PHILOSOPHICAL
TRANSACTIONS
OF THE
ROYAL SOCIETY OF LONDON.
SERIES A
CONTAINING PAPERS OF A MATHEMATICAL OK PHYSICAL CHARACTER.
VOL. 193.
LONDON:
PRINTED BY HARRISON AND SONS, ST. MARTIN'S LANE, W.C.,
{printer* in *rbinarji to $«
1900.
9 It
LSSL
«i J
CONTENTS.
(A) VOL. 193.
Advertisement page vjj
List of Institutions entitled to receive the Philosophical Transactions or Proceedings of the Royal
Society jx
Adjudication of Medals for the year 1899 xvii
I. On the Recovery of Iron from Overstrain. By JAMES MUIR, B.Sc., Trinity
College, Cambridge (1851 Exhibition Science Research Scholar, Glasgow University). Communicated by Professor EWING, F.R.S. .... page 1
II. On the Nature of Electrocapillary Phenomena. — I. Their Relation to the
Potential Differences between Solutions. By S. W. J. SMITH, M.A., formerly Coults- Trotter Student of Trinity College, Cambridge; Demonstrator of Physics in the lioyal College of Science, London. Communicated by Professor A. W. RUCKER, Sec. R.S. 47
1 1 f. The Electrical Conductivity and Luminosity of Flames containing Vaporised Salts. By ARTHUR SMITHELLS, H. M. DAWSON, and H. A. WILSON, The Yorkshire College, Leeds. Communicated by Sir H. E. ROSCOE, F.R.S. . 89
IV. Tlie Diffusion of Ions into Gases. By JOHN S. TOWNSEND, M.A., Dublin, Clerk- Maxwell Student, Cavendish Laboratory, Cambridge. Communicated by
Professor J. J. THOMSON, F.R. S. 129
a 2
V On the Vibrations in the Field round a Theoretical Hertzian Oscillator, By KARL PEARSON, F.R.S., and ALICE LEE, B.A., B.Sc., University College, London page!5'J
VI. OH the Constitution of the Electric Spark, By ARTHUR SCHUSTER, F.R.S., and
GUSTAV HEMSALECH . .
VII. On a Quartz Thread Gravity Balance. By RICHARD THRELFALL, lately
I'rofessor of Physics in the University of Sydney, and JAMES ARTHUR POLUH-K. Demonstrator of Physics in the University of Sydney. Communi- cated by Professor J. J. THOMSON, F.R.S. 215
VIII. The Colour Sensations in Terms of Luminosity. By Captain W. DE W. ABNEY, C.B., D.CL., F.R.S. 259
IV Un the Comparative Efficiency as Condensation Nuclei of Positively and Nega- tively Charged Ions. By C. T. R. WILSON, M.A. Communicated by the Meteorological Council 289
X. On the Resistance to Torsion of Certain Forms of Shafting, with Special Reference
to the, Effect of Key ways. By L. N. G. FILON, M.A., Research Student of King's College, Cambridge, Fellow of University College, London, 1851 Kxhibition Science Research Scholar. Communicated by Professor M. J. M. HILL, F.R.S. 309
XI. BAKKUIAN LECTURE.— The Crystalline Structure of Metals. By J. A. EWINU,
F.R.S., Professor of Mechanism and Applied Mechanics in the University of Cambridge, and WALTER ROSENHAIN, St. John's College, Cambridge, 1851 Exhibition Research Sclwlar, University of Melbourne . .... . . 353
XII. On the Least Potential Difference Required to Produce discharge through
Various Gases. By the Hon. R. J. STRUTT, B.A., Scholar of Trinity College, Cambridge. Communicated by Lord RAYLEIGH, F.R.S. 377
Index to Volume 395
LIST OF ILLUSTRATIONS.
Plates 1 to 7.— Professor K. PEARSON and Miss A. LEE ou the Vibrations in the Field round a Theoretical Hertzian Oscillator.
Plates 8 to 12.— Messrs. A. SCHUSTER and G. HEMSALECH on the Constitution of the Electric Spark.
Plates 13 and 14.— Messrs. R. THRELFALL and J. A. POLLOCK on a Quartz Thread Gravity Balance.
Plates 15 to 28.— Professor J. A. EWING and Mr. W. ROSENHAIN on the Crystalline Structure of Metals. — Bakerian Lecture.
f '
r vii i
ADVERTISEMENT,
TIIK Committee appointed by the Royal Society to direct the publication of the Philosophical Transactions take this opportunity to acquaint the public that it fully appears, as well from the Council-books and Journals of the Society as from repeated declarations which have been made in several former Transactions, that the printing of them was always, from time to time, the single act of the respective Secretaries till the Forty- seventh Volume ; the Society, as a Body, never interesting themselves any further in their publication than by occasionally recommending the revival of them to some of their Secretaries, when, from the particular circumstances of their affairs, the Transactions had happened for any length of time to be intermitted. And this seems principally to have been done with a view to satisfy the public that their usual meetings were then continued, for the improvement of knowledge and benefit of mankind : the great ends of their first institution by the Royal Charters, and which they have ever since steadily pursued.
But the Society being of late years greatly enlarged, and their communications more numerous, it was thought advisable that a Committee of their members should be appointed to reconsider the papers read before them, and select out of them such as they should judge most proper for publication in the future Transactions ; which was accordingly done upon the 26th of March, 1752. And the grounds of their choice are, and will continue to be, the importance and singularity of the subjects, or the advantageous manner of treating them ; without pretending to answer for the certainty of the facts, or propriety of the reasonings contained in the several papers so published, which must still rest on the credit or judgment of their respective authors.
It is likewise necessary on this occasion to remark, that it is an established rule of the Society, to which they will always adhere, never to give their opinion, as a Body,
upon any subject, either of Nature or Art, that comes before them. And therefore the thanks, which are frequently proposed from the Chair, to be given to the authors of such papers as are read at their accustomed meetings, or to the persons through whose hands they received them, are to be considered in no other light than as a matter of civility, in return for the respect shown to the Society by those communications. The like also is to be said with regard to the several projects, inventions, and curiosities of various kinds, which are often exhibited to the Society ; the authors whereof, or those who exhibit them, frequently take the liberty to report, and even to certify in the public newspapers, that they have met with the highest applause and approbation. And therefore it is hoped that no regard will hereafter be paid to such reports and public notices ; which in some instances have been too lightly credited, to the dishonour of the Society.
1899.
LIST OF INSTITUTIONS KVIITI.KD TO RECEIVE THE PHILOSOPHICAL TRANSACTIONS OR
PROCEEDINGS OF THE ROYAL SOCIETY.
Institution* marked A are entitled to receive Philonophk-al Traiuactioiu, Seriei A, ami I'roeeedinga. „ • .. „ ., - Seriei B. and Proceeding*.
„ AB „ „ „ Seriei A and B, and Proceeding*.
„ p „ „ Proceedings only.
America (Central). Mexico.
p. Sociedad Cientifica " Antonio Alzate." America(North). (See UNITED STATES and CANADA.) America (South). Buenos Ayres.
AB. Mnseo Nacional. Caracas.
B. University Library. Cordova.
AB. Academia Nacional do Ciencias. Demerara. p. Royal Agricultural and Commercial
Society, British Guiana. La Plata.
B. Mnseo de La Plata. Rio de Janeiro.
p. Observatorio. Australia. Adelaide. p. Royal Society of South Australia.
Brisbane.
]>. Royal Society of Queensland. Melbourne.
p. Observatory.
p. Royal Society of Victoria.
AB. University Library. Sydney.
Australian Museum.
Geological Survey.
Linnean Society of New South Wale
Royal Society of New South Wales.
University Library.
P- P- P-
AB. AB.
Austria. Agram. p. Jagoslavenska Akademija Znauosti i Urn-
jetnoati.
p. Societas Historico-Natu rails Croatioa. VOL. CXOIII. — A.
Austria (continued). Brunn.
AB. Naturforschender Verein. Grate. AB. Natnrwissenschaftlicher Veruin for Steier-
mark. Innsbruck.
AB. Das Ferdinandeum. p. Natnrwissenschaftlich - Medicinischer
Verein. Prague. AB. Konigliche Bohmische Geaellachaft dor
Wissenschaften. Trieste.
B. Museo di Storia Naturale.
p. Societa Adriatica di Science Natural!.
•
Vienna.
p. Antbropologische Gesellschaft. AB. Kaiserliche Akademie der Wissenschaften. y. K.K. Geographische Gesellschaft. AB. K.K. Geologist-he Reichsanstalt. B. K.K. Naturhistorisches Hof- Museum. B. K.K. Zoologisch-Botanischo Gesellschaft. p. Oesterreichische Gesellschaft fur Meteoro- logie.
A. Von Kuffner'sche Sternwarte. Belgium.
Brussels.
B. Academic Roy ale de Medecine. AB. Academic Royale dee Sciences.
B. Musee Royal d'Histoire Natarelle de
Belgiqne.
p. Observatoire Royal. p. Societe Beige de Geologic, de Palconto-
logie, et d'Hydrologie. p. Societe Malaoologique de Belgique. Ghent. AB. University.
Belgium (continued).
AH. Societc des Sciences.
p. SociM Oeologique de Belgique. Lonvaiu.
B. Laboratoire de Microscopic et do Biologie Cellalaire
AB. University. Canada.
Fredericton, N.B.
p. University of New Brunswick. Halifax, N.S.
p. Nova Section Institute of Science.
Hamilton.
p. Hamilton Association. Montreal.
AB. McQill University.
p. Natural History Society. Ottawa.
AB. Geological Survey of Canada.
AB. Royal Society of Canada. St. John, N.B.
p. Natural History Society. Toronto.
p. Astronomical and Physical Society.
p. Canadian Institute.
AB. University. Windsor, N.S.
p. King's College Library.
Cape of Good Hope.
A. Observatory. •
AB. South African Library.
Ceylon. Colombo.
a. Museum. China. Shanghai. p. China Branch of the Bx>yal Asiatic Society..
Denmark. Copenhagen.
AB. Kongelige Danske Yidenskabemes Selskab.
Egypt Alexandria.
AB. Bibliotheqne Mnnicipale. England and Wales. Aberystwitb.
AB. University College. Bangor.
AB. University College of North Wales. Birmingham.
AB. Free Central Library.
AB. Mason College.
p. Philosophical Society.
J
England and Wales (continued). Bolton. p. Public Library.
Bristol.
p. Merchant Venturers' School.
AB. University College. Cambridge.
AB. Philosophical Society.
p. Union Society. Cooper's Hill.
AB. Royal Indian Engineering College.
Dudley.
p. Dudley and Midland Geological and
Scientific Society. Essex.
p. Essex Field Club. Falmouth.
p. Royal Cornwall Polytechnic Society. Greenwich.
A. Royal Observatory. Kew.
B. Royal Gardens. Leeds.
p. Philosophical Society.
AB. Yorkshire College. Liverpool.
AB. Free Public Library.
p. Literary and Philosophical Society.
A. Observatory.
AB. University College. London.
AB. Admiralty.
p. Anthropological Institute.
AB. British Museum (Nat. Hist.).
AB. Chemical Society.
A. City and Guilds of London Institute. p. " Electrician," Editor of the.
B. Entomological Society. AB. Geological Society.
AB. Geological Survey of Great Britain.
p. Geologists', Association.
AB. Guildhall Library.
A. Institution of Civil Engineers.
p. Institution of Electrical Engineers.
A. Institution of Mechanical Engineers.
A. Institution of Naval Architects. p. Iron and Steel Institute.
AB. King's College.
B. Linnean Society. AB. London Institution. p. London Library.
A. Mathematical Society. p. Meteorological Office. p. Odontological Society.
r xi '
England and Wales (continued). London (continued). p. Pharmaceutical Society. p. Physical Society. p. Quekett Microscopical Club. p. Royal Agricultural Society.
A. Royal Astronomical Society.
B. Royal College of Physicians. B. Royal College of Surgeons.
p. Royal Engineers (for Libraries abroad, six copies).
AB. Royal Engineers. Head Quarters Library.
p. Royal Geographical Society.
p. Royal Horticultural Society.
p. Royal Institute of British Architects.
AB. Royal Institution of Great Britain.
B. Royal Medical and Chirurgical Society.
p. Royal Meteorological Society.
p. Royal Microscopical Society.
p. Royal Statistical Society.
AB. Royal United Service Institution.
AB. Society of Arts.
;-. Society of Biblical Archaeology.
p. Society of Chemical Industry (London Section).
p. Standard Weights and Measures Depart- ment.
AB. The Queen's Library.
AB. The War Office.
AB. University College.
p. Victoria Institute.
B. Zoological Society. Manchester.
AB. Free Library.
AB. Literary and Philosophical Society.
p. Geological Society.
AB. Owens College. Netley.
p. Royal Victoria Hospital. Newcastle.
AB. Free Library.
p. North of England Institute of Mining and Mechanical Engineers.
p. Society of Chemical Industry (Newcastle
Section). Norwich.
p. Norfolk and Norwich Literary Institution. Nottingham.
AB. Free Public Library. Oxford.
p. Ashmnloan Society.
AB. Rodcliffe Library.
A. Rndoliffc Observatory.
I 2
England and Wales (continued). Penzance.
p. Geological Society of Cornwall. Plymouth.
B. Marino Biological Association.
p. Plymouth Institution . Richmond.
A. " Kew " Observatory. Salford.
p. Royal Museum and Library. Stonyhnrst.
p. The College. Swansea.
AB. Royal Institution. Woolwich.
AB. Royal Artillery Library. Finland. Helsingfors.
;>. Societas pro Fauna ct Flora Pennies,
AB. Societe des Sciences. France. Bordeaux.
p. Academic des Sciences.
p. Faculty des Sciences.
p. Societ^ de Medecine et de Chirnrgie.
p. Socie'te des Sciences Physiques et
Naturelles. Caen.
p. Socie'te Linneenno de Normandie. Cherbourg.
p. Societe des Sciences Natnrelles. Dijon.
p. Academic des Sciences. Lille.
p. Faculte des Sciences. Lyons.
A n. Academic des Sciences, Belles- Lettres ct Arts.
AB. University. Marseilles.
AB. Faculty des Sciences. Montpellier.
AB. Academic des Sciences et Lettres.
B. Faculte de Medecine. Nantes.
p. SocieU) des Sciences Natnrelles de 1'Onest
de la France. Paris.
AB. Academic des Sciences de 1'Institnt.
p. Association Francaise pour 1'Avanccment
des Sciences.
p. Bureau des Longitudes. A. Bureau International des Poids et Mesnms. p. Commission des Annales des Fonts et
Chanssees. p. Conservatoire des Arts et Metiers.
r
France (continued). Paris (continued). p. Cosmos (M. L'ABR£ VAI.KTTK). AB. Depot de la Marine. AB. Ecole des Miues. AB. Boole Normale Snperienro. AB. Ecole Polytechniqne. AB. Facnlt^ des Sciences de la Sorbonne. B. Institut Pasteur. AB. Janlin des Plantes. p. L'Electricien.
A. L'Obscrvatoire.
p. Revue Scientifique (Mons. H. DB VARIONT).
p. Societe de Biologie.
AB. Societe d'Encouragement pour I'lndustrie
Nationale.
AB. Societe de Geographic. p. Societe de Physique.
B. Societe Entomologiquo. AB. Societe Geologique.
p. Socie^ Mathematiquo.
p. Societe Meteorologique de France. Toulouse.
ATI. Academic des Sciences.
A. Facult^ des Sciences. Germany. Berlin.
A. Dentsche Ghemische Gesellschaft.
A. Die Sternwarte.
p. Gesellschaft fur Erdknnde.
AB. Konigliche Prenssische Akademie der Wissenschaften.
A. Physikalische Gesellschaft. Bonn.
AB. Universitat. Bremen.
p. Naturwissenschaftlicher Verein. Breslan.
p. Schlesische Gesellschaft fur Vaterlandische
Knltur. Brnnawick.
p. Verein fUr Naturwissenschaft. Carlsrnhc. See Karlsruhe. Charlottenbnrg.
A. Physikalisch-Technische Reichsanstalt. Danzig.
AB. Natnrforechende Gesellschaft. Dresden.
p. Verein fur Erdkunde. Emden.
p. Natnrforechende Gesellschaft. Erlangon.
AB. Physikalisch-Medicinische Societat.
Germany (continued). Frankfurt-am-Main.
AB. Senckenbergische Natnrforschende Gesell- schaft.
p. Zoologische Gesellschaft. Frankfurt-am-Oder.
p. Natnrwissenschaftlicher Verein. Freibnrg-im-Breisgau.
AB. Universitat. Giessen.
AB. Gix>8sherzogliche Universitat. GOrlitz.
p. Natnrforschende Gesellscliaft. Gottingen.
AB. Konigliche Gesellschaft der Wissenschaften .
Halle.
AB. Kaiaerliche Leopoldino - Carolinische Dentsche Akademie der Natnrforscher.
p. Naturwissenschaftlicher Verein fur Sach-
sen und ThUringen. Hamburg.
p. Naturhistorisches Museum.
AB. Naturwissenschaftlicher Verein. Heidelberg.
p. Natnrhistorisch-Medizinischer Verein.
AB. Uuiversitat. Jena.
AB. Medicinisch-Naturwissenschaftliche Gesell- schaft. Karlsruhe.
A. Grossherzogliche Sternwarte.
p. Technische Hochschule. Kiel.
p. Natnrwissenschaftlicher Verein fur Schleswig-Holstein.
A. Sternwarte.
AB. Universitat. Konigsberg.
AB. Konigliche Physikalisch - Okonomische
Gesellschaft. Leipsic.
p. Annalen der Physik nnd Chemie.
AB. Konigliche Sachsische Gesellschaft der
Wissenschaften. Magdeburg.
p. Naturwissenschaftlicher Verein. Marburg.
AB. Universitat. Munich.
AB. Konigliche Bayerische Akademie der Wissenschaften .
p. Zeitschrift fur Biologie.
[• • • n Xlll ]
Germany (continued). Monster.
AB. Koniglicho Theologische and Philo-
sophische Akademie. Potsdam.
A. Astrophysikalisches Observa tori urn. Rostock.
AB. Univorsitat. Strasbnrg.
AB. Univcrsitat. Tubingen.
AB. Universitat. WUrzburg.
AB. Physikalisch-Mi'diciiiiseho GopelUchaft. Greece. Athena.
A. National Observatory. Holland. (See NITHBRLANDS.) Hungary.
Bada-pest.
p. Konigl. Ungarische Geologischo Anatalt. AB. A Magyar Tud<5s Tarsasag. Die Ungarische
Akadomie der Wissenschaften. Herraannstadt. p. Siebenbiirgischer Verein fur die Natur-
wissenschaften. Klansenbnrg. AB. Az Erde'lyi Mnzenm. Das Siebenburgische
Museum. Schemnitc.
p, K. Ungarischc Berg- and Foret-Akademie. India. Bombay.
AB. Elphirmtone College. p. Royal Asiatic Society (Bombay Branch). Calcutta.
AB. Asiatic Society of Bengal.
AB. Geological Museum.
;>. Great Trigonometrical Surrey of India.
AB. Indian Museum.
p. The Meteorological Reporter to the
Government of India. Madras.
B. Central Museum. A. Observatory.
Roorkee.
p. Roorkeo College. Ireland. Armagh.
A. Observatory. Belfast.
AB. Queen's College.
Ireland (continued). Cork.
p. Philosophical Society. AB. Queen's College. Dublin.
A. Observatory.
AB. National Library of Ireland.
B. Royal College of Surgeons in Ireland. AB. Royal Dublin Society.
AB. Royal Irish Academy. Gal way.
AB. Queen's College. Italy. Acireale.
p. Aocademia di Science, Letters ed Arti. Bologna.
AB. Accademia dello Science dell' latituto. Catania.
AB. Aocademia Gioenia di Science Natural!. Florence.
p. Biblioteca Nazionale Centrale
AB. Museo Botanico.
p. Reale 1st it uto di Studi Snperiori. Genoa.
p. Societa Ligustica di Science Natural: e
Geografichc. Milan,
AB. Reale Istituto Lombardo di Science, Lettere ed Arti.
AB. Societa Italians di Science Natnrali. Modena.
p. Le Stacioni Sperimentali Agrarie Italiane. Naples.
p. Societa di Naturalist?.
AB. Societa Reale, Accademia dello Science.
B. Stazionc Zoologica (Dr. DOHRN). Padua.
p. University. Palermo.
A. Circolo Matematico.
AB. Consiglio di Perfezionamento (Sociota di Science Natnrali ed Eoonomiche).
A. Reale Osservatorio. Pisa.
p. II Nnovo Cimento.
p. Societa Toscana di Science Natural!. Rome.
p. Accademia Pontiticia do* Nnovi Lincci.
p. Rassegna delle Science Geologiche in Italia.
A. Reale Ufficio Centrale di Meteorulogia e di Geodinamica, Collegio Romano.
AB. Reale Accademia dei Lincei.
p. R. Comitato Geologico d' Italia.
A. Specola Vaticana.
r
Italy (continued). Rome (continued).
AB. Societi lUliana delle Science. Siena.
p. Reale Aocademia dei Fisiocritici. Turin.
p. Laboratorio di Fisiologia. AB. Realo Aecademia delle Scienze. Venice.
p. Atenoo Veueto. AB. Reale Istituto Veneto di Scienze, Lottere
ed Art i. Japan. Tokio.
AB. Imperial University. p. Asiatic Society of Japan. Java.
Buitenrorg.
p. Jardin Botnniqnc. Luxembourg. Luxembourg.
p. Socie'te des Sciences Naturelles. Malta.
p. Public Library. Mauritius.
p. Roynl Society of Arts and Sciences. Netherlands. Amsterdam.
AB. Koninklijkc Akademie van WetenscJiappen. p. K. Zoologisch Genootschap 'Natura Artis
Magistra.' Delft.
p. Ecole Polytechnique. Haarlem.
AH. Hollandschc Maatfichappij der Weton-
schappcn. p. Muscc Teyler. Leyden.
AB. University. Rotterdam.
AB. Bataafsch Genootschap der Proefonder-
vindelijke Wijsbegeerte. Utrecht. AB. Provinciaal Genootschap van Knnsten en
Wetc use happen. New Zealand.
AB. New Zealand Institute. Norway. Bergen.
AB. Bergenike Museum. Christian!*.
AB. Kongelige Norske Fixxlorika Uuiversitet.
Norway (continued). Tromsoe.
p. Mnsenm. Trondhjem.
AB. Kongelige Norske Videnskabers Selskab. Portugal. Coimbra.
AB. Univeraidado. Lisbon.
