rel Ww Pr ero bee TSR CLE DEED OS Vy Sri vglb vane ded Be We a t ait ee ‘ eee A ) 71 on V8 ah Nie retyite ath (ef) A Aiage Wee Aye hy Shy Oa BU, tH i Hi mit re fir Hf TAAL te ie taal bee Ce ATM H y os earns Sf nea SSS ——— Spee tatboese'a pr More roan ian ae ta ah SWE a Pedaarthse iti LOE eh AI Giporunii itt f ikke { Hie s i St : « ae F xe I * i Veeh ) ‘ % . "i % hy ay 1 Cha vilay hia fy Meals a) hoe Boye) al bast i ue li lee t af 8 i evra DAIL et 4 uh us iat OF Me NEN E | = Sie Sa So ey re = SG SEReret: poe ees : - 1) if ; Tapas rs ith eae Tt it Fifteen any abst 4 eH fy i “st i at = Sees & yt 223 bt ‘3 3 at ali ry af ah ite LELSONIEIEI ILS SIEMENS IES rw [% ® SCIENTIFIC LIBRARY ws % x) £s2 Ke KS iv) (ay w Da 2 a rw cS 4 8 : mi wo ox Q ay o ay Pp (a) wo se 2 © a 6% Q Oo 2 De Q QO ww cs QD. (aN iw is iV) ay a % &) UNITED STATES PATENT OFFICE “ 2 2 (a) w wa % S E % 4 ose iy @ SMaraacamMawMAMMamm a aK GOVERNMENT PRINTING OFFICD 11—8625 —- eS THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. CONDUCTED BY TORO KELVIN, G.C.V.O. D.C.L. LEAD. ERS. &e. JOHN: JOLYS MAS D Scs Paes? EGS. 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. Lips. Polit. lib. i. cap. 1. Not. VOL. XIV.—SIXTH SERIES. JU Ee EMBER, 1907. LONDON: TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET SOLD BY SIMPKIN, MARSHALL, HAMILTON, KENT, AND CO., LD, SMITH AND SON, GLASGOW ;— HODGES, FIGGIS, AND CO., DUBLIN; YEUVE J. BOYVEAU, PARIS ;—AND ASHER AND CO., BERLIN. 56637 ey Seba “Meditationis est perscrutari occulta; contemplationis est admirari perspicua .... Admiratio generat questionem, queestio investigationem, investigatio inventionem.”— Hugo de S. Victore. “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. ipa - ree a CONTENTS OF VOL. XIV. (SIXTH SERLES). NUMBER LXXIX.—JULY 1907. Page Mr. W. Sutherland on Ionization in Solutions and Two EMemmaypes Or VISCOSILY (ii) Sova so aye Sek in syhsloy< ol dithep enced oh i! Mr. J. H. C. Searle on the Effect of Rotatory Inertia on the BORA MS NOL ATS 4 a. 0st oP at nol suoe cia G a, a oy ci eydiepenas gush be 30 Lord Rayleigh on the remarkable Case of Diffraction Spectra described ‘by IEA OO 0 © teamed he one aye Sa or PE aes oi 60 Messrs. K. Honda and T. ‘'erada on the Effect of Stress on Magnetization and its Reciprocal Relations to the Change of Hlastic Constants by Magnetization. (Plates I—-V.) .. 60 Mr. A. Stephenson on the Forcing of Oscillations by Distur- pameesvor Witteremt Wrequencies . a5. 54 00% ves ee ets 115 Mr. 8. H. Burbury on Ditfusion of Gases as an Irreversible 1 TEDESS 130 SR AI A ees BON ae aes Sia De Rein pein We 122 Mr. W. L. Upson on the Electric Arc. (Plates VI. & VII.) 126 Prof. R. W. Wood on the Magnetic Rotation of Sodium Pepoumar ities): Wines. (Plate VI). tye. oe oe a be 1465 Lord Rayleigh on the Passage of Sound through Narrow Slits. 153 Prof. P. Lowell ou a General Method for Evaluating the Surface-Temperature of the Planets; with special reference comme mlemperabire On MAGS ele i ease me ies op eys ee + « 161 Prof. A. Stanley Mackenzie on Secondary Radiation from a Piaveroxpesedi to Kays trou Nag@ium 2.4. sacs... . 176 Prot. R. A. Millikan and Mr. G. Winchester on the Influence of Temperature upon Photo-electric Effects in a Very High Vacuum, and the Order of Photo-electric Sensitiveness of the Wierale Mra ensure Re toate Shae ie oT oa! ake 6 9 o: eee 188 Mr. G. A. Schott: Note on the Explanation of the Radios SiCBU ME OE a CSIC MAUI "Als GR Alle Reece On Ae ee RPE IR 2 210 TOL NV. Ny len on Kays of Positive, Electricity .. 2 q.)suaa 2 02 lv CONTENTS OF VOL. XIV.—SIXTH SERIES. Page Proceedings of the Geological Society :— ie : Mr. H. H. Arnold-Bemrose on the Toadstones of Derby- shire, their Field-Relations and Petrography. ...... 213 Prof. J. W. W. Spencer on Data bearing on the Age of Niagara Malls nc. 2 <2 4 siete ee rele eee ea eee 214 Mr. H. J. Lowe’s Petrological Notes on the Igneous Rocks lying to the South-East of Dartmoor ........ 215 Intelligence and Miscellaneous Articles :— Electrical Ionic Conductivities, by Philip Blackman .. 215 NUMBER LXXX.—AUGUST. Prof. J. J. Thomson on the Electrical Origin of the Radiation from Hot Bodies = .0 2095s. see te cee sem & eee 217 Mr. A. 8. Eve and Dr. D. McIntosh on the Amount of Radium present in Typical Rocks in the immediate Neigh- bourhood of- Montreal <5 i). 0.4 See. ieee oe eee 231 Prof. E. Taylor Jones on a Short-Period Electrometer, and its use in Determining the Frequencies of Slow Electrical Oscillations. (Plate LX.) 1). .51.0-.0 ate. eee 238 Prof. J. A. Fleming on the Poulsen Arc as a means of obtaining Continuous Electrical Oscillations ............ 254 Dr. 8S. Tolver Preston on Certain Questions connected with Astronomical Physics.—Part I1:)...).0..... 2 ae 265 Messrs. F. Soddy and JT. D. Mackenzie on the Relation between. Uranium and Radium) ~.. 2... 2... .2)- os eee 272 Prof. J. J. Thomson on Rays of Positive Electricity ...... 295 Mr. I. O. Griffith on the Relation between the Intensity of the Ultra-Violet Light falling on a Negatively-charged Zine Plate and the Quantity of Electricity which is set free from the SUtiace ices eine lee es ee mee lee ee eee 297 Mr. G. H. Martyn on the Discharge of Electricity from Hot Bodies: (Plate: X90. ak... oes oie esa crene sie annoys eee 306 Prof. J. Larmor on the Range of Freedom of Electrons in MCtals: oe cassie euelens cw cies wtete lot w at cuete hah ole a Meta aa 312 Notices respecting New Books :— E. Gerard et O. De Bast’s Exercices et Projets d’Electro- HOCH NIGME 7 sso os ele des Siete gs wit ea eo ogee gene eee 316 NUMBER LXXAL—SEPTEMBER. Lord Kelvin on the Motions of Ether produced by Collisions of Atoms or Molecules containing or not containing Electrions. 317 Mr. G. Le Bas on the Unit-Stere Theory : The Demonstration of a Naturai Relation between the Volumes of the Atoms in Compounds under Corresponding Conditions and that a1 Combined Hydrogen {cies a... a ee ee 9 ee 324 CONTENTS OF VOL. X1V.—SIXTH SERIES. V Page Lord Rayleigh on the Light dispersed from fine Lines ruled upon Reflecting Surfaces or transmitted by very narrow Ren RN Atos Spaces 5s oi onthe RMS Sd hel ay oh = shag acest eso ake 390 Prof. J. J. Thomson on Rays of Positive Electricity........ 309 Dr. J. W. Nicholson on the Scattering of Sound by Spheroids SDT, LAISISS/ 5 Sh geen eh, De eee IP 2 yr 364 SIGTLES > 40 Se PAS Oh chi Matec Ct ae rr 377 Mirsex. S.-Eive on Jonization by Spraying ................ 382 Mr. E. A. N. Pochin on Experimental Mathematics........ 395 Messrs. W. Wilson and W. Makower on the Rate of Decay of ine Active Deposit from Radiwm .....5.......-2:4. 40+ Dr. C. G. Barkla and Mr. C. A. Sadler on Secondary X-Rays auderie atone Weteht of Nickel ... 0. ...2..0..000-5- 408 Mr. S. H. Burbury on the Work which may be gained during pmembbmarire. OF Gases. SP) 8% iia: sis )rattie: oes; 08a Mins 0 oe 422 Prof. W. H. Bragg and Dr. W. T. Cooke on the Ionization Be rom EV CU MATIC oc. keira wo. 6 Sueneiey in ie Vevey Sood.» < Braise 425 Intelligence and Miscellaneous Articles :— The Photanthistan: a New Instrument for the Com- parison of Luminous Intensities and Absorption Coefficients, by J. J. Taudin Chabot .............. 428 NUMBER LXXXII.—OCTOBER. Prof. W. H. Bragg on the Properties and Natures of various 499 ae rert EMT ATVOUIS aoe tens i A oie esele slot voce iem, mye af dota Prof. G. Melander on the Production of Statical Electricity iyerae Action of Heat and Light-' >... 2 22). 0 532.005. 450) Prot. D. N. Malhk on Magnetic Induction in Spheroids .... 455 Mr. J. Russell on the Superposition of Mechanical Vibrations (Hlectric Oscillations) upon Magnetization and conversely, mebron, steel, and: Nickel: "(Plate Ail.) oy... ee 468 Prof. RB. W. Wood on a Simple Treatment of the Secondary Miemanaromcrravine” Speebra.. ss6 2... Me SST es 477 Mr.J. Prescott on the Figure of the Earth .............. 482 Mr. A. Campbell on the Measurement of Mutual Inductance by the Aid of a Vibration Galvanometer. (Plate XII.) .. 494 Mr. P. V. Bevan on Lloyd’s Fringes tor Internal Reflexion, and the Change of Phase of Ordinarily Reflected age CIPS e ES ng AOS ge ae ee pec Ue Dr. G. Bakker on the Theory of Surface-Forces .......... 509 Messrs. Gwilym Owen and A. L]. Hughes on Condensation Nuclei produced by Cooling Gases to Low Temperatures.. 528 Mr. E. Cunningham on the Electromagnetic Mass of a Moving IRI@CHROINS, so dto an Oe 6 OER ORE ot ee Rep Oe ee o v1 CONTENTS OF VOL. XIV.—SIXTH SERIES. Page Dr. G. Riimelin on the Rate of Transformation of the sae tae Hmanation 00. 022 Le a a err 990 Notices respecting New Books :-— , A. W. Stewart’s Stereochemistry ........:2. 0.2095 003 hk. De Valbreuze’s Notions Générales sur La Télégraphie Sans Ful? (225.260. a2 hess in eeee es 504 Proceedings of the Geological Society :— Mr. . W. Harmer on the Origin of certain Canon-like Valleys associated with Lake-like Areas of Depression. 555 NUMBER LXXXIII—NOVEMBER. Prof. O. W. Richardson: A Theory of Displacement of Spectral Lines produced by Pressure .....).:...--neeeee 557 Prof. H. H. Barton on the Lateral Vibration of Bars treated simply: (Plate XTVs)..0 66 ase ese. J ee O78 Mr. C. V. Raman on the Curvature Method of determining the Surface-Tension of Liquids. (Plate XV.) .......... 591 Lord Rayleigh on the Relation of the Sensitiveness of the Ear to Pitch, investigated by a new Method ..-. 2): 02 2e8 ee 596 Mr. R. T. Beatty on Secondary Rontgen Radiation in Air .. 604 Dr. J. Kunz on an Abrupt Limit of Distance in the Power of the Positive Rays to produce Phosphorescence .......... 614 Mr. R. D. Kleeman on the Secondary Cathode Rays emitted by Substances when exposed to the y Rays ............ 618 Mr. J. 8S. Dow on a Form of Cosine Flicker Photometer. (Plate XV1) shies eee tae bebe ee 644 Mr. J. A. Crowther on the Secondar y Rtontgen Radiation on Gases and Vapours 0.040... kU. 6 653 Notices respecting New Books :— Prof. M. H. Bouasse’s Bases Physiques de la Musique.. 675 Proceedings of the ‘Geological Society: <2 J.) 7.) he eee ee 676 Intelligence and Miscellaneous Articles :— “¢ Hxperimental Mathematics,” by F. J. Jervis-Smith .. 676 NUMBER LXXXIV.—DECEMBER. Dr. J. A. Fleming on Magnetic Oscillators as Radiators in Wireless Telepraphy °..). 00... err 677 Dr. J. W. Nicholson on the Asymptotic Expansion of Bessel Punctionsyot High Order 2.22). 00.) a 697 Mr. A. Stephenson on the Stability of the Steady State of Koreed ‘Oseillatiom (7.10.70). ee teicher e cle oletel sols chy ener 707 Dr. 8. J. Allen ona Null Instrument for Measuring lonization. 712 CONTENTS OF VOL. XIV.—-SIXTH SERIES. Mr. A. 8. Eve on the Amount of Radium Emanation in the mimosphere near the Harth’s Surface.............-+:-: Prof, H. Rutherford on the Production and Origin of Radium. Prof. J. H. Poynting on Prof. Lowell’s Method for Evaluating the Surface Temperatures of the Planets ; with an Attempt to Represent the Effect of Day and Night on the Tempe- ramones GMe Marble Wawasan sel Ame ne ab bs ees oes alerts Prof. J.C. McLennan on the Radioactivity of Lead and other BAe ANSEF yo) eel ives ch sp Seno eo at ais ESS eee Saks ooo Ses Dr. R. v. Hirsch and Mr. F. Soddy on a Gas generated from eetnmarmnmmn’: Wleetrodes.: 2.5 sage. ss 2 ops oe tase es os Prof. E. Castelli on Gradual Modification of the First Linear Spectra of Emission of Mercury. (Plate XVII.)........ Proceedings of the Geological Society :— Mr. Rk. D. Oldham on the Constitution of the Interior of the Earth as revealed by Earthquakes: Some New Light ompthne Oriemot the Oceans (2c 5.6) o ie yee oe oe Dr. C. Davison on the Swansea Earthquake of June 27th, IO enol hats sfoud 2614S Sud » oyisuaxecershave £6 afousbadhinespaccia + Dr. C. Davison on the Ochil Earthquakes of September 1900 to April 1907 ereereereereorvreeeeerFeRaeeeeeeteereeeee ts Peewee eeeeteees PLATES. I.-Y. Illustrative of Messrs. K. Honda and T. Terada’s Paper on the Effect of Stress on Magnetization and its Reciprocal Relations to the Change of Elastic Constants by Mageneti- zation. VI. & VIZ. Illustrative.of Mr. W. L. Upson’s Paper on the Electric Arc. VIII. Illustrative of Prof. R. W. Wood’s Paper on the Magnetic Rotation of Sodium Vapour at the D lines. IX. Illustrative of Prof. E. Taylor Jones’s Paper on a Short- Period Electrometer, and its use in Determining the Frequencies of Slow Electrical Oscillations. X, Ilustrative of Mr. G. H. Martyn’s Paper on the Discharge of Electricity from Hot Bodies. XI. Illustrative of Mr. J. Russell’s Paper on the Superposition of Mechanical Vibrations upon Magnetization, and conversely, in Iron, Steel, and Nickel. XII. Illustrative of Mr. A. Campbell’s Paper on the Measure- ment of Mutual Inductance by the Aid of a Vibration Galvanometer. XIII. Illustrative of Mr. P. V. Bevan’s Paper on Lloyd’s Fringes for Internal Reflexion. XIV. Illustrative of Prof. E. H. Barton’s Paper on the Lateral ' Vibration of Bars treated simply. XV. Illustrative of Mr. C. V. Raman’s Paper on the Curvature Method of Determining the Surface-Tension of Liquids. XVI. Illustrative of Mr. J. S. Dow’s s Paper on a Form of Cosine Flicker Photometer. XVII. Illustrative of Prof. E. Castelli’s Paper on Gradual Modifi- cation of the First Linear Spectra of mission of Mercury. INDEXED. THE LONDON, EDINBURGH, ayn DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. ara Gaia ; 3 ER a f i A, A ‘ rm \ a JUL 12 1907 [SIXTH SERI A pte pe IEEE YS A9OK, SATENT or fC I. Jonization in Solutions and Two New Types of Viscosity. By WILLIAM SUTHERLAND *. N a previous paper on “ lonization” et cet. (Phil. Mag. [6] i. p. 161) it was shown that the theory of the conductivity of electrolytic solutions is complicated by the entry of the dielectric capacity of the solvent and of the ions. In the present paper it will be shown that the subject is still further complicated by the operation of a new type of viscosity; but that when the electrical and dynamical com- plications are taken into account, there emerges an ideally simple result, namely, that the ionization of all ordinary electrolytic solutions, aqueous or other, is complete at all concentrations. Almost all the literature about the degree of ionization in solutions will need to be interpreted afresh, because this so-called degree of ionization, instead of being a fraction expressing a certain condition of chemical equi- librium between ionized and un-ionized solute, gives a physical measure of the mobility of the completely dissociated ions of the solute. The distinction is an important one for the whole theory of solutions. The present paper is a con- siderable amplification of that just cited, and will consist of the following parts about electrolytic solutions :-— 1. The transfer of energy in them when carrying electric current. * Communicated by the Author. mel. Mag. 5.0. Vol. 14. No. 79. July 1907. B 2 Mr. W. Sutherland on Ionization in Solutions 2. Two new types of viscosity of electric origin, and funda- mental for the theory of electrolytic conduction. 3. The theoretical equation for molecular specific con- ductivity. 4. Verification of the equation by represents experi- mental data for typical solutions, and proof that ionization is almost always complete at all concen- trations. 5. A special consideration of typical aqueous solutions. 6. Some exceptional cases of ionization. 7. Comparison of the equation for the coefficient of diffusion in non-electrolytic solutions with that for molecular specific conductivity in electrolytic solutions. 8. The dielectric capacity of atoms. 6. The use of molecular conductivities and diffusivities for calculating molecular and atomic sizes. ro) 10. Summary and general conclusions. 1. The Transfer of Energy in them when carrying Electric Current. In my previous paper I drew attention to the effect of dielectric capacity in determining the electric force acting upon the electric charge of an ion, but I ignored the effect of electric force on the dielectric polar ization accompanying the charge. Although the distinction between the two effects is important for electric theory, it was not carried out in such a way as to make the dynamics of ionic motion complete in my previous paper. The omission of the transfer of energy by dielectric polarization, pointed out by Larmor, will now be made good. As shown in Section 2 of the previous paper, if the intensity of electric force in a conducting solution is. dE/dx, then the force on an ionic charge e in an ion of dielectric capacity Ky, the dielectric capacity of the solvent being Ky and all the ions making up the fraction ¢/D of the whole volume of solution, is KK \ “0 e “AD Ky "1-a— Dy die oe (1) But the total force doing work on the ion must be edH/dz, the difference between which and (1) gives the force acting on the polarization in the ion and and it. Thus in the complete electric force acting on the whole ion dielectric capacity does not appear, but it does.enter into the complete expression for the resistances encountered by the ion, as will be shown in the next section. and Two New Types of Viscosity. 3 2. Two New Types of Viscosity of Electric Origin, and Fundamental for the Theory of Electrolytic Conduction. In the peenlons paper, the resistance to the motion of an ion was written down simply as that calculated by Stokes for the motion of a sphere through a viscous fluid. That expression suffices for the electrically neutral molecule diffusing in a non-electrolytic solution, But in an electro- lytic solution the electric forces acting amongst the ions introduce powertul stresses and in association with them important viscosities of an interesting type. As the solvent in ionizing the solute pulls the ions of the molecule asunder against their strong electric attraction, we must suppose that in general it keeps a positive ion as far as possible from its nearest negative neighbours. Thus the positive and the negative ions are uniformly distributed through the solvent, which preserves the average uniformity in such a way that each of 2¢ions ina volume 1 is at the centre of a domain 1/24, and the domains are arranged in regular order, those of positive and negative ions occurring alternately. In this way an ionized solution is the seat of a powerful distribution of polarity similar to that which I have taken to be the basis of rigidity (“The Hlectric Origin of Rigidity,’ Phil. Mag. [6] vu. p. 417). On the sudden application of electric force to an ionized solution the positive ions begin to move with the force and the negative against it, straining the polarization from its state of uniformity. There is an instantaneous resistance due to the rigidity of the regularly distributed ions. But the actions which produced the original uniformity tend to restore it, so that the ions move so as to relax the strain. The rate at which they yield is best specified by Maxwell’s time of relaxation (‘The Dynamical Theory of Gases,” Phil. Mag. [4] xxxv. 1868). Maxwell’s method of passing from rigidity to viscosity, founded upon conceptions of the great fe eh +67 UV” ceptert ) + O7ruyna,/(1 + ¢/a,), | Cc { / —L ‘ —vyed B/dx = —vy7y7F (uy — Us) {in(ny + Ng) $F + Orr ugye” Gade | + 6m uoHdy/(1 + ¢/a9"). An additional factor v, or v, goes with € because the viscous effect on ve is v times that on é. Now the electric current across each cm.? section of the solution is etn(nyvyuy—NgVetz)/h, and to express this more compactly let us put in (5) A=A/n and 1/Ay = Graygl{C'v22/4a Kal +1/( e/a) /en, (8) OH 8 Mr. W. Sutherland on Jonization in Solutions with a similar meaning for A,. Then EU (2440 — NgVgQUy)/h di 24V1A4 + NgVolhs 9 da 14 2r(A, + Ag)Cryvefin(ny+ne)/h}3/3BKTA, ~ e) In the majority of experimental cases = in Vo Ve = Wee and the coefficient of nn,dE/d« is the molecular specific con-. ductivity in electrostatic units in which e is measured (Ay + Ad) X= a 1+ Qe (Ay As) Cry, an (y+ Ny) / hte 2/3K IN) (10). At infinite dilution n=0 and 7 becomes 7, the viscosity of the pure solvent, 2 is assumed to become 1, and 2 has the value Ag = Aoi t Ags © | sey! et oie ate (11). where 1 / qo Ag = Ora hi Cv Pe /Aa Kya lA +1/14+ c/ay?)tey. (12) Thus (11) expresses Kohlrausch’s principle that the limiting conductivity is the sum of two independent ionic conductivities. usually called ionic velocities. Noticing that A, depends upon 7 and upon quantities independent of concentration, we: write ie ss 2 Nonny 1+ 2ar( Ay + Ag) Cryry,{ in (x my + 9)/ Ne / SK ING: (13), 4. Verification of the Equation by Representative Lxperimental Data for Typical Solutions, and Proof that Ionization is Almost Always Complete at all Concentrations. Years ago Kohlrausch discovered that for dilute aqueous solutions /Ay is linear in ns, as (13) shows it must be when 2=1 in Ay and nis small. Since then he has neglected this. clue in pursuit of empirical expressions for 2 which might express chemical equilibrium between ionized solute and that not ionized. That in dilute solutions A is linear in m3 has been shown by the recent measurements of Noyes & Coolidge (Journ. Amer. Chem. Soc. xxvi. 1904) for aqueous solutions. of NaCl and KCl at temperatures up to 306° C. It appears from (13) that what has been called the degree of ionization of a dilute solution 2 measured by A/Ao or and Two New Types of Viscosity. Y) An/AyM may be only a fraction expressing the dependence of molecular conductivity upon viscosity of electric origin, standing in fact for 1 —2r( A, + Ag) Cryve{n(iy + rg) /h 15 3KTAg, while z itself is really 1. It will now be shown that this is the case. The most satisfactory verification of (9) is to be obtained by applying it to electrolytic solutions in general. After a number of American investigators had opened up the important experimental field of solutions other than aqueous, Walden brought out his comprehensive researches on organic ionizing solvents and certain inductive conclusions drawn from them (Zeitsch. f. phys. Chem. liv. 1906, p. 129). He investigated electroly tic solutions of tetra- ethyl- ammonium iodide N(C.H, ),I in 49 organic solvents of 14 chemical types. From this wealth of dita he made the discovery that those solvents whose solutions of N(C,H;),I have a given value of 7 (that is, of /Ao) exhibit the following principle, namely that K/nz is constant. In general his solutions were so dilute that y= and A,+A,=Ay. For example, with nitromethane bes for which K=40, the value of 7 is 0°66 when n=1/28000, and for ethyl Alcohol with K=21-7 the value of 7 is 0°66 when n=1/256000. For these two substances K/ns has the values 1220 and 1390. Altogether Walden gives 27 instances illustrating the correctness of his induction. But the right interpretation of Walden’s discovery is con- tained in (13), which shows that the true degree of ionization must be taken to be complete, that is7=1, and that the usual so-called degree of ionization 7 given by An/Agy will be the same for a given solute in different solvents if n is chosen so as to make K /ni the same for all the solvents. The law of Walden verifies (13) in a comprehensive manner. But his data carry the confirmation farther. We can write it in abbreviated form N/A = 1fi = 1+n'G/K, Md pied bee (14) where G is a constant for a given solute. That is to say, for a given solvent ),/A or 1/2 is to be linear in ns. This for any dilute solution is a more rigorous form of the law discovered by Kohlrausch for dilute aqueous solutions. It holds so long as 7 for the solutions can be identified with that for the solvent. or concentrations too strong to admit of this sim- plification, the measured values of 7 “must be used in (13). To verify (14) two illustrative cases will be taken from 10 Mr. W. Sutherland on Jonization in Solutions Walden’s data. For N(C,H;),I in acetic anhydride he esti- mates, by empirical and graphic methods, the value of A, at 25° to be 74°5 with which he calculates ne from his experi- mental values of 2 at the different dilutions given below. I find that his values of X/A can be repr esented “by Ag/A=0°908 + 34:3n5 as is shown by the comparison : WO 2700. areas 1 2 + 8 16 32 TOOOWN Nvexuniee: 594 . 669 733 788 832 864 7 Galena 607 669 728 782 832 879 The differences are within the range of experimental error shown in Walden’s measurements. It is to be noted that the 0°908 of our formula ought to be 1:0. ‘This shows that Walden’s empirical and graphical estimate of A, is about 10 per cent. too small. It ought to huve been 82 instead of 74:5. The theoretical equations (13) and (14) enable A, to be found from measured values of A. With A»=S82 the formula for these experiments becomes A/Ap=1+37°8n5. In our second example relating to N(C,H;),I dissolved in ethyl alcohol, we shall go direct to the experimental data of Walden and deduce both A» and the coefficient of ns-im (14). Thus I find A,=81-9 instead of 60 as given by Walden, and then A,/¥=1+ 73ns with the following comparison : NV MOZ a) sean 30) 64 128 256 512 1024 2048 Ns OXDs egos 24°49 28°87 34:08 38°90 43°18 46°60 49:05 Neale. ...... 24°49 29°88 33°48 38:15 42°86 47:94 52°04 The agreement is again within the limits of experimental error shown in Walden’s data. The next verification of the theory is contained in the instalment of his work which Walden has devoted to the connexion between Ay and 7, (Zeitsch. f. phys. Chem. lv. 1906, p. 207). Kor eon of N(C,H;),f in 29 organic solvents he finds that at 25° Ayy, ranges from 0-595 to 0°860, with a mean value 0:70, ee: mj, ranges from 0°00316 for Aeon to 0°08 for benzoyl- acetic. ethylester. rlycol gives a value 1°32 and water a value 1:00. According to (8) and (11), for a given solute in different solvents X97 ought to be constant. For Walden’s 29 solvents the average departure of Aon, from 0-700 is 0°037. The general ve erification of the constancy of AyM) required by (11) is fairly satisfactory. But we have seen that Walden’s values of Ay are liable to considerable error through being estimated graphically and by an empirical formula. So | have used his experimental data to find the and Two New Types of Viscosity. if mean values which they give for A, and the coefficient G/K n (14). The results are collected in the following table, in shih A denotes the molecular specific conductivity of N(C,H;),I in the solvent named, while 7, and K denote the viscosity and dielectric capacity for the solvent taken from the data collected and determined by Walden. added containing the products \oy, and K(G/K). Tassie I. Solutions of N(C,H;),I at 25° Columns are | Solvent. [Methyl alcohol .............s0-++-. ‘Kthyl ay ee -ethyl sulphite (symmetric) (asymmetric)... ie -methyl sulphate faeneueacsees Di-ethyl PARNER lou. needaaas TRIO IMAC. oe. oe sa cecee sean ess PMebOMMEN Cl sc cese.cccunais--ec++0s: weropionitrile ........ pegadoneoosee ‘Benzyl CYMUIGE! eenkes shisasescn ds Gerkycollonitrile -22 02.0. 6ee60-+-e 204: PETE LOviNeMe 57, J. ac) le neve s+ 5 (Methyl thiocyanate ................: K Ethyl Pee teat Mesa settee Ethyl isothiocyanate. .............- | Mbeomeb ame 6.02 ..csccteeeecs eet PINTUFODENZENE), \26occ0- 2: aoe evens on Nitrosodimethylin (CH,),NNO ..., BANG LOINC iy Stale atc ein ara ne sw a scien NEEIVIACEHOMNEN 6.42. aassaeetesacene 6 yen GIST ao aee Noy. eee es Mean (excluding Glycol) ..... | ee ay S77 GSI > eae eee ee 22 LE eee eee MpeMiaaMenye 62o...cec.c-se-cceeee sairealdehigde .,./....s ye" K,/6mnay Ky e ; e 0 2 (29) This is erroneous through omission of the effect of the dielectric polarization accompanying the ion. Yet it leads to values of K, the dielectric capacity of the ionic atom which are of the right relative magnitude for many atoms. In the form K, = 2807,/A,;By2 . ° Sh ts e (30) it was used in “The Dielectric Capacity of Atoms” (Phil. Mag. [6] vi. p. 402 ; Austr. Assoc. Adv. Sci. 1904) for the calculation of K, fon many atoms, and these values have been used in “The Molecular Constitution of Aqueous Solutions ” (loc. cit.), and in “The Nature of Chemical and Electrical Stimulation” (Amer. Journ. of Physiology, xvii. p- 266). But now in place of (29) we have from (8), AG = Grrmyayh§ C'vPe?/4ar Kya lA + 1/1 + e/ay”)} Je’. (31) It is important to see clearly how these apparently incon- sistent relations are really consistent. ‘This comes to pass through two remarkable relations. When giving values of K,, I pointed out that K,’B,/v? is approximately constant, suggesting in “The Hlectric Origin of Rigidity and Con- sequences ” (loc. cit.) how this might have a very fundamental slenificance in the theory of matter. Using this in (31) we see that the term in y,/K,a,’° can be sanilien as a term in KX,/v;. We shall see that for ordinary atomic ions, especially the small ones, this is the larger of the two terms. If we were to neglect the other term, we should have 1/A ; proportional to Kya,/r4 as in (30). Baik Boe lw ge ions the first term in (31) is made small by 1/a,*, and in the limit that equation reduces to WAg =Omnaiheyi, - - sy ee) depending only on ordinary viscosity, the induced viscosity and Two New Types of Viscosity. : 29 disappearing. Hence for large ions we have 1/A , propor--. tional to a,, andor small ones to Ky,a,. But for the large compound radical ions K, falls to a nearly constant value averaged from those of the component atoms, so that at both limits we may say 1/A,; is proportional to a,. If the con-. stants of proportionality are suitably related, we can include both limits approximately in the one formula, making 1/A), proportional to K,a,/y,. As this is approximately true in the limits, it has a good chance of being approximately true in general. In this way we come back to (30) as an empirically convenient simplification of (381). The proof from experience. that this is so was given in my previous paper on Ionization, where it was shown that this formula (30) avplies to the. fatty acid ions from HCOO to C;H,,COO as well as to atomic ions. ‘I'his relation has since been investigated by Carse and Laby (‘ Nature,’ Ixxv. 1906, p. 189), who find Ape, sensibly constant for the ions of 22 amines with a mean value 20-2. For 7 anilines the mean value is 18:8, for 13 pyridines and quinolines 20°3, and for 5 phosphines 17:6. These results confirm the conclusion that with an appropriate value of K, treated as an approximate constant for large ions (30) becomes a useful formula for obtaining the size of large ions whose molecular mass cannot be measured by the usual methods. I have applied it to Hardy’s ionic velocity of globulin (loc. cit.), obtaining a result in reasonable agreement with that obtained by (28) when applied to the diffusion coefficient of egg-albumin (Phil. Mag. [6] ix. p. 781). For small ions of measured Ao;, (30) becomes a means of finding K, the effective dielectric capacity in electric fields which change with a frequency small compared with that of light. For changes of the frequency of light we have Maxwell’s relation K=N?, where N is the index of refraction of the stuff of the atom. For most ordinary ions I have shown that K, from (30) and N’ from refraction equivalents show a fair general agreement, but that the halogen ions are quite exceptional, K, varying inversely as N*. This exceptional behaviour of the halogens I attribute to the large amount of latent valency in their atoms. We shall now consider (31) in detail. The main problem is to determine from the experimental results the relative magnitude of the two terms on the right-hand side, that is to determine C’. Now we shall see that for small ions the first — term becomes large compared to the second. In the first mo/A stands for 1/A9, and approximately for 1/2Ao,, so that for these ions (31) reduces almost to the identity 1/Ap,=1/Ao; and becomes unsuitable for giving reliable values of Ag. ‘30 Mr. W. Sutherland on Jonization in Solutions But my previous paper gave the approximate result that 1/Ao, varies as 4 K,/y,, so 1/A varies as a,K,/v,, and if we use this approximation in the right-hand side of (31), it becomes, on determination of the constants from the data in the next table, the manageable equation 1 _ 00365 | _0-0022 BA, Bi — v(1+e'/B*) ’ (33) in which ¢/ is a constant and B® stands for a. In my paper on Diffusion the value of ¢’ was found to be 220/21=10°5. In the following table the values of Ay calculated by (33) are compared with the experimental. The values of B are taken from my previous papers. ine Nae K boi (Csige Miss ie as Sr. Ba 1 BSG! 2 CE IS:6 7) 7344 V.56 56 86 10:6 “TGs BAN EXD). ae 395 444 653 673 678 48 53) 54 573 A, calc... 841° ° 503 618 676 693 47:3 543 oi oee Lite Cd Ae, 2 (ek: F. Cl. - Jar: L. DE a 106 125 68 9°8 3) 19 26 36 INT MOK WG: cissee Ae O2) a Oui eno T 46°L 365°9" iGo bout A cale: .0.\ Ono | 09:0 . 49°2,\ 56:2 53:0) (62:2 iGo oaies) This table shows that (33) gives the general connexion between the volume of an ion and its ionic conductivity, but not the details of the relation. The details cannot be given by any formula which makes A a function of B and vy only, because, for example, Na and Ag have nearly the same B and yet Ajp=44'4 and 55:7, and again, Sr and Zn with the same B give Aj>=54 and 47°5. But it must be remembered that we are dealing with a formula which expresses the effects of two distinct viscous resistances. In the case of [a the term in (33) arising from induced viscosity is nearly 80 times that arising from ordinary viscosity, while in that of Cs the first is only double the second. It is rather remark- able that the ionic conductivity of Li comes out only about half of that for Cs. Probably we are not entitled to super- pose the ordinary viscous resistance on that of the induced viscous resistance of electrical origin in (8a) as if they did not affect one another. Probably the latter makes the conditions different for the former, altering the slipping and otherwise interfering with the motion caused by ordinary viscous resistance. Probably (8 a) and the equations derived from them need to be completed by repeating the calculation of Stokes with express provision for three sorts of viscosity and Two New Types of Viscosity. dL In simultaneous operation. If we turn to the experimental data for the ions of the fatty acids, we find evidence of a mutual influence between the ordinary viscous resistance. and the induced. In the case of a compound radical the ionic charge is probably lodged in one atom and produces its most important inductive effects in the other atoms of the jon, so that these effects are carried with the ion. Only a residual inductive electrical effect reaches the solvent, so that the induced viscosity of coefficient @ may be expected to be smaller than for a single atomic ion of the same volume as the ionic radical. Moreover, the induced viscosity will interfere less with the ordinary in such a case and at all events as B becomes large for a compound radical ion, the — induced viscous resistance becomes small compared with the ordinary. From the data in the next table we can find the constants in (33), so that for the fatty acid ions 1) 0:0365 0-0097 Bota B (1+ 10°5/B*) ’ whence the calculated values of A, in the table are obtained. (34) alto HCOO. CH,COO. C,H,COO. C,H,COO. C,H,COO. C,;H,,COO. ee 24°5 42 59°5 5) hd 94-5 5 112 A, exp. ... 47:2 35°4 318 28°3 26°5 Dao A, eale. ... 39°9 30°1 ‘3 ir) 28°4 26°8 25°1 Except for the formic ion the agreement is very close. Here again we have obtained 1/A) as the sum of two resist- ances, neither of which is proportional simply to B®, although their sum is so proportional, as the following products AjB* show :—137, 123, 124, 120, 120, and 122. It is to be noticed that for these compound ions the induced viscosity term is identical with that for the atomic ions, although I had expected it to be less because of the inductive effect being mostly operative inside the compound ion. But, on the other hand, the term from ordinary viscous resistance has a coefficient which is 4-41 times as large as that for the atomic ion. Here we have the effect of ordinary viscous resistance apparently much less interfered with than in the case of the atomic ions. The outcome of this inquiry then is to show that, when the induced viscous resistance and the slipping associated with ordinary viscous resistance are taken into account, they yield a sum which varies as B*, as though it were derived from a single ordinary viscosity free from the complication of slipping. Moreover, the case of atomic ions and that of compound ions can be united in the one By Mr. W. Sutherland on Jonization in Solutions approximate formula (30), which can be used for finding the dielectric capacity of atoms of known ionic conductivity and volume. J.J. Thomson and Nernst have suggested that ionization is caused by large dielectric capacity of the solvent. This means, of course, large in relation to the mean dielectric capacity of the solute. Many authors have sought to show that the degree of ionization in different solvents is propor- tional to their dielectric capacity. But as we have proved ionization to be almost always complete, this attempt to give greater definiteness to the suggestion of Thomson and Nernst falls to the ground. Large dielectric capacity in the solvent facilitates ionization by reducing the electric forces between the ions, by reducing their mutual potential electric energy. By the samme action it causes the ions to space themselves approximately uniformly, and with each ion as far from its neighbouring oppositely charged ions as is consistent with uniform distribution. In my previous paper I suggested that large dielectric capacity and ionization are both con- nected with the electric doublets of latent valency in certain atoms. A general theory of dielectric capacity both normal and exceptional is much needed in the present state of molecular physics. 9. The Use of Molecular Conductivities and Diffusivities jor Calculating Molecular and Atomic Sizes. In my previous paper it was shown that ionic sizes can be calculated from ionic velocities, but, the theory of that paper being incomplete, the ionic size calculated came out approxi- mately correct only by a certain compensation of errors. But with the more accurate evaluation of atomic sizes by the kinetic theory of gases, carried out by Jeans (Phil. Mag. [6] vill. p. 700), with the aid of the magnitude of the electron charge obtained by J. J. Thomson and his pupils, it is possible to apply a fairly stringent test to the theory of the present paper by using it in the calculation of atomic sizes. The evaluations of Jeans could be improved by taking account of the effect of cohesioval forces on the viscosity of gases. Butfor present purposes his results suffice. He finds the radius of the hydrogen molecule to be 1x 10-' cm. We shall now calculate the radius of the hydrogen molecule in the two following ways:—First from ionic conductivities. Here we shall find first the radius of the largest fatty acid ion in the last table by comparing (31) and (84). This ion is selected because we have seen that it belongs to a group where the induced viscosity seems not to interfere seriously and Two New Types of Viscosity. | 33 with the effect of ordinary viscosity. or it the resistance due to induced viscosity in (384) is only one-fifth of the whole resistance. From (34) and (31) we get that 62nah/e’v in electrostatic units is the same quantity as 0:0097B* in ohm-}, which becomes 0:0097B2/9 x 10" in electrostatic units ; hence we have the equation 9 x 104 x 6rnah/e’v =0-0097B", with h/e=0-0001035/3x 10, e=3x 10-%, v=1, 76=0-0106, <6 a, the radius of C;H,,COO, is 2°26x10-§ cm. Now B, the limiting velume of a gram-molecule of hydrogen, is 8°6, so for the radius of the hydrogen molecule we wet the value (8°6/112)? x 2°26 x 10-$=0-96 x 10-8, which is practically identical with that obtained from the kinetic theory of ases. With the coefficient of diffusion we shall proceed in a similar manner, that is we shall first find the radius of a molecule of about the size of C;H,,COO, say that of glucose CgH120,. For this the value of B used in my paper on diffusion is 134, which is perhaps 10 per cent. too large for the gram-molecular volume of glucose in the solid state, but such an error affects only minutely the ultimate estimate of the radius of the hydrogen molecule. From (27) and (28) RTA(1+ 10: 5/Be ) Oana Now at 0° C. RT for 2 grams of hydrogen is 226 x 10%, and so at 16° C, the temperature of the diffusion experiments of Thovert, cee 7359 * 10", h=ch/e=0-0001055 x 10-, and »#=0-0111, and so a the radius of a molecule of glucose is 3:14 x 10-° cm., and the radius of the hydrogen molecule is (8°6/134)3 x 3:14 x 10-8119 x 10-8. The agreement of these two new estimates of molecular size with that from the kinetic theory of gases is as satisfactory as could. be expected. It shows that there is no need to adopt the hypothesis of Kohlrausch and other writers that different ions attach to themselves different envelopes of solvent in such solvents as water. It has been proved that the ion in electric conduction and the molecule in diffusion move independently. Phil. Mag. 8. 6. Vol. 14. No. 79. July 1907. iD 1) 34. Mr. W. Sutherland on Jonization in Solutions. 10. Summary and General Conclusions. The ionization of all ordinary solutions at all strengths is complete. This is proved by showing ‘that the fraction currently called the degree of ionization really originates in a resistance which the ions offer to one another’s motion because of their forming with the solvent through their electric action on one another a medium which offers a special viscous resistance to the motion of each individual ion. This is one new type of viscosity of electric origin. But the charge of each ion causes electric induction through the surrounding solution, and with this is associated a second new type of viscosity also of electric origin. These with the ordinary viscosity cf the solution give three resistances to the motion of anion. When the sum of these is equated to the electric driving force, the formula (10) is obtained for the molecular specific conductivity. This formula is tested by comparison with experimental results of very wide range, especially those of Walden for non-aqueous solutions, those of Kohlrausch for aqueous at ordinary temperatures, and those of Noyes and Coolidge for aqueous at high tempera- tures. Incidentally some insight has been obtained into the properties of the effective force which keeps a solute com- pletely ionized (Section 5). It is shown that the dynamical theory already given for diffusion of non-electrolytes joins on consistently with that developed here for conduction, if the same empirical allowance for slipping is made in each. The equations for conduction and diffusion lead to values of the radius of the hydrogen molecule in good agreement with that yielded by the kinetic theory of gases, namely 1x10-%cm. There is no need to imagine each conducting ion or diffusing molecule surrounded by an ‘atmosphere ”’ of solvent. The formule for conduction and diffusion, enabling the radii of ions and molecules to be found, become means of determining large molecular masses for which the usual methods fail, as I have elsewhere shown in the cases of egg-albumin and globulin. The current theory of solutions will need to be entirely re-written. The idea of partial ionization, while it can give a formal qualitative account of the chief phenomena of solutions, being dynamically wrong, cannot furnish a correct quantitative correlation’ of their properties. The theories of the raising of the boiling-point and the lowering of the freezing-point of solutions will have to be put upon a sound molecular dynamical basis. With the knowledge that ionization is complete, the neglected theory of the energetics of solutions will become much more Effect of Rotatory Inertia on the Vibrations of Bars. 35 simple to attack. Physiological chemistry, which ultimately concerns itself mostly with complex solutions, will also be considerably simplified. It is interesting to find the attempt, which I made to give a dynamical account of conductivity in metals through a theory of their rigidity, supplemented by a theory of electrolytic conduction in which temporary rigidity and its associated viscosity play a fundamental part. I have sought to show also that nerve impulse is propagated by rigidity of electric origin, and that the luminiferous ether, if it contains electric doublets, must have a rigidity and a density so related as to give the velocity of light through it. Tf ever viscosity is discovered in the eether, it will ke of similar origin to that of the two types discussed here. The ions of a solution give just such a distribution of polarity as I have assumed to be at the basis of all rigidity. Hence the deduction of the two new types of viscosity in electrolytic solutions is a sort of confirmation of the electric origin of all rigidity. A solution is in many respects a perfect model of a polar medium interpenetrating another. | Melbourne, April 1907. *% % Il. The Effect of Rotatory Inertia on the Vibrations of Bars. - By J. H.C. Starts, B.Se.* I. BT is well known that the rotatory inertia of a rod modifies the notes emitted when transverse vibra- tions are excited. The matter is referred to by Lord Rayleigh in his ‘ Theory of Sound,’ and the correction calculated for a special case by the method of assuming normal functions of unchanged type. I have not been able, however, to find any complete treatment of the subject in the usual biblio- graphical authorities ; and it seemed worth while deducing the exact and special formule for the several cases, as well as discussing the chief properties of the new normal functions. If it be suggested that the work will not repay the labour involved as there are other corrections arising from the dis- tortion and change of size of the cross-sections which are of the same order, z. e. (width of bar/length of bar)?, the answer must be that this is fully admitted. But all such corrections are to a first order additive, and they can thus bs inde- pendently found and allowed for. I shall hope to return to the subject of what may be termed the elastic theory cor- rections on another occasion. The present paper attempts to deal fairly completely with the rotatory inertia terms and * Communicated by Prof. Kar] Pearson, F.R.S. D2 36 Mr. J. H. C. Searle on the Hifect of the corresponding normal functions for the various cases which may arise. The complexity introduced into the normal functions is not very great, and it is some mental satisfaction to see how the correction suggested by the use of unmodified normal functions actually arises as an approximation to the accurate equations. The sequence of my paper will be (1) to obtain full equations for the notes in the six possible combinations of terminal conditions, (2) to solve these nume- rically and table the values of the fundamental note and the overtones. Lastly (3) I shall discuss the form of the suitable normal functions in these cases, and the fundamental integral en which not only solutions in these functions depend, but which determines also the influence of a generalized force of corresponding type on the vibrations of the bar. (I. 1. Equation of Motion. Let OQ be a straight bar of uniform cross-section and material. Let 1 = length of bar. v = displacement transversely of an element distant v from O. m = mass per unit length of bar. A = area of cross-section. kK = swing radius of cross-section about a line through centroid perpendicular to plane of bending. E = Young’s Modulus for the material of the bar. S = shear across bar M = bending moment $ Y = transverse body force. at any point. Then Pas E; my SL) ere and dv aM 2 oak inated ) MK Pip area wee ‘oi ale ae) where ne (3 7 7, oP ) Rotatory Inertia on the Vibrations of Bars. 3 Also pagel”. | MEE a hc «sen d?v 4) +BAeS 4 — MK 2 d*v me dap t™Y 8) The first term in the ee member represents the rotatory inertia, and is usually disregarded. 2. Normal Functions. In the last equation take Y=O and put v=> f,(2)(A, sin pi+ Bi cos pt). . . . (6) Thus, on pnene terms of type p, NYO ae — HA | OF ma Kp ae The, or, putting b= KE and mK"p? 94 I Pee nae a) KA J Gy ye Eh k ie Res oe The solution of this equation is fo=dp cos WE + dy’ sin W\E+dp" cosh yoE+dp'" sinh y2£, (A) where y, and y, are given by the roots of yt tAty? —A*=0. en We Ne fala MEAN ENT ey ee 9) 3. Terminal Conditions. The end of the rod may be clamped, supported, or free; and these conditions determine the ratio of any three of the constants d in (A) to the fourth. ; dv (i.) At a clamped end v and dag are always zero. a dA : ot) eae. a) dx 38 Mr. J. H. C. Searle on the. Effect of Gi.) At a pivoted (supported) end v=0 and M=0. 2 6 f,=0 and (4; afe ==(). . ee (iii.) Ata free end M=0 and S=0. dv av ov 3) & (4 (ehh) ware == Agee ( ) ( ) a dadt? due? Thus, remembering 7=«€, ae Ufo a) | age? 5) | sd (12) antl a fp _ 25 dé The latter equation contains the small term ee alo due to. the rotatory inertia. dé Six combinations present themselves :— (a) Clamped-free, _ (L) Clamped-clamped, (c) Free-free, (4) Pivoted-clamped, (e) Pivoted-free, (f) Pivoted-pivoted. III. 1. Clamped-free Bar. We have, dropping suffixes, f=d cos y,£+d' sin 71€+d” cosh y.€+d' sinh yg. . (13) Taking origin at clamped end, jamboree 0. d=—d". a =(0 when €=0. md=t+yd". f=d(cos yyE—cosh yo2&) +d (sin y,é— 7 sink yt) At the free end, d*f SD ay when &= = say, Rotatory Inertia on the Vibrations of Bars. a9 d{—y1’ cos y,l’ — y," cosh yl"? +d" —y? sin ¥;l/— yo sinh yol’t =0. (14) aa ue aj a= 0 when €=(/’; d{(—A*y, + y:°) sin yl’ + (— y24— y,°) sinh y2//} +d'{(Aty1— y1°) cos yl! + (— y1A4 — yy) cosh Fol O05 GiD) In virtue of relations (9), (14) and (15) become re- spectively : . a — cos y,l/ — i cosh yo! \ +d’ { —sin y,l/— ! 2 sinh vol! } =U, ay sin y,l/— a sinh y2l’ \ +a’! —cos y,l/— . cosh y,!’ ; == (i Hliminating d and d’ between ee we have Ba Y Bi ma if as Or, again using (9), 2+ (2+A4) cos y,l’ cosh yol’ — 20? sin yl’ sinh yol’=0. . (B) On neglecting X’ and putting y;=y.=A, there results cos Al’ cosh Al’ +1=0. The ordinary equation obtained by neglecting the rotatory inertia first given by Euler * cos Y,!’ cosh -+y2l’— sin y,/’ sinh yod'=0. 2. Correction for Rotatory inontia in a Clamped-free Bar, To obtain the roots of (B) we proceed as follows :— By (9) we have y= B/S FEN AN, 2=4[)/ 0 +IN—y]. Expanding these and es all terms of order }°, 7 Pues (0) X itself is a small quantity but Ke aoe small * 1740 circa. 40 Mr. J. H. C. Searle on the Effect of Put, therefore, ) 2 =, Hence, on substituting the values (16) in (B) and neglecting terms of order A‘, we have 4 ? Ne 5 ' 2+2 cos n( 1+ *, )eosh n (i- 5)-™ sin vn. sinh n=(, - - } 2 _.. 2+2%cos ncosh n—2n% (cos 2 sinh n+sin 2 cosh n) —}’%sinn sinhn=0, Now take N= hy + Bye deca sw ea where 7p satisfies , cosn, cosh ng 1=0,.--. 4) st. ES) and 7 is small. “. 24+2(cos my—7 sin no) (cosh n+ 7 sinh 79) : mtg Me : —2n(sin no cosh ng —Cos ny sinh no) — 27% re (cos mp sinh 70 —+sin np cosh mo) —X’ sin ny sinh ny» =0. oe susimen (als) e e . m4 e e Nod2 } COS No sinh 7) + sin m cosh m+ 7, Sint Mo sinh 4 0 S1N Ng Cosh M9 — COS Mg inh ny n= 4 2 nr2 § tan m+ tanh r+ — tan, tanhn eOlenk No Y 8 ue ee tan 2)— tanh no By (18) cosh Np= —SeC No. «. sinh m9= +tan m, according as mp lies in the 3rd or 2nd quadrar 2.) tambien = 1 sim 724: Be a ms 2nd or 3rd I Thus, n 9 K- 7 n — (@) “ Oy G a ra) UE ek A) {cot sain ot 4 Ie ae aa hee a i 2 Ke n 2 n a. Olly ae | tan ~° — —tan "o | ; 4. E \ ? No D) according as s is even or odd where m) approximates to Rotatory Inertia on the Vibrations of Bars. Al (2s +1) Hence a oy | nN, n=mo| 1— 5 5 ” ny Cot +2 | ng cot” . dake f a) or aft 1 _ | Mo tan —2} nytan 4 If pp=period when rotatory inertia is rejected, = eae. = 3 retained, oe ae) (19) ‘a 1 “h No — nC +2 ae | i Ke i ° (20) or 1+ — aes No tan = P= 2 bm tan 70 When the order of the tone is inoderate cot a becomes od closely =1 and tan a — 1p In this case, p liek? igs eae: Giga: 2)vig,esensibly, he) (21) Lord Rayleigh *, by considering the addition to the kinetic energy when rotatory inertia is retained and using the value ot the normal function and its derivatives (rotatory i inertia being neglected) integrated over the length of the rod, has deduced a formula (), § 186] which becomes identical with (20) when the ratio pee is replaced by its equivalent in terms of half-angles. te It will be seen that the effect due to rotatory inertia increases with the order of the tone and is smallest in the fundamentai. For this tone Strehlke t gives No = 1 Slo 104. = 107.26) 77-96, From this we find for the gravest Sie De Pom 1 + 2°323889 gee (22) * Rayleigh, ‘Theory of Sound,’ vol. 1. § 186. + Strehlke, Poge. Ann. Bd. xxvii. p. 505 (1833). 42 _. Mr, J. H.C. Searle on the Luffectiof For the same tone Rayleigh gives pi po=1+2°3241 5. His value, however, would become identical with the above had he taken the correct value of «, viz., #=17° 26’ 8”, instead of a=17° 26’ as used by him. IV. 1. Clamped-clamped Bar. f=d cosyétd' siny,E+d” cosh y&+a”™ sinh y2€. Origin at either end. ia ae when €=0 0) d+d"=0, and yd’ + 9.d” —0- “. f=d(cos y,&— cosh yok) +d’ (sin yie— vsinh ee). (23) Also ie dy 0 : when §= i = kK dé 0=d(cos yl! —cosh yo’) + d (sin yl — 4 sinh y!') 2) ae (24) and 0=d(—y sin yal/—yz sinh yol’) + d'(y1 cos Yul’ — yx cosh yal’) ~ ., Eliminating d and ad’, 1—cos y,l' cosh yol’— oe sin yl’ sinh y,l’=0; ea alla Or, using relations (9) Es : 1—cos y,/' cosh y2l/— 3 sin y;U' sinh yo! =O2tee) Neglecting 0’ and writing y,;=y2.=A, we have 1— cos Al’ cosh Al’ = 0), the ordinary equation when rotatory inertia is neglected. (23) in virtue of (24) now becomes f= DI (cos yy£—cosh y2€) (y2 sin yl! —y, sinh yol!) — (y3 sin 4% —y1 sinh yE) (cos y,l"—cosh yal’) |. . (D) Rotatory Inertia on the Vibrations of Bars. — 43 2. Correction for Rotatory Inertia in a Clamped-clamped'Bar. Substituting in (C), { ae > es m=r| b+ al: y=r| 1 | i ; and calling, as before, X— =Al’=n, we have K 1l—cosn (14 ‘r)eosh n(1— ) — sin n sinhn=0. a Wee ae des ; ~. L—2 cosn—n— sinn i cosh n—n— sinh ae Sala SETI Simin 7s 4 t 4 he 2 M : ; Se atone 1—cosncoshn+n 7 (cos n sinh n+ sin n cosh x) — >-sin n sinhn=0. Put N=No+yY, where 7, is now a root of COSe ACOs ale yale nasa eaann (a) and 7 is small. *, 1—(cos r9>—7 sin Ng)(cosh rg +7 sinh nj) Nn ain 2 (0) 2 2. / = le e a5 a A’(COS Np Sinh 7g + SiN Np Cosh ny) — y S10 No sinh ny =0. Therefore, remembering 1—cos np cosh np=0, (08 Ny sinh m)—sin 7 cosh 79) Ln ne cate saa | ree. ; = YN (COS Np Slah N+ S81N %p COSN 79) — 3g Sin Ng sinh ny =0. : No xo | COS Np Sinh np + sin 79 COSA 2%) — > sin 1% sinh 1, ee i] = xX 9) . COS N sinh rg—sin Ng Cosh ng 4 2 Be on tan m+ tanh ng— ee No tanh ny tan my—tanh n or, transforming by means of (25), oe nN K n Z Ty) a 9 2 19 “0 = 0 V—— Nyiaa 4 COL 2 == COb — | TR OIE ch OS i or n Ke n 2? Ny 0 2 ~ Sites te Ss ae 4 | 2 No 23 according as 7 lies in the Ist or 4th quadrant. 44 - Mr. J. H. C. Searle on the Effect of r 2 Thus = E = - = ' No cot oi —2 \ No cot % | ’ -2 ns —= Np [1— : = No tan = 2 : No ian 29 | : In this case, Poi pHn sn? =(m+n>) : we ; K2 [O° 8 hip llap = 24% cot 5 cot — 2h ng cot 5, ao (26) a she's Le eee ie or — wien aa a according as m lies in the first or fourth quadrant. When the order of the tone is moderate the ratio becomes pi po=l— 5 (= 2 hor 04. eens Vas eee For the first root of nee Strehlke gives Ng = 4°7300408, = 2 3650204, "21352 30) 20 27 tan“ —=— “JoZ400g 5 ny tan > = —4°6471132 ; 3 p:po=1+6 15131115 for the fundamental of a clamped-clamped bar. V. 1. Free-free Bar. f=dcosyé+d' sin y,£+d” cosh y&+ a” sinh yé. Origin at either end. Hence, from (12), igo ; when €=0. and 4 df fi df ay - dy = d''y,’, and d'(Aty,;—913) ta” (My2 +928) =0. Rotatory Inertia on the Vibrations of Bars. — 45 By means of (9) the latter equation reduces to Yoel! = yd!" Thus fad(oos y+ 7, cosh yn6) +d! (sin E+ sinh 996). (28) Again, Gy OL iO) dé ee l Ly aren id ne, > Walle ra = en ° de" Ge = i 3 “.d(—cosy,l' + coshy,l!) + d!(— siny,l’ + i sinh yol’)=0 | 1 and 209) y? [(29) d(—sin y,l!— a sinh yl!) + d'(cos y,l’—cosh yl’) =0 J Thus, eliminating d and d’, Os 6 ‘ , 1— cos y/' cosh yol' + a ’ zie sin y,/’ sinh y,/’=0, 2y1°Y2 Hquations (9) make pars ie = 1 4 Saag ite) Pelee 5) vo ae. (OO) 2 2 “. L— cos yy’ cosh yol! + * (3 +24) sin y,/’ sinh y,/’=0 (EK) is the period equation for a free-free bar. Using (29) in (28) we find f= DI (y2" cos mE +," cosh y&) (qr? sin yl! — 9? sinh yal’) —yPy2? (yy sin WE + ye sinh y2&) (cos yl/— cosh yql')]. (F) 2. Correction for Rotatory Inertia in a Free-free Bar. The period equation omitting \* and substituting = TS 2) m=A1 +70") es 1)2 y2=AC1— 7A’) becomes cos n(1+ +4”) cosh n(1—2A?) —1— 3)? sin n sinh n=0. ee cos n cosh n— 4 (sin n cosh n+ cos n sinh n) —1—3$)’sin n sinhn= 0, l where n=N—. K 46 Mr. J. H. C. Searle on the Effect of *, Putting n=n0+y7, where 'm, is a root of cos ”pcoshn,=1, 2 am and 7 is small, *. COS (M9 +7) cosh (2 + 9) — _ (sin 2, cosh 2, + Cos Np sinh no) —1—3) sin n, sinh n»=0; *, remembering (31) (COs Ng sinh ny—sin np cosh 2) — + *\7(sin n, cosh n, + cos n, sinh ny) — 8? sin np sinh np=0. 6 tan ng + tanh ny + —tan ny tanh n, No P SS 7 4 tan no—tanh ng By (81) this becomes 9) 2 No a Aon 8 No H=— | No (cot 5 + — cots 5 4 l y 1g Z or n K TO n =— 4 0 ge ( tan’ oI ak mae 2} according as mp lies in the 1st or 4th quadrant. ‘Thus ney [1-5 lt cot 5 = 4 6 Jn cot 5 =] ; 1 Kx? j n o1 ae ii ae (no tan” = 8) tans? | . The period ratio is aN 1K? 7 ‘ Pt Po=ltsoq p SEG 32 ans Ln lth G oa 1% tan knot ar In the case of the fundamental, n, tan z = —4:64727596, as before. K? p: po= 1+ 247404148“ In the case of a short thick bar this may become important. Rotatory Inertia on the Vibrations of Bars. 47 VI. 1. Pivoted-free Bar. f=dcosyE+d' sin y€+d" cosh y.€+d'” sinh y2§. Origin at pivoted end. Hence, by (11), pel Cf fhe a); Mee d+d"=0, and yp d=yrd", = a= 7=e signed simlgyeet es 1s (33) Also, by (12), oi ue sitet ea i) de SOE. iy is) —yd' sin y,l/=—y7d'" sinhyl, . . (34) and = d’/(My,— 1) cosyyl’ +d (A4yn+¥5°) cosh vol’ =0, or, since Atyety. A+” Yo ( M7) Ye 11 yy vi uy 1 Te sh v1 gi Yo dys cos yl’ —d!""y, cosh yol/=0. . . (89) Eliminating d and d' between (34) and (35) 9 yi? sin yl! cosh yo! =y.3 cos yl’ sinh y,/', . (36) or oi tal —oe daniel) 2 a CG) By means of (35) we obtain for (33) : sl sinh y& apf nnd Qh] J 608 yl! © 7 cosh yl! up 2. Correction for Rotatory Inertia in a Pivoted-free Bar. Before proceeding to find the correction from (G) we require the roots of tenes tamhi eee) |. ke ae) These may be found ‘ es Aa : 5a Oar (i.) by noticing that these roots lie very close to Teg T and putting m= 7a +e, where ¢ is small, for the 1st root. 48 Mr. J. H. ©. Searle on the Hfect of ns tan (F aa )= tanh = + e); or, expanding and rejecting squares, &c. of e, 1 — —I| Sap? 2 tanh Ta tanh E=—= which gives the roots correct to six places of decimals. For greater accuracy we may retain squares of «. We then have v2r—1-T Hye IL Z ee where T=tanh OT ’ 4 or (ii.) by observing that tan m = tanh m* reduces to - cos 2m cosh 2m=— 1, 7), ee) This is the period equation for a free-free or clamped- clamped bar when rotatory inertiais neglected, and the roots of (38) have been found by Strehlkey. That the periods of vibration of bars under these different terminal conditions should coincide to this extent is obvious also from physical reasons {. , The roots of tan n,=tanh mp are N= 3°9266023 n= (0689827 np OA NMOIE AS IE m3 = 1373517688 n= 16°4933614 n; = 19°6349541. Using the values rn n= + 4 9 ir” p=M1— :) E ; ss 3 a we find (“') =(1 EN), rejecting M4-&e. Y2 A ; * Greenhill, Mess. of Math. xvi. 1887. + Loe. cit. ante. t Rayleigh, ‘Theory of Sound,’ vol. 1. § 180. Rotatory Inertia on the Vibrations of Bars *, substituting in (36) 2 2 (1+ 3X7) sin n( 1+ *) cosh n(1—” ) = cosn (es - )sinhn (1-5). i Ie DINE *. (1+ 28)’) (sin n+ ~ cos 2) (cosh n — —- sinh 2) mr” F nr = (cosn—~ — sin n) (sinh , -. sinn cosh n—cosn sinh n 49 n). ? e = 7 | —2ncosncoshn—6 sin n cosh n }. Put N=N+N, where ny is a root of Camas VAI. eu) ai (39) and 7 is small. (sin 2 +7 Cos 2)(cosh np + nsinh rp) — (Cos 2 — 7 SIN 2p) (sinh nr +4 cosh np) a [ 229 cos 2 cosh ng + 6 sin 9 cosh n, | (sin n, cosh p— cos 7 sinh ng) + (cos 7 cosh ny + sin ny sinh ng + sin 7 sinh 1g — cos ng cosh ny) 2 —. —| 2n, cos n, cosh n,+ 6 sin n, cosh np |. 4. 0) (0) 0 0 0 rn | n= re [7 Cot np coth ny + 3 coth n9] r2 7 = per [2% cot ro + 3! cot no, which for higher harmonics becomes N2. Villas kale (m+ 38). Hence K I — Mo _— iP (229 Cot 29+ 3)n, cot ro}, and 2 Lik aE (19 COt Ny +3) Ng Cot Ng ; for the gravest tone this becomes Pi p=i+ pj — ane: 6155760 —— po PR Mag. S16) Vole 14 Noy 19. July 1907. 50 My. J. H. C. Searle on the Effect of VII. 1. Prvoted-clamped Bar. f=dcosyE+d' sin yF +d" cosh y£ +d!” sinh y€. Origin at pivoted end. Hence, by, (8) f=0 ae iar Bea) Brom d+d”=0. dy =a ye =a 0. . f=d sng, é4+d sinhygé. . > (40) Also, (10), fet oe ae d when os : =e ae) JV=d' sin yl’ +d" sinh yol’ } and O=qy,d' cos yyl! + 2d" cosh yal! yi cos yl’ sinh yl’ =. sin y,/ cosh yl’, . (48) or yi tanh yol' =, tangy!’ = een) Substituting from (42) in (41) pev[snn_sohnby y siny,l’ — sinh vol 2. Correction for Rotatory Inertia in a Pivoted-clamped Bar. Substituting for y, and y, in (43), 2 2 (1- v) sin n(1+ T) cosh nf (i-+ :) Vi rv : r2 =i + 5) cos n(4 =b *) sinh (1 i} ae 2 nr? a (1- 7) n+ as cos n) (cosh n— a sinh n) rn? 2 2 = (2 + T )(cos n— a sin n)(sinh n— “cosh n). *, sinz cosh n—cos n sinh n 2 ae [cos n sinh n +sin n cosh n—2n cos n cosh n]). Rotatory Inertia on the Vibrations of Bars. OL Put N=Nn +N, where np is a root of tan np=tanh np. (sin 29 +7 Cos 29)(cosh ny +7 sinh n,) — (COs Ng —7 SiN no) (sinh n)-+7 cosh ng) n ; : _ [cos ny sinh ny + sin Ny Cosh ny — 29 COS rp Cosh no]. But sin ny cosh ny = COs Ng sinh no, Nor te (a 2n sin ny sinh n= ae [2 sin np cosh n)— 2g Cos No Cosh no]. 2 No K Avan at [29 Cot Ny —1] cot 9. h IL as n==no[1— 55 {Np Cot Np — 1} ng cot no]. ik ee pe po 1-F 9° {ig cot 1% — IL) COU) oe (44) which for higher harmonics becomes ik Do po lt 5B (19 — 1). For the fundamental, D : py=1+5°7562650 =. VIII. 1. Pivoted-pivoted Bar. J = deosy,é+d' siny,E +d” cosh wéE+d' sinh yo&, f= 0 af when Se=(0), dé? cae d+d'’=0 ; rind y 2d pcalt yerd, ; d=d"=0. - f=a@ smyc+a sinbye. . . . (45) Also f =0 Pf f whe oe da 0=d' siny,l’ +d!" sinh yl", and O=—d'y,? sin y,l' +y,7d'" sinh vol’, d'’=0 and siby,. =0. K 2 52 Wee JEL, Ch Senda on aie Liffect of Hence yl Sur Os . tT 9 = as de” v= fp(x) (Ap sin pt + By cos pt) p o4 _ Mr. J. H.C. Searle on the Effect of Similarly, Paar pe 7 fa=e det se 0h WE ° £ : eee ‘| So Jaté =a" {age = fe Get } aes (° qe pee ae =o | LY dg where £= _ AD; : . (p* ht Ir fadé= él i fae oe Ae ta 4 op 7 a des dé dé fp _ dp a a LAs Tie viel. =| 2 dig _ (fa al x Ts a? At a clamped or pivoted end ail terms except integrals vanish by (10) and (11). At a free end ie = e Ja = |(), and by (12) é e *, at a free end all terms except the integrals vanish. Hence, odf, d ie fp fd + i a “ed =O, | Nay Consider the potential energy of bending. It is vaibAe |S af 4 NG de cee d?v dv ae’v d‘v i wale dave? die dx? + orode a But by (5) ae Shee Loy K FS ee == 0K ede 4 Lotatory Inertia on the Vibrations of Bars. By) . = A L d2y p div? V=}BAe?| 0! of ola | Ds mys ore oe a ——. dn, or, putting c=Ké IA le ,, , [88 mK ‘oes vot —ol"o] + SE “os UE AO 0 |e, l where & = im and dashes now refer to &. Now v = DX fodbp. p Considering only the integral in mk (0 d2-d2v 2 |, ae ie —2 | df MK = FP SCib dE jade [GE wh | a ==" °3cibn3r'o [GE pm | ae ie sr (Ga Ge- hh) e =— yrs, [i Ue — (He Gat (p,n08 | => Sebo [0 GF |. ae a nan |” (47 +4 “Ip | Bde, P4 by equation (47). De 2 AA $0 oder Now ee | o'o! —0'"0 | vanishes identically if each end 0 be clamped or pivoted. If both ends be free it is — [oe ]”. BA 0 2 mKp leo) on dt» =P [w= Fave. [alt In any case V reduces to vera are (be. - ao 56° Again, if T=kinetic energy, Mr. J. H.C. Searle on the Effect of L \2 tL 72,, |2 Dedn{ ql dot hme — dae du? dr =e" [5 elk des Gp C = tne” ane db tLe Ts bots |e d =pmes$i {a+s 4 yy a hae, by (2m) eon Thus, d or - ie at O¢ foley) ‘ m«(b, +p", )" PAS oe \ ig= (50) X. Evaluation at |. | 24 (2) Vag. We have Dane Sip dé* +r dE = hoy Of d'fy ndq Wie caer dé TX d& =N'T¢° Sie ee Oar Pe d oem (i iule=({ Gp —feget | ae+ (ata Get ay Ge at ae ie Uy Of lp dfq a fp - —Jogs + de ae t ap de! ae 14 OE q fp Ce a GY, 4 Ufp _ fp df me as a [oae dE (eo dE dé |— pate Lieut de oe ie dé]. Therefore, varying 2, rp p 40h dd, dip efy df, d &, ari, oe Ioan, dB dn dB dn dE d& ~~ dé dn d& ap @ fp sp Up Uo OD th ap) eT ria he ( ae Hence, nsf ars { { prs Ge) de=/ d dif, dfpdiy, | & dfp dip mrmene } Pax de dy d& ' dx dé dB dé dy dB? se © Up se Up _ str Up ite de} N/? de” a ee Rotatory Inertia on the Vibrations of Bars. aT which may be expressed more compactly by 2 | dh Ee a qeeenoe: Ne, de becoming, when rotatory inertia is neglected, se Yo Paes tL oe dé!” dy\ f, dé XI. Normal Function Relations applied to Special Cases. 