hie nitty Bate ee tity if Ba Be it Fy ee ew ee = tee HIE ON A Vk es a } a eutad : bs AW ai al! anti Pini tatyhetan tot yh I Ey ket A i Da o ite i ately Ace ner MASAMI ada tbs gage pits iat i fi Hateuaaeltea aly tt UAV Giaee ata Maleda aba a ith BAD he } : weit ‘ } iu ) SEG SOI : ms ‘ che ee Ieee ay a | Ahh EE ALR Peau i { . Y, Wey d a 0 ‘it rt e599 1 f hy i$ a) i Hf ‘ ins {) my ity tHGA i Mi i} : ( E ie ft gi i , Hi a { ri) Y bata) as h A aja Rhea rp iy p Pam Es A ap ; iy Hie i { if sr >: nego a Sas Pak ee oe eee | ft + tik iil ee ee Haars ee eel rig. ee 4 ye a ua : ahhh at PSs See ota === <= Se 5 = 55 ; en Saas = ie. fo ‘+ ae ey ess ee = eae eam Sane tip oe = 2 we == ise 3 to oe ee ee eae: fed: “Sy Se RE Lena ashi MET att in aa te iW +i at ve at emi Bare in ce Hh ee ait ; Ai aly Aaah Tha he } Lat r is ie Mi ih has Sareea ae iH Mie inate \e pa dil cae Fy! he Cs ee sore eee the ail Heh a i dated aa Y R iF oe } i oe ie : iy sata i Pt vain: bt o ian ie Mar Hype att ida fe Aa tt a8. May H | aah tt i it 7 iit edit See Hah if Ha VF pith Syne) 9 4 ae: Taian a ¥ : bs by ‘ Lien ae hei aan * ) ty ae as Peckt Bah iy ae rH Ate as ' I oe itt ie Pha i a pena a san ib a i dite ; sep hi ite eas a asi iellsih ae int a i thee te ; ¥ tit Mr HE Hy f Hi : die ‘ piretalan ‘ ret i adj stint aeanaya tates te tbs LDEY ees: “<=> ; aaaetets es ie iets tft Phi ii ats a4 Vis ais Be 5 Wi Lat ohy a np —s — —— = : ieee ems hi pati . ihe! é mnie ——— eth Cie Blt eek ‘ind viet ad oe wii 96 hen Py as BED ok LE reat ha Abhi eras ihe cu phyA. Ted sali Ny as Liter es Mate bene ATE ih et 5 } ee by sleet TM Ast da sf in| ied a) Mat Aaatea aa phad aed ga Ip tistiias ‘ Ce Wino 3 j i f° , i 49) de | i es a oe ae ce —— — THE LONDON, EDINBURGH, anp DUBLIN PHILOSOPHICAL MAGAZINE ANB» »& 2 JOURNAL OF SCIENCE. * @oNDUeTeD By!” LORD KELVIN, G.C.V.0. D.C.L. LL.D. F.R.S. &e. JOHN JOLY, M.A. D.Sc. F.R.S. F.GS. AND WILLIAM FRANCIS, F.L.S. ‘Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster vilior quia ex alienis libamus ut apes.” Just. Lies. Polit. lib.i. cap. 1. Nos. VOL. X.—SIXTH SERIES. JULY—DECEMBER 1905. LONDON: TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET. SOLD BY SIMPKIN, MARSHALL, HAMILTON, KENT, AND 00., LD.—T. AND T. CLARK, EDINBURGH ;—SMITH AND SON, GLASGOW ;—HODGES, FIGGIS, AND CO., DUBLIN ,;— PUTNAM, NEW YORE ;—YEUVE J. BOYVEAD, PARIS ;—AND ASHER AND CO,, BERLIN. S4E650 >. i — yay eX i Fr f : ¢ | es € 1G ne |) CO Cleh ig eS oie era CG ec c Gree ce ¢ cc € GN c ZOE . c ¢ AX . SEM NEL Mie tromignmelne uenG a ¢ € 3 Cc ee c C a Medit-tionis est perscrutari, oceulta ; contemplationis est admirari perspicua . . Adniitatic genes at quaistionem, gneestio investigationem, uence tanner: is ~ Hugo de 6. Victores:. ¢ Ge ~ € Cc € C le @2¢ € F € ee Sar Ge ce CHPCHE PSOE wees Ch One Cc Co » € ToT — £ c ¢ eae ACH MCE gaye CMtcives ¢ Cec c € @igie ae € € c ee € oe € €¢& Yar; € MY, © Cle eres © “Cur spirent venti, cur terra dehiscat, Cur mare turgescat, pelago cur tantus amaror, Cur caput obscura Phoebus ferrugine condat, Quid toties diros cogat flagrare cometas, Quid pariat nubes, veniant cur fulmina ceelo, Quo micet igne Iris, superos quis conciat orbes Tam vario motu.” J. B. Pinelli ad Mazonium. lan y ALERE FLAMMAM. \ Reon Le CONTENTS OF VOL. X. (SIXTH SERIES). NUMBER LV.—JULY 19085. Page Mr. P. 8. Barlow: Osmotic Experiments on Mixtures of PMICOMOLM AMOR NY AGERE: duce Barattit de weddisnichasl® bre be,ne lar. Mr. R. A. Houstoun on the Effect of a Surface-Film in Total SECO gn ee en nS a 12 Mr. R. A. Houstoun on Total Reflexion at the Second Surface Caan lanesearallel Plate. 244 Osa. 2 a Wel oda cd aie 2Q4 Mr. 8. H. Burbury: Lord Rayleigh on the Virial Equation.. 33 Dr. T. Godlewski on Actinium and its Successive Products... 35 Dr. T. Godlewski on some Radioactive Properties of Uranium. 45 Mr. J. W. Sharpe on the Boomerang .............2.-005- 60 Mr. J. Peck on the Effect of a Transverse Magnetic Field on the Discharge of Electricity through a Vacuum-Tube .... 67 Prof. D. B. Brace on the Negative Results of Second and - Third Order Tests of the ‘ther Drift,” and Possible First TRUSTS UIT EST TNO Fe aR op Be gees en ae (a. Prof. A. Wehnelt on the Discharge of Negative Ions by Glowing Metallic Oxides, and Allied Phenomena........ 80 Mr. J. H. Jeans on the Partition of Energy between Matter ERMUMBEN IMC Erie Arena afar Morena td ara arte a G)ai-e'k sch hs. gral sa) « 91 Mr. A. 8. Eve on the Radioactive Matter present in the PaO POSES Err ose aR i cih Sots Taha Sie hes eae ecg ret 98 Mr. J. Morrow on the Lateral Vibration of Bars of Uniform AMY TVA SCCHIONALM ATER. . ea. yh s 6+ ms cial e sg 2 os 2 te 113 ev. J. Stoney on ‘An Optical Paradox” ..2..02.. 20.2.2. 126 Dr. W. Watson on the Determination of the Moment of Inertia of the Magnets used in the Measurement of the Horizontal Component of the Earth’s Field... .......... 130 Dr. H. H. Barton and Mr. C. A. B. Garrett on the Vibration Curves simultaneously obtained from a Monochord Sound- ese sicrsveme go crlate Vo)! cto gues ae cents ta ec. ey 149 Mr. H. C. Jones on the Theory of Electrolytic Dissociation : REE OMIS seny em kick Paws ee re ew ece es aie haa 157 lv ‘i CONTENTS OF VOL. X.—SIXTH SERIES. Page Mr. W. C. Clinton on the Voltage Ratios of an Inverted : RotarysConverter <..2 ses usec s+ be ss ohn 160 Prof. E. Rutherford on some Properties of ince Rays from MVAOUUU Coe snes ele ee Mau One ot ee aes ea 163 Dr. O. W. Richardson on the Structure of Ions formed in Gases.at High Pressures «..,...¢s-1.).: 21. - ee eee Wer Mr. R..J. Sowter:on Ellipsoidal Lenses: .... 2.2 S52eeeeeee 180 Mr. W. A. D. Rudge on the Properties of Radium in Minute Quantities. 625s ces co ce abns gee +e ese 183 Notices respecting New Books :— Miss Ida. Freund’ s The Study of Chemical Composition.. 184 Dr. G. Jaumann’s Die Grundlagen der Bewegungslehre. 185 Messrs. H. Le Chatelier and O. Boudouard’s High-Tem- perature Measurements ..............2) oe 185 Bulletin: of the (Bureau of Standards’ -.)... 72 2) eee 186 Dr. A. N. Meldrum’s Avogadro and Dalton .......... 186 Dr. F.M. Perkin’s Practical Methods of Hlectro-Chemistry. 186 Proceedings of the Geological Society :— Messrs. H. J. O. White and L. Treacher on the Age and Relations of the Phosphatic Chalk of Taplow........ 188 Mr. R. H. Rastall on the Blea- Wyke Beds and the Dogger in North-Hast: Yorkshire... 2.0.5) 0... . ee 189 Mr. G. F. J. Preumont on the Geological Aspect of some of the North-Eastern Territories of the —s Free State.) Lee POC Gee OR SOG 1 190 Dr. P. Marshall on the Geology of Dunedin (N. Zealand). 191 Mr. T. F. Sibly on the Carboniferous Limestone of the Weston-super-Mare District NUMBER LVI.—AUGUST. Prof. E. Rutherford on the Charge carried by the a and (3 Rays of Radium: i. ley ane dlodas oie eo se sels i see rr 193 Dr. J. A. Fleming on the Ratio between the Mean Spherical and the Mean Horizontal Candle-Power of Incandescent Electric Lamps ’...). 6.0 pon os. eee eee: . 208 Mr. G. B. Dyke on the Flux of Light from the Electric Arc with Varying Power-Supply (Plate IL.) .............. 216 Mr. J. W. Nicholson on Electrical Vibrations between Confoeal Elliptic Cylinders, with special reference to Short Waves.. 225 Mr. A. A. Robb on the Conduction of Electricity through Gases between Parallel Plates .................25 eee 237 Dr. QO. W. Richardson on the Rate of Recombination of Ions in Gases CONTENTS OF VOL. X.——SIXTH SERIES. Mr. K. Honda on a Portable Aéro-mercurial Tide-Gauge. Gillie auton V «eae a iene as ok Se ee bs ide a we Mr. F. W. Lanchester on the Pendulum Accelerometer, an Instrument for the Direct Measurement and Recording of PAECel Kab TONY. Nol eMMme fe ats 'elo, 6:3) ows Anya Seheial s Gam o's Mr. R. V. Stanford on a new Form of Pyknometer........ Dr. A. D. Denning on a Simple Method of Determining the Radiation Constant: suitable for a Laboratory Experiment. Notices respecting New Books :— Dr. V. Goldschmidt’s Ueber Harmonie und Complication, and Ueber harmonische Analyse von Musiksticken .. Or Vinders Dre Hormelzeichem +). Giese hh as yer vague « NUMBER LVIL—SEPTEMBER. Lord Kelvin on the Statistical Kinetic Equilibrium of Etber in Ponderable Matter, at any Temperature ............ Prof. E. Rutherford on Slow Transformation Products of LEPFEXUSIEEITTEY Go-go ra a pe aeRUP1oPee Dr. C. Chree: Deductions from Magnetic Disturbances at SHAS STIRNGICLEL 2 racy cee Pane Wel CRN Se ANE NAME re te ee Prof. W. H. Bragg and Mr. R. Kleeman on the @ Particles of Radium, and their Loss of Range in passing through vanious roms aria, Molesules 02 00-2 oe alas tnldes » ale « Prof. Dr. J. Traube on the Space occupied by Atoms: The Theories of Th. W. Richards and J. Traube ............ Mr. W. A. Price: The Electrical Resistance of a Conductor the Measure of the Current passing .................. Lord Rayleigh on the Momentum and Pressure of Gaseous Vibrations, and on the Connexion with the Virial Theorem. Dr. T. Godlewski on the Absorption of the G and y Rays of Vv Page 260 269 270 279 284 285 290 306 318 340 ELGIIIUTAUTTICT ole Saar ft AR ar BCE a eae tet ee a a 370 Prof. A. M. Worthington on a Fundamental Experiment in JST SCUTGIIRY BAG oe Bom Sake keaetke Ne ty arom eRe 380 Prof. D. B. Brace on the Aither ‘ Drift” and Rotary JE QU EEIZENTNO I ea Nan) AD Br em: Mee eet ce een a erat eet ea 383 Mr. R. T. Lattey on the Mutual Solubilities of Diethylamine RCM NAc Mra ee eM ne SAME, os AS DU ACN ay aha, Sule. Gey 397 Notices respecting New Books :— HE. Gerard’s Lecons sur l’Electricité.. ................ 400 The late Sir G. G. Stokes’s Mathematical and Physical 400 [PAY NSIESS NOs leh ia ony SS plas UN ae SUA al CONTENTS OF VOL. X.—-SIXTH SERIES. NUMBER LVIIL—OCTOBER. Lord Rayleigh on the Origin of the Prismatic Colours Prof. R. W. Wood on the Magneto-Opties of Sodium Vapour and the Rotatory Dispersion Formula. (Plate V.) ...... 408 Prof. R. W. Wood on the Scintillations produced by Radium. (Plate VIL) Og See Se Oe 5) 427 Dr. J. A. Harker on the Specific Heat of Iron at High Tem- DETALUTES (onic co Sree hie alle he ca MRR ot ee rrr 430 Mr. A. Hi. Harward on the Transfinite Numbers .......... 439 Miss J. M. W. Slater on the Emission of Negative Electricity by Radium and Thorium Emanations...)5....... ee 460 Rev. P. J. Kirkby on the Union of Hydrogen with Oxygen at Low Pressures caused by the Heating of Platinum .... 467 Dr. Harold A. Wilson on the Electrical Conductivity of Blames 2... eee ee ee in a ec 2 rr 476 Mr. Rollo Appleyard on Contact with Dielectrics D+ er 485 Lord Blythswood and Mr. H. 8. Allen on Dewar’s Method of producing High Vatua 7.2.25. 0.02. 2 See 497 NUMBER LIX.—NOVEMBER. Prof. R. W. Wood on the Fluorescence of Sodium Vapour and the Resonance Radiation of Electrons. (Plate VII.).. 513 Mr. Walter Makower on the Method of Transmission of the Excited Activity of Radium to the Cathode ............ 526 Mr. W. H. Jackson on a Paper by W. Makower entitled “*On the Method of Transmission of the Excited Activity of Radium to the Cathode sl S200 .).2 0 200 2 ee 532 Prof. A. Stanley Mackenzie on the Deflexion of a Rays from Radium ‘and ‘Polonium. * (Plate VUEI.)..0-.:...) eee 538 Messrs. K. Honda and 8. Shimizu on the Magnetization and the Magnetic Change of Length in Ferromagnetic Metals and Alloys at Temperatures ranging from. — 186° C. to ° 4+ 1200° ©.) (Plates TX. ER.) 548 Dr. J. Larmor on the Constitution of Natural Radiation .... 574 Prof. J. J. Thomson on the Emission of Negative Corpuscles by the Alkali Metals... 0.0. ne oe 584 Prof. D. B. Brace: A Repetition of Fizean’s Experiment on the Change produced by the Earth’s Motion on the Rotation of a Refracted Ray sc.5 07) as asa ee th oe ag9l1 Prof. W. H. Bragg on the q Particles of Radium ......aae 600. Dr. T. H. Havelock on Surfaces of Discontinuity in a Rota- tionally Elastic Medium CONTENTS OF VOL. X.—SIXTH SERIES. Vil Page Notices respecting New Books :— Dr. A. H. Bicherer’s Mathematische Einfubrung in die PNA OMe MME OLIO rk crale, ve-v ato cpa el ccale. Suse a sie as opie) ® 4) 613 Mr. J. H. Jeans’s The Dynamical Theory of Gases .... 614 Dr. O. Frélich’s Die Entwickelung der Elektrischen Pease eran ee a Bea bed. gone ate BEN eines sah wee ¢ 614 Proceedings of the Geological Society :-— Mr. J. V. Elsden on the Igneous Rocks occurring between St. David’s Head and Strumble Head (Pembrokeshire). 615 Mr. Linsdall Richardson on the Rhetic and Contiguous Deposits of Glamorganshire, and on the Occurrence of Rhetic Rocks at Berrow Hill, near Tewkesbury .. 616 NUMBER LX.—DECEMBER. Mr. Glenn Moody Hobbs on the Relation between P.D. and Spark-length for Small Values of the latter. (Plate XIII.) 617 Mr. H. E. Schmitz on the Thermoelectric Circuit of Three eB eM ge Bi aiey he) fhe 5 a). BAIayE drones Bal Aine OMMayeia Olea « 8 4 631 Messrs. K. Honda and 8. Shimizu on the Magnetization and Magnetic Change of Length in Ferromagnetic Metals and Alloys at Temperatures ranging from ~—186° C. to he LEAP CIR, ghee RR RAR ane ee AES aR RN cee eiAA ca SER bel bt an 642 Prof. Louis Kahlenberg on the Theory of Electrolytic Disso- ciation. (A Rectification of the ‘‘Correction” by pforessarm larry C. Somers) v. ai... . ss pectepehOe oe oss + 8 662 Mr. A. A. Robb on the Conduction of Electricity through Gases between Parallel Plates —Part II. .............. 664 Prof. Louis T. More on Dielectric Strain along the Lines of “SIDS 4. CMa aM a aI ae Seas ea Aa ah g Slat Se 676 Lord Kelvin: Plan of an Atom to be capable of Storing an Electrion with Enormous Energy for Radio-activity...... 695 Notices respecting New Books :— Mr. E. T. Whittaker’s Treatise on the Analytical Dyna- mues of Particles and Rigid Bodies... oo. 0d. 0 ws 699 Mr. James Walker’s Analytical Theory of Light ...... 700 Landolt-Bérnstein Physikalisch-Chemische Tabellen .. 701 Mr. G. Martin’s Researches on the Affinities of the Elements and on the Causes of the Chemical Similarity or Dissimilarity of Elements and Compounds ...... 701 Prof. Dr. A. Werner’s Neuere Anschauungen auf dem Gebiete der Anorganischen Chemie .............. 702 Dr. W. Marshall Watts’s Index of Spectra, Appendix P. 702 J. Bronn’s Verflissigtes Ammoniak als Losungsmittel .. 703 Proceedings of the Geological Society .............. 703-707 ii eer es he. Le ee ieee Pe Tee 708 IL. 1, ee DY V. VI. XIII. PLATES. . Illustrative of Dr. E. H. Barton and Mr. C. A. B. Garrett’s Paper on the Vibration Curves simultaneously obtained from a Monochord Sound-Box and String. Illustrative of Mr. G. B. Dyke’s Paper on the Flux of Light from the Electric Arc with Varying Power-Supply. Illustrative of Mr. K. Honda’s Paper on a Portable Aéro- mercurial Tide-Gauge. Illustrative of Prof. R. W. Wood’s Paper on the Magneto- Optics of Sodium Vapour and the Rotatory Dispersion Formula. Illustrative of Prof. R. W. Wood’s Paper on the Scintil- lations produced by Radium. . Illustrative of Prof. R. W. Wood’s Paper on the Fluores- cence of Sodium Vapour and the Resonance Radiation of Electrons. . Illustrative of Prof. A.S. Mackenzie’s Paper on the Deflexion of « Rays from Radium and Polonium. . Illustrative of Messrs. K. Honda and 8. Shimizu’s Paper on the Magnetization and the Magnetic Change of Length in Ferromagnetic Metals and Alloys at Temperatures ranging from —186° C. to +1200°C. Illustrative of Mr. Glenn Moody Hobbs’s Paper on the Relation between P.D. and Spark-length for Small Values of the latter. =~ INS F ye tan ¥ 4 } 3 THER 2 +% : pT LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SIXTH SERIES.] ETE LG0D. & XK I. Osmotic Ewperimenis on Mixtures of Alcohol® d pepy E> Ss. Bartow, -B.8e. (Vict), St. John Cambridge * 4 tem experimental work of this paper was undertaken by way of examining a curious and unexpected result obtained ms S. U. Pickering T in an osmotic experiment with propyl alcohol. The most recent estimate of the importance of this experiment as bearing on the theory of the action of the membrane in osmotic phenomena is given by W. C. D. Whetham f. The following is a quotation taken from a letter written by Pickering to ‘ N ature,’ dealing with the hydrate theory of solution S. It serves here the double purpose of describing his experiment and giving his own estimate of its value in supporting the hydrate theory. He writes :—‘“ On the other (the hydrate) side we have two experiments, which would seem to be conclusive, but which the dissociationists have hitherto thought fit to ignore. “Osmotic pressure, they hold, is due to the quasi-gaseous * Communicated by E Professor J. J. Thomson, F.R.S. t+ Ber. Deut. Chem. Ges. xxiv. p. 3639 (1891), and ‘ Solution,” Art. iL, Watt’s Dict. of Chem. { Whetham, ‘Theory of Solution,’ pp. 96, 97. § Nature, lv. p. 228 Phil. Mag. 8. 6. Vol. 10. No. 55. July 1905. B y, Mr. P. S. Barlow: Osmotic Heperiments pressure of the solvent and dissolved substance acting on a diaphragm, which, being permeable to the solvent only, renders the pressure of the dissolved substance inoperative, and hence causes the total operative pressure of the solution to be that of only the solvent present in it. Now, I have shown that if we take a solution such as that of propyl alcohol in water, and place it in a semipermeable vessel surrounded by | water, the latter will pass through towards the solution, ergo, the vessel is permeable to water but impermeable to the alcohol ; but if the same vessel with ils same contents is surrounded by propyl alcohol, itis the alcohol that passes through towards the solution, ergo, the vessel is permeable to the alcohol, but not to) the water .. 2... The obvious conclusion to draw from this experiment is, that it is the solution. and not either of the substances separately, to which the membrane is impermeable, and this is just what we should anticipate on the hydrate theory, the molecules of hydrates being necessarily larger than those of their constituents.” The experiment is thus accepted as a ‘ crucial’ one. The experimental work, of which a short account is given in this paper, shows that the observation of an increase in the osmotic pressure after the cell is placed in the alcohol is correct, but that it is not due to an inflow of alcohol. Had more time been given to the experiment, it would have been found that this increase is not permanent as when the cell is in water. The permanent result is an outflow from the cell into the alcohol. And further: had the cell containing the solution been placed by Pickering again in water, he would most likely have found a decrease in pressure; and obviously the outflow causing it would have been the reverse of the anticipation based on the hydrate theory as above quoted. The explanation of what are here called “temporary” rise and fall (or inflow and outflow) is given after some account of the experiments. The Cells. It is not intended to give here a full account of the pre- paration of the cells. This was by far the most tedious part of the work. That some cells should prove useful and others prove failures, after exactly the same treatment, seems only to be accounted for by the presence of flaws within the ot. The membrane used was that of copper ferrocyanide obtained by diffusion. Of the thirty-one cells used in the preparation, fifteen proved sound. Of the others, their failure on Mixtures of Alcohol and Water. 3 was generally due to a fault within the cell-wall, but not always ; ; sometimes the leak was through the glass at the joint being strained or through the joint itself. The cells were very hard ‘and close-grained, having walls between 4 cm. and °5 em. thick. Their internal length was about 6°5 cm., and their internal diameter 1°6 cm. TL ese cells of more porous clay and slightly thinner walls, kindly given by Mr. Whetham, were also used and proved very serviceable. The cell was prepared by washing in dilute alkali and then in dilute hydrochloric acid. It was then washed and boiled in several changes of distilled water and allowed to become nearly dry. Close-fitting glass tubing was ground into the end of the cell by nate of wet emery-powder, and was fixed by litharge and glycerine cement. This hardens to a mass apparently unaffected by alcohol. This cement is rather porous, and any flaw in it may make it impossible to obtain a sound membrane. There is always the same risk of failure due to want of uniformity in the cells themselves. The joint obtained by using sealing-wax is more suitable for formation of the membrane, but had to be abandoned on account of the ease with which it is attacked by alcohol. Of the cells with sealing-wax joints a much larger percentage proved sound, The air in the pores of ane cell was driven out by means of electric osmose and afterwards by placing under the water- pump and drawing freshly boiled distilled water, still sightly warm, through the cell-walls. Its own volume of water was drawn through several times. In the case of the more porous cells, drawing water through in tnis way seemed sufficient. The cell was then placed in copper-sulphate solution and was filled with potassium ferrocyanide soiution. With the harder cells, ten to fourteen days in these solutions seemed necessary for the formation of a useful membrane. The cell was then fitted with a gauge and tested by a sugar solution of known strength. — In the gauge attachments there were two T-pieces arranged in H form. Below one vertical portion was the cell ; below the other the gauge was fixed. In this way the cell and gauge could readily be washed out without detaching the gauge. The opening immediately above the cell was closed by thick-walled rubber tubing wired over a flange on the glass, and a screw-clip. The opening above the gauge was closed by fusing the drawn-out glass. The rubber tubing made it possible to add pressure by means of a pump, and to B 2 4 Mr. P. 8. Barlow: Osmotic Euperiments relieve slowly any pressure set up during an experiment. The volume of the air enclosed within the cell was very small, so that any change in the volume of the cell’s contents immediately mov ed the gauge-level. The bore of the gauge- tubing was small, in the largest having a volume of ‘0358 c.c. per em. length. The Experiments. In the experiments with the alcohol solutions, no attempt was made to get the actual values of the osmotic pressures. In most cases, the solutions were too strong and generally the pressure was not allowed to reach values greater than those for which the cell had previously been tested, thus keeping the experiment within the known limits of the cell’s str ength. However, in more than one case, a cell left overnight got up. a pressure large enough to bur st the rubber tubing or force it over the flange, below which it was wired. The cells still remained sound. What pressure the best cells could bear before breaking down is not known ; and for obvious reasons it has not been sought. Experiments were performed with varying strengths of solutions, going up from 15 per cent. alcohol by steps of 5 per cent. to 70 per cent. Strengths below and above these limits were also used, all with the same result. This gradual increase of the strength of the solution was thought to be advisable, because it seemed not unlikely that when the alcohol was in great excess the sign of the osmotic current might change. In other words, the alcohol might become the solvent and the water the solute. This, however, was not found even when the water was present in very small quantity indeed. In these experiments, where water was always present, the alcohols were not further rectified. They were supplied to the laboratory as pure and so used. The specific gravity (compared to water at 4° C.) of the ethyl alcohol was *7948 at 16° C. ; that of the methyl alcohol, *7940 at 18° C.; that of the propyl alcohol, +8274 at 14°8 ©. This last was taken some time after the experiments were completed, and is there- fore likely to be much higher than when first used. On removing from one liquid to another, the cells were dried by folding in filter-paper. on Mixtures of Alcohol and Water. dD Tasue I.—Cext 8. Ethyl-aleoho!l solution. Strength for maximum contraction. | | | . | | Gauge Readings THA. | “mm. scale). | Cell in water. ...... | Aug. 13. 12.50 | open 290°8 closed 291°5 Aug. 14. 10.0 | 428 Internal pressure | Placed in alcohol. | [nearly 5 atmos. 10.20 open 289 closed 290-5 10.30 299 | 10.50 319° | ' 11.8 311 Max. of temporary 11.20 3085 [rise. 7) 12.25 283 em | | ‘open 288: \ Fall in pressure. | | 11.45 300 : Placed in water. 12.30 | closed 288°5 12.36 | 237 | 12.45 | 988 | | Falling. | 3.0 | 273 | ) 4.20 | 315 | Steady rise. / Placed in alcohol | | without relieving 4.30 | 323 pressure. 4.35 | 327 d.3 | 336 Max. of temporary| | | 5.36 | 354> Wh] [rise. | . ey = | | a8 | 28 aes! } Permanent fall. | open 288 | | | Tasie I].—Critt XXIV. Solution of Propyl Alcohol : 60 c.c. of aleohol in 100 c.c. of solution. Time. Gauge Readings Cell in water. Monday 12.35 closed 268 2.20 303 | 4.20 349°-4 | Steady normal rise. Opened and placed ' | in propyl alcohol. 4.28 closed 2716 | 4.34 ‘276-4 | Rising. d.17 300 | 8.0 269 Falling. | Tuesday a.m. Beyond thebend; Showing consider- of the gauge-tube [able outflow. | Placed in water. | | 9.45 2145 j 11.20 270-2 Temporary fall, 12.10 270 | 5.5 Bs | ae a ed \ Rapidly rising. open 277 6 Mr. P. S. Barlow : Osmotic Experiments TArie Mid; Ceti X XIV.—The cell was first soaked in methy] alcohol. The solution consisted of 49 c.c. of methyl alcohol made up to 50 ¢.c. with water: i.e., nearly 24 molecules of alcohol to 1 of water. { | | } } Time. Gauge Readings Cellinmethylalcohol) Monday 5.0 open 126-4 | closed 126-9 | | | Gini, 122-4 | Immediate per- / | 5.59 120 [manent fall. Tuesday 11.50 10] ae | | open 125 | | Placed in water. : 4.32 126 4.38 124-8 | Temporary fall. | 5.0 | 1239 | J | | . 5.46 126 ' | 6.22 130 [vise.. Wednesday A.M. , 250 Permanent normal | | | TABLE LY. CELL XII.—In this case the solution was outside the cell and and alcohol inside. Solution of ethyl alcohol: 60 grs. alcohol in 100 c.e. solution. Gauge | due: Readings. | | | Cell standing in | Thursday 12.20| 289 the solution. 4.35| 2926 | Friday 10.0 | 305°5 Saturday 11.45| 323 Monday 10.40, 354 | |Tuesday 10.0°| 361 ! Wednesday 10.20 |. 378 Shows permanent rise and inflow from the solution. | After the above experiment, the alcohol was withdrawn and the cell was filled with water. This would give a weak solution of alcohol (but not very weak, owing to small capacity of cell) inside. During the next 24 hours there was a large decrease in the internal pressure, indicating a current from the weaker to the stronger solution. on Mixiures of Alcohol and Water.’ 7 The above tables of results are typical of those obtained from experiments with other solutions and with other cells. Considering the results in Table I., we find a rapid rise of pressure when the cell is surronnded by water, The normal rise of pressure is spoken of as ‘‘ permanent” for the purposes of this paper. When placed in alcohol, cell @ showed an increase of pressure, the gauge rising through 20°5 mm. in 48 minutes. There was no further rise. The level then feil steadily. The above rise was “temporary”’: this fall is “‘ permanent,” that is, 1t would have continued until the liquids on both sides of the membrane had the same composition, or until further outflow was stopped by the difference between the internal and external pressures. That this outflow was permanent in this sense, and not temporary, was readily shown by repeatedly opening and closing the cell while it remained in the alcohol; there was always a fall of the gauge-reading. Jt was- necessary to open the cell at intervals to avoid the mercury being sucked back beyond the bend of the gauge. In this connexion the experiment of Table IV. is important. The arrangement in this case is the reverse of having the solution inside and the alcohol outside. The osmotic current, which in the latter was the permanent outflow, now becomes a steady inflow and may be allowed to show itself over a long interval of time. The rate of rise of pressure is much slower than in the case when pure water is outside, as would be expected. The results given in Table IV. are spread over a week. Obviously, if the current can only be from the single liquid to the mixture, as expressed in Pickering’s account, then results like those of Table IV. would be impossible. When the cell was placed in water after being removed from the alcohol, there was a temporary fall in all cases. In Table I. this fall continued for about three hours, and was succeeded by a steady increase of pressure. On being placed in alcohol again without relieving the internal pressure, there was a temporary rise as before ; but this time the rise was less. ‘The internal pressure opposed the temporary inflow. The case in Table III. is slightly different. The cell was first soaked in the alcohol, and then the solution was added. The cell being in alcohol, there was no temporary rise ; the permanent fall began at once. When placed in water, the temporary fall was that usually found. All the experiments point to the conclusion that the water tends to cross the membrane in that direction which will promote its equat distribution on both sides. This conclusion has been put to the following severe test. 8 Mr. P. &. Barlow: Osmotic Haperiments A cell was soaked in methyl alcohol, the outer vessel being closed by a cork covered with melted wax. With changes of alcohol, both sides were obtained osmotically similar; that is, the closed cell showed neither increase nor decrease of pressure. This being so, the cork of the outer vessel was fitted with a water manometer. The absorption of the water vapour by the alcohol caused a slow but steady increase of the internal pressure. In the case of ethyl alcohol exposed to the air of the laboratory, the same result was obtained. In these cases, it might have been thought on a priori grounds that the alcohol was in so very large excess, that it couid have been regarded as dissolving the water. Experimentally, the water acted as the solvent (in the osmotic sense). The explanation of the temporary effects is very simple. After the preparation of the cell in the ordinary way, the cell-wall is soaked with water. When the solution is within the cell, the membrane soon gets into what may be called the osmotic condition ; that is, the condition of having water at its outer surface, aad solution at its inner surface. The normal inflow of water takes place. When placed in alcohol, the outer face of the membrane remains in contact with water, until the alcohol diffuses through 2 or 3 mm. of the small pores of the pot. While this diffusion is going on, the water in contact with the mem- brane is passing into the cell under normal osmotic conditions. This gives the temporary rise. This inflow of the water between the outside alcohol and the membrane helps the alcohol to reach the membrane in a shorter time than would be required if the water within the pores were stationary. When the alcohol is in contact with the membrane, the fall in pressure begins. In support of this explanation there is the absence of any temporary: rise in the experiment of Table III. | This explanation also accounts for the temporary fall when the cell is taken from the alcohol and is placed in water. Now there is a layer of alcohol in the pot between the mem- brane and the outside water. So long as this remains there is an outflow. When the water reaches the membrane, the permanent and normal rise of pressure begins. If this way of accounting for these temporary effects be the true one, it follows that, if the cell remain in the water until the pressure set up is at its maximum value and be then placed in alcohol, there will be no temporary rise. The | osmotic equilibrium will last so long as water is in contact with the outer face of the renner and further, since there is now no inflow, the alcohol will have to diffuse thr ough a layer of water whose thickness is not reduced by any passage on Mixtures of Alcohol and Water. 3. through the membrane as before. The interval of time between placing the cell in alcohol and the commencement of the fall of pressure will be greater than that in the ordinary experiments. The results given in Tables V. and VI. show this very clearly. TasLe V. Ceti XVI.—Solution of Ethyl Alcohol : 25 ¢.c. of alcohol in 100 ¢.c. solution. Cell in water till the gauge-reading was constant (after d days). | | | . Gauge || | ee Readings. ! Cell in water. Friday 5.0 389 | Maximum. Cell dried and placed in | | aleohol without opening. 5:2 389°2 | The small rise due to | nT | 3891 handling the cell | DAT 389 during the drying. | For every 5 min. | until 6.12 389 7.99 389 9.0 388 Saturday 10.30 376 Monday 8.50 307 11.15 296°'8 Placed in water without opening. 12.30 290°3 | 5.15 268 Temporary fall. | Wuesey da oS | Permanent rise. | open 221 | TasLe VI. Catt X XIII.—Solution of Propyl Alcohol: 20 c.c. of alcohol in 100 e.c. of solution. Time. Gauge Readings. Cell in water. Tuesday 10.0 | open 256 closed 382 | Pressure added by 1.15 419 [pump. | Wednesday 10.0 465 3.20 | 465 | Maximum. Placed in propyl alcohoi. 3.29 465 3.30 464-] 3.40 464°1 Every 10 min. until 4.30 4639 9.0 459 Thursday 9.30 3536 | | 10.0 B47 | Permanent fall. | 10 Mr. P. 8. Barlow: Osmotie Experiments When placed in water after the above there was a temporary fall of nearly 80 mm. succeeded by a large and steady rise. In Table V. the time required for the permanent fall to set in is about four hours; in Table VI. probably less than four hours. In Table I. the fall began in a little more than half an hour; in Table IJ. the gauge had risen and fallen again below its starting point in less than four hours. In this way, therefore, the temporary effects seem satisfactorily accounted for, and the true explanation of Pickering’s observations given. These experiments nave shown that what was claimed as a ‘“‘ crucial’? experiment in support of the hydrate (as distin- euished from the dissociation) theory of solution can no longer be claimed as such. Nevertheless it would not bea justifiable inference to conclude that therefore a hydrate theory of solution is untenable. A large amount of work has been done on the properties of solutions of various solvents— among other workers mention may be made of Fitzpatrick *, Lincoln +, Schlundtt, H. C. Jones and Carroll §,—-and all goes to show that the infiuence of the solvent is con- siderable and that some kind of complex of solvent and solute is formed. Some kind of “hydrate” theory seems necessary; but in this sense it must not be regarded as excluding dissociation. It may justly be concluded that these experiments prove that the part played by the membrane in osmotic phenomena is not a sieve-like one. For in the experiments where the outside alcohol got its water by absorbing the aqueous vapour in the air above it, the ratio of the alcohol molecules to the water molecules must have been very large; hence it is very probable that each water molecule would be the centre of an aggregate of alcohol molecules, which is carried along with it. LHverything really seems to be in favour of the pure alcohol getting through to produce a current from within outwards. For if we consider the alcohol within the cell, it has none of its molecules hampered by the aggregating influence of water molecules; and therefore on any theory accepting a quasi-gaseous pressure exerted by the liquids, there would be a larger number of effective alcohol molecules inside the cell. This would lead us to anticipate an outflow of alcohol from the cell; a decrease, instead of an increase, * Phil. Mag. xxiv. p. 377 (Nov. 1887). + Journ. Phys. Chem. iii. p. 457. t Ibid. vi. p. 159. § Amer. Chem. Journ. xxxi. 6 Dec. 1904, p. 521. on Mixtures of Alcohol and Water. Le of the pressure. In support of this there is the long-known fact that a copper ferrocyanide membrane is permeable to alcohol, though not in an osmotic sense*; and from experiments recently performed by the writer, there is evidence that, under mechanical pressure, alcohol gets through the membrane more easily than water. This removes the argument based on the larger molecular volume of alcohol. which might be put forward in favour of a sieve-like action. However, with all this in support of the alcohol passing outwards, we find an increase of the internal pressure; the water, though present in so small quantity, gets through the membrane. Any form of hydrate theory assumes an attraction between the two kinds of molecules. This attraction is the result of what has been called “ residual affinity ”’ +, a conception since revived by Lodge t and Traube §. Its origin is most likely “chemical,” and its action must be one of the causes of which - osmotic pressure is the effect ; most probably it is the cause. In consequence of this attraction there is mutual potential energy between the solvent and the solution. This tends to reach a minimum, and in doing so under the restrictions of an osmotic experiment, an opposing pressure is set up which hinders dilution and the consequent reduction of potential energy of solution. I. Traube || has very recently put forward the theory that difference between the surface-tensions of the solvent and solution is the cause of the osmotic current; and that the latter will be from the liquid of weaker surface-tension. In connexion with this there is the experiment at the end of Table IV., where the current was from the weaker solution : that is, from the one with the greater surface-tension. In the same way, many similar experiments both with copper- ferrocyanide membrane and animal-parchment membranes are not in agreement with this theory. The only method of finally testing such a theory would be to use a membrane equally permeable in an osmotic sense to both liquids of the mixtures. The existence of such a membrane seems highly improbable. In any adequate theory of osmotic pressure, the part played by the membrane must be taken into account. This necessary part is that the membrane must absorb that liquid * Tamman, dunn. Phys. Chem. [2] xxxiv. p. 309. ft Pickering, Ber. Deut. Chem. Ges. xxiv. p. 3629. { ‘Nature,’ Ixx. p. 176. § Phil. Mag. viii. (Aug. 1904) p. 162. || Phil. Mag. viii. (Dec. 1904) p. 708. 12 Mr. R. A. Houstoun on the Liffect of a which, in going through, forms the osmotic current *. On this point the work of Nernst + and Flusin t may be referred to. During the last year the writer has been working on the osmotic pressure of ethyl-alcohol solutions with different membranes. One experiment may be mentioned here (it is not put forward as original). Pure alcohol and pure water were separated by a gutta-percha tissue, the water being within the cell. A large pressure was set up, showing an inflow from tke alcohol to the water. With a copper- ferrocyanide membrane the direction is reversed. The cause of the current is the same in each case, namely, the mutual potential energy of solution of the liquids; the direction of the current 1s conditioned by the membrane. ~The experimental work of this paper was carried out at the Cavendish Laboratory. I wish to take this opportunity of thanking Prof. J. J. Thomson for his kindness during the progress of the work. Il. The Effect of a Surface-Film in Total Refleaion. By Ropert A. Hovustoun, J0A., B.Sc., Glasgow University 1851 Hehebition Scholar §||. T is well known that Fresnel’s Laws for determining the phase and amplitude of a reflected or refracted li oht-wave from those of the incident wave have not been found to give the exact experimental result, when investigated with the most accurate experimental means. There is a difference between the calculated and observed results, greater than the experimental error. Itis assumed in deriving Fresnel’s laws, that at the surface where reflexion takes place the index of refraction changes discontinuously in going from the one medium to the other. The deviation from Fresnel’s laws has te satisfactorily explained on the assumption that there is “ surface-film ” between the two media. This surface-film can be regarded as a transition-layer, in which the index of refraction changes continuously from the value it has in the * Since this paper was written, a similar view has been arrived at by Prof. Kahlenburg (Phil. Mag. Feb. 1905, p. 228) on similar lines of work. t Zeit. Phys. Chem. vi. p. 37 (1890). t Comptes Rendus, exxxi. p. 1308 (Dec. 31, 1900). § Communicated by Professor A. Gray, F. R8. || “ Wirkuug einer Obertlichenschicht bei Total-reflexion.” R. Houstoun, Gottinger Nachrichten, 1903, p. 852. “Ueber die W ae einer Oberfliichenschicht bei Total-reflexion.” RB. A. Houstoun, Phys. Zeitschrift, vi. p. 208. Surfuce-Film in Total Reflexion. ke one medium to the value it has in the other; er it can be regarded as a nearly homogeneous layer with a definite index of refraction, produced in polishing the surface. The formula for the deviation has been proved experimentally by Jamin * and Quincke { for the case of ordinary reflexion. ‘This paper describes some observations made to prove the formula in the ease of total reflexion, which was first given by Drude f, though it follows naturally from the formula for the case of ordinary reflexion, which was found some years earlier. Fresnel’s laws for the case of total reflexion were proved by Jamin § and Quincke ||, who worked with fresh surfaces for which the effect of the surface-film would be naturally very small. The apparatus used was a spectroscope, the collimator of which was fitted with a polarizing nicol, and the telescope of which was fitted witha Soleil-Babinet compensator and an analysing nicol. A sodium-flame was the source of light. The incident light was polarized at 45° to the vertical ; after total reflexion it was once more made plane-polarized by the compensator, and then cut off by the crossed analyser. The Soleil-Babinet compensator consists essentially of a quartz plate and two quartz wedges with equal angles. The two wedges have their optical axes in the same direction, parallel or perpendicular to the edge of the wedge; the wedges are parallel, but in opposite directions. The axis of the plate is perpendicular to the axes of the wedges. The relative phase-difference produced by reflexion &e. is com- pensated by moving the one quartz wedge relatively to the other wedge and the plate, which are fixed together. The elementary theory disregards the reflected waves. It assumes also that the axes of the two wedges and the plate are Jamin, Ann. de Phys. et Chim. (3) vol. xxix. p. 263 (1850). Quincke, Poge. Ann. vol. exxviil. p, 355 (1866). P. Drude, Wied. Ann. vol. xlii. p. 146 (1891). J. Jamin, Ann. de Phys. et Chim. (3) vol. xxx. p. 257 (1850). G. Quincke, Poge. Ann. vol. exxvii. p. 217 (1866). % ii ib § | 14 Mr. R. A. Houstoun on the Effect of a set exactly. This second cause of error was investigated theo- retically, and does not seem to be an appreciable cause of error in the observations made. ‘The first cause of error, the effect of inner reflexion, has been discussed by Prof. W. Voigt *. In the instrument used, the rays reflected on the surfaces C and D form separate images in the field of vision, and the intensity of the light reflected at B and again at A is too small to be taken into consideration. There remains only the light reflected on the surfaces Hi and A, the intensity of which is perhaps 7}, of the intensity of the light that comes direct through. As the distance between the surfaces A and H is ereat, and the light is not absolutely homogeneous, this error does not come into consideration. In the elementary theory it is assumed that light is propa- gated in quartzin two waves, plane-polarized at right angles to one another. Prof. Voigt has, however, shown in a recent article t, that it is propagated in two elliptically polarized vibrations, the ellipses being long and thin, having their long axes perpendicular to one another, and being traversed in opposite directions. The effect of the ellipticity of the vibrations on observations made with the compensator was investigated, and a result in accordance with Prof, Voigt’s theory obtained. The investigation is given here. For simplicity we can consider the compensator as con- sisting of two plane parallel plates of quartz, with their axes H, and H, exactly at right angles to one another. Let us We Hy suppose that the incident light consists of two vibrations, Hsin T along H,, and H’sin T’ along H,. To take account of the elliptic propagation in the quartz we must replace these two linear vibrations by four elliptic vibrations, a right- handed and a left-handed vibration having their long axes in * W Voigt, Wied. Ann. vol. xxii. p. 236 (1884). Tt W. Voigt, Gott. Nach. 1908, p. 155. Surface-Film in Total Reflexion. 15 each of the directions H, and H,; 7. e. we must write H({1—«*} sin T+.’ sin T) + E'(« cos T’—« cos ny in the direction Hy, and oa ip (x cos T—« cos T) + B’((1—«’) sin T’+«? sin T’) in the direction Hy. «is very small. The underlined terms are right-handed or negative ellipses. Let the right-handed vibrations receive the phase-retardation 7, in passing through the first plate, and the left-handed vibrations the phase-retardation /,.. Then, if we disregard the x” terms, after the first plate the two components are Hem (Er, )--li(« cos (Th) —« cos (I —7;)) and H(« cos (T—7,)—« cos (T—1,))+ EH’ sin (T'— 4). These may be written / (H? + H’«°*)? sin (1 —7r,—tan—" ) +l cos (’—1,), (1) and (BH? + H’x?)? s1D (oe i,—tan~? a ) + EH cos (die r). (I1.) Let 7, and 7, be the corresponding phase-retardations pro- duced by the second plate. Then, if we consider only that portion of the phase-retardation which varies with the thick- ness of the plate, we shall have, after the second plate, in each of the directions H, and H3;, four vibrations with the phase- retardations r, +172, rth, LZ+7, and 1,+4,. Hence we shall have vibrations with those phase-retardations in the principal plane of the analysing nicol. In the ex- pression for the resultant intensity there will occur a number of terms, of the form A cos { (7 +79) — (4+ 2) + a} + Boos (ri +72) — (rth) +0} + Cos {(r +72) — (1; +72) + ¢}+ D cos { (71 +l) —(, +172) +a} + Boos 4 (r+) —(h +4) tet + F cos {(h+7)— (hth) +f. Write r,—2,=6, and r,—/,=—6,. Then we may write the six phases 8;— 8 +4, — +8, Ot, oy tentd, oy +e, and —Oot+/. 16 Mr. R. A. Houstoun on the Hifect of a As the one wedge is moved past the other, 6, changes ; and each of the six terms gives a similar system of maxima and minima. It is the system with the phase §,—6§,+4 on which the working of the instrument depends. Its intensity is s times the intensity of the others; and the position of its minima is not appreciably affected by the other systems. Hence we can disregard the other systems, 7. €., we can disregard the second terms in the expressions Ci} and (Tey: On entering the second plate the first terms become 1 ah | (EE? + Ex?) (1~x?) sin CSS < a sin( P—rj—tan fs 5 ) } | Ey) | + (EH? + Ex’)? } K COS cS Licey: ane COs (v4 tan a5 ) } | / and | 1 ! fy’ CH? + HK?) | COS Gee ~ tan ) —K COS (Tn tame =) } + (B’? + E2«?)? | = #) sin (7 —/,—tan7! ay +e sin (T’——tan~ 1 If we disregard the x’ terms, on leaving the second plate the two components are (Hi? + E’?x?)2 sin( T—7y —7y— tang le (BD? + Bx 22 | « cos (2 —4-b-tan 5 fy #605 cos | (1, rian) and | ee) KW’ = KH’ \ | (EH? + B?x2)? 7 K COS (T—1—r— tan =) —«cos(T—m—2 a iE ) | \ J i) DONS ac KEY | + (B24 Be)! —AjA,— a4 Boe ar lee fe) ie) 484 | 420 | 458 | 38 | 41 | 514 430 | 466 | 36 | 37 | 51:9 | 432 | 46-4 | 32 | 3:5 | 528 | 428 | 462 | 34 | 34 | 548 | 421 | 454 | 33 | 3:0 | 548 | 421 | 454 | 33 | 31 | 561 | 425 | 446 | 21 | 28 | 565 | 41-4 | 442 | 28 | 28 591 | 393 | 420 | 27 | 24 | 584 | 403 | 426 | 23 | 26 59-9 | 885 | 412 | 27 | 24 | 596 | 393 | 414 | 21 | 24 — 62-9 | 35:8 | 380 | 22 | 20 | 628 | 355 | 381 | 26 | 21 | | | * —0-035. £ —0:038. nN 1 The accuracy does not seem to be very much greater than in the former case, when the light was only once totally reflected, probably because here the light was not always totally reflected on the same parts of the surface, and the thickness of the surface-film will vary from place to place. Surface-kilm in Total Reflexion. 23 In both the above cases the film was the natural surface- film, and not a homogeneous layer due to polishing, as the glass surfaces had not been polished for a very long time. An attempt was then made to verify the theory further by depositing very thin artificial surface-films of collodion on the hypotenuse surface of a prism—which had previously shown no trace of such an effect. The artificial film should produce the -same effect as the natural films. The films were made after the manner of Wiener, by putting two or three drops of a very dilute solution of collodion in ether and alcohol on the hypotenuse surface of the prism, pressing them down with a similar surface, until they filled all the space between, and then drawing the two surfaces apart. The ether and alcohol then evaporated, leaving a homogeneous skin of collodion. The prism used was right-angled and isosceles, and the index of refraction for the D-lines was 1°513. The refractive index of collodion is greater than this; and so we had a uniform layer, the index of refraction of which did not lie between that of the glass and that of the air, and which gave an effect in the opposite direction to that produced by the natural film. The film was kept dry during the observations by placing a quantity of calcium chloride on the spectrometer-table. ‘The presence of dampness was easily detected; it lowered the index of refraction of the film to below that of the glass, and we had a deviation from Fresnel’s formula in the other direction. Some trouble was experienced in getting a film of a suitable thickness ; if the film is too thin, the effect is comparable with the errors of measurement, and the formula does not hold when it is too thick. The set of observations given, however, shows the effect of the film very well. Collodion Film. Limiting angle of total reflexion, 6=41° 22" | R A A Mean | a a A’ AlanA | $- : WI Ge Error, faa : Da A: ©} eh @) yi | fe) fo) fo) fe) fe) fe) | 42, 30 34296 | 25-4 D2, Ol oe 21°6 — 0-6 44 0 86 58 | 353 30:7 03 3'6 ot +10 45 30 91 31 AUS awe 0-4 er 30 ==) 47 0 96 2 | 43°D 40°3 0-2 32 40°2 (| 48 30 | 100 36 ADD a) Ag 0-2 2°8 42-2, —0-2 50 0 | 105 10 459 43°5 Ol 2-4 43°1 —O-+4 51 80 |{ 109 44 4671 43°4 Oe 27 43°95 +01 53 0 ll4 18) 45°8 43°2 O-1 2°6 43°4 +(0:2 54 30 118 54 45:2 43:0 0:3 2:2 42-9 (NPI. 56 0 123° 28 44°3 42°] 0°3 | 21 42:2 +01 | ) e=U:029. o@, RK, A,, A, and A’ have the same meaning as before. 24 Mr. R. A. Houstoun on Total Reflexion at the Attempts were then made to observe the effect of the collodion film in ordinary reflexion and refraction. In the first case the one component was too weak at the polarizing angle to give good results. The phase-difference produced by a surface-film in refraction is given by tan Ag=—esin ¢ tan (d —¢')*, where @ is the angle of incidence and ¢’ the angle of refraction. The following measurements were obtained :— R. p. Aa (air to glass). Aq (glass to air). oer ie fo) ©) fe) 154 0 a0 0-7 =O 1s4 12 38 06 Se 153 22 46 08 — 0:0 Lola? D4 OP —I1 Owing to some unknown circumstance the measurements from glass to air are not:so accurate as those from air to glass. The theoretical value, obtained by using the value of ¢ already found from observations on total reflexion, is +0°°6. lil. Zotal Reflexion at the Second Surface of a Thin Plane Parallel Plate. By Rosert A. Houstoun, M.A., B.Se., Glasgow University 1851. Exhibition Scholar fF. ie method used in the experiments described in the preceding paper was also employed to investigate total reflexion at the second surface of a thin plane parallel plate. A prism, the same as the prism used in the collodion experi- ment, was coated by Bottger’s method with a thin homo- geneous layer of silver on its hypotenuse surface. Sodium light, plane-polarized at an angle of 45° to the plane of incidence, entered the prism, was reflected by the silver layer on the hypotenuse, and the relative phase-ditference produced between the components, parallel and perpendicular to the plane of incidence, was measured with the Babinet compen- sator and analysing nicol. The angle of incidence on the hypotenuse surface was usually such that the light would have been totally reflected, if there had been no silver film there. The silver film was then changed into silver iodide, and similar measurements were made. Theoretically this is the case of the plane parallel piate, the thickness of which is small in comparison with the breadth of the incident light-wave, for the case that the three media * P. Drude, Wied. Ann. vol. xliii. p. 145 (1891). | Communicated by Professor A. Gray, F.R.S, Second Surface of a Thin Plane Parallel Plate. 25 are all different, and that total reflexion takes place at the second face. The mathematics is rather complicated ; the rigorous formula in the case of silver iodide was found capable of taking a relatively simple form and agreed perfectly with the experimental result. An approximate formula was used for the silver film. The necessary formule are given in Voigt’s Kompendium, 1. p. 643 and the following pages, but must be considerably transformed. The formula for the silver iodide will be derived from first principles, as that can be done more shortly than is generally supposed by means of the reciprocal property of Maxwell’s equations, and will be compared with experiment. Then the case of the silver films will be treated from the formulee in the Kompendium. When the wave in the glass falls on the film on the hypo- tenuse, it gives rise to a reflected wave in the glass, to a refracted wave in the film that is repeatedly reflected back and forwards in the film, and to a wave in the air beyond. We write down exponentials io represent those waves and substitute them in the boundary conditions. Consider the magnetic vector as the light vector. We can consider separately the components polarized in and perpendicular to the plane of incidence. Let us consider the component per- pendicular to the plane of incidence. We can write the incident and reflected waves in the glass He"; Rel, Then summing all the waves in the film incident on the second sinters, and all those reflected by it, we may write them \ Bee Lee Rye?” Let the wave in air be represented by qn De~4, 1 ; 5 wuere 20 “sin d, + 2 cos L4 = — (- a P), Cue: Vy t is the period of the ive non v, the velocity, and ¢, the angle of incidence in the medium, The z axis is perpen- dicular to the surfaces and is measured positive from glass to air. Let J be the thickness of the film, w the magnetic inductivity, and K the electric inductivity of the medium in question. If H is the component of the magnetic vector perpendicular to the plane of incidence, the boundary conditions are that H and az-7- go through the boundaries z = Omantcerce— 6 26 Mr. R. A. Houstoun on Total Reflexion at the continuously. Therefore we have E,+R, = H.+ Ro. eee __,2nl cos 5 . 27 cos Py 2rl cos ah es alee Reset 2) pI en tear ~ Ke 72 + Rye ie ie aa BY Tete hes - (2) cos cos (yee RSE! ep : ill — oan 2 ° ° . e ) ik Uy ( 2) Kea Co ea 2rl cos Ps _2nl cos Py A 27lcos Ps ( Hee TV9 —R,e ‘ TV2 Ve Pe ae De TVs GOs Ps (4) Kote Kye; ; Put 2arl cos L= Ps . Cos @; is imaginary. TV9 s Pat 1 Cos ds Kets tan @ = cos d, Kv; " Then dividing (1) by (3) and (2) by (4), H, +R, cos¢, — B.+ R, cos dy H,—Rh, Kove a H,—R, Kye, : Bom Se Boers 5 . = == COM: Bye — Roet® © Therefore Rye poe 1l—i cote Kee” 1+i cota cos a@—?sin Now ve ag? therefore E,+R, pene US COS d, sh ae e2i(a—L) E,—h, KK, po cos oy) ] — e2(a-L) Kp; cos ats saat a ot (a—L). Ky, cosy Put R : ss = pse'*s : Ky A K.p; cos | —tan =a/ KL = cot («—L). - Kup, COs D2 A, is the absolute phase-difference produced in the com- ponent polarized at right angles to the plane of incidence. The absolute phase-difference produced in the magnetic vector polarized in the plane of incidence is the same as that Second Surface of a Pin Plane Parallel Plate. 27 produced in the electric vector perpendicular to the plane of incidence ; and by the reciprocal property of Maxwell’s equations the above discussion holds for this electric vector, if we interchange K and wu. Kips COs Pi ae Bie oe NY lc, cae cot (@—L), where 1 COS ds [Lal's tan 8 = — Pa Me fs COS hy (33 Hence putting w=1, and writing A,—-A,=A, we have K [ee VK ee ON ee cos db i at cos oe cos b; - Cot (2 L) cot (B- L) ae bs A z = arc tan where ee [Kz cos h an a NS K X3 COs h and K, cos od» bale, = 7 K, ay This formula gives the relative phase-difference for any angles of incidence, when /, the thickness of the plate, is coat To find 7 in terms of A, i. e. to find ap thickness of the film from the observations, put x=a—hL, y=B—L. Then V/ Ke “cot , A / K, COS @7— ie COU 7 2 | = és: ong x COS DMs 1 . BRA aie: t2 ic cos d, + cot £ co i rd cos ae cos Su — COS & COS ¥ cos py COs oy) ea. (vw +y)—sin (e-~y)) if Wha (a +y)+ + sin (ey) = i ae (cos (@—y) —cos (w+y)) + a 21 cos c +y)+cos(#—y) ) COs d, * C08 So / Ky K K. ix sin ( @+y(r/ i ae A/ ies) — sin @-y\(a, [2 “F \ i) cos gd; Cos 2) (cos i , 608 =) = Gg ~~ = re pat oS cos dy. ete or? " COS Gy, 28 Mr. R. A. Houstoun on Total Reflexion at the Theretore K ‘ sin (o+y)( ie -\/e)- tan cos (e+y) (coe ae oe ds) \cosg: cos dy am 2 oo eee A (cosg, . cos dy q : rf un if Vv any ee 2 (= Py * cos 9) ca (oy ¥e Now uty =a+P—2L, bY == a—B, i 271 cos dy TUo Put COS @; COS dy —cosd, Cos dy 2 K, Ky ey kK tan y = tan Therefore Aqr COs dy ety—y=atp— —y- = Ky, A /cos COS \ | et -n/%) )sin( ao 8) +tan 5 ( an P20 Gey | A cosehy ls ze ial w/e Ke) + tan Las ie . “ie | ) . ¢,, K,, K, are known; dy, «, 8, y can be calculated ; A is observed ; hence from one observation / can be deter- mined to a multiple of 277, and if we have a series of obser- vations, J can be definitely determined. The method, according to which the silver-iodide film was prepared, was found to be very important. If warm iodine vapour in excess was allowed to act on a silver film, we obtained an opaque dull yellowish film; but if a small grain of iodine were left near the silver film for ten or twelve hours, a transparent film that gave beautiful interference-colours was obtained. Observations on a film produced according to this method agreed with theory. A set of such observations is given below. ¢,, the angle of incidence, is calculated from the angle between the directions of the telescope and colli- mator. The thickness of the film, /, was determined by formula (6) from the observations A, and then substituted in formula (5) and A’, the theoretical value of the relative phase-difference, calculated. 1t was found necessary to take ~ the positive value of the imaginary cosine, otherwise a = arc A Second Surface of a Thin Plane Parallel Plate. 29 negative value of / would have been obtained. The silver iodide was screened from light as much as possible, and test readings showed that sensibility of the films to light was not an appreciable source of error. The agreement is very satis- factory, when we consider how imperfectly the mathematical conditions are realized experimentally. The auxiliary functions a, 8, y used in the calculation are given, also the difference between the observed and calculated values. / was 1°40 2. Observations on Silver-lodide Film. p. —a | —8£. —y. | A’ A | Ala. SULT Gas hoe Se Obs fo) fo) fo) fo) O.. ° 230 | 311 68 | 155 | 639 | 613 | +26 44 0 | 30-4 92 | 210 | 752 | 732 | +20 | 45 30 | 461 DO. ViS@5-1 s | STO |802 } +08 47.0.| 507 | 136 | 282 | 840 | 828 | +14 48 20 | 542 | 154 | 312 | 848 | 851 | —03 500 | 570 + 17-1 | 823 | 848 | 828 | +20 5130 | 597 | 188 | 3438 | 824 | 821 | +03 53-0] 611 | 197 | 365 | 799 | 821 | —22 54.30 | 626 | 21:0 | 359 | 768 | 764 | 40-4 56 0 | 640 | 221 | 369 | 732 | 740 | —08 57 30 | 652 | 233 | 3872 | 682 | 700 | —18 59 0 | 662 | 242 | 364 | 644 | 640 | +04 60 30 | 671 | 252 | 392 | 598 | 648 | —5~0 62 0| 680 | 262 | 367 | 553 | 567 | —1-4 The rigorous formula becomes much more complicated in the case of the silver film. Even when we make several approximations, it is still impracticable and not so instructive as the method used. In the case of silver, as in silver iodide, we have a number of repeated reflexions in the film, but as the silver absorbs light we shall disregard all but the first. SILVER AiR Consider the vector polarized at right angles to the plane of incidence. Let ps be the ratio of the amplitude of the reflected 30 Mr, R. A. Houstoun on Total Reflexion at the vibration to the amplitude of the incident vibration at M; and ps’ the similar ratio at N. Let 6, be the ratio of the amplitude of the refracted to the amplitude of the original vibration at M. Those ratios are here complex. Write : -, I -, TT ee AE ty pul t 5 [A/a Su ese ps = pels 3 Os = dé A, >; Ps = 1s EAs ; where 7;, ds, and 7,'’ are real. Then A,, A,’,and A,” are the changes of phase which the waves undergo. Let us represent the incident wave in the direction H M by sin T. ‘hen the reflected wave in the direction MQ is r,sin(T+A,).. The wave which enters the glass at P has been twice refracted and once reflected. Its phase has been retarded by an amount L owing to its having to traverse the distance MNP. Then to take the absorption into account, we multiply by a factor k, like L dependent on the thickness of the film. The wave which enters the glass at P is therefore kd?r,'' sin (T+2A,’+A,”’—L); and the resultant reflected wave, polarized at right angles to the plane of incidence, is resin (T+ A,) thkdgr," sin (T+ 2A,'+A,""—L), Similarly the resultant reflected wave, polarized in the plane of incidence, is r, sin (T+A,) +kd,?r," sin (T+ 2A,'+4,'""—L). When we sum the two simple harmonic motions, of which each of these waves consists, we find that their phases are hdr. sim QNa A mee) ret kdgr,|' cos (2A, +4,’ —A,—L). PAP tan = Ty A. Seen and : hdy?ry'' sin (2A,' + Ap’ —A, —L) | rare ee p Dee) ia ey ee r,t kdp*ry'' cos (2A,/ +A,'—A,—L) Y+A,+P (8) The relative phase-difference which we measure is approxi- mately the difference of these two expressions. If «, and y, are the sine and cosine of the angle of incidence in the glass, and if ay. and asy3 are defined by Noa = N(1L—iK) a = as, ay” + YQ” = ag’ +3 = I, then (Voigt’s Kompendium, i. page 646) AN AVe ) = Bere AY 11 A2Y2 * atatys + tie Sees. 2aiy1 ve Zany O11 + S22 ho + 22 Second Surface of a Thin Plane Parallel Plate. dl p (inn AP) meas) p tin. 23 Ys Our Sane Pe rp (a AaVo + 2373 Axo + HoY3 Mmiyoln(l ik) and __ Ariyzin(1—iK) ket =e x No is the index of refraction of the glass, n(1—7K) the index of refraction and absorption for the film, / the thickness of the film, and A the wave-length of the light in question in air. When the silver film was thick, the relative phase- difference showed no effect due to the silver-air surface, but was the ordinary phase-difference produced by reflexion in glass on a silver mirror. When the film was thinner, however, there was a marked deviation from this curve. Instead of studying the relative phase-difference produced by the film, we studied _ the deviation of the relative phase-difference from the ordinary glass-silver curve, or in other words the effect of the “ thin- ness.” The formula for the deviation is the difference of the tan—! s in (7) and*(8), P—S. It has been found by different observers that the optical constants of silver in thin films are different from the values obtained by Drude from observations on silver in mass. This may be due to the thickness of the film being comparable with the mean free path of the free electron. Fortunately this difference affects only one of the functions p,", p, Xe. appreciably, namely A;”. It was found P could be dis- regarded in comparison with 8 ; also that 2A,’ was equal to A, to a sufficiently high degree of aproximation, This simplifies the formula for the deviation to kd.?r,'' sin (A,'’— L) rstkd?rs'' cos (As —L) * The variation of k and L with the angle of incidence could be disregarded. Asa result of trials, the values nK=3°'67 and n=0'61, as against Drude’s nK=3-67 and n=0°18, were found to give the best results. Six series of observations on the deviation are given in the next table, together with the fale theoretical value calculated for the values ‘= 0-070 and 0-055 and the values of d,? and ,'’ used in the calculation. When we compare the experimental and theoretical results, there is not much similarity. The deviation is in the right direction and has its maximum near the proper place, but the shapes of the curves are different. We cannot improve matters by taking into account the terms that we have dis- regarded. The agreement—such as it is—is the best that 32 Total Reflexion at Second Surface of Parallel Plate. can be obtained using the theory of the plane-parallel homo- geneous plate. W hen the silver film is as thin as one-twentieth Silver Films. | Observed Deviation. | Calculated Deviation. Angle of | ig e: | - | incidence. | 1 ) hw} @ @)| | | @ |% =0055. = = 007. || de | mal — , ea ae Oo he (e) ae Lees fe} nae o z 39 50 es Sole ae. 8 2 4 5 28 | O85 41D 2 GSS 2) 4 1 1 2 |} 28 0:89 42 30 1 ha if 4.| 15-} 12 == —4 les 1:00 44 0 Oo at 3 6125 | - 23 —7T —9 |. Dee 2732 eas eee ec ics be |g Se oie Mine | gh ne 45550 Op se | Ol 354 30 [eee ar 6U 27 4-85 tO ass 6 | 12 | 39 | 39 18 41 2°7 361 48 30 |42| 5; 9 | 11) 41 | 42 15 36 2-6.) ea: 50 0 ||—2)| 2] 44°99) 32) 39] 12 26 2°6 2°69 ee Pre |e 1S a Se ane See eo. / 51 30 | -l ieee Peery) 10 DA 2:5" |} 256 53 0 (| -1 | 1 | 8| 25) 34] 10 20 25 | 240 54 30 1 3048 18 | 32 | 9 18 24 | 296 56 0 1 16 | 24 | 8 16 24.1 215 feos Pe Ce. ae Dy. oO | 10 | 19 |i 8 15 23 | 2-08 59 «~O | ae aa 7 14 25 | 1:99 60 30 1 Fada] a 13 22 1:96 62 0 | 1 5 || 6 12 9-9)" Sas of the wave-length of sodium fight, as in the above experi- ments, then we can no longer consider it homogeneous ; and apparently cannot expect an agreement with the formula derived on that supposition. | The values ot ds and r,’’ are very striking, particularly the value of »,'’.. In the ordinary case of total reflexion d, can be as large as 52: but 7,’ can have much larger values than that. If we w te fn = m+ ip and asy3;= —?s, where Mm, ps and s are real positive quantities, then mt+i(pt+s) m+iup—s) m is small in comparison with p for the metals gold, silv er, and sodium. Consequently 7,’’, the maximum value of 7,’ ' is 2p : PL is the ratio of the imaginary to the real part of asyo, m m or the ratio of the imaginary to the real part of a, since 7 is approximately veal. Now a, 1s given by I} 4 — My, = n(1 = i Jag. On the Virial Equation. 33 Hence ay 2 7, = ae = DKK. m If we take Drude’s values of n and nK, we obtain the following values of 7,/'’:— Metal. n. nk, ag Dilver iiss 02h. 0°18 rat Ale Goldner. 0°37 2°82 15 Sodimm | oe... 0-005 2° Oil: 1043 If » were zero, and nK not zero (Lord Kelvin’s “ ideal silver”), 7s!’ would be infinitely great! If we had a very thin film of sodium, and a ray of light were repeatedly reflected within the film at the proper angle, its intensity would be very much increased. This would be contrary to the conservation of energy. The explanation of course, is, that in such thin films the geometrical laws of reflexion and refraction do not hold. The observations recorded in this and the preceding article were carried out in the Physical Institute of the University of Gottingen at the suggestion, and under the continual advice of Prof. W. Voigt. IV. Lord Rayleigh on the Virial Hquation. By S. Hy BuRBURY, f..8.* N his paper on this subject in the Philosophical Magazine 4 for April 1905, Lord Rayleigh considers a system of molecules, elastic spheres, which also exert on each other finite forces. And concerning these forces he assumes that within the effective range of any type sphere there are many others, and that the forces which the type sphere exerts on the more distant molecules within this range are not in- appreciably small compared with those which it exerts on its immediate neighbours. In his own language, the forces are “‘of the character considered in the theory of capillarity, that is extending to a range which is a large multiple of molecular distances, and not increasing so fast with diminish- ing distance as to make the total effect sensibly dependent upon the positions occupied by neighbours.” Then he goes on to say: “‘ Under these restrictions symmetry ensures that the resultant force upon a sphere, situated in the interior and not undergoing collision, is zero; and the whole effect of such forces is represented (Young, Laplace, Van der Waals) * Communicated by the Author. Phil. Mag. 8. 6. Vol. 10. No. 55. July 1905. D. 34 On the Virial Hquation. by an addition to the pressure of a quantity independent of the temperature e and inversely proportional to the square of the volume.” By this he means one of two things, namely, (1) the re- sultant force on a molecule is zero on average of time; or (2) the resultant force is actually zero at every instant for a sphere not at that instant undergoing collision. If he means the first alternative, the resultant force must be zero on average of time if ihe moulon We stationary. If,then, X, Y,Z be ae compenent forces on a molecule, Ne Vee fee vale on average of time, X—Y=Z=0. But it does not follow that Kon Wa toe =() on average of time, that is that the time average of the Virial for ‘molecules in the interior is ZeYO. In fact, as admitted in Lord Rayleigh’s paper, it is not true for the collision forces between elastic spheres. Neither then can it be true if the molecules are centres of repulsive force, becoming evanescent at distances very small compared with molecular distances. There is in fact no proof that Xa-+ Yy+Zz=0 for molecules in the interior, and therefore no proof that the whole effect “can be represented by an addition to the pressure of a term independent of the tempe- rature and proportional to 2 om If we take the second alternative, that at every instant the resultant force is actually zero for every sphere not at that instant under going collision, Lord Rayleigh must mean by “symmetry,” ‘that his spheres , although in motion relatively to each other, are at every instant in some symmetrical ea rangement such, to take an example, as at the angles of cubes or reoular keholiedrore: Is a motion possible in which ie shall ‘be the case at every instant ? Without going so far a to say that no such anton is possible, we may say, I a with confidence that it cannot be motion in accordaman with Maxwell’s law. Lord Rayleigh’s system, then, is not a rare eas. Perhaps it may be a liquid, or a dense gas, to which Maxwell’s law is inapplicable. In order to form a theory of the motion of a system of mutually acting molecules, to which we cannot apply the ever recurring “assumption of infinite rarity, we require to know what part is to be played by the potential, vy, of the intermolecular forces. In a statical system in stable equi- librium x is minimum. What is the corresponding law for stationary motion in a dynamical system? I think Lord Rayleigh is the man to answer that question, if he could be induced to do so. Actinium and its Successive Products. ay, In the silence of the authorities, I have myself suggested that Boltzmann’s e-?'X law supplies the necessary ouidance. The chance that any group or system of molecules shall be in a configuration in which the potential of their mutual forces, soe of the external forces if any, is y, is proportional to e~*x. Or,if you prefer so to state it, the time during which on the average of any very long time they will be in that configuration is proportional to e =x, That gives the minimum yx for a statical system as a particular case. Tor if yo be the see in the configuration Aj, and x, in the configuration A,, and if Xo< Xi. ae is more probable than Ay in the ratio @04- Xo), that is in an infinite ratio in the statical system, for which & is infinite. The statical system must therefore be in minimum potential. Also if there be only external forces acting, Boltzmann’s law gives e7—?'X as the density at the point where the potential is y, as in Max- well’s vertical column of air. I worked out the consequences of the application of the law to the general case in a former paper (Phil. Mag. for October 1901), and I think my con- clusions were in the main right. If so, the law would be inconsistent with Lord Rayleigh’s symmetry, and with its consequences. In fact it seems to me that Lord Rayleigh’s symmetry and Boltzmann’s Jaw cannot both be true for one and the same system in the same state. It may be said perhaps that Boltzmann’s law holds only for external, and not for intermolecular forces. Some English writers, notably Dr. Watson, while not expressing their dis- agreement with the law as applied to intermolecular forces, prefer to let it alone. That I think arises from excess of caution, or perhaps because the law, if so applied, leads to results inconsistent with some favourite doctrines of the orthodox theory of gases. The proof of the law given by Boltzmann at p. 134 of his Vorlesungen, Part I., is formally applicable to intermolecular forces. Why may we not so apply it ? V. Actinium and its Successive Products. By T. Gopiewsk1, Ph.D. (Cracow) * R UTHERFORD and Soddy, in their well-known investi- &% gationst on the activity of thorium, have shown that it is possible to separate from it a very active constituent * Communicated by Prof. E. Rutherford, F.R.S. Presented before the Academy of Sciences in Cracow, April 8, 1905. * Rutherford and Soddy, Phil. Mag. Sept. and Nov. 1902; Trans. Chem. Soe. lxxxi. pp. 321 & 807 (1902). D2 36 Dr. T. Godlewski on Actinium which they call ThX. The activity of this product decays with the time according to an exponential law; 7. e., the equation of monomolecular chemical reaction, falling to half value in about four days. At the same time, the thorium, which by the removal of thorium X had been deprived of about 75 per cent. of its activity, recovered its activity, the recovery curve being complementary to the curve of decay of ThX. The substance UrX, discovered earlier by Crookes, acts in a manner analogous to ThX. The & activity of this substance decayed according to an exponential law with the time, falling to half value in twenty-two days. Rutherford and Soddy have explained these phenomena on the supposition that the radioactive bodies are producing fresh radioactive matter at a constant rate, and that the activity of the matter so formed decreases according to an exponential law with the time. The discovery of these phe- nomena supplied the basis for the disintegration theory, which supposes that the atom of a radioactive body breaks up through a series of well-marked stages. The resulting products are quite distinct bodies, though they escape detection by chemical methods on account of the minute amount of the substance under investigation. Their existence is proved first of all by electrical measurements which allow us to make the quanti- tative investigations of the rate of change of these products. On looking over the series of successive products arising from different radioactive bodies, striking similarity between the products of thorium and actinium is at once manifest. Thorium produces ThX, ThX the emanation, this gives rise to the active deposit which undergoes two further transfor- mations, the first slow change being a rayless one, the other emitting all kinds of rays. Actinium in like manner pro- duces an emanation which is transformed into an active deposit which undergoes two further changes, the first being a slow rayless change and the other a rapid change. This analogy in “the number and nature of the products pointed to the possibility* that there existed between the actinium and its emanation an intermediate product which bore the same relation to actinium that ThX bears to thorium. In a letter to ‘ Nature’ (26 Jan. 1905) I gave the prelimi- nary results of the investigation which proved the existence of this product. Taking into consideration the similarity of actinium and thorium, I applied te the actinium the same method which * See Rutherford, Bakerian Lecture : ‘‘The Succession of Changes in Radioactive Bodies,” Phil. Trans, Royal Soe. ser. A, vol eciyv. pp. 190 & 204. and its Successive Products. 37 had been used by Rutherford and Soddy for the separation of ThX from thorium. The experiments were made with the emanating substance of Giesel, which, according to numerous investigations®*, has been found to contain the same radioactive constituent as the actinium of Debierne. The saturation current due to the a-ray activity of the products under investigation was measured with a quadrant electrometer of sensibility 120 divisions per volt; the needle was kept at the standard potential of 300 volts. The @ activity was measured by means of a sensitive electroscope. Four different sets of experiments were made which gave very concordant results. In each case 0°15 gr. of the emanating substance, of activity about 300 times that of uranium, was dissolved in 250 cm. of hydrochloric acid (about 8 per cent. concentration). The solution was evaporated on the water-bath to about 100 c.cm. When ammonia was added to the solution, a reddish-brown substance (probably hydroxide) was precipitated. The pre- cipitate, collected on a filter-paper, was dried as quickly as possible, and then its activity was measured. The filtrate was then evaporated to dryness, and when ammonium salts were driven off by ignition a small amount of a brown-black residuum was left behind on the dish. On raising this to a red heat, the colour of the residue changed from black to white. This residue was intensely active compared with the weight. Immediately after the dish was cold the activity of the residue was measured and was found to decrease slowly with the time according to an exponential law. In the same period the actinium, which by precipitation had been rendered almost inactive, recovered its activity, the recovery curve being complementary to the curve of decay. From analogy to ThX, which it so closely resembles in radio- active properties, the active substance separated from actinium will be termed Actinium X (AcX). The results of one of the series of experiments are given in Table I. and graphically represented in fig. 1. In Table I. the first column gives the days measured from the time of separation; the second column gives the activity. The activity of AcX is expressed as a percentage of the initial activity, the maximum activity soon after separation being taken =100. But for actinium (deprived of AcX) the final value is taken =100. In fig. 1, curve A represents the activity of AcX as a function of the time, the activity of AcX being expressed in the same units asin TableI. In the recovery curve B the differ- ence between the maximum and the first value is taken=100. * See f. i. Rutherford, Bakerian Lecture, Joc. cit. p. 188. 38 ACTIVITY. Dr. T. Godlewski on Actinzum TaBeE I. AcX. Actinium. ¢ in days. Activity. ¢ in days. Activity. 0°25 87°5 0-1 5°25 0-9 100 0-7 9:22 19 92°6 il 167 30 86:0 2:7 24:0 40 81:5 37 29°6 59 72:6 oT 39°38 6:9 10°7 67 48:0 8:9 59°2 8't §2°5 9°9 54°5 97 56°5 109 50°8 10°7 61-4 129 43°6 Wg. 62°5 13:9 41:2 13°7 68:6 14-9 40-5 15°38 76-2 15°9 36°2 17-0 78:0 17:1 ook 20°7 82'3 179 34-0 22:7 85°7 21°0 26°5 25°0 88°6 229 24-4 27-0 90°0 249 21°8 30°8 92°3 20-2 18°5 36°95 97-1 29°2 17:6 45:0 99'5 30°9 161 52:0 99:0 34-0 13°5 64:0 100 36:0 12:1 67-0 100 42°0 8:82 45:0 777 52:0 5°89 59-0 4:63 67-0 3°69 0) 30 TIME IN DAFS, and its Successive Products. 39 The activity of AcX immediately after removal was weight for weight more than a hundred times as great as that of the original actinium. In the various experiments the value of the initial activity of AcX was proportional to the amount of actinium used, but was by no means proportional to the total weight of matter obtained from the filtrate. In some cases, for example, only a few milligrams of the substance were obtained, which exhibited as great activity as a few centi- grams obtained in other cases. ‘This shows clearly that in the case of actinium, the substance obtained from the filtrate, which we see and weigh, does not all consist of AcX. The substance contains some impurities; in the present case, probably some of the rare earths. The amount of actinium X actually present is so minute that it precludes the pos- sibility of a direct chemical investigation of its properties. We see from Table I. that the activity of AcX increases in the first day after removal to about 15 per cent. of its original value, reaches a maximum, and then decays with the time according to an exponential law, falling to half value in 10°2 days. This exponential law of decay is clearly seen in fig. 2, where the ordinates represent the logarithms of the activity of the product AcX, and the abscissze the time after separation. On subtracting from the quantities given in the Table I. the number 2°70, which represents the activity of the residue which did not decay with the time, the points fall accurately on a straight line, as in the figure. This non-decaying residue comes probably from the small amount of actinium, which is not precipitated, and is therefore present in the filtrate. The activity of actinium, from which actinium X was removed, increased so that the recovery-curve was approxi- mately complementary to the decay-curve of AcX. The small difference between the experimental and the theoretical curve, as expressed by the equation 1,=],)(1—e), where X has the same value as in the decay-curve, is probably due to a variation in the rate of escape of the excited activity, which is extremely volatile. In all cases the decay-curve agreed more closely with the theoretical equation than the recovery-curve. The initial increase of activity of AcX immediately after removal (see fig. 1 A and fig. 2) is analogous to the similar increase of activity of ThX. The only ditference is that the recovery-curve of actinium does not show the same initial decay as found in the case of thorium*. This fact. is ex- plained by the different properties of the excited activity * See Rutherford, ‘ Radioactivity,’ pp. 180 & 295. AO Dr. T. Godlewski on Actinzwm Fig. D> f | i 60 70 50 Seomentan Sere pe Se ieee ee aoe ee Pe ee = oo Soin ee oe ce eee Se ee aL aan Cnnamnm~ O© YO Ff ND es “ALIAILOY JO *907 /N DAYS. TIME and its Successive Products. Al of actinium and thorium. The active deposit of actinium is soluble in ammonia, and is volatile when heated*. The active deposit of thorium, on the other hand, is not soluble in ammonia and is not so readily volatilized. he initial increase of activity of AcX is thus explained in the following manner. When actinium is precipitated with ammonia, the active deposit is left behind in the filtrate together with AcX. In the moment, however, when we heat, the volatile active deposit is driven off also. But as soon as AcX is separated, it at once produces the emanation which gives rise to the active deposit. The activity of the latter, at first, more than compensates for the decay of activity of AcX, which has a comparatively slow change, and in consequence the activity of AcX first of all increases. On the other hand, the actinium, when treated with ammonia, was deprived not only of AcX but also of most of the active deposit. Any of the latter, if still remaining in the precipi- tate, would be driven off during the process of drying. In consequence, when we start the measurements of the activity of the precipitate itself, no excited activity is present. The activity at once commences to increase, since a fresh amount of AcX is produced which in turn gives rise to excited activity. In consequence we do not observe the initial decay in the recovery-curve of actinium as in the corresponding curve for thorium. Disregarding these small peculiarities, the behaviour of the product AcX, and of actinium deprived of AcX, is, as we have seen, completely analogous to that of ThX and of thorium deprived of ThX. There is, however, the following distinct difference. After removal of ThX, thorium always has a certain amount of residual activity about 25 per cent. of the maximum value. A similar effect is observed in the case of radium, where the “ de-emanated”’ radium has always a non-separable activity of about the same (25 per cent.) value. In the case of actinium, immediately after removal of AcX the actinium is almost inactive, its activity being only 5 per cent. of its maximum value. I tried experiments to see whether this activity could not be removed by means of successive precipitations with ammonia, but although eight precipitations were made in the course of seven hours the residual activity always remained. Nevertheless, the smallness of the initial amount of activity pointed to the probability that in reality __* The more complete account of the physical and chemical properties of the active deposit of actinium will be published later, as the experiments are not yet completed. 49 Dr. T. Godlewski on Actinium the actinium itself is not active, and that the residual activity observed is due to a small quantity of AcX, which is left behind. The interval between the last precipitation and the first measurement was always one hour or more, but this alone would not account for the observed current. It seems very probable that at the moment of the removal of AcX, if the separation were complete, actinium would be entirely devoid of activitv. From the point of view of the theory of radioactive changes, this shows that the change of actinium into AcX is not “accompanied by either a, 8, or y rays or, in other words, is a “ rayless”’ change. By means of an electroscope, 1t was found that actinium X gave out all three kinds of rays «, 8, andy. Now the pro- ducts of excited activity are very quickly formed owing to the very rapid change of the emanation. The activities of these products are consequently measured together with AcX. It was separately proved that the active deposit gave out Brays*. Taking into consideration the analogy with (acre and even with ra adium, we should expect that the measured 8 activity of AcX arises not from AcX itself, but from the excited activity resulting from it. There is, however, strong evidence that in the case of actinium the 8 and probably the y rays are emitted also by AcX itself. For instance, the curves of decay of activity of AcX measured by @ and 6 rays are throughout identical, even from their beginning ;) and further, the activity of ex measured by @ rays, five Set after strong heating, when all the volatile excited activity should be driven oft, exhibits a very great initial value, which could not be the case if the rays were emitted only by oxcited activity. It is thus most probable that AcX itself gives rise to all three kinds of rays. Source of the Actinium Hmanation. In the case of thorium the product ThX was intermediate between thorium and its emanation. In order to see whether AcX occupies the sams position in actinium, I measured the rate of change with time both of the emanating power of AcX and of actinium from which AcX was removed. The measure- ments of activity of the emanation were made in a cylindrical brass testing-vessel+, in the interior of which three insulated * Tt was found that the excited activity of actinium, measured by B rays, after a long exposure decayed according to an exponential law with the time, falling to half value in 36 minutes. The complete account of these investig ations will be elven in another place. t+ See Rutherford, ‘ Radioactivity,’ p. 199, and fig. 37. and its Successive Products. 43 electrodes were placed ; during the measurements one of the electrodes was connected with an electrometer and the other two were earthed. Both actinium X and actinium deprived of AcX were placed in solutions of ammonium chloride in two bubbling flasks, and these could be successively connected with the testing cylinder in which the amount of emanation was measured. For the purpose of comparison with a substance of a standard emanating power, the following arrangement was used. The current of air passed through the bubbling bottle and earried with it the emanation of the product to be investi- gated. It thus passed through the testing cylinder, in which the activity of the emanation was measured. On leaving the cylinder, the current of air entered a glass tube 2 cms. in diameter and about 3 metres long. At the end of this glass tube some fresh solid actinium was placed, and the emanation from this was carried into the second testing cylinder where its activity was measured. In this manner the same current which carried the emana- tion from the product under investigation also carried the . e . o) . emanation from the standard actinium. In passing through the long and wide glass tube the emanation which left the first cylinder decayed completely before reaching the second cylinder. By this method of measurement, the emanating power of AcX was directly compare with the standard emanating power of solid actinium. The experiments made in this manner showed: (1) That the actinium immediately alter removal of AcX gives practically no emanation. (2) That the rate of increase of the emission of emanation of actinium after removal of AcX is the same as the rate of increase of its activity. (3) That the emanating power of AcX decreases at the same rate as the activity of AcX. Since the emanation is only observed when actinium X is present, and is always proportional to the amount of actinium X, it must be a product of actinium X. The changes occurring in actinium are shown in the following graphical representation*, together with the period required for transformation to half value. [or comparison the changes taking place in thorium are also given. * See Rutherford, Bakerian Lecture, oc. c7t. pp. 180-190 & 204; also Miss Brookes, Phil. Mag. Sept. 1904, pp. 382-884; also Bronson, Amer. Journ. of Science, vol. xix. Feb. 1905, p. 187. 44 On Actinium and its Successive Products. It is seen that there is a very striking similarity between the number and nature of the changes for actinium and thorium. But the periods of decay, the r adioactive, chemical Fig. 3. wR aS) 2. %S yo e as = ‘ s ie LRH —THEMAN.— —THA-— ~TH B= -THC— 3 10°yrs 4days S482. thrs SS min. 7 ~ : eae = & , & Oyen 8 i, fo) O a we 4 rats — ACTIN — — ACTIN. X— ACE EMAN--ACTIN.A- —ACTINB= enh Gc ? 10.2dAys =.7 Sec. 36min 1Smtn and physical properties of the products of actinium all point conclusively to the fact that we have in actinium a distinet chemical element. Whilst writing this paper, the December number of the Jahrbuch fiir Radioaktivitat und Elektronik was received con- taining a paper by Giesel on Emanium*. In this paper Dr. Giesel gives an account of his investigation, in which he finds that it is possible to separate from emanium by preci- pitation with amimonia a small amount of very strongly active substance. The method of separation employed by him was then identical with the method I have used. I cannot, how- ever, compare quantitatively my results with his, inasmuch as Dr. Gtiesel does not publish any measurements. A short account will now be given of some experiments which are still in progress on the “nature of the 8 and y rays of actinium. * Giesel, “ Untersuchungen tiber das Hmanium (Actinium),” Jahrbuch f. Radioakt. vol. i. pp. 875-358. Some Radioactive Properties of Uranium. 45 The @ rays of actinium are completely distinct in their character from the 8 rays emitted by the other radio-elements, inasmuch as they are completely homogeneous. This fact was established by the measurements of absorption of 6 rays in passing through solid bodies. The activity measured by 8 rays decreased strictly according to an exponential law with the thickness of matter traversed. The equation I=Ije-*4, where d is the thickness, was applicable even in the case when I was less than 1 per cent. of its original value. The @ rays from actinium differ also from the 6 rays of other radioactive elements in the absolute value of the ab- sorption constant A, which is about 2°5 times as great with actinium as with uranium. Thus the 8 rays of enim have less than half the penetrating power of those emitted by any other radio-element. The existence of the y rays from actinium was also dis- tinctly proved. The absorption measurements showed that the y rays of actinium are fairly homogeneous, and their penetrating power was only about one quarter of that ob- served for the rays from radium. A more complete account of these investigations will be published later on. In conclusion it is my most pleasant duty to express my deepest gratitude to Prof. Rutherford for suggesting these investigations, for his kindness in the advice he has so freely given to me, and for placing at my disposal all the plentiful 5 resources of his laboratory at McGill University. McGill University, Physics Building, February 24, 1905. VI. Some Radioactive Properties of Uranium. By T. GopuEwsx1, Ph.D. (Cracow) *. 1. The Discovery of UrxX. “N 1900 Sir William Crookes + showed that it is possible to separate from uranium by a single chemical operation a small amount of radioactive substance to which he g gave the name UrX. This substance was, weight for weight, many hundred times more active photographically than the uranium from which it had been separated. ‘The uranium deprived of this substance was almost inactive. Similar results were afterwards observed by Becquerel tf, * Communicated by Prof. E. Rutherford, F.R.S. Presented before the Academy of Sciences in Cracow at the sitting of 9th of May, 1905. + Crookes, Proc. Roy. Soc. Ixvi. p. 409 (1900). } Becquerel, C. #. exxxi. p. 1387 (1900) ; exxxiul. p. 977 (1901). A6 Dr. T. Godlewski on some who also noted the important fact that uranium recovered its activity with the time, while the activity of the separated substance decayed. This phenomenon was then quantitatively investigated by Soddy *, by Rutherford and Grier T, and by Rutherford and Soddy t. These investigations proved that the activity of UrX, when ineasured by @ rays, decayed with the time according to an exponential law, falling to half value in 22 days. In the same period uranium ‘which, by removal of UrX, was deprived of all its 8 activity recovered it, and the recovery curve was complementary to the curve of decay of UrX. From the point of view of the disintegration theory, this fact indicated that UrX is a successive product of uranium, and the change of UrX into its successive product was accompanied by the emission of @ particles. 2. The Experiments of Meyer and Schwedler on Uranium. In 1904 Meyerand vonNSchweidler § repeated the quantitative measurements of Rutherford and Soddy with the difference, that while the latter used for separation of UrX the method of Becquerel, they made use of Crookes’s method. The aqueous solution of uranium nitrate was shaken with ethyl ether, and then the ether and water portions were separated from one another. The ether portion contained uranium nitrate deprived of UrX, and the @ activity of this portion increased according to the theoretical curve, to half of its total value in 22 days. The uranium nitrate, however, when crystallized from the remaining water portion, lost its B activity at a different rate, decaying to half value in 2 days instead of 22 days. This unusual fact, that the recovery and decay curves of a radioactive product were not complementary to one another, either pointed to the existence of a new product, or indicated some unknown radioactive phenomenon. In order to elucidate this question, Meyer and Schweidler started a series of investigations on the radioactive properties of uranium nitrate freshly crystallized from the water solutions. They substantiated the fact that uranium nitrate crystallized from the hot-water solutions in the form of compact plates exhibited a peculiar radioactive behaviour.. The activity of these * Soddy, Trans. Chem. Soc. lxxxi. p. 860 (1902). + Rutherford and Grier, Phil. Mag. Sept. 1902, p. 315. { Rutherford and Soddy, Phil. Mag. April 1905, p. 411. § Meyer and v. Schweidler, ‘‘ Untersuchungen wher radioaktive Sub- stanzen, II.: Ueber die Strahlung des Uran.” Svtzber. der Wiener Akad. Mathem.-naturwiss. Klasse, Bd, 113. Abt. I. a. pp. 1057-1079, Juli 1904, Radtoactive Properties of Uranium. AT plates decayed in the first few days after crystallization to about half of its original value, reaching a minimum after four or five days, and then increased slowly for a very long time. The time in which the minimum was reached and the initial form of the curve were both dependent on the thickness of the plate. As regards the meaning of this phenomenon, the authors suggest “two possibilities: either that there is a change in the activity itself, or that the absorption of the rays is modified by the physical alteration of the crystallized plates *. Prof. Rutherford kindly suggested to me, that I should make some investigations to explain these phenomena. 3. The Separation of UrX from Uranium by means of Fr actional Crystallization. The experiments were first made in order to find out the conditions under which this first rapid decay of the @ activity of uranium is obtained. As in the experiments of Meyer and von Schweidler, equal weights of uranium nitrate ¢ and water were taken, and this solution was shaken with an equal weight of ethyl ether. The ether solution was then carefully separated from the water solution, and both were evaporated to dryness. In the case of water solution, the evaporation was continued until even the water of crystallization was driven off. The a and B activity of both portions were then measured. The 8 activity was measured by means of an electroscope { of the type of C.T. R. Wilson ; the bottom of the electroscope was removed and replaced by aluminium foil 0:08 mm. thick, which absorbed all the a rays. The measurements showed that uranium nitrate from the aqueous solution which contained the excess of UrX, derived from the ether solution, lost the corresponding excess of its activity according to an exponential law with the time, falling to half value in 22 days. The ether portion, which was at first almost completely inactive, when measured by * “ Beziiglich der Deutung dieses Verhaltens ist zunichst die Moelichkeit gegehen, dass es sich um Ander ungen der Aktivitat selbst handelt, oder dass durch physilkalische Zustandesiinder ungen der Kristallplatten ihr Absorptionsvermogen beeinflusst wird. Eine definitive Hntscheidung zu geben ware verfriiht.” Meyer und vy. Schweidler, loc. cit. p. 1075. + The uranium nitrate under the experiments was obtained from Merck in Darmstadt and was labelled ‘extra pure.’ { See Rutherford, ‘ Radioactivity,’ p. 71 & fig. 11. 48 Dr. T. Godlewski on some rays, recovered its activity according to a complementary curve *. The only difference between my experiments and those of Meyer and Schweidler was that my uranium nitrate was deprived even of its water of crystallization by evaporation, while in the experiments of the above named authors the uranium nitrate was crystallized from the solution. This proves that the rapid decay of activity occurs only when uranium nitrate is crystallized, but it does not occur when it was obtained from the solution by evaporation which had been carried so far that the water of crystallization was driven off. This fact being established, the subsequent experiments were made in the same manner as the experiments of Meyer and Schweidler. After separation of the ether solution, the aqueous solution containing an excess of UrX was concentrated on the water- bath, and was then left for a short time at the temperature of the room. The great part of the uranium nitrate crystallized at the bottom of the dish forming a compact plate, on the surface of which the rest of the solution remained. This mother liquor was poured off into another dish and was kept on the water-bath until the solution lost all except the water of crystallization. The solution after it was taken off the water-bath crystallized at the temperature of the room, forming a compact dry plate. The whole process of preparation and measurement was repeated many times. Table I. gives one of the series of experiments. T denotes the time in days from separation to measurement. The @ activity is expressed as the ratio of the activity of the investigated product to the 8 activity of a standard amount of uranium oxide taken as 1000. The 6 activity is expressed in the same units throughout this paper. These results are graphically represented in fig. 1], where the ordinates give the activity, in the same units as before, the abscissee the time in days after separation. Curve I gives the activity of the ether portion, curve II that of the first plate of crystal, curve IIL the activity of the plate of crystal obtained from the mother liquor. * I omit the detailed numbers obtained in these measurements because the results are completely normal; and further, during the time when these investigations were being made Meyer aud Schweidler published a short paper (Wiener Sitzungsber. Dec. 1904) in which they showed that when avery small amount of water was present in the solution, the decay of activity of UrX was quite regular. Radioactive Properties of Uranium. AY TABLE I, Ether portion. | Water portion. Plate cf crystal First crystal plate. from mother liquor. T. |G Activity. T. |B Activity.) T. | Activity. | | | 0:25 | 19 | 0-10 366 | O12 2190 ot | DT | 0-32 281 0:33 1370 Bah pee ey He OTS. pe 210 Pyar Vt270 3 131 fe det 219 1:12 1125 53 | 190 1°64 236 1:68 1090 6:3 220 2-9 285 2-9 1090 73 260 4:9 344 49 | 1100 8:3 273 5-9 368 60 | 1120 93.9) “B11 7-0 399 Boe GEO 3 | ALG sl 427 Sa ROO 14:3 | 446 | 9-1 440 Os |) 1210 15°23 460 tO Bb ar Bag 199 | > 11200 165 | 480 |i Bars 545 13-8. | 1210 | || 14:8 572 15-7 1190 | | 164 | 598 18-7 1200 | | It is seen that the activity of the ether portion increases with the time according to the theoretical curve, reaching half final value in twenty-two days. The activity of the first part of aqueous solution, which contained the first crystals, falis to about half value in about one day, this value being almost the minimum, and then increases slowly with the time. As we see from fig. 1, the second part of curve IT is parallel to curve I, which shows that the activity of the first plate of crystal increases at the same rate as that of the ether portion. ; The plate obtained from mother liquor (curve IIL) lost its activity during the first few days after crystallization. Tis activity after reaching a minimum and after a small increase remained practically constant. After two months it was observed to have decreased only 10 per cent. Disregarding for a moment the first rapid decrease of activity of both aqueous portions, which is exactly of the same nature as observed by Meyer and Schweidler, we see that we have the @ activity in two cases increasing at the same rate, 7.e. the increase of activity of the ether portion and of the plate of crystal first obtained. This points to the fact, that UrX was removed not only from the ether portion, but also in some degree from the first obtained crystals. Phil. Mag. 8. 6. Vol. 10. Mo. 55, July 1905. 1D) 200 Dr. T. Godlewski on some ° 2 —— ALIANILIY — TIME IN DAYS Radioactive Properties of Uranium. 51 The mother ‘liquor must contain then the greater excess of UrX. In connexion with this, experiments were made with fresh uranium nitrate, and they showed that by even one erystallization it is possible to separate the uranium nitrate into two parts, namely the crystals and the mother liquor ; the latter part containing seven times as much of UrX as the former. By means of several fractional crystallizations we can deprive uranium almost completely of the substance UrX, which is so readily soluble in water. This at once explains the radioactive behaviour of the erystals first obtained from the aqueous solution after treat- ment with ether. A large part of the UrX remained in the mother liquor, and the crystals themselves contained even less than the equilibrium amount of UrX. In consequence, the activity of the crystals must increase according to a recovery curve of UrX. The experiments show that this is really the case. (See curve II on fig 1.) In a similar way we can equally well explain the increase of activity observed by Meyer and Schweidler * in the crystals of uranium nitrate obtained from water solution. If in these experiments some part of mother liquor was poured off the surface of the plates of crystals, the uranium erystals would contain less of UrX than the uranium itself ina state of equilibrium. The increase of activity would thus be due to the recovery of the separated UrX. And in fact the authors state that this part of curve corresponds to the constant of 22 days. The activity of the crystals obtained from the mother liquor at first decayed very rapidly and, after reaching a minimum, inereased a very small amount and finally remained almost constant, falling only 10 per cent during two months. This is shown in curve III. The percentage decrease observed in this experiment is smaller than the percentage rise observed in curves I and II. This is due to the fact that the laver of crystals finally obtained from the mother liquor was about three times as thick as in the previous fractions. In other experiments, where the thickness of the plate was ° relatively very small, the excess of 8 activity diminished regularly and in a more marked degree. * Meyer and Schweidler, doc. cit. p. 1074, figs. 6 & 7. EK 2 52 Dr. T. Godlewski on some A. The Effect of Crystallization on the B Activity of Uranium Nitrate. , We shall return now to the initial rapid decay of the @ activity of uranium nitrate immediately after it was crystallized in the form of plates from the aqueous solution. A decay quite analogous to that shown in the first part of the curves II and III was also obtained, when uranium nitrate had been crystallized from the pure aqueous solution, when no ether separation was applied. The following is one example :— 25 grams of uranium nitrate was dissolved in a small amount of water; the solution was evaporated on a water- bath till it lost all its excess of water. This solution of uranium nitrate in its water of crystallization was kept for some minutes at the temperature of the room, where it erystallized, forming a compact dry plate. The variation of activity with the time was then measured, and one of the examples is given in Table II., where Tis time reckoned in hours from the moment of crystallization. TABLE II. T (an hours). B Activity. LORRI lace eis a 3° a 30) 2120 shes ame eet 1 LARD BD aie ue es. NOs) ZB tt nr, Oey BAGS 1 SNS eee. SSO) OOP i, Te eC 5 Bay Ck Oe ee Bias DOU ci a ne... OOO 20H A ere NE 24 ARB OG We see that immediately after crystallization the B activity decays, reaching a minimum after about two days. The measurements of Meyer and Schweidler were then once more confirmed. The fact that the minimum was reached in a shorter time after crystallization in the experi- ments of the writer than in those of Meyer and Schweidler, is fully explained by the difference in experimental con- ditions which greatly influence this period. This decay of activity after crystallization at first suggests the existence of some other product besides UrX. But the absence of the complementary recovery curve contradicts this supposition. And further, the rate of decay of radio- active products is generally independent of conditions. In these experiments, however, the time when the minimum was Radioactive Properties of Uranium. 53 reached, as well as the form of the curve, was dependent upon many factors. In different experiments, the relative values of the activity at the minimum point and the rates of decay were dependent upon the thickness of the plate of crystals, and upon the concentration of the solution from which the crystals were obtained. In consequence, it would be difficult to suppose the existence of some other product. The supposition of Meyer and Schweidler* that the phenomena are produced by some changes in absorbing power of the plates of crystals cannot explain the observed fact, when we take into consideration that the activity measured by a rays does not exhibit -the same behaviour. The experiments of Meyer and Schweidler showed that the a activity remained practically constant. The writer made also experiments which completely confirmed this fact. And every change in absorbing power of the plates would be, of course, first of all shown by variation of @ activity. Since these results can neither be explained by the existence of a new product nor by a change in absorbing power, there remained the possibility that the process of crystallization alone influences the @ activity of uranium nitrate. In order to show whether this was really the case, the following experiments were undertaken. The hot solution of uranium nitrate containing only the water of crystallization was put under the electroscope. After about two minutes the disturbance of the gold leaf, produced by the neighbourhood of the hot body, ceased, and it was then possible to investigate the effect due to the process of crystallization by measurements of the activity. The experiments showed that at the moment when the crystallization started, the 8 activity commenced to increase very rapidly, reaching the maximum when the crystallization was finished. The following is an example of the experimental results obtained. 25 grams of uranium nitrate were dissolved in some water and evaporated in a flat glass dish on a water- bath until it lost all the excess of water. The dish containing this hot solution of uranium nitrate in water of crystallization was then put under the electroscope. After three minutes the activity could be measured with accuracy. The results are shown in Table III., where T is the time in minutes from the moment when the solution was taken off the water-bath. * Meyer and Schweidler, loc. cit. p. 1075. 5A Dr. T. Godiewski on some Tagen CE. T (in minutes). Activity. Origen eee 900 | oat f a rood harder. 3h, Come 890 GRR ee oe re ae 910 Oo 4, Spe SEA Be earners: 5 900 At this period the crystallization started. So me ews OOO 10 ee ees LL SO 2 See ae ee eee LOD 14° 4 ee ee | TBBG 7 Seems ee Lay 227 NO ees Mette Fo Pa) D7 Aree eee os ASO At this period the crystallization ended. 30)... Wiehe eoeeeeatel st Vio) SO 3D)» (one are. (6 LFSC On the surface of the plate some drops of distilled water were now added, and the dish was placed again on the water-bath, so that the crystals melted in the water of crystallization. The measurements were repeated in the same manner as before. In the moment when the second crystallization started, the activity of the solution was 1530 ; when it was finished the activity of the plate was 2830. After the third crystallization the activity was 2940. The fourth and fifth and sixth crystallizations did not cause a further increase of the activity. This maximum activity then decayed with the time and reached the value 935 after three days, and, disregarding small irregular oscillations, remained constant at this value through many weeks. Similar experiments were repeatedly made, and gave the same qualitative results. These experiments show that the 8 activity of uranium nitrate is very considerably augmented by the actual process of crystallization, and it will be proved later that the decay of activity noted immediately after crystallization is due to the loss of this excess of activity produced by crystallization. The explanation of the increase of activity at the moment of crystallization is very simple. We know that all the @ activity of uranium proceeds not from the uranium itself, but from UrX. But UrX is so readily soluble in water that it is possible, as we have seen, to separate UrX from uranium by fractional crystallization. If, as usually the case, the hot Radioactive Properties of Uranium. 419) uranium solution starts to crystaliize from the bottom of the dish, first of all uranium itself crystallizes and UrX is pushed in the direction of the surface. When the whole mass 13 solidified, we get a plate which contains on the surface an excess of UrX, and in the lower layers a deficit of this substance. The @ rays, which come from the UrX present near the surface, emerge with little absorption in | the mass of uranium itself, and thus the @ activity must be larger than when UrX is uniformly distributed throughout the plate. In the same way we can explain the steady growth of activity during the actual process of crystallization when UrX is continually passing to the upper layers. Many observed experimental facts prove with certainty the correctness of this explanation of the increase of 8 activity produced by crystallization. For instance, we do not get the increase of § activity when the solution is continuously stirred during the crystallization, so that instead of a compact plate there is a powder composed of very small crystals. Moreover, under suitable thermal conditions the crystallization may be started at the surface instead of at the bottom, and then the increase of activity is not observed after crystallization but, on the contrary, there is often a decay. This last fact suggested to me a decisive test. If the increase of activity during the crystallization is due to the fact that UrX is pushed to the upper layers when the crystallization starts from the bottom of the vessel, then the lower layers of the plate of crystal should contain less of UrX. In order to see whether this was really the case, I took a plate of crystal of which the 8 activity was 1840. The plate was cat across so that it could be removed from the dish, and it was then taken out and inverted so that the under surface faced the electroscope. The 8 activity was found to be 528. This experiment shows quite clearly the truth of the explanation of the rise of activity during the process of crystallization. By the crystallization, UrX was pushed to the upper layers ; when we turn the plate, the upper layers containing the excess of UrX are now underneath and, before reaching the electroscope, the @ rays, which start from UrX, must pass through the whole thickness of the plate whereby they are to a great extent absorbed. And for this reason the activity of the plate, when it was turned over, was only one-third of the activity measured from the upper side. 56 | Dr. T. Godlewski on some 9. Diffusion of Urx. The results obtained in the preceding section can now be used to explain the first rapid decay of 8 activity of uranium nitrate after crystallization from the water solution. We saw that in the case when uranium nitrate was obtained by evaporation from the solution, and not bv crystallization, this first decay was not exhibited. Moreover, it was pointed out that when the hot solution was stirred during crystallization, no increase of activity at the end of the crystallization was observed. It must now be noted that in this case we did not get any decay after crystallization. We see then that the first rapid decay is the decay of the excess of activity produced artificially by crystallization, when the latter caused the uneven distribution of UrX throughout the plate. 7 This suggests the probability that the decay of 6 activity in the first days after crystallization is produced by the diffusion of UrX from the upper layers of the plate, where it was in greater concentration, to the lower, where its concentration is smaller. Thus, if we observe the decay of activity when the upper surface is turned to the electro- scope, we should expect to see the analogous increase when the bottom of the plate faces the electroscope. Experiment showed this to be the case. Some of the experimental results are shown in Table IV., where T gives the time reckoned in hours from the moment of crystallization. Tasue LV. B activity of the plate | 8 activity of the plate when turned with the when turned with the De upper surface to the 1M lower surface to the ’ electroscope. electroscope. Uae nen sates rN Woy i) Omens. H2E UG a, Ree oa er ete Sl tn Moti ees TAT AD he Ve ee eso mee of e) gcihe fou Cota ie ai te OMe he es ge 950 The same experiment made with a very thin plate. 0 750 Rae fod We 570 il, 740 1 Ty a Ae et 600 ae 730 21 ea 620 Dis 20.5% BOAO sep 630 4D. 700 pipe Ay ns". Mies weee 650 es 690 22 LENS 680 In order to completely establish that we here have to do with the diffusion of UrX through the plate from the layers Radioactive Properties of Uranium. Kw of higher to lower concentration, the following experiment was made. Fifty grams of uranium nitrate were treated with ether and from the remaining ether solution 15 grams were obtained consisting of uranium nitrate but almost completely freed from UrX. When the ether had been evaporated, some drops of nitric acid were added to the uranium nitrate and this was dissolved in hot water. The solution was evaporated till it lost all the excess of water, and then was kept at the temperature of the room for some minutes while it crystallized forming a dry plate of crystal. The @ activity of this plate measured 65. : In the other vessel 25 gr. of uranium nitrate were heated on the water-bath till it melted in its water of crystallization. This solution was then taken off the water-bath, and when the crystallization started 9 gr. of the hot solution were poured on the surface of the first plate of crystal. The solution crystallized then in a few minutes, forming the upper layer of the former plate. In this‘manner a plate was made artificially which did not contain in the lower layersany UrX at all, but on the surface it did contain an excess of UrX. The plate was cut off from the dish and the activity from — both surfaces was measured. The results are shown in the table, where T gives the time in hours after the crystallization. | TABLE V. Activity of the plate Activity of the plate when turned with when turned with T (in hours). the upper surface T (in hours). the lower surface to electroscope. to electroscope. Derren OBS Oper eis eng PROM kiss 5:85 Oro LU cm r ee alt Ta iy hay sud OOS | POON ccd rel, | oe IDET ie ie ENan ne OS ¥ Spe lie eb asedeiad’ SOU te welo OO te A, ROL ALN wi gitiy, SYLOOO I Oks ton) ee dehy pan eo) | ASTM) Sere AOS It is seen that the activity measured from the upper surface decreases, and that from the bottom surface increases, buth approximating to a common value. This experiment shows that when we have a plate of crystal of uranium nitrate in which the substance UrX is unequally distributed, UrX diffuses from the piaces where it is in higher concentration to places where its concentration is lower. ; | “This diffusion of UrX therefore explains the first rapid 58 Dr. T. Godlewski on some decay after crystallization. We see also that the period during which the minimum activity is reached should depend on the thickness of the plate, and such is the case. 6. The Possible Causes of the Diffusion. The question now arises, in what manner and under the influence of what forces does this diffusion take place? Only two explanations appear possible. It may be supposed that some part of the UrX is dissolved in a small amount of water and diffuses in a state of solution between the crystals under the influence of capillary forces. The crystal plates under investigation, however, seemed to be completely dry *, and the diffusion took place even when a part of water of crystallization had escaped from the crystals on the surface. Therefore, the supposition that the UrX diffuses in the state of solution does not seem to be probable. And if the diffusion does not take place under capillary forces, we are here dealing with a “solid soluticn.” The crystals and the total mass of uranium are the solvent and UrX is the dissolved body. And then the UrX diffuses through the crystals from places of the higher to lower concentration. We define the solution as a mixture of two substances, which is not a mechanical one, but is accompanied by the molecular penetration of both substances. The process of formation of UrX points to the fact that we really have here a mixture of this kind. An atom of uranium, breaking up by expulsion of one « particle, changes into an atom of UrX, but it always remains surrounded by the other atoms and molecules of uranium. It is not possible to imagine the deeper molecular penetration as existing for the atoms which previously were the atoms of the parent body. Throughout a given mass of uranium, single atoms of UrX are dispersed. Thus if we consider the total amount of UrX present at a given moment in a given quantity of uranium, we may assume that all this UrX is “dissolved ” in the uranium. The observed fact of the diffusion of UrX confirms this supposition. The diffusion of UrX goes in the direction from higher to lower concentration ; we may * Meyer and Schweidler, who first observed this decay of activity after crystallization, due, as we saw, to diffusion of UrX, pointed out that the plates investigated were completely dry (vollkommen trocken). Loc. cit. p. 1068, Radioactive Properties of Uranium. a9 conjecture from higher to lower osmotic pressure. But this osmotic pressure, whilst it might control the diffusion, cannot be imagined as completely analogous to the osmotic pressure as known in fluid solutions. In the case of extremely weak concentration of UrX, the ordinary osmotic pressure would be a vanishing quantity. But in the present case, the forces which guide the diffusion must be extremely great in order to overcome the immense resistance due to friction. These forces can only result from the reciprocal action between the molecules of the parent body and the atoms of its product, and appear to be a special radioactive type. Just as UrX is dissolved in its parent uranium, so the other radioactive products should be dissolved in their parent. There are some experimental facts which confirm this sup- position. We know that radium and thorium give out a gaseous emanation as one of their successive products. The emanation is produced at a constant rate, which does not depend on any physical or chemical agencies, but the escape of the emanation from the body is variable in character and dependent on different conditions. [or instance, radium and most of the compounds of thorium give off little emanation when in a solid state. The emanation is stored in the body itself in considerable amount. We may suppose that in reality just as UrX was dissolved in uranium, so the radium and thorium emanations are dissolved in radium and thorium. When the parent body is dissolved, the emanation is no longer held bound in the solid solution, and it can readily escape from the water. And it is a fact that all substances have the maximum emanating power when dissolved. The increase of emanating power in presence of moisture can be explained in the same manner. We know further that generally the solubilities of the gases decrease with the temperature. And indeed the eman- ating power of almost all radioactive bodies increases when the temperature is raised, reaching a maximum at a dull red heat. At this temperature the solubility should be a minimum and all the emanation should escape. But the solubility of thorium emanation is not the same in all compounds of thorium. A compound like the hydroxide or carbonate possesses an equal emanating power in the solid state as in solution. This would indicate that thorium emanation, readily soluble in thorium nitrate and soluble in thorium oxide, is not soluble in thorium hydroxide or carbonate. We should then expect that in the last cases the emanating power should not be influenced by variation 60 Mr. J. W. Sharpe : of temperature. The experiments of Rutherford and Soddy * show that this is the case. The existence of “de-emanated” products after strong ignition whereby many physical and chemical properties of the compound are changed, can be also explained by the change in dissolving power of these compounds. Further investigations will show if this generalization of the fact observed in the case of uranium is justifiable. Further experiments on this subject are in progress. Analogous experiments will also be tried with other radioactive products in order to see whether this explanation is general. In conclusion I wish to express my best thanks to Prof. Rutherford for the interest he took in this work and for the encouragement I received from him. McGill University, Physics Building, April 3, 1905. VII. The Boomerang. By J. W. SHaren, M.A.F T’ is easy to show in what manner the leading peculiarities of the boomerang’s motion depend upon fundamental dynamical principles. Though the instrument is not perfectly flat, it will be con- venient to use the term “ principal plane” for its average piane. The C.G. is somewhere within the concavity, and the two horns are symmetrically disposed with regard to it. The normal through the C.G. to the principal plane will be called the axis of the boomerang. The three principal axes of inertia at the C.G. are one along this axis (this one’ has the maximum moment of inertia), and two others in the principal plane, respectively parallel and perpendicular to the line joining the horns. Imagine the boomerang held in the right hand, upright, with the concave edge forward and the principal plane vertical, which is in fact the ordinary posture for making a returning throw. The surfaces are both slightly convex, the one next the thrower (to be called throughout the motion the “upper” surface) being always the more curved one of the two. Also the whole instrument has a slight twist in it, so that the “upper” side of the upper horn and the “lower” side of the lower horn are slightly turned towards, and facing, the thrower. ‘This twist is such as to make the boomerang screw itself upwards in the air when thrown with its principal plane horizontal instead of vertical. Its bent form has the * Rutherford and Soddy, Phil. Mag. April 1903, p. 453. + Communicated by the Author. On the Boomerang. 61 important effect of increasing the moment of inertia about the axis without increasing its weight; and the swift spin with which it is thrown causes the initial angular momentum of the rotational motion relative to the C.G. (this will be called simply “the angular momentum ”) to be very large relatively to the total angular momentum which the air reactions can impart during the flight. Were the air absent the C.G. would describe a parabolic path, and the rotational motion, being a rotation about a principal axis of inertia, would remain entirely unchanged. But on account of its twisted form, and the convexity of its _ upper and lower surfaces, the boomerang never presents a fair cutting-edge to the air. Consequently the air pressures that are due to the motion relatively to the air continually act upon both horns, always the more effectually upon the one whose rotational motion at the moment conspires with the velocity of the C.G., in such a way as to set up a very small additional angular momentum in each revolution. Of the three components parallel to the principal axes at the C.G. into which this angular momentum may be resolved, the one of which the axis is in the axis of the boomerang merely effects a very slight reduction, per revolution, in the rate of rotation; but the other two cause a slow alteration, always in the same direction, or rather sense, of the orienta- tion of the axis (barely one complete revolution in an ordinary returning flight of about 9 seconds), without affecting to any appreciable extent the rate of the spin. Consequently the plane of the missile, and therefore also the direction of its flight, undergoes a steady alteration, always in the same sense, 2. e. that of a right-handed screw about an upward vertical axis. Therefore, as the boomerang must on the whole move edgeways through the air, it constantly steers itself round to the left of an observer standing behind it, from whom it is moving away. At the same time the twist, acting like that of the propeller of a screw-steamer, causes the boomerang to screw itself leftwards and upwards through the air; for the axis continually rises from its initial, hori- zontal, position towards the vertical, turning upwards from left to right in front of the thrower, and so sets the principal plane more and more nearly horizontal. The effect of this lifting action is to prolong the flight of the boomerang by maintaining it longer in the air ; and, by raising it to a con- siderable height, commonly about 30 feet, it makes it possible for the missile to lose, without falling to the ground, a large portion of its forward velocity, even coming almost to rest, the spin nevertheless being well maintained ; for in its 62 Mr. J. W. Sharpe : downward flight the C.G. will again recover much of its former speed. When it is approaching the summit of its path, at its greatest elongation from the point of projection, its speed is attaining a minimum ; and therefore, in this portion of the path, the orientation of the principal plane has its maximum rate of change per unit of distance traversed by the CG: consequently at this period the steering effect is much more marked than at any other. From this description of the circumstances of the boomerang’s flight, it is clear that the reaction of the air sets up a precessional motion of the axis, like that imparted to the Harth’s polar axis by the attractions of the Sun and Moon upon the equatorial protuberance, the orientation of the axis being altered by a very small angle. always in the same sense, in each revolution of the body. If a thin piece of slate be thrown into still water, its motion underneath the surface will give a good illustration of the boomerang’s motion in air, the slate steering itself through the water in the same way as the boomerang steers itself through the air. | To explain more particularly the action of the air:— Consider the boomerang just after it has started. It is whirling with great rapidity in a nearly vertical plane, the axis of the whirl being coincident with the maximum principal axis of inertia at the C.G., ¢. e. with the axis of the instrument; and this axis points leftward, and is very nearly horizontal. Take the motion at an instant when the line joining the horns is vertical, and the convex edge is facing forwards. The upper horn, owing to the twist, has its forward surfave shghtly turned against the air; this surface is slightly convex, and the other surface, the hinder one, is still more convex. The result of this is to cause the com- ponents, in the principal plane, of the air pressures upon the forward face of the upper horn to be a maximum towards the convex edge, as indeed would be the case even if both surfaces were flat, according to the law of the reaction of a fluid upon a plane moving through it, whereby the plane tends to set itself at right angles to its course, 7. e. to the path of its centre of inertia. Now resolving the air pressures in three directions, parallel respectively to the principal axes at the C.G., it will be seen that those components which are at right angles to the line joining the horns tend to twist the upper horn backwards, that is they impart a very small angular momentum about that principal axis which is parallel to the line of the horns, and the axis of this angular momentum is directed upwards and outwards from the centre of the boomerang ; and that the action upon the lower horn opposes On the Boomerang. 63 the action upon the upper one, and this too in all phases of the rotation. But the components which are parallel to the line of the horns tend to twist the upper horn over, so that its convex edge, which is in the present position the forward one, tends to turn slightly inwards towards the left ; and the lower horn experiences a similar and similarly directed action. This effect occurs chiefly just before and just after the line of the horns is at right angles to the path of the C.G. The bend in the boomerang is the chief factor in this effect ; but the rounding, i. e. convexity, especially that of the “upper” surface, materially assists it. Thus this action upon the two horns imparts to the missile, in each revolution, a very small angular momentum about that principal axis at the C.G. which is at right angles to the line joining the horns, and the axis of this momentum is directed backwards. Again, the components which are in the direction of the boomerang’s axis, and which, on account of the slightness of the twist, are much larger than the others, set up, by their action upon the upper horn, an angular momentum about the same axis as the last set of components, 7. e. directed back- wards in the principal plane ; and therefore their effect con- spires with that of the last set. In this case, however, the lower horn opposes the upper one. Now the actual speed of the upper horn is the speed of the C.G. plus that due to the rotation about the U.G.; whilst that of the lower one is the difference of these two speeds, the speed due to the rotation being far greater than that of the C.G. Consequently in each revolution the angular momentum imparted by the 1st and 3rd sets of components of the air reactions are not the sum, but the difference, of the momenta imparted to the two horns, the upper horn, 2. e. the one with the greater velocity, prevailing in this respect over the lower one; and the most important phase of each rotation is that in which the line of the horns is passing through the position in which it is at right angles to the path of the C.G. When this line is nearly parallel to the path, these differential effects hardly exist at all. | Combining all the above described results, it will be seen that the axis of angular momentum (and with this the in- stantaneous axis ot rotation and the axis of the boomerang itself are always either very closely, or exactly, coincident) is in each revolution dispiaced through a very small angle upwards to the right by the first set of components, and by the other two sets is rotated backwards towards the thrower, the latter effect being decidedly the larger of the two by reason of the superiority of those components which are 64 -Mr. J. W. Sharpe: parallel to the axis of the boomerang. This agrees with the result in Mr. G. T. Walker’s paper in the Phil. Trans. vol. 190, p. 25, viz.: that the latter is about double the former. From this paper have been taken the descriptive details here given, of the form and length and height of range, of the Australian boomerang. Considering now, not the rotational motion, but the motion of the C.G. itself, for which purpose the whole mass may be imagined to be condensed into one particle at the C.G., and to be there acted upon by all the air reactions and by its own weight, it will be seen that the third set of components, ¢. e. those parallel to the axis of the boomerang, impel the C.G. in the direction of this axis, at first moving it leftwards and afterwards lifting it in the air; whilst the other two sets, with much less effect, check its flight, and very slightly divert it, at first downwards, and then leftwards. Owing to the bent form of the boomerang, it might be thought that the third set of components would have some slight effect in setting up angular momentum about the principal axis parallel to the line of the horns ; but whatever effects in this way they may have will cancel themselves in each complete revolution of the boomerang. For non-returning flight (see Mr. Walker’s paper) the boomerang is thrown with the principal plane leaning a good deal away from the vertical, outwards towards the right. As before, it steers itself at first towards the left, whilst its plane steadily becomes more and more nearly horizontal, the axis leaning more and more over towards the right. When the principal plane has passed the horizontal, and the axis is leaving the vertical, and inclining to the right of it, the co) boomerang will then begin to steer itself also to the right ; co} and hence the path is now composed of two curves joined at a point of intlexion, the first concave towards the left, and the second concave towards the right. The range is greatly extended by the effect of the twist, through the 3rd set of components of the air reactions, in raising the missile and maintaining it in the air, and also by the peculiar action of the convex form of the surfaces, especially that of the upper surface, which is the more curved of the two. As explained above, this, in conjunction with the bent form of the weapon, through the action of the 2nd set of components, causes the axis to incline backwards towards the thrower, as indeed do also the drd set of components ; hence the forward edge tends always to lift itself against the air, so that, even if there were no twist, there would nevertheless be a lifting effect arising from the upper, or rightward horn, the speed On the Boomerang. 65 of which is always greater than that of the other one, owing to its velocity being the sum of the velocity of the C.G. and of that due to the rotation. The motion of a cardboard model follows exactly the same principles ; but, on account of the flatness of the surfaces and the absence of twist, the precessional motion has to be brought about in a different manner. The shape is not con- fined to any particular pattern. In fact the following is a most convenient form, yielding curious and complicated flights. It can be cut out from a visiting-card. The head, which ought to be comparatively large, consists merely of a narrow rim about a large hole ; and a long arm is attached to it. This arrangement secures a considerable moment of inertia about the axis without making the weight too great. If supported with its plane sloping upwards, and struck sharply and fairly at the end of the arm so that its edge cuts the air truly, it will rise in front of the thrower without turning either right or left, come to rest, sull whirling, at the summit of its path, and return to the point of projection. But if the line of the projecting blow be very slightly in- clined towards the plane of the model, the precessional motion will be obtained. To explain the precessional motion, take a model of the ordinary boomerang form. This is projected with its plane nearly horizontal, and inclined slightly upwards; and it is so struck that the initial axis of angular momentum is not exactly coincident with the axis of the model, 2. e. with the normal to its plane through the 0.G. The consequence is that throughout the motion these two axes, as well as the instantaneous axis of rotation, are never quite coincident, but always very nearly so. In each revolution the axis of angular momentum receives only a very small displacement, whilst the other two circle once round it, the plane of the model always touching the surface of a right circular cone of very flat angle, whose axis is coincident with the axis of angular momentum, and is directed upwards. There is now no screwing effect, like that of the propeller of a screw- steamer; nor is there any assistance to the precessional Phil. Mag. 8. 6. Vol. 10. No. 55. July 1905. F 66 Mr. J. W. Sharpe on the Boomerang. motion from convexity of the surfaces; but otherwise the analysis given above for the case of the boomerang will suffice also for this case. In both cases the momental ellip- soid at the C.G. has its least axis normal to the principal plane; and owing to the thinness of the boomerang this axis is very much smaller than the other two. The boomerang, but not the model, is thrown with the axis of angular momentum, and therefore also the instantaneous axis of rota- tion, initially coincident with this least axis of the momental ellipsoid : and, in the absence of the air, these three axes would remain coincident, and their orientation would remain un- changed, throughoutthe motion. The actual motion, however, as disturbed by the reaction of the air, 7. e. the rotational motion, is very stable, by reason of the relative smallness of the minimum axis of the momental ellipsoid at the 0.G., and the high rate of spin imparted by the thrower. Those disturbing air couples which are in planes parallel to the principal plane merely reduce the angular momentum with- out deflecting its axis; but all the other couples, in planes, that is, parallel to the axis of the boomerang, effect in each revolution a very slight displacement of this axis without appreciably altering the actual amount of the angular mo- mentum, or that of the kinetic energy of the rotational motion, because their axes are at right angles to the axis of angular momentum, or, at all events, very nearly so. The invariable plane alway s touches the momental ellipsoid very near the extremity of the least axis*, and the C.G. remains very nearly at a constant distance from this plane, and the ellipsoid is there much flattened. Consequently the instan- taneous axis, the axis of the boomerang, and the axis of angular momentum, are always nearly coincident, the two former following the displacement of the latter. In conclusion it i interesting to note that similar actions on the part of the air cause rifle-bullets and conical shells to set themselves tangentially to the path of their C.G., instead of keeping their axes unchanged in orientation throughout their motion, which would be the ordinary effect of the co- incidence of the axis of figure with that of angular momentum. Take the case of a bullet fired from a barrel with right- handed rifling. The result is just the same with left-handed rifling. The “C.G.. and the axis of angular momentum are in the axis of figure, the latter being directed forward. Now, owing to the downward concavity of the path of the C.G., the bullet tends continually to meet the air more and more * Because the angular momentum and the kinetic energy of the rotational motion remain nearly constant. Discharge of Electricity through Vacuum- Tube. 67 with the under surface of its conical head. On account of the angular momentum the effect of this is, not to turn the point of the bullet upwards, but to deflect it very slightly to the right Gn the case of left-handed rifling, to the left), because the axis of the very small angular momentum im- pressed upon the bullet in one revolution points horizontally to the right. The bullet now begins to experience an excess of pressure upon its left front, upon the whole in a horizontal plane. Sivee the angular momentum thus imparted in one revolution has its axis directed vertically downwards (N.B. every diameter of the bullet through the C.G. which is at right angles to the axis is a principal axis of inertia) the bullet is now compelled to turn its point downwards, and to bring its axis into parallelism with the tangent to the path of its O.G.; and the disturbing couples steadily decrease as the axis approaches this position. Should the axis dip below the tangent, similar actions will at once begin to bring it up again. The pressure upon the left front of the bullet must deflect the trajectory slightly to the right. Wocdroffe, Bournemouth. VILL. On the Effect of a Transverse Magnetic Field on the Discharge of Electricity through a Vacuum-Tube. By JOHN Prcx, B.Sc. * S is well known, the general effect of a transverse mag- netic field on the discharge through a vacuum-tube is to produce an increase in the potential-difference of the electrodes ; this being probably due to the deflexion of all the ions to one side of the tube so as to diminish its effective section and thus increase the resistance in the gas. It has, however, been shown by Dr. Willows f that a trans- verse magnetic field acting at the cathode reduces the resistance in the tube if the pressure of the gas is below a certain value, although it increases it at higher pressures. Quite recently { the same investigator has suggested that this reduction of the total resistance in the tube is caused by the magnetic field decreasing the fall of potential taking place near the cathode owing to the deflexion of the cathode rays, which, instead of passing directly through the dark space with great velocity, are now bent back so that they have a much longer path, and therefore a much better chance of producing fresh ions by collision, in the cathode dark space * Communicated by the Author. + Phil. Mag. Feb. 1901. t Phys. Proe. ee 27, 1905. 