AB. Academia Real das Scienciaa.
p. Seccao dos Trabal hos Geologicos de Portugal . Oporto.
p. Annaes de Sciencias Natnraes. Russia. Dorpat.
AB. University. Irkutsk.
p. Socie'te' Imperiale Russe de Geographic
(Section de la Siberie Orientale). Kazan.
AB. ImperatorRky Kazansky Universitet.
p. Socie'te' Physico-Math£matiqne. Kharkofp.
p. Section Medieale de la Societe des Sciences Experimentales, Universite de Kharkov. Kieflf.
p. Society des Natnralistes. Kronstadt.
p. Marine Observatory. Moscow.
AB. Le Musee Public.
B. Societe Imperiale des Naturalistes. Odessa.
p. Societe des Natnralistes de la Nouvelle-
Rnssie. Pulkowa.
A. Nikolai Haupt-Stemwarte. St. Petersburg.
AB. Academic Imperiale des Sciences.
B. Archives des Sciences Biologiques. AB. Comite Geologiqne.
An. Ministry of Marine.
A. Observatoire Physique Central. Scotland. Aberdeen.
AB. University. Edinburgh.
p. Geological Society.
p. Royal College of Physicians (Research Laboratory).
p. Royal Medical Society.
A. Royal Observatory.
p. Royal Physical Society.
p. Royal Scottish Society of Arts.
AB Royal Society.
! xv
Scotland (contiaaed). Glasgow.
AII. Mitchell Free Library. p. Natural History Society. p. PhiloHophical Society. Servia. Belgrade.
p. Academic Royale de Scrbie. Sicily. (SeeltALT.) Spain. Cadii. A. Instituto y Observatorio de Marina de San
Fernando. Madrid.
p. Comision del Mapa Qeoldgico de Espina. AB. Real Academia de Ciencias. Sweden. Gottenburg.
AB. Kong] . Vetenskaps och Vitterhets Samhallc. Land.
AB. Universitet. Stockholm.
A. Acta Mathematics.
AB. Kongliga Svenska Vetenskaps-Akademie. AB. Sveriges Geologiska Undergo kning Upsala.
AB. Universitet. Switzerland. Basel. p. Natnrforechende Geeellschaft.
Bern.
AB. Allg. Schweicerische Gesellschaft.
p. Natorforachende Gesellschaft. Geneva.
AB. Societe de Physique et d'Histoire Natnrelle.
AB. Institnt National Genevois.
Lausanne.
p. Sociote Vaudoisc des Sciences Naturelles. Nenchatel.
p. Societe dea Sciences Naturelles. Zurich.
AB. Das Schweicerische Polytechniknm.
p. Naturforschende Gesellschaft.
p. Sternwarte. Tasmania. Hobart.
p. Royal Society of Tasmania. United States. Albany.
AH. New York State Library.
United States (continued). Annapolis.
AB. Naval Academy. Austin.
p. Texas Academy of Sciences. Baltimore.
AB. Johns Hopkins University. Berkeley.
p. University of California. Boston.
AB. American Academy of Sciences.
B. Boston Society of Natural History.
A. Technological Institute. Brooklyn.
AB. Brooklyn Library. Cambridge.
AB. Harvard University.
B. Museum of Comparative Zoology. Chapel Hill (N.C.).
p. Elisha Mitchell Scientific Society. Charleston.
/'. Elliott Society of Science and Art of South
Carolina. Chicago.
AB. Academy of Sciences.
p. Astro-physical Journal.
p. Field Columbian Museum.
p. Journal of Comparative Neurology. Davenport (Iowa).
p. Academy of Natural Sciences. Ithaca (N.Y.).
A. Journal of Physical Chemistry.
p. Physical Review (Cornell University).
p. Wisconsin Academy of Scii-n. Mount Hamilton (California).
A. Lick Observatory. New Haven (Conn.).
AB. American Journal of Science.
AB. Connecticut Academy of Arts and Sciences. New York.
p. American Geographical Society.
A. American Mathematical Society.
p. American Museum of Natural History.
p. New York Academy of Sciences.
p. New York Medical Journal.
p. School of Mines, Columbia College. Philadelphia.
AB. Academy of Natural Sciences.
AB. American Philosophical Society.
p. Franklin Institute.
p. Wagner Free Institute of Science
United States (continued). Rochester (N.Y.).
p. Academy of Science. St. Louis.
p. Academy of Science. Salem (Mass.).
p. American Association for the Advance- ment of Science.
AB. Essex Institute. San Francisco.
AB. California Academy of Sciences. Washington.
AB. Patent Office.
United States (continued). Washington (continued). AB. Smithsonian Institution.
United States Coast Survey.
United States Commission of Fish and
Fisheries.
United States Geological Survey. United States Naval Observatory. United States Department of Agriculture. United States Department of Agriculture
(Weather Bureau). West Point (N.Y.) AB. United States Military Academy.
AB. B.
AB. AB.
P- A.
[ xvii ]
ADJUDICATION of the MKDALS of the ROYAL Sorir.iv for the year 1899,
by the PKESIDKXT and COUNCIL.
The COPLEY MEDAL to the Right Hon. Lord RAYI.KKJH, F.R.S., in recognition of his contrihutions to Physical Science.
A ROYAL MEDAL to Professor G. F. FIT^GERALD, F.R.S., for his contributions to Physical Science, especially in the domains of Optics and Electricity.
A ROYAL MEDAL to Professor W. C. McLvrosH, F.R.S., for his important mono- graphs on British Marine Zoology and on the Fishery Industries.
The DAVY MEDAL to Dr. EDWARD SCHUNCK, F.U.S., for his researches on Madder, Indigo, and Chlorophyll.
The Bakerian Lecture for 1899, " The Crystalline Structure of Metals," was delivered by Professor J. A. EWINU, F.R.S., and Mr. W. ROSENHAIN, on May 18, 1899.
The Croonian Lecture for 1899, "On the Relation of Motion in Animals and Plants to the Electrical Phenomena which are associated with it," was dflivnvd l>v I'mfessor BITRDON SANDERSON, F.R.S., on March 16, 1899.
VOL. cxciu. — A.
I'll I LOSOPH 1C AL TRANSACTIONS.
I. On the Recovery of Iron from Overstrain.
By JAMES Mrm, R.Sc., Trinity College, Cambridge (1851 K.i-hihiiii,,, S, •'„>„<••• Ifesearch Scholar, Glasgow University).
Communicated by Professor Ewixo, F.Il.X. Received January 25,— Read Fe!»n«r.y 9, 1899.
IT has long l>een known that iron which has been overstrained in tension — that is to say strained l>eyond the yield-point so that it suffers a permanent stretch — possesses very different elastic properties from the same iron in its primitive condition. The material is said to be " hardened " by stretching,* since the ultimate effect of such treatment is to raise the elastic limit and reduce the ductility of the material.
More recently, attention has l>een called to the fact that, primarily, the result of tensile overstrain is to make iron assume a semi-plastic state, so that the elastic limit, instead of l>eing raised by stretching, is first of all lowered, it may be to zero.t This plasticity may be shown by applying a comparatively small load to a liar of iron or steel which has just been overstrained by the application and removal of a large stretching load. When the small load is put on, the bar will l>e found to elongate further than it would had the material been in its primitive state ; and a slight continued elongation — a "creeping" — may occur after the small load has lieen applied. If this load l)e withdrawn, a quite appreciable permanent, or semi- permanent, set will l)e found to have been produced ; a set which diminishes slightly.
* Kwixu, " On Certain Effects of Stress," 'Proc. Roy. Soc.,' No. 205, 1880. The raising of the clastic limit due to stretching seems to havo been first noted in 1865 by TM M.KS. See a translation of his paper in tin- • I'liil. Mag.' for September of that year.
t B.U's< 'inxiiKR, " Ueber die Veriinderung der Elasticitatsgrenze," ' Civilingenieur," 1881, or " Mittlicilungen aits dem mechanisch-technischen Laboratorium der K. Polytechnischen Schulc in Miinrhcn." An account of BAfscniMiKit's work is given in Uxwix's book on "Testing of Materials of Construction."
Kwixci, "On Measurements of Small St ruins in the Testing of Materials and Structures," 'Proc. Roy. S .<-.,' vol. 5K, April, ls<>5.
vol.. , \riii.— A. B 31.7.P9
MI;, .i MI-IK ON mi: IM-COVKIIY OF IRON FROM OYKI;XTI;.UX.
and. it' small, in.iv vaiiisli. provided time U> allowed for 1 Mick ward creeping to take it, It may also U- shown tliat, it' tin- re-applied load l>e increased, tlie elongation produced will increase in a greater proportion. Thus, if a stress-strain curve V ..l.taincd from a recently overstrained bar of iron or steel, it will show, even for small loads, a marked falling away from the straight line which would indicate oljedience to H"»KI:'S law.
It is the recoverv from this semi-plastic state induced by overstrain to a condition of jK-rfect or nearly perfect elasticity with raised elastic limit, that is referred to in the title of this paper. Such recovery is known to be effected by mere lapse of time,* and the object of the experiments about to be described is to show the effect of moderate temperature, of mechanical vibration, and of magnetic agitation, on this slow return to the elastic state, and further to illustrate this recovery by means of compression tests. One section of the paper deals with +he phenomenon of hysteresis in the relation of extension to stress, which is exhibited in a marked degree by iron in the overstrained state. Incidentally, attention will be called to subsidiary points of inten
The experiments were carried out in the Engineering Laboratory of Cambridge I'niversity. and were the outcome of suggestions by Professor Ewixo. It was on his suggestion that the effect of moderate temperature on recovery from overstrain was tried, and the result of that trial led to much of the work incorporated in this paper.
Uefore going into details of the experiments it may l)e of interest to give, drawn to a vma II scale, an ordinary complete stress-strain diagram, such as is obtained in the testing ,,f in>n or steel. The period in the history of iron subjected to tensile stress which is about to l>e investigated, may thus be more clearly indicated. The curve given in Diagram No. I. was sketched by hand, roughly, from data obtained from the experiments which will lie described later. It applies to steel not previously sub- mitted to overstrain.
For the portion ab of this curve HOOKE'S law is ol>eyed. At b the yield-point
occurs, and as soon as this point is passed the material Incomes overstrained. During
the large yielding which takes place at the yield-point the load may be reduced with-
out pausing the extension to stop. After stretching by a large amount as compared
with elastic extension, the material will lie found to have hardened ; so that to pro-
duce further yielding the load must be increased. The stress-strain diagram may
If represented by some such curve as cd. If at d the load be removed,
and at once gradually replaced, then the stress-strain curve may follow a path such
These curves de and ef, when obtained in such a manner that the exten-
•PIXCSI.KR'S Journal,' vol. 224, p. 5, and papers already cited. KWI.M:, Wh papers cited above.
,,»Kht also 1* ,,,,1, .„ Lord KKLVIS'S discovery of the effect of a Sunday's rest on wires Reeled to torsi.mul vibrations throughout the preceding week—See article, "Elasticity,"
V 01. I »I I* .
MI;. .1. Mill; ON Till: i;i:rovi:i;\ oi- II;ON n;o.\i OYKIISTKAIN. 3
sions cun IK.- plotted to a inucli larger s.-ale. sli<>\v the imperfect elasticity <»i' recently overstrained iron which -lias l»een referred to above; that is, they slmw tliat the material is semi plastic. It' time l>e allowed to elapse between unloading and reloading, tin- recovery l'n>m the effect of overstrain may be shown in a diagram like the present, liy some such curve as ef. When no interval of time is allowed to elap^- U'tween the removal and the replacement of the load, then the stress-strain curve i> continued in the manner shown by /</, until a j>oint g is readied, at which local
Diagram No. I.
Extensions in tenths of An inch.
sets in. When this hap]>en8 the stress may be diminished, and fracture may take place at a load lower than that at which local extension occurred. The stress per square inch of fractured area is, however, found to In- much greater than the stress per square inch of the actual area when local elongation began.
Tin- A/1/inratnjs and (lie Material.
The straining and testing in the following experiments was done by means of the 50-ton Wicksteed single-lever hydraulic testing machine of the Cambridge Engineer ing Laboratory. With this machine the magnitude of the load applied could In- read in tons to a second decimal place by means of a vernier, and to a third decimal place roughly by estimation. Thus a load could be applied accurately if necessary to, it may he said, 5,',,,th of a ton.
The small strains of extension \\eiv measured by Professor EWI\I;'S extensometer.*
* Km- ;i full description of this instrument sec the jcinci already cited "On the Meiwuruniuiit of Snmll stiains, \c.," ' Proe. Koy. Soc.,' vol. 3*, April, 1695.
Ji 'I
MIJ. I-
OK T11H IJKI-OVKKY OK IKON «0* OVKKSTKAIX.
he length of
Tins instnnuent gTO the extend, ««ring « * -JJ* * i
tll, s,K,imen under test. It enabled elongations to * measured to ^-00th of an
ill(,, S to be measured to that degree of precision w,th ease ••ft."**"* . lh.;'
^tnment was iound especially convenient on account -of the facility with winch it
,;,,,, a! the ,,id „»• „ distance-piece) be immediately re-apphed to a specimen winch
,,,,1 just l*en strained beyond its yield-point ; and also on account of t „ readme**
with' whirl, the correct adjustment of the instrument itself could be tested
Th, s,H,i,n,ns e.nployed were, with one or two exceptions, 18 to 20-mch lengths ,„ steel-.-*!. I inch in diameter, of a quality which may be descnbed as semi-mild. detail, of the particular rods employed in the various experiments will be given when these C....U- to be described. Here, us illustrating the general character of naterial the chemical analyses and elastic characteristics of two of the bars made use of will IK- "iven The first is that from which diagram No. IX. has been obtained. \ neeimen imm it showed a well-defined yield-point at a stress of '23 tons to the snuaiv inch, and gave an ultimate strength of 36£ tons per square inch of original an-,, with an elongation of 2'4 l»er cent, on an 8-inch length. The second bar is that from which diagrams Nos. IV. and VII. have been obtained ; it was characterised small Haw running up the centre through the whole length of the bar. A well- d.-tined yield-ix.int was not obtained with specimens from this bar; there was si distinct departure from obedience to HOOKE'S law, at a stress of about 22 tons per squaw inch, but the yield-point should, perhaps, be placed as much as 6 or 7 tons higher than this stress, at which elastic behaviour broke down* The ultimate strength of the material as obtained from a short specimen was 39 tons per square inch, the elongation being only about 20 $ per cent, on a 3-inch length. The chemical analyses of these two bars were kindly supplied by Messrs. EDGAK ALLEN and Co., Sheffield, from whom the material was obtained ; they are as follows :—
|
Bar of diagram No. IX. |
Bar of diagrams Nos. IV. and VII. |
|
|
0-430 |
0-450 |
|
|
Silicon |
0-112 |
0-093 |
|
Sulphur |
o-oio |
0-012 |
|
1'h<MtphoMi« |
0-016 0-150 |
0-021 o-no |
|
| |
||
|
Iron (l»y elilVctrtirr) .... |
98-982 |
99-014 |
|
I |
100-000 |
100-000 |
- tlic tii^t mlnnm nf tht ta'ili; on ji. 15.
Mil. .1. MI'Ii; ON THK UKCOVKKY OF IKON FK<»M oVKl;M l;.UN. The Mftlu,<l .«/
The general procedure adopted in experimenting will now be described. First, the iliameter < >t' the specimen WHS determined from the mean of ten micrometer readings, taken at five equidistant places along the 8-inch length to which the extens.. meter \\.i.s to l» applied. For example, the following readings were obtained tor a certain unturned specimen :—
{r-0069 71 65 64 61 1 J. = 1"-0066. 70 71 71 59 54 J
Not only was this done for virgin specimens, but whenever a yield-point had U-eu jMissecl, the diameter was re-determined by means of fresh readings. For example, the specimen already instanced was subjected to a pull gradually increasing to 35 tons to the square inch of original section, the yield-point occurring at 23 tons per square inch. After the removal of this large stretching load the new diameter was deter- mined from the following readings : —
(V-9918 21 18 20 25 1 Diameter = 4 > = 0'9920 of an inch.
14 *?•? Oji 1 *\ *? * ,4 — — — * ' *' -
After the determination of the diameter of a specimen at each stage of an experi- ment, a table was formulated, from which the total load applied could be translated into tons per square inch of section, the stress being in every case measured with reference to the section at the beginning of each separate test.
These preliminaries having been completed, the specimen was put into the testing machine, the extensometer was attached, and the load was gradually applied. Extenso- meter readings were token sometimes only after the addition of every four tons of .stress, sometimes after each ton, sometimes after each half or quarter ton, according to judgment.
The l'"ll' >\v'mg two series of readings aire given for a typical experiment; they will -. i ve to explain the usual procedure. The first series shows the elastic properties <>!' a certain virgin specimen; the second shows the plastic nature of the same immediately after the overstrain produced by the primary loading.
Mi;. .1. Mill; <>N Tin. IM-PIVKKV OF IKON Ki:«»M (»VKI;STI;AIN.
Stress in tons por square inch.
Total l".i' I in t"»-
I-;\icn>«iinetcr readings.
'""it = nmnr of an inafc.
0
1
•I
4
6
8
10
II
14
16 18 •20 22
21 »
26 87
0 0-79
l •:..< 3-16 Sec.
27J
30 put on
0
30
60 30
120 60
180 60
240 60
;500 60
360 60
421 61
481 60
r,40
600 K. . T. ••'-•• ifift
660 60 ,
720 60
750 30
780 30
810 30
still 810 after 4 minutes, but 830 „ 6 „
iVc. &c.(seeCurve No. 1, Diagram II.) 1595 after 20 minutes 1700 and then quickly out of range gradually and kept on for 3 minutes, the beam of the testing machine remain- ing steady
These figures show that this specimen has accurately obeyed HOOKE'S law, until a stress of -7 t«>ns per square inch was attained. At this load the yield-point w;is exjiected tn occur, and although the exteusometer reading obtained gave HO evidence <>f the proximity of such a point, by simply allowing the load to remain on for a short time (4 minutes) the creeping recorded above set in, or perhaps spread from without to within the 8-inch length under test.* The yield-point, with this specimen, has. therefore, coincided with the elastic limit as accurately as the extensometer can measure. Usually, in testing, imperfection of elasticity is shown before the yield- jMiint is reached, and if a load less than that at the yield-point be allowed to act for some time, then a slight creeping probably supervenes. When, however, a l>ar, like that referred to above, has shown very perfect elasticity up to the yield-point, it is pr< 'liable that a load verv little under that at which the yield-point occurs could be sustained for an indefinite time without creeping taking place. Even although slight imjiertection of elasticity be shown before the yield-point, experiments showed that no creeping need necessarily occur for a pause in the loading of at least a night's duration. .
k The fact tlmt yielding take* some time to start has already licen recorded by Professor Kwix<; in liis piper ciu-d aU»ve, "On McaatirctmmU of Small Strains, \-c." (see pp. 135 and 130). He hiw noticed that yielding may k-gin in ;i part of the Kir lying outside the 8-inch length to which the extensometer is .ippliud. and may gradually sprr.nl .-ilcm^ tliu liar.
MI;, .i. \n ii; i IN TIM: i;i-:m\i.i;\
ICON n;o\i <>\ i I;STI; \i\
'I'll.- manner in which vic'ldin^ umli i a constant load proceeds after tin- yield-jxiint has just IMMMI passed is often \ erv iiregulw. Tin- curves gi\ en on I Jia^ram II. ilhis- tmto this yielding with time for two entirely different sjwciiiit-iis. Tin- tirst shows tin- creeping referred to a hove as having started 1 minutes aftei- the application of the load whii-li \va.s its cause. Tlie second curve sliowH n larger yit-ldinix of mucli longer duration. It occurred under a load of •_'(', tons JH.M- 8<|iiare inch, luit U-fore this loml
NCI. II.— (Manner in which yielding occurs at the yield-point.)
mini. tOt —
mm :
40
30
O»
LOA J-£7i OHA/if *
Cu,
00
'ensiOfis
voo^ in,
Load
Curvet*
If 00
t6toia/in*
inch.
1,6 X)
{400
SflOO
Extensions in iojooo -of&n inch. (Zero extension *hen no load on).
.ittained \\lien •_'.") and 'Joi tons per square inch were acting — considerable creeping |,ad already taken place. The readings from which these curves have heen obtained were taken at intervals of one minute.
To return to the tahle of figures given above, the maximum load (of 30 tons to the sipiare inch of original section) was found, after its removal, to have produced a permanent set of (>"J'J of an inch on the 8-inch length ; this corresj>onds to an extensonietei reading of 1 1,000 ; such a reading is, of course, far beyond the range of the e.xtenscimeter. Immediately after the maximum load had been removed, the
g
readings o
Mi: .1. MI-IK ON THE KKC'OVKKY OK IHOX FUOM OVERSTRAIN.
of the speci.nen was re-measuml and the mluoeil section determined The- tl.,... re-applied, the lpe«h»ai was re-l<.ade,l. and
|
Tons per sq. in. (of reduced section). |
Extensometer readings. |
Differences. |
|
0 |
0 |
|
|
\J I ( = 0-77 ton of |
30 |
30 |
|
total loiid) 2 |
61 |
31 |
|
4 |
125 |
64 |
|
G |
190 |
65 |
|
8 |
260 |
70 |
|
10 |
329 |
69 |
|
12 |
399 |
70 |
|
14 |
469 |
70 |
|
16 |
539 |
70 |
|
18 |
613 |
74 |
|
20 |
687 |
74 |
|
22 |
764 |
77 |
|
24 |
845 |
81 |
|
26 |
930 |
86 |
|
28 |
1028 |
98 |
|
SO |
1150 |
122 |
The load was now removed, and during its removal the following three readings were taken :
Tons/inch2.
Extensometer.
20
10
0
830 477
60 but diminishing slightly with lapee of time
The series of increasing differences shown in this second table plainly indicates a change in the elastic state of the material. HOOKE'S law is no longer obeyed.
This augmentation of the differences is, to some extent, associated with creeping, and to a greater extent, the higher is the applied load. Thus it is essential, if consistent results are to be obtained, that the interval of time which elapses between successive readings should always be kept the same. If a pause had been allowed to occur after the addition of any of the higher loads in this second table, then, owing to prolonged creeping, a larger difference would have been obtained than is recorded above. On proceeding with the loading, however, the immediately succeeding difference, or ditVerences, would have been smaller than according to the table. For had there been no interruption, part of the creeping which occurred during the pause would have been recorded on the addition of the subsequent loads.
Ml; .1. Ml IK ON Till; RECOVERY OF IRON FROM OVERSTRAIN .9
In experiments on !i virgin piece of which the first table given ulx>\r is typ'u-al.the time eli-int-nt dors not enter, for there is no perceptible creeping until the yield point is all but reached.