1. Formule for y, and y2.—The following formule con- necting ry, and y will be found useful in applying the terminal conditions to the above. y= Veer dri +n4]; ey caer NY=™ YY =e VW Ye =v 2 5 or a: 2" eae dye oi te cl dn NYP +H” OPE yt ye? dys 2 2N Loot 2X5 yp IN 2 YP + on? nv +2?” d | an tI gy 2M Lt] = 3 dy; ae! G 58 Mr. J. H. C. Searle on the Effect of 2. Free end.—At a free end we have | {i+ (GE) t= [ean ae ano ae df en oo +t fea an de + AN fp dé" Now /,=Acosyé+B sin yé+C cosh yo# + D sinh yé 5 = (a) +W(P) 5 where a=3€; B= 28 - o f=Hbty; df dé =p +72" ; Claas , : iam — b+ 72 ; Oey oe =— yh! +92 5 d df ! | a, / / ae =P +h! — nm Eb + 272 EY 5 ) d / ! / ! . pe = — Qh + 2y 22 W— yy EP + 212 EW 5 d d°f dn de = ae + Bey'ya'h! + yin EG + y2 92 EW- Dita ie =(¢+)[- Ma ma i + Sey yeh! +r yn Eb + y2°¥2 Ey + rho! h! + yo'ae! — ann Eb + yore’ Eb} ae ANP Lyi! ah yo’ ¥ | — (yb! + yah’) —2qiya'b + 2yaye’ bh — Wy EP! + 279! Ey" = bd! [— Bye! +Atyy' + 40 y1 + Dey y?y2" | tab’ | Syey1! + Nye! + 4M 2 — 2y07¥0' | + bf ys yy — Moya TE + Lye? ya! + Meas’) € ot: ¢v [ya 1 a5 Yo Yo! or riny ae Moyyye, lé + day [Sey2?y2" +o + Any. + 27271 | a GD) | 39 YY a roy! + 40391 — 2yryVo¥2"] — (aid! + yb!) — yea b+ yey DE. Rotatory Inertia on the Vibrations of Bars. a9 Now, at a free end, hp _ cam —y b+ ~=0, ee 1 O=%'¥- Also poi Opes Ritts is MnP + ev) + (—mn'b' + yeh) =0 5 PMI )yi + (M +997) ¥2= 5 yP' =n". Using these relations and those in § XI. 1, | fe+( +( a2) | dE=3y.h0! + 2. +72) P+ 23-40) O"E, a a) rotatory inertia is neglected, ) = f°, thus agreeing with Rayleigh when the necessary trans- formations have been made. De Clamped end.—Ata spr end AC OR ae es wil { os Se oe ae Also, ia (ie) ) at a clamped end. ~ =:6' +yp'=0 | Using these relations and those in § XI. 2, we find i 2| {r+ + i) Lugs PEZ+M) tnbp +y°Eb™. 4, Pivoted ‘G a pivoted end, ae) ae CUP PN On a lpre bay fh papas, ans| {724 ( + ( page= Bi ged OL dE? GN de a. Now — f=Obty, and at a pivoted end yr=0, always. dj Le s dé =0 , a WW Ee, a?f 5 a a? 9 a a ie oe 60 Lord Rayleigh on the remarkable Case of Using these we have {{r +(e) | de= zee (Lt): 5. General Conclusion.—By combining the above we obtain the value of | ] | (+ (Ge ie ja for a bar under any terminal conditions whatever expressed in terms of @ and ¢$’, where o=A cosy,€+Bsinyé. Thus the changes needed in the notes, in the form and relations of the normal functions and in the equation determining the influence of a generalized force have been fully dealt with for the case in which rotatory inertia terms are retained. It will be seen at once, that while the analysis is somewhat lengthy, the results reached are not of a very complicated character. My best thanks are due to Prof. Karl Pearson, both for suggesting the above investigation and for his constant help during the progress of the work. IIT. Note on the remarkable Case of Diffraction Spectra described by Prof. Wood. By Lord RayurieH, O.M., P_R.S* N the Philosophical Magazine for Sept. 1902 Prof. Wood describes the extraordinary behaviour of a certain grating ruled upon speculum metal which exhibits what may almost be called discontinuities in the distribution of the brightness of its spectra. Thus at a certain angle of incidence this grating will show one of the D-lines of sodium, and not the other. “In! tig. 1p. 398; Prot. Wood) sives ten diagrams fixing the positions (in terms of wave-length) of bright and dark bands in the spectrum at various angles of incidence ranging from 4° 12’ on the same side of the normal as the spectrum to 5° 45’ on the other side. In general there may be said to be two bands which approach one another as the angle of incidence diminishes, coincide when the incidence is normal, and open out again as the angle increases upon the other side. In the tenth diagram there is a third band whose behaviour is different and still more peculiar. In the move- ment of the two bands the rate of progress along the normai spectrum is the same for each. The above represents the cycle when the grating isin air. “Ifa piece of plane-parallel glass is cemented to the front of the grating with cedar-oil * Communicated by the Author. Diffraction Spectra described by Prof. Wood. 61 the cycle is quite different. In this case we have a pair of unsymmetrical shaded bands which move in the same direction as the angle of incidence is changed.” An important observation relates to polarization. “ It was found that the singular anomalies were exhibited only when the direction of vibration (electric vector) was at right angles to the ruling. On turning the nicol through a right angle all trace of bright and dark bands disappeared. The bands are natur ally much more conspicuous when polarized light is employed.” The production of effects changing so ‘suddenly with the wave-length would appear to require the cooperation of a large number of grating-lines. But, as the result of an experiment in which all but about 200 limes were blocked out, Prof. Wood was compelled to refer the matter to the form of the groove. To this cause one would naturally look for an explanation of the difference between this grating and others ruled with the same interval, but it does not appear how the discontinuity itself can have its origin in the form of the groove. | The first step towards an explanation would be the estab- lishment of a relation between the wave-lengths of the bands and the corresponding angles of incidence; and at the time of reading the original paper | wasinclined to think that the determining circumstance might perhaps be found in the passing off of a spectrum of higher order. Thus in the’ spectrum under observation of the ‘first order, an abnormality might be expected at a particular wave-length if in the third order light of this wave-length were just passing out of the field of view, 7. e. were emerging tangentially to the grating surface. The verification or otherwise of this conjecture requires a knowledge of the grating interval (e). This is not given in the published paper ; but on hearing trom Prof. Wood that there were 14,438 lines to the inch, I made at once the necessary calculation. If @ be the angle of incidence for which light of wave- length » is just passing off in the nth spectrum, ECEs pole tue veg ss 1 (L) In the first diagram the angle of incidence is 4° 12’ and the wave-lengths of the bands are given as 609 and cle om im centimetres so:09\ x 10m? and) 5:17 x 10—°. Also 2°540/14438 cm., and sin@=:0732. Using these data in a) we find for the larger wave-length n=3 10, or n= 2°68, according as the upper or the lower. sign is taken. Again, for the smaller wave- length we find with the upper sign n=3'65, and with the lower n=3'15. To reconcile these numbers with the suggested relation it is necessary to suppose 62 Lord Rayleigh on the remarkable Case of that 609 is passing off in the third spectrum on the same side as that on which the light is incident, and 517 in the third spectrum upon the other side. But the agreement of 3°10 and 3°15 with the integer 3°00 seemed hardly good enough, and so the matter was put aside until recently, when my attention was recalled to it in reading an article by. Prof. Ames * on Rowland’s ruling-machines, from which it appeared that gratings have been ruled with three different spaces, viz. 14438, 15020, and 20000 lines to the inch. If we permit ourselves to suppose that the number of lines in the special grating is really 15020 to the inch in place of 14438, the alteration would be in the right direction, 3°10 becoming 2°98 and 3°15 becoming 3°03, so that the mean would be about correct. In view of this improved agreement it seems worth while to consider how far the position of the bands recorded in the other diagrams would accord with the formula N=te(l+sin), . sa eee) taking e to correspond with ruling at the rate of 15020 to the inch. In one respect thereis a conspicuous agreement with Prof. Wood’s observations. For if Ay, A, are the two values of X in (2), we have at once My + ro = 2 €, ° e e e ° e ° (3) so that the two bands move equally in opposite directions as @ changes. The results calculated from (2) for comparison with dia- grams (2).... (10) (fig. 1) are given below. Calculation. Observation. 9 ne , Mee ne No DIO sino. 590 | 588 589 537 2 (onan: 566) | eal 566 559 3 Oy: Oioedh ee ee O04" fl eG on san aaG 661 4 OF: Oi Bes 564 064 561 561 by) QO Deasaar OH | BRB CORR Re aiaedens, ee 6 lined eet 576 551 575 549 a ODS eae: o&e2 =| 545 581 | oz 8 Zo Oh eecne 590 = 588 089 538 9 Be Diesedes 620. | 807 619 | , 43065 1 eiaane * Johns Hopkins University Circular. Notes from the Physical Laboratory, Ap. 1906. Diffraction Spectra described by Prof. Wood. 63 The numbers headed “ observation’? are measured from Prof. Wood’s diagrams; but owing to the width and unsym- metrical form of some of the bands they are liable to consi- derable uncertainty. It would appear that (with the exception of the third band in diagram (10)) all the positions are pretty well represented by (2). As regards the observations when the face of the grating was cemented to glass with cedar-oil, we have in place of (1) e(1+sin 0’) =nNn’, where 2’ is the wave-length and @’ the angle of incidence in the oil. Now if » be the refractive index of the oil, ie, Srin @) —erpm(e) 6) ie so that C(O NN aay comes | (A) if as usual 8 and X are measured in air. In the diagrams of Prof. Wood’s fig. (2) there are four angles of incidence. The bands are markedly unsymmetrical and the numbers entered in the following table are those corresponding to the sharp edge. The values for n are calcu- lated from (4) on the supposition that w~=1°5, the lower sign being chosen if the angles on the first side are regarded as 0 N: n Se Se ths. 541 4:03 OGD 3 Be 3 590, 469 3°94, 4:96 en Denice wee sk 610, 489 3°97, 4:95 — 2° 29! i.e. 695, 529 3°99, 4:93 | | positive. ‘The wave-lengths observed correspond pretty well with the passing off of the fourth and fifth spectra on the opposite side to that upon which the light is incident. There seems to be nothing corresponding to the passing off of spectra on the same side. Upon the whole there appears to be con- firmation of the idea that the abnormalities are connected with the passing off of higher spectra, especially if the suggested value of ¢ can be admitted. The argument which led me to think that something peculiar was to be looked for when spectra are passing off may be illustrated from the case of plane waves of sound, incident upon a parallel infinitely thin screen in which are cut apertures small in comparison with X. The problem for a 64 Remarkable Case of Diffraction Spectra. single aperture was considered in Phil. Mag. xlili. p. 259, 1897 *, from which it appears that corresponding to an incident wave of amplitude unity the wave diverging from the aperture on the further side has the expression eT thr y=M (9) where k=27/\, r is the distance from the aperture of the point where the velocity-potential yy is reckoned, and M represents the electrical capacity of a conducting disk having the size and shape of the aperture, and situated at a distance from all other electrical bodies. In the case of a circular aperture of radius a, MS 2 aiiar ee (6) The expression (5) applies in general only when the aperture is so small that the distance between any two points of it is but a small fraction of >. It may, however, be extended to a series of equal small apertures disposed at equal intervals along a straight line, provided that the distance between con- secutive members of the series is a multiple of >. The con- dition is then satisfied that any two points, whether on the same or on different apertures, are separated by a distance which is very nearly a precise multiple of A. The expression for the velocity-potential may be written Pe ear, e esi) eee dial 2 SOPs 5 (i) where 7, ”, &c., are the distances of any point on the further side of the screen from the various apertures, and M”’ is the electrical capacity of each aperture, now no longer isolated, but subject to the influence of the others similarly charged. It is not difficult to see that if the series of apertures is infinitely extended, M’ approaches zero. For, if ¢ be the distance between immediate neighbours, and we consider the condition of the system when charged to potential unity, we see that the potential at any member due to the charges on the other members has the value 2M' € Accordingly M’=0, indicating that the efficiency of each aperture in allowing waves to pass to the further side of the screen is destroyed by the cooperative reaction of the series of neighbours. The condition of things now under contem- plation is that in which one of the lateral spectra formed by ye 5): a (eR ole Lu ME aeek * Or ‘ Scientific Papers,’ iv. p. 288. The Effect of Stress on Magnetization. ‘60 the series of holes (considered as a grating) is in the act of passing off, and it is evident that the peculiar interference is due to this circumstance *. The argument applies even more strongly, if less s simply, to an actual grating formed by a series of narrow parallel and equidistant slits cut in an infinite screen. The case of a reflecting grating differs in some important respects from that above considered. An investigation appli- cable to light is now nearly completed. It confirms the general conclusion that peculiarities are to be looked for at such angles of incidence that spectra of higher order are just passing ‘of, but (it is especially to be noted) only when the polarization i is such that the electric vector is perpendicular to the grating. Terling Place, Witham, May 4. P.S. June 5.—In answer to further inquiry Prof. Wood tells me that he thinks the ruling may perhaps be 15020 to the inch, but (the grating being ane the time out of his hands) he is not able to speak with certainty. IV. On the Effect of Stress on Magnetization and its Reciprocal Relations to the Change of Elastic Constants by Magnetization. By K. Honpa and T. Terapa, Lecturers on Physics in the Tékyé Imperial University t. \ [Plates I—-V.7 N our previous experiments, we investigated in some detail the change of seis constants of several ferro- magnetic metals ae alloys caused by magnetization, with special regard. to the order of applying the stress and the field, and found that in some cases the change is considerably large, and moreover that it differs more or less for different orders of applying the stress and the field. In order to find the proper explanation of these facts, it will be necessary to investigate with the same specimens as in the previous experiment the change of magnetization by stress, with * If e« be not a precise multiple of A, the series 1+3+i1.... ad win. would be replaced by - e—the 4 1e—2ike 4 1le—sikey ,, which is equivalent to —log {2 sin (3ke) } +37 (ke—z). + From the Journ. Coll. Sci. Tokyo. Communicated by the Authors. Phil, Mag. 8. 6. Vol. 14. No. 79. July 1907, F 66 Messrs. K. Honda and T. Terada on the special regard to the order of applying the stress and the field. Since J. J. Thomson* gave his theoretical exposition of the reciprocal relations between magnetism and_ strain, several theories f in the same field have been published, and the present investigation may also afford interesting materials for testing the validity of these theories. In this direction, we have been preceded by Rensing t and Cantone §, in the case of iron and nickel; but a more extended research may not be undesirable. With this view, sets of experiments have been undertaken, firstly to investigate the change of magnetization by applying successive stresses under constant fields; and secondly, to investigate the magnetization by applying the magnetizing field under different constant stresses and thence to deduce indirectly the change of magnetization by stresses. Specimens used had the following dimensions :— Specimens. Length. | Diameter. ee eae Swedish iron. 21°30 cm. 0:903 mm. 000089 Tungsten steel. 26°85 0-885 000050 Nickel. 26-87 0:863 000056 28°74 per cent. Ni. 26°80 0-964 | 0-00063 50°72 per cent. Ni. | 27-00 0-880 000050 | 70°32 per cent. Ni. 26°86 0-891 000068 S Ji, AU BARTOS The intensity of magnetization was measured by the ballistic method. This method was preferred to the magneto- metric one, since in our experiments fields up to 400 c.«.s. units were required, and consequently the adjustment of a very sensitive magnetometer placed close to a pair of com- pensating coils traversed by a strong current would be extremely troublesome. The magnetizing coil, which was * J.J. Thomson, ‘Application of Dynamics to Physics and Chemistry,’ Chap. iv. a Kolacék, Ann. d. Phys. xiii. p. 1 (1904); Ann. d. Phys. xiv. p. 177 (1904). A. Heydweiller, Ann. d. Phys. xi. p. 602 (1903). R. Gans, Ann. d. Phys. xiii. p. 684 (1904). 8S. Sano, Proe. Tokyo Math.- Phys. Soc. ii. p. 175 and p. 207 (1904). t Rensing, Ann. d. Phys. xiv. p. 363 (1904). § Cantone, Rend. d. Ist. Lomb. (2) xxxvii. p. 485 (1904). bid. pp. 474, 535 & 567. Lifect of Stress on Magnetization. | 67 one that had been used in our previous experiments, was placed in its vertical position. The length and the constant of the coil were respectively 40 cm. and 392°6. A secondary coil was wound on a glass tube (external diameter 1°5 cm.), consisting of 1246 turns of well imsulated copper wire (diameter=0°56 mm.) in six layers, the length of the coil being 14cm. ‘This secondary coil was fixed coaxially in the magnetizing coil, so that the former might lie in a uniform field excited by the latter. To compensate for the induction due to the magnetizing field alone, a similar secondary coil connected in series with the above secondary coil was inserted within another coil equal to and connected in series with the magnetizing coil, so that by sliding the secondary within the primary, the induc- tion could be compen- sated to any desired degree. These two pairs of coils were placed at a sufficient distance from each other to prevent their mutual action. The ballistic galvano- meter for measuring the induced current due to the magnetization of the specimen was drum - AQ omg Sis shaped, with 08 0 NS Z 3 APS . resistance ; a mirror QP evenee, with a small magnet wy a Ai aS a —!] was suspended in the centre of the coil by a spider thread. Its period of oscillation was about 9 seconds. The galvanometer was connected with the secondary circuit of the system and placed at a distance of about 15 metres from the magnetizing coil to avoid its direct action. The galvanometer was, however, still disturbed when a strong current was switched on to the magnetizing coil. To prevent this, the compensating primary F 2 68 Messrs. K. Honda and T. Terada on the was so directed that the direct effect of the combined system on the galvanometer was null. To determine the constant of the galvanometer, we should have used the compensating secondary coil, if it had been wound in one layer, so that its effective sectional area could be determined with sufficient accuracy. But, as the ambiguity of the sectional area in the secondary coil of 6 layers was inevitable, another coil was constructed with a thin copper wire wound on a wooden cylinder of 5:04 cm. diameter, in a single layer ; the number of turns of the coil was 48. This was always put in series with the secondary circuit and piaced at a sufficient distance to be safe from any sensible influence of the magnetizing circuit during the experiments for magnetization. When the constant of the galvanometer was to be determined, the compensating secondary coil was removed from the primary coil and replaced by this coil; then the magnetizing coil for the specimen was shunted off, a weak magnetizing current of known strength switched on to the primary coil, and the consequent deflexion of the galvanometer was measured. The constant of the galvanometer was thus determined from the field in the primary coil and the dimensions of the secondary circuit in the usual manner. The resistance of the whole secondary circuit was 10°80 ©. The deflexion of the galvanometer was read by means of a scale and telescope with a scale distance of 1527 m. The sensibility of the arrangement was such that one scale- division corresponded to a change of 1°42 c.¢.s. units of intensity of magnetization. To obtain a smooth motion of the galvanometer mirror due to the induction, it was found necessary that the two primaries as well as the two secon- daries should have nearly the same dimensions respectively ; the kick, which was observed when the dimensions of these coils were different, was probably due to the self-inductions and the capacities in these coils. Compensation for the earth field was effected by a special coil of fine copper wire wound on a glass tube in a single layer. This coil fitted closely to the inside of the mag netizing coil and to the outside of the secondary. It was fed by a current from two Daniel cells with adjustable resistance in the circuit. The current in the primary circuit was measiired by Ee Siemens and Halske ammeter with two shunts, 5 and 4. This was occasionally compared with a Kelvin’s ampere- balance. The specimen to be tested was cut to a suitable length (about 27 em.) so that, if placed centrally, it might lie in a nearly uniform field of the magnetizing coil ; it was brazed Lifect of Stress on Magnetization. : 69 at both its ends to thick rods of brass. The whole was hung vertically in the axial line of the magnetizing coil, and consequently of the secondary coil, the upper rod_ being firmly clamped to the rigid frame above the coils. To the end of the lower rod a hook was attached; from this hung a flexible cord which, after passing thr ‘ough a system of two pulleys, was stretched by a weight, without imparting any injurious pendulum motion to the specimen. Near the end of the lower rod, a rigid pin was screwed on perpendicular to the red. The ends of the pin fitted to the two V-shaped grooves cut lengthwise and diametrically opposite to each other on the inside of a brass cylinder, which could be turned about a fixed vertical axis to any desired angle. The angle of twist was read by means of a graduated circle and the 1 index attached to the torsion oli dlen LOM Oldies reer sin the experiment of the tension effect, the above arrangement served to prevent any accidental twisting of the specimen without causing a sensible friction to the stretching. § 2. MerHop or EXPERIMENTS. Our procedure was usually made in the following order :— The direct effect of the magnetizing coil on the galvanometer was tested first of all. The specimen was removed, the secondary circuit opened, and the maximum current was passed through the primary. If there were any constant deflexion of the galvanometer-mirror, the observer signalled to the experimenter, who adjusted the orientation of the compensating primary coil til the deflexion on breaking, making, or reversing the current was brought to zero. Next the secondary circuit was closed, a strong current was passed through the primary, while the observer was watching the galvanometer; the compensating secondary was slid within the primary till the ballistic deflexion was reduced to zero. Next the compensation for the earth field was effected. For this purpose, the specimen was introduced into the magnetizing coil, clamped firmed and stretched by a suitable tension, care being taken to place the wire co-axially with the coils. The specimen was carefully demagnetized by reversals ; the secondary was closed, a weak field excited in the primary, and the consequent deflexicns noted. After a complete demagnetization, the same magnetizing current was passed in the opposite direction. If the two corresponding deflexions of the galvanometer were not equal to each other, the resistance in the compensating circuit was so adjusted, that 70 Messrs. K. Honda and T. Terada on the the reversal of the magnetizing field, if it was repeated two or three times, caused an equal deflexion of the galvanometer. This method was found to be very sensitive, a very small change of the current in the compensating system producing a decided inequality of the galvanometer deflexions in opposite directions. The tension effect was first tried. To wipe out any uncertain remanent stress of the specimen, cycles of tensions, from zero to the greatest to be used for the specimen, were passed through before commencing any experiment. As a preliminary test of the working of the arrangement, a series of increasing fields was applied step by step under a constant tension, and the increase of magnetization was observed by the galvanometer. After a complete demagnetization, a weak field was applied and kept constant. While the observer was watching the galvanometer, the experimenter applied a series of increasing tensions step by step; the throw of the galva- nometer at each step was recorded. Then the tension was decreased step by step, and the corresponding deflexions were sometimes noted. After passing through several cycles of the tensions, the observation was repeated. After a complete demagnetization, the procedure was repeated for another higher field and so on. The number of fields chosen was naturally large for the region where the change of magnetization was considerable, but few where it was small. The magnetizing current was found to remain nearly constant during an experiment, except in strong fields, where it was sometimes found to vary 2 or 3 per cent. The reading of the ammeter was always observed both before and after the experiment, and the mean was taken. Instead of increasing the tension step by step, the maximum tension was often applied at once; but it was found that the consequent deflexion of the galvanometer was nearly the same as the sum of the deflexions obtained by the application ot tension in successive steps. Another series of experiments is possible in this direction. The specimen was demagnetized with the smallest initial tension; it was then magnetized, and then the deflexion of the galvanometer due to an additional weight was observed. After several alternate additions and removals of the additional weight, the changes of magnetization due to the addition and removal were observed. Then the demagnetization with the initial and added weights was effected, and the change of magnetization due to a second additional weight was measured, and so on. Next, the magnetization under constant tension was deter- mined. The specimen was first thoroughly demagnetized by Effect of Stress on Magnetization. Zz fe! reversals, loaded with the empty pan only. A series of successively increasing fields was applied step by step, and the throw of the galvanometer corresponding to each incre- ment of the field was recorded. Demagnetization was again effected, after the specimen had been loaded with an additional tension, and the magnetization tested in the same way; and so on. In this way, the magnetization under different constant tensions was obtained. The procedure in the experiments on the effect of torsion was similar. The torsion was increased step by step under a constant field, andthe change of magnetization corresponding to each step was observed. The effect of cyclic twist was also investigated. The effect of the maximum twist applied at once does not differ from the sum of the deflexions obtained by graduated application of twists, as in the case of tension. The magnetization under constant torsions was next measured. These sets of experiments were repeated for several tensions nearly equal to those used in our previous experiments on the change of rigidity by magnetization. The standardization of the ballistic galvanometer was made for each set of observations, though the constant remained fairly uniform during the whole investigation. Instead of using each time the special coil made for the standardization, we often used the compensating secondary coil for a set of experiments, recording the deflexions of the es corresponding to a series of magnetizing currents, and at the end of a set, the induction of this coil was compared with that of the standardizing coil. In this way, time and labour were coo) economized, without the risk of introducing any sensible error in the estimation of the constant of the galvanometer. § 3. Resutts oF EXPERIMENTS. The intensity of magnetization was calculated in the usual manner from the eee of the ballistic galvanometer with a known constant, the numbers of turns of the secondary and the standar dizing coil, and the sections of the specimen wire and the standar dizing coil. The necessary correction for the reduction to tangent was made for considerable deflexions. The magnetizing field was calculated from the reading of the scnnnetes of known constant combined with the lowe number of turns of the coil. The demagnetizing force, though it was very small, was also iaken into ‘accourns Tensions were all reduced to weights per square millimetre, and torsions to twists per unit length. In the following pages, I denotes the intensity of magneti- zation, H’ the external field applied and H the intern val or 12 Messrs. K. Honda and T. Terada on the effective field, all expressed in c.c.s. units; T denotes the tension in grams per square millimetre, and 7 the twist in minutes of are per unit of length. I. SwepisH [Ron and TunGstEN-STEEL. The effect * of tension or of torsion on the magnetization of iron and steel is so well known that it is superfluous to enter into a detailed description of the effect. Only the general features of the change of magnetization will be given here. It will, however, be noticed that our investigation has one shavagenetite: that several effects of the ‘Stress on magnetization were studied on the same specimen with special attention to the order of applying the stress and the field. The specimens were also those on which strains caused by magnetization had been fully studied ; hence the numerical results of the present experiment should be of some use to theoreticians, who have either already obtained, or may attempt to obtain, some reciprocal relations between mag- netization and stress, so that they will be given in their proper places. (a) Change of Magnetization by Tension under Constant Jiyelah 2 (uly SU) As will be seen from figs. 1 &3 (PI. I.), the change of mag- netization oI; due to the initial effect of loading increases up to a moderate field, and then decreases with it. In Swedish iron, curves (6];, T’)n in weak fields initially bend upward, and after passing through an inflexion-point, the curvature changes sign. As the field is iner eased, the point of inflexion appr oaches the or igin ; in strong fields, ol; is very small, and the curve is nearly straight. In tungsten-steel, curve (6];, T)u has a slight curvature for all fields. In weak fields, the effect of removing the suspended weight is very small and slightly increases the magnetization. Subsequent loading causes an increase of magnetization ; and unloading, a decrease. In strong fields, the initial and the cyclic effect of loading nearly coincide with each other. Curves (61,, T)n for cyclic effects are given in figs. 2 and 4 in magnified scale. Curves (61;, H)x as deduced from the initial effect of (6];, T)n are given in full lines in figs. 5, 6 and 7; they rise and then fall steeply 1 in low field, and after- ward decrease slowly, cutting the axis of H at the Villari * See Wiedemann’s Llectricitidit, i. chap. 4; Ewing’s ‘ Magnetic Tnduction,’ chap. 9; Winkelmann, Handbuch der Physik, Zweite Auflage, V.., pp. 801-807, 313-319. Effect of Stress on Magnetization. 73 points. The decrease of magnetization reaches a maximum, and then gradually diminishes tending to approach zero, as the field is increased. This maximum decrease had been anticipated from the theory of magnetostriction * by Professor Nagaoka and one of us. Curves (61;, H)r as deduced from (51., T)a of the cyclic effect rise only slightly in weak fields ; but in strong fields they nearly coincide with curves (o1;, H)r for the initial effect. The following are the numbers obtained by experiments. Swedish Iron. Initial T=152 er./mm.?; ¢ II fom oO 2 Ot = P1562, r|"P—S086 er: | P4648 gr. | T6211 gr. | T=71777 er +. ate jot... | OL. | of. | 6I,. 7 ee ery i ey | ol; ol,,. 175) G&) 0:9| 232 | 1:9) 568] 32° 100°9 4°5| 1463 6-9 2°56) 313] O8! 944] 1:75) 184-4 2°3 75°8 | 31) 3437 61 4-37 (106-4) ~0-1 | 226-2 |—0-2) 3269|)— O°6| 397-3/— 1:0] 4440)— 08 5°88 |115°5|—1:1| 197-8 |—1°9| 251°7 |— 2:8 2859'— 40) 3069 — 5-0) 775) 68°7)—1:7| 11i-1 |-34 1409)— 50 1607\|— 67) 1716 — 85 11°90; 253/—2°6| 40°77 |-—S2) 510)/-— 79 > 57°3)—10°5) 61:1)—13-2) 2418, 15\|—34) 18 |-—67 1-1 |—102 — O1|/—15°9|— 19 —174: 30°55 |—2°7 |—3°8| —5:1 |—-7'8 — 75 —116 —103|—1535|—13'3 —196 971 —40 —7-8 | ... j—-11:6] —147| ... |—182 | 204-7 |—3°8 =7-3 | —10°8 | S944 2s, ie ee Oy 51) — §0| Sag Gl 2 183 | | | Tungsten- Steel. Tnafsal P= 159: or./mm25 += 140-2 C. } } | T=1625 er./mm.2 | T=4837 gr./mm.? T=8092 gr./mm.? iy: cl, cI, 7 db], oI, él, 4:08 0-4 0-2 2-6 O-4 65 O-7 10°65 32 166 130 Ls ew, 32 15°70 Set 1G 42-1 4-2 98-4 81 19°34 40-0 26 142°5 OT 2449 9 23°85 39°3 2°0 98°3 6-1 149: 10°9 32°16 16:2 16 43°6 4-5 67°6 ca 43°36 6-9 1-2 21:0 a4 328 56 98-4 O-4 O-4 19 O-+ ol Ol 210:0 —U4. 0-0 —16 —13 —26 —28 | 841-0 —0°3 —O03 —1°5 —1i7 —28 —3+4 * Nagaoka and Honda, Jour. Se. Coll. xiii. p. 69 (1900); Phil. Mag. xlix. p. 340 (1900). 74 Messrs. K. Honda and T. Terada on the The effect of applying the maximum tension at once is nearly the same as the effect of the graduated applications of tensions. The change of magnetization by tension under different initial loadings, where the demagnetization was always effected with the initial load, was also tested. For an equal increment dT of T, I; decreases rapidly, as the initial T increases, whereas in the graduated applications of tension, ol; increases nearly proportionally to 6T. The difference between these two values of 61, is considerable. | (b) Magnetization under Constant Tensions: (1, H)r. The magnetization increases rather rapidly in low fields and gradually approaches saturation. The effect of tension is, in its general features, similar to that obtained from (6I, T)x. With low tensions, the increase of magnetization is con- siderably less than the value of the initial effect obtained from the latter experiment, while with high tensions, the contrary is true. ‘These facts will be seen in the following tables and curves (61, H)r in dotted lines in figs. 5 and 7. Swedish Iron. P= O25 (Os No 2fer,/mm |) ie osname = 1 O29) on, maaan H I le I H I 0:87 18°5 0°88 Doi 0:84 213 1:63 52:7 PAT) LF 1°63 59'8 2°89 161°3 3:12 Q3O°9 3:16 269°8 4-42 509 3°67 441°3 3°86 495°4 | 6°35 835 AO) a iO) 4:48 G2 | 848 1000 644 946 6:57 982 | 13°60 1141 Le Ieezs} 1180 isis 1149 Lg 1229 24-10 1238 23°85 Ss 35°60 1275 35°83 1280 35°88 1251 58:39 1328 58°39 1331 54°34 1300 1273 | 1416 1266 1419 1248 1337 219°4 | 1493 1974 1478 1956 1448 SOT al 542 319-1 1547 296:8 ireyial 386°5 | 1569 | 383°0 1575 381°9 1547 Effect of Stress on Magnetization. | 75 Tungsten-Steel. i i | T=159 gr./gnm.2 | T=1784 gr./mm.? | T=4996 gr./mm.? | T=8251 gr./mm.” H I Hi S| ld eae I, H iL [ssn 7) 144] 235 | 149 | 277 | 176 | 233 | 142 | 468 B12 54 353 | bw 38°5 4-60 29-8 7:90 588 8:85 69°1 9:07 2a || 7-99 60:3 me Ors | loth i te TOS Oke ely | Lis eee) 2 2023 NP liG- 76012 232-90) L676? | 22Bber) 1680, | 241-8 19:29 | 3047 | 19:00 | 341-2 | 1898 | 381-7 | 1899 | 449-0 22°29 | 532 | 22:06 | 597 PILOGE | Oole miee202) |) 695 | 27°73'-|. 788 | 27:66 | 837 27-46 | 8h2 27-64 77 33:94 | 918 S0O0N dg 000 i OarOle OGD 33-98 | 976 Argo) 1005 «=| 42:38 | 1041 «=| 4272 | 1045 «| 42°68: | 1046 63-2 | 1115 G36) olla) | 6328m) Vis7)— | 63-2" lelis3 | 105-2 | 1207 NOS 2) Sesame 052, eo23 1056 | 1215 | 1583 | 1265 S42 | 1291 | p77 | 1279 =| 1585. | 1268 2 1308-2127 | 1327) | 210-9 | 1311 211-6 | 1304 Prem o2e) (2691 |.1842) | 267-1 | 1339) | 2687 | 13880 3452 | 1354 | 3463 | 1380 | 3438 | 1364 | 343°8 | 1356 (c) Change of Magnetization by Twist under Different Tensions: (61, T)1,7. In Swedish iron and tungsten-steel, the curves (61;, T)u, (figs. 8, 10, and 12) are similar to those for (ol, T)s for the initial effect. In mark fields where the twisting considerably increases the magnetization, the effect of the first untwisting is very small and slightly increases the magnetization. In Swedish iron, the cyclic effect of twisting (fie. 9) under low tensions 1s always to diminish magnetization. With high tensions (fig. 11), the effect has a singular character: for a small twist, the magnetization increases, but for a large twist, it is diminished. In tungsten-steel, the cyclic effect of twist is similar to the cyclic effect of tension in Swedish iron, but in amount it is very small. Curves (61,, H);,7 as deduced from (61;, T)n,r are given in figs. 13, 14, & 15 (PI. IL.) in fall lines. They closely resemble those for the tension effect, having points corresponding to the Villari points. With considerable twist, (61., H);,7 (figs. 13 and 14) is always negative. The experimental numbers are given in the table below :— “Swedish Iron. Wi t52 or./mim2 > tr on: Messrs. K. Honda and T. Terada on the 7=42/9 7=69'8. ie ee, Elta elle H'. | dI,, | 1:34 1:26 | 186 122 | 368/— 42 2-43 247 | 39-4 238 | 73:2/—11-2 4-12 4:22 | 90:8 4-24 | 1147 /—200 5:86 573 | 84:7 573 | 125-0|—21-4 7-79 779 | 485 787 | 46-7 |—22:5 13°56 13°60: | 28 13°59 |= "S33 |e 24-04 23-78 | —42 93°74 |—141 |—18°3 48:95 42-01 | —3-9 39-29 |10:3/—11- 114-4 Tees) poole 1168 |— 25/— 3-0 212-7 2190 | 0-0 N52 AS a ae 367-1 3706 |— 04|— 09 T= 3233on./mam:?s lly ome: 7=14'6. F302 | —=cn © ony Polke aoe SEW | OL, 7) Cee oI. 57 1:22) 302| 33) 1-22 | 3:8) Wen ~17-1 22-4 261/1168 | 64) 2:54/2960 |-20 2:55 — 322 13-7 4:05 |}1940 | 57) 417 (=70 403) ~37-2| | 47-0 578) 1162 | 40) 576 -68 6-00 — 356 O73 776 564 | 30) 7-80 (63) T7L| 768 |—326 114 | 13°57| 242] 1-7) 13°63 (-47 1863) 166 |—22°8 58 | 21-70) 12-4 | 1-1) 22-47 | —30 | 21-42 —14-4 | 4-4 31 | 06) 49-21 | 11 48-90 — 55 0-4 1-0 | 00/1112 | | 0-1 [105-0 =o 18 0-0 O1 | 0-0 |2141 | | 0:0 2102 = tal) | | Effect of Stress on Magnetization. (i Tungsten-Steel. iar lorem, <7. C. AO, | E1072. | By —isb3) | Hi =18:39. | H’=2240- ee sero ea ke Hees 0:9 | 12-9! | 22.) 12:9") 4:0 | 1358! 398 | 22 | 475 | 71 | 391 | 144 | 38-4 | 326 | 41-4 | 37-0 692 | 49 | 692 | 157 | 69-2 | 293 | 695 a—o0-07 HY = 46°05. iE = 98:8: E’=—209:05 |) 3620; T. ol,, T. ol. T. oL., “e 19-9) | 84 | 13-4'| 13 | 145’ | O2 | 180'| 0-0 | 21-4") 00 “4 | 348 | 12 692 | 272 | 692 | 91 | 692 | 23 48:4 66 | 42°7 ape a6 3 0:0, = = = (07 = 08 [=O 4 |—0°3 —0-2 | The numbers in the last row give the cyclic effect of twist corresponding to the maximum twist. The effect of the graduated application of twist does not sensibly differ from that of applying the maximum twist at once. (d) Magnetization under Constant Twist combined with Tensions: (1, H)zx. The effect of a constant twist on magnetization is very small; in a small twist, the magnetization slightly increases, but above a moderate twist, it is decreased by twisting. With a moderate twist, curves (61, H);,r as deduced from (i, H);,7 have an opposite sign to those deduced from (S1,, T)x,r; but they have the same sign as curves (61,, H)-,2 obtained from (6l., T)u,r. The following tables and the dotted curves in figs. 13, 14, & 15 (PI. II.) will show these _ changes of magnetization. | Messrs. K. Honda and T. Terada on the 18 Swedish Iron. Palo? or./mimi2s)t— se) a 7=0. rT=31'9. 7=70':3. Fe 7 18[- i A: if O77 16°8 0°68 14:8 0-68 12°5 1:68 A783 1:29 33°3 1°39 oo 2°38 95:1 2°29 79:5 ep N) 66:0 3°49 256°9 ool 211-0 2:93 1293 4-05 406°1 4°21 4162 3°86 Zed, 4:69 571 5:06 632 4-49 41071 591 776 651 838 5:74 683 7°58 933 8°33 975 8:68 945 11°45 1094 12:29 1110 12°47 1064 20°51 1215 20°64 WT 20°65 MRE 30°81 1266 31°08 1264 oleslal: 1238 50°90 1320 50°83 1319 50°91 1299 1108 1408 1102 1409 ilalicalt 1405 173°5 1466 1728 1467 liaseity. 1462 263°5 1524 261-0 1526 263'5 1521 358: 1 1568 By 2) 1569 BY She 1566 | Ray ere) Giese Gea IL C. rT=0. r=14'2 7 =29'°3. 7 =58'°3. r=88''3 | H. I Ee I. ERS eh: EL. ale ie | I 0-66) 15:9) O68 16°38) 0:71) V2) O19) Sa Oar alee LEESON oo s2y 20)) we leolal males 1-32) 3762 1:54) 43°5 2°23| 98:0) 1:94) 79°3)| 2:19) 100-4 2:20) °94:3)) i224 315) 257-7 | 2:73*) 192°) 32:85) 192789) 295i) 163-41 ean meee 3°77| 4509; 3°51} 4240) 3:54) 4184/] 3°78) 3515} 3°82) 3008 4-48| 719 | 419] 6385 | 433/708 | 460] 645 | 4-81) 609 5:69 | 940 5:o7 | 929 5:75| 963 6:05 | 925 6°57, 890 6°75 |1028 6:67 |1023 719 1064 7:99 1048 825 1005 13°74 |1196 15:27 |1210 14°75 1219 15°30 ':1196 12:53 1114 | 90°98 |1250 | 21:09 1248 | 21:36)1265 | 21-2111242 | 207411906 | 31:06 |1292 30°99 |1288 31°57 |1805 30°79 1288 al COM265: 7 50°50 |1342 Malas 51°65 1356 50:91 1346 50°62 11330 _ | L157 143 1157 (1436 |113:3 |1449 |112-4 \1444 1t-ORNeSaee 180°5 |1499 1180°5 {1499 |177-4 |1511 |1759 |1506 [175-1 |1496 | 25:2 1562 274-7 1561 1270°8 (1573 267-73 11568 | 266:a S68 3762 {1610 |8761 {1610 /3870'4 1621 3656 1616 |3656 1608 Eject of Stress on Magnetization. an) Oe Tungsten-Steel. a 5511 orm i 13-7 C. a 7 =69'2 He it H: ily, 2-71 167 222, i3-4 4:68 ets bay | 4°61 29'S 7:98 60°5 10°56 87:0 12°03 109-0 | 14-72 1532 16°80 222°6 16°80 209°8 19:03 364-2 18°98 39972 22-04 630 21:97 622 27-65 S44 27-45 &40 ors 958 33°OT 958 50°26 1083 42-41 1033 85:9 1185 63-2 1136 132-2 1247 105°6 1223 179°8 1272 1584 1279 210-5 1307 212°4 1318 267°7 1334 269°1 | 1B4L 344'1 1359 343 8 1366 From the results thus far described, it may be concluded that in Swedish iron and tungsten-steel, the final magnet- ization is affected in no inconsiderable degree by the order of magnetizing and straining. This fact stands parallel to the result of our previous experiment that in these metals, the change of elastic constants by magnetization is considerably affected by the order of applying the stress and the magnetizing field. DiecNickmn, The effect of stress on the magnetization of nickel has been thoroughly studied by several physicists, so that there remains little to be studied about the effect. Our present investigation has, however, this characteristic, that several effects of stress on magnetization were studied with the same specimen over a wide range of the magnetizing. field and with special attention to the hysteresis effect. (a) Change of Magnetization by Tension under Constant Field: (81, T)n. The initial effect of loading on magnetization in very weak fields is an increase of magnetization by low tension, and a decrease by high tension ; but the cyclic effect is always a decrease, unlike the Villari reversal in iron. Above 2 c.as. 80 Messrs. K. Honda and T. Terada on the units, however, the initial and the cyclic effects are always a decrease of magnetization. In low tension, 61; or dI, decreases almost proportionally with 'T’; as I’ is increased, the rate of decrease becomes great, and after passing through an inflexion-point it begins to decrease, as shown in fig. 16. As the field is increased, the decrease of magnetization passes through its maximum. Except in weak fields, the cyclic effect (61, T), (fig. 16, dotted lines) fairly coincides with the initial effect. Curves (61, H). deduced from (61,, T), are given in fio. 0 am eal lines. In weak fields, they fall steeply and then gradually rise ; as the field is further increased, they slowly tend to approach the axis of the field. . Nickel. Enitial T= 167 on-j/mm.7's e142 ane Ise (aen/omins| Aes wre, T=421 gr. T=5089 gr. T=8513 gr. H’. i ol. | 0, | olp | of, | oly | Ol,. |) (ole 0] (eres aa eeeienmn eerie: 114/ 4 66 |—-135|+ 97 | 322 |4 35/— 8l0/— 41|— 994)= "99/1086 235|— 58 |—184 | —184 | 42:8 |= 62-7 |—1026|— 855 |= ek) ogee 3°89| —10°9 | —20°2 | 29-2 | —47-7 |— 83:0|—109-4|—113:8|—148.4|— 1391 |= 1636 10°77 | —23-4 | —28:0 | —52°5 | —58-7 |—119-2|—129:3|—-170:2| 181-8 |—921-3)| 993-2 31:06 | —23'°3 | —24°5 | —54-0 | —55:1 |—122-'8|—121-2|— 189-2 | 185-5 | 267-5 |— 2611 62:54| —12:4 | —127 | —29°5 | -29°5 |— 76-0|— 76-2 |—129°6 |—129°9|—235:5 | 234-6 | 135-2@)— 48 |— 46|—106|—10-7 |— 258|— 261|— 464|— 47-5 |= mao) 144 2055 |— 20|)— 20|— 46 |— 49 |= 11-3)— 191|/— 905 |= Sane ets 9 364-7 - — 03 wo) = 0'6 sete anlar mecha a nell Pr 3) | The effect of applying the maximum tension at once is nearly the same as that of the graduated applications of tension. The change of magnetization by tension under different initial loadings, where the demagnetization was always effected with the initial load, was also tested. For the same increment oT of T, éI is ina marked degree less than that in the last experiment. (b) Magnetization under Constant Tensions: (1, H)s. The magnetization increases steeply in low fields, and after passing through an inflexion-point gradually approaches saturation. he effect of tension is considerably large and always to diminish magnetization ; curves (I, H); become less steep in weak fields with the increasing tension, and tend to approach each other in strong fields. If we compare Effect of Stress on Magnetization. sl ol obtained from (1, H)z with that from (61, T)y for the same values of H and T, the former is found to be numeri- cally a little greater than the latter. The dotted line in fig. 17 represents the values of oI as deduced from (I, H),. Nickel. f= NAO (Ce ane cr mm: lO22ior) | M=1e/Sier: |) P—3a88 er, | = 5256 or. | P8680) er: orp ties ea) Wet er) ee Neem ime ov, a Oe -093 | 93 0:92 10:0 0:93 9:1 0:86 5:0 1:66 76 2°06 58 1°68 | 82°3 202 Ware 1:91} 389 1:76} 116 3°50 | 16°7 441) 12:9 3:19 | 1476 3:36 | 1dl:3 3:24| 911 3°44} 26°8 6°64) 348 7°78 | 23°4 4:12 | 170°4 4:02 1544 4°43 | 115°8 4°81/ 42:0 | 10°76! 60-4 | 13°38! 41-7 6°62 216°7 6°65 191:2 6:70 | 1516 775| 73-4 | 15°96) 93°8 | 26:01! 81°5 10-48 | 266°8 9°66 | 226°5 | 10°52) 1942 | 12°14 | 1151 ae ae ee ae 16°14 | 3166 | 15:54 | 2793 | 15°72 | 23771 | 17°98 | 159°3 | 26°56 | 144:3 fie ae 26°31 | 373:0 | 26°30 343°0 | 26°32 301:2 | 27°18} 214°5 | 39°31 | 202°8 | 39-24/ 119°3 38°88 | 413-4 | 39°09 | 392°4 | 39:11 | 3546 | 39°62| 270°9 | 62:9 | 291°6 | 59°8 | 176-2 62°5 4660 | 62°99 | 4445 | 63°2 |420°8 | 63-4 | 352-0 |106°3 | 392:1 |105°6 | 296°8 133°5 490'0 (133°9 | 491°4 |184:9 | 482°8 |1388°4 | 451-0 |186°1 | 460°5 |185°8 | 420-°0 205°7 5063 (20671 | 508-2 |206°8 | 502-7 |\206°7 | 479-7 |211:7 | 470°8 |227-1 | 449°5 269°8 511°0 (269°9 | 515-5 |270°5 | 511°6 |270°4 | 491°5 |287:0 | 487-9 |284:1 | 473-0 366'6 514°5 367-9 _620°0 368°7 517°6 |3867°3 | 499°5 1358°9 bar 354:0 | 488-7 (ec) Change of Magnetization by Twist under Different Wonsnons & (Olly Ge a In weak fields the magnetization is increased by twist, but in strong fields it is shghtly diminished. As shown in eels a5 EO Cel. Lil.) the curves (Ol) a)x. bend slightly, towards the axis of the twist ; the curvatures become less as the tension is increased. Except in weak fields, the initial effect is inconsiderable ; it also becomes less as the tension is increased. Curves (6!;, H),, from (61, 7)z,7 are drawn in figs. 20 and 21 in full lines; they have steep positive maxima from which the curves slope down gradually to the higher field, cut the axis of H, become negative, and after passing through very inconspicuous negative maxima, very slowly bend towards the axis; the maxima become flatter with the greater tensions, and the positions of the maxima as well as the points of intersection with the axis move toward higher fields with increasing tension. The course of the curves is thus quite similar to that of curves (61, H), in the case of iron. The following tables give some of the numerical data obtained. Phil. Mog. 8. 6. Vol. 14. Ne. 79. July 1907. G 82 Messrs. K. Honda and T. Terada on the Nickel. Mee LL area ivaventens peak). (Cy Et 0:60" eee Ea OR. H'= 2:31, 7. Ol,;. T. él T. ol, 84" 221 | 99a 342) 160" 105°3 |) 12°2'7 50:9") 162) 27-83) Sloe 21:8 72:8 | 236 91-7 | 269 1583 | 289 109:4 | 3447952 | 302 5I2i6 36°9 1806 | 41°38 1863 | 40°7 196°6 | 41°8 1375 | 463 152°3 | 438°3 150-9 542 1888 | 552 1556 | 54:0 221-2 | 583 161:0 | 63:1 2163 | 587 174-9 69:2 2211), 69:2) 1719 | 69:3 239°5 | 69:0! 172:9 | O94" 232 55 Ooi sere gen) re ——eoile Fi’ 10562: H’=23-22 Tr Oly, all gz. ol © ol,. ag os T 1; ia ol, 102' 602] 80’ 293] 108 456] 71’ 138] 88! . 46 PSOE As 93-7 121-0) 263 918] 226 75:4) 227 480) 2836 200] 381-7 156 | 90%) P1519) (38:2 SUNT 372) W060 F395 A732) \e38iae ao Uren eee oft O30 1798 | 48:7 1833) 507 12270 | 540) (881 | 529) oien eal i zonO | 69:0 1982 | 692 1548 | 693 136-7 690 97:8 | 693 41-1 | 693 311 | T. OL... u 118° + 73/101’ + 30| 98 + 24/154 0 | 99 4 P2/1T7 4 06 98:8 — 34/268 — 76 258. — 66/326 —125 385 —122 27 — 52. 164 — 76/450 -122 439 -187 477 —220 580 —214 420 148. 689 —108 693 -157 694 —307 69°3 —318 693 —29-4/698 —301 | 13) 0:3) 149) 00/188" oo a Ge | 239 — 49/289 — 46 3887 — 43/296 — 23 466 —133/480 —13°6 535 —104/520 — 96 1693 —25-6/69°3 —193/693 —142/693 —15:8 Effect of Stress on Magnetization. 83 P= 6286 ens /ammesss 16 == 14°71 C: H’=2:38. W'=3-99. | H’=10°64. | : ileal ; a ol,. 7 oI. as él. i. OL rg A o1;. ie Olan Boh 2: zs SUE | 93' 18) 38' 154] 101’ 13:9] 116’ 245] 71’ 169] 9:9' 19-4 | 240 55 298 430) 248 363 261 55:0 | 204 428/268 535 B81 113 454 662/398 619) 41-7 888/338 738 | 42:3 91-8 i>)... |. 1582 953 | 506 1072 | 563 1165 | 670 121-0) 688 873 688 1008 688 116-4 688 1424 | 688 1525 688 1415 H’=24-08. | H'=49-02. H'=919, | EM sate ats! (gk) seth [cs ole ees Ne 66 «79| 93 104/109 47/112’ 30) 86 35|144' 15) 238 367 | 26-9 40:8 | 285 207) 273 214/229 47/318 26) Seles gy 40) 175:9-| 403. 742-0 | 45-4 | 443°) B87 "63 Oe | at emi.S)| 563° 97-6 | 57-0 (61-7 |... SBE iRES 7508p) ard | 688 1204 688 1155) 683 729 688 677/688 104 688 79) H'=168-7 H! = 254-0. H’=3512 | ee ers ls) a les al Rais a aay faa er at on ive nraNuaeyTt OR: She ode Cee eee pie hy | ese et 105) 09) 78) + 11! 99" +. 0-9) 11-7’ | 4 0517.0") = 05) 232 = 59/292 — 94.989 — 64/285 — 56/298 — 40/346 — 64 1435 —154|503 —193' 454. —149 1496 =121 487 —13-1| 683 —25°8 68S —26-0 —20°9 68:3 —222. | 688 —264 688 --281) 688 The effect of the graduated application of twist does not sensibly differ from that obtained by applying the maximum twist at once. (d) Magnetization under Constant Twist combined with Wensponsie (lesb). The effect of a constant twist on magnetization is to increase the magnetization in weak fields and to diminish it G 2 84 Messrs. K. Honda and T. Terada on the in strong fields. As for curves (61, H),,~ (dotted lines in figs. 2() and 21) deduced from (I, H),,>, the general course is quite similar to that of the curves obtained from (61: 7)s, 73 but quantitatively there is some difference between these two. The difference, however, becomes less with increased tension. Nickel. P= 1197 orefomees t= ee) =), i GOL 7=67'0. hes al, IL 15t, I Ish 1 Hi. | 0:87 | 65 | O81 | 61] O79 | 42 50 | Ves | 570 | 176 | 474 | 200 | 805) eae 471 | 151-7 | 3:07 | 1020 | 3:40 | 1353 | 768 | 1960 | 499 | 147-1 | 532 | 211-7.) 404 | 2626 | 10-05 | 2220 | 811 | 1953 | 836 | 2737 | 844 | 3105 1449 2621 | 12-48 | 2485 | 11:95 | 3026 | 1361 | 3288 | 35°74 | 871:0 | 3412 | 3609 | 33°79 | 368-4 | 33:30 | 366-2 | | 604 | 4999 | 527 | 4061 | 52:85 | 1251 | 4840 | 1041 | 4635 | 1053 | 448-7 | 1046 | 425-7 1822 | 5027 | 169:1 | 491-0 | 171-0 | 4787 | 1693 | 454-2 218-4 | 509:2 | 2204 | 5016 | 2225 | 4911 | 220-4 | 4680 ‘6 | 289:9 | 5081 | 2828 | 500-4 | 2797 | 47971 —369:1 | 5220 | 356-9 | 512-7 | 363-2 | 507-9 | 3873 | 4894 (Su) we) ee) J on IN or) (0.2) Ss) (o) a ~J cs S are as Or — ee) (=P) P= 3546 atm: clone: 7=0. pes iley 7=34' 6. 7=66'°9. H. IE. H. dh, lel, I. H. J. 0-80 4°8 OO ae 0:80 35 0-79 27 2°01 13°5 1:98 12°3 1-77 9-4 1-75 14:8 3°80 29°9 311 22°1 2°98 24°6 2°84 | 106°4 6°55 59°5 4°65 373 4°53 O76 £06) | OieS 9°73 91°5 6°86 60°35 6°98 | 123-0 6:52 | 248°5 15:03 | 136-4 11-67 | 107°3 12°08 | 195-4 11-22 | 277-4 23°30 | 191°4 Tol 36:0 22°53 | 250°5 22:08 | 3106 33°86 | 245:°0 33°48 | 249°7 33°68 | 287:2 33°15 | 333°9 | 54°1 321°3 57-28 | 322°6 51°85 | 3322 52°87 | 367°3 | 1136 430°2 | 101-8 4149 | 1133 418:8 | 112°3 4256 | 170'7 | 4626 41623 | 458:9 | 171-0 4543 | 169°3 456°5 253°7 483-7 | 275°8. | 4874 | 252°8 479°5 | 2516 482°2 | 3040 499-1 | 3069 | 494-7 | 353°7 493°1 | 350°5 500°1 Eject of Stress on Magnetization. 85 T=6286 or./mm.2; t=13°7 C. rT=0 is 7—ot 7=69'0 H. L H. i H. if H. L. 146 | 56 1-17 38 139 | 40!) os8| 26 303 | 117 2-53 8-4 312 - 14 314, 255 504 | 219 426 160 489 | 217 5:40 | 158-4 892 43-1 9:89 | 43-9 7380 | 588 S16 211-9 14299 | 723 1538 | 743 | 11:58 | 1197 13-27 | 232-0 93-67 | 1148 | 2386 | 1195 | 2335 | 1759 23-77 | 2603 3477 | 1568 3493 1622 3498 | 2110 35°36 | 285-7 5733 | 2297 568 | 2347 | 562 | 2689 56:38 | 325-7 986 | 3410 888 | 3216 | 851 | 3385 881 | 3725 161-7 | 4290 1343 | 3963 | 1476 | 4123. 1473 | 4276 1955 | 4512 1904 | 4419 1963 | 4446 1962 | 4452 HAT | 4787 2702 | 4715 | 2675' | 4714 | 2675 | 4813 381-7 | 465°7 380 4898 3754 | 4913 373: 503'8 It is to be noticed that in nickel, the initial and the cyclic effects of tension or twist on magnetization nearly coincide with each other except in weak fields, and that the change of magnetization does not much depend on the order of magnetizing and straining. ‘Thus, in nickel, the hysteresis effect is comparatively small except in weak fields; and therefore the agreement between the theory regarding magnetostriction and the experiment might well have been expected. Thus, in our previous investigation, we found that the changes of the modulus of elasticity by magnetization for different orders of magnetizing and straining fairly coincided with each other, while in the case of rigidity, the ditference was somewhat greater. In the present investigation also, the tension effect shows a better agreement for different orders of magnetizing and straining than for the torsion effect. II. Nicket-StEELs containing 28°74, 50°72, and 70°32 per cent. of Nickel. As for nickel-steels, experiments on the effect of stress on magnetization have been very few. So far as we know, the effect of tension only was studied by H. Tomlinson * with * Tomlinson, Proc. Roy. Soe. lvi. p. 103 (1894) ; Bezbl. xviii. p. 952. 86 Messrs. K. Honda and T. Terada on the nickel-steels of 22, 25, and 30 per cent. of nickel, and by Prof. H. Nagaoka and one of us* with nickel-steels of 35 and 45 per cent. of nickel. Hence somewhat detailed descriptions of the phenomena will not be unnecessary. (a) Change of Magnetization by Tension under Constant Wels (lL, Wyse The magnetization increases at first rather rapidly, but afterward slowly with the tension. The increase in low fields is tolerably large, but in strong fields it is very small. The initial effect is significant only for weak fields, where the cyclic is remarkably less than the initial. The following tables and figs. 22, 23, & 24 (PL ILL.) show these changes of magnetization. Curves (61,, H): from (61;, T) rise rapidly with the field, attain sharp maxima at low fields, fall at first rapidly and then gradually to asymptotic values, as shown in figs. 25, 26, and 27 in full lines. The maximum of 61 increases with tension. For the same tension, the maximum rapidly increases with the percentage content of nickel. 28°74 per cent. Nockel-Steel. Gavin yee eve vores suave oy — I) (0. 049 | 46:7 4 ILL Oar oles anos On tno. o: | T=1370 gr./mm.2 T=2706 gr. T=4077 gr. T=6818 gr, | | | Mies EC se a ik Plehe ned | | | | [lg | ele ele [ole | OR, 1 ales aaa POUL PRY MB Bib ee, es) 1) 92221), 80:30 36 OMe 025 | 201 | 264 | 624] 575] 975 | 776 1303 | 941 | 7 1202 | 861 1555 1040 6 i) 164 | 113:0 90-0 7| 633 | 561 (22 | G45 0) DSO Malco 26:8 | 952:2)) 045: | 465 | 188 | 172 | 289] 270) 340 | 320 386 363 1068( 59) 53 4... | 2. | 10 | 10:0 7 emia 24:32 23 DOP mie de: BN oO 5:3 8:8 8-0 55:48) [VLSI deOL hk cote cb 2G) 0) i eee 1729 V5 ES cide eh 24, |, 4 ieee [3748 16 1 Wide iiss hess |) 40.) 48:07) | een * Nagacka and Honda, Jour. Coll. Sci, xvi. Art. 8 (1902). | 0-29 r O70 1-27 1:95 | 2-76 Pas? | 10-71 f 23277 | 51-44 (151-4 | 360-0 | { | 227-0 393-2 Kiject of Stress on Magnetization. 50°72 per cent. Nickel-Steel. filial’ T= 1 60ers 5) t= 13°F C. | $7 P1645 gr./min.* T=3249 gr. | T=4864 gr. | T=6540 gr. | T=8185 gr. Meee) ci.) ol, | ok aby eal.,| ot, | atz;| age an “033 910 2226 1988 [8778 1532 3003 1551 S110 11537 | 2667 ©1405 437-9 212-1 | 503-9 | 233'3 5283 | 2351 539-7 | 232-0 3198 1573. 4763 233-4 [53848 254-9 | 5523 | 2559 | 557-1 | 250-0 2531 148-7 359-2 215-4 [392-0 | 2303 | 397-7 | 2275 390-2 | 219-4 196-6 1368 2763 193-9 |298-7 207-3 2993 2041 294-0 | 195-2 1345 1088 186-4 1513 | 2025 | 1625° 2040 | 161-1 199-1 | 154-4 844 75-4 1138 102-0 | 122°5 | 109-4 | 123-4 109-4 1205 | 106-0 342 | 328 | 461!) 435 | 49-4 | 46-6 | 466 47-9) 45-0 79 | «77 | 107/| 105] 11-7) 110] . | 102] 92 | o7 | o4| 09! 04] 09] 04) 02! 00 econ 00 | 60} 00) 00))..00 00} 60 | \f=1604 er./mm-?, T=3170 er. 70°32 per cent. Nickel-Steel. initial R= loo er. fmm. se 145-5: C. T=6379 gr. | T=7984 gr. 58:1 1113 109°6 —O82'4 66672 The effect of applying the 65:1 | 107‘0 8o-2 | 1192 2963 635°1 > | Syeh ce | ol,. 663 | 94 132-4 | 91°35 maximum tension at once does not materially ditfer from that obtained by graduated application of it. The change of magnetization by tension under different initial loadings nearly coincides with the above result in the case of 28°74 per cent. Ni; but in 50°72 per cent. Ni and 70°32 per cent. Ni the change is generally greater in the present case than in the former. $8 Messrs. K. Honda and T. Terada on the (b) Magnetization under Constant Tensions: (1, H)s. Among other ferromagnetic metals and alloys, nickel-steels are characterized by the extraordinary steepness of the curve of magnetization; in a field of 5 c¢.G.s. units, the magnet- ization attains a value which is only a little short of its saturation value. The steepness increases with tension, first rapidly and then gradually to an asymptotic value. The enormous values of susceptibility « are given in the following | table and plotted in fig. 28. It will be noticed that the maximum value increases with the percentage of nickel. In 70°32 per cent. Ni, the susceptibility even attains a maximum value of 1015 for T=4930 gr./mm.?, which is several times as great as the maximum susceptibility of a well annealed Swedish iron. In very weak fields, the magnetization is considerably increased by tension, but in higher fields comparatively little. | 28°74 per cent. Ni. | 50°72 per cent. Ni. 70°32 per cent. Ni. HH. K. | K. K. | | | | T=134 gr, |T=60952 er. T= 160 gr. T= 8344er.)T=156 er. T=4930 gr. 0-20 75 OOF IN 65"), au alo HO ee 0°30 110 390 OS 25 17 95 0°40 125 530 153 | 75 23 200 0-60 145 AOR WN W243) Nose 64 470 0-80 150 SO eap (raw ben 700) 120 1015 1-00 WO ep oO GLO. eh eel 230 860 1:30 PQA ay 280 aN AG OOo minal mmecoa 677 1-60 113 ICO pe EE als OSB 288 570 2:00 99 157 307 | 808 270 | 470 3°00 | 73 LOG i 2S Os Aer) 220 322 5-00 50 Of e202 Te aie roe 160 196 7:00 36 AG Team elo) | 170 123 140 Curves (6], H)» (figs. 25, 26, and 27, dotted lines) deduced from (I, H), take a course quite similar to those deduced from (6I, T)y. In 28°74 per cent. Ni the maximum 6I is generally greater, and the asymptotic value decidedly greater than in (6I,;, T)x for the same tension and field. On the contrary, 61 of 50°72 per cent. Ni is always less than the corresponding value in the last experiment. In 70°32 per cent. Ni there is a fair coincidence between the two values of él. Lifect of Stress on Magnetization. 89 28°74 per cent. Nickel-Steel. fede 10) Oe T=134 gr./mm.?;) T=1504er. | T=4211 er. T=6952 gr i | | Hi: Eee) ed lies 1p ergs T, Ei? |. ga 023 | 208 | 022 | 268 0-13 79 0:09 38 O72 | 1086 | O73 | 178-4 C24 63:0 0-24 416 O77 | 1140 102 | 204°8 0°33 167-9 0°30 | 118-9 PSS Il626. || 1:4) | 225-2 052 | 2433 0°53 | 260°6 ZAM AZ 1b) . 203° | 2a7-4 O82 | 27271 On| -280:9 326 | 2255 | 363 | 2741 1520 G2865 1-24 | 295°5 Pee oe 2d o-l |) Fd | 2997: |. 408. |) 3203 3°36 | 3176 bee} 287-1 | 12°83 | 3120 | 11°57 | 3396 11-28 | 338-6 120 42960 1912 | 3180 | 18°96 | 3461 18°96 | 345°6 24°06 | 2997 | 2444 | 8214 24°31 | 349°1 24°32 | 349-0 50:1 | 3088 d0'1 330°2 | 49°75 | 357-7 49°9 307°8 123°8 320°3° | 125-5 341°0 | 122-4 368°5 | 122-4 368:°7 230°5 3200 | 22970 | 349°7 | 227:9° | 377-2 | 227-5 3772 3748 | 3372 | 3726 3078 | 370°2 - | 3852 | 370-9" | 385-1 D2°72 per cent. Nickel-Steel. t= a1 C.- | j T=983 er./m : T=3450 er. T=5054er. T=6699 er. | T=8344 or. TE ele TMM STE led Ws cg tg MRR Ss 2a UA a: 0°30 34:0} 0:32) 286) 033) 24-7) 0:31 | 23°3| 0°38 15-4 051 96:5} 0-48] 180-0 0-50| 160-4 0-49] 113-7} 049: 806 0-75 262°6| 0°59] 3147, 062) 361-1, O66] 4586) 063; 285°9 148 | 739 0°85| 597 0-89) 681 1:08; 8389 | O80 561°8 173 810 1-41| 899 1:38.) 928 |. 164) 996 | 0°93 cal 2°62 949 2°15 | 1043 2°12 | 1062 2°83 | 1118 158 964 401 1028 3°83 | 1143 4-42 N77 4°58 | 1180 3°05 1106 4:92 1064 5°49 | 1181 6°87 | 1215 TOT | 1224 C20 }ZOE 17-01 {| 1210 10°88 | 1229 | 11°96) 1244 | 13°79) 1253 | 12°94) 1232 Zaft | 125 9 226211260 | 22:78) 1267 | 23817) 1271 | 22°95) 1253 43°47 | 1267 | 43°06) 1279 . 4280/1283 | 43-22)1287 | 42°81 1269 110°9 1290 (1070 |1295 14056 |1298 |105°3 | 1302 |105°3 | 1284 2348 | 1298 |228:0 |1302 |225°5 |1305 |2246 | 1310 |2261 1292 3841 | 1302 e715 /1306 367°9 | 1309 3673 | 1314 366°7 1296 90 Messrs. K. Honda and T. Terada on the 70°32 per cent. Nickel-Steel. f= Ivo OF | ‘T=156 gr.jmm.*) T=959 gr. | T=1761 gr. | T=3366 gr. | T=4930 gr. | ‘ , rae | | | del il. ii. I. i. Sy ean if Jel. I. | | | 0:25 | 185] 0:23] 21-9) 031) 269, 026) 185 O24] 95 0-79 945) O75) 1288) 0-70) 162:2| 046) 132°9, 043) 1806 0:86 | 1279) 0-90) 3275) 0°85) 557-8) 0:57) 2063) 060) 2890 113} 3254) 1:53} 609 UMies) Tals | 0-74 4788 064) 347-7 1-52 |) 4304). 1-78) Got 280; 841 | 085 738 O71) 532°0 1:30 | 5036) 2°77| 763 3°83| 884 | 2:20 903 076) 734 GO OOM VOrh doo 6°32) 937 | 3:56) 946 145] 906 8:04 | 871 | 10:00} 955 | 11:53) 985 | 672) 981 | 3:38) 970 11-93 | 927 | 19:28) 1008 | 19:67| 1016 | 19-26 | 1026 | 6:75), 996 2654 998 | 2476/1022 | 2514/1028 24:33 1084 | 24-02| 1032 D099 | 1022 | d1:2 | 1045 | 52°0 | 1047 | 51-1 (1049 | 509 | 1043 1044 | 1030 1032 | 1052 {1043 | 1055 (1025 1054 | 99:0 | 1048 204-4 | 1083 (204-1 | 1054. [2023 | 1057 (2006 | 1056 /201-0 | 1049 370:0 | 10384 368°5 | 1055 (865°0 | 1057 362°6 | 1057 3651 | 1001 (c) Change of Magnetization by Twist under Different A ARSHOOS S {CONS te) 3. ee In very low fields the magnetization considerably increases with twist; in higher fields it first increases, but afterward begins to decrease with the twist, and in still higher fields the magnetization decreases nearly uniformly with the twist, as shown in figs. 29, 31, 33,35, 37, % 38 (Pie) aie change of magnetization rapidly increases with the percentage content of nickel. As for the cyclic effect (figs. 30, 32, 34, 36, 37, and 39), it coincides fairly with the initial, except in weak fields. With 28°74 per cent. Ni and 70°32 per cent. Ni, the increase of magnetization is only observable in very weak fields, and the magnetization generally decreases with twist. With 50°72 per cent. Ni, the magnetization first increases with the twist, attains a maximum, and then decreases. As the tension is increased, the change becomes gradually less. Curves (6L, H)7,» (figs. 40, 41, 42, 43, 44, 45, & 46 (Pl. V.) in full lines) obtained from (61, T)u,> rise and fall steeply in a very low field, cut the axis of H, become negative, andatter passing through rather conspicuous negative maxima, slope away gradually toward the axis, with the increasing field. 61 is numerically greater for a greater twist. With 50°72 per cent. Ni, however, 6I for a smali twist is always positive, tending to zero as the field increases. Kiffect of Stress on Magnetization. Curves (6!., H)z,. for cyclic effect shown in the same figures are similar to the above curves, and become coincident with them above a moderate field. The increase of magnet- ization with small twists becomes less as the tension increases ; and for 28°74 per cent. Ni and 70°32 per cent. Ni, it almost vanishes at a high tension. { { 28°74 per anne Nickel-Steel. Fy SG) oe, none ee llZLo 7K Silt H’=0°10. | W’=0-21. H’—0-48. T. ol,. ce Olle | ¢. ol, Ti oI. Tener OH. ar) Olle | Pee bs. ee ge 9 oy Gale 158 |iz6 41s 345 127/369 09/388 233) 356 27/402 286] 411 ~01 683 189/683 16/682 362/683 20/683 310/683 —27 H’=1-07 | W=1°86. H’=3°70. | ee ol,. Fo Ciba IN uaa) ep Tet aOllies Te poly Te eos | 187 248 | 15:8’ —21 | 17-8 —2-4 | 145 —39| 159° —53| 1564 —5-4 | 374 +493) 354 —7-92| 436 —19-2 | 382 -13-9 | 56-4 —15-9 | 41:8 —19°8 683 —42 | 68:3 —22-0 | 68:3 —20-9 | 683 —246 | 683 —30-7 | 68:2 —31°7 H’=6-70. W=14-51 W’=30°56. T. ol. T. ol,. T. ol;. T. OMe ae vee ol; P- ol... | 148° 89 | i477 —47 | 135’ —1-3 | 124 —11| 159’ —0-4 | 183° —0-9 43-4 —18°5 | 367 —15-7| 387 —72 138-7 —76| 394 —231491 —31 | 682 —299 | 68:3 —30:5 | 633 —158 | 682 —16-6| 682 —59| 682 —61 HV61-0. H’=168°5. Hl’ =355°7. a ol;. Trolls coy i) Ole mi Ol, roy ale Bs ily ol, 32:9’ 0-6 | 30-4 —041379° 0-0) .. “361 —0-1 632 97 | 682 90 | 682 01 | 68-2’ —01 | 682 —O-1 Messrs. K. Honda and T. Terada on the T=4211 or./mm.?; <=14°2 C. ay | ge 149° —09 | 16:67 —12 088 —45 388 —4'8 1S V==(o sy. r= 022 | H’=0-48. ol,. T of,. T ol, T a ol,. 