68 Mr. Peck on the Kifect of Transverse Magnetic £ ield than they normally possess. Hence the resistance in the dark space would be diminished. According to this view, the reduction of the resistance caused by a transverse magnetic field at the cathode depends on the existence of the normal large fall of potential near the cathode ; therefore anything which does away with the cathode fall of potential should also eliminate, in whole or in part, the effect noticed by Dr. Willows, and cause a trans- verse magnetic field in this region either to reduce the resist- ance less than it generally does or to have no effect, or finally increase it as it does at other parts of the tube. Now Wehnelt * has found that when the cathode is coated with certain metallic oxides (caicitum oxide for example) and then raised to incandescence, the cathode fall of potential is very largely reduced. It therefore seemed desirable to investigate the effect of a transverse magnetic field on the resistance in a vacuum-tube when the cathode was heated and coated with calcium oxide. The results of the experiments are given below. The Apparatus —The vacuum-tube contained air, and was supported vertically with the cathode at the bottom. The cathode consisted of a small inverted U-loop of platinum wire joined on to stouter copper leads. The cathode was heated by joining the leads to a battery ; an adjustable resistance being placed in the circuit. The piatinum was coated with calcium oxide by alternately dipping it into a strong solution of calcium nitrate and heating in the blowpipe-flame. When prepared, the cathode leads were cemented into the lower end of the glass tube with sealing-wax. The lower part of the tube was surrounded with cold water to prevent the wax from melting when the heating-current was passed through the copper leads to the cathode. , An electromagnet was arranged with its pole-pieces level with the cathode, and the direction of the magnetic lines of force was parallel with the plane of the U-loop. The cathode was earthed, and current passed through the tube from an induction-coil. The variations in the potential-difference between the electrodes of the tube were measured with a Kelvin electro- static voltmeter. A tube containing xylene was joined up to the induction-coil in parallel with the vacuum-tube, and one terminal of the voltmeter was connected with an end of this tube while the other terminal was connected with the xylene ata suitable point between the ends of the tube so as to give a readable deflexion on the voltmeter. In every * Ann. d. Physik, xiv. 3, pp. 425-468. on the Lnscharge of Electricity through Vacuum-Tube. 69 case, therefore, only a fraction of the total volts across the ends of the vacuum-tube was measured. A large number of measurements were made with the cathode at different temperatures, keeping the pressure of the gas and the strength of the magnetic field constant. As the cathode was gradually heated, the reduction in the volt- meter-reading was small at first and altered only slowly, but when a certain temperature was reached a very slight increase in the cathode temperature produced a large fall in the voltmeter-reading. When the cathode was only heated sufficiently to produce a comparatively small decrease in the voltmeter-reading, it was found tnat turning on the magnet decreased the potential-difterence between the ends of the tube to a considerable extent, as in Dr. Willows’ experiments. Upon making the cathode hotter, the fall of potential pro- duced by the magnet became’ smaller until it was reduced to zero and finally became a rise. The following is a typical series of measurements :— | Pressure. | D, | M. | mies © | | | | | | | | | | 005mm. | Cathode at dull red heat ...! 205 Drop. lO; wl | | i | 0-05 ,, Cathode somewhat hotter .... 41 | Drop 106 | O05: | Cathode bright red heat... 473 | Drop 45 ' | } 0-0d._,; | Cathode white hot ............ | 638 | Rise 28°6 | Where D = Percentage drop in voltmeter-reading caused by heating - the cathode ; nd M = Percentage alteration on voltmeter-reading pro- duced by turning on the mea the witede stili being hot. These results are evidently in agreement with the theory stated above, for they show that the decrease in the resist- ance caused by a magnetic field at the cathode depends on the existence of a large cathode-fall of potential, and that when this cathode-fall of potential is sufficiently reduced a transverse magnetic field produces an increase in the resist- ance here, just as it does in other regions of the tube. The change in the magnitude of the effect with variations in the strength of the magnetic field was also investigated. The pressure of the gas and temperature of the cathode were kept constant while the current passing round the magnetizing 70 Discharge of Electricity through a Vacuum-Tube. coils was altered. A typical set of observations is given below :— Drees Magnetizing | Change in Voltmeter Reading caused | ‘ current. by putting Magnet ‘ on.’ 0-11 mm. 6°3 amp. From 225 to 350 = 125 volts Rise. Dhl ia, TB. 5 eee 55, COU == ee be ORI APD ae nee 220, 280. GOL %» OnLy 4°05 ,, - Os 3p LO | DO aes - Gane 5 ag tae ab peas)! 2aO =. 20s en The relation between the rise in the voltmeter-reading and the magnetizing current is shown graphically in fig. ils ioe. Arise «nw Votts’ causeo BY MAGNET. 60 | | | | ‘4 | | | © | | | | | ' | | | | ae | | | | | | | | or | j o) | | | | | | j | | 0 | | / 2 3 4 5 6 MAGNETISING CURRENT IN AMPERES The connexion between the magnitude of the effect and the pressure of the gas was not investigated. I desire to thank Dr. Willows for suggesting this experi- ment, and for assistance during its performance. The Sir John Cass Technical Institute, Jewry Street, E.C. ig ta IX. The Negative Results of Second and Third Order Tests of the “Aither Drift,’ and Possible First Order Methods. By D. B. Brace*. ROFESSOR LARMOR F in his analysis for a system moving through the ether has shown how first and second order effects may be annulled in certain optical and electrical tests of the ether drift. He has not shown, how- ever, how to annul third and higher order effects ; but he states, “‘if indeed it could be proved that the optical effect is null up to the third order, that circumstance would not demolish the theory, but would rather point to some finer adjustment than it provides for: needless to say the attempt would indefinitely transcend existing experimental possibilities”? f. Attention should therefore be called to the results in my experiment on the double refraction of water moving thro: gh the ether. The sensibility attained was such that “the greatest difference in velocity or in index between the two components which could exist, referred to that of water for green light, X=-00005 cm., was less than 7°8 x 10—¥ of the whole. If (10-*)§ be taken as the third order magnitude, this result is then easily within the limit. It was not pos- sible to attain this sensibility with a solid—glass; but, since the physical state of the substance does not enter into the theory under consideration, the results for a liquid should be equally valid. The conclusion as to the amount of double refraction as deduced from what might be expected in comparison with accidental double refraction in a solid—glass, should not be considered as defining the mode and the amount of any double refraction arising from molecular reactions due to a system moving through the ether. Granting the FitzGerald-Lorentz “ contraction-hy pothesis,” we should have for this experiment a complete correspondence as regards molecular activities between the moving system thus shrunk and the same at rest, up to and including second order quantities, as the analysis of Larmor shows. But the negative results of such athird order test, showing as it does the absence of any difference between the moving and the _ fixed system, up to and including third order quantities, may * Communicated by the Author. Read in part before Sect. B, Amer. Assuc. for Adv. Sci., Philadelphia Meeting, 1904-5. + ¢ Aither and Matter,’ Chap. xi. t Phil. Mag. June, 1904, p. 624. § Phil. Mag. April, 1904, p. 318. 72 Prof. D. B. Brace on Negative Results of indicate a complete correspondence, to all orders, of the molecular phases in the moving and in the fixed systems. On the other hand, Lorentz * has shown in his analysis for ‘electromagnetic phenomena in a system moving with any velocity smaller than that of light” that, with the aid of the contraction-hypothesis, many electrical and optical effects will be independent of the motion of the system for all orders. This assumption of a shrinkage, although bold and thus far entirely hypothetical, is not impossible, and is the only suggestion yet made which is capable of reconciling the negative results of second and third order experiments with a quiescent ether. Poincaré} has raised objection to the electromagnetic theory for moving bodies, that each time new facts are brought to light a new hypothesis has to be intro- duced, This criticism seems to have been fairly met by Lorentz in his latest treatment of the subject. The deductions, however, from his theory make it untenable without further development. The physical consequences, at least, seem at present to be beyond experimental examination. So far no valid reasons have been brought forward which necessitate the shrinkage hypothesis in the electromagnetic theory. In this connexion, reference should be made to the proof which Hasenohrl {, reasoning from a cyclic process in a moving radiating system, has given, that the second law of thermo- dynamics i is contradicted unless either a second order con- traction takes place in the direction of drift or the emission varies with the velocity, which latter he considers impossible. On the other hand, Abraham § finds, neglecting fourth and higher order quantities, the ratio of the transverse to the longitudinal mass of the moving electrons to be 2/(v 6/-v 4Af/v\ 1+ 3(¥): i+ s(4)= al s(y)> while Lorentz requires the ratio to be (+ GY) = 0- GY) (a) for perfect compensation : thus leaving a double refraction of the order al) to be accounted for, which would have been detected several thousand times over in my experiment. The * Amsterdam Proc. April 1904, p. 809. + Rapports du Congres de Physique de 1900, Paris, i. pp. 22, 23. t Annalen, Band xiii. p. 367. § Annalen, Band xiv. p. 236. Second and Third Order Tests of the ** Hither Drift.’ 73 analysis of both Lorentz and Abraham seems to be equally consistent with Kaufmann’s results on the deflexion of Becquerel rays, Lorentz conforms Abraham’s theory to his own, by shrinking the undeformable spherical electrons of the latter into flattened ellipsoids in the line of drift; while Abrakam himself shows that these will be unstable unless the greatest axis isin this direction. The latter writer shows* that work must be done against the electrical forces to produce this deformation, so that the total energy in any acceleration is greater than that furnished by the outside forces. Hence there must be inner forces as well which determine the form of the electron. Thus the hypothesis of Lorentz is incomplete without defining the law of forces further. Hence we must either abandon the contraction hypothesis or modify it. The assumption that the quasi-elastic forces, which maintain the electrons in their positions of equilibrium, experience the same changes as the electrical forces, may possibly be varied, and, together with a moditication of the previous hypothesis, be adapted so as to agree with all observations. While the negative results of the first order experiments involving a study of pbase relations between periodic dis- turbances from the same radiant, optical or electrical, moving with the system, are quite as consistent with a,mobile—if we neglect second and higher orders—as with a fixed eether, the explanations of the negative results of second and third order tests are still not in full harmony or free from criticisms, notwithstanding the bold assumption in the premises. It becomes then a serious question, whether to seek still for decisive results with experiments involving the higher order tests, on the one hand, or direct entrainment tests on the other, in order to settle the question. The recent repetition by Morley and Miller + of the original Michelson-Morley interference experiment, with a sensibility one hundred times the calculated effect, leaves perhaps no question as to the absence of any such second order optical effect. Lorentz’s analysis requires a negative result, likewise, if the rays pass through a transparent substance instead of a vacuum: and it seems desirable therefore that this point should be tested for water, say. The interferometer method might also be used to test for double refraction if the light were polarized so as to make the electric displacements perpendicular to the plane of the intex- fering rays, 7.e. respectively parallel and perpendicular to the * Phys. Zeit. Band v. p. 576, t Phil. Mag. Dec. 1904, p. 753. 74 Prof. D. B. Brace on Negative Results of greatest axes of the ellipsoidal electrons of the equivalent system at rest. Otherwise the effect would be masked in using natural light, since, with this type of interferometer, the above components may be as low as 25 per cent. of the total interfering light, as Mills has shown”. The remaining second order tests first proposed by FitzGerald t and developed and carried out by Trouton{, by examining the couple on a suspended condenser, gave negative results, This is completely explained on “the assumption of a shrinkage. Direct experiments on the entrainment of the ether have also given negative results. Thus Lodge § sent two inter- fering rays in opposite directions several times around a rectangle between two rotating steel disks, without being able to detect any displacement of the interference-bands. He estimates that if the disks had communicated one eight- hundredth part of their velocity to the ether, he would have been able to detect it. Zehnder ||, using a different method, attempted to detect any dragging of the sether by a metal plug moving within a cylinder whose ends were circuited together by parallel branching tubes through which two interfering rays could be sent in opposite directions. If the ether had moved entirely with the plug, the effect would have been a thousand times larger than this sensibility. Fizeau’s well-known experiment on the entrainment of the ether, repeated by Michelson and Morley q. showed no effect after allowing for the reaction of the moving water itself upon the interfering waves. Had the ther been carried along completely, the displacement would have been nearly two and a halt bands, instead of approximately the single band actually observed, due to the reaction of the water alone. We may conclude from these experiments that the ether was not entrained in any way in the experiments of Morley and Miller, and that their results are therefore valid, although performed within an enclosure. Nordmeyer **, carrying out the experiment first proposed by Fizeau Tf on the change in intensity of a radiant due to the earth’s motion, found that this variation could not have been * Annalen, Band xiii. p. 854. + ‘Scientific Writings, p. 557. t Trouton & Noble, Roy. Soc. Trans. A. 202. p. 165 (1903). § Lodge, Roy. Soc. Trans. A. 184. p. 727 (1893). || Wied. Ann. Band lv. p. 65. q| Amer. Journ. Sci. (8) vol. xxxi. p. 377. a* Annalen, Band xi. p. 284. TT Poge. Ann. Band xcii. p. 652 Second and Third Order Tests of the “Aither Drift.’ 75 as great as 1/300000*. This agrees with the analytical theory of a quiescent ether, which shows there should be no effect if second order quaatities be neglected. Maseart T and Rayleigh’ s{ negative results on the difter- ence in rotation in gnartz with and against the drift are not decisive, since the calculated effect, although not of the second order, is the difference between 4 first-order effects. A reexamination of the problem with greater experimental refinements should give important results. With the present uncertainty on both the analytical and the experimental sides, decisive results, which will be free from any hypothetical explanation, seem only possible in the direct comparison of the velocities of light with and against the ether-drift. (Of course if a negative result were obtained, it might be open to such a hy pothetical explanation by saying that the group velocity, relative to the medium itself, was a function of the absolute motion of this medium.) Thus Wien $ proposes to use two synchronized Foucault mirrors or two Fizeau toothed wheels. This plan is of course of long standing, but has been recently revived. The mechanical difficulties in the way do not give much encouragement to hope for success ; but with present refinements the test is not beyond possibility. The objection which Newcomb and Michelson || have raised to this mode of comparison, that the phases of the synchronizing systems would be affected by the earth’s motion in the same way as the propagation of the light, does not seem to be well taken. For. granting a certain phase difference in the rotating-mirror or wheel systems, this difference in phase of the two systems can still be so changed as to give an eclipse, say, along the drift. If now we observe simul- taneously the light propagated over the identical path in the ‘opposite direction, there should not be a complete eclipse if the ether wereat rest. Any method, therefore, which allows a comparison of two rays, pr opagated over the same path in opposite directions, is a valid test of the problem. It remains then to devise a method which will certainly show a difference between these two intervals of time equal to one part in ten thousand. The method proposed by Michelson{, of * As this experiment was performed in the latter part of November, when the motion of the solar system has to be subtracted from the earth’s motion, this limit is far too high, and the experiment ought therefore to repeated at some other time of the year. + Annales de 1 Ecole Normale, tom. i. p. 157. t Phil. Mae. Aug. 1902. § Physikal-Zeit. Band vy. p. 585. || Michelson, Phil. Mag. Dec. 1904, p. 716. Silo Gs pe G lite 76 Prof. D. B. Brace on Negative Results of determining the difference of time required by two inter- fering rays “to traverse circuits in opposite directions, would require a path one kilometre square in a horizontal plane to give a displacement equal to -7 of a band for latitude 45°. This would necessitate a very high degree of refinement indeed over any previous attempts at interference. The method of determining the velocity of light which I devised as far back as 1889, and tried a number of years ago*, and which consisted of an eclipsing system made up of a rotating double mirror and a grating, thus combining the principles of the toothed wheel and rotating mirror methods of Fizeau and Foucault, would be delicate enough to show a variation of one part in ten thousand, providing synchronism could be maintained during a short interval of time. With a suitable system of mirrors and observing telescopes, a single observer would be able to bring into his field of view both beams of light after their passage through the eclipsing systems. if now one of the rotating mirrors were either gaining or losing on the other, the observer would see, alternately, eclipses of one ray and ‘the other, if their times of transit were ditferent. If their times of transit were the same, then the two fields would maintain a constant relative intensity, each going through its maximum and minimum simultaneously as the relative phases of the eclipsing systems varied. The latter would correspond to the condition of a moving, the former to that of a quiescent ether. Thus the experiment would be possible, even if perfect synchronism were not attainable, but only sufficiently so to make the frequency of the successive maxima in the field of view less than a few times a second, or slow enough for the eye to resolve the fluctuations of intensity. If, by means of mirrors, a common source of light weré employed, the half-shade principle in the field of view could be used which would be very sensitive in showing any difference in intensity (even if rapidly fluctuating) between the two portions of the field due to any slight ditference in the time of propagation of the two rays with and against the ether drift. If we take the conditions in the experiment referred to +, namely, an aperture of 2°5 cm. and a distance of ‘02 cm. between the lines of the reflecting grating, with a radius of 1 m. and 250 revolutions per second, 10,000,000 eclipses per second could be obtained; and, if we carried this to the limit in speed and resolving power, four times as many * Vice-Pres. Address, Sect. B, Amer. Assoc. Adv. Sci., Pittsburg Meeting, 1902; Science, July 18, 1902. i This apparatus was the phototachometer, modified for the purpose, which Newcomb used in determining the velocity of light. Second and Third Order Tests of the “Atther Drift? 77 would be possible. With the former conditions, and allowing a frequency in fluctuation of 10 per second for good resolution to the eye, a difference in speed not greater than one part in a million of the two eclipsing systems would be requisite. While this seems extremely small, experience shows that such an approximation is entirely practicable. Thus Newcomb * records a “run” in his measurement of the velocity of light, in which his micrometer showed “ beautitul bisection” during the greater portion of the duration (2 minutes) of such a “run.” Allowing this setting to one part in ten of his unit, which was 2’”-4, out of a total deviation of 7500" of arc for a period of 90 seconds, we have a fluctuation in the speed of only one part in 27,000,000. If the two mirrors could be regulated to this degree, we should still have less than one-tenth the fluctuation of our limit, from the two mirrors combined. Hence, so far as speed regulation is concerned, a much higher eclipse frequency, say the forty-million limit, is possible. The other disturbances would be of the same order as encountered by Newcomb over his total “‘ go” and “ return” distance of 5000 m. Supposing the eye could detect a dif- ference in intensity of two per cent. between the two fields (under very favourable conditions this sensibility is one-half of one per cent.), we should need an interval corresponding to one hundred eclipses to detect a change in velocity equal to the aberration constant, since we have to add the effects from each ray. This would mean a distance between the mirrors of 3000 m. for the lower and 750 m. for the higher eclipse frequency referred to, which is much within the distance given above in Newcomb’s experiment. ' Of the other methods proposed+, several do not require a return of the ray in the determination of the velocity constant. _ Thus the rotation of a polarizing system, such as a half-shade nicol or tourmaline system, could be carried up to 3000 revolutions per second. Polishing machines are now run up to 2000 revolutions per second. Allowing a sensibility of 0°01, a distance of 15 kilometres would give a variation in velocity of one part in ten thousand. The objection to the above methods and other similar ones. is the great distance required. If we could increase the eclipse frequency, the distance could be reduced accordingly. This can be attained by the use of electric oscillations in con- junction with suitable optical systems. Two methods proposed * Astronomical Papers of American Ephemeris, vol. ii. pts. iii., iv. Delis: { All the methods referred to in the paper were devised as far back as 1889-90, and have been developed experimentally to a greater or less extent since. 78 Prof. D. B. Brace on Negative Results of ical in the article referred to for measuring the velocity of light can be readily adapted to the problem before us. The first depends on the Faraday “ effect,”’ the second on the Kerr electrostatic “effect” *. The second method, in conjunction with a half-shade elliptical pola- rizer +, which I devised several years ago, has given pre- liminary results indicating a superiority over those de- scribed above, quite beyond my expectations, in the arrangement as originally planned for determining the velocity of light a number of years ago. In fig. 1, &, &' are two con- densers containing, say, the dielectric, carbon disulphide or nitrobenzol, giving the Kerr “effect,” and placed with their azimuths so as to give a “crossed” system. p, ¢,a@ and p’, c’, a’ are the polarizer, elliptical half-shade compensator, and analyser of the two respective optical systems placed in juxtapo- sition. g is the spark-gap and m a half-silvered mirror system for sending identical beams in opposite directions through the optical systems pik ic ad and pk hea. A and A’ represent the azimuths of the various ele- ments as seen from the one side or the other. Thus at A, p, and a, are the azimuths of the polarizer and analyser, k and k’ the traces of the 7) ES} 72 Y L EP < doth DD <6: ose aS eae SS Ses if a i ee nrg ee " Bee aS eS eae Ce So ie ee ts ee Se Pe ee et Y 7a > -E4 i f ‘ t ‘ i ' ' ' i ' 4 CS ¥ —- allay a(!] Y I wv] * Abraham and Lemoine, J. de Phys. 1899, p. 866, used an analogous arrangement to determine the retardation of the Kerr and also of the Faraday ‘ effect.” T Phys. Rey. vol. xviii. p. 70, also vol. xix. p. 218. Second and Third Order Tests of the “Aither Drift.’ 79 planes of the condenser, and ¢ the principal axis of the sensitive strip. Similarly at A’, 44, py, a, q are new positions of these elements due to any constant rotation of all of the elements of the second system except k’. If now there be any damping of the electric oscillations, the effect of the one condenser on the polarized ray for, say, ‘the first oscillation, may be made equal to that of the other condenser for the second oscillation by such a rotation, and so on. Thus these two condensers become an equivalent “crossed” system, the one compensating completely the effect of the other, even if the electric stresses in each arenotthesame. This would hold for electric oscillations which produce successive stresses that are in a cunstant ratio to each other. If now the interval of passage cf the beam of light between & and k’ is any multiple of a half period ot the vibration, we may obtain compensation, and hence retain the settings for a match in the two half-shade systems eandc’. If there should be any difference in the interval of passage in the two opposite directions, we should not obtain a match in the one if we set for the same in the other, after the frequency had been varied so as to give this exact multiple of the half period in this latter system. This would be determined by noting when the intensity of the field approximated a minimum intensity. For low frequencies sunlight has been used; but for the higher frequencies this source has not giv en satisfactory results on account of the very brief duration of the spark in the exciter, and, consequently, the integral time of the electric stresses due to such a discharge. In this case the spark itself may be used to advantage, since here we have a very much greater intensity during the period of the electric stresses. The greater uniformity and intensity of a vapour spark-gap, e. g. of mercury, recommend its use in connexion with the half-shade system. To maintain greater uniformity in the amplitude of the oscillations, and hence in the Kerr ‘effect,’ a secondary or resonance circuit itself, with its condenser system, may be used, as this will give sufficient double refraction in the dielectric to make accurate settings. Such a half-shade Sees where the photometric sensibility is as low, say, as 2 per cent., will show a change of phase of Oa L0O--XA*.) Since now the maxima of the Kerr “effect” occur every half oscillation, the distance between the condenser k and k’ needs only to be equal to the space traversed by the ray in half an oscillation, or d=4, where L is the wave- length of an electric oscillation. This would give us a change of phase in the one direction of 0°3 x 107 2) and an * Phys. Rev. vol. xviii. p. 85 80 Prof. A. Wehnelt on the Discharge of opposite amount for the reverse direction; or, if we set for a match in the one system, the other system would show a change in phase of 0°3 x 10-*7=-2, which is seven times the required effect 10—*, the aberration constant. With con- densers larger than needed for the optical condition, 50,000,000 oscillations have been obtained. Thus 65 ee rox vO MT dale 205 110° a distance small enough to allow a rotating mount for the system. Higher frequencies are undoubtedly possible; so that, if the above optical sensibility is not attainable, we can still use a rotating support, with a reduction in this factor of, say, ten times. ‘This method thus contains the requisite con- ditions, if all the experimental difficulties in connexion with the uniformity of the oscillation and the source of light can be overcome. ‘The present stage of the work seems to warrant this conclusion. Physical Laboratory, University of Nebraska, Lincoln. April 26, 1905. —3M, X. On the Discharge of Negatiwe Lons* by Glowing Metallic Oxides, and Allied Phenomena. By A. WEHNELTT. Na recently published paper { Mr. Owen has investigated the emission of negative ions by glowing Nernst burners both at atmospheric pressure and in vacuo. As some time previously to the publication of Mr. Owen’s paper I had, in two articles, investigated the discharge of negative elec- tricity by metallic oxides, among which were the oxides composing Nernst burners, perhaps I may be permitted to present here a short account of my experimental results. For details and fuller bibliographical references, the reader is referred to the original articles. I. Emission of Negative Ions by Glowing Metallic Oxides at Atmospheric Pressure. The metallic oxides to be investigated were in each case supported by carefully cleaned platinum wires of the same length and thickness, which were in turn fixed along the axis of a hollow brass cylinder. The wire and cylinder were enclosed in a glass tube to prevent convection currents of air. * Negative ton=electron=corpuscle. . + Communicated by the Author. Cf. A. Wehnelt, Sttzwngsber. der phystk.-medicinischen Soc. Erlangen, pp. 150-158 (1903); Ann. der Physik, xiv. pp. 425-468 (1904); Verhandl. d. Deutsch. physik. Gesellsch. v. pp. 255-258 & pp. 428-426 (1903). { G. Owen, Phil. Mag. vill. pp. 230-257 (1904), Negative Ions by Glowing Metallic Oxides. 81 The platinum wire was heated by an alternating current from a small transformer having a well-insulated secondary, and could be raised to any desired potential by connecting it to one pole of a high-voltage battery, whose other pole was earthed. The cylinder was connected to earth through a galvanometer. In the case of a pure platinum wire, as well as in that of one covered with oxide, no well-marked saturation currents are reached at atmospheric pressure. Hence the current was in every Instance measured at the same constant potential difference of 1000 volts. The oxides of the following metals were investigated :-— (1) Barium, strontium, calcium, magnesium, zinc,cadmium, yttrium, lanthanum, zirconium, thorium. (2) Beryllium, aluminium, thallium, titanium, cerium, iron, nickel, cobalt, chromium, uranium, tin, lead, bismuth, silver, copper. Oxides belonging to group (2) showed an emission of cor- puscles which was ‘either not at all or else only very slightly higher than that of pure platinum, while oxides of the first group showed a considerably stronger discharge of negative electricity. The oxides of calcium, barium, and strontium exhibited an abnormally powerful discharge, and this led me to select these oxides for a more detailed quantitative examination. Table I. contains the currents which flowed through the TaBe I. Relation connecting current (¢, in 10-° amp.) with temperature (‘I’), at atmospheric pressure. Pure Platinum Wire. Wire coated with BaO. np +2 —74 +4. —1 880 0°95 0:95 970 Eat hae 0:95 3°8 1050 1:14 0:95 1:14 23°7 1070 < Rae ae B07 1090 is os na 87°5 1105 a ane es 200 1120 By EY fhe Ee: 400 1140 ; re ie 780 1220 1 9 0:95 1:52 1300 4°75 0:95 2°85 1380 10-1 2-28 8:56 1460 26°6 27-6 43-7 [+72 and —2 indicate, respectively, positive and negative potential of the glowing wire. | i. Mag. ©. 6. Vol. Ke No. 55. July 1905, G 82 Prof. A. Wehnelt on the Discharge of galvanometer at various temperatures of the pure or barium- oxide-coated wire when maintained at a potential of + 1000 volts. . These results are exhibited in the curves of fig. 1. The Fig. 1. Saturation-current 800 500 9000... eo Wedd. 9300 1400 ° Celsius Temperature. full-line curves show the connexion between 7 and T for pure platinum wire. From them it will be seen that tor tempera- tures below 1450° there are sent out more positive than negative ions*, while at higher temperatures the reverse appears to take place. Much more marked than this slight difference between the numbers of the positive and negative ions in the case of pure platinum is that which occurs when the wire 1s coated with barium oxide (dotted curves of fig. 1). While the currents corresponding to a positive potential do not appreciably differ from those obtained with a pure platinum wire, the currents with the wire at a negative potential are extraordinarily large even at low temperatures. Similar results, both qualitatively and quantitatively, were obtained with the oxides of calcium and barium. Il. Emission of Negative Ions by Glowing Metallie Oxides at Low Pressures. According to the united testimony, of all investigatorsf, a platinum wire heated zn vacuo emits principally negative ions. * This result is in accordance with those obtained by other workers. Detaile2 bibliographical references will be found in J. J. Thomson’s ‘Conduction of Electricity through Gases,’ Chapter viii. (1903). + J. Elster and H. Geitel, Wied. Ann. xxxvii. p. 315 (1889). J.J. Thomson, Phil. Mag. xlviii. p. 547 (1899). O. W. Richardson, Proe. Gambr: Phil. Soe. xi. pp. 286-295 (1901) ; Phil. Trans. eci. p. 516 (19038). McClelland, Proc. Cambr. Phil. Soc. xi. p. 296 (1991). H. A. Wilson, Proc. Roy. Soc. Ixxii. pp. 242-276 (1903), and Phil. Trans. cecil. p. 252 (1905). Negative lons by Glowing Metallic Oxides. 83 The number of corpuscles emitted by glowing platinum was investigated in detail by Messrs. O. W. Richardson* and H. A. Wilson}, according to whom—as had already been found by J. J. Thomson—the relation between the number of negative ions and the absolute temperature may be repre- sented by an exponential formula, into which the number of corpuscles contained in unit volume enters as a constant. This number, according to Richardson’s researches, amounts in the case of platinum to about 10”. Now I have investigated the emission of negative ions by platinum wires coated with the oxides of calcium, barium, and strontium, and found that, for equal temperatures, the oxide-coated wires emit far more corpuscles than the pure platinum wires. The experimental arrangements were essentially the same as ‘in the previous investigations, only in this case various leading wires to the electrodes were melted into the glass, and the tube was fused on to a mercury pump having no greased jointst. At pressures less than 0:1 mm. of mercury, well-marked saturation-currents were observed which were independent of the pressure. At pressures exceeding 0:1 mm., ionization already occurred by ionic impact, the saturation currents were not well marked, and were in addition dependent on the pressure. Hence, in order to find the relation connecting the saturation current with temperature, pressures less than Q°1 mm. were invariably used. In what follows, the results will be given for BaO alone, as those obtained with CaO and SrO were very similar, both qualitatively and quantitatively. The results cannot, of course, be expected to be perfectly concordant, as a perfectly uniform coating of the wires with the oxides is unattainable. Table IL. contains the results obtained with BaO; instead of the saturation-current, the saturation current-densities are given—. e., the currents per unit of area [2cm.~?]. Taste [].—Relation connecting Saturation Current-Density (¢em.~?) with Temperature (T). Wire coated with BaO. p=0-'04 mm. of mercury. | | | } ees) O000 » (rk OO": 1140°. | 122087) L300°. 1880°. | 1460°. | | tem.—2 | 5. 10-7|3'8. 10-8 3:14. 10-5 21810-41610 8-1.10-3/2-4 .10—2 | | | * Loe. cit. + Loe. cit. t Sealing-wax joints and joints rendered air-tight by means of grease were avoided, as the vapours of organic compounds are decomposed by the glowing wire, whereby the coating of oxide on the wire is destroyed. The carbides formed cause a black deposit on the walls of the glass tube. Gy 2 34 Prof. A. Wehnelt on the Discharge of These results are graphically exhibited in fig. 2. eo, bag | POV ee eae Aeon a ee See: abe aoe acim “TT hewn cla aud iaiea gaol cle aCe co) ee ice Pale aid Current-Density Temperature. On comparing these curves with those obtained by Mr. O. W. Richardson* for pure platinum, it is found that they possess precisely the same character. An application of the test suggested by Mr. O. W. Richardson to my results showed that his exponential formula satisfactorily represents the con- nexion between the number of corpuscles emitted and the temperature in the case of metallic oxides also. From the much stronger emission of negative ions by the oxides, I concluded that the latter contain more corpuscles per unit of volume than platinum. A calculation of the number contained in unit volume leads, on the other hand— as has recently been shown by Mr. O. W. Richardson f—to * O. W. Richardson, Proc. Cambr. Phil. Soc. xi. p. 291 (1901). + O. W. Richardson, Jahrbuch fiir Radwaktivitat und Elektromk, 1. p- 313 (1904). Negative Ions by Glowing Metallic Oudes. 85 the same value as that for platinum. From this Mr. Richardson concludes that the corpuscles proceed not from the glowing oxide, but from the platinum, and that the action of the oxides is confined to a reduction of the amount of energy required to liberate the corpuscles. Experiments to settle this point are in progress at this Institute. Ill. Glowing Metallic Oxides as Cathodes in Discharge Tubes. According to our modern views, the cathode dark space of a glow discharge represents a region poor in negative ions*. If this impoverishment is prevented by introducing into the dark space corpuscles produced by any convenient method, their presence results—as has been shown experimentally by Herr G. C. Schmidt—in a lowering of the potential drop at the cathode. | Now glowing metallic oxides emit, as we have seen, numerous negative ions. Hence, when used as cathodes they should produce a lowering of the cathode drop which increases with increasing temperature. Hxperiments on this point confirmed the truth of this conclusion. In what follows are given the results of quantitative ex- periments made to determine the connexion between the cathode drop on the one hand, and the current, pressure, and temperature of the metallic oxide cathode on the other. The spherical discharge-tube used in the experiments had for cathode a platinum wire coated with the oxide under investigation, the wire being heated by an alternating current. The temperature was measured by means of a very thin platinum-platinum-rhodium thermocouple. An _ exploring electrode near the cathode enabled the cathode drop to be measured. A wire of aluminium served as anode. Connexion between Cathode Drop and Current.—In the first place, I investigated the dependence of the cathode drop on the current at various temperatures of the cathode. The results for the oxides of barium, calcium, and strontium are almost identical, qualitatively as well as quantitatively, so that I here give, in Table II1., only the values obtained with CaQ. * J. J. Thomson, Phil. Mag. xlvii. p. 253 (1899). J. Stark, Ann. d. Physik, 11. p. 62 (1900). G.C. Schmidt, Ann. d. Physik, xii. p. 622 (1908). A. Wehnelt, Ann. d. Physik, x. p. 569 (1903). 86 Prof. A. Wehneit on the Discharge of TABLE III. Relation connecting Cathode Drop (K) with Current (2) at a glowing CaQ-Cathode, at Constant Temperature (T) and Constant Pressure ( /). T—752° || 7, 10-3 amp.| 0°026) 0:053 p=0'83 mm. Hg. || K in volts. 1-2 : : an teem |e eazP | BBO SE | 92 03 Le Lae ieee ae paoen oO [Ea pme | CERT OT | 0 os) ote ee T=—984° || 7, 1O—3 amp. | tee tee wane lee ne Ree 3 ae p=0°87 mm. Hg. | K in volts. || Fig. 3 exhibits these results graphically. The curves show Volés, 60 (Tr | ae en if Giemsa ee ea [ eeceuee ce Ee Mitt eee ae Gee ESL Gen ee Peceeeeeocee BinRB ae GES ce Jaws RARE ARR ee [eae ae ia palaoaciag cele SL OK OT) Os. oan Om mns O78 10 Milliampere. that up to a certain value of the current, characteristic of each temperature and increasing with rise of temperature, the cathode drop is nearly constant and very small [the small. residual potential difference of from 1 to 2 volts between the Negative Ions by Glowing Metallic Oxides. 87 exploring electrode and the cathode is, no doubt, due to the fall along the positive column], but that it rapidly increases as soon as the characteristic current is exceeded. This current I have named the limiting current. Since the limiting current increases with rise of tempera- ture I have investigated the relation connecting the two quantities somewhat more closely. Connexion between Limiting Current and Temperature.— By slowly increasing the current at various temperatures, that value of it was determined beyond which the cathode drop just commenced to increase—z. ¢., the limiting value of the current. The relations so obtained between the limiting current and temperature are nearly identical, qualitatively as well as quantitatively, for the oxides of calcium, barium, and strontium ; hence, in this case also, I give, in Table IV., the results obtained with CaO only. 3 TABLE LV. Relation connecting Limiting Current with Temperature (CaO cathode). p=about 0°01 mm. Hg. Memupetature % i... 0. eees eee a 1012/1075 |1133 1192/1252) 1313| 1367 |1485° Limiting Current, 10-3 amp. .0:1 0:56 1-68) 5:6 11-8) 26*| 35-4) 56:1* T00* | | | Limiting Current - density, ) 9.5 ieee F z Z é ’ 10:2 -) AN 2 25 [=< lord F in 10-3 amp. cm.—2 ...... } O41 | 3°57| 1 5 | 55 | 75 | 120 | 1500 | In the third row of the table are given the limiting current- densities, 2. e., the limiting currents per unit of area [7 cm.~?| of the glowing oxide. As will be seen, the current-density reaches a very large value at high temperatures. The curves drawn in fig. 4 have been plotted from Table IV. With increasing pressure the limiting current decreases, but otherwise the relation connecting limiting current with temperature remains unaltered ft. Meaning of Linuting Current.—As already mentioned above, according to modern views the cathode dark space represents a region poor in negative ions. If into it we introduce cor- puscles generated by any suitable method, the cathode drop will decrease. If now we increase the current through the discharge-tube, we do away with more negative ions, the * With large currents, the walls of the tube became strongly heated, so that the pressure could no longer be kept constant, but increased almost to 1 mm, . y A. Wehnelt, Ann. d. Physik, xiv. p. 451 (1904). 88 Prof. A. Wehnelt on the Discharge of impoverishment as regards such ions again increases, and hence the cathode drop will increase. a ee ed [ol RE fe es ae (A ES Ee ee Mi Gi BCE ere ee || ee ae aaa fl | ee a EG / shod a | BOOS |e era Bec tae mene te oat O TOG 1100 7200 4300 1400 Limiting current, per cm.’. v0 Temperature. Now the glowing oxides emit, as we have seen, numerous corpuscles. If the number emitted exceeds the number absorbed by the passage of the current, there will be no im- poverishment, 7. e., the cathode drop will be zero. As the | current through the tube is increased, 1t finally reaches a value such that the number of ions absorbed per unit of time by the current becomes exactly equal to the number furnished by the glowing oxide during the same interval. Up to this value of the current, no impoverishment as regards negative ions takes place, so that the cathode dropis zero. If now the current through the tube be further increased, more corpuscles will be absorbed than are generated, and the cathode drop will begin to rise. Hence the current which I have defined as the limiting current is that for which the absorption of negative tons and the impoverishment thereby brought about just ceases to be com- pensated by the corpuscles emitted by the glowing owides. Negative Ions by Glowing Metallic Oxides. 89 If this view is correct, then the limiting current must in- crease in proportion to the number of ions emitted by the oxide. But the number of corpuscles emitted by the oxide is directly proportional to the measured saturation current, so that the limiting current should increase in direct proportion to the saturation current. An examination of the experimental results from this point of view showed the correctness of this conclusion. IV. Applications of Glowing Metallic Oxide Cathodes in the Construction of Discharge Tubes*. 1. When the glowing oxide cathodes are at a very high | temperature, the limiting current-density reaches a value of several amperes per unit of area [cm.?]._ These high limiting current-densities enable us, by the use of glowing oxide cathodes having areas of several square centimetres, to send much stronger currents through the discharge-tubes than has hitherto been possible. This is due to the fact that with ordinary tubes the cathode drop even with feeble currents already far exceeds the normal value of 300 volts. The con- ditions are essentially different in the case of the strong currents which may be sent through mercury vapour. The fall of potential along the positive column is, as has been shown by special measurements, under low pressures and within the range of 0:1 to 15 amperes, entirely in- dependent of the current and lies between 1 and 2 volts per em. More exact measurements on this point are not yet available, as the heating of the walls of the tube by the strong currents liberates a large amount of gas from them, whereby the pressure and with it the potential gradient along the positive column is greatly increased. The small drop along the positive column, combined with the absence of a drop at the cathode, renders it possible to work fairly long tubes by means of voltages such as are furnished by electric light circuits [110 to 220 volts]. The regular positive layers which are formed with strong currents glow with extraordinary brightness, and promise to supply a valuable aid in the examination of gas spectra in spectrum analysis. The ultra-violet rays might be allowed to escape through quartz windows cemented into the tube. 2. If in a discharge-tube the anode be brought close up to the glowing oxide cathode, the positive column disappears, and there remains only the anode drop of some 20 volts ; 2. é., a potential-difference of little over 20 volts is sufficient * The tubes here described are obtainable from E. Gundelach, Gehlberg, in Thuringia. 90 Jhscharge of Negative Ions by Glowing Metallic Oxides. to send a current through the tube. But if the polarity were reversed, so as to make the glowing oxide electrode the anode, and the cold metal electrode the cathode, then at low pressures several thousand volts would be necessary to send a current through the tube. Hence, if such a discharge-tube be in- troduced into a low-voltage (110 to 220 volt) alternating current circuit, it will act as a valve, allowing only one half- wave of the alternating current to pass through it. The tube may then be used in a manner similar to that of Gritz’s aluminium rectifier, for the purpose of charging accumu- lators, or working induction-coils having electrolytic inter- rupters, by means of alternating currents. 3. If the limiting value of the current be exceeded in a discharge-tube with glowing oxide cathode, the cathode drop may be given any desired value, and so the cathode rays any desired velocity. | By the use of a cathode consisting of a narrow bare strip of platinum foil, having only a small circular patch (about 1 mm.’ in area) of CaO on it, the entire discharge, when the. platinum glows, may be made to pass through the CaO patch, so that from this latter there issues a very thin pencil of cathode rays, having a direction normal to the foil. These rays may be given any desired velocity by a proper choice of the temperature and the current. They are extraordinarily bright, so as to be visible even in a fairly large darkened lecture-room. If the tube be introduced into a uniform magnetic field whose direction is perpendicular to that of the cathode rays as they leave the cathode, the rays are bent into completely closed circles, whose radius of curvature is easily determined. If in addition to this the total discharge potential-difference be measured by means of a voltmeter, and from it there be subtracted 20 volts to allow for the anode drop, the cathode drop becomes approximately known, and thus it becomes possible to demonstrate to a large audience, in a simple and easily intelligible manner, the determination of the ratio of charge to mass \< | and of the velocity [v] of cathode rays. pe By varying the cathode drop within wide limits (5 to 200 volts or more) it then further becomes possible to demonstrate e E e . e . . . that the ratio — remains constant within these limits, while la v, on the other hand, increases with increasing cathode drop. Erlangen, Physical Institute of the University, April 1905. pal] XI. On the Partition of Energy between Matter and Asiher. By J. H. Juans, M.A., Fellow of Trinity College *. , $1. > sae question discussed in the present paper is one which I stated in an earlier paper on the Theory of Gases (Phil. Trans. exevi. p. 397, 1901) as follows :— “If an interaction between matter and sether exists, no matter how small this interaction may be, the complete dynamical system will consist of the molecules of the gas, together with the ether, and must therefore be regarded as a system possessing an infinite number of degrees of freedom. Applying Beltzmann’s Theorem to this system, we are merely led to the conclusion that no steady state is possible until all the energy of the gas has been dissipated by radiation into the ether. This application of the theorem may or may not be legitimate, but it is, 1 think, certain that no other application is legitimate.” The same question has recently been discussed by Lord Rayleigh in ‘Nature’*. In the present paper, I have tried to investigate the legitimacy of applying the theorem of equipartition to a system consisting of both matter and eether, assuming for the present that this matter is in the gaseous state. Let us, to take the simplest case first, consider a gas of which the molecules are rigid spheres or point centres of force, possessing no internal degrees of freedom, and acting on one another partly through ‘‘ material ”’ forces and partly through their interaction with the ether, this action being very small except when two molecules are near together. If there are N molecules (A, B, C,...), we can suppose the configuration of the system to be specified at any instant by G.) GN coordinates 22, Yo, 2a; Yay Var Way £5; Yd x -«. Giving the positions and velocities of the molecules, and Gi.) m coordinates £, &,..... En (e.g. components of electric and magnetic force) giving the state of the cether at every point, these coordinates being independent. We here suppose that any relations which must be satisfied in the free ether (e. g., the vanishing of the divergence of the electric and magnetic forces) have already been taken into account. * Communicated by the Author. ~ + April 18th and May 16th, 1905. The present paper was written in March, and was sent to the Phil. Mag. immediately after the appearance of Lord Rayleigh’s first letter. It is therefore not intended as a reply to the second letter, although the questions discussed happen to be much the same. The postscript was, however, written with special reference to the letter of May 16th. 92 Mr. J. H. Jeans on the Partition of The system is accordingly specified by 6N +m Lagrangian coordinates, and the energy is some function of these 6N +m coordinates. § 2. If there is no interaction between matter and ether, this energy can readily be expressed as a sum of squares of these coordinates. The energy is of the form zm D3 (ear Opear a8, Hy (&1, E, Sue. te Em) The last term represents the energy in free ether which, if we assume the exact linearity of the electromagnetic equations for all electric intensities with which we shall ultimately he concerned, is known to be i ‘ 79 79 TJ2 9 9 9 alll (ee ee ere 4 y) dx dy de The energy is not yet expressed as the required sum of squares, for the quantities X, Y, Z, «, 8, y, are not inde- pendent Lagrangian coordinates. Let each of the quantities X, Y, Z, a, 8, y, regarded as a function of 2, y, 2, be expressed in the form oa) pw if e e (cee) = 73 \\h Ai) f (Au, ¥) cos p (N—w) cos J (u—y) Cos 7 (v—2) | 0 “Te | dp dq dr dean and let the right-hand integral be further transformed into the sum of an infinite number of terms of the form | Ot (petqy tre), or again «~ COS a ot ! eA | C 28 «-(la+ my + nz), where l, m,n are direction cosines, c=p?+g?+7°, and C is independent of w, y, and z. The value of any one of the six quantities X, Y, Z, a, 8, y, say the first, can now be expressed in the form to 7 an : x=(|{ (X, cos + X, sin)(xv sin 0 cos #+y sin @ sin ¢ +< cos @) ia desmoue db...» aaa where X, and X, are functions of «, 0, and @¢ only. ON ON ero : re emia i -+—— =() ls now satisfied if Of: OU Tr X, sin @ cos ¢@ + Y, sin Osin@+Z,cospP=0;: . (2) * Cf. Whittaker’s solution of y°V+ V=0, ‘ Modern Analysis,’ p. 321. { | The condition Energy between Matter and Atther. 93 and there is a similar relation for X,, Y>, Z,, and ‘similarly for a1, Pi, 0G. and a2, Bo, Y2- The quantities X,, X,, Y;, Yo, a, #, 81, Be caninow be taken to be the independent Lagrangian coordinates &, &... En, the values of Z,, Zs, 91, y2 being given by relations of the type (2). Substituting from equations (2) we find that “allies +Y? +2? a2+ B47) da dy dz becomes a sum of squares of these coordinates. The total energy is accordingly of the form = 3m>(u, +? +w?) + 2a,&,’. The dynamical equations which regulate the variation of &,, &... are obtained from the electrodynamical equations oA _1dy_ 08) ,, Semin ae As a typical equation we have 2 il Qe (sin? 6 sin? b —cos? 6) B,+sin? Osin b cos ¢. a,b. cos @ J£ 91, pi are any pair of coordinates of position and momentum of the material system, we have the variation of Pp 4 determined by the usual Hamiltonian equations 5 ay lel 5 Grol 1 ie OL 11 9p,” SP Cota at Si 4a (4) and equations (3) and (4) contain between them the dynamics of the system. Let us represent the motion in a generalised space corre- sponding to the 6N +m dimensions Pi Q1> +++ &, E,, cee Eun: If p is the density of a fluid moving in this space, the equation of continuity 1s 1Dp Cio Oe p Dt =e 5 a ae ah If the fluid moves in accordance with the dynamical equa- tions, the first sum vanishes as usual by equations (4), and the second sum vanishes by equations (3). Thus Dp/Di=0, so that the fluid, if initially homogeneous, remains so through all time. | | : (3) 94 Mr. J. H. Jeans on the Partition of 83. As a result of the assumed absence of interaction between matter and ether, the condition of “‘ continuity of path” is not yet satisfied: the fluid moves as though the space were divided into water-tight compartments. The equations of the divisions between these compartments are simply the integrals of the equations of motion (3) and (4), such, e. g., as the family of surfaces X,?+ Y,?+a,7+ 8,7 =constant. If the material system is divided into separate masses of gas, we have as further integrals E,=const. E, =const. &c., where H,, H,... are the material energies of these systems separately. 4. If we now admit a very small interaction between matter and eether, the conditions are changed. The equations of motion are changed by the introduction of cross-terms which link up the material system with the zether, and we may assume that no integrals are left except the energy equation. Thus the whole system of water-tight compartments is broken down except for the family of surfaces H=constant where E is the total energy. The new coordinates of position and momentum differ from the old by terms which depend on the interaction just introduced, and so may be regarded as approximately unaltered when this interaction is small. The whole system, regarded. now as a single electromagnetic system, will still have equations of motion of the Hamiltonian type, so that the equation De/Dt=0 remains true accurately. The conditions for the theorem of equipartition are now satisfied, so that the expectation of the energy of each of the degrees of freedom is the same, namely | oy 3N4+m § 5. When we have a finite amount of matter in infinite ether, N is finite while m is infinite, so that the ratio of energy of matter to that of ether, namely 3N/m, is infinitesimal. Definite though this result may seem, the partition of energy is not yet completely known. If we attempt to find the law of distribution of energy in the radiation-spectrum, the equipartition theorem directs us to assign equal amounts of energy to each coordinate, and therefore to each value of 4, but gives no information as to the “ density ” of coordinates within the different range of values of &. This circumstance Energy between Matter and Aither. 95 suggests that the physical problem is not yet fully threshed out. § 6. Let us assume, as a preliminary to carrying the inves- tigation a stage further, that the transfer of energy from matter to ether does not occur at all on the free-paths of molecules, but that vibrations are set up in the ether at collisions. If T is an average time of duration of a collision, the frequency of the waves “ forced ”’ in the zether is less than or comparable with 7, waves of frequencies much greater than 7 being, as can readily be shown by analysis which I have already given %, of infinitesimal amplitude. We now see that the ultimate distribution of energy in the spectrum would depend on the temperature from which the material system had started, and the radiation at any instant would depend on the temperature at that instant. A mass of gas might at one time emit a spectrum extending into the ultra-violet ; by the time the gas had cooled to half its former temperature, the spectrum would be a heat-spectrum only. The actual temperature at which the light-spectrum would disappear is easily found, from the analysis already quoted, to be comparable with 1000° C. § 7. Suppose, however, that we now consider a mass of gas shut up in a perfectly reflecting enclosure. The coordinates of the ether must no longer correspond to plane waves in un- limited ether; they must correspond to the principal vibrations of the ether inside the enclosure. The number of these vibrations is still infinite, but the number of which the frequency is below any given limit is finite. Let us suppose that the average time of a collision is 7, and that of the infinite series n of principal vibrations in the ether, a finite number s have periods which are less than, or at most comparable with 7, the remaining n—s having periods small compared with r. Then, of the n degrees of freedom of the ether, only s receive any perceptible amount of energy from the molecules at collisions. We may say then that the transfer of energy between the material degrees of freedom and s degrees of ether freedom is comparatively rapid, while that to the remaining n—s degrees is very slow. For an enormous time these n—s degrees of freedom will not receive their due share of the energy, while the energy will rapidly equalise itself between the remaining 3N+s degrees of freedom. During this time, the ratio of the energy of the ether to that of the material system is s/3N, and this will generally be very small. § 8. For instance, let us enclose gas at atmospheric pressure *¢The Dynamical Theory of Gases, Chapter IX., or Phil. Mag. August 1908: “On the Vibrations set up in Molecules by Collisions.” 96 Mr. J. H. Jeans on the Partition of and at a temperature of 15° C. in a cubical enclesure of edge equal to / centimetres. For this svstem N =4 x 10¥/? very nearly. The free vibrations of the sether are known (c/. Lord Rayleigh’s ‘ Sound,’ § 267), each vibration corresponding to values of X, Y, Z, 2, 8, y of the type cos (Qe cos quy cos UES tee): > . ‘@) where p, g, r are integers. These principal vibrations cannot be compounded into plane waves, as was done in § 2 when the space was unlimited. The frequency « of this vibration is given by Ke TW eg en = yar + (6) where V is the velocity of light. For air at 15° C. the mean duration of a collision is of the order of 10-! seconds. Let us suppose the s degrees of freedom to consist of ail those for which the period is greater than 10-14 seconds. The period given by equation (6) is 20 Dt «7 Vi/pagar If we take V=3x10", we find that the upper limit of WA p+q?+7* in order that the vibration may have a period of not less than 10-!* seconds, is 20000//3. The number of sets of positive integral values of p, g, 7 for which ,/p?>+q?+7" <9, where @ is large, is approximately 176°, so that in the present case the number of sets of values of », g, 7 is approximately Aq x 10!" 2 ee Each system of values of p, 9, 7 gives four principal co- ordinates, so that for our present purpose ge, one Taking the value N=4 x 10¥/?, we find Sut Aqr 3N 243x107 so that the energy of the ether is almost inappreciable, no matter how large the enclosure may be. =) als ouohly, Finergy between Matter and Atther. 97 § 9. We can now trace the course of events when one or more masses of gasare left to themselves in undisturbed ether, At first we may suppose that the total energy is entirely that of the principal degrees of freedom. ‘The transter of energy between the different degrees of freedom of the gas at any point is,as we know, extremely rapid. The first phenomenon, then, is that the energy of these degrees of freedom arranges itself according to Maxwell’s Law. The time required is a small fraction of a second. The next phenomenon, at any rate if the masses of gas are small, is an equalization of temperature by conduction through each mass. Simultaneously with this, however, a transfer of energy is taking place between the principal degrees of freedom of the molecules, and the vibra- tions of low frequency in the ether. ‘This equalises the temperatures of different masses of gas, and endows the ether with a small amount of energy, equal to that of a finite number of molecules of the gas, but small compared with the total material energy. The time required for these phenomena must be measured in minutes, days, or centuries, according to the linear scale of the system. After this, a third transfer of energy begins to show itself, but the time required for this must be measured in millions or billions of years unless the gas is very hot. A transfer takes place between the energy of the principal degrees of freedom of the gas and that ‘of degrees of freedom which may either be in the ether or in the atoms of the gas, but which have the common characteristic that they represent vibrations of high frequency. If the gas is in vacant space, the energy set free streams away into space, but if the whole system is enclosed by an ideal perfectly reflecting boundary, the energy accumulates in the ether. ‘Posrscrier, added June 7th. § 10. As in § 8, the number of degrees of freedom of the ether, of which the fr equency is less than k, inside a cube of edge 1 is 20°k3/m?V?. Hence the number of vibrations of frequency between k and k+dk is = k?dk. At absolute temperature T each degree of freedom possesses energy ZRT, where, if the units are those of the C.G.S. system and of the centigrade thermometer, the value of R is 9:3x10—" (cf. “The Dynamical Theory of Gases,” § 130). Thus the Phil. Mag. 8. 6. Vol. 10. No. 55. July 1905. H 98 Mr. A. 8. Eve on the Radioactive energy per cubic cm. of vibrations of frequencies between k and k+dk, is 13d aes ~aya* dk, or, in terms of the wave-length A in free ether, the energy of wave-lengths between A and A+ dA is SeRTAtd.. . nr This is one-eighth of the amount found by Lord Rayleigh (‘ Nature,’ May ‘L6th), but agrees exactly with that given by Planck (Drude? s Annalen, iv. p. 553) for large values “of x. It seems to me that lord Rayleigh has introduced an un- necessary factor 8 by counting negative as well as positive values of his integers &,7, ¢ From formula (7), it follows that the total energy of radiation at temperature T is (e.) Ao sek nt | f0,1,)0a, Ao 0) in which Ay is the shortest wave-length for which the vibrations may be supposed to possess their full energy, and the second integral represents the energy of waves of wave- length less than Xo, the energy of radiation of these waves being a function not only of T and 2, but also of ¢, the time which has elapsed since the closing in of the ether. Formula (8) does not, of course, claim to express the partition of energy in the radiation emitted by a hot solid: it is the radiation when a mass of gas has been shut up for time ¢ in a perfectly reflecting enclosure. And the formula applies only to the continuous spectrum of the gas produced by molecular motions; no account is taken of the line spectrum, produced, so far as we know, by atomic vibrations. AIT. On the Radioactive Matter present in the Atmosphere. By A.S8. Hive, M.A., McGill University, Montreal *. ‘dia presence of radium in the earth, and cf the emanation of radium in the atmosphere, has been well established. Exact measurements of the amount of the radioactive sub- stance in the air are, however, needed. Professor Rutherford was kind enough to propose to the writer some methods and experiments by which to estimate the quantities present, and to throw further light on their effects. The main objects of these investigations were :— 1. To estimate the amount of radioactive matter present in * Communicated by Professor E. Rutherford, F.R.S, Matter present in the Atmosphere.: 99 a known volume of the atmosphere, measured in terms of the mass of radium required to maintain the supply constant. 2. To ascertain if the natural ionization of the air can be entirely attributed to the radioactive matter present in the atmosphere. 3. To determine the rate of formation of ions due to the active matter in the air. 4. To find the distance from which active matter can be collected on a wire maintained at a high negative potential. I. On the Amount of Radioactive Matter present in the Atmosphere. If a wire is raised to a high negative potential for two or three hours in the open air, it is known that it collects active matter from the air. The rate of decay of the activity of the deposit thus obtained approximates closely to the rate of decay of the matter similarly collected from the emanation of radium. It is not necessary to repeat here the summary of evidence collected by Professor Rutherford in the last chapter of ‘Radioactivity.’ It appears certain that the radium in the earth gives rise to radium-emanation in the atmosphere, and that the emanation in turn disintegrates successively into the three products of rapid decay, radium A, B, C. Bumstead has accurately compared the decay of the active deposit obtained from the air of Newhaven, Connecticut, and has shown that it must be ascribed to radium. He has also observed in the same locality the presence of thorium emanation. It may be of interest to compare the rate of decay of the active deposit obtained from the emanation of radium, as given by Professor Rutherford in his Bakerian Lecture *, with the rate of decay of the active deposit derived from the atmosphere in Montreal, as determined by the present writer. These results are shown in Table I. and in the curve (fig. 1). ti is possible that some of the observed difference is due to the presence in the air of active matter from radioactive elements other than radium, such as thorium, but in any case the difference is not large, and it may be partly experimental. {In order to measure the quantity of emanation present in a given volume of the atmosphere, a simple method of comparison was employed. A negatively-charged wire was * Phil. Trans. Roy. Soc. ser. A, vol. cciv. pp. 169-219. H 2 7 100 Mr. A. 8S. Eve on the Radioactive used to collect the active deposit from a known volume of air, and the amount was measured by an electroscope. A known weight of pure radium bromide in solution was then TABLE I. Decay of Excited Activity. a Radium Atmospheric ime eS 1 < Differe io ates manation. ceposit. lilerence. ° Rutherford. Kve. 10 52 52. | ee 20 45:4 48 +2°6 30 40:4 42°5 +2°1 40 35'6 oa +1°9 50 30°4 32°5 +21 60 25-4 278 +2°4 TORS. RR mee ere 22:8. | 80 17-4 18:5 +11 907 a Sa es 145 aa 100 11°6 11:0 — 6 LIQ) on Aare ees 80... |) 120 76 6:6 —1:0 fo} TO gO 1DO "a 120 Time in Minutes taken, and the resulting emanation was collected and trans- ferred to another closed vessel; the excited activity was again obtained on a negatively-charged wire and measured by the same electroscope. In this way the emanation in the air was measured in terms of the amount of radium which would be required to produce it. In all cases the charged wire was exposed for almost three hours, so that practically Matter present in the Atmosphere. 101 a maximum amount of activity was obtained. A Wimsburst influence-machine, driven by a small electric motor, was used, and the potential of the wire varied from about —9000 to —11,000 volts. It was necessary to work with a large vessel in a building into which no radioactive matter had been introduced. ‘The conditions were satisfied by the Engineering Building at McGill University, which is situated at a considerable distance from the Physics Building. In the hydraulic laboratory there is a large water-tank 803 cms. high, and 152 cms. square, with a total volume of 18:7 cubic metres. ‘The sides are made of iron 3°5 cms. thick. The tank is filled from time to time with water supplied by the City of Montreal, and derived from the rivers St. Lawrence and Ottawa. The river water is practically free from radio- active matter, nor could any appreciable activity be discovered in the mud and slime deposit left at the bottom. The tank was placed at the writer’s disposal by the courtesy of the authorities of the Engineering Building, and a series of experiments were made, extending from November to April. In all cases the activity was measured ten minutes after the Wimshurst machine was stopped. For the sake of simplicity the activity is expressed in terms of the scale-divisions of the reading-microscope used to observe the fall of the gold-leaf of the electroscope. It may be noted that one scale-division was about equal to a fall of 3°6 volts, and that the capacity of the system as shown in fig. 2 was 3°5 H.S. units. The wire, after removal from the tank, was rapidly coiled on a metal reel, somewhat similar to the outer part of a large fishing-reel, and was then placed in a zine cylinder connected to earth. Along the axis of the cylinder was a brass rod, insulated by a sulphur support, and directly connected with the gold-leaf system of an electroscope placed beneath the zine cylinder. The fall of potential per minute, due to the active matter collected on a wire 8 metres long placed in the iron tank, ten minutes after removal, corresponded to 36 scale-divisions. This is the mean of the results of a large number of obser- vations, taken on different days, and the readings varied from 2°3 to 4:3. Thus the active matter collected from 18°7 cubic metres of air caused a fall of potential measured by 3°6 scale-divisions per minute. A relatively small, air-tight, zine cylinder 154 cms. high and 25 cms. in diameter was then taken, and the emanation derived trom 2x 10-* mgs. of pure radium bromide was introduced into it. The volume of the cylinder was 76,000 c. cms., and the emanation was distributed through the 102 Mr. A. 8. Eve on the Radioactive contained air by means of convection currents caused by heating the outside of the cylinder. After charging for three hours the wire was removed and wound on the reel, Fig. 2. and then placed as before in the zinc cylinder above the electroscope. The activity, ten minutes after the charge stopped, caused a fall of potential of 7:8 scale-divisions per minute. The solution of radium bromide, initially freed from emanation by passing a current of air through it, had been allowed to stand for fifteen hours in a closed vessel before introducing it into the zine cylinder. Since the constant of change, A, for radium emanation 1s about °18, it can readily be shown that only one-tenth of the full supply of the emanation had been obtained from the radium bromide. Thus the total active deposit, which could be obtained from 2x 10-4 mgs. of radium bromide in radioactive equilibrium, Matter present in the Atmosphere. 103 corresponds to 78 scale-divisions ; and from 1 gramme of radium bromide to 3°9 x 10° scale-divisions. Hence we can determine the amount of radium bromide required to maintain the supply of emanation contained in 1 cubic kilometre of air at Montreal. For the emanation in the iron tank, whose volume is 18°7 cubic metres, caused a fall of potential corresponding to 3°6 scale-divisions, and 1 gramme of radium in radioactive equilibrium would supply emanation corresponding to 3:9 x 10° scale-divisions ; therefore 1 cubic kilometre of the air contains emanation supplied by -49 gramme of pure radium bromide. Thus, making certain assumptions, we can form a rough estimate of the probable amount of emanation in the atmo- sphere. We can first of all calculate the amount of emanation, supposed equal in quantity per cubic metre to that in the air at Montreal, distributed in a spherical shell around the earth 1 kilometre high. Since the surface of the earth is 5 x 10° square kilometres, the amount in this shell corresponds to the emanation released from 2°5 x 10° grammes of radium bromide in radioactive equilibrium. Several observers have shown that the excited activity at high altitudes is equal to, if not greater than, that on the plains ; and it thus seems probable that this distribution of emanation might extend for at least 10 kilometres. In that case, the emanation in a shell 10 kilometres high must be released from 2°5 x 10° grammes, or 2460 tons. Now, three-quarters of the surface of the earth is covered with water, and if we further suppose that the emanation arises from the land alone, we obtain one-quarter of the above value, or 610 tons. This is an estimate of the total amount of radium required to furnish the emanation in the atmosphere over the land of the earth’s surface. It is probable that a vastly larger amount exists in the earth, since the greater part of the emanation would be transformed without ever issuing from the earth’s surface. : An objection may be raised to the above estimate, inasmuch as the measurements were taken in the building, and not out-of-doors. It was found that air driven from the room through the tank did not affect the result, und the production of ions was proceeding at a very slow rate, as will be seen in Section III., so that there was no reason to suppose that the conditions within the building were different from those outside in respect to the amount of radioactive matter present in the air. Nevertheless, it was decided to make some measurements 104 Mr. A. S. Eve on the Radioactive out-of-doors, and for this purpose a large hollow zine cylinder was used, 610 cms. long and 77 cms. in diameter, having a volume of 2 8 cubic metres, or about one- seventh of that of the large iron water-tank. This cylinder was placed on the College Campus, at some distance from the Physics Building. The active deposit was collected as before on a negatively- charged wire along the axis of the cylinder. When the ends of the cylinder were left open, the amount of observed activity showed the usual variations, and was affected by the velocity of the wind, humidity, and the atmospheric conditions. When the ends were _ closed, fairly steady results were obtained. A comparison of the results is given in the following table :— TABLE II. Total activity in |Activity per cubic metre scale-divisions, in scale-divisions. Zine cylinder out-of-doors : (1) seins openicn wo eese aes "34 "12 (2) indszelosed \.52 oe .eesene ee 15 054 - Zinc cylinder in the Engineering Sunalding ?{) hee Aes es eee ee eee ‘50 "18 Iron tank in the “Engineering Building, ese. satis celet ERENCE ane 3°6 "19 The ratio of the volumes of the tank to the cylinder is 6°7:1, and the ratio of the activities is 24:1, so that the excited activity collected in a vessel out-of-doors was between one-third and one-quarter of that collected within the closed tank in the Engineering Building. In order to see whether the effect was apparent or real, the wire cylinder was put in the Hngineering Building, not far from the water-tank, and the excited activity was then exactly proportional to that obtained in the large tank. No s satisfactory explanation of the difference between the values in the building and out- of-doors has at present been found, and the point w vill receive further investigation. Radioactive matter has not been introduced into the Engineering Building, and it will be shown later that the rate of production of ions, g, was as low as any observed. If we take the values obtained in the cylinder out-of-doors, we must reduce the estimate of the radium bromide required to supply the emanation, in a shell 10 kilometres high over the land-surface of the earth, from 610 to 170 tons. Matter present in the Atmosphere. 105 Il. On the Collecting Distance of a Negatively-charged Wire. An estimate was next obtained of the approximate distance from which excited activity can be drawn from the air to a wire raised to a potential of —10,000 volts. On a still day the amount collected on 6 metres of wire was almost the same whether the wire was suspended at some distance from the ground, or was placed within the zine cylinder with open ends. In the cylinder the potential gradient was steeper, but the wire was to some extent screened from slight air- currents. The collecting distance was therefore approxi- mately equal to the radius of the cylinder, or to 40 cm. Two wires were then suspended in the air about 90 cms. apart, and the third wire was fixed at a distance of 10 metres from this. It was found that all three wires collected almost the same amount of excited activity, so that the two neigh- bouring wires were not drawing radioactive matter from overlapping volumes. Similar experiments were made with wires hung in the Engineering Building at various distances from the outside of the tank. The experimental evidence is not easy to summarize, but the general conclusion was obtained that a wire raised to about —10,000 volts collected activity from a cylindrical volume of about 40 to 80 cms. radius. This result is not in agreement with previous suppositions, for some observers have wrongly concluded that the collecting distance is very great. III. On the Rate of Production of Tons. It is important to obtain as many determinations as possible of the value of g, or the rate of production of ions per cubic centimetre of the air. A well-insulated wire was there- fore hung down the middle of the large iron tank in the Engineering Building, and the wire was connected to the wold leaf system of the electroscope used throughout the experiments, but from which the zine cy linder was now removed. On charging the wire to two or three hundred volts, it was: found that a saturation current was not obtained. Twelve wires were therefore taken (fig. 3), and fastened to a few zinc disks, 13 cms. in diameter, so that the wires were along the generating lines of a cylinder of that diameter. This system of wires, connected to the electroscope, and charged to 300 volts, was found to give a saturation current. By this arrangement, the whole tank practically became a very large electroscope, and the discharyve of the central wires was due to the radioactive matter present in the air within the tank. The capacity of the system was found by connecting 106 Mr. A. S. Eve on the Radioactive Big to: ial Uy : I 800 cms, ee Matter present in the Atmosphere. 107 the wires to a condenser of known capacity consisting of two concentric cylinders, and by observing the potential, both before and after the connexion. The subsequent calculations are similar to those given by Rutherford in ‘ Radioactivity,’ page 72. Since 8, the volume of the tank, equals 18°7 x 10° ¢.c., and C, the capacity, was 140 E.S. units, the current, 2, is equal to CV, when V is the fall of potential per second; g is the number of ions produced per second in a cubic centimetre, and e, the charge on an ion, is taken as 3°4x 107°. But the gold-leaf fell at a rate measured by 2°3 scale-divisions of © the microscope in one minute, and a scale-division represented 3°6 volts or a E.S. units. 300 Hence 2= 644 x 10-2, and a 1 = Se == 10'1. A large number of similar experiments were made, and the values ranged from 9°1 to 10°2, with a mean value g = 9°6 ions per c.c. per second. This is the smallest value yet obtained, and I think that the error is not more than five per cent. H. L. Cooke, using a well-cleaned brass vessel, found g=10 in the Physics Building at McGill University about two yearsago. Professor Schuster, in the laboratory at Manchester, found g = 12. These small values for g are only obtainable when the instru- ments employed are well-cleaned, and removed from the neighbourhood of radioactive substance. IV. An Estimate of the Total Depth in the Earth from which the hadium Emanation passes to the Atmosphere. Professor Rutherford has given in ‘ Radioactivity’ an estimate of a higher limit to the amount of radium which can be present in the earth. If this amount were exceeded, the temperature of the earth would have a value in excess of that observed. He calculates that, on an average, not more than 4°6 x 10-™ grammes of radium can be present per one gramme of the earth’s constitutents. But the mass of the earth is 6-1 x 10° orms. Hence the total amount of radium in the earth cannot exceed 28 x 10 kilos, or 28 x 10’ British tons. The consensus of observers seems to show that the emanation 108 Mr. A. S. Eve on the Radioactive in the air escapes from the earth; and if we suppose that radium is uniformly distributed to the above amount, we can readily calculate the depth from which the emanation must freely come in order'to keep up the supply in the atmosphere. Let « be the average depth through which that radium is distributed which gives rise to the emanation in the atmo- sphere. Since 610 tons of radium suffice to produce the amount of emanation over the land of the globe, we have an 010 28 x 10” ae where 7 is the earth’s radius, and since move 1) ems: uv = 18 metres. If we take the lower estimate of 170 tons of radium, the corresponding depth is about-5 metres. Emanation arising from greater depths than these would prevent disintegrate before reaching the surface of the earth. IV. On the Cause of the Natural Ionization observed in the Atmosphere. The question arises whether the natural ionization of the air at the surface of the earth is due to the radioactive matter contained in it, and whether this cause will wholly account for the effect, or whether there are other causes at work, known or unknown in character. Take, for example, the discharge of the cylinder of wires suspended in the large iron tank in the Engineering Building. This wire lost its charge at the same rate whether it received initially a positive or negative charge. The saturation current from the wire to the sides of the vessel was 6°44 x 10°? ELS. units, and the rate of produgtion of ions was given by g=9°6 per ¢.c. ina second. Is such ionization of the atmosphere to any extent an inherent property, or would air entirely free from radiating matter, or its influence, cease to produce ions, and would it become a non-conductor? ‘The only ionizing agents under such conditions are (1) radiation due to radio- active matter contained in the air, (2) radiations due to active matter on the surface, or in the material of the sides of the Matter present in the Atmosphere. 109 vessel, (3) penetrating radiation through the sides of the vessel, due to radioactive matter in the surrounding bodies. In the present experiments, the sides of the fonke consisted of iron one inch thick, and were sufficient to cut off all but y rays coming from without. The deposit on the sides of the tank could not have been appreciably radioactive, or the low values of g (9°6) would not have been obtained. For in no apparatus, however carefully cleaned, has a lower value of the volume ionization been noted. The chief factor , probably the only factor, in producing the discharge of the wire is the emanation in the air, and the successive products of rapid decay. And of this there is undoubted evidence, inasmuch as the excited activity was actually collected on a negatively- charged wire in the tank. The experiment shows that the radioactive matter is in the tank, and the only question is whether it is sufficient to account for the effect obtained. In order to test this point, Professor Rutherford proposed to me a new method of directly determining this important point. I venture to describe it at some length, because it is desirable that similar experiments under various conditions should be carried out in other places. Such a radioactive survey of the atmosphere would be of interest at the present time. If the radioactive matter in the air is the sole cause of the ionization observed, there should be a direct and proportional relation between the excited activity and the ionization ; for both these effects must originate from the same cause, namely, the emanation present at any given moment in the mass of air under observation. The method employed was as follows :—The natural ioni- zation of the air in the tank was observed, and the active deposit in the tank was then collected ; the first with a cylinder of wire connected with the electroscope (as in fig. 3), the second on a wire suspended in the tank, and char ged to —10,000 volts. The wire after removal was wound on the reel, and measured by the same electroscope, as in figure 2. Thus, if C, be the capacity of the cylinder of wires in the large tank, V, be the potential fall per minute in the electro- scope whose mold-leat system is connected with the central wires, then C,V, is a measure of the natural ionization. Again, if C, be the capacity of the electroscope, fitted with the upper cylinder and reel as in figure 2, and if V, be the fall of potential per minute due to excited activity on a negatively-charged wire, as observed ten minutes from the 110 _ Mr. A. S. Eve on the Radioactive cessation of the charge, then C,V, is also a measure of the emanation present in the tank. Therefore, whatever may be the amount of emanation, whether naturally present or artificially introduced, we should have, under all circumstances, a constant value for the following percentage, namely, ON CLV, The constancy of the quantity must, of course. depend upon the current being fully saturated, and on the active deposit being completely collected in every case. If a smaller vessel be now filled with the emanation of radium, so as to give a discharge large compared with that due to the natural ionization, the same value for (1) should be found for the air mixed with emanation in this small tank, as for the natural air in the large iron tank. The advantages of this method are due to the fact that the measurements are all taken with the same electroscope, and may be expressed in terms of scale-divisions of the same instrument, which need not-even be disturbed from its position. Now, in the actual experiment with the iron tank, C,=140, C3=3'9 E.S. units. V,=2°17, V.=8:6 scale-divisions per minute. O2V» ree OK. $100.) Oa OO 41. This rasult is the mean of many experiments extended over some months. The emanation from radium bromide was next blown into a small tank of 80,000 c.c. capacity, and a similar series of experiments were made. C, was now equal to 21, and C, to 3°95, and the following values of these quantities were obtained for various strengths of the emanation :— Mi. V,. ae x 100. 1-44 4-4 55 0:93 2-6 6-0 1:85 63 4-9 132 58 4-4 Matter present in the Atmosphere. 111 Thus we obtain 4:1 from the natural air in the iron tank, and 5:2 from the air mixed with the radium emanation in the smaller vessel.. These figures are of the same order, and the difference between them is probably caused by the difficulty of drawing all the excited activity to a wire charged even to —10,000 volts from a tank whose sides measure 150 cms. These results show that the ionization in the large tank was very largely due to the presence of radium emanation, and cannot be ascribed to radiations from the walls of that vessel. But the results obtained were not altered after air had been freely driven through the tank, and we thus come to the con- clusion that the rate of production of ions in the air of the tank was probably the same as from the air outside the building ; and if such is the case, we have seen that the ionization can mainly be attributed to the presence of radio- active matter in the air itself. Since the activity is due to the emanation which decays to half value in four days, its amount cannot have sensibly decayed in passing from the outside air to the tank. The results strongly indicate that the radioactive matter in the atmosphere near the earth will fully account for the rate of production of ions observed in it. V. Summary. The o@ general conclusions derived from these experiments are as follows :— (1) An estimate of the amount of radium required to main- tain a steady supply of the emanation in one cubic kilometre of air near the earth’s surface, lies between -14 and -49 gramme. (2) This amount of emanation and its successive products cause a production of ions at the rate of about 9°6 per cubic centimetre per second. (3) The radium emanation in the air is probably sufficient to account wholly for the natural ionization observed in large closed vessels consisting of non-radioactive materials, and for the rate of production ~ the ions in the atmosphere near the earth. (4) The collecting distance of a wire charged to —10,000 volts is about 40 to 80 ems. The active matter derived from the carriers is not drawn in appreciable quantities from. still air at a greater distance. 112 Radioactive Matter present in the Atmosphere. (5) Assuming that the radium in the earth is equally distributed in amounts sufficient to maintain the temperature gradients actually observed in the earth, then the radium emanation in the air is derived from an average depth estimated to be between 5 and 17 metres. All these estimates and results are based on the assumption that the conditions at Montreal are normal, and represent the average. It must be remembered that the country was covered with snow from one to three feet deep, and that the temperature was sometimes as low as 10 degrees, or 15 degrees below zero Fahrenheit. But after the snow ihe melted, and the frost had left the ground, the active deposit on a wire in the zine cylinder on the College Campus was almost equal in value to that obtained in the depth of winter. Allan also found that the summer and winter values at Montreal showed but slight variation. It is most desirable that experiments should be repeated elsewhere similar to those described in this paper, particularly that suggested by Professor Rutherford, and described in Section IV. If any investigators have at their disposal a very large tank which can be “yendlerad absolutely air-tight, it would be interesting to observe whether the natural leak of a well-insulated wire suspended in it and connected to an electroscope would fall in a few days at the same rate as the decay of radium emanation. iresh air cculd then be intro- duced from without, and the experiment repeated. Such an investigation would determine absolutely whether the natural ionization is entirely due to the emanation present in the air. There might be a small residual ionization due to the sides of the vessel. A large steam-boiler might serve as a tank. Observations at sea are also needed, both on the rate of production of ions, and on the excited activity which can be collected. In conclusion, I am indebted and grateful to Pratece Rutherford, both for suggesting the experiment, and for his advice, encouragement, “and resourcefulness when difficulties occurred. McGill University, Montreal. ord April, 1905. bay tl2.] XIII. On the Lateral Vibration of Bars of Uniform and Varying Sectional Area. «By Joun Morrow, M.Sc. ( Vict.) ; M. Eng. (Liverpool) ; Lecturer in Engineering, University College, Bristol™. CONTENTS. . Introduction. Approximate Method of Solution. . Clamped-Free Bar. Bar “ Supported ” at Both Ends. Free-Free Bar. . Clamped-Free Bar of Varying Breadth (6 = Ax). » (6 = Ax”). Depth (d= Az). 7 ] CO OO MIO Or B Colo » ” . Kirchhoff’s Investigation. I. Introduction. N the theory of vibrating rods expressions for the frequency and the form of the displaced bar are ob- tained from the equation d* Tg a MY in which y is the displacement at a distance w from the origin. The solution is y=A sin we+B cos wa +C sinh we+ D cosh pa, A, B, C, D being arbitrary constants to be determined by the end conditions. In the case of a uniform bar supported at each end the numerical solution presents no difticuity. In other ele- mentary cases the results are deduced from the values of the roots of equations which would be troublesome if not previously tabulated. Lord Rayleigh + has shown that the natural period of a bar may be obtained approximately by simpler means. For example, he supposes that the curve assumed by a clamped- free bar whilst vibrating is the same as that which it would take up if displaced from its position of equilibrium by a lateral force acting on the bar at some point in its length. He shows that the period is given with considerable accuracy if the point of application of the force is one quarter of the length from the free end. More recently, Garrett { has investigated this subject and, * Communicated by the Physical Society : read March 10, 1905. + See Rayleigh’s ‘Sound,’ vol. i. pp. 233-285. t Phil. Mag. Nov. 1904. Phil. Mag. 8. 6. Vol. 10. No. 55. July 1905. I 114 Mr. Morrow on Lateral Vibration of Bars of from instantaneous photographs of the vibrating bar, has concluded that a better approximation to the centre-line of the bar is obtained if the lateral force is assumed to act at a point one-fifth of the length from the free end. Rayleigh’s method is, of course, applicable to rods under other conditions of support. It rests on the fact* that a close approach to the true period can be obtained by assuming a type of vibration which is admissible as an initial con- figuration, as a considerable departure from the true type leads to only a small error in the estimate of the frequency. — Garrett’s method and results have been further investigated and compared with Lord Rayleigh’s by Dr. Chree {, and it is shown that, whilst Rayleigh’s depends on a recognized dynamical principle, Garrett’s apparently has no such basis. These simple solutions may be of considerable importance in acoustics and mechanics. They have been employed in problems of the “ whirling ” and vibration of rotating shafts by Dunkerley { and later by Chree §. It is the object of the present paper to show that by assuming an equation which completely satisfies the end conditions a better approximation is obtained, and that, by a process of continuous approximation, the vibration curve and the period of the fundamental are given to any required degree of accuracy. The treatment is capable of very general application, and will be chiefly useful in problems of which the solution has not previously been obtained. ‘The first three cases dealt with will serve as illustrations under various types of terminal conditions. It is a noteworthy fact that, whilst Rayleigh’s approximations are necessarily overestimates, the method described below gives initially too small a value for the frequency. When the density and flexural rigidity of a bar are variable from point to point in its length, its treatment by the ordinary method of analysis presents difficulties which have not yet been completely overcome. Many ot the solutions are obtained easily by the method here given, and several special cases are considered. 2. Approximate Method of Solution. If a bar is vibrating so that every point in it has the same ~ period, the ratio of the acceleration to the displacement is constant for all points. * Rayleigh’s ‘Sound,’ vol. 1. §§ 88, 89, 182. + Phil. Mag. Jan. 1905, p. 184. t+ Phil. Trans. A, 1894, p. 279. § Phil. Mag. May 1904, p. 504. Uniform and Varying Sectional Area. 115 If yz be the displacement at a distance z from the point ae yz . ie chosen as origin, so that — is the acceleration, and if y, be the displacement of any chosen point (say that at which the displacement is a maximum), then the above statement may be expressed by the equation Pyz | Py, | de Tea ge |? or ; ee ete Pal hah a. ae te (1) This is equivalent to the usual relation in frequency problems denoted by Ge — COS 1) \ 2). Now, if we consider the reversed effective forces due to the acceleration of an increment of the length of the bar, we have, by the ordinary Euler-Bernoulli theory, that the couple at any section in the direction tending to increase 2 is equal to the product of the curvature and the flexural rigidity at that section. That is, in view of the approximate straightness of the rod, ay). Mh am Sa ont ke where M is the couple due to the reversed effective forces, E=Young’s Modulus, : and I=Moment of Inertia of the cross-section about th neutral axis. Since M is a function of the mass per unit length, the end forces, and the accelerations, we can express it in terms of A yz and the density and cross-sectional area of the bar. And JL ; assuming for yz a hypothetical type of vibration satisfying the end conditions, we can insert the value of M thus obtained in the equation (2). Solving for y we have a second approximation to the centre-line of the bar, and can calculate the period by fe 7. : ee eee, me ae (3) The next approximation consists in using this solution for y I 2 116 Mr. Morrow on Lateral Vibration of Bars of to find a more accurate expression for M, inserting this in equation (2) and again solving. , The process can be repeated to any extent, but in common with other methods it neglects the rotatory inertia of the rod. In the following work the bars will be considered to be of uniform sectional area, density, and flexural rigidity except when otherwise stated. 3. Clamped-Free Bar. Taking first the case of a rod “ clamped ” or “ built-in ” at one end and free at the other, let the origin, O, be at the free end. | i p = density of material of bar, @=cross-sectional area, then the Moment of the Inertia forces about X (distant «x from QO) = ( po yz(4—z)dz, - 2/0 and therefore the differential equation of the centre line of the beam is, by (1) and (2), 7 (ep ad 0 mee = ae | Yy2(@—z)dz, $ 5 . E (4) 0 p» being taken from under the integral sign on account of the uniformity of the density and sectional area throughout the length. The object is now to find the solution of this equation in ascending powers of 2, and hence to obtain the period of vibration. Assume a value of y, which satisfies the end conditions. Thus let y=A+Ba+ Cv’? + Dx? + Hat. The end conditions at the free end, =O, are Pe a®a tie ne aK D Y aa Yi» vs A = Yv and at the fixed end, # = J, vi —a0, erie (), mie en ML Sane Cae Uniform and Varying Sectional Area. 117 and the equation is y=n(1—35 +57) Prarie an! ah Co) Substituting for y, in equation (4) ne Pere he Ae fae: Rh oa za” me), (1- 33+ 3x) 4 2? = 7 and performing the integrations, evaluating the constants by the end conditions, —y= pet ( 08194 lt— -112,698,41 Pa+-0416 a! = ore a == 2) Le +-000,198,41% ), | hie) which is approximately the curve of vibration of the bar and gives = ,=-08194 92 jn, or from (3) where k=radius of gyration of cross-section, pon) Lae velocity of transmission of longitudinal p vibrations in the rod. The expression given by Rayleigh may be put in the form Nn 375160 kU Dar On 4 showing that the ratio between the two values of N 1s die See The next approximation gives a still closer value and a ratio of 0°9998. Itis obtained by inserting y, from equa- tion (6) in (4), and using the value just obtained for y, whence qd? ° ae . ay = Eee: ii (-osio4 i —-112,698,41 Pe + 04162! 5 . 8 015 + 000,198,415; )(w—2)de é celia ii(-04097 > Ita? —-018,783,07 Px? +-00138 2° a Pa — 000,264,557 +-000,002,21% ) 118 Mr. Morrow on Lateral Vibration of Bars of y= err ("663084 [8 —-912718 Ua + 341435 Fart KI?’ —°093915 Ba +:002480 2° wi? ~ 0003672 +: 000002, 7 “). This is a more accurate expression for the vibration-curve than is (6), but it-can be seen that the difference is not great. i == "0809227 onl tas and oloD WU. AS Or «OP? which is correct to 0°02 per cent. of the value given by exact methods. 4. Bar “ Supported” at Both Ends. This is the case in which the directions at the ends are free, but the ends themselves are constrained to remain at rest ‘by « supporting ”’ forces of the required magnitude. For a uniform bar these forces must each equal one half of the total force due to the inertia of the bar, that is, taking O at one end, Equation (2) then becomes d*y Ce. wrt = apo! —(" ydo— pro! | y,(2 =a) dee 7) l/r Taking y=A+Be+Ca?+ Da? + Ex*+ Fo’, a=0, y=—5=0, -, A=O=0 Eady es : 3 DP+4 BE+.5, Fl eS) eae 5 gee) Tray eS a ea HE + 5°. BN al ; l ip Gs g fot ine a poe Dan +Ba5 Gas) 6 es, .. O=Bl+ DP? +E + FP ; “= l Cy iy “. O=6D/412H/? + 20F?; Uniform and Varying Sectional Area. ILS and the last four of these give Hence the type to be assumed as a first approximation is 16% Be) fe (Ca—2Qla* + 2"), and (7) becomes @y poy, {1-a ("16 ,, ie ep te _ Lt (Pa—2la’ +2x*\dx ay (Pz—2lz* + 2')(2z— ade} ie se ee ca ie Mae an i ae moet 10 — 55) Integrating and keeping the end conditions in view, =3 a (016 Lx” —-0083 Pa® +-002,380, 953107 —°000,595,24 2®—°010,119,05il'v), . . (8) which is the a vibration-curve, and 1) — 97-1098 or te ol For the second approximation, using (8) in (7) / and simplifying as before, 2 Y oY — +310 151 22% (— 1:02513 Pa +1:68650 Ua" —-83 Pv’ +°19841 827 —:03307 Ie’ + °006622"’) SES THR , y= 31075 1 (10386 U2 17086 Pa + 0843341" —01984 Px" +-00276 lx’ —-00030 le” +-00005 2”). This is a close approximation to the equation of the centre- line, and gives —y, =0102725°0 yj, _ 9°866 kU oN a7 120 Mr. Morrow on Lateral Vibration of Bars of The correct value of the numerical constant in the numerator is 7°, so that the ratio of the two values is 0°9996. The last expression for the displacement may be con- veniently compared with the exact type. Thus it may be written San 17086 «? "08433 ut a "00030 a oe ie vf "10386 22 Wee °° °° “10386 2° "10386 ju ? whilst the method indicated at the commencement of this paper gives, by the insertion of the end conditions, Til l yo sin or y=Neh 1 a ( efl)? ‘ q*(/L)4 7 (ell E (5 ee @ e@ © —e [11 Js ° Comparing the coefficients of 2”, 2, &c. inside the bracket shows how the accuracy alters in passing from the lower to the higher powers. For example, AIOS6 Be apa “T0386 — 1845: ee ie 08433 ce Beaty re mss6 Pee ie iin 00030, mW? TOaRG = (000289. > 000235 5. Free-Free Bar. In the case in which both ends are free and no external forces act on the bar, the conditions at each end are GE d°y peng dx* Y=Yy Assuming y=Ast Bas Co? 4+ Da’ + Ea’ + Fa’ 4+ Go’, the conditions at z=0 give A=y,, C0. and those at r=/ give Uniform and Varying Sectional Area. 121 To determine G we have that, since the total force on the bar vanishes, ae Bou Wr — eine dhval a ier. | (9) 12/0 that is *] (y,-4 Gat 3 Gla'—3 Gla + G2’ \dze=0 "0 ere an? and hence the equation to be assumed is Age 80 oh) er BB awl Zp +g 8 +3) Equation (2) becomes for this case _ #1 _ po yp dx? Bl z("; BNP ie, and substituting for 7, Cy po.. “( Pe athe ake. BO 2 Verte a. laa! Bi! Al : Sr+ gn Bp tg pee = Fahl 52" 7 PT br +16) Integrating twice and evaluating the second constant by virtue of (9) Lise aaa 001,993,14 —-00925 Px +0416 w'—-0387 l — 01382 — ‘0092 25 + 00185 ~% F =) and 22°399 kU Dae ee The more correct value is 22°373, so that in this case the first approximation gives a ratio of the two values as near as 0°9988. 6. Clamped-Free Bar of Varying Breadth. (b=Azx.) Let b be the breadth of the bar, and d its depth in the plane in which the vibration occurs. 122 Mr. Morrow on Lateral Vibration of Bars of Let d=constant, and 6=Az. Equation (4) then becomes ee ey { PW 2 Wz (w%—z2)dz by virtue of (1) and (5). —y= sel 122,619,04 /'—-173,469,38 Px + -083 a" | —-087 +-000,850,34 h = OT76Ee th pl In the next approximation the differential equation re- duces to : Q7- : ey esleeae A (-020, 436,51 Ua? —:014,455,78 Pa’ a= hal +-001,984,13 «°—-000, 595235 +-000,007 38s) = whence , | | se Se a 40053 2 —°340. Te et ao 4A —y= Eel 240053 340800 U2 +°170304 lta —-0722790'x* + 003543 x —-000827 = : - +-000006 7) F 2 5h, Kal p! yee oo aU and ae 2 ~All clamped-free bars in which the depth is constant and the breadth proportional to the distance from the free end will vibrate with a period which is independent of the breadth at the fixed end (that is of the value of A), as given by the above formula. 7. Clamned-Free Bar of ee Breadth. (b=Az?.) Here d?y 1p Gol phew de ge = Ea? y (2 a) 4 = Ph, feat gt | -*07142857 Lah Uniform and Varying Sectional Area. 123 Ying -9= $4 098,928,57 I! —-143,537,41 Pa +083 2 = he F x? ; x ar —-04% +-001,275,517 my) 5 t = fe 1 10Roe pl y For the second approximation ee eae ae die Hee : ; ea OPEL ITN! ae —Z (- Co Z ' —’ e 41 Pz +083 -'—-04= dais 001,275,515 Se Me ee Be ihe Poets ie = Sk (8 244.05 Ua? —7°17687 Pa* + 1:48809 w x vr? —5— +-00966 =) pe ae oor [ —1-09782 la + 68700 Lx* »12 — +35884 (22? 4--02657 2*— 00772 ~ z + -00007 ) == 1()- gg12 2% : an pl This gives Wee 3°313 dU ork as For a third approximation the differential equation re- duces to 2 eee ee 062562 [’a? —-054891 Ua +°012268 Ta° da d*l —-004984 P'2° + -000201 x°—-000049 . oe 5655 [2 +8275 [a +-52135 Pat —°27446 172° + °02191 I’a® —:00692 Pa” +°00015 21?—-00003 ) Whence Os — 11-063 oF 1 and N= es ae This is again independent of the breadth of the bar. 124 Mr. Morrow on Lateral Vibration of Bars of 8. Clamped-Free Bar of Varying Depth. (d= Aux.) The exact form of the equation first assumed for the type of vibration is immaterial to the final result, but, by choosing a suitable equation, the labour involved in obtaining this result to any required degree of accuracy is reduced. 2y In the present case (as, indeed, in the last two) is not necessarily zero when w=0, for there the area of the section of the bar also vanishes. Hence we may start with an equation . 24 2 y=y(1— 7 +E) te which, inserted in dy eon, | 7 oe | ~ da? = BAB? a) bAz(a—a)y,. dz gives fy _ Bh (o_ 22 4.52%, da? ~ BA? ay P): Y, y= on 483 21:2 le+22- 3° 4+° 0575 =) and ais _ 60 BA2 7 20 ae) In the second approximation fey. (20a dx? 29 BA? i 08052 — "Ile + 050° —-01% +001,190,48 3 2 ae ifayp (1742064 4468254 Px +-4027 Pa? 29 BAY s : a s ae vw — "16 la? +-0416 a*—-005 +-0003968 ) ‘ — 91 9.939 HA tee YW pl? and in the third approximation 2 ew ae is vat 99034 1t—'37235 la +:2014 Px? ) —-05 Ia? +:0099 a — 0001), Uniform and Varying Sectional Area. 125 = fe (06192 16 —°15936 Px +°14517 U2? —-06206 Px’ +-01678 2xt—-0027 Ix* +-0003 2°) — ha9-3445 22 yi ph 153812 AU Die eS In this case the period is independent of the breadth of the bar, and the influence of the depth is exhibited by means of the constant A. aad N= (11) 9. Kirchhof’s Investigation. The solution for some cases of non-uniform cross-section was considered by Kirchhoff in 1879 *. He remarked that the general equation d”y d*y S3(BLT ; in) +P pede sia can be solved in general terms when the depth and breadth of the cross- section are of the form d= ay, (x) b= LaF, (x), x being any variable quantity. The only cases he investigates fully are (Ga) m=1, a — x = constant. ()” m= I, n=, v= constant. The former corresponds to that in the last section and the numerical result obtained by Kirchhoff may be written ae 1-534 AU t pps 0 Agreeing well with equation (11) above. University College, Bristol, January 1905. * Berliner Monatsberichte, 1879, p. 815. t+ Rayleigh’s ‘Theory of Sound,’ vol. i. art. 187 84650 mee XIV. On‘ An Optical Paradow. By G. Jounstone Stoney, .A., Se.D., FRS.* JN the June number of the Phil. Mag. vol. ix. p. 779, Lord Rayleigh describes and discusses an experiment by which he was at first puzzled. The experiment is illus- trated by a diagram, which is here reproduced. i ee L A is a point-source of light of nearly wave-length A, L is a lens forming an image of A upon the middle of C, which last is the objective of a telescope T. The telescope is to be focussed upon lens L; and the boundary of this lens is then the object which will be more or less satisfactorily seen by an observer who looks through the eyepiece of the telescope. The excellent definition of L as seen in the telescope was unexpected. It would seem paradoxical to a person who, remembering that most of the light from A is concentrated within the minute “spurious disk ” of its image formed at C, was disposed at first to infer that this little disk may be regarded as determining the effective aperture of telescope T. Lord Rayleigh interposed a material screen cutting down the aperture of the telescope to nearly the above small size. This greatly impaired the image of L as seen through the telescope ; and this satisfied him that the effective aperture of the telescope before the interposition of the screen was not so small as had been supposed. Lord Rayleigh was led by this to make a closer theoretical discussion of the pheno- menon, and obtained the definite integral upon which the question turns. Lord Rayleigh also considers the effect of enlarging A, the source of light; and expresses the opinion that if the enlarged source is a self-luminous body, there will be “no possibility of bringing into play the interferences upon which the advantage of a large aperture depends,” inasmuch as with a self-luminous source of light it was supposed that there can be “no phase-relation between the lights which act at different parts of the object-glass.” This view, as it appears to the present writer, is based upon an oversight. The in- terferences upon which resolution depends are of quite another kind as will be explained in a subsequent paragraph, * Communicated by the Author. On an Optical Paradow. 124 and they in no degree depend upon phase relationships between the puncta of A, the enlarged source of light. Lord Rayleigh’s experiment is one familiar to the present writer, whether made with a collimator, an intermediate lens and a telescope; or with a microscope: he prefers the latter form of the experiment, as it lends itself more conveniently to an investigation of the successive phenomena with the powerful aid of au analysis of the light into its component undulations of flat wavelets. The experiment is one of those which it has been his intention to describe and explain in the next of the series of papers on “ Flat-wavelet Resolution ”’ which is being published by the Phil. Mag. The full dis- cussion will be postponed till that paper appears ; but some of its results may in anticipation be stated here. The analysis into undulations of flat wavelets makes it easy to understand the way in which the image of L is fermed in telescope T. It is formed by the mutual interference of all tne undulations of fiat wavelets which advance in the direc- tions indicated by the so-called “rays” that pass into the telescope from the several optical puncta of the image of A produced at C by lens L. In the case where the source of light is a single punctum or physical point, this image con- sists of a distribution of light upon C which is nearly* Airy’s “spurious disk ” along with its diffraction appendages. Telescope Tis to be focussed on L, and then, in order that the observer may be able to distinguish between the parts of an object so small as lens L (and, therefore, to exhibit the outline of that object), the analysis indicates that, if A the source of light be a single luminous punctum, the aperture of the telescope-objective C must take in, in addition to the spurious disk, some part of the appendage rings; or else portions of two or more of these rings if all light from the spurious disk is excluded. To exhibit lens L in the most satisfactory way the aperture of objective C must be large enough to include the spurious disk and all its diffraction appendages that have any appre- ciable brightness. If the objective be anything smaller than * Conceive the lens L to be divided into two lenses L’ and L”, of which L’ parallelises the light from the point source A, and L" concen- trates this approximately parallel beam to a focus at C. Then the image at C would be exactly Airy’s image, if the parallelised beam were an exact beam of parallel light; but this it cannot be, since it can be shown that to form an exact parallel beam would require a small amount of other light than that from A to be incident upon lens L’. Accordingly, the light which is concentrated by L” upon C is only an approximately parallel beam of light, and the image it forms differs slightly from Airy’s image of a star. 128 Dr. G. Johnstone Stoney on this, the definition of the image of L as seen in the telescope will fall short of what the light that passes through lens L is capable of producing ; if the aperture of the objective is re- ' duced to so small a size that it admits the light of the spurious disk only and excludes the whole of the diffraction rings, then the definition will have become so bad that even the outline of L cannot be seen. Moreover, we can by this analysis ascertain the poor character of the image which results from employing in its formation the light of the spurious disk and the innermost ring only ; as also the greatly improved definition, which is obtained if the aperture of the objective admits the light of the central disk and of two rings ; and the slightly further improvement which results from still more enlarging the aperture. All these particulars are easily investigated by employing the analysis into undulations of flat wavelets. A full examination of phenomena of this kind will be given in the next of the Flat-wavelet Resolution papers. The same method of proof shows that when the source of light is enlarged there is no necessity, such as Lord Rayleigh speaks of, for any phase relation between the portions of light emanating from the several luminous puncta of the source A when enlarged. In fact, the phase relation which needs to be present is of a totally different kind. It is the phase relation which necessarily subsists between the light forming at C the spurious disk of each separate punctum of the enlarged A, and the light forming at C the annular appendages asso- ciated with that particular spurious disk. his is a phase relationship which will prevail, however unrelated may be the portions of light emanating from different puncta of A*. Accordingly, it may safely be affirmed (and is fully confirmed by experiment) that, without any loss of definition, the source of light may be a self-luminous body. It seems necessary to point this out, because an insufficient appreciation of the way in which images are produced is still prevalent. In Lord Rayleigh’s paper, and in the present paper, the simplest case, viz. where the image of a point-source A falls * This makes it plain, why when Lord Rayleigh employed as the source of light, light coming through a narrow slit situated at A, he found that the definition of L as seen in the telescope did not suffer, “the vertical parts of the circular edge (paralle! to the slit) being as well defined as the horizontal parts.’ or, in fact, the light issuing from the several puncta of the slit independently formed good images of L, and the simultaneous presence of these independent images of L, made a re- sultant brighter image and somewhat modified in other respects, but of which the definition was equally good. an Optical Paradouw. 129 centrally upon the telescope objective C, is alone considered. In order to deal adequately with what happens when the source of light though central is of sensible size, the inves- tigation needs to be extended to the case where the image of a point-source falls excentrically upon C. When this is done some instructive results emerge into view. Lord Rayleigh’s experiment, and others related to it, can be most conveniently made with the microscope, which, besides, enables us to experiment with numerical apertures up to 28 times the numerical aperture of an ordinary refracting telescope*. To see that the experiment can be made with the micro- scope—Remove lens L of the apparatus represented by the figure in the text, and replace it by two lenses L/ and L”, of which lens L’ collimates the light from A, while L’’ con- centrates the collimated beam to a focus at C. It is obviously legitimate to make this substitution. When the experiment is made with a microscope, the source A is to be light passing through a small hole (or slit) in a stop placed under the con- denser. The condenser of the microscope then takes up the duties of lens L’, and at the same time the objective of the microscope discharges the functions of the combination con- sisting of lens L" together with lens C. The image of A produced at C then becomes that image of the hole (or shit) which may be seen in the ‘‘ Concentration Image” of the _ microscope—/. é., in the image which comes into view on removing the eyepiece and looking down the microscope tube. Furthermore, when the experiment is made with the micro- scope, any desired object can be put upon the stage of the microscope and becomes the object to be resolved. So far as the writer knows, far the best object to employ is one of the bands of Grayson’s Rulings, supplemented by observa- tions upon a single pair of lines such as may here and there be seen to project from one or other end of a band. The hole in the stop may, if desired, be made to behave as a self- luminous source of light, by focussing the light of the lamp- flame or other luminary upon the stop. This will be found in no degree to impair definition, whether the hole in the stop be large or small. * The numerical aperture( z.e. the sine of half the angular aperture) of the objective of an achromatic telescope is seldom so large as 0:05 ; while the numerical apertures of dry microscope objectives and con- densers range up to 0:95, and the numerical apertures of immersion objectives and immersion condensers range up to 1°4. Phil. Mag. 8. 6. Vol. 10. No. 55. July 1905. K OM aO | XV. The Determination of the Moment of Inertia of the Magnets used in the Aleasurement of the Horizontal Com- ponent of the Earth's Field. By W. Watson, A.R.C.S., D.Se., FRS., Assistant Professor of Physics at the Royal College of Science, London”™. NE of the constants required when determining the horizontal component of the earth’s magnetic field by the ordinary method, is the moment of inertia of the magnet which is used in the vibration experiment. Nearly all the magnetometers which are used in English-speaking lands are tested at the Kew Observatory ; and the custom there has been, I believe, to determine the moment of inertia of the cylindrical brass bar supplied with each instrument by caleu- lation from its dimensions, then by measuring the period of the magnet alone and when loaded with this bar to calculate the moment of inertia of the magnet. This method pre- supposes that the density of the inertia-bar is uniform throughout. Now it is by no means easy to secure a bar of which the density is uniform throughout, and further it is difficult to test whether such uniformity has been secured. This question as to the uniformity of the inertia-bars supplied with magnetometers has been brought into some prominence lately; for the differences at first obtained when comparing the magnetometers intended for the Indian Magnetic Survey with the Kew standards were finally traced to want of uniformity in the inertia-bars. It seems to me that more reliable and uniform results would be obtained if a somewhat different procedure were adopted. Namely, to determine once for all, with very great care, the moment of inertia of a standard bar, and then to determine the moment of inertia of the bars supplied with the different magnetometers sent to be tested by comparing them experimentally with the standard bar. Even if the standard adopted were slightly wrong, so that the values given for the bars belonging to the different instruments were uniformly either too high or too low, the confusion caused would be much less than where, as at present, the values obtained may, owing to want of uniformity in the bars, be sometimes too high and sometimes too low. In the following paper is described an instrument suitable for comparing the moment of inertia of bars, together with some experiments made with a view to determining the moment of inertia of a standard bar, and an investigation on the influence of the air on the period. * Communicated by the Physical Society: read April 14, 1908. Moment of Inertia of Magnets. enn § 1. Determination of the Moment of Inertia of a Standard Bar. The instrument is shown in fig. 1. It consists of a cradle A, suspended by a stout quartz fibre (length 30 cms., diameter 0°37 mm.). The bar, B, to be tested rests on this ? WS HKU | 1 Wa / Oooo = - Seececuts | aera LL i NAN == (a) cradle while the position of the cradle is read by reflexion of a scale in the mirror C. A table, I, which can be raised or lowered by a lever, K, has a hole-slot-and-plane on its upper surface, and the three feet, F, G, H, of the cradle rest in these when the table is raised. The conical hole, O, in which the leg I rests is so placed that the cradle when supported on the table lies about half a millimetre to the left of its position when hanging free. The object of this arrangement is that K 2 132 Dr. Watson on the Determination of the the position of the bar B, with reference to the cradle, can be adjusted by means of the’ screw J, and yet, when the cradle is released, the bar may swing clear of the point of this screw. Two small weights D serve to adjust the balance and period of the cradle. The quartz fibre is soldered to a clip E which hooks on to the cradle and another clip which hooks on to the end of a rod carried by the torsion-head LL. An arm, M, attached to the torsion-head can be moved between two adjustable stops N. This arm serves to give the torsion-head a small to-and-fro motion of adjustable and fixed amount, and thus allows of the bar being set swinging. The bar, &c.,is enclosed ina wooden box the sides of which are removable. A window P allows of the mirror being seen; while a hole Q, which can be closed by a cork, serves for the removal of the bar from the cradle. The torsion-head is supported by a brass tube 30 cms. long attached to the top of the box. This brass tube is wound round with a layer of felt to reduce the temperature changes. The method adopted for adjusting the instrument is as follows. The base of the instrument having been levelled, the cradle is supported on the table with the bar in position, and a striding level is placed on the bar. By adjusting the screws G and H the bar is brought into a horizontal position, and a telescope and scale are set up at a distance of about 70 cms. from the instrument, and so adjusted that the horizontal cross wire coincides with the ends of the division-lines of the scale as seen reflected in the mirror C. The bar is then removed and the cradle released. The weights D are adjusted till the horizontal wire of the telescope again coincides with the images of the ends of the division-lines of the scale. When this adjustment is complete the line joining the V’s of the cradle will be horizontal. The bar having been placed in position, the screw J is adjusted till on releasing the cradle the hori- zontal wire of the telescope again coincides with the ends of the division-lines of the scale, and therefore the axis of the bar is horizontal. | The vertical cross wire having been brought into coin- cidence with some well-marked division of the scale, the arm M is moved from its position against one of the stops N up to the other stop and back again, thus starting the bar swinging. The two thermometers.T are read, and the period is determined by means of a chronometer in the usual manner. The fol- lowing is an example of such a determination of period, though in some of the observations, particularly those in | which the air effect was being investigated, the vibrations were allowed to continue for over 30 minutes. Moment of Inertia of Magnets. 133 A t encement 4° £1499 14°:9 Amplitude { 2 Beat leans 1° 30’ Repu nate orm (40-7 | | ie Team Times of Transit. [pesckom calms Times of Transit. Pane | | Scale moving to right. | eels: Scale moving to left. ae 'hm Ss lie nes | in Ss | hom -'s De Sa cs ms pbeeo tesG) | 12 6 toh) 20. fb Ub.46 3842: ) 12 °6 3h°7 20" 1°5 47 13°7 Oe saan AT 344 7 30:0 16 48 13:8 | Sho oie 15 48 34-5 8 36:0 15 49 14:0 9 ASA | 1:4 49 346 9 36:0 ce: 50 14:0 LO” 1S"6 16 | 50 34:6 10 3671 hed 4 0-4 Mean 20 1:50 | 4 0-4 Mean 20 1°50 1G) “26 | 16° £6 16. 15°6 | i bk? (62.362 Approximate period determined with stop-watch =3°75. Hence in 60 secs. there are 16 vibrations, and in 4 m.0‘4 5. there are 64. Thus in 16 m.1°6 s. there are 256. Hence the number of vibrations corresponding to each of the above differences is 320. Mean time for 320 vibraiions . . 20m. 1°50 s. 2 sone: Vibration. 1)! 41.01 COAT SeG. The period of the cradle alone has alse to be determined, and it will be found convenient to adjust the period by the weiyhts D to nearly one second, so that the method of co- incidence may be conveniently employed. The following table gives particulars of the different inertia- bars which have been compared. Distinguishing number. Material, &e. nes he Rolled brass. Ep eed His cs Cast silver. 2 Peete Rolled copper. Ae stays 4 Copper with 0°5 per cent. zinc. Cast. Sele AA Copper with 0-5 per cent. phosphide of tin. Cast. CS Ree eae Gun-metal. Cast. I UNE oS NG Rolled copper. Shame ees tame Rolled copper. 9. Rolled copper. RO s.r. A rolled brass bar with slightly rounded corners and gilt. _ Note.—Bars 2, 4, and 5 were made from castings prepared with very great care at the Royal Mint under the direction of Dr. Rose; and Lam much indebted to him for the trouble he has taken in the matter. The bars were turned and then ground true, while special care was taken to have the ends plane and perpendicular to the axis of the cylinder. I1n the case of bars numbers 7, 8, and 9 the ends were ground and polished to an optical surface, 134 Dr. Watson on the Determination of the which was tested by obtaining Newton’s rings between the metal surface and a piece of plane glass. The ends were slightly rounded ; but as this did not amount to more than about five half wave- lengths of sodium light, and this only near the edge, the accuracy of the measurements did not necessitate any correction being applied *. To measure the lengths of the bars two cylindrical palpers having the same diameter as the bars were prepared, one end of each being turned to a spherical surface. A fiducial line was scratched on one cylinder. These cylinders rested in a V-groove in the iron bed of a comparator fitted with micro- meter-microscopes, one palper bedding against a stop. The two palpers being placed in contact, by means of a force of 70 grams weight, the right microscope was adjusted to the fiducial mark on the left-hand palper. The bar to be mea- sured having been introduced between the palpers, which were kept pressed together by the same force as before, the left-band microscope was adjusted to the fiducial mark on the left-hand palper. The micrometers having been read, the bar was turned through 90° and the adjustment repeated. In this way four measurements were taken, each measurement consisting of four readings of the micrometers, the bar being turned through a right angle between each measurement. To obtain the distance between the micrometers a nickel steel (Invar) metre which had been calibrated at the International Bureau at Sevres was substituted for the bars, and the micro- meter-readings taken for two divisions 10 centimetres apart, care being taken not to displace either micrometer more than necessary from the position it occupied when setting on the bars. In the case of the bars with optically worked ends, the length was also measured by setting the micrometers halfway between the point of a needle and its image as seen reflected in the end surface of the bar. At first this method gave values which were consistently 0°001 centimetre lower than those obtained by the contact method. This difference was found to be due to the objectives of the microscopes not being aplanatic, for in this method only half of the objective of the microscope is used. On replacing the objectives with others which were optically much better, and taking care to focus accurately, the measurements obtained by the two methods were in exact agreement. * This question has also been tested at the National Physical Labora- tory, where they measured the lengths of the generators of two of these cylinders across two diameters, and found that the lengths were constant except at the very edge, and that there the “ rounding did not amount to more than ‘0006 cm. Moment of Inertia of Magnets. 135 The diameters were measured at three places along each bar by means of a Brown and Sharp micrometer-screw gauge whicn had been tested against the standard metre, measurements being taken along different diameters at each place. The masses were obtained by means of a Bunge balance, which reads easily to a tenth of a milligram. The method of double weighing was employed, the weights used having been calibrated and compared with a standard 100 gram weight the error of which has been determined at Sévres. Except in the case of the silver bar no correction has been applied for buoyancy, as all the weights, except the fractions of a gram, were of brass. In the following table are given the dimensions of the bars and the calculated values of the moment of inertia :— Logarithm of No. of Bar es oe. Hees Mass, the Moment ; : ; eve grams. of Inertia em. cm. = at. bbe: ip opie Ait 99755 ‘9909 65°230 2°73633 AAA ea ae 99-9811 “9974 81814 2°83525 : 4 ee eee en 9-9998 ‘YOTA 69204 276416 A ee ee acat | 10-0044 "9979 69°437 2°76602 Ute Ae eee 10-0017 ‘9985 69°391 276049 0) Sl 9-9878 -9972 68°516 2-75878 Be LGR. ae aise 3 99964 “9994 63°745 2°76099 | ol eae eer ea 9-9837 ‘9973 68-414 PT TOLLO oe ae | 99856 | ‘9976 | 68:481 2°79837 | | All the observations of period used in the comparisons of the moments of inertia of the bars were made at temperatures not greatly differing from 15°C. In order to be able to allow for the small departures from this temperature, a series of observations were made with the whole instrument heated ina well-stirred air-bath to a temperature of 30°. The change of period with change of temperature is very small, owing to the fact that the rigidity of quartz increases with rise of temperature, and thus produces the opposite effect to that due to the increase in the dimensions of the bars owing to expan- sion. In the case of the copper bars the coefficient of increase of period with temperature is 0°00004, and in the case of brass 0:000035. By means of the coefficients the observations of period recorded in the following table have been reduced to what they would have been at 15°, the actual temperatures at which they were made being included between 14° and 18°. In the case of bar 1, since the observations with this bar 136 range over a very considerable time, the dates of the various measurements of period are given to indicate the constancy which can be obtained with such a quartz-fibre suspension. Dr. Watson on the Determination of the No le No. 5. No. 9. Date Period. | 3°7726 3°7446 ooo 05) | Seopa) 23 AT PAM x03: qu 22 49 265 (03; Oss (5 48 Di ae 11 Mean... 3°7724 Ks Toy xi? 03: 38) Mean... 3°7448 2s xt OS. 12 26. x1. 03. 13 No. 6. 20 xi. O83: 14 eat: No. 10 St 70m Ii aa cara ge 36682 fy, oats (O45 in é 81 . 04, a9 83 a a Caan teat: 57460 oF Mean 36612 84 ‘ N 84 No. 7. 81 No. 2. a 31 4:0543 Sei 43 45 Mean... 3°6683 Mean... 4:0543 fs Mean... 3°7547 Cred No. 3. 1:2427 3°7672 69 5 3°7421 2 Mean... 3°7670 | a ; 24 6 No. 4. ime | sae 3:7751 | Mean... 3°7423 | Mean... 1:2425 48 - 48 Mean... 3:7749 If ¢, is the period with a bar of moment of inertia K, in the cradle, while ¢, is the period of the cradle alone, Ky being its moment of inertia, we have b ernie ty = amy | ee ¢ ne ig Bataly/ one where ¢ is a constant depending on the suspension fibre. Hence KG C bac erat bag Ag? Thus if the bars are uniform in density and diameter we Moment of Inertia of Magneis. a7 have, subject to variations due to errors of experiment, that the quotient Ky /(ty? —?,”) ought to be the same for all the bars. The following table a the value of the quotient for the different bars :-— | f | Mabes of Bae. ; = a | Difference from | ea meal. Mer 5s Se oe So Bde 45°944 + -008 rsh aa ae a Rs 47 +011 33) ee OR ot 40 + ‘004 72 Aue oi amt oe ee mA | — 015 2 ea a a oe 3l —‘005 (TE ae he Ae ras 23 —'013 (0 Cee AO ee 41 +005 inet RL eta aoe 44 +-008 ee 37 +001 | | Mean 45-936, | +-007 | | Ky , however. The mean value for gon s 45°936, Ido not, however, consider that this mean is e best value to take, as owing to the extra care taken in making the three bars numbers 7, 8, and 9, I consider it advisable to give the results with these bars treble weight. Doing this the mean becomes 45938. By means of this mean value we may calculate the moment of inertia of the standard bar No. 10. The value obtained in this way at 15° C. is 5AT-94 Owing to the fact that the rigidity of fused silica increases as the temperature rises, the period changes very little with temperature. Thus for the cradle alone the percentage increase of the period for a fall of temperature of one degree centigrade is ‘0036. Witha brass bar of the dimensions used in these experiments, the percentage increase of period for a fall of temperature of one degree is ‘0035. As long, there- fore, as care is taken to have the temperature uniform throughout the instrument, the correction for changes of temperature can be made without difficulty. In order to obtain some idea as to the accuracy with which the moments of inertia of bars may be compared by the method employed, we may take the differences from the respective means of the determinations of period given on page 136, taken irrespective of sign. The number obtained isQ°00014. Thiscorrespondstoa mean difference fromthe mean of 0:0037 per cent. This value, if we neglect the error 138 Dr. Watson on the Determination of the produced by an erroneous value obtained for the period of the cradle, which error can easily be made negligible, corresponds to a mean error of ‘018 per cent. in the ratio of the moments of inertia. To test the question as to whether the vibrations were strictly isochronous, that is whether the period was independent of the amplitude, a series of measurements were made with different initial amplitudes, and the results are shown in the following table :-— Amplitude. eet ode | Period. | Atcommencement. | At end. 14 94 7 29 | 3-6616 12 32 4 15 3°6613 4 5d 2 25 36611 2 44 120 36611 It would thus appear that with an initial amplitude less than 5° the period is not, within the limits of the accuracy of the observations, feed by the variation in the amplitude. This point was also brought out because in many of the observa- tions of period startiny, with an initial amplitude of between 4° and 5° one set of period observations were made, and then, without altering the amplitude of the vibrations, another set was made. The values obtained for the periods were, how- ever, as often larger with the smaller amplitude as smaller. As a further precaution the initial amplitude was in all cases taken as about the same. > ae : K i When obtaining the expression for ——1_. above it has been = “ lean t0 assumed that the torsional rigidity of the suspension fibre is the same whether the cradle is empty or loaded with one of the bars. ‘To test whether this assumption is allowable, a set of measurements were made in which the period of the cradle alone was measured. Then its period when loaded with each of two bars separately, and finally when loaded with the two bars*. The results obtained in the case of two fibres are shown in the following table :— * The cradle used differed slightly from that shown in fig. 1, in that a second pair of V’s were provided to allow of two bars being suspended simultaneously. Moment of Inertia of Magnets. 139 Weight of = Value of | | Suspended System_| Bony | C. | Peale withys (225 2.0c4oedend! 27 grms. 12426 | é Peradie+-No..1 +... ¢ LO," Now 3mnV’=heating effect of « particles expelled per second from radium C. =3°'6 x 10° ergs. Substituting again the value of the ionic charge e and the 2 mV" =1-03 x 10". e In this result the value of e has not been assumed, since value of n, 2 e 7 n =-, where i was the measured current due to the charge e carried by the a rays. We have previously seen that ee —4+(0) x 10°. From these two equations, it is seen that V=2°'6 x 10° cms. per second and _ e/m=6'5 x 10? electromagnetic units. These values are in surprisingly good agreement with those previously deduced by Des Coudres, and myself, from the amount of deviation of the rays in passing through a magnetic and electric field. Des Coudres found that V=1-6 x 10° and ema 1)? while’ 1. found - that “V=2°5 x 10°, and e/m=6 x 10°. While the application of the heating effect of radium to determine the values of the constants of the @ rays is of interest, I do not think that at present much weight can be given to the results, on account of the uncertainty attaching to the value of n, which is very difficult to measure with accuracy. When the experiments at present in progress on the electric deflexion of the « rays from radium C are completed, it is hoped that the vaiue of e/m will be obtained with sufficient accuracy to settle definitely the important question, whether the « particle is a projected helium atom. 170 Prof. E. Rutherford on some Decrease of Velocity of the « particle in passing through matter. Some experiments were made to determine the relative velocity of the « particles from radium C after passing through known thicknesses of aluminium. The apparatus shown in fig. 1 was employed, and successive layers of aluminium-foil of thickness ‘00031 cm. were placed over the active wire. The amount of deviation of the rays is inversely proportional to their velocity after their passage through the screen. The impressions obtained on the plate were all clear and distinct, and the breadth of the band was very nearly the same in all cases. This shows that the rays after traversing a metal screen were still homogeneous, although their velocity had been reduced. A clear photographic impression was obtained with twelve layers of foil over the wire, but it was not found possible to obtain any effect through 13 layers. This result shows that the photographic action, like the ionizing action of the & rays, ceases very abruptly. The photographic effect of the « rays ceases after they have passed througha thickness of aluminium- foil greater than ‘0037 em. and less than ‘0040 em. The results obtained are shown in the following table. Assuming that the value of e/m is constant, the third column gives the velocity of the « particles after passing through the aluminium. This is expressed in terms of Vo, the velocity of the « particles when the screens are removed. Number of layers Distance 2d Velocity of of aluminium-foil. between bands. # particle. | 0) 1°46 mms. 1:00 Vo 5 eae 35 e 8 eon. 71603) 10 2-01, eye 12 229 | ‘he The velocity of the « particle is thus reduced only 36 per cent. after passing through 12 layers of aluminium. _ Since the « particle produces approximately the same number of ions per cm. of path in air over its whole range, the simplest assumption to make is that the energy of the a particle is diminished by a constant amount in passing through each layer of aluminium-foil. After passing through 12 layers, the kinetic energy of the « particle is reduced to 41 per cent. of the maximum. Lach layer of foil thus absorbs about 4°9 per cent. of the maximum energy. The observed kinetic energy of the @ particle after passing through different thicknesses of aluminium-foil, and the value Properties of the a Rays from Radium. 7a. calculated on the above assumptions, are shown in the following table. | Number of layers Observed Calculated of aluminium foil. energy. energy. 0 100 LOO a) D8 61 | 10 D3 d1 12 | 41 4] The experimental and calculated values agree within the limit of experimental error. We may thus conclude, as a first approximation, that the same proportion of the total energy is abstracted from the « particles in passing through successive layers of aluminium-foil. Velocity of the a Rays from other products. Knowing the velocity of the « particle expelled from radium C, the velocity of the « particle emitted from the other radioactive products can at once be deduced, provided the maximum range of its ionization in air is known. This velocity can be determined from the data already given of the decrease of the velocity of the « particle in passing through screens of aluminium-foil. The ionizing action of the « rays ceases after passing through 12°5 layers of foil, which is equivalent to a thickness of 6°7 cms. of air. Each layer of foil corresponds to a depth of 0°54 cm. of air. The velocity, for example, of the rays from radium itself which have a range of 3 cms. in air, that is, which would be stopped by 5°5 thickness of foil, corresponds to the velocity of the rays from radium C which have traversed 12°5—5°5 =7 layers of foil. For convenience, the velocity of the a particle from different products which have ranges in air from 1 to 6°7 cms. are given in terms of Vo, the velocity of the « particle from radium C. Maximum range of the Maximum velocity ot # particles in air. e particle. 1 efile 2 ‘165, 3 “Bova 6 4 Biv. 5 92 | 6 ‘96, 6:7 OU pee sa) o ; > E+ = | gs. oOo an = 5 O > oS Hy | 2S. mrsieey D4) Sak ES) O -[| so ea) (02) 22 on : ° Beet my s n os. of Ficures in € OS of Pizures in Column 3 3 requencie s of string aes for Columns 2 & 3 § s. of os of Figures in Column 2 cures in Column 2 LR 83 2) £ 30 a 4 . Eo lo] ay So a Ss a} = 23 5 ° Lol LI] 4 o2 (e) Ee (e) rete w > aa a s a a ca oe n a . 5 4 Zz Soy = mu & hfe P v 3 HI Suc . = S fe) caecc ; =O €.2 4 BS & cal i) cd jon of Figures in Column os. of Figures in Column 1 a | + i reque ‘lly responding to e') Belly responding to note , | 7 . . wae ie : lucked at 1, String at frequency 153, Belly i g Bowed at .1_ Bowed at 1 Bowed at 1 Two under like conditions Two under identical conditions Bowed at 3: bad quality. Bowed at 4: good quality. Plucke 1 eating from belly eee (aaGn vountiedr eh af frequency aa from 10" iwi > but showing different amplitudes. Ss second partial (306), mug hana) Gharmoniauametine! INDEXED THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAT, OF SCIENCE.—_ 4 at A r~ | 4 Ve ey a (SIXTH SERIES.) - OFF \ AUGUST 19056 ae eR LIE —_ XXV. Charge carried by the a and B Rays of Radium. By i E. Ruruerrorp, /.R.S., Macdonald Professor of Physics, Me Gill University, Montreal*. 