Slow Recovery of Elasticity with lapse of Time.
l'..-f"iv proeri'din^ t-> di-si'i-ilic tin- i-tl'.-.-t ,,(' -.p.-.-ial tivatm.-nts on recovery from tensile overstrain, I give two instances of the slow recovery from overstrain \\ith lapse of time, similar to the examples already given by Professor EWINO.*
The curves in Diagram No. Ill A. illustrate this slow recovery for a specimen of 1 inch round steel rod, which has been strained to or very little beyond its yield- point. The material had an ultimate strength of 37 tons per square inch of original area, the total elongation being almost 23 per cent, on an 8-inch length. The yield- point was well defined and occurred at a stress slightly under 27 tons to the square inch. The readings from which the various curves have been plotted are given in the table on p. 11. The curves were obtained in the usual manner, the stresses being plotted as ordinates, and the corresponding extensions as abscissae.
Curve No. 1 of Diagram IIlA. is a record of the primary test of the specimen. It shows that HOOKE'S law has been obeyed up to a load of 26 tons to the square inch ; and that before 27 tons there was a well-marked yield-point. This load of 27 tons per square inch was kept on for two minutes, by which time rapid stretching had ceased, as was shown by the beam of the testing machine remaining stationary. There was still a slow creeping, which probably would have continued for hours or days, becoming however slower and slower. Curve No. 2 represents a test performed as shortly after the removal of this load as the remeasurement of the diameter and the calculation of the reduced area would permit : it illustrates the semi-plastic condition of the material immediately after overstrain. In the plotting of this, and all subsequent curves in the diagram, it will be noticed that the origin for the measurement of extensions has been displaced ; this was merely to keep the curves distinct and to facilitate comparison.
Curves Nos. 3, 4, 5, and 6, obtained at succeeding intervals, illustrate the gradual recovery of the elasticity lost by the overstrain. This recovery will be noticed to be quickest at first, and latterly to be very slow. In Curves 3, 4, and 5 the load was not allowed to exceed 27 tons per square inch. Curve No. 6 shows the recovery to have been nearly, though not quite, perfect after the material had been allowed to rest for 6 days 3 hours. In this test the load was gradually increased beyond the 27 tons, and a new yield-point was not obtained till rather over 30 tons to the square inch was reached.
Curve No. 7 shows the plastic nature of the material immediately after this second
overstrain, and No. 8 the condition after 4 days' rest. Thus after 4 days the recovery
• * See page 139, &c., of his paper " On Measurements of Small Strains, &c."
VOL. CXCIII. — A. C
10
MR J
MUIR ON THE RECOVERY OF IRON FROM OVERSTRAIN.
|
I
f
'ffH*
. tf\ ^ <-v •**!
MR J. MUIR ON TIII: I;KC<>VI;I;Y OF IKON KKOM OVKKSTRAIN.
11
was liy ii<» means perfect, and on increasing the load l*-y<>nd the 30 tons an almost immediate lulling away was observed, and (as is shown in the curve) a third, rather indefinite, yield-]x>int w;is indicated. Further yield-points might have beeu obtained had this treatment been proceeded witli.
TABLE giving readings i'»v I Marram NI>. 111. (Sl..\\ recovery with tiim-).
|
Extensometcr readings for various curves of Diagram III. , |
||||||||
|
Load in tons/in9. |
No. 1. Zero time. |
No. 2. 10 min-. |
No. 3. 4 hours. |
No. 4. 23 hours. |
No. 5. 2 days 22 hours. |
No. 6. 6 days 3 hours. |
No. 7. 20 rnins. (No. 6, zero.) |
No. 8. 4 days (No. 6, zero.) |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
2 |
60 |
62 |
62 61 |
61 |
60 |
61 |
60 |
|
|
4 |
121 125 |
128 125 |
122 |
122 |
127 |
120 |
||
|
6 |
1*2 192 |
191 l-> |
186 |
186 |
191 |
181 |
||
|
8 |
2i:t |
262 |
260 |
249 |
248 |
249 |
260 |
243 |
|
10 |
304 |
333 330 |
311 |
310 |
309 |
330 |
305 |
|
|
12 |
368 |
405 |
401 |
J7fl |
372 |
370 |
397 |
368 |
|
14 |
428 |
481 |
477 |
444 |
434 |
433 |
471 |
429 |
|
16 |
491 |
553 |
550 |
511 |
500 |
498 |
542 |
489 |
|
18 |
:.:,:; |
631 |
625 |
581 |
562 |
560 |
626 |
549 |
|
20 |
618 |
709 |
701 |
658 |
630 |
621 |
700 |
610 |
|
22 |
680 793 |
779 |
738 |
698 |
687 |
778 |
678 |
|
|
24 |
742 |
855 |
817 |
765 |
750 |
860 |
740 |
|
|
25 |
772 933 |
902 |
658 |
801 |
781 |
|||
|
26 |
803 999 |
'.'.:; 900 |
841 |
816 |
942 |
810 |
||
|
27 |
Out of 1068 to"! range 1117 in > 3 min-. J |
1010 toT 949 to 1 1035 in ^ 978 in ^ 3 mins. J 3 min-. J |
881 to 1 897 in <[ 3 mins. J |
850 |
||||
|
28 |
... ... |
... ... ... |
884 |
1035 |
889 |
|||
|
29 |
... ... |
921 |
||||||
|
30 |
972 |
1152 |
964 |
|||||
|
31 |
1251 and |
1262 tol 1004 |
||||||
|
then very |
1382 in ^ |
|||||||
|
1.. • |
2 mins. J |
|||||||
|
yielding |
||||||||
|
32 |
... ... |
... |
1055 |
|||||
|
33 |
... ... |
. . . |
1166 |
|||||
|
34 |
... |
... |
... |
Very laim yielding |
||||
|
Load |
||||||||
|
removed. |
||||||||
|
0 |
1 ' |
128 to "I 113 in ^ 4 mins. J |
61 to I 39 in I 4 mins. J |
36 to "I 2!i in i- 15 mins. J |
23 to 17 |
241 to 228 |
c 2
12 MR J. MUIR ON THE KKCOVERY OF IRON F1I»M OVERSTRAIN.
The "Shearing Back" of the Curves.
It will have been noticed that, owing to the extensions being plotted to an unusually large scale, the curves occupy an inconvenient amount .of space. This may te avoided by adopting a geometric artifice, suggested by Professor EWING, ot "shearing back" the curves; that is, retaining the same scale of measurement, an amount is deducted from each extension proportional to the load producing it. F..r example, if extensions of 120, 240, 360 were produced by loads of 4, 8, and I-J tons IHT square inch respectively, the extensions might be diminished by, say, 100 units per 4 tons of load, and plotted as 20, 40, and 60. Another way of expressing this is t.» say that in the diagram the axis from which extensions are measured may .simply be considered as tilted back in the manner shown below by fig. 2. Fig. 1 shows a curve drawn with ordinary rectangular axes, and fig. 2 the same curve " sheared back."
Extension Extension.
Referring again to Diagram No. I HA., the process of " shearing back" is performed graphically on the single Curve No. 6 by adopting an oblique base line, OY', the distance from which of each point of the curve is measured horizontally and re-plotted from the vertical base line. Curve No. 6' being obtained. Besides the convenience of space gained, this foreshortening of the curves by diminishing the rates of extension renders a more obvious comparison of similar, but slightly different, curves, and emphasises any irregularities there may be in the extensometer readings. It should thus be remembered that in a stress-strain curve which has been " sheared back " inequalities in extension are exaggerated, since the relations they bear to the total extensions are not shown.
In Diagram No. Illn. all the curves of Diagram No. IIlA.* are shown sheared back by the method just explained, and in all similar diagrams to be shown in this paper the curves will be subjected to the same treatment. In all cases the amount of shearing of the curves is the same — the extensions are always diminished by y^^ths of an inch for e\vry 1 tons of stress. The scale for the measurement of extensions
Since Diagram H!A. has been reproduced one-half full size, while Diagram Ills, (and all other diagrams in the paper) have been reproduced to a two-thirds scale, the two Diagrams IIlA. and IIIu. are not absolutely comparable. Besides this difference due to reproduction, the scale for the measurement of load in IIIn. was originally only half that in IIlA.
Mi: .1. MIIR ON THE RECOVERY OF IKON Fl;i >M < >Vi;i;s I ]; \]\
13
will be kept the same for all analogous diagrams, but that for the measurement of load will IKS varied, in order to get the different diagrams suitably spaced.
Diagram No. IIIu. — (Slow recovery with time.)
I
r
|
^-0^- |
a. |
•o |
. • — • |
• 7 |
||||||
|
x^ |
* |
S* |
*^ |
|||||||
|
J |
y |
. |
X |
|||||||
|
t |
ff |
/ |
^ |
|||||||
|
// |
y |
— /» |
||||||||
|
J. |
w |
EX |
i m |
6 £< 7. -* A-4 |
>e ttbc •)mir» d*fS |
i/e after |
A^. |
|||
|
/// |
/ |
.K
I
Extensions- diminished <u explained on page if. Scale : - 1 unit - <af(B of an inch. °. ' 1
Second Example of Slow Recovery with Lapse of Time.
In Diagram No. FV. there is shown the slow recovery from overstrain of a slightly different quality of steel under somewhat different conditions from those of the last example, while in the accompanying table the figures are given from which the various curves of that diagram have been plotted. The material is that described second on p. 4.
An examination of the differences given in the first column of the table on p. 15 will show that, although during the primary loading of the specimen, considerable yielding set in at a stress of 22 tons {>er square inch, it was not until almost 29 tons that such
14
MK. .1. MI'IR ON THE RECOVERY OF IRON FROM OVERSTi; .UN
yielding as is usually associated with a yield-point occurred. Before this stress of 29 tons per square inch was reached, the stretching was not sufficient to cause the skin of oxide to spring off in the manner characteristic of a yield-point, and the removal and gradual re-application of a load of 28 tons was found to show compara- tively little semi -plasticity of the material. Thus the specimen cannot be said to
Diagram No. IV. — (Slow recovery with time).
tons
\
Extensions -diminished AS explained on p*ge 12. Scale -.- 1 unit • of an inch. ? ( _f
Curve No. 1— primary test of specimen. „ „ 2 — after load removed from No. 1. „ „ 3— about 2 days after No. 1. » » ^~~ » 7 „ l.
» 5- ,, 17 „ l.
> been thoroughly overstrained until after 29 tons per square inch had been The primary loading was continued beyond this amount until a stress of ••MS {)er square inch of original area was attained. Curve No. 1, Diagram IV, illustrates, so far, the primary loading of this specimen.
iHMhml manner in which this specimen yielded was perhaps, directly or indirectly, by a small flaw which ran up the centre of the bar (see p. 4).
Ml: .1. \iriu ON THE RECOVERY OF IK"N | I;M\I <>Yl.l;sTi;.\IN.
15
( 'in ve No. 2 illustrates the semi-plastic condition of the material immediately after the removal of the overstraining load ; while Curves Nos. 3, 4, and 5 show the pro- gress iniulr towards recovery, '2, 7, and 17 days respectively, after the material had
TABLE of Readings for Diagram IV. (Slow recovery with time.)
|
Extensomcter readings for the variotu curves. |
|||||
|
T ,1 " |
|||||
|
I j i.ui in tons/in'-'. |
. No. 1. |
No. 2. |
No. 3. |
No. 4. |
No. 5. |
|
Zero time. |
15 iniii-. |
2 days. |
7 days. |
17 days. |
|
|
0 |
0 Differences. |
0 |
0 |
0 |
0 |
|
2 |
60 61 |
62 |
61 |
61 |
60 |
|
4 |
121 60 |
129 |
122 |
122 |
120 |
|
6 |
181 |
190 |
l>s |
IHL- |
179 |
|
8 |
241 |
259 |
247 |
242 |
IM |
|
10 |
301 |
329 |
309 |
MS |
299 |
|
12 |
361 5° |
398 |
370 |
363 |
:;.v.» |
|
14 |
'--' GO |
468 |
43.1 |
l_'l |
419 |
|
16 |
482 5° |
559 |
499 |
MB |
479 |
|
18 |
543 |
609 |
:„;-, |
545 |
539 |
|
20 |
604 30 |
681 |
637 |
612 |
600 |
|
21 |
634 50 |
719 |
669 |
643 |
630 |
|
22 |
';>l 66 |
755 |
706 |
674 |
661 |
|
23 |
760 |
791 |
740 |
705 |
692 |
|
24 |
810 |
830 |
779 |
737 |
725 |
|
25 |
889 .JS |
869 |
815 |
770 |
757 |
|
26 |
998 j» |
909 |
851 |
802 |
788 |
|
27 |
1140 IJr |
949 |
890 |
834 |
819 |
|
28 |
1440 |
991 |
930 |
Mfl |
uo |
|
on |
Out nf |
1AQI-. |
Q70 on<l |
AM |
|
|
m9 30 |
range, say 6500 |
&V0U 1079 |
•71V 1011 |
vw 934 |
OOfl 915 |
|
31 |
. . • |
1124 |
1058 |
967 |
948 |
|
32 |
• . * |
1171 |
1104 |
1002 |
979 |
|
33 |
Load slowly in-"\ |
1225 |
1149 |
1036 |
1012 |
|
34 |
creased to 35 1 |
1279 |
1199 |
1074 |
1048 |
|
38 1 1 minute J |
tons, and then f removed. J |
13491 1368/ |
12501 1262/ |
1133 |
1079 |
|
tons/in*. |
|||||
|
35$ 1096 |
|||||
|
30 |
1207 |
1108 |
980 |
36 1111 |
|
|
25 |
i oa- |
940 |
820 |
36 J 1129 |
|
|
20 |
ses |
772 |
666 |
37 1146 |
|
|
15 |
689 |
601 |
510 |
Extcnsometcr re- |
|
|
10 |
601 |
425 |
352 |
moved. |
|
|
5 0 Time |
0-31 of an inch. |
305 851 6 mins. 78 V 2 days 63 J |
237 391 6 mins. 30 J |
187 15 |
Break in grips at 41 tons/in. |
been overstrained. The manner in which contraction takes place during the removal of the load is shown by dotted lines in Curves Nos. 2, 3, and 4, and it will lx) noticed that comparatively great retraction takes places as the lowest loads are removed. The test illustrated by Curve No. 5 shows that after 17 days' rest recovery was practically
1C, Mi;. .1 Mr lit ON THE RECOVERY OF IRON FROM OVERSTRAIN.
perfect, the material approximately obeying HOOKE'S law up to the maximum stress of 35 tons per square inch. The load in this test was therefore increased beyond its previous maximum amount. The extensmncter, however, was shortly removed for fear of a suddea break, so that the top part of Curve No. 5 (shown dotted in the diagram) was not obtained from extensometer readings. At a stress of about 41 tons per square inch the specimen suddenly broke, unfortunately in the machine grips ; before this stress was reached no yield-point had been passed, or it would have been detected by a rapid falling of the horizontal beam of the testing machine.
Recovery under Stress, and Effects of Hysteresis.
Experiments were carried out to test the effect of keeping an overstrained specimen loaded, instead of allowing it to rest in an unstressed condition, and it was found that the material, whether kept stressed or unstressed, recovered at practically the same rate.
In the following table extensometer readings are given, which show the gradual recovery from overstrain of two specimens, A and B. A was kept loaded to the maximum stress employed to produce overstrain, while B was allowed to rest free from load.
TABLE comparing Recovery under Stress and Recovery when no Load was Acting.
|
Load in llw./in*. |
Extensometer readings. |
|||||
|
Immediately after over- strain. |
10 days after. |
40 days after. |
||||
|
A. |
B. |
A. |
B. |
A. |
B. |
|
|
500 10,000 20,000 30,000 40,000 50,000 55,000 |
0 137 88fl 446 610 795 901 |
0 135 287 448 612 805 925 |
0 121 269 426 587 759 842 |
0 129 270 427 589 760 859 |
0 129 265 410 560 717 795 |
0 129 269 410 561 719 799 |
m experiment was carried out during a vacation in the Engineering Laboratory
Jnivermty (Professor BAKR having kindly granted the use of apparatus
tory), so that the conditions of experiment are somewhat different from
ined at the beginning of this paper. A 10-ton single-lever testing machine
and the load applied by thousands of pounds, instead of by tons
*>r EWINGS extensometer was still used. The material tested was a half-inch
MI: .1 MI n; UN TIIK i;i;c(ivi-:i;v <»F ii;«>N i'i;n\i U\T.I;STI;AIN.
17
rod of fairly mild steel. It gave an ultimate strength of about .'!'_' tons JMT sijuaie inch, with an elongation ()f 2G£ per cent, on an 8-inch length. The jirimarv vield- jioint occun-ed at a stress of 48,000 Ibs., or about 2t£ tons JMT square inch. It will IK- noticed from the table of figures that this material recovered very slowly, for even after forty days" rest recovery \\as !.\- n.. nie:ms complete. S|M-.-]M,.-'; A of th« ftbovt table \\as further tested after about three and a-half months, an<l considerable imjier- fection of elasticity still found.
Although the table given above shows close agreement U-tween the elastic state- of the material in the two cases, there was really an interesting difference l*-t \\een them. This is clearly shown by Diagram No. V. Curves A and B in that diagram illustrate
Diagram No. V. — (Recovery under stress.)
pool**'* A * B,*min*.
S3 -~*Z-
Scale .— / unit -
Fig. A represents the elastic condition of an overstrained specimen, which li.nl ITCH
resting for forty days at a stress of 55,000 II*. in -'.
Fig. B represents the clastic condition of an overstrained specimen, which had Wen resting for forty days free from stress.
the testing of the two specimens after the forty days' rest referred to above ; the last thirty of these days were uninterrupted by any intermediate testing, and during that time A was in the testing machine, \\ith a load of 55,000 Ibs. per square inch ajiplied to it. The extensomettr having been applied to A, the load was gradually removed,
\,,i. exam. — A u
Mil. J. MUIR ON THE RECOVERY OF IRON FROM OVERSTRAIN.
ami readings taken, from which the part of Curve A lettered abc was plotted. This shows that, while a considerable proportion of the l»ail was being removed, contraction occurred quite elastically, a straight line being first obtained at an inclina- tion giving the Young's modulus for the material. Latterly, however, as more load was withdrawn, the retraction became more rapid, and after all load had been removed, creeping was observed to continue in a marked fashion for a few minutes, as is shown by the horizontal line cd. The load was now increased, and the curve def obtained. At the maximum stress slight creeping occurred, and then the load was once more removed, and curve a'b'c was plotted from the extensometer readings taken. This curve differs distinctly from abc (obtained on first removing the load), the material behaving less elastically during the early part of this second removal of the load. The curve defa'b'c, however, represents an approximately cyclic state, which illustrates the imperfectly elastic condition of the material of specimen A at the time in question. When such a cycle — due to hysteresis in the relation of extension to load — is performed, work is done on the specimen, and the energy so spent is no doubt dissipated as heat.
Specimen B, which had been resting for forty days free from load, was next put into the testing machine, and the load was gradually applied. The result of the first li lading is shown by the part of fig. B, Diagram V., lettered «/3y. This curve is straight for a considerable portion («^8) — the material at first approximately obeying the elastic law — but latterly greater extension occurred, and at the highest load creeping continued very obviously for a short time. The load was then removed, and curve 8e£ obtained. This curve resembles closely the part a'b'c of Curve A, not the part abc. Specimen B was next reloaded, and curve «'/3'y' illustrates the manner of yielding. This curve differs from a/3y just as a'b'c differed from abc. A cyclic state has now been attained, and the cycle a'/6'y'8e£ closely resembles that got with specimen A, which had been allowed to rest under high stress. The readings for curves def&nd a'^y' of these cycles were compared in the table given above.
It will have been noticed that it is not only the cycles ultimately obtained which are analogous in the two figures of Diagram V., but that, if one of the figures, say A, be turned upside down, then the three curves of that figure closely resemble the three curves of the other figure, B. Considering in particular the curves first obtained in the two cases, viz., abc and a/?y, it will be seen that they consist of two parts. There is first a range of almost perfect elasticity, then an elastic limit is passed, and greater extension or retraction obtained, according to the curve in question. The breaking up in the structure of the material, which occurs after this elastic limit has been passed (by a decreasing or an increasing load, as the case may be), is probably analogous to the much greater breaking up which occurs on the passage of a yieldr point.
In Diagram No. VI., there is illustrated the effect, on an overstrained specimen, of keeping an intermediate load acting for some time ; and it will be seen that the process of recovery tends to produce an elastic range about the position of continued
MI;. .1. Mm; ON TIN-; i;i.co\ i:i;v (IF H;MN n;nM < )Yi:i>Ti;.\iN in
fi. The experiments illustrated hy this diagram were carried out in the Cambridge Engineering Laboratory, hence the loading is performed in tons (not in jtnundsi p. r
sjuaieinch. The material iisnl is very similar to that employed to ohtain hi:
No. III., so that the rate of ivroveiy j'lom ovei'stiain is much quicker than with the
material of I li.i-i.uii \'.
Diagram No. VI. tona/mt
40
\ \.
A
7
Load
far/7
//»*
t
!
j»
ȣAoi r&i, iifiA.
f
r
Extvt&ons- diminished tta explained on page ie. Scale : - 1 unit -tsfoofdn inch. 9 I
Curves 4, 5 Rnd 6 are displaced to the right — they should be continuotw with one another and with Curves 2 and 3.
Curve No. 1 of Diagram VI. shows the primary elastic properties of the sti-el r<«\ considered. AHer this tirst test, the specimen \vas largely overstrained and allowed to ivco\er. (>n (estini;. it uas then found t<> Ljive a yield-jn.int at ulx>ut 40 toii-
D 2
•_•„ MI; .1 \irii; ON THK KF.COVKKY OF IKON KKOM OVERSTRAIN.
square inch, ami immediately after this yield-point had been passed, Curve No. 2 was obtained.
h will }»• n..ti(v<l t'mm the diagram that in Curve No. 2, the removal of the load was stopped midway and the stress of 20 tons per square inch allowed to act over a niijlit. Had the load l>een entirely removed, then Curve No. 2 would have continued in some such fashion as is illustrated hy the dotted line in the diagram.
The continued action of the load of 20 tons was found in the morning to have produced the slight extension shown. On then testing the specimen by first increasing and then decreasing the load for a short range on either side, Curve No. 3 was first obtained, and then Curves Nos. 4, 5 and 6.
Curve No. 3 shows a short range of nearly, though not quite, perfect elasticity. A slight discrepancy of sooooth of an inch was obtained on each side of the starting !><>sition.
( 'urves Nos. 4, 5 and 6 show how elastic behaviour is departed from, and greater and greater indications of hysteresis obtained as the range of loading is increased.