144° 86 | 17-1’ 1437 163] 15-4" —1:3 | 14-97 16 —4-4 | 29°7 | 396 46°3 | 40:1 —69 | 39:2 39:36 —16°7 41:7 | 69:0 61:0 | 69:0 —12:2 | 69:0 69:0 —29°9 209) H’=1°90. H’=3:60. eto le. ie OM Nizete Molise igs me, Olle 161’ —1:6 | 156’ —5-1 | 13-6’ —26 | 189’ —61 | 149° 16-5’ —40 41:6 —14:°8°) 386 —18:7 | 43:4 —152 | 42:3 —19:2 | 42:56 —153 | 40:5 —1da2 | 69:0 —28°9 | 69:0 —34°6 | 69:0 —31:2 | 69°0 —33°2 | 69:0 —27:'7 | 69°0 —29°1 | Rel ener b i H’=6°78. 1a Sailers, H’=35'58. co. Olle re ONO Were) Olas Tie. toll —0-4 | 206" —03 | GSR vee 69:0 0:0 | 69:0’ —02 41:7 —11:0 | 405 —10-4 69:0 —218 69-0 —11:0 | 69:0 —11°2 —3°3 | 690 —3°5 H’=66°7. H/—=179;9 H’=354'6. T ol; T Men) re Olt, FS Te 19-7’ —0-1 MO 10704 e 0:0 | 69:0’ —0 Effect of Stress on Magnetization. 93 50°72 per cent. Nickel-Steel. (De UE eyeliininn“5 Ue Ee Oe 677 —11) 677 —15 | 677 —0-2 | 67-7 —03 | 67-7 —0- H! =0-28. H'—0°68. HW =1°38. ee) xO. Tino. cpm Olle: Wea OU cry bly, To en Olle: Wy 994/172 87/128 5131104 62/130 559| 105° 93 99-4 577 | 352 19:81 276 11881307 1691269 1179] 325 234 43-2 100-2 | 533 303 | 543 2941 | 489 21:8 | 47-4 19901 546 11°33 | 67-9 171-7 | 682 3471| 680 3056 681 162] 67-9 2250 | 679 —39 H! =1°83, a3. HAG, = fy ig ae ee eae ed 107 422 | 149° 152/148" 356/124’ 1661109 1981139! 17-4 96-9 1068 | 346 27:3) 293 567/278 287]|261 3811 314 266 46-0 1496 | 51-4 180) 45:7 608/490 1971 51:0 3361 496 155 67-7 1509 | 679 —4:7 | 679 378) 677 —9:0 1! 677 1251677 —96 H/—12-62 H/=2457 H’=49°61. Tie, 9 Olli fin) Ol: ge Olle. (pe NOS ieanres Ol ia | tO momma! os Se liso 81/166 101 liso” 2s L177! 48 382 228/310 189/406 120/307 120/404 57/390 5-4 RSMEANS 3) mors Pore ee PM IN We oF oh 67-7 —2-7 | 67-7. —83 | 67-7 —36 | 67-7 —47 | 67°7 —18 | 677 2:7 H’=1088 H’=211°8, H’=377-4, | es fo) ll. Ge Pails. ie Olle ie) OL, is Cll, ie feiss ipo aioe’ =) 06 | 10-9" —lo-2 | le Ae een) 486 1-5 | se 07 (B36 ° 0-6 SEE EEneEeeeee 94. Messrs. K. Honda and T. Terada on the T5409" or./mmn.75 fe a0. H’=0-28. H/=0°69. H’=1-28. T ol,. T. oI, T. ol,. T. ol. T. ol,. T. ro 12-4/ 135 | 11:2’ 21 | 12-6’ 882) 11-1’ 45 | 121° 850 | 1357 93 297 424/301 41/289 8831277 90/277 886/307 155 | 520 91:7 | 462 56/460 1316] 465 9:0] 43:3 1923] 496 11-4 679 1215 | 679 5:6 | 679 1829] 679 3:0] 679 1532) 679 —26 H’=1°82. H’=416. H’=10-54. ae ol,. T. Ol ss T. ol,. T Ole Te oI;. T. OL. 11:9’ 356/107’ 95] 110’ 180/112’ 117) 11:2’ 101/118’ 90 | 312 8131269 1861278 35:0 | 280 92:0) 29711 ean emai a|| 53:0 1080 | 465 152/465 361) 479 155/476 188] 505 89 679 1082 | 679 —47| 67-9 180 | 679 —56| 677 —27 | 677 —62 | H/=24-62 | H’'=49'35 | H’=109°0. Tenn Wolly. Ten Ol | Trea vill: Taaear oles: | Tan) wrOlles Goines, || — P| at PL A | pe ee =! 113’ 57.) 109’ 48/118’ 30 107’ 27 | la 2) een eleO meant 277 9812986 89/280 45) 254 48 | 41:9 ab) eens Ap3 (69 | 486 57 '| 510 241/467 35. )) 7 ee re 677 —33 | 677 —42 | 677. —24 | 679 —23 | 677 =O6)| 677 )—05 | | | H'=212'8 | H/=376'8. PAO Gl gs) col. | rl. 0) | | 17777, 103 | 132", 0:8 \°23:0’. 0:0 | 21-07aOw 35a 10:3) 937-8. 108 | ~ leer 67-7 0867-7 +03 | 677 —03'| 67702 | Liffect of Stress on Magnetization. 95 70°32 per cent. Nickel. 23 ons mmeg re — 21 CO. H’=0-29. H'=0°69. | H '=0°'89. T. ol,. T. Olle a oL,. | oe elope T. ol,. | or, oL Bea TT 0)| 253! 44 | 162’ 89:0'| 23:27 141 28-2) | 17-9 ae PP | Oh Oe ee GMa. \B24-0 | 42-01" Baty 435 1181 | 489 19 | 545 2950} 494 340] 557 3946] ... ... 69:3 1219 | 693 -—-1:0| 693 341:0 | 69°3 42:9 | 693 4203 | 69:0 44:5 T. ol,. rT. OL T. oI,. T. CS RIP a Olle T. oI. 14:3’ 49°3 | Poumon 22 To) LOIS 4, es) 201 04) ) OtOf 9-0 371 988) 488 106/487 22:8 | 449 —148 | 361 —81 | 476 —336 Soop LOA 2. 235 de Me av as sive a6 nee ston Goa t50) 1693 13:0!) 69:4 20:2 | 694 —220 | 69:4 —276 | 69:3 —44°9 | H’=8:96. H/=235°23. | Tl ’'=47:04. Pee OR We ORS ie” Sen tee on. HG! Mer 1 de C ~ ! 185’ —58 | 25-1/—17-1 | 25-8’—102 | 201’ —5-2 | 161’ 25 | 219’ 25 | 458 —449 | 485 —49-4 | 46:5 —35:1 | 480 -358 475 -170 479 —178 | 693 —67-2 | 69-1 —69-4 | 693 —60-2 | 69-3 —608 | 69:3 —32-6 | 69:3 —33-2 | H’=92:0 H’=208-7 H'= 367-2. | Teed Oil. Tend Olle cy peal. cia ON ee Te Olle T Ol TEND) 795) (eat Sa IOS SOU) | Ae es ey S00 eG th Ge een me oe ae i GOs 80s GOR 1s | Messrs. K. Honda and T. Terada on the 96 = So06 or./mm.-; bie 7 Oe. | i} H'=0-29. | H/=0-68. | H’=0°88. | | eo eee mn ee at | =. 23-9’ 769 | 236' —39 22:6’ 81-6 | 236’ —80 15-6’ 1118 | 243’—11-4 | 492 976 | 488 —145 47:6 1396 | 47-5 —257 365 2458 | 486 —341 691 1009 69:3 —205 | 69:2 1433 69:2 —363 | 69:2 284-9 | 692 —47-4 H’=1-68 H'=3-06. H’'=5-00 T ol,. Tet ole T lig ol,. i Ole moh oe 198’ 27-8 | 22:3'-126| 15:8’ 03 | 182'—10-4 | 152’ —38 | 171' —9-7 404 217 | 48:5 —43°5 | 335 —169 | 38:3 —37°6 | 31:0 —33-4 | 36-1 —360 ete fore ee | 5B —857 | 597 605 | 51:3) ete eae 692 16 692 —61:2 | 690 —485 | 689 —68-9 | 69-1 —65°3 | 691 —731 H/=10-75 H/=23°43. H'=47-06. T. oI ,. Fo ol,. aa ol; ait alls lie ol,. T. oI,. 154° =47 |) 188’ —31 | 189” =4-7 | 1467 —2:1|)o1e See eaten eee 35:1 —27-3 | 31-3 —23:2 | 34-7 —17°3 | 85:3 —173 | 462 —139 | 41-9 —19-1 555 —52-8 | 551 —53-4 | 551 —87-2 | 51-5 —33-0 | ROP ial 69:1 —67°5 | 691 —680 | 69:0 —50-6 | 69:0 —50-2 69:0 —28-4 | 69-0 —29°3 H'=1046. | H’=190°9. H'=348-9. + Ol |e ol, |, ol, | g. Ol. | 7a OI 162' —0-7 | 15:0' —06 | 189’ —O-1 /184' —0:3 363 —33| 465 —44 | 443 —-1-5 443 —0-7 690 —11-2 | 690 —101 690 —40 690 —1:7 Fiffect of Stress on Magnetization. OT The effect of giving a maximum twist at once does not materially differ from that of a graded twisting. (d) Magnetization under Constant Twist combined with Tensions: (1, H)r,r. The effect of a constant twist on magnetization is com- paratively great, especially in high fields. In 28-74 per cent. Ni, the magnetization is slightly increased by a small twist, but above a moderate twist it decreases. In 50°72 per cent. Ni, the increase of magnetization by a small twist is not appreciable, but the magnetization always decreases with greater twist. The magnetization of 70°32 per cent. Ni is also decreased by twisting, except in weak fields in which a slight increase is observed. In all cases, the change of magnetization decreases with increasing tension. In 28°74 per cent. Ni, curves (61, H)-,r (fig. 40 in dotted lines) deduced from (I, H);,r show a somewhat different aspect from those deduced from (6éI, T)ru, especially for a small twist. For a small value of twist, 5I is always positive and has a faint maximum; for a greater twist it is first negative and afterward positive; and for a still greater twist it is always negative, and, except in weak fields, it takes a course parallel to the corresponding curve obtained from the last experiment, but the former lies somewhat below the latter. In 50°72 per cent. Ni, curves (61, H);,r (figs. 41 and 42 in dotted lines) deduced from (I, H);,r have a quite different aspect, 7. e. dL is always negative. It rapidly decreases in weak fields, and after passing through a negative maximum, slopes away very slowly towards the axis of H with in- creasing field. Tension reduces the decrease of magne- tization. In 70°32 per cent. Ni, curves (61, H);,r (figs. 43, 44, 45, and 46 dotted lines) deduced from (I, H);,7 take a course similar to those obtained from the last experiment, but the difference is that in the former the positive maxima in weak fields are considerably smaller, the points at which 51 changes its sign lie in a lower part of the field, and 51 tends more slowly to zero than in the latter. The effect of tension is to push the points of intersection with the axis of H towards the origin. For these alloys curves (61, H);,. as deduced from (I, H)-,r rather resemble the curves (6I,, H);,r obtained from the last experiment. Phil. Mag. S. 6. Vol. 14. No. 79. July 1907. H 98 Messrs. K. Honda and T. Terada on the 28°74 per cent. Nickel-Steel. 909 or./mm.4; t= Waeo CO psleee H. I. 0:28 349 0°42 85°5 0°52 112°4 0°85 | 1653 1:19 192°9 3:15 | 261-9 5:35 | 288°9 690 | 299°6 19:04 | 322°4 24:30 | 326°0 50:00 | 3349 128:°7 3460 238°8 359°6 366°1 367°5 7T=34'8. H. ie 0:29 28°1 0:39 778 0-57 | 1138 0:89 | 162-2 1°41 197-0 2°89 | 243°3 4°82 | 2726 675 | 286°5 19:04 | 3187 24:18 | 3231 50:0" soz 127°3 343'5 236:7 307°2 362'6 3647 50°72 per cent. Nickel-Steel. T=1151 ory mum t= Lowes rT=—0. H. I 0:29 35°6 0°42 82:8 0:58 1218 0:90 165°8 1°34 | 1967 Ziel aoe 4°54 | 2718 6°91 290°3 18°93 | 3145 Dats) oro 49:20 | 3268 129°4 Salut 239'8 850°5 348'5 3570 | 7T=0. boats & ba I | 1:43 787 2-73 | 1016 3°90 | 1085 | 604 | 1155 | 12:39 | 1240 22°58 | 1288 | 39°94 | 1319 - 100-9 1345 2169 1354 | 3516 1358 — 11”°7. H. 1h, 15°8 ’ 220°7 ; 528 1:08 635 1:37 755 2°41 $81 4°95 1115 868 | 1193 15:43 1251 21°61 1279 40:74 | 1316 99'9 1346 214°5 1350 349°8 1355 Goofs H. iI 016 13°8 0-50 89°3 0:64 217°3 0-75 399°5 110 624 1:45 739 2°05 882 3°56 | 1013 642 | 1112 10:83 | 1183 22°82 | 1257 40°30 | 1297 101°3 13382 2172 1344 3007 1348 7=68'0. H. I. 0:30 23°6 0:44 63:0 0:59 966 0:92 | 1387°3 164 | 179°5 2785) 2Lrg 468 | 2388 6°89 | 258°3 19:09 | 297°8 24:35 | 303°8 50-1 316°4 126°6 3290 234-2 $42°6 341°5 349°4 ON oe H. I. 0-18 12:3 0:49 726 0:65 182-1 0°91 480°6 1:18 585 2°02 804 3°34 929 4:60 994 7°84 | 1084 14:20 | 1163 22°45 | 1215 39:97 | 1206 101°3 ale hiirg 217°2 1334 3511 1340 Effect of Stress on Magnetization. r=0. r=11"7. 7=68"2. H., 1 H. I. H. I. 0°21 12°6 0719 14°4 0:20 26°4 0:49 128°9 0:50 1156 0°50 1278 0°61 296'9 0°62 309-6 0°62 330°7 0:90 676 | 0°79 578 1:02 671 1:13 863 1:02 751 37 7389 2°43 1073 52 932 1:64 859 3°16 1125 2°44 1070 a 22 1031 4:47 1169 5°04 1178 4°34 1077 7-60 1220 8:03 1219 8:08 1151 14:56 1256 13:09 1246 13°51 1193 22:08 1273 22°43 1270 22°61 1229 40°81 1291 40°34 1290 40:67 1264 98°1 1308 97°4 1308 99°2 1300 213°0 LS] 209-9 1317 213-7 1315 343°8 132i 340-7 1321 3845°9 1317 70°32 per cent. Nickel-Steel. Zo) Ole mime lou 0) ©. 7=0. reais uri r=3)"5 7=68''3. H. I H. I. H. I, 120 Fe 0°25 23'6 020 162 0:20 10:0 0:29 ill 0°74 161°9 065 | 1144 0°65 144°1 0°63 108-2 0°93 423°4 0:87 802°7 0:91 376'2 0°95 310°2 1:12 575 1:03) 3) 555 1:25 672 22, 689 1°49 688 1:27 635 1:50 7Ol 1°47 713 2°50 809 2°55 | 790 2°61 774 2°45 764 3°85 890 4°35 | 883 4:91 834 3°96 809 8:07 988 687 9389 7:09 888 PD 858 12°64 | 1029 10°46 983 11°82 937 11-21 895 17°62 | 1053 16°66 1020 16°97 970 16:99 930 22°71 | 1065 21:60 | 1087 21°86 990 21°93 951 46°73 | 1090 44-44. | 1065 44-90 | 1030 45-18 | 1005 92-7 1098 87-4 | 871 1047 87:1 1035 181°7 1101 1746 | ie 1729 1053 172°5 1049 368°1 1104 345°4 | 1081 3429 1056 341:2 1055 | T=3409 gr./mm.?; t=13°3 ©. 99 H 2 100 Messrs. K. Honda and T. Terada on the L=33606 or.jmm.?; +=". C2 { 7=0. 7=12'8. Zao te 7=69'-0. H if 15 (ame eae H. I. H. I 0:21 9-4 0-21 9:0 0:25 31-4 0-22 61 0-56 | 186-2 0:58 | 193-6 0:64 | 232°5 0-67 | 155°9 0-74 | 442-9 073 | 4866 O71 | 528 0°72 | 245-1 0:93 | 784 0:99 824 0:90 | 768 0:81 | 400°8 1:33 | 863 1:34 | 866 1:45 | 839 0-94 | 767 240 | 934 218 | 924 3:25 | 912 1:23 | 800 3:64 | 973 370 | 972 4:64 | 936 2-51 | 863 7-83 | 1016 7-25 | 1011 8:37 | 967 3-75 | 890 11:86 | 1035 11:44 | 1033 12°55 | 989 9°74 | 941 16:56 | 1048 16:81 | 1047 17°65 , 1006 17°63 | 976 21-48 | 1057 21-78 1056 22:78 | 1018 22:72 | 991 44-84 | 1074 44-83 | 1074 46:43 | 1044 46-44 | 1029 86:7 | 1081 86:0 | 1082 89:9 | 1056 899 | 1051 170°8 | 1084 1715 ©1084 172-2 | 1062 1722 | 1062 359'8 1086 3613 1086 361-7 1065 3640 | 1067 | Thus in the case of nickel-steels, the change of magnetiza- tion by tension does not differ much for the different orders of straining and magnetizing. So also in the change of elasticity, we found a fair agreement between the values for different orders, especially at high tensions. On the other hand, the change of magnetization by twist differs sometimes. in a considerable degree for the different orders, while in the change of rigidity the agreement between the values for different orders is generally good, if the tension be large, especially in 28°74 and 70°32 per cent. of nickel.. In general, alloys, for which the hysteresis effect is small, have also a small difference in the changes of elastic constants by magnetization for the different orders of magnetizing and straining. Thus far we have seen that generally the change of magnetization by stresses differs more or less with the dif- ferent orders of applying the magnetic field and stress. In some cases, the difference is not only quantitative but also qualitative, as for the effect of twist in Swedish iron or in 50°72 per cent. Ni, if the initial effect of twisting under constant field be compared with the results of magnetization under constant twist. On the other hand, there are examples. of good coincidence, as in the case of the tension effect in nickel and 70°32 per cent. nickel-steel. Generally speaking, the tension effect shows a better agreement for the different orders of magnetizing and straining than for the torsion Hifect of Stress on Magnetization. 101 effect ; and the discrepancy is remarkable in low magnetic fields, as may be expected from the consideration of the hysteresis effect prominent in that region. In our preceding paper, we have remarked that the de- pendence of the change of elastic constants on the different orders of magnetizing and straining is probably due to the hysteresis effect accompanying magnetization. This ex- planation agrees well with the facts brought out by the present experiment. § 4. RECIPROCAL RELATIONS. Among several important reciprocal relations obtained by J.J. Thomson, the two relations which have connexion with the present experiment are referred to below. Let a cylindrical bar of soft iron, whose axis coincides with the axis of x, be magnetized along its axis. Let e, 7, g, be the dilatations of the bar parallel to the axes of wx, y, z . ; J. J. Thomson obtained the relation n= 2 3{1-H (51) ey 4a, al KL 2) H.fg m—n “(= 3m—n Kl Sle. where J, H, « have the usual meanings, n represents the coefficient of rigidity, and m is connected with the modulus of compression k by the relation k=m—n/3. In his original work the factor 4 is dropped in the right-hand member of the above equation; the error is to be traced back to his equation (41). Since dl=«xdH + Hdk, we have the relation, supposing the strain to be ae constant, -H(S; efg eee ie oH 6, fig Hence equation (1) may be written 0e/ ol m—n (Ol Si SH). ,,7 Gaxa\se >). iy rani A (2) Again, if T is the tension per unit of area, we have 102 Messrs. K. Honda and T, Terada on the en ah (37 uaa St an * (35 nae St) Se uve( Stet eee oe |, hahaa since we may put f=g. If H is zero, we have (50). oe m of m—n or n(3m—n)y Or a: 2n(38m—n) , hence, neglecting the change of elastic constants by mag- netization, we have, from (3), Ol NG id: m ol oe eee | OT) n(3m—n) sa Tee Gy Hence, by (2) and (4), we get B t o (Sa 7 Gn U ($5 T sid (Sa)... * fC + GA mG) i) (5) ahi (2 Bee hence finally we get Oe vor (2 : =(S5)_- . hing As to the twist, J. J. Thomson obtained a relation which, strictly speaking, holds in the case of a thin tube, 2.e., net = 51(S {1- H(S aK a " Here again in his original work, the factor 4 is dropped ; ¢ is not the twist t per unit-length, but it is connected with 7 by the relation c=rt, where r is the radius of the thin tube. As in the former case, we have -H(5) 1) = (24) * nd (SF a), = (SH) . Effect of Stress on Magnetization. 103 in which L is the twisting couple. Equation (6) then becomes ; ai(sut), =(3ir), = a(S» a or, very nearly, 2(07\ _1/ol ASH oiaa he The last equation, if it be integrated over the cross-section of the wire of radius R gives a ( ca a : (2 { Serle Ms ce ee where I,, is the mean intensity of magnetization. Hence finally ; From a thermodynamical consideration, A. Heydweiller obtained two relations, neglecting small quantities, ‘oe Ol, L(1—2c) See ee ee BNE ASD Sab x . (8) fot. ot le ot 9) meee tare cur ap ey ree oil where E is the modulus of elasticity, and o the Poisson ratio. In his original paper, o was put equal to 4. Hquation (9) was obtained by differentiating equation (8), considering o and E to be constant. But in magnetic fields, both co and B vary considerably with tension, as is shown by our previous experiment, so that if we retain the second term in the right- o( a must be subtracted from it. But these terms being small compared with the first term, they may be neglected without causing any considerable error. The second term in equation (8) is also very small. ) On another occasion*, Heydweiller gave relations which are very nearly equal to the last two with the second terms suppressed, and remarked that they are correct. Heyd- weiller’s equation (8) differs from that given by J. J. Thomson by a term of second importance. hand side of equation (9), the term I * Rensing, loc. eit. p. 377. 104 Messrs. K. Honda and T. Terada on the Rensing experimentally tested relation (9) in the case of iron and nickel, and showed a fair agreement between the theory and the experiment. R. Gans criticised Heydweiller’s equations and proposed his own, 2. é., Oe odo wea (2 OB ) ROS Sine AH nee oe inky Vaso ea If the medium surrounding the magnet be air, we may put Mp=1; hence Oe) wo loa = 26) i 27 Ol? aH © ee E E OH’ é A 5 (10) Thus, Gans’s equation differs from that of Heydweiller by 270? the tert EH” which generally is not very small, but in weak fields it sometimes overweighs the first term. As in the case of Heydweiller, differentiating the above relation with respect to '!, Gans obtained an expression for the change of elasticity which differs from that of Heydweiller by the 27 C7 I? E OToH’ E are independent of T, a supposition not admissible in a magnetized wire. By a similar consideration as Heydweiller, A. Kolacék obtained equation (8), and also a relation between magnetism and twist, 2. é., term — Here again, it was assumed that o and 9H aL’ ee where s is the cross-section of the wire. Since L= a Rtn, the above equation becomes OT va ol Tl aR . (12) which coincides with equation (9). M. Cantone obtained two relations by equating the change of magnetic energy due to a tension or a twist to the change of elastic energy caused by magnetization, %. e., o (Har & (aan en = nf d and mas ( d 9 Liffect of Stress on Magnetization. =, AOS where ¢,, and T,, are the magnetic strains. By differentiating the above equations with respect to H, we have or = op(H Se), . aac) or seer (Sa). - Res ) Cantone tested the second relation by experiment and found a satisfactory agreement in iron and nickel. For the first relation, he also made a comparison between theory and experiment, but the data he used were taken from experi- ments by different physicists, so that they do not refer to the same specimen. Though the comparison shows a satis- factory agreement, it is not certain whether it was by chance or not. By a direct method, Dr. 8. Sano obtained the relation de _dI_, 1—2c) , 27 3(«7H?) Als ol’ eee Peon” . (15) where #9 is a term in the expression of susceptibility, which is independent of the strain. Since l-==« )H, Sano’s equation practically coincides with Gans’s. For the change of elasticity, Dr. Sano obtained (16) which is practically the same as Heydweiller’s equation, but different from Gans’s by a term not negligibly small in weak fields. The above equation was obtained independently of the relation for ae As to the effect of twist, Dr. Sano obtained an equation which can be transformed into (12). Thus far, the relations for Be given by Heydweiller, Gans, oH Kolacék, and Sano all agree with one another in the first : I important term ee Relation (1) given by J. J. Thomson does not differ in reality from others. Relation (13) given by Cantone also coincides with others in the first term, provided « is independent of H. ‘The second term -I(1—2e)/E in (8) and (10) may be neglected for the first 106 Messrs. K. Honda and T. Terada on the approximation; the third term in relation (10), which becomes important in weak fields, is properly to be added. The relations for ok oH Sano see agree with each other in the first term — given by Heydweiller, Gans, and folly aT: Gans’s differs principally from the others by a term not generally small in weak fields. a Kolacék’s and Sano’s coincide with each other. Thomson’s relation (6) also does not differ from the others. If « be independent of H, Cantone’s formula coincides with the others. Thus, the chicf relations to be tested by experiments are as follows :-— As regards the relation for de _ OI, nar Olly Ol Alon? Lob ol Hea pole ee 25 Ole ne) OH nk?0r ~ Pra Our present experiments combined with the previous investigations on the change of elastic property due to magnetization furnish us with good materials for the testing of these relations. Our results taken as a whole, give for the effect of tension as well as of twist two different sets of experimental data corresponding to the different orders of applying the magnetic field and the stress. The mutual correspondence of the results in the previous and the present experiments in this respect is tabulated below :— Change of Strains by Magnetization. 1. Magnetic elongation under constant tension. Elongation by tension under constant field. 2. Magnetic twisting under con- stant couple (Barus’s method). Change of rigidity under con- stant field (oscillation method). Change of Magnetization by Strain. 1’. Magnetization under con- stant tension. Change of magnetization by tension under constant field. 2'. Magnetization under con- stant twist. Change of magnetization by twist under constant field. Fiffect of Stress on Magnetization. 107 The theoretical relations to be tested were, however, deduced on the supposition that the magnetization is independent of the order of magnetizing and straining, so that in comparing the theory and the experiment, too much weight is not to be placed on the above correspondence. a : es and a were deduced from our previous experiment, while the corresponding values for aL Ol aT or” and o were obtained from the present experiment. In the following tables Ea and Ea are the values of ~ iS OT ba Ol’ Ja The values of these differential coefficients obtained from curves (61, T)x; 2 while EA and [S| are the values of the coefficients T T ror : from curves (I, H)>. Oe | 5H cs the value obtained from the results of the elongation method ; while = E K? LOH Ir is that obtained from the tension effect on magnetic elonga- tion. a a is the value of the coefficient obtained from tLOHJIy it the result of the oscillation method, and | 2 that Ty oH T Warel! obtained from Barus’s method; while : B — ; en - are the values obtained from curves (61, 7)g and (1, H), re- spectively. To find the values of these differential coefficients, corresponding curves were carefully drawn on section papers ; a fine straight line drawn on a thin glass plate was brought into contact with the curve at the required point and the trigonometrical tangent of the inclination of this straight line ie evaluated. Some of the calculated results are given elow :— 108 Messrs. K. Honda and T. Terada on the Swedish Iron. | \T=1627 er./mm.? 1'=5535 gr./mm.* pce jel ies yee ~ ge [rary | fouqie ° | oH a or E9H oH En H 1n'Coah Measured in 10 eS 59 \18 14729 | +68. 1483 | -+1-0)| 220 eeenm 1L-Oyeri4. 4-13 || 19 Fea 0:7, | eo o ma eG 242 |4+ O8/+ 0O6/ + 33 |+ 47) —10] — 08 —7'0 366 |— O7|— 17) + 20 |+ 27) -17 |) — 19 —6'2 971 |— 1:8 \/— 24 ae + 12)-—21 | — 2:0 —5:0 207 |— 20/— 22 +07/-19 |) — 2:3 —8-0 367 — 14\/— 17 + 04/)/—14] — 19 ah =4754 gr./mm.?2 H oh os] E or oH |r Or | u ot | Measured in 1Osne 59 | =i¢ ne | am 11:9 = 19 —29 | 4 24-2 88 — 28 at 36°6 — 33 — 10 —12 97°1 + 0:05 ae =a 207 + U:03 — 06 —34 367 + 0:00 — 03 wee T=8255 gr./mm?. 7=6'3 7™=6'3 7T=6"3., s o- | sfol H. a | Bah I =| TLOL Ju ae T Measured in 10m 4 anil +128 464 6 —13 + 92 — 80 8 a esc + 48 — 48 14 H028 | — (36 4 24 iw 22 =O Pe an 12 " 50 Fi200 1 11 + 30 110 =g40) |= 20:38 ee nOT 200 +012 | — (Ohilil + 00 300 La G Tae 10:07 zs Effect of Stress on Magnetization. 109 Tungsten-Steel, T=1693 gr./mm.? | T=5762 er./mm.2 | oe Qn OL? eas oe | pat) | ary oa H. aH Gel. | mi Tlr} E 9H or or Measured in <= 106 | +09 | 4+ 33 | 4+ 00 |/+ 065} 4-07 | +46 | +00 Pea) oleh) 23-0) | E24. | 890:6) || Ob 4218. |. 4218 434/434 |+43 /4 00 /+48 | +55 | +44 | +00 984 | +057 | + 038] — 29 |+ 12 | 40:35] +040] —5:0 210 —010 | — 0:32/ — 30 |+ 050] —025] —038| —36 341 | —0:25 | — 032] — 31 |+ 023] —0-29] —036| —36 | T =4947 gr./mm2 See eel. ee ea | i? bee H kK? Ee ea or? ju | or? jr Measured in 1072", 23-9 —36 ay Pores 243 43-4 S55, 2a5 — 62 0-0 98°4 =1s — 0:83 — 00 4 1-2 210 —0:0 —0°32 — 00 + 42 341 +041 —0:17 | — 00 | 0-0 T=3340 gr./mm?’. | | 7=20'0. 7=20'0. sTol He 2[f5 H a is r a H Measured in 10° * 10-7 +0:23 F +15 Teed +0°10 —10 +79 | 301 —0:04 — 0:53 +32 98'8 —0-03 —0-15 +03 364 —0:03 | —0:03 —0:04 110 Messrs. K. Honda and T. Terada on the Nickel. inaacp | T=1540 or./mm.? T=5240 gr./mm.” | Qa OI? ic (Gall u Ea | Eon | ar |u Messnredaan Ome 108 63. | a7 7 ipa 8) oe) | 2640 lee ees Bb) e277 | 8387] 249 | Lon \ 2 ice eee eee Qh | 293 | 99 | 2e8 | 40-06 | = 3a | ea a eee 135 —068 | —0-71 | —0-66 | +002 | -20 | —16 —18 206 0°32 | —032) =038 | 0:01 | —0:80 | 20720 = ie 365 —0-05 | —0-05 | —0-05 | +000 | —0-17 | —017 | —03 T=4498 gr./mm.? By cares ol ol ieee ae 7 eee om |e Sek Measured in 107 /° | 10°8 42:3 4+ 2:3 +20 + 00 31-7 Ee ar 4+ 492 +89 +153 62:5 +76 413-7 —26 4 78 135 —3°3 — 52 —3°6 4+ 4] | 206 Dicy = 18 ~0:85 + 34 365 a Twas 0:39 | 4 BA Tm = 3400 gr./mm.? fee col Oe: | o09Gior sl eeeto er: 3546 er. r=12'6. H lpor -| 2 s E S [2 ; OH_|n 7LQH_JIr 7LQLJn 7LoLtiz | Measured in 10° 2:4. +.0:20 Sled! +19 a 4:0 40:27 — 3-4 +36 +030 10-6 +0750 425 435 43°5 93°8 + 1:28 ow +1:9 +18 49:6 41:24 +04 410-7 +0:96 97-0 —0-02 —0-48 40°78 —0°39 168 — 0-26 —0'50 +017 —0:26 | 358 —0°20 —0-20 +0-05 q Effect of Stress on Magnetization. 111 28°74 per cent. Nickel-Steel. | T= 1497 gr./mm.2 T=4856 er./mm2 ee! | 7 anor ||| eat) |e oP aH 1 Ver EoH | of |Latlu|Larir Measured in 10° 4:7 8:0 11 25 271 2:2 2°4 41 10°6 30 2:2 16 0-4 1:2 16 2°9 24°3 43 16 17 0-2 1:0 12 2'6 5D'O 1:0 1:3 16 0-04 1:0 11 2'6 173 1:0 1:2 15 0:03 O-9 11 ol 374 1:0 1:0 15 0:00 0:9 1:0 3'4 T=4170 gr./mm.? = Sala|—wl Sale| [Se Bride |) 8? On ja E? | 9H Jr OL? In ar Ir Measured in 1072" 4-7 —4°] —3°0 —15~— a 10-6 —3'0 —2°6 a —dl 94°3 —16 —1°6 —0°3 Wen 55°5 —02 —0°3 —O0'1 ae 374 —0:2 +01 —0:0 —5dl1 T= 4200 gr./mm.? ie) 4096.er. |) 4240 er. | 4240;er) | 4201 er.) |) 4a21 ler. 17 or i KE =| |, T L H TLOQH_Ir 70 oe eS? |) p= 8e9. | r=19"1. Measured in 107* 3°6 ey —30 —2:9 —45 —3 68 —1'3 272 —2°0 —3:2 —2-0 14°8 —0°95 —0°50 —0°65 —1-2 —0:96 35°6 —(0'25 —0-20 —O17 —0-44 —0°31 66°7 —0°15 —0'10 —0-03 —0:00 —0'00 112 Messrs. K. Honda and T. Terada on the 50°72 per cent. Nickel-Steel. T=890 er./mm.? * T=6652 gr./mm.? mi eld ol E 2x Ql" | 02 E E | ; oH E nj LOTiIt}) EQ@H | OH or ts] Lettre | Mereureda alone 19 | 11:9 20 9-0 11:2 | —062 | —0-16 | —0-78 Bd 6:3 8-2 71 22 | —083 | —016 | —0-42 10°7 3-7 57 4-0 10 | —0-25 | —0-08 | —0:57 23:8 17 2-2 1-9 01 | —009 | —0:05 | —0-51 51-4 0:34 061 | 0-70 6-07 —005 | —0:02 | —051 151 0:04. 0:03 | 0:32 0:01 —001 | —0-01 | —0°51 360 0-03 0:0} | 0:25 : 0:01 | —0:00 | —0:00 | —0-36 | T—5003 er./mm2 1 [OE | or Ea [Se] H. 7) Je (SF H | BE? [ee T Ol? ju ol? _Ir Measured iatOn 5D —019 —0-20 —051 —0°66 10:7 —0:13 —0-15 —0:10 —0:56 23:8 —0-10 | —0-09 —0:10 —0°36 51-4 —0:04 —0:03 —0:00 —0-41 151-0 —0-01 —0:01 —0-00 —0°:34 360 —0-00 —0-:00 | —0-00 —0'23 i | Tm =3400 gr./mm.” m ...| 8277 gr. | 3445 gr. | 3445 gr. | 3409 gr. | 8409 gr. | 3409 gr. Ir or 1 OF | s fol s [ ol | st H aL H_J7- T e H 7LQLJjr H. | r=62' | r=186 | r=69' | r=028" |) r= I7-4! Measured in 107°. Mey. |) anes 18 Eg 49:1 —1-2 —16 10:5 —1'8 —17 —1-4 45-0 aca —15 24:5 95 |) —_-0 —090 | 42:4 —0°69 078 496 040m 0'47 4 0:47 ||) Es —0:35 —0:44 1090 Oza 0:27 Wie 0-17 || 0-48. | 0718 —012 212 _0-07 | —0:05 | —0-05 | +0:09 | —0-04 —0-00 377 _0-02 | —0-02 | —002 | +000 | —0-00 —0-00 * Under a high tension, this specimen slightly contracts by magnetization, which is also to be expected from the effect of tension on magnetization. Liffect of Stress on Magnetization. 113 70°32 per cent. Nickel-Steel. 806 gr./mm,? | | Ss T=3277 gr./mm.? eee: | fol) | pola) |2nor | oe. tt aca "| oH He ek 1 oi | oH | olin Lotiz | Measured in 107! Ae. |. 19 Path 20 BL 38 d1 Ay ple lh 14 12 3 2°3 4-6 37 Dil 6:2 (fal 9:2 IIs 16 2-4 2-6 10-7 ile 3°6 4-1 0°56 0°89 1:0 1-0 24:5 0-4 0-6 ol O13 O17 03 0:0 49°8 0-09 0-20 2°6 0-03 0:08 0-1 0-0 129 0-01 0:03 2-0 0-V0 0-01 OLOF | 00 300 0-01 0-00 2:0 0:00 0:00 0:00 0-0 a oye ulvay tau elas He ob : ‘orl | ot : ol eel st ln st |. Measured in 10”. 51 72 —6°7 ate Ome ie Gal 10-7 —2:3 —16 —153 —6'3 PAIRS) —0°77 —O%7 —0°5 —16 49-8 —0-08 —0°10 —0'0 —0°0 129 —0-:02 —0:02 —0-0 ae 300 —0-00 | —0-00 —0-0 Tm = 3336 gr./mm.? 7 _,,| 3198 gr. | 336i gr. | 8361 gr. | 3366 gr. | 8366 gr. | 3366 gr. | [8 aon 2 | =| S|, | 7 LOL Lr H. r=118',| r=18:0!.| r=11-8'.) r=18-0'.| r=345'. Measured in 107”, 31 —24 —1'8 —1-4 —0°35 —0-70 —l1 5-0 2:8 —2:0 —1:2 —0°83 —14 —1-0 10°7 —1'3 —15 —12 —0-76 —079 —0°95 234 —0-76 —0°84 —0°72 —0'52 —0'48 — 0°67 47-2 —0°82 —0°35 —0°32 —017 —0'18 — 0°56 105 —O12 | .—0:10 —0'10 —0:04 —0:07 —0°53 191 —0 04 —0:03 —0:02 —0:00 —0°02 —0°53 349 —0°01 —0-01 —0-01 | —0-00 | —000 —0°53 Pin Maga. 0. Volta: No. 79. July 19C7. if 114 On the Effect of Stress on Magnetization. Among all the specimens tested, nickel affords the best evidenee in favour of the theories above tested. The dis- crepancies due to the difference of the orders of applying the stress and the field, are generally small, when compared with those in the case of other specimens. The agreement is especially good in the case of tension effect, if the term Ae (ole E 3H be suppressed; the differences between the values of and or are of such an order of magnitude that they may be explained by the errors introduced in estimating these values from the corresponding diagrams. For the rest of the specimens, the agreement is tolerably good in many cases, except a few cases in which it completely fails. Generally speaking, the tension effect shows a better agreement between : -n OC : ol theory and experiment, if aH be compared with E : It H while Ea deduced from the (I, H)r curve is often of a different order of magnitude, as in the case of 28°74 per cent. te iol O71 Ni. As for the comparison between — eH and owe the agreement is less remarkable, but the discrepancies may in many cases be due to the errors introduced in estimating a aq 2 the curvature of the curves for obtaining Ea Ss Bal deduced from (I, H)r curve is often of a different order of magnitude, as in the case of Swedish iron. For torsion effect, things are much more complicated, except in the case of nickel and nickel-steels of 28°74 and 70°32 per cent. of nickel, in which the agreement is fairly good. For the last : Be. two specimens, aan generally agrees with — EE x T rl ea or ~[2a |: while in the case of 50°72 per cent. Ni, the former is of a different sign from the latter for small twist. In all cases, the discrepancies become less in high fields. 270 P As to the term B a obtained by Gans and Sano, it may be noticed that its introduction makes the agreement between theory and experiment rather worse. The origin of this term is, however, to be traced to the fundamental assumption that at the ends of the specimen wire, the lines of induction issue On the Forcing of Oscillations. 1015: normally from its end faces—an assumption far from being realized in our actual experiments. Hence the importance of this term must be reduced, when applied to the case usually ‘subject to experiments. Thus far, the agreement between theory and experiment is in general to be considered as fairly good, it we consider the difficulties encountered in measuring the minute strains caused by magnetization, and also the considerable dependence of the magnetization upon the order of magnetizing and straining. Since the theories, which are based upon quite different considerations, all agree with one another in the first important term, it may be concluded that for the first ap- proximation, they are all verified by the present experiments. It seems, however, impossible to decide experimentally the correctness of the terms of second importance for ferro- magnetic substances, in which the hysteresis effect appears in no inconsiderable amount. In conclusion, we wish to express our best thanks to Dr. S. Sano for useful suggestions in working out the theoretical part of the present investigation. V. On the Forcing of Oscillations by Disturbances 2 Different Frequencies. By ANDREW STEPHENSON * les HE simple oscillation of a system may be influenced in two distinct ways: either by a force which is a function of the time alone, or by a force which is a function of both the time and the configuration of the system. In the former case resonance occurs only when the period of the force is equal to the free period of the system ; in the latter the effect of the disturbance is cumulative when the ratio of its period to that of the system has any value within a certain range in the vicinity of 47, where 7 is any integer +, the intensity being maximum when r=1. We now enquire as to the effect of the two different types in joint action. Will the two together under any circumstances produce and con- tinually intensify an oscillation when each acting separately would have no appreciable result ? * Communicated by the Author. + “On a class of forced oscillations,” Quarterly Journal of Pure and Applied Mathematics, no. 148 (1906). The case of double frequency, r= 1, was examined by Lord Rayleigh, ‘“ On the maintenance of vibrations by rcee of double frequency, and on ene propag ation of waves through a ‘medium endowed with periodic structure,” Phil. Mag. vol. xxiv. (1887), 12 lace Mr. A. Stephenson on the Lorcing of 2. The equation of motion under such action is w& +p? (1+ 2a, cos nt + 2a, cos 2nt +...) v=asin (gt+e). The properties of the forced motion follow readily from consideration of the free motion, the solution for which we shall therefore briefly recapitulate*. For the free motion, 2.€. a=0, we have w= > A;sini(e—rnjite} where =o Ay we (e—rn)?} + pert ay(Ap—1 + A+41) + a(A,—9 =e Ap«2) +.. f ails On eliminating the A’s, we obtain the infinite determinant : : , a les ° 2D) ay [— 1] ay a9 ° ° as ay [0] ay as ots te oe lL eerie where [7] denotes u?—(e—rn)?. This equation determines ¢, and the roots are all included in the form +cey—rn. If ¢ is real the motion is made up of simple elements of constant amplitude, but if ¢ is complex the amplitudes continually increase, as one part of the solution contains a factor e™, where A is a positive quantity. The forced motion due to asin (gt+e) is given by e= > A,sin {(q—rn)t +e, where — A, fu? — (9g —rn)*} + p74, (Ap-1 + Ani) +ay(Apot Arie) +...$= 0, except in the case r=0, when | A (we — 9?) tet a(A_1+ Ar) +a(A_o+ As) +...}=a. (0)’ These equations determine a convergent series whatever the value of «. The conditional equation (7)/ is the same as the corresponding equation (7) in the free motion with gq for c, except that in (Q)’ the right-hand side is a instead of zero. If, therefore, ¢ is real, the A’s become large without limit as g is taken nearer and nearer to ¢ ; and in the limit when g=c the solution passes over into the form w=t>Br cos {(¢—rn)t +e} + LC, sin { (g—rn)t e}. * The method is due to G. W. Hill, “On the Motion of the Lunar perigee,” Collected Works, vol. i. The properties of the infinite determinant and the numerical evaluation of ¢ are dealt with therein. (7) OF Oscillations by Disturbances of Different Frequencies. 117 Thus a large oscillation is forced if qg is nearly equal to + ¢) — rn and the effect is continually cumulative ig= +¢j—7n; 2. e, af the frequency of the forcing disturbance is equal to the frequency of any periodie element in the free motion under variable spring. If the variable spring ‘deel forces an osciliation ¢ is complex, and therefore whatever the value of g the forcing disturbance cannot help in the continual intensification of the oscillation, although it may force a motion of amplitude large compared with a. 3. In the above it is assumed that the variation in the force of restitution is periodic. If, however, it is made up of two elements of incommensurable frequencies, @ +m? {1 + 2a; cos (nyt +€,) + 2a cos (not + €) }a=asin gt, and for the free motion 2=DA,,.sin {et +r(nyt +e) + s(ngt +) }, where the summation includes the zero and all positiv ye and negative integral values of 7 and of s. On substituting for we find A,,.(w?— (e+rn, + sng)? ] + we? {ay (Aras + Aris) + 42(Ar, ort Arsti) f= a system of equations determining a convergent series: c is obtained as before by eliminating the A’s, and the roots are all included in the series +cey+7n,+sn:. The examination of the forced motion follows a similar course to that of the preceding case, and we find that the forcing disturbance has a continually cumulative effect if g= +c9+7n,+sn, where vy and s have the zero or any positive or negative integral values. 4, If the system is subject to kinetic friction, & + 2hke+w?{1+ 22, cos nt + 2a cos 2nt-+...}w=asin (gt +e). To find the free motion we pub s=¢ “y ; then yt wel —R |p? + 2a, cos nt + 2a, cos 2nt+...by=ae* sin (qt+e). The complementary function is found as before: itis clear that in all cases, whether the “ec”? of y is real or complex, # must in part contain a harmonic series with an exponential function of ¢ as factor. Now the free motion is also given directly by x= > [Arsin {(c—rn)t+e} + By cos {(e—rn)t +e; ], 118 Mr. A. Stephenson on the Forcing of where A, mw? —(e—1n)?} + po? fey (A,—1 + Ay 41) + ao(A,-2 + Appod +... }—2k(c—2n)B,=0 . (274) Br{y?— (c—rn)?} + 4? {a (Bri + Bry) + #5(B,2+ B, 2) +... + 2k(e—rn)A,=0. © (79) Comparing the two solutions, we observe that ¢ must be complex. For the forced oscillations we replace ¢ by g and the right-hand side of (0)' by a: ¢ being complex, it follows by the argument of § 2, that there is a definite limit to the amplitude of the forced motion due to a sin (qt+e), although this limit may be large compared with a if the frictional resistance is sufficiently small. It may be noted that for the numerical evaluation of a forced oscillation under friction, it is expedient to replace the. trigonemetric functions in the equation of motion by their exponential equivalents and to solve in exponential series. 5. When the variation in the spring is small, the solution for the forced motion may be obtained readily by approxima- tion. We shall investigate this in the frictionless case, apart from the general theory, thus arriving at a more distinct, conception of how the magnifying effect is produced. If the equation of motion is & + pw?(1+ 2a cos nt)v=asin (qt +e), for the forced oscillation “a=>A,sin : (q—rnjt+e}, Mr | GS (— of”) | 7 | fT (4? —(g—mny} provided w?—(q—rn)? is not small for any of the values of r. In general, therefore, the motion approximates to the forced motion under constant spring. In the exceptional case when pw’ —(q—rn) is small for some value of 7, m say, we consider the solution as made up of two parts, y and z, where y is that part of the series in (i) which lies on the same side of the term in sin {(q—mn)t+e} as the term in sin (gt+e). Thus yt w(1 + 24 cos nt)y=a sin (gt+e)+bsin {(g—mn)t+e}, (— ctf” ) nv| |m| approximately, where A,=a where b=a i 5 my TT {u?—-(g—rn)?} 10) Oscillations by Disturbances of Different Frequencies. 119 and therefore z+ p?(1+4+ 22 cos nt)z = —b sin ; (g—mn)t + et : On putting g—mn=p—p, where p is small, we have ss B,sin {(u—p—rn)t+el, in which ae B,(rn + p)(24—p—rn) +eu7(B,-1+ Bei) =0; hoa tor r—(, By p(2u—p) + au?(B_1+ By) =—D. In order that B, may be large compared with a, p must be of order 2? and be adjusted correctly to the order a!”!+!, If p has the value obtained by putting =O in the con- ditional equations and eliminating the B’s, the solution for the forced oscillations passes over into the form ro) ltoa s=t> B,cos}(u—p—rn)jt+et}+ C,sin{(u—p—rnit+et, —o -—oto -1 where Ba@nt+p)2+p—rn) + ap?(B,_1 + B,41) =0 an —2B,(u—p—rn) + C(rn+ p) (24 —p—rn) + ap? (C,-1 + Chir) =0, except for r=0, when —2B(u—p) tau?(C_1+C,)=—0. Hence Bo=+6/2u, and B,=B,— Ses approximately. Irn(24—rn) 1 Thus the rate of increase of amplitude is proportional to |a™, a result which shows how rapidly the intensity of the magnifying effect diminishes as m increases. In practice, the equation of motion is not linear in «, the force of restitution being in general an odd function of w containing z? and higher powers; nevertheless the above investigation holds good so long as x? is negligible compared with 0, i. ¢., if a? is small compared with nv—— ‘ [m| m ; as Gre eli (97%) j- 1 If this condition is not satisfied the linear equation does not furnish a sound approximation, and higher powers of wx 120 Mr. A. Stephenson on the Forcing of must be included. ‘he magnifying effect of the joint dis- turbance depends upon the adjustment of the frequencies ; and as the frequency of the free motion is a function of the amplitude, the action can have appreciable effect in any particular case only for a certain range of amplitude. 6, The examination above brings out the interesting fact that when the system is sensitive to the disturbance the oscillation generated is approximately of free period (under variable spring): thus a system of which the spring under- goes periodic variation furnishes, in these cases, an exception to the rule that forced vibrations follow the period of the exciting cause. If a crowd of direct disturbances acts on the system each in general produces a forced oscillation of its own period; but these e'erments are small in comparison with the oscillations of approximately natural period gene- rated by those disturbances to which the system is sensitive. In this action, therefore, energy is given out by the system in the period in which incident energy is most readily absorbed. The phenomenon of fluorescence is the outstanding physical case of a direct disturbance exciting an oscillation of different period, and it has beeu shown that in glowing sodium vapour ‘“‘ the fluorescence spectrum is the exact complement of the absorption spectrum”™*. Thus an assemblage of simple systems of variable spring furnishes a mechanical analogue to the vapour with regard to fluorescence, at least in so far as the main features are concerned. It is specially to be noted that the fluorescent spectrum depends upon the frequency of the incident monochromatic light; this is in accordance with our analogy, for of the assemblage of systems only a certain definite group is sensi- tive to a disturbance of given frequency. From this point of view, again, the lengthening and the shortening of the period of the incident disturbance in emission are essentially similar phenomena, and the exceptions to Stokes’ law cease to be exceptional. 7. Owing to the counteracting influence of friction it is difficult to realize more than a few cases of the joint action in practice, but the effect may be observed readily in the two * “The Fluorescence and Absorption Spectra of Sodium Vapour,”’ by Prof. R. W. Wood and Mr. J. H. Moore; Phil. Mag. Sept. 1903. Prof. Wood found subsequently, Phil. Mag. Nov. 1906, p. 499, on more detailed examination that many absorption lines do not appear in the fluorescent spectrum. In our analogue these would correspond to vibra- tions of constant spring. It may be noted that the equidistance of the lines of a group in the fluorescent spectrum produced by monochromatic stimulation is in accordance with the properties of the mechanical system. Oscillations by Disturbances of Different Frequencies. 121 leading cases given by g= c+n|. A body suspended by a light spring forms a convenient system for this purpose. When the body is set into vibration vertically and the spring seized at the point of suspension and oscillated horizontally, a. comparatively large pendulum motion is generated if the sum or difference of the vertical and free pendulum fre- quencies is approximately equal to the suspension frequency. In a system with two, or more, degrees of freedom, if one normal coordinate is subject to direct forced oscillation, a variation of frequency n, say, is In general produced in the spring of the other coordinate, which will therefore respond to a direct force of frequency ¢+rn. 8. If a system containing a cyclic coordinate is making small oscillations about a state of steady motion under the action of a periodic disturbance, the effect of the disturbance at any instant depends partly upon the configuration of the system in the small oscillations. If only two coordinates are affected the equations for the small oscillations in frictionless motion are of the form & + ap (1+ 2a, cosnt +28, sin nt+...)y +u?(1+ 24, cos nt +28,sinnt+...)v=H sin gt+F cos qt, y t+a'p! (1 + 24,’ cos nt + 28,' sinnt+...)e+u?(1+ 2a,! cos nt +28,’ sin nt+...)y=E’ sin gt+ F' cos gt, where powers and products of « and y are neglected. The complementary function is of form s SS > [A+ sin (e—rn)t+B,cos (e—rn)t], ay = a [ A, sin (c—rn)t +B, cos (ec—rn)t]. On substituting for x and y and eliminating the coefiicients from the conditional equations the frequencies ¢, and ¢, are obtained. Complex values of ¢ indicate that the disturbance acting through the spring alone produces a cumulative effect. The forced oscillations are of similar for m, but with g for ¢; and if ¢ is real it is evident, by the argument prev iously employed, that the oscillation is of continually increasing amplitude if =e TOF ak — TA. The approximation made in taking the equations of motion as linear holds good for r=m if the amplitude of the forcing disturbance is small compared with the mth power of that of the spring; otherwise higher powers of « and y must be taken into account in the equation of motion. 122 Mr. 8. H. Burbury on Diffusion of As an example, consider the question of the stability ofja symmetrical top spinning in small oscillation about the vertical when acted on by a periodic force through a point in the axis. If the force is vertical the equations of motion are : —Ant+ Cmé+ Mgh(1 +2 cos nt)n=0, A£E+ Cmn—Mygh(1 + cos nt)E=0, so that the effect of the applied force, to this degree of approximation, is to produce a variation in the spring alone ; hence a comparatively large oscillation is generated if n lies near to a certain value in the vicinity of 2u,/r or 24,/7, where #1 and py are the natural frequencies and r any integer. If, on the other hand, the force is horizontal the spring is not affected, and there is instability only when g=p, or py. When the horizontal and vertical forces act together, —Ant+ Cmé + Mgoh(1+acos nt)n=Mogh asin (qt +e), AE+ Cm —Mgh(1 +2 cos nt)E=0 ; so that the joint action produces a large effect when g=|ern|, where ¢ represents either of the frequencies under the vertical force alone. The spring and direct disturbances may be produced by giving the point of suspension periodic motions in the vertical and horizontal directions respectively ; and for readily ap- preciable magnification it would be necessary to have the vertical vibration of large amplitude, VI. Diffusion of Gases as an Irreversible Process. BYES. Le Ss URBUR Vel vhetSee epee G. H. Bryan in his recent work on Thermo- dynamics (Leipzig, Teubner & Co.) states (p. 125), “when two gases at equal pressure and temperature mix by diffusion, the loss of available energy and consequent gain of entropy is the same as would occur if each component were to expand by rushing into vacuum till it occupied the same volume as the mixture.” This statement appears to present some difficulties. If in a cylinder of volume 2v, one half on one side otf the piston is occupied by oxygen at given pressure and tempera- ture, and the other half is vacuum, we have in_ that arrangement available energy. We might, by placing the axis of the cylinder vertical with the oxygen at the bottom, * Communicated by the Author. Gases as an Irreversible Process. 122 cause the oxygen by its expansion to raise a weight, and so convert part of the energy of the oxygen into "mechanical work W. If the gas is allowed to escape into the vacuum, no such mechanical work is done, or thereafter can be done, by the arrangement. We have lost an amount W of avail- able energy. If instead of vacuum, the upper half of the cylinder be filled with oxygen at the same pressure and temperature as in the lower half, no mechanical work can be done by that arrangement. And therefore none can be lost by allowing the two volumes of oxygen to mix by diffusion. In fact if they do mix, the whcle system remains in the same physical state, and therefore, by Art. 86 ot Bryan’s work, no entropy has been gained, nor available energy lost. If the second half of the cylinder instead of with oxygen is filled with nitrogen at the same pressure and temperature, there is according to Bryan a loss of available energy tor each component. But it is no more possible to use the oxygen-nitrogen arrangement for the practical purpose of doing work than to use the oxygen-oxygen arrangement. Where then is the loss of available energy when the oxygen and nitrogen are allowed to mix by diffusion ? The explanation is probably as follows :—Bryan asserts (p. 123), and he is a very high authority, (1) that when two gases mix by diffusion the process is an irreversible one. And I understand him to imply (2) that every irreversible process is attended by a loss of available energy. Both these positions (1) and (2) seem to be disputable, even against so high an authority. Weed as to the diffusion of gases being an irreversible process. We know by familiar experience, that if two gases mixed in different proportions but at the same pressure and temperature are separated by a partition, then, when we remove the partition, the gases begin to mix. That experience however, so far as regards the initial stages of the process, is as consistent with the diffusion being a cyclic—i. é. reversible —process as with its being an irreversible one. Yor if there be a cycle, it may be described in either of two directions, ABC or CBA, one of which, in the given initial state of the system, is towards, and the other from, more uniform mixture. By removing the partition we determine the direction to be towards more uniform mixture. For let the gases be oxygen and nitrogen in a cylinder et ioce axis shall be that of a, ad. let the partition be at right angles to it, the oxygen being say at the left. Before the partition is removed, oxygen molecules striking it with velocity wu parallel to « have that 124 Mr. 8S. H. Burbury on Diffusion of velocity reversed, and owing to these reversals the mean # velocity of all the oxygen molecules is zero. A short time after removal of the partition, those oxygen molecules which, but for the removal, would have had their 2 velocities u changed to —u, will still retain their original 2 velocity wu. So by removing the partition we have in effect given to the oxygen gas a mean momentum towards the (originally) nitrogen half of the cylinder, and to the nitrogen gas an equal — mean angaaenina towards the oxygen half. We thus determine the direction in which the cycle, if there be a cycle, is described. In the limiting case of molecules having infinitely small diameters, so that collisions will not occur, it is evident that the motion must be cyclic. But it will be argued that the cyclic motion is destroyed by the collisions which actually occur. Before considering the general effect of this, we may note the application of it to the inference (2), which ‘I under- stand Bryan to draw, namely, that the diffusion process, if irreversible, must on that account be attended by gain of entropy. May we not reason thus: The gain of entropy due to all the collisions is the sum of the gains of entropy due to the collisions separately. Therefore it is zero, because each separate collision is a reversible process attended by no gain of entropy? Is not the implied assumption that if the diffusion is an irreversible process, it must on that account involve gain of entropy, erroneous ? As to the general question of irreversibility, let the two diffusing gases be equal in quantity, and both at the same pressure and temperature. And let their respective densities at any point at any instant be denoted by p and p’. Let = (aa ven the integration being ie oe the containing vessel. Then alee dK x doa! Ve =| (o-6 SEN dt. It can then be proved on practically the same assumptions as those which are necessary in the proof of Boltzmann’s H theorem, though not by identically the same method, that Ke qe 28 On average negative, so that K diminishes until it c acquires its minimum value zero when p=p’' everywhere. The necessary assumptions are, in Boltzmann’s language, ‘dass die Bewegung moleculiir ungeordnet ist und fiir alle Folgezeit bleibt.” I have tried to give a definition of the Gases as an Irreversible Process. 125 expression “moleculir ungeordnet,”’ namely this :—The chance that any molecule at any instant shall have assigned velocities is independent of the velocities and positions of all the other molecules for the time being. ‘This I cal! condition A. That, if it be accepted, is, so long as 1t remains dH true in fact, a sufficient foundation for the proof that —— dk ae” assumed to exist cannot possibly continue to exist indefinitely in a system completely isolated, that is completely protected from external disturbance. With my definition, therefore, the proof fails altogether that H or K continues irreversibly to diminish if the system be isolated. If my definition be not accepted, will anybody make a better one? I think if he does he will find that ‘‘ moleculir ungeordnet” represents a state of things which, like my condition A, cannot possibly continue to exist indefinitely in the isolated system. The Loschmidt objection, that if you were to reverse all the velocities, the system would retrace its course, applies only to the isolated system, and as applied to the isolated system is in my opinion a conclusive objection to the theorem that the diminution of H or K is in that system irreversible. The defence of the theorem which has met with wide acceptance, is that the reversed motion, although possible, is infinitely imptobable compared with the direct motion. But if Maxwell’s law prevails—and it cannot be denied by advo- cates of the H theorem—any set of velocities and the reversed set are equally probable. If on the other hand the system be not isolated, but subject to disturbances, Loschmidt’s objection is not true in fact. For on reversal oO: the velocities, the svstem would not retrace ats course, beyond the point at which the last disturbance occurred. It may therefore be true that if disturbances are always occurring, e.g. if you keep stirring the mixture, H or K will go on diminishing ¢ to minimum. I venture to suggest the following as the true theory. The motion Is in theory cyclic—z. e. reversible—in both cases, the H theorem and the diffusion—that is it is cyclic prov ided that the system be completely isolated. But that condition of complete isolation is impossible to realize in nature. How for instance can you prevent the gas in a closed vessel from being affected by vibrations coming from the surrounding medium? That is a sufficient reason w hy we can never expect the cyclic motion of two diffusing gases to become 36657 Vie , Or is on average negative. But the state of things thus 126 Mr. W. L. Upson: Observations apparent. It is of no avail to say that the disturbances from without are very small, because a very small impulse may change the direction, and because the disturbances continue acting for an immense time. In the H theorem, when H is near its minimum, say H=H,)+2, where w is very small, an is a small quantity of the second order, compared with dt x; so that in the cycle,.if there be a cycle, H will remain near its minimum for very long periods of time. The same is true of K and ie in the diffusion theory. The effect of disturbances coming from without is, as I pointed out in ‘ Nature’ for November 1894, always to main- tain or to renew pro tanto the state— moleculiir ungeordnet,” whatever that may mean—which is assumed to exist at every H dK aE 5 ge » IS negative. They must therefore be sufficient to destroy the possible cyclic motion. In that sense the diffusion of gases will, in any experiments that can practically be made, be found to be irreversible. instant, as the necessary basis of proof that or VII. Observations on the Electric Are. By Water Li. Upson, H.E., 1.S., Princeton [Plates VI. & VII. ] LTHOUGH numerous investigators have studied the ve phenomena of the electric are in air, between carbon terminals, and also between metal terminals, yet the use of the electric arc in the production of electric oscillations raises some new questions with regard to it. While I was working in the Pender Electrical Laboratory of University College, London, during the present session, Prof. J. A. Fleming, F.R.S., suggested therefore to me that it would be interesting to make a further examination of the are between metal and carbon terminals, in air and hydrogen. I am indebted to him for the facilities for carrying out the work, and also for many suggestions during its progress. The following apparatus was first constructed with the kind assistance of Prof. W. C. Clinton, B.Sc. * Communicated by the Physical Society: read June 14, 1907. on the Electric Are. ve TOM DESCRIPTION OF APPARATUS. Two upright brass tubes are connected across the top by a brass casting through which is bored a hole, to provide a means of causing cold water to circulate through a metal electrode. From the centre of the casting, extending downwards, is a cylindrical piece of copper, which ends in a tip about 4 inch diameter, on to which may be fitted the upper metallic terminal of the arc. The brass tubes are clamped to a slate base, and extend through it. Thus, by connecting the end of one of them to a water supply, a steady flow is obtained, and this is directed on to the very tip of the upper metallic terminal holder (see fig. 1, p. 128). Through the centre of the slate base passes a screw of four inches’ length, which is capable of being turned by means of a milled ebonite head, fixed at its lower end, and thus being made to approach or move away from the upper terminal holder. This screw likewise ends in a tip, by which the lower are terminal may be held. Surrounding the whole apparatus above the slate base was placed a bell jar,in the neck of which was a rubber cork holding a tube whose end was covered with wire gauze. ‘There was also a tube let into the slate base, by which connexion could be made to a gas reservoir of any kind. The gas thus admitted was expelled through the tube fixed in the cork, and could, in the case of hydrogen or coal-gas, be made to burn at the end. The two terminals of the are were connected with the source of electric supply—wusually the street mains at 110 volts, continuous current—the upper, through one of the tubes of the water circulation, and the lower through the central screw. Potential leads were connected to the other tube of the water circulation, and to the terminal leading to the central screw. The electrodes used were ordinary solid carbons, 0°47, 0°4, and 0°37 inch in diameter, cored carbons 0:47 inch diameter; also metal terminals of copper, iron, and aluminium, either as solid rods about 5 inches long, set into the lower holder, or pieces of the shape shown in fig. 2 (p. 129), fastened to the upper holder. The solid rods used were of the following diameters copper #2 im. iron $ im., aluminium 4 in: and 2 in. The light of the are was passed through a double convex lens, and projected onto a sheet of squared paper, at such a distance that the arc length could easily be read off from the image, in fractions of an inch. The arc was magnified f [LLL LLL LLL LL LLL RUA WARS SAEEA SERRA ESHA TEER REEL LE EER EEETE SUL ECE CHINESE SEE OBRERS EE ASN ZN Sean PSap SASS SESS SELES UKE DESL SSERALATE CELTS CUCL ES aas | | IK LILIIOLTADDSEOTALERERLOPLEOBEETAAE GY = LIEEMEELOL EEL AIDLEOILEEOE Es KK y G d L | ROVAVLASREALS ST BATS TE RAPE BASE SF CESARE EE Oe EEA OSCILLA S EEO NA AN SSSI IN AE: Observations Y iy SY Mr. W..di. Upsonm® Se o> O> AisppshsssssssssLessssessLEsTPLsSSTLELsSSESll aaa N on the Electric Arc. 129 to ten diameters. Its length could be kept constant by means of the screw holding the lower terminal. Fig. 2 When carbon terminals were used, the ends were pre- viously shaped into the general form ‘they would after use have assumed. By this means much time was saved, as it appeared that, with a given arc-length and current, terminals once shaped do not eive variable volt readings according to the time the arc has “burned, but may be considered in their normal state as soon as they have reached their normal temperature. When metal terminals were used, the ends were rounded, but it was found better not to make them too pointed, owing to the tendency of the are to bow out and become of uncertain and variable length. DESCRIPTION OF ARCS. In what follows, the arcs will be designated by the chemical symbols of their electrodes, followed by the gas in which they occur. Thus, Cu-C in H. The first elec- trode is always positive, and, except where carbon, or other- wise stated, isthe upper terminal, cooled by water circulation. Observations were taken on ares in air and hydrogen, using carbon, copper, iron, and aluminium in all combinations, both positive and negative ; also several of them in coal-gas. The following is a summary of the observed phenomena. Ares in Air. Cu-C and Fe-C ares are probably more or less familiar. ° Al-C. The characteristic aluminium flame is pale blue, being hardly distinguishable from that of iron. The Al was oxidized rapidly, but was only slightly eaten away. Very little deposit was left on the globe and framework. A strong odour was emitted, however, but a match applied at the end of the tube did not light the gas which should have been escaping. The are could be lengthened to 0°5 in. with 10 amperes. Phil, Mag. 8. 