1 the Bakerian Lecture (Phil. Trans. A 204. pp. 169-219, 1904), I gave an account of some experiments made in order to measure the charge carried by the a rays, with a view Of determining the number of « particles shot out per second from a given mass of radium. The method employed is clearly shown in fig. 1. A known small quantity of pure Fig. 1. AOL cee — — ic Pump FF Ta NG . MOOQNNQOON radium bromide was dissolved in water and the solution spread uniformly on a metal plate A, and then evaporated to dryness. The process of solution and evaporation liberates the radium emanation and about three hours afterwards _ * Communicated by the Author. A briefaccount of the results included in this paper was published in a letter to ‘ Nature,’ March 2, 1905. pei wag. Sm. Vol. 10. No. 56, Aug. 1905. O ‘ — 194 Prof. E. Rutherford on the Charge the excited activity practically disappears, and the activity, measured by the @ rays, is reduced to one quarter of its equilibrium value. Experiments were made with the radium as nearly as possible at this minimum activity in order to avoid possible complications due to the presence of @ rays. The latter have almost completely disappeared about three hours after the emanation is removed. The @ activity is gradually recovered, rising to half its maximum value in about four days. A second insulated plate B was placed parallel to the lower plate and a few millimetres distant from it. The plates were insulated in a brass vessel which could be exhausted to a high vacuum by means of a mercury pump. ‘The lower plate A was connected with one pole of a battery, the other pole of which was connected to earth. The current passing between the two plates was measured by a Dolezalek electro- meter with a suitable capacity in parallel. | If the a rays carry with them a positive charge, this will — be communicated to the upper plate in which they are absorbed. At ordinary pressures of the air, however, the amount of ionization produced by the a particles in their passage through the gas is so large that this charge is rapidly dissipated. lei is necessary to work ata very low pressure of the gas, in order to reduce the ionization to a very small value. Under such conditions, it was to be expected that the upper plate would acquire a positive charge. A very different result, however, was observed : on diminishing the pressure of the gas, the current between the plates decreased directly as the pressure, but finally reached a limiting value, corresponding to about 1/1000 of the value at atmospheric pressure. This current was about the same whether the lower plate was charged positively or negatively, and, although an extremely high vacuum was produced, it was not found possible to further reduce its value. This minimum current was not much altered when hy Thoret was present in the vessel instead of air. No certain evidence that the « particles carried a charge could be obtained. It was suggested that the failure to. detect this charge might be due to the presence of a number of slow moving ” electr ons, liberated from the plates by the action of the rays. The following explanation (loc. cit.) was given :-— “The apparent absence of charge on the a particles would be explained if an equal number of negatively charged particles, or electrons, were expelled at the same time with a slow v locity. If the electrons had about the same penetrating power as the @ particles, it would be difficult to detect. their: carried by the 2 and B Rays of Radium. 195 presence by the electric method, as the ionization produced by the « particles would probably mask that produced by the electrons. The electron should be readily deflected in a magnetic field, and experiments are at present in progress to examine whether the « rays show any trace of positive charge when the rays are exposed to a strong magnetic field.” If a strong magnetic field is applied parallel to the plane of the plates, any slow moving electrons, which escape from the plates, will describe curved paths and return to the plates from which they set out. Owing to work in other directions, experiments of this character were not begun till November 1904. The apparatus of fig. 1 was placed between the pole-pieces of a large electromagnet, when a striking alteration of the values of the current between the two plates was observed. The currents in both directions were much reduced in value, and the upper plate was found to gain a positive charge, whether the lower plate was charged positively or negatively. While these experiments were in progress, an abstract of a paper by Professor J. J. Thomson (Proc. Camb. Phil. Soc. Noy. 14, 1904) appeared in ‘ Nature’ (Dec. 15, 1904). In this an account was given of some experiments made with a view of detecting the positive charge carried by the « rays. A plate of radio-tellurium, which emits only a rays, was used. It was found that a number of slow moving electrons were emitted from the active plate, which could readily be bent by a magnetic field. I did not receive a copy of the paper itself until my experiments were com- pleted, and was not aware until after a publication of my results in ‘ Nature’ (March 2, 1905) that Prot. Thomson had previously succeeded in detecting the positive charge carried by the @ rays. As the method employed by J. J. Thomson is especially well suited to show the presence of the electrons expelled with the a particles, a brief account will be given of his experiments. A plate of radio-tellurium was placed in a vacuum-tube 3 cms, away from a metal plate connected with a gold-leaf electroscope. Whena very good vacuum was obtained, the electroscope was observed to leak very rapidly if positively charged, and very slowly if negatively. The positive leak was at least 100 times that of the negative. This result indicated that the plate of radio-tellurium expelled a number of slow moving electrons, which gave up their charge to the electroscope. This was confirmed by placing the apparatus in a strong magnetic field. The positive leak was almost stopped, showing that the electrons had been bent away by the action of the magnetic field. The small negative O 2 ‘196 Prof. E. Rutherford on the Charge leak without a magnetic field shows that the electrons are projected with such slight velocity that they cannot travel against the electric eld, Pui later experiment, where the plates were closer together, it was found that the electro- scope gained a positive charge in a strong magnetic field, proving that the a rays carried a positive charge. The experimental method used by the writer was not so much for the purpose of detecting the charge carried by the @ rays, as to measure this charge and so deduce the number of @ particles expelled from a known quantity of radium. The use of radio-tellurium as u source of a rays is very advantageous, as the @ rays are altogether absent. It has been shown, however, that in the case of radium the disturb- ance due to the 8 rays can be avoided by using radium at its minimum activity. An account will now be given of the details of the experi- ments. 0°484 milligram of radium bromide was taken, dissolved in water, and the solution evaporated uniformly on a polished aluminium plate, about 20 sq. ems. in area. This amount of radium bromide was not directiy weighed, but determined by comparison of the y ray effect in an electroscope with that produced by 23°7 milligrams of radium bromide. The latter had previously been used in experiments to deter- mine the heating effect of radium, and gave out heat at a slightly greater rate than 100 gram-calories per gram per hour. The radium bromide was thus probably pure. Assuming that the radium was uniformly distributed on the plate, the weight of radium bromide per sq. cm. of surface was 2°-4x10-° grams. This film of radium was so thin that only a very small fraction of the @ particles shot out from the surface was absorbed in the radium itself. This is seen to be the case, when it is remembered that half of the a particles emitted by radium are stopped by about ‘0004 cm. of aluminium, that is, by a weight of aluminium per unit area of about -001 gram. Assuming that the absorption is proportional to density, only a few per cent. of the rays can have been absorbed by the radium itself. The saturation current due to this deposit of radium at its minimum activity was measured between plates 3°5 cms. apart by means of a high-resistance galvanometer. The current observed was 8°4 x 10~-° amperes. A second set of experiments were made with a glass instead of an aluminium plate. The deposit of radium was covered with a layer of aluminium-foil ‘00034 em. thick. The saturation current, observed as in the case of the aluminium plate, corresponded to 3°3 x 10~-§ amperes. From this, it was concluded that the number of « particles issuing through the carried by the aand 8 Rays of Radium. 197 aluminium-foil corresponded to about 0°19 milligram of radium bromide. It was thought possible that some of the radium might be absorbed in the pores of the aluminium plate, and it was for this reason that a set of experiments was made with a glass plate. The agreement of the results, however, obtained with the two plates indicate that such an effect, if it exists, is small. One of these radium-coated plates was placed in the vyacuum-vessel D in the position of the plate A. With the view of reducing as far as possible the number of electrons emitted by the impact of the « particles on the absorbing plate, the 2 particles were shot into a rectangular copper vessel BC, the bottom of which was covered with a layer of aluminium-foil -00034 em. in thickness. Most of the a particles passed through this aluminium-foil, and were stopped by the metal walls of the vessel. The brass vessel D was exhausted by means of a mercury pump to a very low pressure. In later experiments, it was found that a low vacuum could be more easily produced by Dewar’s method of absorption of the residual gas by charcoal. A side tube, containing cocoanut charcoal immersed in liquid air, was connected to the vessel D. ‘The air was first partially exhausted by means of a mercury pump, the cocoa- nut charcoal being heated to drive off ‘the absorbed g gases. This method was found to be very convenient to keep a “good vacuum without the necessity of continuous pumping. The apparatus was placed between the pole-pieces of a large electro-magnet, so that the field was parallel to the plane of the plates AB. The followi ing table gives the numbers obtained for the current, when the lower plate was charged positively or negatively, and when the magnetic field was on or off :— | Current in arbitrary units. Potential of lower — Peet —_— —_ —_ plate. _ Without magnetic With magnetic | field. field. | 0 ORB bees wed + 56 + 2 volts | 20 | +46 | .o9 ont | 25 Pie tials a alae, / | A, -++ 28 Saal | Be Ba | orgs f “A | oe: ee alae ees | =e — 40 Riche tc | +84 | a5 477) | mtd - at i 10 )5) | — 84 | 5-2 The above numbers refer to the radium-coated glass plate. 198 Prof. E. Rutherford on the Charge When once the magnetic field had attained a certain value a considerable increase in its strength did not affect the magnitude of the current observed. This showed that the field was strong enough to bend back all the electrons and to prevent them reaching the opposite plate. The field was not sufficiently strong to appreciably deflect the a@ particles themselves. The magnitude of the charge carried by the @ particles can readily be deduced. Let 7 be the current due to the ioni- zation of the residual gas between the plates. A very small H.M.F. is required to produce saturation at such a low pressure, and this current should be equal in magnitude but opposite in sign when the potential is reversed. Let i i; be the charge per second communicated to the upper electrode when the ier plate is charged positively, and 2, the value when charged negatively. Let n be the number of « particles, carrying a “char ge e, projected per second into the upper plate. ‘Then j=l +ne Adding eet te a= : 2 Now in she third column of the table above, it is seen that yt? a be ie ? are 1395, -41, 435 for 2, 4, andueawolte the values the respectively. The numbers are thus in fairly good agree- ment. The charge communicated to the upper ‘plate when the lower plate is earthed, is, as we should expect, slightly less than that calculated from the mean of the two currents, since the ionization of the residual gas tends to dissipate it as soon as the potential of the upper plates commences to rise. It will be observed that the current between the plates before a magnetic field was applied was greater when the lower plate was negative, and for the potential difference of 4 volts was about 9 times the current due to the « particles alone. A very different result, however, was observed when the radium-coated aluminium plate was used. In this case, the film of radium was not covered with aluminium-toil. Voltage. Without magnetic field. With inagnetic field. +8 volts. GO 1-23.0> —3s ,, 14-0 “03 carried by the a and B Rays of Radium. 199 The negative current was about twice as great as the positive, and over twenty times as great as the current carried by the particles alone. A very similar result was observed when the upper electrode BC was replaced by a thick brass plate, fixed at a distance of about 2 mms. from the lower plate. We must thus conclude that the escape of electrons from the lower electrode was considerably reduced by placing a layer of aluminium-toil over the radium. ‘The results obtained in the different experiments were fairly concordant. The current due to the charge carried by the @ particles was not small, and the electrometer-needle moved at a con- venient rate when a capacity of °0024 microfarad was added to the system. For example, using the aluminium plate as a source of rays, the mean value of ne was found to be 25 x10- ampere. Assuming that each @ particle carries the same charge as an ion, viz. 34x 10- electrostatic units, or 1:13 x10—- coulombs, the number of « particles projected per second into the upper plate was 8:7x10% This is the number from -484 milligram of radium bromide ; and remembering that half of the « particles projected from the radium are absorbed in the lower plate, it can be readily deduced that the total number of a particles expelled per second from 1 gram of radium bromide at ?ts minimum activity is 3°6 x 10". The corresponding number obtained for the *19 milligram of radium bromide on a glass plate was 3°36 x 101°, and for the -484 milligram, when the upper plate B was of brass, 3°96 x10!°. The mean of these three determinations is 3°6 x 102°, and this may be taken as the probable value. Assuming the composition of the compound employed as RaBr,, it follows that the total number of « particles expelled per second from 1 gram of radium at its minimum activity ts 62x10". Now the @ ray activity of radium in radio- active equilibrium is four times this minimum value, and includes three products, viz. the emanation, radium A, and radium C, which emit a2 rays. We may thus conclude that the total number of « particles expelled per second from 1 gram of radium in radioactive equilibrium is four times the number at its minimum activity, and is equal to 2°5 x10". This number is in good agreement with the number 2 x 10", previously deduced from direct data, based on the heating effect of radium and the observed volume of the emanation *. I think these experiments show conclusively that the erays from radium do carry a positive charge. We have seen that * Rutherford (loc. cit.). 200 Prof. E. Rutherford on the Charge the numbers obtained are in good agreement, although the magnitude of the current due to the electrons varied consi- derably in the different experiments. The fact that the current either in the positive or negative direction was independent over a wide range of the strength of the magnetic field, when once a certain small value of the magnetic field had been reached, shows that the strength of the field was sufficient to bend back all the slow-moving electrons emitted by the plates. The failure of the earlier exper iments to detect the charge carried by the @ rays led to the suggestion that the @ particle was uncharged at the moment of “expulsion, but gained a positive charge i in its passage through the gas. It is probable 5 that the a particle, if initially uncharg ‘ed, would lose a negative electron by collision with the gas molecules, and so retain a positive charge. This point came up in the discussion at the close of the Bakerian Lecture (loc. cit.) last year, and was referred to by me in the paper “ Present Problems of Radio- activity,” read before the Internatianal Con egress of Arts and Sciences, St. Louis, 1904. The same suggestion was also made by Brage”. There does. not, however, now seem any doubt that the a particle is char ved at the moment of its expulsion. The pressure of the gas in the experiments was so low that oniy a small fraction of the a particles could come into collision with the gas molecules. This is brought out by the com- parison of ‘the values of the positive and negative currents in a strong magnetic field. The difference between the currents. in the two directions is probably due to the small ionization produced in the residual gas by the passage of the particles through it. In some cases the value of this ionization current was not more than one-tenth of the current due to the charge on the @ particles alone. This indicates that only a small fraction of the @ particles come into collision with gas molecules. On the other hand, the magnitude of the char: ge carried by the « rays was independent of the state of the vacuum over a considerable range, showing that the residual gas had no effect in altering the number of charged @ particles absorbed in the upper plate. We may thus conclude that the @ particles are positively charged at the moment of their release from the radium ae and, remembering that the film of radium used in the experiments was very thin, there is no obvious reason for supposing that they are. not char ged at the moment of their expulsion from the radium atoms. * Phil. Mae. Dec. 1904. carried by the a and B Rays of Radium. 201 Origin of the Slow-Speed Hlectrons. We have seen that J.J. Thomson has shown that a number oh slow-speed electrons are emitted with the @ particles from i plate of radio-tellurium. The experiments described above ors that this is equally the case with radium. The mag- nitude of the current due to these electrons is sufficient to completely mask the effect due to the charge carried by the a particles, and in some cases is twenty times as great. The question now arises, whether these electrons are projected from the radioactive matter itself, or are emittted from the plates on which the « particles impinge. The fact that the current without a magnetic fieid is greater when the lower plate is negative than Gehon it is positive shows that a greater number of electrons are emitted from the lower plate. It the electrons were only emitted from the lower plate, the positive current should greatly exceed the negative. The results indicate that these electrons arise from both the upper and lower plate, but to a greater extent from the latter. This is borne out by the experiments when the radium film de- posited on the lass plate is covered with thin aluminium-toil. The negative current is still the greater, but the difference is not nearly so marked. Since he Sica are probably not projected with sufficient velocity to pass through even one thickness of aluminium-foil, it seems probable that the electrons liberated from the radium deol and the glass plate would be absorbed in the aluminium-foil. The experiments as a whole indicate that the electrons escape both from the radium piate and from the surface in which they are absorbed. It seems probable that these electrons constitute a type of secondary radiation which results from the impact of the’a particles on matter. Since half the « particles emitted from the radium are projected into the lower plate and the other half are pro- jected upwards, it is to be expected that more would escape from the lower than from the upper plate. It is difficult to settle whether the radium itself emits any of these slow-speed electrons at the moment of expulsion of the « particle. There is no reason, however, to doubt that such electrons would be Fhemated by the bombardment of the radium by the a particles projected from its own mass. The existence of this type of secondary radiation, set up — when the « particles pass through matter, readily explains some resuits obtained by Mme. Curie in her experiments on the absorption of the # rays from polonium. The ioni- zation current between two parallel plates was compared when two screens of different materials, placed over the 202 Prof. E. Rutherford on the Charge polonium, were interchanged. For example, with screens of aluminium and cardboard, the current was greater when the aluminium was uppermost. Similar results were obtained with other materials. These results indicate that different amounts of secondary radiations—probably in the form of the slow-speed electrons in question—were produced at the surface of the matter through which the rays passed. Charge carried by the B Rays. It is of importance to determine the total number of 8 particles emitted from one gram of radium in radioactive equilibrium, as, theoretically, it is to be expected that this number should bear a definite relation to the total number of a particles expelled. Now radium in radioactive equilibrium contains four substances, viz., radium itself, the emanation, radium A, and radium ©, which emit a2 particles. On the other hand, @ particles are only expelled from one product, radium ©, These substances are successive products of radium, and, when equilibrium is reached, the same number of atoms of each break up per second. If the disintegration of the atom of each product is accompanied by the expulsion of one a particle and the case of radium C also of one @ particle, the number of « particles emitted from radium in radioactive equilibrium will be four times the number of @ particles. The number of 8 particles from radium in equilibrium will thus be equal to the number of « particles expelled at its minimum activity, when the emanation and its turther products are absent. Some experiments have been made by Wien™* to deter- mine the number of # particles expelled from a known quantity of radium. About 4 milligrams of radium bromide were enclosed in a platinum cylinder, which was insulated in a larger tube, and the air exhausted. The platinum cylinder was found to gain a positive charge, since the @ particles, some of which were projected through the cylinder, carried with them a negative charge. The rate of escape of electricit from the platinum cylinder corresponded to 2°91 x 107” ampere. If each £ particle carries the observed ionic charge of 1:13 x 10-1, this corresponds to an escape of 2°66 x 10 8 particles per second. From one gram of radium, the corre- sponding number would be 1-14 x 10”. It is known from experiments upon the absorption of the 8 rays from radium that some of the f particles are easily absorbed in passing through a small thickness of matter, o The above estimate is for this reason far too small. * Wien, Physik. Zeit. iv. p. 624 (1903). carried by the a and B Rays of Radium. 203 In order to eliminate as far as possible the error due to absorption of the 8 rays in the radium itself and the envelope containing it, I employed a different method. Instead of using the radium compound itself, a body made active by exposure in the eee of the radium emanation was used asa source of Brays. A lead cylinder 4cms. long and 4 mms in diameter was made the negative electrode in a vessel con- taining a large quantity of radium emanation. After about three hours exposure, tlie excited activity reaches a maximum. The lead rod was then removed, and the intensity of the v rays from it was compared directly by means of an electro- scope with that due to a known weight of pure radium bromide ~ in radioactive equilibrium. The y rays, rather than the 8 rays, were chosen as a means of comparison, as the ab- sorption of the y rays in the lead rod or the radium envelope is very small. Suppose, for example, that the y ray effect from the active deposit in the lead rod was equivalent to m vailligrams of radium bromide. Now the Band y¥ rays from the radium or tle active deposit on the rod arise only from the one product radium C. Since the 8 and y¥ rays always oceur together and in the same proportion, the total number of 8 particles emitted by the lead rod is equivalent to the number emitted by m milligrams of radium bromide. Since the active deposit on the rod is extremely thin, half of the & rays projected from it escape without absorption. The stoppage of the @ particles by the active matter itself, such as would occur if radium bromide were directly used, is thus avoided. Immediately after testing, the lead cylinder was wrapped with a thickness of aluminium-foil just sufficient to com- pletely absorb the a rays. It was found experimentally that the « rays were completely stopped by 13 layers of foil, each of thickness ‘00031 cms. 17 layers of foil, that is a thick- ness of aluminium of -0053 cm. were added in all. This ensured that the absorption of the @ particles in the aluminium screen Was a minimum, consistent with complete absorption of the a rays. The lead rod was made the central electrode A in the apparatus of fig. 2. The outer cylinder B was con- nected with one pole of a battery, the other pole of which was earthed, and the central electrode with a Dolezalek elec- trometer, using a suitable capacity in parallel. The air was exhausted as rapidly as possible, and measurements were begun usually about 20 minutes after the removal of the active rod from the emanation. The potential of the external cylinder was alternately re- versed, and the currents measured. As we have seen in the 204. Prof. E. Rutherford on the Charge experiments on the charge carried by the @ rays, half the algebraic sum of the currents observed with reversal of the Fig. 2. An en Hanvy7 <= potential represents the value ne, where n is the number of & particles escaping from the central electrode per second, and ¢ the charge on each particle. The value of ne was found to decrease with the time at the same rate as the rod lost its 8 activity, measured in the usual way by an electroscope. Knowing the curve representing the variation of the @ ray activity with time, the value of n e at any time can be expressed in terms of the value of ne at the moment of removal of the rod from the emanation. The following numbers illustrate the experimental method. At the moment of removal, the y ray activity of the rod corresponded to 4°20 milligrams of radium bromide. The value of ne was determined after the rod had been removed 33 minutes. From comparison with the known curve, the 8 ray activity had during that time fallen to 74 per cent. of the initial value. The value of ne, reduced to the initial value, was found to be 1:05x 10-1! ampere. Taking e¢ as 1°13 x 10—" coulomb, the value of n is thus 9°3 x 10%. This is the number corresponding to 4:2 milligrams of radium bromide. Remembering that half of the @ particles are projected into the lead which absorbs most of them, it can carried by the «and B Rays of Radium. 205 readily be calculated that one gram of radium in radioactive equilibrium emits 7:6 x 10" 6 particles per second. A second series of experiments made under different con- ditions gave a value of 7°0 x 10". Taking the mean of these two values, we may thus conclude that the total number of B particles expelled from one gram of radium per second ts 7°38 X 1019, The total number of @ particles expelled per second from one gram of radium at its minimum activity has been shown to be 6°2 x10". The approximate agreement between these numbers is a strong indication of the correctness of the theoretical views, previously discussed. It is to be expected that the number of 8 particles, deduced in this way, should be somewhat greater than the number of «@ particles, for the B particles give rise to a secondary radiation, consisting also of negatively charged particles moving at a high speed. These secondary 8 particles, arising from the impact of the @ particles.on the lead, will pass through the aluminium screen, and add their effect to those directly shot out. For this reason, probably, the experimental number is somewhat too large. The results, however, indicate that four @ particles are expelled from radium in radioactive equilibrium for each @ particle, and thus confirm the theory of successive changes. Deductions rom the Results. The determination of the total number of « particles ex- pelled per second from one gram of radium is of great value, for by its means we are enabled to directly deduce the magnitude of other important physical constants in radicactivity. The methods of calculation of some of these quantities will now be briefly given. Life of Radium.—We have seen that one gram of radium at its minimum activity expels 6°2 x 10!° e particles per second. It seems probable that only one « particle is expelled during the disintegration of the radium atom, so that 6°2 x 10! atoms of radium break up per second per gram. The number per gram per year is 1°95x 10°. It has been experimentally deduced that one cubic centimetre of hydrogen at standard pressure and temperature contains 3°6x10" molecules. Taking the atomic weight of radium as 225, it follows that one gram of radium contains 3°6 x 1074 atoms of radium. The fraction X of the radium atoms which break up per year is thus Ja x 20'S “3-6x 102. or OE x LO *. 206 Prof. E. Rutherford on the Charge Thus in a gram of radium about half a milligram disintegrates per year. ” Now it is probable that, as in every other radio- active product, the number of atoms of radium which break up is always proportional to the number present. Thus if n is the number present after an interval t, and m the initial n ie number, then — =e“. The value of 2X is 5-4 x 10 (year)—}, 2o so that the time required for the radium to be half trans- formed is about 1280 years. The average life of radium is thus 1850 years. Volume of the Emanation.—Hach atom of radium in break- ing up is supposed to produce one atom of emanation. If g, is the number of atoms of emanation produced per second per gram, the total number of atoms Ny present when radio- active equilibrium is reached is given by No= = , where 2X is the radioactive constant of the emanation. Now gy=6'2 x 10%, and 1/A=480000, thus Ny=3°0 x 107°. But one cubic centimetre of any gas contains 3°6 x 10” molecules. Thus the maximum poles of the emanation to be obtained from one gram of radium in radioactive equili- spl UUs brium is equal to ————— c.c.=0°83 cubic millimetres. 2 3°6 x 10 Now Ramsay and Soddy found experimentally that the volume of emanation to be obtained from one gram of radium was about one cubic millimetre. The numbers are thus in good agreement. Heating Effect of Radium.—Rutherford and Barnes have shown that the heating effect of radium and of its various products is due to the bombardment of the a particles expelled from them. From measurements of the constants of the a particle, I deduced that its kinetic energy was about De) DGLOr ere. Radium in radioactive equilibrium emits 2°5 x 10" & particles per second per gram. ‘The emission of energy in the form of kinetic energy of the @ particles thus corresponds to 126 oram-calories per gram per hour. This number is in fairly good agreement with the value 100, first determined experimentally by Curie and Laborde. If the heating effect of radium is assumed to be a measure of the kinetic energy of the @ particles, we may conversely deduce that the average energy of the « particle emitted from radium and its products is 4°7 x 10~® erg. Number of Ions produced by an « particle-—Knowing the number of @ particles expelled per second from a thin film carried by the « and B Rays of Radium. 207 of radium, and the saturation current produced when the radiation is all absorbed in the gas, we can at once deduce the number of ions produced in air at atmospheric pressure and temperature by the passage of a single « particle through it. A weight of -484 milligram of radium bromide spread in the form of a thin film on an aluminium plate emitted 8°7 x 10° a particles into the gas per second. The saturation current observed between parallel plates at sufficient distance apart to absorb most of the rays was 84x 107% ampere. ‘Taking the charge on an ion as 1:13 x 10—® coulomb, this current corresponds to a production of 7°5x 10" ions per second in the gas. But this number was produced by 8-7 x 10° particles. The average number of ions produced by each a particle, expelled from radium itself, is thus 86000. Now Bragg has shown that an «@ particle passing through air pro- duces nearly the same number of ions per unit length of its path, and the ionization ceases fairly abruptly. The range in air for the 2 particles from radium at its minimum activity is about 3:0 ems. The number of ions produced per cm. of path in air at normal pressure and temperature is thus 29000. The number per cm. of path at a pressure of one millimetre of mercury would be 38. Townsend found that the maximum number of ions pro- duced by an electron per cm. of path at a pressure of one mm. of mercury was 21. At this maximum it was deduced that each collision of the electron with the molecules in its path resulted in the production of ions. Since the @ particle pro- duces 38 ions under the same conditions, we may conclude that an « particle is nearly twice as efficient an ionizer as the electron at its maximum efticiency. Such a result indicates that the a particle has a somewhat larger sphere of action than the electron, and is able to ionize about two molecules for the electron’s one. This is not unexpected, since the a particle is of atomic dimension, while that of the electron is small compared with an atom. Energy requred to produce an Ion.—A deduction of the average energy required to produce an ion by collision of the a particle with the gas molecules can be made, if the range of velocity, over “which the a particles ionize the gas, is determined. I have shown in my paper* “ Some Properties of the 2 Rays from Radium,” that the @ rays, emitted by a thin film of radium at its minimum activity, are initially projected with a velocity 88 v, where’ vw is the initial velocity of projection of the a particles from radium C. The « particles cease to ionize the gas when the velocity falls * Phil. Mae. July 1905. 208 Dr. Fleming: Ratio between Mean Spherical and to 64 v). From this it can at once be deduced that °48 of the total energy of the @ particle, shot out by radium itself, is absorbed when it ceases to ionize the gas. Now it can be calculated from the heating effect of radium at its minimum activity—25 gram-calories per hour per gram— that the kinetic energy of the @ particle is 4°7x 10-° erg. The amount of energy absorbed when the a@ particles just cease to ionize the gas is 2°3xX10~-® erg. Assuming that this energy is used up in ionization, and remembering that the a particle from radium itself produces 86,000 ions, the average energy required to produce an ion is 2°7 x 107!' erg. This is equivalent to the energy acquired by an ion moving freely between two points differing in potential by 24 volts. McGill University, Montreal, May 1, 1905. XXXVI. Onthe Ratio between the Mean Spherical and the Mean Horizontal Candle-Power of Incandescent [lectric Lamps. By J. A. Foemine, WA. D.8Se., FS., Professonioy Hlectrical Engineering in University College, London*, A PAPER was read before the Physical Society ‘on é November 11th, 1904+, by Mr. G. B. Dyke, B.Sc., in which, amongst other matters, he gave the results of numerous measurements made in the Pender Electrical Laboratory of University College, London, of the ratio of the mean spherical candle-power of incandescent electric lamps to the mean horizontal candle-power, taken when the lamp was rotating round a vertical axis. In all cases the ratio of the mean spherical to mean horizontal candle-power ‘was experimentally found to be a number near to 0°78 for about nine different types ot electric glow-lamps. This constant ratio must depend upon definite optical facts, and cannot be a matter of accident. That this is the case can be shown by considering a typical instance. Let us suppose a short straight filament ab (fig. 1) ren- dered incandescent to be placed vertically in the centre of a sphere described by the revolution of a semicircle PH Q round a diameter P Q, coinciding with the direction of the filament. Let the length of the filament be small compared with the radius FH=~, of the sphere. Let Iy represent the * Communicated by the Physical Society: read June 16, 1905. + See Mr, G. B. Dyke, “On the Practical Determination of the Mean Spherical Candle-Power of Incandescent and Arc Lamps,” Phil. Mag. ser. 6, vol. ix. p. 186, Jan. 1905; also Proc. Phys. Soe. vol. xix. p. 399 (1905). . Horizontal Candie-Power of Incandescent Lamps. 209 intensity of the light emitted or the candle-power of the filament in a horizontal direction FH, and let I be the in- tensity in any direction FN making an angle NFH=@ with the horizontal direction. Let Is be the mean spherical candle-power. Bion fi Let us then start with the assumption that l=Iqcos @. The justification for this is found in the fact that if a long straight incandescent filament is placed behind a smail rectangular- shaped hole in a metailic plate, then inclining the filament to the plane of the plate within certain angular limits makes no sensible difference in the quantity of light which comes through the hole*. Consider then a zone of the sphere swept out by an elementary arc NN’ of the semicircle. The surface of this zone is 27r?cos@d0, where d@ denotes the angle N’EN. | Hence the quantity of light falling on the whole zone is Ig27r’? cos? 0d, and the total quantity of light incident on the * For the limits within which the above statement is confirmed by experiment the reader is referred to the Appendix to this Paper. Phil. Mag. 8. 6. Vol. 10. No. 56. Aug. 1905. p 210 —Dr. Fleming: Ratio between Mean Spherical and entire surface of the circumscribing sphere is cE) Amr? I | 2 cos? 6d0 0 Hence by the definition of mean spherical candle-power I, we have wl Arr? .= dor] “cos? @ dé, 0 or 1s =| cos? adda | * (te?) 49 = =0°785. 0 0 2 : Accordingly for such a short straight filament the ratio experimentally found by Mr. Dyke, viz., Is/Im=0°78, holds ood. : Conversely, the fact that experiment shows that for any incandescent lamp Is/Iq=7/4 nearly, is a proof that the cosine law of luminous radiation from the filaments in different direction holds good, with considerable exactness. The departure from the above rule when the filament is pot short compared with the radius of the sphere can be found as follows :— Consider a straight incandescent filament of length 2/ the half of which is represented by the line AB (see fig. 2) placed Fig. 2. B at a distance AP=D from a photometer-disk P, the filament being parallel to the photometer-plane. Let an element of length at C be denoted by d/. Let the angle APB subtended at Horizontal Candle-Power of Incandescent Lamps. 211 P by half the length of the filament be denoted by ¢, and let the angle APC be denoted by 8. Let the intensity of the light sent out or the candle-power per unit of length of the filament in a direction normal to itself be denoted by Iy, then the illumination on the photometer-disk, assuming it to follow the above mentioned cosine law, due to an element d/ of the fila- ment at C subtending an angle d@ at P will be given by the expression Iyecos? Bdl _ Ty cos* Bdl (CRY D? Also from the geometry of the figure we have | D.d@ i : cos? 8 Hence the illumination on the photometer-disk due to the element di of the filament at C is given by the expression IyD.cos * Bd |)? This is the same illumination as that which would be given by a vertical element of length Dd placed at A, but having a horizontal intensity or horizontal candle-power per unit of length equal to Iq cos? 8. To obtain the whole illumination on the photometer-disk due to the whole filament of length 2/, we have to integrate the above expression for one element, between the limits 8=0 and B=4, and then multiply by 2, where ¢ is half the angle subtended by the whole filament. Since i ieee ees Cos Pa +8, 0 and since lcos d= Dsin 9, we see that 2f “te Buse SP uN la iS p rn d cot a) poe 0) ye 2 2 Hence the correcting factor when photometering a filament, the apparent length 2/ of which subtends a finite angle 2¢ at the photometer-disk, is (cos? 6 + ¢ cot d). Accordingly the ratio of mean spherical to mean horizontal candle-power in this last case is given by the expression ae ——— Ft eee ee p+¢ cot d- : If the filament is not a straight filament but a loop as in a! 212 Dr. Fleming: Ratio between Mean Spherical and an actual lamp, which may be so coiled that the different portions lie in different planes, we have an additional small correction to make. We may first notice the effect of the inclination of a straight filament in various directions. Let three coordinate planes be drawn through the centre of the sphere of reference. Let one of these planes be horizontal. Let the photometer-disk be placed with its plane vertical. Let two other planes be described through the centre of the sphere which are respectively parallel and perpendicular to the photometer-disk plane. Then consider a straight filament lying in the plane, per- pendicular to the photometer-disk and having an inclination to it. It is clear that if the cosine jaw of radiation holds good, the light sent out by each element of the inclined filament in a horizontal direction will be the same as that of its projection on a plane parallel to the photometric disk. Hence we may substitute for the inclined filament its projection ona vertical plane, and if we assume the filament and its projection have the same candle-power per unit of length, the horizontal illuminating power will be the same in the two cases. If, therefore, the filament lies in any plane we may consider it divided into equal elements of length, each of which makes its own contribution to the mean spherical and the mean horizontal candle-power. Disregarding for the moment the effect of distance from the horizontal plane on the illu- minating effect of each element on the photometer-disk, we see that the ratio of the mean spherical to the mean horizontal candle-power must be greater for each element of. length of the filament the more it is inclined to the vertical plane or the less its inclination to the line joining it to the photometer- disk. Hence if the whole filament lies in one plane placed per- pendicularly to the photometer axis the ratio Is/Iq must be m/4. fit does not lie wholly in that plane the ratio will be somewhat greater. In the case of filaments coiled in various ways a small correcting factor is also necessary, providing for the reduced illuminating effect of each equal element of the filament, into which the filament may be considered to be divided, the further the element 1s removed from the axis of the photo- meter, that is, from the horizontal plane. In the case of simple horseshoe-shaped filaments, so placed that the whole filament is visible, this correcting factor will be the factor 2 | cos? d+ d cot Horizontal Candle-Power of Incandescent Lamps. 213 where @ is half the angle subtended by the whole filament at the centre of the photometer-disk. If the filament has a double or multiple loop, then the precise correcting factor for angular magnitude of the whole loop is not quite so sharply defined. It will, however, always operate to increase the fraction or percentage which represents the ratio of mean spherical to mean horizontal candle-power. It will always be a small correction if the whole filament subtends an angle, say, of not more than 10° at the centre of the photometer-disk, as in the ordinary photometry of an incandescent electric lamp. These considerations show that incandescent lamp manu-_ facturers can without much difficulty furnish the figures required to give the true photometric efficiency of any “ty pe of lamp. Instead of stating, as at present, the value of the maximum candle-power taken in one direction, viz., the direction perpendicular to the axis of the lamp in which the whole of the filament is seen exposed, they should furnish the mean horizontal candle-power taken in the same direction when rotating the lamp around its vertical axis, using for this purpose well-known mechanical devices. If this reading is taken at such a distance from the lamp that the whole filament does not subtend a greater angle than 5° to LO° at the photometer-disk, then the mean spherical eandle-power of the incandescent lamp is for practical pur- poses very nearly obtained by multiplying this mean horizontal sandle-power by the factor 7/4. From the measurement of the electric power in watts supplied to the lamp, we have at once the means of calculating the total flux of light per watt -which fixes scientifically the efficiency of the lamp as an energy-transforming device. APPENDIX. To enable a judgment to be made as to the validity of the assumption that the intensity of the light proceeding from a filament in any direction varies as the cosine of the angle between the ray and the normal to the element, the following experiments were tried by Mr. G. B. Dyke at the suggestion of the writer. A tubular incandescent carbon-filament lamp was prepared with a straight filament about 10 inches in length. This was placed ona photometric gallery at a distance of about 40 inches from a Lummer-Brodhun photometer, and two baffle-screens interposed having circular holes in them about 1 inch in diameter. These screens were a so as to divide the 214 Dr. Fleming: Ratio between Mean Spherical and space between the photometer and the lamp into three nearly equal parts. The tubular lamp had a protractor attached to it, and could be tilted over at various angles to the vertical line, keeping it in one vertical plane normal to the photometer-disk. It is obvious that if the illumination sent out from unit of length of the straight filament obeys the cosine law above mentioned, then tilting the lamp as described to various angles should make no difference in the observed illumination on the photometer. Asa matter of fact, the observed illumination decreased rapidly as the lamp was tilted over, in accordance with the figures in the following table. Angle between the straight Observed candle-power or filament and the plumb-line illumination through the through its centre. two baffle-screens. ) 2°33 15 2°27 30 2°23 45 2°19 60 1°96 (i) 1:06 It is clear, however, that some part of the decrease of light at high inclinations is due to the loss of light by reflexion at the inner surface of the tubular glass bulb. To obtain the correction for this reflexion a sheet of glass was interposed between an ordinary lamp and the photometer, the plane of the glass being tilted at various angles to the plane normal to the ray. The photometric readings were as follows :— Angle at which sheet of glass was placed to the Observed intensity plane normal to the ray. of the light. 0 ZOU Sep. 15 29°9 + ,, 30 2S has 45 Zorn ce 60 ES 5: 75 Lente It follows therefore, that if the carbon filament in the tubular lamp could have been used without a glass envelope, the light sent by it through the baftle-screens would have been greater in the ratio of the first term in the right-hand column of the previous table to any succeeding term in the same column corresponding to the same angle of inclination of the filament. If therefore we call the intensity of the light sent through the screens unity when the filament is vertical, then its true Horizontal Candle-Power of Incandescent Lamps. 215 intensity corrected for reflexion when the lamp is tilted to various angles is as follows :— Angle of Corrected Value of Intensity of Inclination. Light emitted per unit of length. 0 2°33 xX 26°1+2°33 x 26°1=1:00 1D 2°27 x 260°1+2°33 x 25-9= °98 30 2°33 x 26°1+2°33 x 25°38=1°00 45 2°15. X 26°1—2°33 x 25°2= °96 60 1°96 x 26°1— 2°33 x 25-4= °86 (5) 1-06 x 26°1+2°33 K16-7= ‘71 The figures in the last column therefore represent the | intensity of the light sent out by unit length of the incan- descent filament at various angles of the normal. If the cosine law were strictly fulfilled these values should all be unity. The easiest way to determine the effect of this departure from the true cosine law on the mean spherical candle-power, is to describe a semicircle (firm line) of unit radius and to set off on its diameter distances from the centre C (see fig. 3) Vi, a = —— che tied SR a I aN proportional to the sines of the angles 0°, 15°, 30°, &., and then through these points to draw ordinates (dotted lines) to the diameter of the semicircle. Fractions of these ordinates equal to the fractions in the last column of the above table are then set off, and the upper ends of these define a curve (dotted line) which is the Rousseau diagram of the photo- metric curve of luminous radiation of the filament. If the value of the mean ordinate of this last (dotted) curve is taken, it gives us the ratio of the mean spherical to the mean horizontal candle-power of the straight filament. For the (dotted) curve as drawn in fig. 3 delineating the obser- vations made with the above-mentioned carbon filament, this 216 Mr. Dyke on the Flux of Light from the mean ordinate or corrected ratio comes out 0°77 instead of Q°785 as it should do if the cosine law had been strictly fulfilled. In this case the dotted line would have fallen on the semicircle and coincided with it. Another similar set of measurements was made with a straight oxide filament taken from a Nernst lamp used without heating-coil, and with the supports of the filament all carefully painted dead-black to avoid errors due to reflected light. In this last case no correction due to loss of light by reflexion from a glass envelope was needed, as the Nernst filament was used in the open air. The ratio of the mean spherical to mean horizontal filament in this last case was experimentaily found to be 0°785, or exactly the value it should have if the cosine law is obey ed. We have therefore in these experiments a justification for the assumption made in this paper for the law of luminous radiation from a straight incandescent filament. My thanks are due to Mr. Dyke for his assistance in the ee portion of this work. XXVIL. On the Flue of Light from the Electric Are with Varying Power-Supply. By G. B. Dyxe, B.Sc.* [Plate IT. ] | i 1896 a paper was communicated to the Physical Society by Dr. J. A. Fleming, F.R.S., and Mr. J. EH. Petavel +, recording the results of numerous observations on the Hlectric Arc, dealing, amongst other matters, with the question of the relation between ano fhe of light, or mean spherical candle- power, and the watts expended in the are. The time and labour necessary to obtain the mean spherical candle-power of any source of light from observations made on the point-by-point method then employed, prevented any very extended study of this relation. The construction ot the integrating photometer, described by the author in bis paper “On the Practical Determination of the Mean Spherical Candle Power of Incandescent and Arc Lamps ” {, having, to a very large extent, removed these difficulties, it was thought that a more extended series of observations in this direction might be undertaken, and facilities for this purpose were kindly granted in the Pender * Communicated by the Physical Society: read March 24, 1905, + “An Analytical Study of the Alternating-Current Are,” by J. A. Fleming, M.A., D.Sc., F.R.S., and G. E. Petavel, Phil. Mag. April 1896, 15. ‘i “ On the Practical Determination of the Mean Spherical Candle- Power of Incandescent and Arc Lamps,” by G. B. Dyke, B.Sc., Phil. Mag. Jan. 1905, p. 186, and Proc. Phys. Soc. vol. xix. Electric Arc with Varying Power-Supply. DAT _ Hlectrical Laboratory of University College, London, by - Prof. J. A. Fleming. The objects in view may be thus stated :— G.) To obtain a series of curves for both continuous and alternating current arcs, showing the relation between the mean spherical candle-power and the watts taken up in the arc. Gi.) To compare the “ efficiencies ” of the continuous and alternating ares as illuminants when supplied at different powers, the “efficiency ”’ being expressed in mean spherical candles per watt. As the field covered by these statements was too broad to be covered in its entirety in the time at the author’s disposal, it was decided to impose the following restrictions :— The make and diameters of the carbons used to remain unaltered throughout the experiments. _ Alternating current of one frequency only to be employed, this frequency to be 80~ In continuous-current experiments the top carbon to be in- variably positive. Arc-lengths not to exceed 0°5 inch. Power to be supplied at rates not greater than 1500 watts. The carbons used may be specified thus :— Upper Carbon— . iMacs Wek ee C. Conradty, Nuernberg. JOSS C114 1000) ce eee emer Cored. Marke W.C. Diameter 62.00 ee 12 mm. Diameter Gk Core ..... 4.02.26... Oe Weight per cub. centim. ...... 1-41 gramme, Weight perc.c.ofoutercarbon 1:43 ‘. Weight per ¢.c. of core ....... 0:93 - Lower Carbon— Wilt ES etd Bi cs an a Sica a C. Conradty, Nuernberg. WCSCri MOM 6. nei deeds oes Solid. Marke C. JDIaNCOVeUS See Aa Rw NE aty 4 Reet Oi 10 mm. Weight per cub. centim....... 1°46 gramme. The mean spherical candle-power was measured directly by means of an integrating photometer. This instrument was described in detail in the paper referred to above, and it will be sufficient to say that it consists of a system of pairs of mirrors arranged in a semi-circle, about 6 feet in diameter, in such a manner that light emitted from a source placed at the centre of the system shall be incident upon a photometer-screen, also situated at the centre, at the same angle with the vertical as that which it made on emission from the source. 218 Mr. Dyke on the Flux of Light from the The intensity of illumination of the screen is then pro- portional to the mean spherical candle-power. As previously arranged for testing incandescent lamps, the photometer measured directly the ratio of the mean spherical candle- power to the mean horizontal candle-power. When dealing with arc-lamps, however, this ratio is not of much practical value, so a small alteration was made to adapt the instrument to read the absolute value of the mean spherical candle- power. This was effected by replacing the horizontal sliding pair of mirrors by a standard incandescent lamp ona sliding support. This alteration will of course alter the constant of the instrument. The formula given before was MISC. 9508 MENG sPe ie Mae where d is the distance in feet from source to screen by way of the sliding pair of mirrors. Now the sliding pair of mirrors reflected 70°5 per cent. of the ight incident on them ; hence it is obvious that if these mirrors are replaced by a lamp of known candle-power C.P. we have os US aioe i M.S.C.P.= 705 GE e Hence the formula becomes C22 MS:CE-— —p Xx C.P. of balancing-lamp, where d is the distance of balancing-lamp from photometer- screen in feet. : As this result is obtained somewhat indirectly the are was replaced by an incandescent lamp, and the polar diagram constructed by opening the slides in front of the mirrors one at a time and making a photometric measurement for each. The Rousseau diagram was then drawn, and the mean spherical candle-power deduced and found to be 22°49. All the mirror-slides were then opened and a balance obtained at 15°95 inches, the candle-power of the balancing-lamp heing 5°51. Hence, applying the formula given above, 22°49 e2e 2 Ser) = 7:21. This check-experiment being considered satisfactory, the value 7°22 was taken as the constant of the instrument. constant of instrument = Electric Are with Varying Power-Supply. 219 When dealing with ares of some 2000 mean spherical candle-power, it was necessary to bring the balancing-lamp very close to the photometer. In this case it was necessary to apply a correction to the Fie. 1. scale-reading of the distance d, due to the angle subtended by the filament of the balancing-lamp becoming applicable. If J is the length of the filament, and i the brightness per unit-length. | Then, considering a flat-loop lamp at a distance d from the photometer (see fig. 1), we have :— Intensity of illumination due to 2 legs of filament 1 en i ad era a 21 ry s 0 OS ) 2 2 i{ (os cos @) co © Nowe J ANTE faete if a4) (<4 . 30) cos 0X i “y 15/4 Ay tan d = cos? 660 a val) L = oe 2/4 27 . ———— [ 0+ 2 sin 20 | ad = ¢ ee ee ea q = F; | tan == + (41) 220 Mr. Dyke on the Flux of Light from the > > } d. r or approximately Wiese ad ae 41d | d i eee hs an VEL + (41) ) Ar CEs, Hence d? must be multiphed by the factor e+ QD} @+d Vd? + (4l (41)? The author is indebted to Mr. W. C. Clinton, B.Sce., for bringing this correction to bis notice. A hand-regulated are was used in the experiments, the length of are being kept constant by observing the image of the are thrown on to a screen by means of a lens. During each series of experiments the are was maintained at a constant length, whilst the power supplied was varied by means of an adjustable resistance. In order to obtain a mean result ten photometric readings were taken at each setting. Altogether eight lengths of arc were employed, ne ig in., sy in., 4 in., and hence by 16ths to 7% in. The table which follows gives the mean esnle of these experiments, involving nearly four thousand observations. If now these results are plotted, taking watts as ahscissee and mean spherical candle-power as ordinates, we obtain the series of curves shown in PI. II., the full-line curves referring to continuous-current arcs and the dotted lines to alternating-current arcs. It will be seen that, within the limits of experimental error, the relation between mean spherical candle-power and watts follows a str aight-line law. This straight line, however, does not pass through the origin, but for zero candle-power there is still an outstanding amount of power amounting to some 200 to 400 watts. The amount of this outstanding effect increases, in general, with the arc-length, and is probably due to the energy dissi- pated as heat by radiation, and as chemical energy in evapora- tion of the carbon at the crater. The author hopes, at some future date, to investigate this matter experimentally. It is found from these curves that for each are-length the point in which the efficiency curve cuts the axis of watts is Electric Are with ena Cae ee 221% | | | | Are | Continuous Current Arc. \ Alternating Current Are. as 7 | | Inches. | Volts. Amperes.| ‘Watts. MS.OP. ‘Volts. Aimperes. Watts. M.8.C.P. ee | 50-0 G4 -) 318 05 1, 39°. |. 56 221 155 4G3 bo RG 855 | 267 || 87-8 | A 968 | 236 AAT | 9:8 AIT 370 =| 37-4 9-2 344) 359 45:1 Lah 544-542 ~— (violent hissing if current increased) 454 | 163 741 777 | 44-2 | 201. | 890 | 1078 || | ee, 50°5 6-7 Boo abr are bh Ge. (ONT L1G 7 489 Oh Ser br B54. lh Aro WW O37) 6 |e BS 293 48:0 9-6 459 AO Sra: | Wl) 44 nt AO toe 56a 7S88e 1.398) | 18-4 Hao on 64 46:4 16:9 736.| 1119 || 401 | 160 | 648 855 453 | 209 fT TATG |) AGF 1987 Wy BOz) | 104 if 538°5 | «6:0 323 290 || 43:8 68 | 299 124 Se 5L0: | 75 $82 | 390 || 42-1 8:6 362 241 BPD) 9.8 As) 6097 41-6" | “TOs 429 297 Ho 123 | G09). 90N) |4i7 | 125.) 20 477 Pag ilGs 1 796 | 1295 421. |. 146 | G16 579 | 47°0 | 26-4 O61) “176 149-2 51878 793 846 | | | 40:3 | 2071 81] 977 He |, 580 57 333 | 237 || 51-0 49 | 250 80 546 viel 386 | 353 || 482 63 304 132 Poo 1 §S-9 462 R24 || 45-4 85 384 Q44 ie cle EL 599 "67 1-435 | 126 547 543 48:8 | 163 796} 1219 || 421 | 158 655 712 | 48-8 | 20-2 985 | 1669 || 422 | 199 | 837 990 20 es 68 AAV | - 410 || 561 46 | 259 87 60:9 Se ST ML GSa" Ws: 54 | 991 154 eee) PDO OT hr RIG 50:6 Zi 1360 196 559 | 154 863| 1532 || 460 | 107. | 490] 432 0 1A 194) TOL) SHOW 456.1159 727 863 Seba Oh |S 8 548 GON Sy SS, 83 | 478 270 | 608 | 10-4 632 77 563) 105 617 382 | 59:0 | 125 F280) G2 PesG 137 9 Fook S96 (585 | 149 871 | 1284 || 49-2 | 17-5 S68 jet 707 1611) 188 | 1150'| 1900 || 489.| 21-7 | 1062 1024 Pian 167-2 68 | 459) 35 57-7 8-1 470 238 | : | 62:5 SOw to 6o b So7. lr aor | eS 602 446 1621 | 122 760 | 1130 || 541 | 14-1 763 | 720 eos) LOO Gop |, 620 5687! 105 593 | 407 : 659 | 11-6 Feo SO. e566" | Ise 7S 660 | G29) 1435 |°.927 | 1202 || 55°6 |, 181 },1003 1070 | De ats Oumar ie. 03.01 | } ! | the same whether the are is supplied with continuous or alternating currents, pointing to the fact that the power ex- pended in forms of ener sy. other than light, e. g. volatiliza- tion of carbon, radiation of heat, sound, &c., is exactly the same for similar alternating and continuous ares. For lengths of arc greater than } in. the ratio of the efficiencies of the continuous and aliernating ares is about 3 to 2, agreeing very well with that obtained by Dr. Fleming and Mr. Petavel, 222 Mr. Dyke on the Flux of Light from the If, however, the arc be made shorter than 1 in. the efficiency line for the alternating-current are will be found to gradually approach the line for the continuous-current are until for an arc-leneth of =, in. they are practically coincident (PI. I1.). The are is quite stable at this point, and even in the alter- nating-current case may be supplied at more than 600 watts without causing hissing. Any further decrease in the arc-length will result in the alternating-current efficiency line rising above the continuous- current line until at an arc-length of 5), in. they have the position shown in the first curve in Pl. I. With so small an arc-length, however, the alternating- current arc begins to hiss badly when suppled at a rate greater than 350 watts, although the continuous-current arc is still silent up to 900 watts. As far as the author is aware, this is the first case in which an alternating current arc of efficiency greater than the corre- sponding continuous-current are has been realized in practice, although Dr. Fleming and Mr. Petavel recognized the possi- bility of such a phenomenon in their paper referred to above Why, then, does the alternating-current arc give the same efficiency as the continuous-current arc at this arc-length ? This can perhaps be most clearly seen by making some simple approximations with regard to the shape of the carbons, and calculating the length of are necessary to give the same candle-power with the same power supply. Mie. 2, Let the carbons be supposed to assume the shape indicated in fig. 2, truncated cores whose heights are equal to their Electrie Arc with Varying Power-Supply. 223 bases; this being approximately the shape found by ex- periment. Also let all the light in the case of the continuous-current arc be supposed to come from the positive crater. Now, the expression for the mean spherical candle-power of a source synimetrical about an axis is — Z I, cos@ dé, = 2 M.S.C.P. =4 | where I, is the luminous intensity in a direction making an angle @ with the horizontal. Now let I be the luminous intensity of the crater when viewed normally. Then, as a rough approximation, assuming the crater to be a flat circular disk, small compared with the arc length, 1, =1siné. Hence for the are MLS.C.P. end cone | bol rH ——, | = aa) ~ sin 26 d@ a 7 € | = | ie cos 26 | Let a be the diameter of the lower carbon (—), and J the diameter of the upper carbon (+). Then, making the above assumptions, all the light, in the continuous-current case, will be concentrated into the zone between the horizontal and an angle « below the horizontal: where 7 t Ate2e ta sean” Hence we get M.S.C.Proc. = }Toc. [— cos 26] Similarly for the alternating-current arc, considering each 224 Flue of Light from the Electric Are. erater separately, we obtain M.S.C.P.4.c. = ¢1ac. (sin? «+ sin’ 8), where Hence M.8.C.P.c CIES Toc. sin? a M.S.C.P.ac x lac. sin? a Seine B ; Some experiments mentioned by Dr. Fleming Mr. Petavel give :— for a continuous-current are O10 when 7 0a Hence ' 910 ic — ce Bee 1400 ; and for a similar alternating-current are I, = 300 when 6 = 60° for top crater, and 1, = 3(0 vyhen 63° for bottom erater. Hence as a mean Tac => 707, So we get leg AO St De — Ow C— ih 99, Therefore MS. Cleo... 1-9 sin? a MSC co sin? «+sin? 8° Hence for equal efficiency we have 1:99 sin? a = sin? a+sin? PB. ° = ENS a ey r OUlsim: @ == sin 6; or putting in the values of the angles Car ae (6+2)? (a+ x)? +°25a7~ (b+ a)? +2507" Now a — V0) mami: eae arine Hence Woon a)? 2 a ae (lO+a)?+25 (1242)? +36" and Electrical Vibrations between Confocal Elliptic Cylinders. 225 Writing out and arranging a*+ 44a° —34027— 6000. + 18000 =0. Solving this equation graphically we obtain as the positive finite value of 2 i= 2° Wi, which agrees very closely with that found by experiment. This consideration, however, by no means gives a complete solution of the problem of the relative efficiencies of the continuous and alternating current arc, but is only intended to account to some extent for the phenomenon of continuous and alternating current arcs of equal efficiency. A complete analysis of the subject could only be undertaken on the basis of the evidence of a much more extended series of experiments, of which the time at the author’s disposal would not allow. In conclusion the author wishes to thank Dr. J. A. Fleming, F.R.S., for bis many suggestions and constant advice, and also for his kindness in placing the resources of the Pender Laboratory at his disposal, and to express his indebtedness to Messrs. J. S. Westerdale and-H. C. Bullman for the very efficient assistance they have rendered him, at great personal inconvenience, in making some thousands of electrical measurements, without which the investigation would have been impossible. 3 XXVIII. On Electrical Vibrations between Confocal Elliptic Cylinders, with speciat reference to Short Waves. By J. W. Nicnotson, B.Sc. (Lond. §& Vict.), Trinity College, Cambridge *. OLUTIONS of the problem of electrical vibrations in confined spaces, bounded by perfectly conducting sur- faces, have hitherto been limited to the cases of the circular cylinder (vide J. J. Thomson, ‘ Recent Res. in Elect. and Magn.’) and the sphere (Macdonald, ‘ Hlectric Waves’). In the present paper, it is proposed to show that the case of the elliptic cylinder, although in general devoid of simplicity, will yet furnish results of great elegance, when the solution 1s merely carried to a close approximation. When the surfaces are perfectly conducting, they cause no * Communicated by the Author. Phil. Mag.:8. 6. Vol. 10, No. 56. Aug. 1905. () 226 Mr. Nicholson on Electrical Vibrations dissipation of energy, and the surface conditions may all be included in the statements :— (1) The resultant magnetic induction at the surface is tangential. (2) The resultant electric force is normal. In an oscillation, these vectors are perpendicularly situated in the plane of the wave-front ; hence the latter plane is tangential or normal to the surface. The problem is confined to the case of an elliptic cross- section. If the section were parabolic or hyperbolic, the energy would be radiated into space, and the oscillation could not be permanent. If the axis of z be that of the cylinders, and (wy) the plane of a section perpendicular to the axis, a point of space is defined by (Auz), where (A, ~) are the roots of a es i. a N=const., w=const., being systems of elliptic and hyperbolic cylinders respectively. The space elements in the directions A, # are du dn= 5 Ny = yee where _ MN (O07 + r), u = yes (say), A—bB Sn A— wu In the usual electrical notation, the current is denoted by (u, v, w), the electric force by (X, Y, Z), and the magnetic force and magnetic induction by (a, 0b, ¢ The two latter vectors are identical, if the medium between the two surfaces be non-magnetic. If V is the velocity of light, and the current is entirely eethereal, Peas Ar V7(u,v, w)=(%, Y,; 4)... >. By the circuital relation of Ampére, UN sy om Mie ato Ban ge Pe fey rai foes ca are NT ON: ee ae te) ar (20), > (2) a ii = & . eile ox 8: 2 between Confocal Elliptic Cylinders. 227 By that of F ack a 3 Toe i mopar (ia p2 Tk ) Se | b Bel SNe 0 eee ga een fea es OE SV Gs. 1 ae an” a % ee 2p, OA oie Onl J Dots denoting differential coefficients with respect to time. The conditions that (2) and (3) should each form a con- sistent scheme are 2a) * aan) 3 delon) en 1 : sl.) - = \its 2 lee) =(). It must be recalled that (X, Y, Z) and the other vectors are in these equations defined by components along the directions A, m, 2, and not by the rectangular components. We now examine the ae of a type of oscillation in which two of the components (X, Y, Z) of electric force are Zero. i ¥=0,Z=0. Then by (4) St Sn ea id Nee tems ie CO: If \ is the wave-length of the oscillation, and k= _ x ow Ve =e. The circuital relations readily give, in this case, | ems oki ea a) a. / (6) and by combination lead to the equation for X, at 4 —P(u) 90 —P(m) +hPX+ ! Vo aie VEG) V Ne On VAs mes ae) But by (5), = ae b(t, 25 SUSE gore aye ab a 8b esd =P 2g Pw) =0 Q 2 (7) 228 Mr. Nicholson on Electrical Vibrations Since ¢ cannot contain A, this gives the two equations s Tie eae < 3a (Py — P(e) =0, 2 Hence . JN : = 4 Gos (he ee cos (EVE er oa ee whence the components of electric force are A | X= —= =. cos (kz +a) cos (kVi-+e), Y=Z— 0a A NSO . ) By equation (6) the first surface condition is satisfied; and since (Y, Z) both vanish, so also is the second. This solution represents the simple case of waves propagated along z; and we note that the force is independent of the size of the boundaries. It holds also inside a single cylinder. X is nowhere infinite, for \ =u only on the imaginary curve (2? +7°—b?)? = —4270?. The magnetic force at any point is normal to the confocal hyperbola through it, and has the value a) = sin (ke-+ a). sin (AVt+ 6). es It isreadily seen that this is the only motion of the kind; for if we had taken (X, Z) =0, we should have found = Y= ee cos (ke+ B) cos (kVt+e), Var | which cannot vanish at the conductors unless B=0. Again, if (X, Y)=0, Z is a mere trigonometric function of z and ¢, and cannot vanish at the conductors unless it does so everywhere. Finally, when waves are propagated along the axis, the electric and magnetic forces are normal to the confocal elliptic and hyperbolic cylinders respectively, and are of magnitudes given by (8) and (9). General Solution. It is readily seen from the equations and surface conditions that the general solution can be built up from two particular between Confocal Elliptic Cylinders. 229 cases. The case of waves along z, already treated, will serve as the first. The second must be obtained by arbitrarily making two components of magnetic force vanish. On addition of the resulting solution to that obtained above, the general values of the forces for all possible oscillations may be found. The case (6, ¢)=0 cannot be made to satisfy the surface conditions; therefore we are reduced to the case CNA Mi ee eee res (10) which'involves, of necessity, . Ai amen a, he eh eee 8 CIT) By equation (4), C=PipPP'A, “), where @ does not contain ¢. Hence AisnOmaALUNCHON. Ol es 8s. oe. ee (12) Substituting in the circuital relations, it is found that ¢ must satisfy the differential equation Bee fon 08 py 0 ere, B, VPA) SV PASS +V Pi) Sv Plu +g me 0. (13) Since Z=0, and the electric and magnetic forces are per- pendicular, both surface conditions are included in Y=0; oc — (vat the surtacesseupa yy 2+) (14) Let c= LM cos (A Vi+e), where L is a function of » only, and M of wu. Born An OME Vila eae i Mom 4 (A—h), . (15) where ={ dn vez dp. leas ©} 7=Ew) We may therefore take 1 ere k igas m Csy * (16) Li da? 4 ok (17) 1 aM = —O+K pe M dp? 4 where @ is an arbitrary constant. The first of these equations will now be considered. 230 Mr. Nicholson on Electrical Vibrations Let 2X=0? sinh? &, and it becomes PL i Peele de (O76 smb? BP whichis known as the equation of the elliptic cylinder. Let E(é), F(&) be two principal solutions. if w= —0? sin? yn, we find similarly ??M a ==—(0+4°)? sin? 7)M. ae And if solutions be E,(7), Fy(), then the magnetic force is given by | c= {E(€) + AF (£)}{Ei(n) + BF;()} cos (kVt-+e), . (20) the summation being for all possible values of 6. While the surface condition gives, by (14), [Se] =05. en therefore if &, & denote the elliptic surfaces, the free periods of the system arise from the values of k given by HN(E,) NE) Pe) = ee ee (22) Owing to the impossibility of finding even adefinite integral to represent the functions H, I, whose properties may be found in Forsyth (‘Theory of Differential Equations’), this solution is of little interest. We now proceed to examine certain approximations. If two very nearly spherical boundaries be considered, L must return to its old value asa point defined by 7 describes a path on a particular boundary. We will therefore regard (—@) as the square of a positive integer, and write it n?. In general, 6= —n? + a)(kb)? +a,(kb)*..., where dp, 4, &c. decrease to zero when v is great. Then the equation for Lis aL 2 279-2 2 5 Tae + kb’ sinh’? ¢)D=0.. 9. It will be noticed that the periods form a doubly infinite system, for the values of n are singly infinite in number, and each value of n gives rise to a singly infinite number of periods. We proceed to the case where n is very great. between Confocal Elliptic Cylinders. 231 kb Let a? when 7 is large, aL d2 +n?(1+e? sinh? =) (0. . “ (24) The approximate value of the solution in this case may be obtained by a method due to Webb (Proc. Roy. Soc. Ixxiv. 1904, p. 315). Put b=e" or, where (wf, d) are functions of &. Substituting in the equation, and equating coefficients of n, n* to zero, since the terms are of different orders, me (3) +(1+é sinh? £) =0, dé and dg dp aa.” ; ee LYRAe Re p= + | a/ Meee simi edey ) a (25) 0 d C tas a ae ner oa(a6) Ua 209s aS np (27) NZ where (A, B) are functions of (7, ¢) only. The free periods are given by =e =0, at $=, 2, which ? leads te . As n(apow '—abyry' ) Co ee aa +b yl To the present order of approximation =." an Voth aye! 28 tan n(@;— $2) = oh ee (28) This can be expressed in terms of elliptic functions, for b=| V1 +e? sinh, «= ep 0 nm Hence if H(@, k) denote the incomplete elliptic function, ’ (rman o ae, Sieh aes css tieat Co) J 0 Boe ‘Mr. Nicholson on Elliptical Vibrations Then p= (Ee). Boe es Ge i (30) where 1 =4/—] _ Hence if ) =? sinh? &, a set of free periods between the surfaces (,\2) is given by | 2 sinh2E 7? tan ind E( & *)\- : & a Z [ a | 31 . ny ( tn : Bon St An (i+é sinh? €)2 i ( ) / | provided n be very great. We may here recall the fact that 0? is the difference of the squared semiaxes of any confocal, and A is the minor semi- axis. Treating the equation for M ina similar manner, m= Ccosh abit Disinhngi | ee ‘ V $y, =| /i—esintn dn, . - |. 5a 0 which is also readily expressible as an elliptic function B(n, 7 The magnetic force is then where 4 A = ae cos (nf + €) cosh (np; + €) cos (AVit en). (34) And the electric force may be obtained by the proper operations. For vibrations inside a single elliptic cylinder, we must have = BT . in order that the forces may be everywhere finite. The period equation for the cylinder defined by &, for large values of n, is accordingly e eV a d | sinh B() lag i & dé (1 +e sink? &)* | kb where the function E has a modulus e= a & between Confocal Elliptic Cylinders. 233 Detailed Investigation of very Short Waves in the Space. In the case of short waves, & is great. We first take the case when n is an integer too small to be comparable with k. The dependence of @ on & ceases when k is very great, by analogy with the corresponding circular problem. Moreover, the result is periodic in , of period 27. Then the equation ‘for L is dé? and by the previous method, the asymptotic expansion for large values of £ 1s found to be L =v cosech £4 A cos (kb cosh &) + B sin (kb cosh E)t. .(38) Similarly, M=v/cosec 7 {C cos (kb cos 7) + D sin (hb cos 7)}. (39) Now ro crn A cos (kyV/ +2) +Bsin (kV/F+A) OF een: (40) +L.b?sinh2€=0; . . . (87) L= The period equation therefore becomes N07 te VPN, tan i: Caines eae r/ b? ae rd) = 2k 2kNg ie ees ie Jur nat DIN since & is lar ge. 2a Hence — a is a ier! possible wave-length, if k is a large root of 1 2 1 | N 2 ¥ >—Xr b? Xr z tan ky (b2 +A2)F -(P +A, Fh = a" + a +») F (41) For a very elongated section, 6 is large, and we obtain p 2—A1): ° ° (42) tan 5 (Ae Ni dles DEAS (A The larger k may be, the more accurate is the approxi- mation to the free period. 234 Mr. Nicholson on Electrical Vibrations For these very short waves, the magnetic force is very approximately = nae » COS (ky\/ 0? +r si €) sinh (ky/ 6? + po—kb) _ Elkvt (43) a= 8=0, and is along the axis of the cylinders. The factor involving w has been so adjusted that it cannot become infinite at any point. In order to test the error involved in this approximation, we a a the asymptotic expansion under the assumption that n? is not zero, but a small positive quantity. Shet - i 7 where @ is very small. ‘Then € }2(6? +? sinh €)L=0. It, following the previous method, we write d= e24") ap ; we find o= | VO¢+6?sinh2édz; . . . (44) a’ { vay as before. V To the second order of small quantities, o=b cosh eco 5 5 low tanh ; and therefore F /b? 4-) is to be replaced by 6? NN. 1 pV DNS log ——__ - AD 205 aan VU24N cy in the period equation. The ratio of the increase, to the original value, is of magnitude Hibes alg eae vey hb ve ea Now = while for light waves k is about 10° mm. sc) Hence the correction is quite inappreciable, even when » is fairly large. between Confocal Elliptic Cylinders. 23 the components of electrical force are ox =), es _ (EY eos en 62) 4 sinh (b/ PEL + 6) VE cosh (kV PERE) as ey > sy y- SN Cae ( 4 aaa ay sin (Aa/L? + \+e;) EE je = ee d cos (kn/ + +€,) t cosh (ky/b? + w+ €2} (47) where ¢, is known from the condition that Y=0 at boundaries, and k is one of the roots of (41). If @ is the inclination of the resultant electric force to the normal drawn to the confocal ellipse through that point, Z b2 - MNT. Y te \ tan (ky/ 624 ee) + eS tan 0= | =|— ee) Cie (48) Se op ea tanh (kn / b? +&—kb) — 5 ( Danes And therefore the differential equation to the rays is dy a fa te th aos b4 +r ie oe ees emer 62 a AVP2+%. tan (kr / 0? + AN+e,)+ oom ae at Vv b*+ w tanh (k 7b? +4 — kb) — oa since they are propagated perpendicularly to the electric force in the normal section, and pee P2 dyn These rays are closed curves round the axis of z, in the plane of each section. When the quantity n becomes appreciably great in the differential equation, if the asymptotic expansion be found, it appears that the ensuing waves cease to be short. The above theory therefore applies to very short waves in general, pro- vided they are possible to the enclosed space. This possi- bility is determined by equation (41), and exists if the root k, to which they correspond, is large. The approximation tan == 236 Hlectrical Vibrations between Confocal Elliptic Cylinders. becomes closer as the successive roots are taken in an in- creasing sequence. In the particular case of short waves inside a single elliptic cylinder, the forces must be finite at X\=0. Hence in equation (43), a 2) = aT kb e == 3? and the wu term must similarly be finite. c= mae sin (ka/0? + —Ad) sinh (ky / 0+ p— kb) _ eke, is the approximate magnetic force for waves such as those of - light. The electric force may be deduced at once from this expression. The period equation for a single cylinder defined by X is d f sin ki\(?+yr)z—b} Ahr ea rn: fa where only the large values of kare chosen, the approximation being closer as they increase. A similar investigation for the case of long waves appears impracticable. The waves peculiar to the cylinders cannot have a length sufficiently great to ensure the utility of a continued approximation to the solution of the equation. The assumption of the existence of very long waves, when tested. is found, as was perhaps to be anticipated, to lead to impos- sible values. The approximate solution given above for short waves is of remarkable simplicity, and almost quite accurate in the case of light. A certain interest attaches to the class of waves worked out in terms of elliptic functions ; but their period equation is so complicated that it cannot readily lead to any numerical caleu- lations, to which, on the contrary, the short periods readily lend themselves. The most general type of oscillation possible in the space consists of the combination ot— (1) Waves of the doubly infinite series of possible periods travelling round the axis of <. (2) Waves of any period whatever travelling along z. In this general vibration, the path of a ray is a spiral curve round the axis of the cylinders, and the following results will hold :— (1) The magnetic force never has a component normal to the confocal elliptic cylinder through any point. (2) The electric force never husa component along the axis uf the cylinders. (50) pergsat | XXIX. On the Conduction of Llectricity through Gases between Parallel Plates. By Aurrep A. Ross *. (HE differential equation FO he ib NG eg ae (RR) UH exe Ry Me eC RAN 7 s (i+ Sir it ae) | (1) occurs in the theory of the conduction of electricity through gases between parallel plates. In this equation X represents the electric intensity at a point defined by the coordinate x, measured in a direction perpendicular to the plates. 7 represents the current per unit area; R, and R, are the velocities of the positive and negative ions under unit electric intensity ; g is the rate of ionization per unit volume and @ is the coefficient of recombination. The equation has been solved by Professor J. J. Thomson for the case when R,=R,; but in general it does not lend itself to solution. Itis proposed here to show (i.) that this equation may readily be transformed so that it becomes a characteristic one for any gas under definite conditions of temperature and pressure; and (ii.) that for any gas for which R, and R, are unequal there exist two pressures at which the equation becomes soluble. In order to effect the first of these objects, we have only to write : a q a ne Lene. q and the equation becomes dy? iL it a ae =tele +) 1- apr Rp iy dy? ( R, dy?\ BE esa Ea SS pesos: 22 )\ : Sar calle (3) The form of this equation does not depend either on the strength of the current or the intensity of the ionization, and therefore is characteristic for the gas. In order to show that for certain pressures this equation ails \ Sir dv * Communicated by the Author. 238 Mr. A. A. Robb on the Conduction of Electricity tekes a soluble form, we shall write it d?y? ae b c dy? € — ae ee e (4) where 8are(R, + Ra) Bb = Me Sra eR, R(R, + R,)’ a(R,—R,) eR, R2(Ry+ R,)’ (== a 4rre(R, + Ry)’ e—— It is to be observed here that ¢ is the same quantity as that introduced by Langevin (Recherches sur les Guz ionisés, University of Paris, 1902), and denoted by the same letter. It follows from the physical meaning which he gives it that e« must be a positive fraction. In order to reduce equation (4) we make the following eee Pedy. bu ages series of substitutions: lst. Puttins = =—-— — and yo > dv zZ we get ae as Ge (TENE Ge te . ; s dz 2nd. Putting w= ee where K is a constant to be after- wards determined, we get b 9 OG sot AN ES ee € ot cK)s oa g Me 9 we é1, aay ord. es §=2s", we have a ae ewe dz ages. ey 2ns— +n(n—1)-. If, therefore, K and n be determined by the equations 1—cK=2n, uae g an) through Gases between Parallel Plates. 23Y we have z given by the equation be a ie a ay SCT) and the differential equation becomes ee IN esa; — n(n—1)@ és Ae peng ce) Now equation (7) has two roots. If n, and ny be these two values, then ny+n,=1; and so unless n,=n,=4 there will be two equations of form (8) corresponding to any one of form (4). Regarded merely as a differential equation, (8) may be solved in several cases :— Gi.) When a=0. ( Gi.) When n=}. (iv.) When n=e or l—e. As regards case (i.), our problem does not allow of a being Zero. Further, € is necessarily a positive fraction, and so case i.) is useless for our purpose. Case (iii.) corresponds to c=0, or in other words to R;= R,, and the equation of conduction under these circumstances has already been solved by Professor J. J. Thomson (‘ Conduction of Electricity through Gases,’ p. 66, or Phil. Mag. vol. xlvii. p. 295, 1699). Case (iv.) requires be b3 e(e—-1) : oh 2(e—1) 2 7 22 (1—2e)® OY Om see 5 - (9) But pert R,R, | De me (geal Thus we get either acted ie ~ R,+R, | ae L (10) aay ~ R,+R, Now both these values of € are positive fractions, and . BK i therefore are possible. For air Rp al22 approximately, i 240 Mr. A. A. Robb on the Conduction of Electricity R R ae and thus the values of =—~, and ,—~,- are respectivel about *45 and °55. Ri + Ry Rit Ry : : Now Langevin gives e="27 at 760 mm. pressure and °62 at 1550 mm. for the case of air. Thus e=*45 corresponds to about 1°53 SIMD 22 eS. and e= "99 to about 1°83 atmospheres. Accordingly, for air at these two pressures the equation has the desired form, and may be solved. Taking, then, for simplicity n=e (n=1--€ gives of course the same final | result), we have d*Q fae ae ds* b This gives where C,; and ©, are constants of integration. By reversing the various steps indicated, we may finally obtain y and v in terms of @ as an auxiliary variable; but it is desirable to introduce a slight change of notation in order that the final result may not contain a third and superfluous constant. We accordingly write dO, 2e—2 (ca ie Se, Cor/ — 0; _ (aa a transformation which is only possible if C, be different from zero, and finally obtain y and v in terms of the auxiliary variable @. Thus iar us aia IV germ! 27 alee). Cs ae : ae? (1 — 2e) | As may readily be proved by differentiation. and = through Gases between Parallel Plates. DAT Besides this solution, there is another corresponding to the case where (Q, is zero, and when therefore the transformation from @ to ¢ fails. In this case the relation between y and v can be expressed directly without the use of an auxiliary variable, and may readily be shown to be l—e 2¢ ee a ban) Te y— 2 IS lg (5 poe eae? The solution (11) may be somewhat simplified in form, for if we ee 1 G Ge = cashiay, and substitute the values of c and a, we get ee ae oe wee Seon eee cosh!-< @ 0 OS os A Jydo+ts}, | where ,/a is to be employed with the same sign in both places and where (13) = R, R, +R,’ or oe Lae Tp according as the pressure is such as to make a=AreR,, or a=AreR,. The integrals in (13) may be evaluated in finite form when ie is an integer, and when therefore the velocity of one ion is an exact multiple of the velocity of the other. In other cases they may be easily calculated*. The other solution (12) may be ae in the form ae Big Ey ae 5, ( ae 1=9e “oe log { 1—2e! (x - x) ane Se!) 42a / =o) Hilts 4 const . (14) 4 * The author has calculated a table of these integrals for «= 7 which Aqre? is approximately one of the values for the case of air. This he hopes to give in a supplementary paper at an early date. Phil. Mag. 8. 6. Vol. 10. No. 56. Aug. 1905. R 9492 Dr. O. W. Richardson on the Rate of R R in which, as before, ¢ has the values eR and Ree corresponding respectively to the pressures at which a=4eR, and «=47eR,. Note.—The idea of adjusting the pressure so as to render the equation of conduction of electricity between parallel plates more manageable occurred independently to Mr. G. W. Walker and myself. It was used by Mr. Walker to complete the integration in the case when R;=R,. It was shown by him (Phil. Mag. Nov. 1904) that this may be done a if on =2, 4, 4, £, and he selected 2 as the simplest. TC I pointed out to him ina letter that according to Langevin’s theory, «= must be a fraction, and that therefore the a Sieh value 2 was physically impossible. He replies that he had not observed the limitation im- posed by Langevin’s theory, and suggests that I should lay a OTe possible if « be constant and R vary inversely as the pres- sure according to McClung’s and Rutherford’s results, yet emphasis on the point that while the value R=? 18 5 3 a according to Langevin {—, can never be greater than i S7eR unity. There is thus a serious difference to be explained. XXX. The Rate of Recombination of Ions in Gases. By O. W. RicHarpson *. VHE following is an attempt to explain the variation of the rate of recombination of ions formed in gases with the pressure of the gas. The basis of the method is a theorem due to Langevin +, which may be stated as follows :—If we describe around each negative ion a sphere whose radius is arbitrary, except that it must be large compared with the mean free path of an ion and small compared with the average distance between two ions—both of which conditions are capable of being satisfied in the case of ionization pro- duced by Rontgen rays and radium radiation, in gases at moderate pressures—then the number of positive ions which * Communicated by the Author. +t Theses de V Université de Paris, A. 481, p. 103 (Gauthier Villars). Recombination of Ions in Gases. 243 will enter such a sphere in time dé is independent of the radius of the sphere and of the external field, and is given by An (hy + ky) Pe dt 5 where 4,, k. are the velocities of the two ions under unit field, P is the number of positive ions perc.c., and e the charge on an ion. If we call each case of an ion crossing one of these surfaces a “collision,” and suppose that each collision is equivalent to nyeomal maniacs we get for the law of recombination dips dre, _- eer ik —Amr(k, + ks)pn, where p, n are the densities of positive and negative electri- fication respectively. Since recombination does not necessarily result every time an ion comes within the Sp shere of action of another ion, the above expression only gives an upper limit to its amount. Langevin puts oP == Z = —Aar(k, =F ky )epn, where e¢ is a function of the pressure whose possible values Be from zero to unity. The coefficient of recombination a is thus equal to 4ar(k, +he)e. We shall now proceed to calculate a value of e. To do this it will be necessary to consider what happens to an ion when it enters the region in the immediate neighbourhood of an ion of opposite sign where the electric force is very intense. If we deseribe round each negative ion a concentric sphere whose radius is 4 x 10~° ems., then by the time that a positive ion reaches one of these spheres the work done on it by the attracting forces will be about one two-hundredth of the total work done during recombination. It is evident that inside this region the ion will be greatly accelerated and its behaviour will be quite different from what it was outside. To fix our ideas, we may for the moment regard the negative ion as fixed and the positive as projected through the spherical boundary. The positive ion will then describe an_ orbit round the negative and in general will return to the boundary at some other point. If this is the case it will have returned to the region where the kinetic energy, which it gains in virtue of the work done by the attractive forces, duri ing its passage through a distance equal to the mean free path, is not great compared with the mean heat energy; in fact it R 2 244 Dr. O. W. Richardson on the Rate of will again behave as a free ion. The criterion for recom- bination then is the condition that the ion should remain permanently within the region in question. The condition that the positive ion should return to the boundary is a well-known result in the theory of attractions, and is that 4mV?+2W is positive: where V is the relative velocity of the ions, m is the mass of one of them, and WV is their potential energy reckoned from the surface of the sphere. Since the number of cases in which the positive ion can enter the sphere without a finite velocity component along the radius is infinitesimal, itis evident that at the commence- ment of the path $mV?+2/Y is necessarily positive ; so that unless something happens which reduces the value of V recombination will not take place. We shall suppose that the necessary decrease in V is caused by collision with un- charged molecules, and try to find out how many collisions are required to produce the observed experimental results. We shall first calculate the probability that an ion pro- jected from the circumference of a sphere of radius r makes a collision within the sphere. To make the calculation possible, we shall make the rather approximate assumption that the path of the ion inside the sphere is straight. It is evident that this assumption cannot change the form of the function representing the probability: it can only modify the values of the constants which enter into it. Of any number of ions starting from a given point P (see fig. 1) the fraction which get over a path of length / without collision is e~7/4, where X=the mean free path of an ion in the gas ; so that the fraction which collide in a path of length J is 1—e-”*. Now the length of the chord 1=2rcos@, and the ions for which this represents the Recombination of Ions in Gases. 245 maximum possible path inside the sphere are those contained in the solid angle between two circular cones whose generators are inclined at 0 and 8+d8 to oneanother. Hence if P ions start from P in directions uniformly distributed throughout the hemispherical angle 27, the number which lie between the infinitesimally near cones is P sin @d@ ; hence the number which collide within the sphere is 7/2 _ 27 cos 8 m (1-¢ Me ) sin ad 0 Ngee 2p 1+3(¢ x 1) }. On the hypothesis that one collision is sufficient to stop the ion ever getting out of the field of force of the other ion, we have now calculated a value of €; for ¢ is the fraction of the number of positive ions, projected into the small sphere surrounding the negative ion, which never succeed in escaping. It is therefore equal to Nie fees 1+ 5,(¢ *—1), A brief examination of this function is sufficient to show that it is incapable of representing the values of e found experimentally *. If we put - =w, then wis proportional to the pressure, and our function may be written J oe j—lt 5 len Sl). It approaches unity asymptotically as x becomes infinite, and takes the value zero when x=0. This, however, is not sufficient to satisfy the experimental curves which, as Langevin t has shown, vary as the square of the pressure at low pressures. Expanding f in powers of « in the neighbourhood of the origin, we find the first term =w, which obviously does not satisfy the required conditions. We shall now examine what results are obtained on the hypothesis that two is the minimum number of collisions within the prescribed region which are necessary for recom- bination. We have to calculate the probability that an ion * Langevin, These, p. 150. + Comptes Rendus, vol cxxxvii. p. 177 (1903). 246 Dr. O. W. Richardson on the Rate of makes two consecutive collisions within the region considered. The general problem, in fact, is to find the chance that an ion, after any one of the above primary collisions, makes a second collision before leaving the spherical enclosur e, and to integrate the value of this over all the primary collisions which oceur. I have not been able to obtain the exact solution of the problem as thus stated ; but it is very easy to obtain an upper limit to the required number, which can be shown to be very near the true value. This may be done by supposing the ions which have undergone a primary collision at any point within the sphere to staré on their next path from the centre of the sphere. The error introduced by this supposition is greatest in the case of an ion which has collided at the surface of the sphere and when A is small. In the most unfavourable case, the probability would be increased in the ratio of two to one by supposing the ion displaced to the centre. But the number of cases near the boundary is necessarily small compared with the total number, so that the average error will be small compared with the maximum error. Thus we see that the upper limit obtained in this will not be far from the true value. The probability that an ion, starting from the centre of a sphere of radius 7, will collide before it reaches the cireum- ference is readily seen to be 1—e~"’; so that, out of P ions projected into the prescribed sphere, we obiain as an upper limit to the number which make two collisions before reaching the circumference the value P(i+ 5 Fe (es -1)) (tena). If two collisions within the prescribed sphere are necessary for recombination to take place, we find that Nf! —* e= {14 5-(¢ s—1)} (1-< s), = (wv) say, where v=r/). Kvidently ¢ approaches unity asymptotically as # becomes infinite ; also on expanding it in powers of # in the neigh- bourhood of «=0 we see that the first term in the expansion is x’, so that 6=0 when 2=0 and ¢ varies as x? for small values of #. Thus the function we have found gives a qualitative explanation of the values of ¢ found by experiment. By carrying the argument a step further we see that an upper limit to the number of ions which make three collisions We) ue ~! Recombination of Ions in Gases. inside the sphere is given by {eh} (res and generally, (MF is an upper limit for the number which make n collisions. For high values of n, however, the above product will cease to repr ‘esent, even approximately, the true value of the number required, since the error is proportional to the number of terms in the product. We should expect from the nature of the preceding argument, that out of those molecules which make a sufficiently large number, s say n, of collistons within the sphere practically the whole would result in recombination. O£ those which made n—1, but not n, collisions a certain definite fraction would become fixed, and of those which made n—2, but not m—1, a smaller fraction, and so on. In fact, if c, be written for Xx ay 20 bls n—l1 (gle Jes) the number of ions which make n collisions within the sphere, n being sufficiently large, we should expect e to be of the form em (Gn) Oh Ae ame. 1) tee Cpe) where @,_;...@, are proper fractions which gradually become smaller as pe suffix decreases. We are now in a position to test the theory by the experimental results. This may be done by referring to fig. 2. The ordinates of the various curves plotted in this diagram represent the following functions :-— e72r J A= ae’ ite SS SK 22 Ee) ca(e Mean \ D=(1+- Bir co ee | Sta, es 1— A ee re ji ; 248 Dr. O. W. Richardson on the Rate of Paes’ 4 3 2 T 0 (2) (2) (20) Pd ed 10) Recombination of Ions in Gases. 249 The reason for the insertion of the last curve will be given later. The other points in the diagram are Langevin’s experi- mentally found values of «. Those for air are shown thus : x, and those for carbon-dioxide, thus: o. In order to compare the results, the scale of the abscissze has been chosen so as to make the observed values coincide as nearly as pos- sibie with the curve C (=c;). The pressures corresponding to any point are therefore different for the two gases; for the air points, x, they are obtained from the abscissee by the relation p(mms.)=691.4, for the carbon-dioxide points, 9, they are given by p(mms.)=438 a. In the case of air the experimental points all appear to be sufficiently close to the curve C or y=c;, but a slight devia- tion from the curve can be detected at the two lowest pressures. ‘The agreement with the curve Y=t,+"1d (€3—¢4)-+°17 (¢,—¢s) seems to be exact, or at any rate within the experimental error, as the following numbers testify :— | | Values of e. p mms. Experimental. Calculated. 152 ‘Ol £009 375 06 ‘O72 760 27 we 1550 62 "62 2320 | 80 “80 3800 ‘90 ‘90 The values for carbon-dioxide do not seem to be capable of being represented by the formula with the same degree of accuracy as those for air. If the scale of «# is adjusted so that observations at low pressures come nearly on to the curve C, then the values at high pressures deviate considerably, the last but one being as much as 20 per cent. too high. It looks as though the experimental values were too large— there would be a tendency this way in the case of a strongly absorbing gas-like carbon-dioxide at high pressures, when the ionization would be large—although it is possible that there is some inherent complication in this case, of which the theory does not take account. | 250 Dr. O. W. Richardson on the Rate of A different view of the nature of e, which explains its variation at low pressures, has been given by Langevin ~. On that view the criterion for recombination is that the two ions should undergo a direct collision, considered quite apart from their previous history. If we imagine a sphere described round each negative ion, the radius 6 being some quantity of the order of, and proportional to, the mean free path; then the probability of any positive ion projected into the sphere striking the opposite ion at the centre is the chance that its originally straight trajectory would pass through a sphere about the negative ion of radius 3 —s es ae ( + TT nets Fo? the mass of the two ions being supposed equal. In this formula e is the charge on an ion, m its mass, v the original relative velocity, and s the radius of the sphere of action of the two ions. It can easily be shown that the probability of an ion projected from the circumference of a sphere of radius 6 striking the opposite ion is 5/\2\3 et) so that Langevin’s theory leads to the formula Ge c=1—(1-(5) i In this formula 6 varies inversely as the pressure and s! is independent of it, so that ¢ is of the form 1—(l—ap’)*. It evidently varies as the square of the pressure for small values of the pressure. The function 1—(1—’.x’)? is the dotted curve H in fig. 2, where the abscissee have been chosen so as to make the curve fit the three lowest experimental values. ‘The agreement is good enough at the three lowest pressures, but at higher pressures, as is readily deduced from an examination of the function, its rate of increase with # goes up continually as x increases, instead of falling off as the experiments require. For values of «>1/8 the function is imaginary. Tor these reasons this view does not appear to afford a satisfactory explanation of the phenomena. Returning to the exponential expression for e, we shall now deduce a value of 7, the radius of the spheres within which collisions have to occur, to determine recombination. Since the charge on an ion appears to be the same for all gases, and r is determined by the field of force, presumably * Comptes Rendus, vol. cxxxvil. p. 177 (1908). + Richardson, Camb. Phil. Proc. vol. xii. p. 144 (1902). Recombination of Ions in Gases. 251 ris independent of the gas. Also since w==7/d, all we have to do is to find the value of corresponding to a particular value of w for any one gas. This may be done by means of the formula for the velocity of an ion under unit field, which is given by the kinetic theory of gases, viz., rape, where e is the mean velocity of agitation of the moiecule. The author * has recently shown that the value of the velocity of the ions indicates that they have a definite complex structure, which is a function of the pressure and probably also of the temperature. In the paper referred to it is shown that at pressures greater than atmospheric the negative ions are practically all com- plex, and probably consist of three gas molecules cemented together by a corpuscle. Hence the mass of a negative ion will be equal to three times the mass of an average molecule in air. The formula for A may be written Zu A= VEmC? V2m— ; Substituting the following values: ime =o bo x 17 4 1 ie ie D- ==505 and Ca eae: we find »X at atmospheric pressure =8'8x 10-° cm. This value for X% seems to be obviously too high, being midway between the values for oxygen and carbon-dioxide. In the absence of any other evidence bearing on the question, we shall take the true value to be somewhere about 4 x 10—® cms. at atmospheric pressure. The value of x at atmospheric pressure we find from the curves to be 1:1. This gives for the radius of the prescribed spheres r=4:4 x 10-6. The work done on the ion by the electric forces before it reaches the boundary of the sphere is seen to be =2°2 x 10-“ ergs, and the kinetic energy thus set free would be equivalent to raising the temperature of the ion to about 200° C. The work done inside the sphere on an ion which recombines is about two hundred times that done outside. If we may assume that the value of r is independent of the gas, the ratio of the pressures corresponding to any given value of e for two different gases should be the ratio of “their mean free paths. Assuming that the values for carbon- dioxide at low pressures are the ones which the curve ought to fit, this gives for the ratio of the mean free path of an ion in CO, to that of an ion in air A//A== "635. * Phil. Mag. [6] vol. x. p. 177 (1905). 252 Rate of Recombination of Ions in Gases. According to the formula v= “== the ratio of the velocities of the ions under unit fields for two different gases NM (m2 should be =< (".) , where m, m’ are the masses of the 1M corresponding ions. In the case of air and carbon-dioxide the mean of the values of the ratio found by Zeleny for the positive and negative ions in the dry gases =°497. This ! D 5 : 0 Me gives for the ratio of the masses of the ions — =1'54. The m ratio of the densities of carbon-dioxide and air is 1°53, a result which indicates that an ion in carbon-dioxide at high pressures contains the same number of molecules as an ion in air. Since it has been shown that a negative ion in air at high pressures probably consists of three molecules held together by a corpuscle, presumably the same is the case for a negative ion in carbon-dioxide. Objection may be made to the present thecry on the ground that almost any function might be capable of being repre- sented by a formula such as that given on p. 247 by taking a sufficient number of terms, each involving one of the un- determined constants d,_;, &c. This is not, however, a valid objection. In the first place, the constants a are not arbi- trary; they are always positive and less than unity, which they rapidly approach as 2 increases. In the second place, reference to fig. 2 shows that in the case of air a single term of the series,viz. ¢, is sufficient to represent all the points but one within the limits of experimental error, and even that is not very far out. So that this very complex curve can be repre- sented with almost the desired amount of accuracy by a formula containing only one arbitrary constant, which is equal to the ratio between the radius of one of the prescribed spheres and the mean free path of an ion when the pressure equals unity. In the case of carbon-dioxide the points which fall off the curve cannot be brought on to it by manipulating the con- stants without making the theory lose ail its physical signi- ficance. The constants a ought to be capable of being | calculated by making some hypothesis about the effect of a collision. At present the experimental results are not sufficiently accurate to enable us to more than guess at their values. It will be noticed that roughly speaking the present theory makes e=/() for different gases depend solely on one para- meter A, the value of the mean free path of an ion in the gas in question. The smaller the value of X the more the curve e=/(p) is displaced towards the axis of e. A Portable Aéromercurial Tide- Gauge. 253 The principal results which have been obtained in this paper may be summarized as follows :— (1) The hypothesis that recombination only takes place after the kinetic energy of the ions has been reduced by col- lision with neutral molecules, when the ions are very near each other, affords a satisfactory explanation of the variation of the rate of recombination with the gas-pressure. (2) The results indicate that’ practically every ion which makes a collision with four molecules becomes fixed; that most of those which make only three, and about one-sixth of those which make only two, collisions, recombine. The terms with fewer collisions become more important at low pressures. (3) The quantity obtained by dividing the coefticient of recombination by the sum of the velocities of the two kinds of ions, when expressed as a function of the pressure, is found to depend, in the cases of different gases, on a single para- meter, which is the mean free path of an ion in the gas in question at some definite pressure. (4) An ion in carbon-dioxide at high pressures probably contains the same number of gas molecules as an ion in air. XXXI. A Portable Aéro-mercurial Tide-Gauge. By K. Honpa, Rigakuhakushi *, [Plates II. & IV.] a novel form of tide-gauge, which is a modification of Richard’s hydrometer, or of W. Seibt’s tide-gauge f, consists of a diving jar, a narrow lead (or copper) tubing and a recording apparatus. Fig. 1 shows the diving jar. A is a closed cylindrical vessel made of brass, 12 cm. high and 12 cm. in diameter ; it is screwed into a heavy lead disk D. By the tube a, water enters the vessel and compresses the enclosed air. The vessel A communicates with the recording apparatus by means of a brass tube b and a long lead tubing / (internal diam. =3 mm. in my case) ; the brass tube is bent in a form as shown in the figure for convenience of transporta- tion. * Communicated by the Author. + Seibt, Instrwmentenkunde, xvii. p. 81, 1897, 254 Mr. K. Honda on a Portable Fig. 2 shows the recording apparatus. The lead tubing / is tightly connected to a glass vessel B (3°5 cm. in diam.), which is again connected, by means of a thick caoutchouc tube, to a glass tube © (1°8 cm. in diam.).. The two arms of the U-shaped system are partially filled with mercury, and _ the pressure of the enclosed air is balanced by the pressure due to the difference in the heights of the two mercury columns. The change of pressure caused by the change of the water- level above the diving jar, appears then as the motion of the mercury column in the tube C. To record the motion of the meniscus, the following arrange- ment* is used. A float made of a ‘hollow ebonite box fits loosely into the open arm of the tube. Upon this, a thin aluminium rod is vertically erected. A pen-holder p, which carries two arms perpendicular to the pen, is fixed horizontally on the upper end of the rod. At the end of the arms, friction-wheels are attached which roll in V-shaped grooves of two vertical guides gg. In this way, the pen is constrained to move smoothly in a vertical line. Though the pen is always pressed’ against the recording cylinder 4 by a weak spring, the friction is quite insensible. The recording cylinder (20 em. high and 9:4 em. in diam.), which contains the clock-work inside it, is vertically placed just behind the two vertical guides and revolves once per day about its fixed axis. The zigzags of the curves recorded on the cylinder, which are due to the surface waves of short periods, may conveniently be eliminated to a desired degree by turning the cock k through a suitable angle. Vig. 3 is the photograph of the apparatus ready for setting ; the reduction is one-sixth of the natural size. The relation between the change of water-level above the * K. Honda, Y. Yoshida, and T. Terada, Reports of the Tokyo Physico- Mathematical Society, vol. ii. no. 16, p. 222; Phys. Zeitschrift, no. 4, p. 115, 1905. Aéro-mercurial Tide- Gauge Fig, 3. z i so=- jar and the mercury meniscus in the tube C can be found in the following way :— Let A, h, (fig. 4) be the levels of the water above and inside 256 ' Mr. K. Honda on a Portable the jar respectively ; hg , h3 be the levels of mercury in the tubes B and C. Let b be the common height of the mercury in the tubes, when the jar is not dipped in the water. If II and P be the pressure of the atmosphere and that within the jar respectively, we have P=I1+h—h=p(h;—h,) +H, where p is the density of mercury. If s;, a be the cross-section and the height of the jar, and So, 83 the cross-sections of the tubes B and C respectively, we have, by Boyle’s law, Pi{sy(a—h,) +v+s,(b—h,)} =const., where v is the volume of the lead tubing, plus that of the part of the tube B lying above the level 0. The differentials of the above two equations are dP = dh—dh,=p (dh; — dhg), dP §8,(a—hy) +0 + 8(b—he)} —P(sydhy + sodhy) ) =0; we have also the equation of continuity Seth, = —s3dhz. Hliminating dh, dh3, dP from these equations, we get dhs enagOp de Sila on i ; dh p (1 + =) | 8\(a—hy) ++ s.(b—hy) + sP } + Ps, 2 Since the first three terms in the denominator of the above expression are very small compared with the fourth, we have, neglecting these small terms, aay dh =) & aD Hence the motion of the mercury meniscus in the tube O is practically proportional to the change of water-level. We may also inter from the exact expression for dh;/dh that the volume of the lead tubing need not be small compared with that of the jar. ven, if the volume of the tubing is equal to that of the jar and the change of the water-level exceeds 10 m., the value of dh;/dh in my apparatus remains constant up to 0°6 per cent., which is sufficient for practical purposes. Hence the recording apparatus can be set up at a considerable distance from the beach. | | I ( A Aéro-mercurial Tide-Gauge. 257 aes : fea It is evident that the reduction-factor ~ of the apparatus dh may have any value whatever, which is less than -, by p suitably choosing the values of s,, s9, s;3, In my case it was 1 MGS 7 factor, by raising the immersed jar by a known height and comparing this height with the vertical line recorded on the cylinder. The effect of temperature may be calculated in a similar way. For this purpose, the product of the volume and the | pressure in Boyle’s law must be put equal to RT, where T is the absolute temperature and R a constant. Blene h is con- sidered to be constant ; we have the equations It is easy to find experimentally the value of the MS 1h dh; (1 oe ). pdhs (1 “= =) fsi(a —hy) + vt so(b—hg)} — P(sydhy + sdhg) = RAT, 2 Seth, = — s3dh3. Eliminating dh,, dhy, dP, we have approximately dhs _ gern: ne R plo(i+2 ata} ‘spP(1+2) If we neglect vin comparison with the volume of the jar, Ri is equal to Ps,a/T ; hence dh; _ a “ pl(t+®) In my case, a2=12 cm., p=13°6, and 1 + =) 91-76... hence ab 10°.C., dhs _ ae = 00-0025 cm. When the temperature changes, the vapour-tension also changes; but the change of vapcur-tension per degree rise of temperature is about 1/3 the change of pressure due to the thermal expansion of air. Hence as the combined effect of these two, we may take a BO 0083 cnt. Phil. Mag. 8. 6. Vol. 10. No. 56. Aug. 1905. S 258 Mr. K. Honda on a Portable I have also experimentally determined this ratio by heating the water in which the jar was immersed, and found 0-004 em.,: which agrees fairly well with the above value. The greater part of the enclosed air, which is in the diving jar, is subject to the daily change of temperature by 3° or 4° C. of the sea- bottom. Hence in the degree of accuracy of the present tide-gauge, which records the motion of the mercury meniscus, the correction due to the change of temperature is quite to be neglected. } To estimate the effect of the barometric change, both h and T are to be considered as constant ; we then have dP=dil—dh,=dil + pdis( 1 + ah dP {8 (a—hy) +0 + 52(b —hy) | — P(s,dhy + sgdhz) =0. Soap = —sodhs. Hliminating dh, dhy, dP, and neglecting small quantities, we get dhs a—h, dik $3 / Pp(i+”) which is, in my case, nearly equal to —0-04 mm. for the change of barometric pressure by 1 cm. of mercury. Hence the barometric change of 10 cm. in mercury only causes the displacement of the pen not amounting to 1/2 mm. Thus in the actual case, the correction due to the barometric change is quite insensible. In the above calculations, I have neglected v in comparison with the volume of the jar; but in the actual case, the influence of v does not materially affect the above conclusions. On the coast at high latitude, when the sea often freezes, the present tide-gauge works equally well. The tide-gauge may also be used for recording the tide at sea. For this purpose, it is better to suspend the recording apparatus by a rope, instead of placing it on the deck of a ship. The diving jar is plunged to the sea-bottom ; if the sea be too deep, it is necessary to hang the jar at a suitable depth by means of a buoy fixed by a three-way anchor-rope. To avoid the distur- bance of surface waves, it is required to keep the buoy itself at a certain depth in the sea. In passing, the following remarks may be made about the records obtained by my tide-gauge. Plates III. and LV. are the copy of four of the records obtained in Kitsha. Aéro-mercurial Tide- Gauge. 259 In the bay of Hososhima on the coast of Hitiga, extremely regular undulations appear superposed on the tidal wave ; the period varies from 17°7™ to 2U™ according to the tidal phase. The period slightly decreases as the tide passes from the low water to the high. In very calm weather, the amplitude of undulation amounted even to 25cm. This regular undulation is a stationary oscillation having its node and loop at the mouth and the end of the bay respectively, as actually shown by Y. Yoshida, T. Terada and the author ™~* in several bays on the coast of Sanriku. The period of oscillation is therefore given by the formula where / is the length and f the mean depth of the bay. In the present case, the calculated value is 19™, which fairly agrees with the observed one. ‘The change of the period caused by the tidal motion has also the range which is to be expected from the above formula. In the bay of Aburatsu in Hitiga, we also observe con- spicuous secondary undulations, though they are not regular. The period varies from 15™ to 22™; the amplitude frequently exceeds 15 cm. ‘The calculated period is 17™, which lies within the range of the observed periods. The tidal wave at Kagoshima is generally very smooth ; but frequently distinct secondary undulations of 19" or 24™ are observed. In the bay of Nagasaki, the secondary undulation is so con- spicuous that it is usually known as “Abzki.””. The undulation is not, however, regular; its amplitude often exceeds half a metre. On one occasion, about ten years ago, the amplitude of the abiki amounted even to two metres, and a large number of boats and steamers are said to have been damaged. According to my observations, the period irregularly varies from 25™ to 43™, Judging from the form of the bay, several nodal lines at the mouth are conceivable ; thus the largest and smallest values of the calculated periods are 28™ and 41™, whose interval fairly coincides with the range of the observed periods. March 30, 1905. Tokyo, Japan. * Honda, Yoshida and Terada, loc. cét. S 2 [. S2bOmaa XXXII. The Pendulum Accelerometer, an Instrument for the Direct Measurement and Recording of Acceleration. By F. W. LANCHESTER *. NE of the problems connected with the testing of locomotive vehicles is that of measuring and recording the maguitude of the starting and stopping efforts, and generally experimentally determining what may be appro- priately termed the “ ballistics of traction.” The instrument that forms the subject of the present paper has been designed to facilitate determinations of this description with a sufficient degree of accuracy for the ordinary purposes of the engineer, without involving any special and expensive preparation. Fig. I. PENDULUM ACCELEROMETER. ‘i tasks iB89 MODEL. 9 12 INCHES. Note to figs. 1 and 4. A, Pendulum-bob. H. Spool of paper. O. Anchorage screws. B-C. Knife-edge supports. J. Datum marker. | P-Q. Clock-work. D. Motion arm. K. Dash-pct bracket. R. Wind. E. Pencil arm. L. Dash-pot piston. 8. Handle. F. Pencil or stilus. M. Frame casting. G. Winding drum. N. Levelling-screws. The fundamental principle on which the instrument works, is that the effect of the algebraic sum of tractive forces and resistances on the vehicle as a whole, is shared proportionately by every portion of its mass, and that consequently the * Communicated by the Physical Society : read June 16, 1905. The Pendulum Accelerometer. 261 tractive effort on the whole vehicle can be ascertained if that acting on any portion of its mass be measured. It is evident that the actual measurement on a known mass carried on the vehicle could be made by means of a spring- balance, the mass being mounted so as to permit of its hori- zontal motion only ; but it is also possible and it is easier to arrive at the same result by arranging the mass as the bob of a pendulum and reading the coefficient of traction directly in the tangent of the angle of its deflexion. It will be recognized at once that the quantity being measured in this manner is the acceleration of the vehicle: hence the instrument is in reality an accelerometer, the measurement of gross tractive efforts and resistances requiring in many instances the instrument to be used indirectly, the direct reading giving the net difference between the pro- peliing and resisting forces. The first pendulum accelerometer was made by the writer as far back as 1889; this somewhat rough model is still in existence (fig. 1), and many of the diagrams taken on the Pic, 2: ea Vv railway in 1889 have been preserved (fig. 9). This instru- ment was not fitted with clockwork, so that the time-scale is irregular. Fig. 2 shows in diagram form the essential working parts 262 Mr. F. W. Lanchester on of the pendulum accelerometer ; and fig. 3 shows the actual proportions of my present (1904) model. Referring to fig. 2 in which a resolution of forces is given, let the angle of deflexion of the pendulum be denoted by 6, “ W ”=forces on pendulum- bob due to gravity, and “ '” = force due to acceleration “7,” then we have :— f=gat | Weg ane. It will be seen, therefore, that the motion of the recording pencil in order to give a uniform acceleration scale must be Fig. 3. PENDULUM: ACCELEROMETER. i +904, proportional to the tangent of the angle of deflexion. It is the form of ‘tan angle mechanism ” that constitutes one of the improvements in the new model. In the 1889 model the pencil was mounted on a sliding carriage (fig. 4) actuated by a forked arm, being an upward prolongation of the pendulum: in this arrangement, in addition to the pencil friction, two additional sources of sliding friction _ existed, those of the carriage mounting and forked operator. the Pendulum-Accelerometer. 263 Fig. 4. La o , ‘$)) Pa ig Y) Z| <| at | O uJ} 2 ul J O z <{ \ ws { LC Inithe present form of instrument the pencil arm is pivotted directly to the pendulum continuation in ‘such manner that the point of the pencil lies always in the plane of the pendulum 264 Mr. F. W. Lanchester on axis. The only theoretical disadvantage of this arrangement is that a small time error is introduced, but provided the pencil arm be made reasonably long this error is infinitesimal. In order that the accuracy of the instrument shall not be interfered with, the pendulum should be made as short as possible. It is assumed in the theory of the instrument, that the motion of the pendulum-bob is substantially that of the rest of the vehicle, and consequently its motion of swing should be negligible in comparison with the motion of the vehicle ; also its time of oscillation should be small in com- parison with the time of change of acceleration that it is desired to accurately record. This point was not overlooked in the original model, in which the length of pendulum was 3 inches only ; in the present model this has been reduced to 14 in., beyond which it is doubtful whether it is desirable to go. : : The dash-pot, which is an absolute necessity for working on road vehicles, in the original instrument took the form of an oil-well of large dimensions in which dipped a vane or paddle of considerable area. On the present model the dash-pot is a simple cylinder with spherical piston making an approximate fit, the cylinder is filled with viscous oil and is adjusted to make the pendulum as nearly as possible ‘‘ dead-beat.” Considered purely as an acceleration meter, a correction -would be necessary for any change of gradient; and if it were required, for instance, to integrate the diagrams to obtain velocity curves, either the precaution would have to be taken to work on level roads, or means found of making the neces- sary corrections. It isa point of great interest and importance that for the purposes for which this instrument is principally required, starting and stopping efforts, frictional and other resistance, &c., the readings are unaffected by gradient and no corrections are required. Put tersely, it may be said that the acceleration produced by the gravity component exactiy compensates or neutralizes the direct effect of the gradient. This point is one that it is quite easy to make clear. Let fio. 5 represent a car standing with brake applied on a gradient whose angle of slope is 8, then the accelerometer will record an amount equal to y tan@ (provided that it has previously been brought to zero on the level): now this will be a correct measure of the brake and frictional effect employed in holding the car up. Now let us suppose the brake removed, then the true acceleration (neglecting friction) will rise from zero to g tan 8, which will bring the accelero- meter reading exactly to zero, which under these circum- stances 1s the } precise measure of the applied tractive forces. the Pendulum- Accelerometer. 265 This reasoning obviously extends to partial removal of the brake, and is in fact general. a Oe Ra dt ee i ie SNe i Fe oaee In order to facilitate the accurate setting up of the instrument, it is fitted with a transverse level to ensure getting the knife-edges approximately level, the pendulum itself being relied on to obtain the correct zero position, a separate pencil or datum-line marker being fitted to the instrument, and the setting being correct when the datum-line and record- line correspond when the car is at rest on the level. When setting up on a motor-car, an approximately level place is found on the road, two trials of the setting are made with the car in opposite positions and the error divided. When on the railway a known level is chosen for setting up. A few typical diagrams taken on the railway and on motor- cars are given in figs. 6, 7, and 8. In fig. 8 we have a group of brake diagrams taken on the original model in 1889 on the Great Western and the Metropolitan Railways. These at once bring out a point of great interest, the sudden change of acceleration that takes place at the exact instant the train comes to rest; this is a characteristic of nearly all brake diagrams and will be referred to again. The max. negative acceleration recorded in these diagrams is about 4 ft./sec.sec. A starting diagram taken on the same journey is given. The maximum starting acceleration here recorded is about °6. There is unfortunately no record of the type or weight of engine or the number or weight of the coaches. 66 Mr. F. W. Lanchester on Fig. 6. Two SPEEO STAAT, 4wvo ® to = Start Stop STOP witw MAxIMUM BAAHE 3 f fEFORT & f N e } lama s ° —— EEE ee -sif | b (secende) } } / a { j JAN, IST 1905 =) Le y kK WHEELS (2 H.P. LANCHESTER. SHIDDING (Froud Surfoce dry) AND EFFECT oF CLUTCH WITH DRAWEL e “Tyee SPEED Sraar Ff CLUTCH WITHORRAGWY i és 1 “ COAST ireg * CS 5 ° t. (Seconds) 2 f ” 2 ” Ny & & TwHRee SPEED STAAT SS bs v € S we BAAHED wity REVERSING Sch Ree * Pe GEAR. ‘ a 2 | ie Ne s vs 5 3 ws . : pear ascn ATO j : as t (Seconds) <<] Aan -10 Ws Jan, 18 §905 IZHP LANCHESTER. Fig. 7. JAN, (ZF 1905 ‘THe Use of tHe BRAKE, (2 4.F. LANCHESTER. OBVIATING Vern. Slop SS = | ‘ | rr) 5 ° rs, —— t t (Seconds) rie ——_ 4S FEVER SING TEST. Novam\Branke ofler Feverse ) VPS Ra IER Dry, roads, wheels jocked) —i_i__1 sie ? t (Seconds) eae if | Jan. 12 1905 - oa es 1995. 12 H.P. LANCHESTER (2A SS ee Figs. 6 and 7 give a few typical motor-car starting and brake diagrams. The greatest negative acceleration here recorded amounts to 11°5 ft./sec. sec. against a maximum of the Pendulum Accelerometer. 267 8:5 ft./sec. sec. positive. These give respectively about 800 Ibs. per ton brake and 600 Ibs. per ton starting effort. Fig. 8. C.WRY, Brake (Leamington stop). — — —- =} — — --2 (2) C.W.RY, Brake i ed af 2) ( Paddingion slop). Sree C.WRY. SrAating. ‘ne (c) 2 eg Ee RE Metropolitan At’, Brake (Neliing Hii Gale ) De - d? ~ (South Kensington) i889 DIAGRAMS. Ordinates. Accelera/zozz. Abscisse. Time. — The ordinate (acceleration) scale employed in the present instrument is 10 ft./sec. sec. per inch, and is not quite open enough to give pleasing diagrams in the railway. The original model with its scale of 3 ft. /sec. sec. per inch was better suited to this class of work; but the much greater range and general compactness of the 1904 model renders it much handier and better for motor-car work, the purpose for which it is primarily intended. In figs. 6 and 7 the time-scale (abscissze) reads from right to left; in fig. 8 the time-scale reads in the opposite direction from left to right. It has been remarked that a characteristic feature of brake diagrams is the suddenness of the drop at the instant of stopping. This is a very interesting and important point, inasmuch as it is the cause of the © jerk ” nearly always experienced just as a train comes to rest; it was in fact in 268 The Pendulum Accelerometer. investigating this jerk in 1888 that the idea of the pendulum accelerometer occurred to the writer. At that time it was currently supposed that the jerk was the effect of the recoil of the buffer springs after stopping; whereas a very little consideration shows that it is in reality sudden change of acceleration that we recognize physiologically as “jerk,” that is d//dt, and not change in the direction of motion. It sug- gests itself in fact that the term “jerk 7 might well be given a scientific meaning and be defined as a s/dt. The value of df/dt at the moment of stoppage in the case of a rigid body sliding on a rigid plane surface would be infinite. In actual fact, in the case of a train brought to rest by its brakes the value of d//dt is so high that the correct form of the curve at the moment of stopping is beyond the power of the instrument to properly record. In all the diagrams the lag of the pendulum will be noticed, and in most cases the line shows that the “dash- pot” has been insufficient and the pencil has overshot the mark. The peculiar form found on diagram 3 fig. 6 is due to a partial vacuum formed in the dash-pot on the sudden release of the pendulum from its extreme position. It is probable that the correct form of the drop would be sensibly perpendicular to the datum-line. It should be more widely recognized that a great part of the art of properly braking a ‘train, or in fact any other vehicle, consists in taking the brake nearly off just before stopping o. itis not easy ‘to obtain a train diagram in which this has been done, but diagram I in fig. 7 is a good example taken ona car in which the driver was paying special attention to the point. Many of the diagrams, figs. 6 and 7, are particularly interesting to the motor-car engineer: the loss of starting effort area (which is equivalent to velocity) during gear change, the exalted starting effort obtained whilst the energy of the flywheel is being drawn upon, the curve of falline effort (largely due to increasing wind resistance) ,—all these are points that repay the most careful study. Other applications I anticipate for the pendulum accelero- meter are its employment in the determination of the lateral (centrifugal) forces and coefficient of friction when rounding corners, ‘the determination of wind resistance at differ ent speeds and other resistances to traction, the determination of the thrusts and resistances of launches ve ; but these and the further discussion of the engineering aspect of the subject does not come within the purview of the present paper. May 11th, 1905. F 260021) XXXII. A new Form of Pyknometer. By R. V. STANFORD*, HE construction of this modification of the common U-shaped pyknometer will be seen from the accom- panying sketch. It may be readily made before the blowpipe, | i} -—S7i- of any desired content from 1 ¢.c. upwards. It is filled with the liquid whose density is desired by attaching at B a tube which dips into the dish containing it, and applying suction at A. The apparatus, entirely filled with liquid at room temperature, is placed upon a stand in a thermostat, and the plunger CD uffixed at B by means of rubber tubing. When the liquid has attained the temperature of the bath, a finger is placed over the aperture E in the piston-rod, and the piston depressed until the liquid meniscus has descended to the mark «. The finger is then removed from E, the plunger detached, and the instrument removed from the thermostat and weighed. The plunger consists merely of a piece of glass tubing some 0°5 cm. outside diameter, into which a smaller tube fits, as shown in the figure. The piston is made airtight by means of a small rubber ring. This form of pyknometer has the advantages that it dis- penses with a wire suspension, and that the adjustment to the * Communicated by the Physical Society: read June 16, 1905, 270 Dr. A. D. Denning on a Simple Method of mark @ is much easier and more accurate with the plunger than is the usual one by means of blotting-paper applied at A, and in addition the ‘horizontal arm permits ot its employment in the common thermostats with opaque sides, while reducing to a minimum the amount of contained liquid outside the bath. The ee Birmingham. XXXIV. A Simple Method of Determining the Radiation Constant: suitable for a Laborator ‘y Experiment. By A. D. Denninc, M.Sc., Ph.D., Demonstrator in Physies in the University of f Birmingham oe HE following experiment was suggested to me by Prof. Poynting, F.R.S., as a laboratory experiment, and as it is by no means difficult to carry out and appears to give good results, it may be useful to give an account of it. The principle of the method followed may be thus briefly described :—A hemispherical radiator, blackened inside, was quickly placed over a flat silver disk of known dimensions and which formed one of the junctions of a constantan-silver thermoelectric couple. From observations, at definite in- tervals of time, of the deflexions of the moving coil of a low- resistance d’Arsonval galvanometer included in the circuit, the initial rate of rise of temperature of the disk was obtained and this result, when substituted in the equation (a), given below, gives o the radiation constant. For, suppose m=mass of silver disk, s=its specific heat, dT/dt =initial rate of temperature change, then ms.dT/dt=initial amount of heat received by disk. But if A =exposed area of disk, : R=radiation trom that area per unit of time, and R,= radiation from blackened hemisphere, then the gain of heat by the plate — (Ry — R) A, 9S. Ly Ab. Using Stefan’s Law, we may write: eo? and! shee where o =the radiation constant, T & T,=the temperatures of disk and hemisphere, respectively, measured from — 273° C. * Communicated by the Physical Society: read May 12, 1905. + The initial rate of temperature rise being taken to avoid gain of heat by disk from conduction and convection effects. Determining the Radiation Constant. 271 Consequently mse atid: —No(l,—T), or fs ms dT (2) o= AT) Sor FI a) Ca ua If the galvanometer readings were proportional to the current existing at the instant of reading, we should have dT /dt by simply noting successive deflexions at known times. But, owing to the moment of inertia of the moving part of the galvanometer and the viscous resistance, the reading will not always indicate the current at the instant, as will be seen from the investigation below (Appendix). In this case, however, the readings did indicate the temperature, when plotted to eliminate oscillations. The actual arrangement of the apparatus is shown diagrammatically in fig. 1. A is a cylindrical vessel of | Fig. 1. 15:3 ems. internal diameter: to the underneath side of this vessel was soldered a polished copper hemisphere, indicated 272 Dr. A. D. Denning on a Semple Method of in the figure by the dotted line, and which, before an experiment, was evenly coated with a layer of lampblack produced by the combustion of camphor. The space between the cylindrical and hemispherical vessels was used as a reservoir for steam or the other substances which were employed to maintain the hemispherical radiator at the temperature T,. The tube B served as an inlet and the tube C as an outlet for the steam; the wider tube, D, was subsequently added for the purpose of covering the hemi- spherical radiator with ice. During the course of a series o! observations this part of the apparatus rested on the wooden board, W. (The stands supporting this latter are not shown in the diagram. ) _ As mentioned above, the elements of the thermo-junctions were silver and constantan. In order to have an appreciably large surface to receive the radiation at the one junction, the silver and constantan wires were soldered on to a silver disk, ii. This disk, after having been thoroughly weli polished, was mounted in a vulcanite frame, FG, which fitted into the wooden board carrying A. The disk also was lamp- blacked before being used. Ifit be considered desirable to prevent the disk receiving radiation at the sides, felt or some other non-conducting material might be so wrapped round the disk that only the top surface of it was exposed to the hemispherical radiator. The wires coming from the disk were led down the arm GH to the binding-screws at the bottom. The other junction of the thermo-couple was placed, together with a thermometer, T, in a test-tube containing oil in the glass beaker, K. The two constantan wires were further soldered to copper wires leading through a mercury commutator to the galvanometer. These last two (the Cu-constantan) junctions were passed through rubber tubing fitting into two holes in the lid of a tin canister packed with cotton-wool. The dimensions of the silver disk were: Diameter =2:015 em. Weight=8°911 er. Thickness=0:275 cm. Sp. Ht. =0-0567. This value for the specific heat was the mean of several determinations made by means of a Joly steam calorimeter. Inasmuch as the source of steam and also the outlet from the vessel A were on the side CD of the apparatus, a long piece of sheet nickel, polished on the one side, was tacked on to the wooden stand W, with the idea of screening the underside of the silver disk from the hot air currents. It was also found advisable to further protect the disk from Determining the Radiation Constant. — 273 draughts by loosely fixing under it a wide pad of cotton-wool, held in position by a wire passing between the retort stands supporting W, since otherwise the opening and shutting of doors, &c., was sufficient to occasion an irregular and jerky motion of the galvanometer-coil. During the boiling of the water, the silver disk was covered by a screen with one edge resting on two thin corks to prevent actual contact between the disk and the screen. This screen was made by taking a piece of sheet nickel, approximately twice the size of the board W, doubling it into two with the dull side inwards and, after placing a layer of cotton-wool between the folds, wiring the two folds loosely together. When steam had passed for some time through the vessel A, the latter was placed on the screen. At a particular instant the screen was removed, A was lowered over the disk and some six to ten readings of the position of the cross-wire image were taken at intervals of five seconds (in the majority of cases). In order to find the temperature equivalent of the galvanometer deflexions, the silver disk was kept at a constant temperature, and the deflexions of the galvanometer were noted when the temperature of the other junction was altered by a known amount—subsequent reference is made to this point. Before beginning an experiment it is necessary to ascertain that the two thermo-junctions are at the same temperature or to know the difference of temperature between them. In these experiments the following procedure was adopted :— By insertion of the shunt-key S the galvanometer was short-circuited and its zero-position found. Did the de- flexions, consequent to the removal of the key, indicate that the temperature of the disk was too low, the hand was held over the disk until the cross-wire image returned to its initial position of rest ; whilst if the temperature were too high, ether was poured on to a piece of cotton-wool resting on a crucible lid, and this was allowed to evaporate in the neighbourhood of the disk. The results of a number of experiments extending over varying ranges of temperature are given in Table I. In the last column but one are given the values of the initial rate of change of temperature, whilst the last column contains the values found for «.10°. It will be noticed that in some of these experiments alcohol and acetone were passed through the radiating vessel and afterwards condensed in a condensing worm (not shown in fig.). But subsequent experiments Phil. Mag. 8. 6. Vol. 10, No. 56. Aug. 1905. E 274 Dr. A. D. Denning on a Simple Method of TABLE I, Temperatures. Date. AU a dT /dt. ae 1 U8 29/11/04 100-0 ©. 18°7 C. 9-44 5-19 5 12/12/04 99°5 156 9°71 5:30 2 12/12/04 99°5 16°3 9°55 5:22 < 17/12/04 98°5 17°4 6:47 3:36 3 19/12/04 786 14:8 4-95 3:92 3 19/12/04 78°6 9-2 7:25 5:39 is 20/12/04 736 14-5 671 5:32 By] 20/12/04 -| 57 12:8 4-24 5-43 3 20/12/04 57 131 4-24. 5-46 E ) 2 21/12/04 0 152 1-06 5:24 = 21/12/04 0 14-7 1-06 5:42 (results recorded in Table II.) showed that easier manipulation and equally satisfactory results were to be obtained by simply placing hot water in A ; owing to the large bulk of water which A could hold (nearly two litres), its rate of cooling was comparatively slow ; whereas the observations necessary for each experiment were made in less than a minute. TaseE IT, Temperatures. Date. T°. T°, dT /dt. o. 10°. ese De Se ta oe ae a 3 ai ToT 3 = a a rate 27/1/05 100°5 ©. 166 C. 9:83 526 | 97/1/05 100°5 178 9-83 5290 98/1/05 75:0 17°8 5:99 530 | 28/1/05 73:0 17°8 5°76 5:32 | 98/1/05 60°5 17°6 4-32, 549 | 28/1/05 60:0 17°8 4:32 5°39 | 98/1/05 45-0 15°5 2:64. 5:32 28/1/05 43°8 15:8 2-40 5-40 31/1/05 0 15°7 1:08 5:14 31/1/05 0 14:9 1-08 548 By quickly removing the radiator after sufficient readings had been taken and placing the cotton-wooi saturated with Determining the Radiation Constant. 275 ether near the disk, it was possible to take several sets of observations in fairly quick succession—especially if a current of air were maintained across the disk. Owing to the small range of temperature prevailing when the ice was used and the possibility of disturbances due to convection, such close agreement with the other results as was actually obtained was hardly to have been expected. It has been thought advisable to include all the experiments made to indicate what kind of accuracy can be expected. A glance at the values for o given in the last columns of both tables will at once show that two of the values are very much lower than the other nineteen. The most probable explanation for this is that somewhere in the galvanometer- circuit there was poor contact and a consequent increase in the circuit-resistance—most likely in the mercury commutator, since these at times are very unreliable. Indeed, deter- minations of the equivalent of the galvanometer readings made from time to time during the course of the first series of experiments showed variations in the sensibility of the galvanometer. Hence it were better to measure the sensi- tiveness of the galvanometer directly before taking a series of observations by arranging that the simple reversal of a commutating-switch might place the galvanometer in circuit with a low resistance, the fall of potential along which is a constant small fraction of the E.M.F. of a storage-cell. Ignoring these two values, we find uniformity and agree- ment among the remainder—the average of the residual nineteen results being about 5:3. The mean of Kurlbaum’s more elaborate experiments was 5°32. The simplicity of construction of the apparatus and the principles embodied in its use will, it is hoped, recommend the experiment as a laboratory method of illustrating an important and funda- mental law. APPENDIX. Note on Motion of Galvanometer Coil. In order to take into account the effect of the moment of inertia of the moving coil and the viscous resistance of the medium, let us suppose that a steady difference of 1° C. between the thermo-junctions gives a steady deflexion of the galvanometer-coil of » radians, then a steady ditference of temperature of T’ would give a steady deflexion @=XIT’. 276 Dr. A. D. Denning on a Simple Method of If the torsional couple per radian exerted by the suspension is w, then the couple on the fibre in a steady state would be poO=wrl, But the observations are taken during the motion of the galvanometer-coil, 7. ¢. when the change of temperature is not steady. In this case 20 do = UA = Kee vires le ne where I=the moment of inertia of coil, K =the viscosity coefficient of the air, T= the initial difference of temperature ; that is a6 dé le +K + pwO=pnrT ; Bae K/I=k and p/l=n?. the equation of motion becomes Ono AG) Pe ae +n7O=nrT. Now, if T be approaching a steady value A, according to the exponential law we have SAN lia) consequently GeO 300 8, ae k ae TG —— nl Nel eee the solution of which gives O=AA(1— anes) —Be 2 sin( / w= t4e), 2 The second term is evidently oscillatory so long as n*> s : but if & be large it dies away rapidly, or to such an extent that it can be eliminated by plotting, and we have only to deal with n2e—Pt O=AA (1 Te) differentiating ap ie? n? di =)pAe P kip — 1} but from the differentiation of the exponential equation, Determining the Radiation Constant. 277 given above, a= pac and since we only want the initial rate of rise of temperature aT ih = (PA ao=P, but dO 14 ApAn? dtin pp? —kp+n® Hence iv | DO ay pepe ae eo on n* * dt K By plotting galvanometer deflexions against the times, we can eliminate the oscillations and obtain the initial rate dt only concerned with the ratio of a | ® we can use galvano- dt meter scale-divisions instead of radians. ) Consequently, then, in order to obtain the initial rate of of change of @, 7. ra | r, from the curve. (And since we are rise of temperature, the observed a X must be multiplied by (p?