Curve No. 7, drawn on the bottom half of Diagram VI., shows the effect of applying a load of 20 tons to this same specimen, and allowing it to act for over sixteen hours liefore proceeding with the loading. That is, the effect produced by a prolonged pause in the loading of an overstrained specimen is shown. After the pause, the curve starts off at a much steeper gradient ; but shortly it falls back again to a rather less inclination than if there had been no interruption in the loading. The dotted line in Curve 7 shows the manner in which the curve would have continued had no pause occurred in the loading. This continuation was accurately known ; for previously the specimen had been loaded to 40 tons, three times in succession, and the last two applications had given very accurately the same curve — no two readings differing by more than yoooo^bs of an inch. At the stress of 34 tons, in Curve No. 7, the effect of a three minutes' pause is shown to be similar to, but of course much smaller than, the effect of the long pause at 20 tons. This slight effect at the higher load may, however, be explained by simply considering that if creeping be allowed to occur at any load, then a small increase of load cannot be expected to produce so great an extension as it otherwise would.
After Curve No. 7 was obtained, the complete cycle represented by Curve No. 8 was gone through. The part of this cycle lettered a represents the partial removal of the load from Curve No. 7. The stress was only reduced to 20 tons, and then one and a-half hours were allowed to elapse. Slight back-creeping occurred instead of forward-creeping, such as happened in Curve No. 2. The load was then increased and Curve b obtained. This curve arrived very accurately at the same top point as Curve a. The load was then entirely removed, and Curve c, which coincides s«. far with Curve a, was obtained. After a pause of five minutes under no load, during which K-.r-k-pivi-ping showed itself, the load was re-applied to 20 tons (<'urvi. </), decreased to /.,-ro (Curve r), and then increased to 40 tons (Curve/),
MI: .1 \irii; ON TIN: i;i:i <>\I.I;N OF IKON I I:»M UVI-:I;STI:.\IN -j|
\\ hidi completed the large cycle of loading. The hysteresis exhibited by a cycle such as this may lx- represented numerically by expressing the breadth of the cycle at any stress, as a fraction of the total elongation of the specimen. If this be done, the hysteresis, in tin- relation nf strain to stress, which recently overstrained iron has JIM U-en shown to exhibit, may IM- compared \\itli that observed with ordinary material l.v Professor EWIM; in experiments on very long wires.* In Professor KWIXQ'S experi- ments, the wires were subjected many times to a certain range of stress, and the extension at half the range was observed l*>th as the load was applied and as it was removed. The latter extension w;is found, due to hysteresis, to be greater than the former ; and the difference being expressed as a fraction of the extension produced l>y the maximum load, values were obtained ranging from ^la in the case of high carbon steel, to TJff in the case of an iron wire in the hard-drawn state, or j^j with mild steel wire annealed and then hardened by stretching. The hysteresis shown at half the range of stress in the cycle described above (Curve 8, Diagram VI.) is about -^ of the extension produced by the maximum load of 40 tons per square inch.
In order to see how far the hysteresis in the relation of strain to stress exhibited by recently overstrained iron is statical in character, or how far it depends on the rate of l«'.-iiling, a cycle was performed allowing ten minutes to elapse after the addition of every 4 tons of stress. The only effect was to produce a series of little notches in the curve obtained, similar to the notch shown at the stress of 34 tons in Curve 7, 1 Magram VI. The area of the cycle was thus not appreciably affected. The time allowed after the addition of every 4 tons was ample so far as the amount of creeping was concerned, as is clearly shown by the creeping at the stress of 20 tons in Curve 7, Diagram VI. If a much longer time had been allowed to elapse, then recovery of elasticity would have taken place as in Curves 3 and 7, Diagram VI., and the question of the static character of the hysteresis would have become complicated.
The back creeping which occurs after the removal of the load from a specimen which has been several times overstrained (for example, the creeping shown to have occurred during ;"» minutes in Curve 8, Diagram VI.) is not simply due to the immediately preceding loading, but to all previous loadings. It was often observed that if sufficient time were allowed to elapse after the removal of a load, the zero reading would become negative. That is, the bar would become shorter than it was before the loading was commenced — an effect which is no doubt to be ascribed t<> previous overstrains, and is analogous to phenomena which have been observed in the residual charge of dielectrics, and in the torsional strains of glass and other materials.
Before leaving this section of the paper, attention should be called to the close analogy between the hysteresis effects shown in Diagram VI.. and the known characteristics of magnetic hysteresis in iron.t
* " On Hysteresis in the Relation of Strain to Stress," ' B.A. Report,' l*s;i. |>. 502. t EWINO. " r.\|» •'imi'iital Researches in Magnetism," • Phil. Trans.,' l»M, or Intok on Induction in Inni and nthi-i Metals."
22 MR. J. MUIR ON THE RECOVERV OF IRON FROM OVERSTRAIN.
Effect of Moderate Temperature on Recovery from Overstrain.
The slow recovery »t' iron from tensile overstrain which has been illustrated by the examples already given, was found to be hastened to a remarkable extent by a slight increase of temperature. Three or 4 minutes at 100° C. were found sufficient to bring alnuit a complete restoration of elasticity ; and this, at the normal temperature, could not be effected in less than a fortnight, with the material considered.
Diagram No. VII.— (Recovery at 100° C.)
.- first S.-zomina. After ft? I
I. 6. 3. * 3. £.
Extensions - diminished as explained onpa.$e IS. Scate :- 1 unit - ^ of an inch. ° '. *
Before describing experiments which show this effect, it may be stated that experi- ments were made (though perhaps they might be considered unnecessary) to show that the tem{>eratures to be dealt with could in no way alter the elastic properties of the material in its primitive condition. A virgin specimen was kept immersed in
MI:, .i. MIII; <>\ THK i;i;cnvi:i;v <>r IKON FK«>M
water for many hours, and another was kept in a sand l»atli at about 250° C. Ibr liall'an hour or so ; in neither case was there found, on cooling, any change in the elastic condition of the material.
In Diagram No. VII. there is shown the history of a specimen \\hii-h was dipped in Ixiiling water, whenever an overstraining load had been applied and removed. By tliis means recovery from overstrain instead of taking days, as in Diagram No. III., was effected in a few minutes. The material and the primary overstrain given to it are exactly as in the second example of slow recovery with lapse of time given above ; so that Curves Nos. 1 and 2 of this diagram (No. VII.) should be practically the same as Nos. 1 and '2 of Diagram IV. In order to show that the two pairs of curves are really to a close approximation identical, some of the extensometer readings taken to obtain these curves are compared in the following table. Curve No. 2 in lx>th cases represents the first loading performed after the overstrain which is illustrated by Curve No. 1.
|
Load in tons/in9. |
Curves No. 1. |
Load in tons/in'. |
Curves No. 2. |
||
|
Diagram IV. |
Diagram VII. |
Diagram IV. |
Diagram VII. |
||
|
0 8 16 20* M 28 29 35 |
0 241 482 604 810 1440 out of range |
0 240 483 606 B3B 1430 (say 6500) |
1 : 16 L't :«•-> 35 |
0 259 539 BSD 1171 1349 |
0 IN 536 829 1167 1335 |
The readings for the other curves of Diagram VII. need not be tabulated.
Immediately after the readings for Curve No. 2, Diagram VII., were obtained, the specimen was taken out of the testing machine and placed in a bath of Ix>iling water for 4 minutes. It was then removed, cooled in cold water and re-tested by gradually applying a load of 35 tons per square inch. Curve No. 3 was plotted from the obser- vations taken. This curve is very similar to Curve No. 5 of Diagram IV., and is distinctly straighter than Curve No. 4 of that diagram ; so that 4 minutes at 100° C. has sufficed to produce more perfect recovery than would have resulted from, say, a fortnight's rest at the ordinary laboratory temjxjrature.
After having been thus recovered and tested, the specimen was turned down in the centre to avoid breaking in the machine grips. About 4 inches at each end were left at the full diameter of 1 inch, a central portion, fully 9 inches long, being turned down to about 0'8 of an inch, and gradually tapered out at each end to the full
Here elastic behaviour may be said to end.
24 Mi;. ,1. MIIU OX Till! l;i:o>VF.KY nF ll;<)NT FROM OVERSTRAIN".
diameter. On n<>\v h-sting the specimen, no change was found in the Ix-haviour of the material; Curve No. 4, which shows this test, agreeing very accurately with Curve No. :t up to the stress of 35 tons per square inch. This maximum loud of 35 tons to the square inch (now 17 '50 tons total instead of 26 '91 tons as before turning down) was kept on for 1 hour, with the result that slight creeping took place, as is shown in Curve No. 4. On augmenting the load a distinct yield-point was got at 37£ tons per square inch. This second yield-point happened at a lower stress than would naturally have heen expected, for in Diagram No. IV. the same material is shown to have been subjected to a stress of over 40 tons per square inch without a second yield-point having been passed. The lowness of the yield-point in the present case, was probably due to an inherent weakness in the specimen, which was shown by the small flaw which ran up the centre of the bar.* Owing to the specimen having been turned down this weakness would exert a greater influence than when the bar was of the full diameter of 1 inch. Experiments on another specimen of the same material, in fact, directly showed that after turning down a yield-point was obtained, at a stress lower than that to which the specimen had already been sub- jected without other than elastic yielding resulting. Such behaviour was anomalous. With other material which exhibited no flaw, turning down was found to have no effect on the position at which subsequent yielding took place.
The second yield-point shown in Diagram VII. having been passed, the material was once more in the semi-plastic state, so to effect recovery it was placed in boiling water again for 10 or 15 minutes. On cooling and re-testing, a third yield-point was obtained at 4l£ tons per square inch, as is shown by Curve No. 5, Diagram VII. The specimen was once more put in boiling water and then tested, with the result that fracture occurred at a stress of 50 tons per square inch. The break was outside the central 8-inch length, close to the tapering neck joining turned and unturned portions.
A short virgin specimen of the same rod as the above was tested (after being turned down in the centre to a diameter rather smaller than in the last case), in order to find the ordinary ultimate strength of the material. The result of this test has already been given on p. 4 ; local extension set in at a stress of 39 tons per square inch of original area, or about 45 tons per square inch of actual stress, and fracture was allowed to occur at that load.
The effect which a temperature of 100° C. had in hastening the recovery process was further strikingly shown by an experiment On one of the specimens employed to obtain Diagram V. This specimen had been allowed to rest for three and a-half months, and was even then found to exhibit considerable imperfection of elasticity. By heating to 100° C. for a few minutes, a marked improvement was made in the elastic behaviour of this specimen.
* See pp. 4 and 14. •
MR. J. MUIR ON THE RECOVERY OF IRON FROM OVERSTRAIN.
25
Effect on Recovery of Temperatures below 100° C.
Diagram No. VIII. , which is in two parts, gives the complete history of a specimen which was allowed to recover its elasticity at various temperatures, after having been overstrained. It shows, among other things, the very considerable hastening produced in the process of recovery from overstrain by even such a moderate temperature as 50° C. (120° Fahr.). A lengthy description of this diagram need not be given, as the side-notes accompanying the diagram give all necessary details. The tables which follow give most of the readings from which the curves of this diagram have been plotted. The material employed differed slightly from that considered last, particularly as regards the position and character of the yield-point ; it resembled more closely, perhaps, the material of Diagram III.
Diagram No. VIII. (First Part).— {Recovery at 50° C., &c.)
Extensions - diminished aa explained on page le. Scaie : - i unit • jgftj of An inch, f < t
Curve No. 1. — Primary last.
.. .. 2. — 30 minutes after No. 1 . „ „ 3.— After 5 minutes at 50° C.
„ 4. — „ 15 „ more at 50° C. „ „ 5. — „ 17 hours at noiniitl
ture (say 13° C.). 6.— After 15 minutes at 50° C.
Curve No. 7.— After 5 minutes at 95° C.
„ 8.— 3 days after No. 7.
„ „ 9.— 20 minutes after No. 8.
„ 10.— 4 hours after No. 8.
„ 11.— After 15 minutes at 50° C.
„ „ 12.- „ 15 „ „ 70° C.
, 13.— 5 „ 95° C.
A comparison of the distances at the top between Curves 3, 4, 5, and 6, strikingly
indicates the large effect of a small increase in the temperature of the restoring bath.
The distance between 3 and 4 (after subtracting ^th of a unit for change of origin),
I •„ units, may be taken as a measure of the recovery due to 15 minutes
\«i|.. c\< in. — A. i:
26
Mi; .1. Ml IK ()N Till: KKCOVEKY OF IRON FROM OVERSTRAIN.
at 50° C. Similarly, only |th of a unit (the distance between 4 and 5) measures the recovery due to 17 hours at the normal temperature (about 13° C.), while -gths gives the recovery due to a fiirther 15 minutes at 50° C.
Diagram No. VIII. (Second Part).— (Recovery at 60° C., &c.)
U. *.A*.
IT.
Extensions - diminished <*s explained on page 13. Sct*li:-lunit
Curve No. 13. — See first part of diagram.
„ „ 14. — 20 minutes after No. 13.
„ „ 15. — After 15 minutes at 60° C.
„ „ 16.— „ 10 „ „ 95° C.
.. „ 17. — „ specimen turned down.
„ „ 18.— 20 minutes after No. 17.
„ 19.— After 5 minutes at 60° C.
Curve No. 20. — After other 15 minutes at
60° C. ,, „ 21. — After 16 hours at normal
temperature.
„ 22.— After 15 minutes at 60° C. „ „ 23.— „ 10 „ 95" C.
Comparison of Curves Nos. 19, 20, 21, and 22, which illustrate the process of recovery after the passage of the fourth yield-point, shows a similar large difference between recovery at the ordinary temperature and that at 60° C. (140° Fahr. ). In this case Curve No. 21 (obtained 16 hours after No. 20) shows that the material has yi.-liled more, after its long rest, except for the higher loads. This apparent weakening is, of course, not due to the resting, but to the fact that the re-applica- :i<»n <»f the load, necessary to obtain the readings for Curve No. 20, has had the effect
further overstraining the material to a slight extent. A curve obtained immedi- ately after No. 20 would have fallen below that curve and also below Curve No. 21, vhile reaching approximately the same top point as No. 20. It may here be emarked that all the curves of this diagram have been obtained from first loadings
MK. J. MUIR ON TlIK l;r.oiYi:i;Y OF IRON FI;OM OYI l>Tl;\|\.
•-'7
READINGS for Diagram No. VIII. (First Part.)
|
Load in tons/in*. |
Curve 1 (first test). |
Curve 2. (30 minutes after 1.) |
Curve 3. (5 Miin ii. at 50° C.) |
Curve 4. (15 lllilllltr.- at 50° C.) |
Curve 5. (17 hours at 13' C.) |
Curve 6. (15 minute* at 50' C.) |
Curve 7. (5 ininiitrs at 95- C.) |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
4 |
119 |
126 |
122 |
.122 |
122 |
120 |
120 |
|
8 |
us |
258 |
248 |
248 |
Ml |
242 |
241 |
|
12 |
360 |
397 |
377 |
371 |
370 |
366 |
366 |
|
16 |
486 |
539 |
517 |
500 |
499 |
489 |
489 |
|
20 |
608 |
688 |
660 |
635 |
633 |
619 |
611 |
|
24 |
729 |
MO |
820 |
776 |
777 |
750 |
734 |
|
26 |
789 |
952 |
910 |
857 |
849 |
822 |
7'.'- |
|
27 |
820 and then off scale |
1019 |
960 \ 965 / |
901 \ 905 J |
8891 890 / |
860 |
828 |
|
20 |
. . * |
800 |
745 |
MB |
670 |
M4 |
612 |
|
10 |
. • • |
459 |
405 |
360 |
348 |
330 |
308 |
|
0 |
... |
63 |
27 |
10 |
4 |
1 |
-1 |
|
Load in tons/in*. |
Curve 8. (3 days after 7.) |
Curve 9. (20 minutes after 8.) |
Curve 10. [4 hours after 8.) |
Curve 11. (15 minutes at 50° C.) |
Curve 12. (15 minutes at 70° C.) |
Curve 13. (5 minutes at 95' C.) |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
4 |
120 |
128 |
120 |
122 |
120 |
120 |
|
8 |
240 |
260 |
248 |
248 |
241 |
240 |
|
12 |
361 |
398 |
379 |
371 |
365 |
360 |
|
16 |
482 |
534 |
518 |
500 |
489 |
482 |
|
20 |
605 |
675 |
661 |
636 |
611 |
607 |
|
24 |
729 |
822 |
811 |
779 |
7:> |
729 |
|
28 |
.-.-,( . |
974 |
940 |
860 |
850 |
|
|
30 |
911 |
1079 1064 |
1029 |
924 |
910 |
|
|
n |
'.•7- |
1195 1170 |
1126 |
989 |
971 |
|
|
33 |
1028 and |
1290 1250 |
1180 |
1022 |
1001 |
|
|
then very large yielding |
in'-'. |
|||||
|
34 1032 |
||||||
|
20 |
* • • |
869 |
829 |
761 |
627 |
36 1094 |
|
37 1128 |
||||||
|
10 |
• • • |
520 |
478 |
419 |
318 |
38 1163 |
|
0 |
. . . |
99 |
.79 |
35 |
10 |
and th( n Inrge |
|
yielding |
2
28
MR. J. MU1R ON THE RECOVERY OF IRON FROM OVERSTRAIN.
READINGS for Diagram No. VIII. (Second Part.)
|
Load in tons/in-. |
Curve 13. (See last tuMe.) |
Curve 14. (20 minutes after 13.) |
Curve 15. (15 minutes at 60° C.) |
Curve 16. (10 minutes at 95° C.) |
Curve 17. (After turning down.) |
|
0 4 8 12 16 20 24 28 32 36 38 |
0 120 240 360 482 607 729 850 971 1094 1163 and |
0 . 128 260 398 536 678 820 973 1133 1320 14401 |
0 122 245 368 490 613 739 865 997 1138 1219 |
0 120 240 360 480 602 726 849 970 1094 1157 |
0 120 240 360 481 601 724 849 970 1092 1152 |
|
large yielding |
1450J |
tons/in2. |
|||
|
40 1212 |
|||||
|
30 20 10 0' |
1190 853 492 78 |
970 662 347 17 |
910 608 303 -3 |
42 1280 43 13301 1365J 43J large |
|
|
yielding |
|
Load in tons/in-. |
Curve 18. (20 minutes after 17.) |
Curve 19. (5 minutes at 60° C.) |
Curve 20. (15 minutes at 60° C.) |
Curve 21. (16 hours at 15° C.) |
Curve 22. (15 minutes at 60° C.) |
Curve 23. (10 minutes at 95° C.) |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
4 |
128 |
122 |
122 |
122 |
120 |
120 |
|
8 |
261 |
249 |
247 |
247 |
240 |
239 |
|
12 |
402 |
380 |
370 |
371 |
363 |
360 |
|
16 . |
547 |
515 |
498 |
499 |
488 |
480 |
|
20 |
691 |
657 |
624 |
629 |
610 |
600 |
|
24 |
832 |
798 |
759 |
768 |
741 |
722 |
|
28 |
989 |
950 |
895 |
907 |
871 |
845 |
|
32 |
1150 |
1100 |
1039 |
1049 |
1009 |
966 |
|
36 |
1320 |
1260 |
1195 |
1207 |
1158 |
1089 |
|
40 |
1508 |
1439 |
1359 ' |
1360 |
1308 |
1212 |
|
43J |
1712 |
1612 |
1518 |
1500 |
1445 |
... |
|
tons/in2. |
||||||
|
44 1336 |
||||||
|
20 |
911 |
820 |
758 |
739 |
700 |
46 1402 |
|
48 1488 |
||||||
|
0 |
100 |
38 |
24 |
19 |
8 |
49 1550 |
|
49£ 1598 |
||||||
|
and then large |
||||||
|
yielding and |
||||||
|
fracture |
Mi: .1 MI'IU ON Till-: KKOiVKKY (»F IKON FIJOM i >Vl.l;sTK.MN
of the specimen at the various stages, so that, as explained when Diagrams Nos. V. and VI. were described, cyclic conditions of material are not represented. The differ- ence between the behaviour of the material when a gradually increasing load was applied for a first time, and when the same load was applied for a second time, was, however, not usually so great as that shown in Curve B, Diagram V., at least with regard to the yielding at the higher loads. At early stages in recovery slightly smaller elongations were obtained on a second loading, but at intermediate stages greater extensions were obtained at the lower loads, and approximately the same exten- sions at the higher. The following table of extensometer readings, obtained from a specimen very similar to the last, may be taken as showing maximum differences, for the material commonly employed in these experiments, between the elongations produced at intermediate stages in recovery by a first and by a second loading. Curves Nos. 6 and 6' of Diagram IX. also show in a striking fashion this difference in elastic condition.
|
Extensometer readings. |
||||||
|
Load in tons/in2. |
1st application. |
. 2nd application. |
Difference. |
1st application. |
2nd application. |
Difference. |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
4 |
120 |
120 |
0 |
120 |
120 |
0 |
|
8 |
246 |
246 |
0 |
240 |
246 |
+ 6 |
|
12 |
368 |
370 |
+ 2 |
362 |
370 |
+ 8 |
|
16 |
490 |
501 |
+ 11 |
488 |
500 |
+ 12 |
|
20 |
619 |
638 |
+ 19 |
618 |
637 |
+ 19 |
|
24 |
7V. ' |
779 |
+ 20 760 |
776 |
+ 16 |
|
|
28 |
930 |
936 |
+ 6 917 |
925 |
+ 8 |
|
|
28} |
961 |
969 |
- 2 939 II |
945 |
+ 6 |
The effect .produced by a third loading of a specimen usually differed from that produced by a second, but the difference was comparatively very slight.
To return to Diagram No. VIII., in the lost test of the specimen (illustrated by Curve No. 23 in the second part of the diagram), the load was increased by a quarter of a ton to the square inch at a time ; a gradual falling away from elastic behaviour was recorded, and finally local extension and fracture occurred at a stress of 49^ tons per square inch. This corresponded to about 46 tons per square inch of primitive area. The total elongation which the specimen had received was estimated to be 12 per cent, on an 8-inch length.
A fresh specimen from the same rod as the above, broken in a single test without allowing intermediate recoveries to take place,* gave an ultimate strength of rather
* Owing to the specimen breaking in the machine grips (at a stress of 38 tons to the square inch) a partial recovery took place while the specimen was turned down in the centre. The strength given above may therefore be a little too great and the elongation a little too small.
30
MR. J. MUTR ON THE RECOVERY OF IRON FROM OVERSTRAIN.
under 40£ tons per square inch of original area. The total elongation in this case \\.iw found to be fully 16 per cent, on the 8-inch length.