6. Vol. 14. No. 79. July 1907. K 130 Mr. W. L. Upson: Observations C-Cu, The are was very steady; of a purple colour, except at the point of junction with the copper, where there was a small region of green colour. A small deposit of carbon quickly formed on the copper. IE this were not continually removed, the are soon assumed the characteristics of carbon-carbon. The deposit on the apparatus was very slight. The carbon terminal burned away quite rapidly, assuming a three-stage form, as shown in fig. 3. Fig. 3. crater. e—~ Bright ull Red Black. C-Fe. This are come miele splutters and hisses, and is very hard to measure. It is very bright; more blue (from iron) than purple (from carbon). “When the iron has reached a certain temperature, bubbles form— probably magnetite—and the energy consumption in- creases. The arc, however, now becomes steady. It was drawn out to 0°5 in. with 5 amperes and 80 volis across the are. (C-Al. This are started more readily than when its poles were reversed. There appears not to be any very heavy formation of aluminium oxide acting as an insulator on the end of the Al electrode. But once started, the are was not very stable, and would not be drawn out to more than 0°3 in. with a current of from 10 to 12 amperes. The Al electrode was deeply pitted and very hard, con- taining a deposit of carbon embedded in it. The apparatus was coated with a light grey deposit of Al, but not so thickly as in the case of “the AIC are 10 hydrogen. The end of the carbon was rounded, and showed in- dications of a crater form. A pungent odour was emitted as in the case of the same electrodes with current reversed. on the Electric Are. IIL u-Cu. A steady green are could be drawn out to 0:2 in with 2°5 amperes. The terminals were very little affected, being somewhat oxidized. A shallow crater was formed in the negative, and a small hard bubble of oxide on the positive. Fe-Fe. This are is very steady at low currents and small are-lengths. It is blue-coloured, with a yellow aureole. As the arc-length and current are increased, yellow fumes are given off in considerable quantity, and. a deposit of yellow-brown powder, no doubt iron oxide, covers the apparatus. The terminals, also, begin to boil and the arc becomes less steady. When the bubbles make their appearance the are begins to hiss, and there appears to be an increase in the amount of power con- sumed in the are. The boiling iron disturbs the are, making it difficult to get accurate readings. There is also a hissing when the are changes its point of attach- ment on the positive electrode. This is accompanied, as in the carbon-hissing are, by a fall in voltage, but is quite distinct from the hiss which accompanies the boiling iron. Al-Al. This arc was found. to be very unstable. The terminals became quickly oxidized where the arc is formed, causing the latter to travel around continually, seeking unoxidized portions, and tending to lengthen out and run up the sides of the terminals, finally going out. The are is a clear blue colour with a thin yellow aureole. On each pole is a bright spot where the are enters. A small grey deposit was formed on the framework. Cu-Fe. The are is bluish, with a yellow aureole. No copper-green is visible. The iron bubbles form a con- ducting oxide (magnetite), which, when cool, may be knocked off the end of the terminal. Also a bubble, or deposit of iron is left on the copper if the are has been burned for a little time. There is also some brown iron- oxide deposit on the electrodes. Fe-Cu. The copper was the upper cooled electrode. The are showed a greenish colour, getting stronger at the copper electrode. Toward the iron it was blue. On knocking off the cap of oxide which covered the end of the iron, a heavy deposit of pure copper was found buried in the iron underneath. Quite a deep crater was burnt into the copper, while in the reverse experiment prac- tically no effect was to be observed on it. The whole copper terminal was covered with a brown sooty deposit. K 2 Mr Weales ipsam Observations Cu-Al. The aluminium was the upper cooled electrode. This are is more persistent than with the electrodes. reversed in polarity. It is easily started, but is very un- settled in character, emitting constantly a hissing and spitting sound, and travelling about, over the surface of the electrodes, tending to lengthen out. But it does not go out as easily as the arc between the same terminals. when the current is reversed. The flame is principally ereen from the copper. Sometimes the whole crater will be green with merely a thin aureole of blue. The alumi- nium electrode was covered with a golden-brown deposit from the copper, and its end was hard and pitted. Al-Cu. The are was blue in colour from the aluminium terminal, and green from the copper terminal, about equally divided. It was very unstable, and acted much like the Al-Al are, being impeded in starting by the aluminium oxide. The are would continually lengthen out until it ruptured itielf. Fe—Al. The aluminium was above and cooled. The are is as to be expected, blue with a yellow aureole. It shows the characteristic aluminium tendency to glide about and play around the edges of the electrodes. It is less steady than the copper arcs. The poles presented much the same appearance as those of the Fe—Cu are. The Al electrode was embedded with iron to a considerable depth. Al-Fe. The aluminium was eaten into very slightly. The iron appeared as in the case of the Cu—Fe are. Arcs in Hydrogen. C-C. The arc was pale blue in colour, with a faint purple core. Its length was difficult to measure on account of heavy carbon deposits. The carbons became shaped so that their ends formed parallel spherical surfaces, the positive being concave. Around the edge of the negative was built up a branching deposit of carbon, extending outward about a quarter of an inch. Compare ares of carbon and iron. Cu-C. The are was small and pale, consisting of a central core of reddish-purple colour, enveloped by a region of green light. It persistently travelled around, finding no point of permanent attachment, and wearing a broad crater in the positive and shaping the negative to fit the A crater. The end of the carbon became very hard, with a deposit of copper, while around the outside edge was soft carbon which easily fell away. The surrounding globe was blackened by a fine carbon deposit. on the Electric Arc. 133 Fe-C. The are is blue in colour with a reddish-purple eore. The iron boils at its point of contact with the arc, its surface becoming irregular. A black deposit covered the apparatus. FEarth-surface heat, A= solar constant, less loss by selective reflexion by the air, M= heat conveyed to the air from other points, i 5) » surface from other points, v=] = albedo of the surface y= radiation constant. 172 Prof. P. Lowell on a Method for Evaluating If we assume clouds to transmit less heat than 20 per cent. we diminish y and inerease (1—°35 e), so that the ultimate result is not greatly altered. Albedo and Air.—-Some interesting conclusions follow on the investigation of planetary albedo. If we classify the various planets according to their atmospheric envelopes, we The values for these quantities found bolometrically for a clear sky are >— a= 'd0 A=1—'79x ‘32='747= whole spectrum — albedo of the air into B= approximately a. visible portion, y=l]—'l1=°89. For the Earth in its entirety M=0 and N=0, since what is lost by convection in one place is gained in another. Applying this same formula to the case of Mars, we have similarly :— #,= 40 approx. ho ne (l1—17 x ‘82) = whole spectrum — albedo of its air 124° into visible portion __ ‘946 ~ psd §,=a) approx. yp, =1—‘138= °87. Whence for the Earth under a clear sky. gt ae sums ed y(l+y— By) | and similarly for Mars, substituting its values for A, ~ and B. Since in both «=8 and y,=y approx., we have T, for Mars, which gives But the Earth is ‘50 cloud-covered and the transmission of cloud being: not more than °20 (the value he takes), we have finally sh 2 BU a ASCO, whence T= 974 cM and T being 519°°4 abs. on the Fahrenheit scale, T= 505°7, that is 46°3 F. or 8° C., a result substantially the same as we have deduced. Had we assumed 8 to be ‘70 and to be in the like proportion to » for Mars, we should have had A i ea ere y T#=1-101%), ] which gives not far from what we had before, since it lowers the resulting temperature for Mars by only about 4° F. or 2° C. and the Surface- Temperature of the Planets. 173 shall discover a significance in their several albedoes. Three classes stand forth distinct :—(1) those possessing no air ; (2) those with air, but wholly or in part cloudless ; (3) those with a cloud-covering. Into these classes the planets fall in the manner below, while the albedoes they respectively present are placed alongside of them. I. Airless bodies. Albedo ICRCUCY. os «a cies seas eit 0:17 MVE Me ny ee acre oe eee On II. Air-enveloped bodies. Venus, cloudless, } medium 0-92 Earth, 50 °/, clouded fair 0°75 Mars, cloudless, thin air ...... 0°27 III. Cloud-canopied bodies. Albedo. ATO" O10 Sy oer ne BSP 0-75 UUM os ares oss Phe ons apc 0°88 or 0°78 by Struve’s UDI Sag eee 6 sess aie es 0-73 [latest measures. ING PUIG hewn oka 7 0°63 The albedo of clond is 0°72. Whence it is clear that cloud cannot account for the albedo of Venus ; but that it accords with the albedo of the four major planets. That an air- envelope increases the albedo of a planet is witnessed, first, by the greater brilliancy per unit of disk of the Harth, Venus, and Mars as compared with the airless bodies, Mercury and the Moon; and, secondly, by the relative specific brightness of Venus and Mars, together with what has above been found as to that of the Earth. It appears that the denser the air surrounding the planet, the more dazzling the aspect the planet presents. This is undoubtedly due not to the gases themselves, but to the solid or liquid particles the gases support in the shape of dust, ice- particles, or drops of water. This testimony of the albedo that Venus is not cloud- covered but atmosphere-hid is corroborative of the observations made by the writer at Flagstaff in 1896 and at Mexico in 1897, from which it appeared that the planet’s markings were not obscured by cloud but seen as it were through a veil, and which also showed the correctness of Schiaparelli’s deduction that Venus, in all probability, turned in perpetuity the same face to the Sun. ‘That she did so was evident from the long- continued observations at Flagstaff and Mexico. Now such a facing always of one hemisphere sunward would . cause convection-currents upward in the centre of the disk, and an 174 Prof. P. Lowell on a Method of Evaluating indraught along its edge, together with an absence of moisture on the sunlit half of the planet. Dry winds of the sort blowing over a perpetual sahara must be laden with dust, which Very’s investigation finds to be the chief cause of reflexion in our own air. The high albedo of Venus thus stands accounted for. ven Light round Venus.—A sidelight bearing on the albedo of air comes from the prolongation of the crescent of Venus when the planet passes in inferior conjunction before the Sun. It used to be thought that the fine circlet of light that then crowns the disk was due to refraction in the Venusian air. But m 1898 Russell at Princeton showed that it is rather reflexion from that air than refraction through it which reaches our eyes. Now that such should be the case follows from the planet’s albedo, if that albedo be of atmospheric and not of nubial origin. This supports the conclusion reached by the visual observations of Venus at Flagstaff. For refrac- tion means transmission, and if the air of Venus reflects 90 per cent. of the incident light it can refract but 10 per cent. at most. The light from it, therefore, must be reflected not refracted light in the proportion of 9 to 1. The albedo, Russell’s observations, and the Flagstaff results, thus all concur to the conclusion that Venus is not enveloped in cloud. Deduction as to amount of Martian Air.—Another outcome of the consideration of albedoes is a means it gives us of approximating to the density of the Martian air. Mars’ surface is chiefly Saharan, and dust, therefore, must be largely present in its air. Now from the albedo of various rocks, of forests, and of other superficies we may calculate the relative quotas in the whole albedo of Mars of its surface and its air. Five-eighths of its surface is desert and therefore of an albedo of about 0°16, as its hue shows: three-eighths of a blue-green, the colour of vegetation with an albedo of about 0°07 ; while one-sixth is more or less permanently white, the white of the polar caps. These would combine to give it an albedo of 0°13. This, however, is Uluminated by so much of the light as penetrates the atmosphere only, about three-quarters of the whole. Whence the apparent albedo of the surface must be about 0°10. As the total albedo of the planet is 0°27, the remaining 0°17 is the albedo of its air. Taking the density of the air as proportionate to its brilliancy, which would seem to be something like the fact, since the denser the air the more dust it wonld buoy up, we have for the Martian air a density about 2/9 our own over each square unit of surface. Or the Surface- Temperature of the Planets. ho Now if the original mass of air on each planet was as its own mass, we should have for the ratio between the Earth and Mars, 9°3 of atmosphere on the former to 1 on the latter. This being distributed as their surfaces, which are in the proportion of 7919 to 4220, must be divided by 3°5, giving 2°7 times as much air for the Earth per unit of omc. The difference between 2°7 and 4°6 thus found may perhaps be ‘attributed to the loss of air Mars has since sutfered on the supposition of proportionate masses to start with. Air-density at surfuce of Mars.—To get the relative density of the air at the surfaces of the two planets, these. amounts must be divided by the ratio of grav ity at the surfaces of the two, that is by 38/100. For the density being epliisaal to its own increase, if D denote.the density at any point, we have dD=— Dade, where g denotes the force of gravity at the surface of the Earth and « is reckoned from that surface outward into space, whence = D=Ae-# A being the density at the surface of the planet. For Mars we have correspondingly D, — Anew, For the whole mass of air over a space dydz we have, for the Earth, Ae Ddz= eee pas a iS WR eS eg Similarly for Mars it is Ay. Ho and as the whole mass of the Earth’s atmosphere over any space dydz=4-6 that of Mars at a similar point and g,='38 g, we have A Ay Pe ee whence, as A=30 inches of barometric pressure, Ay=2°5 inches. Boiling-point on Mars.——Owing to the less amount of the Martian air and the smaller gravity at the surface of the planet, the boiling-point of water is greatly reduced, being probably in the neighbourhood of one hundred and eleven 176 Prof. A. Stanley Mackenzie on Secondary Radiation degrees Fahrenheit. If the whole mass of air be aot the Earth’s. while gravity is ‘38 of ours, the pressure is : 8 ny ) Pp Myg9,='09 of the Earth’s, whence the boiling-point is 44° C. or 79+32=111° F. For the same reason, sublimation takes place more freely at identical temperatures there. Proportionally, therefore, there would be more water-vapour in the air. | Results —In conclusion we may summarize the results for the more probable values of the following quantities for Mars :— Mean temperature ........... 5 482 for One Boiling-point of water ........ 111° F. or 44° C, Amount of air per unit surface... 7 in. or 177 mm.; 2/9 of the Earth’s. Density of air at surface ...... 2°5 in. or 63 mm.; 1/12 _,, + The look of the surface entirely corroborates the tempe- rature results of this investigation. XI. Secondary Radiation from a Plate exposed to Rays from Radium. By A. STANLEY Mackenziz, Ph.D., Munro Professor of Physics, Dalhousie University, Halifax, N.S.* Sl ae following experiments were made to examine more carefully than has been done the secondary radiation from the back side of a plate bombarded by the rays from radium, and to see what light a comparison of this radiation with that from the front side would throw on the mechanism involved in the production of secondary rays ; and, further, to see what evidence it would give of the secondary radiation of penetrating type, of which other experiments seem to show the existence. In order to restrict to a definite bundle the beam of radium — rays employed, and to shield as far as possible the rest of the apparatus from rays leaving the radium in other directions, the radium was put at the apex of a conical opening of 19° half-angle in a massive block of lead. The accompanying diagram (fig. 1) will make the arrangement clear. A hole was bored through the lead block along the axis of the cone, and the radium (5 mg. in a glass tube) was put in its place by being inserted in the end of a brass rod which fitted the hole. The lead block had a circular cross-section of 10°7 em. diameter, and its greatest length was 16 cm. As the radium was inserted to a depth of 7-7 em. in the block, no rays could emerge from it without passing through at least 5 cm. of * Communicated by the Author. from a Plate exposed to Rays from Radium. Ig lead, except through the conical opening. The shape of the block was so arranged, with a corner sawed off at a, and a prolongation added at 6, that no secondary radiation from the sides of the conical opening, nor from the absorbing plates A, nor from the surfaces at that end of the block, | G) i! = i} é = — t& caxth could enter the ionization-cell I, as the direction of the dotted line ad will show. A channel ¢ was cut in the protuberance 6 to hold the ends of the plates A, which were used as absorbing layers to cut down the primary radiation. A conical frustum of lead C (shown in position in the diagram) could be inserted in the conical opening when still further reduction of the beam was required. The height of the frustum used was 1°18 cm. The axis of the block made an angle of 34° with the horizontal. The intensity of the secondary radiation was measured by allowing the rays to enter an lonization-cell I which was connected with a Wilson tilted-electroscope. This cell was a brass cylinder of 24-2 em. and 7:2 cm. diameter, haying a central wire insulated by sulphur with an earthed guard- ring. The mouth of the cell was covered by thinnest aluminium-leaf. The central wire was connected to the gold-leaf of the electroscope, which was situated about a metre distant, and the connecting wire was surrounded by an earthed metallic conductor extending from the earthed guard-ring to the box of the electroscope. The cell I and Pla. Mag. 5. 6.-Vol. 14. No. 79. July 1907. N 178 Prof. A. Stanley Mackenzie on Secondary Radiation the plate of the electroscope were brought to the required high potential by connecting with one pole of a battery of small storage-cells, the other pole of which was earthed, in the usual way. The axis of the cylinder made an angle of 23° with the horizontal. The radiation entering the ionization-cell al be absorbed by screens 8 placed against the aluminium end of the cell. The position and inclination of the cylinder were so arranged that the radium lay in the plane of the aluminium- leat, as shown by the dotted line cd : this is to reduce to a minimum the secondary radiation set up in the screen 8 by the y rays from the radium, and was sufficient to make any leak due to this cause so small as to be negligible. | When a plate was to be bombarded it was put either in position R or in position T. Position R was such as to make equal angles with the central axes of the lead block and the lonization-cylinder, in which position the reflected radiation entering the cell was found to bea maximum. | It is inclined toward the lead block about 10° from the vertical. The distance from the radium to the plate measured in the line of the axis of the block was about 13 em., and from the aluminium-leaf to the plate, measured along the axis of the cylinder, about 6 cms. Position T was horizontal, and the lower surtace of the plate 8 mm. below the corner of the block 6. The distances from radium and aluminium, measured as before, were 18 and 12 cm. respectively. ‘The plates were 30 x 40 em. in area, and of various thicknesses. It was found that the same effect was produced by a single plate of given thickness as by a pile of plates of the same agoregate thickness. The secondary radiation from the front side of a plate has been carefully investigated by Eve*, McClelland f, Allen {, and others, and the chief properties of these rays are now beyond doubt. The interpretation of the results of experi- ments of this kind is very difficult on account of the complex character of the radiations involved, and what seems to be a penetrating radiation may be easily confused with one which is only of a tertiary nature, and so on. It was hoped that in the apparatus as here set up the various radiations could be kept fairly well distinct. The stream of radiation which enters the cylinder, especially when either the reflecting plate Ror the transmitting plate T is used, is made up of many components, consisting of (1) y rays direct from radium, and the secondary rays they * Phil. Mag. Dec. 1904. ft Phys. Rey. Aug. 1906: + Phil. Mag. Feb. 1905. from a Plate exposed to Rays from Radium. 179 produce ; (2) the secondary rays sent out from the air, due to the passage through it of the primary rays ; (3) the secondary rays from the lead; (4) the air-rays produced by (8) ; and (5) various tertiary rays, ke. The first of these is always present, and with the so-called spontaneous ionization constitutes an invariable amount of leak, which is always added to that from other sources. The second group was first studied, that is, the rays from air due to the passage through it of 8 and y rays. A few numbers are given in Table I. to show the power of the puna rays of different penetrability to produce these air-rays. The numbers denote the rate of leak as observed by the movement of the gold- leaf of the electroscope. In order to preserve similarity of conditions and ensure greater accuracy, the numbers actually observed were for the time in seconds required for the leaf to move over 20 scale-divisions, and these numbers divided by 20 are added in brackets to give a general idea of the actual magnitude of the times involved. The leak as given is 100 times the reciprocal of the above time, or the number of scale-divisions passed over by the leaf in 100 seconds. The leak is given for the full unobstructed beam, and also for the rays left when various plates of lead A (and C) are interposed in the path of the beam, over a large range of thicknesses from -02to15-4mm. The method was s susceptible of an accuracy of $ of 1 per cent., and where necessary to interpr etation the Seeiece can be relied on to that degree ; in general an accuracy of 1 per cent. may be claimed for them. A BEROL Thickness | | | | | | lead plate A + | 0°00 | 0-020 0°095/ 0-225 1:00 | 1:80 | 3°60 5:60 15-4 | in mm... | | | ee a ee Time in sec. for 1 ese-| (00 00) (18-9) (37-2) 4s) (49-6) (50 6) (61-5) (52: 0) (6 3:0) (2-02 | 1-98 | 1-94 1-92 | 1:89 | 100 sec. ... | | ie a | | | | | The leak 1°89 for an absorbing layer A of 15°4 mm. is the smallest noted during the course of the experiments, and is useful as an index when asking whether the leak is as crate in any given circumstances as there is a possibility of its being. From the table it is seen that, although the easily absorbable INE? 9 180 Prof. A. Stanley Mackenzie on Secondary Radiation rays are the most effective in producing these air-rays, there is an appreciable amount of radiation set up by the y rays, or, at least, set up after a layer of lead is interposed sufficient to cut out all the @ rays, equal to several per cent. of the maximum, It will, however, be shown later that there is a large radiation sent out from the side of the lead plate which is not bombarded, what we may call for convenience ‘transmitted’ rays; and although the apparatus is so arranged that these transmitted rays cannot directly enter the ionization-chamber, yet they may produce air-rays to an unknown extent, and it is impossible now to estimate how much of the leak which we observe when a plate say of 6 mm. is at A is due to the y rays which strike the air after getting through the plate, and how much is due to the rays which are set up in the lead and then strike the air. If these numbers are plotted, it will be seen that the law of absorption over the whole range is very far from being an exponential one, being too steep at first and then too flat. But before trying to find an equation to the curve, it would be necessary to subtract from the numbers given the leak which is always present due to spontaneous ionization and the direct y rays and their secondary effects. This I have not found a way of estimating with any accuracy. The leak when the radium is out of range and out of the room (a room never contaminated by having had open radium in it) is small) being about *24 on the scale adopted. In order to test the type of these rays as to penetrability, the leak was observed with lead screens S of various thicknesses over the aluminium end of the cylinder. The results are found in the second column of Table II. It will be seen that these air-rays are mainly of the easily absorbable kind, and that about two-thirds of the whole is absorbed by lead-foil 02 mm. in thickness, and five-sixths by + mm. of lead. One of the most interesting results is that the remaining one-sixth is of a seemingly very penetrating type, like y rays, the leak through 11 mm. of lead being only about 3 per cent. less than through +mm. The question as to whether these are y rays or not will be considered later. By referring to Table I. it will be seen that as a rough statement we may say that the proportion of the beam of secondary rays of any given penetrability is about the same in order of magnitude as the effectiveness of primary rays of that penetrability in producing secondary air-rays. These results are in the main in agreement with those found by others. : from a Plate exposed to Rays from Radium. 181 TABLE IT, | | a Thickness of plate ay Differ- “Dhicknes of plate A. Differ- i) “ence; l | ence. Minielness 0:00 | 15°4 mm. 0:00 154 nm. | of screen | Giving the leak when air is Giving the leak when plate : exposed to | R 18 mm. thick is exposed to in mm. | B+y rays.| y rays. | 6 rays. || 6+y rays.| y rays. | 6 rays. Srey | ee EO Pea “2 eee | 0000 || 12°50 1-89 106 104:2 2°85 TOES im | 0020 | 304 | 1-91 203 || 544 | 2:38 | 520 0225 | 200 | 1-94 06 5:59 «| 2-02 3°57 TOO,» || 1-97 1-96 ‘01 is Se a aly 1:80 1:95 | 1:95 00 2°02 1:96 06 Oe, All, (21:93 1-92 ‘Ol 200 | 1:94 06 | | | In these observations both @ and y rays were present to affect the air, and in order to determine whether both soft and penetrating rays were produced by both @ and y rays, another set of observations was taken with the y rays only falling upon the air. To be perfectly certain that no @ rays would be present the cone C of 11°8 mm. of lead was put in the opening, and for fear the chance of its not fitting exactly might allow some stray @ rays to emerge, a plate of 3°6 mm. of lead was put at A. The total, 15-4 mm., is more than enough to ensure the passage of nothing but y rays. The results are given in the third column, and the differences of the second and third columns will show the leaks due only to the 8 rays ; these are found in the fourth column. It will be seen that the radiations set wp in air by @ rays are practically all of the soft kind and are absorbed by 1 mm. of lead. To return to the observations on the effects of the y rays, as given in column 3, which are of considerable interest. The numbers are at first sight rather surprising and anomalous. With no screen the rate of leak is 1: elo) 5 when a screen 8 is put in the path of the rays we expect a reduction of the leak due to absorption of the radiation by the screen; but we find that a layer of =4, mm. thickness increases the leak to 1:91, and that the leak increases with increasing thickness of screen, until for 1 mm. the leak is 1:96, nearly 4 per cent. greater than with no screen. For still greater thickness of sereen the leak decreases again, but even after a plate 182 Prof. A. Stanley Mackenzie on Secondary Radiation 11 mm. thick is put before the ionization-chamber the leak is still 1:92, or nearly 2 per cent. greater than without any plate. In other words, you can increase the leak in a vessel in certain circumstances by merely making the walls thicker. If the rays here approaching the cylinder are of an absorbable type, we could explain this phenomenon by saying that when they meet the plate they start up both a radiation of similar type as well as a very penetrating type, the sum of the two being a maximum for a lead plate 1 mm. thick, more only acting as an absorber. If they are of the y type, we could say that they themselves pass easily through the thickest screen used, and at the same time start up a secondary radiation in the cylinder of ionizing activity more than enough to make up for the absorption of the original rays. We shall have evidence later of the existence of both these phenomena, but the latter explanation is probably the main one. In order to put this peculiar behaviour to a further test, a plate of 6 mm. thickness was put at A instead of the cone and plate used before ; this must absorb all but a few of the very fastest @ rays and let through a quantity of y radiation cut out before. The results were similar to those just described, but the changes were noe so great. The leak with no screen at 8 was 1°92 ; with 8; mm. thick the leak was not measurably different fon that with no screen ; with §S °225 mm. the leak increased to 1:96 ; and later decreased again. The proportion of less penetrable secondary air-rays due to the impact of the less penetrable primary rays has begun to mask the effect due to the rays coming from the impact of the very penetrable ones; and there must be a certain thickness of plate A for which the phenomenon in question would just disappear. It is not present when the whole beam is used. [Further discussion of this behaviour is reserved until experiments on “transmitted” rays are described. Jinaliy, with regard to the data of columns 2 and 3, we may say that the y rays passing through air produce no great amount of radiation except the peculiar kind just described, and that practically all the absorbable radiation produced is by the 8 rays, and that it cannot penetrate more than 1 mm. of lead; the leak shown in column 2 for thicknesses greater than 1 mm. is that due to the y rays referred to, since the numbers are the same as the corresponding ones in column 38 within the limits of accuracy of the experiments. Before giving the results obtained from investigating the ‘. condary rays reflected from varying thicknesses of lead bombarded by the primary rays, the proportion of the from a Plate exposed to Rays from Radium. 183 secondary beam from lead due to the @ and to the y rays and the penetrating powers in each case may be referred to and compared with the corresponding results for air just described. These results are given in the last three columns of Table II. for a reflector of thickness 1°8 mm., which was found to be more than sufficient to produce the maximum effect. In the first place, the 6 rays produce a greater proportion of penetrating radiation from lead than from air ; tor whereas in thee ease of air only one-fifth of the stream of rays gets through =, mm. of lead, now one-half of it does so. As before, the leak does not fall to the possible minimum of 1°89 for an absorbing screen of 11 mm., but after the thickness of S reaches beyond 1 mm. the jeak remains in the neighbour- hood of 1:95 for the y rays, and -06 for the @ rays. Another obvious result is that the y rays now produce considerable absorbable radiation, sufficient to mask entirely the peculiar effect noticed in the case of air. The final leak after 11 mm. of lead is interposed is 1'94, and is diminishing very slowly with increasing thickness of lead, and is nearly 3 per cent. greater than that we know to be a possible minimum. The last column of the table shows that the secondary rays set up by @ rays are still effective in the case of the greatest thickness of screen S used, that is, are able to produce by striking lead rays of the highly penetrating kind. Secondary Radiation from the Front Surface of a Lead Plate. “ Reflected Rays.’ The plate was put in position R of the diagram, and various thicknesses were used in order to find when the intensity of the reflected beam reached a maximum. The position of the front surface of each plate was alwaysthe same. Observations were made with no absorbing plate at A, and with 15-4 mm. of lead at A, and their differences taken, as before. Table III. contains the results. TABLE ITI. | j 1 | ere) 4. | | | | PPiniekness of reflector 999 |-040 -060 |-080 /095 | -190 | -225 |-45 | 1-00. 1-80 | 3-60|5-40 7° Te ee ee | mee ce No plate) = [B+ 62-1 179-4 87-7 91-7 95-2 | 101-01104-2| ... [104-2 1042 1042) .. at A. m | rays. | | repent leer aun amie eo Lyf.) ¢ |_Y. 212/230 2392-49 258) ... | 2732-77] 279| 282) 283 284 6: lead at A.| 5 | rays. | | SSS rs ee 2 SS SSS | | ee ul Bence lacs enolase el cs oq gs eee ence, |" |raye, OOO NTI 85S 892926) .. [lo] ... HOl-4 101-4 Nord! i — } | 184 Prof. A. Stanley Mackenzie on Secondary Radiation From this we see that the @ rays cease increasing their effect after a thickness of lead of about + mm. is reached. But for the y rays it requires more than 6 or 7 mm. before the limit is reached. An important conclusion from this is that some of the secondary rays from lead produced by y rays passing into it are of a highly penetrating character and can return through 6 or 7 mm. of lead. Moreover, we saw before from Table IT. that the y rays produce comparatively little absorbable radiation as compared with that from the @ rays ; so that it seems that a large part of secondary radiation is always of a similar type to the primary. Curves A and B of fig. 2 show the growth of the secondary radiation with ie s alas ¢) L A. Reflected radiation from B rays. Unit abse.='5 mm. Unit ord.=leak of 100. B. Reflected radiation from y rays. Unit absc.=5 min. ; Unit ord.= leak of 5. C. Transmitted radiation from 8 rays. Unit. absc.="5 mm Unit ord.=leak of 50. — DP. Transmitted-radiation from-y rays. Unit-absc.=5 mm. Unit ord. =leak of 5. thickness for the 8 and yrays respectively. They are drawn to different scales, but it will be seen that they follow the same general law. They suggest the equation y=a(1—e™), but the rise is too steep and they flatten too quickly after passing the knee. from a Plate exposed to Itays from Radium. 185 Secondary Radiation from the Back Surface of a Lead Plate. “ Transmitted Rays.” The plate was put in position T of the diagram. The position of the bottom surface of each plaie was always the same. The results are in the following Table. TaBLeE LY, T { | | | | | | | Thickness of reflector} q99 |.9G0 095 -190 -225 | 45 1-00 1:80 3:60 5:60 9:20 156 Tin mm. | | | re || eee seal eS No plate| 3 [8+ l35.9 53-7 [195 11-9 10-1 510 380 309 287 2-62 238 22 at A. 2 rays | | | = ae lhe: rE Leseas em leat ligt in ia Sah ROE se 154mm, e| y 2-05 210 2-16 |2-23 |2°25 2:27 |2°27 |2-24 2-19 |2°16 2-03 |1:99 lead at A.) a | rays. | | | | eee. || = ee cae roo (ere ee Ree Sok bore ale cette oo Differ- “4 | B 36.8 /31-6|17-3 19-7 |7-8 23 103] °85| °68| -46| -35) -23 ence. an | rays. | | | | | | Fla! | ) | | = 18 mm. ; 9.99 | lo. 7 |)--Q Ip. 9.12. TA | Reenter eee ee 333 a | Ve 287 ee Pe Ags | 2 18 — ee ‘225 mm. | | | | lo.74 | 9.25 | ieadat A. fates (miele saree wiajaveta wed cats | eee caren aes arate ot ao An examination of these numbers discovers a_ rather surprising result. The @ rays which ceased giving “re- flected’ rays after the thickness of lead traversed reached + mm., now give “transmitted” rays up to the limiting thickness used, 15°6 mm., and the intensity even for this thickness is relatively great. The result was so unexpected that it was considered it must be due to the more absorbable y rays cut out by the 15-4 mm. of lead. To test this some measurements were made with a thickness of the absorbing plate A only 1-8 mm., which would keep back only the more absorbable @B rays. The results are appended to Table IV., and show that these 8 rays which had been cut out must give i very decided stream of “transmitted” rays. For instarjce, with a plate T of thickness 9°2 mm. the leak when all the @ and y rays struck the plate was 2°38, and when the rays which could not pass through 1°8 mm. of lead were cut out the leak was only 2°31, showing that a leak of 07 was due to the easily absorbable @ rays. That is, the rays which cannot pass through 1°8 mm. of lead will yet start up rays. from the far side of a plate of lead 9°2 mm. thick, when they strike the near side of it. Even more astonishing is the evidence of the last row of numbers in Table IV., which shows that even the softest @ rays (those totally absorbed by 186 Prof. A. Stanley Mackenzie on Secondary Radiation 1mm. of lead) cause these transmitted rays in a 9-2 mm. plate. Since the pelle rays due to incidence of 6 rays do not increase after + mm. of lead is used, one would expect the transmitted rays aa to the same 8 rays ‘to cease incr easing after about double that amount ; but there seems to be no limit of even that order of magnitude. Another important result is 5 shown by the numbers of the second row of the Table, the “ POSS IB y ray leak. For the smallest thickness used, lead-foil .4, mm. thick, the leak is 205; as the thickness is incre eased the leak increases instead of decreasing, as was the case for @ rays, and as one might at first sight expect. The leak reaches a maximum for a thickness of about 2 mm. of lead and thereafter decreases steadily, but remains large for a thickness of even 156 mm. These ver y penetrating y rays are evidently not very largely absorbed by =i, mm. of lead, and it requires many times that thickness “before their maximum effect is brought out. The existence of this maximum for the y ray. leak suggests that there should bea similar one for the 6 ray leak. The values were accordingly plotted, and are found in fig. 2 as eurves D and C respectively. The shape of the curve © leads one re expect that there is a maximum for a thickness of about =!, mm., and I have drawn that part of the curve on that conjecture. It would then be very like the curve whose equation 1s y=ae—’ — be”, Referring back to the discussion of the results in Table IL, it will be seen that the anomalous behaviour of the air-rays due to y rays with increasing thickness of screen 8 there observed, is precisely the same as that we have just been considering ; in that case also the leak increased with increasing thickness of screen up to 1 mm. and then de- creased, but very slowly, even after a thickness of 11 mm. was used. This gives further evidence that we were there dealing with y rays entering the ionization-chamber, and hence that these y rays were made by y rays striking alr. In the case of lead, Table II. shows that @ rays also can set up these secondary y rays. It remains to account for the radiation from the back of a thick lead plate the front surface of which is struck by easily absorbable primary 8 rays. It is usually stated that these primary rays are practically all absorbed by 2 mm. of lead, and we might have expected some little Bile: from the back of a 4 mm. plate ; but instead we find a relatively very large effect with 10 and 15 mm. It seems reasonable to ee ————————— 4 from a Plate exposed to Rays fron Radium. — 187 conclude that the process is not a single action, that the primary ray is not simply deflected nor simply absorbed (consider, for instance, the production of 8 rays by y rays, and the reverse) ; but that the mechanical process is some- thing more like a convective transference of energy, in a manner suggested by electrolytic convection. As a working hypothesis « one might say that the atoms which are bombarded absorb energy y until internal instability is reached, and then a sort of Seolebiols takes place with the expulsion of electrons and y rays ; these in turn provide energy to be absorbed by the next layer; and so on through the plate. Since the limiting layer required for maximum “reflected’’ rays at the angie here employed is small compared with the maximum layer capable of giving “transmitted”? rays, we would have to assume that the propagation of the energy obeyed a law somewhat similar to that known for the propagation of wave- energy, a maximum In the direction of and a minimum in the opposite direction to the stream of entering energy. The primary beam of rays would produce, as it were, an ‘E.M.F. in the direction of the beam. The relatively large intensity of these “transmitted ” rays would seem to have a be: aring on the method of investigating spontaneous ionization. The general results of this paper are in agreement with those of Cooke and others on the influence of the secondary 1 rays due to the radiations coming from outside the ionization-vessel ; but they do not seem to fall in with some of the shermating of Campbell * on the influence of plates of ordinary materials placed before the thin aluminium side of his testing- -vessel, The method of measuring. the absorption of a beam of radiation caused by a plate of given material, by noting the change of ionization in a vessel “when different thicknesses of that material are put in the path of the beam, gives not the absorbing power of the material, at least in the sense one is apt to associate with the term, but the difference between what it absorbs and what it radiates; and as the latter quantity can be quite large, the method is open to objections. Physical Laboratory, Dalhousie University. May 9th, 1907. * Phil. Mag. [6] vol. ix. April 1905. XII. The Influence of Temperature upon Photo-electric Lffects ina Very High Vacuum, and the Order of Photo-electric Sensitiveness of the Metals. By R. A. MILLiKaNn, Associate Professor of Physics in the University of Chicago, and GroRGE WINCHESTER, Assistant in Physics at the University of Chicago ™. 1. 7 pee RODUCTION.—Two views have been advanced regarding the mechanism of the discharge of cor- puscles for metais under the influence of ultra-violet light. According to the first view, the discharged particles are the free or “metallic” corpuscles of the body which, by absorb- ing the ultra-violet light, acquire sufficient kinetic energy to enable them to escape from the attraction of the metal T. According to the second view, the escaping electrons are not free from the atoms before their escape from the metal, but are rather constituents of complex atomic systems which become unstable under the influence of the ultra-violet light and project electrons from themselves with velocities not greatly different from those which these electrons possessed within the atom tf. If the first view is correct, then it is to be expected that the ease with which the corpuscles escape from a given -metal, and therefore the number which escape per second under the influence of a given source, will be an increasing function of the temperature ; for “‘the higher the tempera- ture the greater would be the initial kinetic energy possessed by the corpuscles, and the smaller the increment required to enable them to escape from the metal.” On the other hand, if the second view is correct, it 1s not to be expected that the rate of discharge will be affected at all by temperature changes, since both the independence of radio-activity upon temperature, and the fact that the ratio of the specific heats of mon-atomic gases by constant pressure and by constant volume reaches the theoretical limit, namely 1°67, constitute strong evidence that the internal energy of the atom is not affected in any way by temperature changes. It is very important, therefore, from the standpoint of the theory of photo-clectric phenomena to determine definitely whether photo-electric effects are or are not dependent upon * Communicated by the Authors. This paper was read before the meeting of the American Physical Society held in Chicago on Noy. 30, 1906. + ‘Conduction of Electricity through Gases,’ J. J. Thomson, Chap. x. ‘Die Hlektrizitat in Gasen,’ Johannes Stark, p. 112. Ramsay & Spencer, Phil. Mag. xii. p. 417 (1906). t Lenard, Ann. d. Phys. ii. p. 355 (1900) ; viii. p. 149 (1902) ; xii. p- 449 (1903). ne Influence of Temperature upon Photo-electric Kjfects. 189 temperature, and, if so, to what extent. This was the main purpose of this investigation. ~ 2. Historical Summary.—Many investigations have already been made upon the effect of temperature upon photo-electric discharge, but the results have not been at all concordant, and none of them seem to be conclusive. Hoor*, working in air, found a decrease in the discharge from zine between 18°C. and 25°C. Stoletow f states that a rise in tempera- ture increases photo-electric effects. Zeleny t found that the effect was more than doubled in the case of platinum when the temperature rose from (0° C. to 650° C., while the dis- charge from iron increased forty-fold between 0°C. and 700°C. All of these experiments, however, were made in air. Hister and Geitel § alone record measurements in a good vacuum, the metal upon which they worked being potassium. In raising the temperature from 20°3C. to 50°3 J. they found that the discharge changed from 27:9 to 4-9 scalé- divisions, an increase of about 60 per cent. Relying chiefly upon the experiments of Elster & Geitel and Zeleny, J. J. Thomson concludes that ‘‘the photo-electric effects of metals are greater at a high temperature than at a low one” ||. He mentions, but does not record, some results of his own on the alkali metals which are in accord with this conclusion. He inclines to the view that the cause of this phemonenon is to be found in the absorption by the free electrons of the metal of the energy of the ultra-violet light and the consequent acquisition “by these corpuscles of sufficient kinetic energy to enable them to escape. ‘This view follows naturally from the fundamental assumption of the electron theory “of conduction as elaborated by Riecke ¥, Drude **, and J. J. Thomson f+, and applied with so much success to the explanation of the relation between the thermal and the electrical conductivities of metals. For according to this assumption, there exist at all times within conductors free or “ metallic ” corpuscles, which, in accordance with the Maxwell-Boltzmann law, possess a kinetic energy of agitation * Hoor, Wien. Berichte, xcvii. p. 719 (1888). T Stoletow, Journ. de Phys. 1x. p. 536 (1890). t Zeleny, Phys. Review, xii. p. 321 (1901). § Elster & Geitel, Wied. Ann. xlviii. p. 625 (1893). | Conduction of Electricity through Gases,’ pp. 237 & 241. This sentence is not found in the new edition of this book which has appeared since the present article. was written. Nevertheless the view that photo- electric effects vary with temperature is still retained. 4 Reicke, Wied. Ann. lxvi. p. 353, & p. 545 (1898). Also Ann. d. Phys. ii. p. 835 (1900). ** Drude, Ann. d. Phys. i. p. 566, & i. p. 369 (1908). Ti lowe Thomson, Rapports au Cong gres International de Physique, iii. p. 188 (1900). 190 Prof. Millikan and Mr. Winchester on Influence of of like value to that possessed by the atoms of the metal at the given temperature. If this assumption is correct, and if the electrons which escape under the influence of the ultra- violet light are these free electrons of the metal, it is obvious that their rate of escape must be an increasing function of the temperature. Indeed, whether the Maxwell- “Boltzmann law can be applied to such corpuscles or not, it is difficult to see how their rate of escape from the surface of a negatively- charged body could be any other than an increasing funeiied of the temperature ; for in view of their mutual repulsions these free corpuscles would be distributed over the surface of the body, and the forces which hold them to it might be expected, from the behaviour of molecular forces generally, to decrease as temperature increases. The other view, namely that the emission of corpuscles is due to atomic disintegration effected through resonance, was suggested by Elster and Geitel *, and is very strongly sup- ported by Lenard f. The most convincing evidence adduced by the latter is found in the fact that the aluminium, carbon, and platinum plates upon which he experimented acquired in a vacuum, under the influence of ultra-violet light, posi- tive potentials which were wholly independent of the j intensity of the source. As Lenard points out, this means that the kinetic energy of projection of the corpuscles—a quantity which is measured by the positive potential assumed in vacuo —cannot have been acquired to any appreciable extent by the abserption of the ultra-violet ight, but must rather have been possessed by. the corpuscles before they were set free by the light, which could in that case have acted only as a % detonating ” agent. Furthermore, the independence of the quantity of discharge upon the potential of the charged body + constitutes an indica- tion, at least, in favour of enende Ss vlew. Again, Elster and Geitel’s t discovery that absorption and emission go hand in hand, whether it be wave-length or chad of polarization of the incident light which is made to vary §, 1s also more readily reconcilable with the theory of * Elster & Geitel, Wied. Ann. xli. p. 175 (1890). + Lenard, Ann. d. Ne il. p. 8359 (1900); and viii. p. 149 (1902). In the new edition of ‘Conduction of Klectricity through Gases’ J. J. Thomson recognizes the strength of Lenard’s argument and adopts in the main his viewpoint regarding ‘the mechanism of emission. { Elster & Geitel, Wied. Ann. lu. p. 453 (1894); lv. p. 682 (1895); 1xi. p. 445 (1897). § This discovery of Elster and Geitel’s as regards the effect of the plane of polarization of ‘the incident light was made by allowing yellow light to fall upon a sodium surface. It does not hold when ultra-violet rays are employed (see Lenard, Ann. d. Phys. viii. p. 168 (1902); and Ladenburg, Ann. d. Phys. xii. p. 558 (1905)). Temperature upon Photo-electric Eqects in High Vacuum. 191 atomic disintegration because of resonance, than with that ot absorption by free corpuscles of the energy of the incident hight. In view, then, of the strength of the arguments in favour of Lenard’s point of view, and in view of the fact that all of the recorded measurements upon the effect of temperature upon photo-electric phenomena, save only those cf Elster and Geitel, are incapable of a positive interpretation because of the failure of the experimenters to eliminate secondary effects due to the medium, while even Elster and Geitel’s experi- ments were made only upon one metal, and one which has a melting-point only slightly above the temperature at which the experiments were performed, it was decided to reinvesti- gate de novo the eftect of temperature upon photo-electric phe- nomena, making all observations in a very high vacuum, and extending the experiments toa considerable number of metals. 3. The Vacuum.—On account of the contaminating in- fluence on the mercury of the usual rubber tube which connects the two reservoirs of a mercury pump, and also on account of the fact that air slowly leaks into the vacuum ——— ee through this tube, this form of tube was discarded altogether after considerable fruitless experimenting with it, and the vacuum was produced with the pump which is shown in fig. 1. This pump possesses no essentially new elements, 192 Prof. Millikan and Mr. Winchester on Influence of although the combination of elements may be of sufficient interest to justify the diagram and a brief description. The pump is composed entirely of glass, no stop-cocks or wax-sealed joints being used anywhere in connexion with the vacuum-chamber. The pressure within the forty-litre bottle, 6, is maintained at from one to five centimetres of mercury by means of an aspirator-pump, p. The mercury is forced into the bulb, 0', by connecting b with the outside air through the two-way stop-cock, ¢, and the drying-tube, ¢. After the bubble of air has been forced out at o, the cock ¢ is turned so as to establish connexion between B and b, when the mercury falls again in 6’. With such a pump the mer- cury remains clean tor an indefinite period, and the vacuum can easily be maintained for months, in which a MacLeod gauge will register ‘00001 mm. of mercury or less. This means, of course, that practically all of the gas save mercury vapour (pressure about ‘001 mm.) has been “removed. 4, Early Laperiments upon Aluminium.—The first series of observations upon the effect of temperature upon the dis- charge was made in May 1905, upon an aluminium electrode. The source of the ultra-violet light was a spark from the zine electrodes e (fig. 1), which were made the terminals of the secondary of an induction-coil as shown, a small condenser }. being introduced for the sake of increasing the intensity of the light. The coil and electrodes were enclosed, in the usual way, in a metallic box, so as to screen the charged system from the disturbances produced by the spark. The ultra-violet light passed first through a hole, 5 mm. in diameter, this box, then, when the shutter s was lifted, through the quartz plate Q, then through a hole 7 mm. in diameter in the metal washer w, then through a wire gauze screen, of one and one half mm. mesh, and finally fell upon the charged plate a 10 mm. in diameter. This piate was connected to one pair of quadrants of an electrometer, which was charged at the beginning of each observation to the potential of —20 volts. For the sake of reducing the natural rate of leak, the capacity of the electr ometer “system was increased by means of the air-condenser ¢c’. The electrometer was an Edelmann instrument furnished with an oil-damping device. The deflexion of the electrometer for the charge of —20 volts was about 200 cm. on a scale 2 m. distant. In these first experiments the leak when the electrode was not illu- minated amounted to about 2 mm. in 30 seconds. When the light was turned on for a period of 15 seconds by lifting the shutter s, the discharge was sufficient to cause a change in deflexion of about 20 mm. The method employed for Temperature upon Photo-clectric Kfects in High Vacuum. 193 separating this discharge due to the light from the natural leak of the system was as follows:—The natural leak was observed during the period of 30 seconds immediately pre- ceeding the time at which the light was turned on, then the electrode was exposed to the ultra-violet light for a ‘period of exactly 15 seconds: after a lapse of 45 seconds more, the deflexion was again observed ; finally, the natural leak was observed during the next 30-second period. The sum of the leaks during the first and last 30-second periods was sub- tracted from the change in deflexion during the intermediate 60-second period in order to obtain the dischar ge due to the light. “In order that the char ged body might be perfectly screened from electrical effects during these observations, the inner wall of the tube was entirely covered with wire netting of 4+ mm. mesh, and this netting was connected to the washer w and the tinfoil envelope g, and the whole system then con- nected to earth in the manner shown in fig. 1 In order to eliminate any possible effects which gases adhering to or occluded in the surface of the electrode might have on the results, the tube was kept at a temperature of about 400° C. during the whole process of evacuation, and in addition the electrode was made the cathode of an induction- coil discharge which was maintained continuously for a period of several hours. A typical series of observations obtained with this electrode is given in Table I. t TABLE I. pons , Discharge in Discharge in Temp. | Seale Dive. Temp. | Seale Dive panna 208 iE —— eh BOOMs 1 16°3 286° C. | 13°8 50, 17°4 ZOO et 1d 100 ,, 16-0 ete a 15-4 142), 14-2 We 20Bn.," | 15:2 169 ,, 17:0 Hee OG Vea es 16:2 IS 16°5 [2S 7a es Laer DD 166 ZO Si | 15:9 Loe 16:3 SOO sie | UBS, 990)-; 17-2 Hh ps ese. of 163 PASTS NS 129 aie 15°3 246 ,, 14-2 He goa A 15°7 254 ,, 136 Hae 304) 15°5 DOO. Lol Veeyee SAO ees es Mt 15°8 264 ,, 13:9 eetore.) el 15°4 269 ,, 13:3 BAe eo 17-0 972 ,, 14:3 256i, "| 16-9 Sa 14:2 Py Obt 17/25) 280 ,, 14:0 Ged 17:0 | | | Phil. Mag. 8. 6. Vol. 14, No. 79. July 1907. O 194 Prof. Millikan and Mr. Winchester on Influence of The observations shown in this table covered a period of about two days. It will be seen that the readings are not very satisfactory from the standpoint of the agreement between observations taken under apparently identical con- ditions, and it was for this reason that the results were not published at the time. Nevertheless, the table is sufficient to show clearly that within the limits of the rather large obser- vational error, temperature has no effect whatever upon the rate of discharge of electrons from aluminium, at least, within the temperature range 50° C. to 343° C. Observations could not be carried much above 343° C., for the reason that between this point and 400°C. the natural leak of the system, consisting of the electrode and the elec- trometer, became so large as to mask completely the effect of the ultra-violet light. “In fact, at 400° C. the electrometer would lose either a positive or a negative charge with equal readiness, and so rapidly that the needle returned to zero in approximately the same time as when it was connected to earth. This leak disappeared as soon as the temperature was again reduced to about 340°C. 5. Laperiments upon other Metals.—In order to obtain observations upon a whole series of metals under identical conditions, the tube shown in fig. 2 was constructed. Within Fig, 2. Purnp == == (f- “ys “if £ UY a glass bulb 8 cm. in diameter an aluminium wheel, VW, 6 cm. in diameter was mounted upon agate bearings a. At equal intervals about the rim of this wheel were screwed metal disks, d, 1 em. in diameter, of copper, nickel, iron, zinc, silver, magnesium, lead, antimony, gold, al untninniait al brass. To the wheel was also attached a small strip of iren to serve as a magnetic control, so that with the aid of a large magnet outside of the tube any desired disk might be rotated to a position in line with the beam of ultra- violet light which Temperature upon Photo-electric Effects in High Vacuum. 195 entered through the quartz plate Q, traversed the metal tube A, and finally fell upon the disk d under examination. The tube A was coated with a dull black finish on the inside so as to avoid reflexions and prevent, to as large a measure as possible, photo-electric effects from its surface. Its left end was closed with a metal stop having a circular opening 7 mm. in diameter, and its right end with a stop having an opening 8 min. in diameter, the size of the openings being chosen so that the whole beam which entered the tube might fall upon the disk d and none of it strike the aluminium wheel IV. Care was taken also so that this beam might not fall upon the inner walls of the tube A. The metal tube A was con- nected to the wire gauze g, which completely covered the inside of the glass tube. It was also connected to the elec- trode /"’, so that tube and gauze might be connected to earth either through E’ or £". The electrode E’ was connected directly to the aluminium frame, 7, which supported the wheel, and / was kept in conducting contact with the wheel by means ofa platinum spring p. ‘The bulb was enclosed in an electric furnace of dimensions 30 em. x 30 cm. x 20 em. This furnace was provided with an electric fan for maintain- ing constancy of temperature. Observations upon the effect of illuminating any particular disk with ultra-violet light were made in both of the follow- ing ways:—1. The electrometer was connected to / and the system ‘charged to a potential of about — 20 volts. The gauze and tube being i in this case connected to earth, observations were made upon the rate at which the electrometer system lost its charge under the influence of the light. 2. The electrometer was connected to the gauze and tube by means of the electrode ” or /"', and the wheel was charged to a potential of from —20 to —300 volts. In this case the charge which was lost by the wheel because of the influence of the light was caught upon the gauze and measured by the amount of the electrometer deflexion. It will be observed that with either arrangement the electro- meter was connected to an electrode which was sealed into glass. As the following observations were taken in mid- summer 1906, this contact of. the charged system with glass made the elimination of the natural leak due to the conduc. tivity of the glass surface of the tube a maiter of exceeding difficulty. The elimination of this leak was, however, con- sidered of the greatest importance, since there was reason to believe that the irregularities in the readings given in the preceding table were due to uncertainty in the corrections due to the natural leak. After some months of experimenting O 2 196 Prof, Millikan and Mr. Winchester on Influence of the following method was adopted and found to work admirably. The small room in which the work was done was kept as dry as possible with trays of sulphuric acid and caleium chloride, and a current of thoroughly dried air was kept blowing against the electrode / or L’, which was connected to the electrometer. The persistence with which moisture adheres to a glass surface is shown by the fact that it required three or four days of continuous blowing to obtain an elec- trode dry enough for our purpose. The success attained in the end, however, is shown by the fact that with a deflexion of 25 cm. the leak was not more than*l mm. in five minutes. Since the following observations never required more than two or three minutes at most, it will be seen that the natural leak was completely eliminated. At temperatures above 100° C., however, another source of leak appeared, for which it was necessary to make a correction in the manner indi- cated below. In the series of observations which follows, the wheel was joined to one pair of quadrants of the electrometer and to this system was connected the negative pole of a battery of 20 cells (one volt each), the positive pole being joined to earth. The other pair of quadrants and the gauze ¢ were also connected to earth. The deflexion was observed, then the connexion between the battery and electrometer was broken. The leak being inappreciable, the deflexion remained constant. At an accurately noted instant the induction-coil was started and the light allowed to fall on the disk under examination for exactly "10 seconds , as measured by a stop-watch. After an interval of about 50 seconds, the electrometer having again come completely to rest, the reading was taken. ‘The difference between the two readings represented the discharge due to the light. At temperatures above 100°C., a leak similar to that observed with the aluminium electrode at 340°C. (ef. § 4) began to make its appearance. > "<0 Pane CCC CERNE eT pee ee SANG Cee rome et SK) ee eee Nae ao Me lie | Pe) |) le | | Ce ae eee i Bim hs — i. im A i, oe i | | = Ae ne | | et | oe 0! rh Seer nepal eset Sp ae | = = a tha Soe WRAnees ase f al a nbn elt =a | — - - aI = ah Sits ee te ee 1 SNS 8 b Vie : | Sia. iy er pore TD | [ = | Nj ae wo | | Ts a a Ss | iS § S s Ss — lex la t——§ Se Nu ae | Sls x & 3| = His TT Ik ae aL me ae ak te ae Il = t | ; RISES SS RS | peepee Ss . T SNS N AS) NN T S s = ae = | ois 9 a | | S) S ie [Leese 3 = ois tod ar co. n : ‘ia ) Upson. Phil. Mag. Ser. 6, Vol. 14, Pl. VI. phil. Mag. Ser: 6: Vo! vie Pe Vee ee i VOLTS, r. i ” or, . + . . Urson. Phil, Mag, Ser, 6, Vol, 14, Pl, VID Hig. 5, Fie. 9. Fe, 7. Tia. 6. 45 - Fie. 8, 45 40 40 : a ra 2 35 2 o a > te — a ° S 35 > > ao EK 30 = > 30 25 25 AL-Fe 20 a 6 7; aT. | ) 2 6 10 14 IL 2 4 6 8 10 12 8 10 12 14 AMPERES. AMPERES. AMPERES, AMPERES, . Fie, 13, Fie, 12. 400 ] Fia. 10, 65 350) = Fie, 14. 120 Fe, 11. 0 500 100 10 2 400 2 a = ae Pec = e i) a w a =< 300 2 80 8 45 = = roe 200, - = = =< 200 40) 60 6 150 100 : 35 Als ar 02: Sa 03 owe TIME IN SECONDS. 16 0 AL — 4 1 0.2 0125 Fi 4 af | | as Oe IRORORTInS a2 a O05 ARC LENGTH GNCHES) Ei : FALL IN INCHES. ) 4 8 12 16 2 A A —15- 2 TINE IN SEC 7 ; 6 AMPERES. AMPERES. a ae ee a arama i Woop. Phil. Mag. Ser. 6, Vol. 14, Pl. VIII. ) Me 360 D, Deas | " Mag viele Ret tim oh Sedum Vib ¥. oe PRE ANY vo. A " * 4 fie ‘ —$ (i ae 2 lag ieee dm tie TRE Rae AN A TOE RGAE LTT GOAT ARTE A AAAS PINE eae a | eed alg Abii; i- i : war 9 19004 a7 ~tund h S ; Pug 12, Add eo: THE SATE NT AOR | ONDON, EDINBURGH, anp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SIXTH SERIES.] A UG US B. 190T. XVII. On the Electrical Origin of the Radiation from Hot | Bodies. By J. J. THomson, M.A., F.RS.