—kp +n?)/n’. Should p?—kp be small in comparison with n?, this fraction may evidently be neglected. But to test this we must first find n, p, and & for the particular galvanometer in use. (i) To find n: If the circuit is open, & is negligible and 2zr/n is the time of swing. Or, if the observed period of free swing be P then n= 2ar/P. Gi) To find k: For the deflexion @ on closed circuit we have ale he d= Be) 2 sin(y /e— © i+B), and if successive deflexions or elongations 6,, 6, 03, and 6, be observed it is easily seen that . 6, —O, poe kar ane a fea 278 Method of Determining the Radiation Constant. (iii) To find p: From the exponential law we have dT | a1 Ape Ph, dt and therefore oe oc Ape Pi= Ape? say. dt Similarly for time ¢, (where t= 2¢,) 0, =A, pe "a= A pe Ph , that 1s 6 |b. = 0%, or pt, = log 04/65. But by plotting the deflexions against the times we get the deflexion curve 6=A,(1—c-¥), and from this curve we may measure 0, and 6, for a pair of times such that t,=2¢,, and consequently we find With the galvanometer used in these experiments the following values were obtained for these quantities : p=0:0069 5 n=—07b045) and) £0 tye which, when substituted, give pe —kpt+n 427 n? 7 4987 which may be taken as 1, that is to say, the observed value of = / rX could be taken as a measure of the initial rate of rise of temperature of the silver disk. 24964 XXXV. Notices respecting New Books. Ueber Harmonie und Complication. Von Dr. Victor GoLDScHMIDT. Pp. 136+ iv, with 28 figures in the text. Berlin: Julius _ Springer. 1901. Uber harmonische Analyse von Musikstucken. Von Victor Gotp- scHmipt. Ostwald’s Annalen der Naturphilosophie: Leipzig, 1904, vol. ii. pp. 449-508. For centuries has it been a favourite study of able thinkers to investigate the fundamental principles upon which the various branches of knowledge have been developed, and to trace a con- cordant relationship in phenomena to all appearance entirely dissimilar and disconnected. No doubt it will be ultimately dis- covered that the varied and apparently divergent paths along which science progresses meet eventually in the same, though may be many-sided, goal—the constitution of matter. In these days of extreme specialization, when each worker sees little more than a small portion of some particular subject, it is of importance to have our thoughts occasionally brought back to the possible re- lations underlying the fundamental principles of different branches of science. Professor Goldschmidt is well known as one of the leading crystallographers of the day ; and his work has always been distinguished by its versatile and philosophical character. In this remarkable treatise Ueber Harmonie und Complication he has, with characteristic energy, undertaken a task requiring a breadth of know- ledge such as is rarely possessed by any individual. Few probably feel at home in all of such a diversity of subjects as are discussed by him ; and, indeed, to many such a conjunction may seem altogether fantastic, to be dismissed with a jest. Nevertheless Professor Goldschmidt submits to the reader a strong case; and the evidence produced is far sounder than the kind met with in most philo- sophical writings dealing with uniformity in the universe. More than a century has elapsed since Haiiy established the sreat crystalline law on which the whole science of crystallography has been built. This law, usually known as the law of rational indices, states that the positions of the natural faces bounding a erystal are not haphazard, but obey a very simple relation. Haiiy himself studied the more complicated question of the arrangement of the ultimate units in a crystal; and the law mentioned is an immediate deduction from the principles laiddown by him. Later writers have, however, seldom gone behind the law, and they mostly ignore the absolute positions of the faces. The habit, that little understood character of crystals, which varies so strangely in crystals identical in other respects, is not considered or explained by this law, beyond that all crystals have the symmetry of one of thirty-two classes. Professor Goldschmidt, in the course of a number of important papers which have appeared in the Zeitschrift fir Krystallographie und Mineralogie during recent years, pro- poses an extended form of this law, which includes the principle of symmetry and at the same time places the relative development 280 Notices respecting New Books. of the faces lying in the same zone ina novel and clearer light, Thus, suppose we have a series of such faces ABODEFGHI, no two of which are parallel; we select the two most prominent faces, A and B, as coordinate faces and the next in importance, C, as the unit face. The remaining faces, then, fall into groups [DE], (FGH1}, and so on, asshown in the following Table. The members of each group will be similar in their characters: size, frequency of appearance, &e. Primary faces: A B N, = 0 co Normal row 0. 1 complication: A C B N, = 0 1 co Normal row i. 2complication: D D C E B N, el) + 1 2 ow Normal row 2. 3 complication: AFDGCHEIB N, = 043313230 Normal row3. The numbers under each face are the ratio of the corresponding indices, supposing that A and B are the pinakoids (0 1) and (1 0). Each row is developed from the preceding in precisely the same way. It was natural to one of Professor Goldschmidt’s philosophical temperament not to confine his attention to the morphological characters of crystals, but to investigate the possibility of a wider application of this same law. His investigations resulted in the vork under discussion, Ueber Harmonie und Complication. The brief introduction deals with the arrangement of the faces on a crystal, from which, as we have pointed out, the author originally deduced his law of complication. Then follows pro- bably the most important and—running as it does to 66 pages— certainly the longest part of the book, on the Sensations of Tones. The science of sound in its physical, its esthetic, and its physio- logical aspect has received so much attention and study as to provide obviously a ready means of testing the principle of compli- cation developed by the author. We may here remark that the later treatise, Uber harmonische Analyse von Musikstucken, is an extension of this part with a somewhat different treatment, as will be explained below, and is intended more particularly for musicians. The notes comprising the diatonic scale of C major and their relative vibrations (z) are ¢ d é ip g a b Cc 9 ia 4A 3 oY 15 ¢ z= 1 8 4 3 2 3 8 2 tonic second third fourth fifth sixth seventh octave Notices respecting New Books. 281 : z—l : By means of the simple transformation p= —— another series z —_— of harmonic numbers is obtained : Cc ad € p=0 F BF which bears an obvious resemblance to the third normal row. It, however, lacks the components p= 32, 3, and 3, and contains two with high symbols which do not occur in that row. The latter notes, as the author plausibly explains, have really no part in the scale of C, but belong to that of the dominant, being the fifth and third respectively in that scale. Of the additional notes required to complete the row, dp( p=3) is very closely related to the tonic, and, indeed, forms the ordinary modulation to the chord of the sub-dominant. The remaining notes f¥ (p=) and ab( p=3) are both associated, though not so closely as the remaining notes of the series, with the harmony of C major. The complete series corresponding to the third normal row is finally ee Gets cSt weil aD! eG Lbs 2g ee a pains ei eis aeptcey cls BBL Since the harmonic numbers increase with the pitch, the author terms this series ‘‘ rising harmony.” Another harmonic series is obtainable in the same way froin the wave-lengths (7) by means of the transformation p = = 4 The wave-lengths are inversely proportional to the vibrations, and we may for convenience assume that z= 7» and consequently pp=2. Applying this transformation to the scale of A minor, we have a Ge as fe € d ¢ Di ine: a Neva iis (ea Mao kee Cee Rae asrd st aleh ge Suda eR jeg) a2 on) ee oh ee eee The bar over the letters distinguishes the method of trans- formation, and has no negative or minus significance. As in the previous case, the note with the high symbol is omitted, and the missing members of the third normal row are introduced, giving the complete series: a if € Ap) cad Chien '¢ b a Res on oan fos aoe Phiul. Mag. 8. 6. Vol. 10. No. 56. Aug. 1905. U 282 Notices respecting New Books. Since the harmonic numbers decrease with the pitch, the author terms this series “falling harmony.” Thus the major and minor scales appear im a new and interesting light as, so to speak, the inverse or the reciprocal of one another. The close connexion. between the scales of C major and A minor is familiar, and is emphasized by the fact that the combination of the two gives the chromatic scale. The author discusses the usual method of developing this scale, namely, by means of successive tempered fifths. Either the rising or the falling harmony may be employed for the analysis of music; but Protessor Goldschmidt finds it more convenient to adhere to one, the msing harmony, even for pieces composed in a minor key. He analyses and discusses in detail seven examples selected from the works of classical composers. To illustrate the method, we will give his analysis of Haydn's tamiliar hymn. ae =i Te pec | i 2 | | | Gott er-hal-te Franz den Kai- ser un-sern gu- ten Kai - ser Franz. 2 | 2s — | | | | ee ee ee ee ees Gott er—hal-te | Franz den Kai — ser unsern guten | Kai -ser Franz Gs sock, Ora C ba ft g F ed: ve CONE Ginn ON AORN a g ¢. @:.b | oe: b" fh .g |. eee Oe ots ; d CLR fo PEPE Gi ee en b |.” Sige eeiar 1g, A he é fee iG NOMA: salto) SL a> Ma TA EiMigaieeereae OZ O1 OF 41 | 0313 O31 0313 0313 OF | 03 $1 0313 03] 032 0332 . OF d d d a ad c C d ee y me g ‘ oe Re: I Le Z g g a Gq ‘Cage Oo O.. Fe ee eee vy) No single cipher occurs which exceeds those included in the third normal row. The importance of the note (p=3) in this selection may be noticed. The next section deals with the physiological and psychological grounds for the harmony of tones. Our knowledge of this inter- esting subject has been enormously advanced by the classical researches of Helmholtz, whose great work Lehre von den Tonemp- findungen marks an epoch. It is still, however, uncertain how the sensation is conveyed to the brain, or by what means an educated ear is able to distinguish almost minute differences of pitch. Helmholtz considered that the fibres of Corti’s organ correspond in a manner to the wires of a pianoforte: others, among them Notices respecting New Books. 283 Professor Goldschmidt, do not altogether agree with him and think that, numerous as these fibres are, they are not sonumberless as to account satistactorily for the minute gradations which are perceptible ; the author believes the drum of the ear to play a very important part. There can be no doubt that the appreciation of musical tones depends wholly on the brain, which can, indeed, act quite independently of the organ of hearing; for do we not think, even dream, of tones ? The second chapter is taken up with the Harmony of Colours, and is analogous to the first chapter, but with some important modifica- tions necessitated by the dissimilarity of the organs by means of which our senses are affected. Since the eye, unlike the ear, has a range of less than a single octave, and, if unaided, 1s incapable of resolving a composite wave into its constituent parts, there 1s nothing con- nected with light which corresponds to music; and the discussion must, therefore, proceed on different lines. The extent of our knowledge of the constitution of matter has been vastly increased by the discovery of the spectroscope. Much of what it has shown us we understand; but there still remains much which is not yet explained. Many writers have endeavoured to trace a relation between the spectral lines of the same elementary substance, and also between the different elementary spectra, but as yet with little success. If Professor Goldschmidt’s principle of compli- cation reveals the existence of some such periodicity in the elementary spectra, aud determines for each the fundamental line which corresponds to the tonic in a musical scale, a great step will have been made towards the elucidation of the phenomena. In the present work the author, however, merely deals with the fringe of the subject; he shows that the Fraunhofer lines in the solar spectrum, with the exception of G, form a series of the falling harmony type, and so do the Imes in the spectrum of hydrogen. Possibly he intends to discuss the subject at greater length in a separate paper. The remaining sections of this chapter deal successively with the various theories of colour-vision which have been put forward, especially that of Young and Helmholtz, and the evolution of eolour-vision in Man and its development in children. In the concluding chapter it is briefly shown that the symmetry involved in the law of complication is discernible in the characters of the lower organisms, in corals and in plants; and further, that the methods of subdividing units of length, weights, and measures, and systems of money, all conform to the same principle. | We have already mentioned that the later paper, “‘ Uber har- monische Analyse von Musikstiicken,” is an expansion of the section in the earlier work treating of the Harmony of Tones, though the discussion is a little different. Since a knowledge of crystallography is not among the ordinary qualifications of musicians, the author has wisely based the discussion on the diatonic scale, and not on the development of faces on a crystal. He here shows that the transformations from the wave-lengths 284 Notices respecting New Books. and the vibrations to the series-numbers have a real physical significance, and are’ not merely juggling with numbers. Thus je Docs ay is the ratio of the two portions into which half a stretched deen is diviled by the node corresponding to the particular harmonic, and pis double of the inverse of this ratio. Musicians should find the author’s method of analysing music of great practical value, since it enables the construction’of the whole com- position to be visible almost at a glance. The notation is simplified by the employment of letters to represent the principal chords ; e.g., d for the major (Dur) and m for the minor (Moll) chord. To illustrate the method, Beethoven’s “Die Ehre Gottes” is analysed in the minutest detail. Professor Goldschmidt has undertaken a great task and has acquitted himself with conspicuous abilitv. The principle which he has enunciated and discussed has already attracted no small attention among continental writers. A new theory not only coordinates, and throws fresh light on, facts already known, but opens out vistas of fields for further research. We anticipate, therefore, that “Uber harmonische Analyse von Musikstiicken ” is only the first of a series of papers in which the author discusses in detail various aspects of this fascinating subject. Die Formelzecchen. Hin Beitrag zur Losung der Frage der algebra- aschen Bezerchnung der physikalischen, technischen und chemischen Gréssen. Von Otor LinpEers. Leipzig: Jah & Schunke. 1905. Pp. 96. THERE can be no doubt that the subject of notation 1s one of growing importance in science, and the desirability of an inter- national system is hardly open to question. The saving of time and worry which would result from the adoption of such a system would be considerable. Efforts in this direction have been made before, and although a few international symbols, such as z, B, H, p, &c., have become firmly established, an extension of the some- what meagre list 1s to be fervently desired. One cannot help admiring the patience of the author in drawing up a table of symbols for no fewer than 871 physical and chemical quantities, giving their dimensions in the C.G.S. system, and their proposed symbols, not only according to his own system, but also aecording to twelve other authorities. In many cases, the columns allotted to the latter are blanks. In his own system of notation, the author presses into service the Latin, German, Greek, and Russian alphabets. The author’s effort is deserving of all praise, and we should be doing him an injustice did we omit to mention that he by no means regards his own proposals as final, but only as tentative and forming a contribution towards the subject; he clearly realises that the time is not yet ripe for the definite adoption of an international system of notation, and that such a step should only be decided upon after very careful consideration and free and thorough discussion of the various systems proposed. z aid = eames a NN Sh + Oe tm a * y # i - eam & by 4 A = - etl > $ s ff f \ 5 ‘ + 4 1 - ni e y a ' 2000 1500 1000 2000 1500 2000 1000 500 0 250 500 750 1000 1250, ~| A\re| LENG TH 1250) Z| Javed 5 250 100 750 1000) Phil, Mag. Ser. 6, Vol. 10, Pl. II. 2000 ArciLENGTH 1500 1000 0 # 5 (0) 250 500 750 1000 1250 2000 1500 1000 500 0 250 500 750 1000 1250 An | 2000 1500 1000 ' zi oes . Le he BGA ig 2 oe ne a ee ~ > Phil. Mag. Ser. 6, Vol. 10, Pl. IID. os GPS55AM Decal O55 EM Dec.29 ‘UL9DI WIS 7OUD L0979 SIM LOY JOY FOOL IAT 807° AM 22. 10”°52”"AM 30 Phil, Mag. Ser. 6, Vol. 10, Pl. IV. 8° 58" AM, Jan. G4 25™AM, Jan.3. fs pon a % = S SS Uj) was JUD LDL, SOM L3Y 714 S061 UO’ a 8°5”AM,¢ 74 5357 AM le LAYYS EE XED Falk Z }, THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SIXTH SERIES.] SEPTEMBER 1909. XXXVI. On the Statistical Kinetic Equilibrium of Ether in Ponderable Matter, at any Temperature. By Lord Kxutviy*. § 1. evn SIDER first the simplest possible case, a piece of solid matter of a few millimetres or a few centimetres greatest diameter, placed in space at the earth’s distance from the sun, say 150 million kilometres ; for par- ticular example, let us suppose two globes of metal, or rock, or glass, or the bulbs of two thermometers, of a centimetre diameter, one of them coated with black cloth and the other with white cloth, side by side, at a distance of a few centi- metres or metres asunder. Tor the most extreme simplifica- tion, suppose no other matter in the universe than ether, the sun, and our test globes. From our knowledge of the pro- perties of matter, it is obvious that each of our test globes will, in a few minutes of time, come to a steady temperature. In these circumstances, each globe sends out by radiation as much energy of waves travelling out through ether, as it takes in from the sun; after it has been long enough exposed to come to a steady temperature. § 2. The internal mechanism in each elobe | consists of atoms of ponderable matter, with ether permeating through the whole volume of the globe, and locally condensed and rarified in the space around the centre of each atom; as I * Communicated by the Author, having been despatched for Section A of the British Association at Capetown. Phil. Mag. 8. 6. Vol. 10. No. 57, Sept. 1905. xX 286 Lord Kelvin on the Statistical Kinetic have assumed, with explanations, in §§ 162, 163, 164 of pp- 412, 413, and in § 3 of pp. 487, 488 of my volume of Baltimore Lectures. § 3. The action of this mechanism in our case under consideration, involves the communication of energy from incident waves of sunlight to the atoms of the solid, in the surface of the hemisphere illuminated by the sun; and the communication of energy from the atoms to ether outside the globe, in the form of waves travelling out zn all directions from the surface of the globe. The travelling of this energy through the volume of the globe is carried on according to the laws of the conduction of heat through solids; modified, but scarcely perceptibly modified, by convection currents in the ease in which the globe is the bulb of a mercury thermometer. § 4. Our present knowledge of the radiational properties of matter does not quite suffice to let us pronounce for certain, which of the two globes will have the higher steady tempe- rature : as this depends, not only on the well-known higher receptivity of the black surface than of the white for sun- heat; but also, on the difference of radiational emissivities of all parts of the two surfaces to surrounding space. It seems most probable that the black globe will be steadily warmer than the white; but we cannot say with certainty that this is true. Suppose for a moment that the steady temperatures of the two are the same; and now whiten the hemisphere of the black globe remote from the sun. This will cause the’ globe which is now black and white, to be warmer than it was, because it wili radiate less into void ether than it did when it was all black. § 5. Now blacken the hemisphere facing from the sun, of the globe originally all white. Its temperature obviously will be lowered. Thus we have, side by side, two globes each with a white hemisphere and a black hemisphere; facing respectively towards and from the sun. The globe of which the black hemisphere is towards the sun, will certainly be warmer than the other, when a few minutes of time has been given for the temperature of each to become steady. § 6. It is not possible for a human experimenter to attain to the extreme simplicity ideally prescribed in §$ 1-5 above. But it has occurred to me (and probably to many others) that instructive experiments might be made by observing the temperatures of two equal and similar thermometers, placed beside one another on a wooden table (or on two similar tables of the same materials) or on a cushion or layer of very fine cotton wool: each thermometer between the folds of a doubled sheet ; one of white cloth and the other of black; both Equilibrium of Ether in Ponderable Matter. 287 exposed in the open air under sunlight, or under the light of a more or less cloudy sky, or under moonlight or starlight, or in the darkest attainable cellar. § 7. Not being at present able to undertake experiments of the kind, I asked Dr. Glazebrook a few weeks ago if he could conveniently allow. some such experiments to be made under the auspices of the National Physical Laboratory. He kindly consented, and asked Dr. Chree to commence an in- vestigation of the kind. I have to-day (28th July, 1905) received the annexed description of his work, and statement of results. § 8. It is very interesting to see in Dr. Chree’s results how large are the differences in the temperatures of the thermometers under black and under white cloth, ranging from +5° to ‘6° cent., even at times when the sky is covered with dark clouds ; and how comparatively moderate are the differences ranging from 1°1 to 3°°6 cent., at times of exposure to direct sunshine. § 9. Returning to § 4 with one of the globes black over its whole surface and the other white: suppose the two to be taken to 1000 times the earth’s distance from the sun; and suppose, all at about the same distance (for simplicity of calculation), 999 stars, each equal to our own sun, to be scattered through space, round the place of our ideal ex- periment. The total of radiational energy coming from all these suns to the place of observation per unit area, will be one one-thousandth of the amount coming from our own sun in the case of §$1, 2, 3; and the difference of steady temperature between the white globe and the black globe may be about one one-thousandth of that which it would be in §$ 1, 2,3. This last arrangement would be some- what similar to an exposure to starlight on a cloudless night, at the top of a high mountain of our earth, with two or three polished silver screens between the tested globes and the mountain top. It does not, however, seem probable that any differences of temperature will be perceptible on the two thermometers exposed only to stellar radiation from the sky. Even less of difference may be expected when the two thermometers are placed in the darkest attainable cellar. The bolometric method would of course be much more sensi- tive than the comparison of two ordinary thermometers : even of the most extreme sensibility: and it will, I think, be worth while to try it in cases in which the thermometric method fails, or almost fails, to show any difference between the temperatures in the two cases. NoZ 288 Lord Kelvin on the Statistical Kinetic Dr. Chree’s Report on Temperatures of Thermometers | under Black Cloth and under White Cloth. National Physical Laboratory (Kew Observatory Department), Richmond, 27th July, 19065. Heperiments with two ordinary Thermometers, Nos. 1184 & 1207. THERMOMETERS placed horizontaily on small stands fastened to the outside window-sill of the wooden room on the Obser- vatory roof, some 40 feet above the general level of the ground. The arrangement was as shown diagrammatically. N. Thermometer . Thermometer. The north side of this upper room is entirely in the shade until well on in the afternoon. The cloths were wrapped several times round the bulbs and a small adjacent part of the stems. The thermometers were interchanged and the cloths were interchanged to eliminate difference between position and between thermometers. Readings were taken at intervals throughout two days. In every single case the (corrected) reading was higher for the thermometer with the black cloth. The conditions at the time were noted either as (a) bright sunshine, (>) sun shining through cloud, (c) cloudy, (d) bine cloud, 2. e. dark generally. An analysis appears in the following sheets. The readings are all centigrade, corrected for scale errors. Woollen Cloths. Juty 12. Position on Rieut. Position on Lerr., Excess of Reading under Black Black Cloth. White Cloth. Cloth, conditions being: Time. No. 1184. No. 1207. No. 1184. No. 1207. | (@) (b) (c) (a) fo) fe) fo) ° fo) 11.0 23'9 BN ine SL punlag 2 4 20 Buy, 25°8 23-4. ae 2-4 AO 26:2 ine Ae 23 8 24 12.0 ie 26°8 24-6 ; 22 i 20 25°5 Bae Ge 24-5 ae ee 1-0 40 oan 25-0 24-1 ! : 09 2.0 25°6 ne, eh 24°8 ie 0-8 10 5a, 26°3 25°3 1:0 20 26°5 a tt 25°8 ‘y (a (ay 30 ute 25'8 24-9 oe 0-9 40 26°4 ah a4 25:2 ts ify 50 ne 27°4 256 Bed 1:8 _ Equilibrium of Ether in Ponderable Matter. 289 Cloths changed over. Juny-12. Position on Riear. Posrrion on Lert.) Excess of Reading under Black White Cloth. Black Cloth. Cloth, conditions being: Time. No. Bon No. ae No. hie No. 4 207.) (@) (2) (c) (d) O 3.0 25° 1 252 yt Eek a 10 24-8 26°1 se Lapa seca 13 20 25'1 ats sae 26:35. oun be pes 30 aa 25°3 26°2 ah le ee ae 0'9 j 40 25°6 a age ps le i a ih ais 0°5 50 ue 24:5 26°1 Me | 16 4.0 25°0 ah 26°2 | 1-2 10 ae 24°5 255 sos Ea 10 Cotton Ciorhe Juty 13. Position on Ricur. Posrtion on Lerr., Excess of Reading under Black White Cloth. Black Cloth. Cloth, conditions being : Time. No. 1184. nee 1207. Nee 1184. No. oe (a) (b) (c) (d) fo) O fe) 11.0 : 54-6 25:3 ames: 0-7 15 23°5 ze 24-8 13 30 Loe 23:0 23°7 sy 0-7 45 23°6 ae we Pea ona a a) ine 23°6 24°5 hhh al depos 0-9 12.10 23°2 «33 a 24-4 1-2 DENG 8 23'3 24:2 a Ng ener fh eee Oh os 30 24°3 24-9 ae ae ree 06 40 ne 24-3 25° ee 0-8 Changed age of Cloths. Juty 13. Position on Rieut. Posrrion ox Lert. Excess of Reading under Black Black Cloth. White Cloth. | Cloth, conditions being: Time. No. 1184. No. 1207. No. 1184. No. 1207.) (a) (dD) (¢) (d) fe) fo) fo) fo) O 2,10 27:0 ae fee 242 | 28 5 20 Ah 26:0 25°2 ee f pee 0°8 35 27°3 ret me 25°5 18 45 sas 26°6 25°3 Ae 13 4 55 26:7 hae ae 25°6 oN, fA 5 3.5 ass 25°5 24-9 aft ins a, ae 0°6 15 26°4 =e oR 25°3 Lt 25 ae 269 25°6 ts ies 35 27°0 an het PO Srer | oe lees Observations made on a stand in the Garden about 4 feet above ground. No shade. Woollen Cloths. Jury 18. Posrrion on Rieur. Posirron on Lert. Excess of Reading under Black Black Cloth. White Cloth. | Cloth, conditions being: Time. No. 1184. No. 1207. No. Bee No. els | (a) (b) (c) fo) fo) fo) 11.50 28-2 rhe ay 250 4h 2 Oe % 12.0 eg 27:1 25°6 Bt 1-5 i TO) 8259 ot - 216 | As Us 18 ZUR a eat 25°6 24-1 iy i 15 30 24-7 ae 23-2 | 15 White Cloth. ‘Black Cloth. 2.50 24°8 ate 7 2a ae O07 3.0 Res 24°6 25°6 ae 1-0 10 249 s tk 26°6 hay 20 ss 24:4 25°3 ae ne an3 0-9 30 24:2 ae at 25:85 I 16 290 : Prof. E. Rutherford on Slow Cotton Cloths. Juty 18. Position on Rigut. Position on Lerr. | Excess of Reading under Black Black Cloth. White Cloth. Cloth, conditions being: Time. No. 1184. No. 1207. No. 1184. No. 1207. (a) (b) (c) O fe) fe) fe) fe) 3.40 29-1 bet Sis Dosis 33 z 50 3s 26°9 25°59 Rs sie 1-4 4.0 27:1 ae oe 25°4 urs s3 10 ae 26°0 24°6 aye he i \-4 White Cloth. Black Cloth. 4.20 ae 24-4 26°3 Se oh 19 a0). 244 i a 28°0 3°6 40 sos 243 26°2 ae e sit BS, HOF) 24:9 aoe aa 26:2 13 Aix-les-Bains, Savoie, Aug. 16, 1905. P.S.—I have made some rough experiments in this place, about 250 metres above the sea-level ; with two small dis- mantled bath-thermometers hung side by side from a horizontal bar in an open window about 12 metres above the ground. The thermometers were double coated; one with black silk, the other with white cotton, round the bulb and up to about 17° cent. of the scale. The black was always warmer during daylight. The greatest difference which I have hitherto observed in the course of eight days was this morning, 37°6—30°=7°6 in bright sunshine. This was with air freely circulating round the two bulbs. In a special experi- ment with the two thermometers laid side by side on a slab of red blotting- -paper, in bright sunshine, the black-coated one ran rapidly up to above 40° (the end of its scale), and had to be removed to escape breakage, as it had no safety space above the top of its tube. The white-coated thermometer did not rise as high as 40°. KELVIN. XXXVI. Slow Transformation Products of Radium. By EK. RutuerrorD, /.L.S., Macdonald Professor of Physics, MeGill University, Montncat 4 [* a previous paper (Phil. Mag. Nov. 1904) I described experiments made to elucidate the changes occurring in the active deposit of slow rate of transformation, which is left behind on a substance after exposure to the radium emanation. I showed that this active deposit contained two distinct substances, called radium D and radium H, the latter of which arose from the transformation of the former. The product radium D gave out only 8 rays, while radium E gave out only a rays. * Communicated by the Author. Transformation Products of Radium. 291 At the time of publication a sufficient interval had not elapsed to experimentally determine the rate of decay of the activity of these substances, but it was calculated from purely radioactive data that radium D should be half transformed in about 40 years, and radium H in about one year. The present paper contains an account of further experi- ments upon the variation of activity of the different products with time, and of the isolation of a new product which was previously overlooked. If a body is left for some time in the presence of the radium emanation, the activity after removal, measured by the a, 8 or y rays, rapidly decays with the time. At the end of 24 hours, the products radium A, B, and C, deposited on the plate, have been almost completely transformed. There then remains a small residual activity, which comprises both a and @ rays. The magnitude of this residual activity depends upon the quantity of the emanation, and upon the time of exposure, but is, in general, of the order of one millionth of the activity observed immediately after removal. ? It was shown that the « ray activity of the body was small at first, but increased nearly proportionately with the time over a period of two months. In another set of experiments, it was shown that the @ ray activity was still increasing after standing for nine months. The @ ray activity was examined about a month after removal, and was then found to remain sensibly constant for a_ further period of nine months. It was considered advisable to see whether the 8 ray activity remained constant during the first few weeks after removal. Tor this purpose, the active deposit was obtained on a platinum plate exposed to a large quantity of radium emanation for 3°8 days. Observations were begun on the @ ray activity 24 hours after removal. The activity was measured by placing the plate under an electro- scope, the base of which was covered with a sheet of aluminium of sufficient thickness to absorb all the @ rays. It was found that the @ ray activity was small at first, but increased with the time, reaching a practical maximum about 40 days later. The results are shown graphically in fig. 1, where the ordinates represent the activity, and the abscissze time in days. The time was reckoned from the middle of the time of exposure to the emanation. The first observation was, in consequence, made after an interval of 2°9 days. If the curve is produced backwards to the origin, its shape is very similar to the recovery curves of UrX and of vther radioactive products, and the activity I; at any time ¢ can be 292 Prof. E. Rutherford on Slow expressed by an equation of the form I — —)At Toe 0 where I, is the maximum activity. The activity reaches half — ACTIVITY SAVO NIFAWIL 4 its final value in about six days. The value of X is given by "115 (day)-?. A recovery curve of this character indicates Transformation Products of Radium. 293 that the @ ray activity arises from a product which is half transformed in six days, and which is supplied at a constant rate from a primary source, the latter being transformed at avery slowrate. The results indicate that the primary source itself does not emit @ rays, but that these arise from the successive product. We have already seen that the « ray activity, tested immediately after removal, is very small. We may thus conclude that the primary matter is “rayless,” that is, it does not emit either 2 or 8 rays, but that these arise from the products of its transformation. In conformity with the nomenclature adopted in the pre- vious paper (loc. ct.) this rayless product will be called radium ~ D. The @ ray product which arises from it will be called radium H}. The « ray product (previously termed radium EH} will be called radium F, for we shall see later that the @ ray product is the parent of the # ray product. We have seen that the increase of the « ray activity to a maximum indicates the existence of a product which emits 8 rays, and which is half-transformed in about six days. We shall now consider a method by which this product radium E can be isolated, and its rate of transformation directly measured. In my previous paper it was shown that if a platinum plate, coated with the active deposit, were subjected to a temperature of about 1000° C., the @ ray activity was nearly all lost, while the @ ray activity remained unaffected. On examining the platinum plate about two months later, it was found that the @ray activity had in the meantime decayed to a small fraction of its original value. This at once suggested a possible means of separation of radium E. A platinum plate, containing an active deposit two months old, was heated in an electric furnace for four minutes at about 1000°C. On testing it, the loss of the a ray activity showed that the product radium F had been mostly volatilized. The 8 ray activity, as before, was not immediately altered by the heating, but was found to lose its activity with the time. The activity decreased to about one quarter of the maximum value and then remained constant. Subtracting this constant value, the activity was found to decrease exponentially with the time, falling to half value in about 4°5 days. This result shows that not only most of the radium F, but also the greater part of the parent substance radium JD, had been volatilized at or below 1000°C.- Radium E was left behind, and, since most of the parent matter had been removed, immediately commenced to lose its activity. The constant activity which remained behind was due to the fact that some of the radium 294 Prof. E. Rutherford on Slow D on the plate had not been volatilized. It is seen that the transformation periods, deduced from the recovery curve (6 days), and from the decay curve (4°5 days), are somewhat different. Ido not think this difference in the periods can be ascribed to experimental errors, but is more probably due to an alteration of the rate of transformation of radium EH, resulting from the high temperature to which it has been sub- jected. A similar effect of temperature on the rate of transformation of radium C has been noted by Curie and Danne. It is intended to continue these experiments in order to settle definitely the cause of this difference in the period obtained by the two methods. The period deduced from the recovery curve is more likely to be the correct value under normal conditions. This method of separation is of interest, and shows in a strixing way how the difference in physical properties of the products can be utilized to effect a partial or complete isola- tion of a substance which is mixed with several others. The volatility of radium D, as welias of radium F, has also been noted in other experiments, for it has been found that the a ray activity of a platinum plate after exposure to i. temperature of 1000° C. does not increase with time to the same extent as that of a similar plate which has not been so treated. Such a result is to be expected ifa large part of the parent matter radium D is removed by the heating. The experiment of heating the platinum plate was also utilized to prove that radium E was the parent of the a ray product radium F. The a@ ray activity of the plate was determined immediately after heating, and at subsequent intervals. The increase of activity of the plate with time after heating is shown in fig. 2. The activity rose far more rapidly during the first two weeks than for equal intervals later. The slow period of increase is due to the production of radium F from the radium Hi, which is continuously produced trom the fraction of radium D which was not volatilized. The rapid initial increase of the activity is at once explained if the excess of radium H changes into F. We may then conclude that E is the parent of F, and that the three products D, EH, F are successive, for we have previously shown that E is produced from D. In the previous paper it was calculated that radium D should be half transformed in about 40 years. This result still holds good, although it has been found that radium D itself does not emit rays. About 40 days after removal, the 8 ray activity of radium E is constant, and the number of Transformation Products of Radium. 295 8 particles expelled from it per second is then a measure of the number of atoms of radium D which break up per second. — ACTIv/ITy — TIME InN OAYS — Thus the activity of the successive product, when in equili- brium with the parent substance, can be utilized to determine the period of a substance which itself does not emit rays. For convenience, the physical and chemical properties of the three radium products are tabulated below. lt will be shown in the next section that radium F is half transformed It is probable that radium EH emits y rays as well as 8 rays, but the intensity of the former in the experi- ments has been too small to measure. : in 143 days. Active deposit of radium of slow transfor- mation. Radium D...... Radium HE...... Radium F...... | i i Time to be haif Radiations. transformed. no rays. 40 years. B (and y?). 6 days. oe 148 days. Some physical and chemical properties of the product. Soluble in strong acids, not deposited on bismuth, volatile below 1000? C. Non-volatile at 1000° C., soluble in acids, not de- posited on bismuth. Volatile at 1000° C., deposited on bismuth, soluble in acids. 296 Prof. E. Rutherford on Slow Decay of the Activity of Radium F. The product radium F is deposited on a bismuth plate from a solution of the active deposit. The surface of such a plate, which has been left for some hours in the solution, becomes strongly active. The activity consists only of a rays, the B rays being altogether absent. In this way the « ray product is almost completely removed. Radium D is not deposited on the plate, for the solution, deprived in this way of radium F, at once commences to grow a new supply of radium F. The solution of the active deposit was obtained in the following way :—The emanation from 30 milligrams of radium bromide was condensed in a glass tube, which was then sealed. After standing for a month the tube was opened, and dilute sulphuric acid introduced. This almost completely dissolved the active deposit on the glass. The solution was evaporated to dryness in a glass vessel, and allowed to stand undisturbed for nine months. During this time a large quantity of radium F was produced by the primary active substance radium D. ‘The deposit was then again dissolved in sulphuric acid, and three bismuth disks were successively introduced into the solution. These three disks, coated with radium F, were then placed aside, and the a-ray activity examined at intervals over a period of about 9 months. The activity of each disk was found to decay according to an exponential law with the time. The results are shown graphically in fig. 3, where the abscissee represent days, and the ordinates the logarithm of the activity in arbitrary units. It is seen that the points lie nearly on a straight line, showing that the activity decreases according to an exponential law. The curves of the activity of the three disks are marked radium F (I.), radium F (I1.), radium F (III.). F (I.) was found to decay to half value in 150 days, F C11.) in 136 days, F (III.) in 142 days. The mean value is 143 days. We may tbus conclude that the activity of radium F decays to half value in about 143 days. The initial rate of decay of two of the curves was somewhat slower than the final value. This may possibly be due to the fact thata small quantity of radium D was also deposited on the bismuth plate. This would produce more radium F, so that the apparent rate of decay would be somewhat less than the true rate of decay of radium F alone. The observations of the rate of decay of the bismuth disks were made with a specially designed electroscope, which was standardized at the time of each observation with the aid of a constant sample of uranium. — SAVONIIFAWIL o¢c/ Cco/ 002 Transformation Products of Radium. Log. OF ACTIVITY Jal EE Si Lo 0 6 |o/ 02 298 Prof. EH. Rutherford on Slow Rise of the «a Ray Activity of the Active Deposit. It was shown in the previous paper that the « ray activity of the active deposit increased for the first 60 days at a nearly uniform rate. Observations of the « ray activity of a platinum plate, coated with the active deposit, have been con- tinued for a period of nine months. The results are shown in the table below. Time in a ray activity days. in arbitrary units. 5 0-127 43 O57 135 i 144 163 1°65 196 1°89 290 lt The results are shown diagrammatically in fig. 4. The activity is still increasing, but not nearly so rapid as at first. Observations have also been made on an active deposit 15 months old. ‘The activity is still increasing, but slowly, and is obviously tending towards a maximum value. The curve of fig. 4, as far as observations have gone, is very similar in shape to the usual recovery curve, in which half the final activity is reached in 143 days. Such a result is to be expected since radium F is transformed far more rapidly than radium D. From a comparison of the experimental curve with the theory discussed below, it can be deduced that the activity should finally reach the value 2°90. The activity after 290 days has thus reached 75 per cent. of the maximum value. The full explanation of the rise of the « ray activity involves the theory of three successive changes, since the substance initially deposited, radium D, changes into radium H, and radium E into radium F’, and the latter substance alone gives out a rays. Since, however, radium E (half transformed in six days) has a very short period compared with radium F (half transformed in 143 days), for the purpose of calculation the intermediate change may be neglected, and radium D may be supposed to change at once into radium F. If X,, A3 are the constants of change of radium D and radium F respectively, then the number g of atoms of radium F present at any time ¢ is given by = Moh (e-Mt— erst), Ns Ay where ng is the number of atoms of D originally deposited. Transformation Products of Radium. 299 The « ray activity at any time is proportional to g, and a maximum value is reached at a time T, when Nica = Neca as Since D is half transformed in 40 years, \y=:0173 (year) ~', and since radium F is half transformed in 143 days, R= Ce wear) eae — ACTIVITY —- og —e2/ O9/ (0) Ore 08 SAVO NIAWIL O9/ Ce2/ 7 OU oor Of2 og2 oof A maximum will be reached after a period of about 2-7 years. The activity will then diminish exponentially with the time according to the period of radium D, that is, it will 300 Prof. E. Rutherford on Slow be half transformed in 40 years. The activity 180 years after the active deposit is formed will be about the same as that observed after an interval of 9 days. Origin of Polonium and Radio- Tellurium. Contemporaneously with the experiments on the rate of decay of radium F deposited on a bismuth plate, observations were made on the decay of activity of a specimen of the radio- tellurium of Marckwald, which had been obtained from Dr. Sthamer of Hamburg. The activity was found to decay exponentially with the time, falling to half value in 148 days. During these experiments, results of a similar character upon the decay of activity of radio-tellurium were published by Meyer and Schweidler*, and by Marckwaldt. The former experimenters found that the activity fell to half value in 135 days, while Marckwald obtained a corresponding value of 189 days. Considering the difficulty of making accurate experiments of the rate of decay over long periods of time, the numbers obtained by Meyer and Schweidler, Marckwald, and the writer are in remarkably good agreement. We may thus conclude that radio-tellurium loses its activity according to an exponential law, falling to half value in about 140 days. In my previous paper I pointed out that there were strong reasons for believing that the active constituent in radio- tellurium was identical with the product radium F. Both active substances possess similar physical and chemical properties. Both only give out @ rays, and both are deposited on bismuth from the active solution. In addition, I showed that the @ rays from radio-tellurium and radium F were identical in their power of penetrating matter. Such a result affurded very strong evidence of the identity of the two products. We have seen that radium F loses half its activity in 143 days—a value agreeing closely with the rate of decay observed for radio-tellurium. The agreement of physical and chemical properties, coupled with the identity ot the radioactive con- stant », conclusively shows that the active constituent in radio-tellurium is identical with radium F. We may thus conclude that the active constituent present in radio-tellurium is in reality a transformation product of radium, and that the radio-tellurium obtained from radioactive minerals is _* Wien. Ber. Dec. 1, 1904. + Ber.d. D. Chem. Ges. No. 2, p. 591 (1905). Transformation Products of Radium. d01 derived from the decomposition of the radium contained in them. The amount of radio-tellurium to be extracted from the radioactive minerals will always be proportional to their content of radium, and, in consequence, also to the content of uranium, for the investigations of Boltwood and others have conclusively shown that the amount of radium in radie- active minerals bears a constant ratio to the content of uranium. The relative activity of radium and radium F, and also the relative amount present in radioactive minerals can easily be deduced. Let N, be the number of atoms of radium F in one gram of radioactive mineral, and N, the corresponding number of radium atoms. Let A,, A, be the constants of change of radium F and radium respectively. In an old radioactive mineral, the amount of radium and radium F have reached a steady state and the same number of atoms of each break up per second. Thus Niwvy = No». Now radium F is half transformed in °38 years, and radium in about 1200 years. Thus Nii MW WOSUN 4 U8 Ma oa 9-4 Nasu aot Now it is probable that the atomic weight of radium and radium F are not very different. Consequently the weight of radium F in the mineral is ‘00032 the weight of radium. Now corresponding to each gram of uranium in a radioactive mineral, there is about one millionth of a gram of radium. Consequently, from a ton of mineral, which has an average content of 50 per cent. of uranium, the amount of radium F present is 0°14 milligram. Assuming that the « particles expelled from radium itself and from radium F produce about the same amount of ionization in the gas, the activity of radium F in the pure state will be 3200 times the activity of pure radium at its minimum activity, or 800 times the activity of radium in radioactive equilibrium. Marckwald * has worked up 5 tons of uranium residues, corresponding to 15 tons of the Joachimsthal mineral, in order to extract the radio-tellurium (radium IF) from it. Simple but very efficient methods of separation were devised, and * Ber. d. D. Chem. Gres. No. 2, p. 591 (1905). Phil. Mag. 8. 6. Vol. 10. No. 57. Sept. 1905. ¥ 302 Prof. E. Rutherford on Slow he finally succeeded in obtaining 3 milligrams of intensely active material. Since the mineral contains about 50 per cent. of uranium, the theoretical yield is about 2°1 milligrams. It is not likely, however, that the total amount would be separated, so that the three milligrams obtained probably contain some impurity. The enormous activity of this substance so prepared has been pointed out by Marckwald. *ax shown a surprisingly good agreement between the content of radium and uranium for n D = 5 localities, which differ very S a widely in their content of ura- nium. This proportionality is a strong indication that radium ea is produced from uranium ; and a conclusive proof of this point "8 of view is given by the experi- ments of Soddy and Whetham, who find that there is a slow growth of radium in uranium which was initially freed from radium. In addition, the actual FONVHIAUdIVY LISOD AG FAIL DY oldvy ‘ ‘-ss4hor | | shilugy Gg-avy Davy SA a V minerals obtained from various a “5 pe a : amount of radium in radioactive x minerals is of the right order oa aes of magnitude to be expected a = from theoretical considerations, a Om "8 if uranium is the parent of oe radium. a8 Soddy finds that the present : 43 growth of radium from uranium Sd ltsae sec is only a very small fraction of = [ck : ®a« the theoreticalamount. ‘This is : 7° 7 most simply explained by sup- > 5 pesing that one or more products & |e of slow period of transformation eal intervene between UrX and c radium. The uranium-radium family and their connexion with one another is summarized below. 306 Dr. C. Chree on Deductions from Uranium. y UrxX. Y ? v Radium and its family of ee eee products, viz., the emanation, radium A, B, an V Radium D=primary constituent in radio-lead. V Radium HE. V Radium F=active constituent in radio-tellurium and po- lonium. No evidence has been obtained that any further active products exist after radium F has been transformed. If the a particle isa helium atom, remembering that five products are present in radium which emit @ particles, the atomic weight of the transformation product of radium F should be 225—20 or 205. This is very close to the atomic weight of lead, 206°7. The view that lead is the final or end product of the transformation of radium is supported by the fact that lead is always found in the radioactive minerals in about the amount to be theoretically expected from the content of uranium, when the quantity of helium, present in the mineral, is used to compute its probable age*. A similar suggestion has recently been advanced by Boltwood ft. McGill University, Montreal, May 1, 1905. XXXVI. Deductions from Magnetic Disturbances at Greenwich. By C. Cures, Sc.0D., LLO.D., FBS. Sa qyN three recent papers in the Monthly Notices§ of 4 the Royal Astronomical Society, Mr. E.W. Maunder has discussed the phenomena of magnetic storms at Green- wich. In the first paper he concluded that magnetic storms tend to follow one another at an interval of 27:275 days. In a review of this paper in the March number of ‘ Terrestrial Magnetism,’ p. 12, 1 pointed out that “ With the 8 storms * A full discussion of this question was given by the writer in the Silliman Lectures, Yale University, March 1905. + Phil. Mag. April 1905. t Communicated by the Author. § November 1904, April 1905, May 1905. Magnetic Disturbances at Greenwich. 307 (2. e. those of sudden commencement)...the irregularities in the hourly distribution shown ... might be fortuitous. But of the ... not-S storms no less than ...71 per cent. are ascribed to the 8 hours noon to 7 pP.M., and there is a most pro- nounced maximum at 1 p.m.”’; adding: *‘ If the phenomenon is a true physical one it indicates a very dominant influence which has nothing to do with the Sun’s rotation period, and which would have to be dealt with in any complete theory, or in any estimate of probabilities.” The question of the diurnal variation of magnetic distur- banees has been treated from a variety of standpoints. Some, e.g. Sabine, have taken a disturbance as existing at any hour — when the observed value of a magnetic element has differed by more than a certain amount from the mean monthly value for that hour, and have treated positive and negative distur- bances separately, finding diurnal variations for each as well as for the two combined. Others have taken the difference between the mean hourly values for all days in a month and those for a few specially quiet days, considering the amplitude of the departure at any given hour as an estimate of the tendency to disturbance at that hour. Van Bemmelen* has specially considered the incidence of the tiny undulatory movements not unusual at times when large movements are altogether absent. In all cases “disturbances ”’ have shown a diurnal variation, but the times of maxima and minima have varied according to the particular standpoint adopted, and for any given definition of disturbance different results have been obtained at different parts of the Harth. A good deal of information on these points is given in well-known treatises, such as Baltour Stewart’s article in the 9th Hdition of the Encyclopedia Britannica and Mascart’s Magnétisme Terrestre. .There was thus nothing surprising in the existence of a diurnal inequality in the figures of Mr. Maunder’s Table L.; but some features of the inequality, especially the sudden- ness of the rise to a maximum at 1 P.m., led me to suspect that the phenomena were not wholly due to Nature. Accordingly, on the appearance of Mr. Maunder’s second paper I examined its figures with interest, and found that they also showed a conspicuous diurnal inequality, but that it differed markedly in some details from the inequality I had found in the first paper. Meantime Mr. Maunder read the third paper referred to above, in which he too recognized the existence of a diurnal inequality, and also noticed the difference between his first two papers. Having seen a * Natuurkundig Tiydschrift voor Nederlandsch-Indié, 1902, p. 71. 308 Dr. ©. Chree on Deductions from reference to the fact-in the ‘Observatory, I waited to see exactly what his conclusions: were. Having now read the paper, I find that there are so many points on which I differ from Mr. Maunder, both as regards the facts and as regards the inferences to be drawn, that it has seemed worth while to put my views on record. § 2. In Table XIV. of his third paper, Mr. Maunder analyses the times of commencement of magnetic storms, treating separately 1882 to 1903 * (the period dealt with in his first paper) and 1848 to 1881 (the period of his second paper). As the corresponding table which I had formed agrees sub- stantially with Mr. Maunder’s, I omit it and pass to the following Table I. For brevity it gives only the total number of disturbances for the twelve hours 0 to 11 A.M., but it subdivides Mr. Maunder’s two periods of years to bring out certain points. Five storms to which no hour of commencement was assigned are omitted. TABLE I. Numbers of disturbances commencing at hours stated. | | | | | Years. Otollam|Noo. 1|2 8|4 5/6)7)8/9|10|) i 1848-58 22 To) O48) 9 TS | 144 12 (49) Cal Oa 1859-69 37 8 |.9/.18|.14) 11) 17 | 24) 16) 10) 8 |e 1870-81 37 2 8 | AS a oo er ON (er as 1882-92 49 6 (204 17/1 12) 41} 064 ad 14 6) Ga esas 1893-1908, 29 17 |/20:).12 | 9 | 8) 4) 41 240 4), Seles | 1848-81 96 12 ‘| 22 | 296 | 30 | 39 | 42 | 45 | 43'| 26 | 24 ede 1882-1903} 7 23° | 40 | 29 | 21) 19' | 10) 15 116 110) 9) eae 1848-1903] 167 35 | 62 | 55 | 51 | 58 | 52 | 60 | 59 | 36 | 33 | 22 | 31 Percentages of Totals. SS eee es 1848-81 Ca aa 58 20 1882-1903] 26 63 | 12 1848-1903, 23 | 60 | 17 | Mr. Maunder’s explanation (J. c. p. 670) of the striking difference between the results for the periods 1882 to 1903 and 1848 to 1881 is that “In (his) Table I. (disturbance data from 1882 to 1903) the times were taken from the reproductions... in the plates of the Greenwich volumes, and these in the majority of cases began with Greenwich noon; hence the * There are a few trifling differences between Mr. Maunder’s hourly figures and those which I had previously given in ‘Terrestrial Magnetism,’ due presumably to difference of choice made in cases where the commence- ment was ascribed to an exact half-hour. Magnetic Disturbances at Greenwich. 309 fluctuations of the early afternoon more frequently caught the attention.”” This suggests a more casual inspection than even a severe critic would have ventured to suggest, especially considering that the times were given to 0:1 hour in the case of all the storms having a notably sudden commencement. Also under the conditions mentioned the hours principally overlooked ought surely to have been the forenovn hours. But, as my Table I. shows, the percentage of occurrences between 0 and 11 A.M. is not conspicuously less, but even absolutely greater, for the period 1882 to 1903 than the period 1848 to 1881. Where the period 1882 to 1903 actually © shows a relatively smaller number of commencements is in the late afternoon and evening hours. The chief difference between the two periods consists in an alteration in the incidence during the afternoon. It is also clear from my analysis that there is a marked difference between the first and second halves of the period 1882 to 1903, theugh one would infer that the whole period was supposed by Mr. Maunder to have been treated in a uniform way. § 3. In discussing the diurnal inequality shown by his data for 1848 to 1881 (which agree substantially with those in my Table J.), Mr. Maunder says (l. ¢. p. 667) “Table IX. rises, with a regularity which precludes the possibility of accident, to a most unmistakable maximum at 18 hours (6 P.m.).” This is surely not an accurate descrip- tion of the facts. There seems a very poorly defined maximum at 6 P.M.,a sort of high level plateau extending from about 4 to 7 P.M., with a sharp drop at 8 p.m. Also of the three sub-periods into which 1848 to 1881 is divided in Table L., only one gives a distinct maximum at 6 P.M. To explain apparently how this supposed maximum at 6 P.M. comes about, Mr. Maunder in his Table XV. gives the “hourly distribution of small wave-movements, 1894-5.”” The nature of these movements is not clearly indicated, but as they are referred to on p. 668 as “isolated ”’ they are presumably not the regular wave-movements con- sidered by van Bemmelen. The diurnal variation in Table XV is certainly very different from that assigned by van Bem- melen (/.c. p. 81) for the regular wave-movements at Kew for the year 1897. However this may be, I cannot regard as satistactory Mr. Maunder’s explanation that in cetting out the times of commencement of magnetic storms the eye was caught by the movements whose incidence he records in his Table XV. What that table shows is a high frequency of easterly movements from 5 to 10 p.M., and a less but consi- derable concentration of westerly mov ements from 0 to3 A.M. 310 Dr. C. Chree on Deductions from Grouping Mr. Maunder’s numbers, we have | | Ba | Easterly. Westerly. | Total. Avenage fi per hour. Oto 11 a.m, (12 hours)......) (12 | +59 71 Gy td Noon to 7 P.m.(8 hours).... 89 3 92 112 | 8 to 11 p.m. (4 hours) ...... 61 9 70 ps isl The average per hour between noon and 7 P.M. is certainly greater than between 0 and 11 A.mM.; but it is just as con- spicuously less than the average from 8 to 11 p.m., a period when Mr. Maunder’s times of commencement of storms are relatively few. § 4. The next point where [ differ from Mr. Maunder is as regards his conclusion (/.¢. p. 669) that in his tables “The ‘oreat’ disturbances are distributed throughout the 24 hours with almost complete impartiality.” As some importance attaches to this point in connexion with the theory of disturbances I shall discuss it in some detail. In Mr. Maunder’s first paper, storms were divided into four classes, G, V, A, M, in descending order of magnitude, and to each storm only one letter was attached. In his second paper he combined the two first classes into one, called G, and when a storm lasted over two or more days a letter was attached to each day. I have adopted the three classes cof Mr. Maunder’s second paper; but have attached to a single storm, however long it lasted, only one letter, that letter corresponding to the most violent part of the storm. It must, I think, be conceded that this is the proper choice of letter if the disturbance be assumed all one storm. Table I. shows what the incidence of the commencements really was for each class of storm, the number occurring in the 24 hours being taken in each case as 100. TaBLe IT.— Actual percentage incidence of storms (for normal incidence 0 to 17 aim, 50; noon tor?’ ?.M., 335 oe (Uh Ti Le | | Midnight toll a.m. ' Noon to7 p.m. 8 to 11 p.m. @ ada eae OR ae |e SG Period Mete Seek 2th lO Ml oe 52 62 2 | eal 22 , 1882-1903] 39 , 1848-1903) 87))| 27 | 1 |, 8.) 66 | oF. | 10.| aa Magnetic Disturbances at Greenwich. 311 Table II. shows, what Mr. Maunder already admits, that the A (“active”) and still more the M (“ moderate’’) storms show a marked concentration of commencements between noon and 7 P.M.; but it further shows a similar though less conspicuous concentration of the G (“great”) storms. In fact, in the period 1848-81 the percentage of G storms commencing between noon and 7 p.m. is greater than that of the A storms *. § 5. There is also reason to think that part of the apparent difference between the different classes of storms arises from a cause wholly unrecognized by Mr. Maunder. In Tables 1. and II. it has been tacitly assumed that there — is no essential difference between one year and another, but this is far from the case. In years of many sun-spots, whilst the amplitude of the regular diurnal changes of the magnetic elements in England seems enhanced at all hours, the increase seems relatively greater by night than by day: the distinction between day and night is thus less marked than usual, As we shall presently see, a similar phenomenon presents itself as regards the times of commencement of magnetic storms, the diurnal incidence being notably more regular in years of many than in years of few sun-spots. We shall also show that the distribution of G, A, and M storms is widely different in years of many and of few sun-spots. In years of the latter type G storms are exceedingly rare, and so the majority of storms of this class are taken from the years of sun-spot maximum; 2. é. from years which, as has already been stated, show an exceptionally regular incidence of commencements. I now proceed to prove these statements, dealing with the latter first. The 56 years of Mr. Maunder’s investigation included the following 14 of exceptionally large sun-spot frequency :— eo, 2 03..00, Ol 70.712, 62, 63, 34,92, 93, 94. This group I shall refer to as S max. years. Amongst the 5€ years the following 15 were of excep- tionally small sun-spot frequency :— 1854, 55, 56, 65, 66, 67, 77, 78, 79, 88, 89, 90, 99, 1900, 1901. This group I shall refer to as S min. years. * Mr. Maunder particularizes storms of sudden commencement only for 1882 to 1903. According to my figures in ‘Terrestrial Magnetism,’ the percentage distribution of these was:--0 to 11 a.M., 47; noon to 7 P.M., 40; and 8 to 11 p.m, 13 (Mr. Maunder’s figures would give 44, 40, and 16 respectively). This suggests a concentration between noon and 7 P.M. even for sudden storms. a4 Dr. C. Chree on Deductions from Table III. gives the number* of storms of the three classes in each of these groups of years, and the percentage which they form of the total number of storms of the same class in the whole 56 years. TaBLE III. S max, years. S min. years. Class of | Storm. Number. Percentage. Number. | Percentage. COE MOOR, Buaiae 57 Y | 6 VAN ies A des en ABD 82 on bl 14 IVE Shits olde Se 112 29 88 23 All classes...... 256 36 126 17 We see from Table III. that the numbers of A storms from the two groups of years are comparatively nearly in the proportion one would anticipate from the total numbers ; but the G storms are relatively few in years of S min., and are so numerous in years of S max. as to form considerably more than half of the total from the whole 56 years. § 6. The data on which the assertion was based that the diurnal incidence is different in years of S max. and 8S min. are presented in Table IV. It gives the number of the storms commencing in the three portions of the day already emploved in Tables I. and II., and the percentages these form of the whole number occurring in the 24 hours. Results are given for the M storms separately, as well as for all the storms irrespective of size. Tasue LY. Numbers. Percentages. Group of EES: Oto | Noonto| 8 to Oto | Noon to 8 to ana 7 P.M. 11 P.M. 1] a.m. Pa 11 p.m. All| M | All| M | All| M || All| M | All| M | All, M 24 | 134) 65 | 49 | 23 || 29 | 21 | 52 | 58 | 19 | 21 S min......| 24/12] 86 66/16/10] 19) 14 | 68 | 75 | 13) 1 * Omitting three whose times of commencement are not given, owing to imperfect registration at Greenwich. Magnetic Disturbances at Greenwich. 313 Whether we consider all the storms, or only the M storms in Table IV., we see a notable difference of the kind already indicated between S max. and S min. years. If the difference had existed between the ‘“‘ All” storms, but not between the M storms, then of course it would naturally have been suggested that the difference was solely a matter of the absolute size of the average storm in the two groups of years ; but the fact that the difference is conspicuous when we confine ourselves to M storms renders this position untenable. . The Gand A storms are so few in the 8 min. years that com- parative data based on them are too uncertain, but the M storms number 88 in this group and 112 in the S max. group; so that the difference shown in Table IV. can hardly be assigned in any large measure to chance. We have now shown (Table LV.) that the diurnal incidence of commencements is notably more uniform in years of S max. than in years of S min., and (Table III.) that an unduly large proportion of the G storms come from the S max. years. It is thus clear that a difference of the kind shown in Table IJ. between storms of the three classes would naturally arise, even if the size of the storm were absolutely without effect on the hour of commencement or its estimate. At the same time, it should be clearly understood that our investigation has not shown that the difference of behaviour in S max.and 8 min. yearsis the sole cause of the phenomena appearing in Table II. In fact it suggests that there is a real difference depending on the size of the disturbance ; for Table IV. shows in both groups of years a greater concentra- tion of M than of “ All”? storms between noon and 7 P.M., and in the case at least of the S max. group the number of G and A storms is sufficient to render chance an improbable explanation. § 7. The difference between S max. and § min. years extends, as will be presently shown, to the annual distribution, a subject to which Mr. Maunder also refers in his third paper. Before dealing with this, I might explain that the tendency to a maximum near the equinoxes in the number of disturbances, to which Mr. Maunder refers on his pp. 680-1, has long been known to occur at certain stations, including Toronto and Greenwich—whose long series of results have been so fully dealt with by Mr. Hllis; but other stations of whose data Mr. Maunder seems unaware show different phenomena. Some of the older results are discussed in Balfour Stewart’s article in the Encyclopedia Britannica, and some more recent results are given by Mascart in his Magnétisme Terrestre (pp. 296 et seq.). old Dr. C. Chree on Deductions from § 8. Table V. advances the evidence of the statement made above, that the annual incidence of storms differs in years of many and of few sun-spots. The data are the times assigned for the commencement of the 726 storms included in Mr. Maunder’s two lists, The year is divided into three seasons: Winter (November to February), Equinox (March, April, September, October), and Summer (May to August) ; the monthly results are given in the order mentioned, i. e., month 1 denotes November, March, or May, according as the season is Winter, Hquinox, or Summer. In the case of the whole 56 years the results for the M storms are given as well as for the ‘‘ All’’ storms. In the case of the 8 max. and S min. years—which represent the same years as in Tables ITI. and 1V.—only the results for “ All” storms are given. Maia. WINTER. | Equinox. SUMMER. al | Month, | 56 years. | | 56 vears. | 56 years. | Shes s jis Sas max.|min. | max./min. max.|min. | All.) M. LAll.| M. All.| M. De ae a | 56 | 27) 24| 7 | 74148) 21 | 19 | 46 | 27 | 10 | 19 Be RON, 40 |21|15| 2/75] 40! 28| 9] 40/18) 16/ 6 BUN i: 59 | 37 | 18 | 14195 | 43 | 2m di) 45) ovo | ae | 78.) 38 | 34) 13 | 88/40 | 28 | 22) 55 134") oo) ace Total .,. 288 118 | 91 | 86 307 171 | 98 | 61 [186 |103 | 69 | 30 | “areas | Percentage’ 32 | 30 | 35 | 28 | 42 | 44 | 38 | 48 | 26 | 26 | 27 | 24 | The total number of storms is too small, especially in the S min. group of years, to give smooth results for an annual variation, and much weight cannot be assigned to the data for individual months. But taking the seasons, there seems an unmistakable difference between S max. andS min. years, at least in Winter and Hquinox. ‘The tendency in § max. years 1s obviously towards a more regular distribution of storms throughout the year. The phenomena are in short exactly analogous to what we have already seen to be true of the diurnal distribution. Also, as the difference between “All” and M storms from the 56 years is, if existent, exceedingly small, the difference between the 8 max. and Magnetic Disturbances at Greenwich. 315 S. min. years can hardly be assigned in any large degree to the fact that M storms form a larger percentage of the whole in the latter than in the former group. ? § 9. Returning to the subject of the diurnal imequality, the conclusion to which our investigations point is that whilst Mr. Maunder’s first paper may be, as he himself now maintains, somewhat affected by a systematic error in the estimate of times, the general agreement between it and his second paper affords overwhelming evidence that a marked diurnal inequality exists in the times of commencement of magnetic storms at Greenwich as estimated by an unprejudiced mind. The consequences of this are hardly, I think, adequately recognized by Mr. Maunder. ‘The ‘local peculiarities,” he says, “tend to blur the evidence for the Interval Rela- tion; but he adds, “they by no means efface it, for the whole of the evidence. ..in my two former papers .. .is still outstanding.” But the certainty of the existence of a pro- nounced diurnal period in the figures, and the admission of uncertainty in the individual data, make the proof of the existence of a true 27 to 28 day period more difficult, and, supposing it to exist, increase the probable error in its estimate. If the determining factor, as Mr. Maunder believes— and as others before him, e.g. Arrhenius and Birkeland, have supposed—be some form of electrical discharge from the sun, the time at which that leaves the sun or reaches the earth’s atmosphere cannot well have anything to do with whether it is day or night at Greenwich. We must thus suppose that the effects at any given station often remain almost entirely latent, for a time determined by circum- stances which if not local, in the ordinary sense of the word, have at least a marked relationship to local time. There is of course nothing very improbable in this, if we suppose that the emanation, or whatever it is that proceeds from the sun, is not the immediate cause of the disturbance, but only introduces conditions which facilitate the development in the atmosphere of electrical currents, similar to but irregularly distributed as compared with those to which the ordinary diurnal inequality is due*. But evidently if this be the case, the determination of the circumstances to which a particular disturbance is due is a less simple matter than would appear at first sight, and we cannot but view with increased reserve estimates such as that of RiccO—quoted by Arrhenius + in support of theoretical conclusions—of the time required for the supposed electrical discharge to travel from the sun to the earth. * Phil. Trans, A, vol. cecil. p. 436. + Terrestrial Magnetism, March 1905, p. 4. 316 Dr. C. Chree on Deductions from § 10. Supposing a period existent in disturbances, it is obviously desirable to determine it as exactly as possible, if only with a view to ascertaining the true source. At least two previous investigators had, unknown to Mr. Maunder, investigated the matter from practically the same standpoint. How closely similar Mr, Allan Broun’s * views were may be seen from his paper in the Phil. Trans. for 1876, p. 400, or from the account given by Balfour Stewart in the Mnc. Brit. ; but the time which he deduced for the period from the Makerstoun disturbances was a day less than Mr. Maunder’s estimate. So again it appears that the Toronto disturbances led Mr. Arthur Harvey+ a year or two ago to conclusions almost identical with Broun’s and Maunder’s, but the period he deduced (27°246 days) differs slightly from Maunder’s. This all suggests the advantage of some more strictly mathematical method, whether the periodogram method of Prof. Schuster or another, which can not merely assign a value for a period, but also afford a measure of its probability. There is also obviously an advantage to be derived from having a variety of data. The horizontal force at least might well be treated, and quite independently of the declination, and the criteria for selecting disturbances should be varied. Even supposing a fived minimum range limit assigned, it is at least highly doubtful whether Mr. Hllis’s is ideal for an investigation of the kind. His limit is such that in the 22 years of Mr. Maunder’s first paper the average interval between two successive storms was approximately 29-1 days, while in the 34 years of his second paper it was approximately 27°6 days. It does not seem desirable that the average interval should approach so closely to the period it is desired to investigate. There ought under the circumstances—period or no period—to be an exceptionally large number of cases in which storms follow one another at intervals of from 27 to 28 days. Obviously if Mr. Ellis’s lowest limit were much raised the number of storms would become so small as to render it difficult to recognize any 27 to 28 day period however real. Thus, if a fixed limit be adopted, the better alternative would be to lower ¢ Mr. Ellis’s limit, though it might be necessary to * My. Broun accepted apparentiy three periods, viz., 26, 27°3, and 29°5 days, as occurring in the small regular changes of horizontal force, attributing the former to the sun, the two latter to the moon. But he. found distinct trace in the disturbances only of the 26-day period. + Trans. Can. Inst. 1898-9, p. 8345; Roy. Ast. Soc. of Canada Selected Papers & Proc. 1902-3, p. 74, 1904, p. xiv &c. t In some months it is difficult to get more than 5 or 6 days free from very appreciable disturbance. Thus any large reduction in Mr. Ellis’s qualifying limit would hardly be compatible with the application of his method. Magnetic Disturbances at Greenwich. dI7 make it a condition that the qualifying movement took place in a comparatively short definite interval of time, otherwise complications might arise from the large size of the regular diurnal range at certain seasons. 9. hie There is at least theoretically a good deal to be said in favour of a limit varying in a definite way. In the average year the regular diurnal variation is much larger in some months than in others. In England the declination range in December is only about a third of what it is in several summer months. Again, the average range may be 40 or 50 per cent. larger for a year near sun-spot maximum than for a year near the adjacent sun-spot minimum. ‘Thus in the course of an ll-year period the regular diurnal ranges in two individual months may bear a ratio such as 4 or 5 to 1. One cannot but doubt under such circumstances whether a system which defines a day as disturbed, and the disturbance as M, A, or G, by reference to an unvarying absolute scale of magnitude is a natural one. If the immediate cause alike of regular and irregular movements be electric currents in the upper atmosphere, whose intensity is increased in years of sun-spot maximum owing to the increased presence of some ionizing or otherwise effective agent, it would seem clearly better to take limits varying with the average diurnal range for the individual month considered. Even if the large disturbances have an absolutely distinct source, an allowance would seem desirable for the movement that would in the natural course of events have taken place between the times when the maximum and minimum were recorded. § 12. The considerations already advanced would suffice to raise doubts as to whether the energy of the source to which a particular storm is due can be supposed to answer in ail cases to the letter assigned to the storm on Mr. Ellis’s and Mr. Maunder’s lists. But an even stronger reason for such doubts remains to be mentioned. On Mr. Hillis’s, or any analogous system, a single to and fro movement may count as a disturbance, whereas a dozen movements occurring in close succession, of but slightly inferior amplitude, may fail to be classed. Again, disturbances in which the extreme range is the same may differ enormously in the number of the oscillatory movements and in the rapidity with which they take place. Thus a classification which takes account only of the extreme range must in many cases fail to arrange dis- turbances according to their real intensity. Consequently the conelusions which have been drawn as to differences between storms of different intensities might have to be modified if some more exact measure of energy were adopted. July 10, 1905. Phil. Mag. 8. 6. Vol. 10. No. 57. Sept. 1205. Z [Bley a XAXXIX. On the « Partecles of Radium, and ther Loss of Range in passing through various Atoms and Molecules. By W. 4H. Braae, I A., Elder Professor of Mathematics and Physics in Ale Unmensie y of Adelaide, and R. Kinemay, B.Se., Demonstrator”. [* previous papers which we have contributed to this Magazine | we have shown that the «# particle moves always in a rectilinear course, spending its energy as it traverses atoms of matter, until its velocity becomes so small that it cannot ionize and there is in consequence no further evidence of its motion. Hach 2 particle possesses therefore a definite range in a given medium, the length of which depends on the initial velocity of the particle and the nature of the medium. Moreover, the & particles of radium which is in radioactive equilibrium can be divided into four groups, each group being produced by one of the first four radio- active changes in which « particles are emitted. All the particles of any one group have the same range and the same initial velocity. The present paper may be regarded as a continuation of the papers cited. Its contents are arranged under the following heads :— ile Improvements j in the apparatus used for measuring the ranges and relative strength of the four groups of rays. 2. Results of experiments with the new apparatus giving the following values of the ranges in air at a pressure of 76 cm. and a temperature of 20° C. ‘Tea Giri Pi, ees ater de ema, Emanation or Bet Radiaimgag ian iied a — Radium A or Tee Himanagions pais inl ee Radimmy Gy ae 7°06 These are correct, we believe, to‘05 cm. The pressure and temperature are stated, since a change of 1 cm. in the pressure or 5° ©. in the temperature would produce an effect which could be observed. We have not yet determined which of the two middle groups belongs to the Emanation and which to Ra A ; but we have constructed a special piece of apparatus which will, we hope, settle the point. * Communicated by the Authors. Read before the Royal Society of South Australia, June 6, 1904, + Phil. Mag. Dec. 1904. On the « Particles of Radium. d19 The results also show that the four groups are alike in all respects save that of initial speed; and further, that the a particle spends its energy at a rate which is approximately inversely proportional to the square root of its speed. 3. Determinations of the loss of range of « particles in consequence of their passage through various substances, from which it appears that for all the materials examined the loss in traversing any atom is nearly proportional to the square root of the weight of that atom. ‘The loss in the case of a complex molecule is proportional to the sum of the square roots of the weights of the constituent atoms. 4. Discussion of these results. ‘aE In the apparatus which we first used for these experiments we found that our measurements were liable to considerable irregularities. The most troublesome of these was an occasional sudden and violent increase of the ionization eurrent which would cause the electrometer spot to fly off the scale. This would occur in the middle of a period of satisfactory working. It appeared to be due to the liberation of emanation from the radium under observation, and we have therefore enclosed the whole of our apparatus in a metal vessel through which a current of dry air is made to pass continually. In other respects the apparatus now used differs but little from that described on p. 728 of the Phil. Mag., Dec. 1904: except that we have added an arrangement by which an aluminium screen can be drawn over the radium so as to cut off all « radiation, and we have made it possible to set the ionization-chamber at any desired depth. Both these arrange- ments can be worked from the outside of the enclosing vessel. It is necessary that the air which is drawn through should be fairly dry. In this country a difference of 30° F. between the wet and dry bulb thermometers is not unusual, and at these times artificial drying is hardly necessary ; but we find it more satisfactory to draw the air at ali times through a set of large calcium-chloride tubes, the current passing day and night during the progress of any series of experiments. The need for dryness appears to arise from the fact that moist air acts on the thin film of radium which we employ and liberates emanation. At one time we endeavoured to secure the complete removal of any liberated emanation by passing the whole stream of air directly over the radium just before it left the vessel; Z 2 320 Prof. Bragg and Mr. Kleeman on but with this arrangement the remaining moisture of the air seemed to do more harm in liberating emanation than the current did good by carrying it away. We now pass the current of dry air through the vessel from one end to the other; but the radium film probably feels little draught, being protected by the set of vertical metal tubes which stand over it (see the previous papers). When this is done the leak which the electrometer shows, the radium being out of range, is very small compared with the principal leak and is fairly constant. In the experiments described later it amounted usually to one or two millimetres in ten seconds, whilst the principal leak might be as much as sixteen centi- metres in the same time. This residual leak is due to various causes. One of them is the leak which takes place from the metal of the ionization- chamber, and the wire which connects it with the electrometer, to the earthed metal case which screens the chamber and its connexions from external influence. This current is supplied by the ions which are continually formed by various agents in the air within the earthed casing, and is driven by the Volta potential-differences between the metals of the connexions and the casing. It can be materially altered by changing the material of the casing, or part of it, e.g. exchanging zine tor copper. If a speck of radium is placed within the casing so as to increase the supply of ions the effect is surprising. As an illustration we allowed the electrometer connexions to end in a brass wire 15 cm. long, which projected horizon- tally in the open air, the ionization apparatus being dis- connected. When a large earthed copper tube containing the radium speck was placed so that the brass wire was along its axis, the electrometer showed a large deflexion, whereas, when the copper was displaced by zine, the deflexion was also large, but in the opposite direction. The whole of the apparatus including the keys which connect the electrometer to earth or the ionization-chamber is enclosed in earthed metal casing. The keys are worked by electro- magnets which are fixed externally to the casing, and operate on iron armatures within. We have found it necessary to be careful as to the contacts of these keys. Want of perfect contact causes incomplete charging or discharging of the electrometer quadrants, shown by kicks and irregular move- ments of the light-spot when the keys are ‘used. We have obtained good results by making the contacts of platinum surfaces, , so arranged as to rub each other at the make or break. This does not introduce any want of definition into the beginning or ending of a leak, since both the a Particles of Radium. 321 these times are determined by the breakings of contacts, and these are done by the electromagnets with great suddenness. . An arrangement which we find to be of great importance, is the ion-trap which is placed under the gauze of the ionization-chamber. ‘I'he space below the gauze B, forming the lower plate of the ionization-chamber AB, is of course a bo QE. cAL ‘ B------ -- > battery Seé of Cubes, AMI ine Lia. on plate. filled with the ions formed by the rays which cross it. When the gauze C is not present, then although B is at a high potential, some of these ions manage to cross it and add themselves to those in the chamber AB, thus disturbing the results to be measured. We were first aware of this effect occurring in any marked degree when we began to use a platinum dish on which had been evaporated a few drops of water containing a speck of very pure radium bromide. We were so very fortunate as to be presented by Mr. Soddy with a milligramme or two of this material; by its use our experi- ments were very greatly improved, as will be described a little later. On the first occasion of its use, however, we were puzzled by a rather curious result. The radium and the tubes above it were rather close up to the gauze B. We were measuring the various leaks as, millimetre by millimetre, we pushed the radium still closer. Every now and then we drew the aluminium screen over the radium so as to discover how much of what was observed was really due tothe « rays. We found that after the screen had been so used and withdrawn, the proper leak was materially lessened, but recovered its old value in a short time. When the screen was drawn over again, the leak (which was then not due to « rays) fell instantly to its usual very small value, and again, when the screen was withdrawn, the proper leak was for a time too small. We guessed therefore that some of the leak, with the screen off, was due to ions made outside the chamber, which afterwards drifted into it. The interposition of the aluminium 322 Prof. Brage and Mr. Kleeman on screen instantly cleared all the space between itself and the gauze B of ions, because the gauze was at a high potential and the screen was earthed. No more ions were made in this space until the screen was withdrawn. When this was done, the space just below the gauze and above where the screen had been was momentarily empty of ions, and though the continued passage of the « rays through it soon refilled it, yet there was a short time during which the ions in the space were below normal value, and therefore the drift upwards into the ionization-chamker was small. If this drift existed, it was certainly to be avoided, and we therefore placed below the gauze B a parallel gauze C about three millimetres away, which was put to earth. No ions could cross the powerful field which existed between the two gauzes. The second gauze cut off a number of « rays which would other- wise have entered the chamber, but there were still quite enough. With this new arrangement the irregularity described above has disappeared completely. Another uregularity has also disappeared at the same time; it was probably due to the same cause, and removed in the same way. It occurred when one or other of the bundles of rays was just out of range of the ionization-chamber, and took the form of a small leak which seemed to prelude the arrival of the real rays; it formed a shght projection on the ionization curve just above the true and large increase which represented the entrance of the rays of the bundle into the ionization- chamber, as the radium was pushed higher and‘ nearer. It often blurred the corners of the ionization curves, and made it more difficult to determine the exact ranges of the rays. The electrometer used in these experiments is of the Dolezalek pattern. It has been been frequently calibrated, either by charging it and causing it to share its charge with an auxiliary condenser, or by measuring a given radium leak, first, when the electrometer was in parallel with the condenser, and again when it was not. The deflexion for a given charge is wonderfully constant over a wide range of voltages of the needle ; though the deflexion for a given potential varies considerably. It is not found satisfactory to maintain the conductivity of the quartz fibre by dipping it in a solution of calcium chloride; in dry weather it does not conduct. It is better to recharge the needle to 250 volts every few hours, if it is used for so long; the needle may then leak con- siderably without alteration of the deflexion for a given charge. Op b cé “6 79 ‘SMMOY YG Loge ‘SUNOY FO L09Je ‘sossou0 Aq poytval sourpvor peyuoTodxgy ‘uotyeavdoad oye ATOIVIpowMUIL Vay JO OAANO MOTYwZIUOT * 'so[0.110 UL SJOp Aq poydeuUt ssUIpPeOd payetno[eO 6c & : (a3 66 ‘sXup Qz 10qye “ai OY OPT oyu Vay JO ALND UOTyezIUOT — ur ix bs pe the a Particles of Radium. OFF Having made these various improvements in our apparatus, and become more familiar with its use, we made a new layer, as already mentioned, from the pure ee bromide which Mr. Soddy had so kindly sent us. results. precision which it was now pos ssible to attain. Ta ie 1 i ' ~~ ps ir ! ri ' 1 x H I yi i i. 1 ° n 1 d23 This at once gave good “The curves shown in fig. 1 show the toacidoncblc > ’ It may be well to repeat here that these ionization curves show the amount of the ionization due to the « rays at various distances from the radium layer, the medium ionized being oT LL 324 Prof. Bragg and Mr. Kleeman on air at ordinary pressures and temperatures. A bundle of copper tubes is placed in a vertical position over the hori- zontal layer, so that only such « particles as move in a direction nearly vertical are allowed to proceed upwards. The bundle used at present contains about 100 tubes made of thin copper, each 2 mm. in diameter and 1 cm. long. The ionization-chamber consists of an upper horizontal plate of sluminium, and a lower plate of brass gauze ; the distance between the plates in most of the experiments described in this paper was set at two millimetres. The ordinates repre- sent the distances from the radium plate to the gauze ; and the abscissee the leaks on the quadrant electrometer. The absolute value of these leaks was not accurately measured, as there was no object in knowing more than their relative values; but it was calculated that the greatest leak measured was about 10-" ampere. Curve A, in fig. 1, shows the ionization due to the a rays when the dish was first prepared. It had been kept at a bright red heat for some minutes after preparation. The shape of the curve shows that all radioactive products except the radium itself had been completely removed. On com- parison with the similar curve on p. 730 of the paper already cited, it will be seen that the new radium layer is thinner than that from which our first results were obtained ; for the maximum value of the ionization occurs at 2°85 cms. instead of at 2°5. The greatest range is about 3°4 as before. This means that the a particles from the bottom of the new layer lose, in coming up through the material of the layer, a range of 5°5 mm. measured in air: the corresponding amount for the older layers was 9 mm. The new layer is nevertheless nearly twenty times stronger than the old. The term layer is, in fact, rather inappropriate. Actually the radium is not distributed over the dish in a thin uniform sheet but is studded over the surface in the form of small crystals which can be easily seen under the microscope. Consequently a weaker solution of radium bromide does not give, when evaporated, a thinner layer; but simply asmaller number of crystals. The various bundles, and in particular those from Ra, Emanation, and Ra A do not therefore stand out any better from each other when a weaker solution is evaporated, as we found on making the experiment. But the greater purity of the new layer gives the result which we formerly sought to obtain by evaporating very weak solutions. Presumably the crystals are now more regularly arranged, and are not overlaid by other matter which acts as a screen. Since the radiation of the new layer is so strong, the the « Particles of Radium. 325 residual errors of the experiment become relatively small. In particular, consecutive readings of the same leak become much more nearly in agreement than before; when the readings are large, the difference between two such readings is generally less than one per cent. of the whole. For small readings it is proportionately greater; and it is quite clear that much of this irregularity is due to some extraneous cause, and is not due to variability of the principal leak, or inaccuracy either of the observer or his apparatus. Other experimenters have made a similar observation. In the case of all the measurements recorded in this paper, the current was allowed to run into the electrometer for ten seconds; the mean of the first and second points of rest of the needle was taken as the correct reading. This was justifiable, as relative, not absolute, measurements were wanted; and as the difference between these two mea- surements was very nearly proportional to the whole defiexion. Curves B, C, and D in fig. 1 show the state of the radium at definite intervals after preparation of the layer. Similar curves were published in our previous paper, but the curves now shown are much more accurate, and supply much more information. In the first place, the division of the & rays into four groups is now seen very clearly, and the range ot each group can be measured accurately. In the former curves, the separation of the two central groups was not well effected, but now it is plain ; the improvement being mainly due to the greater thinness and evenness of the radium layer. In the same figure, curve Ei shows the state of the radium when 28 days old. According to Rutherford’s theory the number of « particles in each group is the same, provided the radium preparation is old enough to be in radioactive equili- brium. This can be proved from the curve E in the following manner. | The curved side ab, belonging to Ra C, is produced to ¢, as shown. The line de represents a certain ionization produced by @ and y rays which is intercepted by the aluminium screen. It is the small difference between the readings at (say) 7-5 cm. when the aluminium is on and off. When the radium is within range, and the ionization of the « rays is measured as the difference between the on and off readings, this small quantity of 8 and ¥y ionization is included in the difference. Its value must be nearly constant over all ranges, as it is a certain fraction of the total @ and ¥ ionization, which latter is found to be constant by experiment. We may therefore 326 Prof. Bragg and Mr. Kleeman on consider the figure bounded by the vertical line through de and by the curved line dabe to represent the ionization by the Ra C particles over the whole of their course except the first two centimetres. This curve is now added to itself, being first lowered through 2°23 cm., and the points represented by dots in circles represent some of the results of the addition. It will be seen how nearly these points lie on the actual ionization curve, on which the experimental readings are marked by crosses. Again the curve dabcis lowered, by 6°0 mm. this time, and added on to the sum already obtained, and the new points which show the result of the addition are also marked as dots in circles. These also lie very nearly on the ionization curve. Tor the last time the curve is added on, being this time lowered 7°3 mm.; and again the calculated points lie on the experimental curve except just at the peak. Thus the full curve is formed by the superposition of four simple curves, each alike in all respects but that of height; and the inference is that the four groups of « particles are alike in every respect but that of initial velocity. The differences of the ranges are in this way given with more accuracy than that with which the actual ranges can be found, for it is hard to avoid all uncertainty about the latter because the gauze of the ionization-chamber is not easily made quite flat. If the curve fg is produced to meet the curve hg also produced, then the meeting-point is at a height 3-4 em. This point should represent the arrival of the Ra rays at the middle of the ionization-chamber, which is 1 mm. higher than the gauze. Hence the range of the particles from Ra is 8°50 em.; and the ranges of the other three groups are 4°23, 4°83, and 7:06. These must be correct to 0°5 mm. Since the ionization curve can now be drawn with some accuracy, it becomes reasonable to make an attempt to dis- cover the relation between the velocity of the « particle and the rate at which it spends its energy. Let » be the velocity of the particle, and s the distance it has yet to run. Suppose that the energy spent per em. = k.v-” , where & and n are constants. We seek a value for n. 2 Then na oe = fey’ 2 —— e ds ive mv'tldy = kds myrt2 oe n+2 the a Particles of Radium. oot Hence the rate of expenditure of energy on ionization If the strip of air (supposed thin) in which the ionization is measured is at such a height above the radium layer that the « rays from the top of the layer pass it by a distance a, and those from the bottom by a distance w—d, then the ionization produced in this strip by the « particles from all parts of the layer where A is a constant. If the rays from the top of the layer pass the strip by x, and those from the bottom do not reach it, then the ionization — Agt*? e In the curves as found experimentally the effect is further complicated by the fact that the ionization-chamber has an appreciable depth of 2 mm., and that the cones of rays have an appreciable vertical angle. We need not, however, take these factors into account in the formula. We can give n different values, plot the corresponding curves as found from the formula, and round off the corners in accordance with the effect which the two disturbing factors must have. When this is done, it is found that n = § gives a curve wnich is very near to the actual form. Choosing the value 5) mm. for d, which seems proper from an inspection of the curve and from trial, the ionization is equal to Aa* from z=0 to e=5 mm., and thereafter to Af{a*—(w—5)*}. The curve obtained from this formula is plotted in fig. 1, P; and the corners are rounded off by the dotted line. The value of A is chosen so as to make the curve more easily comparable with the experimental curve H (portion da bc). Curves Q and R are derived trom the formula when n is put equal to 1 and to 1/3 respectively. It will be seen that they do not approach the experimental form so well, and err in opposite directions. 328 Prof. Bragg and Mr. Kleeman on The conclusion is that the a particle spends its energy at a rate which is approximately inversely proportional to the square root of its velocity. § II. From the results described above as well as from those de- scribed in the previous papers (Phil. Mag., Dec. 1904) it will be clear that the law of the absorption of the @ rays is consider- ably different from that which has been generally assumed hitherto. It has been supposed that a stream of radiation gradually diminishes in power as it penetrates any material substance, the rate of loss being approximately expressible by an “absorption coefficient,” and the law being therefore nearly exponential. It is true that it has been pointed out. that this coefficient is not constant for any one stream in any one gas, but varies with the distance of the stream from the source. If this variation were small, there might be some ground for considering that the law was fundamentally dependent on an exponential form, but varied from it on account of some secondary cause. As a matter of fact, how- ever, the variations are far too great to permit of such a supposition. The true state of affairs is very different. There is no such absorption coefficient, nor any approach to an exponential law. Hach « particle pursues a rectilinear course, no matter what it encounters: it passes through all the atoms it meets, whether they form part of a solid or a gas (or in all proba- bility of a liquid), suffering no deflexion on account of any encounter until, at any rate, it is very near the end of its course. It loses energy as it goes, a portion of this at least being spent in producing ions. This drain on its energy, at least, robs it of its extraordinary powers of penetration and lonization. From this it will be clear that there are two quite independent characteristics of a stream of @ radiation: one, the number of « particles in it, the other, the energy of their motion. The latter may more or less be evenly distributed amongst the various particles. It is possible for the latter of these characteristics to vary considerably whilst the first does not change at all. For example, in the curves described above, the & particles from Ra C remain unchanged 11 number up to nearly 6°5 cms. from the commencement of their motion; but their energy has almost vanished at the longer distance. Again, as will be seen later, a thin metal plate the e Particles of Radium. 329 may be placed in the way of the stream, and so rob every particle of some of its energy, but not a single one is brought to rest by collision with the atoms of metal, and the number of particles in the stream remains unchanged. In our experiments two different quantities are measured, one the range of the « particles, the other, the ionization which they produce. The range of the @ particle in a given substance is the distance it can penetrate before losing its power of making ions in that substance, which can be collected and measured by electrical means. We assume that when it ceases to have this power, the energy has fallen to an amount which is very small compared to its initial energy (say 1/500), so that even if it varies in different substances, such a variation cannot affect the rangeappreciably. As a matter. of fact, it is probable that no such variation exisis. The range of an e particle in any substance is therefore dependent on the original energy of projection. It is not quite proportional to it, because, as we have pointed out already, the 2 particle does not spend energy at exactly the same rate at all periods of its flight ; towards the end of its range its rate of expenditure is somewhat increased. If the particle is made to pass through some material other than air, its range may be much altered. For example, if it passes through a thin silver film whose thickness is ‘001 cm. its range in air, supposing it to be allowed to complete its course in that medium, is diminished by more than 3 cms. Or again, the a particle which has a range of 7:0 cms. in air has only a range of 3°3 cms. in methyl bromide at the same pressure and temperature. Consequently, if we measure the range of the @ particles in different gases, or after their passage through thin films of matter, we obtain a measure of the comparative rates at which energy is expended by a particle in passing through these gases and materials. The second quantity which is measured by us is the ionization produced by the particle at various distances from its source. From this measurement we are able to discover, amongst other things, whether the stream has suffered in any other respect than that of loss of range when it has passed through thin material films, supposing that the rest of the flight is in ordinary air ; and if we compare the quantities as measured in different gases, we are enabled to compare the conductivities which are imparted to these gases by 2 particles moving through them under conditions otherwise similar. These two quantities are independent of each other. It is true that if the conductivity of a gas were proportional to the 330 Prof. Bragg and Mr. Kleeman on number of ions produced by the particle, and that if the total number of ions produced by an a particle were the same, no matter the gas in which it completed its course, then ‘the product of the ranges and the ionization per cm. of path would be a constant. Now Rutherford has made measure- ments of the total ionization produced by the particle in some substances, and found it the same in each case. But there are other substances for which this is not true; e. g., ether, ethyl chloride, and methyl bromide ; and in consequence the sedan of these suppositions is not justified. It is even possible that the first may also prove incorrect. It is conceivable that the « particle may spend energy on ionization whilst passing through a molecule, especially a complex molecule, and that the products may never get away from the molecule so as to be separated by the electrical field, and measured by the electrometer. That this actually occurs certainly seems a natural inference from some of the fellowing results. Let us now consider the experimental evidence. In fig. 2 are drawn three curves, A, B, and C. The first of these repre- sents the ionization curve of radium in air. Curve B shows the result of placing a number of thin sheets of silver-leaf over the radium, so that the rays had to traverse these before reaching the ionization-chamber. Curve C shows the effect of substituting thin silver-foil for the leaf. The product of the density and the thickness was in the case of the leaf "00213, and in the case of the foil ‘00967, ‘These figures were readily obtained by weighing a measured area of the material in each case ; the leaf was not easy to handle, and the loss of range in its case not very great, so that the foil experiment is the more reliable. The curves ABC are clearly similar in shape, and differ only in their height above the zero line. The silver sheet has not in either case caused any modification of the a stream, except that it has cut off an equal amount from the range of each particle. If some of the particles had been stopped by the metal, or if some had lost more energy than others, there would have been more or less distortion of tbe curve. But the former condition does not occur, as has been already explained, and the latter was also prevented in this case by the great uniformity of the foil, which was polished on both sides. The loss of range in the case of the silver-foil is 33°5 mm. If we take the density of the air to be ‘0012, we may say that a silver stratum for which thickness x density =: 00967 is equivalent to an air stratum for which the same product = 3°35 x :0012=°00402. The ratio of these quantities is 2°41. ‘So8V.0 UI}.100 U1 ( the a Particles of Radium. 331 In fig. 2 are shown the results of some of our experiments of this kind on other metal films. All do not show the same regularity as the silver: for we have found great difficulty in obtaining uniform films in the majority of cases. The 2 ie ali pied Ann ea % ai aa eee _— _ wie N 5 = IN iS) Ee je ’ ! i i 1 Ay 1 J x = Nieee Wes a0) i 7h Mieke a ea Se i x p {eyo jo Artsuop =d) vy oy} 10A0 poorzd ore spvzour urez.100 eae laa a ace bAL70) | JOU Ke % "4, 4, rolls used by the jewellers are not fine enough to give perfect results, and we believe there is no goldbeater in Australia at present. Nevertheless the metal workers have managed to roll for us films of gold, platinum, and copper which have given us fair results : ; aluminium leaf was procurable and 332 Prof. Bragg and Mr. Kleeman on thin tinfoil. When a film is not uniform, the fact is made evident by a distortion of the curve, e. g. in the case of copper. It will be seen that the top of it slopes too much, implying that the « rays do not come into the ionization- chamber as suddenly as they ought to do. Some have, in fact, been less checked than others because they have passed thr ough thinner portions of the somewhat uneven film. We have measured, in such cases, the drop ot the curve as shown by its amount ‘at the middle point of the top of the RaC portion. #.g.,in the case of platinum we have measured the depth of the middle point of the top of the curve below that of the middle point of the top of the normal curve. The results of these experiments are shown in the following table. The first column of figures gives the product of the thickness of the metal film and its density, the second the corresponding drop of the curve, multiplied by the density of air, and the third the ratio of these two products. if | 20 tate IV. | Ratio 1V./IEI. Gold ...cscc.c8) (OLLI) 00896501) 3: 0oe eine 4-65 IPIEWG UMC Bo sa6 ‘00633 WOT92 | Soo ee aks (lan 4:25 ‘Uinriesaaeieemens ree 0051 | OOZ12 sy) 24 10:85 4°50 Silver’ i5062.5, 00967 | °00402 | 241 | 10-4 4°30 Copper <2... 00873 | -00492 WATS, lan (6 4°45 Aluminium ...) ‘00258 | 00209 NGS ee Oval bed) 4:20 * Tinfoil contains a certain proportion of lead; but this could not affect the result very appreciably. It is remarkable that the numbers in the third column are nearly proportional to the square root of the atomic weights of the metals. To bring this out more clearly, the square roots are shown in a fourth column, and in a fifth the ratios of the numbers in the two previous columns. Moreover, air itself falls approximately into line with fh metals. Its ionization ratio should be entered in the third column as unity, and the average square root of its alomic weight as (4714+ /16)/5=3°79. The corresponding entry in the last column should be also 3:79. Also it is easily seen that hydrogen is not far away from the others. For it has been shown by Strutt that its con- ductivity under ionization as compared with air is *226. As- suming for the present that this means that a 1 cm, layer of hy drogen has the same effect us a °226 cm. layer of air, then the ratio of the product of the thickness and the density in the case of the hydrogen to the similar product in the case of the air is 1/144 x° 296=-31. The square root of its atomic weight is 1, and 1/°31=3°2. the a Particles of Radium. Jom Since the atomic weight is of such consideration in this law, it is more direct to state the results in another way. Instead of comparing the stopping powers of strata of metal and air of equal weights, we can compare the stopping powers of strata containing equal numbers of atoms, and therefore the stopping powers of individual atoms. For example, a stratum of silver produces the same effect as a stratum of air whose weight is 2°41 times greater. Thus for equal weights silver stops 1/2°4i times as much as air; but for equal numbers of atoms it stops 108/14°4 x 2°41 times as much as air. This ratio, which is equal to 3°11, may be called the “stopping power” of the silver atom, referred to the air atom asa standard. The latter is an imaginary atom having an atomic weight 14:4, a molecular weight 28°8, and an atomic square root 3°79. The stopping powers of the various metals examined will be set out below, in conjunction with those of certain gases. When we found that a simple law seemed to cover the behaviour of substances differing so widely in all their pro- perties as those enumerated, we thought it advisable to examine such other substances as were available. We were unable to obtain other metal films; and we therefore turned our attention to gases. Now no striking evidence for the square-root law could be obtained from an examination of gases whose atomic weights were nearly the same as that of air, such as oxygen or nitrogen. Indeed, it had already been shown by Strutt that their behaviour was very much the same as that of air. Nevertheless, it was not to be forgotten that their proved properties were not against the square-root law. We therefore made experiments with the following gases, which contained atoms whose weights were very different from those of air atoms :— Methyl bromide, methyl iodide, ethyl chloride, carbon tetrachloride, ether, and hydrogen. Methyl bromide was a most suitable gas for our purpose. The ratio of its molecular weight to that of air is 3°28. If, then, the loss of range in passing through this gas were proportional to the density, the range of the particle from RaC would be only about 7/3°28 or 2°3 cm., provided the gas were at atmospheric pressure. But if the square-root law were true, the range would be much greater, and could be calculated thus :— The carbon atom should contribute a stopping power pro- portional to W712, the three hydrogen atoms to 3,/1, and the bromine atom to /80. Total 3:46+3+48°95=15°41. In air the stopping power should be the average of that of Priteag. S265 Vol: 10, No. 57. Sept. 1905. 2 A 334 Prof. Bragg and Mr. Kleeman on four molecules of nitrogen and one of oxygen. ‘The stopping power of nitrogen should be proportional to 2/14 or 7°48, that of oxygen to 2,/16 or 8. Now (4x 7:48+8) /5=7558. Therefore the stopping power of the CH;Br molecule as compared to that of air should be 15:41/7:58= 2-03 ; and the range of the a particle of Ra C should be 7/2°03=3°4 em. A sufficient quantity of methyl bromide was prepared and kept liquid in a freezing-mixture. The vessel containing our apparatus was joined to an air-pump and exhausted till the remaining pressure was equal to about 6 cm. of mercury. The liquid was then allowed to pass in under atmospheric pressure until the vessel was full of the gas. The pressure was again reduced to 6 cm., and vapour introduced until the pressure in the vessel was once more equal to that of the atmosphere. The ionization curve was then obtained. It is plotted in fig. 2, and shows that the range is nearly as calculated from the square-root law. It was not advisable to take it for granted that the vessel contained vapour only; and after a little time we hit upon a method of determining this point satisfactorily. The method also proved particularly useful in the case of mixtures of air and vapours, as will be described presently. Immediately after measuring the range of the particle in the gas, we opened a communication between the vessel and an exhausted globe of about one litre capacity. The capacity of the vessel itself was 6 litres. The weight of the gas so drawn over was compared with the weight of the air that came over under similar conditions when the larger vessel contained air only; and from this ratio the proportion of air and vapour could be deduced. For example, the weight of the mixture of air and methyl bromide was 2°599 grams. The corresponding weight of air was ‘800 gram. (It was not, of course, at atmospheric pressure.) Hence if w= the ratio of the number of air molecules to the number of molecules of CHBr, #£+3°28 ft eS Sh) e+ Loe e800? = one, ee 1 iD: The extreme range of the « particle of RaC in CH;Br is shown by the curve to be 3°32, This is the distance from the radium to the gauze of the ionization-chamber. ‘The the a Particles of Radium. aa latter was 2 mm. deep, and half this, viz. 1 mm., should be added in order to get the true range, which may therefore be taken as 3°42. The corresponding range in air is 7:06. Hence, if w« = stopping power of the methyl-bromide molecule, wor. «06 et Ap Deere CO O42 ue re) which is very nearly the value already calculated on the square- root law. The errors of experiment were not so small that this almost absolute agreement can be looked on as more than accidental. It will be seer, however, that all the gases ex- amined gave good results. The curve of a gas is different in some important respects from that which is obtained in examining the loss of range in metal films. In the latter case, all the ordinates are re- duced from those of the normal air-curve by nearly the same amount ; in the former, they are reduced in nearly the same proportion. Again, in the case of the metal film (provided it is uniform) the abscisse are unaltered ; in the case of the gas, the abscissee are all altered in the same proportion and show the amount of ionization produced by the @ particle in traversing the gas. For example, the extreme abscissa of the RaC group has the value 666 in the gas and 547 in air; thus the ionization per cm. is 666/547 or 1°27 times greater in the gas than in the air. Since, however, the range is 2:07 times shorter, the ratio of the total ionization in the gas to the total ionization in air is only 1:27/2°07 =-62 nearly. In most of the complex gases examined the « particle produces less ionization than in air. We propose to make a further examination of this point. In the case of the other gases, the procedure was very similar. Carbon tetrachloride, methyl iodide, and ether are liquid at ordinary temperatures and pressures, and in their case we introduced the necessary quantity of liquid to give a vapour pressure of about two-thirds that of saturation, and then filled up with air. We found it better to do this than to attempt the experiment with low pressures in our vessel, for the latter had so many joints and stuffing-boxes that it would not keep a vacuum very well. It was, however, quite airtight enough to retain a mixture unchanged for hours provided it was at atmospheric pressure. The proportion of air to vapour was afterwards determined in the manner already described. 2A2 336 Prof. Bragg and Mr. Kleeman on Hthyl chloride was tried before we used the method of weighing a definite quantity of the yas. But the vessel was emptied and filled three times, and there must have been very little air in it. It cannot give a decisive answer as to the validity of the square-root law, because, as it happens, the square-root law and the simple density law give nearly the same value. On that account we have not yet repeated the experiment. Hydrogen presented some special difficulties. The range (on the square-root law) of the «& particle of Ra C must be about 30 cm., and our apparatus only measures up to 8 cm. We therefore placed a piece of silver-foil over the radium, which was equivalent to 3°3 em. of air. This cut down the range of the Ra C particles to 3°63, and the ranve of the swiftest of the others to 1:43. The former when multiplied by four would still be out of range, but the latter would be within it. : Fig. 2 (p. 331) shows that this was the case. With a mixture of hydrogen and air in the proportion (by pressure) of 9 to 1 it wasat4°6. With mixtures containing a greater proportion of hydrogen it rose somewhat, but a small proportion of air made little relative difference. The curve is of course very much drawn out vertically, and drawn in horizontally. The results obtained for all the above substances are collected in the following table :— TaBLE, showing “stopping power” of various atoms and molecules as compared with that of air. The atomic weight of the supposititious atom of air is taken as 14:4, and the “atomic square root ” as 3°79. Stopping power| Ratio of Ratio of atomic of atom or square or molecular molecule, roots. weights. iyo o gem: 45 ..2 Ser Lehaety 246 20954 6 ‘069 AVI Pr Ee clas als esate 1 1 1 PAUITIMTNNAUNTINA ee oe 2 ace noceee 1:53 1:38 1:88 Wappeltiet sess. iv en. cae 2:42 Fl 4:53 SLUT EIS oN Ger Ae ce ee ee 311 ZO TO) ADE vs sees tare eee 3 42 2°88 8:2 Eerie aie epee sinc <4 | 4-12 37 13°5 Gold Beetles ss 8.2's.: | 4°45 | 37 | 15°7 Methyl bromide ......... 2:09 | 2:09 | 3°28 Ethyl! chloride ............ 2°30 | 2°36 223 Methyl iodide ............ | 2-49 | 2°35 | 4:9 Either) (tae teen c. kek | 3°30 | 3°68 | 2°56 Carbon tetrachloride ... 38 361 5-41 the a Particles of Radium. 337 These results are shown graphically in fig. 3, in which the ordinates and abscisse represent the numbers in the first Kio, 3. WG 7 7/\ Ze 47 Y and second columns respectively. It is curious that the metals and gases seem to lie on rather different lines. Pos- sibly this is due to the difference between solid and gas; possibly again to the fact that the gases tested have such complex molecules. Further research may make the point clearer. Several other points arose in the course of the experiments, which deserve further inquiry. [For instance, the metal films did not cause exactly the same drop through- out all the curve; the slower « particles were a little less affected than the swifter. i From these results it appears that the following law is _true for certain elements, at least to a first approximation. The energy spent by an « particle in its passage through an atom is proportional to the square root of the atomic weight. It can never be said that this is a law which is general to all the elements until all the elements have been experimented upon. In the case of many of them, the ex- perimental difficulties will be very great. Since, however, the law holds with some accuracy in several cases, it becomes desirable to consider whether any physical interpretation can be placed upon it. 338 Prof. Bragg and Mr. Kleeman on Now the energy which is spent by the a particle 1 is certainly spent, in part, in producing ions. If the rate of the expen- diture of the energy as a whole is related to the atomic weight by so simple a rule as that of the square root, it is probable that the part which is spent on ionization obeys the same rule. or if not, and if the expenditure on ionization follows some other law, then the remaining expenditure must follow such a law that the two together compound into the simple rule of the square root. It is proper to put aside this more complicated hypothesis until we have considered the simpler one. We may therefore advance the law one stage and state it thus :—The energy spent on ionization by an a particle i in its passage through” an atom is proportional to the square root of the atomic weight. The question now arises: Is the variation from atom to atom due to a difference in the number of ions produced, or in the energy required to produce an ion, or in both these quantities? Because an oxygen atom absorbs four times as much energy as a hydrogen atom, are there four times as many ions produced from an oxygen atom, but the energy per ion the same; or is the act of ionization four times as difficult, but the number of ions the same; or are neither of these suppositions true, and is the difference between oxygen and hydrogen in this respect due to a variation in each of the two quantities ? Now the total conductivity imparted to a gas by the passage of a particle through it is very nearly the same for the simpler gases. This is true even though some of them differ widely from each other in their atomic weights, e. g. oxygen and hydrogen. From this it appears probable that the energy required to produce an ion is always the same. It is true that in some of the complex gases the total conductivity is less than in the simpler gases, but this can be explained on the hypothesis that the same number of ions is made in these heavy molecules, but that they find a difficulty in escaping from the molecule and are recombined, so that they add nothing to the conductivity of the gas. If this hypothesis is not entertained, we are driven to suppose that the energy required to make an ion is not the same in some of the complex molecules, and that the number made varies by just so much as to make the total loss of energy of the particle in each molecule follow the same simple law as holds for the simpler molecules. For the present at least this complicated supposition must also be set aside, and again we may make an advance in the statement of our law. It now stands :— The nunber of ions made by an « particle in passing the a Particles of Radium. 309 through an atom is proportional to the square root of the atomic weight. It should, perhaps, be pointed out that this does not mean that the a particle makes the same number of ions out of each atom of the gas through which it is passing ; but merely compares the average per atom. It asserts, for example, that in going through oxygen the a particle makes a number of ions which is four times as many as the number made by the particle moving with the same speed in passing through hydrogen at the same pressure and temperature. It is possible that this rule implies that a particle must make more than one pair of ions in passing through any one atom, unless ionization is only rarely the consequence of the encounter. or if only one pair could be made in each atom, and if the « particle made one pair in crossing each atom of hydrogen, then in oxygen at the same pressure and temperature as the hydrogen, only the same number of ions would be made per centimetre, which is not the case. Nor does it appear possible to suppose that ionization does not occur at a large proportion of encounters ; the number of jons made is of the same order as the number of atoms traversed, according to Rutherford. The most reasonable interpretation of these results seems therefore to be (1) that the a particle makes the same number of ions during its course no matter what the gas which it traverses ; (2) that the energy required to make a pair of ions is always the same ; and (3) that the observed variations in the conductivities in some cases are due to the failure of ions to get free from the molecule in which they are made. Under these circumstances we must look for the origin of the square-root law in some disposition which limits the number of ions that can be made in an atom. It is not to depend on any variation of the energy required to make a pair of ions; but must be due to some condition which only gives the « particle such an opportunity of making ions as is to be measured by the square-root of the atomic weight ; and, where it forbids the act of ionization, forbids also the corresponding expenditure of energy. We can only make guesses as to what this condition may be. It has been maintained, on good evidence (see Meyer, ‘Kinetic Theory of Gases,’ § 112), that the atom has a disk-like form, and that the various atoms and molecules differ in two dimensions only. It is possible that an ex- planation of the square-root law may be found in the hypothesis that ions can only be formed on the circumference of the atom’s disk, for the amount of that portion of the atom 340 Prof. J. Traube on the which lies on the circumference is proportional to the square root of the whole. Under such circumstances an @ particle, if it struck the atom anywhere except at the edge, would pass through without result. Since the energy required to make a pair of ions is probably the same no matter what the atom or molecule may be in which they are made, and no matter whether it be solitary or a constituent of a complex molecule, we seem driven to the belief that ionization consists in breaking bonds which are always the same, both in character and in strength. The electron is torn from its union with something else which is always the same, and must form some constituent of all — atoms. This hypothesis also makes reasonable the supposition that an act of ionization may be performed within a complex molecule, and yet no conductivity be imparted to the gas. For the act would then consist in the breaking of an electron from its attachment to this common constituent, and would not of necessity imply separation from the system of the molecule. The idea of a common constituent is, of course, an old one. It is certainly strengthened by the discovery that radium and its successive products emit a particles which are exactly alike. | We wish to express our gratitude to Mr. J. P. V. Madsen, B.Sc., for the generous assistance which he gave us during several weeks of full work, and to Professor Rennie, D.Sc., and Mr. A. J. Higgin for their kindness in making the chemical preparations. XL. On the Space occupied by Atoms: The Theories of Th. W. Richards and J. Traube. By Prof. Dr. J. TRAvuss, Berlin *. et several years f I have been busy with investigations regarding the space relations of different forms of matter, and have repeatedly pointed out the extraordinary importance of this much neglected domain of science. To my satisfaction, so distinguished an investigator as Th. W. Richards has recently { taken up the same problem, * Oommunicated by the Author. + See, especially, my Jatest work, Drude’s Ann. d. Phys. Bd. v. p. 548 (1901), ana Bd. vii. p. 267 (1902); further, the account in the Boltzmann-Festschrift, p. 480 (1904); also Zeitschr. f. anorg. Chem. Bd. xxxiv. p. 413 (1903), Bd. xxxviii. p. 399 (1904), Bd. xl. p. 372 (1904); and the older account: ‘Ueber den Raum der Atome, F. W. Ahrens, Samml. chem, techn. Vortrdge, Bd. iv. p. 1 (1899), and my Grundriss der Physikal. Chemie (Enke, Stuttgart, 1904). t Th. W. Richards, Zeitschr. f. Physik. Chem. Bd. xl. pp. 169 & 602 (1902); Bad, xlii. p. 129 (1903) ; and Bd. xlix. pp. 1 & 15 (1904). Space occupred by Atoms. 341 and in aseries of memoirs has arrived at conclusions and results which substantially agree with my own, which partly form extensions of them, but which partly also, in one essential point, present so characteristic a difference in the point of view that it may be worth while to compare the two theories. More especially, however, do I wish, by a brief résumé of my work, to establish my priority in regard to many of the problems treated of by Richards. Although Mr. Richards is good enough, in a concluding note, J. ¢. vol. xlix. p. 17, to refer in terms of approval ,to my work, I am_never- theless of opinion that the note in question is liable to be» misleading. The space occupied by matter may be regarded as con- sisting of (1) The true volume of the atoms and molecules; and (2) The co-volume, or space within which the atoms are free to move. Now while in the case of the “ideal ” gases the true volume is negligible in comparison with the co-volume, Budde and especially J. D. van der Waals have shown how, from the behaviour of gases under high pressures and near the con- densation-point, the coefficient } in van der Waals’equation (p+ S)@—H=RT may be taken into consideration *, and how, by the aid of this well-known equation, the cohesion coefficient a, the true volume 0, and the co-volume v—b may be calculated, as a first approximation, by taking into account the deviations of strongly compressed gases from the ideal gaseous laws. It is sufficiently well known with what success van der Waais applied this equation to the transition from the gaseous to the liquid state, and further to the theory of corresponding states; and how, by means of the coefficient b, it became possible to determine the absolute dimensions of the atoms. The proof that the equation of van der Waals also holds good for homogeneous liquids and even for solids—so that the * J may take this opportunity of remarking that I regard the establish- ment of van der Waals’ state equation as one of the greatest advances in physical chemistry. If we take into consideration the fact that a and 6 are not constants, then the equation holds with much greater accuracy than has hitherto been supposed ; in any case, it is in general much to be preferred to those complicated equations which have been proposed in place of it, and which, perhaps, come nearer the truth, but are far less well adapted to purposes of calculation. 342 Prof. J. Traube on the modified gaseous laws ure applicable to all three states of matter —was first given by myself*. Now the method which I first adopted in investigating the volume relations of liquids was to compare, according to Kopp’s method, at the ordinary temperature, the molecular volumes (molecular weight~density) of such organic sub- stances as had the same composition-difference, e. g. CH, H,, &. It appeared that—as a first approaimation—cor- responding to equal composition- difference there was equal volume-difference. On comparing, for a given compound, the atomic volumes so determined with the molecular volume, it appeared, contrary to Kopp’s calculations, that the sum of the former was less than the molecular volume. Thus the molecular volume of a liquid consists of a sum of atomic volumes }V,, but in addition to this also of a second term, which obviously represents the co-volume. ‘The values calculated by the above method of this co-volume, per gramme- molecule, mostly oscillated about 25 ¢.c. at 0° as a rough approximation, and only in the case of associated substances were the calculated values considerably less, for reasons which are easy to understand, when the simple molecular weight was made the basis of calculation. The values v; and v2 of the volumes corresponding to two neighbouring temperatures T, and T;, calculated by means of the coefficient of expansion of the liquid, were next substituted in the equation of van der Waals, and thus the values of b and v—b calculated. The values of b so obtained were found to be in agreementt with the }V. calculated according to Kopp’s method—7. e. with the sum of the atomic volumes. Thus the equation of van der Waals was found to hold good for homogeneous liquids. The same two methods led to the desired result in the case of solids. Kopp’s method tf, as in the case of liquids, led to 70 an equation of the form ee +, where — denotes the .aolecular volume, >V, the sum of the atomic Talat and ® the co-volume. When, on the other hand, by using the soefficients of expansion Bf the elements the v oie b= SS ve and ®=v—b were calculated by means of van der Waals’ equation, the following result was obtained §:— On the supposition that when a solid element is heated * Drude’s Ann. d. Phys. Bd. v. p. 548 (1901) ; and Zettschr. anorg. Chem. Bd. xxxiv. p. 415 (1903). t J. Traube, Drude’s Ann. Phys. Bd. v. p. 552 (1901). tT See the author’s Graundriss der Phy ystk. Chemie, Enke, Stuttgart 1904, p. 207. § oso anorg. Chem. Bd. xxxiv. p. 418 (1908). Space occupied by Atoms. 343 only the co-volume expands—as in gases—and not the total volume, the coefficient of expansion was referred to the former instead of the latter, and it appeared that this coefficient of expansion is equal to 34 for all the elements (halogens excepted). Therewith a proof was obtained that van der Waals’ equation applies to all three states of aggregation, and that it enables us to calculate the true volume and the co-volume for all three states. Now the separate consideration of each volume leads to remarkable consequences. (a) The true volumes (the quantities b). The atomic volumes as calculated by Kopp’s method and by means of van der Waals’ equation are only mean values, which may be used for purposes of calculation much in the same way as the mean molecular velocities are used in the kinetic theory of gases. The volume of an oxygen atom is, e. g., least when it is in combination with hydrogen, it is appreciably larger in combination with carbon, and increases in homologous series, in combinations such as methyl, ethyl, &. The contraction, ¢. g., undergone by chlorine when combined with the atoms of various metals depends on the chemical affinity of the metal concerned for chlorine. I was the first—several years before Mr. Richards *—to * In the Zeitschr. Physik. Chem. Bd. xlix. p. 19, Richards remarks :— “Tt is a pleasure to me here to draw attention to the entirely independent investigation of J. Traube in this direction. It is remarkable that quite simultaneously he published in Drude’s Ann. Bd. v. p. 555 (20 June, 1901) the following proposition :— ‘The atomic volume of an element changes from one compound to another; it decreases as its attraction for the neighbouring atoms increases ’—while on June 15 of the same year my version of this relation appeared in the Proc. of the Amer. Acad. Ivil. p. 17: ‘The atomic volume is not constant, but is a function of pressure and temperature, and probably of electric strength.’ ” Mr. Richards has evidently overlooked the fact that in my monograph, which appeared already in 1899, quoted by him and published in Ahrens, Samml. chem. u. chem.-techn. Vortrige, Bd. iv. p. 22, there is contained the following proposition :— - “The vibration space (the quantity 6) changes, according to the nature of the atom, more or less from one compound to another, and in accordance with the mutual influence which the various atoms contained in the compound exert on each other. The less the attraction of neighbouring atoms, the more nearly does the vibration space approach its maximum value (maximum vibration volume), and, on the other hand, the vibration volumes decrease the more the greater the mutual attraction of the atoms.” I may also remark that I undoubtedly have the claim to priority in the matter of the doctrine of the compressibility of atoms (the quan- tities 6) as against J. D. van der Waals (cf. my statements in Zeztschi. anorg. Chem. Bd. xxxvii. p. 242, 1903). 344 Prof. J. Traube on the arrive, as a result of my researches, at the following funda- mental proposition regarding atomic space:— The spuce occupied by an atom changes from one compound to another; it is the smaller the greater the affinity of the atom in question for the neighbouring atoms with which it 1s combined. The importance of this proposition lies, on the one hand, in the conception of atoms as compressible spheres, and, on the other, in the fact that the contraction of the atom is regarded as a measure of chemical affinity. Special attention must be drawn to the fact that the atomic contraction forms the only measure of chemical affinity; and although Richards cannot claim priority regarding the above and a few other propo- sitions enunciated by him, he has rendered one of the most valuable services by showing * that in general the change in the free energy is just as little a measure of the chemical energy as the heat development. | In accordance with the above I have propounded the problem of calculating the atomic contractions from the results of chemical reactions, considering this to be the most important problem of chemical dynamics + (Mechano-chemie)— the sister science to thermo-chemistry. The effect due to “affinity pressure” must be similar to that due to other pressures, and in particular to the intrinsic pressure of liquids, which in most cases amounts to about 1000 atmos. at 0°. From tbis it follows that the true atomic volumes corresponding to the liquid state must frequently be considerably less than those corresponding to the gaseous state, and that accordingly during evaporation not only the co-volume, but the true volume of the atoms as well, frequently undergo very considerable expansion. A gason is greater than a fluidon. By means of this simple doctrine of the compressibility of atoms, among other things various difficulties of van der Waals’ theory may be explained, notably the third volume of the isothermals may be enterpreted f. * Leitschr. Physik. Chem. Bd. xiii. p. 129 (1908). t Cf. my Grundriss der Physik. Chemie. t Cf. my Grundriss der Physik. Chem. p. 107, 1904. I had also (cf. Drude’s Ann. Phys. (4) Bd. vii. p. 267, 1902, and Zertschr. anorg. Chem. Bd. xxxvii. p. 226, 1903, and Bd. xxxvui. p. 399, 1904) appealed to the theory of gasons and fluidons in order to interpret the observations of de Heen, Galitzin, and especially also those made in my laboratory by Teichner, which apparently are not in accordance with Andrews’ theory of the critical state. I note that—as Teichner and Bakker have shown (Zeitschr. Physik. Chem. Bd. li. p. 345, 1905)—other suppositions are also possible. But when Verschaftelt (in the Berichte der Akad. von Wetenschappen, Amsterdam, 24, Dec. 1904) once more attempts to miinimize Teichner’s experiments by ascribing them to the effect of slight Space occupied by Atoms. 345 The determination of the true atomic volumes of an element in its elementary state and in its various combinations is also of considerable importance in other directions. Thus the determination of the space occupied by, for example, an oxygen or a nitrogen atom is helpful in arriving at the constitution. Ring compounds—such as the benzene ring— are characterized by so greata reduction in the volume of the carbon atom, that by means of the molecular volume it becomes possible to determine the number and even the nature and tension of the rings. The small space occupied by the carbon atom in its elementary state as compared with the large space which it occupies in compounds, is characteristic throughout of the behaviour of carbon in its elementary and combined states—and what holds for carbon is equally applicable to other elements. Already in my first memoir * on chemical volumes I drew attention to the intimate connexions which primarily exist between the molecular volume and the thermo-chemical constants, especially the heat of formation. Now although Richards was not the first to point out the close relation between atomic volume contraction and heat of formation, he nevertheless first showed, in a large number of cases, that a far-reaching paral- lellism exists between heat of formation and atomic contrac- tion, and that the heat of reactzon is, as a first approximation, equivalent to the work represented by the contraction of the atoms. Now when we consider that the electrical energy which a galvanic cell is capable of generating may, as a first approxi- mation, be equated to the heat which under ordinary circum- stances the reactions taking place in the cell are capable of developing, it necessarily follows from the relation of this heat development to the dynamical contraction-energy, that the electric energy of acellis to be attributed to the mechanical work accompanying atemic contraction Ff. In this respect my views are in complete agreement with impurities, I beg to refer him to my own experiments, Zeztschi. anorg. Chem. Bd. xxxvili. p. 399, especially p. 402. When in using Teichner’s method it is found that after the equalization of the densities during cooling these ditferences of density again appear above the critical temperature, then surely this cannot be due to admixtures! IJ¢ will be necessary to get accustomed to the supposition that Andrews theory is in need of a very essential modification ; that the temperature at which the meniscus vanishes ts not the critical temperature ; that this latter has, unfortunately, not been determined accurately in any case, but that in all cases it lies considerably higher than has hitherto been supposed. : * Zettschr. anorg. Chem. Bd. 11. p. 23 (1892). + J. Traube, Zeitschi. anorg. Chem. Bd. xl. p. 382 (1904). 