In order further to call attention to one or two features of this recovery from overstrain and the effect of temperature on it, the history of another specimen is given in Diagram No. IX.
The steel rod from which this specimen was cut differed but slightly from preceding ones. The rod was 1 inch in diameter, but the specimen was turned down, except at the ends, to a diameter of about 0'8 of an inch. The yield-point occurred at a stress of 23 tons per square inch, and was well defined like those shown in Diagrams III. and VIII., unlike those in Diagrams IV. and VII. The position of the yield-point was, however, sometimes found to vary even with specimens taken from the same rod. Thus, the specimen of the present diagram (No. IX.) gave apparently a perfectly steady extensometer reading after 22 tons per square inch had been applied — steady for, say, half a minute. The addition of the next half- ton produced rather greater elongation than was in accordance with the elastic law, but the reading was still steady. With 23 tons, however, creeping set in shortly after the extensometer reading — a rather large one — had been observed. This yielding continued, becoming greater and greater, and the skin of oxide began to spring off in the manner characteristic of the yield-point. Another specimen taken from the other end of the same bar (a 10-foot one) showed creeping and the springing off of the oxide after 22 tons of stress had been applied.
After the passage of the yield-point, illustrated in Curve No. 1, Diagram IX., the specimen was put into boiling water, and kept there for over 12 hours. This was to see if the position of the second yield-point would be affected by such prolonged treat- ment. As was expected, on cooling and re-testing the specimen a yield-point occurred at a load which agreed with that obtained from an adjacent specimen of the same rod, which had been immersed in boiling water for 3 minutes only. A third specimen from this same rod, after being overstrained, was put in a sand-bath, and kept at 250° C. for half-an-hour. On slowly cooling and then re-testing, the material behaved exactly as in the case of the comparison specimen, which had been restored by 3 minutes' immersion in boiling water. Had the specimen been annealed by heating to redness and slowly cooling, then, of course, the effect of overstrain would have been entirely annulled, and a yield-point obtained at a load corresponding to the stress at which the primary yield-point occurred.* It was found, however, that no effect (other than the recovery from the temporary effect of overstrain) was produced, until a fairly high temperature was attained.
To return to Diagram No. IX. After the second yield-point had been passed, the bar was re-measured and re-tested in the usual manner, Curve No. 3 being obtained. In this test the maximum load was kept on over night, and the creeping which
• See paper by UNWIN, "On the Yield-point of Iron and Steel, and the Effect of Repeated Straining and Annealing," ' Roy. Soc. Proc.,1 vol. 57, 1895.
MR J. MUIR ON THK ICKCOVERY OF IRON FROM OVERSTRAIN.
31
occurred during the first 5 minutes is shown to have been considerable ; for the next 15 hours it was perhaps not so great as might have been expected. This creeping \\rnt tn the production of permanent set. Curve No. 4, Diagram IX., was obtained
Diagram No. IX. — (Temperature effects.)
Settle-- I unit •
Curve No. 1. — Primary test.
„ „ 2.— After 12 hours at 100' C.
„ „ 3. — 15 minutes after No. 2.
„ „ 4. — After load removed from 3. S(>ccimcii now at 45° C., see table, p. 32. Curve No. 5.— After 3 minutes at 60° C.
Extensions - diminished as explained on page if.
of *n inch.
Curve No. 6.— After 4 minutes at 70° C.
„ „ 6'. — Immediately after No. 6.
„ „ 7.— After 4 minutes at 70* C.
„ „ 8.- „ 3 „ „ 100° C.
„ „ 9.— „ process A, diagram X.
ii ii I". „ .. D, ,, \
immediately after the removal of the load from the test illustrated by Curve No. 3, and t hen the specimen was kept at 45° C. for 5 minutes, and afterwards for 15 minutes. The effects produced — which were slight — are shown in the following table. The
32
MR. J. MUIR ON THE RECOVERY OF IRON FROM OVERSTRAIN.
second column under each heading in that table gives the extensometer readings for a test performed immediately after that given in the preceding column.
|
Extensometer readings. |
||||||
|
Load in tons/in1. |
Curve No. 4, Diagram VIII. |
After 5 minutes at 45° C. |
After 15 minutes at 45° C.- |
|||
|
- |
1st. |
2nd. |
1st. |
2nd. |
1st. |
2nd. |
|
o |
0 |
0 |
0 |
0 |
0 |
|
|
4 |
121 |
122 |
120 |
121 |
120 |
120 |
|
g |
251 |
251 |
242 |
249 |
241 |
245 |
|
12 |
387 |
388 |
378 |
384 |
369 378 |
|
|
16 |
525 |
521 |
519 |
520 |
503 |
511 |
|
20 24 |
670 818 |
662 812 |
661 818 |
661 814 |
650 802 |
658 808 |
|
28 |
987 |
979 |
988 |
981 |
978 |
969 |
|
29} J minute (say) |
1059 \ 1061 J |
10481 1050 / |
1061 \ 1070 / |
1049 |
1050 |
1039 |
|
20 |
762 749 |
766 |
751 |
755 |
739 |
|
|
8 |
348 336 |
350 |
339 |
339 |
324 |
|
|
0 £ minute (say) |
22\ 14\ It/ 10 J |
25 |
20 |
29 1 20 J |
14 |
These figures show that an immediate re-application of the load has produced iia each of the three cases less total elongation than the first application, in consequence of the bar's gradual settlement into a cyclic state through successive loadings. After the recovery has become fairly perfect, this considerable diminution in the total elonga- tion obtained by a second application of the testing load does not occur. This was clearly shown in the table on p. 29. In the present diagram Curve No. 6' (shown dotted) was obtained immediately after No. 6, and it shows almost no change in the total elongation produced.
The tests made immediately after treatment at 45° C. are shown by columns 2 and 3 of the table above to have given slightly greater total elongations than those obtained from the loadings performed immediately before warming. This is perhaps contrary to what might have been expected, since increase of tempera- ture has been shown to hasten recovery. But although the total elongations are greater, the process of recovery really has been aided. This is shown by the fact that distinctly smaller yieldings are obtained with low loads after the bar has been heated to 45°C. But though the bar is more perfectly elastic under low loads, under- higher ones the yielding which occurs has not been decreased ; so that, as the specimen is subjected to a gradually increasing load, there is a transition from more elastic l>ehaviour to less, which is suggestive of a yield-point.
To return again to Diagram No. IX., the specimen, after being warmed to 45° C. in
MI: .i. MTU; MX Tin-: KKCOVKKY OF IKON KI:<»M <ivi,i;.xn;.\i\
33
the manner just explained, was subjected to the treatment recorded in the notes accompanying the diagram, and finally, as shown by Curve No. 8, complete restoration of elasticity was effected. The load was therefore increased until a yield-point was obtained at a stress of about 35 tons ]>er square inch. The recovery from the <>\ strain produced by the passage of this third yield-i»oint is shown by means of a curve at A in Diagram No. X. This curve was obtained by plotting amounts of recovery—
Inch
Diagram No. X. — (Time-recovery Curves.)
|
300 £> / |
A • Recov sho* |
try from the •> in dug? |
^ |
Temp AT' to |
6J'C |
\—f^ \min& 33' to 63 |
am/us. iufC 'C |
|
X |
Pdrdbold |
||||||
|
i n |
7 |
Tempert Maximut |
\Cure 60'C n lodd.tSti |
ins] in* |
Time in minutes, during which specimen mcu kept <tt 60'C.
|
i 0 i |
B Ret •M |
overy from •sttniij in dt |
tt,e*$~ *&• a : i-B— minaff °°CA . |
C.K( |
cowry fron |
1 d 4^0*** |
strain |
|
|
Ate* dC 1C |
||||||||
|
7_ |
,..-- |
^o » |
||||||
|
1 |
||||||||
|
/ |
, |
/Vd/t |
boU. |
|||||
|
/ |
^ |
|||||||
|
£ |
Temi *, MAX, |
I KfC |
ChenA |
o*C |
/ |
Temp MAX. I |
eo'C OAd."4ft0n |
t/tftf |
|
load,- |
4OtOI |
H/tnf i |
||||||
|
) 10 IA tO ""< Time in minutes |
) 9 to & eo Time in minutes.- |
measured in the manner described on page 25 (that is, by the diminutions in the extensions produced by the maximum load) — against the time taken at 60° C'. to produce the recoveries. This method of measurement is of course faulty, for it has Ix-en shown above that a slight remvery may have occurred, although a greater total elongation has been obtained. But if the nro\ery is tolerably rapid, the method may be justified, for the sake of comparing the rates of recovery at different stages of completion, by means of a time-recovery curve. At C, Diagram X., there is shown a VOL. r\i in. — A. F
34 MR. J. MUIR ON THE RECOVERY OF IRON FROM OVERSTRAIN.
curve of this kind obtained from a specimen whose history will not be given. This curve was more fully and carefully determined than those obtained from the specimen of Diagram No. IX. ; but any of the curves in Diagram No. X. show that in the earlier stages the amount of recovery is approximately proportional to the squaiv
root of the time.
The heating of the specimens was accomplished by immersing in a hot water-but!) at the required temperature for the required time, and then cooling by at once dipping in cold water. Had the specimen been aUowed to cool slowly in the air, then greater recovery, due to a long and indefinite time at lower temperatures, would have been obtained.
Curve A, Diagram X., shows that at 60° C. a long time would have been required to produce perfect recovery, so the specimen (of Diagram IX.) was finally put in boiling water for 5 minutes. After cooling, a gradually increasing load was applied, and a fourth yield-point obtained at a stress of 40 tons per square inch. This test is shown by Curve No. 9, Diagram IX.
The recovery from this fourth overstrain is illustrated by Curve B, Diagram X. First GO" C. and then 80° C. were employed, perfect recovery being again obtained by bringing the piece to 100° C.
On load being once more applied to this specimen, elastic behaviour was shown up to the stress of 40 tons per square inch. At the 43rd ton, creeping was detected, and this load was allowed to remain on for 20£ hours. Considerable extension resulted, as is shown by Curve 10, Diagram IX. On now further increasing the load, the yielding was found for the subsequent three half-tons to be in close accordance with the elastic law. With the fourth half-ton (i.e., at 45 tons per square inch) creeping was again detected. After 12 minutes, however, this creeping became very slow, so another half ton was applied, with the result that local extension and fracture occurred at that load of 45^ tons per square inch. This stress was equivalent to rather over 42| tons per square inch of primitive area ; the total elongation was about 0'81 of an inch, or rather over 10 per cent, on the 8-inch length.
A virgin specimen from an adjacent portion of the same bar as the above, gave, when tested at once to breaking, an ultimate strength of 36 J tons per square inch of original area ; the total elongation in this case was 1*82 inches or nearly 23 per cent. on the 8-inch length.
It will be noticed that the distance in tons between the successive yield-points shown in Diagram IX. is roughly constant, and further that fracture has occurred where a yield-point (if not a fracture) would naturally have been expected. More correctly, it is the distance between a yield-point and the previous maximum load that is the same throughout. Thus a specimen from' the same bar as that employed for this diagram, No. IX., was overstrained primarily by 27 tons to the square inch, and the subsequent yielding was obtained at 33 tons. That is at about 4 tons higher than the second yield-point shown in Diagram IX., when the primary loading was only carried to 23 tons jxjr square inch. This regularity in the raising
MR. .T. MUIR ON THE RECOVERY OF IRON FROM OVERSTRAIN.
35
of the yield-point was also shown in Diagram No. VIIL, the material being slightly different from that which has just been considered; and, further, it will be shown in Diagram No. XL, whicli gives the history of a specimen of unhomogeneous wrought iron. The distance between the yield-points is 3 to 3^ tons with the common wrought iron and 5 or 6 tons with the semi-mild steel usually employed in these
Diagram No. XI. — (Common iron.)
tons/in* SO
.
Extensions- diminished as explained on page Scale - 1 unit* of AH inch. 1.
Curve No. 1 . — Primary test.
„ „ 2. — Immediately after No. 1 .
»» ii •*• — ii ii it «••
4>> • ii it ii •*•
„ „ 5. — 16 hours after No. 4.
„ „ 5'.— After a few minutes at 100° C.
„ „ 6. — Immediately after No. 5.
Curve No. 7. — Immdiatcly after No. 6. lf „ 8. — After a few minutes at 100* C. „ „ 9. — Immediately after No. 8. „ „ 10. — J hour after No. 9. „ „ 11.— After 5 minutes at 55° C. 12.- 10 , 100° C.
experiments. In Diagram No. VIIL yield-points were obtained at loads of about 27, 33, 38, 43^, and 49J tons per square inch, — fracture occurring at the last mentioned stress. With another specimen from the same steel rod the primary loading was carried to 30 tons per square inch, and after recovery of elasticity a 2nd yield-point was obtained at about 35 tons per square inch. On again restoring elasticity a 3rd yield-point was found to occur at a stress somewhat under 40 tons,
F 2
MI:. .1. .\iriu ON THI: I;KO>\T.I;N <>|- n;<>N FI;<IM <>VKI;STI;.\I\
when recovery from overstrain had once more l)een effected fracture took place at 45 tons per square inch. It is however probable since this material is the same ;i* in Diagram VIII., that had the primary loading in the present case been carried only to 29 tons per square inch, then a yield-point would have been obtained at a stress of 44 tons, and fracture would not have taken place until a load of over 49 tons per square inch had been applied. A yield-point obtained at a high stress is thus a crisis in the history of the specimen under test ; the material is in danger of giving way, but if it does not, then, after recovery it will stand, before fracture occurs, a stress 5 or 6 tons higher than that at the critical yield-point.
It should, perhaps, be pointed out that in Diagram No. VII. no uniformity exists in the position of the yield-points. In this case the specimen cannot, perhaps, be taken as illustrating the behaviour of a certain material, for it will be remembered that a small flaw ran through the centre of the bar from which this specimen was taken, and probably this flaw had a considerable influence in determining the position of the yield-points.* Chemically this material differed only slightly from that of the other steel rods used, as is shown by the analyses given on page 4.
Before concluding this section of the paper, attention should perhaps be directly called to Diagram No. XL, which has already been incidentally referred to. It gives the history of a specimen of common wrought iron, the diameter of the specimen being 1 inch. Curve No. 1 illustrates the primary loading and shows that the yield-point has occurred at a stress of 15^ tons per square inch. After the large stretching had ceased, and the load had been removed, the 8-inch length of the specimen was found to have been stretched about 0'20 of an inch. On re-loading, the material exhibited comparatively little semi-plasticity, as is shown by Curve No. 2. The load was, therefore, increased until a stress of 20 tons per square inch was attained, the specimen being thereby stretched further by about a quarter of an inch on the 8-inch length. On re-testing, the curve obtained was still found to agree closely with Curve No. 2 up to the stress of 15 tons, but as the loading was now continued to 20 tons the semi-plasticity was more clearly shown. Curve No. 5 shows that a night's rest at the ordinary temperature has been sufficient to produce complete recovery of elasticity ; so common iron recovers much more quickly than the semi- mild steel employed for the most part in the course of these experiments. It may be of interest here to recall that the half-inch specimens of comparatively mild steel, employed for Diagram No. V., recovered at a very much slower rate than the harder steel usually employed in these experiments.
After Curve No. 5 was obtained the specimen was put in boiling water for a few minutes to ensure perfect recovery. On testing, Curve No. 5 was repeated, and on increasing the load a yield-point was got at 23£ tons per square inch, as shown by Curve 5'. Curve No. 8 shows that a few minutes in boiling water has effected perfect recovery from this second overstrain. The maximum load of 23£ tons was kept on in this test for 45 hours, and only the slight creeping shown in the diagram occurml.
* Sec p. 24.
Mi:. -T. MUIB ON THE RECOVERY OF li;o\ n;. >\| ( .Yi.KM I:.\1N
37
( >n inn-easing the load, a well-defined yield-point was now got at a load of 26j per square inch. Comparison of Curves Nos. 9, 10, and 1 1 shows the remarkable hasten- ing in the recovery from this overstrain, produced by a temperature of 50° ('. ; \\liil.- Curve No. I1-' shows the material once more in the perfectly elastic condition. On now carefully increasing the load a fracture was obtained close to the upper machine grips, at a stress of 29 £ tons per square inch. The specimen was gripped and loaded again, with the result that fracture occurred close to the lower grips at 29 j tons per squan- inch. This was repeated a third and a fourth time, so that the occurrence of the fracture close to the grips was not due to a primary effect of the gripping, that is, it was not due to the gripping having prevented the material from becoming hardened by overstrain. The breaking load, of over 29 J tons per square inch, was equivalent to a stress of fully 27 tons per square inch of the original area of the specimen. Another specimen of the same rod was found to give a yield-point at 14 tons per square inch, and on steadily increasing the load fracture occurred, near the centre of the specimen, at slightly under 23 tons per square inch of original area. The elongation was alxnit 21 percent, on an 8-inch length. Common iron thus. exhibits the same features as steel in respect of recovery from overstrain and the effect of temperature on it; but in the case of common iron recovery is comparatively rapid.
The Effect of Mechanical Vibration on Recovery from Overstrain.
Diagram No. XII. illustrates the effect of mechanical vibration on recently over- strained iron, and shows that such treatment has an opposite effect to that of increase of temperature — instead of the recovery process being hastened, the material is made distinctly less elastic. The following table gives most of the figures from which various curves of this diagram have been plotted. The material employed is t In- flame as that used for Diagram No. IX., but the specimen in this case was not turned down, and so was of the full diameter of 1 inch throughout its length.
|
Load in tons/in*. |
Curve No. 1. (2nd — aftor vibrating.) |
Curve No. 2. |
Curve No. 3. (i hour's rest.) |
Curve No. 4. (After vibrating.) |
Curve No. 5. (16} hours' rest.) |
Curve No. 6. (After vibrating.) |
|
lat 12nd |
( .ml loading) |
|||||
|
0 |
0 0 |
0 |
0 |
0 |
0 |
0 |
|
•-> |
60 |
61 |
60 |
N |
60 |
60 |
|
4 |
1 •_'•_' 120 |
1 •_'•_' |
120 |
119 |
121 |
120 |
|
6 |
isi! 181 |
188 |
187 |
185 |
188 |
185 |
|
- |
L'l:. 240 |
251 |
251 |
248 |
249 |
|
|
10 |
307 300 |
|||||
|
II |
361 |
390 |
387 |
m |
374 |
379 |
|
It |
429 421 |
|||||
|
1C |
489 482 |
539 |
539 |
MO |
MM |
518 |
|
18 |
549 r, 1 1 |
|||||
|
20 |
609 601 |
699 |
58Q |
718 |
639 |
|
|
n |
659 |
797 |
771 |
818 |
709 |
749 |
|
23 |
Off the |
851 \ 10 |
825 \ 3 |
8681 10 |
71.-. 1 3 |
790 |
|
scale |
1008 J min". |
840 J mins. |
919 J mins. |
750 J mins. |
38
ME. J. MU1R ON THE RECOVERY OF IRON FROM OVERSTRAIN. Diagram No. XII.— (Mechanical vibration.)
Extensions-diminished as explained on page IB Scaie - 1 unit = j^n of An inch. 1 —
Curve No. 1.— Illustrates primary loading.
1'. — Is after mechanical vibration. „ 2.— Immediately after No. 1'. 3. — | hour after No. 2.
Curve No. 4.— After mechanical vibration.
„ 5.— A 2nd loading, 16 \ hours after No. 4. 6. — After mechanical vibration. 7.— 4 minutes at 100° C.
Before the experiment corresponding to Curve No. 1 was performed, a test was made to ensure that such vibration aa was contemplated would have no effect on the elastic properties of the primitive material. The specimen was loaded tffl a stres; 20 tons per square inch was attained, and the load was then removed. The extenso- meter readings obtained are shown in the first column of the table given above. The specimen was then taken out of the testing machine and vigorously tapped with a hammer, so as to make it ring in various modes. It was then re-tested and the second column of readings shown above was obtained. These readings are slightly less than those obtained during the first loading, but this was to be expected on a second loading, though, perhaps, to scarcely so great an extent. Large yielding occurred during this test at 23 tons per square inch, which is the known yield-point of the material Hence violent vibration may be said to have had no effect on the primitive material, or if it had a slight effect, it was shown in the annihilation of the causes of small departures from accurate obedience to the elastic law.
Curve No. 2 of Diagram No. XII. shows the specimen to be in the ordinary semi-
Ml; .1 Mi III ON THE RECOVERY OF IRON FROM OVI l;MI;.\IN 39
plastic condition produced by overstrain, and Curve No. 3 the condition of the material jitter half-un-hour's rest. After this test the specimen was taken out of the testing machine and vigorously tapped with a hammer. On re-testing Curve No. 4 was obtained, which shows that not only has the effect of the half-hour's rest been annulled by the vibration, but that the material was rather more plastic than it had been immediately after overstrain. The specimen was next allowed to rest for H'i.1 In mrs and was then re-tested, Curve No. 5 showing the progress made towards recovery. The specimen was then taken out of the testing machine, and once more struck with the hammer so as to make it ring. On again testing, the elasticity was found just as before to have been made more imperfect, Curve No. 6, which illustrates this test, lying below No. 5. The specimen was then put in boiling water for a little, and Curve No. 7 shows that recovery was complete. Hammering was found to have no appreciable effect on the elastic condition of material whose elasticity had been thus restored.
In concluding this section it may be of interest to state that the effect of turning down the diameter of a recently overstrained specimen was to produce partial recovery of elasticity. This was in all probability due to the warming which accompanied the cutting action — the bar being heated by conduction, and only the surface subjected to severe mechanical vibration.
The Influence of Magnetic Agitation in Hastening or Retarding the Recovery
of Elasticity.
The experiment which is now about to be described was made with the object of finding the effect on recovery, of magnetising and de-magnetising an overstrained specimen.
A coil (Ij inch diameter X 7^ inches long) was made which gave a field strength at the centre of about 140 C.G.S. units, when a current of 10 amperes was passing. This coil was put round a specimen and supported at the 8-iiich length, to which the extensometer was to be applied.
The material used was the same as that of Diagrams IV. and VII. ; the specimen, however, was not in its virgin condition, it had been largely overstrained and had recovered its elasticity again, so that a yield-point was not expected till a stress of about 40 tons was attained. During the loading of the specimen, a current of 10 amperes was passed at intervals through the coil, and it was found that the extenso- meter could clearly detect (when the current was passed) the slight elongation due to magnetisation. This elongation occurred only at the lower loads ; at the higher ones the slight contraction, which is known to occur, was quite readily observed.*
At a stress of 40^ tons per square inch a yield-point was obtained, and while the bar \\as stretching rapidly at this load the current was put on and off several times, its direction being constantly reversed. The contraction, which had been noticed just In fore the yield-point had been reached, was still clearly shown at each "make," by
* For tho chnnge in length caused by magnetisation, when iron is under various stresses, see papers l,y Sin i IMKI. Uii.wKi.i, 'Phil. Trans.,' A, 1888, and 'Roy. Soc. Proc.,' 1890.