* O many investigations, theoretical as well as experimental, have been made on the radiation emitted by bodies at various temperatures, that a paper on this subject seems to call for some apology. Some of the theoretical investi- gations, however, are of such an extremely general character, that perhaps others besides myself may have found some difficulty in following them and in appreciating their rigour: and it is possible that there may be room for an investigation ‘in which the radiation is supposed to be produced in a way which admits of comparatively simple treatment. The idea on which this investigation is based is, that the radiation from hot bodies is analogous to Rontgen radiation ; i. €., consists of a series of electromagnetic pulses produced by the stopping or starting of charged corpuscles in the hot body. I suggested the possibility of this origin of radiation in a paper presented to the International Congress of Physics at Paris, 1900 (Rapport, t. mi. p. 148); but the subject acquired importance by a remarkable investigation by Lorentz (Amsterdam Proceedings, 1902-3, p. 666), who showed that, on this view, the energy in the radiation with exceedingly long wave-length is given by the expression 1 mv? Ua eee! * Communicated by the Author. Phil. Mag. S. 6. Vol. 14. No. 80. Aug. 1907. Q 218 Prof. J. J. Thomson on the Electrical where EH, is the energy carried by waves with frequency between g and g-+ dq, mu’ is the kinetic energy of the corpuscle, and V the velocity of light. If we suppose that the kinetic energy of the corpuscle is the same as that of a molecule of a gas at the temperature of the hot body, mu? = 200, where « is a constant equal to 1:4 x 107" on the C.G.S. system of units, and @ the absolute temperature. Hence 8S WO DP Been ye and this has been shown by Lorentz to be in good agreement with experiments made on the very long wave radiation from hot bodies. Lorentz’s investigation is limited to frequencies so small that a corpuscle describes very many free paths during the time taken by light of this frequency to make a complete vibration. The preceding expression represents a radiation increasing indefinitely as the frequency increases ; whereas the radiation from hot bodies attains a maximum at a frequency depending upon the temperature, and then diminishes as the frequency increases. The following in- vestigation is an attempt to find an expression for the radiation which does not involve the assumption that the frequency is small. If a particle carrying a charge e is moving with an acceleration 7, waves are emitted by it and the rate at which 2 £2 energy is radiated is as where V is the velocity of light ; and if f is an harmonic function of the time having a frequency gq, the radiation will be light having this — frequency. If by Fourier’s theorem we express fin the form f=5|e@edy where $(g) is some function of g, then, since the rate of 2 £2 1D Oq? dq; radiation is — the radiant energy emitted by the moving particle through the whole of its career is Origin of the Radiation from Hot Bodies. 219 Lord Rayleigh has shown (Phil. Mag. [5] xxvii. p. 460, 1889) that when / is expressed in the form (1), then +0 2 Fa 2 (ore Hence the energy radiated Eee ar, 2 J =sav | (o@} ay Thus the amount of the energy in waves whose frequency is between g and g+dq is Say is@ta ZorV (Pd cs Let us now apply this result to the case of a corpuscle moving through a body and coming into collision with its molecules; and let us follow a corpuscle from the beginning to the end of its free path. At its start it is subject to a great acceleration for a short time; then it proceeds without acceleration, and when it collides at the end of its p-th the acceleration is again very great. After the end of the collision it 1s again zero. We have, by Fourier’s theorem, Fie) — a) { f) cosg(t—A)drdq.. . (2) Now we may represent the acceleration during the free path by ee that f(A) is zero, except when 2X is between -* and + — a , or between b- and ode when it is very large ; thus 4, and A, are the times occupied by the col- lisions, and t, is the interval between them. If the accelera- tions are symmetrical with respect to the beginning and end of each collision, then equation (2) becomes ie) = = nC cos gt + $, cos ¢(t—ts)) dq; where a d,= | /A)cosgqr.dr, " 1 +% do, = “A) cos gv dh. t—3 Q 2 220 Prof. J. J. Thomson on ihe lean Hence i yi) ee 1¢° (§p, +. cos qty}? +,” sin? gta) dg Say (pr? + hy’ + 2pidy Cos Gty) dg. Thus the energy of the waves with frequency between g and g+dq is equal to , =, (hi? + ho? + 212 Cos qe) dq. If the accelerations when the particle is stopped are equal and opposite to those when it is started, ¢,= —dz., and the preceding expression becomes 8 9 ae “roe sin? oe Ads). ws: aati ene We shall now proceed to find te value of ¢, in special cases. If the acceleration is constant and equal to @ during the collision, then 3 | 26 sin soe o, = C08 GMa = - uae 2 Z a where A, is the duration of the collision. If the collision reduces to rest a particle which was moving previously to the collision with the velocity w, then ay 2 Sar=u, AL a (ON Sa) Hence On sin 12 or Pao gry 9 and the energy radiated from the beginning to the end of the free path is by (3) LGN s Sines "nD i 5 ag sin? = Lemme Sisn sh | (45) Instead of supposing that the acceleration abruptly changes Origin of the Radiation from Hot Bodies. 221 from the large value ,; to zero, let us suppose that it increases from zero quickly up to a very large value and then quickly diminishes to zero again. Such a case could be represented oy supposing Re i Ae @, where a is small compared with X,. In this case A ae Ie i, = af ,€& 700s gn. an. 2 If A, is large compared with a, we may substitute —o and 1 My nr ’ s +o for the limits, instead of ae and 3? without making any appreciable error ; so that +20 2 ?i = Af € @cos gn dr g2a2 =2A\/Tae 2. If this acceleration reduces a particle moving with a velocity u to rest, +o 2 = At e @dnr =2AW/ tra. Hence q2a® cas Aaa RE MEE CSE SST PAIN 1) and the energy radiated is 9 “= 2 ga : 3 = ie €e 2E sim oe GREE EIR ES, Since the acceleration is only appreciable for a time com-. parable with a, we may regard a as the time occupied by a collision. | Another form for 7, which also has the property of being very large at a particular time and diminishing very rapidly on either side of that time, is A F(X) my Cy where a is very small. This is very large when % is com- parable with a, and small when X is large compared with a. 922 Prof. J. J. Thomson on the Electrical Thus a may be regarded as the time during which the collision lasts : Ay "+2 Cos gr — A zl dn 3 Pr Jon a+r? aD and if 2, is large compared with a, this may without appreciable error be written +c COS GA AY ea gaat” aa ak = 7 7 If this acceleration reduces a particle moving with a velocity u to rest was A eer sos BN eae ede i eat ad thus pee, and the energy radiated is equal to eg OE 3 ay S ; sin lon ° dq. ° #1 ile (8) By taking other expressions for / we can get other forms of ¢, but it will be found that db is always of the form uyr(qa), where a is the time occupied by a collision, and that yr(qa) vanishes when ga is infinite and is equal to unity when gis zero. In the preceding investigation we have only considered one collision ; in considering the effects of a large number of collisions we must distinguish between the case when there is any regularity in the occurrence of the collisions and when these occur entirely at random. If there are fixed phase . relations between the collisions, the energy radiated in a number of collisions will not be the sum of the amounts of energy radiated when the collisions occur separately. Thus, take the case of two collisions occurring simultaneously and in close proximity. If the two collisions were of the same character, 2. e. if the accelerations were the same in the two cases, the energy radiated by the two collisions occurring simultaneously would be twice as great as that radiated when the collisions were separated by a long interval. If, on the other hand, the accelerations in the two collisions were equal and opposite, the energy radiated by the two collisions would be infinitesimal in comparison with the energy radiated when the collisions did not coincide. If, however, the collisions occur quite at random, we may take the energy radiated in these. Origin of the Radiation from Hot Bodies. 223 collisions as the sum of the amounts of energy radiated when they occur alone. If N is the number of free paths which are described in unit volume of the substance in unit time, then, when the collisions are numerous and at random, the energy having frequency between g and g+ dq radiated from unit volume in unit time is equal to This is not the amount of radiant energy in unit volume at any time, for the energy is absorbed after passing over a very short distance; we can, however, deduce from it the actual density of radiant energy in the substance as follows :— When the system is in the steady state, the energy radiated from unit volume in unit time must equal the energy absorbed by that volume in that time. Let EH be the energy in unit volume of the stream of radiant energy of the body when in the steady state, X the electric intensity in the stream, 7 the current parallel to w; then the energy absorbed per unit volume per unit time is Xi, or, if ¢ is the conductivity of the substance, X?c. If K is the specific inductive capacity of the substance measured in electrostatic units, V the velocity of light in a vacuum, = KX? o | Amn? hence =e eye Xe = K J 5 thus the rate of absorption of energy per unit volume is equal to Ray? c - i. | As this in the steady state must be equal to the rate of emission of radiant energy, we have 47 V? K When Ez, denotes the part of the energy corresponding to waves having a frequency between g and ¢+dq, we see from (3) that E se oly AU LN 3 Ver sin” ae dq. oF C Ly — Na apvier sin’ 9 4: e - e (9) When the heat produced by the current represents the 224 - Prof. J. J. Thomson on the Electrical work done by the electric field on the corpuscles during their tree path, we can easily find an expression for ¢. If the electric force X is represented by Xy cos (gt +e), then the equation of motion of a corpuscle during its free path is Aza mg = eX, cos (gt+e); | and hence mo = a sin (gt-+e)+ mu sin €, if w is the velocity of projection of the corpuscle at the beginning of the free path when t=0. The work done by the electric field on the corpuscle during the free oe feXda = he 0 eX — pedi=| eX tees Gh ae - | Substituting the value of we see that the integral DAU ae am 4 ; | ' Saye 1° (gt, +e) —4 sin? e—sine en (gto+¢) —sin e)} | +-u— ; of (sin (pt, +e) —sin e) ee =5= “= (sin (qt,-+€) —sin €)? + EE i (pt, +e)—sin e}. The last term on the right-hand a will vanish when we take the average, and the expression will reduce to 9 OX - og Gtr <2 ges a ee sin 9 cos ey, a3 |b Since the phase e at the beginning of the free path may have any value, the mean value of the last factor is 4: hence the average rate of absorption of energy per free path is WO hie sin? 22 ni 2 7 m g 2 Since there are N free paths completed in unit volume per unit time, the rate of absorption of energy per unit volume is equal to 2 Ya Ne? x2 1 2 m io g? This expression must be equal to 4cX,?, for the rate at Origin of the Radiation from Hot Bodies. 225. which energy is absorbed is cX?, and }X,? is the mean value of X?. Comparing these expressions, Substituting this value in equation (9) we find 1 mk Ey= oy aaysPL dq. If we take the form given by anaron (5) for d; we have Lm? K. =e E,= 5 5 aya’ 2 GaAs ide ae T! 82S CTOH while if we take (7) we have UR a Nore Dig == —S BR aoe © ee ia: g dq. e e ° e (@a) In each of these expressions a represents the time of a collision. When the waves are so long that qa is small, these two expressions are identical and agree with that given by Lorentz, provided we assume that the kinetic energy of the corpuscle is the same as that of a molecule of a gas at the temperature of the radiating body, 7. e. is equal to 20 if 0 is the absolute temperature and a=1:42 x 10-¥, On this assumption (11) becomes 2 adh 9 Ky= Se “dq. _ If, as is usual, the radiation is expressed as a function of 27V the wave-length A, then since (= , H,, the rate at which radiant energy with a ote between X% and 7~A+dXr passes through unit area is given by the equation 47 V BE te. snd jar 2h Ese Wa We know from the researches of Wien and others that if the Second Law of Thermodynamics holds for radiant ener ey HB, must be of the form Ik where $(A@) is a function of A@ and the same for all bodies. 226 Prof. J. J. Thomson on the Electrical Comparing this with (12) we see that sa Chon B must be of the form ¢ 4%, where } is a. constant and inde- pendent of the radiating substance. Thus a, the time occupied by the collision of a corpuscle with an atom of the substance, must at the same temperature, 7. e. with the same average velocity of the corpuscle, be the same for all substances, and — when the temperature varies must be inversely proportional to the temperature, 2. e. to the square of the average velocity of the corpuscles. The measurements which have been made of the radiation at different temperatures enable us to find the duration of the collision for any velocity of the corpuscle. We see from equation (12) that for a given value of dd, Hy is a maximum when AwVa=An, OF tees ar a= _ (time of vibration of the light of maximum radiation). Now at 0° C., the radiation is a maximum for light whose wave-length is about 10-3 em., and the time of vibration of this light is 3°3 x 107" see. Hence the time of collision at 0° C. when the corpuscles are moving with a velocity about 10’ cm./sec. is 1-1x 10-™ seconds. In this time light would travel through 3°3 x 10~* em. If the time of a collision varies inversely as the square of the velocity, this time for cathode rays moving at the rate of 10° em./sec. would be 2°1 x 10- sec.,and the distance travelled by light in this time, 7. e. the thickness of the Réntgen pulse, would be 3°3 x 10-8cem. For cathode rays moving at the rate of 10" cm./sec.,the thickness of the pulse would be 3:3 x 10—!® em. In an ordinary Réntgen-ray tube the velocities of the cathode rays, and therefore the thickness of the pulse of Roéntgen radiation, are probably between these limits. Sommerfeld, from a discussion of the results of experiments by Wind and Haga, estimates the thickness of the pulses used by these physicists as 2°5 x 10-8, a value which is within the preceding limits. Radiation produced by the impact of Cathode rays.——An interesting application of the preceding results is to the effect produced when a stream of cathode rays impinge on a solid body, without any ordered connexion between the time at which the impacts occur. In this case we see that the energy corresponding to a frequency between gq and g+dq radiated Origin of the Radiation from Flot Bodies. 227. per second in consequence of the collisions is equal to 2 Ne? Barve where N is the number of collisions per second : taking the value of ¢; given by equation (7) this equals 9 Ne? 3 at end: where wu is the velocity of the cathode rays. Hxpressing it in terms of the wave-length instead of the frequency, Ha, the energy between wave-lengths X and A+dA is 4 Neu? aN, Se This is a maximum when 7X=27Va. When the cathode rays are moving with a velocity of 108 em./sec. or over, a will be less than 2:1 x 107~"*, and the * dq, dn. 47é terme 4° will be very nearly equal to unity all through the visible spectrum, and the energy in the visible part of the spectrum, say between X=7x10-° cm. and A=3°5x10° cm., will be A Ne?u? 2x AO.” Now if each corpuscle only makes one collision, Ne=7:, the current carried by the cathode rays, and since e=10~”, the energy in the visible part of the spectrum is 4 : 5 : 91210 HR or if the velocity of the cathode rays is 10%, the energy radiated will be 19 x 2 ergs. Now by the use of Wehnelt tubes with lime cathodes we can get a stream of cathode particles carrying a current of a milliampere. Hence putting i=10~“*, the energy in the visible part of the spectrum would in this case be 1S) Selle crete: Radiation carrying as much energy as this ought to be 228 Prof. J. J. Thomson on the Electrical easily visible. Lord Rayleigh (‘Collected Papers,’ vol. iv. p- 128) estimates that from a standard candle the energy in the luminous radiation is about 5x 10° ergs per second. Hence the quantity of energy crossing one square centimetre at a distance of 100 metres from the candle would be 5 x 10°/4ar x 108 or 4x107* erg per second, considerably less than the energy in the luminous radiations sent out by the cathode rays in the case just considered ; so that this light ought to be bright enough to affect the eye. The intensity of the light could be materially increased by ac- celerating the corpuscles given out from the lime by an electric field. If the velocity were increased tenfold, the intensity of the light would be increased one hundredfold. The energy in the light in the octave of wave-lengths from 3°5x 107° em. to 1:75 x 107° em. would be twice that in the octave corresponding to luminous radiation, and until we approached the wave-length 6:°3x10~° em. (supposing the velocity of the corpuscles to be 10° cm./sec.), the energy in each succeeding octave would double as the wave-length diminished. Thus we must have here a source of ultra-violet light cf much smaller wave-length than any yet investigated, and by increasing the velocity of the corpuscles to 10° cm./sec. or further, we ought to be able to produce light with a wave- length of less than 107° cm. ; in fact, to completely fill up the gap between the infra-red radiation and Roéntgen rays.: I am at present engaged in experiments with this object, making the corpuscles given out by hot lime impinge against a solid obstacle. We see from equation (8), tf being large compared with a, that the total amount of energy radiated per unit time is equal to 2 NeW? 3 7Va’ or, since a is the time of a collision, to 2 Ne?u? { 1 te Th space travelled by light in the time of a collision _ Thus the energy in the visible part of the spectrum will be to the whole of the energy radiated as the thickness of the pulse in the Rontgen radiation is to a length -comparable with the wave-length of visible ight. When the cathode particles are moving at a speed of 10° cm. per sec., the thickness of the Réntgen pulse is only about one-thousandth part of the wave-length of sodium light. Hence only about Origin of the Radiation from Hot Bodies. 229 one-thousandth part of the radiant energy appears as light : practically the whole of it is in the radiation whose wave- length is comparable with the thickness of a Réntgen pulse. The preceding estimate is based on the assumption that the cathode ray is stopped at the first collision; if it has to make several collisions before losing its energy, the amount of radiant energy emitted by it will be reduced. For suppose instead of being stopped by one impulse P it is stopped after n collisions by n impulses each equal to P/n, then though the number of collisions is increased n times, the amount of energy radiated at each collision, being proportional to the square of the impulse, will be reduced to 1/n? of its former value. Thus the amount of energy radiated will be 1/n of that calculated on the assumption that there was only one impulse. The total amount of radiation when N particles moving with a velocity w are stopped is 2 Ne2u? 3 7Va’ a being the time taken by a collision. Now we have seen grounds for believing that a is inversely proportional to the square of the velocity of the corpuscles. If this is the case, however, the energy radiated varies as Nu*; i. ¢., the energy in the Rontgen radiation is proportional to the square of the energy in the cathode rays, provided the number of corpuscles striking against the anti-cathode in unit time is constant. I am not aware of any experiments on the connexion between the effect of the velocity of the cathode rays on the proportion between the energy in the Rontgen rays and the cathode rays which give rise to them. | We have seen, too, that if the Second Law of Thermo- dynamics applies to radiant energy, then a the time of a collision must, when the velocity of the corpuscles remains the same, be the same for all bodies. Now the amount of energy radiated as Rontgen rays when a given stream of * cathode rays is stopped depends only upon a ; and hence, if the preceding considerations are correct, ought to be the same whatever may be the material against which the cathode rays strike. We know, however, that far fewer Rontgen rays are produced when the stream of cathode rays falls against an aluminium target, than when they fall upon one made of platinum or lead. It must be remembered, however, that the impact cf the cathode rays, in addition to producing Réntgen rays, produces also secondary cathode rays; and these secondary rays, both at their starting and afterwards 230 Llectrical Origin of the Radiation from Tot Bodies. when they come into collision with the surrounding mvle- cules, will give rise to Réntgen rays ; and thus the Rontgen rays emitted from the target struck by the cathode rays consist of two parts, one due to the impact of the primary cathode rays; this part, if the preceding considerations are correct, ought to be the same for all bodies ; the other part, due to the stopping and starting of the secondary cathode rays, will depend upon the metal of which the anti-cathode is constructed. If the collision between a corpuscle and a molecule is regarded as arising from a strong repulsion between the two when they come very close together, then we can show that if, as the Second Law of Thermodynamics requires, the time of a collision varies inversely as the square of the velocity of the corpuscle before it came into the neighbourhood of the molecule, the repulsion between the corpuscle and the mole- cule must vary inversely as the cube of the distance between them. By taking the acceleration during impact to be propor- we have arrived at the law of distribution i tional to eae expressed by the equation anaes B, « as aug which is the form suggested by Lord Rayleigh (Phil. Mag. tipi] pdlixtp-' 939): At high temperatures this expression does not seem to agree with the experiments as well as the one suggested by Planck, 2. é., To find the kind of collision that would give Planck’s form, we see that if f(A) represents the acceleration at the time A, we must have Hee Dr 2 f amet = HPD COIN 10 \ same or, since no +a A) 2 i F(A) cos gr. cos gt .dq. dn, 0 —o pee tee a aoe \Md FAS) a Ost ata! 2h qame=ammie Radium present in Typical Rocks of Montreal. 231 The amount of energy transformed per cubic centimetre of a metal into radiant energy per second is surprisingly large : nearly the whole of this is absorbed by the metal, and passes into a form other than that of radiant energy. We have seen that if E is the radiant energy per unit volume in the body when in the steady state, the amount of radiant energy produced in a cubic centimetre of the substance per second is C. 4a V? aa) i Now VE is the stream of radiant energy passing through the substance ; by Stefan’s law it is equal to of* at the absolute temperature 6, and uv is about 10~™” gram calorie. For silver c, the specific conductivity, is about 1/2000 ; hence at the temperature 27° C. or 300 absolute the radiant energy produced per cubic centimetre of the silver per second is equal to | it = PAs? x (00) er K bx 10° calories. Thus if K were unity the radiant energy produced in a cubic centimetre of silver represents about 8000 horse- power. Thus, though a cubic centimetre of silver does not distribute its radiant energy well, it produces as much as a good-sized electric-lighting station. XVIII. The Amount of Radium present in Typical Rocks in the immediate Neighbourhood of Montreal. By A. S. Eve, M.A., and D. McIntosu, D.Sc.* ie 1906 Strutt made a careful and thorough investigation of the amount of radium present in specimens of rocks obtained from sources differing widely in geographical dis- tribution and in geological time. His results, published in the Proceedings of the Royal Society (May 14th and August 18th) were most remarkable and important; and it may be convenient to reprint them in the present communica- tion. But it is necessary to apply a correction depending on the ratio of radium associated with uranium, which in the results first published was not correctly assumed, because the value ultimately found by Rutherford and Boltwood was * Communicated to the Royal Society of Canada. Communicated by the Authors. 22, Mr. Eve and Dr. McIntosh on the Radium not then known. The results obtained, expressed in grams of radium per gram of rock examined, are as follows :— Igneous Rocks. Granibey ys Aemeismet «+: Rhodesiasc) 00. sche pean 4°78 x 10-12 SES NCS Ca Cornell Se eee ener 4°67 a Zircon Syenite ........ INOEWOY: 4000 ee ee 4°65, Granivey cere eee. ss ac Cornwall yi eee a ee Wy eee nee 85's aha Cape of Good Hope .... 357 ,, SA MGS.) 3) aCe, ¢ Compal, 0% es ee 345, i Rie = ake tenete Westmoreland 37. e oO. ae SVEMILC Geer... tere eee Norway! i) ee 244, Gramibe. ee... Sear Devon ta nse ine 1 Sao Gee iblueyeroumd) |. gaan. Kimberley (42°22. Ssence 63 Vike Leucite basanite ...... NV CSUunWIUS) 24.) cbr cee 12661 gyi Elorniblende oramite = 2).).) Meyvpt no. eee 22 oe Bipehstone eae yo, Isle of Nico)... eee 0s ae iElornblende diomte’ ... delerdelbers) 2. sae “OO Sato Augite syenite ......... Norway itics) ot. See OSs phks IETUCOUILE D heWs Graven cs Iisleyot cE uni ey) a eee "GS accel Olivine euchrite........ a Sy) hy See a 64 se Olivaneybasalti eee aes ce- IVC leer nee cee Ie are Kimmeridye clay ...... Iya ae eet A aera oleae On-bearine sandstone Ve eu Oollciaters ms nae 52 tee ooime slate sa... AWinlleste tees St o's Urano 2S cee Gritty slates el see « @ornyyalleen. . eee 12d) Ty, Cerne clinaegs ase 4: =i iacambrideer iy. seer ee LOD gee OE pi a ae SOE LoPs armas ISG OX Ge Bac herectev errs Ceeeee Sos eee eae Red sandstone ........ Hast Wothiant 45s SOA ghee imenoravel ey When tea ISSO yr oy ae ofa ta edt chal avai hes. Elunstanton ) Shee. vere foo Oa AUG aNG PTV eROIRE ee ce baci eer Essex; ) pti eee (Do. A Wihitemarnble airs sr <<. Mnidia). t-te ea gubeeee eae 7 ee Marble ec ee ai a ead Rast Lothian sce aor 6) Chalke bottomior pit j-2) Cambridge eee p10 fs pe os » top of same pit .. A ih MMR NE IN Si clo Ye 2) OE These results show that the amount of radium in the rocks near the earth’s surface is greatly in excess of that required to maintain the earth at its present temperature. present in Rocks in the Neighbourhood of Montreal. 233 For Professor Rutherford has shown by his calculations that the heat from ‘05 x 10-” gram of radium in every gram of the earth would be sufficient to compensate for the loss of heat from the earth by conduction and radiation. But the averages obtained from Strutt’s determination are :— Homeous rocks ......... 1:7 x 10-¥ gram of radium. Sedimentary rocks ... l:1x10-¥ 55 ‘3 Mean value. ............ PAX 10" 09 29 Hence it appears that near the earth’s surface there is about 28 times as much radium present as will account for the existing temperature gradient within the earth. This result is so unexpected that it seems desirable to check all available data before embarking on speculative hypotheses. Moreover Strutt, in his work, ignored the twin continents of North and South America, for he did not select a single specimen for investigation from the New World. For these reasons the present writers decided to examine representative rocks obtained in the immediate neighbour- hood of Montreal. Professor F. D. Adams kindly recom- mended a typical series, and his assistant, Mr. Bancroft, was good enough to procure specimens from the field. Three igneous rocks were selected :—Hssexite, which forms the main mass of Mount Royal; Nepheline Syenite, a sub- ordinate part of the same mountain, and Tinguaite; which occurs as a large intrusive sheet. All these were thrust through the Ordovician plain in Devonian or later times. The sedimentary rocks selected were Trenton Limestone of the Ordovician system; and the Boulder-Clay, Leda-Clay, and Saxicava-Sands. of the Quaternary or Post-Tertiary period. Thus the specimens examined cover a wide extent in point of geological time. The rocks were chemically prepared in the following manner : —Fifteen to twenty grams of the rocks were oround so as to pass through an eighty-mesh sieve. One hundred to one hundred and fifty grams of fusion mixture (Na,CO; and K,CO,) were added, and, the whole fused in a platinum dish for several hours in a muffle furnace. The fused mass was detached from the platinum dish, acidified with HCl, and evaporated to dryness ; then taken up with dilute HCl and the silica and insoluble matter removed by filtration. This insoluble matter was treated with hydrofluoric acid, evaporated to dryness, and the small amount of residue was fused as before, and added to the soluble portion. The whole was evaporated until a reason- able amount of liquid was left, and this was stored in a tightly stoppered flask for subsequent examination. Phil. Mag. 8. 6. Vol. 14. No. 80. Aug. 1907. R 234 Mr. Eve and Dr. McIntosh on the Radium After a definite period, usually about a week, the solution was thoroughly boiled, and the expelled air and emanation were collected over water. These were drawn into an electro- scope which previously had been almost exhausted of air by a water-pump. Three hours later, when the active deposits had nearly reached maximum activity, the movement of the gold-leaf was measured by a microscope with a graduated eyepiece. Since the emanation in the flask increases to half its maximum value in about 3°8 days, it is easy to calculate the maximum from the amount measured after any definite period. It was found by experiment that the emanation was not lost to an appreciable extent by absorption when collected over water, if placed in the electroscope without delay. The electroscope, as shown in the figure, consisted of a to Water Pump. filter-flask silvered inside. Strips of tinfoil moistened with phosphoric acid connected the silver coating to the earth wire. The flask was closed by a rubber stopper to which the. usual gold-leaf arrangement was attached. It could be ex- hausted by a water-pump to a pressure of 1 or 2 cms. of mercury. Air and emanation could be admitted through a capillary-tube and a bulb of phosphorus pentoxide. The natural leak of the electroscope was 3°9 divisions an hour, and this remained remarkably constant, provided the electro- scope was exhausted and refilled daily. The electroscope was not influenced by exterior electrification, nor by atmo- spheric conditions. Blank tests were made involving all the chemicals and all apparatus used in the experiments. No radioactive matter could be detected by these tests. The electroscope was standarized by inserting the air and emanation boiled from a flask containing 1:57 x 107° gram of radium, and the resulting effect was a movement of 10°3 scale-divisions per minute after 3 hours. The standard solution was that used by Rutherford and present in Rocks in the Neighbourhood of Montreal. 285 Boltwood in their determination of the amount of radium associated with uranium in radioactive minerals. It was prepared from some radium bromide which Rutherford and Barnes found gave per gram a heating effect of 110 gram- calories per hour. | The solutions prepared from the specimens of Montreal rocks were tested two or three times to insure accuracy. The results obtained were as follows :— Peri Rocks in order of age Grams of Radium eriod. . ’ of formation. per gram of rock. 1/2 Ordovician ...| Trenton limestone, Sedimentary. ‘92 x 10 14 crystalline * ...| Trent limestone, i 91 weathered. *Devonian? ...| Essexite. Igneous. "26 As Tinguaite. aes 4:3 e Tinguaite (different - 30 locality). a ...| Nepheline syenite. af 1-1 Quaternary ...| Boulder-Clay. Sedimentary. "80 ‘a ...| Leda-Clay. " or) - Saxicava-Sand. i = "16 * These igneous rocks ail cut the Upper Silurian, and are of late Palseozoic age, probably Devonian. ~The mean of these values is 1:1 x 10-!%, and as this result is of the same order as that obtained by Strutt (1:4 x 10-¥) we did not think it necessary to examine a larger number of specimens. It will be noted that in every case the substances examined contained much more radium than that required to account for the existing temperature gradient of the earth. It is difficult to understand how the earth can have remained at its present temperature when radium is so plentifully dis- tributed in the constituents of the earth’s mass. There appear to have been three explanations offered :— 1. Strutt has suggested that the interior of the earth is different in constitution to the earth’s..crust. The great density of the earth lends some weight to this suggestion. Moreover, Milne’ finds further support to this hypothesis in the rate of propagation of earthquake waves. 2. Ithas been conjectured that the disintegration of radium is retarded or stopped under the extreme pressure in the earth’s interior. If thatis so, the heating effect of the radium would also be diminished. This suggestion is capable of experimental test. In the meantime it may be remarked R 2 236 Mr. Eve and Dr. McIntosh on the Radium that the disintegration of radium is not affected by large changes of temperature, and it is difficult to conceive of the radium atom so closely surrounded by other atoms that the « particle would be prevented from escaping. 3. Joly has suggested that radium may reach the earth from external sources. At present there is little experi- mental evidence in favour of this view, and it 1s not easy to reconcile it with the fact that in radioactive minerals uranium and radium exist in constant proportions. : It must be remembered that in these investigations no allowance has been made for the heating effects due to radiothorium, uranium, and actinium. There is evidence that radiothorium must be distributed in the earth, both widely and in considerable quantity, for the active deposits of thorium have been found in the atmosphere in most places where an attempt to discover them has beern’made. This fact is the more remarkable because the thorium emanation decays so rapidly that only a minute proportion of it can escape from the soil into the air. - | As the work of obtaining rocks in a state of solution is somewhat lengthy, involving the expenditure of time and materials, some experiments were made in order to ascertain | if the emanation could be driven off by simple heating. Fifty grams of each specimen investigated were powdered and passed through an 80-mesh sieve. The powder was placed in a porcelain tube and heated for an hour in a com- bustion-furnace. The air driven off by expansion was collected over water, and at the end of the heating the air in the tube was blown out, and all the gases thus obtained were introduced into the electroscope and tested. The results were compared with those obtained when portions of the same specimens were in a state of solution, and the emanation driven off by boiling. The amounts found by heating ex-— pressed as percentages of the amounts found by boiling are as follows :— Urentoneliinvestoneqeannere: ia: 27 per cent. Anno Wee ee Beeb a: see Bed « oe AQ 5's WISSERIECH Ha HS He Sibel Giles 10 is Nepheline Syenite .........2..:.- ay) & lueda Cla yuens mee Mab sf ut tre pl. hase: AT im Saxicava Sand Fee oe Poa ar ee rom at It is, therefore, clear that the method does not give con- sistent or accurate results. But when a large number of present in Rocks in the Neighbourhood of Montreal. 237 rocks have to be examined, the extraction of the emanation by heating may serve as a valuable preliminary test, and furnish an indication of the amount of material which should be reduced to a state of solution, in order to obtain an accurate determination with the least expenditure of time and chemicals. Some tests were also made of the effect of adding a little sulphuric acid to the solution of Tinguaite. The radium was then probably precipitated, for the emanation was not freed by boiling. In one experiment the amount obtained was only one-fifth of that measured previous to the addition of the sulphuric acid. A special experiment was made with Tinguaite, which was finely powdered and the soluble portion was leached out with water. When tested, the insoluble gave about eight times as much emanation as the soluble. The addition of HCl made no change in the ratio nor in the total amount obtained. In the case of clay, Strutt found that the total emanaticn could not be stained until HCl was added. The ratio of the emanation derived from the acid and alkaline solutions, as found by Strutt for various substances, is about the same as that found by us in Tinguaite. In a previous paper published in this Magazine (Sept. 1906) an account was given of an attempt to measure the amount of radium in the earth from the penetrating radiation due to it. The result found was 10°5x10—-¥ gram of radium per gram of rock, and it depended upon Cooke’s value of the enetration radiation measured on the College campus at Montreal. The subsoil consists of Saxicava sand and Leda clay ; and it is clear that the value found by the penetrating radiation method, although of the right order, is too lar ge, unless there is a large quantity of radiothorium in the eround. Or a partial explanation may be found in the value of the coefficient of absorption of the y rays by rocks. Wigger has found that the value of \ for the most penetrating rays is considerably less than that assumed in the paper in uestion. We are indebted to Professor Rutherford for his interest and advice in this work, and to Professor Adams and Mr. Bancroft for their assistance in matters geological. McGill University, Montreal, May 1907, LAP 2BBF Gi XIX. A Short-Period Electrometer, and its use in Determining the Frequencies of Slow Electrical Oscillations. By Hi Taytor Jonns, D.Sc., Professor of Physics in the University College of North Wales, Bangor”. [Plate IX. ] N the “ Rapports présentés au Congrés International de Physique,” vol. ii. (1900), a description is given by Blondel of various methods which have been employ ed for the direct demonstration of varying currents and potential differences. Most of the instruments designed for this purpose (oscillographs, rheographs, &e.) depend upon electromagnetic action, a fine wire or strip carrying the current, a small bar or strip of soft iron, or a beam of cathode rays, being deflected by an electromagnetic force proportional to the current. The Braun tube may also be used as an electrostatic instru- ment, the beam of cathode rays passing between two plates connected to the source of varying H.M.F’. and being deflected by the electrostatic force between them, So far as I am aware, this is the only electrostatic method hitherto employed for rapidly varying electromotive forces, and it appears to be difficult by this method to obtain a ver y clearly defined wave-curve, while according to Zenneck + the Braun tube method has not hitherto been found to give very accurate quantitative results. For the study of slow high-potential electrical oscillations an electrostatic method would seem to require simpler apparatus than most of the electromagnetic methods, and to have the advantage that no additional self-inductance is introduced into the cireuit. The experiments described in this communication constitute an attempt in this direction. (1) Apparatus. A piece of phosphor-bronze strip, 8 (fig. 1), is soldered at one end to a terminal on an ebonite pillar, P, and at the other to a small spiral spring, L, attached to a screw. A second ebonite pillar supports the screw which can be drawn through by a nut, thus allowing the tension of the strip to be varied. ‘The strip. rests horizontally against two vertical glass rods, R, about 2 cm. apart. To the middle of the strip is attached a small mirror, M, of very thin silvered glass, rectangular or triangular in form, and one or two square * Communicated by the Author. . + Elektromagnetische Schwingungen u. arahtlose Telegraphie, p. 360 (1905). A Short-Period Electrometer. 239 millimetres in area. In front of the strip and connected to the terminal by a thin wire is a thin plate of copper (not shown in the figure) bent so that its edge faces the strip and is less than 1 millimetre from it. A gap in this plate allows Fis, 1 NAAAARAAAANS EES P, P, ebonite pillars; R, R, glass rods; 8, strip; M, mirror; L, spiral spring; K, ebonite sheath containing attracting plate; N, movable platform. a beam of light to pass to and from the mirror. Behind the strip is another thin plate of copper imbedded in a sheath of ebonite, K, and also with its edge facing the strip. The whole is mounted on an ebonite support, ‘and placed in an ebonite vessel’ provided with a small window and filled with a transparent, insulating oil of suitable viscosity and of fairly high dielectric strength. It is also advantageous that the oil should have a high specific inductive capacity *. A small platform, N, of ebonite tipped with cork can be raised by a screw until it comes into contact with the lower edge of the mirror. A horizontal adjustment of the platform then allows the mirror to be tilted so that the reflected ray can be made horizontal, or can be given any desired small elevation. The phosphor-bronze strip is thus between two plates to one of which it is connected. If the plates are charged to a difference of potential, the strip is repelled by one plate and attracted by the other. The mirror then, since one of its edges is fixed, is deflected through a small angle proportional to the square of the difference of potential of the plates, as in the idiostatic use of the quadrant electrometer. A beam of light, proceeding from a small circular aperture illumi- - nated | vy an are lamp and condenser, passes through a convex _ * The oil found most suitable was a mixture of about equal volumes of castor-oil and Singer’s machine-oil. _When freshly mixed it is slightly yellow, but the colour deepens after a few weeks, and the oil must then be replaced by a fresh mixture. 240 Prof. H. Taylor Jones on a lens and is reflected by the small mirror on to a rotating concave mirror, driven by a motor. It is finally focussed so that an image of the aperture is formed on a plate of ground glass or on a photographic plate. A tuning-fork carrying a small mirror is mounted vertically in front of and close to the window of the oil vessel. The plate BB is glued on to the ebonite ring EH, which is 1°3 ems. deep and whose outer and inner radii are 3°2 and 1°5 cms. respectively. A quartz plate fixed to the zine plate BB and a brass disk CC cemented to the opposite side of the ebonite ring, render the chamber air-tight. An ebonite plug fitted into a hole in this disk served to hold firmly a brass rod d to which the zinc plate AA was attached. | AA was connected to one set of quadrants of an electro- meter, BB to the positive pole of a battery of small lead cells, the other pole of which was earthed, while the brass disk CC was permanently earthed, and thus prevented any electricity creeping over the surface of the ebonite to the insulated system connected to the electrometer. Under the action of the light the plate AA gives off negatively charged electrons, ‘and acquires accordingly a positive charge. Owing to the collisions which take place between these electrons and the molecules of air in the detector, positively charged ions are generated which are attracted to the plate AA, and thus increase the actual effect due to the light. from a Zinc Plate by Ultra- Violet Light. 299 If the field of force is uniform, the number of ions which reach the positive plate is given by _ Ml e— Be? 5 at a— Belr—P4 ? vr where 1, is the number actually discharged from the plate, a, @ are constants depending on the electric force and the pressure, d is the distance between the plates. The resultant positive charge is shown by the motion of the electrometer-needle, but in practice it was found ex- pedient to use an induction-balance, owing to the large range of intensities used and to avoid the inherent defects of the ordinary method of electrometer deflexions. The method used is shown diagrammatically in fig. 2. Fig. 2. TO ELECTROMETER JOEARTH 70 EARTH CC is a parallel-plate condenser consisting of seven plates set up in a brass case which was permanently earthed. The plates c,¢,¢; were insulated from the other plates, and a short connector from each plate terminated in an insulated mercury cup placed outside the case. The four plates d were connected together and insulated from tbe case, while some of the plates ¢,¢:¢3 were always connected to the insulated quadrants of the electrometer, * Prof. J. S. Townsend, Phil. Mag. Noy. 1903. X 2 300 Mr. I. O. Griffith on the Electricity set free As the plate AA acquires a positive charge, the plates d are brought from zero to negative potentials so as to keep the electrometer-needle approximately at rest. At the end of the experiment the potential V of the plates d required to bring the needle exactly to zero is found. The quantity of electricity given out is measured by VC, where C is the capacity of the plates in use. The potential of the plates is adjusted by a potentiometer method. A set of 50 equal resistances of 20 ohms each were arranged in series, and by means of a sliding contact it was possible to connect the plates with any one of the junctions of the 20-ohm coils. The two terminals of the 1000-ohm resistance were joined to a battery of known E.M.F. H, the positive pole of which was connected to earth. The value of V can now be estimated accurately by ob- serving the small deflexions on opposite sides of the zero when the plates are in connexion with two consecutive junctions of the resistances. Quantities of electricity can thus be measured accurately over a large range, as C and H can be easily altered. Further, the electrometer is only used as a detector, so that its capacity need not be determined and all errors due to unequal values of the readings at different parts of the scale are eliminated. The electrometer used was of the Dolezalek pattern and gave a deflexion of about 3000 divisions for 1 volt. The source of ultra-violet light was a spark-gap in a circuit in which a leyden-jar discharge took place, the spark passing between aluminium terminals in air. The leyden-jar was charged from the secondary of a Ruhmkorff coil. All the apparatus in connexion with the spark was enclosed in a metal-lined box permanently earthed in order to prevent induction effects on the insulated conductors. With a proper adjustment of the current in the primary circuit of the induction-coil and a proper rounding of the terminals, the spark in air was found to be very constant. Methed of performing an Haperiment. Various intensities of light of known relative values can be obtained by varying the distance between the spark and the detector. If we assume the intensity of the light falling on the detector to vary inversely as the square of the distance from the spark-gap, it will be necessary to ensure that the same quantity of light is absorbed for the different distances. from a Zine Plate by Ultra-Violet Light. 301 A description of the procedure adopted in the case of two distances will show how this was secured. In fig. 3, S denotes the spark, D the detector, Q; Q, two quartz plates placed so as to allow the light to pass through Fie. 3. ~ “VACUUM Le 70 PUMP them normally. The spark was allowed to run for 10 seconds and the effect n, noted. DS was then increased from 7 to y+d, and a tube of length d was inserted between D and 8. This tube, when the quartz plates are fixed on to its ends, can be rapidly exhausted until the pressure of the residual air in it is less than 1 mm. The spark was again run for 10 seconds, and the effect nz, noted. The above process was repeated, n, and nm, being measured alternately and the mean of several readings taken as the final result. The value of r was never less than 10 ems., so that the maximum error in reading the distances could not exceed J per cent. By using tubes of different lengths a range of intensity of 1: 190 was obtained. In order to work with weaker intensity and avoid the inconvenience of very long distances, a quartz cell containing water was placed between the spark and the detector. Results. I denotes the intensity of the light in arbitrary units. q is a factor which gives the effect in amperes per square centimetre of surface. r is the distance between the spark and the detector in centimetres. 302 Mr. I. O. Griffith on the Electricity set free A.—Light obtained by sparking between aluminium terminals in air. g=—2x10-" ampere. Vin | if ie E=1. tom. |) 196 318 ¢ 2:52 576 863 IST 9 1:82 110-2 1 q 1:00 138 | 64 43q/.. ‘67 Several other experiments under similar conditions gave similar results. B.—In the following table the initial intensity of the light is reduced in the ratio 1 : 50 approximately by passing it through water, and it will be noticed that H/1 does not increase so rapidly with increasing intensity. The quality of the light is not the same in the two cases as the water has very marked selective absorption and cuts out certain kinds of rays more than others. q= s X1l0s) ampere: r. I. E, | B=E 10 126 Hog) | 28 110-2 1 Y 1-00 C.—The following table gives the results when the spark took place between iron terminals in an atmosphere of hydrogen. r i EK. K~+I 10 126 225 1:78 376 8:63 11°8 1:37 110-2 1 1 1:00 from a Zine Plate by Ultra-Violet Light. 303 The above experiments were all performed with a pressure of about 5 mm. of mercury in the detector. As this pressure could be easily reduced to about 1 mm, by means of the Fleuss pump which was used in the experiments, it was thought desirable to find what effect, if any, this change of pressure had on the results. D.—The relation between H and I for a pressure of 1 mm. is shown in the following table :— E. Idk | | 126 211 1°67 11032 ee 1 1-00 The variation in H/I is still very marked and for the same range of intensity almost equal to that in C. Too much stress, however, should not be laid on this coincidence inasmuch as the initial intensity of the light is not necessarily the same in both cases. All that can justly be deduced is that in all cases the ratio E/I increases with increase of intensity at a gradually increasing rate. Absorption Haperiments. As the apparatus employed in the preceding experiments was well adapted for investigating the absorption of the light by different gases, the following cases were considered, viz., the absorption due to air and hydrogen of the light produced by sparking between :— | (a) aluminium terminals in air ; | (>) iron terminals in hydrogen. _ The method of procedure with a given spark was as follows : One of the tubes of length d was introduced between the detector and the spark-gap and readings were taken : (1) when the tube was exhausted ; _ (2) when the tube was filled with air at atmospheric pressure. (3) when the tube was filled with hydrogen at the same pressure. If I, I, J; denote the successive Pade. the ee” due to a column of air of length d was assumed to be ee : TL 304 Mr. I. O. Griffith on the Electricity set free Spark between Aluminium terminals in Air. | iene Reading. Reading |Reading when) Fraction | Fraction of ig when tube is when air in) hydrogen | absorbed |absorbed by ores exhausted. tube. in tube. by air. | hydrogen. ; In cms, | 100 27-6 163 21-6 +409 217 O7 sen < || oh os2 31-4 221 138 16 47-1 Wohi 42°6 . UTS: 095 Spark between Iron terminals in Hydrogen. 100297 215 | 280 273 | 259 27 33°1 aire | 29:0 alt “124 16 12°] 10°1 11°4 “161 055 The results are ae diagrammatically in fig. 4. The curves show very clearly the effect of selective absorption. It is evident that a portion of the radiation is rapidly absorbed and a more penetrating part passes through. Fig. 4, Sparkin Air. (1) Absorption by air. (2} Absorption by hydrogen. Spark in Hydrogen. (3) Absorption by air. (4) Absorption by hydrogen. 0 Key Sf 2e/ 100 froma Zinc Plate by Ultra-Violet Light. 305 It should be stated that other investigators have as a result of their experiments asserted the constancy of the ratio i/I. Lenard (Ann. d. Phys. viii. 1902, p. 154) assumed that the light-intensity for normal incidence varied as the inverse square of the distance between the spark and the detector, but did not apparently make any correction for the absorption of the light by the intervening medium. As shown in the present paper ‘this for the larger distances will only reduce the intensity of the light in a certain fixed ratio, so that the following results extracted from Professor J.enard’s paper will still hold good :— r. i E. [pie i 20:6 23:6 231 977 46:3 4-64 369 7-94 86°5 1-44 106 7-42- t will be observed that for a change of 1 : 22 in the light- intensity the corresponding variation in E/I is approximately 25 per cent. If in spite of this E/lis assumed to be constant the degree of accuracy could not have been very high, and probably the matter was not investigated with a suitable apparatus. Ladenburg (Ann. d. Phys. 1903, p. 578) varies the angle of incidence of the light and assumes that the light-intensity is proportional to the cosine of this angle. W hen we consider that the effective portion of the light is that which is absorbed by the zine plate, and that this fraction varies with the angle of incidence, the above e assumption seems hardly justifiable. But even if this is permissible, it should be observed that the angle of incidence ranged in value from 0° to 80°, so that the range of intensity was from 1 to 5°8. From 0° to. 60° the intensity is only reduced by one-half, so that the greater part of the variation took place in a limited region of about 15°. It would be impossible, with our-present limited knowledge of the way in which the light acts on the molecules of the gas, to form a theory which would indicate the connexion between E and I. A little consideration, however, would show that there is no particular reason for supposing that the ratio between these two quantities is constant. Assuming that the ions are set free owing to the action of the electric force (F) in the.beam of light, the experiments 306 Mr. G. H. Martyn on the Discharge determine the number of ions (7) at the surface of the metal which are affected by the various forces, these forces being proportional to the square root of the intensity. The experiments show that for small intensities, n diminishes much more rapidly than F?, so that it may be that for very small forces n would be zero. In conclusion I wish to acknowledge my indebtedness to Professor Townsend, in whose laboratory the experiments were performed, for his kindly interest and valuable sug- gestions throughout the course of the investigation. XXV. The Discharge of Electricity from Hot Bodies. By G. H. Martyn, B.Se., Wheatstone Laboratory, King’s College, London ”™. [Plate X.] Re following paper contains an account of some expe- riments on the rate of loss of electricity from negatively charged hot platinum in air and in hydrogen at atmospheric pressure, and also on the effect on the rate of loss produced by coating the wire with calcium oxide. H. A. Wilson (Phil. Trans. A. vol. exevii. 1901) measured the leak from hot platinum in air at various temperatures, and showed that the energy required to produce an ion could be calculated from the rate of variation of the leak (a), due to a small difference of potential, with the absolute tempe- rature (8) by means of the formula where Q is the energy required to produce one gram-mole- cular weight of ions of either sign. O. W. Richardson showed (Phil. Trans. A. p. 343, 1903) that the negative leak from hot platinum in gas at low pressures could be represented by a formula of the type Q x= Are” 26, where «=the current per square centimetre, 9=the absolute temperature, and A is a constant. | H. A. Wilson found (Phil. Trans. A. p. 352, 1903) that the leak in hydrogen was enormously greater than in a vacuum. * Communicated by Prof. H. A. Wilson, F.R.S. of Electricity from Hot Bodies. 307 ‘A. Wehnelt (Ann. d. Physik, vol. xiv. p. 3, 1904, and Phil. Mag. vol. x. 1905) found that the negative leak from hot platinum was very much increased on coating the metal with a thin layer of calcium oxide or barium oxide *. In the following experiments an attempt was made to. determine whether these two effects were independent or not. _ The apparatus was arranged as follows :— _ A loop of pure platinum wire ‘1 mm. diameter and about 8 cms. long was sealed to platinum electrodes passing through glass tubes. These were fitted into a rubber stopper so that the platinum loop could be introduced into the middle of a wide glass tube. A brass tube to which a copper wire had been soldered was passed up from the lower end of the glass tube so as to surround the platinum loop, the copper wire being sufficiently rigid to hold it in position out of contact with the glass. This wire also passed through a narrow glass tube fitted into a rubber stopper which closed the end of the glass tube. OC Re c ——— 4a i cauecuae aeee FLATINUM WIRE. VAGUS: VOLTMETER. 70 BATTERY OF 500 CELLS ©) | GGiites GALVANOMETERS. C.CC,...:... KEVERSING COMMUTATORS: RRR 5 Ry Rs.AESIS TANCES. Ieee eee Ae Hydrogen or air could be passed into the tube through two delivery-tubes passing through the rubber stoppers. The stoppers and various tubes were sealed into position by means of sealing-wax which was found to keep the apparatus sufficiently air-tight. The platinum loop was heated by a current from a secondary battery which was measured by an ammeter, and could be * See also “On the Discharge of Negative Electricity from Hot. ee and from Lime,” by F. Horton, Roy.|Soc. Proc. p.. 528, if | 308 Mr. G. H. Martyn on the Discharge varied by means of a variable resistance in the circuit, and so the temperature of the loop altered as desired. A volt- meter was connected to the ends of the platinum loop, so that from its readings and the current the resistance of the platinum could be determined. The resistance of the loop was measured at 15° C©., at the melting-point of pure K,SO, (1066° C.) and just at its own melting-point (1710° C.), and from its resistance its tempe- rature on the platinum temperature-scale could be calculated. The temperatures on the platinum scale were reduced to the ordinary scale by means of the parabolic formula t -t ‘p= A(ioe3 —1) 068 where ¢=temperature on centigrade scale, pt=temperature on platinum scale. The constant A was obtained from the observed resistances RMS Orne JE? Op | The platinum loop and the brass cylinder were maintained at a difference of potential of 200 volts, and the current from the brass cylinder to the wire was measured with a galvanometer. The hydrogen was prepared from pure zine and hydro- chloric acid, and was dried by KOH and passed through the glass tube for a considerable time. The calcium oxide was deposited on the platinum by immersing it in a strong solution of calcium nitrate and heating. It was found that the leak was considerably increased when the platinum wire was in hydrogen, and also that a coat of lime increases the leak, the two effects being added when the lime-coated wire was heated in hydrogen. The following tables give the results obtained. V is the P.D. between the ends of the wire. A is the current through the wire in amperes. T” is the temperature of the platinum. . C is the corresponding current from the brass cylinder to the platinum wire. . 7 I. Platinum wire in Air. AW A. | ALS Gy | C (amperes). 3:2 42 1570 6x1078 | 3°35 4-3 1621 tt) Glo 3:5 4-37 1690 300k of Electricity from Hot Bodies. 309 IT. Platinum wire in Hydrogen. Vv ia ONC: C (amperes). 3:7 59 1190 6x 1073 3°85 6:0 1228 12 4:0 6°] 1267 16a, 4°31 6:2 1335 S2DeuE., 4°53 6:3 1346 4644 | 4°5 6:4 1400 PAT ATS) 46 6:5 1419 48,300 __,, 4:8 6°6 1472 154,500 ___,, 4:95 67 1493 240,000 __,, 52 6:9 1539 266,400 ., 5°35 70 1576 266,400 _,, III. Lime-coated Platinum wire in Air. Vv. A. ABO (6) C (amperes). 2-25 36 ee 9x 1078 2:4 3-7 1242 oe 2-5 3:8 1274 DO. 2:6 39 1317 360, 2:75 4-0 1404 Arie 2-95 41 1450 525, 3:1 4:3 1451 BSd 3:25 4:38 1512 540, IV. Lime-coated Platinum wire in Hydrogen. V. A. Mon@s C (amperes). 2-62 52 865 30x 107° 2°77 5:28 922 EO 2:9 54 953 730), ol 56 994. 4,035 __,, 3:3 5:7 1037 18,990 |. 3:4 5:8 1081 34,500 _,, 36 59 1148 60,390 __,, 3°8 6:0 1200 95,100 ,, 39 ea! 1220 103,800 ,, 4:0 6:2 1243 108,000, 4:2 6:3 1300 110,610 .,, 4:3 6:4 1317 108,000 4-4 65 1325 108,000 _,, 4-6 66 1382 108,900 __,, 5:2 70 1512 114,000 _,, Theabove results are shown graphically in diagram I. (PI. X.). The coordinates of the points are the reciprocals of the tempe- ratures and the logs of the corresponding currents. The 310 Mr. G. H. Martyn on the Discharge resulting curves are straight lines except at the highest tem- peratures in each case. It will be noticed that these lines are roughly parallel. The diagram shows that the effect of an atmosphere of hydrogen is identical with raising the temperature of the wire about 320° C.; the effect of coating it with lime is identical with raising the temperature about 340° C., and the effect of using a lime-coated wire in hydrogen is identical with raising the temperature about 670° C.; and thus that the effects produced by hydrogen and by coating the wire with lime are in this sense additive. | It will be observed that the lines obtained cease to be straight for higher temperatures, the negative leak seeming to reach a maximum value. It is to be noted that though the lime has almost exactly the same effect as the hydrogen on the temperature at which a certain small leak is produced, the maximum leak obtained with hydrogen is very much greater than that obtained with lime. i The occurrence of a maximum leak in this way is probably due to the ions at high temperatures becoming attached to minute particles of platinum or lime which are lost by the wire. The speed of these ions will thus be reduced, and the potential-ditference between the wire and the cylinder will become insufficient to saturate the current. If this is the explanation, it will be seen that the ions become so weighted much more easily when lime is frequent than in its absence. In order to test whether the current was no longer saturated at the temperature at which the curve obtained ceased to be straight, the apparatus was modified as follows. The platinum wire and the brass cylinder were connected to the two poles of a secondary battery so that any difference of potential could be introduced up to 1000 volts, this difference being measured by an electrostatic voltmeter. In order to measure the temperature of the platinum, this and a standard resistance formed the two arms of a Wheatstone bridge arrangement, the other two arms being formed by a resistance-box, so that the ratio of the platinum-wire resistance to that of the standard could be measured, and hence the platinum temperature calculated. The apparatus was con- nected as shown in the figure. The experiments were conducted as follows :—The platinum wire was heated until the ratio of its resistance to that of the standard was of some fixed value. The leak was then mea- sured with a certain P.D. The P.D. was then increased and the corresponding leak noted, care being taken that at the of Electricity from Hot Bodies. 311 moment of observation the resistance of the platinum wire, and so its temperature, had the required value. In this way the relation between the P.D. and the leak for this particular temperature was obtained. The platinum wire was then heated to another temperature and the experiment repeated. When the temperature was such that the current was pro- perly saturated, the curve showing the relation between the leak and P.D. was similar to that shown in diagram ILI. No. [X., in which the current becomes saturated at about 100 volts, and on increasing the P.D. ionization by collisions sets in between 200 and 300 volts. It was found that as the temperature rose the P.D. for saturation became nearer the P.D. at which ionization by collisions occurred, as shown in III., VIII., and at a slightly higher temperature no indication of saturation could be observed. In diagram II. will be seen the curves obtained for lime- o coated platinum in air. Each line shows the relation between the leak and the P.D. On plotting the logs of the leaks with the P.D. diagram III. was obtained. Very similar results are obtained from lime- coated platinum in hydrogen, as shown in diagram LV. From III. or IV. we can get the relation between tempe- rature and leak for different P.D.’s; and so we can plot the relation between the reciprocal of the temperature and the log of the leak, which according to the equation _2 v=Abie 9. should give nearly a straight line since the variation in @ is small. Diagram V. gives the result obtained for lime-coated platinum in hydrogen at potentials between 50 and 300 volts. It will be seen that the curves are precisely analogous to those originally obtained. We get a series of parallel lines for lower temperatures, and a maximum leak indicated at higher temperatures. With increasing P.D. this maximum oceurs at higher temperatures, indicating that it is due to non-saturation of the current. The curves obtained for greater P.D.’s than 300 volts are of little value, as ionization by collisions then affects the results. | If it is assumed that the leak in each case, if saturated, would at all temperatures obey the law of variation indicated by the straight parts of the curves in diagram I., then the 312 Prof. J. Larmor on the Range of leaks in each case at a particular temperature can be calculated. In this way the following numbers were obtained for the temperature 1600° C. Mealknmbarr 2.0720)... ee 5x10‘ ampere. Airowath limmets were ee 5 x LOgauaee elo ment 2. aa pere ee 10 es Hydrogen with lime... LOA hee Thus the leak with hydrogen, as with lime, is about 10° times greater than with air alone, while that with both hydrogen and lime is 10! times greater. These ratios do not vary much with the temperature. In conclusion I have to thank Prof. H. A. Wilson, at whose suggestion these experiments were undertaken, and who was ever ready with kind advice and assistance. XXVI. On the Range of Freedom of Electrons in Metals. By Prof. J. Larmor, #_R.S.