346 Prof. J. Traube on the those of Richards, and we also agree in thinking that this way of regarding the electrical processes leads much further than the application of the electron theory to electrolytic processes, and especially as regards the conception of elec- trolytic solution pressure. While fully acknowledging the additions due to Mr. Richards in this respect, I regret that my earlier remarks-in this connexion should have been over- looked byhim. I have at a much earlier date * established a connexion between the solution pressure of a metal and the difference in the affinity of the solvents for the metal and the affinity of the metal for itself; and I have even repeatedly pointed out the very remarkable fact—which had not as yet been noticed by Richards—that the atomic contraction of potassium, sodium, silver, 5c. cons in water is the same, and is independent of the nature of the ton, and that this proposition is strikingly analogous to Faraday’s electrolytic lawt. It is to be hoped, now that Richards also expresses similar views, that my former views will receive greater attention. (b) Lhe Co-volumes (the quantities v—}). Not less significant are the conclusions to which we are led by a discussion of those volumes which we denote as co-volumes. Since at ordinary temperatures the intrinsic pressure is in most cases not very different for different liquids, the molecular co-volume is also in general so nearly constant that frequently it may be used to determine the molecular weight as well as the approximate degree of association. specially is this the ease for substances soluble in water without ionization. The molecular volume in solution, or the solution volumet of a dissolved substance is also equal to a sum of atomic volumes, increased by a co-volume, which in the case considered, owing to the contraction which takes place in water, is considerably less than for the undissolved substances, but which for all substances not undergoing ionization was found to be approxi- mately 12°4 ¢.c. per gramme-molecule as determined by Kopp’s method. * J. Traube, Ann. Phys. Bd. Ixii. p. 505 (1897) ; and Richards, Zettschr. Physik, Chem. Ba. xl. pp. 179-181. { J. Traube, ‘Raum der Atome,” Ahrens Samml. Chem. und Chem.- Techn. Vorti. Bd. iv. p. 76 (1899), and Ann. d. Phys. Bd. \xii. p. 505 (1897). t Cf. J. Traube, F. W. Ahrens Samml. Chem. u. Chem. Tech. Vortr. 1899, 7. c. Space occupied by Atoms. 347 This law—of Avogadro—is, as I yet hope to show, of funda- mental interest in connexion with the notion of osmotic pressure. The above proposition also furnishes a very simple method for determining the molecular weight from the specific gravity of a solution. The study of the co-volumes of solids led to values which were mostly not greater than half the molecular co-volumes of homogeneous liquids. Now since in the case of some such compounds as racemic acid &c. the molecular volume was undoubtedly doubled, but was accompanied by twice as great a co-volume as in the case of other solid compounds, the _ assumption did not appear too bold that in general the apparent halving of the co-volume during the passage from the liquid to the solid state was to be attributed to a doubling of the molecular fact that during the Sree from the solid to the liquid state the increase of volume is proportional to the decrease in the degree of association of the liquid*. Onthisis based the only reliable method of determining the molecular weights of homo- geneous solids, As regards the effect of temperature on the co-volume, the iaw of Charles-Gay-Lussac-Dalton applies to all three states of aggregation. Hspecially in the case of the solid elements (including most metalloids) did I supply the proot 1 that the coefficient of expansion of the co-volume is = ae If the known co-volume per gramme-molecule for the gaseous state— 22,400 c.c.—be divided by the molecular co-volume at 0° for the liquid state, we obtain the intrinsic pressure S Using this method, I calculated the intrinsic pressure tor most organic liquids to be between 800 and 1000 atmospheres; for gold in the solid state, 176,000 atmos.; and for the diamond, 5,460,000 atmos. ‘These intrinsic pressures were, for an element obeying Dulong and Petit’s law, equal to exactly three oe the value ae where C stands for the atomic heat sag a “ for the rate of change of volume with temperature fF. The intrinsic pressures of the metals were found to follow the * Cf. my Grundriss der Physik. Chem. pp. 207 & 208. t Richards has (/. c. Bd. xl. p. 174), unlike myself, calculated the intrinsic pressure not by the aid of van der Waals’ equation, but by putting Cdt=Kdv—an assumption which is not permissible, since ihe heat has to do work other than that involved in overcoming the internal pressure. 348 Prof. J. Traube on the changes in the hardness, elastec modulus*, and coefficient of friction Ff. It was further found { that the length of free path of the metallic atoms as calculated from the difference between the diameter of the total volume and that of the true volume (the quantity )) was in agreement with that found from the diffusion-coefficient ; also, the atomic coefficient of compressi- bility of the metals was the greater the greater the ¢o-volume. Van der Waals’ equation leads to the value = for the heat of vaporization §, if, as in the case of monatomic substances, it is permissible to neglect the work connected with the passage from a fluidon to a gason. I have shown that in the case of mercury, observation and calculation are in agreement. In the case of poly-atomic substances, the heat of vaporization a é . came out to be 2—. Since according to Deprez-Trouton’s vO rule the heat otf vaporization is proportional to the absolute temperature of ebullition for non-associated substances, it follows that the boilzng-point also becomes a simple calculable function of the volume, and finally I showed that in the case of metals the absolute boiling-point is inversely proportional to the ewpansion-coefficient || . (c) Internal and Haternal Atomic Volumes. So far we have only considered two volumes: the true volume and the co-volume, or the quantities 6 and v—0. According, however, to the calculations of van der Waals, the quantity 5 is by no means the space which is completely filled by the mass of the atoms, but the four-fold multiple of this space. We may, following Clausius, picture to ourselves the quantity b as the space occupied by the atom together with the ether envelope into which no other atom can penetrate. The znternal atomic volume would thus be pro- portional to the external volume, or to the space occupied by the envelope of “bound” ether. Now the theories of Clausius, Mossotti, and Exner lead to the conclusion that an approximate measure of the internal volume is furnished by * J. Traube, Zeitschr. anoru. Chem. Bd. xxxiv. p. 413 (1903). + J. Traube, did. Bd. xl. p. 877 (1905). t J. Traube, zbed. Bd. xxxiv. p. 425 (1903). § J. Traube, Ann. der Phys. Bd. viii. p. 298 (1902); and Zertschr. anorg. Chem. Bd. xxxiv. p. 428. || J. Traube, Zettschr. anorg. Chem. Bd. xxxiv. p. 422 (1903). Space occupied by Atoms. 349 2 abot .“; and it has, as a matter of n-+2 d ; fact, been shown by me* that, in accordance with this as- sumption and with the theory of van der Waals, the quantity b is, at the critical temperature, in general about 3°5 or + times as great as the molecular refraction. According to this, the refractive index also becomes a simple volume-function. The molecular refraction is also dependent in a similar manner on pressure—i. e., 71s compressible like the quantity b. Although the influence of the internal pressure is only de- monstrable in the case of the quantities 6, the considerably stronger affinity pressure acts also on the refraction. From this it follows that we have to consider not only the surrounding ether envelope, but also the atom proper, as elastic. I do not, however, go so far as T. W. Richards, who concludes from this result that the distinction between the internal and external volumes is unjustifiable; but I conclude, from the above com- pressibility, as well as from the multiple relations between the internal volume, the external one and the co-volume (at corresponding temperatures), that ultimately wther and che- mical matter are identical. The consideration of volume thus leads to views similar to those which are developed in the theory of vortex atoms, and even the more modern views regarding electrons are by no means so far removed from those here developed as would at first sight appear to be the case ft. It might be specially pointed out, that the doctrine of the three volumes is not only in accordance with the theory of van der Waals, but also with that of Fresnel, who distinguishes the eether bound up with the atoms from free ether. The difference between the external and internal volumes corresponds to the space occupied by the bound wether, while the co-volume is filled with free ether. I have pointed out { that the various properties of matter are related to the atomic volumes much more simply and directly than to the atomic weights (e. g., hardness, elasticity, viscosity, length of free path and velocity of diffusion, boiling-point, melting-point, heat of vaporization, surface-tension, refraction, isomorphic, valency, compressibility, cohesion, affinity, heat of formation, electromotive force, K&e.). Lhave further drawn attention to the fact that the numerical relations among the atomie spaces are likewise simpler than those among the atomic weights, especially when the effects due to intrinsic pressure the molecular refraction * J. Traube, Ann. der Phys. |4] Bd. v. p. 552 (1904). { Cf. J. J. Thomson, ‘ Electricity and Matter.’ { J. Traube, Zeztschr. anorg. Chem. Bd. xl. p 372 (1904). Pil siiagas. bo: Vol. 10. Ne. 57. Sepi. 1905. 23B 350 Protea Traube on the are eliminated and the elements compared in their gaseous state *; I have further shown that 7 to the changes in the pro- perties which an element undergoes as it passes from the elementary state to that of a definite class of compound, there correspond throughout simultaneous volume changes. All these facts, combined with the well-known defects of the periodic systems, have led me to enunciate the proposition— The properties of the elements and their compounds are primarily functions of the atomic and molecular volumes. A satisfactory systematic presentation must primarily be based on the relations con- necting the volumes (and possibly also the shapes) of the atoms. The fact that, according to the well-known volume curve of Lothar Meyer, the atomic volumes are periodic functions of the atomic weight, and that thereby all other properties become functions of a function, is best interpreted as follows : When the elements are arranged according to their atomic weights, there are frequently found at periodic intervals elements whose atomic volumes and atomic shapes stand in simple nume- rical relationship; only when such is the case are the elements also related to each other in their remaining properties. The periodic interval is thus by no means the essential determining factor; the determining factors are volume and shape of atom. I would particularly draw attention to the fact that these views of mine regarding the periodic system are in excellent agreement with those of J. J. Thomson} regarding the structure of atoms—views which, though hypothetical, are strikingly original and worthy of allattention. J.J.Thomson shows, by building up the atoms out of negatively charged corpuscles, that at definite periodic intervals there recur atoms of similar constitution, and hence also similar space relations, and that it is these forms of matter whose properties are related. Jt seems to me very remarkable that the views which I have for a long time advocated solely on the ground of my studies of volume-relations, should have been arrived at in a totally different way by so competent an authority, on the basis of the electron theory. | | I now wish to return to the investigations of Mr. Richards, and say a few words about them. | Starting from the compressibility of matter and the con- traction of the atoms, Richards arrives, although considerably * LC. Diolo; e + “Raum der Atome,” F. W. Ahrens Samm. Chem. und Chem.-Techn. Vortr. p. 14. 5 { J. J. Thomson, Phil. Mag. | 6] vol. vit. p. 237 (1904) ; also ‘ Electricity and Matter.’ ee Space occupied by Atoms. dal later than myself, yet independently, at the important relation between contraction and affinity. By means of the equation Cdt=Kdv he calculates the “energy-quotient” K as a quantity which is proportional to the intrinsic pressure calcu- lated by me from van der Waals’ equation. In accord with myself, Richards points out that hardness, elasticity, and other properties vary in accordance with this intrinsic pressure. To Richards is, as already pointed out, due the great credit of having verified for the first time, in a large number of cases, the relations, among others, between the heats of for- mation and the atomic contractions already recognized by myself. As regards the relations connecting electromotive force, solution-pr essure, and atomic contraction, Richards has arrived at results which accord with my own. Of fundamental interest is the already quoted memoir on the change of free energy, as well as the recently commenced experimental investigations on the coefficient of compressibility. Although I regret that Mr. Richards did not make himself acquainted with my work before commencing his own, yet, on the other hand, it is satisfactory to find that he has, on the whole, inde- pendently arrived at similar conclusions. On one very important point only do we differ. Richards remarks,. /.,¢. vol. xlix..p. 17: “The bulk of Traube’s reasoning is rendered difficult to follow by his hypo- thetical assumptions of ‘co-volume,’ ‘ core-volume,’ ‘ bound ’ and ‘free’ ether, but nevertheless to him is due the credit of having recognized the importance of many of the facts.”. _ _ In my opinion, the value of my views lies precisely in what Richards reproaches me with. . W hile I distinguish three volumes : internal, external, and co- volume, Richards assumes for the hquid and solid states only a single velume. He regards the atoms as something in the nature of elastic spheres, which are in contact and undergo contraction, without any intervention of a free space between them. The effect of heat manifests itself in condensations and rarefactions within the atom. While [ have proved the generality of the gaseous laws ag expressed by van der Waals’ equation, and their applicability to all three states of aggregation, from the assumptions made by Richards it would follow that this equation is not applicable to the liquid and solid states, since Richards equates the co-volume v—b for both these states to zero, not only at the absolute zero of temperature, but at all temperatures. But if Richards is right, how are we to account for the fact that the coefficient of expansion of the solid elements = wep provided the total expansion be referred not to the Zire 302 Mr. W. A. Price on the Electrical Resistance of total volume, but to the co-volume as calculated by myself? This resuit alone is enough to show the advantage which my views possess over those of Richards. The co-volume is, in fact, that part of the total volume which changes with tempe- rature, while the true volume can only be altered by pressure. Further, I would reter to all the other consequences which are rendered possible by the separate calculation of the co- volume, such as the calculation of the intrinsic pressure (this is proportional to Richards’ ‘‘energy-quotient”), and the relation of the co-volume to the most varied properties. Had Richards separated the notions of co-volume and true volume, many of his investigations—especially that in Zectschr. Physik. Chem. xlix. pp. 16 et seg—would have taken a much simpler form. Not only, however, the notion of co-volume, but also the consideration of the mutual relationship between external and internal volume must I defend against the views of Mr. Richards. Now I am not only in agreement with Mr. Richards, but may even claim priority regarding the view that not only the envelope but also the core of the atom is compressible; but the two ideas must be maintained separate—this is confirmed by the theories of van der Waals, and of Clausius, Mossotti, Exner, as well as by my verification of both theories. Finally, I have already pointed out the agreement of my volume-theory with Fresnel’s theory of a bound and free wether; and it also appears to me that the various zther theories, such as those of Lord Kelvin, are in agreement with my views, but not with those of Mr. Richards. Charlottenburg, Technische Hochschule. XLI. The Electrical Resistance of a Conductor the Measure of the Current passing. By W. A. Pricz, Fellow Phys. Soc.* 1. ¢NHANGE in the length of a platinum wire is a con- venient measure of the current, but the ordinary hot-wire instrument is net sufficiently precise for some purposes. The experiments in this paper were made by Mr, C. H. Wright, in Crompton & Co.’s works at Chelmsford, to ascertain whether the resistance of a conductor would be a better measure of the current than its length where consi- derable accuracy is required, the practical object in view being the calibration of alternating-current instruments. It was hoped to retain the advantage possessed by the dynamo- meter of calibration by direct currents, and thus of direct * Communicated by the Physical Society : read May 12, 1905, a Conductor the Measure of the Current passing. 353 reference to the Clark cell and standard resistance ; to get the precision of other resistance measurements ; and to avoid the use of apparatus which is easily put out of adjustment. 2. To try whether the resistance of a conductor carrying alternating current could be easily measured, the connexions were arranged as in fig. 1. The mean fall of potential over R. carrying a current from the alternating supply A was compared with that over 8, a standard; a small direct current being passed through the system from the accu- mulator H. The potential-differences of R and S were compared on the potentiometer. B, K were regulating re- — sistances, and highly inductive coils at M, N the primaries of Bro. 1. O/B POTENTIOMETER small high-voltage transformers reduced the alternating currents in circuits where only direct-current effects were required. If the alternating current in R be I, and the direct current 2, the heat developed « I’?+7*; so that if I be large compared with 7, say 100 times as great, the heating effect of 2 is negligible. The experiments of fig. 1, in which I was several hundred milliamperes, and z was 1 milliampere, were designed to show whether the resistance of R carrying alternating current could be measured by a superimposed direct current so small that it would not affect the heat developed. It was found that using the Chelmsford town- supply for the alternating source observations could be made 354 Mr. W. A. Price on the Electrical Resistance of without any difficulty, the widening of the galvanometer-line by the alternating current producing no appreciable incon- venience in reading. With the workshop supply readings were impossible, as the line was given a violent jerk every time a motor was started or stopped. 3. It was assumed that the temperature of R, a thin con- ductor, will be the same for a direct current as for an alter- nating current of the same root mean square; so that if R can be constructed to measure direct currents, it can be cali- brated with those, and used to measure alternating currents. All the subsequent experiments were accordingly made to ascertain the conditions for its use with direct currents. 4, Silver was chosen for trial. Being a pure metal, its resistance changes rapidly with temperature, and its molecular condition is unlikely to change with repeated heating and cooling as might be the case with an alloy. Being a good conductor, it is heated rapidly by a low potential-difference. It was available as foil -5 mil thick, in which form it has a large radiating surface for a small heat capacity. In the end we found this foil gave irregular results, probably from being too fragile, and platinum-foil of 1 mil in thickness was used instead, A few preliminary experiments showed the results to be exceedingly sensitive to draughts; and a great many different arrangements were tried to “protect con- ductors from ir regular cooling by currents of air. Conductors of thin foil were enclosed in large vessels and in small, packed in mica slips and in slag- wool. The containing vessels were protected in various ways, or immersed in water or paraffin-oil. ~The net results were clear. If any considerable free body of air is near to the conductor, currents of air and irregular cooling are produced when the conductor is heated, and no comets in! measurements are obtained. If, on the other hand, the containing vessel or any solid packing is near to the conductor, its heat capacity affects the temperature, which only slow ly reaches a permanent value. These results indicate that the conductor must be contained in a relatively large vessel, exhausted of air, and suggest that an incandescent lamp may be suitable for small currents and large. pressures, and a slip of metal foil for large currents and small potential- differences. 5. Experiments on the above lines were started on— A. Carbon-filament incandescent lamps. B. A platinum ligament in a metal box, exhausted by a Fleuss pump. ©. A platinum ligament sealed into an exhausted glass bulb. a Conductor the Measure of the Current passing. 355 All these experiments were directed to the establishment of a relation between the resistance of the conductor and the direct current passing. The connexions are shown in fig. 2, where K is the conductor under test, shown, e. g., as an incandescent lamp, § is a standard resistance of known value, B isa regulating resistance, Ha storage-cell, and C a standard cell. The potential-differences of R, 8, and the H.M.F. of C were compared on the potentiometer P fora series of different currents obtained by regulating B; and from the three readings the current through and the resistance of R are calculated. In each case there are four leads to the resistance, two carry- ing the current, and two which carry no current connected to the’potential points, and the resistance measured is in every POTENTIOMETER case that between the potential points. The potentiometer lends itself admirably to experiments of this class, since all the data are obtained from adjustments on one calibrated wire, while the whole of the conductor whose resistance is measured may be inside the exhausted vessel, so that the leading-in wires are not involved. With a bridge the current could not be measured with the resistance, while the resistance of leading-in wires would have to be taken into account. _ 6. The resistance of a 50 volt, 8 ¢.p. Stearn lamp was measured witha small testing-current immersed in a paraffin- bath warmed up to 56° C. to obtain an idea of the change of resistance with temperature. The mean change over a range of 40° C. was —:0224 per cent. per degree. In the resistance was included in this case that of the leading-in wires ; and 356 Mr. W. A. Price on the Electrical Resistance of it may be mentioned as a curiosity that a particular 4-volt lamp tested at the same time showed a very nearly constant resistance over the same range, the increase of the platinum and the decrease of the carbon resistance just balancing one another. The combination of a carbon lamp and a metallic conductor might be useful for some purposes as having a small or negligible temperature-coefficient. 7. To determine the effect of external temperature a 50-volt 8 c.p. lamp was tested in a paraffin-bath, with the following results :— Current in Resistance in ohms. milliamperes. Bath at 7° C. Bath at 50° C. me 160 159 | 30 150-35 149:97 | 50 142-84 142-6 | qu 137-14 136:83 89°98 131-96 13182 | As would be expected, the effect of the external tempe- rature diminishes as the current employed increases. A current of 110-120 milliamperes just made the above lamp incandescent, the above measurements being taken with the filament black. Observations on the lamp in air, quite un- protected, gave closely similar and consistent results, showing that air-draughts outside an exhausted bulb are of no appre- ciable importance. 8. To ascertain how far the resistance of the lamp is affected by use, the following results were obtained, on a lamp when new, and after it had been run for 6 hours and 17 hours respectively at its full voltage of 50 volts. @uerent in Resistance in ohms. milliamperes.| — === 529 The figures A were taken as the bulb was received from the maker; B were taken ten days afterwards, a good many experiments with currents not exceeding *5 ampere, alternating and direct, having been made in that time; C were taken shortly after B, the slip having been heated previously for one hour to a bright red by a current of ‘9 ampere; D were taken after a further heating for # hour of the same current, ‘9 ampere. The resistance of the slip when cold was unchanged throughout. It had been raised to a bright-red heat before originally sealing into the glass bulb. It seems clear that. _ the explanation of the changes between A, B, C, D must be looked for in the small quantities of gas occluded by the platinum betore sealing in, and given off when subsequently heated 7m vacuo; and this effect may also explain the changes in the resistance of a carbon filament noticed in § 8 above. If a conductor of this kind is to be used asa gauge for the measurement of current, either, as Prof. Callendar has suggested to me, the exhaustion of the vessel must be poor, so that the absorption or occlusion of gas by the platinum does not make any appreciable change in the amount in the vessel, giving the case of the results of § 13; or else the exhaustion and sealing must be performed when the platinum is at a bright-red heat, so that no occluded gases are left. Hither course seems to promise a satisfactory result. Ps Beg XLII. On the Momentum and Pressure of Gaseous Vibrations, and on the Connexion with the Virial Theorem. By Lord RayuzicH, O.M., F_R.S.* iL a paper on the Pressure of Vibrations (Phil. Mag. iii. p. 338, 1902) I considered the case of a gas obeying Boyle’s law and vibrating within a cylinder in one dimension. It appeared that in consequence of the vibrations a piston closing the cylinder is subject to an additional pressure whose amount is measured'by the volume-density of the total energy of vibration. More recently, in an interesting paper (Phil. Mag. ix. p. 393, 1905) Prof. Poynting has treated certain aspects of the question, especially the momentum asso- ciated with the propagation of progressive waves. Thus prompted, [ have returned to the consideration of the subject, and have arrived at some more general results, which how- ever do not in all respects fulfil the anticipations of Prof. Poynting. I commence with a calculation similar to that before given, but applicable to a gas in which the pressure is any arbitrary function of the density. By the general hydrodynamical equation (Theory of Sound, § 253 a), pe a where p denotes the pressure, p the density, @ the velocity- potential, and U the resultant velocity at any point. If we integrate over a long period of time, @ disappears, and we see that Vardi 4) U% des 1.0. | aaAom retains a constant value at all points of the cylinder. The value at the piston is accordingly the same as the mean value taken over the length of the cylinder. If , p; denote the pressure and density at the piston, and Poy Po the pressure and density that would prevail throughout were there no vibrations, we have p= (p)=f(pot+p—po) - + - - (@); aud approximately f' (00+ P—Ppo) = -—1 '( \ 1 —— is aH = ») =| p Jp} o=| aipeaiph P= op ae BOs (Pp — po)” a I met (P,) + ne {pot (Po.)—F' (po) s - (4). * Communicated by the Author. Momentum and Pressure of Gaseous Vibrations. 365 For the mean value of @ at the piston we have only to write p; for p in (4) and integrate with respect to ¢. And at the piston U=0. For the mean of the whole length J of the cylinder (parallel to #), we have to integrate with respect to # as well as with respect to ¢. And in the integration with respect to w the first term of (4) disappears, inasmuch as the mean density remains the same as if there were no vibrations. Accordingly : Purdeoga fy ( U? dx dt is co) | Po w=1|| / SH Oly "dad ae, 2 + {pof”(p0) —/'(p,)$ - {| (p a 0) ae a} (5); the terms on the right being of the second order in the quantities which express the vibration. Again, J (pipe) dt=f (f(x) —F (00) fat — La NA =po foo) ® Po dtr ptf) | Peed 3 Po Po so that by (5) U? dz dt fo. — po) dt= = \| = : ss — po)? dx dt — po)? + {po (po) — Pot (Po) {fe 5 En) pees (a) | 0M a “Po ‘Po | (6). The three integrals on the right in (6) are related in a way which we may deduce from the theory of infinitely small vibrations. If the velocity of propagation of such vibrations be denoted by a, then f’(p,)=a?. By the usual theory we have ib p—p 1 dd joe eee Bee : dx’ Po loge tie Oniae (7). If we suppose that the cylinder is closed at e=0 and at “=l, a normal vibration is expressed by Tv § t p=cos cos ; Set Me Cot Phil. Mog. 8. 6. Vol. 10. No. 57. Sept. 1905. 2C 366 ~ Lord Rayleigh on the Momentum and where s is any integer, giving a (pi— po)”, 24) (Ba Por art i Uda dee =| oe dt=a ae 7 = \\> 7 (9), the integrations with respect to « in (9) being taken from 0 to 7, that is over the length of the cylinder. The same conclusions (9) follow in the general case where g is expressed by a sum of terms derived from (8) by attri- buting an integral value to s. The latter part expresses the equality of the mean potential and kinetic energies. Introducing the relations (9) into (6), so as to express the mean pressure upon the piston in terms of the mean kinetic energy, we get as the final formula I/ J2 { @=po dt= fo ed ies) Te ue eas » A IODE Among special cases let us first as that of Boyle’s law, where p=a’p, so that F(po)=u*, fp) =. We have at once U2 dx dt f-na=n |] a The expression on the right represents double the volume- density of the kinetic energy, or the volume-density of the whole energy, and we recover the result of the former investigation. According to the adiabatic law pip=(pieg). oo > so that ! ‘ Po { =) Fol=P2, Fo PBT. 4, Hence from (10) \ (pp ae po | The mean pressure upon the piston is now $(y+1) of the volume-density of the total energy. We fall back on Boyle’s law by taking y=1. Tt appears “therefore that the result is altered when Boyle’s law is departed from. Still more striking is the alteratvan when we take the case treated in ‘Theory of Sound? § 250 U? dz dt i (14). Pressure of Gaseous Vibrations. 367 of the law of pressure p=Const.— oP Mtithes 2h (LD) . According to this I’ (Po) =@, I (po) = —2a7/po . ° ° (16), and (10) gives i Cpipdt— On havin ag eto in( LT). The law of pressure (15) is that under which waves of finite condensation can be propagated without change of type. In (17) the mean additional pressure vanishes, and the question arises whether it can be negative. It would appear so. If, for exampie, apo p=Const. — Sad a (18), P(p)=e, — f'' (Po) = — 82"/pp; d Be an | (rp) pe 4p || Uae sReiec teenage 5.))5 I now pass on to the question of the momentum of a pro- gressive train of waves. This question is connected with that already considered ; for, as Prof. Poynting explains, if the reflexion of a train of waves exercises a pressure upon the reflector, it can only be because the train of waves itself involves momentum. From this argument we may infer already that momentum is not a necessary accompaniment of a train of waves. If the law were tbat of (15), no pressure would be exercised in reflexion. But it may be convenient to give a direct calculation of the momentum. Yor this purpose we must know the relation which obtains in a progressive wave between the forward particle velocity u (not distinguished in one-dimensional motion from U) and the condensation (e—po)/po, usually denoted by s. When the disturbance is infinitely small, this relation is well known to be w=as, in the case of a positive wave. Thus ii ays 0a (ap ido) wae te st. (20). The following is the method adopted in ‘ Theory of Sound,’ § 351:—“If the above solution be violated at any point a wave will emerge, travelling in the negative direction. Let us now picture to ourselves the case of a positive progressive wave in which the changes of velocity and density are very gradual. but become me ey accumulation, and let us 368 Lord Rayleigh on the Momentum and inquire what conditions must be satisfied in order to prevent the formation of a negative wave. It is clear that the answer to the question whether, or not, a negative wave will be generated at any point will depend upon the state of things in the immediate neighbourhood of the point, and not upon the state of things at a distance from it, and will therefore be determined by the criterion applicable to small dis- turbances. In applying this criterion we are to consider the velocities and condensations not absolutely, but relatively, to those prevailing in the neighbouring parts of the medium, so that the form of (20) proper for the present purpose is w= /(P). a =|,/(4)-* Lo ee which is the relation between wu and p necessary for a positive progressive wave. Equation (22) was obtained analytically by Earnshaw (Phil. Trans. 1859, p. 146). In the case of Boyle’s law, ,/ (dp/dp) is constant, and the relation between velocity and density, given first, I believe, by Helmholtz, is whence u=a log (p/po); if po be the density corresponding to w=0.” In our previous notation dpldp=f'(p)=@ +f'(p0) « (Pp —po)s a being the velocity of infinitely small waves, equal to Vif" (po)s3 and by (22) —e iy ——_— age ee an en . (28), Po pPo\ 2a Po 2 the first term giving the usual approximate formula. The momentum, reckoned per unit area of cross section, =| dx =po|(1 + oa) uadx. 0 Introducing the value of uw from (28) and assuming that the mean density is unaltered by the vibrations, we get F'(po) , @Y ( (e= poy? a _ Pressure of Gaseous Vibrations. 369 or, if we prefer it, eeu (po) +h fura pris (20). The total energy of the length considered is po) wu’ da ; and the result may be thus stated oe Pos pos (Po) momentum = x total energy (26). This may be compared with ce If we suppose the long cylinder of length / to be occupied by a train of progressive waves moving towards the piston, the integrated pressure upon the piston during a time ¢, equal to //a, should be equal to twice the momentum of the whole initial motion. ‘The two formule are thus in accordance, and it is unnecessary to discuss (26) at length. It may suffice to call attention to Boyle’s law, where /’’(p,)=0, and to the law of pressure (15) under which progressive waves have no momentum. It would seem that pressure and momentum are here asso- ciated with the tendency of waves to alter their form as they proceed on their course. The above reasoning is perhaps as simple as could be ex- pected; but an argument to be given later, relating to the kinetic theory of gases, led me to recognize, what is indeed tolerably obvious when once remarked, that there is here a close relation with the virial theorem of Clausius. If a, y, z be the coordinates ; v,, vy, vz the component velocities of a material particle of mass m, then ama 2 ; 42mv.= —$>Xe4+3 Pea with two similar equations, X being the impressed force in the direction of # operative upon m. If the motion be what is called stationary, and if we understand the symbols to re- present always the mean values with respect to time, the last term disappears, and 1>mv,= —1> Xx 2" SA aI (ea aN The mean kinetic energy of the system relative to any direction is equal to the virial relative to the same direction. _ Let us apply (27) to our problem of the one-dimensional motion of a gas within a cylinder provided with closed ends. ov Lord Rayleigh on the Momentum and As in other applications of the virial theorem, the forces X are divided into two groups, internal and external. The latter reduces to the forces between the ends (pistons) and the gas. If p, be the pressure on the pistons—it will be the same on the average at both ends—the external virial is per unit of area $p,/ simply. As regards the internal virial, I do not remember to have seen its value stated, probably because in hydrodynamics the mechanical properties of a fluid are not usually traced to forces acting between the particles. There can be no doubt, however, what the value is. If we suppose that the whole mass of gas in (27) is at rest, the left-hand member vanishes, so that the sum of the internal and external virial must vanish. Under a uniform pressure jo, the internal virial is therefore tpl. Inan actual gas the virial for any part can depend only on the local density, so that whether the gas be in motion or not, the value of the internal virial is 1 -3|y dG. LiL |) Oe Hence (27) gives 1 St . > Y — il 1 f kinetic energy = 43p)/ -3{ dx 0) Ll =Hn—pl-4| (p-pede - 42a 0 If the gas be subject to Boyle’s law, pressure is proportional to density, and the last term in (29) disappears. The additional pressure on the ends (p,;—j,) is thus equal to twice the density of the kinetic energy. In general, P—Po=l(P—po) +3" (Po) - (P— Po)” and 1 a | (p—po)da=stf" (00) | (Pp —po)?dx. 0 If we introduce expressly the integration with respect to ¢ already implied, (29) gives 1\ (py —po) dt = po) | U*dx dt +47" (py) \\(e — po) "da dt 211 ; = Po =F Rov aay pat) ; || cae it, regard being paid to (9). Equation (10) is thus derived very simply from the virial. Pressure of Gaseous Vibrations. atl In all that precedes, the motion of the gas has been in one dimension, and even when we supposed the gas to be confined in a cylinder, we were able to avoid the consideration of lateral’ pressures upon tbe walls of the cylinder by applying the virial equation in its one- -dimensional form. We now pass on to the case of three dimensions, and the tirst question which arises is as to the value of the virial. In place of (27) we have now ism WV= —43 (Xx + Yy+ Zz) . : c (30), U_ being the resultant ee Y, Z impressed . forces parallel ‘to the axes of YF and 2 Let us first apply this to a gas at rest under pressure 7%. “The total virial, represented by the right-hand member of (80), is now zero ; that is, the internal and external virial balance one another. As is well known and as we may verify at once by considering the case of a rectangular chamber, the external virial is 3p9v, v denoting the volume of gas. The internal virial is accordingly —gpov ; and from this we may infer that whether the pressure be uniform or not, the internal virial is expressed by Spa diy dans) 2) ah ia (31): The difference between the internal virial of the gas jn motion and in equilibrium 1 1s —3\{{ (ppidadyde so. Cl"). According to the law of Boyle, (31*) must vanish, since the mean density of the whole mass cannot be altered. The internal virial is therefore the same whether the gas be at rest or In motion. | A question arises here as to whether a particular law of pressure may not be fundamentally inconsistent with the statical Boscovitchian theory of the constitution of a gas upon which the application of the virial theorem is based. If, indeed, we assume Boyle’s law in its integrity, the incon- sistency does exist. For Maxwell has shown (Scientific Papers, vol. 1. p. 422) that on a statical theory Boyle’s law involves between the molecules of a gas a repulsion inversely as the distance. This makes the internal virial for any pair of molecules independent of their mutual distance, and thus the virial for the whole mass independent of the distribution of the parts. But-such an explanation of Boyle’s law violates the principle upon which (31) was deduced, making the pressure dependent upon the total quantity of the mass and not merely upon the local density ; from which od2 Lord Rayleigh on the Momentum and Maxwell concluded that all statical theories are to be rejected. Tt is to be remarked, however, that our calculations involve the law of pressure only as far as the term involving the square of the variation of density, and that a law agreeing with Boyle’s to this degree of approximation may perhaps not be inconsistent with a statical Boscovitchian theory *. Passing over this point, we find in general from (30) 43 mU?=3(pi—po)v— 3) \\ (p—po) da dy dz. (32), whenever the character of the motion is such that the mean pressure (p,) is the same at all points of the walls of the chamber. Further, as before, \\\ (p — po )da dy de=$f''(po) \\i (Pp —po)°*dax dy dz, and finally, regard being paid to (9) as extended to three dimensions, '/ (pi— py v= (5 oP Past po!) x total energy . (33). In the case of Boyle’s law *’”=0, and we see that the mean pressure upon the walls of the chamber is measured by one-third of the volume-density of the total energy. For the adiabatic law (12), (13) gives (Pi-— Po) v= € 15°) xtotal energy. . (64): In the case of certain gases called monatomic, y=1%, and (34) becomes (p1—po)¥ = 2X total energy . . 2 (Gd): oO Thirdly, in the case of the law (15) for the relation between pressure and density, (pi—po)v = —#xtotal energy. . . (36), the mean pressure upon the walls being less than if there were no motion. So far we have treated the question on the usual hydro- dynamical basis, reckoning the energy of compression or * [ think the difficulty may be turned by supposing the force, inversely as the distance, to operate only between particles whose mutual distance is small, and that outside a certain small distance the force is zero. All that is necessary is that a pair of particles once within the range of the force should always remain within it—a condition easily satisfied so long as small disturbances alone are considered. O13 (we) Pressure of Gaseous Vibrations. rarefaction as potential. It was, however, on the lines of the kinetic theory that I first applied the eal theorem to the question of the pressure of vibrations. In the form of this theory which regards the collisions of molecules as instan- taneous, there is practically no potential, but only kinetic, energy. And if the gas be monatomic, the whole of this energy is translational. If V be the seevece velocity of the molecule whose mass is m, the virial equation gives Sri > NF) ach ae ere Lee ey), p, denoting, as before, the pressure upon the walls, assumed to be the same over the eae area. If necessary, p; and YmV* are to be averaged with respect to time. Tt is usually to a gas in equilibrium that (37) is applied, but this restriction is not necessary. Whether there be vibrations or not, p; is equal to 2 of the volume-density of the whole energy of the molecules. © Consider a given chamber whose walls are perfectly reflecting, and let it be oceupied by a gas in equilibrium. The pressure is given by (87). Suppose now that additional energy (which can only be kinetic) is communicated. We learn from (37) that the additional pressure is measured by 2 of the volume-density ot the additional energy, whether “this additional energy be in the form of heat, equally or unequally distributed, or whether it take the form of mechanical vibrations, 7. e. of coordinated velocities and density differences. Under the influence of heat-conduction and viscosity the mechanical vibrations gradually die down, but the pressure undergoes no change. The above is the case of the adiabatic law with y=12 already considered in (35), and a comparison of the two methods of treatment, in one of which potential energy plays a large part, while in ‘the other all the ener gy is regarded as kinetic. suggests interesting reflexions as to what is really involved in the distinction of the two kinds of energy. If we abandon the restriction to monatomic molecules, the question naturally becomes more complicated. We have first to consider in what form the virial equation should be stated. In the case of a diatomic molecule we have, in the first instance, not only the kinetic energy of the molecule as a whole, but also the kinetic energy of rotation, and in addition the internal virial of the force by which the union of the two atoms is maintained. It is easy to see, however, that the two latter terms balance one another, so that we are left with the kinetic energy of the molecule as a whole. For 374. Momentum and Pressure of Gaseous Vibrations. general purposes a theorem is required of which I have not met a complete statement. For any part of a wider system for which we wish to form the virial equation, we may omit the kinetic energy of the motion relative to the centre of. gravity of the part, if at the same time we omit the virial of the internal forces operative in this part and treat the forces acting from outside upon the part, whether from the remainder of the system or wholly from outside, as acting at the centre of gravity of the part. In applying (87) to a gas regarded as composed of molecules, we are therefore to include on the right only the kinetic energy of translation of the molecules. If a gas originally at rest be set into vibration, we have 3(pi—po)v=additional energy of translation. (38). The pressure p, does not now, as in the case of monatomic gases, remain constant. Under the influence of viscosity and heat-conduction, part of the energy at first translational becomes converted into other forms. A complete discussion here would carry us into the inner shrine of the kinetic theory. We will only pursue the subject so far as to consider briefly the case of rigid molecules for which the energy is still entirely kinetic—partly that of the translatory motion of the molecules as wholes and partly rotatory. Of the additional energy E representing the vibrations, half may be regarded as wholly translational. Of the other half, the fraction which is translational is 3/m, where m is the whole number of modes. The translational part of H is therefore $H(1+3/m) ; so that (P1—Ppo Jo=E(3 += Li m=3, as for monatomic molecules, we recover the former result ; otherwise p,;—py is less. In terms of y we have y= 1S Oi eee 0). - 2 eee (39). m and accordingly ay | : (p1—po)v=H (5 —75- ‘) uN, Ont 2, aa in agreement with (34) where what was there called the total energy is now regarded as the additional energy of vibration. In the case of a diatomic gas, m=9, y=12. Terling Place, Witham, July 26. as 750) 4 XLIII. On the Absorption of the 8 and y Rays of Actinium. By T. Goptuwsx1, Ph.D.( Cracow) *. | aes numerous investigations of the absorption of 8 rays emitted by thorium and radium have established the fact that the @ rays of these elements are complex in their character and consist of electrons projected with a wide range of velocities. It has been shown that their penetrating power does not remain constant but increases with the thick- ness of matter traversed. Consequently, the absorption does not follow an exponential law, such as is shown by the more homogeneous rays of uranium. In the case of radium and thorium, the value of the absorption constant is dependent on the thickness of the matter traversed. For instance, the following values of the absorption constant % for aluminium were found by Hve + for the 8 rays from radium: Thickness in mms. A cm.—1, 0 to ‘85 6°5 85 4, 25 5°7 5 | Al 16 As we see, the value of X varies in a marked manner with the thickness of matter previously traversed. In my previous paper on actinium, I pointed out that the activity of actinium, measured by the 8 rays, decreases accurately according to an exponential law with the thickness of traversed matter. Thus, in this respect, the @ rays of actinium are distinguished from the f rays of other elements. The measurements were made in the following way :— About 2 grams of emanating substance of Giesel (of activity about 300 times that of uranium) were spread uniformly on the bottom of a dish (7 cms. in diameter). The dish was covered with a very thin plate of mica, which was sealed with wax, in order to prevent the escape of the emanation. The measurements of activity were made by means of sensitive electroscope of the type of C. T. R. Wilson. The bottom of the electroscope was removed and replaced by an aluminium plate, 0:08 mm. thick, which absorbed all the arays. The dish, containing the actinium, was placed under the electroscope and covered with the plates of metal whose absorption power was to be examined. * Communicated by Prof. E. Rutherford, F.R.S. Tt Phil. Mag. Dec, 1904. | 376 Dr. T. Godlewski on the Absorption of The results are graphically represented in fig. 1, where the ordinates give the logarithms of the activity expressed in — LOGOF ACTIVITY = = S Leas ,-Olk WW NI SSANMOIHL ercentages of total activity, the abscissas the thickness of P g y> the absorbing matter. For comparison, the corresponding "T Su the 8 and y Rays of Actinium. 377 curves of absorption for the @ rays of radium and uranium are also given. The experimental points obtained for the @ rays of actinium lie on a straight line. The equation I = I,e-**, where wz is the thickness, is applicable even when I has a value smaller than one per cent. of Ih. This indicates that the @ rays from actinium are homogeneous in character, and that their pene- trating power does not change with the thickness of matter traversed. The second characteristic property of the @ rays of actinium is their relatively small penetrating power. While the @ rays from uranium are -half absorved in passing through the thickness of 0°5 mm. of aluminium, the 6 rays of actinium are reduced to half value in 0°21 mm. Thus the @ rays of actinium have only 40 per cent. of the penetrating power of those of uranium. A still greater difference is observed when we compare the penetrating power of the @ rays of actinium and radium. The average penetrating power of the 8 rays from radium is more than three times as great as for actinium. It must be pointed out, however, that the value of X for radium rays changes very considerably with the thickness traversed. From fig. 1 we see that the initial portion of the absorption curves for radium and actinium rays are nearly the same. This shows that some of the @ rays of radium are of the same penetrating power as those from actinium. ‘Tasie IJ. ACTINIUM. Uranium. |; MRapium. | Thickness of metal | | | in mms. x 10—? Eee. ees X Substance. to absorb half the | \ cm. = a° r. a | a rays. | | | Aluminium , 21°2 32% | 129) 140 | 54 | 116) 4:30 | Mica ......... 21:0 330 | 120| 172] 51 | 108 | 3-94 | Brass ......... 65 Qe Oe gamba de > at ae | Copper ...... 63 139 | 159! 60 | 70 | 492) 5:50 Tinfoil ...... 4°5 154 WT] oe | | oe | pic 23-5 | 4°25 163 | 141 | 122 | 10°38 | 62°50 | 5-48 | | A reference to the absorption constants X given in Table II. for different substances traversed by the @ rays of actinium shows that the absorption is nearly proportional to the 378 Dr. T. Godlewski on the Absorption of : : nN density d. For comparison, the values of % and — for d uranium given by Rutherford*, and for radium given by Strutt +, are added. ny e . We see that although the value of 7 is not constant, its variations are considerably smaller than in the case of the other radio-elements. Thus the absorption law of density holds better for the @ rays of actinium than for those of radium and uranium. y Rays of Actinium. The absorption of the y rays was also investigated in a similar way. The ratio of the ionization produced by the 8 rays in the electroscope employed to that produced by the y rays of actinium was found to be about 300. The absorption of the y rays could not be investigated over so wide a range as that of the @ rays, owing to the smallness of the effect produced. The results are graphically represented in fig. 2, where the ordinates give the logarithms of the y activity, expressed in per cent. of the total y activity, and the abscisse the thickness of absorbing matter. The initial value of the y activity was obtained by graphical extrapolation of the curves. Fig. 2. lL kK S | Q o" ER e WS > ‘ on’ i) y) ° to a So 25 ee Ke) ——— THICKNESS IN MM-1Q7 It is seen that the activity measured by the y rays decreases according to an exponential law with the thickness traversed. This law is applicable over the range examined, viz., to * Rutherford, ‘ Radioactivity, p, 114. + Strutt, Nature, 1900, p. 439. the B and y Rays of Actinium. 379 30 per cent. of the initial value. In order to show whether the y rays of actinium are entirely homogeneous, it would be necessary to repeat the experiment, using a more active preparation of this substance. The y rays of actinium differ also very considerably from the y rays emitted by other radioactive elements in having a very small penetrating power. The following table gives the constants of absorption, and the values of ® for the metals d investigated , for comparison the corresponding values for radium * are also given. Tasze IIT. ACTINIUM. RADIUM. Misernacw oe | Less penetrating. More penetrating. | metal in mms. ts nN | | Poa to absorb half | *¢™- le tek r r r | of the rays. | picid: Oe a aad = ee = ae | a eros a Iron’ ... 5°70 mms. 1-23 aliorn | es Wee [Ya cerns eet ond eee. | paoncie..| 5:60. ,; 124 0-17 O28) | 1.07039. |) 0-24 0:033 Lead...) 192 ,, 454 | 040 | O64 | 0056 0-44 | 0037 | We see from this table that the y rays of actinium have a penetrating power of only about one-tenth of that of more penetrating rays of radium. This unusually small penetrating power of the y rays of actinium may perhaps be the cause of the great divergence from the density law for these rays +. Further experiments are in progress to examine the behaviour of the @ and y rays of actinium in a magnetic field. An investigation of this character may perhaps throw some light on the peculiarities of these rays. In conclusion the writer has pleasure in acknowledging the kind advice received from Prof. Rutherford. McGill University, Montreal. April 7, 1908. * See McClelland, Phil. Mag. July 1904, p. 67. + See J. J. Thomson, ‘Conduction of Electricity through Gases,’ p. 312 ; also McClelland, Phil. Mag. July 1904, p. 67. boo XLIV. A Fundamental Experiment in Electricity. By Prof. A. M. Worruincton, C.B., F.RS., Royal Naval Hngi- neering College, Devonport *. be object of the experiment which I desire to record was to ascertain whether any difference could be detected between space at a high electrical potential and space ata low potential, quite irrespective of the existence of any electric field in the space in question. Any easily noticeable difference was not to be expected. Such would probably have been long since discovered; for, if it exists, it can only correspond to some small residue of energy not accounted for in the well-established relations of the electric field. To most people the question may seem to have been settled once for all by the experiments recorded by Faraday in his ‘Experimental Researches,’ vol. i. p. 1174, in which he describes how he constructed a hollow, insulated, conducting cube, inside which he went, “and lived in it, and using lighted candles, electrometers, and all other tests of electrical states, could not find the least influence upon them, or indi- cation of anything particular given by them, though all the time, the outside of the cube was powerfully charged, and large sparks and brushes were darting off from every part of its outer surface.” It must be observed, however, that what Faraday was looking for was some sign of what he called an absolute charge—. ¢., as he explains, a charge existing by itself and not connected by lines of induction with an equal charge of opposite sign; and it will be noticed that the tests he mentions were tests of ‘electrical states.’”? He does not seem to have employed tests of other physical conditions. It therefore seemed to me worth while to examine whether any difference could be detected in the velocities of lght passing through two tubes, the interior of one of which was at a high, and of the other at a lew potential. The arrangement employed was that of a Rayleigh interfero- meter, and is shown in the diagram. The light of a Cooper-Hewitt mercury-vapour lamp A passes through a fine vertical slit B, at the focus of a colli- mating lens C. (This lens was an achromatic object-glass of 126 cm. focal length.) The light then passes, as a beam of parallel rays, to the two fine vertical slits D D, and thence through the two open brass tubes E H, each 5 feet (152'4 em.) long, and separated by a partition of ebonite about 2 mm. * Communicated by the Author. A Fundamental Tux periment in Electricity. 381 thick, 183 cm. long, and 30 cm. wide. The two beams are then received by the telescope-lens F (a Steinheil achromatic) 28°4 in. (7271 cm.) focal length, and produce interference- bands in the focal plane of a cylindrical eye-lens G, made of a well-worked glass rod about 4 mm. in diameter. F1G./. Voy msnursr MACHINE The brass tubes were half-cylinders, obtained by splitting a complete tube about 5 cm. in diameter and 3 mm. thick into two equal halves, by sawing it from end to end. The sawn edges were then planed flat, and between the two halves was placed the sheet of ebonite, along the middle of either side of which was pasted a strip of tinfoil a little wider and a little longer than the tubes. The edges of the tubes were pressed firmly against the tinfoil, and the tubes were held in position by a series of stout insulating ebonite bars carried by a light wooden frame, not shown in the diagram. In this way the separating wall of ebonite was prevented from warping and was kept pretty accurately plane, at any rate along its middle part, which was necessary on account of the nearness to each other of the two slits D D. From the middle of the outside of each tube projected a brass rod with a knob, and these knobs could be connected with a Wimshurst induction-machine (see fig. 2). When the machine was worked a potential-difference was established between the two tubes, and this increased untila spark passed between adjustable knobs at K, which were kept about 1} inches apart (30 mm.). The optical apparatus at one end, and one end of the frame carrying the tubes and partition, rested on a table standing on a base of concrete, the other end of the frame and the remainder of the optical parts on a similar table; the Phil. Mag. 8. 6. Vol. 10. No. 57. Sept. 1905. 2D 382 A Fundamental Haperiment iu Electricaty. electrical machine was placed below the middle of the tubes between these two tables. The experiment consisted in watching the interference- bands as the potential-difference rose and then suddenly fell on the passage of the spark, and looking for a shift of the bands. To aid in the detection of the shift, the edge of a fine silk fibre, fixed in the middle of the field of the cylindrical eyepiece, served as a fiducial line. When care was taken not to touch either table, no shift whatever could be detected either when the spark occurred or while the potential- difference was accumulating. With the slits D D about 4mm. apart the bands as viewed were just about 1 degree of are apart, and a shift of =; of this distance could have been easily detected. Sometimes the slits D D were placed wider apart and the beams brought together by means of a parallel plate Jamin separator shown at H in fig. 1. With this arrangement the separation of the middle of the bands was about 8 of a degree, but the definition was not so good. Sometimes the slits D D were traversed by the light after it had passed through the tubes, instead of before; but the result was always the same. The difference of potential when the spark passed was ascertained to be about 60,000 volts. The wave-length of the light to which the predominating part of the illumination was due may be taken as 57 X 10-6 cm., and the experiment therefore shows that a difference of potential of 60,000 volts does not, in a length of 152 cm. of air, produce a relative retardation of as much as a of 57x10-§ cm.; so that, if there is any difference in the velocities through the tubes, 1¢ A 1 1 ate 4 ‘ is less than jg5 X59 X qos Of the whole, z. e. less than one-millionth of the whole. 1 53 of Observations on the Haperiment. It is satisfactory to notice that the observations were not appreciably disturbed by any secondary effects due to dis- placement of the optical parts through the action of electric forces. Even if such effects had, however, been observed, they could have been distinguished from the effect sought, through their remaining unaltered when the charges of the tubes were reversed in sign. The sensitiveness of the experiment could probably be considerably increased by extending the length of the tubes, for this should not increase any secondary disturbance due to electrification. There might be some difficulty in procuring The Atther “Drift” and Rotary Polarization. 383 very long sheets of ebonite: indeed that which I used had to be specially rolled. But it is not necessary for the tubes and sheets to be continuous; a succession of short lengths could be employed. I think, how yever, that a practical limit must exist to the total length of tube that can be advantag geously employed, for the definition was always better when the tubes were removed, and was better with tubes 1 foot long than with tubes 5 feet long, a fact which must, in part at any rate, be attributed to reflexion of diffracted and scattered light, at grazing incidence from the partition into the field of the eyepiece. It was to diminish the effect of such reflexion that in some experiments the slits D D were set wider apart and the beams subsequently brought nearer together by the parallel-plate Jamin device. But the gain was apparently more than compensated by the loss due to the dispersion, by refraction, of each beam in traversing the Jamin plates, since the light was not homogeneous. With a homogeneous source, if one bright enough can be found, this would not happen. July 22, 1905. XLV. The Ather “ Drift” and Rotary ee By D. B. Brace*. ASCART+, some thirty-five years ago, first examined the effect of the motion of the earth on double circular refraction, using R- and L-quartz, from which he ee that the rotary power of quartz is not altered by the sp}oo part when the ray is reversed in the direction of motion of the earth. Lord Rayleigh { recently repeated this experiment, also using quartz, in which Me found that such a reversal does not alter the rotation by toolooo part. By using an active oil—the oil of caraway—and reversing the ray so as to compensate for rotary dispersion, I have been able by means of a sensitive-strip analyser, giving a much higher accuracy, to carry the limit certainly twenty-five and probably fifty times as far, so that we may conclude that the effect of the motion of the earth an the rotation in active substances is certainly less than =5o)p99 and probably less than yo900000 Of the total rotation. Lorentz §, in his early analysis, gives two first order terms, * Communicated by the Author. + Ann. del Ecole Normale, vol. i. p. 157 (1872). { Phil. Mag. Aug. 1902, p. 215. Versuch einer Theorte, Leiden (1895), p. 118. ZW 2 38 t Prof. D. B. Brace on the in one of which this coefficient is the ratio of the velocities of light in quartz and in space, or approximately two-thirds. The presence, however, of two first order terms might imply still a zero first order effect if these terms completely com- pensated one another. It is difficult, however, to see how this could be; and hence, from such a mode of reasoning, we might still expect to find a residual first order effect which would be represented by the aberration term with a small coefficient, and which even the refined experiment of Rayleigh could not show. Ina later paper, Lorentz*, ina reply to a criticism of Larmort, gives the relation of the action between two elements arising from the electric forces which must obtain in order that the earth’s motion may not influence the rotation of the plane of polarization to the first order. As this is not the only possible mode of action, and as further it is only true when second order terms are neglected, a definite conclusion can only be reached by direct experimental examination. While the following test does not fully attam a second order sensibility, it does establish the absence of first order terms, or, at least, a compensation up to one part in five hundred and probably to one part in one thousand. Instead of quartz, which both Mascart and Rayleigh used, I employed finally an active liquid, the oil of caraway-seed (ap = + 103°33! per decimetre). Although its rotary power is much less than quartz (a)p>= 21°67 per millimetre), I found it preferable in the arrangement used. Both Mascart and Rayleigh point out some of the difficulties in such an experiment, involving as it does such enormous rotations. Thus, with the five pieces of quartz which Rayleigh used, the total rotation for sodium light was more than 5500°, and this would give a difference of rotation for the two D-lines of 11°, thus making the use of such a source impossible. He actually used the yellow helium line. Even then the field in his half-shade plane polarizer was “‘ decidedly inferior to that obtainable when the quartzes were removed.” ‘This inferiority due to residual light in the field seems to have originated more largely in imperfections in the quartzes themselves. We should infer from this that, even if the dispersion due to the actual ‘rotation were compensated for, the field would, on account of such imperfections, be far less dark than that attainable with ‘a perfectly homogeneous substance. This was borne out by * Amsterdam Akad. v. Wet. March 29, 1902, p. 669. } ‘Atther and Matter,’ Cambridge, 1900, pp: 214 215 ; also Phil. Mag. Sept. 1902, p. 367. Atther “Drift” and Rotary Polarization. 3895 my own experience in attempting to use quartz successfully in the experiment. It is well known that if the direction of propagation of a ray in an active substance is changed by a single reflexion, the rotation is completely compensated for after passing over the same distance. If such a compensation could be brought about and still allow the influence of the earth-motion to be unaffected, we could use white light, and hence approximate to the normal polariscopic sensibility of say 0°-01 or less, a sensibility usually some ten times that attainable with homo- geneous light from the same radiant under like conditions. My first plan was to mount two equal lengths of the active substance (in this case, quartz cylinders) at right angles to each other, with one. in the direction of drift, and then rotate the system through 180°. This arrangement would give complete compensation if the details of the system could be realized. As this plan involved a change in the direction of the ray of 90°, reflecting surfaces were necessary ; and since, with white light, the azimuths of the various vibrations would be at different incidence on the reflecting surface, the rotations produced by this surface would, in general, follow a different law from that of quartz, so that, to this extent, compensation would be prevented. If, however, these rays should all strike a second surface at the same incidence, but in azimuths which are the complements of those at the first surface, the effect due to reflexion would be completely com- pensated for. This of course may be realized by making the planes of incidence at right angles to one another. Thus, if the plane of the paths within the active media is horizontal, the plane of incidence of the first mirror may be vertical, for example, and the ray be sent upward and then horizontally from the second mirror, the plane of incidence of the latter being also vertical but in an azimuth of 90° to the incident plane of the first. Since now a single reflexion reverses an axial displacement, 7. e., a right-handed to a left-handed one, a second reflexion would reverse this to a right-handed one again, thus restoring the relative order, and so on. An odd number of reflexions therefore reverses the relative axial displacement, while an even number restores it* This * Mascart, in his experiment, realized a reversal by means of a half- wave plate, following the method of Fizeau and Foucault, who used _ the two parallelepipeds of Fresnel instead. He was in this way able to use consecutively R- and L-quartz, their effects being added together. The tetal rotation which he thus obtained was approximately 6300° for the green thallium line. This rotation is somewhat greater than that obtained by Rayleigh, but the former’s polariscopic sensibility was several times less, depending, as it did, on the appearance or disappearance of the thallium line as seen with a spectroscope between crossed nicols. . * 386 Prof. D. B. Brace on the principle of reversal is often lost sight of in connexion with rotary polarization problems. Thus it is true that by a single reflexion the rotation of a ray is neutralized in returning through an active substance and doubled in a magnetic one. If, however, two reflexions were used, as may sometimes oecur, the relative rotation for the different colours would be doubled in active substances and destroyed in a magnetic field. The total rotation of any one ray, however, would depend on its azimuth, which changes sign with respect to the normal to the incident and reflected rays, at each reflexion. The resultant rotation would be the sum of the initial and final azimuths of the vibrations on entering and leaving the re- flecting system. White light, returned through an active substance by two mutually perpendicular surfaces, would not show a recomposition, as it does with a single reflexion. Thus, in the arrangement proposed (fig. 1), equal lengths of right- and left-handed substances, e.g. quartz, would give perfect colour neutralization, as well as plane-polarized light, if the double-mirror compensation, described above, were used. Asa length of one metre for each cylinder was con- templated, the question of the realization of the normal sensibility of a half-shade system had to be answered. This requires, for its application, a uniform field of sensible area, a condition apparently unrealizable with paths of such great lengths in double-refracting substances. In this case, we should have the well-known spirals resulting from the passage of white light through equal lengths of R- and L-quartz, since the number of reflexions is even in this case and they do not enter. However, these spirals, at the centre, intersect each other at right angles, and a partial compensation at this point of the field might be realized by means of a crystal of opposite sign placed so as to forma “ crossed ” system with the quartz cylinder, the cross in the former being tangent to the spiral of the latter for a short distance from the optical axis. It was proposed to use Iceland spar of the proper thickness to give the best result,if this mode of compensation should prove effective. Quartz is positive and the difference in index between its two rays is only about one-twentieth that of spar, which is negative, so that a cylinder of the latter of much less length would be sufficient. As the area available in the field would necessarily be small, the amount of material for cutting could be reduced by using a small cross-section. Samples of both R- and L-quartz crystals of various sizes were secured, mainly from the Hot Springs region of Arkansas. These were cut into prisms (something over a total length of one metre for each kind) approximately parallel to the 387 cation. Drift” and Rotary Polari Aither “Di YS 388 Prot) Dab: Brace on the optic axis, and their ends polished in order to make a pre- liminary examination of their optical qualities. Many of these showed traces of the double spiral over various points of their end faces, indicating the presence or both R- and L- formations to a greater or less extent, so that perhaps less than a third of the cuttings could be used. The entire lot was finally sent to an expert cutter, who declined to under- take, with this material, the making of cylinders which should give the optical conditions necessary for realizing the normal polariscopic sensibility. Cylinders one-fourth as long, built up from sections some 5 cm. in length of purer material from Swiss sources, were proposed. Even then the final outcome as to the polariscopic sensibility was much in doubt, while the importance of the extension of this test did not seem to me to warrant the great expense which the proposal contemplated. The use of quartz was finally abandoned for other available active materials. These I sought among the active oils. The success of the same plan, as proposed for quartz, seemed somewhat doubtful, since we should need two R- and L-substances which for suitable lengths—not necessarily equal—would give identical rotary dispersions. With the great rotations proposed, any slight relative irrationality would at once make itself evident by the corresponding increase of the residual light in the field of the half-shade, which would present the same order of difficulty as that from impure quartz. Such oils would also have to be very clear indeed to allow the passage of sufficient light through the much greater distances necessary to produce the same total rotation asin quartz. Several of the commercial oils fulfil these conditions to a greater or less extent. Two of these, caraway oil, «p= + 103°33', and eucalyptus oil, ap = —52’ 22”, as prepared by Schimmel & Co., Miltitz-Leipzic, are quite colourless and suited to the above arrangement. The expense of the latter (8 marks per pound) precluded its use, but the former (1 mark per pound) was entirely available, if the optical conditions referred to above could be met by a single substance. It did not at first occur to me that an arrange- ment for testing the “ drift”? was possible with a single sub- stance which would allow the use of white light, thus giving the normal polariscopic sensibility. Both of the previous experimenters had failed to make use of this idea. If the motion of the earth produces an effect on the rotation of the plane of polarization, we should of course expect this effect to be reversed on changing the direction of motion. Thus the plane of a ray propagated along the drift would show a Atther “Drift” and Rotary Polarizateon. 389 slight increment, say ; then, if it be reflected back, there would be a corresponding decrement over what would oecur if either there were no motion or the direction of propagation were across the drift. Thus in fig. 2, if AB is the initial direction of vibration, and if the active substance rotate it through a whole number of circumferences without motion, it would be Bie, 2. slightly increased, if propagated along the drift say, and the emergent vibration be in the direction of A' B’. If now this ray is reflected back by a single reflector against the drift, it would be rotated in the opposite direction (toa fixed observer) by the same number of circumferences less the angle between AB and A'B’, vibrating on emerging in the direction of A’ B”. Hence we should have a recomposition of all the colours to this extent. If now the optical system be turned 390 Prof. D. B. Brace on the about through 180°, the first passage would make the emergent vibration along A,’B,’, smce now the propagation is against the drift. On reflexion the final vibration would be along A,'’B,’’.. Thus, on reversing the optical system, we double the effect. Hence we are entitled to reflect the ray backward and forward, compensation being attained when the total distance in the liquid in one direction is equal to that in the other. Such an arrangement contains at once the possibilities of far greater sensibilities than any previous attempts. The same mounting for the optical system was used as in my former experiment ‘on the Double Refraction of Matter moving through the Aither”*. The optical system, however, was somewhat different. Instead of using plane-reflecting mirrors, as before, which allowed the beam of light to spread too much, with the con- siderable distances gone over, concave reflectors mounted with adjusting screws were used instead; their centres of curvature being approximately at the axis of rotation of the mount (fig. 3). The distance between the two sets of mirrors at the end of the trough was 410 cm., and it required some 60 to 70 pounds of the oil to fill the trough. This arrange- ment conserved the light without allowing it to spread out continuously, which would have required a much larger trough and consequent amount of liquid. This would have produced greater distortion in the ray by its passage through larger portions of the liquid. fo} ° ° ° [) 0) ° ° ° 120 I25 130 135 140 lae5) 150 155 160° TEMPERATURE —> X GUTHRIES RESULTS. © f-.7.L’s RESULTS. unreasonable when we read Guthrie’s statement that “the 62°35-per-cent. solution caused the surface of the glass (soft Solubilities of Diethylamine and Water. 398 German) to peal off in visible scales when heated to 150° 15052 An experiment with Miiller’s new “Resistance ” glass showed that even the slightly greater solubility of this giass as compared with Jena glass caused a lowering of the tem- perature of over 2°. It seems therefore probable that the present results are slightly vitiated by the solution of glass, but the extreme insolubility of Jena glass makes it likely that the inaccuracy due to its solution is but slight. It is interesting to note that the form of the curve is more » that of the curve for trimethylpyridine (Rothmund, Zeit. Phys. Chem. xxvi. p. 462, 1898) than of that for triethylamine (bid. p. 461). An attempt was made to determine the densities of saturated solutions of the amine and water at various temperatures by heating a solution containing 40°5 per cent. of amine in a graduated tube and observing the volumes of the layers at various temperatures; the weights of the layers being calculated from the percentage composition of the saturated solutions as read off from the solubility curve. The attempt proved abortive since the values obtained are so largely affected by small errors in the data used ; it was, however, obvious that there is (1) practically no sudden change in total volume on separation, and (2) very little difference in the densities of the two saturated solutions which are in equilibrium at temperatures between 14375 and 153°. EHaperimental Details. Suitable quantities of water and diethylamine were weighed out from “ weighing pipettes’ into a small stoppered bottle. The mixture so made was transferred as soon as possible to a tube sealed at one end and drawn toa capillary in the middle ; by changes of pressure the liquid was got into the lower part of the tube, which was then sealed off at the capillary. A tube so prepared was heated in a paraffin bath so arranged that the filament of an incandescent electric lamp could be viewed through the tube. The appearance of a fog was very easily seen in this way, and consequently the temperature at which the mixture under observation separated into two layers could be ascertained with a fair degree of accuracy. The tube was supported by a simple mechanical device whereby the contents could be remixed between observations without removing the tube from the bath. Oxford, May 1905. [ 400 ] XLVI. Notices respecting New Books. Lecons sur VElectricité. Par Eric Gurarp. Tome Second. Paris: Gauthier- Villars, 1905. Pp. viii+ 888. 4 ee publication of the second volume of the seventh edition of this work has not long been delayed after the appearance of the first volume, and the high terms in which we spoke of the latter must also be extended to the former. A perusal of the work cannot fail to produce the impression that it is a wonderfully com- plete and well-balanced account of the present state of electro- technology. There is hardly a single aspect of the subject left unnoticed by the author, and yet the book is extremely readable and not overloaded with detail. It is in every respect an ideal student’s book. | : The present volume deals with alternate-current transformers, their theory, construction, design and testing ; induction-coils and their applications ; systems of distribution, overhead lines, under- eround conductors, submarine cables, telegraphy, telephony, electric lighting and lamps, photometry, motors—continuous current, polyphase, single-phase, induction and synchronous—rotary con- verters, power transmission, electric traction, electro-metallurey, and electro-chemistry. The diagrams and illustrations are characterized by simplicity, but their reproduction is far from perfect, and leaves a good deal to be desired. This is about the only feature of the book which calls for adverse criticism, and to which the publishers would do well to give some attention. Mathematical and Physical Papers. Vol. V. By the late Sir GEORGE GABRIEL STOKES. Reprinted from .he Original Journals and Transactions, with brief Historical Notes and References. Cambridge: at the University Press. 1905. Pp. xxv + 370. Dr. Larmor’s task of editing those papers of the late Sir G. G. Stokes which had not been included in the first three volumes— the third being the last which their illustrious author was able personally to prepare for publication—has now been completed. The present volume contains various short papers and notes, very frequently having reference to the work of other investigators who asked for that advice and guidance which were always so generously and freely given. In order to render the volume self-contained, contributions by other authors are included where necessary to the complete understanding of Sir G. G. Stokes’s criticisms or suggestions. We notice a paper “On the Maximum Wave of Uniform Propagation,” which has never been published before. An appendix contains Mathematical Tripos and Smith’s Prize Examination papers set by Sir G. G. Stokes. The volume opens with the masterly Obituary Notice by Lord Rayleigh, reprinted from the Proceedings of the Royal Society, and it is adorned by an excellent portrait of Sir G. G. Stokes in his later years. INDEXE Sho gh 18, LONDON, EDINBURGH, AND DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. — (SIXTH SERIES.] OCTOBER 1905. XLVIIL. The Origin of the Prismatic Colours. By Lord Rayuricu, O.V., F.R.S* a. fact that by the aid of a spectroscope interferences may be observed with light originally white used to be regarded as a proof of the existence of periodicities in the original radiation; but it seems now to be generally agreed that these periodicities are due to the spectroscope. When a pulse strikes a grating, it is obvious that the periodicity and its variation in different directions are the work of the erating. The assertion that Newton’s experiments prove the colours to be already existent in white light, is usually made in too unqualified a form. When a prism, which has no periodicities of figure, is sub- stituted for a grating, the modus operandi is much less obvious. ‘This question has been especially considered by Schuster femh Mac xxxvit. pe 009) £894: vis pre; 1904), and quite recently Ames has given an “ Hlementary Discussion of the Action of a Prism upon White Light” (‘Astrophysical Journal, July 1905). The aim of the present note is merely to illustrate the matter further. I commence by remarking that, so far as I see, there is nothing faulty or specially obscure in the traditional treat- ment founded upon the consideration of simple, and accord- ingly infinite, trains of waves. By Fourier’s theorem any arbitrary disturbance may be thus compounded; and the method suffices to answer any question that may be raised, so long at least as we are content to take for granted the * Communicated by the Author. Pipi. Mages. 0.; Vol. 10; No. 58. Oct. 1905. 2K 402 Lord Rayleigh on the character of the dispersive medium—the relation of velocity to wave-leneth—without enquiring further as to its con- stitution. For example, we find the resolving-power of a prism to be given by ny d aap ae a Do in which A denotes the wave-length zn vacuo, T the “thickness”’ of the prism, w the refractive index, and dd the smallest differ- ence of wave-length that can be resolved. A comparison with the corresponding formule for a grating shows that (1) gives the number of waves (X) which travel in the prescribed direction as the result of the action of the prism upon an incident pulse. But, although reasoning on the above lines may be quite conclusive, a desire is naturally felt for a better understanding of the genesis of the sequence of waves, which seems often to be regarded as paradoxical. Probably I have been less sensible of this difficulty from my familiarity with the analogous phenomena described by Scott Russel and Kelvin, of which I have given a calculation*. ‘When a small obstacle, such as fishing-line, is moved forward slowly through still water, or (which, of course, comes to the same thing) is held stationary in moving water, the surface is covered with a beautiful wave-pattern, fixed relatively to the obstacle. On the up-stream side the wave-length is short, and, as Thomson has shown, the force governing the vibrations is principally cohesion. On the down-stream side the waves are longer and are governed principally by gravity. Both sets of waves move with the same velocity relatively to the water, namely, that required in order that they may maintain a fixed position relatively to the obstacle. The same condition governs the velocity, and therefore the wave-length, of those parts of the wave-pattern where the fronts are oblique to the direction of motion. If the angle between this direction and the normal to the wave-front be called @, the velocity of pro- pagation of the waves must be equal to vg cos@, where vw represents the velocity of the water relatively to the (fixed) obstacle.” In the laboratory the experiment may be made upon water contained in a large sponge-bath and mounted upon a revolving turn-table. The fishing-line is represented by the impact of a small jet of wind. In this phenomenon the action ofa prism is somewhat closely imitated. Not only are there sequences of waves, unrepr esented (as would appear) * “The Form of Standing Waves on the Surface of Running Water,” Proc, Lond. Math. Soc. xv. p. 69 (1883); Scientific Papers, 11. p. 258. Origin of the Prismatic Colours. 403 either in the structure of the medium or in the character of the force, but the wave-length and velocity are variable accor ding to the direction considered, For the purposes of Scott Russel’s phenomenon fli localized pressure is regarded as permanent ; but here it will be more instructive if we suppose it applied for a finite time only. Although the method is general, we may fix our ideas upon deep water, subject to gravity (cohesion neglected), upon which operates a pressure localized in a line and moving transversely with velocity V. In the general two-dimensional problem thus presented, the effect of the travelling pressure. is insignificant unless V is a possible wave-velocity; but where this condition is satisfied, a corresponding train of wavesis generated. In the case of deep water under gravity the condition is always satisfied, for the wave-velovities vary from zero to infinity. The limitation to a wave-train of velocity V is complete only when the time of application of the pressure is infinitely extended. Otherwise, besides the train of velocity V we have to deal with other trains, of velocities differing so little from V that during the time in question. they remain sensibly in step with the first. Asis known”, the behaviour of such aggregates is largely a matter of the group-velocity U, whose value 1s given by (6 2 AD Oa k being proportional to the reciprocal of the wave- tenets in the medium. In the particular case of deep-water waves O=sV. From this point of view it is easy to recognize that the total length of the train of waves generated in time ¢’ is +(V—U)#. Ifr be the periodic time of these waves, the wave-length in the medium is Vt, and the number of waves is therefore V-U?' eyes ar eae | ee T But for our present purpose of establishing an analogy with prisms and their resolying-power, what we are concerned with is not the number of waves at any time in the dispersive medium itself, but rather the number after emer gence of the train into a median which is non-dispersive; and here a curious modification ensues. During the emergence the * See, for example, ‘Nature,’ xxv. p. 51 (1881); ‘Scientific Papers,’ i. p. 540. 22 404 Lord Rayleigh on the relative motion of the waves and of the group still continues, and thus we have to introduce the factor V/U, obtaining for the number N of waves outside V—U?’ ‘ If X be the distance through which the pressure travels, X= Vit'; andif V, be the (constant) velocity outside and X the wave-length outside, X=V,7. Thus VV ae N=(7ogis - - - ae =(q V aN, 9) To introduce optical notation, let w= V,/V, so that pu is the refractive index. In terms of yu N= i so that finally N= — AS e ° e ° . e ° (Wa), in close correspondence with (1). A very simple formula thus expresses the number of waves (after emergence) gene- rated by the travel of the pressure over a distance X of a dispersive medium. The above calculation has the advantage of being clear of the complication due to obliquity; but a very little modifi- cation will adapt it to the case of a prism, especially if we suppose that the waves considered are emergent at the second face of the prism without refraction. In the figure, AC repre- sents an incident plane pulse whose trace runs along the first face of the prism from A to B. AF’, BE is the direction of pro- pagation of the refracted waves under consideration, to which the second face of the prism is per- pendicular. As before, if 7 be the period, V the wave-velocity of the waves propagated in di- rection BE, U the corresponding group-velocity, ¢’ the time of travel of the pulse from A to B, the number of waves within the medium 1s We NU a: Origin of the Prismatic Colours. 405 giving on emergence the number of waves expressed in (4). If V, be the velocity in vacuum, T=2/Vo, and t'= BC = AD, VY vis ae so that | AD, T MN Thus, as in (5), (6), (7), Vea WV AD d N=(7-¥y oe Ven SN. in agreement with (1). : Although the process is less easy to follow, the construction of a train of waves from an incident pulse is as definite in the case of a prism as is that of a grating ; and its essential features are presented to the eye in Scott Russel’s phenomenon. The above treatment suffices for a general view, but it may be instructive to give an analytical statement; and this [ am the more inclined to do as affording an opportunity of calling attention to a rather neglected paper by Lord Kelvin entitled “Qn the Waves produced by a Single Impulse in Water of any Depth, or in a Dispersive Medium” *. When we know the effect of an impulse, that of a uniform force applied for a finite time can be deduced by integration. It may be con- venient to recite the leading steps of Kelvin’s investigation. Let /(£) denote the velocity of propagation corresponding to wave-length (in the medium) 27/k. The Fourier-Cauchy- Poisson synthesis gives u=| dkeosklu—t f(k\| . - ae (9) 0 for the effect at place and time (a, t) of an infinitely intense disturbance at place and time (0, 0). When w#—t/(A) is very large, the parts of the integral (9) which lie on the two sides of a small range, «<—« to «+a, vanish by annulling interference ; « being a value, or the value, of £, which makes | {kat (B)]}=0 AAS (10) or Peery (eve e.) te CLG), * Proc. Roy. Soc. vol. xlii. p. 80 (1887). 406 Lord Rayleigh on the U being the group-velocity. By Taylor’s theorem when k—k is very small, Bet $(R) | f(K) eee) — fc) — 2a Using this in (9) and integrating with the aid of + co « +00 dco cos =| do sin o? = Vv (4m), —0o Hae we find as an approximate value woe (27) .cos {tx?/'(K) + 1a} Vt. {—K FM) — 27" ()} As a particular case, for deep-water gravity waves IM=V(9/k), f' (Ha=—3gtk-?, —kf"(B) ~2f' (= 3g h-§ and finally with use of (11) | i Paley ie T - uamigttateos( —T) . . . (13) This gives the effect of the impulse at (0, 0). If the impulse be at 2’, i’, we are to write w—a’ tor « and t—@t' for ¢. For our purpose of finding the effect of a travelling force, we are to make 2’ =Vt' and integrate with respect to t' from 0 to ¢’, ¢' being the duration of the force. The integral will depend mainly upon the part where (¢—t')? o— Vt’ under the cosine, is stationary. This occurs when 2e=V E-+t) oi. g(t—t')? LgINGS2) i(a—Ve) mas ee (15). Omitting the variation of the other factors as less important, we see that, when sensible, the effect is proportional to cos {A Fh 0 a) Ii representing simple waves of velocity V. But this is limited to such values of w and ¢ as make ¢’ in (14) he between 0 and t’. Thus if ¢ be given, the range of 2 is from $Vé¢ to 4Vi+iV?’; so that the train of waves covers a length 4V¢, * An almost equally simple formula applies when more generally S (k) x kn. Th (12). and then Origin of the Prismatic Colours. 407 agreeing with the general value given before, since here U=4V._ If, as would be more convenient in order to find the length of the train after emergence into a non-dispersive medium, we regard x as given, we find that ¢ ranges from 2x/V to 2x/V +t’. I have taken the particular case first, as the reasoning is rather simpler when we have, as in (15), an explicit expression in terms of z and ¢*. In general « cannot be eliminated between (11) and (12), and we must proceed rather differently. The question is when will Pe TAMU cig Waehoms n eeD) Pease dt ye a1) enemas CE), be stationary with respect to ¢', e—V¢’ being substituted for « and t—¢' for fin (17), (18)? Now with dead is dic, di\f . dt kf (ky } of which the second term on the right vanishes by (18). The variation of (17) vanishes when V=/(k). Accordingly kLa—Vi' —(t¢—t') f (£)] e—Vi'=(t-t){ (+k f'(W} is stationary with respect to t’/, if V=/(4), and then assumes the form with kl a—Vet]. Here ¢’ must lie between 0 and ¢’. Thus if ¢ be constant, x has a range Vt —U{ f(A/\)+ES (Ef =(V—U)U. And if x be given, ¢ has a range M7 Ae _vU(U—V) FHF) U These are the limits over which the waves of velocity V extend. And (19) shows that the number of waves which pass a fixed point, either within the dispersive medium or on emergence from it, has the expression t’ U—V mus? where 7 is the periodic time, in agreement with (4). f! (19). * For an admirable discussion of the general problem of deep-water waves arising from a localized disturbance, see Lamb, Proc. Lond. Math. Soe. vol. ii. p. 371 (1904). P aOB | XLIX. The Maygneto-Optics of Sodium Vapour and_ the Rotatory Dispersion Formula. By R. W. Woop, Pro- fessor of Experimental Physics, Johns Hopkins University *. [Plate V.] T has been shown in a previous paper} that the vapour of metallic sodium is an ideal substance for investigating the effect of a strong absorption-band on the magnetic rotation of the plane of polarization. The preliminary work was not very satisfactory, however, as the method employed did not admit of very accurate determinations of the wave- lengths, and the verification of the rotatory dispersion formula could only be considered as approximate. Improve- ments in the methods of observation and design of the apparatus have been accompanied by an increase in accuracy, which could scarcely have been hoped for, as will be seen by the following comparisons. In the preliminary work no readings of the rotation for wave-lengths between the sodium lines could be obtained, while in the present case accurate readings have been made for as many as nine different values of X between D, and Dp. Rotations as great as 1440° (four complete revolutions) have actually been observed, and this with a 10 em. column of not very dense vapour, in a field of only 2000 C.G.S. units. This was for a wave-length midway between D, and D,. In the earlier work it was only with the greatest difficulty that the bright lines which appeared in the region of the red and green channeled absorption spectrum could be seen. The have now been photographed to the number of about 160 with the 14-foot concave grating. Comparatively few of the absorption-lines show any trace of magnetic rotation, scarcely one per cent.; and the fact seems to have been established that these lines coincide with the bright lines of the fiuores- cent spectrum of the vapour, which has been found to be by no means the exact complement of the absorption spectrum as was at first supposed. In the present paper the magneto-optics of the vapour for light travelling along the lines of force will be discussed. The double-retraction of the vapour, which occurs when the rays are perpendicular to the field, has also been studied, and will be reported in a subsequent paper. An exhaustive study of the fluorescence of the vapour has been made, and the lines of the spectrum to the number of several hundred * Communicated by the Physical Society: read June 30, 1905. + Wood and Springsteen, “The Magnetic Rotation of Sodium Vapour,” Phys. Review, July 1905. | The Magneto-Optics of Sodium Vapour. 409 accurately measured. Very remarkable effects have been observed when the vapour is illuminated with a very narrow band of approximately homogeneous light, the lines in the fluorescent spectrum changing their position and appearing to dance about in the liveliest manner with the slightest change in the wave-length of the exciting light. The motion is of course only an illusion, lines disappearing and others reappearing, like the sparks of a spinthariscope. Stokes’s law is violated ina most flagrant manner, bright lines coming out on both sides of the excited region. The behaviour of the spectrum indicates that we are dealing with a number of groups of electrons, each group containing a large number — of vibrators. The excitation of one of the vibrators sets the whole group agoing, but does not start disturbances in the other groups. These and other remarkable phenomena will be fully discussed in the following Number of this Journal; they are mentioned here only on account of the appar ent relation between magnetic rotation and the fluorescence. In the earlier experiments referred to above, the sodium was heated in a tube of hard glass, the ends of which were closed with thin plate glass. The tubes lasted but a short time, owing to the chemical action of the metal, and in fact usually cracked on a second heating. In the present work a tube of thin steel has been used, the ends of which projected from the helices of the magnet. It was found that the field- strength within the steel tube did not differ greatly from that obtained when glass tubes were used. The arrangement “of the apparatus is shown in fig. 1. A o piece of thin seamless steel tubing of such a diameter as to iach: slip easily through the hollow cores of the electromagnet, from which the conical pole-pieces have been removed, is procured. A short piece of small brass tubing is brazed into one end, through which the tube is exhausted. It has been found that a good vacuum is essential, all-trace of the rotation disappearing in hydrogen or nitrogen at atmospheric pressure. In the earlier work this fact was not known, and the tubes 410 Prof. Wood on the Mayneto-Optics of Sodium Vapour were exhausted and then sealed off from the pump. The hydrogen liberated from the sodium must have raised the pressure to at least 15 cms. in all of these experiments. In the light of what is now known, it is surprising that any results at all were obtained under these conditions. A lump of sodium the size ofa walnut is melted in an iron erucible, and poured out into a V-shaped trough made of thin sheet iron. As soon as the bar is solid it is placed in the iron tube, one end of which has been previously closed with a small piece of plate-glass cemented on with sealing-wax. The tube is introduced into the magnet, the sodium bar pushed to a position midway between the helices, and the other end closed with a piece of glass in a similar manner. The ends of the tube should be coated while hot with sealing- wax before the introduction of the sodium. One has then only to wave a Bunsen flame over them and press on the piece of glass, previously heated; the sealing-wax should come into optical contact with the glass to insure an air-tight joint. The tube is now connected with an air-pump which will produce a vacuum of a millimetre or two. If the air- pump leaks, it is a good plan to place a glass stopcock between the pump and tube to prevent the entrance of traces of air after exhaustion. For purposes of demonstration it is sufficient to heat the tube gradually with a Bunsen burner turned down low. In the present work, however, where constancy of temperature was essential, electrical heating was invariably used ; the tube was wrapped with a thin sheet of asbestos board, around which was wound a spiral of iron wire, and the whole subsequently covered with an asbestos jacket. The light from an arc-lamp, made parallel by a lens, is passed through a Nicol prism, the steel tube, and a second nicol, after which it is brought to a focus by means of a second lens upon the slit of a spectroscope. In the present case, the instrument in question was a concave grating of i4-foot radius, the observations being made both visually and by means of photography. We will now consider briefly the phenomena which are presented when the sodium vapour is formed in the magnetic field. The nicols are crossed and the spectrum vanishes completely. The magnet is now excited and the Bunsen burner placed under the tube, the tip of the flame barely touching it. In a few minutes we see two bright yellow lines exactly in the position of the D lines. The light constituting these lines comes, however, from the crater of the are, as we can easily see by intercepting the beam. The lines are in reality double, though they appear single with low resolving powers, while even with the 14-foot grating their duplicity and the Rotatory Dispersion Formula. All cannot be made out when they first appear. As the density of the vapour increases, the components separate, four lines being distinctly visible. This condition is shown in Plate V. fic. la. The lines are formed by the constituents of the white light bordering the two absorption-lines, which having suffered a rotation of 90° in the magnetic field, is enabled to pass the second nicol. The lines continue to separate, becoming broader, and presently we see between them a second pair of lines, for which the rotation is 270, the two dark regions between representing rotations of 180. This stage is shown in fig. 16 and c, Plate V. In fig. 1b, the two inner 90° lines are beginning to fuse together, the centre being partially dark however. Jn fig. 1c, the fusion is com- plete and the centre of the system of lines is bright. With a further increase in the vapour-density, the outer lines (90°) separate still further, and widen out into broad flares of light, and cther lines appear between them, corresponding to larger rotations, the system resembling a set of diffraction fringes, as shown in fig. 2. The centre of the system, as I il shall designate a point midway between D, and D,, becomes bright and dark in succession, as is shown in the succeeding figures of Plate V. fig. 1. Only a few of the inner lines show in the photographs, as they are very close together, and the vibration of the building prevented their resolution in the photograph. They could be distinctly seen with the eye- piece, and accurate settings of the cross-hair could be made. Their position with respect to the D lines was very accurately determined by means of a filar micrometer, settings being 412 ‘Prof. Wood on the Mayneto- Optics of Sodium Vapour made on the dark lines between as well. A little practice was necessary before a complete series of readings could be taken without error, but consistent results were finally obtained. The method adopted was as follows. A current of given strength was turned into the iron spiral, and as the vapour-density increased the alternations of brightness and darkness at the centre were counted. No measur eee were commenced until a steady state was reached, which was indicated by a fixed condition at the centre. The positions of the bright lines and dark spaces were then measured, the readings being taken down by an assistant. If at the end of the series any change was tound to have occurred at the centre, it was rejected. As soon as the series was completed, the heating current was shut off, and the tube aliowed to cool. During this process the alternations of re at the centre were counted, and if the number of changes differed from that originally recorded the series was thrown out. The rapid changes which occur as the tube cools, especially an unjacketed tube, are most interesting ; the centre of the system changes from bright to dark with great rapidity. The largest number of complete alternations ob- served was eight, corresponding to a rotation of 1440 degrees, one alternation (7. e. from bright to bright) cerresponding to 180. The whole thing lasts but a few seconds, the bright band “ winking ” almost as fast as one can count. We can, as it were, see the plane of polarization actually turning around and around, for four complete revolutions. Beyond this point the absorption becomes too strong to admit of further observations between the D lines, but readings may be taken above and below them in the spectr um, with vapours of very great density. When the vapour peta a considerable density, a most magnificent bright-line spectrum appears in the red and green- blue region. Each bright line corresponds to a dark line in the absorption spectrum, but only a small percentage of the dark lines appear to exercise a rotatory power. Some of the strongest absorption-lines are absoluiely unrepresented in the magnetic rotation spectrum, which indicates that there is some radical ditference in the absorbing mechanism. Much time has been spent in a further photographic study of the channeled absorption spectrum,:a piece of work which was commenced three years ago by the writer in collaboration with Mr. J. H. Moore. It has since been found that the presence of hydrogen, nitrogen, or carbonic acid modifies the appearance ot the absorption spectrum. The photographs previously obtained were made by passing the light through and the Rotatory Dispersion Formula. 413 a steel tube containing sodium vapour in an atmosphere of hydrogen, under which condition the absorption spectrum has a most beautiful shaded appearance, being made up of fluted bands, each band containing a very large number of fine lines. If the hydrogen is removed, and the sodium vapour formed in vacuo, the fluted appearance disappears almost entirely, although the individual lines remain. Many new lines appear, however, which are broader and more distinct than the others, and these lines appear to coincide with the bright lines in the rotation spectrum. This point will be more fully investigated in the future, the work on the absorp- tion spectrum not having been completed at the present time. | Returning now to the measurements obtained in the vicinity of the D lines, we will discuss them in their bearing on the theory of magnetic rotation. The rotation has been measured over a considerable range ot wave-lengths in the case of very dense vapours, by the method described in the previous paper. In brief this method consisted in rotating one of the nicols through various angles and measuring the position of the two dark bands which move, the one up, the other down the spectrum. ‘The dispersion of the 14-foot grating was too great for this part of the work, and a large plane grating was accordingly combined with a pair of telescope objectives of six-foot focal length. A very brilliant spectrum was obtained in this way, and the dark bands were not so broad but that the cross hairs of the micrometer could be set on the centre of the band with a fair degree of accuracy. Readings of the rotation were obtained throughout the region comprised between A= 5840, and 7~=5932. The dark bands cannot be pursued with accuracy to greater distances from the D lines, on account of their increased breadth. It will be understood from what has been said in the previous paper, that these dark bands retreat from the D lines when one of the nicols (originally parallel) is rotated towards the position of extinction. The bands enter the red and green regions when the nicols are very near the crossed position, under which circumstances the bright lines appear, and completely obliterate all trace of the dark bands, which by this time have become very broad. The rotation for the wave-lengths corresponding to the dark bands, is the angle through which oue of the nicols has been rotated, measured from the crossed position. The values found with vapours of various density are recorded in the following table. The tables are designated by the magnitude of the rotation midway between the D lines. 414 Prof. Wood on the Magneto-Opties of Sodium Vapour CENTRE 30°. | Centre 90° con. | Crntre 450°. CENTRE 540° con. 58971 90 | 58945 270 59021". 30 58880 630 58968 180 | 58044 180 59022 40 5887°8 540 5896-5 270 589334 90 5900°3 60 5887-4 450 58054 270 | 5891-9 180 5899-4 90 58871 360 58953 180 |. 5891-5 270 5898-7 180 5886-7 270 5894-9 90 5891°3 360 58980 270 | 58861 180 98932 9/30) | oSot ra 5897-°7 360 58846 90 5891-4 90 5890°86 640 5897°5 450 | 58832 60 58909 180 , 58890 450 5897-3540 5881-5 40 58893 270 | 58885 270 | 58947 810 5889-0 180 | 58882 180 58945 720 Centre 720°. 58887 90 | 58875 90 58942 630 Kone 58°66 60 58940 _ 540 oor ee Spon | oesOOn eaUet 98082. 0 450 58763 25 Centre 50°, | 58960 30 58923 5A) 5880°5 50 5897°3 4d : ae oe 58832 95 kK -. 0 d e ; | al = ee a Crencre 180°. 58883. 720) Bee bn 5e0y © ate) ya eoools) | 20 5885'l 630 = 58967 270 | 59003 30 pea ‘9 2% 58935 720 52949 180 | 58990 60 | 58874 360 BS ae 58046 90 | 58982 90 | 58669 270 59018 80 Seo OA ROO 9 8978 20a) Pees ee) 59036 «BO beol4t 2180 | 58971 Bed )| 28832 60 5908-0 295 Boot 270 | O806- 9) 50 ees ay 59097 20 58891 270 | 58949 540 | 58803 30 5888-7 180 , 59947 450 58883. 90 | 58945 360 Curren Sue Bas78 «GO| «801 ~~ 270 || “Gay nen 540° 58876 45 | 58932 180 5903-9 60 5886-9 30 | 5891-9 270 59028 40 59020 90 5891-6 360 | 5901-5 60 5900-2 180 L Peet aae til (Sola MaG0 5900-1 90 5899-6 270 Contre 90°. | e912 540 5898:8 180 58992 360 5899-7 20 | 58886 540 58983 270 58988 450 58993 30 | 58884 450 5898-0 360 cog me 58988 40 | 58882 360 5897°7 450 58983. 60 | 5887-9 270 5894-4 720 5886-6 540. 5897-8 90 | 58875 186 58937 630 5886-3 450 5897-45 180 | 58868 90 58935 540 5885-9 360 5897-1 270 | 58862 ° 60 5892-4 630 58851 270 53968 360 | 5885-4 40 5892-1 720 58845 180 58053 451 | 58846 30 5891:8 810 58813 90 5895-0 360 | 58832 20 5891-7 900 5880-0 60 A number of photographs of the spectrum with the dark bands in different positions were made with a large three- prism spectrograph, recently constructed for the study of the fluorescence spectrum (Pl. V. fig. 2). It was at first thought that by measuring the positions of the bands on the negatives, more accurate results could be obtained than by visual observations ; but the reverse proved to be true, though fairly good curves were obtained. The density of the vapour was and the Rotatory Dispersion Formula. Ald much greater than that employed for the visual observations, and the dark bands were found to be symmetrical with respect to the D lines, that is the rotation was the same at points in the spectrum at equal distances (measured in wave-lengths ) to the right and left of the D lines. This was not the case with less dense vapours, the rotation being greater in the vicinity of D, than in the vicinity of D,. The rotation con- stant of D. was found to be about double that of D, ; but. since the direction of rotation is the same on opposite sides of the absorption-bands, the effects of the two bands are addi- tive, and lack of symmetry will be less noticeable with very dense vapours, where the measurements are made in a region not very close to the lines. Verification of the Rotatory Dispersion Formula. Drude, in his Lehrbuch der Optik, has given two formule for the magnetic rotatory dispersion, the first of which, developed from the hypothesis of molecular curreats, calls for an anomalous effect on crossing the band, and obviously does not apply to sodium vapour. The second, developed from the Hall-Effect Hypothesis, predicts rotations of similar sign and equal magnitude for wave-lengths symmetrically situated in the spectrum, with respect to the centre of the absorption- band. The formula deduced for the rotation is ae bd? O= n (5 ai Ce =k m , In the case of sodium vapour n differs so little from unity that it can be left out of account. Investigations of the refractivity of the vapour by the writer, have shown that with very dense vapour (comparatively speaking) the value of n may be as great as 1°3 in the immediate vicinity of D,, hut calculations showed that in all of the cases dealt with in the study of the magnetic rotation, n was practically equal to unity. When working very near the D lines the vapour was extremely rare, while observations made with denser vapours covered regions not very near the absorption-lines. Since, moreover, the rotation is zero for very short waves, the first term in the formula drops out, i.e.,a=0. Precisely the same thing was done in the case of the ordinary dispersion formula, since the refractive index was found to be unity for very short waves*. The similarity in the sign of the rotation on opposite sides of the bands results from the fact that the * See previous paper on the “ Dispersion of Sodium Vapour,” this Journal, vol. viii. p. 293 (1904). 416 Prof. Wood on the Magneto- Optics of Sodium Vapour quantity (A7—A2) (which changes sign on crossing the absorption-band) is squared. An attempt was first made to verify the simplified formula by writing X,,=5893, 2. e., assuming the D lines to be a single absorption-band. The value of the constant could then be determined from a single observation, and the rotations for different values of 2 cal- culated. The calculated values agreed very closely with the observed on one side of the double absorption-band, but the agreement on the other side was very poor. This was at once seen to be due to the fact that the rotatory power of the two lines was very different, and the following formula was con- sequently adopted :— __ au an? i bn? Woy * Wa? The constants a and 6 were calculated from two observations of X, one greater than D,, the other less than D.. In almost. every case the ratio was found to lie between the limits 1°8 and 2°03. Writing D,=5896 and D,=5890, the values of the constants a and ) for vapours of different densities are recorded in the following tahle. The densities are defined by the magnitude of the rotation for a wave-length midway between D, and D.. : Centre AD OMSTEY. | a. eset er a. b. a/b. Rotationeate Cemene ¢ — O05 e esce 1123 587 19 ‘ls GS) ah tne Ocoee 2217 1350 165 Sisie Bee LCOS 4309 1&60 2°3 1GES pees OO pe ade d11l 2571 1:98 Za ie ee Ores cee 9279 4545 2°03 369° Fa OaOe ooneeee 10326 4607 2°24 392° elas RULOS Ri a itee 12750 7100 1°8 538° Boe) OO naan 23873 | 10333 26 893° | The ‘‘ centre’ as defined above does not in fact fall at A=59893, but at 5893°5, 7.¢., when the bright bands unite, the point of unison lies nearer D, than Dy. Thies is owing to the tact that the expansion of the ‘bane from D, is more rapid than from D,. It was found that if the constants a and } were calculated from different pairs of readings, there was considerable difference between the values, a circumstance which indicates either that the formula is at fault, or that the observations were not sufficiently accurate. We are dealing with very steep curves, as will be seen by reference to fis. o, ale and the Rotutory Dispersion Formula. AIT Fig 3. me | | Wee ry fl [| PL a 02 0] 590099 98 97 96 95 94 93 92 Si 90 89 88 87 86 8&5 8 5883 TM Phil. Mag. 8. 6. Vol. 10. No. 58. Oct. 1905. 2G 418 Prof. Wood on the Magneto-Optics of Sodium Vapour small errors in wave-length readings will make large errors in values deduced from them. The severest test of all is to calculate the rotation at the centre from values of the constants determined from two medium values of 6 (say 90 or 180). outside of the D lines. This has been done in each ease, and in almost every case the calculated value has turned out too small. Ihave given all of the tables of data thus far ob- tained, and some of them are doubtless less accurate than others. By means of an improved heating coil (which is in process of construction), of porcelain and strip platinum, I hope to be able to hold the conditions more nearly steady and obtain still more accurate results. It will also be necessary to secure greater rigidity of the grating. Yor large rotations at the centre, say above 180, we cannot be quite sure of the exact value, as the best thers can be done is to regulate the heat so that the condition at the centre is either of maximum brightness or darkness. Errors ot say 15 or 20 degrees can be made easily. It is quite possible too that the formula is incomplete. It seems more than likely that the molecular currents play some part, and that the formula built up on the hypothesis of the Hall effect is incomplete. As we shall see presently, however, it represents the rotation outside of the D lines with a surprising degree of accuracy, while between the lines it gives in most cases a curve which is elevated somewhat above the experimental curve. It is possible that the refractive index plays some part, though I regard this as very doubtful. Midway between the D lines the refractivity is equal to unity, rising and sinking rapidly to the right and left of this point. It is not worth while to experiment further with the formula until still more accurate data are at hand, which I am confident of obtaining in the autumn. oO Another matter still to be determined is whether the variation of the ratio ; results from errors, or whether it increases with the density of the vapour, as appears to be the case. These points will be taken up again in the second paper. For densities giving rotations of 50°, 90°, and 180°, at the centre, the calculated value agrees with the observed to “ovine the probable experimental error, for, as I have said, it is impossible to fix the rotation at the central band to within say 15. In the case of denser vapours the discrepancies are much too large to be attributed to errors of this sort. Outside ot the D lines the calculated values agree re- markably well with the observed, even in the case of the densest vapour used, as will be seen by referring to the and the Rotatory Dispersion Formula. 419 curves shown in figs. 3 & 4. The observed values are re- presented by circles, the computed by crosses. The observed values are, of course, for values of 6 which are multiples of 90. In the computations, values of X were selected, which Fig, 4. ig ae aT BE a a a 0 ee IGa | i fe a HSER REeewes Ce a a i a a SEBSREL Ee Eee sae RASS MPs aia Sessasaae a | | a a Lee (RSW e ae Sees (oreo Bee Gt al wel ee | 04-0302 5900 9998 97 96 95 94.93 92 91 90.89 88 8786 85 B+. 8382 Bl 80 D, Dp could be accurately represented by five figures, consequently we judge of the accuracy with which the formula represents the dispersion by seeing whether the calculated values fall on the curve determined by experiment. The computations are easily made. One has but to determine the value of r? d rn CEE ah oe. een? for wave-lengths in the region under investigation. These terms being independent of the vapour-density, can be used 2G 2 420 Prof. Wood un the Magneto- Optics of Sodium Vapour in all cases, the rotations being found by multiplying them by the constants a and 6 as determined for a particular density, and adding the two products. On fig. 3 will be found two curves, A and B, for centre rotations of 50° and 360°. The values of 6 calculated for the curve A, will be seen to fall in most cases exactly upon the curve of observed values. Fig. 4 shows that the agreement is also good for a density giving a rotation of 450° at the centre. Fig. 5 represents the rotatory dispersion of the densest vapour investigated by visual methods. The bright band Fig. 5. rs, 5850 5860 5870 5880 5890 530) 5910 5$20 between the D lines had disappeared completely owing to absorption. This corresponds to a rotation at the centre of about 1500, since 1440 is the largest rotation actually observed. ‘I'he observed values in this case were obtained with the plane grating and long focus telescope-lenses of five inches aperture. The positions of the broad, dark bands were measured with a micrometer eyepiece for different settings of the nicol, and readings were also taken on the arrow bright and dark bands lying between the broad ones and the D lines, whenever they were distinct enough. In this case, the calculated values lie on a curve slightly lower than the observed curve. This may be due to the fact that the value of X for which the rotation is equal to that of the nicol may not lie exactly at the centre of the band. On the whole, the e formula may be said to represent the rotatory dispersion, and the Rotatory Dispersion Formula. 421 exclusive of the region between the D lines, with a fair degree of accuracy. If, how ever, the constants a and b are calculated from different pairs of readings on the same curve, different values are found. On this account, it seems desirable to redetermine the curves with still greater precision, which will be done in the autumn. Vapour of a still greater density was investigated by a photographic method. The spectrum of the light transmitted through the two nicols and the sodium tube was photog raphed with the three-prism spectrograph. Seven exposures were made on a trichromatic plate, with the second nicol in seven different positions. A sodium flame, burning continuously in front of the slit of the spectrograph, recor ded the D lines on the plate. The tube was heated electrically, and the density of the vapour remained constant throughout the total time of exposure. Hach exposure amounted to less than half a minute. One of these multiple photographs is reproduced on Plate V. fig. 2. The picture may be said to show the dispersion curve. “The positions of the dark bands, which appear on each side of the D lines, were measured on the dividing engine, and the wave- lengths determined from the calibration curve of the spectro- graph. For these dense vapours it was found that the rotatory dispersion curves Were symmetrical with respect to a point midway between D, and D,. The a should therefore be well represented by a single-term formula an? o= 722 2? (Vi —A5) in which A»=5893. This was found to be the case, as the following table shows. Value of constant a= 135600. | ny ieat@aseere § Caleulated. | A 5980 | 5 447 5950 | 10 10-4 5933 Nibeiane ea) 20-2 5923 | 40 38-0 5917 | G0 589 5912-5 | 90 89-2 5874 | 90 93-1 5859 43 13-0 5864 40 40-6 58A2 20 20-2 5833 | 10 9-2 5814 5 52 The value of the constant was determined from the value of 6 at wave-length 5869, as given by the curve. 422 Prof. Wood on the Magneto-Optics of Sodium Vapour Lhe Bright Line-Spectrum produced by Magnetic Rotation. Attention has already been drawn to the remarkable bright line-spectrum which presents itself when the nicol prisms are crossed. ‘This spectrum, which at first could only be seen with the greatest difficulty, was finally obtained of such briliancy that it could be photographed with the 14-foot concave grating. A good vacuum was found to be the most essential condition. In the earlier work with tubes sealed off from the pump, the pressure due to the liberated hydrogen was probably responsible tor the faintness of the lines. The density of the sodium vapour must be just right. If it is too rare, the rotation is insufficient to bring out the lines, if too great the absorption weakens the spectrum. When the conditions are exactly right, the lines are almost as bright and numerous as the metallic lines in the are. Photographs of the complete spectrum were made on trichromatic plates, made by the Cramer Dry Plate Co. of St. Louis. These plates were found to be sensitive up to the red lithium line (~=6705). An exposure of fifteen minutes was sufficient with a small concave grating of abouta metre radius. Two of these photographs are reproduced natural size on Plate V. fig. 4. I have never observed a doubling of any of these lines such as occurs in the case of D, and Dz. So great is the quantity of the light transmitted by the second nicol, that a brilliant orange-coloured image of the crater of the are appears on the slit of the spectroscope the moment the current is turned into the magnet, notwithstanding the fact that the nicols are crossed. Inasmuch as it seemed desirable to investigate these lines under higher dispersion and determine their wave-lengths as accurately as possible, the apparatus was transferred to the concave-grating room. The Ruhmkorff magnet was abandoned at this point, as it was found that an exposure of four or five hours would be necessary, and the magnet became dangerously hot in half an hour, when fed with the necessary current. In its place a very large magnet, built by Professor Rowland for the study of the Zeeman effect, was used. This magnet could be fed with a 110-volt current without resistance, and operated continuously for any necessary length of time. A steel tube nearly 3 cms. in diameter could be used with this magnet, which increased in no small degree the amount of light available. After a number of failures, a very satis- factory negative was secured with the 14-foot grating show- ing the rotation spectrum and the absorption spectrum side and the Rotatory Dispersion Formula. 423 by side on the same plate. The plate showed over 60 lines in the blue-green region, some of them so faint that they could scarcely be seen under the microscope of the dividing engine, while others were strong enough to yield prints capable of reproduction. Another plate was exposed and a comparison iron spectrum recorded by the side of the rotation spectrum. The wave- lengths of the rotatory lines were measured on both plates, using the iron lines and the sodium absorption lines as standards. Some of the latter were redetermined, as it was found that they were much sharper when the sodium was heated in a high vacuum, than when heated in hydrogen, as in the previous work by Dr. Moore and the writer. A print obtained from the plate on which the rotatory spectrum and absorption spectrum were recorded, is shown on Plate V. fig. 5. The absorption spectrum is above. Many lines are, of course, visible on the negative which do not show on the print. The rotatory lines in many cases coincide with the heads of the groups of absorption-lines, though the centre of the line appears to be slightly displaced beyona the head of the group of absorption-lines. The displacement is, however, very slight, not more than half the width of the line. A list of the wave-lengths of all the lines visible on the negative follows. The approximate intensities are repre- sented by numerals, 10 indicating the maximum intensity and 1 the minimum. Lines marked with an interrogation point were so faint as to be doubtful. Green Rotation Spectrum. Le ro225°34 1 9053°54 2 4839-56 1 5218-49 19%'5025;66 9 4837°49 Lt 5212702 1 5003712 broad 2 4819-43 i olsor7 0 10 500157 1 4814-60 Inolioral Dd 4979°34 L 4812-68 1 5172-98 1 4970°85 3 4810-16 OL71'93 1 4967-10 3 4802-62 1 5169-04 1 496439 » 4792°67 5165°85 9 A962°85 3d 4782739 1 514071 1 4958-62 eee 00) 2 5133°73 1 4933°93 1 4766-94 2 5126°54 3 493264 6 4756°69 1 5119-54 2 4924-32" 1 4752-04 2 5094-78 4A A9I210 2 4738-51 7 5087-31 1 4904-67 | 4 4727°52 8 5079-78 1 4903°38 | 1 4716-90 1 507158 1 4896-65 1 4715°63 1 5052°83 1 4894-58 1 4703°78 1 5049-56 WAST 2 4692-54 3 504849 2 4883°81 2 4670-30 7 5040°65 2 4865°59 ~ 424 Prof. Wood on the Magneto- Optics of Sodium Vapour It is especially noteworthy that many, in fact most, of the strongest absorption-lines are not represented at all in the rotation spectrum. This fact is of fundamental importance, for it indicates that the absorbing mechanism is different in © the two cases. Just wherein the difference lies cannot as yet be definitely stated. On either hypothesis as to the cause of the magnetic rotation, the effect will diminish as the mass of the electron increases. ‘The lines of the rotatory spectrum may correspond to the negative electrons of small mass ; the other lines in the absorption spectrum which show no rotatory power may be due to positive electrons, or at all events to some form of vibrator having a much larger mass than the negative electrons. The fact that the bright lines in the fluorescence spectrum coincide with the lines of the rotatory spectrum appears in accord with this assumption ; for the agitation of the electrons by the light vibra~ tions will be greatest for those having the smallest mass. Tt will doubtless be possible to speak more definitely in regard to this point, after the fluorescence spectrum has been more carefully studied. The matter will be discussed further in the paper on the fluorescence of the vapour. The rotation spectrum in the red and orange region is more brilliant than the green-blue one, but it was found impracticable to photograph it with the 14-foot concave erating. Excellent photographs of it were secured with a small concave erating of about a metre radius. One of these, together with the absorption spectrum, is reproduced in fig. 3, Plate V. As the red lines could be seen without difficulty with the 14-foot grating, a method was devised for mapping them which may prove useful in other Jines of work. A brass rod, on which a short brass tube had been fitted, was fastened into the grating camera just below the groove which held the plate. To the movable tube was soldered a second tube of 2 mm. bore, into which was fitted a short piece of brass rod. This rod carried a needle point. The whole arrangement is shown in fig. 6. A plate of thin glass was carefully smoked over a gas-flame, and then wiped clean with the exception of a narrow strip 4 mms. wide along the centre. This plate was inserted in the camera in place of the photo- graphic plate, and the spectrum brought into such a position that the lines crossed the smoked strip. The positions of the lines could be accurately recorded by bringing the needle- point in contact with the glass exactly on the centre of a line and the Rotatory Dispersion Formula. a and then pushing it up across the soot-film. Intensities could be recorded approximately by varying the length of the lines. The sodium lines were also recorded on the plate in the same manner to serve as reference marks. An iron are spectrum was then photographed together with the sodium lines, and by means of the two plates the wave-lengths of the lines of the red rotation spectrum could be determined. The Fig. 6. smoked plate was fixed by flowing it with a very dilute solution ef collodion in ether. A print from the plate mounted “in register,’ with a photograph of the absorption spectrum, is shown in fig. 6, Plate V. Owing to the inequality of the absorption in the different parts of the spectrum above the D lines, it was necessary to take photo- graphs, at three different vapour densities, to represent the entire set of lines. The prints have been carefully registered in mounting. The small percentage of lines which exercise rotatory power is very marked in this case. The position of the D lines is indicated on the left-hand end of the plate, the red being to the right. The wave-lengths of the lines in the red rotation spectrum are given in the following table :— 426 Magneto-Optics of Sodium Vapour. Red Rotation Spectrum. 8 6005-26 3 6218-94 | 2 6427-45 8 6019-22 5 6280°59 7 6434-23 4 6023°45 7 6285°96 2 6435°05 5 6027 47. 3 6240-19 3 6488°30 i 6031779 | 5 6252718 | 3 6441°62 + 6060 25 | 4 620573 3 6445-24 6 6063°91 A GvAG VR 10 6449°86 7 6067-47 10 6262°55 1 6470°58 2 6075:42 6 6272-78 10 6481°89 10 6107°73 3 6283-40 10 6490°36 9 6108'25 3 6283°84 7 6501-45 4 6113°59 10. 6314714 3 6515°69 2 611381 6 6317-09 4 6545°91] 10 6125°67 TO WG6525;81 3 6995°71 HO OL Sooke 2 6358°65 5 6556°66 8 6162°74 10 6374-11 7 6079-55 2 6166°10 4 6379-24 8 6609°80 6 6172°32 10 6886-50 7 6623:96 4 6179 92 6 6399-79 3 6676°88 8 6183°93 | 3 640584 4 6692°60 9 619693 | 8 6419-69 A O(a 8 6216°56 - 38 6426°85 | 2 6761-19 The fact that ne rotatory effects of the vapour only manifest themselves in a vacuum is of fundamental import- ance. The exact nature of the changes which occur when an inert gas is admitted have not as yet been determined. The fact that no trace of the red or green rotation spectrum could be seen when the vapour was formed in an atmosphere of hydrogen at atmospheric pressure, and that only a very slight restoration of light was visible at the D lines, led me to infer that the rotatory power had been destroy ae On experi- menting with helium light, however, it was found that the rotation measured in degrees was the same after the ad- mission of the hydrogen as before, the intensity of the trans- mitted light bemg however very much less. On this account it seems probable Shan the effect of the chemically inert gas is to modify the absorbing power of the gas. It has been found that the presence of hydrogen or nitrogen interferes in a very marked degree with the fluorescence of the vapour. The same thing is true in the case of iodine vapour, which has been found to possess a very great rotatory power for green light, when the vapour is formed in an exhausted tube. A small bulb, containing a few crystals of iodine, is exhausted and sealed off from the pump. On placing it between the poles of the magnet between crossed nicols, a most beautiful emerald-green light is restored the moment the current is turned into the coils. The spectrum of this light has been photographed and observed visually. It resembles the ab- sorption spectrum so closely as to lead to the belief that the narrow black lines in it are produced by absorption. Little The Scintillations produced by Radium. 427 or no rotatory power is exhibited for red or yellow light, though this portion of the spectrum is filled with fine absorp- tion- -lines, and the blue region is also wanting in the rotation spectrum, though the absorption is strongest at this point. These effects are at present under investigation, and will be reported in a subsequent paper. The investigation reported in the present paper is one of a series made possible through substantial aid received from the Rumford Fund, two grants having been made by tbe American Academy, for a study of the optical properties of sodium vapour. Much assistance has also been rendered by Mr. A. H. Pfund, for whose services I am indebted to the Carnegie Institute. L. The Scintillations produced by Radium. Bueno sta, Wes, WOOD: [Plate VI.] HE scintillations of phosphorescent zine sulphide, when subjected to the bombardment of the radium corpuscles, does not appear to have been satisfactorily explained up to the present time. Crookes regarded each flash as due to the impact of a positive electron or “alpha particle, while Becquerel regards the production of light as a secondary effect resulting trom cleavages of the crystals brought about by the action of the rays. Neither hypothesis, as it stands, seems quite convincing. I do not know whether any estimate has ever been made of the actual number of alpha particles emitted in unit time from a given amount of radium, but it certainly seems as if the number must far surpass the number of fiashes of light as seen in the spinthariscope. As to the second hypothesis, the only argument advanced in support of it appears to be the circumstance that zinc sulphide crystals when rubbed or crushed show similar flashes of light. This argument is not very convincing, for it amounts to saying that similar effects must result from similar causes. On the other hand, the cleavage hypothesis removes the trouble regarding the number of flashes as compared with the probable number of electrons, as well as the difficulty in the conception of an appreciable flash being produced by a single electron. The experiments described in this paper were completed just a year ago, and were undertaken in the hope of settling the question of the cause of the flash. As they did not lead to sufficiently definite conclusions to satisty me, * Communicated by the Author. 498 Prof. Wood on the I refrained from publishing the results, in the hope and belief that some one else would succeed in solving the question in a more conclusive manner. As no further work appears to have been done, and no more satisfactory theory bas been advanced, I have decided to publish them for what they are worth, together with the conclusion which I have drawn from them. It was hoped that the cleavage hypothesis could be either strengthened or weakened by determining the duration of the spinthariscope flashes, and the flashes produced by cleavage. If the order of magnitude was found to be different in the two cases, it would be a very strong argument against the hypothesis of Becquerel. The duration of the flash due to the radium bombardment was determined without difficulty. The rim of a wooden disk, mounted on the shaft of a small electric motor, was coated with zine sulphide, and a speck of radium supported above it on a needle-point. The bombarded surface was viewed in a dark room with a small lens. The flashes remained sharp even when the motor was running at a pretty good rate, but on further increasing the speed they became less distinct, being drawn out into cher: streaks. It ro) was pretty definitely determined that ue duration of the flash was somewhere between ,.\,, and ap of a second. The only method I was able to devise for determining the duration of the triboluminescence was the simple expedient of touching the rim of the revolving disk with the point of a slender rod of glass. The glow due to the crushing of the crystals extended halfway around the disk, even when it was running at low speed. In addition to the long streak of light, there is alw ays a bright star at the point where the rod is in contact with the sulphide surface. ‘This is probably due to the fact that some of the luminous crystals are held back, by the rod, stick to it in other words, and does not necessarily indicate that the first flash is of very brief duration. It the latter were the case, we should expect the glowing star to be slightly drawn out at very high speeds, which is not the case. This experiment appears to indicate that the flashes due to the radium bombardment have a much shorter duration than the flashes which result from fractures of the crystals, and there seems to be no way of escaping from the conclusion that the two phenomena are not very closely related. A photographic study of the phenomenon was then under- taken to determine the integral effect of a large number of fle au for it seemed possible that the flashes might recur at certain points more often than at others. Scintillations produced by Radium. 429 A small heap of the phosphorescent sulphide was pressed flat with a clean piece of glass. A perfectly flat smooth sur- face was thus formed, free from any cement or other binding substance. A speck of radium was mounted above it, and the scintillating surface photographed with a Zeiss microscope, using a low-power objective, the magnification not exceeding 20 diameters. An exposure of three days was given, w hich was sufficient to yield an excellent negative. ), also a+ QBs (it is necessarily >a). 5. We are now in a position to tackle the cardinal numbers. Since every aggregate can be arranged in a well-ordered series, it follows that of two dissimilar aggregates one must be similar to a part of the other, for when they are arranged in well-ordered series, one must be similar to an initial segment of the other. ‘It is not possible for two dissimilar aggregates to be each similar to a part of the other *. For let A be an aggregate of cardinal number &@ and B an aggregate of cardinal number BD and let A be similar to a part of B and B be similar to a part of A. Let A be arranged in a well-ordered series, and let a denote the ordinal type of this. This contains a part B, similar to. B, let 8, denote the ordinal type of this, B, contains a part A, similar to A, let a, denote the ordinal type of this; A, contains a part B, similar to B, let 8, denote the ordinal type of B, and so on. We thus get a progression + of parts of the agoregate A similar to B and A alternately. It follows from $46 that * This is Schroder & Bernstein’s theorem. I have not seen their proofs, but the proof which Mr. Jourdain gives (Phil. Mae. Jan. 1904, pp. 71-73) appears to me defective. See Note A at the end of this article. + It should be observed that this argument is not open to the objection which I have urged against the argument used in the proof given by Mr. Jourdain. We do not require any step by step process of selection to get the series of partsof A which are similar to Band to A alternately. The whole series is completely determinate when once we have defined the correlation of all the elements of A with some of the elements of B and of all the elements of B with some of the elements of A. 446 Mr. A. E. Harward on the 2>Bism>+f)...&c. Since there cannot be a progression of ordinals in inverse order of magnitude, it follows that we must after some finite number of steps come to a stage where a,=8n+1 OF Bn=eny 1} in either case we get a part of the aggregate A which is similar both to A and B. Therefore A is similar to B, and A=D. We are now in a position to assert that if @ and B be any two different cardinals then either A>D or b>€; i. ec. the cardinals are a simply-ordered class *. 6. It is easy to prove that the finite cardinals form a progression, and that N) which is defined as the cardinal number of the agoregate of the terms of a progression, is the smallest transfinite cardinal, for any initial segment of a progression is finite. Since any transfinite well-ordered series with a last term can be converted into a series with no last term by merely transferring a finite number of the terms from the end to the beginning ; it follows that any infinite aggregate can be arranged in a well-ordered series with no last term, and since the type of such a series is unaltered by substituting for each term a finite series of n terms, it follows that nA=a, if a be transfinite. If «bea, at+bea+a=a; bub atbsa; «. at+b=a(bza). By diagonal enumeration of a progression of progressions it is proved that &o?=No. It is easy to prove now that N,d—=€4 if & be any transfinite cardinal. For an aggregate of cardinal number @ can be arranged in a well-ordered series with no last term, ¢. ¢. a series of type w8 where @ is some ordinal. By substituting for each term of this series a progression of terms we convert the series into one of type w’8 and the cardinal number of terms in the new series is Na. But in this series each component of type w? can be rearranged in a series of type w ; the series is then of type w. e. Na =a. 7. We are nowin a position to classify the ordinals. I use * By following Cantor’s method of procedure it can be proved, with- out using Schr ider & Bernstein’ s theorem, that the cardinals form a well- ordered series. 8. & B.’s theorem can then be inferred as a corollary. But the course of the argument is much simplified if S. & B.’s theorem be first proved. Transjinite Numbers. 