40
Mi; .1 Ml IK ON THE RECOVERY OF IKON FROM OVERSTRAIN.
a temporary check in the rate of extension. Time readings — of a few minutes duration taken while the bar was stretching, detected no change in the rate of extrusion when tin- current was allowed to pass for some time, and so the bar for that time kept magnetised.
When the stretching at the yield-point had practically ceased, the specimen was re-measured and the curve showing semi-plasticity obtained. The specimen was then allowed to rest for two hours, and the recovery effected was recorded by a curve. The current was next passed through the coil for periods of from 10 to 15 minutes, and was reversed all the time rapidly by hand, so that the bar was subjected to con- siderable magnetic agitation. Such treatment was found to have no appreciable effect on the recovery of the specimen, the curve obtained on re-testing being almost exactly the same as that obtained after the 2 hours' rest.
Compression Experiments.
The experiments which are now about to be described illustrate the recovery of iron from tensile overstrain by means of compression tests. These tests were carried out on small cylindric blocks, l£ inches diameter by 1-J- inches long, compression being applied by means of the 50-ton testing machine. The small compressional strains obtained were measured by an instrument specially designed by Professor EWING. This instrument resembles in principle Professor EWING'S exteusometer, especially a more recent form of that instrument, and like it is self-contained, and is entirely supj)orted by the specimen under test. A detailed description of this instrument, which is shown attached to a compression specimen in the following illustration, need
not be given here, but it may be stated that with a mechanical multiplication of 10, and further optical magnification, a contraction of u^nnF^ of <™ inch can be measured. This corresponds to a corapressional strain of srAooth, since the length of specimen actually tested is only 1± inches. It may be recalled that the unit of t In- raulings of Professor EWING'S extensometer represented an elongation of ^oWoth, tin- length of specimen tested V-ing 8 inches.
The following two series of readings, obtained with the new compression instru- ment, clearly show by comparison the semi-plasticity which is induced in iron by
MI:, .i Mm; ox THI: m-;o>\ i :I;Y «\- n;n\ FI;OM
tensile overstrain. Tin- curves wliidi have been |>I«>tted tV«.m these readings are
slmuii in Diagram XIII. The first series was nhtaim-d trnm ,-i virgin ^] imi-n »\'
1| iiH-li roiiiul steel ml, very similar in quality to the 1-inch r<xls usunllv
tonafinf
JO
I >i;if,'r,-iin NIL XIII.— (Compreasion experiments.)
specimen aimiiar to ff?e, hue After it fad been for
* A e
Contractions - diminished by f^5o °^d/7 inc^ P*1" ton- Scdte - lunit- of An inch. ? - i - 5
in the tension experiments. The total length of the-specimen was only if diameters, and the ends were carefully faced, so that "buckling" may be said to have been avoided, and the compressional stress applied in as uniformly distributed a manner as was practicable.
vol.. i \riii. — A.
42
Mil. .1. MI-IK "N THK KKCOYKKY «>F IK'.N FIJMM « )VKi;Ml;.\l.\
|-|,;>, BeneB of Compression Instrument Readings. (Test on a Virgin illustrated I iy Curve 1. Diagram XII M
|
Load in tons per sqtwe inch. |
Contractions in = :nnnnftn<* °* an inch> |
1 >ifference |
|
o |
0 |
|
|
1 |
20 |
20 |
|
2 |
43 |
23 |
|
4 |
88 |
45 |
|
G |
134 |
46 |
|
8 - |
183 |
49 |
|
10 |
827 |
II |
|
li' |
^'77 |
50 |
|
14 |
.'•I' 1 |
44 |
|
1C |
367 |
4G |
|
18 |
410 |
43 |
|
20 |
168 |
58 |
|
21 |
505 1 |
|
|
time 510 J |
||
|
22 |
555 1 |
|
|
time 560 J |
87 |
|
|
23 |
685 |
|
|
24 |
705 |
150 |
|
25 |
800 |
|
|
26 |
1000"! |
295 |
|
1 min. 1075 J |
||
|
The load was now removed and the follo\ving readings taken |
||
|
20 |
990 |
|
|
15 |
915 |
75 |
|
10 |
815 |
100 |
|
5 |
705 |
110 |
|
1 |
622 |
|
|
0 |
588 |
117 |
The difference column given above shows that the material has behaved elastically until a load of 20 tons per square inch was attained. Beyond that load there is shown a gradual but tolerably rapid departure from HOOKE'S law ; there seems to be, however, no very definite yield-point. In a tension test of this material creeping was first noticed at 23 tons per square inch, and at 24^ tons a very large yielding occurred. YOUNG'S modulus, as calculated from the compression readings given above, was found to agree with that obtained from tension experiments to two significant figures ; in both cases the third figure was rather doubtful. Thus, the modulus as got from a first loading in tension to 20 tons per square inch, was 13,100 tons per square inch, while from a second loading to 10 tons per square inch it was found to be 13,300 tons per square inch. The modulus, as calculated from the contraction shown to have occurred in the table above, between 4 and 18 tons per square inch, is 13,600 tons per square inch.
The second series of compression instrument readings was obtained from a specimen
MI: .1. MI IK <>\ TIII-: i:i-:n>\ I-.I;N <>K II;M\
HVKKSTBAIN
It
iif tin- same I J-inch n>d, but after the rod had U-eii overstrained largely in tension 1»\- a |..;t(l of :V.\ tons |,,.| square inch. The compression specimen was cut from the strained \x\r immediately after the large stretching load wan removed, care lx-in£ taken t«. piv\ . -m uarming during the cutting and mechanical manipulation necessary to the making »\' the small compression block. To test the eti'e< •( of such mechanical treatment on the elastic condition of the material, a tension specimen was overstrained, tested, immediately turned down to n smaller diameter and tested again. As has already been recorded on page 39, considerable, though by no means perfect, recovery of elasticity was found to have been produced. Owing to the precautions taken in making the compression specimen used for this second series of readings, the mechanical manipulation may be assumed to have produced no effect on the elastic properties of the material.
SKI CM > Series of '( '.impression Readings. (Material freshly overstrained,
Curve 2, Diagram XIII.)
|
I, owl in tons per square inch. |
Contraction* in •-• j<nnn>th« o* »n inc1'- |
Difference*. |
|
0 |
0 |
|
|
1 |
w |
20 |
|
•_' |
l-'i |
u |
|
1 |
94 |
51 |
|
6 |
148 |
01 |
|
8 |
L'lT |
n |
|
10 |
315 \ |
98 |
|
time 350 J |
||
|
r_' |
500 |
185 |
|
14 |
'170 ' |
170 |
|
."> iiiin-. 768 |
||
|
16 |
948' |
178 |
|
.1 niins. 1010 |
||
|
1260 |
312 |
|
|
20 |
i ii.")0 T |
|
|
•J iniiis. I7.">0 > |
390 |
|
|
•JO mins. 1816 J |
||
|
1 .n »l wiw now renic. MM! ami the following i witlings taken : |
||
|
10 |
1610 |
|
|
I |
1466 |
|
|
:.> |
1410 |
|
|
0 |
1360 |
\ oiu|>ari*oii of' the difference column of the present series of readings with that of the \;>^ \ei-y clearly shows tlie change in the elastic condition of the material, pro- duced by tensile overstrain. There is now not even approximate conformity with HOOKK'S law at the lowest load-.
The recovery of elasticity, which is brought about either by prolonged rest at
o 2
44 M1; .,. M, ,,; OH T11K RKCOYKKY OK IKON KKOM OVF.KSTKMN.
normal temi»-ratu,vs. « by keepiug the piece for ,, *» mim,t,s !lt a temperature uch as 100° C is shown in the following series of OOmpre«» instrument readings. This third series of readings was obtained from • compression specimen taken from the same overstrained rod as the last; but in the present case the specimen WM boiled in water for 6 minutes before being tested. This test is illustrated by Cum- No. 3, Diagram XIII.
T.mii. Series of Compression Readings. (Showing Recovery of Elasticity produced
by 6 Minutes' Boiling.)
|
Load in tons per square inch. |
Contractions in ^TinrorjU18 of an inch. |
Ditt'erences. |
|
0 |
0 |
|
|
V/ i |
29 |
|
|
J. 2 |
48 |
26 |
|
4 |
99 |
51 |
|
6 |
152 |
53 |
|
g |
208 |
56 |
|
10 |
-.'62 |
54 |
|
12 |
319 |
57 |
|
14 |
382 |
63 |
|
15 |
428 (creeping |
|
|
noticed) |
||
|
16 |
482 |
100 |
|
17 |
558 |
|
|
18 |
660 |
178 |
|
19 |
795 |
|
|
20 |
970 \ 1 min. 1020 J |
310 |
|
On removing the load the following readings were obtained : — |
||
|
15 |
912 |
|
|
10 |
788 |
|
|
4 |
639 |
|
|
2 |
589 |
|
|
0 |
540 |
Comparison of the differences in this table and those in the last, or comparison of Curves 2 and 3 of Diagram XIII. , clearly shows the large effect produced by the 6 minutes at 100° C. Comparison of the first and third series of readings, or of Curves 1 and 3, Diagram XIII., seems to indicate that the 6 minutes' boiling has not sufficed to produce quite perfect recovery of elasticity. In Curve No. 4 of this diagram— the readings need not be tabulated— there is shown the testing of a specimen very similar to that employed for Curve No. 3, but in this case it was certain that recovery was complete. The specimen was not taken from the same overstrained portion of a bar as that from which Curves Nos. 2 and 3 were obtained, but from another portion of the same material, which had been similarly overstrained. Before the compression specimen was cut off, the overstrained tension specimen had
MI;, .i. Mm; ON Till-: i:i:mvm <>K II;<>N H:<I\I «.\ i .KM i;\lN. 45
been allowed to rest for many weeks, and had been tented and found t<> I*- <|iiite elastic up to a stress of 35 tons per square inch. The tension specimen was, however, 1 ><>iled for some time as a further precaution, and then the compression specimen was cut from it, and the test illustrated by Curve No. 4 was performed. The modulus given by this curve agrees very well with that obtained for the virgin material from Curve No. 1. The marked discrepancy shown in this curve, No. 4, at the lowest loads may evidently be discarded ; it was probably due to imperfect facing of the ends of the specimen, or some such cause.
Curve No. 4, further, very clearly shows that tensile overstrain — which raises the yield-point in tension — lowers that in compression, or, it may be more definite to say, lowers the load at which anv arbitrary amount of plastic contraction occurs. This is in agreement with Professor MAI >• IIINUER'S conclusion with regard to the elastic limits. \i/... " that the elastic limit in tension cannot be raised without lowering the limit in compression, and vice versd."* Professor BAUSCHINUER draws a further conclusion from his experiments, namely, that when the elastic limits of a material are varied by overstrain, the range of perfect elasticity seems to remain constant, so that, if the elastic limit in tension l>e raised, then that in compression is lowered by an equal amount. The author's experiments do not bear this out. They show that such a proposition cannot be applied to the yield-points, for the yield-point in tension of the material in the condition whose compression properties are illustrated by Curve 4. Diagram XIII., was found to occur at a stress between 12 and 13 tons per square inch, above the yield-point of the material in the primitive condition, and no matter where the yield-points in Curves 1 and 4 be supposed to exist, the lowering, which is the result of the tensile overstrain, cannot be greater than 4 or 5 tons of stress.
The characteristics of overstrained iron in respect of hysteresis and imperfect elasticity may be considered as illustrating MAXWELL'S views on the ' Const it ution of Bodies,' as set forth by him in the ' Encyclopaedia Britannica.' t In that article all bodies are assumed to be composed of groups of molecules oscillating about more i >r less stable configurations. If the oscillations are such as to cause all the groups to be continually breaking up, then we have a viscous fluid. But if "groups of greater stability are disseminated through the substance in such abundance as to build up a solid frame work, the sxibstance will be a solid, which will not be permanently deformed, except by a stress greater than a certain given stress." A solid, however, is not assumed to be entirely composed of these stable groups of molecules, or say of sensible particles, but to contain groups of less stability, and also groups which break up of themselves. When a solid has been permanently deformed or overstrained
* See UNWIX'S hook on ' Testing of Materials of Construction," p. 386, or BAI:SCHINGER, " Ueber die Veriindciiing der Ehinticitategrenze iind die Festigkeit de« Eisens und Stahls," ' Mittheihmgen aus dem Me. h. Techn. Lalwratorium in Miinchen,' 1886.
t Or Ha tin- 2nd volume of CI.KKK MAXWKI.I.'S 'Collected Paper*.'
Mi
\||; .1 \ir||;
TIIK KKO tVKKN
Ii;<>\
< iVKKSTKAIN.
thru " son it- <>t' the less stable groups have broken up and assumed new configura- tions, but it is quite possible that others more stable may still retain their original configurations, so that the form of the body is determined by the equilibrium between these two sets of groups : but if, on account of rise of temperature, increase of moisture, violent vibration, or any other cause, the breaking up of the less stable groups is facilitated, the more stable groups may again assert their sway, and tend to restore the body to the shape it had before its deformation."
The semi-plasticity exhibited by recently overstrained iron may thus, on the above theory, be attributed to the less stable groups, which after overstrain are in comparative abundance. And since these less stable groups will tend to break up of themselves, there will be a slow recovery through lapse of time towards elastic behaviour which is associated with the idea of stable groups.
Increase of temperature has been shown in the present paper to hasten recovery from overstrain to a remarkable extent. This, as indicated by the quotation given above, may be ascribed to a greater facility given by slight warming, to the breaking up of the less stable groups, and possibly to the re-formation of more stable groups.
Violent mechanical vibration, however, seems to break up the rather more stable groups, rendering the material more semi-plastic and hindering the recovery process.
That recovery from overstrain, or more generally, that the phenomenon of " elastic after-action," is associated with complexity in the physical structure of the material, is further borne out by the fact that a crystalline body, such as a quartz torsion fibre, exhibits little or no after-action (in the form of zero-creeping) ; while a complex body like glass shows such action in marked degree. An analogy to this difference in the behaviour of material, according as it is simple or complex, is found in the phenomenon of the residual charge in the Leyden jar. Condensers with pure dielec- trics such as sulphur, quartz, air, exhibit little or no residual charges ; while with complex substances like glass, gutta-percha, caoutchouc, the phenomenon is par- ticularly observable.
I '' !
II. On the. Nature of Ekctrooap&CH'y /'/"'nomena. — I. Their Jf>/'itin,, t<> tin- !'<
I Differences between Solutions.
By S. W. ,T. SMITH, M.A., /»,;,«• rltl ('„„//*- 7Y..w,r Student of Trinity College, ( 'ninln'idge ; Demonstrator of Phy.*i<-x in tin- Ifni/al College of Science, London.
Communicated by Professor A. W. KIVKKK. .S-< . Jt.S. Received .laiuuiry 5, — Bead January 26, 1899.
TAULK OK < 'ONTKNTS.
FV
Introduction 48
The 1 .ippmann-Hclmholtz theory of elect rocapillary phenomena 49
1. The first hypothesis of the Lippmunn-Helmholtz theory. The effect of depolari-
zation. Experimental determination of the magnitude of the depolarization current. 50
2. The second hypothesis of the Lippmaim-IIrlinholtz theory 87
The relation Iwtween the Lippmaiin-IIclmholtz theory and other theories of clectrocapilliu y
phenomena 58
The discrepancy between the Lippmann-Helmholtz theory and the Nernst-Planck theory of
the potential difference between solutions 59
Solutions of potassium chloride and potassium iodide 62
1. The potential difference between equally concentrated solution* 62
•2. The nature of the electrocapillary curves for the same solutions ........ 62
a. General character of electrocapillary curves 62
A. Definite nature of the " descending " branched 63
Method adopted in the present examination of the electrocapillary curves and
discussion of the degree of accuracy attainable in the experiments 63
</. The electrocapillary curves for KCI and KI 66
1. Preliminary experiment M
2. Final experiment* showing the agreement of the first hv|x)tliesis of the
Lippmann-Hchnholtz theory with the Ncrnst-Planck theory of the
potential difference between KCI and KI 69
. i mi nation of other known discrepancies between the Lippnmnn-Helmholu theory and the
Nernst-Planck theory 74
1 . Solutions of potassium chloride and potassium sulphocyanide 74
2. Solutions of potassium chloride and sodium sulphide 74
The relation Iwtween the nature of the kation of the solution and the form of the electnt-
capillary curve 77
Experiments with equally concentrated solutions of potassium and sodium chlorides .... 77 Relation l>etween the surface tension for a given potential difference and the concentration of
the solution employed in the electrometer . . . 80
Relation between the electrocapillary curve measurements for KCI and KI, and dropping
1 nir.iMiii'incnts fur >iilutinii< of these salts 83
U.7.M
4K Ml!. S. W. J. SMITH ON THE NATURE OF ELECTROCAPILLARY PHEXtiMI N A
THK phenomenon of surface tension exhibited at the surface of separation l>etween two homogeneous liquids may be regarded as arising from such a variation in the distribution of the matter composing each of the liquids, in the immediate neighlxnir- hootl of the surface of separation, that the energy of given quantities of the two liquids is greater when these are in the neighbourhood of the surface than when each is in the homogeneous interior of its corresponding liquid.
On such a view, the tension per unit length in the surface will be equal to dE/dS, where dE is the increase in the potential energy of the system of two liquids, resulting from an increase, dS, of the surface of separation l>etween them. The distribution of energy here referred to may be considered independent of possible electrostatic effects at the surface of separation.
There is little doubt, however, that there is frequently a potential difference of considerable amount at the surface separating two such liquids as mercury and a solution of a salt in water. There must, therefore, be a corresponding separation of electricities of opposite sign at the surface, and we may regard these as forming a condenser-like " double-layer." This double-layer will give rise to an electrostatic surface energy, whose value we may write as E' = -JcSTr2, where c is the capacity of the double-kyer per unit surface and TT is the potential difference across it. S is, as before, the area of the surface separating the two liquids. Now, if a small change of this surface, dS, be supposed to take place while the potential difference across the double-layer is kept constant by an external electromotive force, we get
This increase in the potential energy of the system, with increase in the surface of separation between the two components, will be an effect that tends to take place under the influence of the external electromotive force, and will be equivalent to a force per unit length tending to increase the surface of separation between the two liquids.
The observed surface tension will thus be
y = dE/dS -
= ya -
where y0 is the surface tension arising from the non-electrical distribution of energy first mentioned. The equation will give the relation between the observable surface tension and the potential difference at the mercury surface.
The above may be regarded as the Helmholtz theory of electro-capillary pheno-
MK. S. \V. J. SMITH ON THK NATURE OF ELECTKOCAPILLAKV I'HKNn.MKNA. in
mena. LIPPMANN found that the curve showing the relation between the surface tension and the E.M.F. applied between the terminals of a capillary electrometer was (for a jKirticular solution of sulphuric acid) approximately j>aral«»lic through a con- siderable portion of its course, and it appeared from this that c was a constant and that y0 was independent of ir.
It is not a necessary consequence of considerations such as the above, that c should be constant ; but if the only effect of the potential difference is to produce an electro- static surface energy represented by fair per unit surface, then the observed surface' tension should have a maximum value when IT = 0, even although c may be variable The assumption, that the maximum surface tension corresponds to zero potential difference between the mercury and the solution, has been much employed in recent years in the deduction of values for the contact potential difference between various electrodes and electrolytes. It must be remembered, however, that the observed variation in the surface tension need not be due solely to variation in the quantity ^cir. The non-electrical surface energy, represented by y0, may vary with the potential difference. A variation in the potential difference at the surface of separation between the mercury and the solution may be accompanied not only by a variation in the electrostatic surface energy, but also by a variation in the distribution of the matter in the neighbourhood of the surface.
If a variation of the kind just mentioned can be traced, it is clear that we cannot consider the phenomena as if they were due to a certain non-electrical distribution ujxm which is superposed an electrostatic double-layer, producing no other effect than that represented by its electrical energy. Hence it nerd not happen that the maximum surface tension corresponds to zero potential difference, for the maximum surface tension may arise from the fact that non-electrical effects, accompanying the change in the potential difference and tending to reduce the surface tension, pass through a minimum value as the potential difference changes. This minimum value need not necessarily correspond to zero potential difference. The possible nature of non-electrical effect*) which may accompany changes in the potential difference is discussed later. The first part of the paper contains an experimental analysis of the Lippmann-Hehnholtz theory.
THE LIPPMANN-HELMHOLTZ THEOIIY OF ELECTROCAPILLARY PHKNOMKNA.
In theLippmann Helmholtz theory of the capillary electrometer there are in reality two distinct hypotheses, either of which may be separately justifiable. The first concerns the manner in which the potential difference at the capillary varies with the electromotive force applied between the terminals of the electrometer. The second deals with the relation between the above potential difference and the tension of the surface separating the mercury and the solution.
\..'. rxmr.— A. n
50 Ml!, s. AV. .1. SMITH ON THE NATURE OF ELECTROCAPILLARY PHENOMENA.
The, First Hypothesis of the Lippmann-Hdmholtz Theory.
The first hypothesis would apply to any electrolytic cell consisting of two polariz- able electrodes placed in a conducting solution. When an E.M.F. (of which the value is kept within certain limits depending on the nature of the electrodes and of the solution) is applied to such a cell there may be a considerable current for a very short time ; but the system almost at once assumes a practically steady state in which there is only a very feeble continuous current through the cell. The value of this current can in general be neglected in comparison with the current value found by dividing the E.M.F. applied by the calculable resistance of the electrolyte. It is therefore considered that the potential fall within the liquid can be neglected in comparison with the sum of the potential changes in the neighbourhood of the electrodes, and that this sum is equal in value to the applied E.M.F. The system is, in fact, considered equivalent to a pair of condensers (supposed existent at the surfaces of separation between electrode and solution) connected in series by a resistance (repre- sented by the resistance of the electrolyte). For electrodes of the same nature in the same solution the respective capacities are taken to be proportional to the areas of the surfaces in contact with the solution. In the capillary electrometer, therefore, the capacity of one electrode would in general be indefinitely small compared with that of the other.
Let AA' and BB' represent condensers (of capacities C, and C2) of which the plates
A' and B' are connected by a resistance R, and of which the " external " plates A and B are at first also connected.