* T has been ascertained that complete metallic conduction is established in a small fraction of the period of low ultra-red radiation. This is proved by the experimental result of Hagen and Rubens that radiation of about ten or more times the period of light is reflected from all metals in * Communicated by the Author. This brief discussion was drawn up in forgetfulness of Prof. Schuster’s estimate of the number of free electrons in metals (Phil. Mag. vii. 1904). His method was, I find, criticised and enlarged on in an interesting way later in the same year by Drude (Ann. der Phys. xiv. p. 936), with a view to greater precision ; but the widely uncertain assumption that the optical frictional term is represented for visible radiation by the full ohmic resistance seems to enter fundamentally. The values there obtained are about 10 times larger than the admittedly very rough estimate in the text. Later in the same paper (p. 956) Drude estimates the Jength of free path of the electrons, obtaining results ranging in order of magnitude from 10—® em. for the nobler metals to 10—8 cm. for bismuth; these were intended to replace estimates (of almost the same order for the nobler metals) deduced by J.J. Thomson and J. Patterson from magnetic influence on the resistance of thin sheets. The lower estimate, about 10—8 cm. for most metals, deduced in the text directly from the time necessary for establishment of complete conduction, is the main point of this paper; the result might possibly be stretched toward 10—%, but hardly further, if the velocities ot the free electrons are really determined by the gas-law. If velocities so small as these are retained, the negative conclusion that hardly any poitions of the paths by which the electrons travel are free, and that therefore estimates of number made in this way are uncertain, seems not unnatural. Freedom of Electrons in Metals. 313 proportions determined by their ohmic conductivities alone. For that type of radiation, the square of the guasi-index of refraction is therefore a pure imaginary quantity. The opposite extreme case, that of radiation of period rapid compared with the times of undisturbed motion of the elec- trons, is also of interest. It will appear that, if the effective electrons are free, the square of the guwasi-index must be wv real negative quantity. The optical determinations of Drude indicate that this is not very far from being true with light- waves for some of the nobler metals; in the case of w ‘hite metals such as silver, the property, moreover, persists over a considerable range of period, though at length it faiis. Thus, both on this ground and by reason of the shorter period, over a rather wide range of optical period the electrons are perhaps not far removed from being free. Moreover, theories of ordinary complete metallic condaction have been developed with some promise which ascribe it to electrons entirely free. When the electrons in the optical problem are supposed to be virtually free, then for each of them, of inertia m and charge e, under electric force (P, Q, R), WE (istin.e4) = ey. G), ta): thus if there are N’ of them per unit volume, and (w’, v’, w’) is the current of conduction, d ; on dt (w’, oS w’) = ee (). R), the sign of the charge e not entering if m is the same for all, Consider a plane-polarized wav elirein travelling along ¢, with electric vector (P) along « and magnetic vector (8) along y. Its equations of propagation are, by the circuital relations of Ampere and Faraday, fo) oP d Oe =—47u, ——-=—-— 9 0: aie dt where ae. A4gqusAdu’ +¢7? : dt the last term representing the guasi-current of zether strain, which will prove to be here neghgible. Thus ? Geet a EA = AT . ae 3 ye =4nN =a al dt?” which determines the mode of propagation. Phil. Mag. 8. 6. Vol. 14. No. 80. Aug. 1907. MG 314 Prof. J. Larmor on the Range of In a simple wave-train of period 27/p, \? zt ine CONG which yields on substitution bee giving for the square of the gwasi-index w (=c/c’) the value For radiation (D line) of wave-length 6.10-> em., 27/p is 20522. so that pee Nte 10-20(9.102)(4.1073) + 1 7 mM oe h FO =—N m8 10-*9 approximately. If the ions are all free electrons, ¢/m is 17.10%, thus v= = NN’, 2.105: For the nobler metals, in red and yellow light, the real (and five times preponderant for gold, silver, magnesium) part of yw? is of the order —10 ; this would give N'=4. 10” *, so that the number of free electrons taking part would be of somewhere about the same order as that of the molecules of the metal. A view of metallic electric conduction, which fits in with its parallelism to thermal conduction, is that it takes place by free electrons whose velocities are prescribed by collisions with the molecules, and so are taken as determined by the law of equality of mean energies in gas-theory. Tor hydrogen under standard conditions, the average velocity in the free path is 2.10’ em./sec.; as the electrons are a thousand times less massive, their average velocity would thus be about 6.10%. And we know that metallic conduction is fully established in a small fraction of the time 2.107 sec., which is the period of ultra-red radiation of ten times the wave- length of light. If then, as theories involving free electrons require, the establishment of conduction is intimately con- * Ifundamped resonance of adjacent free molecular periods contributes sensibly to the real part of —p?, otherwise than by shaking out more electrons into freedom, this would be an over-estimate. ~ Freedom of Electrons in Metals. 315 cerned with the duration of the free paths*, the mean free path of the electrons must not much exceed 10—8 em., so that their excursions must in fact be largely confined to the spaces between each molecule and the next. If their free paths were larger than this, complete conduction could not become established in so short a time. ! If a free path longer than this were demanded, then the optical incipient conduction would have to be ascribed mainly to the gradual deflexion of the path by the electric field with- out introducing limitation due to interruption of the path by eollision with the molecules ; and the theory of propagation which has been developed above would be the one applicable to ultra-red radiation. The results of Hagen and Rubens seem emphatically to preclude that type of hypothesis. If then metallic conduction is due to free electrons, their freedom is spacially very much restricted, almost in fact within molecular limits. While if it is inferred from the approximation of p? to a real negative value, that the tnc/pient conduction, which is the main agent in the optical phenomena of the nobler metals, must be largely due in the above manner to deflexion of paths of electrons, effectively free for times exceeding the period of the vibration, it would appear that the number of them that are concerned is roughly of about the same order as the number of the metallic molecules. The value of the mean velocity of the free electrons, above employed, about 6.10°, is involved in Drude’s form of the theory (Ann. der Phys. i. 1900, p. 577), in order to get the right (universal) ratio of electric to thermal conduction, on the assumption that both of them are effected through the agency of the free electrons. If, however, their velocity were of the order 3.10°, like the electrons from radio-active substances, then the free path might be as much as 5.10~—4 em. without vitiating the conditions laid down. The work of __ * Because the mean additional velocity imposed upon the electron by the electric field is proportional to the duration of the free path. This view of conduction, as stated by Drude, seems to require tacitly that the average velocity is in most instances restored by collision at the end of each free path. Moreover the conductivity varies as the tem- perature for pure metals: thus N x free path x velocity must be constant. These conditions are difficult to interpret, unless each molecule may be taken to emit electrons at a constant rate and absorb a definite proportion of those that encounter it, the same at all temperatures, thus establishing an equilibrium ir which N’ varies inversely as the velocity. Such increase of N’ at low temperatures would make p”, and also the absorbing power, for those shorter wave-leneths for which —p° is large, tend to vary inversely as the square root of the temperature. 316 Notices respecting New Books. O. W. Richardson, on the escape of ions from incandescent solids, which he finds to agree with the requirements of the gas-law, supports the former view, in fact seems to be its main experimental support ; he concludes, moreover, (Phil. Trans. 1906) that the number of free electrons in platinum ranges somewhere about 10’, which is not discordant, under the circumstances, witb the goneral estimate 4. 1072 mi ade above. The conclusion reached above, that in fact the free. electron is deviated or entangled by e each molecule which it meets or traverses, also points to the smal'er velocity, as the rapid electrons are known to pass straig 2 metal. But the free path now seems hardly long or definite enough to substantiate, except very roughiy, Drude’: formula for metallic condiction as effected entirely by the steady deflexion of the free paths by the electric field. It the rough generai estimates of order of magnitude, made above, for the number of free electrons and their velocities and free paths in the best conducting metals, are substituted in Drude’s formula (loc. cit.), they give ‘a conductivity of the order 12.10%, which is about one-fiftieth of that of silver, and errs on the wrong side, though hardiy so far as to cause surprise when the necessary vagueness of the data is kept in view. Cambridge, ae 16. oo Notices respecting Ne ew Boos Exercices et Projets d Llectrotechnique. Publiés sous la direction de Eric Grrarp et Omer De Basr, Tome Premier. Paris : Gauthier-Villars. 1907. Pp. 240. rHYHIS is the first instalment of a collection of problems primarily intended for the use of students attending the electrotechnical courses at the Montefiore Institute. It is devoted mainly to general magnetic and electrical theory, and deals with magnetic moments, intensity of magnetization, electrostatic theory, the laws of the electric current, electromagnetism, electromagnetic induction, and alternate current theory. his latter subject is treated very tully, and with special reference to its technical applications. The total number of problems is 104, and each problem is followed by a fully-worked solution. A book of this type should prove of ereat use to all students of electrotechnology, but especially so to those who are more or less thrown on their own resources, and can only occasionally take advantage of the guidance of a teacher. The solutions supplied should have an excellent effect in training students to those systematic methods of attacking problems which so many find it difficult to acquire. Altogether, the work is to be very highly commended, and should find a wide sphere of usefulness as a companion volume to Eric Gerard’s well-known Lecons sur U Electricite. oht-through thin sheets of ar <5 A ri rt i Awe . v 2 i he Taytor JONES. Oscillations of secondary of induction-coil. T =-‘o113 second. Oscillations started by sparking method, with the electrometer and fork spots. Phil. Mag. Ser. 6, Vol. 14, Pl. IX. IPG, ©: Three successive interruptions of the circuit of an electrical tuning-fork. IEG. We NAINA AIA ASA AV Oscillations of secondary of induction-coil produced by an alternating current of 35 amp. in primary. No condenser in secondary. Fie. 8. Oscillations of secondary circuit with condenser nearly in tune with alternator. Primary current = 1 ampere. LIME-COATED By acest 1,000,000 100,000 10,000 LOGARITHM OF LEAK. ° 100 i POTENTIAL Df LIME-¢ 0906 “0007+ “0008 “0009 -0010 “O01! 0012 PPEC/PROCALS OF TEMPERATURES CEN TIGRADE. Phil. Mag. Ser, 6, Vol. 14, Pl. X. Draanam I. Diagram LY, i Lurk-coitrp PLarrnum iN IlypRoGEN AT DIFFERENT TREMPRRATURES. C0 a ear [——~ L eet 1006 ——— tt =| I 100,000 es = 7 F wn & in Vv § eed Dracram III, | = + pace 10,000 ale a hos 4 i Lime-coarep PLAviINUM IN ATR AP DIFFERENT TEMPERATURES. Vv g 009 1000 é , na & wo sear iy 0010 1000 = Vt t Ry T (295°C * ai = 1 ; ea wl Ir (225° « © 1 CLeaw Prarinymin AR N 100 eet = | e227 & ieee . HYyOROCEA N / WV 10a? « t wT HE Lime con: WOM INH: 100 asl ° & Viena - HYOROGE, | S Rane © « | s VT 948° « ¢ }0 - >} Fie eg he 07 to-® {o-° 1o~4 10> N } rere LOGARITHM OF LEAK IN AMPERES ——+ < 8 Diaaram II, ~ ’ Lime-coatip PLATINUM IN Arr AY piIrrERENT Temperatures, 100 200 300 400 500 600 700 POTENTIAL DIFFERENCE IN VotTs Draaram V, Link-coarry Pravrovum in Ilyproamn, 1432°C Sf § § e S N S iS | g xs | S S «| | 50 100 150 200 250 300 350) ForentiaL DIFFERENCE Iw VoLTs | FECIPROCALS OF TEMPERATURES CEN igi anand ae do 8 oe ¢ oy im i i , a & ty j iBit dad dig /\ [4] CN a ate dl z ee Bia THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. oa [SIXTH SERIES.) SHPTEMBER YP90%. XXVIII. On the Motions of Ether produced by Collisions-of Atoms or Molecules containing or not containing Electrions. By Lord KEtvin*. Gul Y atom is meant an indivisible element of ponderable (cravitational) matter, or of electricity ; by mole- cule, an assemblage of two or more ponderable atoms, held together by mutual attractions balanced by mutual repulsions. § 2. In the atomic theory of electricity, electrion means an atom of resinous electricity, commonly hitherto called nega- tive electricity. It is at present commonly assumed, and I believe in all probability rightly assumed, that all electrions are equal and similar. § 3. An ancient hypothesis, which has had large considera- tion among philosophers in all times, assumes that there is only one kind of atom, and that groups of equal and similar atoms constitute the chemical elements, with all their marvellous variety of quality. But, though no doubt some important and interesting differences of quality, such as the difference between ordinary, and red, phosphorus, are due to differences of grouping in assemblages of one kind of atom, it seems extremely improbable that differences of grouping of atoms all equal and similar suffice to explain all the different chemical and other properties of the great number of sub- stances now commonly called chemical elements. It seems * Communicated by the Author, having been read before Section A of the British Association, August 1, 1907. Phil. Mag. 8. 6. Vol. 14. No. 81. Sept. 1907. Z 318 Lord Kelvin on the Motions of Ether indeed almost absolutely certain that there are many different kinds of atom, each eternally invariable in its own specific quality ; and that different substances, such as gold, silver, lead, iron, copper, oxygen, nitrogen, hydrogen, consist each of them of atoms of one invariable quality; and that every- one of them is incapable of being transmuted into any other. § 4. The sole properties of an atom are:—(1) its mass (being the measure of the inertia of its translatory motion), (2) its law of mutual force between itself and every other gravi- tational or electrical atom in the universe, varying according to the distance between them. As to the mutual force between ponderable atoms, we have strong reason to believe that this law is practically the Newtonian Law of universal gravitation, for all distances exceeding the millionth of a centimetre. For distances considerably less than the millionth of a centimetre, the Newtonian Law of attraction according to the inverse square of distance merges into repulsions resulting in mutual pressure of two bodies resisting joint occupation of space. For smaller distances, we have attraction again, in the inevitable theory of Boscovich, constituting cohesions and chemical affinities. . § 5. The assumption, that the mutual force between two - atoms depends merely on the distance between their centres, implies that each atom is utterly isotropic. An seolotropic atom, that is to say, an atom having different attractive and repulsive forces in different directions, is conceivable: and may possibly come in future to have a place in atomic theory. Hitherto it has been universally assumed that every atom, whether gravitational or electrical, is thoroughly isotropic, and I do not propose at present to enter upon any theoretical consideration of zeolotropic atoms. § 6. 1 do not propose to enter on any atomic theory of ether. It seems to me indeed most probable that in reality ether is structureless; which means that every portion of ethsr however small has the same elastic properties as any portion however great. There is no difficulty in this concep- tion of an utterly homogeneous elastic solid, occupying the whole of space from infinity to infinity in every direction. We sometimes hear the “luminiferous ether” spoken of as a fluid. More than thirty years ago I abandoned, for reasons which seem to me thoroughly cogent, the idea that ether is a fluid presenting appearances of elasticity due to motion, as in collisions between Helmholtz vortex rings. Abandoning this idea, we are driven to the conclusion that ether is an elastic solid, capable of equi-voluminal waves in which the motive force is elastic resistance against change of shape. produced by Collisions of Atoms or Molecules. 319 _ § 7. We now meet the question :—Is ether incompressible ? We should be compelled to answer— Yes, it is incompressible, if it is subject to the law of universal gravitation. But, presently, when we ‘try to account for motion produced in ether, by ponderable or electrical atoms moving through it, we shall feel ourselves persuaded that. ether is compressible”. Believing this, we are forced to believe that it is non- gravitational. Thus we find ourselves settled in the con- viction that ether is compressible, and that ether experiences no gravitational forces between its parts. § 8. Suppose now that an atom, whether ponderable or electrical, disturbs ether solely by attracting it or repelling it with a force varying according to distance; and that, with no other mutual influence than this, the atom and the ether jointly occupy the same space. If ether were incompressible, this attraction or repulsion would be utterly ineffective. The atom would move through the space occupied by the ether, without giving any motion to the ether, and without itself experiencing any influence of force due to the ether. Hence, in order that atoms may take energy from motions of ether, and that ether may take energy from motions of matter, we must suppose the ether to be compressible and dilatable ; and to be compressed, or to be dilated, or compressed at some distances, and dilated at other distances, in virtue of the force exerted on it by the atom. § 9. While assuming ether to be compressible, we suppose its resistance to compression (positive or negative) to be so very great that the velocity of condensational-rarefactional waves in pure ether is practically infinite, and that the energy of whatever of such waves may be produced by collisions of atoms or electrions is practically nzl in comparison with the energy of the equi-voluminal waves, constituting radiant heat and light, which are actually produced by these collisions. It is only under the enormous forces of attraction or repulsion exerted by atoms on ether that augmentation or diminution of its density is practically influential. § 10. By purely dynamical reasoning, it may be proved to follow from the hypotheses of §§ 4, 6, 8, and 9, that an atom, (supposed for a moment to be infinitely small,) kept moving _ through ether at any velocity, g, greater than v, the velocity of light, produces no disturbance in the ether in front of a cone having its vertex at the atom and semi-vertical angle equal to smoot but that the moving atom produces, in its * ‘ Baltimore Lectures,’ Appendix A; Appendix B, § 3. t ‘Baltimore Lectures, Appendix B, §§ 6, 7. ZL 2 hel 320 Lord Kelvin on the Motions of Ether rear, wholly within the. cone, an ever growing disturbance of ether, and therefore requires the application of a continual pull forward to keep it moving uniformly at any constant velocity exceeding the velocity of light. In 1888, Oliver Heaviside* arrived at a correspondin ¢ conclusion by purely mathematical work, from Maxwell’s electromagnetic tormulas, without any dynamical foundation : and in 1897 tT, still without assuming any dynamical or chemical properties of ether and atoms, he corrected an erroneous hypothesis, that no force however great could give an atom a velocity equal to the velocity of light, which has been somewhat extensively adopted within the last ten years in speculations and reckonings regarding radioactivity. § 11. Purely dynamical reasoning { on our physical assumptions of $$ 4, 6, 8, and 9, teaches us further that :-— (a) No force is required to keep an atom moving uniformly through ether, at any velocity ie than the velocity of light. (b) “To start an atom suddenly into motion from rest, causes a spherical pulse to travel outwards with the velocity of light, from the place in which the atom was when it was receiving the supposed velocity. (c) The magnitude of this spherical pulse is a maximum in the plane through the centre perpendicular to the line of motion, and is zero at the two points in which the spherical surface is cut by that line§. (d) This spherical pulse carries outwards through infinite space a finite quantity of energy, /, due to a part of the work, w, done by the force which was applied to the atom to start it in motion. The sharper the suddenness of the stopping, the greater is . (e) If at any time a resisting force suddenly stops the atom, work is done on the ether, in virtue of which another pulse carries away an amount of ener gy, /’; and work is done on the stopping agent amounting to w—/—I’. (7) If the suddenness of the stopping is equal and similar to the suddenness of the starting, the second pulse is equal and similar to the first, and /’ is equal to J. § 12. To understand clearly the meaning of (e), take an example. Let three equal and similar ideal non-electric atoms, A, B, C, be given in a straight line; B at rest, A moving with velocity g towards B, and C moving towards B in the contrary direction with a velocity just great enough that B is * Heaviside’s ‘ Electrical Papers,’ vol. ii. pp. 494,516. + Heaviside’s ‘ Electromagnetic Theory,’ vol. 11., Appendix G. t ‘Baltimore Lectures,’ Appendix B, §§ 4.. .7, § ‘Baltimore Lectures,’ Lec. viir., p. 88; Lec. x1v., p. 197. produced by Collisions of Atoms or Molecules. 321 left ‘at rest after its collision with C. The initial distances must be such that the collision between A and B precedes the collision between Band C. Amounts of energy equal to /and l’ are carried away into infinite space in the pulses produced by the two collisions. In the arrangement now described, the suddennesses of the starting and stopping of B are not pre- cisely equal and similar ; and, because of their difference, I’ might generally be somewhat less than /; but the law of force between the atoms might be such as to render /’ equal to, or greater than, /, for certain ranges of values of gq. | _ Take an analogous case of collisions between three ideal billiard balls, each perfectly elastic. The clicks of A on B, and of B on C, cause losses of energy, / and U', to be carried off through air by sound-waves. - § 13. Consider now the collisions in a_ non-electrified monatomic gas, that is to say, an assemblage of single atoms, each having within it its neutralizing quantum of electrions; except a small proportion, from or to which electrions may have been temporarily taken or given. Tor simplicity we shall first take the case in which a single electrion is the electric. neutralizing quantum for each ponderable atom. The collisions will keep the electrions continually in a state of vibration within the atoms ; except, in the comparatively rare case of an elec- trion being knocked out of an atom, or in the infinitely rare case of the relative motion of an atom and electrion being reduced exactly to zero, by a collision. § 14. The law of force between the electrion and atom may be such that the centre of the atom is the only position of stable equilibrium for an electrion within it. | § 15. Or the law of force may be such that there are any number, 2, of concentric spherical surfaces within the atom, on each of which an electrion may rest in equilibrium radially stable; and others, on each of which an electrion would be in equilibrium radially unstable *. In the statistical average of collisions, the electrion may, immediately after a particular collision, be ranging, in non-sinusoidal vibration, across several spherical surfaces of stable and unstable equilibrium, and losing energy by sending out irregularly reciprocating waves through ether. Before the next collision, the electrion may probably have settled down into very approximately sinusoidal vibrations in and out across any one of the surfaces of radial stability. ! § 16. This last condition we may suppose to. be generally prevalent during the greater part of the free path between # “Plan of an Atom to be capable of storing an Electrion with Enor- mous Energy for Radio-activity,” by Lord Kelvin, Phil. Mag. Dec: 1905. 322 Lord Kelvin on the Motions of Ether successive collisions. We may indeed suppose it to be more frequently the immediate result of a collision than the wilder vibration described in § 15, which, however, must undoubtedly be an occasional, though probably a rare, condition immediately after a collision. § 17. We are not bound to assume thata single electrion is the saturating quantum of any particular ponderable atom : nor are we bound to suppose that it is electrically neutralized by any integral number of electrions* The most general supposition we can make is that, with 7 electrions to each atom, the atom and electrions act externally as a vitreously electrified body, and, with 7+1 electrions, the atom and electrions act as a resinously electrified body. § 18. It seems to me indeed exceedingly probable that the persistence of the two-atom molecule in the common diatomic gases, Oo, No, He, Cly, is due to the impossibility of electrically neutralizing the ponderable atom by any integral number of electrions. Suppose for example that one electrion suffices to electrically neutralize two atoms of Nitrogen. A monatomic Nitrogen gas (N), if non-electrified as a whole, would have half of its atoms without electrions, and therefore vitreously electric, with electric quantity equal and opposite to half that of a single electrion. Hach of the other half of its whole number of atoms would have one electrion within it, and therefore its external action would be resinous, with half the potency of a single electrion. Thus there would be a strong electric attraction between the atoms destitute of electrions and the atoms each containing one electrion, within it. This attraction would tend to bring the atoms together in pairs, No, each pair containing one electrion, of which one position of equilibrium would be at the middle of the line joining the centres of the two ponderable atoms. In seems quite probable that this is the real condition of ponderable atoms and elec-. trions, in the ordinary diatomic gases. § 19. The dissociation of a considerable number of such pairs of atoms would be exactly the “ionization” by which, following Schuster’s and J. J. Thomson’s theory of the conduction of electricity through gases, the latest developed theories of radio- activity explain the specially induced electric conductivity of diatomic gases, such as Lenard found to be produced in air by ultra-violet light traversing it, and Becquerel found in air all round an apparently inert piece of metallic Uranium, or a Uranium salt. | § 20. But, to give electric conductivity toa monatomic gas, * “ Aepinus Atomized,” §§ 5,6; Baltimore Lectures, Appendix E. produced by Collisions of Atoms ori Molecules. 323: the “ionization ” could not be anything else than dissociation of electrions from ponderable atoms. This kind of disso- ciation might be produced in a very hot gas by mere impacts between the atoms of the gas itself, withthe large translational velocities to which high temperatures are due. Or it might be produced by extraneous bodies, such as the “a” or “@” particles shot out with high velocities from radioactive substances. We are now however chiefly concerned with the motions of ether produced by collisions of atoms, in circumstances less abnormal than those in which dissociations and recombinations are largely influential. § 21. The pulses described in §§ 11, 12, as due merely to mutual collisions between ponderable atoms (without con- sideration of electrions whether present or not), constitute a kind of motion in the ether, which, if intense enough to pro- duce visible light, would, when analysed by the spectroscope, show a continuous spectrum without the bright lines, which, when seen, prove the existence of long-continued trains of sinusoidal vibrations of particles of ether, in the eye perceiving them, and therefore also in the source, and in all the ether between the source and the eye. On the other hand, the vibrations of electrions referred to in § 13 would, if intense enough, produce bright lines in the spectrum. § 22. There is another kind of vibration in the source, which might produce, and which probably does produce, bright lines in the spectrum. If there are two or more ponderable atoms in the molecule of a glowing gas, not dissociated by the violence of the collisions, each atom of the molecule must have a vibratory motion, of which an isolated ponderable atom is incapable ; and these vibratory motions of the atoms of a group must give rise to bright lines in the spectrum, when the. frequency of the vibrations in any one, or in all, of the vibrating modes, is between four hundred million million and eight hundred million million per second, if we take this as the range of frequencies for visible light. § 23. The spectroscopic phenomena to be accounted for in a dynamical theory of light include continuous spectrums, with large numbers of bright lines superimposed on the more or less bright background of continuous spectrum. Even when every care has been taken, in artificial sources of light, to eliminate influence of more than one of the substances com- monly called chemical elements, the number of bright lines is generally very large: indeed we are not sure that we have’ been able to count the whole number of those which are presumably due to any single element. oa ay § 24. In a glowing monatomic gas, with just one electrion 324 : Mr. Gervaise Le Bas on to each atom, and only the central position of stable equilibrium for the electrion in the atom, there could be only one bright line in the spectrum. But in reality, every one of the known monatomic gases, Mereury vapour, Argon, Helium, Neon, Krypton, Xenon, gives a highly complicated spectrum with a large number of bright lines. We infer; that, if there is just one electrion to each atom, it has many positions of stable equilibrium ; or that there are many electrions, with only the central position of equilibrium for one of them alone; or that there are several electrions, and several. stable positions for one of them alone in the atom. '§ 25. It seems as if only on the third supposition—several electrions and several positions of stable equilibrium—we can imagine the great number of bright lines, and the great complexity of their arrangement in the spectrums of the monatomic gases. . § 26. But we can feel little satisfaction in this, or any other, attempt to discover details of dynamical theory, unless it gives some reasonably acceptable explanation of the laws of arrangement of trains of bright lines in the spectrums of different chemical elements, which have been experimentally discovered by Runge, Kayser, Rydberg, Schuster, and others. XXIX. The Unit-Stere Theory: The Demonstration of a Natural Relation between the Volumes of the Atoms in Compounds under Corresponding Conditions and that of Combined Hydrogen. By GERvVAISE LE Bas, B.Sc.* I. THE RELATIVE VOLUMES OF CARBON AND HYDROGEN IN THE Liquip Normat Pararrins C,H,,,, UNDER CoRRE- SPONDING CONDITIONS. e fie author has shown (Trans. Chem. Soc. 1907, xci. p- 112) that, in the liquid normal hydrocarbons from undecane C,H, to pentatriacontane C3;H7. at the melting- point, carbon has a volume almost exactly four times that of combined hydrogen. ‘This ratio is similar to the one existing between the fundamental valency numbers of the above atoms.. It thus follows that the molecular volumes of the paraffins in question are, at the melting-point, proportional to their respective valency numbers. These facts are regarded as evidence in favour of the view that valency is a volume property. i * Communicated by Prof. W. J. Pope, F.R.S. the Unit-Stere Theory. 32), Valency has also been shown (Le Bas, Proc. Chem. Soe. xxiii. p. 134) to be an energy property by means of the molecular heats of combustion of the normal paraffins. (See also Chem. News, xlv. p. 247, xevi. p. 58.) These results are intrinsically interesting, and, if accepted, would no doubt be of the highest importance. The writer proposes, in this and succeeding papers, to subject the molecular volumes of the members of a number of organic series under corresponding conditions to a critical examination, in order to show the generality of the above relation. _ The idea that the volumes of the atoms in compounds are. simply related is not new, for it was considered by Schréder so far back as 1877 (Ber. x. pp. 848, 1871 & foll.). Traube has shown, from a consideration of molecular solution volumes, that there is a connexion between volume and valency (Ber. 1894, xxvii. pp. 3171-3179). Following the suggestion of Barlow and Pope, the above author has recently demonstrated the fact that the molecular — refractions of compounds belonging to many series are pro- portional to the atomic refraction of combined hydrogen ° (Ber. 1907, xl. (1) pp. 130-139). Traube has also applied the above principle to his theory of molecular volumes (Ber. 1907, xl.. (3) pp. .723-733, 734-736 & foll.; Annalen, 1907, . XX1l. pp. 518-542). es Recently Barlow and Pope have developed the view that . crystalline form and molecular structure can be correlated (Trans. Chem. Soc. 1906, Ixxxix. p. 1675). Their theory is based upon two fundamental concepts : (1) That the volumes of crystalline solids are simple additive - functions of the- fundamental valencies of the compounds. - ~ (2) That these solids may be supposed to consist of structural . units in tactile arrangement and built up from the spheres of influence of their component atoms. a In 1905 the author developed the present theory, sub- stantially as it is now being presented, but was prevented by circumstances from publishing it at that time. The molecular volumes of many compounds were shown to be integral multiples of that of combined hydrogen when examined under corresponding conditions, so that thereisa - — proportionality between volume and valency. Views regarding the compact structure of liquids and solids similar to those of Barlow and Pope were at that time entertained. At the present time it is proposed simply to investigate the valency relation, and to show that the laws of correspondence and additivity are very closely connected. 326 Mr. Gervaise Le Bas on The Volume Relations of Combined Carbon and Hydrogen at the Melting-point. Some very interesting relations have been met with among the volumes of solid compounds, leading to the conclusion that the valency law and the law of corresponding states are. valid for the solid state; but, until the latter shall have been definitely proved, it seems wiser to limit investigation for the present to the liquid volumes of compounds, the constitutions of which are known, and to commence with substances which are not believed to be associated in the liquid state. The author has previously dealt with (Joc. cit.) the mole- cular volumes of eighteen liquid normal hydrocarbons at the melting-point, the determinations of which have been made by Krafit (Ber. 1882, xv. p. 1716). TasLe I.—The Saturated Normal Hydrocarbons C,H nm 2n+2° No Hydrocarbon. | W. eat A for CH,. — | V/W. bier es 1, | Undecane, C,,H,...|, 68) 201-4 | ae 0527/2962 201-96 2. | Dodecane, Ci,Hecs | T4|\249:9 sha 0°526 | 2°971 | 219°78 3.| Tridecane, ©,,H,3...) 80) 237°3 | Fe |0°524 |2:966 | 237-60 4,| Tetradecane, C,,H, 9...) 86 | 255°4 | ie 0°520 | 2:970 255°42 5, | Pentadecane, CORE eel Bra eiatAs | a 0:520 ee 273°24 6. | Hexadecane, Cy, He yae) Cozole2) We 0519 | 2971 291°06 7.| Heptadecane, C1735... 104 | 309-0 | 17-9 0:513 (2971 308-88 8. Octadecane, Ci,He | LOrSs26:9 | 173 0-512 (2972 326°70 9.| Nonadecane, C,,H,4,...| 116 | 344-7 | eee a 0:506 | 2971 344°52 10. | Hicosane, » OFA a Uawee | 2 | 362°5 17-8 | losis +) HCHOmES 36234 11. | Heneicosane, ©, Hy. s:| 128) 6803 Pedr ti facts! | 2-971 380716. 12.| Docosane, C,,H,,...| 134 | 398°3 | ing | = 2972] 39800 13. | Tricosane, C,H ys...| 140 | 4162 17-9 incronsa zi). | 415°8 14. | Tetracosane, C,H 9..-| 146 | 434-1 avira tie ad 2°973 | 433-62 15. | Heptacosane, Coie ya. | Woe | 4e0 4 lasci-y6 J abe | 2972 487-08 16.| Hentriacontane, C,,H,,...| 188 | 558°4 178 ee | 2970 558°36 Le | Dotriacontane, C,,H,,...|194' 5762 84178 be.) pare 57618 18. | Pentatriacontane, C,,H,,...| 212 629°5 2°969 629°64 Mean values’ .......2:.+..+. 1 ate Rett wes IG. The volumes of the above hydrocarbons are seen to be proportional to the volume of combined hydrogen which, = 2°97(); that of carbon = 4x 2:°970=11°88. The volume the Unit-Stere Theory. 327 of CH, is thus calculated to be =11°88+5°94=17°82, while that observed is 17°83 on the average. It is however possible, by an independent method, to verify the above numbers for carbon and hydrogen. The volume of hydrogen may conveniently be called the unit stere, and be represented by the symbol 8, thus :— 28 = @V. of Cis lHss + ¥; of Ci6H3,) —YV. of C3, Hes = 6. S == 3u The average volume of hydrogen obtained in this way confirms that previously found. That of carbon is also determined directly as follows :— V. ot ©=17-83 —9°94=11°89=4 x 2:972=48. A similar method based upon the constancy of the volume of CH, gives very good results :— ; 28= Vol. of C,H,,,,.—n Vols. of CH, ; = Vol. of C,gH3g—18 x 17°88 ; = 326°9—320°94=5°96. p= 98: The conclusion is thus drawn, that the molecular volume V of anormal paraffin of the molecular composition C,H,, ,., in the liquid state, at the melting-point, is given by the formula v= (6n+2)8 == VS. W representing the valency number and 8 the volume of hydrogen. S=2-970 at the melting-point. - The above computation, which verifies the relation C=45S, necessarily excludes the following :—C = 2H (Kopp), and C = H (Schroder). Kopp’s constant for hydrogen at this point would be 4:398 and that for carbon 8°796; so that Vol. of CH,=17°59. Schroéder’s constant = 5°987 for carbon and hydrogen, and his calculated volume of CH = 5.x 9,981 = 17-96. Oa so far as the differences are concerned, it is found that : time observed -volume of CH,: . : -...... 17°83; theorciica! C=4H (Le Bas)... ...) . 17°82; #3 Cee re oppy eo ho. ap . QLiCOO: me OS He(Schroder) . . 5. 1¢-9Ge In order to further show that the 4:1 rule is alone capable of explaining the facts, the following method, which involves no preliminary assumptions, is followed :— ‘The volumes are taken just as they stand, and are compared with, say, that of tetradecane. The ratios are then examined in the light of the 4:1 rule and of the relations advocated by Kopp and Schroder respectively. A Mr. Gervaise Le Bas. on 328 LG10-0- 6680-0- L860-0- 2160:0— $CG0-0— 6L10-:0- 0910 0- OFLO-0— L110-:0- ZO10-0— 1800-0— €100-0- £900-0— 1700:0- c100-0— 1Z00-:0+ GZ00-0+ Vv eoofee SIPEG GLGG-G 1691-4 0988-1 8189-1 9g19-1 OSPe-T GLLF-1 160F-1 60PE-T LGLG-1 CFOG-T I9GT-T 6890-1 0000-T 81€6-0 898.0 ‘H=0 ‘Tepoayog Suess mats ting Se SIOLL9 Uva, TG9F-3 | L69r-3 | ¢-629 gees | 0996-3 | .9LG 1981-3 | 98-6 | F896 0106-1 | 7806-1 | -L8F 1169-1 | 2669-1 LPP 6129-1 | 9629-1 | &-9IF 1gc¢-1 | 9699-1 | -¢:868 OSsF-1 | O68F-1 | $088 QgtF-T | €61F-T G.Z0E GOPS-L | 96PES-T LFPE 164-1 | 0084-1 | 6-968 e60GT | G660GL | 0-608 G6EI-1 | ZOPT-1 G-166 8690-1 | 2690-1 | &82z 0000-T | 0000-1 | ¥¢ez 086-0 | 1666.0. | $182 4098-0 | 01980 | 6-6IG any = Kn ys : Page Pe aan wee ete e eer oeeee ee ree eee ete rene seninee 9000.0 — EOtF-G F000-07 PIPG-G 2000.0 — 6GL1-G §000-0 — 0G68.-T FL00:0— 1689-1 0cz00-0—- L0G9-1 L100-0—- LIGG.T ¢100:0—- Sc8F-1 OL00-:0— SSIP-1 1000-0 —- SPrs: 1 §000:0+- 6EL16-T 6000-0 — 6906-1 9000-0 — GLET-T 4000-0 — 6890-T 1000-0 + 0000-1 i ee O1&6-0 1100-0+ 0698-0 €000-0 — ‘HZ=0 | : Hae Vv 5 lel ©) OI}eYy Ol} JO UOIVoTsoAUT—'T] AAV], Shrr*’C ‘UBIMOOVIA} EUS | FT — ‘OuURJTODVTAVO(L tes ‘QueyuMoOdVIAjU PT rao) ‘guvsooeydopy Cee) ‘QUBSOORIIOT, Sako ‘QUBSOOLAT, ea ESTO) ‘guvsoo0q TieeTLSG ‘guesOdIoUd PT Sra 4G) ‘guesOoIn ura PNG) ‘QUBOOPLUO NT Sars ENG) ‘QUBIOPLIO Beet) ‘gueoepeydoxy Te ‘QUBDOPLXOTT Cor ‘quRdepeyued mera vNG) ‘uRdEpLA9 T, Mera Elio) ‘QUBOOPLLT, STAONG) ‘queda pod ‘ucqrvo0IpATT the Unit-Stere Theory. 329 The above table shows conclusively that the molecular volumes of the above compounds are additive, and .the only satisfactory additive relation is that of valency. Having established additive relations at the melting-point it is now necessary to discover what are the conditions for the existence of similar ones above the melting- -point. This is possible, for Krafft has given the specific gravities of a large number of compounds for several temperatures up to about 99° (Ber. 1882, xv. p. 1687). Krafft’s determinations are suitable for the purposes of this investigation for the following reasons :— (1) Owing to the purity of the compounds, that is, because of their freedom from admixtures of other normal members of the series and of related isomers. (2) On account of the undoubted accuracy of the experi- mental results. It will be found that interpolation formule with two constants are, under the conditions, quite satisfactory. The general formula is as follows :— d,, = d,,{1—at + BP}, in which d,, and d,, represent the specific gravities at the temperatures T and T’, the latter sienityine the melting- point, <=T—T’, and a and 6 are temperature coefficients. able of Constants. No.| Hydrocarbon. IAW aD Aya | exces chee oe B. |;-——- 1.|Dodecane, ©,,H,,...| 170 | 74) 261 |-7730 |—-0008668 | —-00000058 . Tridecane, C,,H,, ...) 184 | 80) 2668 -7755 |—-000902 |—-00000013 Tetradecane, O,,H,,.../ 198 | 86) 277-5 -7753 |—-000897 —-000000106 Pentadecane, C,,H,, .../ 212 | 92| 283 | -7758 |—-000889 —-000000106 |: Hexadecane, O,,H,,...| 226 | 98) 291 |-7754 |—-000864 |—-00000028 Heptadecane, O,,H,, ... 240 | 104, 295°5|-7766 |—-000895 |-+-60000027 st ast Ges eee Octadecane, ©,,H,, ...) 256 )110/ 301. |-7768 |—-000896 + 0000005 ee In column 4 (Table LV.) the ratio V/W has’ the same sl@ni- fication as before. In column 5 fhe ratios “* are calculated oe by means of the expression 1-at+ i. A comparison —— Mr. Gervaise Le Bas on 330 is also made between the calculated and observed specific gravities, TasBie LV. (1) Dodecane, CigH. M.W.170. W. 74. MP, —12%, d,, = °773{1—-0008668 ¢ —-00000058 #7}. d (calculated). Sp. g. (observed). 7730 d_y9 AGOUCaUOON yh oncdddc A Bei "7649 ‘7655 dene. ‘7546 7548 Nae elas ‘7511 7511 ay ee ye 6931 6930 T, d. M.V | V/W. | dp[Ayt | | Ea DG lealide: ‘7730 21993 | 2970 — 1:0000 Salen. ‘7663 991-84 | 2997 | 09913 LSI a "7594 993-86 | 3025 0-9824 20 aes 7525 22591 3053 | 0:9735 BOLS ches: "7456 29804 | 3081 | 0:9644 Bile oe 7384 23023 | S111 | 0:9552 Solan ae "7312 939-49 3141 | 09459 sant yeh 7241 93477 | 3172 | 0-9368 Al aie 7166 23722 | 3206 | 0-9270 Bh a: ‘7090 23980 | 3240 | 09172 (2) Tridecane, C;;3Hy.. M.W.184. W. 80. M.P>6:2. d, = °1755{1—°000902 ¢ —-00000013 #3}. Sp. g. (calculated). Sp. g. (observed). "7755 1 a re ee ee Gc: tem ‘7711 ‘7713 Eee Melee 7606 ‘7608 = ¢ RES LAS, 7571 “1571 ee hae, 7010 7008 T. d. M.V | v/W | dnfden 266'8 T7155 237-3 2-970 1-0900 276'8 7685 239-41 2993 | 0-9909 286'8 7614 241-66 | 3020 | 0-9819 296'8 7544 24390 | 3049 | 0-9728 306-8 7473 246-22 | 3-078 09637 3168 7403 24855 | 3107 | 0-9546 326-8 7381 25099 | 3187 | 0:9453 336'8 "7260 953-44 | 3168 | 0-9362 346'8 ‘7188 25600 | 3200 -| 0-9270 356'8 "7117 95853 | 3232 | 09177 the Unit-Stere T heory. 331 (3) Tetradecane, Cy F30- M.W. 198. W. 86. M.P. 4°53. | d,, = '7753{1—+000897 t —:000000106 #}. Sp. g. (calculated). Sp. g. (observed). Pere hie ol vi Cain. 7753 LE AN ‘TT15 ‘TT15 soe Wares 7680 ‘7681 ene "7645 7645 EN amet "7088 "7087 a, d. M.V. V/W. d/dyi. Pa T7153 255°38 2:970 1:0000 287°5 . "7684 207-71 2997 0:9910 2903: i ‘7613 260:03 3023 0°9820 307°5 .. "7543 262°45 3051 0:9730 317-5 “7473 264-96 3081 09639 327°5 “7404. 267°42 3°109 0:9550 337°5 "73395 270'01 3139 0:9458 347°5 "7262 272°64 3170 0:9367 357'5 “ON 275°34 3201 0:9275 367°5 ‘7120 278°09 3°234 0°9184 (4) Pentadecane, Cy;H3. M.W. 212. W.92. M.P. 10. d =°7754{1—-000889 ¢ —-000000106 ¢?}. Sp. g. (calculated). Sp. g. (observed). Ef Sal San Ml ‘7758 ee ee 7624 ‘7624 NE se ‘7689 7689 Dis ae ‘7135 7136 T. d. M.V V/W. | dyl dey). 28B) aso ‘7758 2732 2-970 1-0000 DOE Bice ‘7689 275-72 2-997 0:9911 30D 7620 278-21 3-024 0-9822 ne aa "7550 280°8 3-052 09732 Sogn 7481 283'38 3080 | 09643 Soa ely ‘7411 28606 3-109 09553 343 ‘1337 288:94 3140 0:9463 Ct ae 7271 991-57 5169. 0:9372 868... 7199 29447 3-200 0:9282 Mr. Gervaise Le Bas on (9) uae Cralalan MW. 2 26. W...98. MP: Ue d= "T7543 1—-000864¢ —: 00000028¢??. Sp. g. (calculated). Sp.g. Haag 2 GENES a mae Meat hen 754 GN oh haere T7107 a 07 AGREE, «A: LON oT LOT T. id: M.V V/W. Ay[Any. QOT eke “TT54 29G2\ 2-971 1-0000 SOL eee | 7686 294-05 3000 0:9913 Oillivenaee ‘7618 296°66 3027 0:9826 By ae “7550 299°34 3054 | 0:9738 Sole. 7482 302°06 3082 0:9650 B41 ...... “7413 30487 3111 09561 SOME Sy: 7344 307-73 3°140 09471 BOL oo. esas 7274 31069 3170 0°9381 yi (lles sacs 7204 313-71 3201 09291 (6) Heptadecane, Cy Hs. M.W.240. W.104. M.P. 2275. d,,=°7766 { 1 —-000895t + °00000023 #7}. Sp. g. (calculated). Sp. g. (observed), ve doe fc eke oy aM aed 7714 ee da Sania 7245 THB fink M.V Vw.) aeons 2955 ...| -7766 309-0 2971 | 1-000 3055 ...| 7697 31181 | 2998 | 09911 8155 || “7627 31467 3025 | 09822 3255 || 7558 31754 3-053. 09733 3355 ...| °7490 320-42 | 3081 0:9645 3455 || °7422 323:36 3110 | 0-9558 353-5 | °7350 39631 3138 | 0-9471 365° ...| 7288 32930 | 3166 | 0-9385 (7) Octadecane, CygH;,. M.W. 254. W.110. M.P. 2.3 d,,==°7768 {1 —:000906 ¢ + *0000005 27}. Sp. g. (calculated). Sp. g. (observed). Ga aaa nan arty ibrar 7768 Gi i Lautner 7719 77 19 i EA SB 7684 ‘7685 Giga sahaeeiase eyes 7288 "7288 T. dl. Mv. | w/w. | do/dy. B01", 2... “7768 326°9 2-972 1:0000 il) Mea 7698 329°95 2-999 09910 321 7630 332'89 3026 0-9821 BOL he: "7562 335°89 3053 0:9732 Salley te "7493 339°0 3082 09645 BOL Fi2..: 7427 3420 3°109 09560 SOL: Cie... ‘7361 34506 3137 0:9474 SAL ees 7295 | 34818 3°166 0:9390 the Unit-Stere Theory. 333 The above method of calculation can be extended to higher members of the series, with similar results. It will be convenient for purposes of comparison to arrange the above results in tabular form. V.—tTable illustrating the Additive Law. Values of V/W. MP. X10. | C,,H,,.| C,,Has- C,,H.,.| (OFM eb yay (OnelelyeMORSEL | (Ou debe ce es | oe ie ae 2970 | 2:970 | 2970 | 2970 | 2971 | 2971 | 2-972 , +10° ...| 2997 | 2993 | 2994 | 2997 | 3000 | 2-998 | 2-999 | | »- +20 ...| 3:025 | 3020 3:023 | 3:024 | 3-027 3025 3°026 | e. | er oo 3°053 3049 3:051 | 3052 | 3:054 3°053 3°053 sees oWel: | 3078 308i | 3080 | 3-082 3081 3°082 Peo ee OL |. 3:107 3109 3109: | 3111 3110 3°109 Spor | ol. | 3137 3139 | 3140 | 3-140 3138 3137 med ee) alia. |» 3-168 3170 | 3:169 3170 3166 3°166 Pee) ees a 206 | 3200 3201 | 3200 | 3-201 mien! 2.1 | o'240 3°232 3234 | | | V1I.—Table illustrating the Law of Additivity. autor) | Ratio | Wales Ratt | V. of bRatie | V. of C\,H5.| a | C,;H;,| B. | OisHy yy. || Ci-Hae- | | | | | 2732 | 1-070] 291-2 | 1140) 3090 | 1-210 » +30°.| 262-45 280°8 | 1:070|| 299-34 | 1:140]) 317-54 | 1-210 eeeGOa 270-01 | 288-94 | 1:070]| 307:73 | 1:140!|| 326-31 | 1-209 | i | | Ratio. M.P. il 255°4 a The volumes of the paraffins are shown by the above table to be additive and to follow the valency law; for 86 CR Gs 0d 86, 92, 98, 104, representing the valency numbers of the compounds in question. It is thus coneluded That the molecular volumes of the complex liquid normal paraffins are subject to additive relations and are proportional to ther respective valency numbers at their melting-points also at equal intervals of temperature therefrom. Phil. Mag. 8. 6. Vol. 14. No. 81. Sept. 1907. ae 334 Mr. Gervaise Le Bas on VII.—Table illustrating the Law of Coincident States. Values of d,/d,'. | | | M.P. +210 | C,H. | C,H5- CyyHyo. | Cy5H 52. | CygHy. ———————— ee ee ee fone MaP weeierase 1:0000 | 1:0600 | 1:0000 | 1:0000 | 1:0000 ae LOS 0:9913 | 09909 | 0-9910 | 0-9911 | 0:9913 » +20 09824 | 09819 | 0:9820 | 0:9822 | 09826 » +80 09735 | 09728 | 0:9780 | 09732 | 0:9738 »» +40 0:9644 | 0:9637 | 09639 | 09643 | 0-9650 set 09552 | 09546 | 0°9550 | 0°9553 | 09561 5 ed) 09459 | 094538 | 09458 | 0:9463 | 09471 5 geod 09368 | 0°9362 | 0-9367 | 0:°9372 | 09381 oy Be) 09270 | 09270 | 0:9275°| 0°3282 | 09291 » +90 09172 | O9177 | 09184 C,7H,,- 1:0000 0-9911 0:9822 0°9733 0'9645 G:9558 09471 0:9385 C,,H,,. 10000 0:9910 09821 09732 0°9645 09560 0:9474 0:9390 The subjoined table further demonstrates the validity of the law of corresponding states under the above conditions: — VIII.—Table illustrating the Law of Corresponding States. V. of : V. of ; Ve of , i WAeerone ; A Ws Oly Tele. Ratio. Chai Ratio. Curie Ratio. O, see Ratio M.P. 255°4 Zia2 || 291°2 309°0 1:027 1:027 ||. 1:028 1:028 » +380°.| 262°45 280°8 299°34 317°54 1:057 | 1:057 | 1:056 056 », +602.) 270-01 28894 | 307°73 32631 It is concluded from the above table That the molecular volumes of the complex liquid normal parafins at equal intervals of temperature from their respective melting-points are equal multiples of their respective volumes at those points. The conditions for the validity of the laws of additivity and correspondence are seen to be represented by intervals of temperature from certain fixed or reference points, and not by equal ratios thereof. | The evidence of the above tables is strongly in favour of the view that the laws of additivity and corresponding states are intimately connected. An investigation of the volumes of the liquid normal paraffins shows that, when the law of additivity is strictly true, the law of corresponding states 1s also true. The melting-points of the above compounds have been shown to he nearly equal fractions of their respective boiling-points, and thus of their critical points. It is true that the boiling- point is not a strictly corresponding temperature ; but the fractions made by the B.P.’s of the simpler paraffins with 330 their critical temperatures gradually increase with the com- plexity of the compounds. For this reason, no doubt, the the Unit-Stere Theory. ratios BP. gradually diminish as the complexity of the compounds increases; and thus it is probable that the melting- points are all similarly related to the critical points of the paraffins under consideration. The Volume Relations of Carbon and Hydrogen at the Boiling and Critical Points. It was Kopp’s fundamental statement, that the differences in volume for the addition of the homologous increment CH, are invariably constant when examination is made of the volumes of homologous compounds at the boiling-point. Schiff and Gartenmeister have, however, shown that this is not quite true ; for the difference in question as a rule rises as the complexity and of course the molecular weight of the compounds increase. This is in part due to the fact that the boiling-point is not a strictly corresponding temperature. Jt is thus necessary to find out if Kopp’s dictum is true under precisely corresponding conditions. Young has given the following table (Brit. Assoc. Address, Cambridge, 1904). It isfound that the molecular volumes and the differences A for an addition of CH, are given under the following con- ditions :— A ot, 0° C. B. At the respective boiling-points under 1 atm. pressure. C, At equal reduced temperatures (0°6396). D. At the respective boiling-points under equal reduced pressures (0°02241). HK. At the respective critical points. TABLE IX. A. B. GC. | D. | E. Paraffin. | | M.Vol.| A. ||M.Vol.| A. |M.Vol.| A. | M.Vol.| A. || M.Vol.]| a nm Butane*...| ....-. TEU Sha a | ee | 251 | | 21:80 eee eal 583 nm Pentane ...| 111:33 117°80 | 116-13 11613 | 309:3 | 15°44 2-13 20-09 1-06) 56°8 nm Hexane .... 126-77 13993 | 136-22 137-19 | 366-1 | 15°69: 29-63 20-18 1-49 | 60-2 nm Heptane..., 142-46 162°56 156-40 158°68 || 426'3 15:88 | 23°7 20-54 1-83 62°6 n Octane 15834 | 186-26 | 176-94 180°51 | 488-9 i * The numbers for butane were not given in Young’s table. a= a 336 The conclusion is that, under the conditions just specified, the differences for CH, are not quite constant when the above four normal hydrocarbons are considered. Mr. Gervaise Le Bas on _ If, therefore, the calculation of atomic volumes be attempted from a consideration of the differences, no reliable results can be obtained. This, however, has been the method followed hitherto in the discussion of physical properties in their relation to chemical constitution. It must not for this reason be concluded that the additive rule may not be very closely followed. The calculation of additive relations by differences virtually assumes that as we pass down a series, the addition of the homologous increment CHa, e. g., leaves the volume of the residue the same as before, provided that coincidence of physical state is maintained. Although very nearly true at the boiling-point, this is not quite the case, and any change from compound to compound affects every atom in the molecule. The method of calculating from differences throws on to the increment the onus of such changes ; so that very serious disturbances are some- times brought to bear on the volumes of the increments, especially if these are small. Moreover, atomic volumes obtained in this way have never any other signification than that which may be given to numbers which are derived from the average of as many numerical coefficients as possible. The method adopted in this paper does not labour under this disadvantage, for, assuming that the 4:1 rule applies very closely between the atoms of any indidual hydrocarbon under all physical conditions, the ratios V/W not only show the validity of the above rule for the different members of a series under corresponding conditions, but they also show the extent of constitutive changes from compound to compound. This is demonstrated in a striking way by the following table. A comparison is made of the above hydrocarbons at the cor- responding pressure, °011795 (see Table XIV.). TaBLE X.—Volumes of CH, at B.P. and at equal reduced pressure. M.V. M.V. for * No Hydrocarbon. ae BoP. |e p/P, = 01179 AS | (6 ViyNVe erate a ee 1. | 2 Pentane, C;H,, | 117-80 11618 21°77 | 22°13 21-06 2. | 2 Hexane, O,H,, | 189°93 137-19 21°66 22°63 21°49 3. | 2 Octane, C,H,,-| 162:56 158°68 21-64 23 70 21 83 4°| nm Octane, (C.Ea | 186-26 180°51 21°66 the Unit-Stere Theory. aor It will be noticed in the first place, that the volume of CH, varies much less under these more precisely correspond- ing conditions than at the boiling-point. Also the value of 6V/W varies but slightly, and in any case, far from there being a rise with complexity, there is a decrease. It is con- cluded that the differences for CH, do not show the true values of constitutive changes, but exaggerate them. They may even be deceptive. For instance, sippose that V/W should not be quite constant, but should reach a minimum and then rise as the complexity increases, as is at any rate probably the case near the critical point; the differences would not show a minimum but gradually rise to the end of the series. This must necessarily happen under such condi- tions, for a preliminary decrease of V/W would cause a depression of the differences between the whole molecular volumes, while the subsequent increase in V/W would make the differences between the whole molecular volumes of con- secutive members of the series too great. The following table gives the values of V/W for the normal paraffins at the boiling and the critical points :— XJ.—Table showing the Values of V/W at the B.P. and the Critical Point. | | | | Nom\gettydrocarbon, |W.) Vi..-| A. | V/W.| Vy..| .a. | V/W. ereatane, C,H, |.26 | 96-0 3:69 | 251-0 965 | 218 | | 58:3 2. \9@ Pentane, C,H, | 32 | 1178 | 368 | 309°3 9°67 22-13 | | 56°8 3. | 2 Hexane, C,H,, | 38 | 139-93 | 3°69 |.366°1 9°63 | 22°63 | 60°2 4. | » Heptane,C,H,, | 44 | 162:56 | 369 | 4263 9°69 | 23°70 | 62°5 5. | m Octane, O,H,, | 50 | 186-26 | 372 | 488-9 9°78 Mean values............ 225 Dv) | SiO9 | oe. 59°5 | 9°68 V/W is fairly constant both at the boiling and the critical points. Octane, however, shows a higher value at both these points. It is usually possible, by means of the independent method adopted at the melting-point, to prove that the value of V/W is in reality that of H. The results are only approximately concordant, owing to the exaggerated deviations shown by the differences for CH,. Nevertheless the method is suffi- ciently good to exclude both Kopp and Schréder’s constants. 338 . Mr. Gervaise Le Bas on The following is a suitable method for the demonstration of the approximate validity of the valency law at the boiling and the critical points ; and it is especially significant owing to the fact that no preliminary assumptions are made. It is also adapted to showing that the following relations are not admissible, viz. C=2H (Kopp), C=H (Schroder). TABLE XII.—Investigation of the ratio i! at the Boiling and H Critical Points. Xt une Boles Theoretical. | Ratios |LeB Laat ae ' atios | LeBas, opp, Schroder, No.| Hydrocarbon. ee WW (obs.). |C=4H A. C=2H A. | 6=H A. 1. | Butane, C,H,, |26| 96-0 |1-0000}1-0000/ ... | 1000 ... | 1000]... 2. | m Pentane, C,H, | 32 117-80) 1:2271) 1-230 |+0-003| 1:222'-0-005| 1214 |—0-013 3.| 2 Hexane, C,H,, 38 | 139-93) 14576) 1-461 |+ 0-003 | 1-444 —0013) 1428 |—0030 4.| Heptane,C,H,, | 44 | 162°56 1-6933) 1-693 |--0-000 1:666 |—0:027.| 1642 |—0-051 5.|2 Octane, C,H,, | 50 | 186-26) 19402) 1-923 |—0:017 | 1-888 —0052) 1-857 |—0-083 Mean errors ............ 0-002 | .. '~0:019 Es —()'045 At the Critical Point. | : No.| Hydrocarbon. | W. We oes Theoretical. A. 1.|2 Butane, C,H,,| 26 | 251-0 1:0000 1:600 ager 29 Bentane, ©. | 32.) 130972 1:2310 1-230 — 001 3. | 2 Hexane, C,H,,) 38 3661 1-458 1-461 +0:003 4.|n Heptane,C,H,, 44 45157) 1:698 1693 —0:005 5.| 2 Octane, C,H, | 50 488'9 1948 1-923 —0'025 Mean. error: 5250.1 25eccneceee eee —0:007 The ratios advocated by Kopp and Schréder respectively are seen to be inadmissible, while, on the other hand, the 4: 1 rule very approximately reproduces the observed results. Kopp’s constants were obtained by means of comparisons between the volumes of members of very different classes of compounds, and, as will afterwards be shown, are not to be relied on. the Unit-Stere Theory. aS) In the following table the volumes of most of the paraffin series up to C,,H., are given. Many of the determinations are those of Bartoli & Stracciati (Beibldtter zu den Annalen der Physik und Chemie, ix. p. 697), and are given for what they are worth, for though the determinations themselves are probably fairly accurate, the substances examined appear to have been the isomers of the normal paraffins or admixtures thereof. They were obtained by means of the fractional distillation of petroleum. XIII.—Table of Values of V/W of the Paraffins at the B.P. No. | Hydrocarbon. | B.P. W. Voc | V/W,.. 3) "Author: 1. | Methane, CH, — 164 8 38'6 4:82 | Olszewski. 2. | Propane, C,H, —25 20 70:0 3°50 | Lefevre. | 3. | Butane, Oe ep all aia L 26 93 3°58 - | 4, | Hexane, C,Hy4 68 3 135°6 357 |B. &S 5. | Nonane, C,.H,, | 136-8 bor |) L941 3°52 , 6. | Decane, C,,H,,| 158-62 62 | 2202 3°55 9 7. | Undecane, C,,H,,| 180-2 68 | 241-9 3°56 : 2), Wodecane, CiLHy,| 198-200) 74 | 2639 3°56 55 | 9, | Endecane, C,,H,, | 218-20 80 | 284-4 3°55 s; 10. | Tetradecane, C,4H,, | 236-40 86 | 3088 3°59 45 11. | Pentadecane, C,,H,, | 258-62 92 | 333:0 3°60 i | 12. | Hexadecane, C,,H,,| 278-82 98 Sooo 3°60 % | The above table shows that V/W for methane is quite discordant with the rest of the series. This fact is, however, not of great significance, since the boiling-point of methane is hardly likely to be even an approximately corresponding temperature. The concordance of the ratios derived from Bartoli & Stracciati’s determinations is somewhat remarkable. This fact seems to be in favour of the view that the liquids were definite isomers of the normal compounds. In any case, the lower boiling-points and the smaller volumes of these compounds are interesting, since they indicate that the branched-chain type of structure depresses both the boiling- points and the molecular volumes of the compounds. This has been shown to be the case for iso-pentane, diisopropyl, and diisobutyl by Young (loc. cit.). 340 Mr. Gervaise Le Bas on A FURTHER EXAMINATION OF THE MoLECULAR VOLUMES OF THE PARAFFIN HYDROCARBONS UNDER IDENTICALLY REDUCED CONDITIONS. A more complete examination of the molecular volumes of the paraffin hydrocarbons and other compounds under corre- sponding conditions, is made possible by the very thorough researches of Young (Trans. Chem. Soc. 1895, Ixvii. p. 1075 ; 1897, Ixxi. p. 466; 1898, Ixxui. p...675; (S003 ixeacm p. 1145). The above investigator has examined the volumes of a number of organic substances under the identically reduced conditions of pressure and temperature, that is to say, at equal fractions of the critical vapour-pressure and the eritical temperature respectively. It was found that, while the volumes of liquids approximately obey the law of correspond- ing states at identically reduced pressures, it fails to a greater extent at corresponding temperatures. It is proposed in this section to show, that the law of corre- sponding states and the additive law are interdependent, and that therefore they may be accounted for similarly. Those features of the physical behaviour of liquids that depend on the one are without doubt intimately connected with the other. (a) At identically reduced Pressures. It will be convenient first of all to show that the law of additivity is very closely followed at corresponding pressures. Use is made in the following table of the valency numbers W, of the four hydrocarbons pentane, hexane, heptane, and octane, which are respectively 32, 38, 44, & 50. As before, the ratio V/W represents the molecular volumes divided by the valency uumbers (see columns 4, 7, 10, 13). Columns 2,5, 8, 11 give the corresponding fractions of the critical temperatures at which the volumes are taken. The evidence of Table XIV.is very much in favour of the significance of the valency numbers W for the respective hydrocarbons, and there cannot be much doubt that under strictly corresponding conditions, the 4: 1 rule is very closely followed. If this characteristic relation can be demonstrated from a consideration of four consecutive members of the series, is zs likely to be true within very narrow limits for every individual compound under all circumstances. 