447 the symbol C(8) to denote the cardinal number of the agoregate of terms of a series of type 8 (@=any ordinal). It is obvious that if B<, C(8) —C(y), because the aggregate of terms in a series of type 8 is similar to a part of the ageregate of terms in a series of type y, and therefore (by the definition of ‘ less than” for cardinals) the cardinal number of the latter aggregate is not less than the cardinal number of the former. Therefore it is equal or greater. The first class of ordinals consists of the finite ordinals. Two transfinite ordinals 6 and y are said to be of the same class if C(8)=C(y), and the cardinal number C(@)(=C(y)) is said to be the cardinal associated with that class. | If B and vy are of the same class then all the intermediate ordinals belong to that class. For if B<éy, C(8) 5 C(y). Therefore the cardinals associated with the classes of trans- finite ordinals form a well-ordered serial class similar to the class of classes of ordinals. | | There cannot be any last class of ordinals, because if there were the associated cardinal would be the greatest cardinal *, Therefore the ordinals belonging to any class form an agoregate, for they are part of the aggregate of ordinals pre- ceding the first ordinal of the next class. : The classes of ordinals are not a series (7. e. not an aggre- gate), for if they were so, there would be an aggregate of * It should be observed that it is at this stage of the argument that I for the first time make use of the axiom assumed in § 3, for the proof that tuere is no greatest cardinal depends on that axiom. A448 Mr. A. E. Harward on the ageregates of ordinals, comprising all ordinals, and the ordinals would be an aggregate. The class of classes of ordinals is therefore an unlimited well-ordered serial class similar to the class of ordinals. The same is true of the class of associated cardinals. Every transfinite cardinal is included in this class of cardinals because every aggregate can be arranged in a well- ordered series. The first ordinals of the classes of transfinite ordinals are denoted by the symbols @, MW}, Wo, eee Dw, Wwy+1>5 eee Ws, eee (@ any transfinite ordinal). The class of which @ is the first is the 2nd class, the class of which @, is the first is the 3rd class, the class of which o, is the first (v finite) is the (v+ 2)th class, the class of which , is the first is the wth class, and the class of which @, is the first (8 transfinite) is the @th class. The cardinal associated with the 2nd class (of which o is the first ordinal) is No and the cardinal associated with the class of which w, is the first (@ finite or transfinite) is designated by the symbol Ng. It is implied by what I have proved above that there can be no cardinal intermediate in value between Ne and Ne. But as the point is of great importance it is as well to restate the proof. The elements of an aggregate of cardinal number Ng can, by definition, be arranged in a series of type w,, and the elements of an aggregate of cardinal number Ng; can be arranged in a series of type w+}. Let the elements of any other aggregate be arranged in a well-ordered series, call the type of that series y. Then, if y < @,, C(y) Ne (it is in fact <, but it is not necessary to assert ye this), ify 5 p41, Cy) S Nei it @,27< ® ae then y belongs to the same class as ws and C(y)=Nz. It is easy to show that the cardinal number of the aggregate of ordinals belonging to any class is equal to the cardinal number associated with the next following class. For let x be the cardinal number of the aggregate of ordinals belonging Transjinite Numbers. AAQ to the class of which 3 is the first term. Then Neii=N ate; if w<&gi1 then «=< Ng, in that case Nei1 = Npte= N 3, which is impossible. v= Neu. 8. At this stage it is desirable to state clearly the con- ditions necessary for proving by induction that a proposition is true for every ordinal (or every transfinite ordinal). If a proposition (or set of propositions) « is true for every ordinal belonging to some initial segment of the ordinals (or of the transfinite ordinals), and if it be proved that if « is true for every ordinal (or every transfinite ordinal) less than @, then itis also true for 8, then it follows that « is true for every ordinal (or for every transfinite ordinal). It should be observed that this statement includes both the case where 8 has a term next before it, and the case where 8 has no term next before it. It is not sufficient to prove that if « is true for @ and the ordinals less than £, then it is true for 8+1. 9. I now proceed to define w° where @ is any ordinal :— @” means ww. @* means wo. w@’+l means ww (vy any finite ordinal). Therefore the meaning of w” is determinate where v is any finite ordinal. w® (@ transfinite) is defined as follows :— In the first place if @ denotes a type of series with no last term (7. ¢. if @ has no immediate predecessor), then w® de- notes the first ordinal after all the ordinals w7 (y<). If B=y+1 then w® means oo. It is clear from this definition that w* denotes an ordinal uniquely determined, provided that w’ denotes an ordinal uniquely determined, for every value of y less than 6. But w® does denote an ordinal uniquely determined when £ is finite. *. w® denotes an ordinal uniquely determined for every value of £. I proceed to prove that w*t%& =o, This follows at once from the definition when £# is finite. Phil. Mag. 8.6. Vol. 10. No. 58. Océ. 1905. 21 A50 Mr. A. E. Harward on the It also follows from the definition that if this proposition is true when B=y, it is also true when B=y + (rv finite). I proceed to prove that if the propesition is true for every ordinal less than #, it is also true for @ in the case where 8 denotes a type of series with no last term. In this case w*t® denotes the first ordinal after all the ordinals wY (y or, in other words, w® also belongs to the 2nd class. 11. I now proceed to prove that x= =, for all values of 8 (finite and transfinite). Consider the two propositions U(o*) =C() | (OEE NEE | aa ee It has been proved that these two propositions are true if 8 be any ordinal of the second class. I shall prove that if they are true for all transfinite ordinals less than @ then they are also true for 8. Assuming the propositions A to be true for all transfinite ordinals < 8, * This can also be verified by arranging the finite numbers in a series of type o, viz., first the primes in order of magnitude, then the numbers with two factors in a series of type w?, then the numbers with three factors in a series of type w*, and so on. ea Ge: 452 Mr. A. E. Harward on the If S=yrt+1, then C(B)=C(y) and w8=oa"a, and C(@®) =C(@”) Xo, =C§(y)No as <8, =O) =C(8). If @ denote a type of series with no last term, then the series of ordinals less than w® (which is a series of type w®) is partitioned by the numbers ea oe Gere ses hy < 8) into segments of which these numbers are the first terms. Each segment is of type o° (6< 8). Therefore the cardinal number of the aggregate of terms in each segment is equal to or less than C() *. The series of segments is of type @; therefore the cardinal number of segments = C(). +. Cw?) Z{C(8)}2 If {C(8)}?=C/(@), then it follows that C(w*) =C(8). Now if 8 be not the first ordinal of a class, there is some ordinal y< such that C(8)=C(y); as the propositions A are true for Y, it follows that {C(@)}?=C(@), and therefore in this case the propositions A are true for £6 also. But if @ be the first ordinal of a class, then we have to prove that {C(8)}?=C(@). This it is easy to do with the aid of the assumption that the propositions A are true for all ordinals less than . Let 8=o« the first ordinal of a class. We can classify all the ordinals less than w, as follows :— (1) ordinals of the type v or w6d+y, (2) ont a ov, Ww d+or, (3) ” ” wy 9 od + w’r, (w) 2 ” OPV ,, ant TO Oy, (y) 99 ” wv 3 o!t16+a’y. In the above scheme y and 6 stand for any ordinals less than we=f, and y stands for any finite ordinal (1, 2, ...). It has to be proved that all these ordinals are less than w,¢. * Because C(w?)=C(6) (6 transfinite) and =, (6 finite). Transjinite Numbers. | 453 This can be shown as follows :— From (A), if y be transfinite C(w”)=C(y), C(o’*?) =O(y+1)=C(y), {Co P=Cy); and if 6 be transfinite, {C(6) }?=C(6). Therefore, if both y and 6 be transfinite, C{o’+1$}=C(y) or C(6), whichever be the greater. Therefore C(w¥t+1§ + w/v) =C(y) or C(6), whichever be the greater. If x be finite and 6 transfinite the above expression equals C(6) ; and if y be transfinite and 6 finite then the above ex- pression equals O(y); and if both y and 6 be finite then it is | equal to XN. - In any case, therefore, wo’ 6+a'V< Wg, provided that y and 6 be less than ax. It follows from this that every ordinal in the above scheme is less than ax. All the ordinals in the above scheme are different, for if otl§ +o17, = w/2*16,+@!2 V>. - . > e ° ° ° (2) Then, since a series of type (#) has a last segment of type w1, and a series of type (@) has a last. segment of type w’2, a last segment of a series of type w”! is in ordinal correspon- dence with a last segment of a series of type w”2, but this is not possible unless y,=., for every last segment of a series of type w” is itself of type ’. Therefore y;= 2, and it obviously follows that v, =v, and = o>. Now as 6 may be any ordinal whatever less than w,, the number of ordinals in each set (z.e. in each horizontal line) is C(w,)=Nx, and the series of sets is a series of type ax, since y may be any ordinal less than w,. Therefore there are Nx sets. Therefore the total number of ordinals in the scheme is x, but the number is also X?: ve) NOS. We have thus proved that if the propositions (A) are true A454 Mr. A. E. Harward on the for all the transfinite ordinals less than 8, then they are also true for 8. But they have been proved to be true for every ordinal of the 2nd class, therefore they are true for all transfinite ordinals. In other words, w8 always belongs to the same class as 8 when £ is transfinite, and NU =Ny for all finite and trans- finite values of ¥. It follows from this, of course, that X}=, (v finite). 12. The whole of § 9 still holds good mutatis mutandis, if instead of m we take any ordinal number. In this way #8 is uniquely defined whatever ordinal « and 8 may be, and it is proved that a®t+’ = aba’, It can also be proved that * aBy = (a®)y, For if this be true for all ordinals less than y, then, if y=6+1, a PO+1) — gPb+8 — (Bo == ede) Dome. and if y have no next predecessor then a” is the next ordinal after all the ordinals at(k<@ry), and (since the law is assumed to be true for all ordinals less than y) it is easily seen that this statement is equivalent to the statement that a®y is the next ordinal after all the ordinals («*)® (8 @,) belongs to the same class as £9. For if this law be true for all ordinals y(#, ), and let y be the term of N with which 2 asa term of M is correlated. Then, since the correlation is one-one, 7 must be common to P,_, and P,,-1, and if z be the term of N with which y asa term of M is correlated, then z must be common to P,_»and P,-»; by proceeding in this way we prove ultimately that P,_, and P have a term in common, but this cannct be because P has no term in common with M. This completes the proof. Mr. Jourdain’s proof that 87=, appears to me to contain an unsound inference of a somewhat similar character. He. proves that the terms of a double series (wg), such that a+ 2, and we can correlate the terms of (,wg) such that r<2+B< 2, with the terms of (4,) such that r a6 eae | Distance between Electrodes. } | | 1 em. | -4°5 ems. 9ems. | 13-5ems. | 18 ems. GOO) volliss. conse 310 304 Vee | 280 270 AOR ete oo): 255 «|S 47 Se 280: el, ES BDU eek, 75 |), x0 165 155 143 2s ace ae 130 | 125 tS | 104 90 ote, a) Be ea 67 64 7 | 53 | 48 70 inde isiet Meee 42 39 35 a2 29 1S eg. PR aie ee how 2 | 20 16 | 14 13 Bh EAR Sh Rie | 9 | 8 rf 6 Dist Do Frege ety, 5 4°7 4 3°5 3 A478 Dr. H. A. Wilson on the It will be seen that in every case the current falls off slowly with increasing distance between the electrodes. The fall of potential between the electrodes was examined by means of a third electrode, consisting of a fine horizontal wire which was put in between the disk electrodes and could be moved along from one to the other. Its potential was measured by means of a Kelvin’s multicellular electrostatic voltmeter. Tig. 2 shows the variation of the potential along the flame obtained as just described. The distance between the disks was 17°7 cms. and the PD. used 550 volts. Wilgnailiiiee seen that there is a sudden fall of potential near each electrode and a uniform gradient in the space between the electrodes. Fig, 2. 6 ao vp om = eee || es Let m;=number of positive ions present per c.c. N= xe negative ae = k,=velocity of positiv e ions due to one alt per cm. ky= oy) negative Dy 9 oy) oy) X=electric intensity in volts per cm, e=charge on one ion. i= current density. Then we have the well-known equation = Xe(kyny + hong). ae Where X is uniform n;=7, so that 2= Xen(k, + fs). According to this equation we should expect the current through the “flame to be proportional to the potential gradient existing between the electrodes. To test this, two: small electrodes were put in the flame 0°5 cm. apart, and the P.D. between them was measured by means of a quadrant electro- meter. It was found that the P.D. between them was very Electrical Conductivity of Flames. 479 nearly proportional to the current through the flame. The following are some of the results obtained :— Current. P.D.=C. (C). ae 270 4:0 volts. “soot | OMS 00148 54 OS | 00148 | | 18 0725: 5, | 00139 The P.D. between the two small electrodes varied to some extent as they were moved along the flame together, owing to the non-uniformity of the flame, but at any one point not very near either electrode it was always proportional to the current. Near the negative electrode the P.D. became too large to be measured on the quadrant electrometer, and very close to the positive electrode it also became large. The fall of potential (V) between the disk electrodes may be regarded as made up of three parts—the sudden fall near the negative electrode, say V.; the fall near the positive electrode, say V, ; and the fall in the uniform gradient, which is proportional to the current and to the distance between the electrodes. Hence approximately V=V,4+ V.+ACd, where A is a constant, C the current, and d the distance between the electrodes. The following table gives the values of (V,+ V2) got by subtracting ACd from V, using the results given above. The value of A was got from the measurements of the electric intensity between the electrodes by means of the equation InCd = (Xa; We have Ga A=008, the current being expressed before in terms of the corresponding galvanometer deflexion. Hence Vi +V.=V—0-03 Cd. | | | | PD. | lem. | 45cms. | Qems. | 135 ems.| 18 cms, | Bie 62 ee =F ns ers a 600 volts.....3... oe 591 | 559 520 487 Ad4. AO ce eter e.| 392 367 | 339 307 284 20a lorie eaters: ORG Sea ne eal Tie 155 137 123 1201 he ee hee 1G tos) |. 89 78 1-4 AQ So is eee ' 38 le aa 24-6 18°6 14:0 QO Ba SS sal 19 ay 106 fig 45 TO Fetes 9 73 7 4:3 2°8 Be — eee as 4 2°9 2°1 16 Et 2. | paper 2 | a 0-9 06 O-4 480 Dr. H. A. Wilson on the In fig. 3 these values of (V,+ V.) are plotted against the corresponding values of the current. The curve drawn is the parabola C=12'8\/V,+V., and it will be seen that nearly all the points lie near thiscurve. It appears therefore | 190 200 300 400 500 600 VozTs. that the current varies approximately as the square root of (V,+V.). Hence we have C=B,/V.+V; nearly, where B=12'8 for the flame used, or V, + V.= =. But e 3 E V=V,+V,+ACd, so that C? Vie Bet ACd. bo Se) L Prof. J. J. Thomson * has given the theory of the variation of V with C in a uniformly ionized gas. He finds that when the current is far from its maximum possible value so that there is a region between the electrodes where the electric intensity is uniform, then the relation between V and C is of the form V=aCl?+bdC, where a and 0 are constants. The significance of a and 6 in Prof. Thomson’s formula is more- over precisely that which has been deduced above for a and A. B? It appears therefore that the conductivity of the flame is due to approximately uniform ionization taking place throughout the region between the electrodes, and, further, that the current is always very far from its maximum possible value even when a P.D. of 600 volts is applied to electrodes only J. cm. apart in the flame. * “Conduction of Electricity through Gases,’ p. 73. Flectrical Conductivity of Flames. 481 To further test the applicability of the formula 2 V= 5 tACd to flames, the current between two vertical parallel platinum disk-electrodes placed symmetrically in an ordinary Bunsen flame was measured. One of these electrodes was 3 cms. in diameter, and the other consisted of a disk 1 cm. in diameter surroanded by a guard-ring 3 cms.in diameter. The annular space between the disk and ring was 0°5 mm. wide. The current between the large disk and the small one was measured, the guard-ring being kept at the same potential as the small disk. The results are shown in fig. 4 for a distance Fig. 4. et A eer 0 10 20 30 A0 VoLrs. 3 YL CURFENT. & of 1 cm. between the electrodes. The current was very nearly independent of the distance between the electrodes, 2 which means that ACd in the formula Vas +ACd was negligible. Consequently we should have C?=B2V. The curve drawn is the parabola C=19-25VV, and it will be seen that the points fall very near to it. The term ACd in this experiment was small, partly on account of the smallness of d and partly because the flame was very hot, which of course diminishes A. In previous experiments on the variation of © with V with the electrodes near together, no guard-ring was used, so that the relation obtained was probably complicated by the non- uniformity of the field at the edges of the electrodes. Plal. Mag. 8. 6. Vol. 10. No. 58. Oct. 1905. co Aly 482 Dr. H. A. Wilson on the (2) The fects due to introducing Salt Vapours into the Flame. The quartz-tube burner enables the effect of putting salt into different parts of the flame to be easily studied. A bead of an alkali salt on a platinum wire was put into different parts of the flame, the electrodes being about 18 cms. apart. It was found, in ‘agreement with earlier results, that the current through the flame was not attected unless the salt vapour came in contact with the negative electrode, when a large increase in the current occurred. This result was previously explained by supposing that the salt vapour is only ionized when in contact with the hot electrodes, but it now appears that the true explanation is that the salt vapour is ionized anywhere in the flame, and that the absence of effect except close to the cathode is due to the non- -uniformity of the potential gradient. Two wires connected to a quadrant electrometer were sup- ported in the flame so that the electric intensity between them could be measured. In one experiment, using a P.D. of 700 volts between the principal electrodes, the electric in- tensity was 1°6 volts per cm. at about midway between the electrodes. On bringing a bead of K,CO; into the flame just below the two wires, the P.D. between them fell toa very smal! fraction of a volt , but the current through the flame was not appreciably inereateds The part of the flame occupied by the salt vapour is thus a much better conductor than the rest of the fame. In the experiment just described, the potential fall at the cathode was 700—18 x 1°6=671 volts, and, as we have seen, C=A,/V>. Now the effect of putting in the salt is to diminish the electric intensity to practically zero in the part of the flame occupied by the salt, which was a length of about 2 ems. of the flame. Thus putting in the salt must have increased the cathode fall by 3:2 volts, which according to the formula C=A,/Vo, since Vz is 671 volts, should have increased the current by one part in 400. Now the deflexion due to the current in this experiment was about 200 mms., so that putting in the salt ought to have increased the deflexion to 200°5 mms.; but since the deflexion was never perfectly steady owing to small oscillations of the flame, so small an increase ‘could not have been detected. It thus appears that the absence of effect on putting in salt, except close to the cathode, is not inconsistent with the view that the salt is ionized anywhere in the flame. ' Fig. 5 shows the variation of the current with the distance betw: een the electrodes for several P. D.’s when some K,CO, Electrical Conductivity of Flames. 483 was put on the cathode. The K,CQO, on the cathode fused and volatilized at a very constant rate, so that the current remained almost constant as long as any salt was left. Fig, 5. f Hany ae a Bec nM 0 2 a 6 8 i i a NCR wane It will be seen that the current falls off rapidly as the distance between the electrodes is increased, this effect being much more marked than in the case of the flame alone. Fig. 6. 10 le Fig. 6 shows the effect of putting salt on the cathode on the potential gradient. It will be seen, on comparing with fig. 2, that the cathode fall is greatly diminished, while the uniform gradient between the electrodes is increased. 21; 2 A84 The Electrical Conductivity of Flames. When the distance between the electrodes is large, the current with K,CQO, on the cathode is about 50 times greater than the current when no salt is present. The electric in- tensity in the region between the electrodes, however, is only three or four times greater, so that it seems as though putting salt on the negative electrode increased the conductivity of the rest of the flame. This effect is of a rather unexpected character, and the writer hopes shortly to carry out further experiments with the object of elucidating its real nature. With salt on the cathode, most of the fall of potential occurs in the uniform gradient between the electrodes, so that the current which is proportional to the gradient varies roughly inversely as the distance between the electrodes and dir ectly as the potential-difference. It has been shown recently by IF. L. Tufts* that coating the negative electrode with calcium oxide gr eatly diminishes the fall of potential at this electrode, and so increases the current. ‘This effect is clearly exactly of the same nature as the effect of putting an alkali salt on the electrode. Tufts also finds that when the negative electrode is coated with CaO, then putting a bead of salt anywhere in the flame between the electrodes increases the current considerably. It was consequently to be expected that with salt on the negative electrode a similar effect would be obtained, and this was found to be the case. With the electrodes 18 cms. apart and K,COs; on the cathode, putting a bead of K,CO; unywhere in the flame increased the current about 10 per cent., and the same effect was-obtained with beads of other alkali salts. Two beads put in at the same time in different positions increased the current about 20 per cent. The portion of the flame occupied by the salt becomes a much better conductor than the rest of the flame, so that the electric 1atensity in it hecomes very small. The electric intensity in the rest of the flame is consequently increased, and the current is proportional to this intensity. The salt from one head occupied about 2 ems. of the flame, so that with the elec- trodes 18 cms. apart an increase of ay in the current ought to have occurred, and with two beads 2. With the eleenmndes nearer together, the effect of putting in a bead was greater, as was tobe expected. With the electrodes 9 cms. apart, putting in a bead increased the current about 20 percent. It appears, therefore, that the salt vapour is ionized anywhere in the flame, and not only when in contact with the electrodes. In an earlier paper (Phil. Trans. A. vol. excii. 1899) the * F, L. Tufts, Phys. Zeitschi. v. p. 76 (1904). See also I’. L. Tufts, & J. Stark, Phys, Zeitschr. v. p. 248 (1904). Contact with Dielectrics. 485 writer suggested that the salt vapour was only ionized when in contact with the hot platinum electrodes. This view enabled a great many experimental results to be simply ex- plained, but it appears now that the true explanation of these results is the smallness of the potential gradient in the fiame, except close to the electrodes. It was supposed previously that when the P.D. used was large, so that the current only increased slowly with increasing P.D., that then the current was nearly at its maximum possible value, and so was a measure of the number of ions formed between the electrodes. It is clear now that this supposition was incorrect, and that the current is really always very far from its saturation value. It is of course probable that some surface ionization on the hot electrodes does occur, but, at any rate, when the elec- trodes are not very near together, it does not appear to be sufficient to appreciably iniluence the conductivity of the flame. The view that the salt vapour is ionized throughout the flame was adopted by Arrhenius (Wied. Ann. xlii. p. 18, (1891), H. Marx (Ann. de Phys. ii. pp. 768, 798, 1900), and by F. L. Tufts and Stark in the papers referred to above. In conclusion, I wish to say that my best thanks are due to Prof. J. J. Thomson for valuable advice and kind interest shown during the carrying out of these experiments. LVI. Contact with Dielectrics. By Rotto APPLEYARD *, OBJECTS. To examine :— (1) Whether tinfoil electrodes, pressed against a sheet of dielectric by indiarubber disks, enable accurate determinations of dielectric- resistance to be made. (2) The effect upon dielectric-resistance of change of load on such tin- foil electrodes, in the case of press-spahn. (3) The effect upon dielectric-resistance of increase or decrease of voltage in the case of press-spahn between tinfoil electrodes. (4) The rate and direction of the change of deflexion in direct-deflexion tests on press-spahn, and to determine in how far these changes result from surface conditions, and in how far from internal stresses. (5) The effect of reversals of voltage upon dielectric-resistance. (6) The effect of prolonged “ electrification.” (7) To indicate the probable limits of accuracy with mercury electrodes. (8) To point out that Price’s guard-wire can be used in sheet tests to eliminate leakage over the sheet surface, as well as over the instruments. (9) The retentive force between electrodes and dielectrics. * Communicated by the Physical Society: read June 16, 1905. 486 Mr. R. Appleyard on CONCLUSIONS, (a) Except in the case of homogeneous dielectrics, it is nusleading to deduce specific values referred to unit cube of the material, from the results of tests on sheets. (6) With tinfoil electrodes, the apparent resistance of press-spahn diminishes as the load increases, and it attains a fairly constant value at a load of about 400 grammes per cm.” (c) If, with tinfoil electrodes, the load is gradually diminished after a load of 543 erammes per cm.*, the resistance gradually rises, but the rise is less rapid than the diminution in the former case (dD). (d) When the full load with tinfoil electrodes is again restored the resistance falls to its minimum value. (e) For small loads, with tinfoil electrodes, the 2nd-minute deflexion is in general greater than the Ist-minute deflexion. As the load increases, a point is reached at which these deflexions become approximately equal, For loads greater than about 360 grammes per cm.”, the 1st-minute deflexion is in general greater than the 2nd-minute deflexion. (f) Increase of voltage, with tinfoil electrodes, especially with small loads, behaves like increase of load, apparently increasing the contact area, aud diminishing the observed dielectric-resistance. Load, voltage, and the normal effect of “absorption”? thus combine to determine the ratio of the Ist-min. deflexion to the 2nd-min. deflexion. ; (g) When mercury electrodes are used, the dielectric-resistance, as measured at different voltages, is sensibly the same, even for abrupt and great changes of voltage. (h) When mercury electrodes are used, the 2nd-minute deflexion is in general never greater than the lst-minute deflexion. The inference is that when, with tinfoil electrodes, the converse is the case, it arises from imperfect contact, and not from the material itself. (2) When mercury electrodes are used, the dielectric-resistance, as measured with a voltage applied in a given ‘direction, i is sensibly the same as that measured with the voltage reversed, and this equality appears to become greater after a few reversals. (7) There is a critical load at which tinfoil electrodes yield fairly accurate results. With greater loads there is danger of crushing the material. With a less load the contact is faulty. (kK) With mercury electrodes under the application of 750 volts, with earthing and reversing, respectively, at every fifth minute, the resistance of a sample of press-spahn fell from 45:2 to 41:7 megohms in 51 minutes, thus indicating the limits of precision of resistance tests on such material on a prolong ed test where the conditions have time to change. (7) The earth- readings, in such an experiment as that described under (i), fall steadily towards zero, and their pairs of maximum values are approximately equal, corresponding to the two directions of voltage. These maximum earth-readings are only about 0-2 per cent. of the maximum readings with the battery. Consequently, if only 1 minute is allowed ior a sample to recover after the application of a given voltage, the degree of precision of the results will be of the order 0:2 per cent., on account of the previous charge left in the sample. (m) The retentive force bemcen a disk of tinfoil and a sheet of dielectric, forming part of a condenser, increases rapidly with the voltage ; and it vanishes, or becomes extremely small, when the voltage falls tO zero. (x) Small variations between the observed capacity of a condenser tested at different voltages may be due to more intimate contact between the electrodes and the dielectrics at the higher voltages. Contact with Dielectrics. A87 N the course of some experiments described by Mr. E. H. Rayner*, the electrical resistance between the faces of sheets of dielectric was measured, using electrodes of thin tinfoil. The dielectric sheet to be tested was laid between two circular soft indiarubber disks, each disk being covered, on its contact-face, with tinfoil, and the whole was surmounted by a brass disk of the same diameter, upon which lead weights could be placed. This interesting arrangement may be regarded as a compromise between the use of unyielding contact-plates and mercury contact. Itis here proposed to investigate the capabilities of this compromise; and as the material known as ‘‘press-spahn”’’ was examined by Mr. Rayner in his tests, it is here selected as a convenient dielectric for the present purpose. Specific Values.—Mr. Rayner reduces his results to kilo- megohms per cm.’*, but it is perhaps better to state the total megohms measured in each case, without reducing them to specific values. The reason for this is that many materials of this class have a varnished surface, and this varnish has a higher resistance than the middle layers, so that thin sheets yield higher specific values than thick sheets, and specific values cannot be said to be representative of the material generally. Specific values should therefore be avoided, except in the case of homogeneous dielectrics. Size of Ilectrodes.—The disks used by Mr. Rayner were 50 cm. This corresponds to a diameter of 7:98 cms. (3°14 ins.). The electrodes used throughout the following tests are 153°3 cms.’, corresponding to a diameter of about 14 ems. (5'5 ins.).. The soft indiarubber disks are of the same thickness as those employed by Mr. Rayner, 7. €. 1 cm. Load on Hlectrodes.—The weight used by Mr. Rayner to press upon the electrodes was 2() Le eta ices, so that the average load was 400 grammes to the cm.’ In order to give an idea of this load expressed in British units, it may be noted that it is almost exactly the same mean pressure as would be exerted by 1 ewt. distributed over a 5-inch disk. To obtain the same mean pressure on a 54 in. disk, it had to be loaded ‘with 135°2 lbs. (61°3 kilogrammes). It is clear that with some dielectrics a load of this magnitude is likely to reduce the thickness of the sample or alter its texture, and so invalidate the results; as press-spahn is fairly hard, it is probably not seriously atfected, but it will be necessary to examine the etfect of changes of load. * “Report on Temperature Experiments carried out at the National Physical Laboratory.” By HE. H. Rayner. Journ. Inst. Electrical Engineers, vol. xxxiy. p. 613, May 1905. 488 Mr. R. Appleyard on Change of Resistance with Volts ——Mr. Rayner observed considerable change of resistance according to the volts applied. For example, using successively 200, 1000, and 200 volts he obtained respectively 22,000, 9600, and 18,500 megohms with a sample of press-spahn. These changes appear to be excessive, and it is necessary to consider whether they are in any way to be associated with the method of applying the test. Abscrption.—Another question of great importance is the change of resistance with time, when the volts are constant. Mr. Rayner, following ordinary usage, calculated the resist- ance from the deflexion observed after “ electrification ” had proceeded for 1 minute, and he states that the deflexion after 2 minutes did not differ by more than about 5 per cent. from the deflexion obtained after 1 minute. In view of the valuable information to be derived from observations of the rate and direction of the change of deflexion, the actual readings at the 1 minute and 2 minutes, respectively, should be recorded. In what follows, this will be done. Surface Leakage-—In the apparatus employed for the following tests, every part of the system was provided, where necessary, witha Price’s guard-wire. A preliminary test was made to examine whether there was surface leakage between the electrodes. For this purpose the edge of a sheet of press-spahn was covered with tinfoil, and this was connected to the guard-wire. It was found, however, that this did not affect the deflexion. The surface* leakage was therefore negligible. Temperature.—The temperature of the room during all the following tests varied from 15° C. to 16°C. Humidity.—Press-spahn, as is proved by Mr. Rayner’s results, is very hygroscepic ; consequently the resistance cannot be regarded as a fixed quantity. Hach set of tests must therefore be considered as distinct from those which precede or follow it. It is assumed that the conditions in regard to moisture remain constant during a short test. Method of Testing.—The direct-deflexion method was em- ployed throughout, the readings being recorded at successive minutes. In order to indicate the rate of change of deflexion, the actual readings, or their equivalent, are in each case tabulated. ‘The dielectric-resistance is worked out from the 1 minute reading, and is expressed in megohms. * It may be pointed out that when I first put a guard-wire intu practical use, at Mr. Price’s suggestion, he mentioned to me that one of its advantages would be that in sheet-tests the surface leakage could be eliminated in the manner here described. Contact with Dielectrics. A89 Haperiment 1. (Tinfoil Electrodes. 150 Volts.) TABLE I, Load in Shunt, Deflexion, | Deflexion, Total, ae ohms. 1 min. 2 min. megohms. 22°3 1000 345 369 268 | ED 3 379 383 24-4. 61-3 7 450 | 453 | 20°6 76:0 700 345 | 347 | 195 90:8 e, 358 | 359 18:7 105°3 ie 367 | 369 18:3 1198 a 378 375 | 178 197-2 ie 430 430 | 15°6 226°7 500 328 329 | 15:0 256°1 af 335 rayo}) | 14:7 289°] st 340 340 | 14-4 311°5 Ns 343 343 14:3 361-1 u Slay 336 13°8 390°5 fe 360 | 359 13°6 449°] ¥ 365 363 13°5 543°3 ne 368 | 368 | 13°3 449-1 . 373 | 370 a 390°5 4 370 368 eee 315-0 is 568 367 13°3 | 25671 : 366 365 13°4 | 196°8 a 362 360 136 149-7 i 345 344 14-2 90°8 $3 335 334 14-7 oly, % 285 287 Wy | 223 a 258 | 259 19:0 | 197°2 4 349 348 | 14:1 | 361-0 - 367 367 134 | 544-1 ba 381 379 | 12:9 | Des Mo 266 268 18:5 | (The above table shows the effect of increase of load. The electrical test at each load was begun within 1 minute of adjusting the load.) Comparing the first and fifth columns of Table I., the resistance is seen to diminish from 26°8 to 13°5 megohms as the load increases from 22°3 grammes per cm.? to 449°] grammes per cm.” ; and it is seen to attain a fairly constant value at that load, which is not far from that used by Mr. Rayner (400 grammes). Mr. Rayner took the precau- tion of allowing 5 minutes for the load to settle before taking a test, so that his results would probably be rather more uniform than these. The increase of resistance as the load diminishes takes place more slowly, and the value 19-0 megohms at minimum foad is considerably less than the initial value. The increase of load at this point to 361 grammes per cm.” lowers the megohms again to 13°4; and the resistance is further reduced to 12°9 megohms when Mr. Rayner’s load is exceeded. When the minimum load is 490 Mr. R. Appleyard on suddenly restored, the megohms rise once more to 18°5. It is especially interesting to note that for small loads the 2nd min. deflexion is always greater than the Ist min. deflexion, whereas for loads from 119°8 to 90°8. in the order shown in Table I., the 1 min. and 2 min. readings are at first equal, then the first is greater than the second, and finally they are again equal. The same general result will be noticed in the tests with tinfoil electrodes, which follow. Increase of voltage, as well as increase of the load, appears to have the effect of improving the contact when contact is imperfect. With small loads, it may be assumed that the surfaces are partially out of contact, and that the effect of the current is to improve the contact, so that the resistance diminishes, and the deflexion increases. Meanwhile the normal effect of “absorption” tends to produce an apparent ¢ncrease in the resistance, and a point is reached at which no change of deflexion is observed, the effects being balanced. J inally, with the greater load, the films are in more intimate contact and the absorption effect preponderates, the second-minute reading being then less than the first-minute reading. Heperiment 2.—In order to examine the change in resist- ance with change of voltage, using tinfoil electrodes, the experiment represented by Table II. was carried out. The dielectric was short-circuited for about one minute between each change of voltage. TABLE I1.— Tinfoil Electrodes. | | yi | Load in : : | grammes | Volts. a Wes oe: Wetee Megobms. | oft ohms. 1 min. 2 min. oS | per em. / En 150 2000 272 285 alo | 9 _ 3800 | 600 288 290 20°2 | i 450, HOO 424 426 aries | aes Panes Oe re) 200) B20 thaws S88 IEG 9 | 750 PANO 341 | 342 148 5 O00) S00 Wi so 300) 4) LOG » 450 500 442 443 jo LOG ae | 300 | 600 316 | ollig 18°4 x fe BO LOW 344 BAT 1 24a ae a 750 | 200 336 | 336 os 150 ie 2000 342 | 345 | 246 545 150 | 1000 334 334 fee Paige sf ie 300 400 306 304 | 13:0 ms | 450 | S007 304 302 | 12°8 ie GOO | 200 325 324 12 s | 750 140 292 291 172 c 600 | 200 326 O24 | 12-4 As 450 | 300 360 396 | 12°6 - 300 400 308 308 12°9 E 150 1000 346 345 13°6 = | 750 140 292 240 122 ‘ | 150 L000 348 347 Ales) | Contact with Dielectrics. AQT In the above table it should be observed that with the small load the first-minute readings are never greater than the second-minute readings ; and that the apparent resistance of the dielectric diminishes as the testing-voltage increases. With the greater load, the first-minute readings are never less than the second- iene readings, and although there is a diminution of resistance with increased voltage, the effect is far less marked than in the case of the small load. Increase of load is again seen to have a similar effect to imcrease of voltage. At the end of these tests the dielectric sheet was tested between mercury surfaces, proceeding exactly as when using tinfoil electrodes. ‘he results are shown in Table III. For this purpose the dielectric sheet is held in a vertical position symmetrically between two flat rings of ebonite, faced on each side with soft indiarubber. Disks of iron, forming in effect the jaws of a large ebonite vice, are then clamped one against the outer face of each ring. Mercury is poured into each of the hollow spaces between “the iron disks and the dielectric, through holes in the top of each disk. The temperature can be conveniently read by placing a ther- mometer in the mercury. TABLE III. Mercury Electrodes. Wolk Shunt, Deflexion, | Deflexion, isola ohims. Ls roar 2 min. = 150 700 325 329d 10°5 300 400 387 386 10°3 450 200 299 298 10-2 600 200 397 396 Oe 750 140 350 348 102 600 200 396 394 10°2 450 200 DOS. 2 10:2 300 400 | JOT 385 10°3 150 700 328 327 10°4 Tea Oar 140 348 345 10°3 150 | 700 330 328 10°3 This table renders it doubtful whether the true resistance of press-spahn varies greatly with the voltage, and it shows that the results obtained with tinfoil electrodes may be mis- leading when imperfect contact is interpreted as high re- sistance of the dielectric. In confirmation of the foregoing results, the sheet was left for a day, and was then tested again between mercury electrodes, the current being reversed as indicated in Table IV. 492 Mr. R. Appleyard on TABLE LY. Mercury Electrodes. | | Volts. | Shunt, | Deflexion, Deflexion, | | obms. | 1 min. Seine yt pelea e | | 6150.) 700%) aan 284 11:9 —150 , 700 | 294 294. | 116 O00 ie A000 342 | 335 | 11-6 | —3800 | 400 | 301 | 300 11:3 — +450 200 | 269 | 261 11:3 rae ADO e200 ia 2379 | 25 11-2 +600 200 | 30870 | SHIGE 113 Ls O00 200° | O04 | 360 | IML) | ee Ro i a yeleO et 319 | 317-5 11:2 _ —750 140 | B24 319 11:0 EGU0R I) 200%" 7 360°) | 305 et — 600 ZOO; a s0rD | 362°5 11:0 — +150 700 B03;0) 2 | 302 11-2 (een) TU 5 304 | 302 11-2 After leaving the sheet for four hours, it was again placed between the tinfoil electrodes, with the following result :— isn Vs Tinfoil Electrodes. Load in | ares | grammes Volts. Ce Bre Pelee Megohms. Aa Oi ms. min. 2 min. 22'3 +800 1000 459°5 466°5: |. 20:10 # — 300 1000 498 494 | des ” | +450 400 356 300°D) |) lo MY — 450 400 3775 380 Bee Oyo: 2: _ +600 200 291 286 Bera ees) 04 |} —600 | 200 292°5 293 | 1di9 bp | -+/750 200 398 384 Wee eee 5s pa ED 200 395 393 | aS 2 jo toboO 1000 232°5 232 |, 2032) hae 55 | —150 1000 217 212 | 2G ae 543 | —150 1000 408 408 10-0 1 1 SOD 100 249 246 10°3 if | —150 1000 423 422 | o7 The final three tests with the greater load were intended to indicate the true resistance, the current therefore was not reversed: they are seen to be fairly uniform, and they justify the use of tinfoil electrodes for rough tests where mercury cannot be obtained. The fact that these three values are all lower than those given with the mercury apparatus on the same afternoon (Table IV.) is probably accounted for by the 493 It was 1} cwts. Contact with Dielectrics. reduction of thickness due tu the heavy load. on a 53 inch disk. The next experiment was made with a view to testing the resistance with tinfoil electrodes, as nearly as possible under the same conditions as those adopted by Mr, Rayner. For this purpose the sheet was allowed to rest for 17} hours. It was then put into the apparatus, and the weights on the disk area of 153°3 cm.” were adjusted to give a mean load of 400 grammes percm.? Five minutes was then allowed, as in Mr. Rayner’s experiments, for the conditions to become steady, before applying the voltage. Only one minute was allowed between the successive voltages. The readings and results were as follows :— TABLE VI. Tinfoil Electrodes. | Walks | Shunt, Deflexion, Deflexion, Meeanee | ohms. 1 min. 2 min. Baume. +150 | 1000 | 266°5 266°5 176 +750 | 140 240°0 238:0 14:9 +150 1000 284°5 283°5 16°5 +750 | 140 237°0 235°5 15:0 The results are fairly uniform, but the diminution of re- sistance with increase of volts is still marked. For purposes of comparison, the dielectric sheet was fie immediately placed in the mercury apparatus, precisely the same way, with the following results :— TasLE VII, Mercury Electrodes. 150 1000 342 339 137 750 1400 | 259 255 138 150 1000 332 Soleoe Te] 750 10s 255 259-5 140 | | and tested in A comparison between Table VI. and Table VII. seems to indicate that although the tinfoil electrodes under a load of 400 grammes to the cm.”, and with an allowance of 5 minutes A494 - Mr. R. Appleyard on for settling e@ down, are brought into fair contact with the dielectric, the contact is not so perfect as when mercury is employed. It is curious to note here, as in all these ex- periments, that where tinfoil electrodes are used the resistance appears to decrease with the increase of voltage, whereas with mercury contact this effect practically vanishes. I have shown (Proc. Physical Soc. vol. xiii. p. 157, 1894) that with celluloid sheets between unyielding metal plates, the change of apparent resistance with voltage is remarkably great. ‘Tt is a matter of considerable impor ood in the study of dielec- trices, and I have purposely described the experiments in detail so as to endeavour to establish the fact that what is often called change of dielectric resistance with voltage is, as a rule, merely a "capa effect, and that it can be gre atly reduced, if not entirely eliminated, by ensuring perfect con- tact with the electrodes. Moreover, the effect is generally found associated with so-called “ negative electrification,”’ the second-minute reading being oreater than the first-minute reading. In order to see how little the true resistance is affected by abrupt changes of voltage, an examination may be made of Tables ILI. Nive ,and VII., where only one minute was allowed between angle change for pe dielectric to lose its charge. The residual effect can ie estimated by switching off the Caen at the end of a given minute, and immediately connecting the insulated electrodes through the galvanometer to earth. With fo) co) a view to avoiding too lengthy a table illustrating this, I have ao d calculated the values of [(deflexions) x (multiplying power of shunt) | in the following case, omitting shunts, and omitting megohms, from the tabulated figures. It may be stated, however, that the megohms, worked out from the Ist, 11th, 21st, 31st, Alst, and 51st mins ., are respectiv ely 43° 2, 42: 6, 42°3, 42:2, 42°0, and 41:7. The procedure was to apply the battery for 5 mins.,and at the end of the 5th minute to switch the battery out of circuit and connect the insulated electrode to earth through the galvanometer, taking earth-readings for five minutes. At the tenth minute the battery was reversed, and the same process was continued in a cycle of revers sals and earthings up to the 53rd minute. In the following table the reversals and earthings are sufficiently indicated by the sions of the ‘deflexions, and by the smallness of the earth- readings | in comparison. with the battery readings. The fall aiter Sch change of connexions was perfectly steady, and in no instanee was there anything approaching a rise after the deflexion corresponding to a given change had been recorded, On another day, after allowing the sheet to rest for 12 hours; Contact with Dielectrics. 495 a similar test was applied, using 150 volts. The resistance calculated from the lst min. (+) was 46°8 megohms. The resistance calculated from the 11th min. (—) was 46°5 megohms, a change of only 0°38 megohm against the change of 0°6 in the corresponding test with 750 volts. The earth- readings at the 6th min. and 16th min. were respectively —3°5 and +2, as against —10°5 and +7°5 with 750 volts. The earth-readings therefore are not directly proportional to the applied voltages originating them. TaBLEe VIII. Mercury Electrodes (750 volts). Min. Deflexion. || Min. Deflexion. | Min. | Deflexion. 1 +4630 |; 19 +3 36 Pio 2 +4589 20 +2 On = 5 3 +4548 21 +4721 38 +3:'5 4 4.4524 22 4.4679 39 Ee! 5 +4499 ae +4638 40 +2°5 6 —10°5 24 +4606 41 +4762 7 ad yA) +4565 42 +4729 8 —60 26 —9 43 +4696 9 —50 || 2 —6 44 +4655 10 45 28 —5 45 +462? EL — 4696 29 —+ 46 | —9 12 —4679 30 —3°5 AT | —6 13 ARRAY, acl —4737 Ae ult e5 14 — 4630 Ve igen, | —4713 49 | 4 15 —4606 i oe — 4696 30 —3°5 16 eri 34 — 4663 Near ch —4787 7 5 | aD — 4639 By) — 4762 18 +375 | 53 —4729 The maximum earth-reading is 10°5 with 750 volts. The effect of this residual charge upon subsequent readings is only 0:23 per cent.; or in terms of resistance say 0°1 of a megohm in the 42 megohms here concerned. In comparison with the effects of changes of humidity, it is probably negligible. The uniformity of the earth-readings in the above table is instruc- tive. The (+) current applied at the 1st min. strikes the dominant note, and gives an earth-reading which at the 6th min. is —10°5. At the 11th min. the (—) current is applied, and gives an earth-reading which at the 16th min. is +7°5, 1. €., d divisions less than the corresponding earth-current of the previous charge ; and we may assume that if the earth- current at the tenth minute had been allowed to act alone it would have fallen from —4°5 at the tenth to —3 at the sixteenth minute. At the 21st min. the (+) current is again applied; the corresponding earth-current at the 26th min. 496 Contact with Dielectrics. is —9. And it is seen, taking the readings at the 6th, 16th, 26th, 36th, and 46th min., that we obtain the sequence —10°5, +75, —9, +7°5, —9; a further indication that with mereury electrodes the apparatus conditions are trustworthy. These earth-readings were taken without a shunt, so that they are actual records of direct deflexions. Retentive Force—It seemed desirable to obtain positive evidence as to the magnitude of the retentive force between the tinfoil and the press-spahn, and to determine whether it was proportional to the voltage. For this purpose, a flat circular disk of gutta-percha, of the same size as the electrodes used in the foregoing experiments, was perforated over about half its surface with holes 1 cm. in diameter. A smooth sheet of thin tinfoil, not perforated, was attached to one side of this disk bya little chloroform. This arrangement allowed a certain amount of freedom of movement to the tinfoil, so that it could conform tv the surface of a sheet of press-spahn when placed in contact with it. The disk was then suspended above a sheet of press-spahn, in a horizontal plane, from the beam of a balance, and its weight was counterpoised. Beneath the sheet of press-spahn was a second sheet of tinfoil con- nected to earth, so that the combination formed a condenser, the upper electrode of which was thus in balanced contact with the dielectric. The weight necessary to counterpoise the disk was first determined with no voltage between the electrodes, and the weight necessary to relieve it from con- tact was then measured at successive voltages. Check read- ings of the weight, taken between the various applications of voltage, never exhibited a difference greater than 1 centi- gramme for the normal (no-voltage) counterpoise. If there was residual coherence, it was therefore very small. The readings in a characteristic case were :— TARE xe DP viaus Counterpoise. | Retentive ml Ratio of Ratio of ‘| Total grammes. grammes. /Retentive forces.) Volts. 0 2204 0 0 0 750 72:00 52 104 5 ORE, 22°04 0 0 0 600 | 50°00 28 D6 4 450 25-00 3 6 3 300 | 23°00 1 2 2 SOR 22°50 5) 1 1 300 23:00 1 2 2 450 | 25°00 3 6 3 Rival QUEM ee 49°00 27 a4 4 a gool 7a! 66°00 44 &8 5 Dewar’s Method of producing High Vacua. 497 The retentive force between the tinfoil and the press- spahn increases far more rapidly than the voltage, the contact must therefore be more perfect with the higher voltage; this accounts in some measure for the changes of apparent dielec- tric-resistance with voltage shown in Tables If. and V. It is possible that a similar effect may account for small dif- ferences of capacity observed with different voltage with some tinfoil condensers, and it may also serve to explain to some extent certain abnormal “ electrifications’’ with cables, where for any reason there is imperfect contact between the con- ductor and the dielectric. LVII. Dewar’s Method of producing High Vacua. By Lord Buytuswoop, LL.D., and H. 8. Atuen, M.A., B.Sc.* § 1. | i has long been known that charcoal, freed from gas by heating to redness, is capable of ‘absorbing ¢ gases in large quantities. The subject was first investigated by Saussure, and a detailed examination of this property of charcoal was made by Hunter (Phil. Mag. [4] vol. xxv. p. 364, 1863, & xxix. p.116, 1865). Ofall the charcoals he examined, that made from the cocoanut had by far the greatest absorb- ing power, one volume of the charcoal : absorbing 1717 volumes of ammonia, 17-9 of oxygen, 15°2 of nitrogen, and 4°4 of hydrogen. In 1875 Professor Dewar employed this property of charcoal to improve the vacuum in a vessel exhausted by amercury-pump. His recent discovery that when the char- coal is cooled to the low temperatures now available it is capable of absorbing still larger quantities of gas, is of great importance. This result promises to be of the greatest service in scientific research, and it is even possible that it may have important commercial applications. § 2. Sir James Dewar has described experiments to test the amount of exhaustien reached by the use of a given weight of cocoanut charcoal. He found that 30 grams, cooled to the temperature of liquid air, absorbed so much air that the pressure in an electric-discharge tube of 1300 ¢.c. capacity fell from 760 to 50 mm. of mercury. Starting with the tube initially ig Jee ea) atmosphere, the exhaustion reached was now beyond the striz stage. A further experiment, starting with one-fourth of an atmosphere, gave a vacuum through which no discharge passed. * Communicated by the Authors. A preliminary account of some of the experiments described below has been given by one of us in a paper a before the Royal Philosophical Society of Glasgow, March 22nd, + Proc. ca Soc. lxxiv. pp. 122-131 (1904). Eile Mage S0n Vole VO. Noy.55.. Oct. 1905, 2M 498 Lord Blythswood and Mr. H. 8. Allen on §3. Experimeuts carried out by the Authors show that it is only necessary to increase the size of the charcoal receptacle in order to produce a high degree of exhaustion in a large discharge-tube without the use ofa pump. The first attempt made (Jan. 30, 1905) was to exhaust an old X-ray bulb, three inches in diameter (capacity 250 ¢.c.). This was attached to a drying-tube containing phosphorus pentoxide, and to a bulb of capacity 200 ¢.c. containing about 65 grams of charcoal*. The apparatus was set aside for some days before it was used so that the air might be dried. Before the charcoal bulb was’ cooled, both it and the discharge-tube were heated strongly to drive off as much gas as possible. The apparatus was then sealed, and when the charcoal bulb was sufficiently cool it was placed in liquid air. During the process of exhaustion the focus tube was heated, and during the later stages the discharge was passed through the iube to drive off gas from the electrodes. The tube was sealed off after the charcoal had been cooled for one hour, and the vacuum produced was so good that the tube had to be heated in order to allow the discharge to pass through it. A second focus tube, four inches in diameter (capacity 675 c.c.), was successfully exhausted with the same charcoal bulb (Jan. 31). § 4. In the next experiment the drying-tube was. discarded altogether, and a new X-ray bulb, five inches in diameter (capacity 1150 e.c.), was attached to the charcoal absorber (fig. 1). The following notes show the progress of the exhaustion :—- 11.25 a.m. Commenced to heat discharge-tube and charcoal. 11.85. Apparatus sealed. 11.45. Charcoal bulb placed in liquid air. HES 0; Discharge begins to pass. 12 noon. Both electrodes covered with a velvet glow. 12.7 p.m. Discharge fills the whole bulb. 12.9. Some green fluorescence. IMAIPA Shadow of the electredes thrown on the tube by cathode rays. 12.30. X-rays beginning. 12.50. Discharge-tube sealed off. The result of this experiment was a somewhat “ soft” X-ray tube. Several similar X-ray tubes were exhausted, and exhibited the same succession of changes at practically the same time * The charcoal used in the experiments we have carried out was of two kinds, the first made from lgnum vite, the second from the shell of the cocoanut. The material was packed into an iron pot closed with a lid provided with a small vent hole, and was heated in a yas furnace for some hours. Dewar’s Method of producing High Vacua. 499 Fig. 1. from the beginning of the experiment. The amount of liquid air used in the course of the exhaustion was determined by weighing the flask in whieh it was stored at the commence- ment and conclusion. ‘Two distinct experiments with the charcoal receptacle already described gave 340 grams and 295 grams as the amount of liquid air evaporated in exhaust- ing a five-inch bulb. About 800 grams of liquid air were required to cover the charcoal absorber, which was placed in a cylindrical Dewar’s vessel 10 centimetres in diameter. §5. Another experiment with a larger absorber, of 550 e.c. capacity, containing 216 grams of charcoal, gave penetrating X-rays after the charcoal had been cooled for an hour and a 2M 2 : 500 Lord Blythswood and Mr. H. 8. Allen on half in liquid air. In this case 420 grams of liquid were evaporated, but the amount required to cover the bulb at the outset was only 570 grams. § 6. In order to obtain a still higher vacuum in a large discharge-tube without the use of a pump, two charcoal receptacles were employed. At first No. 1 was cooled in liquid air, whilst No. 2 was strongly heated to drive off as much gas as possible. Then No. 1 was sealed off with the blowpipe, and No. 2 was cooled. One hour was devoted to each operation. After the X-ray tube was sealed off and had been allowed to cool, it was found that the discharge from a large induction- coil would pass across a five-inch “spark-gap rather than go through the tube. § 7. These experiments show that it is practically possible to apply Dewar’s method to the exhaustion of large receivers, and that this method requires but a moderate amount of liquid air. It is particularly useful when it is desirable to avoid the presence of mercury vapour in the vacuum-tube, as in Geissler tubes for spectroscopic analysis. It is possible to dispense with drying-tubes, though this procedure is not recommended in general as the charcoal is rendered less efficient for subsequent work. ‘The method is a rapid one, and a further recommendation to the amateur glass-blower 1s the simplicity of the apparatus required. EXPERIMENTS TO DETERMINE THE AMOUNT AND RATE OF ABSORPTION OF AIR BY CHARCOAL COOLED TO THE TEMPERATURE OF LIQuID AIR. (i.) Absorption by Charcoal in Presence of an acess of Air. § 8. A number of experiments were carried out to find the absorption by charcoal in the presence of a volume of air greater than the charcoal could absorb when cooled to the temperature of liquid air. A small quantity (2 grams) of charcoal was placed ina glass bulb in communication pie a barometer-tube. Glass veal of known volume could be attached to the apparatus in order to determine the effect of altering the initial volume of air experimented upon. Let v denote the volume of the bulb which is cooled to the temperature of liquid air, V denote the volume of the connecting tubes and the attached vessel. Initially we have a volume V+v at pressure P and tem- perature T. Suppose that when the small bulb is cooled to a temperature ¢, without any charcoal in it, the pressure in the apparatus is petted to p’. Dewar’s Method of producing High Vacua. DOL Then we have a volume V at pressure p’ and temperature T, and a volume v at pressure p’ and temperature ¢. So that V p a (V+o")E =Vte. ey ane pares te) When the bulb contains charcoal the final pressure reached will be less than when it contains air, in consequence of the absorption of air by charcoal. Denote this pressure by p. Then the volume of air not absorbed by the charcoal (measared at pressure P and temperature I’) is | =(V+ 7 from ‘(i.) Therefore the volume of air absorbed by the charcoal =(V+o)(1-%), Deer koi) $9. The following table gives the results of experiments carried out in this way :— TABLE I. Total Volume. ; Volume of Air | Vt+u. Je P- "| absorbed by Charcoal. 1 Oa 33°95 CC. 393 mm. | 180 min. 18:1 c.c. ITPA Teed BRowronep 520 mm. | 3886 mm. 18:2 c.e. TSBs 93-4 ¢.c. 558 mm. | 428 mm. 217 ce. EVirss 125°0 c.c. 598 mm. | 495 mm. 21:5 e.c. Vite: 674:0 c.c. 726 mm. | 702 mm. 22°3 c.c. The figures in the last column show that the volume of air absorbed by the charcoal is, to a first approximation, independ- | . ent of the quantity of air present in the apparatus at the commencement of the experiment. The small ditferences observed in the figures giving the amount of air absorbed may be attributed to the influence of pressure*. In accordance with the principle of Least Action the effect of raising the pressure is to make the reaction take * Mellor, ‘ Chemical Statics and Dynamics,’ p. 435. 502 Lord Blythswood and Mr. H. 8. Allen on place in that direction which is accompanied by a decrease in volume, that is in this case to increase the volume of air absorbed. § 10. For comparison with these results, the amount of air absorbed by the charcoal at atmospheric pressure was deter- mined by direct experiment. The charcoal bulb was immersed in liquid air for six minutes, as it was considered that this time was long enough for the charcoal to absorb its full supply of air from the atmosphere. ‘The bulb was then allowed to regain the temperature of the room, and the air expelled was collected over water in an inverted burette. The mean of three readings gave 69°3 ¢.c. as the total volume. A blank experiment was then carried out without the charcoal. The mean of three readings was 41°2.c.c. The difference, 28'1 ¢.c., gives the volume of air absorbed by 2 grams of charcoal when cooled to the temperature of liquid air*. $11. Observations were made with the apparatus already described to determine the rate at which air was absorbed by the charcoal. Readings of the height of the mercury column were taken at intervals of a quarter of a minute. For one minute after the application of the liquid air. the readings were irregular in consequence of the cooling of the bulb, but at the end of that time the liquid air had ceased to boil violently, and regular readings could be obtained. The mercury in the barometer-tube reached a steady height within from six to ten minutes after the commencement of the experiment. The readings obtained in Experiment No. 1 are given in the following table (Table II.) :— TABLE II. | ineyt 1. | 1c) ap! 18. | 2, | 28.) 25. |) 234) 8.9) 84), 28. | 32.1 eee Free: 400 | 440 | 475 | 500| 520 | 535 | 546 | 556/565 | 571| 575/580 583] 593 Dursses2| 873 | 382 | 298 | 273 | 253 | 288 | 227 | 217] 208! 202! 198} 193/190] 180 p—po...'193}153|118) 93| 73| 58| 47| 37| 28] 22/ 18] 13] 10 * This result illustrates a point frequently observed in the course of these experiments. If the charcoal is left exposed to the atmosphere it rapidly deteriorates in its capacity for absorbing air, probably through the absorption of moisture. In an experiment made eight weeks previously over 100 c.c. of air were collected from the same bulb. The power of absorption may be partially restored by heating the charcoal, and driving off the condensed moisture, but it appears never to regain its original value. Charcoal bulbs intended for the exhaustion of vacuum tubes should always be kept sealed when not in use, Dewars Method of producing High Vacua. 503 The readings in the first row (¢) give the time in minutes from the first ‘application of the liquid air, those in the second row (fh) the height in millimetres of the mercury in the gauge. The values in the third row (p) are obtained by subtracting the figures in the second row from 773, the atmospheric pressure in millimetres of mercury. In the last row are the values of p—vp,, the excess of the pressure at any instant over the final pressure. These last figures were plotted as ordinates on semi- logarithmic paper, with the corresponding values of the time as abscissse (fig. 2, p. 504). It was then found that the points lay ona straight line, showing that the pressure was connected with the time by the relation los (pp) =A=M, a ss GR) where X is a constant whose value in this experiment is 0°428. _ Similar results were obtained in the experiments numbered Z,3,&4. It is not necessary to give in full the readings in ie cases. as they are represented in the diagrams (fig. 2), and the results in all four cases are summarized in Table III. The values of X were found from the inclination to the axes of the straight lines in the diagrams. It will be noticed that the value of 2 is approximately the same in each 1 experiment, the mean value being 0°406. TABLE ILI. Reading Reading Final Initial after 1 min. | after 4 min. Reading. nitia g X Volume. bE Wop ie pp. Pre af 30°5 @.e at 400 193 bso 10 593 180 | 2°714|-428 ZAS 126 | 330-| 14 344 | 428 | 2-480 |380 Bs) 70:S.6.c at PaO) L3G") old g 385 | 3886 | 2°555 |-421 | NG ashes LIZ) 265) |. £2 277 | 495 | 2-443 |-394 J h=height of mercury column in mm. p=pressure In apparatus in mm. » H. 8. Allen on Lord Blythswood and Mr o04 “FYUNSSIA DWYIHISOWLY LY YI 10 NOlLdOSEY @ | V Y “NIW NIWO “NIW { ‘qwoony) hg up 0 Al oN @ “NIN 2 NIN | uoyduosgp fo ajynar Dewars Method of producing High Vacna. 505 §12. In all the experiments which have been described, the relation between the pressure in the enclosed s}:ace and the time since the commencement of the absorption is given by the formula log (p—po)=A—AE. : a ae at tte ge AV.) But we have already seen that the volume of air absorbed by the charcoal (which we may denote by «) By differentiation where V’ is the total volume of the exhausted space. So that the rate at which air is absorbed by the charcoal is daz ____V'dp Oe pat Vx = yp (Pp—Po) SSNs ay hata ety Lia! Gs de Ve) where £ is the amount of air absorbed when equilibrium 1s established. § 13. An experiment was also made with the same saimple of charcoal used in Experiments Nos. 1-5, in order to determine the rate of absorption of air at constant (atmospheric) pressure. For this purpose the bulb containing the charcoal was connected through a T-piece with the stopcock of a burette, inverted over water. During the preliminary cooling of the bulb, which lasted three-quarters of a minute, the third limb of the T-piece — was left open to the external air. At the end of this time the aperture was closed and the charcoal commenced to absorb the air in the burette. Readings of the volume of air absorbed were taken every 15 seconds, the pressure exerted by the column of water in the burette being neglected. The observed volumes were subtracted from the final reading obtained when the absorption was complete, and the resulting values (repre- senting the volume of air still to be absorbed before equilibrium is established) were plotted on semi-logarithmic paper with the corresponding times as abscisse. The points were found to fall ona straight line, showing that log (E—w) is connected with ¢ by a linear equation. On differentiation we obtain as before dx , The value of X in this case is 0°380. 506 Lord Blythswood and Mr. H. 8. Allen on TABLE IV. é(mums.) 2: .) 7 13 13 12 2 22 25 £—w#(cc.) ..| 23° | 19-2 15:5 | 12°4 9°9 79 6:2 Re RO ae DAS 31 | 88 33. | 4 4h GENE Iie esinone 5:0 4:0 33 2°6 21 lor 1-5 The results are plotted in fig. 2. § 14. This value for A is very nearly the same as the vale found in the previous experiments in which the pressure altered as the absorption proceeded. The constancy in the value of leads to the important conclusion that, within the range of the observations, the rate of absorption is practically independent of the pressure. The rate of absorption will be different for different samples of charcoal, and there is a wide field awaiting Investigation in the determination of this constant for various kinds of charcoal, and what is more important the determination of the rate of absorption of pure gases by a particular sample of charcoal. (ii.) Absorption of a Linuted Volume of Air by a large quantity of Charcoal. § 15. In order to trace the course of the absorption at low pressures, a charcoal bulb was sealed to a McLeod gauge and barometer-tube. The capacity of the McLeod gauge was 232-4 c.c., the capillary portion being 10 cm. long and haying a capacity 0°125 ¢e.c. The internal volume of fie barometer- tube and the connecting tubes was estimated at 142 c.c. The charcoal bulb first used contained about 65 grams of charcoal, its volume being 200 c.e. The vessel containing liquid air was brought up underneath the charcoal bulb and gradually raised until the whole was immersed. This process generally occupied about two minutes. At the end of this time, readings of the height of the mereury column were eouimeneenl and noted at every hulf minute, until the motion became too slow to give trust- worthy results. In ten minutes the difference between the height of this column and that of the barometer was less The one millimetre. No readings of the McLeod 0 gauge could be obtained until about haif an hour after the commencement of the experiment. Dewar’s Method of producing High Vacua. D07 As soon as the mercury could be got to enter the capillary of this gauge (corresponding to a pressure of about ‘08 mm.) readings were taken every five minutes. The process of filling the gauge with mercury, taking the reading, and emptying it again occupied almost exactly a minute. During this interval of time, the air contained in the gauge was cut off from communication with the charcoal. § 16. The results obtained with this absorber are recorded in Table V. TABLE V. Charcoal Bulb containing 65 gms. of Charcoal. Values of X. Tnitial Final Pressure. _| Pressure. Baro- | wieLeod meter. PMU MESH ya |oc he)! mone ciate ices sea 763—153 mm. | ‘0109 | -258 | 0468 =610 mm. April 10th...| Charcoal bulb had been |757—380 mm. | ‘0163 | ‘863 | -0476 strongly heated. =3/77 mm. April 12th...| P,O; drying-tube inserted. |766—403 mm. | ‘0214 | ‘315 | -0467 Charcoal bulb again heated. =363 mm. The figures in the first two columns show the pressure in the apparatus at the commencement and at the conclusion of the experiment. It is noteworthy that the final pressure attained is greater each time the charcoal is used, illustrating the deterioration that takes place when the charcoal is ex- posed to a damp atmosphere even though the exposure is of short duration. § 17. The pressures in the apparatus, as determined by the height of the mercury in the barometer-tube, were plotted on semi-logarithmic paper with the times as abscissee, and the resulting curve was found to approximate very closely to a straight line. The pressure at any ipstant may accordingly be represented by the formula loop — A — Nb, which is of the same form as that already found (iii.), being now so small that it may be neglected in comparison with p. The values of X from these experiments are given in the Table in the last column but one. The pressures recorded by the McLeod gauge were treated ina similar manner, but in this case py can no longer be 508 Lord Biythswood and Mr. H. 8. Allen on neglected. Consequently the relation between the pressure and the time must be expressed by the more general equa- tion (ili.). This was found to agree well with the experi- mental results. The values of X are given in the last column of the Table. § 18. It will be observed that the rate of absorption (as measured by 2) is about eight times as large in the earlier portion of the experiment as it is in the later part, when the value is deduced from the readings of the Mcleod gauge. If we compare the pressures under which the absorption is taking place, we find an immensely greater ditference. In the first part of the experiment, the pressure is of the order of 200 mm., in the second part it averages only 04 mm., so that while the ratio of the pressures is of the order of 5000 to 1, the ratio of the corresponding values of 2 is only about 8 to 1. This result emphasizes the conclusion arrived at from the experiments formerly described, that the rate at which ab- sorption of gas takes place is influenced to only a very slight extent by the pressure of the gas. $19. It must be remembered that in the experiments de- scribed we are dealing with a mixture of gases, so that. the results are more complicated than they would be if we had to do with a pure gas. Dewar®* has shown that one cubic centi- metre of cocoanut charcoal can absorb 155 ¢.c. of nitrogen, or 230 c.c. of oxygen at a temperature of —185° C. Con- sequently, in the present set of experiments the percentage of nitrogen in the unabsorbed gas will increase as the absorption proceeds, so that the velocity coefficient deduced will not be constant. Both the alteration in the composition of tle gaseous mixture and the effect of diminution of pressure on the velocity, will tend to give a smaller coetticient of velocity as the experiment advances. 7 | § 20. Three separate experiments were carried out with the large charcoal receptacle already referred to (§ 5) sealed to the Mcleod gauge. By means of a Fleuss pump the whole apparatus was exhausted uatil the mercury stood at 740 mm., the barometric height being 780 mm. After the charcoal had been cooled to the temperature of liyuid air, the pressure in the apparatus fell for over three hours ; the tinal pressure registered being ‘(0009 mm. ‘The readings of the McLeod gauge obtained in experiments on three consecutive days showed remarkable agreement, and it has been thought worth while to tabulate these not only to illustrate the regularity of the absorption, but also to strengthen the confidence that may be placed in the readings of the gauge (Table VI.). * Proc. Roy. Soc. Ixxiv. p. 124 (1904). Dewar’s Method of producing High Vacua. 509 TaBLE VI. Experiment with McLeod Gauge. po=*0009 mm. t Values of p—p,. t | | mins. April 18th. | April 19th. | April 20th. } Mean. 0 0271 (0295 0271 | 0279 5 0192 ‘0185 ‘0179 = ||, = 0185 10 ‘0131 ‘0131 ‘Olz1 | 0128 15 0100 ‘0086 ‘0081 | 70039 20 ‘0069 ‘0061 0061 | ‘O04 25 0053 ‘0046 0046 ~=—s||_—=S 0048 30 0040 | ‘0033 0040 = || — 0038 35 ‘U031 0026 ‘0027 | 0028 4) 028° |. *-Q022 (0022) |i -0024 4d ‘YU2D “OO19 ‘O0L8 00 20 50 ae | ‘OULG ‘Q016 ‘O16 § 21. The mean values of p—po have been plotted as ordi- nates, with the corresponding values of the time as abscissz in fig. 3,p.510. It will be seen that the points so obtained fall approximately on a straight line, so that in this case also the relation between the pressure and the time is of the form log (p—po) =A—At. The value of » in the equation is ‘0245. TABLE VII. Ce oe Bulb containing 216 ems. of Charcoal. eS SE a a re a a a Values of A, Initial Final Pressure. Pressure.’ Baro" | MeLeod. ineter. April 17th.| New bulb attached, strongly | heated and sealed. | PACE UL LORE AFORE. 10. Uramede- cence oe sane = -780—603 min. | 0095 | °313 teal =177 mim. Afternoon. Exhaust appa- 7°0—740 mm. Mean of ratus with Fleuss pump. =40 mm. three ANTo AUIS (THO aie | ee Benen ae 780—768 mm. | ‘0009 "0245 ane = 12mm: April 20th. SS eae See ee 777—763 mm. | ‘0009 =14 mm. April 21st.| Let in air to atmospheric |775— Omm. | -0093 | -220 > pressure. =775 mm | Mein of April 22nd} Mercury stands at ............ 783—136 mm. | ...... \. two =647 mm. (OG May Sth. | Apparatus left sealed since |785—155 mm. | -0097 | -206 | J April 22nd. = 680 im. | SIKO) Lord Blythswood and Mr. H. 8. Allen on § 22. Two experiments were made with the same absorber starting from a pressure that was nearly atmospheric. The results of these and the former experiments are summarized FRessure i MILLIMETERS OF MERCURY. (M4°LeE0D GAUGE) Fig. 3. -0030 0020 0010 5 10 15 20 9) 30 35 40 45 50 Time IN MINUTES. Rate of Absorption of Air by Charcoal. Experiment with McLeod Gauge. in Table VII. and in figs. 3 and 4; and it is unnecessary to enlarge upon them. We need only note that the rate of absorption is practically constant, and that the final pressure Dewars Method of producing High Vacua. 511 attained is ten times as great as that reached in the experi- ments in which the apparatus was first of all exhausted by Fig. 4, 300 ae) rosa Ea 200 20 10 | 2 3 4 5 6 7 SAME] 0 Rate of Absorption of Air by Charcoal (April 21st). PRESSURE IN MILLIMETERS w & § TIME IN MINUTES. means of the Fleuss pump. The latter result has an im- portant practical application, for it shows that if we desire to obtain the best possible vacuum in any vessel, the vessel 512 Dewars Method of producing High Vacua. with its attached charcoal absorber should be exhausted to as high a degree as possible before the charcoal is cooled to the temperature of liquid air. § 23. Reviewing the results so far obtained, we see that they may all be included in a relation of the form given in equa- tion (v.). This expresses the fact that the rate of absorption is proportional to the difference between the total amount of air absorbed and the amount which has been absorbed at the instant in question. In other words, the rate of absorption stands in a constant ratio to the quantity of air that will still be taken up by the charcoal. The constant is bunt little affected by alterations in the pressure under which the absorption takes place. » The simplest explanation of the result appears to be to consider each element of the charcoal (probably a superficial rather than a volume element) capable of taking up a definite amount of gas. When the element has received this quantity it becomes useless so far as further absorption is concerne 1. On this hypothesis it follows that a given sample of charcoal ean absorb a definite amount of gas, the amount being inde- pendent (or almost independent) of the pressure. Moreover, the rate at which the absorption is proceeding at any instant will be proportional to the number of elements which have not yet taken up their quantum of gas; that is to say, to the quantity of gas that the charcoal is still capable of absorbing. This hypothesis is sufficient to account for the facts observed in the simpler cases, but it may require some modification when we are dealing with a limited quantity of air. For we know that in this case the whole of the air is not absorbed by the charcoal, but the pressure tends to a definite limiting value. | | | It is to be expected that further light would be thrown on the value of this limiting pressure, by a study of the absorp- tion of pure gases by charcoal. In the case of air, the residual pressure is due to some considerable extent to the less easily absorbed gases, hydrogen, neon, and helium. Consequently, if an extremely high vacuum is required, it is advisable to remove as large a proportiun of these gases as possible by a preliminary exhaustion. Blythswood Laboratory, Renfrew. * In the experiment made on April 12th (Table V.) the final pressure recorded was not altered by keeping the charcoal bulb in liquid air for a further period of three and a half hours. Red. Vere, 3, Green. ABS. MAG. Ro. RPE RTRNPE TNT HRT Rr rrr T ETE et 4837 Phil. Mag. Ser. 6, Vol. 10, Pl. V. 7 Didi Absorption Mag. Rotation. Mag. Rotation. Absorption. eee (4 eae + J y WN, ‘ if i, v , Ss - \ ‘ ‘ a ‘ . 1 ‘ ‘ » I 7 . Phil. Mag. Ser. 6, Vol, 10, Pl. V. ~ ~ 3 =~ = is) > iS) te = Low! = ~ : 2 3 e : i a . G E : o : 5 > E : : = | & i : S ay ee} ce > Ons Go 2 a p 5) Absorption Mag. Rotation. Mag. Rotation. Absorption. Phil. Mag. Ser. 6, Vol. 10, Pl. VI. 18S, des Fig, 2. Fig. 3. Tie. 4. = ~ . & - + ‘eh - ys on tl om t 2 a y ti - * ay aioe + & PY é 4 " io : % + ~ te ae e%., = > 2 f . ? ws - ra . - + . Sail 7% bs x 4 * 1 See = s = ‘ , : 3 : i a - iar Saat : >a = ee so" f Sei aides me Sy i = oy ee nr : hs td 2 t y INDE TTR, INDEAED. A hye 3 LONDON, EDINBURGH, ayp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SIXTH SERIES.] NOVEMBER 1905. LVI. The Fluorescence of Sodium Vapour and the Reso- nance Radiation of Electrens. By R. W. Woon, Professor of Experimental Physics, Johns Hopkins University *. (Plate VIL] ly the modern theories of absorption we find frequent use made of the conception of a re-emission of radiant energy by an electron which is vibrating in unison with the incident light-waves. The emitted energy should, however, be of the . same wave-length as that of the exciting waves, ead while we have plenty of examples of photoluminescence, it seems probable that in these cases the phenomenon is extremely complicated, for the emitted radiation consists of a hetero- geneous mass of waves, usually of slower period than that of the incident light. Repeated efforts have been made by various investigators to detect a-lateral emission of yellow light by sodium vapour when in the act of absorbing sodium light. These efforts have been unsuccessful for reasons which will be presently given. ‘The phenomenon has at last been observed: a dense mass of non-luminous sodium vapour radiating a brilliant yellow light when illuminated by the light from a very intense sodium flame. The same pheno- menon has been observed in the region of the channelled absorption ; in this case, however, radiations of other wave- lengths are emitted, as well as those of the same period as that of the exciting light. This seems, to be the first case found of the phenomenon, which it may perhaps be well to * Communicated by the Physical Society: read June 30, 1905. Pinl.-Mag- S. 6. Vol. 10. No. 59. Now. 1905. 2N S14 Prof. Wood on the Fluorescence of Sodium Vapour style resonance radiation, to distinguish it from fluorescence. The intimate connexion between fluorescence and phospho- rescence, and the almost indisputable evidence that the latter phenomenon is associated with chemical changes produced in the substance, makes it appear probable that fluorescence and resonance radiation are two entirely different phenomena, though the former is doubtless caused in some roundabout way by resonance. In the present paper, however, I shall, for convenience, ‘use the term fluorescence, though we may eventually have to distinguish between fluorescence spectra and resonance spectra. The very remarkable fact has been ascertained that the stimulation of the vapour with approximately monochromatic light, furnished by the monochromatic illuminator (spectro- scope), results in the emission of light, the spectrum of which consists of a number of more or less reoularly spaced bright lines of different intensities. The slightest change in the wave-length of the exciting ight results in the disappearance of these lines, and the appearance of another set ; the pheno- menon indicating that the molecule contains a number of groups of electrons, the excitation of any one of which sets the entire group in vibration, without however disturbing the other groups. As the wave-length of the exciting light is slowly changed, the fluorescent spectrum presents a most remarkable appearance. The lines appear in rapid motion, the luminous bands moving in a rippling manner, like moon- light on water. ‘The motion is of course an illusion, due to the continual disappearance and reappearance of the bright lines, the phenomenon reminding one forcibly of the scintil- lations produced on a screen of zinc sulphide by the electron bombardment produced by radium. In the earlier work on the fluorescence of the vapour, carried on by the author in collaboration with Dr. Moore, the metal was vaporized in a tube of seamless steel. Owing to the distillation of the metal to the cooler parts of the tube, it was necessary to open the tube and introduce a fresh charge after two hours’ heating. This was a great gain on the exhausted glass bulbs used by Wiedemann and Schmidt, which blackened, and became useless in half a minute or i but something better was obviously necessary for the large number of long exposures necessary for a careful study of the remarkable changes in the fluorescence spectrum, which accompanied changes in the wave-length of the exciting light. For purposes of demonstration a plain tube of steel, or even brass, is all that is required. Steel is preferable, for and the Resonance Radiation of Electrons. 515 it is probable that the sodium would eventually eat its way through brass. The latter metal can, however, be used if a large steel tube cannot be procured. The tube should be 2 or 3 inches in diameter and about 2 feet long. A small piece of brass tubing is brazed into one end, through which the tube can be exhausted to a pressure of a few millimetres, for it is only at low pressures that a fluorescence of any brilliancy can be obtained. A piece of clean sodium, obtained by melting the metal in a crucible and pouring it out on a plate, is introduced into the tube, and the ends closed with » plate glass, cemented on with sealing-wax. One window should be attached before the introduction of the sodium. ‘The following method gives the best results:—Heat the end of the tube and apply the melted sealing-wax smoothly to the rim, building it up to a depth of about 2 mms. Stand the tube on end, heat the glass plate, wave the flame over the wax until the surface melts, and then immediately apply the plate. The wax must be in optical contact with the metal and the glass, otherwise the joint is sure to leak. It is a good plan to go around the joint with a very minute pointed gas-flame, heating the wax until it runs freely over the surfaces. A mercurial or mechanical pump can be used for the exhaustion. If the pump leaks ever so slightly, a glass stopcock should be put between it and the tube, and all the joints made of glass and sealing-wax. With a little practice the whole apparatus can be set up in fifteen minutes ; and the tube, once prepared, can be put away for future demonstrations, care being taken to close it hermetically with wax. Sun or arc-light is focussed in a slightly oblique direction, by means of a lens, directly over the lump of sodium, which should be brought to the centre of the tube. On heating the tube, the brilliant spot of green fluorescent light can be observed through the opposite end, care being taken to keep the eye out of the emergent beam of white light. Tubes of this description, while perfectly satisfactory for demonstration, are unsuitable for long continued spectroscopic study, and various devices were accordingly tried. The apparatus in its final form consisted of a seamless tube of thin steel 3 inches in diameter and 30 inches long, with a steel retort at its centre in which a large amount of sodium could be stored. The retort was made by fitting two circular disks of steel to a short piece of tubing, just large enough to slip snugly into the larger tube. ‘The circular ends of the retort were provided with oval apertures as shown in fig. 1 (p. 517). The retort was half filled with sodium, the molten 2N 2 516 Prof. Wood on the Fluorescence of Sodium Vapour metal being poured in through one of the apertures. It was then introduced into the tube and pushed down to the centre, after which the plate-glass ends were cemented on as shown in the figure. This arrangement prevented the rapid diffu- sion of the vapour, and enabled a large supply of metal to be kept at the centre of the tube. The tubes used in the earlier work required re-charging after two hours’ continuous operation, while the retort-iube could be operated for several hundred hours on a single charge. The illuminating beam was focussed just inside one of the oval apertures in the retort, being received by the opposite wall just to one side of the other aperture. The end of the large tube was covered with a black cloth, by which device it was possible to view the fluorescent spot against the dead- black background of the second aperture. | A large three-prism spectrograph was constructed for photographing the spectra. The prisms were of clear dense flint 4 inches in height, and the focal length of the lenses 36 inches, The monochromatic illuminator, which furnished the ap- proximately homogeneous light by which the fluorescence was provoked, was arranged as shown in fig. 2. A small strip of silvered glass 2 mm. wide was mounted in front of the second slit of the instrument, by which the emergent beam was thrown into the sodium tube. By means of a split lens the lght was focussed upon the aperture, and an image of the fluorescent spot thrown upon the siit of the spectrograph. It was found necessary to split the lens and separate the two halves a trifle, as otherwise the image of the fluorescent spot was thrown back upon the small mirror. The arrangement figured was found to be the only one capable of yielding an image of the fluorescent spot upon an - absolutely black background. It was extremely important to accomplish this, as otherwise it would have been im- possible to ascertain whether or not the fluorescent light contained the same wave-lengths as the exciting light. For the same reason it was important to get rid of all traces of floating particies of oxide. These gave a good deal of trouble in the earlier work, but in the new tube it was found that after a half-hour’s operation all trace of them disappeared. To prove the purity of the atmosphere in the tube and the blackness of the background, it was only necessary to adjust the prisms of the monochromatic illuminator for some wayve- length incapable of exciting fluorescence. The brightest part of the spectrum in the yellow region, not far below the sodium lines, answered the purpose admirably. and the Resonance Radiation of Electrons. 517 By means of two right-angled prisms it was possible to substitute a powerful beam of sunlight for the mono- chromatic beam, by which the spectrum of the fluorescence provoked by white light could be easily photographed or observed. tS Y Joz2wounly OL With white light illumination the fluorescence spectrum is made up of a large number of hazy lines, which in the vellow and yellow-green region are arranged in groups or 518 Prof. Wood on the Fluorescence of Sodium Vapour bands, which lie close together in the vicinity of the D lines, ‘widening, however, as the blue region is approached. Coincident with the D lines there appears a hazy band, the surrounding region being nearly devoid of light, which, if the vapour is not too dense, can be resolved into a double line, the components of which coincide with D, and Ds. These lines only appear when the vapour is stimulated with light of the wave-length of the sodium lines, z.e. the fluor- escent light can be regarded as an emission of light by the electrons, in virtue of the vibrations excited by the incident light. This was proven in two ways: first, by illuminating the vapour with the light of a very intense sodium flame, which provoked a bright yellow fluorescence; secondly, by illuminating it with light from a spectroscope, and varying the wave-length continuously. The yellow band only appeared when the spectroscope furnished light of the wave- lengths of the D lines. Further work, it is hoped, will show whether the D, vibration is independent of that giving rise to D,. To solve this interesting question, it will be necessary to illuminate the vapour with the light of D, only, and ascertain whether both lines are present or not in the fluores- cent spectrum, a difficult observation, but one which can doubtless be made. ‘There is in addition a red fluorescence, the spectrum cf which Wiedemann and Schmidt believed to be devoid of bands or lines. This, however, is not the case, for the spectrum in the red was found to be crossed by a large number of dark bands. They are much more difficult ve observe than the green bands, and are only very conspicuous when the density of the vapour is considerable, which accounts for their having been overlooked previously. The general appearance of the fluorescence spectrum stimulated by white light is shown in PI. VII. fig. 1. In this photograpb the red region and the double band at the D lines are not shown. In the blue and ereen-blue region the lines and bands of the fluorescent spectrum are irregularly spaced. From A=5050 to A=5071 we have a regularly spaced. system of lines, which get closer and closer together as we approach the less refrangible end of the spectrum. These lines col- lectively form 2 system of bands, the spectrum having a fluted appearance. The spacing between the bands also becomes less as we approach the more refrangible end. With white-lght illumination the bands cannot be distin- guished in the yellow region, but by exciting the fluorescence with blue-violet light, the bands can be traced up to the very end of the spectrum (A=571). The bands change their position slightly as the wave-length of the exciting light is altered, but the lines of which they are composed remain and the Resonance Radiation of [lectrons. ale fixed in position. What actually happens appears to be a redistribution of intensity among the individual lines. The yellow-green-blue fluorescence spectrum can _ be divided roughly into three parts, which we will designate me, B, and G. Region A, comprised between wave-lengths 571 and 500, is made up of regularly spaced lines which collectively form a system of bands, owing to the periodic fluctuations of intensity. Region B, between 500 and 477, is made up of irregularly spaced lines, often hazy on one side, and of varying width. This region contains the first three bands of the group already alluded to, though special precautions are necessary to bring them into view. With dense vapour, and illuminating light of the proper wave- length (about 460), the region is seen to break up into three very broad patches; in other words, there is a periodic fluctuation of intensity as in region A. . Region © between wave-leneths 477 and 468 is made up of very broad lines, spaced w ith a fair amount of regularity and arranged for the most part in pairs. These three regions are indicated by brackets in fig. 1, ie VIL. The positions of the bands, which apparently have their origin in the periodic Auehuetions of intensity of the lines, are recorded in the followi ing table :— A791 | D415 4882 5465 4971 5010 5050 ddol 5120 5989 9185 5620 5246 5645 5316 5665 0361 The centre of the bands cannot, of course, be very exactly located, especially in the case of the first three which are found in region B. These bands apparently obey the same law as the oxygen bands in the solar spectrum, 7. e. if we plot their wave-lengths as abscissee, and take ordinates which increase by equal amounts, we obtain a curve which is approximately a parabola. In this way we can calculate the position of the head of the group, which was found to fall at wave-length 5715. Two bands were therefore missing, one of which at 5676 was sub- sequently found in the spectrum obtained with blue-violet exci- tation, dense vapour, and long exposure: still longer exposures would probably record a trace of the first band at 571. As has been said, these bands shift their position as the wave-length of the exciting light changes. The shifts are 520 Prof. Wood on the Fluorescence of Sodium Vapour greatest in the region between X=515 and 7X=545, where it may amount to the full width of the band or 25 A.E. The bands in the vicinity of X=555 remain fixed in position, as is probably true of all the less refrangible ones. It was at first thought that the head of the group remained fixed, the group opening out, or expanding so to speak, but this appears not to be the case ; and the law governing the motion of these bands, if one exists, cannot be determined until a larger number of photographs have been obtained. The probable cause of the motion will appear presently. The wave-lengths of the lines which collectively make up the fluted bands were determined from the calibration curve of the spectrograph, and are recorded in the following table. It was at first thought that they would obey the law of constant second differences, but such was not the case. It has not yet been possible to measure the lines above A=555, though the bands extend to 571. Wave-lengths of bright lines in Fluorescence Spectrum of Na Vapour. 5553 | 5315 | 5040 48 | 09 3 43°5 | 02 25 39 £2965 | 5000 35 | Pot) 4995 31 | &3 &8 14 | 76 su 10 70 G4 05 6+ | 59 5499 | 58 34. SH) | 52 25 91 46 12 S6 39 | 04 81 | 32 | 4895 a 26 85 62 19 iD 58 | 13 | 67 ae | O06 | 60 47 Banat o2 5O 4?°5 o194 | 39 Sih fala) | 21 3 80 12 26 ie 03 Di GG A795 oa99) * | Faint 59 | 5 OB) | 49 | 78 87: 41 : 69 Si 34 59 TOM | 27 | 53 Os 20 | 43 64 : | 15} | o9 59° C5 | 33 Faint 5l | E096 | 28 44 $8 16 38 80 O-+4 32 we | 4695 2H 49 a4 and the Resonance Radiation of Electrons. 521 Stimulation with Monochromatic Light. Having described briefly the general appearance of the spectrum when the fluorescence is provoked with white light, we will now consider the case of monochromatic stimulation. In all of the earlier work with Mr. Moore, and during the first stages of the present investigation, no trace of any emission-band at the D lines was observed, neither was any fluorescence whatever observed when the prisms of the mono- chromatic illuminator were adjusted so that the instrument delivered light of wave-length approximately that of the D lines. A bright band at the D lines had, however, been observed by Wiedemann and Schmidt, and independently by the author in the case of sodium vapour formed in exhausted glass bulbs, which observations have been confirmed by Pucianti, who has recently published an interesting paper on the subject *. It seemed probable that in the case of a large mass of vapour in a steel tube, the radiations capable of exciting the D line fluorescence were absorbed in the outlying mass of comparatively rare vapour before coming to a focus in the dense mass. As it was found difficult to observe the pheno- menon in glass bulbs on account of the formation of a sodium dew on the walls, and the speedy discoloration of the glass, NES. 5) Figs .3. to pulp ¢ the arrangement shown in fig. 3 was adopted. A small piece of clean sodium was placed in a large test-tube, hermetically * Accad. Lincei, Atti, xiii, pp. 480-440 (1904). 922 Prof. Wood on the Fluorescence of Sodium Vapour sealed with a glass plate, and furnished with a tube for ex- haustion. Since a much more powerful D line radiation can be obtained from a bright sodium flame than from a selected portion of the spectrum, the monochromatic illuminator was abandoned, and a small oxy-hydrogen flame, heavily charged with sodium, substituted for it. An image of this flame was formed by means of a lens, at the centre of the tube immediately above the lump of metal. On gently heating the tube and viewing the interior through the cover- glass, a faint cone of yellow light was observed which, however, only extended to the centre of the tube, owing to the inability of the effective radiations to penetrate | to a greater depth. This stage is shown in the upper diagram of fie. 3. As the temperature rose and the density of the vapour increased the fluorescence increased in brilliancy, the region retreating towards the wall, until only a bright skin of yellow light remained, which lined the wallvar sane tube at the point where the exciting radiations entered, as shown in the lower diagram. This experiment proved con- clusively that sodium vapour is capable of re-emitting a yellow light, when in the act of absorbing the light of ‘the sodi flame. The appearance of .the yellow cone and its behaviour as the vapour-density incr eased proved that it was a true re-emission of absorbed light, and not a scattering of light by floating particles of. oxide. An attempt was next made to observe the same pheno- menon in the steel retort-tube. On focussing an image of the flame upon the window of the retort a distinct spot of yellow light was observed, though it proved too faint to admit of satisfactory observation in the large spectrograph. Re- turning once more to the monochromatic illuminator, I was surprised to find no difficulty at all in obtaining a bright emission-band at the D lines, which proved to be double when the vapour-density was not too great. The band was of considerable brilliancy when direct sunlight was used. The failure to observe this band in the previous experiments may have been. due to an insufficiently high vacuum, or to insufficient density of the sodium vapour. It has been found that long-continued work results in a steady improvement of the spectrum as to brilliancy, though it is quite impossible to ascertain the precise reason. It is probable that the proper conditions are unconsciously found, and the detri- mental ones discarded, by what Prof. James would call» the “Sub-conscious-self’? The band at the D lines only appeared when the light from a corresponding part of the spectrum fell upon the vapour, showing that the electron system which produces these lines is independent of the and the Resonance Radiation of Electrons. 52> system which gives rise to the channelled spectra. Whether D, and D, are connected has not yet been determined. To do this it will be necessary to free the illuminating beam from the D, radiations, and observe whether or not the fluorescent band is double. An attempt will be made to accomplish this. We will now consider more in detail the appearance of the fluorescence spectrum, when the illuminating light consists of a more or less monochromatic beam from the ieee As has been said, the yellow end of the spectrum appears only when the stimulating light is blue-violet. It is probable that oO the yellow light will also be radiated when the stimulating light i Is of the same wave-length, though such a radiation | has not yet been detected. The ‘absorption for radiation m this region (A=971 to 560) is very small, and the vapour appeared practically black in all cases thus far observed. The region of maximum fluorescence moves down the spec- trum as the stimulated region moves up, as is weli shown in the series of photographs in fig. 8 (PL VII.). In this series of photographs the stimulated region is indicated by the luminous region to the left. The lowest one, e, shows very clearly that when the stimulation is at the violet end only the first five bands at the yellow end appear. In spectrum “a” the stimulation is at the centre. The change in the hie of the groups or fluted bands is best shown in figs. 4 and 5. The same thing can be seen in fig. 3. by moving a vertical straight edge along the series. That the ‘spectra are in perfect “‘register”’ can be seen by noting the position of the D lines at the right. These were recorded by holding a soda flame in front of the slit for a few seconds during each exposure. Radiations both above and below the excited region are present, showing that Stokes’s law is not obeyed. This is especially noticeable in fio. 2 (PI. VII.), where the excited region is indicated by a white rectangle. ‘The plate-holder of the spectrograph was arranged so that it could be moved up and down, and many as seven spectra could be photographed on a single plate if necessary. After recording a fluorescent spectrum, the plate was elevated and the beam from the monochromatic illuminator thrown back into the instrument by means of a mirror. In this way it was possible to obtain a record of the extent of the region of fluorescence below the excited region. It was thought desirable to obtain a more homogeneous type of exciting light than that furnished by the monochromatic illuminator, and a mercury arc in a quartz tube was accordingly tried. Though the light was extremely intense, and though its radiation contained a number of lines in the region de- sired, it was found impossible to obtain the slightest trace of 924 Prof. Wood on the Fluorescence of Sodium Vapour fluorescence. No one of the periods happened to be quite right; and the electrons remained quiet. The light of the cadmium spark, bone much less intense, excited the fluorescence ; but it has not yet been ascert tained to what degree the “ con- tinuous background ” of its spectrum was responsible for the phenomenon. Work along these lines will be continued during the coming year. The shifting of the bands, which results in all probability from a change in the distribution of the intensity among the individual lines, when the wave-length of the exciting light is altered. has been already alluded to. In the earlier stages of the investigation, it was necessary to work with the slits of the monochromatic illuminator wide open. Later on, as the methods improved, it was found possible to narrow them by degrees, until finally a fluorescent spectrum of sufficient in- tensity for observation was obtained with the slits not much wider than a hair. A remarkable phenomenon was at once observed: the slightest change in the wave-length of the exciting light caused the spectrum-lines to flutter about in a most extraordinary manner. It was quite impossible to follow the changes by the eye, they were so complex. As a line disappeared or appeared, the sharp and shaded edges often changed place, the appearance reminding one of a flag flying first on one side of the mast and then on the other. Obviously a vast amount of information regarding the nature of spectra is to be obtained by a careful study of these changes, which can only be done by photography. I have estimated that fifty or one hundred photographs will be necessary for a complete record of the changes which occur when the wave- length of the exciting light is shifted over the range 450 to 550, and as each picture requires an exposure of four or five hours, the task is seen to be no small one. If the spectra were then printed in succession on the film of a kinematograph and projected on a screen, it would be possible to follow at leisure the wonderful changes which occur. At the time of writing this paper only half a dozen photo- graphs have been obtained, three of which are reproduced in fig. 6, Pl. VII. Much of the detail is lost in the process of printing and reproduction, and on this account a careful drawing has been made on coordinate paper of all the details which are to be made out on the original negatives, fig. 7, Pl. VII. The white-light fluorescent spectrum A is recorded on the lower line, and the spectra obtained with nearly homo- geneous radiation above, as is the case in the photograph as well. A number of the lines in the complete spectrum shown in fig. 6 have been lettered A, B, C, D, etc. These letters correspond with the letters in the diagram, fig. 7. The and the Resonance Radiation of Llecirons. Hyp) letters at the left-hand side enable the spectra to be identified with the diagrams. The line at which the excitation occurs is indicated by a double-headed arrow. This line always appears in the fluo- rescent spectrum. For example, in spectrum B the excitation is at wave-length 4962. In this case three lines of shorter wave-length appear, as well as the line at 50, and the lines at 504 and 5071, which belong to the groups of lines or bands already referred to, indicated by brackets. In spectrum OC we are stimulating the vapour at 4935, and we obtain the second line in each of the first two groups. In spectrum D we stimulate another member of the same series, — and also get the second line in the first two groups; while immediately above (EH) by stimulating 4866 we obtain the third line in the second and third groups, this line being wanting in the first group, even when the vapour is excited — by white light. In spectrum F, with a stimulation at 4839, we get another set of lines. The cause of the shift of. the bands previously observed is at once apparent, the individual lines belonging to different groups of electrons. The number of groups has not yet been ascertained, but the photographs indicate that there are at jeast four, and probably more. It has not yet been possible to study the minute details which accompany the appearance or disappearance of a line, which are even more interesting, but another year’s work on the subject will doubtless yield fruitful results. Longer expo- sures will doubtless enable these relations to be traced throughout a wider range of wave-lengths, but from what is already known it is clear that the shift in the apparent position of a group of lines results from a change in the dis- tribution of the intensity among the individual lines consti- tuting the group. These experiments show in a striking manner the com- plexity of the piece of machinery which we will call the sodium molecule. Professor Rowland once said that a mole- cule is much more complicated than a piano. In most cases, all that we have been able to do is to strike the entire key- board at once, but in the case of sodium it seems possible to strike one key at a time. SS SSS Reaorm Soturion To Pume- - - =os | ! peek , : SSS eee ieee positive pole of a battery of thirty small storage-cells. The wire AB (14°5 em. long) was screwed into a stouter rod AC connected to the negative pole of the battery, and passing through a rubber stopper E fitting air-tight into the neck of the vessel V. The portion AA’ of the rod AC projected about 6 cm. into the vessel V, and another rod BD 6 cm. long was screwed to the lower extremity of AB, which was therefore exposed to a uniform electric field. To obtain a constant supply of emanation, a strong solution of radium salt was placed in the glass bottle R provided with 528 Mr. W. Makower on the Method of Transmission a stopper, through which passed a long capillary tube C reaching to the surface of the solution but not dipping into it. The air inside R was thus always kept at atmospheric pressure, and by making C sufficiently long the rate of escape of emanation from the bottle by diffusion was rendered small. After standing for some weeks, the concentration of the emanation in the air above the radium solution was found to have become sensibly constant. To transfer a definite volume of gas from R into V, the closed limb a of the three-way capillary stopcock ¢ was con- nected by the capillary 6 with the vessel V, to which it was attached by rubber 7 By means of a pump the whole was exhausted to a low pressure, when the pump was discon- nected by closing the tap T. The stopcock ¢ was then turned so as to connect a with R, allowed to stand for a short time and then again turned into its origina! position. In this way the volume a (about *2 ¢.c.) of gas was transferred from R into V, and by repeating the operation any required volume of emanation could be introduced into V. As the volume of a was always small compared with that of V. practically ail the emanation in a was discharged into V at low pressures; at higher pressures it was easy to apply a small correction for the quantity of emanation left in a. The pressure in V was registered on a mercury manometer at the higher pressures, and on a McLeod gauge at the lower pressures. The rod AB was exposed for 30 minutes to the emanation, and then transferred to another metal cylinder in which its activity was tested in the usual manner by means of a quad- rant electrometer. As under these conditions the activity of the rod remains constant for about 10 minutes*, it was possible to take several observations of the activity, the means of which are recorded in Tables I., I., and III. 3. Observations and Results. Hxperiments were performed with three vessels V of diameter 1*1 cm. (vessel I.), 2°6 em. (vessel II.), and 8°3 em. (vessel III.) respectively. The pressure of the air with which the emanation was mixed was varied and the activity acquired by the rod in 30 minutes recorded. With vessel I. it was found difficult to prevent the rod CD from touching the sides of the cylinder. The arrangement described above was therefore slightly modified by * Miss Brooks, Phil. Mag. [6] vol. viii. p. 880 (1904). of the Excited Activity of Radium to the Cathode. 529 making the cylinder V somewhat shorter and fixing the rod BD into a rubber stopper fitting into the end of the cylinder. In the case of vessel I. it was necessary to work with very small quantities of gas in order to get to sufficiently low pressures, and the capillary a was discharged once into V. With vessels II. and ILI., a was discharged twice and three times respectively. The maximum value to which the activity deposited on AB tends at high pressures is not the same for the three vessels, on account of the difference in their dimensions and of the variation in the quantity of emanation used. The results obtained are given in Tables I., II., and III., in which the pressures are given in cm. of mercury and the quantity of activity on the rod in arbitrary units. TaBLE I. (Vessel I.) diameter 1:1 cm. Pressure Activity in cm, mercury. on rod. 15°3 180 39 174 6°39 167 43 161 2°69 134 17 120 0°95 93 TaBuE II. (Vessel II.) diameter 2°6 cm. Pressure Activity in cm, mercury. on rod. 9-3 209 S7 219 6-2 224 20 214 3°3 198°5 yaa 183 2°6 198 2:2 OW ee Jkt Th E33 182 0-95 158 0°8 150 0°44 LOO 0-32 87 0-12 d0 Phil. Mag. 8. 6. Vol. 10. No. 59. Nov. 1905. 20 530 Mr. W. Makower on the Method of Transmission TasueE ILI. (Vessel ILI.) diameter 8:3 cm. Pressure Activity in cm. mercury. on rod. a3 O94 15 410 A*15 413 2°0 409 tah 398 1°4 385 IOS) 386 0°35 367 0-41 332 0°38 346 O-17 268 0-10 178 0086 170 4, Discussion of Results. The experiments described above show that, at low pres- sures, the excited activity produced from radium emanation contained in a closed vessel is not confined to the cathode, as in the case at high pressures, but is distributed over the walls of the containing vessels and appears both on the anode and cathode, even in a strong electric field. This is precisely what has veen previously found with thorium emanation”, and shows that the method of transmission is probably the same. It will be further noticed from the results given above that ina large vessel the influence of pressure on the con- centration of the excited activity on the cathode becomes appreciable only at low pressures, whereas with smaller vessels this influence is noticeable at much higher pressures. If, therefore, we assume that at the moment of its production the excited activity is uncharged, it is evident that the pro- portion of particles of excited activity which can traverse the gas in which it is formed, and reach the anode without becoming charged, is a function of the length of its path through the gas. As has been pointed out by Rutherford f, there are two ways in which the excited activity may be supposed to acquire a positive charge. (1) The excited activity condenses on the positive ions existing in the gas and is thus transferred to the cathode; and (2) The excited activity possesses the property of expelling * Rutherford, loc. cit. ) t Rutherford, Phil. Mag. [6] vol. v. p. 111 (1903). of the Hxcited Activity of Radium to the Cathode. 531 negatively charged particles, and so becomes positively charged. To decide between these two hypotheses, Rutherford per- formed experiments in which the number of ions in the vessel containing the emanation was increased by external means, and found that the amount of activity deposited on a cathode in a given time was not increased by this means. For this reason he rejected hypothesis (1) in favour of (2). The experiments were, however, carried out at atmospheric pressure; and it is possible that, under these conditions, the number of ions produced by the emanation is sufficiently great to remove the excited activity as fast as it is formed, | in which case any further increase of the ionization would be without further effect. To test this point still further, some similar experiments have been made at a low pressure, using vessel II]. The walls of the vessel were made the cathode and the central rod the anode; 20 volumes of the capillary a (fig. 1) of emanation were introduced into the vessel and allowed to stand for 34 hours, the pressure being atmospheric. The emanation was then compietely pumped out as quickly as possible, and a new inactive rod AB intro- duced and the field reversed. One volume of the capillary a was then introduced into the vessel, and the rod exposed to the emanation at a pressure of 1 mm.of mercury. Although the ionization in the vessel must have been increased about five times by the excited activity deposited on the walls of the vessel during the previous exposure to the emanation, the activity collected on the rod was found to be the same as when the walls were inactive. In a subsequent experiment 7 milligrams of pure radium bromide were brought close up to the vessel during the exposure of the negatively charged rod, without affecting the quantity of excited activity de- posited on the cathode in 30 minutes. Supposition (2) is therefore the only one capable of explaining the observed phenomena. It is of interest to speculate as to the mechanism by which a negatively charged particle is expelled from the excited activity during its passage through the gas. At the moment of formation of excited activity, the emanation from which it is produced expels an @ particle* whereby the residue must itself be projected with considerable velocity. In their flight *® The negative charge left on the excited activity by the expulsion of an a particle may be neutralized by a simultaneous expulsion of slowly- moving electrons similar to-those which Prof. J. J. Thomson (Proc. Camb. Phil. Soc. vol. xii. part 1, p. 49) has shown to be given off by radio-tellurium. 202 Doz Mr. Jackson on the Method of Transmission of these particles of excited activity would collide with the molecules of the gas in which they are produced, and it is suggested that in a certain percentage of these collisions a negative particle is expelled, leaving the excited activity positively charged. To explain the results obtained in this investigation on this view, it is necessary to assume that the particles of excited activity, when mixed with air at 1 cm. pressure, travel a distance comparable with 1 cm. before becoming charged. This distance is great compared with the mean free path of a molecule of air at the same pressure, and therefore only a very small fraction of the collisions can be effective in causing a negative particle to be expelled by the excited activity. - I am indebted to Professor Schuster both for placing the resources of his laboratory at my disposal and also for much valuable criticism during the course of these experiments. LX. Note on a Paper by W. Makower entitled “ On the Method of Transmission of the Hacited Activity of Radium to the Cathode.” By W. H. Jackson, M.A., Assistant Lecturer in Mathematics in the University of Manchester*. S a result of some experiments on the method of trans- mission of the excited activity of radium, Mr. Makower has arrived at the following hypothesis:—The molecules of excited activity, initially uncharged, are projected from radium emanation with velocities large compared with those of gas molecules, and at a certain percentage of encounters with the gas molecules a negative electron is shot off, leaving the activity positively charged. It gives additional force to his argument to further show that the deviation of the experimental results obtained by him from those required by the above theory are actually less than the errors of observation. Since the number of ions present in a gas ionized by a small quantity of radium emanation is exceedingly small compared with the number of molecules of gas, it is safe on this view, even though the positive ion influences a much larger field of force than an ordinary molecule, to assume that the importance of encounters with positive ions is negligible. The amount of activity which, in the experiments described by Mr. Makower, is deposited on the cathode, is to be taken proportional to the number of excited activity molecules * Communicated by the Physical Society. the Excited Activity of Radium to the Cathode. 533 which have encounters with air molecules on their way to the sides of the cylindrical vessel. Consider a number of particles travelling a distance «x through air in which the average distance between molecules is X, and the effective radii of moleculesis o. The distance may be divided into N layers each of thickness X, in which e f e each layer contains, on the average, x2 molecules per unit area, and the proportion, on the average, of encounters in each layer 2 is = Hence the proportion of the particles which have 7 2\ N 2 = ; no encounters is ds <7) = ( 1— =o , and this for small : - 3 values of X is equal to e L, where L ae and is the “ mean free path ” of the particles in air. Supposing now that the proportion of encounters effective in displacing a negative electron be R, the above result will be modified and the proportion of particles experiencing no R “ effective encounters” will bee ©”. In the experiments with which we are dealing, the central rod on which the activity was deposited was shielded at both ends, so that the calculation may be simplified by con- sidering the problem as a two-dimensional one, that is by taking the cylinder to be of unlimited length. It is con- venient to calculate the proportion of particles which reach the side of the cylinder without having any effective encounters, and then to subtract the ratio from unity. Consider the number of particles which reach a small area of magnitude A, containing a point O. Use polar coordi- nates 7, 6, d, with O as origin; if P be any point of space let OP=v7, and if Q be the projection of P on the right section of the cylinder through O, of which C is the centre, let COQ=¢@; and.QOP=¢. Let M be the number of particles projected by the emana- tion per unit volume. The number of particles reaching the area A from an element of volume 6V at P is proportional to the solid angle subtended by A at P, which is“$c03 CORRS in particular, the number reaching A from P is R De sae cos 6 cos d oV. Agr? 534 Mr. Jackson on the Method of Transmission of This expression is to be integrated over the infinite cylinder, and then it is clear that the deposit on any portion of the sides is proportional to its area. The area of unit length of the cylinder is 7d, where d@ is the diameter, and the value of 6V expressed in terms of 7, 0, d is 7? cos 6 606¢ dr. Denote the number of particles reaching unit length of the sides by N, we have =e] N=iMd iene cos’ bcos 0 dl drdd .. \. aie The limits of integration being P- 2 Gp 6. —cos ae cos @ \to cos —!| = cos ) ae ee a 0 to d sec , é LG d, = 5 to + o° Performing the first integration with respect to 0, we have 5 ( asec © R 2 2 --¢ - 7 9 > é N==Ma| | 28" cost g(1— 5 cost d Jdrdg. . (2) In this integral substitute r=ad sec ¢, whence . 1 = zd see N=Me ( ( pat * cos? @ (L—a2)t dx AD... aan e0 ef The maximum value of this integral is obtained by omitting the exponential factor, and corresponds to a vacuum when all the activity would reach the sides. Denoting the maximum value of N by No, we find, as is otherwise obvious, that No = st Me?. pa on ee Let the ratio N : No be denoted by s. An effective approximation to the integral expression for the value of s may be found by expanding (1—2”)? in powers of «x. Introduee the notation 1 m(e)= 4 ee LC aa ee - Seen Vv and write ——. : ; c 5 : é (6) the Excited Activity of Radium to the Cathode. 53 Or HKquation (3) may now be written xt cos byl seep) —Srslseseed)—dys(useeg)— 16 (7) We also have Also y,(z) decreases continuously as either z or n increases. If —— we have, if z=psec @, | i Ce ie ae OL, e w iL iu i 9 Yo(<) < °) y2(e)< O19, and with an error of order 3 per cent. we may write 4. (: % ] s= —]}2 cor’ ddd=— . 9 wmf Oba = ) This simplified result should therefore hold if the defect from the maximum deposit of activity on the cathode is less than 30 per cent. Hence, with this restriction, the deposit of activity y should be given by the formula y=N(1—) =i (1— 7). ° ° : (10) But the mean free path varies inversely as the pressure, and hence, if Ly be the mean free path for a pressure of 1 cm. of mercury, and w cm. denote any other pressure, we obtain Ly , — N ae e e e e ’ e ata This equation affords a means of determining the values of No and is which best suit each of the Tables I., I1., III. obtained by Mr. Makower. Owing to the restriction that the value of y must be greater than’7Ng, it is found that this is an 536 Mr. Jackson on the Method of Transmission of ; L inexact method of determining the value of R- In the accompanying figure, the maximum activities have all been reduced to 100, and the three curves are calculated by L assuming the mean value of R to be ‘7 cm. The values of Np and = were determined as follows :— Assuming that the set of m points in question, 7. ¢.(@, Yi), +++ (nr, yn) belong to a curve of form we make s ( and k \? i: > %—a+ — ) a minimum. Up By differentiation this leads to the equations Dap a —nst ek wv ib niie—(SE2) }. ores uF na= kd, eas Ly In the curves for vessels II. and III. all the points for which the deposit was greater than 70 per cent. of the maximum were used in the above formule. In the curve for vessel I. the point slightly below this value was used because the next point was clearly inaccurate. The result so obtained was practically identical with that obtained by leaving out both the points in question. On account of the difference in the values of lig caused by omitting even R single points, this value is reliable only to one figure. The results are given in the following table :— Ne = in cm Messel 1. ae Li Tal Messel klar) oe 221 “13 Messe M2)... tee A\4. 64 the Excited Activity of Radium to the Cathode. Dab It has only been possible to test the values of No, as given by equation (4), very roughly, owing to the difficulty of ACTIVITY ° 3 8 3 = S $ <3 S S 8 €l uh 0 WD NI JUNssIud AUNIYIWS Ghee at 9} finding the volume of vessel V and its connexions, with sufficient accuracy to determine the relative values of M in the three sets of experiments. hveoae le LXI. The Dejflexion of « Rays from Radium and Polonium. By A. STANLEY Macxkenziz, Munro Professor of Physics, Dalhousie University, Halifax, N.S.* (Plate VIIT.] {| ae following investigation was begun with two aims in view: first, to measure from the deviations of a beam of @ rays in a magnetic and in an electrostatic field the value of the velocity v, and of the ratio of the charge e on an a particle to its mass m, for the rays from radium and from polonium; and, secondly, to see it there were any evidence of achange in any of the quantities v, e, or m as the rays travelled in an ordinarily good vacuum. The former problem for the case of radium was first treated by Rutherford, using an electroscope to determine the deviations ; and later by Des Coudres{, who let the rays fall directly upon a photographic plate. Both used radium in radioactive equilibrium, and this method was foilowed in the present case; but it has the disadvantage that the beam of a rays not being homogeneous, it gives only the mean velocity of the rays. The method employed by Rutherford was admittedly not well adapted to give accurate numerical determinations ; and Des Coudres states that too much stress must not be laid on the accuracy of his electrostatic experl- ment. In a paper just published Rutherford describes some very suggestive experiments made on the magnetic deflexion of the « rays from radium C, and promises to give later similar results for the deflexion in an electric field. The great advantage gained by the use of a thin coating of radium © on a wire is that the rays all leave the wire with the same velocity, and the beam is accordingly homogeneous. An accurate determination of the values of v and — is to be expected from his completed measurements. : An effort was made to find a way of observing the position of the beam of rays coming through two slits without having to let them fall directly upon a photographic plate, since in the case of a path longer than a few centimetres this necessitates the use of a closed vessel and the production of a vacuum each time an observation has to be made. After experiment- ing with a thin layer of powdered zinc sulphide on glass, and finding that the scintillations were still quite brilliant when observed after transmission through the glass, I adopted * Communicated by Prof. J. J. Thomson. Tt Phil. Mag. Feb. 1903, p. 177. t Physik. Zeitschr. iv. p, 483 (1903). § Phil. Mag. July 1905, p. 163. Deflexion of a Rays from Radium and Polonium. — 539 this method of observing the position of the end of the beam ot arays. I learned later that Mr. F. H. Glew of London has used this arrangement in his “ scintilloscope,’ and he kindly consented to make for me the excellent zinc-sulphide screens used throughout these experiments. It was hoped that the position of the line of scintillations could be observed by means of a microscope, but the amount of light was found to be too faint to enable one to make a setting with a cross-hair. The method adopted was to put the film side of a photographic plate in contact with the glass side of the zinc-sulphide screen, and photograph the scintil- lations. In order not to increase the width of the line unduly, the thickness of the glass of the screen had to be as small as was consistent with strength to withstand the atmospheric pressure inwards when a vacuum was made in the vessel. The thickness used was from three to four fifths of a millimetre according to the size of the opening to be covered by the screen. Magnetic Deflexion of « Rays from Radium. The design of the tube finally adopted for the measure- ment of the deflexion of the a@ rays from radium by a magnetic field is shown by figure 1. The vacuum-box is Fig. 1. To pump i Pe ee A res ‘ | |) oD U o ie) m (a) made of brass, and consists of a solid disk A at one end, a hollow cylinder D at the other, and a tube BC joining them. The shape of the latter is shown by the small drawings (a) and (0b) in the figure, its dimension parallel to the length of either slit being the same, 9 mm., at all parts to enable the 540 Prof. A. 8. Mackenzie on the Deflexion of pole-pieces of the electromagnét to be placed at any part of its length and as close together as possible. The wedge- shaped part of the tube was to allow for the deflexion of the rays; but this expansion of that part of the box and the size of the cylinder D were made large, in order to prevent as far as possible secondary radiations from the walls of the box from affecting the photographic plate. The disk was bored almost through to receive the slit-tube, and the bottom was pierced by a slit 8 mm. long parallel to the slits in the slit-tube when the latter was in its proper position. This slit was covered on the outside by a piece of mica about ‘0006 cm. thick through which the « rays passed into the vacuous box. The mica was put on with sealing-wax, and was as thin as would safely withstand a difference of pressure of an atmosphere on its two sides. The slits were } mm. wide, and 5°75 cm. apart. The circular opening in the end of the cylinder D was covered with the glass zinc-sulphide screen, powdered side inwards, put on with sealing-wax. A light-tight cover E fitting over the end of D served to make this end a sort of camera. The distance from the zine sulphide to the nearest slit is 15°4 em. The radium was contained in, and filled, a shallow depres- sion in a disk of brass, R, of the same diameter as A. This cell was attached to A when required, and the joint covered with soft wax to prevent the escape of emanation into the room. As the radium filled the depression in the cell, it was practically in contact with the mica when it was attached to the box, and thus the distance through which the @ rays had to go in air at atmospheric pressure was very small. A photographic impression of the line of scintillations when undeflected by the magnet could be obtained in two or three hours; but when deflected the exposure had to be increased several times, due in part to the absence in this case of the @ and y rays and in part to the dispersion of the beam of @ rays. In erder to see whether the « particles always retain their charge when they travel, and whether the seintillations are in part due to uncharged particles, the magnetic field was applied over lesser and greater extents of the path of the rays and to different parts of the path. For this purpose it was necessary that the path of the rays from their source to the far end of the slit-tube should be always shielded completely from the magnetic force. This was satisfactorily attained by winding round this part of the box many turns of a thin ribbon of varnished soft iron. Measurements were made with four different arrangements a Rays from Radium and Polonium. 541 of pole-pieces and their positions as regards the length of the path, as shown in the following table (two measurements are given for position III. with different magnetic fields). In the first three positions the main part of the field begins at about the same place, but extends over lengths of the path which are as 1:5:10 approximately. In position IV. we have the same pole-pieces as in II., but displaced 4 cm. further along the path of the rays from the slit. The value of the field H at every point of the path of the rays was determined by means of a small throw-bobbin and a ballistic galvanometer in the usual way, and the value of \de\H da found graphically for use in the equation _ (see J. J. Thomson, ‘ Conduction of Hlectricity through Gases,’ p. 92), where dis the deflexion to either side of the centre. ao | 3 = 6 re = io) Bie male ee meee 23 " = © fan =) Eo : oS zo ; me 55 Bs = Se) SS Selne CaS Seige ore. ara ee ee ORs ies: 5 8 Pepe | So a) oe Sl eee 2 a e Ss = Hoa |/ 4.95 | doe eS es ere ee Zs 2s S oF do | CS% | o o-m Se 2 a 8 ao e 8 crea ue |e be as se > Sys ao § Sy 4 ee 5 2 = |< — o ~~ ~ (o} S TD ot HH = ao =al je! eS | «= © O og 2) sama SS a5 = = A > «a eOoNe: IVES Oe peo io: 5,0) S08», /h4540w-,. LiOB2Z be 9G co 04. Mean value of = = 3°00 x 10° c.a.s. electromagnetic units. co The main error in the measurements comes in when determining d, the deflexion ; for the bundle of a rays is very heterogeneous in velocity, and under the action of the magnetic field is spread out into a spectrum. The length of this spectrum is of course determined up to a certain limit by the length of exposure given, as it is strongest in the middle and weak on both sides. The deflexion measured was to the middle of the spectrum. An error of at least 3 per cent. is D42 Prof. A. 8. Mackenzie on che Deflexion of possible in this measurement, and it will be seen from the mv Me above table that the values obtained for > agree to this approximation for the very different arrangements used. In figure 2 (Pl. VIII.) is given a copy of the negative used in measurement II. of the table, where the dispersion of the beam is about 3/8 of the mean ‘deviation. The agreement of the values obtained for — points to the conclusion that the « particles, in a very rare gas of this kind at least, retain their charges unaltered along their path (that is, assuming that their velocities and masses remain unchanged, which is probable at low pressures). As one can mark by a use of a magnifying-glass the position of the scintillations, is further proved that these scintillations are aways ie by the field, and that they are caused only by the a rays and cannot be due to uncharged particles, if such exist. The fact that with this apparatus one can make eye measurements is of great assistance in roughly checking up one’s results and in arranging the conditions for the par rticular determina- tion in hand. fhe The mean value of the average — found was 3:00 x10”. e The values of the extremes of ~ as given byfig. 2 (Pl. VIL.) are” 270 x 0) and 377 x0? i Wee The value A MV é Rutherford in his earlier experiment was 3:9 x 10°, and by Des Coudres 2°56 10°. The value I have found is between the two, and not far from that of Des Coudres. In his paper in this Magazine for July, Rutherford shows the amount of decrease in velocity of thea rays due to their passage through successive lay -ers of aluminium ‘00031 cm. thick. The decrease in the present experiments due to the thin plate of mica through which the @ rays have to pass betore entering the vacuum box would be equal to that due to two or three of Rutherford’s aluminium sheets, and so amount to about for radium in radioactive equilibrium found by F m. : 6 per cent. Assuming that — is constant this would make e m the value of the average | for the rays as they left the surface of the radium 3°18 x 10°, and of the extreme ones 2-65 x 105 and 3°92x10°. Since the fastest rays are those from radium C the value 3°92 10° must belong to them, a Rays from Radium and Polonium. 543 and this value is in entire agreement with the value 3:98 x 10° found by Rutherford in his paper just cited. Rutherford found that the power of acting on a photographic plate and of producing phosphorescence ceased for the « rays when their velocity fell to 64 per cent. of the maximum, that is when = is 2°55x 10°. The minimum velocity which I have found above is 2°65 x 10° approximately, and if the scintil- lating action ceases at the same time as the rays fail to affect a photographic plate, this value of = would be that expected. Electrostatic Deflexion of « Rays from Radium. The general form of the apparatus used in measuring the os PP Caen electrostatic deflexion of the z rays from radium is like that already described, and is shown in figure 3. The radium cell Fig. 3. R, the mica window M, and the camera end E are as before. The charged plates BB were 6 cm. long, 1°87 cm. wide, and # mm. thick, and were placed 506 cm. apart. They were attached to and supported by the metal slit-tube by means of two quartz rods AA soldered to them. The distance from the end of the slit-tube to the nearest edges of the plate was 1:72 cm., and from the end of the slit-tube to the zinc sulphide was 14°61 cm. The main tube was of glass with side tubes D44 Prof. A. 8. Mackenzie on the Dejlexion of for the entry of wires to connect the plates with the Wims- hurst machine employed for charging them. The greatest difference of potential used was 10,000 volts, and the follow- ing table gives the deflexions observed with that and lower voltages :— Deflexion to either Voltage between | Observed deflexion |...) | plates. to either side. side redne ea for 10,000 volts. | 10,000 | “30 em. | 30 em. 10,000 “0 a5 3) 0 8,000 24 ,, | ‘SOL 6,000 Aa: S38) 5 | 6,000 | 20-;; seh aes 10,0v0 | a Bihhe s Average deflexion d to either side produced by 10,000 volts=°31 cm. If we call F the electrostatic force along the path of the rays in the plane midway between the plates, the value of \ dx \ Fdx was calculated graphically after the equations given by Clerk-Maxwell in his ‘ Electricity and Magnetism, § 202. The value of 7 calculated from the equation (see J. J. Thomson, ‘ Conduction of Hlectricity through Gases,’ p. 93), is4°11x 10%. The effect of the lines of force beyond the plates is thus to give a value 8 per cent. larger than if we had assumed that the field was bounded by the plates and everywhere uniform. No account was taken of the smaller effects due to the thickness of the plates, the distortion of the field by the metal slit-tube, or to the fact that the beam of rays is deflected from the central line, as they are of the order of magnitude of the other errors necessarily involved in the observations. The distance d was measured to the centre of the deflected line, but the dispersion of the beam is not nearly so noticeable as in the magnetic experiments. This is in part due to the fact that the deflexions are smaller, and may be also in part due to the exposures used, but I think itis safe to say thai the dispersion is not half so great as in the other case. In fig. 4 (Pl. VIII.) is shown a copy of a negative where 10,000 volts a Rays from Radium and Polonium. DAS were applied in one direction only ; the inner narrow line is the undeflected beam, and the other narrow line the deflected a beam. Thus it will be seen that the dispersion cannot be much more than 10 per cent. of the deviation. If there were different kinds of particles sent out by the radium, the lesser dispersion in the electric field than in the magnetic field would be explained if the energies of the different kinds of particles were much more nearly the same than their momenta, as these are the physical qualities involved in the two cases respectively. The wide fuzzy line in figure 4 on the opposite side of the central line from the deflected « rays must be due to 6 rays. They are deflected about two or three times as far as the arays. Ifthey are ® rays from the radium itself, they must be exceedingly rapid and have a velocity nearly that of light; but they may be secondary § rays. Further investigation is needed before one can state their real source. We have thus for the average ray =e 4°11 x10") and = =3°00 x 10’; whence the average v=1°37 x 10° cm. per sec., and a = 4:6 x 10° electromagnetic units. The extreme velocities would be from the values given : TUG ET. : : . above for — in the magnetic deflexion experiments, and ¢ assuming no dispersion in the electrostatic observations, 1-11 x 10° and 1°64x10°; or, increased by 6 per cent. to allow for the absorption by the mica, we have for the slowest, the average, and the fastest 2 rays leaving the surface of a small quantity of radium (12 mgr.) the velocities 1°18 x 10°, 1-45 x 10°, and 1:74x 10° cm. per sec. respectively, about sip of the velocity of ight. To be compared with my value of v=1°37 x 10° are Rutherford’s earlier estimate of 2°5 x 10° and Des Coudres’ value of 1°65 x 10°. My value of 1°74 x 10° for the fastest rays observed is decidedly less than that deduced by Rutherford in his paper on the rays from radium ©--vin. 26x 107, The value of = = 4-§ x 10? is much smaller than the values previously found by Rutherford and Des Coudres, which lay between 6 and 6°5 x 10°. Assuming that the charge on the a particle is the same as that carried by the hydrogen atom, ; Bie for which the value of — is 10* in the units used above, we 0 Phil. Mag. 8. 6. Vol. 10. No. 59. Nov. 1905. pel Be 546 Pref. A. 8S. Mackenzie on the Deflexion of see that the mass of the « particle is 2°2 times that of the hydrogen atom, or about that of the hydrogen molecule. If helium is monatomic its atomic weight must be 4, and the above experiments do not lend any weight to the view that the a particle is either a hydrogen or a helium atom, but suggest that it is a hydrogen molecule. LHven if we take the mv . Ari 8 Da ae 3 extreme value of — in one direction, viz., 3°7 x 10°, and an é 9 MU" . cS ° . extreme value of —— in the opposite direction, let us even e suppose that the dispersion in the electric experiment were great enough io extend to 10 per cent. on either side of the 9 me Ae mean and that —— could be as small as 3°7x10", the e calculated mass would be only 3°7 times that of a hydrogen atom. 121-5 1279 102-2 985 110-5 989 | 1690 1310 | 187-4 1002 203-5 1007 |, 2248-3 || 11882 341 1014 350 i tOr2 =) | 396 sie | 436 1015 473 1013 | 450 lis § |) 598 | 1016 662 | 1014 || _ 636 1 B67 | 657 1017 | | Nickel-Steel 29°24 per cent. i220 CO. /=—186° C. t=06° oC, H. ik H. I. lai, 1 1°58 4} 32 39 0-69) 5) 2°46 66 12°97 146 4:00 27 4°41 92 24°48 382 8:45 63 22°40 138 29°38 464 18:14 180 28°5 144 43-2 D783 26°45 316 30'3 147 50 658 38°4 394 once 150 71-0 696 541 A04 83'6 156 LOT 793 91°5 544 20:5 Uyak 152-4 836 eS o92 324 18] 2350 981 210-4 677 440 189 307°4 1050 320 740 504 193 4031 1080 465 789 O92 197 519 112) 951 808 657 201 591 1135 623 887 192 el Nickel-Steel 29 per cent. t=12°-0 0. ¢=—186° ©. ¢=16°-0ne H. I. H. ie | Jal i, 1:00 11 2°24 9 220 8 2°95 131 L013 95 4-52 29 7:60 207 13°39 155 9°35 75 196 272 20°74 321 12-92 123 67:1 307 29-5 505 15°95 180 143°7 315 376 608 | 24°72 305 243°6 321 480 708 44:2 582 400 328 790 858 74:5 708 515 333 139°6 1036 105°7 Cs) 32 333 182°9 1104 174-9 874 738 341 36 1247 279°3 954 424 1276 378 1004 | O17 1306 547 1052 631 1330 664 1079 Nickel-Steel 28°74 per cent. C— en) ©. t= — 186° C. t= 26701, Hi. It Hi. IL He L. 0:29 6 2 OF Es 0°85 4 161 70 6°85 39 8:91 AF) 4:20 156 11-42 106 Tepe hy 128 13°70 242 18:28 201 17-01 193 29°20 278 2 se2, 378 22°38 325 46°2 292 30°8 427 30'0 453 87°0 305 39°5 D49 48°] 566 159°3 314 66°7 730 796 658 233'3 319 178°9 991 111°8 746 320 32] 235°3 1060 207-7 851 406 327 316 1098 307 SIT 472 328 370 1153 457 966 627 333 461 1191 543 987 672 335 523 1227 662 1110 17°3 226 182 Nickel-Steel 28°32 per cent. G—i--5 GC t= —186°2 C. fea to arid Op H. | ie | H. DL Jal. I. 0-52 6 3-06 og) 1 37 24 Day 23 5:21 yas | 6°56 dl 6°40 37 9°54 107 | 12:34 134 14:58 48 122435 156 | 21:09 262 24°24 53 23°45 one 28°10 342 | 43:1 59 Ae 558 | 44-0) 452, 97:2 69 86:0 759 96:0 609 206:0 84 128°8 866 188°4 726 ont 98 1759 944 | 264°6 799 493 112 253-4 1029 | 438 886 596 119 360 1104 | 504 904 672 126 429 1132 602 931 752 128 51d oe LG! 578 1178 (0) 145 141 Nickel-Steel 26°64 per cent. | | ¢=20°°0 C. t= — 36210! Gea | H. I H. I, H, A fs | 23°2 2 aon 18 387 2 716 5 8:72 45 9-03 49 124:3 8 13:90 105 16°47 129 295'0 11 18:10 194 23°89 267 aes oa 14 28°15 369 38:7 488 524 17 48°5 605 50°5 613 635 18 AT-2 671 65-2 721 744 20 739 764 89:2 836 107°6 893 145:7 982 169°8 1023 230-0 1085 246'0 1118 307°2 1161 383 1219 422, 1231 | 466 1260 501 1255 559 | 1293 621 1287 Nickel-Steel 25 per cent. na OC. t= —186° C, i=15°-0 ©. Ee 1, jah ie H. I. 32:9 1 fs Wi an of. 53:71 23 58:3 0-6 a of 128-1 54 155°8 2-3 354 0-4. 209-5 8-0 344-8 Be a HM 313 1L-0 401 a 516 2-0 498 15-2 529 a 605 17-5 749 33 752, 20:3 958 Messrs. K. Honda and 8S. Shimizu on Nickel-Steel 24:40 per cent. t=18°7 ©. i= — 186° ©. t=23°°5 C. H I H. I H it 29-5 1:9 6-22 23 1:03 3 71-0 3:4 12-54 60 12-92 i 126-2 54 28-15 241 19-16 153 230°4 78 40-4 359 26-2 260 412 9°3 62:7 529 ay 408 541 106 93°6 675 47-6 508: ) 207-2 24:8 363 23°5 98 2 230 our 26°4 482 24-1 449 24-0 506 267 673 DAT 561 Da) 665 26-7 783 24:9 695 24-3 835 26°8 Nickel-Steel 46 per cent. | 1=20°-0 ©. t= —186° C. =21°-0 ©. | | ie es eal (Ve H. a x 10° H 2 x 10° 4-0 03 5-0 09. 4-0 0-6 70 28 iat 28 4:8 ie; Po: 6 2 26-4 9:2 9-4. 40 763 18°5 82-0 20°4 28°1 10°5 168-0 297 1130 22:0 88°7 19:0 259°5 23'°8 310 28:6 207°9 22:8 440 24-8 522, 29°) 326 2a hk 608 25:3 728 3U0'7 442 24-0 760 25°4. 603 QA-4. 746 24-4 Nickel-Steei 36 per cent. G=202- OC: eae ©. 