Supjx)se the condensers are charged, and let A and B be at zero potential while A' and B' are at the potential — TTB. Let now an E.M.F. irt be introduced in the external circuit connecting A and B, and let the resistance of this circuit be R'. Let TT, IT' and TT" be the final potentials of A, A' and B' respectively, — B being supposed kept at zero potential. Then it is easy to show that
MR. S. W. J. SMITH ON THE NATURE OF ELECTKOCAI'ILL.MtY NIKM i\ll IN A 51
in which the integral represents the quantity of electricity that has passed in tin- circuit during the time r taken by the system to acquire its steady state. Also
IT = IT, if
1 fT = (IT, — irn) — I i (It
C| Jo
and
IT" = i dt — ir» = IT'.
c, .'0
N"\v if the condenser A A' is very large comjKired with the condenser 1515. \\e nuiy
neglect in comjKirison with — , so that we get c, c^
it
IT = IT, — 1Tn
and
t
7T ^~ 7T — 7Tn«
Thus the effect of introducing the E.M.F. irt is that the potential difference at the small condenser is changed from — IT* to ir, — TT,, while the change at the large condenser is negligible.
If the supj>osed analogy were complete, we should, therefore, have the result that in the capillary electrometer the variation of the potential difference at the capillary electrode is the same as the variation of the E.M.F. applied between the terminals. The analogy between the condenser system and the electrolytic cell cannot, however, be complete. In the latter case the original potential difference (corresjw Hiding to — ir.) is not arbitrary, but represents one of the conditions of the equilibrium at tin- electrode. Any cause which tends to alter the "natural" potential difference — IT., at the small electrode — the nature of the solution in the neighlxmrhood of the elect r< '(It- remaining sensibly constant — must in general be accompanied by a "depolarization" current representing the continual tendency of the " polarised " electnxle to revert to the original potential difference. We cannot, therefore, have i = 0 in the final steady state ius in the condenser system.
The E/ect of Depolarization.
It' we assume, however, that the effect of the depolarization Is to produce a fall i>t' potential within the electrolyte according to Ohm's law, the nature and magnitudi- of the effect can be readily specified. Thus, taking the symlM.ls ;)s alxi\e to In- appli.-ahl.- t.. tin- capillary electrometer, we shall have
r.-» = B'./(»")
and
TT'-TT" = 11. II •_'
52 Mil. S. W. J. SMITH ON THE NATURE OF ELECTKOCAFILLAKY HIF.NnMKNA.
in which the continuous depolarization current is written as a function of IT", because of the assumption that if the area of the capillary electrode is kept constant, the magnitude of the current will depend only on the potential fall at that electrode. It is not to be expected that the depolarization current will remain constant for an indefinite time. Owing to the variation of the concentration of the solution in the neighbourhood of the electrode, which must necessarily accompany the passage of the current through the electrolyte, the relation between IT" and the depolarization current will alter ; but an effect of this kind will be gradual, and we may consider the depolarization current to be constant for some time after the introduction of TT,. In like manner, the accumulated effect of the continuous current upon the potential fall at the large electrode will only be gradually perceptible.
Adding the two above equations, and putting TT — IT' = irn, we get
It therefore follows (as is otherwise obvious), that the effect of depolarization would be to cause the potential difference at the small electrode to change less rapidly than the applied E.M.'F. Hence, before one can proceed beyond the first hypothesis to examine quantitatively whether the second hypothesis, concerning the relation between the potential difference and the surface tension, is true, it is necessary to determine whether the effect of the depolarization can under any circumstances become appreciable.
The magnitude of the effect will depend upon the value of (R + ft') /(""")• The internal resistance, R, will, of course, depend upon the nature of the electrolyte employed, upon the internal cross-section of the capillary tube and upon the distance between the mercury meniscus and the point of the capillary tube. Its value may range from something like 50,000 or 100,000 ohms to a million ohms or more. So that, under usual circumstances, the external resistance, R', can be neglected in comparison with R. The value of / (IT") will depend upon the area of the mercury meniscus. It will, therefore, be possible in a given electrometer to vary the value of R/(TT") fora given solution, and (by comparison of the curves for two different positions of the meniscus) to determine whether the form of the curve is appreciably affected by the change. On the other hand, the effect may be rendered directly evident and measurable by interposing a very high resistance in the external circuit, so that, although /(ir"), and even R/(TT"), may be very small, R/(TT") will have an easily observable magnitude.
Experimental Determination of the Magnitude of the Depolarization Effect.
I have used this latter method, and the following experiments may be given in illustration of it. The high resistance consisted of graphite rulings upon ebonite, and
Mil. S. W. J. SMITH ON THE NATURE OF ELECTROCAHLLARY I'lII.NoMl-NA. 53
in the experiments in question had on approximate value of 10 megohms. The ;u ran^cinent was as in the diagram :—
-it-
|
w, |
"fc |
|
|
/ |
The graphite resistance could be cut out of the circuit by means of the key K. For each E.M.F. applied, the direct reading with R' cut out of the circuit (as in thr ordinary method of determining capillary curves), was taken ; the "indirect" reading with R' in the circuit was then observed. The results for a solution of sulphuric acid are shown in fig. 1. The ordinates are the scale readings of the summit of the
Fig. 1.
|
** |
_~ |
**^ |
te |
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|
• «c |
jt |
(!? |
*%. |
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|
* |
/r |
X |
"••v. |
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— -r |
|||||||||||||||||||
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/ |
K |
^ |
" |
K |
— — ... |
K |
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r |
: |
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m m |
i |
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' a |
B ' |
1 — z |
a — ' |
12 |
H ' |
— a |
|
E |
— I |
• |
B |
1 E |
mercury column of the electrometer, and the abscisste denote the values of the resistances unplugged in the resistance box W2. 1000 ohms correspond approxi- mately to 0'28 volt. These depolarization experiments were made in June, 189G, with an electrometer slightly different from that described later in the paper.*
* These experiments were described in a Dissertation presented at Trinity College, Cambridge, in August, 1896. I have since fotiml that WIEDEBURO has also indicated, theoretically, the effect of depolarization. ' \Viol. Ann.,' 59, 1896 (October). WIEDEWIUJ'S conclusion concerning the possible magnitude of the depolarization effect is not supported by the experimental results contained in this paper. For example, when the surfiice tension has its maximum value at the capillary electrode in an electrometer containing a normal solution of potassium iodide, ho suggests a possible potential fall of about 0'25 volt within the electrometer solution (due to n depolarization current) as a means of reconciling certain results, mentioned l.-itor, with tin- ordinary I.i|>|uiiaiin Hclinholt/. theory. The actually observed dojxilurization current for a KI solution is far smaller than that required to substantiate WiKDEUl'Kd'.s suggestion, and, apart from this the relations established later are at variance with his view.
54 MK. S. W. J. SMITH ON THE NATURE OF ELECTROCAPILLAKY IMIKNo.MKNA
The method of taking the electrometer curves and their degree of accuracy is
discussed later.
The dotted curve represents the indirect curve, while the continuous one represents the ordinary capillary curve. In this particular experiment it apparently happened that for some accidental reason (such as difference in purity of the mercury of the large and small electrodes) the " natural" potential difference at the small electrode was appreciably different from that at the large. In consequence of this, the surface tension of the small electrode began to increase immediately the connection between it and the large electrode was broken. As I have subsequently observed, this is an effect which can be obviated when due care is taken, with pure mercury and a solution of uniform concentration. The phenomenon does not affect the conclusions in the present case, but in fact rather increases the interest attaching to the observations. When the electrodes were joined by a short wire, the surface tension was different from what it was when they were joined by the graphite resistance. The reading in the latter case was not appreciably affected by reversing the resistance, so it could be assumed that the graphite did not introduce any appreciable E.M.F. into the circuit.
At first the indirect readings for a given external E.M.F. give higher values for the surface tension than the direct. The curves cut one another at an E.M.F. corresponding to about 0'28 volt, so that for this E.M.F., the surface tension assumed by the mercury is the same whether the E.M.F. is applied directly or through a very high resistance. Hence, when the surface tension at the capillary has this particular value, there can be no appreciable continuous current through the electrometer. It was found that the surface tension in question was practically identical with that assumed by the capillary, when the electrometer was disconnected from the rest of the apparatus— the electrodes being also unconnected. From this it is highly probable that this surface tension corresponded to the natural potential difference at the small electrode, and the significance of the disappearance of the depolarization current becomes immediately clear.
The horizontal distance between two points corresponding to the same surface tension, one on each curve, is a measure of the depolarization at the small electrode when the potential difference there has the value corresponding to the given surface tension. The actual value of the current is equal to the above horizontal distance (expressed in volts), divided by the value of the graphite resistance in ohms.
The curve in fig. 2 shows how the depolarization current varies with the externally applied E.M.F. The depolarization, apparently for a considerable range, is nearly proportional to the extent by which the potential difference at the small electrode has teen displaced from its natural value. The ordinate of any point on this curve is the horizontal distance between a given point on the direct curve and the corresponding point on the indirect curve ; the abscissa is the sain.- as that of the given j)oint on the direct curve. Since each of the curves has a maximum
Ml; s \\ .1. SMITH ON THE NATURE OF ELECTROCAPILLARY PHi.NCMKXA. 55
onlinate, they cross one another a second time. In the neighbourhood of the maxima tin- horizontal distances between the curves are not very accurately determinable ; In it the general nature of the depolarization curve is obvious.
Fig. 2.
|
f |
|||||||||||
|
1000 790 |
|||||||||||
|
/ |
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|
/ |
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too 0 -too |
i -*- |
,*-*^' |
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h. |
, |
«------ |
— »- — |
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The vertical dotted line in fig. 1 is drawn as nearly as possible through the highest point of the capillary curve. Immediately to the right of this line there is a dotted curve. The points required to determine this curve were obtained by bisecting the horizontal lines drawn between points on the direct curve corresponding to the same surface tension. Considering any horizontal line, therefore, the intercept made on it between the vertical line and the above dotted curve represents the extent by which a point on the descending branch departs from symmetry with the corresponding point on the ascending branch, with respect to the vertical axis. The whole curve, therefore, represents the manner in which the descending branch of the capillary curve departs from symmetry with the ascending branch, with respect to a vertical axis through the point of maximum surfluv tension. The internal resistance of the electrometer used in the experiment above described was certainly less than 100,000 ohms, and probably not much above 50,000 ohms. Hence the depolarization effect upon the form of the curve, due to the internal resistance of the electrometer, lay between 0'5 per cent, and 1 per cent, of the corresponding effect due to the external resistance of 10,000,000 ohms. From an examination of the horizontal distance between the ascending branches of the direct and indirect curves we therefore see that the depolarization effect (due to the internal resistance) upon the ascending branch of the direct curve is negligible within the limits of observation.
The a.seenilin^ Kraneli of the curve can, therefore, be taken to be sensibly inde- pendent of the depolarization. It is seen from the indirect curve, however, that the depolarization current continues to increase after the maximum is passed, and that, eventually, the rate of increase becomes very rapid. It is also evident from the curves that the rate at which the descending branch of the direct curve departs from symmetry with the ascending branch is very similar to the rate at which the depolariza- tion current increases. The departure from symmetry might, therefore, be very well due to the depolarization.
56 Mi; s. W. J. SMITH ON THE NATURE OF ELECTROCAPILLARY PHENOMENA.
In order to determine whether the depolarization is the sole cause of the olxserved flattening of the direct curve, an accurate knowledge of the relation between the graphite resistance and the internal resistance of the electrometer would be necessary. But an approximate knowledge of this relation is quite sufficient to show that the depolarization must soon affect the form of the curve. Thus, to take an example, the horizontal distance between the direct and indirect descending branches for a surface tension corresponding to 150 is not less than 64 horizontal divisions (see fig. 1), equivalent to a potential difference of 1600 (= 1/6 X '28 volt), and even if the electrometer resistance is not above 50,000 ohms, the effect of the latter will be a displacement of the direct curve to the right to the extent of one-third of a horizontal division — a quite perceptible amount — due to the potential fall within the electro- meter. As the actually observed displacement is considerably greater than the above, it seems probable that the flattening in the upper portion of the curve is not due to de|K)larization alone. This is rendered still more probable when the curve for such a substance as hydrochloric acid (in which the ascending branch is very much steeper than the descending) is considered."
Fig. 3.
140
ao
izo
no
ICO
SO
60
70
..-*
-<ooo
3 gives a portion of another pair of direct and indirect curves, showing how the depolarization increases when the potential difference applied, between the terminals of the electrometer is reversed in sign.
In order to show how the depolarization for kathodic polarization of the small electrode varies with the nature of the kation, curves (corresponding to those above described) are given for a dilute solution of caustic potash (fig. 4).
The curves show that in this case, for a given surface tension, the depolarization IB
than when the kation is hydrogen of the same order of concentration.
known, the magnitude of the depolarization in an electrolytic cell depends
Mi;. S. W. ,T. SMITH ON THE NATURE OF ELECTKOCAPILLAKY Till N« '\||.N.\ 57
not only upon the chemical nature of the ions, but also ii]x>n their concentration in the solution. This can be readily rendered obvious by the above method.
Fig. 4.
|
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i 4000 tjooo afloo 4000 ojooo op |
For the above solution of potash it is clear that within the range of the experiment the effect of depolarization upon the direct curve can be considered negligible. The same can be said of most of the solutions considered later.
The Second Hypothesis of the Lippmann-Hclmholtz Theory.
The second hypothesis in the Helmholtz explanation of electro-capillary curves is that the electrical effect upon the surface tension is a purely electrostatic effect d«'|H-!idmg at a given potential difference upon the capacity of the electrode per unit area. It supposes that, in general, the capacity per unit area is independent of the chemical nature of the solution employed in the electrometer. From the approxi- mately parabolic nature of some of the curves through a considerable portion of their course, the Helmholtz theory leads not only to the view that through the range considered the capacity per unit area is constant, but also makes it possible for the value of this capacity to be calculated. Assuming the inductive capacity of the dielectric of the double layer to be unity, the theory further allows an estimate to be formed of the dist:m<v between the parallel charges forming the double layer. That the distance so calculated is of the same order of magnitude as molecular distances calculated in other ways is, however, no proof of the validity of the Helmholtz view. For the distance l»et\veen the layers, as so calculated, might have amounted to some- thing very much larger without standing in opposition to other known data concerning molecular distances. In other words, there is no <i priori objection to a view which supposes that the rapacity per unit area of the common surface may really be much
VOL. c \< III. — A. 1
58 MR. S. W. J. SMITH ON THE NATURE OF ELECTROCAPILLARY PHENOMENA.
smaller than the Helmholtz view requires.* If such a view as this were true, the electrostatic effect would be insufficient to account for the observed variation in the surf'atv trnsi.ni. Assuming tin- potential difference, the existence of the electrostatic effect is scarcely o{>en to doubt, it is only the relative importance of the effect that may be questioned. The electrostatic effect apart, the Helmholtz view assumes that the nature of the transition from the solution to the mercury is (through a con- siderable range) independent of the potential difference and of the nature of the solution.
Several published observations show that there are cases for which this assumption cannot be true. There are many facts in favour of the view that for a given potential difference there is a corresponding condition (of the partly physical, partly chemical kind, pictured by WARBURG) of the space bounded on the one side by the mercury, and on the other by the sensibly homogeneous solution. Obviously the surface tension will depend upon the nature of the transition through the surface layer. The mode of transition may depend only on the chemical nature of the solution and the potential difference across the space in which the transition takes place. On this view the electrostatic effect and the mode of transition for a given solution will l>e determined by the potential difference, and therefore the surface tension will l)e fixed by the potential difference. It remains to determine how the relation between the surface tension and the potential difference depends upon the chemical nature and concentration of the solution.
It is scarcely necessary now to set forth the arguments against the second hypo- thesis of the Helmholtz theory of the electrometer ; but I shall endeavour to show by consideration of observations of the type held to throw greatest doubt upon the theory, that the first hypothesis gives results in close accord with the facts, and need not therefore be abandoned, even if the second should be proved untenable.
RELATION BETWEEN THE LIPPMANN-HELMHOLTZ THEORY AND OTHER THEORIES OF
ELECTROCAPILLARY PHENOMENA.
It may be well to point out the relation such results bear to the theory of WARBURG, which is, perhaps, the most strongly advocated in opposition to the Ilrlmholtz theory. Strictly speaking, the Warburg theory deals only with the ascending branch of the curve. It ascribes the increase in surface tension to the diminution in the concentration of a mercury salt in the neighbourhood of the capillary meniscus. According to WARBURG the effect of an E.M.F. established IK -tween the terminals of the electrometer is to convert the latter into a kind of concentration cell. Part of the E.M.F. of this cell will presumably be due to a potential difference within the electrolyte. The conclusions drawn later depend upon observations of the descending portions of capillary curves, which are usually much
* Cf, WARBURG, 'Wied. Ann.,' 1890, vol 41.
Mil. S. W. J. SMITH ON THE NATURE OF ELECTRQCAPILLAKY 1'IIKM'Mi \ \
more definite and more accurately measurable than tin- ascending jMU-tinns ; hut unless the concentnition E.M.K. within the electrolyte is supposed to be the same for quite different liquids subjected to very different degrees of polarization, there does not seem to l>e any simple method of reconciling the results with the Warburg theory. G. MEYER* has attempted to complete WARBURG'S theory of the phenomena by supposing that the descending portions of the curves :uv produced by formation of an amalgam between the mercury and the element forming the kation of tin- solution, while Li i. «. IN I has endeavoured to show that the descending branch of the curve is absent when the solution does not contain hydrogen. The experimental evidence adduced in favour of these views is mainly qualitative in nature. An extended examination of the quantitative relation between the capillary curves for differently concentrated solutions of the same salt shows that difficulties arise in the quantitative application of the idea that the surface tension in the descending branch de]*»nds only upon the concentration of the amalgam ujxin the electrode surface.
While it is unnecessary to deal with the nature of these difficulties at present, since they do not immediately concern the experiments first discussed, it may be jointed out that if the first hypothesis of the Helmholtz theory be true, it is possible to trace (by means of the capillary curves) the relation U'tween the variation of the jx.tetitial difference at the capillary electrode, the surface tension and the nature and concen- tration of the electrolyte. Probably it is only by the investigation of the relation l>etween these quantities that the value of the capillary curves, as a method of determining "single potential differences" in voltaic phenomena, can be definitely fixed.
THE DISCREPANCY BKTWKKN mi: LIIM-MXXN HKLMHOLTZ THEORY AND THE NERNST- PLANCK THEORY OF THE POTENTIAL DIFFEI:KS< i: BETWEEN SOLUTIONS.
The result, derived from the Helmholtz theory, that the E.M.F. which must be applied between the terminals of the electrometer to cause the capillary electrode to assume its maximum surface tension, is equal to the natural potential difference between the large electrode and the solution, is so important, if true, that this E.M.F. has been observed for a large number of solutions. It is, however, impossible to test directly the validity of the numbers so found, since no other independent means <.f determining single potential differences has, up to the present, been discovered — if we except the dropping electrode method (which will Ixj referred to later).
We may set up and measure the E.M.F. of a cell of the type
MX.
MX.
* MrvKi:, • WiM. Ann.,' 45, 1892. t Luooix, ' Zeita. f. Physik. Chemie.,' 16, 1896. I 2
60 MR. S. W. J. SMITH ON THE NATURE OF ELECTROCAPILLAUY PHENOMENA.
where M,X, and M2X2 signify two solutions which have been examined in the capillary electrometer ; but the E.M.F. found cannot be applied to test the Helmholtz theory of the electrometer unless we know the value of the potential difference between the two solutions.
The state of our knowledge of the potential differences between liquids is not satisfactory. Within recent years, however, NEKNST,* starting from the dissociation hypothesis, has given a theoretical investigation for the case in which the two liquids are solutions of the same salt, but of unequal concentration. PLANCK! has extended the investigation to the case in which the liquids are solutions of different salts. In many cases the values found experimentally agree very closely with those calculated ; but it must be borne in mind that in the experiments the potential difference between the liquids only formed part of the E.M.F. actually measured. For example, in testing the formula as applied to two solutions of potassium chloride of different concentrations, it is necessary to introduce a fresh hypothesis in order to calculate the difference between the potential difference between mercury, covered with calomel, and the stronger solution, and the potential difference between mercury, covered with calomel, and the weaker solution.^ In order to show the nature of the agreement between the calculated values and those found experimentally, some results for KC1 solutions are given below. In the first column are given the concentrations in gram equivalents per litre ; in the second the observed E.M.F.s of cells of the type ;
HgCl KC1 KC1 HgCl
dilute
concentrated
Hg,
and in the third the calculated values of these E.M.F.s.
|
Concentrations. |
||
|
Gram equivalents |
Observed E.M.F. |
Calculated E.M.F. |
|
per litre. |
||
|
3-0 and 0'5 |
volts. •0443 |
volts. •0402 |
|
1-0 0-1 |
•0533 |
•0525 |
|
0-5 0-1 |
•0359 |
•0367 |
|
0-1 0-05 |
•0162 |
•0162 |
|
0-1 0-02 |
•0387 |
•0380 |
|
0-1 0-01 |
•0545 |
•0548 |
|
0-05 0-01 |
•0387 |
•0384 |
These observations form part of a series of experiments which will be described later.
* NEUXST, 'Zeits. f. Physik. Chemie,' 4, 1889.
t PLANCK, ' Wied. Ann.,' 39, 1890, and 40, 1890; cf. also NEGBAUR, ' \Vied. Ann.,' 44, 1891.
J NERXST, ' 7eits. f. Physik. Chemie,' 4, 1889.
Mi; S. W. J. SMITH ON TIIK NA'ITIIK <'F I.I.Ki I 'l;< •CAl'II.l.AKY I'HKNo.MKNA. Ill In a cell of the type
M,X, MX.
II-:
let irni and irnt be the respective potential differences between mercury and the solutions (calculated on the Helmholtz theory of the capillary electrometer), and let 7Tr. l>e the potential difference between the liquids and TT, the observed E.M.F. of the cell, then we should have
"ft = ""it, fl"*, ~\~ f|2'
ROTHMUND has made observations upon cells of this type and has found values for irt, TT,,, and TT^ for a number of different solutions. The following table gives the results of some of his experiments : —
|
M.X.. |
MX:. |
«V |
»„,. |
*:• |
«•« — (»«i — 'lO' |
|
nKCl |
nKI |
•349 |
•560 |
•437 |
•226 |
|
•KG) |
nKCNS |
•172 |
•560 |
•534 |
•146 |
|
fiNiijS |
nKCl |
1-006 |
-MO |
-•030 |
•416 |
He estimates the possible error in the determination of irHl and irni from the curves to be not greater than O'Ol volt.*
Referring to such experiments, NERKST says : — " While, therefore, the Ilelmholtz hypothesis concerning electrocapillarity is found to be in good agreement with the osmotic theory ... as far as the qualitative side of the phenomena goes, we come upon ferious contradictions so soon as we proceed to a quantitative OomparMOO. As results of the electrocapillary meth<xl of measuring contact potentials, we obtain the following table : —
Ha
KCl KC1 KCl KCl
11,80, HQ KCNS KI
•025 •022 •IGl •247 •419
•010 •028 •000 •000 •000
Column 1 gives the symbols of the solutions examined ; column 2 contains the values of the potential differences between them deduced from the Helmholtz theory of the electrometer ; and column 3 gives the values of the same potential differences calculated according to the osmotic theory. The differences are great, and not explicable as errors of observation."!