341 OEY. Red. Press. ‘001474 ‘002949 005898 0011795 ‘022411 042352 ‘088465 "144744 ‘20642 29488 44232 ‘58978 “73721 82568 88965 ‘94363 ‘97313 1:00000 the Unit-Stere Theory. eereeroes Ceseeeree eereeeees Pentane, C;H,.. W=32. Table of Volumes of the normal Paraffin Hydrocarbons taken un Hexane, C,H, 4, W=88. Heptane, C,H,,, W=44. T/T. | M.v. | V/W. ‘D414 ae ‘D707 Be bike “6040 | 113:20 | 3:537 6396 116713 3'629 *6824 | 12015 | 3:°755 Tool 125°62 3'925 “7769 alezi 4101 ‘8091 186:05 4-251 "8460 142:66 4-458 ‘S917 | 153885] 4:808 ‘9278 | 166°35 | 5198 9574 | 181:°55 | 5:673 O727 193:80 6:05 "9826 205°60 6:42 ‘9916 ic ee ‘9963 | 238:90 | 7:46 1:0000 | 309°20 | 9°66 der reduced pressures. Octane, O,H,,, W=50. VN | EN | EINE | 5524 | 127-98 | 3:368 5814 | 13051 | 3435 6144 | 13365 | 3°517 6489 | 13719 | 3:610 6907 | 141-95 | 3:736 ‘7406 | 147-48 | 3:907 7831 | 15509 | 4-082 8145 | 160-91 | 4-234 8504 | 16890 | 4-444 8955 | 181-80 | 4-784 9308 | 196-25) 5164 ‘9591 | 214-80 | 5640 9740 | 229-20] 6:03 9833 | 242:20 | 6:37 9922 | 26310 | 6:93 9965 | 28230 | 7-43 10000 | 36630 | 9:64 Ay WOVEN, POA ‘5371 | 145-44 | 3:306 ‘5625 | 147-94 | 3:363 ‘5912 | 15094 | 3-430 6237 | 15458 | 3-513 6579 | 15868 | 3-606 6987 | 164-02 | 3728 ‘7483 | 171-78 | 3-904 7904 | 179:62| 4-082 8205 | 186-21 | 4-283 8560 | 195-29 | 4-435 8999 | 21036 | 4-781 9835) || 297-17 F 5168 ‘9608 | 24818 | 5-640 ‘9752 | 26525 | 6-03 9841 | 28091] 6:38 9923 | 304-76 | 6-92 9964 | 32551 | 7-40 1:0000 | 425:7 | 9-67 Lao WAS | NAW 5462 | 165:39 | 3-308 5714 168°32 3'366 "5995 lee 34384 ‘6313 175°83 oO 6650 180'51 3610 ‘7060 187:02 | 3:740 7544 195°84 3916 ‘7954 | 20462 | 4-092 "R255 212°39 4°248 8598 ve on "9026 | 241-11) 4-829 "9352 | 260°3 5:206 ‘9619 2844. 5 688 ‘9758 | 3052 6°10 ‘9845 hae ea 9926 Cah fn ‘9965 ss a: 10000 | 488:9 O70 342 Mr. Gervaise Le Bas on An additional test of the above rule, under the conditions stated, is furnished by the subjoined table. XV.—Table showing the validity of the Valency Law. P/P,,.. | C,H, |Ratio «| C,H;, | Ratio B.| C,H, | Ratio. | Clee Miaciero: 001474 165°39 1 Wasa ORGIES I ce ie sine 002949 168°32 1 147-94 0°8790 | 127:°98 | 0:7603 Bie a ‘011795 175°83 1 15458 08792 | 133-65 07601 | 11320 | 0°6438 022411 180°51 1 15868 O-8791 | 187-19 0-7600 | 1167138 | 06453 Mean values (obs.)...| 1 08792 0-7601 0°6435 Theoretical (4:lrule)) 1 08800 0:7600 0:6400 TPOr Wc hese O — 00008 —0-0001 —0°0035 It will be noticed that the values of V/W for octane cease to show any difference from those observed for hexane and heptane, so that the deviations only hold under conditions of high vapour-pressure. They are thus a maximum at the critical point. The conclusion to be drawn from the above observation is, that additive relations are best seen at some considerable distance from the critical points. It appears also to be probable that the divergences from the additive rule which doubtless obtain at the critical point (for compounds more complex than octane) disappear when the vapour-pres- sures become relatively small. The very strict observance of the additive rule, made by the liquid volumes of the complex hydrocarbons, at the melting-point and above it, shows that the above conciusion is true. While the law of additivity holds within narrow limits for the hydrocarbons under con- ditions of corresponding pressure, Young has demonstrated the approximate validity of the law of corresponding states for the liquid volumes of the paraffin hydrocarbons under similar conditions (Trans. Chem. Soc. 1900, Ixxvii. p. 1142). Nevertheless, his calculated values cf V/V,, V, and V, being the observed molecular volumes, and the critical mole- cular volume respectively, under conditions of reduced pres- sure, for the four normal hydrocarbons above mentioned, are not nearly so constant as the values of V/W (see following table). Th reason is to be found in the imperfection of the standard of reference, viz., V,. The constitutive differences which appear among the paraffins at about the critical point, attain a maximum at that point. They, however, disappear for hexane, heptane, and octane at about the equal reduced pres- sure ‘04232. It follows, therefore, that when the volumes under identically reduced pressures are compared with the the Unit-Stere Theory. 343 molecular critical volumes, influences are introduced which have similar effects to those of constant errors. This is par- ticularly the case with octane, which possesses values of V/V,, consistently lower than those for hexane and heptane. If now the volumes under the equal reduced pressure ‘002949, viz., that at which the additive law is very approximately true, be taken as standard, the multiples that the volumes at higher reduced pressures make with this standard are much more nearly equal, and further, the divergences are seen to exactly follow those of V/W. XVI.—Table of Comparison of V/V, and V/V’, V’ the volumes at equal reduced pressure ‘002949. | V/V,, (Young). | V/V’ (Le Bas). | | | : | | P/P x, ! C5H,.. C,H, | CH. | CsA). | C,H, 4. C-Hy.. C,H, 5. 002949 | pie 3494 | -3475 | «3443 || 1-CO0 | 1-000 | 1:000 005898 || ... 3963 "0049 8513 || 1-020 | 1-020 | 1-020 | 011795 | © 662 "3649 "3631 3597 || 1044 | 1:045 | 1-045 | 022411 || 3756 "3746 3127 3693 || 1-072 | 1-073 | 1-072 | 44232 || 4976 4969 494) 4932 || 1-419 | 1-422 | 1:4382 | ‘58978 5320 5857 "5886 93824 || 1-533 | 1536 | 1-547 |} “3721 |, “5872 5851 5830 5818 || 1-674 | 1-678 | 1-689 Wee2oos. «|; “6268 6258 6220 6243 || 1-790 | 1-793 | 1-813 | 100000 |, 10000 | 1:0000 | 1:0000 | 1:0000 ||2°86 |2°87 | 2:90 The ratios V/V’ show that hexane and heptane follow one another very closely right up to the critical point, and on the other hand, octane, while agreeing with the other two hydro- carbons from P/P,,=:002949 to :022411, shows higher values of the ratio from P/P,="44232 to 1. Vv This is exactly what the values of the ratio W teach. The conclusions are as follows :— (2) The molecular volumes of the hydrocarbons from pentane to octane are very nearly proportional to their respective valency numbers under conditions of corresponding pressures. (>) The law of corresponding states and that of additivity are interdependent, and they may no doubt be similarly explained. (c) The ratios V/W are very well adapted to show the extent of constitutive differences. (d) The law of additivity is the more closely followed the further from the critical point that observations are made in this series at any rate. 344 Mr. Gervaise Le Bas on (b) At corresponding Temperatures. If an examination of Table XIV. be made, it will be seen that, while the values of V/W are nearly equal for the four compounds pentane, hexane, heptane, and octane at corre- sponding pressures, the reduced temperatures are not identical but increase from pentane to octane. It follows, therefore, that if the volumes were taken at equal fractions of the critical temperature, the values of V/W would be found to diminish in the same direction. The following table shows how far this is true. In order to further show the close relationship between the law of corresponding states and that of additivity, an additional table is included which — gives the values of V/V, at identically reduced temperatures. XVII.—Table of Values of V/ W for the Paraffin Hydrocarbons at identically reduced temperatures. C5H.. C,H). C,H. | C,H. mes || ¥. M/W. cv. |v. || we | V/A) a alee 6805 || 11133 | 3:48 |180°6 | 3:44 |149°8 | 3-40 || 169°25 | 3°38 625 114-72 | 3°58 || 1845 | 3°54 | 1542 | 3°50 || 17465 | 3:49 ‘7959 || 181-90 | 4:18 | 157-3 | 4:14 || 180-5 | 4:10 || 2047 4-11 "8917 || 153°85 | 481 | 1806 | 4:75 | 207-1 | 4-71 sh oae | | 9963 || 238°9 746 || 282°3 | 7:43 || 3255 | 7-40 sis sie 10000 || 309°2 9°66 || 8663 | 9°64 ||425°7 | 9:67 || 488°9 9°77 | | In spite of the diminution in the value of V/W with complexity, the very similar rise in the case of the four hydrocarbons is unmistakable. The limits within which the law of additivity holds are still narrow. XVIII.—Table of Values of V/V, for the Paraffin Hydrocarbons at corresponding temperatures. C,H... C,H... C,H. l. .CxEne T/T VSM /MEG OV VINES Vee VN ave rg 58085 ||111°33 | -3600 || 130°6 | -3546 || 149°8 | °3519 || 169°25) -3642 6231 1114-72 | -3710 |) 134°5 | -3672 || 154-25) -3628 || 174°65, -3572 ‘7959 1131-90 | -4530 || 157-3 | +4295 || 180°55| 4241 || 20475) -4188 "8917 ||153°85 | -4970 || 180-65} -4937 || 207°15| 4868 |} ... |... '1:0000 |}209°2 |1-0000 || 366°3 |1:0000 || 425:7 |1-0000 | 488°9 1:0000 | | \ \ K° +i eS a the Unit-Stere Theory. 345 The above tables show that :— (a) Both the values of the ratio V/W and those of V/V, diminish from pentane to octane at the corresponding temperatures. (b) The deviations from the additive law and the law of corresponding states are in the same direction and are about the same fraction per cent. of the whole. These facts are additional evidence in favour of the close mutual dependence of the two laws. Application of the 4:1 rule to the Critical Coefficient Te Young has shown that the following relation is approxi- mately true for the most various substances fe 1B dle aed =) Goleta (GS) UCGE nin) eC i V,=055 since z= Pe K P 1890, xxi. p. 206) is subject to similar additive relations to those found from a consideration of V,. The following Table gives the critical coetticient for the four hydrocarbons (column 5), the pressures being expressed in centimetres of mercury. .—The critical coefficient of Guye (Ann. Chim. et Phys. ii ize Column 6 shows the values of the ratio = Pp and column 8 Vv those of a se K K ; Price ee XIX.—Table showing the proportionality between —* and W for the Paraffin Hydrocarbons. ee | | Compound. NAY Pee A he Bs) ee I AWE a. | ~ C kK | Pentane, C,H,,...) 32 |2510 | 4702) -1873 | -00585 | 309-2] 1650 Hexane, C,H,,...| 38 |2251 | 507°8] -2256 | 00594 | 366-3) 1631 Heptane, C,H,,.... 44 | 2041-5] 539-9] -2645 | -00601 | 425-7! 1609 Octane, C,H,,...| 50 |1873-4| 5692] -3038 | 00608 | 488-9! 1609 346 Mr. Gervaise Le Bas on The chief point to be noticed other than the approximate ve ; constancy of EF pT is the gradual increase of this relation Wes from pentane to octane. This evidently corresponds with 3 Pv. | the gradual diminution of pres in the same direction, for if K the two be multiplied the products which represent the ratio ale are approximately constant. These are :—9-65 for C;Hypo, W 9°688 for C,H, 9°67 for (Craig, and OSS for CyH)e. It is Ke Kk ry ss thus concluded that the variations in the values of Je are due to the factor 7: ay THe UNIT-STERE THEORY IN THE Liagut or MOLECULAR REFRACTIONS. The law of corresponding states implies the fact, that the apparent volumes of liquids under coincident conditions are measures of the space actually occupied by the molecules. There should therefore be a proportionality between their apparent volumes under the above conditions, and their molecular refractions as found by means of the Lorenz and Lorentz formula. lf w represent the fraction of the space actually occupied by the molecules, then this formula supplies the relation pa ial a i ee awe pw vepresenting the index of refraction for light of infinite wave-length. It will be sufficient to refer the refractions to the D sodium-line. Then The volumes V of the four hydrocarbons pentane, hexane, heptane, and octane at corresponding pressures are referred to. Under these circumstances the ratio wis the same for the substances now being considered. R XX.—Table of Determinations of — for the four the Unit-Stere Theory. 347 Vv Hydro- carbons under conditions of identically reduced pressures. Beige R951. CHH,, ; BL =29-7 0,1; R, =3435, O,Hyy; RB, =38'95. | BP meme, |) > Wis |. keer ela aD Va) 9) oa Na 1 aes aA V V 001474 a cae | | 14544 | -2360 | 165°39 | +2355 “005898 aie ee 130-51 | °2276 | 150°94 ‘2274 ito 2268 ‘011795 || 113°20 918 SSO) | 2292 | 154258 SPA 175°83 2216 °022411 || 116:°13 2161 137719 | -2166 | 158°68 -2164 180°51 *2158 "04232 || 120715 2089 141°95 | °2092 164:02 *2093 187:02 -2083 "088465 || 125-62 “1999 ae 71:78 -1999 195-84 1988 1:00000 309°2 ‘O811 366'3 0811 495°7 ‘0806 4889 ‘0797 Since the characteristic relation between carbon and hydrogen has been found under all corresponding conditions, it is concluded that the molecular refractions themselves are subject to similar additive relations. R XX1I.—Table showing the Values of the Ratio —2 W for the Paraffin Hydrocarbons. | | { R Hydrocarbon. | W. R,. nD) W lees sd Re Reser antas ewe ae iventames (Cre ea. | 32 2571 ‘784 |Hexane, ©,H,,...... | 38 | 29-7 "782 Hieptane, CEH. se... 44 34°33 “780 Octane, OEE ac ear 50 38°95 ‘779 Decane, @ lesa toet 62 48°3 179 It is thus seen that the apparent molecular volumes of the (normal) paraffin hydrocarbons under corresponding con- ditions are approximately equal multiples of their molecular refractions and thus also of their real volumes. The appli- cation of the valency rule to the apparent volumes under the above conditions depends on this fact, although the reason for the proportionality between the real and apparent volumes under corresponding conditions remains unexplained. Traube has already studied molecular refractions from this R point of view, that is, he has shown that the ratio —¢ W 348 Mr. Gervaise Le Bas on is approximately constant for the hydrocarbon and other series, W representing an integer, which in this instance is the fundamental valency number (loc. cit.). CONCLUSIONS. St may be useful to summarize the results so far obtained. (1) The law of additivity is exactly followed at the melting-points of the complex liquid normal hydrocarbons from undecane C,,H.3 to pentatriacontane C3;H-», and at equal intervals of temperature therefrom. The volumes of the compounds in question under such conditions are propor- tional to their respective valency numbers for the reason that the atomic volumes of combined carbon and hydrogen are as 4:1, a ratio which is the same as that between their respective valencies. This is best represented by the following formula : M.V. of C,H, ,2=(6n+2)S= WS, W representing the valency number of the compound, and S the volume of hydrogen under the conditions, that is to say, the volume of the unit-stere. 2. The specific gravities of the above hydrocarbons at equal intervals of temperature from their respective melting- points are equal fractions of their specific gravities at those points. | If the melting-points are considered to be corresponding temperatures, the above results show that the law of corre- sponding states is valid near the melting-point and possibly below it. This is also true for the law of additivity. (An experimental investigation of this point is in progress.) Thus there appears to be a remarkable mutual dependence between the law of corresponding states and the law of additivity. This indicates that those features of the pro- perties of liquids and possibly also of solids which account tor the one, also account for the other. (3) The volumes of the simpler hydrocarbons under corre- sponding conditions have also been studied. At Corresponding Pressures.—The valency law is approxi- mately true at the critical points. Octane, however, is somewhat divergent. Similar relations are found at equal fractions of the critical pressures. The additive relation is much more closely followed at considerable intervals of temperature from the critical points the Unit-Stere Theory. 349 than at the critical points themselves. Octane ceases to be divergent. (4) Just as the additive law is very approximately true at equal reduced pressures, so also is the law of corresponding states. This is especially shown when the volumes at the equal reduced pressure ‘002949 are taken as standard instead of the molecular critical volumes. (5) At Corresponding Temperatures.—The laws fail some- what under conditions of equal reduced temperature. The departure from the law of additivity is in the same direction as that from the law of correspondence and is proportional to it. This shows that if the one were true under the above conditions, the other would be also. It may be demonstrated that the condition for the validity of the laws of additivity and correspondence depend, not on the ratio T/T,,, but cn the difference T,.—T. T,—T may not be always quite the same for the different members of a series of homologues, as we pass from one condition to another, but often is so, the complex normal paraffin hydrocarbons near their melting-points being a case in point. i (6) The critical coefficients P of Guye, being subject to K similar additive relations to those of the molecular critical volumes, are approximately proportional to the valency numbers of the compounds. (7) The apparent volumes of the liquid hydrocarbons from pentane to octane under conditions of equal reduced pressure are approximately equal multiples of their molecular re- fractions as calculated from the Lorenz and _ Lorentz formula. Tt thus follows that the molecular refractions are similarly subject to the valency law. The above relations seem to be strongly in favour of the view that valency is a volume property, and also that the laws of additivity and correspondence are very closely related. The validity of the law of correspondence for liquids has hitherto been supposed accounted for by Van der Waals’ theory. The law of additivity, however, does not appear to be deducible from Van der Waals’ equation of condition. Tt is further remarkable that both laws are far more strictly followed under conditions such that the assumptions upon which the above theory is based are less likely to be valid Phil, Mag. 8. 6. Vol. 14. No. 81. Sepé. 1907, 2B 350 Lord Rayleigh on Light dispersed from than near the critical point, that is under conditions such that the repulsive forces have just overcome the attractive forces which hold the molecules in their places in the solid or crystalline structure. The assumption of a co-volume, that is a space in which the molecules as such are moving, does not seem to be at all necessary so far as the additive relations are concerned. Traube’s theory is based upon this conception of liquid structure, and since an unnecessary complication is thereby introduced, it ceases to be significant. Municipal School of Technology, Victoria University, Manchester. XXX. On the Laight dispersed from sine Lines ruled upon Reflecting Surfaces or transmitted by very narrow Slits. By Lord RayueicH, O.W., Pres. R.S.* di age problem of the incidence of plane waves upon a cylindrical obstacle, whose radius is small in comparison with the length of the waves and whose axis is parallel to their plane, is considered in ‘Theory of Sound,’ § 343, also Scientific Papers, iv. p. 314; but it is now desired to carry the approximation further and also to make some applications. On the other hand, we shall confine ourselves to the cases of perfect reflexion where the boundary conditions are simplest. The primary waves, travelling in the negative direction, are represented by d=e@+*), where a is the velocity of propagation and k= 27/), X being the wave-length. Dropping the time-factor for brevity, we shall write b= eh — orcs” — J (kr) + 22 Jy (ker eos + oo. Qt), (er) COSMO ere (1) J, being the Bessel’s function usually so denoted, so that zn ae WO= SEED LI aD) eS ” Ok (Qn 20) (nee ioe (2) In (1) # and v are measured from the centre of the section of the cylinder, whose length is supposed parallel to the axis of 2. * Communicated by the Author. fine Lines or transmitted by narrow Slits. 30L ' The secondary waves diverging from the obstacle are represented by ; ap = BoDo(kr) == B,D, (kr) COS 6 + B,D, (kr) COS 20 tas *5 (3) where T z —iz [2 12, 37 Do(e)=— (5; )*e Soe ye iz 22 oA 2 26 om gs ute) 2 aa pete et y being Huler’s constant (‘5772 ...), and the other D’s are related to D» according to D,(2) =(—22)" as) DH Heda ened © The first expression in (3) is available when z is large and the second when ¢ is small. It should be remarked that the notation is not quite the same as in the papers referred to. The leading term in Dy when ¢ is large is Di=—-(F) Saat. 4G) and in finding the leading term in Dn(z) by (5) it suffices to differentiate only the factor e~*. Thus when z is great D.@)=—i* (sa) e*. - eae on) Qizg Accordingly when in (3) y is required at distances from the cylinder very great in comparison with A, we may take be —( aim) Bot iB, cos 9—B,.cos20+...}. . (8) We have now to consider the boundary conditions to be satisfied at the surface of the cylinder r=c, and we will take first the condition that Die Og a ie youl. Loree) at this surface. We have at once from (1) and (3) in virtue of Fourier’s theorem i —Jo (ke) + Do (ke), B, = —2iJ, (kc) —D,(ke), and generally Ba= — 22" In (ke) — Dn(ke). Bath ose dee (10) 2B2 352 | Lord Rayleigh on Light dispersed from In like manner if the condition to be satisfied at the surface of the cylinder is A uae ae 2 we get, using (, C, &c. in place of Bo, B, &c., | Cyo=—JIo' (ke) = Dy (Ke), Cr=—2iJin'(ke) = Dn' (ke), .% ees the dashes denoting differentiation. The next step is to introduce approximations depending upon the smallness of ke. In addition to (4) we have dD iL A +(y+logZ) {5-...}-S4.5 (13) Ds =4— Stuy ony 2 and so on. Also Di()= > 17 3(7+log5 ), - ee 5) Di@= 3+ 3(1+5 + 85) Mis cs Di@=5. 4.) Using these, we find —Bo'=ytlog (dike) +4P(14+8,h) . . . (18) ~iB, =Pc{1+4e(y—J tog (Hike))} 2 2. (19) Bela ok 3 Ee Referring to (8) we see that when ke is small the pre- dominant term is the’ symmetrical one dependent on By. Retaining only this term, we have as the expression for the secondary waves Se Petar OR PRE Y= 7+ log(dike) Gar - + + (2) as in the papers referred to. Relatively to this, the term in cos @ is of order kc”, and that in cos 26 of order k'c*. fine Lines or transmitted by narrow Slits. 353 Passing on to the second boundary condition (11), we have h2¢? k?¢? _3 ake ie 5 ike \ Y Ly) Pe dee 2 Bee he7 41 5 (r+ —~ + log = 1 ee (23) hte! —C,= Sart <= . ah ets cM Pccxcs che is cea BS (24) When these values are introduced into (8), we see that the terms in Q, and C, are of equal importance. Limiting our- selves to these, we have p= — Bee (so) + cos O) a0 ehti, 225) the symbolical expression which gives the effect of the incidence of aerial waves upon a rigid and fixed obstacle (‘Theory of Sound,’ § 343). Fully to interpret it we must restore the time-factor and finally reject the imaginary part, thus obtaining 2 2 \ aa ($+ cos @) cos Cai) (20) corresponding to the primary waves 20r p=cos\— (a +x). Po ee on In the application to electric or luminous vibrations the present solution is available for the case of primary waves Ca Cees ae iia be C2) incident upon a perfectly conducting, 2. e. reflecting, cylinder, c™ denoting the magnetic induction for which the condition to be satisfied at the surface is dc*/dr=0. Accordingly the secondary waves are given by (25) with ¢* written for +. This is the case of incident light polarized in a plane parallel to the length of the cylinder. For incident light polarized in the plane perpendicular to the length of the cylinder the primary waves have the expression SGM R Ree Steer Sa Meas (PA y. where R denotes the electromotive intensity parallel to z. In this case the secondary waves are given by (21) with Rin place of wy. It appears that if the incident waves in the two cases are of equal intensity, the secondary waves are of different orders of magnitude, R preponderating. Thus if 354 Lord Rayleigh on Light dispersed from unpolarized light be incident, the scattered light is polarized in the plane perpendicular to the length of the cylinder, and the polarization is complete if the cylinder be small enough. It is now proposed to make application of these solutions to meet the problem in two dimensions of the incidence of plane waves upon a perfectly reflecting plane surface from which rises an excrescence, also composed of perfectly reflect- ing material, and having the form of a semi-cylinder whose axis lies in the plane. We shall show that it is legitimate to substitute the complete cylinder, provided that we suppose incident upon it two sets of plane waves adjusted to one another in a special manner. In the figure ABECD represents the actual reflector, upon which are incident waves advancing along PO,a direction POD=P0D=«; QOD=¢. making an angle a with the surface OD. The secondary disturbance is required tat a great distance (7) along OQ inclined to OD at an angle @. But for the present we suppose the cylinder to be complete and the plane parts of the reflector AB, CD to be abolished; and in addition to the waves advancing along PO we consider others of the same quality advancing along a line P’O equally inclined to the surface upon the other side. The angle @ of previous for- mulz is represented now by POQ, P’OQ whose values are g—aandgd+a. Thus we may write cos 9=cos(@—a), cos @’=cos (pP+a), so that cos 0+ cos @’=2 cos @ cos ¢, cos @—cos 6’=2 sin « sin @. jine Lines or transmitted by narrow Slits. 3D0 The two sets of waves advancing along PO, P’O will be supposed to be of equal amplitude; but we shall require to consider two distinct suppositions as to their phases. In dealing with R the supposition is that the phases are pre- cisely opposed. In this case we obtain from (8) as the complete expression of the secondary waves: R= = one e~*r} 27B, sin a sin 6—2B, sin 2x sin 26+...}, (30) the term in By ee while the values of B,, B, are given by (19), (20). Bach of the ae separate solutions here combined, primary and secondary terms included, satisfies the condition R=0 at the surface of the cylinder and so of course does the aggregate. It iseasy to see that the aggregate further satisfies the condition R=0 along AB, CD where 6, 6’ are equal, the contributions from the two solutions being equal and opposite. Hence (30) gives the secondary waves s due to the incidence of primary waves along PO upon the reflecting surface ABHCD; and the expression for the primary waves themselves is R= eke cos a+y sin a) — ghz cosa—y sin oy. : P F (1) x being parallel to OD and y parallel to OG, so that e=rcosd, y=rsin d. In like manner the c* solution may be built up. In this case we have to give the same phase to the two component primaries. Corresponding to the incident o* = eik(@ cosatysin a) ae gik(@ cosa—y sin 2. Shi 1e Hee (3 2) we have for the secondary disturbance c= —(57. ) e—¥rF IC + 271C, cos a cos h —2C, cos 2acos26+ ...s. . + (33) Each solution, consisting of primary and associated secon- dary, satisfies over the surface of the cylinder dce*/dn=0, dn being an element of the normal. And over the plane part AB, CD the two solutions contribute equal and opposite components to dc*/dn. Henceall the conditions are satisfied for the incidence of waves along PO upon the papi reflecting surface ABHCD. The pr sroblem is now solved for the two principal cases of polarized incident light. If the incident light be unpolarized, 356 Lord Rayleigh on Light dispersed from the condition as regards polarization of the scattered light turns upon the value of = iB, sin «sin o— By sin 2xsin 2+ ... (34) "+70, cos a cos 6— C,cos 2a cos 264+...” in which the values of B,, Ba, ... Cy, C, ... are to be sub- stituted from (18), (19), (20), ‘end from (22), (23), (24). a we stop at the ae approximation, neglecting B,, Cz, &e., we have 2 sin asin d 1+2cosacosh™ ~ From (34) or (35) we see that the value of II is symme- trical as between @ and @¢, an example of the general law of reciprocity (‘Theory of Sound,’ § 108 &c.). If «=0, or if ¢=0, II vanishes without appeal to approxi- mations. This means that c* preponderates, or that the scattered light is polarized in a plane parallel to the length of the cylinder. The conclusion follows approximately although @ be not very small, provided ¢ be also small. According to (35) II becomes infinite when 1-+'2'cos a cos d6— 0, . eee for example when «=45°, 6=135°. If we take a=40°, 6=130° so as to avoid the directly reflected rays, we have II=—67, so that there is nearly complete polarization in the plane perpendicular to the length of the cylinder. If we suppose 6=180°—a, so that observation is made nearly in the direction of the regularly reflected rays, (35) becomes ee (35) 2 sin? a HN ee erm a) (20) The scattered light is unpolarized when T=+1. If we make this supposition in (37) we find 2a=30°. This angle separates the two kinds of polarization. Thus when a is small, II =2 sin? a; when a=30°, II=1; whena=45°, l=» ; when a—O0-. We 29 By use of (34) the approximation may be carried further. As an example we may take the case of perpendicular in- cidence and observation, so that a=90°, 6=90°. Thus by (34) ee eo (38) CRaCATin- 4 sk mee Jine Lines or transmitted by narrow Slits. 307 It may be well to recall that in the results which we have obtained the angles «, ¢ are measured from the surface and not, as is usual in Optics, from the normal. Again, if it be desired to attach significance to the sign of II, we must re- member that in one case we were dealing with c* and in the other with R. The above given theoretical investigation was undertaken in order to see how far an explanation could be arrived at of some remarkable observations by Fizeau*, relating to the light dispersed at various angles from fine lines or scratches traced upon silver and other reflecting surfaces. In every case the incident and dispersed ray is supposed to be per- pendicular to the lines, so that the problem is in two dimen- sions. The most striking effects are observed when the incident and dispersed rays are both highly oblique and upon the same side of the normal to the surface. The dispersed light is then strongly, sometimes almost completely, polarized, and the plane of polarization is parallel to the direction of the lines, 2. e. perpendicular to the plane of incidence. A silver surface, polished by rubbing with ordinary rouge in one direction, shows these effects well, and even a piece of tin- plate, treated similarly with cotton-wool, suffices. The plate is to be held obliquely and the incident rays should come from a window or sky-light behind the observer. It is of importance to avoid stray light and especially any that could reach the eye by specular reflexion. Observation with a nicol shows at once that the light is strongly polarized and in the opposite way to that regularly reflected from a glass plate similarly held. Under the microscope a single line may be well observed, especially when strongly lighted by sunlight. Fizeau found that when the incidence 1s oblique and the observation normal (a=small, 6=90°), or equally when the incidence is normal and the observation oblique («2=90°, @=small), the above specified polarization obtains, provided the line be very fine ; otherwise the polarization may be reversed. When the in- cidence is oblique and the light nearly retraces its course (a and @ both small and of the same sign), the polarization is more complete and also less dependent upon extreme fineness. Whenz« and gare both in the neighbourhood of 90°, the polarization becomes insensible. If the incidence is oblique and the angle of observation in the neighbourhood of the regularly reflected light, traces of reversed polarization are to be detected. : if piniene de Chimie, |xiii. p. 885 (1861); Mascart’s Traité d’ Optique, 358 Light dispersed from Lines or transmitted by Slits. My own observations are in essential agreement with Fizeau. At first accidental scratches upon silver surfaces which had been worked in one direction were employed. Afterwards I had the opportunity of observing specially fine lines ruled with a diamond by a dividing-engine, for which I am indebted te Lord Blythswood. In the latter case the plate was of specuium-metal. | It will be seen that the theory agrees with observation well in some respects, but fails in others. When « and } are both less than 90° and of the same sign, the polarization expressed by (35) sufficiently represents the facts. But there is little in the observations to confirm the strongly reversed polarization which should oecur when the denominator in (35) becomes small. One defect of correspondence in the con- ditions of theory and experiment is obvious. The former relates to semi-cylindrical ewerescences, while the observations are made upon light dispersed from scratches which are mainly depressions. In order to examine the question thus arising, a glass plate provided with suitable scratches was coated chemically with silver upon which copper was after- wards deposited by electrolysis. When the coating thus obtained was stripped from the glass,a highly reflecting surface was obtained in which the original scratches are represented by precisely fitting protuberances. But even with this I was unable to find the strongly reversed polarization to be expected according to (85) when (36) is nearly satisfied. If we trace back the denominator in (35), we find that it is derived from the factor ($+ cos@) in (26), and that its evanescence depends upon the antagonistic effects of the terms which are symmetrical and proportional to cos@. The precise form of this factor is doubtless connected with the assumption of a circular cross-section, but the discrepancy from observation seems almost too complete to be attributed to such departures from the theoretical shape. . As other possible sources of discrepancy we may note the assumption of reflecting power which is absolutely complete, and again that the dimensions of the line are small in comparison with the wave-length. It may be that lines sufficiently fine to justify (35) in its integrity would not reflect enough light to be visible. At the same time the evanescence of IL with a or @ does not demand such a high degree of fineness. In the memoir already cited Fizeau treats also the polari- zation impressed upon light which traverses fine slits. Thus (p. 401): “Une lame d’argent trés-mince, déposé chimique- ment sur le verre, a été rayée en ligne droite, avee de l’émeri tres-fin; c’était un fragment de la lame désignée précédem- ment par la lettre (A), et dont l’épaisseur a été trouvée de / / / / f ne On Rays of Positive Electricity. 399 1/3400 de millimétre. Un grand nombre de stries avaient traversé la couche d’argent de maniére 4 donner naissance a autant de fentes d’une ténuité extréme. Ces lignes lumi- neuses étant observées, a Vaide d’un analyseur, au microscope éclairé par la lumiere solaire, ont présenté les phénomenes de polarisation déja décrits, c’est-a-dire qu’un grand nombre dentre elles étaient polarisée dans un plan perpendiculaire a leur longueur. “Mais en observant avec plus d’attention les moins lumi- neuses de toutes ces lignes, c’est-a-dire celles qui devaient éire les plus fines, on en a trouvé un certain nombre qui présentaient un phénoméne de sens opposé, c’est-a-dire qu elles étaient polarisées dans un plan paralléle a leur lon- gueur, les unes totalement, les autres partiellement; cet effet étant accompagné de phénomenes de coloration semblables a ceux qui ont été signalés dans les lignes qui donnent la polarisation perpendiculaire.” The passage of electric or luminous waves through a fine sht in a thin perfectly conducting screen was considered by me in a memoir published ten years ago”. If the electric vector is parallel to the length of the slit, the amplitude of the transmitted vibration is proportional to the square of the width of the slit; but if the electric vector is perpendicular to the length of the slit, the transmitted vibration involves the width only as a logarithm—see equation (46)—much as in equation (21) of the present paper. If the incident vibra- tion be unpolarized and the slit be very fine, the latter com- ponent preponderates in the transmitted waves, viz. the direction of polarization is parallel to the length of the slit, in accordance with Fizeau’s observations upon light transmitted by apertures of minimum width. Terling Place, Witham, July 1907. | XXXII. Rays of Positive Hlectricity. By J. J. THomson, M.A., FRS.F i On a paper on the rays of positive electricity (Phil. Mag. May 1907) I showed that these rays in gases at very low pressures consisted mainly of streams of two Kinds of positively charged particles, the value of e/m for one stream ‘being 10* and for the other 5x 10%. As these are respectively the values of e/m for charged atoms and molecules of hydrogen, it might be thought that the rays of positive electricity were dependent on the presence of hydrogen in the discharge-tube. The results described in the previous paper were not, as I * Phil. Mag. xliii. p. 259 (1897); ‘Scientific Papers,’ iv. p. 283. See also Phil. Mae. July 1907. ) t+ Communicated by the Author. 360 Prof. J. J. Thomson on pointed out, in accordance with that view; and direct mea- surements have shown that the intensity of the rays in different gases is not connected with the amount of hydrogen in the tube. The method adopted was to measure photo- metrically the brightness of the phosphorescent patches produced by the rays with the aforesaid values of e/m on a screen covered with willemite. This was done as follows:— Light of the same colour as the willemite phosphorescence was produced by sending the light from an incandescent lamp through a weak solution of fluorescine: with a little care it is easy to get a solution in which the fluorescence produced by white light is a very good match for the fluor- escence produced by the positive rays on the willemite. A small glass tube A (fig. 1) containing such a solution was Ries. placed! against the willemite screen on which the rays impinged ; the tube was illuminated by light whose intensity was adjusted in the following way. A Nernst lamp was placed at the end of a long tube B; the light from this, after passing through a lens, went through two Nicol prisms N, N placed in graduated holders: after passing through the nicols the light was reflected parallel to the screen from a mirror M and produced in the fluorescine a phosphorescent patch side by side with that produced by the rays on the willemite. — When the planes of the two nicols were at right angles to each other, no light got through; when the planes were parallel so much light got through that the phosphorescence of the fluorescine was greater than that of the willemite. By rotating the nicols the angle between them could be adjusted so that the light passing through made the phos- phorescence of the fluorescine equal to that of the willemite. The angle between the planes of the nicols in this position gave a measure of the intensity of the light from the fluores- cine, and therefore of that produced by the positive rays. The current passing through the discharge-tube was mea- sured by a galvanometer. The brightness of the positive rays depends upon a good many things besides the current through the tube; but the currentis one of the important factors, and Rays of Positive Electricity. 361 it would not be legitimate to compare the intensity of the phosphorescence on the willemite if the currents were very different. | The procedure was as follows:—The discharge-tube origi- nally full of air was exhausted, and measurements of the brightness of the patch of phosphorescence produced by the rays for which e/m=10* were made for measured values of the current through the tube: the tube was then further exhausted until the discharge only passed with great difficulty. Sealed on to the discharge-tube was another tube containing potassium permanganate: this was connected with the discharge-tube by a long spiral tube dipping into a reservoir which was kept filled day and night with liquid air, so as to prevent any water-vapour reaching the discharge-tube. A similar spiral in liquid air was placed between the discharge-tube and the pump. The permanganate was heated and the tube filled with oxygen ; this was pumped out and the brightness of the phosphorescence measured ; the exhaustion was then carried to the stage when the discharge only passed with difficulty; the permanganate was again heated and the process repeated. This procedure was kept up for six days, the total number of fillings with oxygen being about 70. The discharge from a large induction-coil was kept .running through the tube for about 6 hours each day, being only stopped during the short intervals when the exhaustion had been carried so far that the discharge passed with difficulty, and there was a danger of breaking the tube by sparking through the glass. Measurements of the brightness of the phosphorescence with given currents through the tube were made from time to time, but there was no indication of any diminution. At' the end of the run the tube was opened and hydrogen let in, when again with the same current the intensity of the phosphor- escent patch was the same as before. The hydrogen was pumped out and helium admitted, and in this case the phosphorescence seemed a little brighter than before, though the difference was not considerable. There is thus no indication that the positive rays are dependent upon the presence of hydrogen in the tube. Positive rays are very widely distributed through the tube. The positive rays are to be found throughout the tube, and not merely passing through apertures in the cathode and in the layer of luminosity adjacent to it. The positive rays which were used in the preceding experiment as well as those used in all the experiments described in the previous paper, were rays which had passed through an aperture :in the cathode. I have found, however, that positive rays are to be found in all parts of the tube which have an uninterrupted view of the ordinary ‘“ Canalstrahlen”’ or of that luminous patch next 362 Prof. J. J. Thomson on the cathode of which the Canalstrahlen are the prolongations. The. first place in which they were found is right in tront of the cathode. The discharge-tube is represented in fig. 2. A perforated plug was placed at the entrance of the tube A, Fig’, 2. and at the end of this tube there was a willemite screen B ; the tube passed between the poles of a powerful electro- magnet of the Du Bois type and contained two parallel plates, which when connected with a large battery of small storage- cells had a strong electric field between them. When & was cathode, the tube was flooded with ordinary cathode rays, but these could easily be turned to one side by a small per- manent magnet: when this was done there still remained a bundle of rays passing through the aperture which were not appreciably deflected by the weak magnetic field, but which suffered appreciable deflexion by strong magnetic and electric fields. The direction of the deflexion showed that they con- sisted of positively charged particles; the magnitudes of the deflexions were comparable with those of the rays which pass through apertures in the cathode ; but even rough measure- ments were sufficient to show that the velocity of these particles in front of the cathode was less than that of the par- ticles which had traversed the cathode. Viliard (Comptes Rendus, vol. vii. p. 674) has described a similar experiment and obtained the same results. The luminosity produced on the screen in this experiment, though quite appreciable, was much less than that produced by the ordinary Canal- strahlen, and was rather too faint to allow of very accurate measurements of e/m and v. I have deferred making these measurements in the hope of improving the appa- ratus so as to get much brighter phosphorescence. Along with the rays which were positively deflected, there were others which were not deflected by the strongest fields I could apply; and, as in the case of the rays coming through the cathode, there were some rays which were deflected in the negative direction, and which consisted of particles having a negative charge and a mass much greater than that of a corpuscle. The existence of the positive rays in front of the cathode and travelling away from it, might be explained by a kind of reflexion of those travelling towards the cathode: we might suppose that some of these, when close to the cathode, Rays of Positive Electricity. 363 got negatively charged by the adhesion of corpuscles. The strong electric field near the cathode would shoot these away from it, and they might in their journey through the tube lose by collision with the gas not only the corpuscles they had acquired, but also an additional one, and thus become posi- tively charged. Another way of explaining these rays is to regard the gas traversed by the positive particles moving rapidly towards the cathode as being thrown into a condition analogous to that of a radioactive substance and shooting out with great velocity positively electrified particles (corre- sponding to the « particles), as well as corpuscles (cor- responding to the 6 particles). If this were the case, the positive particles might be expected to be shot out in all directions; while on the other view they would tend to follow the lines*of force in the tube and be mainly right in front of the cathode. : To test this point the following arrangement was used. The cathode k (fig. 3) was an aluminium disk with a hole at the centre through which the Canalstrahlen passed ; after passing through the tube these rays fell Fig. 3. on a copper plate ¢ rigidly attached by an arm to the cathode but insu- lated fromit. The cathode floated on the mercury in a barometer- column, and by raising or lowering , the level of the mercury different regions near the cathode could be brought opposite to the end of the side-tube T; at the mouth of this tube there was an insulated metal plug with a hole bored through it. The tube passed between the poles of a powerful electromagnet of the Du Bois type ; a willemite screen was fastened to the end of the tube: the anode was at A. Starting with the cathode in such a position that the axis of the hole in the plug passed through /, the luminosity produced by the positive rays above the cathode, it was found that rays of positive electricity passed down the side-tube; gradually raising the cathode, these rays remained until the plane of the cathode just got above the opening in the plug, when they disappeared. On raising the cathode still 364. Dr. J. W. Nicholson on the Scattering further, the rays were absent until the bottom m of the tube in. the cathode came opposite the opening, and the axis of the opening therefore passed through the Canalstrahlen, when they reappeared ; they became brightest of all when this axis passed through the part of the plate C struck by the Canal- strahlen passing through the tube. The fact that the rays were not visible when the slit was opposite the tube indicates that the rays are not mainly due to the metal plug getting charged negatively by the cathode rays and acting as a secondary cathode. We see from this that particles of positive electricity are shot off in all directions from the gas traversed by the Canalstrahlen. The results just described were ob- tained when the tube was filled with air or with hydrogen; other gases have not yet been tried. The intensity of rays emitted sideways is small compared with the intensity of those observed in front of the cathode in the preceding experiment, so that there must be considerable reflexion of the direct rays. This view is also supported by the fact that the velocity of these rays is not constant, but increases with the velocity of the Canalstrahlen. T wish to thank Mr. Everett for the assistance he has given me in these experiments. Cavendish Laboratory, Aug. 6, 1907. XXXII. The Scattering of Sound by Spheroids and Disks. By J. W. Nicnouson, D.Sc.,.B.A., Isaac Newton Student in the University of Cambridge*. W HEN a plane train of sound waves falls on a small spheroid or disk, formule expressing the scattering effect have been given by Lord Rayleight, who employs a method based on an analogy with potential theory. The formule are first approximations, holding only when the ratio of linear dimension to wave-length is very small. The deduction of more accurate expressions requires the use of harmonic analysis. This analysis has been given by Lord Rayleigh t for the case of the sphere, but the furthér exami- nation of the problem of the obstructing spheroid or disk does not appear to have been carried out. The object of this paper is to develop a suitable harmonic analysis, and to * Communicated by the Author. + Phil. Mag. Jan. 1897; Scientific Papers, iv. p. 305. t ‘Theory of Sound,’ vol. ii. § 334. of Sound by Spheroids and Disks. 365 obtain more comprehensive results for obstacles of other than spherical shape. The differential equation to be solved is of common occurrence in physical theory, and two important solutions have been given. Niven* has discussed the equation in detail in a general manner, but his treatment is not well adapted to problems of the ‘class here contemplated, which admit of a comparatively simple analysis. The same remark applies to an investigation by Maclaurin tf, which has little in common with that of the present paper. Maclaurin’s method is peculiarly appropriate to problems in which periods of a vibrating system are sought, but, like that of Niven, is unsuited to diffraction problems concerning small obstacles, mainly because the exact correspondence between solutions valid near the obstacle and at a great dis- tance is left undetermined to the extent of an arbitrary constant. In other words, the asymptotic expansions, at a - great distance, of the functions must be definitely known. The method of operators used by Lord Rayleigh in the case of the Bessel functions is here applied to a determination of these expansions. The initial reduction of the equation of wave-motion CUeaRer ie Os MoMA 2 CE) proceeds on the usual lines. Treating the case in which the spheroid is ovary, and writing c=pcosd, y=psin ®, SO se COSMA(e | UO) Me Ce vs (2) or z=ccoshacos 8, p=csinhesinB, where (a, @) are ellipsoidal coordinates in the plane of any section (defined by @) through the axis, the equation (1) becomes os + ey + cothe 2 ow + eee (cosech*« + cosec?p) & us Oz (oye) + @*(cosh? a—cos? B)ap== y) where w denotes ke. In the symmetrical case in which waves impinge along the direction of the axis, 0/O¢=0, and y== A (a) B (Bp), * Phil. Trans. 1880, p. 188. + Camb. Phil. Trans. 1903. Phil. Mag. 8. 6. Vol. 14. No. 81. Sepé. 1907. 2C 366 Dr. J. W. Nicholson on the Scattering where — + coth 2S +(w? cosh?a—rA)A=0 . (8) a’B ag t cot BS 3tO- w” cos? B)B=0;. . (4) the summation being for ie possible values of >, which have been determined by Niven from the consideration that must recur on moving round any confocal spheroid. They will here be chosen to make yf finite everywhere, the two ~methods being really equivalent. When o=0,r’\=n.n+1, n being a positive integer; and therefore when @ is small, A=n.n+1teo'?+6,o0'+....... Stead sl En) Writing cos B=p, and H, (z) for a typical function B(P), ail oN + 0%) =0. RG dp ne du H, is a non-hypergeometric type of zonal harmonic, and cannot be simply expressed unless @ is smal], a condition valid in this discussion. Calculation of the Harmonic Functions. Writing H,=P,(1+o°H,), and neglecting w', it is readily shown that Lait dp aoe 2 B=| | (u'—e.)E dun Thus (" ly ) gr eer ry In order that Ey may be finite when p= +1, 1—p* must be a factor of © —e€ , and therefore : 2 é&)=4, Ko(w) = — = : The iower limit has been ignored, for any value may be given to it, so far as the order w? is concerned. This indefiniteness is to be expected, and does not vitiate the harmonic expansion subsequently used, for it only repre- sents multiplication by a constant series in powers of @. In all subsequent work, the harmonics are all so chosen, for clear definition, that the lower limit may be ignored. The corresponding associated functions are then selected in accordance with these harmonics. of Sound by Spheroids and Lnsks. 367 To the second order of a, We 2 H,(u)=1- a Ss a) a Again, E(w) ae du ,(&— e, ” which can only be finite at all points if e,=32, leading to 2 @” 3 (ape EL Gli es Further, te dp Jeo +6 ie i OGne \, BW=| Ce —1) {oi 5 als a i ee and if 1— a is a factor of the numerator, ¢.= as 21 whence H,(u)=4(3u2—1) + Ee Gly) In the same manner, 2a €2 — 45, Hl (uw) = t(dp? ~34)— 599 ( 125W°—T5y?— 24). (11) In order to obtain higher approximations, it is only neces- sary to write, in the differential equation for the harmonics, He,.= iL a= wi, == oF, aa wG,, == wo K, Haha and A=n.n+1l €,0" ae 6,0" a5 K;,00° ain nnw® eee (12) The following results are readily obtained: i dp E r=| 1—p2.P (" (3 2—e,)] 1B ji dpe @ = Me dy eae EF SE P %& i, yrs ese a) Bre Se j Pelee n—*,) n dp c \ Lae ewer K,= 1—p?.P? | (u hao Gene Ken an) Pvdu, (13) and so on, the riod of formation being now obvious. The higher approximations to A, are obtained by making these expressions finite for all values of pu. 202 368 Dr. J. W. Nicholson on the Scattering Thus, quoting the results, ot Bat | dot Ue tog en0) ets 30° 6o A@°® Tee bY IST 5 05.625 Lie? (94et pegs hana piae a 23 Ne = 12 = ino? aot a8 Ay = 20+ qe + He Ob . . ° 0 . : (14) in agreement with the results of Niven’s general calculation. The first two harmonics become Qe 8 249 4 i ee etsy) wp 4 Ope + 20 p? Hy(w)=p— Oe +01. SO me N i) From the differential equation, it may be shown in the usual manner that mM fnu—m.ntm+1+o?.¢,—€,+0'6,—6,+ ee Weert! dpe a =(1—p?. H,H,’—H,H,’)-4. The quantities e¢, 6,... being algebraic in m and n, and Ee EE and \ithem Aseevatiee eee at p’=1, it follows! that when m and » are unequal | H,H,.de=0.. 7] es eaeaemens il Again s C21 28: elie Cr ee ah tt ee =S asain 5 + 5095 + a “a =;(1 3a" 267 a4 —! while to the second order, ‘ieee 44q* {Hee = 5{14 = Me For all important applications H;(~) may be taken as P3(#). - bo of Sound by Spheroids and Disks. 369 Expansion of an Incident Wave. A plane wave travelling parallel to the axis (z negative) of a spheroid may be represented by a velocity potential ro) — er= eOe., | bg TOMI t Weeds Ohi (20) where 0=ke cosha., Since 2 sin 8 —_—_— = eve dp, ve d and H 4° "ay 70H — He (wer, Therefore Rae x udp =2H (= ) cele Y l A toy OG Thus if o= a AnH, (4), then zA.{ Hi de= a anf igh bed G10) The function on the right will be called w,(a). It must obviously be a typical associated function satisfying the differential equation (3). A knowledge of these functions at once determines the coefficients A of (21). si d : : Writing D= Ie? and expanding sin @ as a series, l wD? 1D? wD ) sin 0 a= eae a ss Oe We) Ne G? wo Oe Ge wt a =1-G + +G(-3 457) +405 + 600 A (c cosh*e + 2 cosh?a+ = an w,(“)= tw cosh « eae ie 2-3 +5 cosh? «) + a (cosh! a 69 +2 cosh? a— aan) ze wale) = ( (1 —3 cosh? a) W3(a)=— 12 (cosh? B= cosa), ss se eee) these being the values when « is not great, that is, in the neighbour hood of the origin, at which the obstacle is placed. 370 Dr J. W Nicholson on the Scattering With the integrals of the squared harmonies the coefficients become A, = Lae ele 3 cosh? a) + wre at+2cosh?a+ ee 135 A,=woosha {1+ 5 (3—5 cosh? a fe (cosh! a 9a" 2 "9 +2 cosh? a) 0 ae (1—3 cosh? a) + ...... ; La? As=— 7p (cosh’a—5 cosh) + ... 2g le eee Associated Functions of the Second Type. It may be proved in the usual manner that a second solution of the equation (3) for w, is given by B n(a)=w, | - da Pe 42" | Wy itol oes 50 where £8 is any root of v,(8)}=0. In calculating the functions v, near the obstacle, we may treat 8 as approximately infinite, the integral between any two possible values of 6 being zero. meee vo(a)= | ue 4% (L+3 cosh? 2) { le sinh @ _ sinha w? (2143 cosh? a 8) sinh a = log coth 5 + = ( —6 cosh a+4—3 sinh? a log coth 5) An additive constant depending on § only is ignored, for the functions v, will all be subsequently differentiated. Similarly (4) =— oF 844 (cosh a.log coth 5 37) + 6 =(6 +5 cosh? a—11 cosh a+ 5 cosh? « log coth ;) } (25) on reduction, it being unnecessary to ignore any constant in this and subsequent cases. of Sound by Spheroids and Disks. onal v, and v3 are usually required to the first order only, and become 75) 4 4 oe) — a (1—3 cosh? a) da sinh a(1—3 cosh? «)? AS fe SRE sh aa ze — Ao? (3 cosh «+ 1 —3 cosh’ a log coth A) 7 ; oa 03(a) = Tats 4—Lcosh? a+ 15 cosh’ « —9 cosha. log eoth st The calculation of these functions rapidly becomes laborious, but enough have been found for our present purpose. Their first approximations are proportional to the values of Q, (cosh a), where Q,,(«) denotes the ordinary zonal harmonic of the second kind. Asymptotic expansions of Vy and Wy. At a great distance from the obstacle, or at all points if it be a sphere, v, and w, become Bessel functions. In fact, under these conditions, H,() may be regarded as P,,(u), and therefore | . Wn (a) =P,(75) ane which has the value oh Wy (a) =o / ace ak mene) where c= ccosh a, which is the major semi-axis of the con- focal through the distant point. Thus wy, admits the expansion u” 3 sin( @— =). LW Oe = tae Now the Bessel function J_,,_:(@), admitting an expansion 2 Z NTT’ — cos { 0— — wh 2) Silas ner 0 dé Satisnes: J l= a1! as.” 7 (U+8) > s=large positive integer, where the lower limit is the value selected for 8 in (24). 372 Dr. J. W. Nicholson on the Scattering Comparing this relation with that in (24) between um and w,, it appears that for a large argument Vv, (a) = a \/= J ini t(@), when a, and therefore @, is large. Accordingly, under this condition, ’ NIT aioe |b corresponds to the functions v, near the origin, with the same limits. The portion of the velocity potential representing the dis- turbance due to the presence of the obstacle must, at a great — kr — distance, be proportional to = , or, ultimately, to = Thus the appropriate function of « for such a diverging wave, associated with the harmonic defined by n, is Uc) = 6a — Ja (ce), |. ee ae Dee = nue COs ¢ (29) : . @ which, at a great distance, has the value me or sechia .¢ ecshe. a ane Expansion of the Divergent Wave. The divergent wave, corresponding to the incident wave 0) == Cre, whose expansion was given in (21, 23), is of the form V=>d, 4,(0,—-40(—)"w,)H,(u). . . (82) At the spheroidal obstacle defined by a= &, if perfectly rigid, 0 is se ae since there can be no normal velocity at the surface. Thus oO p— — )” =— 29 % 52 ("n to(—)"w )= SE: ee (33) where the values of A, appear in (23). The values of a, may now be calculated. I will denote log coth 5 oe UE ee of Sound by Spheroids and Disks. 373 ~ It will be convenient to write also M=coth €—L sinh & | (34) N=143 sinh? £31 coshf sinh’ gf’ 7 The final values of the coefficients become, after some reduction, a,=— = sinh?€ cosh f1-% — —..12 cosh? £+7+15L coshé sinh? “snl b = SC aie oe “= oy ech E 2 50 At" 141 sinh &—4 coth € m= 7 - — eink? E cosh &. (35) The next coefficient a3 is ef order oe , and those succeeding decrease continually by the factor wm. a) and a, are of the same order, but a, is two orders higher. The orders have been so reed that the result will be correct to order o*. Thus ae summation in (32) is readily found to be, to w*, a <= | (M sinh’ & cosh &+ sinh & cos @)e-*" _ ke? sinh? & cosh & { Ba ae: re eee 4—12cos?0 aaa 15 cos*6+54 cosh oO ON Te Nae ae k4*¢@ sinh & cos 6 | 5 eo 2 10 coth & | ee ; ~ 1507M cee | op ots yt (36) corresponding to an incident train ¢=e”. The functions M and N depend only on the eccentricity of the boundary, which is given by e=sech &. Thus l+e L= 5 logs, MyPage (1-2) log — Saha, Né=e(3—2e)—5(1—e) logs **. . (87) When the obstacle is spherical and of radius p, the corre- sponding result may be deduced by making ¢ zero, and & infinite so that oar ee (22) } j ike 374 Dr. J. W. Nicholson on the Scattering Retaining only the significant portions, M= =sech? & ae N= a bo sech? €, and finally ) : y= i se cee 03 Ve eu cos — 5 coe Je, (39) which agrees with on result " Tora oe. analysis by spherical harmonics and Bessel functions. This agreement extends also to the first approximations for the spheroidal obstacle. Prolate spheroidal obstacle of small ellipticity. When e is small, sinh €= “(1-§ a —.) | 2 Te ese (142) ee a 15e? Mea.) and to the first power of the ellipticity «= 5° eee 3 i | eats ot ,—tkr ce inaitca | este fend oe eh 2 —whr = H(1+5 cos 8 Je ANGIE) a one 5 C8 aye iP k “ae ne S p—vkr ka’ s Ges 83 21 2 2A i «3 ) —kr- 3 (a+: 5 COs 0) a 189 + 5 C088 — 91 098 Q- cos? 6 Je where a is the major axis. ea (4G Long thin blade. The effect of any thin obstacle placed with its length along the direction of propagation of the incident waves, may he estimated by considering a very prolate spheroid, in which Eis very small. If the greatest breadth is 2b, and length 2a, De b? ile on &= tanh ; au) & 4 b N ou” c=./a— =a (1- i2) i lie since — 1s small. a. of Sound by Spheroids and Disks. 375 Pighe SOF ='lop =2) ete CLL: Thus a OS ee (41) and ultimately, the first order effect is ee —ikr 49 y= a CePecseicat ia) ty.) 2 (42) the higher order being readily calculated if required. The effect is zero at the extremity nearest to the incident waves, and a maximum at the other. This was to be expected. Diffraction by an oblate spheroid. In this problem the.sabstitution p+4z=c cosh (« +48) may be employed. The equations so obtained for the harmonics and associated functions are identical with those for the case of the prolate spheroid, if the sign of ? be changed, and if (a, 8), in the latter, correspond to (a— =; p- ) respec- tively in the former. a ‘ L thus becomes, for the oblate spheroid, utan— cosech & + isz, and it is readily seen that s=0. The expression for the effect of an oblate spheroid on waves incident along the direction of its axis is then readily deduced from the previous case of the prolate obstacle. Hmploying now the notation L=tan~! cosech &, M=cosh & tan-! cosech €—tanh &, N=1—3 cosh? €+3 sinh & cosh? &.tan— cosech &, . (43) ‘it appears that, corresponding to an incident wave, d = Qe, there is a divergent system Ph aes =— a (M sinh E cosh 2 E+ Cos @ cosh £)e— ihr hic’ ue 2 RO ORD 1a) ties mE 2 Vert a 970- nh E cosh g(10N 6 cosh? E—15cos?9—48 nil 3co0s’ @ je (14 —5 cos*O+ ee . (44) a) ki? cosh Ecos@ 1507M 376 Scattering of Sound by Spheroids and Disks. Approximately spherical planetary body. If e be the small eccentricity of the axial section, tan-! cosech € = sin~‘e, and it appears that eM =sin-1e—e,/1—2& oN=3,/1—e sin“ e—e(3—e), . . . (45) and for small values of e L=e+ oY Dose: Bee M=- 2 = ele a Si Ar 4e hi Bee (14% 5 and finally, if a is the unequal axis, and e the ellipticity, hq? e ae ic — = p— thr —ur abs oF (1+ 7 088)e 3. ‘(L449 cose hia? =A; 22 cos 6 — ‘one 135 * 20 9 a eas 40 1 5 il See z (3, + 3 9 cose poe = (0) ae 90 2° Ae 2) a PeLO) Circular disk. The case of the circular disk may be deduced from that of the oblate spheroid by making the axis zero. Thus €=0, and ¢ becomes the radius of the disk. The result is 2 Wa ae Tea? Wa? 25 * 10 cos” 0) cos Oe 7 an) If the disk thickens towards the centre it may be roughly treated as an oblate spheroid of small minor axis 26, where 26 is the maximum thickness. Jn this ease, END OL ioe Me e=a(1— 6? ) L=- -— — — a oe Sees Logarithnuc Lazytongs and Lattice-works. and to the first order of b/a, 2 Kea? tha? iat SS ee a) gs. Ge wr d am 7 ( SN AOU oki, Coan kath 8 cos 4 me ea 2niecosy 1 = ee 27, + - =e or 2 yy: ip 45 (O70 90 att 9 4 cos’ f — 3-9 (48) Cos” a) When the incidence is oblique the analysis is much more cumbrous, and there is little interest in carrying it beyond the approximations given by Lord Rayleigh in the paper cited above. XXXII. Logarithmic Lazytongs and Lattice-works. By Tomas H. BLaKkEsLey *. .) (ae point of view in which the Equiangular Spiral is usually regarded is that implied in its name, viz., the curve which makes the same angle with its radius vector, dé dr == RN 22. I fe Té is rather from what I may perhaps call its polygonal character that I shall present and apply it in this paper. By this I mean that it is a circumscribing curve to polygonal figures following simple laws. If a series of equai straight lines form a consecutive number of the sides of a regular polygon, the circumscribing circle is absolutely determined. But if those straight lines, still maintaining the equality of the angles between any consecutive two, g in magnitude form a geometrical series, the circumscribing curve will be the equiangular spiral. According to the value of the angle between consecutive lines, one may speak of the figure as a regular logarithmic entagon, hexagon, octagon, &c., and more generally as a Pp sou, ) 5S ’ bg regular logarithmic polygon. The regularity ‘consists in the equality of the angles between the lines, and in those sub- tended by them at the pole of the spiral. Consecutive chords are those straight lines which form consecutive sides of a logarithmic polygon. * Communicated by the Physical Society : read March 22, 1907. 