1A SO. © He 2 10° Hi = x 10°. H e x 10° ba 0:3 56 0-6 53 0:3 10:2, DET 10°4 1-4 13:0 oo 37°38 8:0 28:2 51 27:9 6°6 101-4 13-5 63 14:0 719 11:8 205°9 16:0 186°4 23°8 174°8 15:5 363 17-4 289°8 26°5 298 16°38 503 18-4 428 23'8 44] 17°6 616 19:0 587 29°83 5Y2 18:6 756 20°3 738 30°5 yews 19°3 566 Messrs. K. Honda and S. Shimizu on Nickel-Steel 29°24 per cent. ~=19°'5C. ~= — 186° C. t=23° be H z >< OE “EL. . x05: H. | = sv allOP: 16-0 0-6 13:5 0:3 20-0 0:3 55:0 ime) 26:0 0-9 52°6 naa 93°3 ee 66°35 a 101°9 o2 149°8 34 142°2 6:0 171°8 49 291°8 36 264°0 9-6 304 | rhes'g 44] 53 422 Heri 444 | 9:8 591 67 524 15-0 565 TES 699 78 75 16°5 08 Taek 897 9:7 837 178 801 | 13°9 Nickel-Steel 29 per cent. t=11° 5a: [——Vool 7=-14°-0C. jB0. - Se 1EE x > 108. H. a 105. ile ihe 22:9 Ol 18:8 0°3 36°9 19 49°3 2°5 31°38 eit 83°6 rat | 105-7 wee 59-6 a2 147°6 374 206°9 12-6 22-2, 5'6 oe 49 3813 164 349 tick 472 6:9 412 18:0 70 12°8 692 9:0 555 201 633 14:5 850 10°3 681 21-6 770 15°8 Nickel-Steel 28°74 per cent. t— 22-6 thao. G: Ge Oe H : x 10° H. = x 108. H. . x 108, 11-4 06 35-0 10 16-0 0-2 46°7 ry 81:0 4:0 37:0 16 92:6 2-4 138°7 67 76:0 3°5 155:°7 ae | 184-7 8:2 Leow 56 281:0 -4:92 948:0 10°3 250 85 419 56 327 11:8 anys 10°3 681 ffl 519 15°4 457 12:4 782 86° 687 LCF 633 14-7 822 19°4 820 16°7 Magnetization and Magnetic Change of Length. 567 Nickel-Steel 28°32 per cent. | t=20°-0 C. t= —186° U. t=21°°5C 5 al igi e Xe LOR is a x 10° Ee Wi SOEs 21-3 0-2 27-0 0-3 15-0 0-2 50-2 0-6 39-0 15 415 15 85:3 08 66-2 2-7 92-0 3-0 I 1690 1-2 101-0 4-4 144-4 4-9 281-6 2-0 231 9-4 275 8-3 | 378 3-0 368 12:9 420 Tio | 455 3:6 454 143 599 14-0 eile: (0. 48 618 16-2 738 16-4 Sion i GL 826 183 878 17-4 Nickel-Steel 26°64 per cent. | t=24°5 C t= — 186° C. t=21°-0C | | | | ee toe) tae i Soetons | im! i Sx 08 Rites; 0 19-6 0-2 2000 | 2og | be 813 0 42-0 16 47-2 24 | | ise 0 92-6 4:8 Oho ho | 18¢:0 0:08 145:0 6-9 168 93 | | 302 0-13 255 108 300 oe aa] 489 0-15 353 129 AGS ae ao | 680 0:17 490 15-4 530 16900 | 390 0-21 593 16:9 668 122 | 774 17-7 778 18°8 | 935 19:5 Nickel-Steel 24°40 per cent. | t= 252-00. f= 186° 0, #=20°'5 C. i a 5 ] H. 7 * LO? Hi aS 10° Hi: Z 108 aeeaee fi 22-7 0-1 19-0 Oak i ei 50:8 1-4 32-0 0-9 ss “fe 91-0 Bl 78-2 3 4 118 0 156-5 52 149 68 236 0 295 9-3 240 9-5 367 0-02 405 11-2 362 12-2 494 0-08 544 13/1 484 14:6 705 0-10 640 139 621 163 886 O11 839 16-9 795 18-4 568 Messrs. K. Honda and 8. Shimizu on Nickel-Steel 24:04 per cent. 72 0G, t= —186°C. t=23°-0C. Aisne 10°. H. : ~ 10°. Ele ox 108. 22:9 0 34:3 07 35°3 10 Or 01 65°7 25 66:7 z9 196°6 0-2 1240 59 112-0 5°4 281-7 0-3 238°5 9:9 253 10-0 429 0:35 334 13°3 398 127 | 600 0:6 468 17°8 508 144 808 07 622 21-6 695 15°9 839 25'6 858 16-9 The effect of cooling on the magnetic elongation in nickel- steels is exactly parallel to the same effect on magnetization. In nickel-steels containing percentages of nickel greater than 28°74 per cent., the elongation is diminished in weak fields and increased in the strong, by cooling them in liquid air ; with other nickel-steels, the initial decrease of elongation vanishes. The ratio of the elongation in liquid air to that at ordinary temperature increases in strong fields, as the percentages of nickel decrease. In 36 percent. Ni, it amounts to about 1-6 in H=500 C.6.8. and in 28°32 per cent..Ni to oye in 24°40 per cent. Ni to 160 for the same field. For reversible nickel-steels, the elongations after and before cooling coincide with each other. The elongation of other nickel-steels, once cooled in liquid air, is always greater than that before cooling. With 26°64 per cent. and 24°40 per cent. alloys, the elongation is even increased, by heating it to the ordinary temperature. 25 per cent. nickel-steel does not sensibly elongate at ordinary temperature nor in liquid air. (2\ Change of Density by Cooling. The density of the irreversible nickel-steels at ordinary temperature suffered a permanent change, if they were once dipped in liguid air. This singular fact was first observed by Hopkinson*. The following table contains the observed values of density :— * Hopkinson’s Original Papers, vol. ii. p. 240. Magnetization and Magnetic Change of Length. 569 TasLe VII. Alloys. 28:32 °/, Ni. | 26-64/, Ni. | 24-40°/, Ni. | 24-04°/, Ni. / | Before cooling... 15 16 | sig 8:06 | After cooling ... 8-01 7-99 | 8:06 794 Thus the density is diminished by cooling them in liquid air; M. Ch. id. Guillaume® specially investigated this point by measuring the coefficient of thermal expansion at low temperatures He found that the irreversible nickel-steels expand on being cooled in solid carbon dioxide and again expand when heated to ordinary temperatures. Hence the effect of cooling is to doubly diminish the density of the alloys. II. Seconp SERIES. To obtain a constant low temperature lying between the ordinary temjerature and that of liquid air, a method of slow cooling was applied. The specimen-holder in the former apparatus was covered with a water-tight brass cylinder, and a suitable amount of liquid air was poured into the interspace between the cylinder and the Dewar tube. The temperatures above —15° C. were, however, obtained by dipping the specimen directly into a freezing-mixture (snow and common salt) contained in the Dewar tube. The experi- ment was commenced with the specimen in the annealed state, and measurements were made at successively decreas- ing temperatures. During one set of observations, which usually required 7 or 8 minutes, the temperature was fairly constant and its change did not exceed one degree in the most unfavourable case. Since the cooling was very slow and the specimen was doubly enclosed in copper and brass tubes, the temperature of the specimen may be regarded as constant throughout its entire length. The temperature of the specimen was measured by a thermo- elactric couple of platinum and german-silver. The wires were insulated with a thin caoutchouc tube. One of the junctions was brought in contact with the specimen at its middle, while the other was insulated with asbestos papers and inserted in a copper tube. The tube was dipped into the water-bath, and its temperature was observed with a thermometer placed in the bath. The thermoelectric current was measured with a low * Guillaume, Bulletin de la Socrété d’ Encouragement, Mars 1898, p. 275. 570 Messrs. K. Honda and S. Shimizu on resistance galvanometer. The calibration of the galvanometer was made by using a mercury thermometer and a petroleum- ether thermometer. ; Since the character of the pure metals and the reversible nickel-steels was not much altered by cooling them in liquid air, the measurements of the magnetization and the magnetic change of length at the intermediate temperatures were confined to only the irreversible nickel-steels, that is, those whose percentage-contents of nickel were less than 29°24 per cent. (excluding 25 per cent. Ni). (a) Magnetization of Nickel-Steels. The observed values of the intensity of magnetization are given in Table VIII. Here H and I have the same meaning as before. Taste VIII. . Nickel-Steel 29°24 per cent. ee) Ch ee oe. (= — 6225 Hy neat H. I. EL it 0-15 10 0-16 8 0:16 15 0-40 41 0:23 48 0:66 v4 0-79 79 0:49 105 2:26 76 1-34 110 1-10 167 540 152 3:19 172 2°19 232 9-01 227 6:88 226 3:89 298 17-07 341 12°33 264 11-22 331 22°65 391 22:81 287 12-49 453 33'8 450) 46-2 297 67°6 530 61-9 561 754 301 1209 565 1200 670 151-5 306 183-0 583 234-7 758 BIS > UN eee 323 590 329 Liens 4g | B15 369 596 408 BIR.) Nickel-Steel 29 per cent. b= 102-AC: t= —37°?:5 C. f= = 1210-8 3G H I H. I H iT 021 18 0°24 24 0:42 8 0-61 69 0:52 52 1:93 53 / 0:98 109 1:01 107 3:93 107 1:84 164 9:30 203 9°87 215 3°00 214 4:19 287 16°30 309 brat 273. 9:20 405 92-58 376 Laaley, a2 15°50 475 45°5 506 26°62 BY 6s) 31-1 521 10-3 614 66-4 382 62-2 539 160°5 740 161-2 387 126:9 544 280'8 813 302 390 261°5 546 395 845 | 438 | 392 416 548 35) | 5 47 Magnetization and Magnetic Change of Length. Nickel-Steel 28°74 per cent. all t= —10°-4 C. (= — D4 ee t= —108°:0 C. 180 Lie Jat. iC. H. I 0:22 16 0°25 te eee 12 0:43 42, 0°63 62 4:29 64 O-9D 95 1°83 ss 9-5 153 2-9 154 2°99 205 14°64 261 3°69 210 Owlif 275 21-40 859 9°68 SF) 10°99 382 29°83 AY4 19°82 383 25°02 AS 49 2 536 32 0 402 69:9 542, 66°9 607 64:8 415 189:0 5d0 L3H 741 189°0 419 325 550 218:0 827 298°8 420 420 5d] 310 874 445 473 380 904 Aes 38 91 Nickel-Steel 28°32 per cent. $= —12°5 0, | t= —45°-0 C. {= —79°-5 C iE. aL Ee I, H. I Oe in woe 0-16 18 0-45 16 O86 5d 0°50 62 0-96 40 2°63 101 141 121 279 86 4°73 128 ecu) 186 6:24 142 14:98 159 7:00 952 10:98 203 32°9 170 15°46 301 17°85 266 Gro 180 98°78 315 ane 336 180-6 193 73'4 onl 63:2 ALT 332 205 168°9 325 90:0 451 450 211 345 327 191-4 502 438 328 305 526 419 542, 05 0-4 19°5 Nickel-Steel 26°64 per cent. i= —9°-6 C. t= —36°5 C. t= —80°-0 C. H. Th H. i I. it 10:0 2°38 3°95 9 2°15 (2 20°2 7:0 11:38 oe 5:96 39 39°3 17-2 94°95 58 11°60 92 94:6 Ouse 36:6 82 16°43 142 195:7 47°8 55:9 122 31:0 290 312 60:0 129°8 168 50-1 386 470 719 2220 PAL) 63:0 437 332 247 97:2 524 446 A(t 169°5 623 224°6 726 3821 736 392 770 Tas 64 166 572 Messrs. K. Honda and 8. Shimizu on Nickel-Steel 24:40 per cent. fas Oa OF t=—138°9 C. t= — 68° 7 C. t= —105°'5 OC, H if H I isk is H. If 11-4 hy) al 21 30 7 2-6 9 16°9 32 11:5 6-1 10-4. 28 9-2 38 27:2 ov4 19-1 13:0 16°8 57 185 108 38:5 Che 28'2 jh 26:0 119 25'1 176 55°9 1d 43°2 33°5 30°8 187 32°] 268 98°9 161 64°5 43°7 57°3 283 456 339 193°9 24°5 102-7 58°4 69-6 330 70°7 481 291-4 315 170-4 79'8 104°9 401 106°8 561 391 37:2 290°5 4. 0% 177-0 488 166-2 651 323 99:2 297°9 569 2264 717 407 618 320 786 396 826 73 33'6 192 226 Nickel-Steel 24°04 per cent. t=—6°°2 C. t= —13°:2 C. t= —60°'8 C. t= —997 Oe. H. L EH. i i. Tae eer i ee 4 a | lo i. eel) © Ome It) 416. | ate eaneg ee 73 | 94 26:2 260 25:2 37 20°6 82 161 66 43°7 46°8 40°5 71 341 Inst 214 125 741 72'8 794 123 49:1 285 29°3 223 B41 | 9581 1505-1 19501 660 363 1 40 ee 9988 | 1198 | 2954 | 219 | 1O11 | 461 | 62:8 | 452 342 | 1373 | 393 239 | 1948 | 580 | 80-4 | 533 457 | 1483 | 450 930 | 2556 || 661 | 125 eae 400 713 | 2408 | 807 9329 | 842 393 870 | 50-4 87 231 266 In weak fields, the intensity of magnetization gradually increases as the temperature falls till it reaches a maximum, and then gradually decreases. As the field is increased this maximum recedes towards lower temperatures, and beyond 50 o.a.s. the maximum altogether disappears. These ehanges are common to nickel-steels of 29°24 to 28°32 per cent. Ni. In 24:04, 24:40, and 2664 per cent. Ni, the maximum does not appear from the outset; 7. ¢., as the temperature falls the intensity of magnetization at first rapidly increases and soon approaches to an asymptotic value for every magnetizing field. Or —~ Magnetization and Magnetic Change of Length. 3 (b) Length Change of Nickel-Steels. The magnetic change of length of nickel-steel is given in Table IX. and in figs. 4 ¢,d, e, f,g,h, 7 (Pl. X.), from which the curves of the change of length for constant fields are obtained and drawn in figs. 5a, b, ¢, d, e, f (PI. X1.). Tasie [X. Nickel-Steel 29°24 per cent. Nickel-Stcel 29 per cent. t=—0°3C. t=—70°-0 C. t= —38°U0 C t= —123°°3 C. fen |2 10%: EL oP rene | He 82) ye!) x10". ay) 0:3 4-2 02 a4 0-7 10°8 0-2 186 15 15°3 03 12:3 2°8 40°5 18 65°1 2:0 46:1 2:2 36°9 ari 1165 56 118°6 27 61-1 38 723 56 241-2 9°3 251°6 4:0 Tee T7 1758 6:5 321 10°6 333 4°8 2876 9°8 302 70 394 11°8 469 57 | 404 | 11:8 || 415 77 Nickel-Steel 28°74 per cent. Nickel-Steel 28°32 per cent. | t=—8°'3 C. j= —-pa -O.€; f= —45° 2.0: t= —77°-5 C. EH. = x10%.| H. 2 x10%,|| HL z x10%,| H. : 108, 63 | 08 yar aaa an Meee eas el eas hes res 172 | 1 Goria we Vil SeO ll toe ioe Willa ers LES Sl i493 | Ase shu ots se ae) | tesa y 67 0483 |. 40). 795. bs OG 316 57 | 299 7-7 || 353 a1 | 1933 | 3-9 430 Ga 408 86 || 443 59 | 23661 BI 417 6-4 Nickel-Steel 26°64 per cent. Nickel-Steel 24:40 per cent. t= 39°50. | t=—78°-40. || t=-69°2c. | t2—97°-7¢. = gee | F. - SehOe, |. = SAO em |i Eb zt sc 108 | H. = x 108. iy | aS ee Tee ee so ee io79 | 10 | 678 | 20 | 478 | 02 | 670] 19 60 | 20 |166¢7 | 438 (11529 | 92 |ir75 | 38 449 38 | 2605 | 7:0 || 240 3-5 | 281 6-6 390 9:5 || 336 48 | 389 79 ‘All 53 574 Dr. J. Larmor on the Nickel-Steel 24:04 per cent. Pesci t= —64°-0 0. i——96°-0 C. , H & 108 H. x 108 H a 10°. 40 9 0-1 43:5 0-5 20:5 0-1 oan 0-2 1140 2-0 44-9 1-0 266 0-6 217-3 3-7 125-4 3-4 463 jet 402 66 2168 56 318 7-7 412 93 From these numbers, we find a parallelism between the change of magnetization and that of the length-change. In weak fields, the change of length gradually increases as the temperature falls till it reaches a maximum, and then decreases. As the field becomes stronger the maximum elongation is displaced in lower temperatures, and at last vanishes. These changes are common to nickel-steels of percentages higher than 28°32 per cent.; for percentages lower than 26°64 per cent. the elongation for a constant field at first increases gradually and then rapidly, soon approaching an asymptotic value as the temperature falls. [To be continued. | LXIII. On the Constitution of Natural Radiation. By J. Larmor, #.RS. * fie recent paper by Lord Rayleigh on “The Origin of the Prismatic Colours” + recurs to fundamental and delicate points in the philosophy of Optics, first effectively expounded by himself in 1881 and the following years {, on which I desire to offer some observations ; especially as the mode of exposition of the dispersive action of a prism which was adopted by me several years ago § has been the subject of criticism in the papers by Schuster and Ames, to which Lord Rayleigh refers at the beginning of his paper. The first part of the following remarks would doubtless bear condensation, as the full force of Lord Rayleigh’s comparison of the dispersion problem with that of a travelling maintained source had not been grasped when they were written ; but ina subject which so largely turns on the mode of expression, condensation might involve obscurity. There * Communicated by the Author. + Phil. Mae. Oct. 1905, p. 401. t Cf. especially ‘Wave Theory’ §7, Ency. Brit. 1888; Scientific Papers, ol. 11. ‘ § ‘ Ather and Matter,’ 1900, chap. xv. Constitution of Natural Radiation. a does not, however, seem to be in what follows anything that stands in definite contradiction with Lord Rayleigh’s published views. That there is room for still further precision of terminology in this subject is indeed suggested by the beginning of Lord Rayleigh’s paper. It would seem that a definite choice can be made between the two modes of exposition, both o£ which he considered to be allowable. According to the first, “The assertion that Newton’s experiments prove the colours to be already existent in white light is usually made in too unqualified a form.”” On a first impression this remark might be imagined to strike at the roots of all the various instrumental methods that have been elaborated for analysing complex radiations ; for if the analysis brings out features that are not already existent in the radiation, two different methods of analysis (e. g., by a grating and by a prism) can hardly be expected to give concordant results. The alternative mode of exposition is to say that each complex type of radiation is constituted definitely of those colours (simple trains of various wave lengths), into which the Fourier mathematical analysis would divide its vibration- curve: and that various analysing instruments (gratings, prisms, &c.) are capable of revealing this constitution with. different amounts of precision, the outstanding differences between these analyses being treated as due to imperfections of the instruments as regards the purpose in question. This (the usual) point of view is claimed as a valid alternative in Lord Rayieigh’s third paragraph: to hold, as is done ¢nfra, that in some cases the resulting analysis is so imperfect as to be valueless, need not disturb the general validity of this point of view. So far, the matter is one as to the most suitable mode of . theoretical description or formulation. But we presently reach questions on which opinions may perhaps differ as to physical fact. In the spectral analysis of ordinary con- iinuous radiation, the prism and the grating give consistent results, when well understood corrections and adaptations are applied before making the comparison. If these instruments are applied to radiation consisting of a system of sharp, entirely uncoordinated, discrete pulses, such as the Rontgen rays are supposed to be, will this general agreement continue ? It is clear that the grating (if of ideal perfectly reflecting quality) will draw out each pulse into a spectrum, and thus will analyse the radiation. It seems open to question whether a prism will not merely gradually dissipate it by scattering, however wide the pulses may be, even if they are of breadth comparable with the wave-lengths of visible light. If this 576 Dr. J. Larmor on the be so, the prism is very badly suited for the analysis of this type of radiation, and no amount of adaptation of the result will bring the prism into conformity with the ideal grating. The Fourier mathematical process*, as also the ideal grating which reflects back the disturbance in échelon so to say, operates by simply selecting and piecing together elements existing in the original radiant disturbance, so as to isolate periodic wave-trains that on superposition would reproduce the form of the original vibration-curve. On the other hand, what the prism may de to a given isolated pulse would seem to depend on its own constitution. The customary mode of investigation would be to replace the pulse by the equivalent infinite system of component Fourier wave-trains, to find the effect produced on each of them by substituting its expression in the differential dynamical equations of the dispersive medium, and to add the results thus found. Though the original Fourier expansion of the pulse is always analytically legitimate and definite, it is not always allowable, without scrutiny as to convergency, thus to operate on its separate terms and add. Indeed, the particular component waves whose period is a free period of the medium would increase infinitely in importance in the result : thus it. _ must be ascertained whether this infinity of intensity is more than compensated by infinite smallness of the element of period over which it ranges, before the procedure which includes it can he accepted as mathematically legitimate. The insertion of a very small frictional term in the dynamical equation will, however, secure that the component vibration remains finite though great at this critical period, and the analysis then becomes entirely valid. But the problem is only shifted ; it has now to be ascertained whether the limit which this solution approaches as the friction is reduced indefinitely is the same as the solution previously arrived at in the absolute absence of friction,—whether in fact there exists a definite limit. That there is in many cases no definite limit is merely another way of expressing the theory of anomalous or selective dispersion, in which the final steady result depends essentially on the magnitude of the small _ viscous term that must be introduced in order to evade infinities, while the mode of the gradual establishment of that result is likewise undetermined. ‘The question thus arises, whether the proportion of the energy of an incident isolated pulse that goes into this selective vibration is capable of determination by operating analytically upon its Fourier analysis in this way,—whether, in fact, a different line of * Cf. ‘ Aither and Matter,’ § 162. Constitution of Natural Radiation. hi attack would not be required in order to determine it. At any rate, such questions of mathematical validity can arise only in regard to the presence of selective or anomalous dispersion *. The argument of Prof. Schuster (Phil. Mag. Jan. 1904, p- 6 +) arrives at the conclusion that a single pulse is split up regularly into a spectrum by a prism. It appears to start from an implied hypothesis that even an abrupt pulse travels unchanged across the dispersive medium, with the velocity appr opriate to a group of waves. Itffora pulse is substituted a train of waves with wave-lengths variable within the narrow limits % and A+6A, so that the train is very nearly simple harmonic, this statement will be sensibly exact except near the beginning and end of the train: and Prof. Schuster’s representation of the emergent radiation, as consisting of groups of waves, most concentrated in the neighbourhood of surfaces which are oblique to the wave-fronts, then affords an instructive view of the process of dispersion, whether prismatic or diffractive. Butif thisargument is to be pressed so as to include a single sharp pulse, what value of X are we to take as applicable to it? The theorem of definite group- velocity is demonstrated oniy for the compound disturbance _ arising from the superposition of simpler trains of some common type but with slightly differmg parameters,—the trains being unlimited and of simple harmonic type in the usual Stokes-Rayleigh theory. A single pulse will thus not have any definite group-velocity with which it can travel; or, what comes to the same, the different parts of it will travel in the dispersive medium with widely different velocities, so that it will spread out and be dissipated. An argument which assigns a definite velocity to a complex dis- turbance can thus be applicable only to very special types of disturbance ft : for them it must of necessity lead to the same * T fear that I have on previous occasions orally assigned to them a wider importance. It is only the fate of the constituent wave-trains that are near the free period that is undetermined. + The paper, as its title indicates, is concerned mainly with a brilliant application of groups of undulations to the instantaneous explanation of Fox Talbot’s interference bands. In connexion with §6 it may be remarked that the dynamical relations require that a limited disturbance, travelling in a transparent medium, must consist of compensating positive and negative parts. { Formation of the differential equation for the forms of disturbances that are propagated without change of type shows that, when simple wave-trains possess this property, there are in general no other solutions ; the existence of a wave-group in fact implies the existence of the wave- train through which it travels. Phat Mages: 62 Vol, 10;, No. 592 Wo. 1905. 2K 578 Dr. 4J. Larmor on the law of prismatic dispersive power as holds by the same argument for a disturbance consisting of uniform trains of simple waves, if the average wave-length of the latter corresponds to this group-velocity. As these considerations relating to the mode of propagation of pulses apply to both Prof. Schuster’s and Prof. Ames’s arguments, it will not be superfluous to fortify them by the following quotation from Lord Kelvin *, written in connexion with the features exhibited near the beginning and end of a regular gravitational train of surface-waves travelling on deep water :—“‘ Our present solution shows how rapidly the initial sinusoidality of the bead and front of a one-sided infinite procession, travelling right-wards, is disturbed in virtue of the hydrokinetic circumstances of a procession invading still water. Our solution, and the item towards it represented in figs. 6 and 7, and in fig. 2 of § 6 above, show how rapidly fresh crests are formed. ‘The whole investigation shows how very far from finding any definite ‘ group-velocity’ we are, in any initially given group of two, three, four, or any number, however great, of waves. I hope... to return to this subject in connexion with the energy principle set forth by Osborne Reynolds, and the interferential theory of Stokes and Rayleigh giving an absolutely definite group-velocity in their case of an infinite number of mutually supporting groups.” It would appear then that there is no certain ground, on the basis of the ideas pertaining to group-velocity, for con- cluding that a prism is competent to disperse any isolated ethereal pulse, or any series of pulses with absolutely irregular statistics, into a series of simple wave-trains, in a regular manner +, as an ideal grating could do, the number of undula- tions in each train being in that case the number of rulings in the grating or a sub-multiple thereof. , But Lord Rayleigh in his recent paper has thrown fresh light on the subject of the general action of dispersive media, by examining the disturbance that follows an impressed travelling aperiodic pulse, maintained at constant intensity, and showing that such a pulse imitates in some respects closely the behaviour of a wave-train {. He in fact points out the analogy with the surface-waves produced by a boat travelling with uniform velocity on a lake, which, as everybody has * Kelvin, “On the Front and Rear of a Free Procession of Waves in Deep Water.” Phil. Mag. vol. vii. 1904, p. 468. + What apples to a prism would probably also apply to colour- perception by the eye. t A more direct investigation than that quoted from Lord Kelvin’s note of 1877 is given in Prof. Lamb’s ‘ Hydrodynamics,’ 1895, § 227. Constitution of Natural Radiation. a19 observed, are dispersed into simple wave-trains each travelling in its own appropriate direction. It would seem indeed that this illustration bears more closely on the action of a travelling source impressed on the medium than on the fate of an un- supported pulse travelling across it spontaneously. In default of a constant supply of power to the boat, to be spent in making new waves, it would soon lose its velocity unless it had a store of kinetic energy great for its size. Thus this close analogy with ordinary dispersion, which is afforded by the dispersed wave-trains excited by a pulse, impressed and maintained from outside, appears to leave where it was the question of the fate of an isolated unsupported pulse, propa- gated into the dispersive medium and then left to itself. The steadiness which in the ordinary dispersion-theory arises from the succession of fresh waves of the train, is obtained in the illustration above by the maintenance of the energy of the pressural source, with results in close analogy in the two cases. It thus still seems dittcult to evade the force of the argument of Sir George Stokes * :—‘* When you let a ray of light fall on a refracting medium such as glass, motions begin to take place in the molecules forming the medium. The motion is at first more or less irregular; but the vibrations ultimately settle down into a system of such a kind that the regular joint vibrations of the molecules and of the ether are such as correspond to a definite periodic time, namely that of the light before incidence on the medium. That particular kind of vibration among the molecules is kept up, while the others die away, so that after a prolonged time—the time occupied by, we will say, ten thousand vibrations, which is only about the forty thousand millionth part of a second—the motion of the molecules of the glass has gradually got up until you have the molecules of the glass and the ether vibrating harmoniously together. But in the case of the Réntgen rays, if the nature ‘of them be what I have explained, you have a constant succession of pulses independent of one another. Consequently there is no chance to get up har mony between the vibrations of the ether and the vibrations of the body.” The distinction may perhaps be put more definitely. White hight from an incandescent solid is made up of a vast number of pulses arising from the molecular shocks incessantly occurring in the hampered spaces to which the molecules are confined. On the other hand, the Rontgen rays are made up * Wilde Lecture “On the Nature of the Rontgen Rays,’ 1897. Math. and Phys. Papers, v. p. 271. | 2R2 580 Dr. J. Larmor on the of the independent sporadic shocks transmitted through the ether from the impacts of the separate and independent cathode particles. Both kinds of disturbance are resolvable by Tourier’s principle into trains of simple waves. But if we consider the constituent train having wave-length variable between A and A+ 6d, 7. e. varying irregularly from part to part of the train within these limits, a difference exists between the two cases. In the case of the white light the vibration- curve of this approximately simple train is in appearance steady : it is a curve of practically constant amplitude, but of wave-length slightly erratic within the limits 6A and therefore of phase at each point entirely erratic. In the Fourier analysis of the Rontgen radiation the amplitude is not regular, but on the contrary may be as erratic as the phase. The origin of this difference is that the body radiating the white light is presumably so far in a steady state that each element of it has a definite temperature at each instant, which implies a statistical uniformity in the vibratory dis- turbance that is emitted. Or, approaching the subject from the side of the thermodynamics of radiation, each elementary constituent wave-train, say that corresponding to the interval 6d above, has its own temperature which it carries permanently along with it, the same as the temperature of its source supposed a perfect radiator. This temperature is at each point of it a function of the energy-density,and therefore of the amplitude of the radiation. If the amplitude were different along two reaches of the train, the reach of higher amplitude could be in equilibrium of spontaneous exchanges of energy with a perfect radiator of higher temperature than its own source, and ideal automatic arrangements involving intensi- fication of the energy would be possible, in opposition to Lord Kelvin’s fundamental principle of degradation. In the internal equilibrium to which a material system nearly instantaneously settles down, in acquiring a definite temper- ature for each element of its mass, such differences of amplitude must thus have disappeared: the state of uniform amplitude is, in fact, the most probable one™*. In the distinction which is here suggested, the average degree of suddenness of the Rontgen pulses is not involved. That would still be capable of estimation by experiments on diffraction of rays travelling in free ether, in the manner of Haga and Wind. But no physical rationale of prismatic dispersion t except the influence of the vibrations excited in the material system seems now to be entertained ; and this * It is hoped to pursue this idea in another connexion. + Propagation in limited systems such as bars is not to the point. Constitution of Natural Radiation. o81 appears to impose a limit to the types of disturbances that are subject to regular dispersion. Hven in the case of wave-trains excited on the surface of water by a travelling source, where, as Lord Rayleigh remarks, there is no structural periodicity *, the presence of the wave-trains travelling in any direction does, at any rate, depend on the persistence of free periodic trains of waves. if we imagined the water replaced by a medium in which no free wave-trains could travel with velocities within certain limits, then we would expect a gap in the wave pattern formed by the travelling source, corresponding to those limits. The passing remark of Sir George Stokes, which likens the syn- chronous optical vibration of a transparent solid body to the sonorous vibration of the sounding-board of a pianoforte, thus assigning it to regions of the material medium in bulk rather than to its individual molecules t, would bring the optical effect somewhat nearer to the water-wave phenomenon. But the feature in the case of the water-waves to which Lord Rayleigh doubtless intends to draw special attention, is the absence of gradual initiation and delay of effects ; as soon as the source begins to move with uniform velocity, the wave- pattern begins to travel out from it, and as soon as motion of the source stops, so does the formation of the wave-pattern. By a legitimate application of the principle of group-velocity, the number of undulations formed is shown to be connected with the distance over which the source has moved ; just as the number of waves formed from a single freely travelling pulse by a grating is determined by the number of its lines over which the pulse has travelled. At first sight, as above stated, it is difficult to detect sufficient similarity to the optical case. But if we consider (with Lord Rayleigh, p. 404) a thin plane pulse incident from free ether obliquely on an infinitely extended plane face of a refracting medium, the intersection of the pulse with the face will be just such a maintained disturbance, travelling * Prof. Schuster (Phil. Mag. Jan. 1904) puts the point as follows :— “As we may imagine continuous media of such elastic properties as to give dispersion, the true explanation must be independent of the sympathetic vibrations,” on which I had relied in ‘ Atther and Matter,’ . 248. The force of this is obvious: yet, when friction is ruled out, what can there be, as a matter of fact, except conspiring periodicities in time (free periods) or space, to modify simple elastic waves, which travel without change, into the dispersive type ? + In the case of a vapour, the molecules, being isolated, must however operate independently. 582 Dr. J. Larmor on the along the face, as we require. If the medium has the dispersive quality fully developed, for all disturbances however sharp, 2. e. if the differential equation determining dispersive vibration has no limits to its full application to such dis- turbances, the resolution into trains of waves must be granted as a necessary consequence of the analysis for a steady travelling source. This rationale of the dispersive refraction, at a plane surface, of an obliquely incident thin plane pulse, is one of those obvious things that when once grasped form a permanent addition to our stock of physical imagery *. One can picture its appilcation to water-waves. A tract of water may be imagined, of small uniform depth h, in which therefore all waves travel with the same ae “gh, separated from a region of deep water, in which the velocity of a train depends on its wave-length, by a straight boundary. A disturbance consisting of a thin plane ridge can advance obliquely towards the deep “water without change of form ; the successive parts of the ridge reach the boundary in the manner of a maintained local disturbance running along the boundary with uniform speed, of which a definite fraction is transmitted across into the deep water, the rest being reflected back. The mode of this transmission is, by symmetry, the same as if that part of the disturbance were doubled and the deep water were unlimited on both sides: regular wav2-trains are shed off dispersively in the different directions s,as in the case of the boat described above, with wave-lengths such that their velocity can just keep up with the travelling source, while the distribution of intensities between the various directions depends on the character of the moving source, 2. e. of the incident travelling ridge of water. The waves must, in fact, form a steady pattern travelling with the source : thus the velocity of free propa- gation of the component train travelling in any direction must be the component in that direction of the velocity of the source. But as the travelling source has finite size, this component train, though nearly homogeneous in wave-length, is not quite so; being nearly homogeneous, the dispersive quality of the medium wil! make its waves travel in croups, which progress in the known manner. with only half the velocity of their component waves. ‘Thus after the train is well formed, the groups of disturbance will recede from the @ Lord Rayleigh considers this explanation of the refraction of a pulse into a dispersive medium to be less simple than his first case of the propagation of a plane pulse in such a medium; but owing to the difficulty described above, regarding the maintenance of such a pulse, I have failed to appreciate the argument in that case. Constitution of Natural Radiation. 583 source with a velocity equal to the difference of these two velocities, and Lord Rayleigh’s determination of the length of disturbance emitted in a given time ensues,—subject, however, to the reservation quoted above from Lord Kelvin as regards the extreme head of the train. The account of the process, which is indicated by Lord Rayleigh, seems in its essentials to be fully verified. Yet the quotation above made from Sir George Stokes, in which the imagery is optical instead of hydrodynamical, appears to show a different aspect of the picture which we are bound to follow out ; though Lord Rayleigh bas guarded himself against it by his reservation, “so long at least as we are content to take for granted the character of the dispersive medium—the relation of velocity to wave-length—without inquiring further as to its constitution.” The postulate thus indicated is that the partial differential equation of propa- gation is to hold true without limitation. This implies that the dispersive medium must be homogeneous in space ; if it had minute alternating structure, then this differential equation could not of course be applied without modification to waves of length comparable with the dimensions of that structure,—a circumstance on which Cauchy reared his original attempt at an explanation of optical dispersion. But it requires also that the medium should, so to speak, be homogeneous in time. An optical dispersive medium is made up of elements which have periods of free vibrations of their own, that are more or less durable ; the differential equation will not hold for disturbances whose scale of duration is so small as to be of the same order as the time of the natural subsidence of free disturbance among the elements of the medium. In connexion (originally) with the dynamical theory of viscosity in gases, Maxwell introduced the term tame of relaxation to express the time, roughly assignable, that it would take for a local derangement of the molecules of the medium to smooth itself out. In optics it is the time needed for the free irregular vibrations of an element of the medium, produced by a local shock or other disturbance, to die out by dissipation into surrounding elements. The theory of regular dispersion of a disturbance into wave-trains caused by refraction, re-stated above for the hydrodynamic case of waves on water, cannot be applied in the optical case unless the scale of duration of the disturbance is long compared with the time of optical relaration of the dispersive medium. In Sir George Stokes’s illustration, taken at a venture, the time of relaxation would be ten thousand times the period of a light-wave ; if so, regular refraction and dispersion would 584 Prof. J. J. Thomson on the Emission of hardly be established for sequences of less than ten thousand similar waves. Perhaps the only means of even roughly guessing at the time of optical relaxation is by the time-lag in such “phenomena as fluorescence, which are connected in part with free internal vibrations excited in the elements o. the medium. Stated in the present form, the criterion that a Réntgen eether-pulse should be regularly refracted and dispers sed into wave- trains, according to a process of which Lord Rayleigh’s rationale has been paraphrased above, is that its duration should be long compared with the time of optical relaxation of the dispersing medium. In the hydro- dynamic illustration the restriction does not arise, for the time of molecular relaxation is far beneath the period of any observable surface-waves. To sum up, it now seems clear that Lord Rayleigh’s application of the phenomena of a maintained moving source gives an adequate picture of the modus operand: of the dispersion of an incident aperiodic disturbance into regular wave-trains by refraction, for all types of disturbance that are slow compared with the period of natural molecular relaxation of the refracting medium,—provided, however, anomalous dispersion, which cannot be included unless a quasi-trictional term is assumed in the analysis, plays a part which is unimportant. But it is still held to be unlikely that ethereal pulses of the type of the Rontgen rays come as a rule within this limit. If this be so, white light, such as can be regularly dispersed by a prism, cannot consist of wholly irregular ethereal disturbance; each Fourier com- ponent, comprised within say the infinitesimal range of wave-lenoth between % and 7+6A, must have sequences of regularity in its amplitude, of dnnaition comparable with the time of optical relaxation of the dispersing medium. Cambridge, October 10, 1905. LXIV. On the Emission of Negative Corpuscles by the Alka Metals. By J.J. THomson, MA. PRS T is well known that the alkali metals when exposed to light give out negative corpuscles, even when the light is of very feeble intensity. Thus Hlster and Geitel found that the light emitted by a piece of glass rod heated to a dull red heat was sufficient to make rubidium emit cor puscles. It has not, however, as far as I am aware, been noticed that * Communicated by the Author. Negative Corpuscles by the Alkali Metals. 585 with these metals there is a small emission of corpuscles, even when all external light is excluded. The following experiments show, however, that rubidium and the liquid alloy of sodium and potassium give out corpuscles in the dark. The experiments showing this were made as follows :—A gold-leaf electroscope with quartz insulation was enclosed in a glass vessel, which was exhausted to an exceedingly low Fig. 1. Ee ps eeenies (Manta: ys pt ve 2 Sy Coes, m0 25S vacuum by means of charcoal cooled to a very low tem- perature by liquid air in the way discovered by Sir James Dewar. The rubidium or Na-K alloy was placed below the gold leaves of the electroscope, care being taken to have the surface of the metal as clean as possible; the metal was earthed by means of a wire fused through the glass. The vessel was placed inside a box made light-tight by means of felt, the tube containing the charcoal which protruded from the box was painted over with lamp-black. ‘To measure the divergence of the leaves of the electroscope, these were momentarily illuminated by a faint light transmitted through a red glass window, the position of the leaves was deter- 586 Prof. J. J. Thomson on the Emission of mined by a reading microscope passing through the side of the box; after a reading had been taken, shutters were put before the window and the eyepiece of the microscope covered withacap. The readings only took a second or two, but even in that time the red light produced an appreciable leak in the electroscope ; this part of the leak can, however, easily be separated from that taking place in the dark as the latter is proportional to the interval between two readings, while the former is independent of this interval. To test the efficiency of the means taken to exclude the light, some of the experiments on the rate of leak were made ina photographic dark room, others with the case exposed to the light of the laboratory ; the leak was the same in the two cases. Another proof of the exclusion of light is that a sensitive photographic plate placed in the case for 48 hours was not fogged. When the leaves of the electroscope were charged with positive electricity there was, even in the dark always, small leak of electricity from the leaves, while there was no perceptible leak when the leaves were negatively charged. The positive leak was entirely stopped by a transverse magnetic field: this proves that it is due to negative cor- puscles emitted by the rubidium or the alloy of Na and K, On some occasions the positive leak was abnormally large. This was traced to the presence in the tube containing the electroscope of minute quantities of hydrogen ; it was tound that this gas had an extraordinary influence on the emission of corpuscles from electropositive metals. To investigate this more fully, an arrangement was added to the glass vessel containing the electroscope, by which bubbles ot hydrogen could be admitted from time to time into the vessel. ‘lhe admission of a very small quantity of hydrogen produced temporarily a very large increase in the rate at which electricity escaped from the positively charged leaves of the electroscope, the rate of leak after the admission of the hydrogen being often ten times its previous value. The increase in the leak rapidly died away, and after about 20 minutes the leak resumed its original value ; the admission of a fresh supply of hydrogen, however, sent it up again. The admission of small quantities of air or carbonic acid did not produce any appreciable increase in the leak. It would appear that while these electropositive metals are absorbing hydrogen, the rate of emission of negatively electrified particles i is greatly increased. The influence of hydrogen on the emission of corpuscles Negative Corpuscles by the Alkali Metals. 587 from a hot platinum wire has been observed by Dr. H. A. Wilson ; the increase in this case is very much greater than that with cold alkali metals. In a previous paper (Proc. Camb. Phil. Soc. xiii. p. 49) I showed that the radioactive substances radium and poloniam emit when cold slowly-moving negatively electrified cor- puscles. The experiments just described show that this property is also possessed to an appreciable extent by substances not usually regarded as radioactive. With more delicate apparatus than that used in these experiments it Is probable that this property might be detected in all sub- stances :—I tried in my apparatus, in addition to the alkali — metals, lead, silver, and mercury, but could get no indication of the emission of corpuscles by these metals. The alkali metals:give out corpuscles when in the gaseous as well as in the solid state ; this was proved in the following way. If the gaseous atoms of sodium give out negative corpuscles, the atoms themselves will be positively charged and so will be attracted by negatively electrified bodies : this was found to be the case. Sodium was heated in a highly exhausted flask, the cooler part of which contained two glass tubes down which ran wires. The wire in one tube was connected to the positive pole of a battery of small storage-cells giving a potential-difference of 600 volts, the wire down the other tube was connected with the negative pole of the same battery. When the bottom of the flask was heated, the sodium evaporated and condensed on the two tubes. When the wires down these tubes were disconnected from the battery, the deposit of sodium was pretty equally distributed between the tubes. When, however, the wires were connected with the battery, there was very little deposit on the tube connected with the positive pole, while the deposit on that connected with the negative pole was very dense. If the connexions with the battery were reversed, the sodium began to deposit on the tube which had previously been clean, while hardly any increase took place in the deposit on the other tube ; showing that the effect was due to the elecirical charges on the tubes, and not to any want of symmetry. In these experiments the tubes were not ab- solutely dark. ‘This deposit of sodium on a negatively electrified surface may be compared with the flow of “radium emanation to a negatively electrified wire. The result at which we have arrived from the preceding experiments, that some substances emit many ccrpuscles, while others at the same temperature only emit few, if any, 288 Prof. J. J. Thomson on the Emission of has important consequences when considered in relation with the Second Law otf Thermodynamics. For, consider an enclosure at a constant temperature containing two sub- stances in electrical connexion, one A giving at this tem- perature a copious supply of corpuscles, the other B few, if any: we see that we could utilize the stream of particles from A so as to do mechanical work. But since everything is at the same temperature, it follows from the Second Law of Thermodynamics that the energy required for this work cannot be derived from a lowering of the temperature of any part of this enclosure; it cannot come from thermal sources, but must come from some change in the state of the working substance, presumably from some diminution in the internal energy of the atoms of this substance. In- vestigations made with the object of seeing whether prolonged emission of corpuscles, such as might be produced by long- continued incandescence, produces any appreciable effect on the properties of the subject, might be expected to give interesting results. There are undoubtedly changes produced in a substance such as a piece of platinum wire by long- continued incandescence, but we do not know as yet whether these changes are such as indicate a change in the platinum atom, or whether they are merely physical, such, for example, as would regult from the expulsion of gases absorbed by the wire. Again, many metals after the emission of corpuscles by exposure to ultra-violet light show “ fatigue,” i. ¢., the rate of emission of corpuscles after long exposure becomes less than it was initially: this is usually ascribed to the formation or removal of films of gas or to a roughening of the surface ; it is possible, however, that it may partly be due to some change in the metal itself. Investigations on these points would be of especial interest because, if the energy of the corpuscles does come from changes in the atomic energy, we have here a case in which this transmutation of energy can be started and influenced by external conditions, such as incandescence or the incidence of ultra-violet light or Rontgen rays. On this view, the energy of the corpuscle emitted is not derived directly from the work done on the corpuscles by the electric field which exists in the Rontgen rays or in the light. The rays act as detonators, causing some of the atoms on which they fall to explode, and the energy of the corpuscle is derived from the energy liberated by this explosion. In the case of radium and other radioactive substances we have probably also the transformation of internal atomic Negative Corpuscles by the Alkali Metals. 589 energy into the kinetic energy of corpuscles and @ particles, but in this case, as far as is known, the transformation is quite uninfluenced by external physical conditions, and is thus beyond our control. If, however, the view we have been considering above is eoneiet the tapping of the internal atomic energy “by corpuscular stre eams 1s to some extent under our control and can be brought about by elevation of temperature or by ultra-violet light. Since the emission of corpuscles goes on to some extent at all temperatures, and since inside a body the energy of these corpuscles would ultimately be transformed into heat energy, there is probably a continual transformation of internal - atomic energy into heat: this would cause the interior of a mass of metal to be hotter than the surface, the increase in the inside temperature depending on the amount of energy transformed, on the size of the body, and on its thermal conductivity. . If the body isa sphere of radius a, of uniform composition, we can easily show that 6, the difference between the tem- perature of the surface and that at the centre, is given by the equation _ 9a an 6h’ where g is the amount of energy transformed into heat per cubic centimetre per second, & the thermal conductivity of the substance. For bodies comparable in size with the earth, a very small amount of transformation of internal atomic energy into heat would produce very large differences of tem- perature between the centre and the surface. Thus, if the conductivity of the sphere were ‘01, which is about three times that of granite at the temperature of the earth’s surface, there would be a difference of 3000° C. between the centre and surface of a sphere the size of the earth if q=45x10-", 2. ¢., if the atomic energy transtormed into heat per e.c. in 100 million years were less than that required to raise the temperature of 1°5 gramme of water 1°C. If the corpuscles were emitted with a kinetic energy corre- sponding to that which would be acquired by the fall of their electric “charge through two volts, the emission by an atom of a corpuscle once in a thousand million years on an average would be far more than sufficient to produce the required transformation of energy. ‘The temperature differ- ence between the centre and the surface being proportional 390 Emission of Negative Corpuscles by Alkali Metals. to the radius of the sphere, leads us to expect that with bodies of the size we could manipulate in the laboratory the differences of temperature would be exceedingly small unless the emission of corpuscles was very copious. It would, however, be interesting to test whether the inside of a block of lime which, as Wehnelt has shown, at high temperatures emits large quantities of corpuscles, is at such temperatures appreciably hotter than the outside. If there is a continual transformation of the internal energy of the atoms into other forms of energy when the atom is emitting corpuscles, we should expect that the internal energy of an atom would vary with the treatment it had received ; that it would have been more diminished if the atom had been maintained for long periods in a state of incandescence than if it had been kept cool ; we should thus expect the internal energy of an atom of an element in the sun to differ from that of the same atom on the earth : if this is so, then this variation in the internal atomic energy must be without effect on some of the properties of the atom. Thus, for example, spectrum analysis shows that the periods of vibration of an atom in the sun do not differ appreciably from those of the same element on the earth ; we have indeed at present no evidence of the existence of any difference in the properties of atoms of the same element. We can, however, easily conceive an atom constructed in such a way that before the internal ener gy had diminished sufficiently to appreciably alter many of its properties, the atom would become unstable and explode, breaking up into atoms of elements of a different kind. Suppose, for example, that the atom consists of a number of corpuscles arranged in layers on the surfaces of concentric shells, and that the loss of internal energy by the atom is mainly due to the loss of kinetic energy by those corpuscles in the outer layer, this will hardly affect the times of vibrations of the corpuscles inside, while the outer layers may lose such a large amount of energy that their configuration becomes unstable, and the corpuscles in the outer layers rearrange themselves: in doing this, such a large amount of kinetic energy may be liberated that the atom explodes and breaks up into atoms of different kinds. Thus, in a case of this kind we should have the atom losing internal energy and yet as long as it remained intact the great majority of its periods of vibration would be unaltered, and the atom would explode before the change in its internal energy was sufficient to appreciably affect the great majority of its properties. Eesti] LXV. A Repetition of Fizeaws Experiment on the Change produced by the Earth’s Motion on the Rotation of a Refracted Ray. By D. B. Brace*. ie following experiment was undertaken for the purpose of re-examining the results which Fizeau + announced he had obtained, nearly fifty years ago, in observing a change in the azimuth of a plane-polarized ray when refracted through a plate of glass, respectively along and against the earth’s motion through space. The results of my observations, made under similar con- ditions, show that the effects which Fizeau obtained must have been due to other causes than those whose effects he | supposed he was examining. This conforms to that which we should expect from the results of other experimenters, examining the problem by other modes of experimentation, and also to the prevailing opinion that the results of Fizeau’s observations were somewhat doubtful. In fact it appears that he has so expressed himself in this matter t. Notwith- standing these facts, reference is still made to the positive results of this experiment, which are the only ones ever obtained by experimental means on the problem of the ether drift.” It would have been highly desirable if Fizeau himself could have repeated his experiments long ago. Perhaps, however, the evidence from other sources did not warrant this; but the undoubted care and skill devoted to this experiment have left an impression that, perhaps, after all the test involved surface conditions which did not enter in the other experiments and which might give the positive results obtained. Hixperience in several similar problems in polarization recently has led me, incidentally, to believe that it would be entirely possible to repeat this experiment with sufficient sensibility to give conclusive results. Two principal factors have made this possible :—first, a sensitive-strip plane polarizer §; and, second, the use of a “ crossed” system of thin refracting plates. This system reduced the double refraction to a minimum, and also compensated for the colour dispersion that Fizeau had to contend with, thus allowing me to use white light with, consequently, a higher sensibility in the halt-shade system. * Communicated by the Author. t Ann. de Chim. et de Phys. (3) lviil. p. 129. t Lorentz, Versuch einer Theorie, Leiden, 1895, p. 2- § Phil. Mag. Jan. 1903, p. 161. 592 Prof. Brace on the Change produced by the Fizeau used a combination of elements to compensate for the dispersion and the unavoidable double refraction and, also, to magnify the expected rotation of the ray. He further readjusted the beam of sunlight, which he used, on reversing the system, and this seems to have given him variations in his readings. These possible sources of spurious effects have been eliminated in the arrangement which I used. His experiment is based on Brewster’s law for a refracted ray, namely, tan @ cos (@—1r) where 2 and r are the angles of incidence and refraction and a and @B the corresponding azimuths, respectively, of the plane-polarized ray. Any change in the index would indi- cate itself by a variation in the angle rv and, hence, in the azimuth 8. Fizeau usually used, for producing the effect, two so-called rotary piles, each containing four slightly prismatic plates of glass 1 to 2 millimetres thick, and mounted slightly inclined to one another. In his experiment the incidence of the ray upon these piles was 70°, and the azimuth of the polarized beam, usually 20°, sometimes 30°. He also generally used two piles, at a smaller inclination, for compensating the elliptical polarization due to the double refraction in the rotary plates. For compensating the rotary dispersion, he inserted during a part of his observations a natural rotary substance, such as quartz, or some of the essential oils. Binally, to increase the effect, he inserted several “ amplifying” piles which magnified the effect some 30 times. His polariscope consisted either of crossed nicols, an interference system, or the sensitive-tint single or biquartz systems. Sucha complicated arrangement necessarily caused a great loss of light and thus reduced his sensibility. In my preliminary experiments I adopted a similar arrangement to that of Fizeau. In order to avoid as far as possible the disturbing factor of double refraction, ten plates were cut from well-annealed optical glass np = 1°5178. These plates were ground wedge-shaped so that the internally reflected images would not enter the field of view. They were 20 mm. long and 15 mm. wide, and their faces made an angle with one another of approximately 50’ in the direction of their greatest lengths, their thickness diminishing from 0-6 mm. to 0°3 mm. These plates were set on rings, upon which they could turn, whose planes made an angle of 70° with the vertical plane, in which plane a second ring, carrying the first ring, could be made to rotate. Thus, with an tan B= ————_~ Earth's Motion on the Rotation of a Refracted Ray. 593 incidence of 70°, the azimuth of the plane of polarization of a ray could be varied at will. These were then mounted, one at a time, between the polarizer and the analyser. Starting with an azimuth of 45°, the analyser was adjusted for minimum intensity, being shifted to receive the light axially, since, on inserting the wedge, the direction of the ray was changed. A second plate and its mounting was then inserted and adjusted so as to receive the ray from the first one in an azimuth of 45°, the wedge-shaped plate being turned in its own plane upon its ring-carrier until the multiply reflected images were thrown out of the field of | view. ‘This necessitated a somewhat spirally-shaped arrange- ment of the system when the analyser and all the plates were finally mounted. A thin strip mica compensator * was placed after the polarizing half-shade system, to compensate for any slight amount of elliptic polarization which might be produced by the plates themselves. This was quite effectual and, with three or four plates, moderately close settings could be made with the plane-polarizing half-shade system. However, with white light, the colour dispersion due to the rotation prevented anything like the sensibility required by the experiment. I attempted to compensate for this by means of quartz, as did Fizeau, but still found that, with white light, the sensibility was far too small, I then tried sunlight, using one of Wilfing’s spectral “ sifters”’ to obtain homogeneous light. But here my intensity was too low. A powerful mercury lamp gave similar results. I then saw that white light and complete compensation of the dispersion, due to the rotation of the plates (this rotation was approxi- mately through one quadrant), would be necessary to attain the required sensibility. Only moderate pains had been taken in grinding the plates, and I found that, with all ten plates in, the astigmatism was so large that the definition of the “ half- shade” was greatly reduced. I therefore decided on a different arrangement which, though apparently unlike that of Fizeau, involved the principle of his experiment and, hence, would be valid in a repetition of the test. This con- sisted in combining pairs of plates into the “ crossed ” system mentioned above. ‘Thus (fig. 1) if in the equation tan a oe ES cos Gay (8—a) is the rotation experienced by a ray after refraction at a single surface, 6(8—a) would be the increment, say, due * Phys. Review, Feb. 1904, p. 70. ; Plul. Mag. 8. 6. Vol. 10. No. 59. Nov. 1905. 28 d94 Prof. Brace on the Change produced by the to the effect of the earth’s motion upon the velocity of propagation in the glass. The total increment for a single plate would be 26(8—a) approximately. If now the ray be reflected back through the second plate, in the same azimuth Pig. i. with respect to the incident ray, it would experience similarly a rotation of 2(8'—a’) ; and, since its direction is reversed with respect to that of the motion of the earth, it would experience a decrement of 26(6'—a’). Hence the azimuth of the ray will appear to an observer to have changed by an amount equal to 46(8—a), approximately, for the pair of plates, if a’ =a and f’=B. Fora second pair of plates, in series with the first, the change would be 86(8—a), and so on. ‘The full lines in the figure show the azimuths of the ray, without the effect of the earth’s motion, and the numbered dotted lines, those with the supposed changes in the planes of polarization. Thus, line 1 is the new azimuth after passing the first plate, and line 2 the new azimuth after returning through the second plate of the pair. Similarly, if the Earth's Motion on the Rotation of a Refracted Ray. 595 system is reversed in the direction of ‘ drift,” line 1’ would be the azimuth after the first plate and line 2’ after returning through the second plate. Thus, the total change in the azimuth is equal to the angle between 2 and 2’, and so on for any number of pairs. It is evident, from the figure, that, neglecting the effect of “drift,” rays of all colours will emerge from the system with their absolute directions of vibration the same as when incident on the first plate. Hence, if we start with our nicols crossed, the insertion of these pairs of plates will not affect the final direction of vibration of the rays, and we shall have perfect compensation of the rotation, as well as of the rotary dispersion. Hlliptic polarization may of course occur to a greater or less extent, due to imperfect annealing. The arrangement, as finally adopted to utilize these various ideas, is shown in fig. 2. I is the radiant (a Nernst filament Fig. 2. of 110 volts), N is a nicol for polarizing the light before entering the half-shade system, in order to reduce the diffused light arising from internal reflexion within the polarizer P proper of the half-shade system PS, M and M’ mirrors silvered on the front surface, L a lens forming a conjugate image of the radiant I on the analyser A, S the sensitive- strip, 1, 2 and 1’, 2’ the two pairs of wedges, T a small telescope of 2 or 3 diameters. and C the reading circle carrying the analyser and provided with a micrometer-screw. The sensitive-strip 8, which I have already described *, consisted of a plate of Iceland spar 0°15 mm. thick and so mounted within a cell containing carbon disulphide that its optic axis was perpendicular to the ray and covering one half of the field of view. The micrometer tangent-screw was provided with a drum so that it could be read directly. The entire system was mounted on a wooden support, so that the axes of the ray were in a horizontal plane, and this was * Phil. Mag. Jan. 1903, p. 161. 252 596 Prof. Brace on the Change produced by the placed upon the same pivoted trough which I used before in my experiments on the double refraction of water* and on rotary polarization +. A seat was also fastened upon the trough so that I could keep my eye uninterruptedly in a fixed position H, before the telescope T, when the system was rotated. The distances IM and MM’A were 40 ecm. and 180 cm. respectively, and the angle MM’A was 10° approxi- mately. The plates 1, 1', 2, 2’, were selected from the ten plates mentioned above, so as to give as far as possible the best definition. The analyser was first set for a match, and then plates 1 and 1’ inserted, and the mirror M’ and analyser A adjusted so as to bring the image of the radiant upon the centre of the latter. Plate 1’ was rotated in its own plane until the multiple images disappeared, and then its carrier was turned in its vertical plane sufficiently to give a match, the azimuth of the plates thus becoming the same ~ with respect to the direction of propagation of the ray at incidence. Plates 2 and 2’ were then inserted and similar adjustments made. After various minor adjustments, 1 found that either half of the field could be made practically black, on rotating the analyser, showing that the ray had suffered but a slight amount of depolarization by the reflexion from the mirror M’ or by the transmission through the plates. The vanishing line, however, was somewhat indistinct, but, by diaphragming the aperture of the system down to about 6 mm. at L,I had a small portion of the field which was fairly uniform with a moderately sharp vanishing line. With carefully figured plates and a more intense source I might have increased my sensibility considerably, but I found this large enough for the purpose as it was. The magnitude of the probable effect Fizeau calculated by means of Fresnel’s ‘coefficient of convection”. for the “ eether drift,” namely, (u?—1)/p?. The change in pu due to the velocity v of the glass plate, the velocity of propagation of the ray being V, becomes yi aw i). In order to find the corresponding change in the azimuth of the ray due to such an effect, he compared the rotations of two piles of plates of crown and flint glasses, respectively, with the difference in their indices. Thus he found 9 (Be a ee ate 0 be * Phil. Mag. April 1904, p. 318. Tt Phil. Mag. Sept. 1905, p. 388. Eartl’s Motion on the Rotation of a Refracted Ray. 597 for the difference 1°6224—1'5134 of the indices of the two kinds of glass. But ot ee from the previous equation, on substituting the values of v and V, where AE 94 ey vy 10 and w=1°5134. 6(B—a)_ 1 Hence he finds Eg) = 9500" For a complete reversal of the ray we should have twice the : : ] - ae ee increment of the rotation, or j559- Correcting this for the obliquity of the ray to the drift, on account of the refraction of the ray within the glass, we have a change in the rotation of we: or, since 8—a=6° 40' for each plate with an incidence of 70° and an azimuth of 20° in his experiment, we have, finally, a0 x 6° 40'=16" as the probable effect on a single v plate of the motion of the earth. In my experiment the incidence, 70°, and the index, 1°517, were, approximately, the same as in Fizeau’s experiment. However, instead of an azimuth of 20°, I used an azimuth of 45°, each plate being adjusted with respect to the preceding one to attain this end. Furthermore, on account of the inclination of the plates and the angle MM’A, the deviation of the path of the ray within the plates was less than in : : : i : Fizeau’s experiment, so that his factor of ;,59 reduced to (Leaiiane : igo 12 my arrangement. Direct measurements of the angles of rotation, for azimuths 45° and 20°, gave 8°6 and 51, respectively, for each plate, using white light. Fizeau obtained with a single one of his plates a rotation of 6° 40’. This made his calculated probable effect 16” for each plate. The corresponding effect in my experiment was 21/7, for each plate, which is 5/3 greater than that for an azimuth of 20°. With the four plates the calculated probable effect should then be + 0°-024. The sensibility of my optical system was such that I could certainly have detected a change of less than 0°°02 under favourable conditions with an unfatigued eye. On reversing the system I was unable to detect any change whatever. In order to give greater weight to my observations, I took a series of settings, on several different days, whose means showed that such an effect would have been detected several times over. Oo (sobs Oh So@+2 ag that 7 So. == n+2 . (25) 2 —1 Having thus found sp, we see that the ionization is proportional to (@ + So) 2/™+2) — (2 +5,—d)/+2), when «particles from the highest stratum of the radium layer 602 On the a Particles of Radium. pass the ionization chamber by a distance measured in air, and those from the lowest by a distance z—d, d being the effective thickness of the layer measured in air. When zis less than d, as in the top part of the ionization curve, the lonization is proportional to ( a+ Ste Eom spel +2), I find that when n is put equal to 1, d being estimated at ‘5 CM., S=2'01 Cm., when #=—2, s,=—1°35 CM, sae n=3, s='8 cm.: and I have calculated a few values on the ionization curves given by the above formule for each of these values of n. I have placed alongside some corresponding actual observations, making all the curves nearly agree at a distance 6°4 em. from the Ra. | Distance Calculated Values of Ionization. | from Observed | Radium. n=l. yy eee Values. | 70 0 0 0 0 68 132 120 116 115 6°4 282 277 283 273 6:0 266 248 237 250 55) 252 223 200 218 50 242 205 176 200 | 4°5 233 191 157 187 | 4:0 224 he i767 144 WT? ay) 217 168 Lee 172 So far, therefore, as the evidence goes, it is now in favour of the value n=2. Itis interesting to observe that when one particle flies at great speed past another which is relatively at rest, the energy given by the ionizing to the stationary particle, in consequence of their mutual attractions or repul- sions, is inversely proportional to the square of the velocity of the moving particle. (Report of the Australasian Asso- ciation for the Advancement of Science, Dunedin, 1904, p. 64.) I am, Gentlemen, Yours faithfully, W. H. Brace. [ 603: ] LXVII. On Surfaces of Discontinmty in a Rotationally Elastic Medium. By T. H. Havetoon, M.A. D.Sc. Fellow of St. John’s College, Cambridge™. § 1. Introduction. HE kinematics of wave propagation have been studied in _ great detail recently by Duhem+ and Hadamard {. Their method consists in following the motion of surfaces of dis- continuity in the fluid and in developing in connexion there- with the idea of compatibility or persistence, due originally to Hugoniot. In $§ 2-5 of the following paper a short account of this method is given, and the rest of the paper consists of an application to the electric ether when this is considered as a rotationally elastic medium; the production and mode of propagation of discontinuities of various orders are discussed, together with the relations of various vectors at the surface of discontinuity. © § 2. Surfaces of Discontinuity im general. The discontinuities which we shall consider are not perfectly general, but are limited by the condition that they are situated on isolated surfaces. Let ® be any function of «2, y, z, ¢ and the derivatives of the coordinates with respect to the time, and let S be a surface on which ® is discontinuous at any time ; let S be given by T(, Ys &, t)=0. The surface 8 divides the space into two regions 1 and 2. At each point of the region 1, ® is continuous and takes a definite value ©, ; further, at each point (x, y,, 2) on the surface 8, ® takes the definite value @? and is said to be con- tinuous provided the path by which (2, y, z) approaches the point (2%, Yo, 2) lies entirely within the region 1. Similarly for the region 2 there is a limiting value ®} which the function ® takes at the point (x, y, 2) when approached by a path lying entirely in the region 2. The difference ©{—° is the measure of the discontinuity of ® on the surface 8 and is written [ ®]. Next suppose that ® itself is continuous on 8, but that its first derivatives are discontinuous; that is, oo: BY) BY], Boje * Communicated by the Author. ft Duhem, Recherches sur ? Hydrodynamique, Paris, 1904. { Hadamard, Legons sur la propagation des Ondes, Paris, 1903. 604 Dr. T. H. Havelock on Surfaces of These latter quantities are not absolutely independent. For if we vary ® along a path on the surface 8, firstin region 1 and then in region 2, we have BeIe+ Be]er BE] ene where the variations dx, dy, 6z are connected by the relation Sf p24 by 4 2 b2=0. Ow Oz Hence we have the relations of Beylar _ pawy (ar _ ay Oxide Lay) oy Oz" Again, if we suppose ® and its first derivatives continuous, but the second derivatives discontinuous on 8, we find in a similar manner the following relations among the second- order discontinuities—)’ being an arbitrary parameter : aR): BIR) BAR) BSR. BRINE Bae And, in general, if ® and its derivatives are continuous up to Radler n—1, the relations between the discontinuities of order n can he written in the form (fae [= ]ev+ [2 Jae) @ WOT EOF RAN WOF ie Oe =n( SE de+ 37 by + 5.82). - aly § 3. The Order of a Discontinuity. We are to consider x, y, z as the actual coordinates of a particle of an elastic medium; thus if a, b, c be the initial or natural coordinates of # particle, we have the displacement (&, 7, 4 se considered ar We shall consider discontinuities in (& 7, &) and their various derivatives with respect to the time ¢ and the co- ordinates (z, y, 2). An absolute discontinuity is one which occurs in (&, 7, 8) itself ; and if n be the order of a derivative Discontinuity in a Rotationally Elastic Medium. 605 such as ks aia ok OuPOyO2" Ot’ where p+g+7r+s=n, then the order of a discontinuity is the lowest of the orders of the derivatives in which discontinuity occurs. § 4. Relations of Identzty. Consider a discontinuity of the first order in (&, y, €). Then from the general results in § 2 we have Be): Bil: BIB | fae }="36* Ley] ray [82 ]="39 where A, w, and v are arbitrary parameters. Thus a single vector (A, “, Vv), given over the surface 8, is sufficient to define these nine discontinuities of the first order. Similarly for a discontinuity of the second order; and in general for one of the nth order the relations between the derivatives not involving the time can be expressed by means of a vector (A, , v) in the form ([o]e+ [2 Ju+ [S]e) Gao =O 1) (SE 80+ SE by + O52)" roe) § 5. Conditions of Compatibility. The notion of compatibility was first introduced by Hugoniot into the study of fluid motions in two regions separated by a surface of discontinuity, and the same idea is used by Duhem under the name of “ persistence.” The relations of identity found in the previous section are those which hold at a given surface of discontinuity Sata given time ¢,. The motions in the two regions separated by S are said to be compatible if the surface § is unique not only at the instant ¢, but also at times immediately before and after that instant ; the moving surface S is then a wave-front and is said to constitute a persistent wave. There are certain kinematical relations which are satisfied whatever be the dynamical equations of the particular medium. 606 Dr. T. H. Havelock on Surfaces of The wave-front S is defined as the position at a given time of a surface given in three-dimensional space by f(a,y,¢0)=0. . 0) es Now consider x, y, Z, t as space coordinates in a four- dimensional space; and let } be the multiplicity given by equation (4). Then the various positions of S are the sections of } by planes ¢=constant. Now the relations of identity were obtained by considering variations on the surface 8, and in an exactly similar manner it is clear that the conditions of compatibility are to be obtained by the same process applied to }. And in general, for a discontinuity of order » in a function ®, we obtain instead of (1) the relation (+ Se E+ Bleye SF bet 9 by + SE de4 Gary OOF fol Thus for a discontinuity of order n in the displacement (E n, €) a single vector (A, w, v) arbitrarily given over = is sufficient to define the variations in all the derivatives of order n, provided the wave-front is persistent. The relations ean be written in the form (( 55 J+ [3y 7+ [3- J+ [oe ]®) G28 =) = 04») (Si b04 BF ay + Uae Vee). (6) which is to hold for all values of dé, dy, 52, O€. § 6. The Ather as a Rotationally Elastic Medium. Having obtained the kinematical relations, we must con- sider now the dynamical equations of the particular medium. Let (X, Y, Z) be the electric force measured electrostatically, and (a, 8, y) the magnetic force in electromagnetic units; then we have the usual circuital relations in the form : : ares Y ; Z) = Curl (a, iS: Y) | . 0 72 (a, By) = Curl (%, ¥, 2) | Discontinuity in a Rotationally Elastic Medium. 607 Now we may introduce a new vector (&, 7, ¢) defined by i. @&N=2EnOs GY, =Cul bn.» ® In a rotationally elastic ether, (¢, n, €) is interpreted as linear displacement ; the constants of inertia and elasticity of the medium must be supposed very large so that all the motions and displacements are small and can be analysed into independent differential strains and rotations*. Otherwise, we may begin with such a medium and take the energy functions to be T=$A\(E 49 + Cjdr ; W=3B((P +9 +h’)dt ; where Gg, i) Our (2 7G). The principle of least action gives the equations of motion ; and comparing the potential energy function W with electrical energy we obtain the correspondence given in (8). Regarding then the eether as an incompressible, rotationally elastic medium, its dynamical equations are te V*(&, UE ee a UE a Ce RO RBs tere (9) combined with Of On ee. Aa Btn ae SEN VRE oe mle Ay Now in order to determine completely the motion in the medium, we must know in addition the conditions at the limiting surface of the medium. For instance, suppose we know the motion of the boundary at each instant, and thus the acceleration of each point ; then this set of values for the acceleration may differ at any moment from those obtained from the internal equations of motion of the medium. Consequently a discontinuity of the second order is set up at the boundary and is propagated into the medium. Again, if the velocity or pressure at the boundary be suddenly altered, a discontinuity of the first order will be set up. In electrical terms, we may be given a boundary in the eether at which the electric or magnetic force is assigned ; then there may be set up a discontinuity of the first order which is propagated into the ether as a wave-front at which the electric and magnetic forces are not continuous. Or, again, if*the electric current is assigned at the boundary, * Larmor, ‘ Atther and Matter,’ p. 332, 608 Dr. T. H. Havelock on Surfaces of © there may be the production of a discontinuity of the second order. Supposing these discontinuities to be produced in some such manner, we proceed to discuss the method of their propagation. § 7. Discontinuity of the Second Order. In this case we have on S S)(2):- BG): Hence, supplying these values in the second-order equations given in (9), we have | (3) + (SF) + Gy = eG + ap Thus the discontinuity is propagated in the medium as a wave-front moving with a constant normal velocity c. Using the notation DEN HOR OF NOT) 0 A, #, VJ=R; ee Oy’ De =N, R.N=scalar product, and R x N=vector product, we have from (10) and (8) R.N=0 [w, v, w)]=2Rxn ot - l= hieay lea He bow Ui iap\e La, B, Y] =(S)) R Hence the vector defining the discontinuity lies every- where in the wave-front. And the discontinuities in the electric and magnetic currents are also tangential to the wave- front and at right angles to each other, while the electric and magnetic forces are supposed continuous. § 8. Discontinuity of the First Order. In this case we have eae OF PTS ra) |S mae: i =n, [$8 J=a%, (43) Bape ol and similar relations in (9, 4) and (€, v). Discontinuity in a Rotationally Elastic Medium. 609 Now in order to use the dynamical equations, we must find the influence of a first-order discontinuity upon the derivatives of the second order*. We shall use the following notation :— POE, by. 8))= oy OF 524 OF of a +f of lz, = (2 ays} ba) heade rie S om’ fl= <5 bu oh OE by + OE Be, (2 r+ [3p J+ [5 J®) € f= sea: | i aay si = = ‘A To form the relations of identity as before, we proceed to the second variation on 8 of the equation [ €] =constant ; then we obtain e+ (2 leet [Se Jey+ [o2 |ee=o, . (5) together with ii | or 2 aw OF 2 of iz j 5 (16) eh OR ico es | Jet zoe oF oy + az 0 Consequently we i from (13), —rfo= 0, when freee Hence for all values of dz, dy, dz we have a relation of the form Beart Bf(Abe + Bly 085 Mage ewe 87) Now vary on § the equation 0€ oF fe 5 oe Then, since a= Or Cae o-f 1 Ofs (5 ant anby + Bags * Cf. Hadamard, loc. ect. p. 121. Phil. Mag. 8S. 6. Vol. 10. No. 59. Nov. 1905. ZR 610 Dr. T. H. Havelock on Surfaces of and similarly Os le, 51 5e1= Da Gep we obtain L0G). Oy Of2 > AG ate alent . «vee elas But from (17) OE, a A iss D A(ba) PSS 53) Hage le 2+ Boy + Céz). Hence on 8 we have | OA= Ade + Boy + Cdz. To obtain the conditions of compatibility in the second order, we take variations as before on the multiplicity > instead of on S; the time variation dt occurs in a similar manner to the other variations, and introducing a fourth undetermined multiplier D, we have on & dA= Ade + Boy + Céz + Dot. And the discontinuities in the second-order derivatives can be expressed finally in the form ([ 5a] &+ [35] [5a] + [5 ]8) # =n (2 b+ 2 ay + 2 824 Oat) 7 of of of are) } ieee 2 t y/: o +2(3 24 oby4 be 2+ Sf e\(ASe-+ By + OB: +D8); (19) together with similar expressions in (7, wp, A’, B,C, D ) and (GA; BC ee Thus for a first-order discontinuity defined by a vector (A, #, v) in equations (13) and (14), the variations in the second-order derivatives are expressible in the form IAB iaN: Bye tohead [|= oe fe swt, ; (20) and similar expressions. Discontinuity in a Rotationally Elastic Medium. 611 Now for the particular medium in question we have the equations :— foe F* boy laa le Se: )* Lseay | + Lege ]=° and three similar equations. Also there are three dynamical eis of the type fe] *[57]*L32] = als 02” Oy” rae Supply in these the values from (20) vig use for shortness the ay notation :— =(A, A’, A’) and similarly for B, C, D; Cr OR 0 made Ns one : ar), ee N)\. also See caer Then we obtain the following equations :— RN=0, V(B.N)p+ (A, B, C).N=—(A+B’+ON, R. on +D.N= —(a+B'40 2 roy t) —2( 2 a3 + Foley sie Re (v i Ce Oe fs) A ioe mee Ot D), From these equations, i a ee: scalar equations, we can deduce the following scalar equation : Oli re ON 4" N.Y(BN)n— 2 RST )=—AtB4C ) {nN 5 (2) de and this equation can be written in the ordinary ia under the form 0 ono M17 of : {rg tee tS 4 eaareroyl{(Xy +| G4 of On Y . Ae | iene Hquation (21) is satisfied for all Ure of the arbitrary parameters c az) * ($5) +(8) ~al5e) =° 612 Surfaces of Discontinuity in Rotationally Elastic Medium. Hence in this medium a persistent wave-front, consisting of a first-order discontinuity separating two states which are compatible up to the second order, is propagated in the medium with constant normal velocity c. Moreover we have [X, ¥, Z]=c[Curl (£, », )]=eRxN ; | [2, B; y|= E (SOE ¢) =r > wid, ied (22) R.N=0 J Thus the two vectors representing the discontinuities in the electric and magetic forces are at right angles to each other and lie in the wave-front. Also if E denote the Poynting radiation vector, we have B]=[X, ¥, Z] x fe, 8, yJ=—0 Rx (Rx®) of 2INY = of ‘ 2. = ae w= (2) Lavette where n is unit vector in the direction of the normal to the wave-front. Thus the discontinuity in the radiation vector is in a direction normal to the wave-front and is of magnitude equal to the square of the discontinuity in the magnetic force. § 9. Stationary and Absolute Discontinuities. Up to the present we have assumed that the equation of the surface of discontinuity contains the time, and we have found that such a surface forms a wave-front expanding out- wards with constant normal velocity. Consider the possibility of a stationary discontinuity of the first order. Then from (22) we see that the discontinuity of the magnetic force vanishes ; also since (21) becomes it follows that the vector R must also be zero. Hence there cannot be a stationary surface of discontinuity at which the tangential electric and magnetic forces do not vanish. In equations (7) and (8), the vector (&, 7, €) is regarded as linear displacement from a natural state of the medium, in which the electric force (X, Y, Z) is everywhere a circuital vector. In order to have electric charges we must suppose the natural state of the medium to include centres of intrinsic Notices respecting New Books. 613 rotational strain. Then a charged surface, or the surface of an electron, might be considered as a surface at which there is given normal discontinuity in (X, Y, Z); such a surface in motion is also the seat of a first order discontinuity in (E, n, ¢), the tangential discontinuities in the electric and magnetic forces being given by equations (22) in the case of compatibility in the first order. Thus if a charged surface S' be suddenly given a velocity v, a first-order discontinuity will arise at S’ and will be propagated outwards as a wave- front S moving with normal velocity ¢ and leaving behind it the steady state corresponding to 8’ moving with uniform velocity v. LXVIII. Notices respecting New Books. Mathematische Hinfuhrung in die Elektronentheorte. Von Dr. A. H. Btcuerer. Teubner: Leipzig, 1904. HIS is an able presentation of the modern electron doctrine as developed by Lorentz, J. J. Thomson, Heaviside, and others. The modifications which the assumption of this theory make on Maxwell’s equations are clearly stated ; and the various interesting problems associated with the motion of charged particles, spheres, and ellipsoids are discussed in considerable detail. The Zeeman effect, the aberration of light, and the electromagnetic theory of dispersion form the concluding sections. The general mathe- matical theorems are given in the particular modification of the Quaternion vector analysis which is familiar to readers of Heaviside’s important papers; and an appendix summarizes the meanings of the formule and symbols used. Any one familiar with quaternions will have no difficulty in understanding the notation, although he will never cease from wondering why vector analysts like Dr. Bicherer should be content with such a comparatively weak imitation of Hamilton’s powerful calculus. The author gives five theorems connecting volume, surface, and line integrals, and connects each with the name (presumably) of its discoverer. Gauss and Stokes very properly get their due; but if other theorems of fundamentally the same character as these are to be named after later investigators, it is simple justice to give the name of him who first published them. Theorems (25) and (26) ascribed to Foppl and B (Biicherer?) were given long ago by Tait; and all the five are special cases of a fundamental theorem first given in its most complete form by McAulay. This historic inaccuracy springs of course from the culpable neglect of quaternions at the hands of certain modern vector analysts, who have wasted time and energy in rediscovering truths thirty, forty, and even fifty years old. 614 Notices respecting New Books. The Dynamical Theory of Gases. By J. H. Juans, M.A. Cambridge University Press, 1904. SEVERAL excellent treatises on different departments of Natural Philosophy have been recently issued by the Cambridge University Press ; and the present volume cannot fail to take high rank among the standard works and memoirs on the dynamical theory of gases. After an introductory chapter stating the nature of the problem, the author develops the foundations of the theory in four chapters on the Law of Distribution, giving not only the usual statistical theory, but also his own investigation based upon the methods of general dynamics applied to space of x dimensions. This leads to a concise demonstration of Maxwell’s equipartition theorem. The whole of Chapter V., dealing with the extension of the theory to molecules of the most general conservative type, is of the highest interest, and paves the way for valuable applications in later sections. Two chapters then follow on the physical properties of gases and the extent to which they can be deduced from the dynamical theory. The significance of the failure of the theory to explain the relation between the specific heats is ably discussed, and leads to the introduction of the dissipative function and the investi- gation of non-conservative systemsalong the lines already laid down. The last nine chapters are grouped together under the title “ Free Path Phenomena,” and take up questions of viscosity, conduction, diffusion, propagation of sound, the problem of the constancy or dissipation of planetary atmospheres, and other topics. The reader who may have no special interest in the mathematical methods themselves, will find a great deal worthy of his con- sideration. All the known physical properties of gases are introduced as illustrations uf the general theory, but apart from this theory in its severe analytical form there is a physical as dis- tinguished from a mathematical charm about the book, which should give it a place in the library of every real student of physical and chemical science. We do not know which is the more to be admired, the mathematical power or the physical insight of the author. This book is a model of fine mathematical printing. Die Entwickelung der Elektrischen Messungen. Von Dr. O. FRoxi0n. Mit124 eingedruckten Abbildungen. Braunschweig: F. Vieweg und Sohn. 1905. Pp. xii + 192. THIs most interesting volume, which forms No. 5 of the series known as Die Wissenschaft, contains an account of the evolutionary process by which our present electrical measuring instruments and methods of measurement have come into being. The book is divided into two sections ; the first section dealing with galvanometers, switchboard instruments, resistance coils, energy meters, and recording instruments, while the second section is devoted to methods of measurement, and deals more particularly with re- sistance and inductance measurements. The subject is treated in a very lucid and interesting manner, and the book should prove most useful to electrical engineers and physicists. fo Gia] LXIX. Procedings of Learned Societies. GEOLOGICAL SOCIETY. (Continued from p. 192. | May 24th, 1905.—J. HE. Marr, Sc.D., F.R.S., President, in the Chair. ee following communications were read :— 1. ‘On the Igneous Rocks occurring between St. David’s Head and Strumble Head (Pembrokeshire).’ By James Vincent Elsden, bee: E.G.S: The author finds that the contemporaneous lavas of the Llanrian area agree generally in character with the eruptive rocks of apparently-Ordovician age in the Strumble-Head and Prescelly districts. These are all of an essentially-acid type. The intrusive rocks of the area are of later date, and belong to three distinct types :—(1) The gabbros and diabases of the Strumble-Head area ; (2) the norites and associated rocks of St. David’s Head and the surrounding district ; and (3) the lime-bostonites and porphyrites of the Abercastle-Mathry district. Detailed petrographical descriptions of the different types are given, accompanied in many cases by analyses and comparisons with corresponding or related rocks of other areas. The lime-bostonites, which have affinities with those of Mena described by Brogger, but are much more basic than the Wicklow keratophyres, are apparently the oldest of the intrusive rocks, and seem to belong to the petrographical province of South- Eastern Ireland. The gabbros and norites were intruded approxi- mately during the same interval; at a later period the norites, enstatite-diorites, and the rest of.the rocks associated with them spread north-eastward from St. David’s Head, and penetrated the area of the Strumble-Head intrusions. Similarly, the gabbros and diabases spread to a more limited extent south-westward into the norite-area. In the overlapping area the gabbro- and norite- provinces are separated by an ill-defined zone, in which some mixture of the two magmas took place. The latest phase of igneous activity was the formation of the Pen-Caer basalt-laccolite, with apophyses penetrating the Garn-Fawr to Y-Garn intrusions, It is not necessary to assume that each of the several intrusions was confined to any single stage of vulcanicity. The laccolites and bosses were probably the result of injections extending over a prolonged interval from coexisting magma-basins, or from a single differentiated magma. ‘There are clear evidences of some further differentiation an situ, but the full extent to which this took place offers a large field for future investigation. 616 Geological Soccety. 2. ‘The Rhetic and Contiguous Deposits of Glamorganshire,’ By Linsdall Richardson, F.G.S. The chief sections in the county are deseribed in detail, the chief being those at Lavernock (near Cardiff), Barry, Tregyff (near Cowbridge), Quarella (Bridgend), and Stormy Down. ‘The Sully Beds, a name given to the fossiliferous portion of the ‘Grey Marls ’” of Etheridge, are determined to belong to the Rhetic Series, on account of the fossils that they contain. They are quite distinct from the‘ Tea-Green Marls,’in which fossils have not been observed. Earth- pressures affected the rocks during the formation of the Sully Beds; the Avicula-contorta black shales rest upon them with perfect parallelism, but even then non-sequentially. Owing to an up- heaval of the Lavernock district early in the age in which the Upper Rheetic Stage was deposited, only a portion of the lowest bed of that stage is found, and this deposit was subjected to sub- aérial denudation during the accumulation of the remaining Upper Rheetic beds elsewhere... But subsidence again in the same district allowed of the deposition of the White Lias, and, as a result, this latter rests non-sequentially upon a portion of the lowest part of the Upper Rheetic deposit. The White Lias, at certain localities in Glamorganshire, contains in abundance Plcatula cintusstriata, Pl. hettangiensis, and Lima valoniensis. .The deposit intervening between the Sun-Bed and the Upper Rhetic near Bath (Newbridge Hill) is over 11 feet thick; at Lavernock the equivalent deposit measures but 2 feet 24 inches. At Lavernock, however, above the probable equivalent of the Sun-Bed, are marls 6 feet 4 inches thick, which are provisionally grouped with the White Lias. Above come the Paper-Shales, succeeded by the Ostrea-Beds. The Upper Rhetic of North-West Gloucestershire and Worcestershire is not the equiva- lent of the White Lias of this or of the Bath district. The White Lias occurs above the Cotham Marble (the topmost bed of the Upper Rheetic) and below the Paper-Shales (which occur immediately below the Ostrea-Beds). Paleontological notes on. certain of the fossils are appended, including Ostrea Bristov., Etheridge MS., which is very abundant in the Sully Beds. 3. ‘On the Occurrence of Rhetic Rocks at: Berrow Hill, near ‘Tewkesbury (Gloucestershire). By Linsdall Richardson, F.G.S. About 2 miles south-east from Chase-End Hill (Malvern Hills) there is a small outlier of Lower Liassic and Rhetic beds, in a basin-shaped area, supported and surrounded by Keuper:Sand- stone. SS Ss pds 00) ae) slat [| SS a LIN i Ar || 35 | | [ H | = tt ip q 240, iD O40 Y v7 Oe | || 24a : 40 ayo S40 1op0) Phil. Mag.'Ser. 6, Vol. 10, Ey Es ett ee ee Sameer le | | | eeleaekege ve] | | | ff oeaannoe ee eee | | | raa6 ttt ee eeaeeteeted Tt TT ie ft ee eet | ee : eee tS ee | 2 CC asses. oe JG Sa |= ee Sea eee Phil. Mag.*Ser. 6, Vol. 10, Pl. X. wey. the, 9.24% [We Is, ix rey. 45, Anat % _ Cl : 20x10 =| i 20x10" 21.0 ¢ }——} = 7 — 5 J | et — (- — aa or 428.4" a ——— | 19; | iS —| ot Seer aia aT zx 2H5'C 4 0 440 24q0 790 £90 sO qo 7) 100 290 I90 400 5qo ayo Lt aL - T LI + oy 4. 2aher0" +—t “ 7 — 1 + ei WW ele by 2dr We. 2) . & f hn ; * a ; 4 i 4 . xy rs 4 j Phil. Mag. Ser. 6, Vol. 10, Pl. XI. ile ae ne ee a ong Se eae ee eae eee | aa ne ee ene ae eee | ES Jee ee ee eZee ee rome ECCEEECE EEE __| SAAB Saas See eeeee _—-_ ESSE EE Se snes i aS Seeecmameeeeee eh eee e _ | Se See a eee vee pop aE _ SSeS Reese J/_ Sele Sa aeaeeee | CS aritirie eae me et le _|_ LS ee aaa sees eaeas a) 22a mee ae pee eee ee SSRs Sa Phil. Mag. Ser. 6, Vol. 10, Pl. XI. [I ee) oe = = oe eh ot a re >| ae i —-_ Phil. Mag. er. Ge Vole £05 Pie xIT. eset OT Ceo SS ESSSe8 SSC] See lonemeee fo woe - ll Ce ee eeeeere: aed ocees ‘Elo es Sse RESSSS 2) 2a SESS08 S500 Goo eoecce SSS. S500 EET STE Se a i ‘| Phil. Mag, Ser. 6, Vol. 10, Pl. XII. ORNS SEAN pe ~ THE TRI OTN INDEXED. ¢/ v4 LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. 3 [SIXTH SERIES.] DEC UM BE kh 1905. LXX. The Relation between P.D. and Spark-length for Small Values of the latter. By GuENN Moopy Hosss *, [Plate XIII. ] 1. Introduction. NHE general subject of spark-discharge in gases has commanded the attention of investigators for many years, but the recent developments of the electron theory have brought it into especial prominence within the last half- decade. ‘he particular investigations on the spark-discharge between two electrodes and the potential necessary to produce discharge with varying distances have extended over a period of forty-five years, the first observations being made in 1860 by Lord Kelvin f. Since 1880, the field has been covered more rapidly and important investigations have been made by Baille{, Liebig§, Paschen ||, Peace], Strutt**, Bouty tt, Warhart tf, and Carr§§. During this period the general behaviour of the discharge between electrodes throughout « * Communicated by the Author. + Lord Kelvin, “Collected Papers on Electrostatics and Magnetism,” . 247. , { Baille, Annales de Chimue et de Physique [5 | xxv. p. 486 (1882). § Liebig, Phil. Mag. [5] xxiv. p. 106 (1887). || Paschen, Wied. Ann. xxxvii. p. 79 (1889). @ Peace, Proc. Roy. Soc. li. p. 99 (1892). ** Strutt, Phil. Trans. exciii. p. 377 (1900). ++ Bouty, Comptes Rendus, cxxxi. pp. 469, 503 (1900). t{ Earhart, Phil. Mag. [6] 1. p. 147 (1901). §§ Carr, Proc. Roy. Soc. Ixxi. p. 374 (1903), Phil. Mag. 8. ©. Vol. 10..No. 60. Dee. 1905. 810) 3 618 Mr. G. Moody Hobbs on the Relation between P.D. large ranges of pressures and distance was investigated, and several important Jaws discovered. The linear relation between spark-potential' and distance for comparatively large values of the latter was established, and Peace noticed the existence of a minimum spark- potential. Paschen deduced from a large number of observations the law which bears his name, viz., that for given potential-differences the product of the sparking distance and the maximum pressure for pro- ducing a spark is a constant. However, it was not until 1900 that any work was done to prove the correctness of these laws for very small distances. At this time, Earhart carried on an investigation in this laboratory in which, by the aid of the interferometer, he was enabled to make accurate observations down to the point of contact. His results were very interesting and, when plotted with potentials 1.—In Arr at ATMOSPHERIC PRESSURE. Fig. 1 ER@REEReeee ae |. SS ES Pht ee | ee) Lae: mr Le es a Na ae 450 400 350 SPARHING FOTENT/IAL /N VOLTS. a ee Hod Ll a Bo | | ea el | eae DISTANCE IN WAVE-LENGTHS. as ordinates and sparking distances as abscissee, gave in air at atmospheric pressure a straight- line curve (see fig. 1) and Spark-length for Small Values of the latter. 619 down to a distance of 3 and a potential of 350 volts. At this point, the curve made a sharp bend and dropped in a straight line to the origin. Harhart also made observations in air at pressures of 228, 152, 40, and 15 cm., and in carbon dioxide at atmospheric pressure. This investigation was begun in 1902, (1) in order to discover why Harhart’s results did not show the minimum which Peace had observed ; (2) to ascertain whether or not the material of the electrodes affected the position of the “elbow,” as it might be expected to do if the metallic ions took part in the discharge at very small distances ; (3) to extend the range of pressures much lower at these small distances than Harhart had done. Since this investigation was begun, there has appeared a paper by Carr * which covers in an admirable manner the third point mentioned above, but leaves the other two points untouched. It would appear from the following results :— (1) That the shape of the curve which is obtained with spherical electrodes is indeed precisely what is expected if there is a minimum spark-potential for flat electrodes. (2) That the material of which the electrodes are composed exerts an important influence upon the spark-potential at small distances. (3) That the carriers of the discharge for small distances come from the metal and not from the gas. II. Description of Apparatus. The apparatus, which is shown in fig. 2, consisted of an ordinary interferometer to which the two electrodes were attached. ‘T'o obviate the necessity of using a tangent-screw and still maintain a sufficient accuracy of setting, the main screw of the interferometer was cut with a fifth-millimetre pitch which made it possible to control variations of a tenth of a fringe (2. e. 0°025 p). | The movable carriage (C) of the interferometer supported the plane electrode (H,), a disk of brass about 1 inch in diameter screwed tightly to a taper shaft which was set in a cearefully-ground socket in the carriage and held in place by a spring (S). A thin gear (G,) 14 inch in diameter was also concentric on the same shaft and, when engaged in the gear (G3) above it which was operated outside of the box, could be turned on its axis. In order to get rid of the troublesome backlash in the nut (N), to which the sliding- carriage was fastened, a stiff coiled spring (W) running * Carr, Proc. Roy, Soc. lxxi, p. 374, U2 620 Mr. G. Moody Hobbs on the Relation between PD. parallel with the screw was attached to the carriage and the latter held in place upon the ways by three spring-clips. This device obviated all drifting contact and made the zero setting very definite. Fig. 2. > , It was found necessary, in order to avoid vibration and similar effects, to attach the support of the spherical electrode to the interferometer-bed itself, insulating it of course so that the circuit would be complete only by the contact of the surfaces. This electrode was also screwed on a taper shaft_ which turned in a perfectly-ground sleeve, so set that the sur- face could be rotated on its axis at an angle of 45 degrees from the outside of the box. Itis easily seen that by this arrange- ment the points of contact of both surfaces couid be shifted after each discharge, and fifteen or twenty discharges taken before removing the box. This box was made of brass and carried on its sides the shafts of the two gears (G_, and G,) by which the rotation of the plane electrode and the main screw (L) of the interferometer was effected. It also carried a socket through which the shaft (H) for turning the spherical surface could be run after the box had heen sealed. The joints of the three shafts were made air-tight by pieces of rubber tubing which allowed sufficient rotation for the and Spark-length for Small Values of the latter. 621 necessary adjustments. The box was connected to an air- pump through the stopcock (P), and after sealing the lower edges with bees-wax any desired pressure could be obtained. A plan of the battery and galvanometer circuits, together with the arrangement of the interferometer mirrors, is shown in fig. 3. The potential was furnished by a battery of about five hundred storage-cells, and the sparking-potential was observed by a direct-reading voltmeter properly standardized. hTERT E ETT TR HO The practice during an experiment was as follows :—~The surfaces were carefully polished with very fine emery and rouge, set in position and the fringes adjusted in sodium light. A small quantity of drying substance was placed inside and the box sealed on. ‘The air was pumped out and slowly let in again through a series of drying bottles, and the apparatus allowed to stand for a period of 6 to 24 hours. On beginning the observations, the surfaces were brought into contact by means of the interferometer-screw, the point of contact being shown by the deflexion of a sensitive galvanometer (G, fig. 3) when the spring-keys K, and K, were pressed. To avoid any possibility of the potential in this circuit effecting a discharge which would tarnish the surfaces, an ordinary dry cell (B,) was connected to a german-silver resistance-coil (R,) and a bit of copper wire (c) im series, and the fall of potential across this copper wire was the P.D. applied to the points between which the 622 Mr. G. Moody Hobbs on the Relation between P.D. discharge was to take place (about 0:01 volt)*. When contact had been established, the reading of the reference point was taken, and the surfaces drawn apart until the required number of fringes had passed the fiducial point. The main discharge circuit was then closed through the switches K; and Ky, and the plunger in the water resistance (R,) raised very slowly until the potential of discharge was reached. In the neigh- bourhood of the discharge potential the P.D. was raised a volt at a time with a wait of a minute between in order that the effect of lag, first noticed by Warburg +, might be eliminated. The discharge was always indicated by the dropping of the pointer of the voltmeter. The electrodes were then drawn apart and fresh surfaces presented for contact by turning G; and H, and after a wait of 8 or 10 minutes to allow the gas to resume its normal condition another discharge was taken. ‘The same pressure was maintained throughout each series of observations. Lil. Results in Air with Brass Electrodes. (1) Comparison of Curve for Atmospheric Pressure with Earhart’s Curve-—The results with brass electrodes at various pressures are given in Table I., and represented graphically in fig. 4 (Pl. XIII.). In order to make comparisons the more easily, the curve for atmospheric pressure has been plotted with that of Harhart, in fig. 1, the latter being the dotted one. It will be seen that the discrepancy which exists at the “‘ elbow ” of the curve is really only apparent; for Harhart’s results (indicated by x ) showa discharge-potential whichis practically stationary at 348 volts for distances from 5A to 13°5a. The difference in slope from the elbow to the origin in the two curves is shown by fig. 13 to be due to the metal of which the electrodes were composed, Harhart’s surfaces being nickel. The agreement. - in the case of the curves for 40 and 15 cm. pressure is not so good, the errors in Harhart’s observations being due probably to imperfect drying of the air. * Notr.—After the departure of the manuscript of this article, the attention of the writer was called to the fact that the indicating potential for different metals should not be below certain minimum values. This explained a difficulty experienced in obtaining definite contact between certain metals, a fact which is mentioned later in the article to explain rather scattered results for zinc, antimony, &c. These curves have been repeated, using a higher indicating potential, and much more consistent results have been obtained. The new results, together with observations on several metals not previously used, will be published in a subsequent article. + Warburg, Ann. d. Phys. vol, |xii. p. 385. and Spark-length for Small Values of the latter. 623 TaBLe I.—Brass [lectrodes in Air. (Fig. 4, Pl. XIII.) Pressure Pressure Pressure Pressure Pressure Atmospheric. 40 cm. 25 em. 15 cm. 1 cm. Dist. |Spark-| Dist. |Spark-| Dist. |Spark-| Dist. |Spark-| Dist. |Spark- in |Poten.| in |Poten.| in /|Poten.| in |Poten.| in | Poten. Wave-| in |Wave-| in |Wave-| in |Wave-| in |Wave-| in Igths. | Volts. | lgths. | Volts. | lgths. | Volts. | igths. | Volts. | lgths. | Volts. 15 95 Por lina AU 2°0 | 165 2:0 | 225 30 | 240 30 | 175 20° 1 17d 30 | 160 30 | 210 30 | 270 35 | 225 25 | 190 30 | 170 40 | 285 40 | 345 4:0 | 275 30 | 150 30) Lio 4:5 | 345 4°5 | 340 42 | 325 3'2 | 265 4:0 | 305 50 | 340 50 | 3850 4:5 | 320 4:0 | 3805 5:0 | 340 75 | 340 75 | 350 50 | 345 4°5 | 335 7) 340" | 10:0. | 350 | 15:0 |, 350 60 | 340 47 | 345 | 100 | 345 | 125 | 3350 | 25:0 | 350 T5 | 345 50 | 355 | 12:5 | 345 | 17-5 | 350 | 50:0 | 350 100 | 345 60 | 317 | 175 | 345 | 25:0 | 850 | 750 | 350 12°5 | 350 75 | 340 | 25:0 | 350 | 37-5 | 3850 15:0 | 860 | 100 | 340 | 35:0 | 350 | 42°5 | 350 175 | 355 | 10:0 | 350 | 87:5 | 355 | 50:0 | 350 25:0 | 400 | 15:0 | 350 | 40:0 | 3830 | 60:0 | 360 375 | 4380 | 17:5 | 350 | 40:0 | 370 | 65:0 | 375 200 | 350 | 40:0 | 370 | 75:0 | 410 22°5 | 350 | 42:5 | 390 225 | 845 | 50:0 | 390 25:0 | 365 | 67:5 | 430 27-5 | 3865 37°5 | 3875 | 37°5 | 395 | 5070 | 415 | 50:0 | 420 (2) Mentmum Spark-Potential for Curved Hlectrodes.— According to Peace and Carr, at a given distance between the electrodes a discharge will take place at the minimum spark-potential (characteristic of the gas) if the pressure has a certain value called the “ critical pressure.” Nowif either the distance or the pressure be decreased while the other is kept constant, it will be found necessary to increase the potential in order to produce a discharge. These facts were observed with the use of plane electrodes; but where one of the electrodes is spherical as in this case, it will be seen, as indeed Carr pointed out, that when the nearest point of the curved surface is closer to the dat electrode than the distance at which the discharge takes place with a potential equal to. the minimum value, the spark can still pass at this potential from a point further out on the curved surface. It will be seen therefore, that with such electrodes the discharge-potential, instead of passing through a minimum 624 Mr. G. Moody Hobbs on the Relation between P.D. should remain constant until the electrodes approach so near that the discharge is effected by the metal ions themselves. To take for example the case where the pressure of the gas was 15 cm., as the distance between the electrodes is decreased the sparking potential falls in a straight line to 350 volts, reaching this value when the sparking distance is 57X (31:64). It then remains absolutely constant until the distance has reached 5A(3), when the potential drops rapidly to zero. An examination of the curve for 15 cm. pressure in fig. 4 will show that the results obtained are in perfect accord with this theory. (3) Effect of Change in Pressure on the Curves.—It will be noticed that the curves for the various pressures reach the minimum potential at distances inversely proportional to the pressure. This agrees with Paschen’s law which has been beautifully verified by Carr, who showed that for a given potential, e.g. the minimum potential, the discharge was only dependent upon the mass of the gas per unit surface between the electrodes. Taking Carr’s value of 4:98 mm. for the critical pressure at 1 mm. distance, it is easy to calculate at what points the curves should reach the minimum potential for the various pressures. The following values were obtained : — Distance in Wave-lengths, - observed. Distance in Wave-lengths, calculated. Spark-Potential. | Critical Pressure. 350 kil. 75 em. 13°2 350 40 ,, 25 350 2D) cs 40 350 LON 66°6 390 Arty, 1000 The discrepancies in the results for the lower pressures are: undoubtedly due to the distortion produced in the field by the spherical electrode, a fact which would seem to indicate a limiting distance of 15, within which the field between the electrodes is practically uniform. The minimum spark- potential of 350 volts agrees with the value obtained by Carr and others. Observations at lower potentials than 150 volts were seldom taken, for the reason that the portion of the curve from this point to the origin has been well explored in an investigation in this laboratory by Professor Kinsley* in connexion with a coherer problem, the apparatus used being susceptible of a higher order of accuracy at these minute distances. * Kinsley, Phil. Mag. [6] vol. ix. p. 692 (1905). and Spark-length for Small Values of the latter. 625 IV. Influence of the Kind of Metal in the Electrodes upon the Discharge. (1) Observations in Air at Atmospheric Pressure with dif- ferent Electrodes.—In order to investigate the effects of the material of the electrodes upon the spark-potential, which was the primary object of the research, observations at atmo- spheric pressure similar to those above given for brass sur- faces were taken with a series of electrodes of exactly the same size and shape but consisting of the following metals : aluminium, silver, bismuth, zinc, platinum, antimony, mag- nesium, nickel. Considerable difficulty was experienced with the crystalline - metals, antimony, bismuth, magnesium, and zinc, on account of uncertainty of contact. The results with these metals therefore show much more scattering observations than the others, and the slopes of the curves are consequently some- what less reliabie. The effect on the discharge is nevertheless so unmistakable that the general conclusion is unavoidable. The table and curve of each metal are given below with the exception of brass, which is found in Table I. and fig. 4 (Pl. XIII.). A first and second series of obseryations for each metal, representing readings taken on widely different days, are given in each table and shown separately on each curve. Taste IT.—Aluminium. (Fig. 5, Pl. XII.) | Ist Series. 2nd Series. | | Distance, Potential, Distance, Potential, r. volts. r. volts. 2 150 2 100 3 210 2°5 140 3 180 2°5 15 _ 230 3 150 4 240 3°5 220 4-5 295 + 280 4°5 305 5 320 45 290 55 350 5) 315 6 390 5 315 6:2 335 6°2 325 75 339 ies | 325 | 10 | 345 | 12°5 | 345 | | 626 Mr. G. Moody Hobbs on the Relation between P.D. Taste III.—Silver. (Fig. 6.) Ist Series. 2nd Series. Distance, Potential, Distance, Potential, d volts. Xe volts. 2 175 if 50 Suet) 210 15 95 27 285 15 165 3°5 305 2 190 4 315 2:5 265 4°5 345 3 250 iF 390 3 310 3°5 340 -: 350 TaBLeE 1V.—Bismuth. (Fig. 7.) Ist Series. 2nd Series. Distance, Potential, Distance, Potential, volts. r. volts. 15 110 15 100 2°2 165 2 160 3 220 Zt 215 32 245 3°2 275 3°5 260 St 275 35 275 | 4:2 “a 4°5 350 | 37 350 TasBLeE V.—Zine. (Fig. 8.) 1st Series. 2nd Series. Distance, Potential, Distance, Potential, x volts. r. volts. 2 170 15 130 2 140 2 20 2 125 2 185 2:5) 185 25 230 3 170 2°5 235 3 1380 3 325 3 230 3 285 3 215 sy) 310 3°D 220 3°5 290 3°5 305 4 260 35 335 4:2 315d 3°5 285 4:5 350 + 305 4-7 320 4 245 5 350 4:2 285 4:9 310 45 38850, 225, 350 4-2 oe 5 350 4:2 350 no 350 and Spark-length for Small Values of the latter. 627 TaBLE VI.—Platinum. 1st Series. Distance, Xr. He 09 CODD RD ND RD NO RE “Io orb Orr Potential, volts. | (Hig. 9:) | 110 225 350 30U Distance, r ored Or ~T CUO bo © OO to Co to be lor Or SOE NO lll call oes Or Potential, 2nd Series. | | yolts. / 90 | 150 | 350 | 230 | 260 350 350 350 350 350 350 360 400 435 Taste VII.—Antimony. (Fig. 10.) 1st Series. | Distance, | ) r. Distance, Potential, : | volts. 2 | 115 2 | 245 2°5 270 25 250 3 | 240 3 220 3 320 | 3:5 | 350 | ao | 350 4 | TSK fe SO NOR SO OO OD el ell Or Or or 2nd Series. Potential, volts. 185 125 285 350 | 160 350 E75 | 180 350 180 | 350 | 110 | } | Taste VITI.—Magnesium. (Fig. 11.) Ist Series. eee : se Or “J OL | oa | Potential, yolts. Distance, Potential, Xr. volts. | 2 170 | 2-5 | 195 2-5 | 110 | = 205 ane 275 | 4 | 325 | 2nd Series. 335 628 Mr. G. Moody Hobbs on the Relation between P.D. Taste [X.—Nickel. (Fig. 12.) ist Series. 2nd Series. Distance, Potential, Distance, Potential, volts. r. volts. 2 170 15 180 3-5 220 2 210 3 250 32 280 od 390 4 350 4 335 4°2 300 4-2 300 5 350 4°5 330 5 350 6 350 (2) Discharges at less than the Minumum Spark-Potentials carried by Metal Jons.—If the discharges corresponding to the above curves from the elbow down are carried by the metal ions, it is to be expected that the nature of the electrode would have an effect upon the position of the elbow, for the force which holds the ions within the metals may be assumed to depend upon the nature of the metal. It will be seen that the above curves completely corroborate this inference. The potential begins to fall below the minimum value at the following distances : Ja hobranyenioueo Game oes e 5)°6 waves. BRASS: ee soln eae 5 Bismiachee ee Ae) Maonesium, 72.5.2 Ard ZINES) Eee, oer eee A-5 Niekellee oun, eee AL, DOLVer see ee ae 3°38 Antimony “nea. 5 3°59 Bhatia. oe S To illustrate this point the curves previously given are all collected in fig. 13 (Pl. XIII.). It will be observed that im all these cases the curves have been checked by two sets of ob- servations taken at widely different times. With platinum, brass, and nickel, the observations are very definite and the points lie extremely close to the line. For these metals, therefore, the results are thoroughly trustworthy. In the case of the other metals the results are less definite, as the and Spark-length for Small Values of the latter. 629 tables show, but the slopes obtained by the two series of observations are nevertheless in good agreement. Further evidence that the carriers of the discharge within the limits specified come from the metal and not from the gas, is found in the fact that the slope of the curve below the elbow is completely independent of the pressure of the gas, us is shown in fig. 4, and also independent of the nature of the gas, as shown in fic. 9. Furthermore, the character of the discharge as observed in the behaviour of the voltmeter is completely different below the elbow from its character on that portion of the curve to the right of the elbow. When the discharge took place at or above the minimum spark-potential, the pointer of the voltmeter experienced a sudden deflexion of a number of divisions towards zero, and quickly returned to the old value as the potential was built up by the cells. On the other hand, when the discharge took place at points on the curve below the elbow, the pointer always fell completely to zero and remained there. Moreover, a test of the circuit with the galvanometer showed that coherence had taken place. That the coherence was not due to any give in the supports because of electrostatic attraction between the electrodes is definitely proved by the facts presented in figures 9 and 13, showing that the elbow varies with the nature of the electrode and with the nature of the gas. (This last result is discussed in the following section.) (3) Observations in Hydrogen and Carbon Dioxide at Atmospheric Pressure with Platinum Electrodes.—In order to check still further the participation of the metal ions in the discharge at small distances, some observations were taken with platinum electrodes in an atmosphere of hydrogen and of carbon dioxide. The results are shown in Table X. and graphically in fig. 9 (PI. XIII). The minimum spark-potentials for these gases are, according to Carr, respectively 280 and 420, while according to these results they are 285 and 420. Now if the metal ions are the carriers of the discharge for all potentials below the minimum value for the gas, then the curve in any gas should follow the slope found for air until the potential reaches the minimum value for the gas, when the curve should bend to the hori- zontal, 2.e. the discharge should at this point begin to take place in the gas. This must be true, for if the curve should hold to the “straight line beyond this point, the discharge would be produced by the metal ions at a higher potential than was necessary for discharge at the same distance in the gas itself. Taking Carr’s values for the critical pressure for 630 Relation between P.D. and Spark-length. TaBLE X.—Platinum in H and COQ,. ™~ Hydrogen. Carbon dioxide. Distance, Potential, Distance, Potential, volts. Xr. volts. 15 175 1:2 140 2 242 2 255 25 275 27 320 2°5 275 34 390 3 280 37 420 + 285 5 420 6 285 | 75 | 420 10 285 | 10 Nh 420 19: 285 | 12°5 420 15 | 285 i 15 430 29 290 25 465 37°5 | 320 37°5 515 50 365 hydrogen, 10°3 mm. at 1 mm. distance and 280 volts, and for CO,, 5°03 mm. at the same distance and 420 volts, the calculations can be made for the distances at which the curves should rise above the minimum potential abscissee. These calculations give 28 A for hydrogen and 12°52 for CQ,, which agree almost exactly with the experimental values obtained (see fig. 9). (4) The lag which is characteristic of the discharge at higher potentials disappears entirely for distances below the elbow. V. Summary. (1) With one spherical and one plane electrode, at constant pressure the spark-potential is directly proportional to the distances between the electrodes, until the potential reaches ihe minimum yalue for the gas. (2) In any gas the potential of discharge reaches its mini- mum value for the gas at distances which are inversely proportional to the pressures existing between the electrodes. (3) For the same electrodes the discharge in air at distances from zero to about 3 is wholly independent of the pressure or of the nature of the gas between the electrodes. (4) For the same electrodes the distances at which the curves - assume a horizontal slope are proportional to the minimum spark-potential of the gas between the electrodes. (5) When a discharge of electricity occurs between two The Thermoelectric Circuit of Three Metals. 631 electrodes at a lower potential than the minimum spark- potential of the gas in which the discharge occurs, the dis- charge is produced wholly or in part by the metal ions. In conclusion J desire to thank Professor Michelson for his kindly interest in my work and for several helpful suggestions. T wish also to thank Professor Millikan for suggesting the problem and for his valuable counsel throughout this work. I can not adequately express my deep appreciation of his efforts in my behalf. Ryerson Laboratory, University of Chicago. April 1905. LXXI. The Thermoelectric Circuit of Three Metals. By H. Es Senmirz, W.A., B.Se.* § 1. Introduction. HE experiments described in the present paper were undertaken at the instance of Professor E. Riecke, and were carried out in the Physical Institute of the University of Gottingen during the months November 1904 to April 1905. Let a circuit be formed of three metals A, B, C ; and let the junctions opposite these metals be at temperatures (centigrade) represented respectively by t,, t:, t3. If we assume that the electromotive force Ei of such a circuit depends only on the temperatures of the junctions, we may suppose intermediate points to be at 0° C., and may therefore write Hy (aC let (Ch Ne (A) tenons ll) where (B, ©)? is the electromotive force of a circuit formed of the metals B, C when the junctions are at temperatures 0°C. and ¢,°C., reckoned in the direction B to C through the junction at ¢,°, and E is reckoned in the direction ABC. If we further assume that the electromotive force of the circuit is zero when all the junctions are at the same temperature t, we have et (C, A) +t Age O25. 5 2 By the use of this equation we may eliminate (CO, A)? from equation (1), and may write E = (B, C))—(B, C)o'+ (A; B) —(A, Bye... (3) * Communicated by the Author. A short abstract of this paper has appeared in the Physikalische Zeitschrift (July 1905). 632 Mr. H. E. Schmitz on the’ Various formule have been proposed as the expression of the electromotive force of a circuit of two metals in terms of the temperatures of the junctions. The simplest of these is the parabolic formula, in accordance with which we may write :— (B, C)i = at4+2b,2%, ] (C14) = ee, | .) 0) aie (A, B)j = at + 2 be0.. | Using these relations, equation (1) assumes the form Bh = aly + dot, + Oats + 4b t+ 20st 4+ oats ee To satisfy equation (2) we must have a, +a, +a; = 0 and 6, +6,+6, = 0. Using these relations to eliminate a, and by, equation (5) assumes the form corresponding with equation (3), namely : BE == ay (t a to) ++ a3(t3— 7) + 3 b(t — t.”) + = b3(t3" as t,”) e (6) Hew: Hquations (4) imply that the lines of the thermoelectric diagram for the metals A and C are straight if the line for the metal B is straight. The diagram is given in fig. 1 for the case where ay, a3, b,, 63; are all positive and t;>¢, >t. Thermoelectric Circuit of Three Metals. 633 The value of E is represented by the area enclosed by the thickened lines. Equation (6) can be written down from inspection of the diagram. Whatever views may be held as to the ultimate causes of thermoelectric phenomena, the experimental evidence for the assumptions on which equations (1) and (2) depend is too strong to be called in question. On the other hand, the researches of Tait *, Dewar and Fleming tf, Holborn and Day tf, and others show that equations (4) do not hold for all metals at all temperatures. In the present paper, the writer confines himself to the application of equations (4), (5), and (6) to the experimental results; and it will be seen that, within the limits of experimental error, these equations are confirmed in the cases examined. The circuits to which the measurements refer are formed from the metals German silver (A), copper (B), and i iron (C), and the limits of temperature are 0° C. and 80° § 2. Standards. The ultimate standard of electromotive force for the present measurements was a Weston cell (No. 445) made by the European Weston Company, Berlin; the electromotive force was taken at its certificate value, 1°015, volts (19°). Four Weston cells were made in accordance with the instructions of W. Jaeger §, except that, following the later practice of the Reichsanstalt, the cadmium amalgam was composed of 12 parts cadmium and 88 parts mercury. Measurements of the electromotive force of these cells, (a) soon after construction, (b) after completion of the thermoelectric experiments, gave the values shown in the following table :— (a) (b) 25th Keb. 15th April. Gell Noot. s. .:.) 1 ORE 1:01935 3 ee 1:0193 10193 - Bed = ar 10194 1:0194 2s. en E-O1G45 1:0194 Cells No. 1, 2, 4 were combined in series, the total electro- motive force being assumed 3°0582 volts; a temperature correction was unnecessary. Cell No. 3 was used to produce an occasional current through 100,019 ohms; wires from * Trans. R.S. E. vol. xxvii. p. 125 (1876). Tt Phil. Mag. vol. xl. p. 95 (1895). t Berl. Sitzungsber. vol. ii. p. 691 (1899). § Elektrotechn. Zettschr. 1897. Phil. Mag. 8. 6. Vol. 10. No. 60. Dee. 1905. 2 oe 634 Mr. H. E. Schmitz on the points on this circuit separated by 8019 ohms gave a prac- tically constant electromotive force of about ‘03 volt, serving, in a manner which will presently appear, to standardize the apparatus for measurement of thermoelectromotive forces. The thermometers on which the main temperature measure- ments depend were two, graduated respectively from —15° C. to + 60° C., and from 450° ©. to +120° C., the length of the degree being about 5 mm.; they were manufactured from Jena glass by F. QO. R. Goetze. In what follows these thermometers are called respectively G) and G,. Com- parisons with a standard mercurial thermometer gave the following approwimate results :— At 20° Gy reads 06° above the gas-thermometer, oy) 60° Gy ” 2063 ” oD) 2 99 80° 29 ” OF bP) 9) 9) The chief temperatures of observation were chosen with the view of minimizing the importance of any error in the correction for the emergent column ; this correction had the following mean values :— + 2° at 20> (Go), zero at 60° (Gy), -+ “O()2 at 80° (Gy) - After the conclusion of the experiments the thermometers were examined at the Reichsanstalt, with the following results :— At 20° Gy reads ‘11° above the gas-thermometer, ry) 60° G, 9 "08° oP) 9 99 9) 80° 7? 99 “03° 99 3 3) The differences here indicated are, very nearly, the true differences between the scale of Jena glass and the scale of the gas-thermometer, the inference being that the actual reading of the thermometer is, very nearly, the true tem- perature on the scale of Jena ‘lass. In what follows the thermometers are taken as correct, and the temperature- scale employed is therefore that of Jena glass. § 3. Method. The observations were directed to determine (1) the electro- motive force of each pair of metals between 0° and 20°, between 0° and 60°, and between O° and 80°; (2) the electro- motive force of the circuit of three metals, ie temperatures Thermoelectric Circuit of Three Metals. 635 of the three junctions being respectively 0°, the aL ature of the water-supply (read on Gp), and 60° (read on G,}. The thermostat for maintaining the temperature 0% was a vessel of diameter 10 cm. packed with broken ice and filled up with water *. The depth of the thermo-junction below the surface of the ice was about 8 cm. The thermostat for maintaining a temperature of 20°, 60°, or 80° was a closed metallic vessel of diameter 8 cm. and depth 15 em., nearly full of water. A powerful stirrer in the base of the vessel, mechanically driven at the rate of 50 to 100 revolutions per minute, together with suitable break- waters in the interior, ensured a uniform temperature. The vessel was, so far as possible, thermally insulated. A coil conveying an electric current projected into the interior of the vessel ; the current was so regulated as to produce a tempe- rature within half a degree of that desired for half-an-hour previous to an observation of electromotive force, and within one-tenth of a degree for five minutes previous to an obser- vation. In most cases an observation was made while the temperature was very slowly rising. The depth of the thermo- junction, which was arranged in the close neighbourhood of the thermometer-bulb, was about 8 cm. below the top of the lid of the vessel f. The third thermostat was a vessel of diameter 7 cm. and height 13 cm. Water was introduced at the base and taken off at the brim. The thermo-junction and thermometer-bulb were about 8 cm. below the water-level. The thermo-elements were in the first instance constructed from soft wires of copper (believed to be pure), iron (believed to be pure), and German silver, each of diameter about 1°5 mm. For a second series of experiments these wires were drawn to a diameter of 0°5 mm. The electrical connexions are shown diagrammatically in fig.2. AB isa resistance of 10,000 ohms ; BB’ an adjustable resistance. CD isa resistance of 10,000 ohms; EF a constant resistance of approximately 100 ohms. Connexions are made either between X, Y,, X2 Yo, X3 Y3, X4 Yu, or between Y; Zs, * Ice and water is much more satisfactory for the maintenance of a constant temperature than ice alone. + In control experiments the water in this thermostat was replaced by paraffin, and in other experiments the first thermostat was modified by the introduction of a small vessel of paraffin (well stirred) surrounding the thermo-junction and the base of the thermometer. The use of par affin in the latter case necessarily gave a somewhat less reliable value for the temperature of the thermo-junction. The results obtained agreed, within the limits of experimental error, with the results of the expences in which water was used. 2X2 636 Mr. H. E. Schmitz on the Y,Z,; the battery current is never interrupted except at the moment of commutation. Let the first system of connexions produce a current 7 through the compensation circuit BB’A. The second system of connexions either produces no current through the cireuit BBA, or, by joining Y; Z), Y,.Z» as well as Y3; Z; and Y, Z,, produces a current approximately TO Meanwhile the battery is producing a current through a resistance which never differs much from 10,000 ohms. The larger current is used when the standard cells are to Fig. 2. = STANDARD CELLS OF THERMO-ELEMENT be balanced, the smaller when the thermo-element is to be balanced. It was undesirable to make the commutation at frequent intervals, and it was therefore of special importance to be able to assume constancy of the auxiliary battery during periods of an hour or two. Accumulators were tried under various conditions, but the rate of fall of electromotive force was in all cases too great. Finally, four large Daniell cells, each containing two litres of saturated copper-sulphate solu- tion and about one-tenth that volume of zinc-sulphate solution of density 1:2, were employed. These could be trusted to give a nearly constant current for several weeks together, the variation during the course of a day being as a rule exceedingly small. In this connection the following record may be of interest :— Thermoelectric Circuit of Three Metals. 637 Dare Laboratory Resistance compensating H.M.F. ; temperature. of three Weston cells. Nie Renee seg) Vitis had. Atey oe 7023 (a few minutes after com- pletion of the circuit) rising to 7044. we ane Die 7050, 7051, 7049°5. Fis oA. 11°-13° 7051°5, 7950, 7051, 7051°5. Re ec: w 11°5 7053 and (after opening the circuit for two hours) 7040. See hee Re 7052, 7053. ar eee 10°-11° 7052°3, 7052°0, 7052°4, 7051°5. ee OU) rasa 11°-12° 7048, 7047, 7046. etka bee 12°-15° 7047, 7046, 7045. Apr. 4.. 10° 7059'5. So8 CoAT EEA ty en mec® Gpeaare ee eee 7056. epg nae 14° | 7056. nt td ig ee Made eae ie 7049, 7051°5. el eee 15°-16° 7051, 7052, 7051. Ri. Las ac: 16? 7052°5, 7052. re LONE Le a5 13°-14° 7056, 7057°5. _ Let W be the E.M.F. of the three Weston cells (see § 2) and let r be the value of the compensating resistance, so that W =7z. Let E be the E.M.F. of the thermo-circuit, and let s be the value of the compensating resistance. Let the current used in this case (approximately iw) be represented by wi, so that K=saz. E is to be determined from the equation iE s = ==. W where # is a fraction depending on the resistances of the eireuit of fig. 1. For the determination of x, Weston cell No. 3 was allowed to produce a current in the manner already defined, and the compensation apparatus was used to balance a definite fraction of the H.M.F. of the cell, the current flowing through the compensation apparatus being alternately i and a. The following specimen of the observations shows the order of magnitudes involved :— | Compensating resistance in ohms (large current). I. he Bae Be et are . ch fap) ARS) v='010004 Compensating resistance in ohms (small current). STRATE 638 Mr. H. E. Schmitz on the The values of W, 7, and « could all be determined with a high degree of accuracy; the accuracy of the value of H depends therefore mainly on the measurement of s. If ¢ is the least recognizable current through the galvanomer and g the resistance of galvanometer and thermo-circuit, then we find E— sai =+(9+s)2, ‘ : ap aes whence proportionate error in H= 222 Yai present HN DP measurements it was found convenient to use a moving-coil galvanometer, in spite of its high resistance (600 ohms), The value of s was from about 50 ohms to abont 400 ohms. Taking z as the current corresponding with a deflexion of a millimetre on the galvanometer scale, its value was 3 5 lhe . 3 jou ampere. Approximate values for x (Foo) and 2 (G00 ampere) give os for = Hence, taking the maximum value (13) for ore we find as the proportionate error in E (or in s) 1 in 1000. This result assumes absence of current through the galva- nometer when the galvanometer circuit is completed by closing the key K after removing all sources of electromotive force, a condition not easy to realize in practice. In the earlier measurements the resistance AB (fig. 1) was provided by a new compensation apparatus of the type described in the Physikal. Zeitschr. vol. i. p.167. The fractions of an ohm in the instrument used were provided by exposed wires of ‘“‘Kruppin,” and the various external and internal contacts almost always produced an appreciable thermo-voltage ap- parently not avoidable by any precautions. In the later measurements the resistance AB was provided by two new ‘precision’ resistance-boxes (Siemens & Halske, No. 19530 and No. 19531) reading from 0:1 ohm upwards. This arrange- ment gave much more satisfactory results. The chief error was now due to the key K, which in this case consisted of two mercury cups connected by a copper wire (unfortunately not well amalgamated) attached to a sealing-wax handle. It was found that a current, large enough to cause a con- siderable error in the measurements, might be produced at the contact of copper and mercury if a fresh surface of mercury were not constantly exposed. Thermoelectric Circuit of Three Metals. 639 § 4. Results. The results of the experiments are given in the following tables. Tables IA. and IB. give the results of final experi- ments made with the thicker (soft) wires of the three metals; the results of preliminary trials with these wires are omitted. Tables II A. and IL B. give the results of all the experiments made with the thinner (hard) wires. In view of the possibility of an alteration in the thermoelectric force of a given junction*, it may be well to state that the observations recorded in Table IIB. were made before those recorded in Table IL a. Owing to the removal of the Physical Institute to a new building the writer was unfortunately unable to carry out his intention of making further experiments with a view to the elucidation of this point. He is however distinctly of opinion that the thermoelectric ‘‘ constants” are (within the range 0° C. to 100° C.) really constant, and that anomalies such as those recorded by Steele (oe. cet.) are due to difficulties of observation. The agreement between ob- served and calculated results is much better in Table IT a. than in Table IIs. This is probably due, not to any alter- ation in the junctions, but chiefly to the better avoidance of the error (previously spoken of) due to the mercury key. TasBLe I a.—Soft Wires. ibetroumoiive force in microvolts of pairs of metals. E.M.F. observed. E.M.F. calculated *. Exp. 1. | Exp. 2.| Mean. Copper-Iron, 0-20 ...... 9315 | 234 | 233 934-2 : O260" 2... 665°5 | 6703 | 668 666°4 x 0-80 ...... 864 865 864°5 8645 Tron-G.8., 0-20 ...... =) ie ee: ates ee 0-60 ...... — 1884 se a. | 13828 53 0-80 .....- —1851 Per 25a) Gp 1851-0 G.S—Copper, 0-20 ...... 923 | 296 |. 2245 223:6 7 0-60 ...... 712 718 715 716°3 ee O=80. 2... 986 985 985°5 985-4 | j | Copper-Iron ...... a=+12°01, b=—-0301. Hron—Gisg yes... a= —22°77, b= — 0092. | G.S.-Copper ...... a=-+10°80, = 03795. * Method of least squares. * See for instance Wiedemann, Elektricitdt, ed. 2, art. 337; also W. H. Steele, Phil. Mag. vol. xxxvii. p. 221 (1894). Mr. H. E. Sehmitz on the: TABLE I B.—Soft Wires. ane force in microvolts of circuit of three metals. 640 res of Junction. Electromotive Force. ie Goopentael Tron-G.S. | G.S.-Copper. Observed. | Calculated *. eo Se ee ———— | ° te) | 60: ON Yo. W7BB 0 + 4917 | + 4872 60 0 7:99 + 7536 + 7539 8:18 0 60 + 816° + 8135 | 0 S20 60 + §33°35 + 5289 : () | 60 | 8°28 —1292°6 —1292°0 | 83l | 60 0 —1275°7 —1284-0 | * From equation (6), which is here used since the values a,, 0), a3, 6, for Copper-Iron and G:.S.- eae are deduced from more observations than the values a,b, for lron-G.S TaBLE IJ a——Hard Wires. Hlectromotive force in microvolts of pairs of metals. E.M.F. observed. le) O° Copper-Iron 0-20 ” ”? Tron-G.S. 9 +} G.S.-Copper 0 3? be 0-60 0-80 we eeee eeeeee ~eeeee 224°5 639-0 825-4 — 4603 — 1390°8 — 1863°3 237°5 75605 1037°5 E.M.F. calculated * . 226'3 638°3 8259 — 459°8 —1391°4 —1863°1 237°4 7562 1037-5 Temperature of Junction. Copper-Iron G.S.-Copper as eer eee a=+11°580, b=—:03142 TroneG: See choses a= —22°891, a=+11°506, 4= —-00995 b= + -03657 * Method of least squares. TasLe Il 3.—Hard Wires. Electromotive force in microvolts of circuit of three metals. Electromotive Force. Copper-Iron. Tr ron-G.S. G.S.-Copper. Observed. | Calculated * . + 441°3 + 444-] + 728-4 + 738:0 + 8782 + 859-2 + 5771 + 5668 — 1298-2 —1294°6 — 12839 —1295°5 * From equation (5). Thermoelectric Circuit of Three Metals. 641 It is well-known that the thermoelectric properties of a metal depend to a marked degree on its purity and on its state of aggregation. The comparison of the constants given in the present paper with those obtained by other observers has therefore no special value. But a rough comparison is not without interest, and the following short table is there- fore appended. The unit of electromotive force for this table is the microvolt. Kohlrausch’s copper was electrolytic. Tait’s copper was probably impure*. Noll’s copper was pure. Tait used pure iron, but not Noll; Tait found that different specimens of iron had thermoelectric properties intermediate between those of pure iron and steel. The numbers giving the results of Kohlrausch and of Noll are from direct observations with the couples mentioned ; those giving Tait’s results are derived from Tait’s thermoelectric diagram. Noll experimented with both soft and hard wires; his results would point toslightly higher values for hard than for soft wires in both the cases quoted. Coupler | a | &. | Observer. Remarks. | Copper-[ron.| +10°2 | —‘030 | Kohlrausch.*} Hard-drawn wires (16°-80°) | Iron-G.s. | —241 | —-039 “, an iM P | G.8.-Copper.| +146 | +°058 ue | Copper-Iron.| +16°0 | —°058 | Tait.? Copper-Steel.| +10°0 | —-042 % 39 ” ” G.S.-Copper.} +134 | +061 2 Constants for G.S. alter above 150°. Copper-Iron.| +10°5 | —O039 | Noll? Soft wires (0°-182°). | G.8.-Copper.| +161 | +°036 i i 5, (0°-216°). el Copper-Lron.| +12°0 | —:030 | Schmitz. Soft wires (0°-80°). | Iron-G.8. —22°83 | —-v09 G.S.-Copper.; +10°3 | +°038 id ss “3 id | Copper-[ron.; +116 | —-031 + Hard wires (0°-80°). Tron-G.S. —22°9 | —:010 3 & Bs - G.S.-Copper. | +11°5 | + °037 3, 33 39 bh) * Pogg. Ann. vol. exli. p. 456 (1870), also Pogg. Ann. Erg. vol. vi. p. 35 (1874). The above numbers are calculated from those given by Kohlrausch en the assumption that the lower temperature in the experiments was 16°. A further reduction of all six numbers by about 3 per cent. is (strictly speaking) necessary to bring them to microvolt-units. 2 Trans. Roy. Soc. Edin. vol. xxvii. p. 125 (1876), also Everett's * Units,’ ed. 1886. 3 Wied. Ann. vol. lili. p. 874 (1894). In conclusion, it is not without interest to compare the differences between soft and hard wires, as found in the present investigation, with those observed by other experi- menters. In constructing the foliowing short table, the * Steele, doc. cit.; Noll, Wied. Amn. vol. liii. p. 874. 642 Messrs. K. Honda and 8S. Shimizu on values given by Noll (loc. et.) and by Maclean * for “ un- drawn” and “drawn” wires have been made use of- Maclean’s “annealed steel” is taken as the equivalent of iron. Excess of ‘* Hard ”’ over “ Soft.”’ | Noll. Maclean. Schmitz. UoRe Hata Mies PE Se cenlil (ey perce ee porcene G.S.-Coppert jn. 2... +2 per cent. | +3 per cent. | +5} per cent. Grsetran: Se. cee | +2 per cent. | +4 percent. | + 43 per cent. | \ LXATI. On the Magnetization and the Magnetic Change af Length in kerr omagnetic Metals and Alloys at Temperatures \ ranging from —186° C. to +1200° C. By K. Eonpa, Tigakuhakushi, Lecturer in Physics, Tokyo University, aa S. Saumizvu, Rigakushi, Lecturer in Phystes, High Normal School. [ Concluded from p. 574. | Ill. Turrp Sertzs. N the third series of experiments the magnetization was measured at different stages of ascending as well as descending temperatures, the measurement of the change of length by magnetization being left for future experiments. The heating was effected by means of an electric current ; a porcelain tube (external diam.