* RoTHMrsn, 'ZeiU. f. Physik. Chemie,' 15. t NKRNST, ' Wicd. Ann.,' 58, Bcilage, 1896.
62 MR. S. W. J. SMITH ON THE NATURE OF ELECTROCAPILLARY PHENOMENA.
SOLUTIONS OF POTASSIUM CHLORIDE AND POTASSIUM IODIDE.
1. Tlie Potential Difference between Equally -concentrated Solution*.
The experiments show that the Helmholtz theory of the electrometer and the Nernst-Planck calculations of the potential differences between solutions cannot both be true. While there are many facts in favour of the view that the Nernst- Planck hypothesis gives the quantitative expression for the potential difference between two solutions, there is one result calculated from the hypothesis which seems to possess greater weight than any of the others, since it would seem to be a conse- quence of almost any form of diffusion hypothesis. This is the result that the potential difference between equally-concentrated solutions of potassium chloride and potassium iodide is so small that in measurements of the type with which we are concerned it can be taken to be zero.
KOHLRAUSCH has investigated the electrolytic conductivity of solutions of KC1 and KI for different degrees of dilution, and an examination of his numbers shows the relative amount of ionization in equally-concentrated solutions of the two salts may be considered identical when the solutions do not contain more than O'Ol gramme molecule ]>er litre (youth normal). Even when the strengths correspond to a gramme molecule in 2 litres (\ normal) the coefficients of ionization only differ by about two per cent.* Again, according to the most recent values, the ionic velocities of chlorine and iodine are practically identical, t When, therefore, dilute solutions of KC1 and KI of equal strength are brought into contact there can be no tendency of the potassium ions to diffuse, while the chlorine and iodine ions will tend to diffuse with equal velocities across the common surface. Granting the ionic hypothesis we may, therefore, safely assume that no forces which tend to alter the quantity of electricity in the unit of volume act across the surface of separation between the liquids, and that, therefore, no potential difference will arise between the liquids.
2. The Nature of the Electrocapillary Curves for the same Solutions.
For the reason given above I have carefully examined the relation between the capillary curves for KC1 and KI in order to determine further the result of the hypothesis that the potential difference between equally-concentrated solutions of KC1 and KI is zero.
(a.) General character of electrocapillary curves.
rhe behaviour of the meniscus in the capillary electrometer is in general very different in the " ascending " portion of the curve from what it is in the " descending "
* KOHLRAUSCH, « Wied. Ann.,' vol. 26, 1885. t KOHIJUUSCH, ' Wied. Ann.,' vol. 50, 1893.
MR. S. W. J. SMITH ON THE NATURE OF ELECTROCAPILLARY PHENOMENA. 63
portion. In the ascending portion the mercury is often apparently sluggish, and the surface tension Incomes iliilimlt to measure. Further, the surface tension may take up a certain value immediately after a given potential difference is established between the terminals of the electrometer, and thru fall gradually as the time of contact emit iiiut-s. In contrast with this, the surface tension in the descending portion of the curve is almost always very definite. Moreover, while the form of the ascending portion is widely different for solutions with chemically different anions, and even noticeahly different for unequally concentrated solutions of the same salt, the form of the descending portion, for a considerable part of its course, is the same (within the limits of experimental error) for equally-concentrated solutions of quite different salts, and only varies very slightly for unequally concentrated solutions of a given salt.
(b.) Definite nature of the descending branches.
While therefore both the ascending and descending branches have been observed, the first conclusions are based upon observation of the descending portions of the curves. These were definite and amenable to quantitative treatment.
(c.) Method adopted in examining the electrocapHlary curves, and discussion of the, degree of accuracy attainable in the experiments. •
The form of electrometer that I have used has a movable mercury reservoir in direct communication with the mercury column supported by the surface-tension effect at the capillary electrode. The mercury reservoir can be raised or lowered by means of a flexible cord, wound upon a bobbin, having a tangent-screw fine adjust- ment. By means of this arrangement the small electrode can be maintained at a
('.instant position in tin- capillary tlll.r. Tin- ilialnet.-r of tin- capillary |1,,. vame "lie
was used in determining the curves for a large number of solutions — was about 0*003 centim., and the usual length of the column of solution between the meniscus and the point of the capillary was 0*057 centim. The resistance of such a column (supposed cylindrical) would, if the solution were normal KC1 at 18°, be approximately 83,000 ohms. The position of the capillary meniscus was fixed by means of a scale within the microscope. The apparent magnitude of a division of this scale is about 1*5 millim. Every tenth division of the scale is marked. When the position of the microscope is so adjusted that the zero of the micrometer scale coincides with the end of the capillary, the fortieth division (marked 4) of the scale is practically in the centre of the field. The meniscus was always made to coincide as nearly as possible with the central division of the scale. The height of the mercury column, supported by the capillary electrode, when possessing its maximum surface tension in such a solution as dilute sulphuric acid, was about 440 millima The variation of the surface tension was observed by means of a scale divided into millimetres placed directly behind the mercury column. The greatest error in the scale division was about 1 part in 500. The conclusions first drawn from the curves are practically
64
Mi; s \v. .1 SMITH ON THE NATURE OF ELECTROCAPILLARY PHENOMENA.
independent of the accuracy of the division of the scale. The zero of this scale «ftl about 12-4 centims. above the capillary point, so that the reading correspond,.,- to the maximum surface tension, in dilute sulphuric acid, was about 31'6 centims. position of the summit of the mercury column relative to the scale could be deter-
mined to within about a tenth of a millimetre. It would not be difficult to arrange for a greater degree of accuracy in this measurement ; but, apart from the increase in the time occupied by the observations, which more delicate determination would involve, the above error does not exceed that introduced from other causes. Usually the solution to be examined was placed in a Clark cell tube of the Rayleigh H form.
Mi;. S. \\. .1. SMITH ON THE NATURE OF ELECTKOCAPILLAIiY I'HKNoMl.NA. 65
The mercury forming the large electrode was placed at the bottom of one limb ; the capillary electrode dipped into the other limb. In order that the definition of the capillary meniscus might be as good as possible, the capillary was placed close to the siile of the limb that received it. After the curve for the solution had been determined, the H tube, containing it, was removed and replaced by another containing a different solution. It would have been very inconvenient to have u i >rked always with the same H tube, as in many cases it was desirable to allow the solution to stand some considerable time over mercury before examining it in the electrometer. A number of H tubes were used, and naturally these were not precisely similar. In every case the definition of the capillary meniscus, when at the fortieth division of the scale, was made as good as possible ; but it did not always happen that the definition of the capillary point was then correspondingly good. However, the maximum error in the setting of the capillary point was not greater than about one of the small scale divisions, while it could usually be set at the zero within two-tenths of a small scale division. The capillary meniscus could be readily set at the fortieth division with an error of less than one-tenth. An error of a scale division in the setting of the meniscus produced a maximum error of about '4 millini. in the reading of the summit of the mercury column. Under ordinary circumstances, there- fore, the error introduced into the surface tension observations by the necessary replacement of one H tube by another was not greater than '08 millini.
In order to remove one solution from the interior of the capillary tube before the introduction of the succeeding one, the following method of procedure was adopted. The capillary tube was immersed in a beaker of distilled water, and by alternately lowering and raising the mercury reservoir, the water could be drawn into the tube and then again expelled along with & little mercury. This process was repeated several times, the excursions of the meniscus in each case being very much longer than any that occurred during the experiments, as the result of electrical effects. The Ix'.ikrr \va.s then withdrawn, and as much of the water as possible was removed from the capillary. A similar process was then adopted in order to fill the capillary with the solution next to be examined. To test the sufficiency of this treatment, a second set of observations upon a given liquid was made, several other solutions having been used in the electrometer during the interval. The first and second sets were found to agree within the limits of experimental error. In a case where one solution was followed by a more concentrated one of the same salt, the intermediate operation with distilled water was, of course, unnecessary.
The potential difference between the terminals of the electrometer was varied by means of an ordinary potentiometer arrangement. The potentiometer circuit consisted usually of a secondary cell (E.M.F. about 2 '03 volts) and two resistance boxes in series. The sum of the resistances introduced into the circuit by these boxes always amounted to 10,000 ohms. Usually the resistance in each box was altered by 500 ohms at a time, so that the corresponding change in the potential difference
Vol.. t \c III. A. K
66 MR. S. W. J. SMITH ON THE NATURE OF ELECTROCAPILLARY PHENOMENA.
applied between the electrometer terminals was about a tenth of a volt. The probuMc error of each of the box resistances was less than a tenth per cent., and the constancy of the potentiometer current was tested by means of a standard Clark cell, of which the E.M.F. at 15° was known to be within one-tenth per cent, of 1'434 volts. The accuracy of the potential measurement was therefore considerably greater than that which could be conveniently given to the surface tension observations.
(d.) The Ekctrocapillary Curves for KC1 and KI.
1. Preliminary Experiment. — Before proceeding to the experiments of the ordinary capillary electrometer type, mention may be made of a simple means by which very suggestive results as to the relation between capillary curves may be obtained.
A vessel for containing the solution is constructed of the shape shown in the figure.
Fhe mercury forming the large electrode is placed at the bottom of the main tube. The point of the capillary is brought within the smaller tube. The vessel is first filled with a solution of one of the salts (say JnKI), and the capillary curve is determined. Withdrawing air from the apparatus by means of the side tube at the top of the main tube, the liquid rises in the latter and falls in the narrow tube. After the small tube has been nearly emptied, it is filled to the level of the liquid in the main tube with a solution of the other salt (say JnKCl), and the capillary curve is again taken.
Fig. 5 shows the forms of the resulting curves for the solutions in question. The numbers from which the curves were constructed are as follow :
MR. S. W. J. SMITH ON THE NATURE OF ELECTROCAPILLARY PHENOMENA 7
Pig. 5.
|
3W |
1- |
|||||||||||||
|
JOG tat |
/ |
si |
0 |
i:1 |
| |
|||||||||
|
M"- |
^ |
'N |
||||||||||||
|
Z |
^ |
|||||||||||||
|
17C ttc |
' |
< |
||||||||||||
|
/]" |
S, |
|||||||||||||
|
• |
||||||||||||||
|
' |
\ |
|||||||||||||
|
ISO |
1 |
5 |
||||||||||||
|
"». |
1 |
\ |
||||||||||||
|
S |
||||||||||||||
|
\ |
||||||||||||||
|
\ |
||||||||||||||
|
\ |
||||||||||||||
|
ffV 160 |
\ |
|||||||||||||
|
\ |
||||||||||||||
|
\ |
||||||||||||||
|
IV) |
"g ifioo tfoo yxn *>oo apoo epoo
|
Applied E.M.F. |
JnKI. |
I* KI with capillary in in KG). |
|
0 |
20-75 |
28-61 |
|
500 |
24-9 |
29-75 |
|
1000 |
26-69 |
30-23 |
|
1500 |
28-3 |
30-1 |
|
2000 |
28-71 |
29-69 |
|
2500 ' |
28-47 |
28-88 |
|
a |
27-73 |
27-88 |
|
8600 |
26-65 |
26-7 |
|
4000 |
25-39 |
25-38 |
|
5000 |
22-2 |
22-2 |
|
6000 |
18-3 |
18-3 |
|
7000 |
13-52 |
13-55 |
The surface tensions in the ascending branches of the curves were somewhat uncertain and difficult to measure. The descending branches, however, were quite definite. It is seen that when the E.M.F. exceeded a value corresponding to the abscissa 4000 (= about '8 volt) the curves were identical. This result can be very readily explained on the double layer view of polarization in an electrolytic cell con- sidered at the beginning of the paper, if we assume that the potential difference between $n K 1 ;m<l \n K< '1 can U> neglected, and that there is no appreciable concen- tration E.M.F. within the liquid. Since the potential difference at the large electrode has not been altered between the two sets of experiments, the potential difference (ir<— IT,) at the small electrode for a given applied E.M.F. will be the same for both i-urviw. When the applied E.M.F. is less than '8 volt., the surface tension does not (It'jK'iid mrivly uix'ii the potent i.-il ilitVcrence at the small electrode, but also upon the chemical nature of the solution. Now the solutions are the same in every respect
68 MR. S. W. J. SMITH ON THE NATURE OF ELECTROCAHLLAKY PHENOMENA.
except that the anion in one is iodine, and in the other chlorine. Until the potenti.-.l difference reckoned from the solution to the electrode reaches a certain value the ..tVcct of the anion upon the surface tension (i.e., in determining the mode of tion from the solution to the mercury) is appreciable ; but this effect gradually diminishes and finally disappears, as is shown by the fact that the form of the curve (beyond 4000) is independent of the nature of the anion.
From this point of view it is obviously futile to consider that the highest point of the iodide curve corresponds of necessity to zero potential difference between the KI solution and the mercury electrode, since it might equally well be argued that the highest point of the curve obtained with KC1 at the capillary corresponded to zero potential difference between the mercury and the KC1. If there is no appreciable potential difference between the KI and the KC1 both results cannot be true. The potential differences in the two cases (maximum surface tension) must differ by about 0-2 volt, or else the potential difference between *nKI and %n KC1 must be about
0'2 volt.
In the fcce of evidence that there is a chemical effect of the anion upon the surface tension, and that this effect increases as the potential of the liquid with respect to the 'electrode decreases, it does not seem advisable to say more than that the potential difference (reckoned from the solution to the electrode) is considerably less at the maximum surface tension when the solution is KC1 than when it is KI. The marked depression of the maximum value of the surface tension observable in the case of potassium iodide solutions is one of the characteristic features of the curves dealt with by ROTHMUND— the actual fact of the depression was apparently first noticed by GOUY ;* but the depression is really a perfectly general phenomenon. The amount of depression depends upon the concentration of the solution as well as upon its chemical nature. The depression for concentrated solutions of chlorides is very pronounced, and for dilute solutions it can readily be observed that the maximum value of the surface tension rises as the concentration diminishes. It is obviously an effect which does not depend upon the density of the solution. For example, a saturated solution of caustic potash (which is soluble in about half its weight of water) has as high a maximum surface tension as a half-normal solution of potassium chloride. The effect of the ions (apart from the electrostatic effect) upon the surface tension would appear to depend, for a given potential difference, upon their nature and concentration in the solution. Whether the surface tension in the neighbour- hood of the maximum is ever controlled by the electrostatic effect alone, depends (on this view) upon whether, when the potential difference between the solution and the electrode is small, the nature and concentration of the ions is such that their non- electrical effect upon the surface tension can be neglected.
In the case above considered the curves are identical when the applied E.M.F. exceeds 0'8 volt. The subsequent variation of the surface tension is therefore
* 'Comptes Rendus,' vol. 114, 1892.
Mi;, s. \v. j. SMITH ON im. X.UTIJK OF J-.u.rri;'n. \I-II.I..\KY I-III;MIMI.NA. <;;•
presumably independent of the nature of the anion ; hut it is obvious tli.-it we obtain im in formation from the curves as to whet 1 MM- their sulisequent course is free from any non-electrostatic influence depending UJMHI the kation. For the kation is the same and of the same concentration in the two solutions. It is, however, easy to extend the ahove observations so as to show that (granting the Nernst calculation gives ;it least approximately the potential difference between unequally concent rated solutions of the same salt), although the form of the lower portion <>f the descending curve varies very little with the strength of tin- solution, yet the surface tension for a given potential difference depends upon the strength of the solution. From this it would appeal- that the surface tension does not depend upon the electrostatic effect alone even when the anion effect has presumably disappeared ; but that, in fact, there is also a kation effect which becomes evident as the solution becomes increasingly positive with regard to the electrode.
2. Final experiments showing tfte agreement of the first hypothesis of the Lippmann- Ililmholtz theory ivith the Nernst-Planck theory of the potential difference between KC1 and KI. — We may, however, first apply to the ordinary electro-capillary curves for equally concentrated solutions of KI and KC1, the result suggested by the curves already given, that ultimately the descending branch of either curve is practically unaffected by the nature of the anion, and that if it is then influenced by the kation, the nature of the. influence is such that, in equally concentrated solutions of salts possessing the same kation, the potential difference for a given surface tension is the same in both solutions. It is found that the descending branches eventually approximate very closely to parallelism. Considering the parallel portions, let IT, be the E.M.F. required to be applied between the terminals to produce a given surface tension for the KC1 solution, and let IT/ be the E.M.F. required to produce the same surface tension for the KI solution. Then ir,—ir.' is very approximately constant. Let — ;rH l)e the natural potential difference between the KC1 solution and mercury (the electrode being considered positive to the solution), and let — «•„' be the corresponding quantity for theKI solution. Then on the first hypothesis of the ordinary electrometer theory (applicable to any electrolytic cell), the potential differences between the solution and the capillary for the two points of equal surface tension (one on each curve) are
IT, — irn and ir,' — «•„'
respectively. Now if we suppose the potential difference is the same in the two cases because the surface tension is the same, we get
ir, — irn = IT, — IT, or
TT. — IT,,' = IT, — irt' = at
where a, an observable quantity, is represented by the horizontal distance between the parallel portions of the curves. Let now a cell be constructed of the form
70 MR. S. W. J. SMITH ON THE NATURE OF ELECTROCAFILLARY PHENOMENA.
Hg
KC1 KI
Hg
and let its observed E.M.F. be b, and suppose irt is the potential fall from the KC1 to the KI solution. Then
"•» — •"•«,' + TT, = 6. If TT, = 0, we must have
a = b.
The following experiments show the observed relation between a and b.
|
E.M.F. applied to electrometer |
Surface tension readings. |
Horizontal distance between parallel por- |
Calculated E.M.F. of cell i Hg KC1 ! KI Hg i |
Observed E.M.F. of cell TT TT^Il T7"T TT |
|
|
[1000 = '202 volt]. |
tions |
assuming P.D. |
Hg KC1 KI Hg. |
||
|
•TO |
fa. |
of curves. (a.) |
between KC1 and KI negligible. |
(b.) |
|
|
volt. |
|||||
|
0 |
23-5 |
20-39 |
|||
|
500 |
26-0 |
24-8 |
|||
|
1000 |
28-0 |
27-1 |
|||
|
1500 |
29-21 |
28-29 |
|||
|
2000 |
30-0 |
28-71 |
|||
|
2500 |
30-49 |
28-5 |
1975 ±6 |
1950 (max.) |
|
|
3000 |
30-6 |
27-81 |
— |
||
|
3500 |
30-29 |
26-78 |
•3990 |
•3940 volt. |
|
|
4000 |
29-69 |
25-48 |
±•0012 |
||
|
4500 |
28-90 |
24-0 |
|||
|
5000 |
27-9 |
22-35 |
|||
|
5500 |
26-75 |
20-51 |
|||
|
6000 |
25-41 |
18-55 |
|||
|
6500 |
23-95 |
||||
|
7000 |
22-29 |
||||
|
Calculated E.M.F. on |
|||||
|
ordinary Helm- |
|||||
|
holtz theory, |
|||||
|
assuming P.D. be- |
|||||
|
tween KC1 and KI |
|||||
|
to be zero. |
|||||
|
•162 volt (approx.) |
MR. 8. W. J. SMITH ON THE NATURE OF ELECTROCAPILLARY PHENOMENA. 71
|
Iv.M.F. applied to electrometer [1000 =-2027 volt]. |
Surface tension readings. |
Horizontal distance between parallel por- tions of curves. |
Calculated E.M.F. of cell Hg KC1 ! KI Hg assuming P.l>. between KCI and KI |
Observed E.M.F. <>f cell Hg KCI KI Hg. |
|
|
. - KC1. |
— KI. |
||||
|
10 |
10 |
(a.) |
to be negligible. |
(6.) |
|
|
vote, |
|||||
|
0 |
24-78 |
19-9 1 |
|||
|
500 |
27-40 |
25-6 |
|||
|
1000 |
29-0 |
28-34 |
|||
|
1600 |
30-2 |
29-73 |
|||
|
2000 |
30-651 |
30-3 |
|||
|
2500 |
31-33 |
30-2 |
|||
|
3000 |
31-41 |
29-57 |
1725 ±6 |
1729 ±-5 |
|
|
1600 |
31-2 |
884 |
^ |
||
|
400D |
30-7 |
27-49 |
•8486 |
•3503 volt. |
|
|
4500 |
29-99 |
26-13 |
±•0012 |
||
|
6000 |
29-1 |
24-65 |
|||
|
6500 |
28-0 |
22-99 |
|||
|
COOO |
26-72 |
21-11 |
|||
|
6500 |
25-33 |
19-13 |
|||
|
7000 |
23-79 |
16-9 |
|||
|
7.-.ou |
22-0 |
14-43 |
|||
|
8000 |
20-01 |
11-73 |
|||
|
8500 |
17-9 |
||||
|
9000 |
15-6 |
||||
|
E.M.F. for maximum |
Calculated E.M.F. |
||||
|
surface tension |
of cell .assuming |
||||
|
P.D. between KI ] T " * • 1 |
|||||
|
and KCI zero, on |
|||||
|
JLKC1. |
foKL |
ordinary Helm- holtz theory |
|||
|
2800 ±50 |
2200 ±50 |
•122 (appro*.) |
7J MI!. S. W. J. SMITH ON THE NATURE OF ELECTROCAPILLARY PHENOMENA.
|
K.M.F. applied to electrometer [1000 = '2027 volt]. |
Surface tension readings. |
Horizontal distance betwtvn parallel por- tions of curves. |
Calculated E.M.F. of cell Hg KC1 KI Hg assuming P.D. Ixitween KI and KC1 |
Observed K.M.F. of cell 1 Hg KCljKI Hg. |
|
|
AKCl. |
n KI. |
||||
|
•M |
20 |
(a.) |
zero. |
(6.) |
|
|
- |
volt. |
||||
|
0 |
25-11 |
19-951 |
|||
|
500 |
27-41 |
25-3 |
|||
|
1000 |
29-01 |
28-35 |
|||
|
1500 |
30-18 |
29-92 |
|||
|
2000 |
30-99 |
30-57 |
|||
|
2500 |
31-45 |
30-49 |
1663 ±6 |
1 608 ±0-5 |
|
|
3000 |
31-5 |
29-9 |
|