=1'7 cm., internal diam. =1:05 cm., length=47 cm.) was covered with a few layers of asbestos paper, and the lower part (36 cm.) was wound anti-inductively with a platinum wire 0:4 mm. thick at the rate of 2 turns per cm. It was then wrapped in asbestos papers to a thickness of about 5mm. To the upper end of the porcelain tube a brass flange was fixed, while a short porcelain cylinder was inserted tightly in its lower end so as: to arrest air currents. The length of this cylinder was so chosen that when the tube was placed in the right position in the central line of the magnetizing-coil the ovoid occupied the central position of the coil. The magnetizing-coil was provided with a water-jacketed arrangement and a coil for the compensation of the vertical component of the earth’s field. The temperature of the ovoid was measured with a platinum rhodium-platinum junction. One of the junctions was placed in contact with the specimen at a point a quarter of the * Proc. Roy. Soc. vol. lxiv. p. 322 (1899), and vol. Ixyi. p. 165 (1900). Magnetization and Magnetic Change of Length. 643 distance from the upper end of the ovoid, the rest being well insulated with asbestos paper. The interspace between the leading wires and the wall of the porcelain tube was tightly filled with asbestos fibres, and thus protected as much as possible from convection currents. The other junction was arranged as in the second experiment. The thermoelectric current was measured with a d’Arsonval galvanometer from Keiser and Schmidt, the reading of which was corrected by the authors with a mercury thermometer containing nitrogen below 550° C., and by Professor Nagaoka and Mr. S. Kusakabe with the melting-point of sodium chloride. A low- resistance galvanometer was, at the same time, employed to measure the temperatures lower than 200° C. A simple connexion permitted us to pass the thermoelectric current through the d’Arsonval or the low-resistance galvanometer as the case might be. The experiment was conducted in the following order :— The adjustments of the magnetometer and the coils, as described in the first experiment, were effected ; the heating- coil with the specimen was then placed in the right position. The magnetization at the temperature of the room was first determined ; then a current from a dynamo was passed through the heating-coil, till the temperature of the specimen became constant. The direct effect due to the current in the heating-coil was tested by breaking or reversing the current. The small deflexion of the magnetometer, when there was any, was completely eliminated by altering the form of the leading wires. The demagnetization by reversals, while the heating-current was passing, showed no trace of residual magnetism, which indicates that the magnetization due to the heating-current was insensibly small. When the tem- perature became constant, the magnetizations at gradually increasing fields were measured. Another stronger current was next sent through the heating-coil and the same processes were repeated as before. In this way, we measured the magnetization in the stage of ascending temperature and then that in the descending stage. During each set of obser- vations the temperature was fairly constant, and even in very unfavourable cases the variation did not exceed 2 degrees. The temperature was always noted both before and after each experiment and the mean was taken. When a series of experiments was finished, the specimen was taken out of the coil and the compensation tested. Hxcepting in a few cases, we found the compensation undisturbed ; when, however, the disturbance was such as to require a correction, it was uniformly distributed. 644 Messrs. K. Honda and S. Shimizu on In the present experiments the strength of the heating- current and the temperature thereby caused were as follows :— Current .s-cpe.ce 1-8 amp. 29 3°8 eri 5°5 Temperature...| 100° C. 300 600 900 1200 | The heating of nickel-steels protected in the manner above described showed only a trace of surface-oxidation, if the temperature did not exceed about 800° C. If, however, the temperature was raised to 1200° C. the surface-oxidation became considerable, so that the heating of some specimens was stopped at about 800° C., if there was nothing of special importance to be gained by heating them above that temperature. (a) Magnetization of Ferromagnetic Metals. The ovoids were first cooled in liquid air ; the observations at ordinary and then at higher temperatures were taken ; the results are given in Table X. TABLE X. Swedish Iron. t= 14°C: Raa siti CE Fok oe (=(6 12302 is Be ib FL: i, ie if vale 16 0°13 49 0713 40 0:05 50 81 118 0:26 115 0-79 220 3°29 121 79°5 39:0 0-50 338 18°42 373 29°39 166 1889 64:5 139 | 533 11156 | 493 | 1258 | 211 | 333 85:3 248 | 597 |258:0 | 542 | 305 241 | 437 97-6 92-46 | 744 | 398 561 | 425 250 78:6 | 829 377 834 t—772° . t—849°C. | z¢=1009°C. 1=1214° ©. H. I. H. IL. H. L H. ie Ronee i Toa) | op 99 | 17 op ||) aa 140° |454°| - 300 | 34 -mopom le 3-4-1 case Mies Dela esa.) 443 )|) 2:9.)) Aebeele SO - |. Aaa 244 | 290 | Magnetization and Magnetic Change of Length. 645 Nickel. | t=205° ©. t—=a19" O. £=362°) C: ve ak Oa | H. I Ee H. I. H. | 1:58 73 1-77 99 32:8 0:8 55 jig at 562 | 190 9:06 | 176 | 182-4 53 179 44 | 1883 | 314 | 31-0 204 | 363 9-0 345 65 | 85:7 390 | 1245 210 | 481 10:8 79 8-1 907-4 398 | 285 213 334 401 | 464 215 | 447 403 | —518° C t=678° C t=—874° C t=1149° C | | el I. H. E Ee L Ee Te a OS eee aes ee ee | 183 3:8 182 35 236 4-6 129 2-3 | 366 6-3 343 5-4 363 5-4 349 51 478 73 477 6-4 479 | 59 481 57 | Annealed Cobalt. £=185° C t=307° C. £=428° C | t=546° CO. C | by CEE I. Biel, H. | i H. eed lars Naeem | Tf BEN eh SG 13°45 49 3:87 45 3:22 | 922 4-27 57 19°52 96 743 | 112 8:23 83 AS | TAR | 32-4 198 | 1469 | 319 | 13-41 | 185 | 13-62 | 406 63-5 325 7-6 570 | 21-46 | 307 | 22:43 | 547 94:3 ALL | 9889). TIO. BT 514 | 59-9 710 | 184-1 568 | 1957 | 913 | 1191 662 | 126-7 832 | 2792 | 677 |319 | 998 | 2401 812 | 253-2 | 928 | 376 758 | 370 | 1018 379 906 | 374 978 | | t—619° C. t= 770° ©. i=919° C t—1060° ©. ia. aciaeal | H. Ee H. L oe H. i | Pas Peleg] S49. |) ng |) fap Bh aia | Baul 4:79 | 108 445 | 151 2-55 a 22°03 84 | 7-88 | 250 | 13:21 | 411 | 13838 | 399 | 51-1 98 | 31°31 | 573 | 2815 | 531 | 4220 | 518 | 900 | 106 — 72:1 716 | 760 674 | 94-4 591 | 2125 | 126 1285 806 | 134-0 749 | 1849 | 639 | 333 | 136 271-4 909 | 262:9 823 | 291-6 665 | 439 | 140 | 378 951 | 386 856 | 400 674 | | | j 646 Messrs. K. Honda and 8. Shimizu on Annealed Cobalt (cont.). z—1066°C. | ¢—1074°C. #=1109° ©. #—1219° ©, H. ie re L ae L H. ie 9.05) | lon | “ins || Bige | aaa || Sato | eo alee mal | a4 | ager | igael 304 || Sea. |) Wea ius 468 62 | 1791 || gae | 446)! 77 | “fase 149-6 87 | 343 41-9 9441 | 100 | 446 45-0 436 107 The magnetization of iron and nickel at high temperatures is so well known that it is superfluous to give all the numerical data obtained by our experiments. Hence in the above table, the numbers for iron and nickel are limited to those at very high temperatures, in which they become of interest. Swedish Iron.—The magnetization at constant temperature was measured at 20 different temperatures in ascending as well as descending stages ; the curves of magnetization were then plotted against the internal field. These curves were cut by an ordinate of constant field. The curves of magnet- ization in a constant field plotted against the temperature were thus obtained, and are given in fig. 6a (Pl. XL). The change of magnetization of Swedish iron with rise of temperature was found to agree well with the results obtained by previous investigators*. The weak magnetization beyond the critical point, as first observed by Curie, was also noticed. Here the magnetization at different temperatures ranging from 800° C. to 1200° C. diminishes very slightly as the. temperature rises. Thus the meaning of the critical point becomes vague; H. Du Bois defines this temperature to be a point of inflexion in the temperature-curve of magneti- zation ; but it is more convenient to define the temperature * J. Hopkinson, Phil. Trans. clxxx. p. 443 (1889); Proc. Roy. Soc. xliv. p. 817 (1888). Lydall and Pocklington, Proc. Roy. Soe. li. p. 22 (1893). D. K. Morris, Phil. Mag. xliv. p. 218 (1897). Ledeboer, C. R. cvi. p. 129 (1888). ‘Tomlinson, Proc. Phys. Soc. ix. p. 181 (1888). Curie, C. A. exv. p. 805 (1892); cxvine pp.)796, 859. \- Wilde; abror Roy. Soc. lL. p. 109 (1891). Kunz, Elekt. Zeits. xv. p. 194 (1894). Wills, Phil. Mag. 1. p. 1 (1900). Nagaoka and Kusakabe, Jour. Coll. Sci. xix. art. 9 (1904). Magnetization and Magnetic Change of Length. 647 as the point of the maximum curvature. The critical temperature so defined is, in the case of Swedish iron, 780° C. for H=406 c.a.s. It is also to be observed that the critical temperatures for ferromagnetic metals and alloys depend more or less upon the strength of the field. The magnetization in a stage of descending temperatures falls a little short of the magnetization in ascending tem- peratures for the same field and temperature. Butat ordinary temperatures they coincide with each other. Combining the above results with those of the magnetizations at the liquid air temperature, we obtain a hysteresis curve with regard to temperature, whose lower range is considerably extended by the present experiments. Annealed Cobalt-—As in the case of Swedish iron, the temperature-curves of magnetization were obtained, and are given in fig. 60. The magnetization of annealed cobalt at high temperatures was first observed by Professor Nagaoka and Mr. Kusakabe™*. The present results generally agree with those obtained by them, but in our case the cooling in liquid air slightly altered the magnetic property. In fig. 66 the point corresponding to the magnetization in liquid air is also included. As the temperature rises from — 186° C. the magnetization in a constant field increases, at first slowly and then rapidly, till it reaches a maximum at about 300° C., after which it decreases. The magnetization reaches a small minimum and then begins to increase, and after passing through another maximum, rapidly decreases, reaching its critical point at 1090° C. for H=400. The descending branch of the curves cuts the ascending branch at about 850° C. from downward to upward ; but its general course is similar to that of the ascending curve. The minimum point in the ascending branch is about 450° C., and nearly coincides with the singular temperature observed by us in the change of length by magnetization f: at this temperature the sign of the length change is reversed for all fields. It is also to be noticed that the course of the curve beyond the critical point is nearly parallel to the axis of temperature. * Nagaoka and Kusakahe, Joc. cit. t Honda and Shimizu, Jour. Coll. Sci. xix. art. 10 (1903); Phil. Mae. vi. p. 392 (1903). 648 Messrs. K. Honda and S. Shimizu on Nickel.—The specimen, which was first cooled in liquid air, was heated, and the magnetizations at ten different ascending temperatures were observed; since the dynamo stopped when the temperature attained 1150° C., the magnetizations at decreasing temperatures were not taken as in the other cases, except for the maximum field only. The temperature-curves of magnetization are drawn in fig. 6c, in which the results of the first experiment are also included. ‘The character of the change of magnet- ization by heating coincides with the results obtained by the former investigators*. Here the range of the temperature is considerably extended on the negative side of zero tem- perature. It is remarkable that though the magnetization falls very rapidly near the critical temperature 360° C., its further decrease is very small, and even at 1200° C. a magnetization of about 6 ¢.G.s. for H=400 is still observed. This important phenomenon was first observed by Curie. (b) Magnetization of Nickel-Steels. In nickel-steels the magnetic state after cooling in liquid air slightly changes as the time proceeds. In some alloys it does not return to its initial state when they undergo a cyelie change of temperatures between —186° ©. and 1100° C. This change of character is greater in the irreversible alloys than in the reversible. The magnetization of the alloys at different temperatures presents a striking contrast between the reversible and the irreversible alloys. Some of the interesting results had already been obtained by previous investigators f. The manner in which the magnetization of the reversible nickel-steels changes with the temperature is similar to that of nickel, as given in Table XI. * J. Hopkinson, loc. cit. Curie, loc. cit. Nagaoka and Kusakabe, doc. cut. + H. Becquerel, C. &. xciii. p. 794 (1881). J. Hopkinson, Proe. Roy. Soc. xlvii. p. 23 (1890); xlviii. p. 1 (1890). H. Le Chatelier, C. R. cx. p. 283 (1890) ; exi. p. 454 (1890). H. Tomlinson, Proc. Roy. Soc. lvi. p. 103 (1894). F. Osmond, C. R. exvili. p. 532 (1894) ; exxviil. pp. 304, 1396 (1899). Ch. Ed. Guillaume, C. &. exxiv. pp. 176, 1615 (1897) ; exxv. p. 235 (1897); exxvi. p. 788 (1898); “Les Aciers au Nickel,” Paris (1898). E. Dumont, C. R. exxvi. p. 741 (1898). L. Dumas, C &. exxx. p. 357 (1900). Magnetization and Magnetic Change of Length. 649 TABLE XI. Nickel-Steel 70°32 per cent. t=11°7 ©. t=104° C. t=410° C. t=658° C. H I H le H. I H | ie 0-34 quiimro-zol (a ig: | “otal Mane 35 | 2:8 107 | 42 108 | 69 1:89 | 368 132 | 9-1 1-73 | 239 125 | 164 8-92 | 485 276 | 186 4-98 | 570 160 | 374 | 31-4 | 536 476 | 29-2 1229 | 716 2:36 | 516 | 641 545 2509 | 9864 | 295 | 867 | 1535 | 559 41-1 047 | 683 | 944 | 2046 | 565 76-4 | 1000 | 166-1 970 | 434 573 193-7 | 1029 | 2646 | 980 393 1043 | 405 989 | | £=733° C. #=900° C. t=753° C. t=11°5 C. H if H me ihre I H I. ee Cea ney ad ee eee 100 | 56 305 | 7:9 WR 5-0 1:08 | 171 248 | 14:3 491 | 10-3 304 | 85 422 | 491 469 | 26-7 488 | 11:0 | 21°64 | 908 56°3 | 1008 | 2044 | 1034 349 1041 405 1045 Nickel-Steel 50°72 per cent. t=12°-0.C. £=126° C. {= 296° ©. t=410° ©. H. I. H. I. Hi I. H. i 186°6 1250 | 215-1 1166 4 404 921 | 305 567 386 1267 Phil. Mag. 8. 6. Vol. 10. No. 60. Dec. 1905. aX 650 Messrs. K. Honda and S. Shimizu on Nickel-Steel 50°72 per cent. (cont.). t—639° CC. 2=607 aC. ¢=—O654-456. t—A9nee H. I, EE I H. i. ii. I. 2] OO 31 eit oll 0:7 30 0°6 113 3°9 206 6:9 136 4:7 98 3°4 267 8:2 487 115 822 9-0 345 10°7 490 11°3 484 116 482 13:6 haat STD OF —w) oS eae OF i= 192° C. €=12°° 270; H. I. H. 1. H. I. H. I 12-7 4-7 0:06 46 0:07 34 0:20 26 34-7 11°5 0:20 169 0:18 432 0:49 87 101°6 al -2 0°45 586 0:70 649 0-77 355 245°1 46:2 85'3 941 6:53 951 0°94. 582 402 58°7 | 269°8 949 94:20 | 1048 45°7 1235 478 65:1 | 408 952 72:0 1069 1430 1259 Mash) 1078 261°7 1264 390 1082 378 1267 Nickel-Steel 46 per cent. pel OSC) pes ih sive Ch, t—260- 1 C: t=o40 1B fp I. H. T, H. I, ihe i 0-78 | 22 | 078)| 28°) lone | a1 0 oo 1:83 60 2°56 144 1:29 96 0:82 U1 3°40 190 J21 319 Du 408 Dea) 227 7:49 549 By 521 5°40 561 4°59 380 9°87 706 9°71 751 15:11 704 13°46 495 17°70 913 22°80 943 34:8 778 40:2 562 49°9 Tatas? 466 1047 789 834 135:3 588 80°3 1201 106°6 1114 913'4 851 253°9 593 195:4 1260 264°4 1140 Bull 7 892 431 597 319 1276 381 1146 409 854 =411° C. ~$=456° C. ~=—624° C. t=488° C. H L. H. L H. ik HL. i iy | 28 | “4 | 06) | (eel) So | Mee 50 6:2 105 2°8 240 73 234 8:7 137 146 305 10:0 387 116 385 IID) 4U7 40°8 483 14:2 479 13°4 475 14:2 Magnetization and Magnetic Change of Length. 651 Nickel-Steel 46 per cent. (cont.). b—oiek- C. =o So OF C—O ee t=33°'2 C. H. 13 H. Ai H. it H. il, 347 168 45°2 592 50°95 887 69°6 1120 459 183 | 1980 626 | 169-4 964 | 161°8 1217 329 631 | 284 974 | 280 1243 | 425 638 | 399 979 | 369 1252 Vickel-Steel 36 per cent. 1—10°0 0. t=161° C. £=295° O. £=259° O, H i H e i. I H I ae ag Web g, |e Poul ese ste: loon. 64:2 954 | 135°1 563 176°2 1021 | 27675 572 299 | 1035 | 437 578 419 | 1039 £=447° ©. £= 828° 0. £=493° ©, 1=303° C. z 0 H. i H. i i. I. See tos | ae ar he "9 | 42 Poe osm | 10-5) le ose. az a) 82..|' tos qeateWisae |) dea. | 171% |. 989-4 Lege -sea~ | 14-7 AeA al, (gale. ty 482k vi 17-8 * In this case the compensation of the magnetizing coil was found to be disturbed, and therefore the disturbance was equally distributed over the whole set. This small increase of magnetization is probably due to the impaired compensation. NG 652 Messrs. K. Honda and 8. Shimizu on —— Nickel-Steel 36 per cent. (cont.). t=218° C. t=182° C. t=145° C. é= 10° 01C? H. I. H, I. HH. ly lek I. 30°5 | 14:7 0°26 54 0:21 42 031 174) 239 1:54 198 0-46. | 127 0-71 118 160°2 | 35°5 8:08 335 151 242 1:66 320 55°3 20:58 364 6°46 459 4°88 556 481 70°6 71-4 379 49°6 582 16°15 801 250°7 391 | 151°4 592 | 1121 1013 447 401 | 292°3 597 | 2479 1027 428 602 | 302 1028 | 375 1029 Comparing the above values for ordinary temperature with the corresponding values in the first series, we notice that except with 36 per cent. nickel-steel, the magnetizability of these alloys had slightly changed by the repeated heating and cooling which the alloys had undergone since the end of the first series. From these results, the temperature-curves of magneti- zation are obtained and given in figs. 7 a, 6, c, d (Pl. XII). In these figures we have also included the results obtained in our first and second series of experiments. As seen from the figures, the diminution of magnetization, after the critical point is reached, is very slight; and to judge from the course of the curve it seems probable that the magnetization does not altogether vanish till the melting-points are reached. The curves of magnetization at a constant field in the ascending and descending stages of temperature do not exactly coincide with each other when the range of tem- perature is large, the two curves thus enclosing a small area - between them. As the critical points of these nickel-steels for H=400, we give the following values :— AOS. Fe. Ee (0532 ©). (VOOH2Y/ sh. 46 Fee 30°9/,. Ascending branch............ 660° C. 490° C. 412° C. 255° C. Descending branch ......... Biecs 460°C. | 395° C. | 2402 a These values nearly coincide with those of M. Osmond and L. Dumas. Thus the critical point falls with the per- centage content of nickel. Magnetization and Magnetic Change of Length. 653 The manner in which the magnetization of irreversible nickel-steel changes with temperature is very striking. The observed values are given in Table XII. Taste XII. Nickel-Steel 29°24 per cent. (ced Ma oe t=140° C. t=2,10°'C. t=352° C. H. t ZC i Is is LE H. I. 3°21 30 5°83 3l 11:27 57 9°87 56 9°33 103 12:57 | 109 18°51 162 18-10 161 14-20 200 29°8 299 291 276 313 275 22°35 355 74:3 433 68:0 428 69°4 399 48°3 507 | 169°5 566 | 1647 566 | 167-7 518 790 | 604 | 329 678 | 2805 | 646 | 308 595 1505 «| «(723 | 449 799 | 449 713. | 445 639 24492 | 810 345 870 417 902 #=499° C. £-=547° O. t= 799° C. 1=466° ©. H. ie ne a H. L H. L 203 | 62\| 51 ce | ae 20 | 52 2-9 560 | 189 | 168 61 | 140 4-8 | 152 58 1932 | 573 | 357 | 109 | 308 93 | 311 | 128 Bape (eee | 405 | sg | 494 | 128) 494) | aay 410 | 946 487 | 1025 £=299° C. 1—192° C, 1—93° C. £—12°-0 C. H I H. ia H I H I 31 eet 3 ie 146 221} O21 | 46 105 49 | 103 51 | 107 58 | 163 | 107 Sete) ide oent | 105 | 972 |isee | isa5 | ise 376 12°83 | 375 1S-G. |py4et 206 | 27-91 250 497 155 | 494 16:2 95°6 265 334 286 654. Messrs. K. Honda and S. Shimizu on Nickel-Steel 29 per cent. 114° 0. 1—168° C. £=268° C. £=388° C. i. 7 i. i. He | ae i. L 4-35 Bil oon | pail eby-43.| 20. bossa 5°31 wl 12°60 86 14°55 71 26°24 153 12°31 214 19°61 176 23°40 173 49°3 230 20°76 367 30°5 254 3671 257 =| 109°7 314 29°1 432 64:5 853 | 115-4 407 | 231-1 387 575 | 585 | 2087 | 503 | 2815 | 512 | 441 446 1252 | 717 | 323 561 | 434 561 2380 | 815 | 436 600 416 889 1=465° ©, 1=515° C. 1=644° ©. t—799° C. H. 1 Ht: Sale H. if H. ie 169 AG | ABy 23 | 54 20 | 94 5 45-4 50 | 1613 | 108 | 280 77 | 989 36 93:3 96 | 340 999 | 475 | 103 | 477 8-9 2124 | 161 | 473 29:9 321 192 448 217 t—601° C. 1—405° ©, £—206° ©. 1—12°3 ©, H. L aE L H. L i. i: 65 23 | 94 34 | 86 54 | 10-41) eee 247 73 | 232 7-4 | 299 30 | 136 | 182 a79. | 10-4 | 344 9-0 -| «858° Je ao-7-|- 4-54 41) ape 476 | 108 | 473 | 122 | 17-32 | 381 1384 | 419 369.9 | 426 466 428 Magnetization and Magnetic Change of Length. 605 Nickel-Steel 28°74 per cent. G= Poe. t=S42€. t= 143° OC. t=228° C. 3072 | 955 | 1851 | 716 | 318 734 | 333 766 422 | 1015 | 313 820 | 436 841 | 450 813 | 499 882 #—327° ©. t—418° C. t=497° C. 1=634° O. He i H. i H. it H. L Sotrieiss | 64m ian |: oa6 a ee oa tee lien | i319) ln | 524. loice ke 214 6-9 25°33 298 22°50 193 97-1 28°4 239 10-2 599 461 33°6 256 | 158°9 426 507 12°6 1099 | 556 | 685 | 352 | 364 79-4 9041 | 659 | 1173 | 428 | 506 93-9 365 796 | 266-7 | 527 443 752 | 446 584 £=795° C. 1=399° C. ‘101°C. 1940-9 C, H. z H. L i. L H. t 60 Piialos. | ao0 fh a4 fee O10. |. 21 157 52 | 262 9-7 | 107 66 | 385 | 207 342 ge iicaiy | | 143. | a6g le re6 ||: 23-07 | 285 Bib) a0 507 | 242 | 961 | 303 575 | 319 656 Messrs. K. Honda and S. Shimizu on Nickel-Steel 28°32 per cent. t=12° 50. #=130°C: ~=300° O. t=453° C. A. 1. H. I, H. I. if. 18 3°28 21 516 26 7°43 33 12°45 28 6°67 75 9°36 qi 17°01. 156 28°82; 72 14°58 183 17:05 233 25°74 293 45°6 114 94°56 328 25°68 348 47:2 434 §9-i 185 41:4 438 | 408 | 432 | 956 582 | 189-2 287 65°6 555 Se7 579 194°3 697 314 339 132:1 713 183°5 734 318 778 469 401 266'6 &61 815 833 439 824 420 962 423 72 t— O04: t=649° C. t=818° C. ¢=hDeleas: ise Ie FD, is H. I, HH. li 22 14 114 4°5 120 3°9 109 39 52 3°9 217 72 263 79 246 79 276 24:3 516 1235 te oS Lia 385 108 506 39°5 | 510 13:7 { | foe $—200°R: 152°C = Loree igh 7B H. i. FL. 1. H. Ie 105 fl .4g° 4 Rates Bl Sant ae 37 | 319 | 20 216 8:2 215 91 111 84 18°38 36 367 11:7 341 13-5 388 Dow 378 46 512 14:2 Hit 159 513 28°8 1252 (2 289 102 492 126 Vickel-Steel 26°64 per cent. @=15°9-3 C. t—1212 -—2Zaoe ©! 4= 3922 ae iff . I. ler ip AB I, 2°55 10 20 25 6:38 Pai 5:03 55 1022 65 9:02 59 13°88 93 9-42 138 16°87 154 16°46 163 19°21 209 13°93 226 9532 292 24:45 297 26°04 341 24°14 364 37°4 - 402 380°2 384 389°1 482 60°6 553 a7°4 581 50:2 5383 54:1 618 111°9 665 10533 737 1049 738 100°9 755 226'4 174 180°1 876 179°4 867 192°3 882 420 849 27171 976 290 969 330 982 406 1064 401 1035 3895 1001 Or Magnetization and Magnetic Change of Length. 6 Nickel-Steel 26°64 per cent. (cont.). | £=—463° C. #=517° C. t=—665° C, $—828° C. H. i eT. L H. L H. L p71 |. 98 .| W50 et ee ve 3-5 i508|| 63 | 204 |103 | 243 | 88 | 301 9-3 9348 | 121 | 484 | 902 | 484 | 139 | 481 | 136 405 | 167 1011 | 297 2161 | 417 352 430 439 538 | #-=514° C. £=401° ©. £—227° 0, 1=8U° C. Hy |e eL. i Tae eal cul H. i) a abe Pac 105 | sui | 124 | 150 | 479 | 166 | 103 4°5 128 a4 124 301 10°3 303 108 301 480 144 479 14°8 480 Nickel-Steel 24°40 per cent. 1=13°-0C. t=101° 0. —4=190° C. t=366° C. He 1p EC I. | H. iF H. I, 3°89 14 8°42 37 12°11 71 9:00 58 12°35 66 19-06 155 19°50 184 16°20 187 20°60 La 27°62 282 27°16 304 23°75 331 27°75 297 48:4 450 49°5 508 40°5 475 56:09 497 81°7 615 61:3 579 62:9 589 126°5 744 | 1524 718- \A4as3 79h, | 1320 733 184°9 837 | 229-5 864 | 261:2 903 | 213°3 805 296 941 | 308 926 | 420 988 | 3120 856 400 1009 | 419 991 ; 427 895 t=466° C, t=490° C. t=392° C. t= 207° C. H. ¥. Jae Ts.” H. he Jak 1 ————— | 5:25 35 8:48 25 12°42 30 10:39 37 10°72 89 18°47 60 15°66 73 23°25 96 25°72 | 234 39-2 138 40°5 125 37°78 | 167 44-7 338 73:2 296 80°3 230 76-7 302 113°7 521 | 145-4 343 | 165°3 362 | 138-5 438 244-9 645 | 296 456 | 279-4 460 | 272-2 575 44) 724 | 458 516 | 455 542 | 447 661 658 Messrs. K. Honda and S. Shimizu on Nickel-Steel 24:40 per cent. (cont.). t= 1499-0. 1=237° C. 1—410° ©. 1=490° C. ae I H. I H. I HL. i 578 | 32 | iy | 98 | da55 | 33 | asc llaee 1339 | 86 | 1648 | 61 | 2355 | 68 | 373 90 20:32 | 155 | 31:36 | 126 | 382 | 126 | 904 | 209 472 | 375 | 749 | 267 | 732 | 2901 | 1841 | 397 77-0 | 543 | 1556 | 425 | 1052 | 270 | 342 493 1648 | 722 | 309 569 | 2306 | 413 | 434 AG5 260 97 | 449 631 | 334 439 412 830 447 538 t—542° C #=591° C. #—851° C. #—1000° C. H. I iz. I i. I i. I pap || ie | sey | BO | B71 | ay | aOponul moe bes || eo | ees | Be | 520 || 47 | Bonn Mee 338 1228 | 3082 | 82 | 3083 | 74 | 483 | 73 472 146 | 49830 | 105 | 486-0 | 8-7 #=1200° C. 1=861° O. #—212° ©. t=-14°-6 0. ae ate H. I H. I H. i ‘oe0 || 34 | 1068 | 99 |. 6441 5a 4 dele aan | 36 | 304 |. 47 | 1634 | 80>) 4qalee ee 480 || 37 | 481 | 54 1.398 | 419 | ‘oogumigee 485 | 138 | 1936 | 176 351 214 464 933 Nickel-Steel 24°04 per cent. #—10°-1C. £—182° C. £=287° C. 1—452° 0. Te Te HH: I H. i EL I mu @ |. 368i 4s) Suen | Sennen i0741| 42 | 11-48 1 (54 | qeaelN 77 | 19-97) 97-60 | 230 | 2048 | 188 | 1863 | 193 | 2491 | 254 356 | 306 | 2697 | 270 | 2306 | 313 | 47-7 | 372 582 | 520 | 391 | 386 | 332 | 497 | 71-9 | 459 80-6 || w64i | 589 | 652 | sie Ml 592 | 1643. (lameee 115-0 | 756 | 907 | 703 | 957 | 760 | 271-2 | 673 i856 | 988 |1747 | 875 | 183-4 | 886 | 447 745 762 | 985 | 2845 | 982 | 975:3 | 954 393 | 1060 | 395 | 1046 | 383 | 1009 Ou wee) Magnetization and Magnetic Change of Length. 6 Nickel-Steel 24°04 per cent. (cont.). | #=581° C. 1—586° O. t=717° ©. :—604° C. | H. i i. i H. r = L 41 Loe ee thee | ie | be Ee 6 3-4 184 79 | 268 | 77 | 348 | 100 | 236 7-7 370 | 137 | 487 | 5 | 487 | wa | 4 | 3 490 | 162 489 | 12-9 #—502° C. t=274° ©. £—193° C. #1193 C. H. L i L H. L. H. L =o Ed ee On oe ee 1s | 57 28 250 GOn |e 1st 77 | (102 Bae nies 8-9 392 11:9 352 141 310 12-9 286 13°8 487 13°8 487 166 494 16°5 484 18°9 From these values, the iemperature-curves of magnetization are obtained and drawn in figs. 7 e, f, g, h, 2, j,k. In these figures, we have included the results obtained in the first and second series of experiments. Here we also notice that, except with 28°74 per cent., the magnetizability of these alloys had considerably changed by the heating and cooling which the alloys had undergone since the first experiment. Hence in some of the figures, the portions corresponding to the first series of experiments were displaced parallel to themselves so as to form closed curves. Thus the displaced portions are given in dotted lines. As the temperature gradually rises from —186°C., the magnetization of 29°24 per cent. Ni diminishes at first slowly, then rapidly, and after passing through an inflexion point, the diminution becomes slow. The curve passing through a second inflexion point begins to descend very rapidly, as the critical temperature is approached. If this temperature be passed, the diminution of the magnetization by heating is very small, so that the curve is nearly parallel to the axis of temperature. rom the course of the curve, it seems probable that the magnetization does not altogether vanish till the melting-point of the specimen is reached. As the temperature is next gradually reduced, the increase of magnetization is very small; this state continues till the temperature falls to about 100°C.; then the increase becomes very rapid. For example, in H=400 c.a.s., the intensity of magnetization at 660 Messrs. K. Honda and 8. Shimizu on the descending temperature is only 20 c.c.s. for a temperature of 80°C., but it amounts to 200 for 20°C., and at —60°C. it increases to 790. Thus the magnetization of the specimen displays a remarkable difference between the ascending and descending branches of the curve. The above manner, in which the magnetization is changed by temperature, is common to all other irreversible nickel- steels. As the percentage of nickel decreases, the concave portion of the ascending branch becomes fainter and fainter ; and with 24°40 per cent. and 24:04 per cent. Ni, it almost vanishes for strong fields. Apparently, the forms of the two curves for nickel-steels of 29°24 per cent. and 24:04 per cent. Ni are widely different from each other; but if we compare the forms of the curves of two consecutive nickel-steels, we can trace transition stages from one form to the other. The critical temperatures of the alloys for H=400 o.as. are given in the following table :— Alloys ..................| 29°24 | 29 | 28-74 | 28°32 | 2664 | 24-40 | 24:04 p. cent./p. cent.|p. cent..|p. cent.'p. cent.|p. cent.|p. cent. Ascending branch... .|530°C.|530°C.)530°C.|510°C.|510°C .|580°C.|520°O. Descending branch ...| 70 140 80 50 10 130 40 Thus, in the ascending branch, the critical temperatures of these irreversible nickel-steels are nearly equal, except with the last but one. The above numbers fairly coincide with those obtained by M. Osmond, except with 24-40 per cent. Ni. With this alloy the critical temperatures are greater, in our case, by about 50°C. for the ascending branch and 100° C. for the descending, than in the experiment by Osmond. The values given by L. Dumas for the first four of these alloys are considerably less than those obtained by us; but for the remaining alloys the contrary is the case. These discrepancies may probably be due to the previous history of the alloys. It remains to mention a singular phenomenon. If at a point in an ascending branch of the temperature-cycle, the temperature be reduced to the ordinary, the path is utterly different from the ascending one. If, however, the tem- perature be again increased to its former value, the path nearly coincides with the former one; the further increase of temperature diminishes the magnetization in such a manner that the magnetization is not interrupted by the cooling process. An instance is seen in fig. 77. Hence in Magnetization and Magnetic Change of Length. 661 irreversible nickel-steels, the magnetization at ordinary temperature can have any value whatever within given limits, if the cooled specimens be heated to a suitable temperature. Becquerel, who first studied the magnetic properties of irreversible nickel-steels, found that in the alloy there were two states of stable equilibrium; but according to our results there are an infinite number of such states, a fact which may possibly prove to be important in the theory of molecular magnetism. Comparing the magnetization at different temperatures in these nickel-steels, we notice that the critical temperature in the descending branch of the temperature-cycle generally becomes less as the percentage of nickel decreases. As the content of nickel diminishes from 70°32 per cent. to 26°64 per cent., the critical temperature falls from several hundred degrees to the ordinary temperature. It is then highly probable that 25 per cent. nickel-steel, which is feebly magnetic both at ordinary and liquid air-temperatures, would become strongly magnetic, if the cooling should be pushed still further. If it once become strongly magnetic by cooling, it may preserve this property, after the alloy is heated to the ordinary temperature. It will be interesting to investigate, whether other non-magnetic alloys, which consist of a mag- netic and a non-magnetic metal, would display a similar henomenon on being cooled to a sufficiently low temperature. The fact that the two strongly magnetic metals form a non- magnetic metal is then nothing more than the lowering of the critical temperature of the alloy to the ordinary tempera- ture. Owing to some changes occurring in the molecular configuration during the process of fusion of the constituent metals, thé. critical temperature of the alloy in the descending branch of the temperature-cycle falls to a low temperature, and therefore the alloy behaves as a weakly magnetic or non-magnetic alloy at ordinary temperature. The same remark will also apply to a non-magnetic alloy which consists of a magnetic metal and a non-magnetic one. The above view is also favoured by the fact that in irreversible alloys the hysteresis-loss at ordinary temperature is markedly small, which corresponds to the hysteresis of iron or nickel at high temperatures, but its value at a low temperature considerably increases, corresponding to the hysteresis of the same metal at ordinary temperature. [ 662 J LXXIIT. The Theory of Electrolytic Dissociation. (A Rectifi- cation of the “ Correction” by Professor Harry C. Jones.) By Louis KanuenserG, Ph.D., Professor of Physical Chemistry in the University of Wisconsin *. HE “Correction” by H. C. Jones+ which recently appeared in this Journal is founded upon an error on the part of its author to which I desire to call attention. The supposed “correction” relates to the following passage which Jones quotes from p. 215 of my paper ¢{ :—‘ In 1901 I pub- lished a list of results of cryoscopic and_ ebullioscopic determinations made with typical aqueous solutions of electrolytes and non-electrolytes, and also a list of molecular conductivity determinations of the same electrolytes at 0° and at 95°. lt is unnecessary to discuss again the details of these results which are rather voluminous. Suffice it to state that a comparison of the freezing-point values with the molecular conductivity at 0°, and also of the boiling-point values with the molecular conductivity at 95°, revealed the fact that there is no such connexion between freezing-points and boiling- points of solutions on the one hand, and their conductivity on the other, as is claimed by the theory of Arrhenius. In numerous cases not even a qualitative agreement exists. The facts presented in the paper cited have since been corroborated by Smits in his careful vapour-tension measure- ments, and by H. C. Jones and co-workers in their molecular weight determinations on solutions.” Now it is clear that this passage relates to aqueous solutions as the first sentence of it explicitly states, which fact has been entirely overlooked by Jones, for after quoting the above he continues § :—‘ Referring to the paper cited by L. Kahlen- berg ||, and turning to page 342, we find the following :— Under the heading ‘ Behaviour of non-aqueous electrolytic solutions’ the following supposed ‘facts are presented.’ ‘Again, many solutions have been found in which the solute according to molecular weight determinations is undissociated, and which nevertheless possess excellent power of conducting electricity.’....‘ According to Dutoit and Friderich, Cdl,, LiCl, Nal, HgCl,, and NH,CnS have normal molecular weights in acetone, and yet these solutions are conductors of electricity.’ Jones then proceeds to give a general statement * Communicated by the Author. + Phil. Mag. (6] x. p. 157 (1905). t Phil. Mag. | 6) ix. p. 214 (1905). § Loe. cit. p. 158. || Journ. Phys. Chem. v. p. 339 (1901). The Theory of Electrolytic Dissociation. 663 of the results of his molecular weight determinations of the salts just mentioned in acetone solutions. It is clear, there- fore, that he has wrongly applied the passage which he quotes from p. 215 of my paper * to non-aqueous solutions, for it relates to aqueous solutions ¢, as has been pointed out above, and his ‘‘ correction”’ is consequently not pertinent. The passage quoted by Jones from p. 215 of my paper does refer to the molecular weight determinations on aqueous solutions made by him and his co-workers,—see the article b Jones and Getman, Amer. Chem. Journ. xxxi. p. 303 (1904)f. In this paper experimental data are presented showing the change of molecular lowering of the freezing-point and also the alteration of the molecular conductivity with change of the concentration of the solutions. A goodly number of the salts which were thus investigated are the same as those I had used, and an examination of the experimental results which Jones obtained with these salts shows that there is no such relation between molecular weight determinations on the one hand and conductivity measurements on the other as the theory of Arrhenius requires. Moreover, the behaviour of the salts which they studied in addition to those which I measured, also substantiates this contention. The deter- minations of Jones and his co-workers therefore constitute, indeed, a corroboration of my work as was stated in this Journal §, | I would like to emphasize here that in my article|| I have not referred to theinterpretations which Jones himself puts upon his experimental data, or the mode of reasoning by which he arrives at his conclusions. A scrutiny of the method of “reasoning” adopted by Jones shows that when summed up it simply consists of asswming for any specific solution just so much polymerization and electrolytic dissociation of the dissolved molecules, together with combination of the latter with the solvent molecules, as may be necessay to make the results of the experimental measurements conform to the * Phil. Mag. [6] ix. (1905). + Indeed, I do not consider the relations between molecular weight and conductivity in the case of non-aqueous solutions till seven pages later in my paper. See Phil. Mag. [6] ix. p. 222 (1905). t The earlier work by Jones and Chambers, and Chambers and Frazer, Amer. Chem. Journ. xxiii. p. 89 and p. 512 (1900), had previously been considered by me, Jown. Phys. Chem. v. p. 359 (1901). § The measurements of Smits, which were mentioned in the same connexion, also confirm my experimental work, which that author has frankly admitted, Zect. phys. Chem. xxxix. p. 885 (1902). Smits mentions the work of Jones, Chambers, and Frazer in the same connexion, J. c. bottom of p. 429. | Phil. Mag. [6] ix. p. 214 (1905). 664 Mr. A. A. Robb on the Conduction of Electricity requirements of the simple gas laws and the theory of electro- lytic dissociation. Such cases as the acetone solutions of CdI,, NH,Cn8S, and Nal, for instance, which are good electrolytes though the ebullioscopic determinations yield molecular weights of 448°6 to 510°7, 88-1 to 101°6, and 133°2 to 143:0 for the respective salts, whereas the corresponding theoretical values are 336, 76°2, and 149-9 *, are consequently readily “harmonized” with the theory of electrolytic dis- sociation by Jones, by assuming the required amount of polymerization and dissociation necessary for his purpose. It is quite unnecessary to dwell upon this further, for in a recent article, which should prove interesting reading to all who belong to what he calls the “dilute school,” J. J. Van Laar t has thoroughly exposed the fallacy of such a course of reasoning as that adopted by Jones and Getman. Finally, as to whether the facts upon which I have based my arguments against the theory of electrolytic dissociation are real or merely “ supposed,”” as Jones would have it, I shall gladly leave to the judgment of the reader. Laboratory of Physical Chemistry, University of Wisconsin, Madison, /) July 1905. y LXXIV. On the Conduction of Electricity through Gases between Parallel Plates—Part If. By Atrrep A. Ross f. HE writer has already shown§ that the differential equation TX” _¢ pla a ( od a da? ae me( a ie ‘eg e’X?(R, + Ry)? ° Ry, dx? . R, axe } ii (4+) (a ae) (1) * The data are those of Jones, Amer. Chem. Journ. xxvu. p. 16 (1902). They are somewhat different from those of Dutoit and Friderich who simply state that the molecular weights are normal, without giving specific figures, Bull. Soc. Chim. Paris, |3]| xix. p. 884 (1898). Jones did not investigate LiCl in acetone on account of its slight solubility, The HegCl, solution had but slight conductivity, and its molecular weight determination yielded the values 267-9 and 271°2 (but two determinations were made) as compared with 271°2, the theoretical. This latter case then presents no difficulties for the dissociation theory, as Jones well states. + Chemisch Weekbiad, ii. pp. 1-16 See also the abstract in Chem, Centralblatt, xxvi. p. 491 (1905). t Communicated by the Author. § Phil. Mag. August 1900. through Gases between Parallel Plates. 665 may be reduced to a form which is independent of both 2and q by putting q nate Sh ind ean oe ied 2) The equation then becomes a if 1 ) { a area. +R) Ut ay R, dy? ( a «(1+ TES — Lae eres ae) The writer also showed that for any gas for which R, and R, are unequal there exist two pressures at which this equation takes a soluble form. The solution is ee Agr aa G dw = = | i=. | +h foosh fe: cosh!—< @ (4) ae R,—R, € v= a/ a sea { Sudo tke i, in which R, ne e€E= Ri+R, " Ry+R, according as the pressure is such as to make a=AreR, or = 47eR,. The integrals which here occur can only be evaluated in , ee finite form when Tug 18 an integer, and when accordingly —e the velocity of one ion is an exact multiple of that of the other. This is not, however, usually the case, and for air the ratio R,: R, is very nearly 5:4. It seemed desirable to render my former paper more useful by calculating the values of the integrals in this case. Different physicists have obtained slightly different values for the ratio, and we can hardly as yet say whether R, : R, in the case of air is greater or less than 5 : 4. The tables which follow are calculated on the supposition that Ry 2 ee ee and that the pressure is such that a = 4qeR. Pil. Mag. ..6. Vol, 10. No. 60. Dee. 1905. 2 2, 666 Mr. A. A. Robb on the Conduction of Electricity This pressure 1s roughly 1} atmospheres, It will be well to give a short account of the method of calculating these tables. | The first function to be calenlated is oer us dw == COCN eo. | “aie l—e ae cosh'~*w This may be expressed as a series in two forms, of which the one possesses the advantage that it converges more rapidly, while the other is better adapted for the second integration. We accordingly give both series. Writing coshw=@ we have do= yeas Thus a pind dw Ms Hees dg : cosh [1 pa es | l—e © aa oS Oi-< ,/@—1 ‘ Hxpanding the expression under the integral sign in descending powers of @ and integrating term by term, we get 1 —e€é = mh oe: rare ieee (1—e) -j.-? eee ! oa 9 (3—De)? Since ees 2"\2) (=e) 7 ro The expression inside the brackets {} represents the integral and clearly vanishes when we put 0=«0. We may thus write 1 w ] re) — cosh !~ w ns ae § cosh a) | fe oe es ae @ mbt ys i vase Wiha Tyee Li See Os if eral t4 5) (3 —2e) cosh2a@ =F 212 (5—4e) cosh*w == ee (5) This series converges for all real values of w including m=Q, and is the one most suitable for calculating the function. We shall next obtain the other series which is adapted for the second integration. Tor this purpose we make use of the formula C dw 1 sinha m+1 dw cosh” w m cosh”! ay ms) cosh”t2 ¢ through Gases between Parallel Plates. 667 By successive applications of this formula we get iN dw we ek sinh w ~cosh™@ = mcosh”t!@ (m+1) sinh (m+1)(m+8) sinh —_— — eeeeeeeeesesesesesesé—==4¥gK m(m+2)cosh™*? @ m(m+2) (m+4) cosh™t5 gw LE arp RG ica i m(m-+2)(m+A4)...(m+2r—2) J). cosh™+?* w ° The former method of treatment shows, however, that 2 do mecosh™ +?" a 1 (m + 27) ly . ~ (m+2r) cosh™*?" » {1 +9 (m+2r+2) cosh? o i a Thus the remainder is m(m+2)(m+4)...... (m+2r) cosh™+?" w 1 (m+ 2r) a x ie Ek er ee ees {14 2 (m+2r+2) cosh? w rae : The coefficient m(m+2) (m+A4)...... (m+2r) is clearly a proper fraction which decreases in absolute value as 7 Increases. The expression 1 it (m+ 27) cosh” +?" @ = 2 (m+ 2r+2) cosh? a clearly has the limit zero so long as cosh a> 1. Thus the remainder vanishes for r=x. We can therefore write aed sf 1 sinha (m+1)_ sinha _ cosh™@ im cosh™*!@ -mim+2) cosh™10, ~~ and this is valid so long as coshw>1. If, however, cosh o=1 then sinh »=0 and each term of the 0 : 5 i leh a de series vanishes. Since we know that the inlegral | ———~—~ ~» cosh” w is not. zero, it follows that the function represented by the series has a discontinuity for @=0. It will be found, 9-7, 9 ai ~ 668 Mr. A. A. Robb on the Conduction of Electricity however, that this does not interfere with the attainment of our object. : 1 Putting for m the value ‘ we get —€ EAS — Cte y a sinhw | (2—e) sinh l—e : 7 — lecoshw (3—2e) cosh? w Cos (ze (tase), sinha ! : (3—2e) (5—4e) cosh? +o which is valid except for o=0. That this series is uniformly convergent for any range of values of w greater than zero is shown if we write it in the form e{a/1 Tee 2, i ~ cosh?w | (3—2e) cosh? w cosh? Q-<) (4-32), /) 1 | (3 — 2e) (5—4e) cosh? w cosh* w If now we select any real quantity 6, greater than but as nearly as we please equal to unity, we observe that the successive terms of the above series are less than the corre- sponding terms of the series it 1 efit get gat f for ail values of cosh o>). Since the last is a convergent series of real positive terms, it follows that our series is uniformly convergent through any interval not including w=0. We are therefore at liberty to integrate it term by term. Now we saw that k,—R, € i == ae og | Sydoths }. Thus putting for y its value we have anh hive 44 € = {— a eel. Dey ee ite (<1. If, however, we apply the usual test we find that the series converges even when cosha=1. Since the part of the series in brackets is a power series in ae it follows by Abel’s continuity theorem (see Chrystal’s Algebra, vol. 1. p. 183) that the value of the series obtained by putting coshw=1 is continuous with those for which cosh@>1. Since these latter represent the integral required and the integral itself is continuous up to cosha=1, it follows that the above series (8) is valid for ali real values of @. We have yet a third integral to evaluate, namely it aus = [cosh 1-€ wy dq, Putting as before cosh w=90, this becomes 1 Gg edg /0—1 Expanding this in descending powers of @ and integrating term by term, we get: ai-egé _l-e oe 1 Ld i \ [ya a Leper pees : or 1 so note — 1 if {cost 8 dia cosh! o {i+ 7 PAT) coal” @ 1 3 1 ue 222 (4e—3) cosh* alee } (9) The usual tests show that this series is convergent even when cosh w=1, _- 3 670 Mr, A. A. Robb on the Conduction of Electricity It thus appears that the three series given by equations (5), (8), and (9) are valid expansions for all real values of a, and therefore may be used to calculate tables of the required functions. It will be shown later that # =0 corresponds to the position of one of the plates. Thus the values of the functions for w=( are of special importance. Although the series which We give are convergent for this value of , yet the conver- gence is very slow, and it appears desirable to obtain other expressions for them in this case. Let us first take © 2 na 7 dia i eosh!s* at Waa ea sa ——— € —— cosh!—¢ w Ww For w=0 this becomes € dw ie ts ae j : cosh!—< w Putting cosha= p72 we have € 1 1 ric5| p= (l=) "dp, and therefore € \ dw € vase)! 1 l oo a i cosh*-* w ; 2(1—e) ) This may be at once evaluated by means of the table of I functions. We shall next find the value of the series given by equation (8), when o=0. The series in this case becomes (2—e) | 1 (Q—e)(4—3e) | 1 (2Q—€)(4—3e)(6—5e) - (3—2e) © 2 (3—26)(5—4e) © 8(8—2e) (5—4e) (7 — 6e) hs + faa Consider now the general hypergeometric series of argu- ment unity F(a, 6,¢,1). This is convergent if c—a—b is positive. It has then (see Whittaker’s ‘Modern Analysis,’ p. 241) the value [T'(e)P'(e-—a—b) M(e—b)(T(e~a) through Gases between Parallel Plates. 671 Thus F(a, b.c,1)—1__ T'(e) (e—a—b) —T(e—b)T (e—a) a ry al (e—6b)T(c—a) epee Dia) Fe) *" T'(c) T(ec-—a—b) —T(ce—/) ~ T(e—a) — a T'(c—a)P(e—8) —a Taking the limit when a becomes zero we have Li Hie a) el Ee 5) oo a eV (eh eb) F But Fp Elbe 1 _) , 10641) | 1041042) 'a=0 ed as Es Cc Bele 1) * 8 e(e+1)(e+2) Las, and if we put 1 b=5q 5th 2(1—e) L ae ae ae this becomes Pe) ee) ease ) id (2—e) (4—3e)(6 —5e) i 3—2e ' 2(8—2e)(5—4e) © 3(8—Ze)(5—4e)(7—6e) © Thus for o»=0 the series as by (8) takes the value 2 =5 *1) tS) ” cn Teg tt) TE) ! (For tables of = functions see Gauss, Werke, Bd. 111. p.161.) (12) As regards the limiting value of the third integral 1 1 ae = | cosh!~*w dw, we have € 1 = (=e 5 eS del 3 = feosni= oadw = ey cosh!-£ w@sinh@ + {cosh poe Gyo ai ha) € = | ig 1 For infinite values of » the value of a cosh !—¢w dw given 1 — cosh =€ ep if the value of e be less eS by equation (9) is as i, Thus, if iS. series is to repr esent the same integral s (13), we must insert « as the lower limit of the integral on the Habe tend side of the latter equation. Further, if e “ prio" (1—p)ildp ; cosh !-€ w __FGa-o PG, (3) mee, r(sq-5 + +5) A similar result may be readily obtained for the value of e greater than 4. We have thus got all the formulz necessary for calculating the tables. lt 1s desirable, however, that the integrals which go to make up v or « should be tabulated with the lower limit zero, as in this way we get w at once measured from one of the plates, and have therefore no trouble with the second constant of integration fk, Thus, putting for e the value z corresponding to - ie we have Bera as the solution of (1) J 4? Aqri VJ ye es ee in which 4 OA pan P= 5 cosh of Sates Ms a ee iu 8 1.3.5 ‘ = 9 Ut 2 Ty cosh®e t 22 29 cosh*a * BB 39 a ee j= cosh® w. “(9 A “he nde H =| & con of cosh? w ) de 1) AC reset =34 (1-9) TG + log cosh w (16) 14 ik es 7) ee -5 19 cosh?w ' 2 19x 29 coshtw 9(° a S= a cosh ae A. 15) | a {13 9 1.3 9 -~\ =; 6) 74a 2 cosh? w - BQ 11 cosh*w ++ f through Gases between Parallel Plates. 673 Now at the positive plate Ry axe dy An Sa de aa doe Woy while at the negative ; Ry dX? dy 4a «Sar da a dv Ry But equations (4) give dy dy _ dw ie eta Nee) gs 4/2 2) tanh de~ de ~~ (= 6)(Re= By)y * e(1—e)(Ry— By) dw 1 . ° For «= Te this gives dy Ar oe a Pye + Jali + i) taboo. Thus at the positive plate w = 0. At the negative plate i, 1 —tn(e +3), + V"(x + yp) tanh o = 0, hea ue — y tanh o = = |, (hus if By, Oi, Ry, ‘ w, are the values of the respective functions at the cathode, (P, + k,Q,) tanh QQ, = Ihe : . e - (17) Suppose / is the distance between the plates, we have a jy Bath CORED biel (Ce aa Mende em l./5}) From (17) and (18) we may eliminate 4, and obtain Say 9 eg = =P) + Rapek.. . Gd) This is a transcendental equation giving the value of w or coshw at the cathode. 67£ Mr, A. A. Robb on the Conduction of Electricity In order to facilitate its solution, the value of the fonction ‘Si geil E Ace =e ee is tabulated along with the corresponding values of P, Q, R, and 8. Having in this way determined the value of coshw at the negative plate we may find 4, thus T,—R | — 20 1 S; ’ ( ) and so complete the solution. ToC ge ee ee cosh w. 2. Q. R. S. | oe 1) B54 1-000 0-000 0000 | 0-000 pf La | (@'8) oo — ~I iyi lace fp) (os) ler) He on =I (op) bo [op) ile} bo aerate le al a ee I Mer ELSE DS SN IDS 2 Sd SON rl ee tae lea og be er eR SIDS CDW HK OOOAIDWUUPWWrCUOUDMDNIDUFWNWH OO KAS Vit & be Ho Or —~I = th i) wy bo _t On — > ft ay foo ow ow) for) OS through Gases between Parallel Plates. i; cosh w. | ie | (MoM ele me 4:9 n oO ‘ SDRAAPRAMNMNAMA A GAM S ~~ ~~ OWUIAGHAMMWHOOWOUARAMIAWNMDHOOMOWAUMAWNWHOCHODAARANAWMHMOH SOMDAMUAWNWH DDO OD OF & OO OG 0 00 00 00 00 09 OH AIT ATAIATAIATAI MAID D | feck 8 wo (o'4) | (=) eeeeae seenee ween ewe sees ee eeeaee eeenee @eeses ecceee scesee te eetee easese aeceae e2csee secece eeeces Q. 16 836 17-472 18-119 18777 19445 20 123 20°812 21-511 22220 22 939 23 668 24-408 25:158 25°918 26687 27°467 28°207 29-057 29:866 30°686 31515 32304 33-203 34-062 34930 35°808 36°696 37993 38°500 39°417 40343 41:279 42-224 43°179 44-143 45°117 46°100 47093 48-095 49°106 50-127 51157 52°196 53°244 54:302 55-369 56°446 57531 58626 59°730 60°842 61-965 63096 675 DIO WNWNKNYNw ty > ec GOW CO MW CO ej a] ~1 -I +] Ww OO ST OV Cs co NT OI Co He ST COR LS Co He OU Or Ce LD S. 22-584 23 397 24°223 25061 20912 26°776 27-652 28°541 29-442 30°356 31-281 32°220 33170 - 34133 35°109 36-096 37096 38°108 39131 407168 41-216 42-276 43°348 44-435 45°529 46637 47-757 48-889 50033 517189 52356 53°536 54°727 55°930 57-144 58°370 59-608 60°858 627119 63°391 64:°676 65°971 67°279 68°597 69°928 71°269 72622 73°987 75363 76°750 TS 149 79°558 80980 ai=p) pyle (Sy ey (ayy fey IO © 8) ST Oi ce &e1OW CIN 676 Prof. L. T. More on Dielectric We append a sample curve drawn with the help of these tables. 0 4 ea ied -FLATE k,=:0/ R, R, +R, plate, while the value at the positive is determined by a transcendental equation. The .case of ¢€ = gives tanhw=0 at the negative LXXYV. On Dielectric Strain along the Lines of Force. By Louis T. Morr, Ph.D., Professor of Physics in the University of Cincinnati *. Ae ee I have reviewed in former papers the work accomplished in electrostriction, yet, as the stress- problem is undoubtedly the fundamental one in the theory of electricity, I may be permitted to summarize briefly what has been done in this branch of the stress-problem before describing any new experiments. By electrostriction is meant the strain in dielectrics and their consequent mechanical deformation, produced by the action of electricity in them. ‘The effect is supposed to occur in solid, liquid, and gaseous non-conductors when they are electrified. The first observations date back to the beginning of the last century. In its early stages, electrostriction was looked upon as an isolated property of electricity, and although laws were formulated, it was not until Faraday and Maxwell adduced the effect as one of the fundamental phenomena on which to build their new theory of etherial stresses, that any * Communicated by the Author. Read in part before the International Electrical Congress, St. Louis, 1904; and in part before the American Physical Society, March 1905. Strain along the Lines of Force. 677 considerable theoretical importance was attached to this property of electricity. That they did so regard it as one of the corner-stones of their theory is clearly shown by their own statements. Thus Faraday says (Par. 1297) :—“The direct inductive force, which may be conceived to be exerted in lines between the two limiting and charged conducting surfaces, is accompanied by a lateral or transverse force equivalent to a dilatation or a repulsion of these representa- tive lines;”? and (Par. 1224) :—“‘ The attractive force which exists amongst the particles of the dielectric in the direction of the induction is accompanied by a repulsion ora diverging force in the transverse direction.” Maxwell (‘ Electricity and Magnetism,’ vol. i. p. 165) writes even more expli- citly :—‘‘ The hypothesis that a state of stress of this kind exists in a fluid dielectric, such as air or turpentine, may at first sight appear at variance with the established principle that at any point in a fluid the pressures are equal. But in the deduction of this principle from a consideration of the mobility and the equilibrium of the parts of the fluid, it is taken for granted that no action such as that which we here suppose to take place along the lines of force exists in the fluid. The state of stress which we have been studying is perfectly consistent with mobility and equilibrium of the fluid, for we have seen that, if any portion of the fluid is devoid of electric charge, it experiences no resultant force from the stresses on its surface, however intense these may be. It is only when a portion of the fluid becomes charged that its equilibrium is disturbed by the stresses on its surface, and we know that in this case it actually tends te move.”’ As is well known, he measures this stress by the famous 2 formula p a where p is the numerical value of the tension, K the specific inductive capacity of the dielectric, and V/d the fall of potential per unit length in the dielectric. In support of this theory and equation a number of in- vestigators have obtained an expansion both in the volume of an electrified glass thermometer and an elongation of a glass tube electrified radially, and have apparently found these deformations agree with the theoretical formula. When the mechanical is substituted for the electrical pressure, by the of dz K 7. ee The left- hand member is the expansion per unit length of the tube under unit electrical conditions at right angles to the lines of force. By taking the average of Cantone’s results we get formula — (Ss = pn we obtain 678 Prof. L. T. More on Dielectric 2 the value . : ae 6:5 x 10-; when the best value for Young’s modulus, w, and the dielectric constant for the glass are substituted in the right-hand member, there results a value of the same order and about one-half as large. Quincke’s average results are in somewhat closer agreement. This discrepancy they assumed to be due to the inadequacy of Maxwell’s formula, which should contain another term, signifying the relation between mechanical and electrical pressures. Passing over the eruder work of early writers, the best direct results were obtained by Quincke * and Cantone +. In previous papers { I attempted to show, by their own results, that both neglected to consider extraneous effects which were of the same magnitude as their recorded values and which, if introduced, would have accounted for the entire deformations observed. These errors are due chiefly to heating, lateral displacements, distortions caused by using thin tubes more or less irregular in diameter and thickness, or by the lack of sphericity in any blown bulb of glass. Quite recently Wiillner and Wien § attacked the problem in an indirect manner, attempting to show that the elasticity of glass is greater when obtained from electrical stress than when found in the usual manner by mechanical or acoustical methods. It is interesting to note the contradictions of these different observers. Wiillnerand Wien confirm Quincke’s conclusions, though not his values, and condemn Cantone’s and mine ; while Sacerdote and Cantone consider Quincke’s to have little value. In the first place, the measurement of the rise or fall of an electrified capillary water column, such as Willner and Wien use, is in my opinion a faulty method, and their agreement with Quincke, who often employed the same method, is natural. J may add that this method is condemned by other investigators. Wiillner and Wien themselves have to introduce elaborate corrections to obviate the irregularities in the motion of the water column. Secondly, their results show great variations in the value of the elasticity, measured mechanically and electrically, for different kinds of glass. For some glass the latter is not more than one-half of one per cent., but for others it is as much as one hundred per cent. * Quincke, Wied. Ann. Bd. x. pp. 161, 374, 513; Bd. xix. pp. 545, 705 ; Bd. xxviii. p. 529; Bd. xxxii. p. 403. + Cantone, Rend. d. R. Accad. Linc. t. iv. pp. 841, 471; Rend. d. R. Ist. Lomb. [2] t. xxxiii.; Nuovo Cim. (41 t. xii. p. 150. _ 1 More, Phil. Mag. [5] vol. i. p. 198, [6] vol. ii. p. 527, | 6] vol. vi. p.1; Elect. World and Engineer, vol. xlii. p. 127. § Wiillner and Wien, Drude’s Amn. [4] Bd. 1x. p. 1217. Strain along the Lines of Force. 679 greater. A variation of such magnitude due solely to differences in the composition of the glass is out of all propor- tion, and certainly if electrifying glass may more than double its ordinary elasticity, such an elaborate method of experimen- tation is unnecessary. Lastly, a variation in elasticity is directly contrary to theory. Lippmann, and his formule are shown by Sacerdote to be essentially in agreement with the other writers on the theory of this subject, states :—‘‘ That the dilatation produced electrically must be due toa direct action of electricity and cannot be caused by a variation of the coefficient of elasticity, or, the coefficient of elasticity 1s indepen- dent of the electrification ; on the other hand, the dielectric constant varies with the electrification.” Some years ago I published a paper in the Philosophical Magazine containing experiments which did not confirm the conclusions just cited, and in fact made me doubt the existence of electrostriction. It was criticised by Sacerdote and Cantone on the ground that my method was faulty ; they claimed I had employed a mechanical instead of an optical device for magnifying the elongations, and that it was not sufficiently delicate to observe this minute effect. The criticism was easy to meet, andina letter to the Philosophical Magazine I demonstrated that my apparatus was an optical system, as sensitive or even a little more sensitive than interference methods, and that their criticism of its lack of sensibility and accuracy was founded on a misinterpretation. Later work has confirmed my opinions. Maxwell’s formula has been discussed by Korteweg %*, Lorberg +, Kirchhoff {, Lippmann §, Sacerdote || and others. ~ Their methods may be divided into two categories: first, the determination of the attractions and repulsions of electrified conducting particles immersed in a non-conducting medium, or in other words the results of a polarization of the dielectric; and secondly the application of the thermodynamic equation and the interdependence of the laws of conservation of energy of electricity and matter. Sacerdote has made a careful synopsis of all the articles published on this subject, with a critical discussion of methods and results. He finds, barring small differences, that both general methods lead to the same conclusion, which may be expressed by the formula KV? p= (K, + a) Sard? * Korteweg, Wied. dnn. Bd. ix. p. 48. + Lorberg, Wied. Ann. Bd. xxi. p. 300. t Kirchhoff, Wied. Ann. Bd. xxiv. p. 52. § Lippmann, Annal. de Chim. et de Phys. [5] t. xxiv. p 159. || Sacerdote, Thése. 680 Prof. L. T. More on Dielectric where a is the inverse of Young’s modulus and K, the varia- tion of the dielectric constant with mechanical pressure, represented by 6K/67/. Itis then Maxwell’s equation with the addition of a second constant. This variation of the dielectric constant must be an exceedingly small quantity, for of the few who have investigated it, some have obtained a positive value, some a negative, and others a null effect. So that the pressure p may be increased, diminished, or unaffected by this quantity. | If one is willing to grant the fundamental assumption made for these theories, there is little doubt that the conclusions are correct. It is easy to see that the assumption made for each of them is essentially the same; namely, that a stress in the eether is communicated to matter immersed in it, or, in other words, the granting of the vital point of the discussion. Those who develope the polarization theory suppose maierial particles to be immersed in a fluid ether, as may be illus- trated by fragments of silk thread in pure turpentine. If charged electrodes are placed in the turpentine, the silk threads are observed to form chains extending approximately along the Faraday lines of force. We may readily imagine the ends of each fibre to be polarized by induction which by their mutual attractions and repulsions form lines of stress tending to shorten along the lines of force and to repel each other perpendicularly to them. In the first place, it is rather doubtful to consider this phenomenon as due to a static system of forces which the Faraday lines demand. But the real error lies deeper,—to assume that particles of matter in the ether act like particles of silk in turpentine is to grant the whole question. We know that a stress in one kind of matter is transmitted undiminished to any other kind of matter, as in this case from turpentine to silk. But we not only have no confirmation, but in fact many reasons for believing that static stresses in the zether are not communicated to matter. Lorentz indeed goes so far as to say that it is absurd to imagine a strain in the ether itself and so impossible to conceive of a strain imparted to matter. One of the chief reasons for the abandonment of the elastic solid theory of — light in favour of the electro-magnetic theory is to obviate the absurdities introduced when the ether was supposed to be an elastic solid. As to the theories viewed from a thermodynamic standpoint, the assumption is just as glaring as it is in fact the same. Sacerdote and the other writers on electrostriction from this standpoint claim that the connecting link between the ether and matter is expressed by the coefficient K,= 6K/6/, that is by the variation of the inductive capacity Strain along the Lines of Force. 681 with mechanical pressure. In the first place, no such varia- tion has been found experimentally, as the results so far are discordant and subject to serious criticism. The question still remains, whether if it were found that K changes when a body is distorted mechanically, electrostriction necessarily exists. We know already that as a general rule this constant is least for gases, greater for liquids and greatest for solids, or it varies approximately as the density of the matter. We may then readily imagine that an increase in density caused by pressure will change the dielectric constant slightly because of a variation in ‘the elasticity ; but the theorists main- tain that electrostriction is due to a direct action of electricity and not to a variation of the coefficient of elasticity, as shown by my former quotation from Lippmann. Wiillner and Wien, who alone regard the effect as being due to such a variation in elasticity, have certainly mistaken the nature of the problem. Their results, as stated before, show large variations, equal at times to the value of the whole coefficient of elasticity, in the elasticity of electrified’and unelectrified glass. And though I believe that this difference must have been exaggerated by extraneous effects, still such a variation may exist in a less degree, but it has no bearing on the subject of electrostriction. The question may be put in this form. Does a mechanical pressure (a stretching force which produces a decrease in density should theoretically increase the dielectric power) cause a variation in the mutual relations of the ether and matter? This is the same question discussed with respect to the polarization theory | There seems to be a considerable degree of confusion pre- valent in regard to the significance of electrostriction. It does not involve the mechanical pressure produced by the attraction of two charged bodies, but is supposed to be a property of the electric flux in a non-conductor. Yor example, two charged bodies attract each other, and if they touch a dielectric, class for example, placed between them, the ID olass must be detormed mechanically whatever theory 1S adopted. But those who believe in electrostriction maintain that if the charged plates be separated from the glass, and if the intervening spaces be filled with a fluid dielectric of the same dielectric constant as the glass and filled in such a manner that the mechanical force of attraction of the electrified armatures cannot be communicated by the fluid to the glass, still the latter will contract in the direction of the lines of force and expand perpendicularly to them. This mechanical deformation, called electrostriction, is due then entirely to the electrical stresses in an eether and communicated by it to Bins Magn so ol. 10: No. 60)Dec. 1905. aA 682 Prof. L. T. More on Dielectric the matter immersed in it. As an illustration, we can make use of the system of glass and liquid dielectrics just described. The lines of electric flux in the ether stretch from one charged armature to the other and may experience, for all we know, the tensions and pressures generally ascribed to them. Since both the glass and the liquid have the same dielectric constant, there is no discontinuity of the lines at the surface of the glass, yet it is supposed to contract in their direction. The only mechanical arrangement I can think of, is to assume that each line does not extend from armature to armature but is like a chain linking particle to particle of the glass. Let us, to be more precise, consider the action of a tension in one of these chain lines on three particles,—one in the surface of the liquid adjoining the glass, a second in the surface of the glass, and the third just within the surface of the glass. Since the dielectric constant is the same in the two substances, the pull on the middle particle is the same in’ the two directions, and there is no tendency to displacement of the surface of the glass. This is also true for any three particles in the glass, and a contraction does not occur. Of course, where there is a discontinuity of the lines, either in passing from one dielectric to another of a different inductive capavity or from a dielectric to a contiguous conductor, an unbalanced force exists, but that is merely the measure of the attraction of the two charged bodies. If the lines of flux are supposed to pass through the glass without being attached to its particles, it is even more difficult to see how the stress in the ether effects the glass. If we assume Maxwell’s formula for electric stress in the ether, and I know no other adequate, we must not lose sight of a most important fact, that theories involving the ether must always remain purely hypothetical, as we have no possible method of experimentation upon it. And only when matter is immersed in the eether does experimentation become possible. Now all our cbservation goes to show, that for static and even for kinetic phenomena, at least where the velocity is less than that of light, the ether is unmodified by the presence of matter and does not affect the properties of it: witness the absence of friction between the earth and eether in its motion about the sun; the Kerr effect of the polarization of transparent matter when electrified ; Brace’s experiments on the action of a magnetic field on transparent media showing that the Faraday stresses affect the velocity of light by an amount less than 2:0x10—-“ for a C.@s. unit of intensity per centimetre ; and many others all supporting the doctrine of the independence of ether and Strain along the Lines of Force. 683 matter. My claim is, not that Faraday stresses may not exist in the ether, but that these stresses are not transferred in any appreciable degree to matter as unbalanced mechanical forces. The fact is, 2 dynamic system in a hypothetical medium may be either affirmed or denied, but it cannot be proved as the question is a metaphysical one. The absence of the electrostrictive effect does not preclude the existence of etherial stresses, but it does prevent it from serving as a fundamental experimental verification of the stress-problem. The recent discussion of Maxwell’s stress theory by Bjerknes* is opportune to this subject, and his conclusion should be quoted :—‘‘ In the meanwhile it will therefore be safest to consider the Maxwell stresses as only fictitious stresses that might have produced the required forces, and not as the real stresses which do produce them. Other authors have also termed them fictitious stresses, especially Lorentz, who also considers the stress formule only as useful analytical formule, but not as representing any physical reality. The reason, however, why he has come to this opinion is quite different from the reason brought forward here. His view is that the stress-problem in itself has no physical meaning. For, according to the doctrine of the immobility of the ether, it is an absurdity to speak of forces acting upon or stresses existing in the ether.” Dielectric Strain along the Lines of Force. Maxwell’s theory, which supposes an expansion perpendi- eularly to the lines of force, also demands an equal contraction in their direction. A test of this latter effect has never, so far as I know, been attempted : it is obviously a much more difficult piece of work, but it also should prove to be of greater importance. In the former method, the effect sought and the extraneous effects are all in the same direction and are difficult to separate. But the effect along the lines of force should be a contraction, and so opposite in effect to the heating and other sources of error. Furthermore, it does not introduce a correction for the little-known value for Poisson’s ratio. Itis besides possible to reduce the magnitude of the disturbances themselves. It is evident that a sheet of dielectric placed between two metal electrodes will be compressed by the attraction of these electrodes when they are charged. We must neutralize this attractive force by making a system of balanced electric forces. This can be best done by building up a pile of alter- nate metallic and dielectric plates, each held horizontal and * V. Bjerknes, Phil. Mag. vol. ix. p. 491 (1905). one 684 Peok Li. T Mlotecon Mictecte accurately equi-distant. Alternate metal plates are then connected by wires into two sets: one set to be charged positively and the other negatively. The number of metal plates must be odd, so that the top and bottom plates may be charged with electricity of the like sign and connected together rigidly by metal rods. Hach plate in this system is thus attracted equally up and down, or is electrically in equilibrium. Whereas, if the dielectric itself expands cr contracts along the lines of force, the whole pile will tend to shorten or lengthen 6d _ nKV* where d is the thick- according to the formula Lo ee ness of each dielectric plate, K the dielectric constant, V the potential, n the number of dielectric plates in the pile, and wu is Young’s modulus. To accomplish this object, it was necessary to cast a large number of plates, which should be exactly parallel. equi- distant and close together, in a dielectric, to form a solid block. A great deal of difficulty was found in getting a dielectric which was a good insulator for high potentials, and at the same time rigid and not viscous, and which wouldinot contract when solidifying. The last was very important and debarred paraffin, as this and similar substances contract sufficiently to tissure in the thin places between the electrodes. The substance finally adopted was a mixture of four parts by weight of the best shellac, one of resin and two of Venice turpentine. This compound gives a clean and smooth surface when broken, and is highly elastic (Young’s modulus about 10°). It melts at 110° and when solidified shows little contraction,—a twoc-litre flask, half full of the hot liquid, presents an almost level surface when it solidifies. Several types of moulds for the casting were made and — tried before the one was devised which answered. ‘Thirty- one brass plates, 5 cm. in diam. and 2°5 mm. thick, were polished and made true. Three lugs, 12 mm. long and 6 mm. wide, were soldered radially to each plate. A seamless brass tube, 21°5 cm. long and 7-4 cm. inner diameter, was then ruled with thirty-one circular lines, each 5°5 mm. apart, and three holes were bored and tapped, equally distant apart on each line. The plates were then placed each in the plane of one of these circles, with a lug opposite each hole and held — in position by three small pointed screws for each plate. Two of the plates are shown mounted in a section of the tube in fig. 1. In the next to the top plate was screwed a brass tooth of the same dimensions as the ebonite tooth shown in fig. 2 (p. 686), and a hole was bored in the top plate so that the tooth passed through it. The bottom plate was tapped with three screw-hoies and a large plate, only a little less in Strain along the Lines of Force. 685 diameter than the mould, was fastened to it by screws. The ends of the moulds were closed by brass screw-caps. After dain the casting was made, the caps and holding screws were removed, and the perfect casting slipped out of the mould by heating it quickly. The large brass plate at the bottom was removed by heating it gently, and the bottom electrode, thus exposed, was fastened to the base plate of the frame of the apparatus, fig. 2. Then the brass tooth was replaced by the one of ebonite. During this operation the top brass plate was slipped off, this being done so that the upper plate of the frame might replace it as an electrode. When the casting was out of the mould, the ends of the three lugs on each plate were exposed, forming two sets of three vertical lines each. Two of these lines of lugs of each set were covered with insulating wax to prevent leakage, and the lugs on the third line of each set were connected by wires so that one set might be charged and the other grounded, fig. 2. After the electrical connexion was made and tested, these terminals were also covered with the insulating wax. We thus have sixteen plate-electrodes (counting the upper plate of the frame as one), connected to the ground, of which the top and bottom ones were fastened rigidly together, and 686 Prof. L. T. More on Dielectric fifteen plate-electrodes connected to the electrical machine. The attraction of these plates when charged is evidently Mig, D5) tes Za em = | | imi Pee te Hh Yesenil ist man, ie Sarees AN ip tlerminals | we Cc Dilelec ~ Jerminals. § i) i) 1) 0-9 ak JA = i” neutralized as they are equally attracted up and down. Between the electrodes are thirty dielectric plates, the whole forming a solid mass except for the discontinuity between the upper dielectric plate and the upper electrode. The greatest difficulty experienced while making these Strain along the Lines of Force. 687 condensers is to avoid air-holes and fissures, as the electrodes are only three millimetres apart. I did not accomplish this until I used the arrangement shown in fig. 3, where the Fig. 3. 72 AIP PUMP AND DRIERS 70 AIR PUMP whole process takes place in a single bath and with a ee vacuum. The constituents, eround and thoroughly mixed, were placed in the two litre- flask, A, in a bath of machine- oil kept at a temperature a little above 110°. From the bottom of the flask a glass and copper tube connects with the bottom of the mould, B, through a stop-cock at C. A second tube from the flask but above the surface of the mixture connected the flask to a water vacuum-pump through driers; and a copper tube from the other end of the mould made connexion with a “‘Geryk” vacuum-pump. The cock, C, was first closed, and the mixture liquefied under a vacuum made by the water-pump. This heating was continued until the mass formed a homogeneous, smooth fluid. The “ Geryk” pump was then started, and when a high vacuum in B was obtained the cock, C, was opened and the fluid gradually forced into the mould by regulating the pressure above the fluid in the flask,—the “ Geryk ” was worked vigorously until the mould was entirely filled. The pumps were then disconnected and the bath allowed to cool slowly. Returning now to the completed casting, a stout frame was made of two brass plates, connected by two brass rods (fig. 2). The bottom electrode was fastened, as stated before, to the base plate of this frame and it, in turn, to heavy beams bolted to masonry piers in a basement room. A hole was bored in the top plate of the frame and a brass cylinder screwed into it so that the base of the cylinder was flush with the lower surface of the plate and the upper end on a level with the top of the ebonite tooth. The legs of a tilting mirror were then placed on these upper ends of the cylinder 688 Prof. L. T. More on Dielectric and tooth. The position of the top plate of the frame was regulated by the set screws at the top of the rods. The dielectric exposed above the uppermost charged electrode was made slightly less thick than that between the other electrodes, and the space between the upper surface of the dielectric and the top plate of the frame was filled with a thin layer of oil of the same dielectric constant as the shellac mixture, and the distance between the two electrodes was adjusted so that this heterogeneous dielectric was electrically equivalent to that between any other two of the electrodes. The ebonite tooth was covered with insulating wax to prevent leakage or sparking from the positively charged electrode. The method of measuring the deflexions was the same as _ that employed in my former work, and the reader is referred to those papers for a detailed description. I give here only a brief account of it. The system of optical levers used to magnify the expansion of the condensers is shown in fig. 4. An incan- descent electric lamp with a ground glass globe was clamped Fig. 4. behind a metal screen pierced with a round hole, five milli- metres in diameter. Across this opening fine platinum wires were fastened horizontally, to serve for the deflected image. The light from the lamp, after reflexion st right angles by a totally reflecting prism, passed through an achromatic lens to a tilting mirror mounted ver- tically on a little tripod table. Upon reflexion, the light again passed through the lens and on, above the prism, to a micrometer microscope. The mirror, 1°5 cm. x 2-0 cm., furnished by Brashear, was silvered on its front face and plane to 1/4 A». The tilting table of brass, 1°6 cm. square, had three legs made of the finest needle points, one of which MIRROP rested on the brass cylinder and the other two on the ebonite tooth. By slightly raising or lowering the cylinder, the beam of light could be directed at a Strain along the Lines of Force. 689 desired angle. Small weights which hung below the level of the table from an arm increased the stability to such a degree that the image showed no oscillation from outside disturbances. The prism and lens were both of the best construction, and the microscope was a new instrument obtained especially tor these experiments. The platinum wires and the microscope were each placed in the principal focus of the lens ; the image was then very sharp and distinct. The least change in length which can be observed is calculated from the following dimensions :— eDimensions for Magnifying Power. ibeallenothrof lens wii eee eink. 100 cm. Distance between feet on tripod I ......... 6 mm. Distance between feet on tripod IIL ......... 3 mm. One division on micrometer of microscope. 0'002 mmm. A deflexion of one division of the micrometer, using tripod I, is equal to a change of length in the condenser 6 ‘ 5) = a) —6 ° me of 2x 1000 * 0:002 =6 x 10-* mm., and with tripod II 3x10-> mm. This minimum deflexion could be easily observed. In compiling readings, they were reduced to the basis of 6x 107° mm. for one division, whichever tripod was used *, The criticisms made on this type of apparatus have been a surprise to me, as I supposed such a standard form would impress all with its capabilities for delicacy and accuracy. In the first place, it is as much a form of optical device as the interferometer, and it has just about the same refinement as all optical devices, namely, its limit involves the wave-length of light just as interference methods do, and on the other hand it seems to me better adapted to the experiments under discussion. During preliminary experiments made to test the insulation and the dielectric strength of the condenser, I inserted a sheet of soft rubber between the lower surface of the top plate of the frame and the upper plate of the dielectric, using no oil. With this arrangement I noticed small deflexions of the mirror, but in every case the deflexion showed an elongation of the dielectric, and not the contraction the theory calls for. This elongation was also much smaller than the theories of electrostriction demand. I thought at first that it was due to * J wish here to express my thanks and indebtedness to Mr. P. B. Evens, the University mechanician, for the skill and patience he has exercised in the making of all this apparatus which made these experiments possible. 690 Prof. L. T. More on Dielectric some action in the dielectric, but later found that it was caused by charges induced on the rubber which attracted the tilting mirror staticall During the final experiments which continued through two months, the rubber sheeting was replaced by pure lard oil. The dielectric constant is almost exactly that of the shellac mixture. The height of the frame was carefully adjusted to make the electrical forces a balanced system, as I have previously shown to be necessary. When these precautions were taken the merror showed absolutely no deflexion when the plates were charged to any potential up to the breaking point for the dielectric. The conditions were varied as far as possible. Sometimes the charging was done slowly and sometimes quickly, ranging from five seconds to a minute or more. and at times Leyden jars were included in the circuit and sometimes not, so that the quantity of charge might be varied. From the nature of the construction of the condenser surface leakage was obviated, as little or no metallic surface was exposed, and in my former work I showed that surface currents were principally responsible for the heating. The currents through the dielectric are always small, and their effect was so much retarded in time by the large mass of dielectric through which the heat must diffuse, that the con- denser could be char ged and discharged before the slow creep of the image due to this occurred. Potentials which produced a spark of 4 millimetres between balls L centimetre in diameter were first used, and then increased gradually a millimetre at a time until a spark of 16 millimetres was reached. This latter corresponds to a potential of about 130 c.a.s. In not a single case did the nurror show ether an elongation or a contraction. When the spark passed, there was usually a slight tremor or jump of the mirror of not more than six or seven divisions of the micrometer, and this was sometimes in the direction of an elongation and sometimes a contraction. These were found to be due to the explosion of the spark transmitted through the air. To prove this, the condenser was dis- connected from the electric cireuit and sparks passed between the balls of the micrometer; in every case the same jump of the mirror was observed, although the condenser was not electrified. Shearer mentions this same disturbance while using an interferometer as a measuring device. That my apparatus was amply sensitive is seen from the following calculation. Strain along the Lines of Force. 691 The equation for elasticity introduced into Maxwell’s formula gives the result : od 2 nK NV” ai FS = eT = eget 6d = nK V?/87rdy, where % the number ot plates 2) 0f2 a K, the dielectric constant ..... ... ed V, max. potential difference ...... == [5S00C-c.S. d, distance between electrodes ...= 0°3 em fo Vounas modulus 2702" ae =a? substituting, od = 168 x 10-7‘ em. This value corresponds to 56 divisions of the micrometer, using tripod II, or 28 divisions using tripod I. These results certainly are difficult to ignore and can lead _but to one interpretation, and that is the lack of influence of the eether on matter in this respect. Dielectric Strain Perpendicular to the Lines of Force. Before the experiments already described in this paper were begun, a series of tests for the dielectric strain perpen- dicular to the lines of force was undertaken with this same shellac mixture for a dielectric. The method of experi- mentation and the apparatus, with the exception that the cylindrical condensers were of the shellac mixture instead of glass, were exactly the same as described in the Philosophical Magazine, vol. vi. p- 1, 1903. Cylinders of the shellac mixture were cast in a mould made of two coaxial brass cylinders. Condensers of paraffin were also cast in the same mould. Dimensions of Cylinders. No. , Composition. , Length. [outer hee al | ; diam. | ciawm. | | | Thickness. yee | | : thai | Shellac. | 64-6 cm. |4°7 cm. eee 0-4 cm. |10'°! 2:5 } | | | | | | | 9. ) Shellac. | 648 4-7 39 | 025 |10°| 25 | | 8. | Paraffin. | 64°8 ae 3 | O-4 10. 2:5 692 Prot. L. T. More on Dielectric These condensers were mounted in the same manner as the glass ones in my earlier experiments. The values for Young’s modulus were obtained in the usual manner by placing weights on the ends of the cylinders and measuring their contraction. They are fairly accurate for the shellac, but the value for the paraffin is not so reliable as the substance is decidedly viscous. The values for both are given rather too large than too small. ‘Tube No. 7 was a little irregular in thickness, as it distorted somewhat when taken from the mould. But the results are of importance as they show the effect of a slightly non- uniform field. Tube No. 9, after removal from the mould, was turned in a lathe and was quite uniform in bore and thickness. Tube 7.—Adherent Armatures. | | | Spark- . Mean elong. | Mean elong.| Time of | length Povenial (gers diy. | o¢x10*. | charging. 50mm.) 60 cas. 200 1:62 0:25 min. | 7-5 85 35°0 2:10 0:25 | 7:5 85 70-0 4-20 1-00 HO A | 00 Ya Eben ll Were 0-25 |10-0 100 100-0 6:00 1:00 10-0 100 | 180-0 10:80 5:00 120 110 alos 8-01 0:25 12-0 | 110 DAP | 14°55 1-00 The elongations, 6/, are the mean in each case of a series of readings. Since one division of the micrometer equals 6 x 10-® mm., the absolute value of the deflexion is obtained by multiplying the observation in divisions of the micrometer by that number. In the first place, for the same time of charging the elongation does not increase as the square of the potential. Secondly, the dependence of the deflexion on the length of time employed in charging is so pronounced as to make it imperative to account for it by the heat evolved by the electrical charge. When the condenser was discharged the return of the image, as Cantone also noticed, is quite irr eoular: : at times the image returned quickly to the original zero, very often about half way, but most often there was no recovery. This is contrary to theory, as there should be no residual effect of the charge. Strain along the Lines of Force. 693 Tube 9.—Adherent Armatures. | Spark- | Mean elong. | Mean elong. | ms: length. Potential. ae ise 37>< 104. Time. | 50mm. 60 ce.s. 30°0 2°10 0°25 min.| 50 — 60 62°5 3°75 1-00 | | | 50 =| «60 675 405 | 250 | 75 | 85 675k Wier Smith Pa aaneyy Greater potentials could not be used as the tube was ruptured with that spark-length. The tube could of course be repaired and used again. According to the theory, the elongation varies inversely as the square of the thickness, thus for the same potential the ratio of the deflexions of tubes 7 and 9 should have been three to eight. This is not verified, as the deflexions for equal potentials and time of charging are about equal. In fact, the effect I ascribe to heating is so preponderant as to overshadow all others. Tube 8.—Paraftin, Adherent Armatures. While experimenting with paraffin tubes the potentials were carried to the breaking point, which occurred at a spark-length of 10 mm., or 110 ¢.a.s. I observed no changes of length at all. I think that experiments with this substance have little significance as it 1s so viscous that not much could be relied upon. Non-Adherent Armatures. The tinfoil was removed from the tubes and the non- adherent brass-tube armatures were mounted in place. The space between the armatures and the dielectric was filled with the lard-oil. Thus the fall of potential between the armatures was uniform, and there was neither a free charge on the surface of the shellac tube nor any discontinuity in the lines of force. The elongation due to the mechanical pressure of the electrodes was eliminated, and according to the value assumed for Poisson’s ratio, a decrease of from one-fourth to one-third of the deflexion for adherent armatures of the same dimensions should result. Again, the distance between the armatures is now increased to 7 millimetres, instead of the former less amount. For number 7 it should reduce the deflexion in the ratio of sixteen to forty-nine; for number 9 of six and a quarter to forty-nine. The results actually obtained are given in the table. 694 Inelectric Strain along the Lines of Force. Tube 7.—Non-adherent Armatures. Spark- . Mean elong. | Mean elong. | : | length. Potenual |S micediy. | ENON = 2a | 10mm.| 100ces.; 3835 | 201 | 025 min, Apr. 13 10 100 SESE Villa), OG Oy wOee 14 12 0 58-0 348 | 0-25 13 12 110 80:5 483 | 0:25 14 16 || 130 610 6©| ) =6366 | (0-5 13 16 130 95° | 591 | 2-00 13 16 130 132-0 792 | O25 14 16 130 170-0 1020 | 200 14 | | | The table shows that the deflexions, though somewhat less, are not nearly so small as they should be. This would be accounted for satisfactorily if we believe most of this elongation to be caused by the heat evolved. Again, the influence of time of charging is clearly shown. ‘he values on different days seem to be consistently different. I cannot account for this except to suppose that the humidity was so different on the two days as to cause a great variation in leakage currents and so a difference in the heating of the tubes. Tube 9.—Non-adherent Armatures. | Spark- Elongation | Elongation Time of ain Oh Falk | micr. div. o/ x 10%. charging. | 10 mm. | 190 c.e.s. 80 4- | 1:00 mm, 10 100 55 33 | O75 10- 100 | 35 21 050 10 100 | 25 1°5 | 0:25 10 100 | 75 4-5 | 1-00 10 100 | 30 1:8 | 0-25 10 - 100 | 35 | 2-1 | 0:25 10 - 100 | 425 | 2:6 0:25 12 110 len M80 78 1:00 12 | 110 115 6:9 1:00 12 110 eA ales 6:9 1:00 12 Pine | 85 51 0:50 12 110 77 46 0°50 12 110 2:5 5:0 0°50 12 110 70 49 0:50 14 120 150 9-0 0:50 14 120 150 9:0 0:50 Vea b 20 165 9-9 0:50 14 | 120 145 | 8:7 0:50 14 120 165 9-9 0:50 14 | 120 160 96 0:50 14 120 150 | 9:0 0:50 Plan of Atom capable of Storing an Electrion. 695 The most convincing results were obtained with tube 9, mounted with non-adherent armatures. The separate readings are here given of a number of observations. With a 10-millimetre spark the elongation for a charging of about one minute is approximately 4°5 x 10-* mm., and this is reduced to one-third of its vaiue when the tube is char ged four times as quickly. This same effect of the time is noticeable thr oughout the table. Evidently very little of the effect would remain if the charging were made instantaneously. The times of charging are only given approximately, and this accounts for the Wariations in the readings when the potentials and the times are the same. There is no evidence of the law that the deflexions are proportional to V?/d?. In concluding this work on electrostriction, which has extended over years, I have some hope that the results given will be sufficiently convincing to prove that the effects which have been observed by myself and others can be fuily accounted for by extraneous effects, and that when these are eliminated the distortion of dielectrics by an electrical charge also vanishes. University of Cincinnati, Jane, 1905. LXXVI. Plan of an Atom to be capable of Storing an Electrion with Enormous Energy for Radio-activity. By Lord KELVIN * al 13 a communication to the Philosophical Magazine of October 1904, I described combinations of atoms and electrions having certain definite qualities of radio-activity : holding myself, for the time, bound to the precise description of the electric property of an atom of ponderable matter, which I had suggested in §4 of “Aepinus Atomised ”’ (Baltimore Lectures, Appendix E). In that description each atom of ponderable matter is supposed to have ideal electric matter of the vitreous kind distributed uniformly through it. No longer binding myself by this limitation to uniformity of vitreous electric density, I now propose to con- sider an atom of ponderable matter intrinsically charged with concentric strata of electricity, vitreous and resinous, of equal electric density at equal distances from the centre ; and with an excess of the total quantity of the vitreous above the total quantity of the resinous. I still suppose (with, I believe, all at present concerned with radio-activity) that free resinous * Communicated by the Author. 696 Lord Kelvin: Plan of an Atom electricity consists of equal atoms. I assume, and I believe there is general agreement in this assumption, that each of these atoms of resinous electricity, which I am calling elec- trions, has, besides its ordinarily defined property of electric attraction or repulsion, a property of somehow acting upon ether, and in virtue of this action having quasi-inertia. The nature of this action I believe to be attraction and consequent enormous condensation of ether around the centre of the electrion. (Baltimore Lectures, Lecture AX. §§ 238, 239.) § 2. My present assumption is Boscovichianism pure and simple. It merely declares that there is, between a single electrion and a single atom of ponderable matter void “of electrions, a definite fin ce in the line of their centres varying according to the distance ; which for distances greater than the radius of the atom is attraction according to the inverse square of distance between the electrion and the centre of the atom. It leaves us absolutely free to assume any law of force whatever that suits our purpose, when the electrion is within the atom. To give capacity to the atom for storing enormous electric energy by placing a single electrion at its centre, or at a very small distance from its centre, I assume, as indicated in the accompanying diagram, fig. 1, that the force on the Fig. 1.—WoRK-CURVE. On the right side of the diagram, slope up to right implies attraction ; slope down implies repulsion, electrion at distances less than a certain distance CM from the centre is towards the centre; and that at all distances capable of Storing an Electrion. 697 between CM, and -CN (the latter being slightly less than the radius of the atom), there is repulsion from the centre, rising to a maximum of enormously great amount at some distance CK between CM and CN, and coming to zero at the distance CN. Between CN, and CA the radius of the atom, the force becomes again attractive, and continues so, varying inversely as the square of the distance for all the distances of the electrion from the centre of the atom, greater than CA. The curve shown in the diagram may for brevity be called the work-curve. It shows by the ordinate PL the work, positive or negative, required to move an electrion from an infinite distance to any point P within or without the atom ; which I denote by w. Thus if we denote CP by 7, we have dw Bt pao et Van teat 3 (LE) where F denotes the force (positive when attractive, negative when repulsive) of the atom on an electrion in the position P. Hence this force is indicated in the diagram by the tangent of the inclination of the curve at any point L, to the line of centres, CA. § 3. For all points outside the atom we have Bay oe PDs) 08.411 1056) where «a denotes the excess of the vitreous over the resinous electricity permanently belonging tothe atom; and e denotes, according to the general usage of scientific writers on radio- activity, the quantity of resinous electricity in any one electrion. Thus for the equation of the curve outside the atom, we have Meta s,s hae poles (3). e By this we see that our curve outside the atom consists of portions of two rectangular hyperbolas. The maximum ordinate through M, and the minimum ordinates through C and N, show that the point M is a posi- tion of unstable equilibrium, and that the points C and N are positions of stable equilibrium ; for a single electrion placed within the atom. The point I on the curve, being a point of inflexion in the branch sloping downwards to the right, indicates that K is a position in which the atom experiences a maximum of repulsive force. Considering a spherical surface Phit. Mag. 8. 6.%Wol. 10. No. 60. Dee. 1205. dB 698 Plan of Atom capable of Storing an Electrion. through any point P within the atom, we see that if Q denote the excess of vitreous over resinous electricity of the portion of the atom within this sphere, we have e woe.) because the resultant force of all the electricity of the atom in the shell of outer and inner radii CA and CP is zero for every point inside its hollow. § 4. We may vary the work-curve within the atom as we please, with a view to trying to explain the different radio- activities of different atoms, and the different modes of radio- activity which seem to be presented by one and the same atom at different times. Thus for example we may draw the curve with four or six or eight or any even number of minimums, instead of the two minimums at C and N. There will of course be in every case an odd number of maximums, being less by one than the number of minimums. Thus we may arrange for any even number of stable positions of equilibrium within the atom. The work-minimum for the stable position nearest to the boundary of the atom is essentially negative, and somewhat less (somewhat more negative) than the negative work required to carry an electrion to the surface of the atom from an infinite distance outside. All the other minimums may be as large positive quantities as we please. ‘The magnitude of any one of them is the explosive energy which will be spent in shooting the electrion outwards or inwards by any shock or any kind of influence, if it is displaced away from its position of equili- brium far enough to reach an unstable position on either side of it. Look for example to the diagram. An electrion placed at C has stability, but only through a narrow range. If it is shaken away farther from the centre than M, the electric force of the atom upon it wiil shoot it out of the atom, with prodigious velocity, which will be but slightly diminished by the attraction of the whole atom when it gets outside. If it gets quite out of the atom, it will be shot through the ether outside with a velocity whose kinetic energy is something greater than the value of w at the unstable position from which it was shot, provided of course we can neglect its loss of energy by motions which, while it is in the atom, it gives to the ether in the atom and outside it. 699 94 LAXVII. Notices respecting New Books. A Treatise on the Analytical Dynamics of Particles and Rigid Bodies ; with an Introduction to the Problem of Three Bodies. By E.T. Wairracser, W.A. University Press, Cambridge. 1904. oS treatise differs in many respects from the usual kind of English text-book on dynamics. With few exceptions these may be described as more or less ingenious collections of modes of solution of abstract problems which may correspond to something natural. The authors of most of such books have had present to their mind the needs of a student whose knowledge of dynamical methods is to be tested sooner or later in an examination hall. One mischievous effect of this system was to bring into special prominence solvable cases without due consideration of why they should be solvable. For why should a candidate waste his precious time over the difficult question of solvability when he was certain to be examined only on cases which could be solved, that is, reduced to elliptic functions? Ever since the publication of Thomson and Tait’s ‘ Natural Philosophy,’ there has gradually grown up a healthier public opinion; and there has been a marked advance in the preparation of our best physical treatisas. And now Mr. Whittaker has given us a treatise, the aim of which is to lead up to the best recognized methods of analytical dynamics as a means towards a great end, namely, the interpretation of nature. Chapter I., on kinematic preliminaries, gets us almost immediately into touch with the real essence of rotation. In the succeeding chapter on the equations of motion, the convenient term holonomic is introduced, Lagrange’s equations established, and the Lagrangian Function or Kinetic Potential defined and used. Chapter ITI., on principles available for integration, discusses ignorable coordinates and the general principle of moment of momentum and energy. Then, and not till then, do we encounter the ordinary well-known simpler problems of particle dynamics. Chapters V. and VI. deal with the dynamics of rigid bodies. The theory of small vibrations about equilibrium configurations form the subject of chapter VII.; and with chapter VIII., on non-holo- nomic and dissipative systems, the more elementary part of the book may be said to end. It corresponds fairly well with the kind of dynamics which the examination paper can attain to; and yet it is but a preparation for the more abstruse developments which follow. Without particularizing too much, we may say that the powerful methods and developments associated with the names of Gauss, Hamilton, Jacobi, Liouville, Lie, Poincaré, Bruns, and others are brought forward and discussed with admirable skill, the later chapters dealing with the problem of three bodies and the - general theory of orbits. Like Lagrange’s great classic, this - treatise is remarkable in the entire absence of a single diagram. eval 700 me respecting New Books. The Analytical Theory of Light. By James Watxur, JA. Cambridge University Press, 1904. THE aim of this excellent treatise is “to give an account of physical optics without haying recourse to any hypothesis respecting the nature of the influence that constitutes light or the character of the medium in which it is propagated. »” In this respect it resembles Lord Rayleigh’s well-known article on Wave Theory in the Encyclopedia Britannica, and differs markedly from Poincaré’s Théorie Mathématique de la Lumiere, which builds on elastic foundations, and from Drude’s Optics, in which the characteristic feature is the electron. It is well perhaps when our imagination is being excited by whirls of charged corpuscles that we should be recalled to what is essentially the original standpoint. of Fresnel’s theory. This is what Mr. Walker has dene, and done effectively and well. Nevertheless, although the notions under- lying the electromagnetic theory of light have not been introduced explicitly, the influence of this theory is shown in the particularizing ot two related quantities which the author calls the polarization- vector and the light-vector. By use of these related vectors the mathematical investigations are in many cases distinctly simplified. It is obvious, indeed, that the author has taken full advantage of the analytical methods which belong peculiarly to Maxwell’s theory without adopting the physical significance of the symbols used. Jt might seem at first sight difficult to take account of the phenomena of absorption and dispersion, without some distinct understanding as to the nature of the dynamical link connecting ether and matter. Buta very general discussion of the facts of absorption and dispersion suggests to the mathematician familiar with workable functions that we have simply to imtroduce an exponentially diminishing amplitude and a forced periodic vibration; and, behold, the deed is done. Similarly, when Mr. Walker comes to treat of magnetically active media, he obtains a sufficient basis for the mathematical representation by introducing a suitable vector perpendicular to the magnetic force and the polarization-vector. In a sense there may be no recourse to any ultimate hypothesis; but the reader can hardly fail to see the modern electromagnetic theory winking at hin through the lines and symbols of the fundamental equations. Nevertheless, the auther has to an interesting degree kept wondrously clear of definite theoretical assumptions as to the inner nature of ethereal and molecular processes. ‘The treatment is instructive as showing how far we can go in coordinating phenomena without committing ourselves to a definite physical theory. In regard alike to the experimental] illustrations chosen to make the argument intelligible. as wel] as to the analytical methods employed, the book is thoroughly up to date; and all students of optical theory will welcome it as a valuable addition to our scientific literature. Notices respecting New Books. 701 Landoli-Bornstein Physikalisch-Chemische Tabellen. Dritte umgear- beitete und vermehrte Auflage, herausgegeben von Dr. RicHarD Borysrern und Dr. Winnetm Meyeruorrer. Julius Springer, Berlin, 1905: pp. xvi+ 861. Tue appearance of a new revised and enlarged edition of this standard and deservedly popular work will be cordially welcomed by all workers in physical science. Since the issue, in 1894, of the previous edition of the work, numerous additions have been made to our knowledge of physical constants, and of these the editors of the present edition, assisted by numerous experts and the Prussian Academy of Sciences, have fully availed them- selves. The workas it stands at present is aremarkable monument of human industry and of that conscientious attention to detail which has been so largeiy instrumental in developing modern science. Among the special features of the new edition. besides the corrections necessitated by more recent researches, may be men- tioned the numerous bibliographical references which occur throughout the body of the work, and the new tables relating to absorption, emission, and reflexion; those relating to thermo- electric constants, sparking potentials in gases, and magnetic properties of materials used in dynamo construction; and lastiy, the very large and important additions to the section which deals with thermo-chemistry and physical chemistry generally. Researches on the Affinities of the Elements and on the Causes of the Chemical Similarity or Dissimilarity of Elements and. Compounds. By Georrrey Martin, B.Sc. London: J.& A. Churchill. 1905. Pp. xii+ 287. Tuts original and interesting work should strongly appeal to all interested in the wider generalisations of modern chemistry. “The chemical properties of an element depend entirely upon its chemical affinities ; and the similarity or dissimilarity of two atoms or radicals depends on the proportionality or otherwise of the affinities of the one to those of the other,’—may be regarded as the text from which the author preaches his sermon, and the text is supported by an immense mass of facts culled from the field of experimental research. Were the affinities of each element in each state of valency known, then it would be possible to construct for each its “affinity surface,” and chemistry would then take rank asa mathematical science. The “affinity surface” is con- structed by the author as follows. In the a-y plane the various elements, arranged according to the periodic law, are represented by points, the «-coordinate corresponding to the group number ‘of the element, and the y-coordinate to its series number. The aiiinity, for any element, of the element whose affinity surface is required is then represented by the z-coordinate, and the surface passing through the extremities of the z-coordinates is the affinity surface. Owing to the absence of sufficient data, it is at present impossible to construct accurately the affinity surfaces. The 702 Notices respecting New Books. general shape of the surfaces may, however, be in many cases indicated, and this is done by the author in a large folding-plate for a number of the more important elements. An examination of these surfaces leads to the “ wave law” of affinity, the affinity surfaces presenting the successive appearances of an advancing wave which repeats itself at the end of every fresh cycle of elements of the periodic system. Numerous questions of outstanding theoretical importance are discussed by the author, and his daring and original interpretation of the significance of alcohol drinking, contained in one of the appendices, will be read with interest even bv those who may not be prepared to agree with him. We wish that the literary merit of the book were equal to its scientific value. Unfortunately, we cannot say that such is the case. The list of errata given at the end of the book is but a drop in the ocean of errors of typography and grammar in which the book abounds throughout. We cannot believe that the proof- sheets were honestly read by any person whose powers of observation are not utterly atrophied. The reader is kept ina constant state of irritation by the altogether inexcusable and frequent violations of the commonest rules of grammar and spelling which assail his eye on almost every page; and it is little to the credit of the publishers that they should have allowed the book to appear in its present state. Neuere Anschauungen auf dem Gebiete der Anorganischen Chenue. Von Prof. Dr. A. WerRNER. Braunschweig: F. Vieweg und Sohn. 1905. Pp. xii+189. Tas interesting and stimulating work forms the eighth volume of the series of monographs now being issued by Messrs. Vieweg & Son under the general title of ‘‘ Die Wissenschaft,” and deals with modern views regarding the periodic classification of the elements, the theory of valency, and the constitution of the more complicated inorganic compounds. The existence of these latter has been very largely ignored by many writers, and the importance of questions of constitution has very generally been supposed to be confined to the domain of organic chemistry. The narrowness and inadequacy of this view are clearly brought out by the author. The gradual abandonment of the old notions regarding valency, and the generglisations of this idea so as to meet the demands of erowing knowledge, form highly instructive and suggestive reading. The author is severely critical and extremely cautious in his exposition, going, indeed, so far as to suggest that the evolution of helium from salts of radium may possibly be capable of some interpretation other than that which attributes it to the breaking up of the radium atom. Index of Spectra. Appendix P. By W. Marsuatt Warts, D. Se Manchester: Abel Heywood & Son. 1905. Pp. 103. THis appendix to the author’s Indew of Spectra contains tables of the spectra of ruthenium and yttrium, and of the line and band spectra of sulphur. Geological Society. 703 Verflussigtes Ammoniak als Losungsmitiel. Von J. Bronn. Berlin: Julius Springer. 1905. Pp. xi+ 252. THE author of this book is to be congratulated on having written a very useful monograph dealing with the properties and methods of handling liquid ammonia, and with its applications as a solvent. Hitherto no sufficiently detailed information on these subjects was available without a very laborious search through the chemical literature of the past forty years; and we can cordially recommend the book to all chemists who are either interested in the subject in a general way, or who may be engaged on experiments in connexion with which the solvent properties of liquid ammonia would prove useful. A special chapter is devoted to the uses of liquid ammonia in physico-chemical researches. LXXVIIL. Proceedings of Learned Societies. GHOLOGICAL SOCIETY. [Continued from p. 616. | June 7th, 1905.—J. E. Marr, Sc.D., F.R.S., President, in the Chair. ps following communications were read :— 1. ‘The Microscopic Structure of Minerals forming Serpentine, and their Relation to its History.’ By Prof. T. G. Bonney, Sc.D., LL.D., F.B.S., V.P.G.S., and Miss C. A. Raisin, D.Sc. The authors, after a brief reference to investigations of serpentine during the last thirty years, which still leave some points unsettled, describe the formation of that mineral from sundry ferromagnesian silicates. Having given a summary of the changes in olivine, they describe more fully the alteration of separate grains in the so-called ‘kimberlite’ of South Africa. Then, after referring to the serpen- tinization of amphibole, as illustrated in the well-known Rauenthal. rock, they enter more fully into the changes, first, of the orthorhombic pyroxenes; then of the monoclinic. ‘To illustrate the latter, they describe the conversion of malacolite into serpentine in the well- known ‘ Hozoon’-rock of Cote St. Pierre, and of some augite-bearing serpentines in the Vosges. An investigation follows of the form of serpentine called ‘antigorite,’ described by Dr. Hussak (in 1883) from Sprechenstein on the Brenner Pass, and asserted to exhibit a ‘netting-like’ (gestrickte) structure, which is a record of the nearly-rectangular cleavage of the original augite. They show, by study of specimens collected in the Sprechenstein district by Miss Raisin, that no such connection exists and that the netting-like structure has often only a subjective existence. The mica-like mineral called antigorite 1s shown to be abundant in the Pennine Alps about the head of the Vispthal, and to lead to the same conclusion, suggesting, no less than the Sprechenstein specimens, a relation between that mineral and pressure. After a brief notice of the chemical changes in the conversion of the various 704 Geological Society :— anhydrous silicates into serpentine, the authors embody their inves- tigations in the following conclusions :—. (1) That both a tint and pleochroism are accidental rather than essential characteristics of antigorite. (2) Neither are low polarization-tints characteristic, unless two mica-like minerals exist, otherwise indistinguishable. (3) That it is doubtful whether any hard-and-fast line can be drawn between antigorite and the more fibrous forms in ordinary serpentine-rocks. (4) That the most typical antigorite appears when the rock has been considerably affected by pressure, but it becomes less so when the latter has been very great. (5) That so far from the nearly-rectangular cleavage of augite originating the ‘gestrickte struktur,’ it is worse preserved than any other original one in the process of serpentinization. Typical antigorite, however, apparently is rather more readily produced from augite than from the other ferromagnesian silicates, but is more directly a consequence of pressure than of chemical composition. 2. ‘The Tarns of the Canton Ticino.’ By Prot. E. J. Garwood, M.A., Sec.G.S. The lakes dealt with comprise the larger Alpine tarns which occur in the Canton Ticino. Most of these drain into the Ticino basin ; one or two, however, flow into the Reuss or the Rhine. Val-Piora Lakes.—These are chiefly rock-basins which lie in all cases along the junction of two dissimilar rock-masses. Detailed soundings prove that the axes of greatest depth of the lakes coincide with these lines of junction: one side being a dip-slope, the other an escarpment. It is shown that in the case of three of the larger lakes, soluble calcareous beds have been brought by thrusts against erystalline rocks. The origin of the lakes cannot be attributed to ice-excavation, as the ice must not only have invaded the district from outside, but must also have come from several different directions at once. Other difficulties in the way of accepting this mode of erigin are also pointed out. They appear to be due to structural peculiarities of the district, aided by solution. Analyses of the rauchwacké are given, and it characters are described. The lakes appear to be connected with a reversal of the drainage of the Piora Valley, consequent on the over-deepening of the Val Levantina in Interglacial times and the elevation of the upper end of the district as the ice-cap melted away. Two of the other lakes of this group lie on or near the water- shed: their origin is difficult to account for, except by differential weathering along the lines of junction. Lago-Tremorgio Group.—tThese tarns are all situated, either on the cale-mica-schists, or on outcrops of crystalline limestone and dolomite. Lago Tremorgio itself is almost certainly due to solution. A typical analysis of the schists gives 75 per cent. of calcium- carbonate. This occurs chiefly in the form of eyes of granular calcite which crumble between the fingers, and is found to be dissolved out in the submerged rock, while sharp reefs run out under water. The Tarns of the Canton Treino. 705 Soundings show a depth of 150 feet near the exit, which is a narrow water-cut gorge. The lake is otherwise entirely surrounded by asteep wall of rock, the lowest point in which is 718 feet above the lake. It is impossible to suppose that ice has scooped out this basin. The fact that springs issue from the side of the valley below the lake all the year round, and that the level of the lake falls 26 feet below its exit in winter point strongly to solvent action. Of the remaining lakes scattered along the southern side of the Ticino watershed, the Lago di Naret has a wedge of crystalline limestone running through the centre, while the Lago Sciundrau is situated on the junction of dolomite ‘and gneiss, and the Laghetti to the east of Lago di Naret le along the junction of the cale- schist and the eneiss. The St. Gothard Lakes.—The rock-basins here also occur along the line of junction of schists and gneiss. The Lago Lucendro is the most important, and soundings show an axis of greatest depth running along this junction. Solution does not appear to have played much part in its formation. Possibly the glacier which descended from Piz Lucerdro has removed fragments along the junction, as a transporting, not an excavating agent, as proved by the soundings at the lower end of the lake. Lago Sella and Lago Orsino are shallow tarns which come under the same category as Lago Lucendro. Lago d’Elio, draining into the Lago Maggiore, is due to reversal of drainage by a landslip. These lakes, then, owe their origin, when they are rock-basins, to the presence of lines of weakness, along which in many cases solution has taken place, while in some shallow tarns ice may have removed detached fragments; but inno case has alake been found which can reasonably be assigned toice-excavation independent of rock-structure. June 2ist.—J. E. Marr, Sc.D., F.R.S., President, in the Chair. The following communications were read :— 1. ‘The Relations of the Eocene and Cretaceous Rocks in the Esna-Aswan Reach of the Nile Valley... By Hugh John Llewellyn Beadnell, F.G.S., of the Geological Survey of Esypt. At the meeting of the Tnternational Geological Congress held in Paris in 1900, “the author brought forward evidence from the Baharia Oasis and Abu Roash to show that there was a marked unconformity between these two systems in the northern part of the country. The Jebel-Awaina succession shows that in the southern part of the country, where the Upper Cretaceous and the Lower Eocene occur in their fullest development, there is no sharp line of demarcation between the Cretaceous and the Tertiary, and no disturbances in the stratigraphical succession. This is confirmed by the succession in the Kharga Oasis, where there is no trace of an unconformity. Dr. J. Ball’s conclusions to the contrary were mainly based on the supposed irregular variation of the Esna Shales; but, where this occurs, it is mainly due to the fact that, with a slight increase of carbonate of lime, these 706 Geological Society :— 2 beds became almost indistinguishable from the overlying marls and marly limestones of the Eocene. The author finds in Jebel Nur el Ghenneiem some 180 feet of green clays between the Echinocorys-Chalk and the Eocene marls and limestones, and a per- * fectly conformable succession throughout. Near Ain Amur there is a considerable development of fossiliferous limestones at the summit of the Cretaceous rocks, and many of the fossils are hardly distinguishable from Eocene species. The author is of opinion that the Farafra succession falls into line with that which obtains in the southern part of the country. An important piece of con- firmatory evidence is furnished by the discovery of a rich fauna in ‘ashen-grey clays’ in the Esna-Aswan Reach of the Nile Valley by Dr.. W. F. Hume, in the clays above the Pecten-Marls in the neighbourhood of Esna. — 2. ‘A Contribution to the Study of the Glacial (Dwyka) Conglo- merate in the Transvaal.’ By Edward T. Mellor, B.Se., F.G.S. The survey of a district lying east of Pretoria and extending from near the Diamond-Fields to Middelburg, has recently afforded much additional information with regard to the Glacial Conglo- merate in this part of South Africa. The district les on the northern edge of the principal area occupied by the Karroo System, and includes a number of outliers, the area between which affords information as to the source of the material of the Conglomerate and the character of the land-surface on which it was deposited. This surface is smoothed, grooved, and scratched by ice-action. The Karroo System is here only 400 or 500 feet thick, and the Con- glomerate usually about 50 feet ; but, where deposited in hollows, it may reach 200 feet or morein thickness. The fragments are usually from 1 to 3 feet in diameter, but may attain as muchas 8 or 10 feet; they are often facetted and sometimes show striations. The majority of the boulders are of local origin. True bedding-planes are rare in the conglomerate, but there are included patches of sandstone, mud- stone, or shale, some of which show ripple- or eddy-markings. The strie are remarkably constant in direction, and they and the transport of boulders indicate an ice-movement from the north-north- west to the south-south-east. In the Prieska district Rogers and Schwarz found the movement to: have been from north-north-east to south-south-west, and the same direction is given by Schenck from near the junction of the Orange and Vaal Rivers. During 1904 outliers of the Conglomerate were found farther north, near the junction of the Hlands and Olifants Rivers. 3. ‘On New Oolitic Strata in Oxfordshire” By Kdwin A. Walford, F.G.S8. The divisions of the Inferior Oolite of North-West Oxfordshire are described, and a quarry on the border of the county cited where the Cotteswold facies dies out in the ‘Purkinsonz ’-stage. A higher division of the same stage (the Trigonia-signata Beds) of North- amptonshire type is shown to sweep over the North-Hastern Cotteswold region. The silico-caleareous beds (Chipping-Norton Limestone) cover the countryside which gives them their name, and are about 30 feet thick. Fossiliferous strata, separated from the : a | aaa. ‘| ¥' Phil. Mag. Ser. 6, Vol. 10, Pl. XIII. Fig. 9—PratintM ELecrroprs wird DIEFERENT GaASnS. seals | Hoe ra EI I] ] tear] 1 »} 0 tL 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 =| 13 DISTANCE IN WAVE-LENGTHS. 5 10 1S 20 e} 25 3 DISTANCE (N- WAVE -LENGTHS. 4p = Se Fig, 4, Ain = — 17 T ai | | | | me | ik | eI f Lol | 4.00 a t et el a | a | Ld [ | | pee Levis =F 400 - a lal 350 : | | 9 a3 r + | awl x 44S = in 350 p73 : | | : a i a | al ae a | te [ R 250 | ATMoskHER|e ARESSURE| = ra _| ge S ae ii = = Sq Ld EL Coe eee © al Lope e Se | Say — ote \: Be _l s {| is ATMOSFHERIC |PRASSURE | | | + g L rT B coo iL = y= - | ‘aa | | TE = 150}-—fh« _| W g { : el IL 8 ] inl gE [ | ee ae a) 150;-—J J =| a HEE es Fee ails | i [2 | I ae) iS | IF I 100} ; iL [ H il aa 50 = a Hh. it Saanr | : came a Lite | Jee | | ae i i ] [ | a | Tie. 5. —ALuminium, Vig. 6.—Si.ver. | Vig. 12.—Nieken. 4.00 Ld 7] — 400 = I ea 4 350 8 ? 6300 4 300 Ic - ® 5 IL Ne N £250) 2250 air ep zi * 200) S200 SI $A T Sse q = /ff Si 7/e4 q =U SAE E 150} Ea 2 & 159 are |i =| 09 § joo) al as = gq | | 50} 50) ia I ali IL i o t 3 4 Saerc 7 r) Y { 2 3 a 5 B DISTANCE IN WAVE-LENGTHS DISTANCE IN WAVE-LENGTHS. Tig. 8.—Zine. 3 4 6 DISTANCE IN WAVE-LENGTHS 3 4a 5 6 DISTANCE IN WAVE-LENGTHS Viv, 10,.—ANTIMONY, Fig. 11.—Magyesro. POTENTIAL /N VOLTS. we! Sa50 4 eee oceans Eo aE | RHA ee Br ote ae ee BA A Rea ors. 2 ANCE jee WAYE- Spee New Oolitic Strata in Oxfordshire. 707 Chipping-Norton Limestone by a bed with vertical markings and a black clay-band, indicative of much ‘ inter-waste’ of these and other beds, are described. They are shown to be similar to the Lincoln- shire (Ponton) strata described by Morris, Judd, and Woodward. A new term is proposed for these beds, which are characterized by the presence of the shell Newra, from the Perna-Marls above the black clays to a higher series of black-and-green clays underlying the Stonesfield Slate. These beds and the Chipping-Norton Lime- stones are classed with the sub-Bathonian. The beds equivalent to those of Oxfordshire have, in Lincolnshire and Northampton- shire, been known in part as Upper Estuarine. In the 20 feet of Oxfordshire strata there appears to be represented the 150 feet of the Lincolnshire Limestone and the Upper Estuarine of the north- eastern counties. The author expresses the hope that his work may help towards the discrimination of the two kinds of deposit known as Lincolnshire Limestones, inasmuch as the fossils charac- terizing each local (Oxfordshire) stratum have been collected from the beds zn situ. Lists of fossils are given. 4, ‘The Causes of Variegation in Keuper Marl and in other Calcareous Rocks.’ By Gerald Tattersall Moody, D.Sc., F.C.8. Analyses of a large number of specimens of Keuper Marl bring to light the fact that the red portion of a variegated rock contains a considerablv-higher percentage of iron and lower percentages of calcium-carbonate and magnesium-carbonate than the green portion. This is in agreement with earlier observations that red strata are usually less calcareous than adjacent green strata; but the author is unable to confirm the hypothesis advanced by Maw, that the lighter-coloured bands in variegated rocks are produced by bleaching or discoloration of red rocks through addition from extraneous sources of lime and magnesia. On the contrary, it is found that the removal of iron existing as ferric oxide from a homogeneous rock-mass is inhibited, if calcium-carbonate, or magnesium-car- bonate, or both of these substances be present. When, however, a chalybeate water (ferrous bicarbonate-solution) permeates a rock containing magnesium-carbonate or calcium-carbonate, iron is pre- cipitated as ferrous carbonate, and an equivalent weight of mag- nesium or calcium passes into solution. Subsequent access of air oxidizes the ferrous carbonate, and red or yellow ferric oxide is produced. The author finds that when a green marl is subjected to the action of chalybeate water in the manner indicated, it is readily converted into a material closely approximating, both in appearance and 1n composition, to the natural red marl of the same rock-mass. The author concludes that the variegation of the Keuper Marls and of other calc: reous rocks has been brought about by the percolation of chalybeate water through the light-coloured mass, the more porous parts of which have in consequence become stained with ferric oxide, while the harder and more crystalline parts, being non-porous, have remained unchanged. The uniformity in distribution of ferric oxide in some red rocks, such as the New Red Sandstone, suggests that the iron contained in them has probably been derived from chalybeate water in a similar manner. iio | INDEX to VOL. X. — ACCELEROMETER, on the pen- dulum, 260. Actinium and its successive products, on, 385; on the absorption of the 8 and y rays of, 375. AXther, on the partition of enerey between matter and, 91; on the statistical kinetic equilibrium of, in ponderable matter, 285. Adther drift, on the, 71, 3838, 591. Alcohol, osmotic experiments on mixtures of, and water, 1. Allen (H. 8.) on Dewar’s method of producing high vacua, 497. Alpha rays from radium, on the, 163, 198, 318, 538, 600 ; from polonium, on the, 588. Appleyard (R.) on contact with dielectrics, 485. Atmosphere, on the radioactive matter present in the, 98. Atom, plan of an, capable of storing an electrion with enormous energy for radioactivity, 695. Atoms, on the space occupied by, 340, Barlow (P. 8.), osmotic experiments on mixtures of alcohol and water, roe, on the lateral vibration of, 118, Barton (Dr. E. H.) on the vibration curves simultaneously obtained from a monochord sownd-box and string, 149. Beadnell (H. J. L.) on the geology of the Nile Valley, 705. Blythswood (Lord) on Dewar’s method of producing high vacua, 497, Bonney (Prof. T. G.) on the micro- scopic structure of serpentine, 703. Books, new:—Freund’s Study of Chemical Composition, 184; Jau- mann’s Die Grundlagen der Bewee- ungslehre, 185; Le Chatelher and Boudouard’s High Temperature Measurements, 185; Bulletin of the Bureau of Standards, I. 1, 186; Meldrum’s Avogadro and Dalton, 186; Perkins’s Practical Methods of Electro-Chemistry, 186; Gold- schmidt’s Ueber Harmonie und Complication, and Ueber harmon- ische Analyse von Musikstiicken, 279; Linders’ Die I’ormelzeichen, 284; Gerard’s Lecons sur )’Elec- tricité, 400; Sir G. G, Stokes’ Mathematical and Physical Papers, vol. v., 400; Buicherer’s Mathe- matische Einfuhrung in die Elek- tronentheorie, 613; Jeans’ Dyna- mical Theory of Gases, 614; Frolich’s Die Entwickelung der Elektrischen Messungen, 614 ; Whittaker’s Treatise on Analytical Dynamics, 699; Walker's Ana- lytical Theory of Light, 700; Landolt- Bornstein Physikalisch - Chemische Tabellen, 701; Martin’s Researches on the Affinities of the Elements, 701; Werner’s Neuere Anschauungen auf dem Gebiete der Anorganischen Chemie, 702 ; Watts’ Index of Spectra, App. P, 702; Bronn’s Verflussigtes Am- moniak als Losungsmittel, 705. Boomerang, on the, 60. Brace (Prof. D. B.) on the negative results of second and third order tests of the “ether drift,” 71; on the “ether drift” and rotary polar- ization, 383; on a repetition of Fizeau’s experiment on the change produced by the earth’s motion on the rotation of a refracted ray, 59]. | Brage (Prof. W.H.) on the @ par- ticles of radium, 318, 600. Burbury (8S. H.) on the virial equa- tion, 33. INDEX. Candle-power of incandescent lamps, on the, 208. Charcoal, on the absorption of gases by, 497. Chree (Dr. C.) on the temperatures of thermometers under black cloth and under white cloth, 288; de- ductions from magnetic distur- bances at Greenwich, 306. Clinton (W.C.) on the voltage ratios of an inverted rotary converter, 160. Cobalt, on the magnetization and magnetic chauge of length in, 548, 642. Colours, on the origin of the pris- matic, 401, 574. Conductivity of flames, on the elec- trical, 476. Contact with dielectrics, on, 485. Converter, on the voltage ratios of an inverted rotary, 160. Corpuscles, on the emission of nega- tive, by the alkali metals, 574. Current, the electrical resistance of a conductor the measure of the, passing, 352. Denning (Dr. A. D.) on a method of determining the radiation constant, 270. Dielectric strain along the lines of force, on, 676. Dielectrics, on contact with, 485. Diethylamine and water, on the mu- tual solubilities of, 397. Discontinuity, on surfaces of, in a rotationally elastic medium, 603. Dispersion formula, on the rotatory, 408. Dyke (G. B.) on the flux of light from the electric arc with varying power supply, 216. Earth’s motion, on the change pro- duced by the, on the rotation of a refracted ray, 591. Elastic medium, on surfaces of dis- continuity in a rotationally, 603. Electric are, on the flux of light from the, 216. conductivity of flames, on the, 476. discharge in gases, on the, GZ, lamps, on the candle-power of incandescent, 208. potential, on space at a high and at a low, 380. ON Electric resistance of a conductor the measure of the current passing, 352. vibrations between confocal elliptic cylinders, on, 225. Electricity, on the effect of a trans- verse magnetic field on the dis- charge of, through a vacuum-tube, 67; on the conduction of, through gases, 257,664; on a fundamental experiment in, 380; on the emis- sion of negative, by radium and thorium emanations, 460, Electrolytic dissociation, theory of, 662. Electrons, on the resonance radiation of, 513. Electrostriction, on, 676, Ellipsoidal lenses, on, 180. Elliptic cylinders, on electrical vibra- tions between confocal, 225. Elsden (J. V.) on the igneous rocks of St. David’s, 615. Energy, on the partition of, between matter and ether, 91. Eve (A.S8.) on the radioactive matter present in the atmosphere, 98. Fizeau’s experiment, on a repetition of, 591. Flames, on the electrical conductivity of, 476, : Fleming (Prof. J. A.) on the ratio between the mean spherical and mean horizontal candle-power of incandescent electric lamps, 208. Fluorescence of sodium vapour, on the, 518. Garrett (C. A. B.) on the vibration curves simultaneously obtained from a monochord sound-box and string, 149, Garwood (Prof. E. J.) on the tarns of the Canton Ticino, 704. Gaseous vibrations, onthe momentum and pressure of, 364. Gases, on the structure of ions formed in, at high pressures, 177; on the conduction of electricity through, 237, 664; on the rate of recombination of ions in, 242; on the spark-discharge in, 617. Geological Society, proceedings of the, 188, 615, 708. Godlewski (Dr. T.) on actinium and its successive products, 35; on radioactive properties of uranium, 45; on the absorption of the @ and y rays of actinium, 375. on the 710 Harker (Dr. J. A.) on the specific heat of iron at high temperatures, 430. Harward (A. E.) on the transfinite numbers, 439. Havelock (Dr. T. H.) on surfaces of discontinuity in a rotationally elastic medium, 603. Hobbs (G. M.) on the relation be- tween P.D. and spark-length for small values of the latter, 617. Honda (K.) on a portable aéromer- curial tide-gauge, 253; on the magnetization and magnetic change of Jength in ferromagnetic metals and alloys, 548, 642. Hloustoun (R. A.) on the effect of a surface-film in total reflexion, 12 ; on total reflexion at the second surface of a plane parallel plate, 24. Hydrogen, on the union of, with oxygen at low pressures, 467. Inertia, on the determination of the moment of, of magnets, 130. Ions, on the discharge of negative, by glowing metallic oxides, 80; on the structure of, formed in gases at high pressures, 177; on the rate of recombination of, in gases, 242, tron, on the specific heat of, at high temperatures, 430; on the mag- netization and magnetic change of length in, 548. Jackson (W. H.) on the method of transmission of the excited activity of radium to the cathode, 532. Jeans (J. H.) on the partition of energy between matter and ether, 91 Jones (Prof. H. C.) on the theory of electrolytic dissociation, 157. Kahlenberg (Prof. L.) on the theory of electrolytic dissociation, 662. Kelvin (Lord) on the statistical kine- tic equilibrium of ether in pond- erable matter, 285; plan of an atom to be capable of storing an _ electrion with enormous energy for radioactivity, 695. Kinetic equilibrium of ether in ponderable matter, on the statisti- eal, 285. Kirkby (Rev. P. J.) on the union of hydrogen with oxygen at low pressures caused by the heating of platinum, 467. TN) ES ' Kleeman (R.) on the a particles of radium, 318. Lamps, on the candle-power of incandescent electric, 208. Lanchester (I. W.) on the pendulum accelerometer, 260. Larmor (Dr. J.) on the constitution of natural radiation, 574. Lattey (R. T.) on the mutual solu- bilities of diethylamine and water, 397. Lenses, on ellipsoidal, 180. Light, on the flux of, from the electric arc with varying power- supply, 216. Mackenzie (Prof. A. §.) on the deflexion of a rays from radium and polonium, 538. Magnetic change of length in ferro- magnetic metals and alloys, on the, 548, 642. disturbances at Greenwich, de- ductions from, 306. —— field, on the effect of a trans- verse, on the discharge through a vacuum-tube, 67. rotation, on the bright line- spectrum produced by, 422. Magneto-optics of sodium vapour, on the, 408. : Magnets, on the determination of the moment of inertia of, 130. Makower (W.) on the method of transmission of the excited ac- tivity of radium to the cathode, 526. Marshall (Dr. P.) on the geology of Dunedin, 191. Mellor (KE. T.) on the glacial con- glomerate in the Transvaal, 706. Metallic oxides, on the discharge of negative ions by glowing, 80. Metals, on the magnetization and magnetic change of length of ferromagnetic, 548, 642; on the emission of negative corpuscles by the alkali, 574; on the thermo- electric circuit of three, 631. Moody (Dr. G. T.) on variegation in the Keuper marl, 707. More (Prof. L. T.) on dielectric strain along the lines of force, 676. Morrow (J.) on the lateral vibration of bars of unifirm and varying sectional area, 113. Nicholson (J. W.) on _ electrical vibrations between confocal elliptic cylinders, 225. INDEX. FAL Nickel and nickel-steel, on the mag- netization and magnetic change of length in, 548, 642. Numbers, on the transfinite, 439. Optical paradox, on an, 126. Osmotic experiments on mixtures of alcohol and water, 1. - Oxygen, on the union of, with hydro- gen at low pressures, 467. Peck (J.) on the effect of a transverse magnetic field on the discharge of electricity through a vacuum-tube, 67. Pendulum accelerometer, on the, 260. Platinum, on the union of hydrogen with oxygen at low pressures caused by the heating of, 467. Polarization, on the ether drift and rotary, 383. Polonium, on the deflexion of a rays from, 558. Potential-difference and spark-length, on the relation between, 617. Preumont (G. F.) on the geology of the N.E. territories of the Congo Free State, 190. Price (W.A.), the electrical resistance of a conductor the measure of the ‘current passing, 352. Prismatic colours, on the origin of the, 401, 574. Pylknometer, on a new form of, 269. Radiation, on the constitution of natural, 574. tadiation constant, on a simple method of determining the, 270. Radioactive matter present in the atmosphere, on the, 98. properties of actinium, on the, 54; of uranium, on the, 45. Radioactivity, plan of an atom capable of storing an electrion with enormous energy for, 695. Radium, on the a rays from, 163, 193, 318, 600; on the properties. of, in minute quantities, 183; on the charge carried by the a and 6 rays of, 193; on slow trans- formation products of, 290; on the scintillations produced by, 427 ; on the emission of negative electricity by the emanation from, 460; on the method of transmission of the excited activity of, to the cathode, 526, 5382; on the deflexion of a rays from, 538. Raisin (Miss C, A.) on the micro- scopic structure of serpentine, 703. Rastall (R. H.) on the Blea-Wyke beds, 189. Rayleigh (Lord) on the momentum and pressure of gaseous vibrations and on the connexion with the virial theorem, 364; on the origin cf the prismatic colours, 401. Resonance radiation of electrons, on the, 513. Richardson (L.) on. the Rheetic deposits of Glamorganshire and on Rheetic rocks at Berrow Hill, 616. Richardson (Dr. O. W.) on the structure of ions formed in gases at high pressure, 177; on the rate of recombination of ions in gases, 242. Robb (A. A.) on the conduction of electricity through gases between parallel plates, 237, 664. Rotation of a refracted ray, on the change produced by the Earth’s motion on the, 591. Rudge (W. A. D.) on the properties of radium in minute quantities, 183, Rutherford (Prof. E.) on some properties of the a rays from radium, 163; on the charge carried by the a and £# rays of radium, 193; on slow transformation pro- ducts of radium, 290. Schmitz (H. E.) on the thermoelectric circuit of three metals, 631. Sharpe (J. W.) on the boomerang, 60. Shimizu (S.) on the magnetization and magnetic change of length in ferromagnetic metals and alloys, 548, 642. Sibiy (T. F.) on the carboniferous limestone of Weston-super-Mare, 192. Slater (Miss J. M.W.) on the emission of negative electricity by radium and thorium emanations, 460. Sodium vapour, on the magneto- optics of, 408 ; on the fluorescence of, 513. Solubilities of diethylamine and water, on the mutual, 397. Sound-box, on the vibrations simul- taneously obtained from a, and string, 149. ae (R. J.) on ellipsoidal lenses, 712 Spark-leneth, on the relation between potential-difference and, 617. Specific heat of iron at high tempe- ratures, on the, 430.° Spectrum, on the bright line, tos duced by magnetic rotation, 499, Stanford (R. Vv.) on a new form of pyknometer, 269. Stoney (Dr. G. J.) on an optical paradox, 126. String, on the vibration curves simultaneously obtained from a sound-box and, 149. Surface-film, on the effect of a, in total reflexion, 12. Surfaces of discontinuity in a ro- tationally elastic medium, cn, 603. Temperatures of thermometers under black cloth and under white cloth, on the, 288. Thermoelectric circuit of metals, on the, 631. Thomson (Prof. J. J.) on the emission of negative corpuscles by the alkali metals, 584. Thorium, on the emission of negative electricity by the emanation from, three Tide-eauge, on a portable aéromer- eurial, 255. Total reflexion, on the effect of a surface-film in, 12; on, at the second surface of a plane parallel plate, 24. Transfinite numbers, on the, 439. Traube (Prof. J.) on the space occupied by atoms, 540. Treacher (Ll.) on the phosphatic chalk of Taplow, 188. Tungsten-steel, on the magnetization and magnetic change of leneth in, 548, 642. Uranium, on the radioactive proper- ties of, 45. ‘Vibration INDEX. Vacua, on Dewar’s method of pro- ducing high, 497. Vacuum- -tube, on the effect of a transverse magnetic field on the discharge of electricity through a, 67. curves simultaneously obtained from a monochord sound- box and string, on the, 149. Vibrations, on the lateral, of bars, 113; on electrical, between con- focal elliptic cylinders, 225; on the momentum and pressure of gaseous, 364. Virial equation, on the, 33, 364. Voltage ratios of an inverted rotary converter, on the, 160. Walford (EK. A.) on new oolitic strata in Oxfordshire, 706. Water, osmotic experiments on mixtures of alcohol and, 1; on the mutual solubilities of diethylamine and, 397. Watson (Dr. W.) on the determina- tion of the moment of inertia of magnets, 130. Wehnelt (Prof. A.) on the discharge of negative ions by glowing metallic oxides, 80. White (H. J. On on the phosphatic chalk of Taplow, 188. Wilson (Dr. H. A.) on the electrical conductivity of flames, 476. Wood (Prof. R. W.) on the magneto- optics of sodium vapour and the rotatory dispersion formula, 408 ; on the scintillations produced by radium, 427; on the fluores- cence of sodium vapour and the resonance radiation of electrons, 515. Worthington (Prof. A. M.) on fundamental experiment in ele: tricity, 380. END OF THE TENTH VOLUME. Printed by Taynor and Francis, Red Lion Court, Fleet Street. < Nice oi flee ie S) ‘wii 3 9088 01 ao 4766