378 Mr. T. H. Blakesley on Logarithmic — Some geometrical matters more immediately arising from this view of the curve may be introduced. The problem of finding the pole when two consecutive chords are given is solved thus:—Let AB, BOC, be the consecutive chords given. Complete the parallelogram, and let BD be the diagonal through B. Make the angle BCP equal to the angle DBC, and make the angle ABP equal to the same angle. Then P is the pole of the spiral in which AB, BC are consecutive chords. As an alternative to the setting off of one of the angles BCP or ABP, the angle BAP may be made equal to DBA. Or, as it may be shown that the product of PB. DB is equal to that of AB. BC: BP may be easily calculated from the data, viz., the values of AB and BC, and the angle between them. If one of the two chords (say BC) is maintained in position, but the other BA is made to turn round B, so as to vary the angle between the chords, the pole P will describe a circle whose centre is in the line CB, produced if required If @ is the angle between the two consecutive chords externally, the characteristic angle of the spiral («) will be given by fan a ana = ne BC : °- AB In any cases therefore in which a C has the same value, the spirals are similar. log AB It follows that, in any mechanical construction of linkages sits BC &c., if we can keep AB constant, but can at the same time cause 0 to vary, we have the power of changing a, that is to say the one thing which settles the character of the equi- angular spiral. Lazytongs and Lattice-works. 379 If now two straight rods or lines, AB, CD (fig. 2) are taken in one plane, and meeting in EK (whether in their actual lengths as shown, or in their geometrical productions, is immaterial), and so conditioned that A, C, B, D lie in one circle, then the products of their segments are equal or CE. HD=AE. EB. ion ——— It follows that E remaining the same for both rods A, C, B, D will always lie on a circle, whatever be the angle between the rods. If DE=n.AEH, and CH=m.AE. then the condition is fulfilled if HB=mn.AE ; n and m may have any values whatever. It will be convenient for geometrical reasoning to imagine or describe the straight lines AC, CB, BD, DA. Then the triangles DEB, AKC, are similar, and DE EB: BD 2: Aw: HC : CA +2: 1. Similarly regarding the triangles CHB, AED, they are fonlare and © > WB) :-BC s: AK: HD; DA :: m : I. Call the angles ECA, HAC, HAD, EDA, a, 8, y, and 6 respectively. Then also the angles HEBD, EDB, ECB, EBC are x, 8, y, and 6 respectively. Now DB may be derived from AC, as regards direction and magnitude, by allowing AC to revolve first through ACE or « in one direction, and then through EDB, or 8 in the opposite direction, and by reduction in the ratio 1: n. Thus DB makes with AC the angle «—8, and DB=n. AC. Similarly CB makes with AD the angle y—6 and CB = 7 AD Se Now suppose another pair of rods DF, BG jointed at H, and similar to the first pair in all respects but bearing the ratio to them of n : 1, jointed on to the first pair at B and D. 380 Mr. T. H. Blakesley on Logarithmic All the lines in this, which may be called the second cell in the direction », including those of the circumscribing circle are homologous ina ratio n: 1 with the corresponding lines of the first cell, and the angular displacement relatively to the first cell is a—f. To the points FG may now be connected a third cell, constituted in a similar manner to the second, and so on indefinitely. 7 To AC may be connected a similar cell bearing to the first cell the linear proportion of 1: 7 and to this another, and 3 : ; ; ete) | so on indefinitely in the direction = Such a line of cells may be called a logarithmic lazy- tongs. It is clear that all such points as A, D, G lie upon an equiangular spiral, the tangent of whose characteristic angle is equal to ; eo og n As all the cells of a series are similar, any motion involving the increase or decrease of the angle between the bars of one cell, will be accompanied by the same change in angle in al! the cells. The sides AD, CB may also have cells attached to them, the same rules as before being observed. m will take the place of n in the change of scale and y—6 the place of «—8 in the change of direction. It is to be pointed out that if two cells in the m direction be applied to BC and BF, the other adjacent points of the two cells will coincide. In other words, the cell on BF may be considered as derived from the first cell either by one move in the n direction followed by another in the m direc- tion, or by one in the m direction followed by a second in the n direction. Whence it follows that the whole of a plane surface may be occupied by a plenum of cells forming an infinite lattice-work, in which, if the angle between the cross- bars of any one cell is changed, an equal change takes place in that between the cross-bars of any other cell. In the m direction the tangent of the angle characterisjic of the spiral through such points as A and C is equal to ye loym- There is a common pole for both the m and the spirals. If for the sake of easy description we liken the plenum of cells so obtained to a chessboard, the rocks’ moves would on Lazytongs and Lattice-works. d81 take place either in the n na ection or in the m direction, or in the z direction or in the dir ection. nr But the bars AB &e. which lie in a would then be called a bishop’s move, would also have their extremities in an eguiangular spiral having the same pole as the other sets of spirals. The angle between successive chords (external) will be in this case a—8+—6, and the change ratio of the chords mn, so that the angle characteristic of the spiral will have for its tangent a—B+y— 6 log smn Cireles and straight lines are only limiting cases of equi- angular spirals. They may therefore be awaited among the cases arising from changing m,n or the angle between the ~ eross-bars. If n=1 the n spirals become circles, and since in that case y=6, the m spirals become straight lines. If m=1 the m spirals become circles and the spirals straight lines. If both m and n are equal to unity, both systems are straight lines. If mn=1, in which case AB is bisected in H, there is no change of scale along the bishop’s move in the direction AB. In consequence the spirals through AB are circles. Similarly if m=n CD is bisected, and such lines lie on circles. Such lines as AB, BK, &c. may under some circumstances lie in a straight line. The displacement in angle of such lines is (2 -@B+y—5S). If this is equal to zero ary= B+6 Thus the circumscribing circle must have AB for a diameter. Therefore as D and C are both on that circle CD must either be equal to AB, in which case the two chords bisect each other (m=n=1), or CD is less than AB. It is therefore only the longer of the cross-bars which, by the variation of the angle between them, can come into a ‘straight line. The longer cross-bar is also that one which is divided most unequally, since the product of the segments is the same in the two bars. Phil. Mag. 8. 6. Vol. 14. No. 81. Sept. 1907. 2D A eeeeuy XXXIV. Lonization by Spraying. By A. 8S. Evz*. S's CE Lenard discovered the presence of negative electri- fication near water-falls, much work has been done and published on the generation of electricity by the splashing of liquids, and by bubbling gases through them. It is not necessary in this paper to refer to these investigations, because an excellent summary of them is given by Professor J. J. Thomson in ‘The Conduction of Electricity through Gases,’ second edition. ‘The electrical effects due to spraying appear, however, to have received little or no attention +. Last year, whilst making some experiments with an Ebert apparatus for measuring the ionization of the atmosphere, I blew, with an ordinary garden hand-sprayer, very fine mist all round the apparatus. The number of ions detected in the atmosphere was thereby increased by many thousands. Negative ions were in excess of the positive, and their ratio was about 1:4. This crude experiment suggested the use of the small sprayers, made of glass, sold by Beckers, shown in figure 1. Fig. 1. >>> > 'cm A steady current of air, filtered through cotton-wool, enters the horizontal conical opening, and draws the liquid up the vertical cone, which has a small hole near its base. With an air-current of about 120 ¢.c. per second, the liquid drawn up * Communicated by the Author. + H. A. Wilson used a sprayer to prove his important result—that the amount of electricity which can be transported by substances in the form of vapour equals the amount required to electrolyse the same amount of salt in a solution. Phil. Mag. July 1902. On Ionization by Spraying. 383 is broken vehemently into a very fine spray, and air and spray pass together through about 50 cms. of tubing into the testing vessel. An ordinary two-chambered electroscope was used, as drawn to scale in figure 2. A rather heavy Dutch-metal Fig. 2. —, idocm leaf was used (and observed by a microscope) when charged between about 500 and 300 volts. To obtain a steady air-current ordinary foot-bellows, as used for glass blowing, were employed. The air was pumped into an iron boiler (0°1 cb. m.), and it passed thence to the sprayer and to a manometer used for regulating the current. Some preliminary tests proved the following :— (1) When the sprayer contained air and no liquid, the 2.D 2 384 Mr. A. S. Eve on natural leak of the electroscope, about 0:4 microscope division a minute, was not affected by a strong air-current through it. (2) That the spray from liquids did not destroy, or impair, the insulation of the gold-leaf system and central cylinder. (3) That a large number of ions, both positive and negative, were generated by spraying, and the total electricity con- veyed by either could be measured by the electroscope. (4) That about 50 per cent. of the ions from water spray were present after passing along 13 metres of glass tubing (6 mms. in diameter) before entering the electroscope ; or along 3 metres of tubing 2 cms. in diameter. (5) That the ions were entirely removed by a cotton-wool filter, placed between the sprayer and the electroscope. (6) That under the conditions of the experiments, not more than 5 per cent. (and generally less) of the ions passed from the testing chamber of the electroscope, if charged, into a second instrument similar to the first. (7) That distilled water always gave rise to more ions than tap water taken from the city supplv pumped from the River St. Lawrence. (8) That distilled water and tap water always gave more negative than positive ions, the ratio being from 1:2 to 1-6. The same result was found for ether. (9) In the case of spray from substances such as chloro- form, amyl, ethyl, benzyl, methyl alcohols, methyl iodide, acetic acid, acetone, aldehyde, and amyl acetate, the number of positive ‘and negative ions were equal for each substance. These substances gave about twice to four times as many lons as distilled water, ‘the conditions being identical. (10) The addition to water of salts, such as caustic soda, sodium chloride, sea salt, sodium carbonate, or of acids such as hydrochloric or sulphuric, reduced the number of ions to lower values than for water alone. (11) That liquids such as benzine, rhigoline, phenetol, cineol, toluene, turpentine, even the most. volatile, gave but few ions, compared with water. (12) Mercury gave no effect that could be detected under the conditions of the experiments. Some of these results for spray might have been predicted from the work of Lenard, Kelvin, J. J. Thomson, and others, in their investigations of the splashing of liquids or the bubbling of air through them. Some of the above obser- vations, such as 9 and 11, appear to be new. In figures 3 and 4 are given a few of the numerous curves obtained for various liquids when the air-current ran for a Tomzation by Spraying. 385 quarter of a minute, during which period about 1800 c.c. of air entered the electroscope, whose volume is approximately Fig. 8. a oe ECs ACh ec a CIEL NESS 2 Q $ “Potential Tonization. Mm w © 2 4 minutes 20,000 e¢.c. Hach curve represents a single actual obser- vation; the abscissee are minutes, and the ordinates, measured from the top line, are the microscope readings of the gold leaf, with the natural leak deducted. In order to save space, and for the sake of clearness, each curve has its origin at its upper end. The fall of potential during the first quarter of a minute of pumping is ruled a straight line, because the conditions are not steady during that period. It will be seen that the curves for positive and negative ions for acetic acid are identical. The same is true of amyl alcohol, and ethyl alechol, so that it is not necessary to publish more than one 386 Mr. A. 8. Eve on curve for these. But in the case of ether. and of water, the curves for positive and negative ions are similar in type, but unequal in magnitude, proving that the number of ions are unequal. Again, the first four curves from the left are somewhat similar in character, and show that the greater part of the ions are drawn to the central cylinder during the time the air enters the electroscope ; hence the curves bend sharply, and the effects end in two or three minutes, after which the curves become horizontal straight lines. These curves are representative of liquids which give rise to mobile ions. But in the case of ether, fig. 3, and still more of benzyl alcohol, fig. 4, the initial quarter-minute fall is but a small fraction of the whole; hence the curves bend gradually, and. the fall of potential can be observed for more than ten minutes before the electroscope returns to ils natural leak. Therefore some of the ions are extremely inert, and move very slowly across the electric field. These differences in character are indicated in the following table, in which the percentage falls of potential, during the periods stated, are compared with the total falls. | TABLE I, Percentage falls of potential. Water, | Amyl | Ethyl | Acetic | : | Ether. | eer7 | Alcohol. | Alcohol. | Acid. | | Aleohol. During first} min. 91-4 81 73 62 26 14-7 second dmin.|. 57 | 157 | 21 26 30 17°6 aoa | 2S | Dy) 8 85 | 20 | Tre remaining time. 0 | 8 16 35 tat 50 It is easy to calculate approximately the velocity of the slower moving ions, treating the electroscope as if it consisted of two long concentric cylinders. The slowest ions of benzyl alcohol have a velocity of about 10-* cm./sec. in a field of 1 volt/em. They are therefore large inert ions such as Langevin has found in the atmosphere, and Giese in the gases from a flame, and Aselmann by the splashing of salt water. An important result may be deduced from these curves. Since their shapes and sizes are identical for positive and negative ions, in the case of most liquids tested (water and ether being notable exceptions), we must conclude that the positive and negative ions are similar in mass and constitution. It does not appear that one set of ions consists of liquid and Lonization by Spraying. 387 the other set of air, but both must consist of the liqiud, or of liquid and air together forming clusters of molecules and carrying a charge. In this respect also, my results are in agreement with Aselmann’s, who found that the large slow ions, whether positive or negative, consisted of masses about equal i in size, all consisting of salt solution, or of salt solution and air together. In figure 5 are drawn more curves, obtained when the air- MAEESLAAIT F MEA EAE eee > ° POTENTIAL | I delh y Alice He MINUTES current carried spray to the electroscope for half a minute. The curve for chloroform is given both for positive ions, indicated by dots, and for negative, by crosses, corresponding to negative and positive charges to the central insulated cylinder. This curve emphasizes the similarity of the two kinds of ions. The curve (fig. 5) for phenetol is typical of those obtained for benzine, toluene, and turpentine. Their total ionization effects are small compared with water. It is not possible to give precise values to the relative ionizing powers of different liquids, because the numbers obtained must vary with the nature of the apparatus used, and the strength of the air-current applied. But I have made a large number of observations, and taken the mean values, and the results are shown in Table II., with the number of positive ions from distilled water as standard. With different experimental conditions these numbers will appear on a different scale, but the general order would not be materially different. I have endeavoured, without great success, to 388 Mr. A. 8. Eve on ascertain the underlying cause of the relative ionization powers of different liquids. Surface tension, and the extent to which liquids are volatile, do not appear to be main factors. Some liquids evaporated so rapidly that they froze on the vertical nozzle of the sprayer and stopped its action. When working with ether, or chloroform, or benzine, or methyl] iodide, the sprayer needed constant refilling. But water or benzyl alcohol will last for days or weeks. The more volatile did not differ in their ionizing powers from the less volatile sub- stances of the same character. Benzine gave low values, ether high. The amount of liquid evaporated did not seem to be an important factor. ‘The number of ions generated is a function of the air velocity, and of the time of its con- tinuance until a maximum is reached. Again, when the sprayer, containing water, was placed in a vessel of water, which was heated from the room temperature to boiling-point, the change did not affect the ionization due to spraying. The small values obtained for the benzine group suggested di-electric capacity as the main cause, but the figures given in the left column, Table II., taken from Drude, vol. xxii. p- 267, Zeit. Phys. Chem., do not entirely confirm this view, water and chloroform being out of place. TasuE II. Relative Ionization. | Dielectric. Substance. | Negative. | Positive. | ieee ion we mae Ec on pee BE | een Merctiny: se aietea a mccecaue es Reea(0) | 0 | ORS Toluene Wiis Oe ee eae | 02 ‘02 Buhigolime ys. assess eeccneees | ‘O07 ‘03 Carbon bisulphide ............... OT Og 2:0 IBENZING janccee rutttie : Again with spray from methyl alcohol, and with ¥ rays, the readings obtained were in the following proportions :— Sy Vy ie) COLO eee ne ae seen 114 \ J 65 Ey RAYS, ALO Et gctcue lh oan, D1 PRAY AO FAVS: | ce evec-- oxy. 140 It will be seen that the effects of spray and y rays together are almost the sum of their independent ionization. 390 Mr, A. 8S. Eve on Recombination of Ions. In order to form an estimate of the rate of recombination of the ions, various lengths of glass tubing, 6 mms. in diameter, were inserted between the sprayer and the electroscope. The results obtained for positive ions from water spray were, to an arbitrary standard, as follows :— Leneth of Tubing. Tonization value. 0°85 metres 100 3°62 92 6°78 79 9°90 60 13°00 49 Thus half the ions disappeared during the three seconds in which the air-current traversed the 12 metres of tubing. With tubes of this small diameter, 0°6 cm., many of the ions must vanish, not by recombination but by contact with the sides. ‘The thin tubes were replaced by 3 metres of glass tubing, 2 cms. in diameter. The loss due to traversing this volume was 50 per cent., so that half the ions disappeared in eight seconds. When the spray was introduced for one minute the losses of potential during successive minutes, including the first, were 47—9—-9, without the 3 m. of tubing, and 19--8—-8, with the 3 m. of tubing. The loss in the tube, therefore, occurs among the more mobile ions, since the catch during the second minute is the same in both cases. As the ions of benzyl alcohol were the slowest compared with those from all the liquids tried, I have made some ex- periments to find out how long these ions may be stored without disappearing by recombination or by diffusion to the sides of the containing vessels. For example, Giese found that the gases from flames could be stored for six or seven minutes and still retain their conducting properties. | If the spray from benzyl alcohol was passed into the elec- troscope for a quarter of a minute, we have already seen that the ions, whether positive or negative, move in a most leisurely manner, and are not extracted until about ten minutes have elapsed. If the air and spray traversed 3 metres of glass tubing, 2 ems. in diameter, there was a loss of 30 per cent. of ions ; corresponding to a loss of 50 per cent. for the ions from water spray, as stated above. This proves that the ions of benzyl alcohol are slower to recombine than those Ionization by Spraying. 391 of water, as may be seen also from the curves in figs. 3 and 4. Another and better method may be adopted. The ionized air may be introduced into the electroscope, which is initially uncharged, and after a stated period the charge may be given and the conductivity of the gases then determined. The results obtained were very surprising, and indicated that the spray from benzyl alcohol contained ions which could be stored for considerable periods. The ions were in all cases removed in ten to fifteen minutes after the charge (whether positive or negative) had been given to the central system of the electroscope. Total fall of gold leaf | Charge given less corresponding _ Per cent, natural leak. Initially | 44 100 after 2 minutes. 23 52 ae af | 17°5 40 5, LO as jie} 25 | lin aa LO) E 8-0 18 | sie) i | 6-4 14 be) 60 99 2°8 | ‘3 120 a 15 or | Thus the ionization may be measured after the ions have been stored for two hours in a vessel where there is no electric field. : In a paper to this magazine (September 1906) it has been proved that the y rays from one gram of radium generate in a zine vessel at one metre distance about 3x 10? ions per c.c. per second. I placed 11 mg. of radium at a distance of 1 metre from the centre of the electroscope. The radium was screened with lead so that the § rays were intercepted. Allowing for the partial absorption of the y rays by the lead, there would be 3300 ions per c.c. per second generated by the y rays, and these, being completely removed by the electric field, gave a gold-leaf deflexion of 24 divisions a minute. This is a simple method of calibrating the electro- scope. Now when the spray from benzyl alcohol is intro- duced into the electroscope the entire removal of the ions, from the time of their formation, over the same part of the scale is equivalent to a fall of 84 divisions. Hence the number of ions initially was 11,200 per c.c. throughout the electroscope. The corresponding value for water spray is about half this, and is in satistactory agreement with the order of the effect produced by a hand sprayer and measured D92 . Mr.. A. S. Eve on by an Ebert apparatus, for the mean value was then 5900 ions per c.¢. , The number of ions after the stated intervals can now be calculated and a curve plotted, shown in fig. 7. The number Lie hc /2000 BENZYL ALCOHOL IONS PEGG /oooo } €c0o 6000 | 4000 2000 MINUTE & of ions satisfy, approximately, the well known recombination 1 1 5 e e e formula — — — =at whence a, the coefficient of recombination, n N equals about 4x 10—7, instead of its usual value 11x 10—%. The loss by recombination must actually be even slower than here appears, because no allowance has been made for dif- fusion and loss of charge to the sides of the vessel. It will be noted that the assumption has been made that the ions carry the usual ionic charge 3°-4x10—10. The curve, fig. 7, is an hyperbola drawn from theoretical calculation. The experimental points show fair agreement. Electrometer Experiments. In order to test the accuracy of these deductions made from experiments with an electroscope, some observations were made with an electrometer. Dr. Bronson was kind Ionization by Spraying. 393 enough to join with me in this part of the work, and he took meastirements witb his direct-reading electrometer*. The instrument is particularly well suited for this purpose, because a constant aifterence of potential is maintained between the imner and the outer cylinder of the testing vessel. To make certain that an insulation leak was not Vitiating the results, a guard ring was used. A testing vessel, as shown in fig. 8, was first employed. Fig. 8 fi (aL ET re 49 C77} The outer cylinder was insulated and kept at a potential of 550 volts. The electrodes are denoted by J, //, IJ in the figure. If J and J/ were put to earth and J/7 to the elec- trometer, and air with water spray passed rapidly through the testing vessel, no current was detected by the electro- meter. Hence all the ions were extracted from the air by Land f/. It £ was joined to the electrometer, the current, for constant spraying, reached a maximum of 170 ee ions. If JZ was put to earth and // connected to the elec- trometer, the current was measured by 16 scale-divisions. Hence about 10 per cent. of the ions were driven past the first electrode without capture, but ali ions were remov ed by. the two electrodes together. In these experiments the air-current was not introduced for a definite time, as with the electroscope, but the current was continued until a steady reading of the electrometer was obtained. The maximum was venerally reached after one or two minutes. For this reason we must not expect the value obtained with the electrometer to coincide with those found by the electroscope method. When the air-current was abruptly stopped the needle returned steadily towards its new position, reaching it in one-half to one minute. After that period less than one per cent. of the maximum value remained. When / and J/ were connected with the electrometer and * Rutherford’s ‘ Radioactivity,’ 2nd edition, p. 104. 394 On Lonization by Spraying. the outer cylinder was charged to 360 volts, the following results were obtained :— TABLE ITT. Electrometer. | Potential difference 360 volts. | ss. = a7 Es || +ions, | —ions. Ratio. Water... ee 1:3 1D slaVs\eye yeeros 420 730 1% | Chloroform sO ll 120 10 | Acetic acid ... 600 630 10 nels CNG eaeeeaee | 3 || 2 These results agree in the main with those found with the electroscope. The negative ions from ether and water are in excess of the positive, and to the same extent as before. The low ionization of benzine spray is again remarkable. The figures for chloroform are lower in proportion than those found with the electroscope, but I have found chloroform rather erratic, possibly on account of impurity. The liquids used have not been dehydrated, and therefore there may be present some of the mobile ions due to water. I have not yet discovered the cause of the inequality in the number of negative and positive ions of water. It does not seem pos- sible 10 attribute it to the different velocities of the two ions. The inequality of the number of negative and positive ions in the atmosphere, as detected by Ebert’s apparatus, is well known. On another occasion with a different testing vessel the results obtained were TABLE LV. +ions. —ions. Ratio. | ae ee es lau a ee Water | enc se igs ol 49 1:3 uginorsoy ye ate oem 235 295 1:25 | Amyl Alcohol ... 490 | 470 ei | Ethyl Alcohol ... 730 750 1-0 Wineol! ete. eee too small to measure In this case it will be seen that the ionization from amyl alcohol was 10 times as great as from water, and from ethyl alcohol 20 times as great. EHeperimental Mathematics. 395 This paper is intended to give a general view of the phe- nomena connected with ionization by spraying. It is clear that much more remains to be done in obtaining more accurate relative values, and in determining the sizes and velocities and rates of recombination of the ions from various liquids. The effect of using various gases in place of air has also to be determined. Perhaps other workers miay find the field interesting and help to throw light on the subject. If large inert ions may in some cases be stored without entire loss for more than an hour in a closed vessel, it is possible that they may exist fora long period in the open air. Thus the “ gros” ions, found by Langevin, may have an important influence in meteorological phenomena. It is important to use liquids free from impurities, and I am grateful to Professor H. Walker for his kindness in pro- viding me with such. I have to thank both him and Dr. D. McIntosh for advice in matters relating to chemistry. XXXV. Hxperimental Mathematics. ig wis AN OC EIEN: 1. A)” ATHEMATICS is an experimental sclence, just as much as Chemistry or Physics.” This very suggestive statement was made, about a year ago, by a friend who held that everything on earth was done the wrong way, and the teaching of mathematics in particular. Being greatly struck by + so original a view, I resolved to give it a trial, and selected e for my purpose, as being the first thing to which I could not attach some visible, material meaning. The method of investigation I now place before you, in the hope that it will be of “interest, not only in itself, but especially as affording a graphical tr eatment of logar ithms, which may be of use to those engaged in teaching. Here is an instrument, for dr awing logarithmic spirals, which is shown diagrammatically i in fio. 1. It consists of a metal boss, with a ‘compass-point at its centre O, and has a smooth steel rod AB sliding freely through it. To one end of this rod is connected a sharp- edged roller D, running in a carriage C, and capable of being clamped at any desired angle with ‘AB by means of a milled nut. Two small guides are added, to keep the carriage upright. By way of illus- tration, I will clamp the roller at 45° to the rod, place it at unit distance—say one inch—from the compass point O, and pressing it firmly into the paper, push it forward, thus describing the curve which will form the main subject of * Communicated by the Physical Society : read March 22, 1907. 396 Mr, E. A. N. Pochin; our consideration. This curve is, of course, a particular case of the equiangular, or logarithmic, spiral, and is commonly known as r=e®, ewe The spiral is again shown in fig. 2, starting from the point 1, and passing through the points marked 2, 3, 4, &c., at which Eaperimental Mathematics. 397 the distance from the pole O is respectively 2, 3, 4, &c. inches. Here also are several sectors of cardboard which have been cut out to fit the various angles 102, 103, 104, &c., and are therefore the Naperian iogarithms of the natural numbers. By means of these sectors, it may be shown experimentally that if we add to the angle 103 the angle 102, we arrive at the angle 1O6—(3 x 2=6), and, conversely, if we take away from the angle 108 the angle 102, we shall be left with the direction 04—(8+2=4). Without further examples, it may be demonstrated in the most general way, that by adding the angle under any one value of the radius vector to that under any other value, we obtain a direction giving their product: or by subtraction their quotient. Evolution and involution follow naturally. For instance, to find the value of 5'° : we divide the angle 105 into ten equal parts, and then by taking 16 such parts we get a direction which at once gives us the desired result. By ordinary arithmetic even this simple calculation is quite impracticable, and it is given to show how the real utility and importance of logarithms may be impressed on the student. The properties mentioned above are common to all curves drawn with this instrument, and not merely to the special case in which the roller is set at 45°. Instead of working direct from the curve, by means of cardboard sectors, or compasses, the values of the various angles may be expressed in terms of some standard angle, such as the radian, and the results printed, in tabular form, for future reference. Here is a protractor, graduated in radians, which we will apply to fig. 2, and by means of which we can read off the values given below. Length of radius vector Corresponding angle in in units of 1 inch, radians, if 0 2 "693 3 1:098 4 1°386 5) 1°609 6 eM a | 1°946 8 | 2°079 9 . ZO 10 2°302 &e. &e. This constitutes a table of natural logarithms, which may Phil. Mag. 8. 6. Vol. 14. No. 81. Sept. 1907. 2 i 398 Mr. E. A. N. Pochin : be used in the ordinary way for making calculations. The highly accurate values, usually published in book form, are not obtained by direct measurement, but by an indirect process which does not at present concern us; and their use is chiefly restricted to those who desire great precision. For the most part, however, we do not require this extreme accuracy, and continue to work direct from the spiral. The radial lines are cut off to a circle about O, and the appropriate length of each is written against it. Two such circles are connected by a pivot through the poles, and constitute one form of the familiar “ watch calculator,” by means of which the desired angles may readily be added or subtracted:— here is a model of this useful appliance. It should be noted that the erreur are not necessarily made from the spiral in fig. 2, but are, like this model, more usually mae from a Ful drawn with the roller set at about 84°—(tan7! 27/log. 10). In this position, the roller will be we inches from O, ee sweeping through 360°. An im- portant advantage arises from this change, to which we shall refer. By rolling one of the dials along a straight piece of wood and copying off the graduations, as each comes into contact, we obtain a straight logarithmic scale; and two of these, when combined, form the device known as a slide-rule. Analysis. So far, the accuracy of our conclusions has a purely con- structional basis, and it is very desirable to apply the crucial test of analysis, and satisfy ourselves that no residual errors exist, which might have eluded our most careful measurements. Fig. 3 is a reproduction, on a larger scale, of the spiral shown in fig. 2. The angle AOe has been drawn equal to one radian, OA being one inch, or unity. This angle is supposed to be divided into one million equal parts by lines OB, OC, OD ... which meet the curve at B, C, D.... Also Ab is drawn perpendicular to OB, Be to OC, &e. Now, from the mechanical construction of the curve, it is clear that the spiral is, at all points, uniformly inclined at 45° to the radius vector ; for the tracing roller was clamped at that inclination to the steel rod. It is also evident that we may, without material error, regard the portions of the spiral AB, BC, &e. as straight lines, and also consider OA equal to Od, ‘ke. Accor dingly. OA OB=06+0B =OA + Ad. Experimental Mathematics. 399 But Ab=OA multiplied by the circular measure of the angle AOB, which is 1/10000U00. Hence writing m to denote one million, we have OB=1+41/m. Similarly OC=OB+ Be. But Be—=OBX Vim: Therefore OC=OB(1+1/m)=(1+1/m)?. Fig, 3. In this way we can write down the values of the radius vector as it proceeds from OA to Oe :— The radius vector is When the angle is iL 0) (1+1/m) 1/m (1+1/m)? 2/m (1+ 1/m)? 3/m (_+1 /m)™ ee m/m, or 1 By calculation, the value of (1+1/m)™ is found to be 2:7 .., and by direct measurement with a foot-rule we arrive a! 400 Mr. E. A. N. Pochin : at an identical result. This expression is usually denoted by e, and accordingly (1+1/m) =e, (1+1/m)?=e/", &e. The previous list may therefore be written as follows :— The radius vector is | When the angle is 1 0 eum | 1/m Galen | 2/m e3/m 3/m | ic eae | Ma de cis | mm, or 1. We have thus secured a most important quantity e, which affords a simple index relation between the radius vector and its angle. Hence we can, as before, multiply together any two values, such as e/™ and e/™, by adding the angles a/m, 6/m, and reading off the value ot the radius vector ¢%/"+4™, which is both appropriate to the angle a/m+6/m, and at the same time, the obvious value of the product. And since this analysis is applicable throughout the spiral, we have shown both experimentally and analytically that log A+ log B = log AB. 669 é. Perhaps we may with advantage pause one moment to consider the full meaning of e. It is usually defined as the sum of 1+1+ 5 oo : Vai , and though undoubtedly correct, I would suggest that this is not really e, but only a method of calculating e. ‘There are, for example, many ways of evaluating 7; but surely our conception of 7 must always be the visible circumference over the diameter, and not an infinite series. In the same way the student might, I think, get a clearer view of e by regarding it as the result of unity growing, in a special manner, through uvit angle: as the amount of £1 at compound interest after one year, interest being paid continuously at the rate of one millionth of the capital per one millionth of the time, or even as the first great milestone along the 45° spiral, with “2-7 miles from London” painted on it in big letters. Change of Base. Possibly you have never seen a modulus. Here is one made of cardboard. Itis called ‘* the modulus of the common Haperimental Mathematies. 401 system,” and is a sector having an angle of 2°302 radians, divided into tenths. If we apply this modulus to the natural logarithms in fig. 2 it will transform them into common logs, and we are able to read off their values, just as we did with the protractor graduated in radians. In adopting a unit angle 2°3 times as big as before, we make all angles measured by it appear 1/2°3 of their previous value. This affords a visible explanation of the method given in text- books for changing from the base e to the base 10. The beginner will doubtless ask why we take the trouble to convert natural into common logs, and the model of the watch calculator, which you have seen, provides a satisfactory answer. After making half a dozen calculations (2x3, 4x5, 6X7,... ) it will easily be grasped that AER Da PAS. LAU, °301 of a revolution. log 20 =1 revolution + °301 , a log 200 = 2 revolutions + °301 45 $5 Had the dials been derived from fig. 2—the natural system —there would be no recurrence, and we shouid be unable, in this simple manner, to adapt a small range of logarithms to cover an unlimited range of values. The state of affairs might be compared to a clock in which the small hand moved over 2°302 divisions during an hour. Instead of obtaining common logs by transformation we may entirely discard the natural system, strike out a new course, and with a fresh setting of the roller describe the spiral, shown by the dotted line, in fig. 2. This curve meets unit angle—one radian—in the point X, distant 10 inches from O, and yields logs to the base 10, by direct measure- ment with the standard protractor graduated in radians. Along this curve, e occurs at an angle of 1/2°302 radians, thus proving experimentally that log,10 is the reciprocal of log@ice. The value 10 may be reached by growing from unity, either along the e spiral at the standard rate for 2°3 radians, or along this new curve at 2°3 times that rate through one radian. We may regard this alternatively as the proof, or the consequence, of the new curve being drawn with an angle whose tangent is 1/2°302. In any case it is clear that tan a=M, and that all equiangular spirals transform from one into the other, by a suitable change in the unit angle. Owing to the rather prevalent idea that common logs can be calculated only by derivation from the natural system, I may perhaps be excused for alluding to the independent, though obvious, method of extracting square roots. 402 Mr. BE. A. N. Pochin: This concludes the graphic treatment of logarithms. Some portions have been made very elementary, and must neces- sarily appear prolix. On the other hand, I have entirely emitted such questions as the limiting value of € = ‘ negative characteristics, and other points which are fully explained in the ordinary books. The short descriptions of the watch calculator and slide-rule, though not essential, have been deliberately introduced, in the belief that such examples are beneficial. 7 I will terminate by mentioning, very briefly, two other properties of the spiral which admit of illustration. Differentiation. ie On the left of fig. 4 is the e spiral; the remainder of the construction being self-evident. The angle POP’ is the increment of the natural log, cor- responding to the increment NP’ of the radius vector. Therefore | dlogw) ia. PN/OP™ fi a is limit of = Wpro=p- On the right of fig. 4 is the “10” spiral, drawn, as we Fig. 4. have seen, with the roller at an angle whose tangent is 1/2°302.... Therefore in this case d logo ay ln ee M Gril DBO a Ws Heperimental Mathematics. 403: Evolute and Involute. It is clear from the nature of the spiral that its evolute must be some form of spiral which also merges ultimately in the pole. at? Here is a logarithmic spiral cut out of wood, from which the curve AP, fig.5, has beendrawn. An adjustable string is Fig. 5, attached, and we find that of all the involutes which can be drawn to this curve, with varying lengths of string, there is one, viz. A’P’, which exactly fits the wooden model. There- fore the spirals AP, A’P’ are reciprocally evolute and in- volute. And we have seen that they must have a common pole; therefore the evolute of A’P’ is the same curve turned through an angle about O. Again, let PP’ be any position of the string ; then the angle OPP’ is complementary to OP’P, and therefore POP’ isa right angle. But the unwound portion of the string PP’ is obviously the length of the spiral from the pole to P. Accordingly the length of the spiral at any point is the intercept on the tangent between the radius vector and its normal through the pole. This of course agrees with sss | secadr =rseca, a being the angle of the spiral. 404 Messrs. Wilson and Makower on the Rate of Conclusion. In the report of a recent Educational Conference, I noticed that whilst differences arose on all other points, there was absolute unanimity regarding the excellence of Euclid I.—-IT1. Now Euclid is, above all, an experimental science—the ex- periment is first performed, then analysed to confirm its accuracy—and the vitality of Euclid is, beyond doubt, due to this pre-eminently rational treatment. This plan is the one J have tried to follow—with what success you must yourselves decide. In more competent hands it might, I am certain, be improved and extended to other problems, with great benefit to all concerned. The larger part of mathematics has arisen in the consideration of practical questions; and by divorcing the reasoning from its original significance, we rob it both of its visible explanation, its interest, and its application. The earlier portions of arithmetic, algebra, trigonometry, &c. are clearly experi- mental, and describe, in symbols, the results of definite opera- tions which any boy can readily understand. As we advance, however, the real meaning gradually becomes obscured, till we are finally left with little more than a notation, intelli- gible only to those possessing special aptitude. When the extensive and growing equipment of our labo- ratories and technical schools is contrasted with the solitary blackboard, it must. surely be admitted that the disparity is excessive. If we will but show diagrams, models, and actual measurements—alluding constantly to the practical applica- tions of the matter in hand, and pointing out its real utility —-we shall by such means do much to awaken interest, stimulate intelligence, and discountenance the idea that this oldest, and most important, of all the sciences is merely a collection of tricks with symbols, culminating in‘a calf-bound volume, neatly embossed with the school arms. XXXVI. Note on the Rate of Decay of the Active Deposit from Radium. By W. Witson and W. MakoweEr*. ife some experiments in which the ionization produced by . the « rays from radium © was balanced against that produced by the more penetrating @ and y rays, it was found that after a short time these two ionizations were no longer exactly equal, however carefully they had at first been adjusted to equality. A similar effect has been noticed by * Communicated by the Physical Society: read May 24, 1907. i Decay of the Active Deposit from Radium. 405 Bronson *, and has been attributed to the slowly moving 8 rays emitted by radium B, recently discovered by Schmidt f. Since these rays are emitted by radium B, whereas the a and the more penetrating rays are emitted by radium C, it is to be expected that the rate of decay as measured by these two types of radiation will be different. Although this explanation seemed probable, it was thought to be of interest to test this point somewhat more carefully, to make sure that this explanation is really the correct one. Fig. 1. VILA QQAQA, The following experiments show conclusively that this is the case. As the whole effect to be measured was very small, it was necessary to make somewhat careful experiments to test the matter, and the method used was 4s follows. Two ionization-vessels A and B (fig. 1) were connected to * Bronson, Phil. Mag. July 1906. + Schmidt, Phys. Zeit. vi. p. 897 (1905). 406 Messrs. Wilson and Makower on the Rate of one pair of quadrants of an electrometer, the other pair of which was permanently connected to earth. The vessel A was 6°4 cms. long and 5 cms. in diameter, and its end was closed by an aluminium-leaf which would allow the a rays to pass through. The vessel B was 15:4 ems. long and had a diameter of 8:4 cms., its end being closed by a copper plate thick enough to absorb all the a rays, but thin enough to allow much of the 8 radiation to pass through. A wire which had been exposed to the radium emanation for a sufficient length of time to allow the deposit to assume a steady state was broken in two pieces, one of which was fixed outside the vessel B, the other being fastened to an iron bar I which, by means of the screw 8, could be moved towards ond away from the vessel A. The vessel A was connected to one terminal of a battery of two hundred small storage- cells, the middle point being connected to earth and the other terminal to B. Two lead screens, LL, were made which could slide so as to leave an opening between them, and were placed close to the end of the vessel A. The distance between the plates could be varied from the whole width of the vessel to nothing. By altering the width of this opening and varying the distance of the wire from the ionization-vessel A, a balance could be obtained between the ionizations produced in A and B by the two wires respectively. After removal from the emanation to which they had been exposed, the wires were left for a sufficient length of time to allow the radium A practically to disappear. The balance was then made, roughly at first by means of the lead screens and then more carefully by the screw 8. In the earlier experiments the difference ot the ionizations produced in the two vessels in one minute was measured at intervals of about five minutes, the value of the whole ionization in the vessel B also being determined from time to time. It was found that the needle did not move uniformly from its position of rest to its final position, but moved irregularly, as is often the case when the difference between two nearly equal large lonizations is being measured*. These irregularities could, however, be to some extent eliminated by measuring the difference of the ionizations produced in five minutes instead of one minute. The results obtained in this manner for two distances D of the wire from the vessel A, 7 cms. and 1:4 cms. respectively, * Bronson, Phil. Mag. Jan. 1906. | Decay of the Active Deposit from Radium. AQT are shown in fig. 2, where the ordinates represent differences between the ionizations in A and B, and the abscisse times reckoned from the moment at which the wire is removed from the emanation. The whole ionization in each vessel was 1600 scale-divisions, 48 minutes after removal from the emanation, Fig. 2. Difference in Ionizations. so that the deviations of the points from the curves (fig. 2) in no case amounted to as much as one per cent. of this quantity. The activity decreased with time according to the usual laws*. It will be noticed that for small distances of the wire from the vessel A the difference in the observed rates of decay of the deposit on the two wires is small, but for large distances (7 ems.) it is considerable. Now it is known that the range of the @ particle from radium C is just over 7 cms.¢; consequently when the wire is at this distance from the vessel A the a rays contribute but little to the ionization in this vessel, which is for the most part due to the rays emitted by radium B. If the observed effect is due to the slowly moving 8 rays emitted by radium B, the difference in the rate of decay of the activity as measured in the two vessels A and B should therefore be greater in these circumstances than when measurements are made with the active wire near to A. Moreover, the ionization in the vessel A should decay more rapidly than that in the vessel B. This is, in fact, found to be the case, so that we may conclude * Miss Brooks, Phil. Mag. Sept. 1904. + Brage & Kleeman, Phil. Mag. Sept. 1805. 408 Dr. Barkla and Mr. Sadler on Secondary that the difference in the rates of decay as measured in the two vessels is due to the slowly moving 8 rays emitted hy radium B. To further test this point, the rays were made to pass between the pole- pieces of a small electromagnet before entering the vessel A. On exciting the magnet, the slowly moving £ rays were deflected and the balance was disturbed, the ionization in the vessel A at once falling below that in B. This fact confirms the conclusion given above. Physical Laboratory, The University, Manchester. XXXVI. Secondary X-Rays and the Atomic Weight of Nickel. By CHARLES G. Barkua, V.A., DSc., Lecturer in Advanced Electricity, and C. A. Sapuer, M.Sc., Demonstrator in Physics, University of Liverpool *. , [ a paper on Secondary Rontgen Radiation, one of the authors suggested a method of determining atomic weights by means of experiments on the more penetrating secondary rays—(those which traversed several centimetres of air and thin sheets of paper and aluminium foil)—emitted by elements in the form of thick plates when subject to #-rays. It was found by graphically plotting as ordinates the per- centage absorptionst by aluminium of the secondary rays proceeding from various elements, and as abscissee the atomic weights of the radiators, a periodic curve was. obtained, in many portions of which the gradient was so great that atomic weights could be obtained by interpolation with considerable accuracy. The curve shown on page 8207 was that obtained by preliminary experiments, and for reasons given was not regarded as accurate in detail, the main characteristics alone being discussed. It was seen that from chromium to selenium the relation between the absorption and the atomic weight of the radiator * Communicated by the Authors. The expenses of this research have been partially covered by a Government Grant through the Royal Society.—C. G. B. +t C. G. Barkla, Phil. Mag. pp. 812-828, June 1906. {| As in previous papers, by ‘‘ percentage absorption,” is meant the percentage diminution in the ionization produced by an 2-ray beam in its passage through an electroscope by placing absorbing plates in its path before it falls on the electroscope. This, of course, is only strictly per- centage absorption of energy when the beam is homogeneous. \ A-lays and the Atomic Weight of Nickel. 409 was approximately a linear one, and that a small variation in the atomic weight of the radiator was accompanied by a considerable variation in the character of the radiation emitted. 7 | As more recent work showed that within these limits very consistent results were obtained from repeated observations, the method seemed exceedingly sensitive. When the elements were examined successively under similar conditions it was found that nickel behaved irregularly, only falling into line when an atomic weight considerably greater than that of cobalt was assigned to it. This exception to what otherwise seemed a general decline of absorbability with increase in atomic weight between the limits named was so striking that we considered it called for more detailed investigation. To determine if this apparent anomaly was due to any special relationship between the radiating and the absorbing sub- stances, similar experiments were made with the same radiators and a number of different absorbers and curves were drawn— one for each absorbing substance experimented upon. It was found that platinum, tin, silver, and zinc absorption curves were very similar to that obtained for aluminium, showing that the relation between atomic weight of the radiating substance and the absorption by aluminium previously found, was a relation between the nature of the radiator and general absorbability of the rays it emits, and nota relation depending on the nature of the absorbing substance. In each of these cases it was evident from the curves that the behaviour of nickel would be perfectly regular if an atomic weight approximately mid-way between those of cobalt and copper were assigned to it. It had previously been shown that the absorbability of secondary w-rays is an atomic property simply, that is it depends on the nature of the atoms from which the rays proceed, and a mixture or even combination with other elements does not affect the nature of the radiation as it pro- ceeds from the radiating atom itself. From this we shvuld conclude that small or even moderate quantities of impurity would not materially affect the results. After preliminary experiments on good commercial specimens, however, samples of the elements of the highest order of purity were obtained and all the experiments were repeated. The results were almost exactly the same as before, indicating that the irregularity was not inany way due tothe presence of foreign substances. 410 Dr. Barkla and Mr. Sadler on Secondary The curves obtained are given in fig. 1. The true relative absorptions by various substances are not here exhibited as 100 FERCENTAGE ABSORPTION GF SECONDARY PAYS. 20 50 55 é 60 65 70 Aromic WeichH7 oF RaolAToR the’absorbing plates varied in thickness. The thickness of each is given in the figure. The absorption of the radiation from nickel by each absorbing substance is shown by a horizontal line cutting the corresponding absorption curve. Thus, by interpolating the experimentally determined absorp= X-Rays and the Atomic Weight of Nickel. 411 tion of the radiation from nickel on the curve obtained from observations on elements of neighbouring atomic weight, values were found for the atomic weight which agreed exceedingly closely for the various absorbers used—aluminium, zine, silver, tin, and platinum. Now as in general the percentage absorption of a beam of Rontgen rays by a sheet of any substance is less after trans- mission through any kind of matter than before, the absorption coefficient calculated as for a homogeneous beam from the relation [=I,e-** differs with the thickness of absorbing plate used, the thicker plate giving the smaller absorption co- efficient X. Absorption coefficients determined in this manner are therefore only rough measures of the absorbability of the rays. The character of the secondary radiation from these elements is, however, quite different, for experiments showed it to be practically homogeneous, while similar experiments exhibited most markedly the heterogeneity of the primary beam. First dealing with the primary beam, the absorption by a sheet of aluminium ‘01 centimetre in thickness amounted to 33°4 per cent. ; after transmission through one, two, three, and four sheets of zinc, each ‘00131 cm. thick, this fell to 31°6, 29°8, 27:9, and 27-2 per cent. respectively. The absorp- tions by a plate of zinc ‘00131 cm. thick corresponding to the first four values were 59, 49°3, 41, 31 per cent. respectively. Thus after transmission through successive layers of zinc the rays were more and more penetrating to zinc, the last 12°6 per cent. being about twice as penetrating as the original beam. The power of penetrating aluminium was, however, not affected to nearly the same extent, the absorption diminishing from 33°4 to 27:9 per cent. only. On the other hand after transmission through aluminium plates the change in the penetrating power to aluminium was much greater than that to zinc. Thus though what we may call the general penetrating power is increased after transmission through one of these substances, the power of penetrating further layers of the same substance is increased to a much greater extent. Results similar to these were obtained by Walter for several substances. If we investigate the secondary rays from copper in the same way we find no such change, the whole radiation detected by the electroscope at a distance of several centimetres from the radiator being almost perfectly homogeneous. This is a 412 Dr. Barkla and Mr, Sadler on Secondary remarkable result; we therefore give in fig. 2 the percentage absorptions of the secondary rays from copper (after trans- mission through various thicknesses of zinc) by plates otf Fig. 2. PERCENTAGE ABSORPTION. 10 PRIMARY BEAM 0 - ) 10 20 30 40 50 60 79 80 Re) 10 FERCENTAGE PREV/OUSLY ABSORBED &yr ZN. aluminium, zinc, and copper. ‘These absorbing plates were not, however, of the same thickness, so again the relative absorptions are not shown. The curves obtained by plotting percentage absorption by a plate of any one substance and the percentage previously absorbed by zinc show that what- ever was the absorbing substance used, the absorbability of the rays from copper did not change even after transmission through plate after plate of zinc. The contrast between the curves given in fig. 2, obtained by experiments on primary and secondary beams, shows the marked difference between these radiations. Another point worthy of notice is the fact that after the transmission of the secondary rays from copper through zine, the ratio of absorptions by other substances does not change— that is to say, the special powers of penetrating certain substances possessed by primary beams after passing through \ X-Rays and the Atomic Weight of Nickel. 413 the same substance, appears to be entirely absent in the case of these secondary rays. That this is on account of the homogeneity of the beam before traversing the plates seems highly probable. We are thus able to determine what are true absorption coefficients for these secondary rays by various substances. These have been calculated and are given for two distinct series of observations in the following table. In the first series the radiators were experimented upon in the order zine to iron, and in the second series from iron to zinc. No attempt has been made to allow for the slight obliquity of some of the rays in traversing the plates, as the conditions were similar in all the experiments. The values given are probably as a consequence 2 or 3 per cent. too high. TABLE I. Radiator. Absorber. | al Fe | @are|| Za. Ag Sn | Pt [eek ae Dine) A | 97:0] 1073 | 514, 342 | 1930 | 1636 | 35350 | Copper 1.0.00... | 121:3/ 1159 | 367] 416 2340 | 1992 | 4270 | is en | 147-3 1229 | 610!| 513 2836 | 2383°| 5210 Cobalt ........ sere 1750, 480 731 625 3456 | 2890 | 5970 in 2160 510 905 789 4050! 3500 | 6520 | a ae | 966| 1063 512 358 1960| 1636 2492 | Domeer cet. one | 119°8| 1159 | 488 434 | 2394 | 1931 | 4170 | Micke st... | 146-9| 1170 , 596 525 2802 | 2430 | 5140 | Grete 1775| 471 | 745 632 3360 | 2904 | 6080 | “it | ae | 218-2) 529) 975) 804 | 4020 | 3470 | 6820 | | | From these results, plotted in figs. 3 and 4, it is seen that the relation between absorption coefficient for a secondary radiation and atomic weight of the radiating substance is almost perfectly a linear one within this range of atomic weights for most absorbing substances. The exceptions were iron and copper, which, it should be observed, were among the radiating substances experimented upon. The values for the atomic weight of nickel obtained by interpolation of the absorption of its radiation on the curves for the absorbing substances aluminium, zinc, silver, tin, and platinum were 61°35, 61°6, 61°45, 61°6, 61°15 respectively, from the first series of experiments. The corresponding values obtained from the second series in which the radiating Phil. Mag. 8. 6. Vol. 14. No. 81. Sept. 1907. 2H 414 Dr. Barkla and Mr. Sadler on Secondary substances were experimented upon in the inverse order were O1-2;, 61:0. 161s a oles. Olea Aromic WEIGHT OF PPADIATOR The curves obtained from the experiments on iron and copper were too irregular to admit the determination of accurate results. ‘These are consequently omitted. The striking irregularities in form shown by the curves obtained from experiments in which iron and copper were used as the absorbing substances were obviously due in one case to the absorption by iron of the rays from iron and cobalt being much lower than might have been expected from observation of the general relation between atomic weight of radiator and absorbability of the emitted radiation and the absorption by copper of the radiation from copper being low. X-Rays and the Atomic Weight of Nickel. 415 It was evident, however, that the deviation from the normal absorption exhibited when the radiators and absorbers had Fig. 4, {o) Atomic WEIGHT OF PADIATOR the same or neighbouring atomic weights, could be best studied by examining the absorption of the radiation from a certain substance by different elements and observing the relation between atomic weight of absorber and the absorption produced. In a paper by Benoist on the absorption of Réntgen rays, the connexion between the transparency (as measured by the mass of a prism of unit cross-section of an absorbing substance which produces a given absorption of an «-ray beam) and the atomic weight of the absorbing substance, is shown by a curve similar to that shown by the discontinuous 2K 2 TRANSPARENCY. “05 | 416 Dr. Barkla and Mr. Sadler on Secondary curve in fig. 5. This was obtained by using the secondary beam from carbon—that is a beam consisting entirely of ATomic WEIGHT OF ABSORBER. scattered primary rays—instead of the primary as used by Benoist, and plotting transparency to sucha beam as ordinates and atomic weight of absorbing substance as abscissee. _ _ The following table gives the thickness of each absorbing ‘plate in centimetres necessary to absorb 75 per cent. of the radiation from each of the substances given in the first column. In the case of the radiation from carbon the numbers are only approximately correct, as they were calculated in the same way as for homogeneous beams. TABLE II. Radiator. | Absorber. | Al. Ble. ai Cus (eZee eA Sn. | Pt. ZY Fe ARRAS See 0586 | 0100 ;-0241 | 0292 | -00758) -0061 | -00839 OL Aas Re A Ae 0309 | 00929) -0338 | 0240 | 00625-00508) -00697 INA Reha ors dielad cei 0254 | 00876) 0203 | 0195 | 00516) -00425! 00571 COMES ese. cn 56k "0214 | 0224 | -0170 | ‘0160 | 00424! 00350} 00498 Cee ok et cinece’ ‘0173 | 0211 | °0157 | 01265) -00362! -00289] -00457 Odeo 14 ae "114 | 0363 | 0242 |-0225 | 0220 | -0195 | -0151 i X-Rays and the Atonue Weight of Nickel. 417 By replacing the primary beam as used by Benoist, or the secondary beam from a substance of low atomic weight like carbon, by one of these secondary beams from metals, a curve showing similar characteristics was obtained (see fig. 5), but a strongly marked deviation occurred in the neighbourhood of the atomic weight of the radiator, exhibiting the special power of the rays emitted by each substance of penetrating further layers of that substance. [The ordinates for the primary curve have been reduced to one-third their true value to make this curve comparable with the true secondary curves. | Treating the radiation from cobalt in this way it will be seen that the curve obtained approximated much nearer to that obtained for the radiation from iron than that from copper, and exhibited the special power of the cobalt rays of penetrating iron, denoting closer proximity in atomic weight to that of iron than of copper. On the other hand the curve obtained by experiments on the absorption of the rays from nickel was very similar to that obtained from copper, and exhibited the special power possessed by these rays of pene- trating copper and zinc, but not iron. This then indicated the proximity in atomic weight of nickel to that of copper. The two series of experiments on cobalt and nickel when taken together appear to furnish very strong evidence that the atomic weight of nickel is considerably nearer that of copper than is that of cobalt, that is, that the atomic weight of nickel is considerably higher than that of cobalt. Not only do the relative positions of the atomic weights agree with those indicated in the previous series of experiments, but though this method dces not furnish accurate numerical results, it will be seen that the value previously given would bring it again into harmony with all the experiments on this special property. In investigating the efficiency of different portions of a heterogeneous primary beam in producing secondary rays from metals, experiments were made to determine the extent to which the secondary radiation was diminished by absorbing portions of the primary beam before it was incident on the radiating substance. Thus when an aluminium plate was placed in the path of the primary beam before it fell on the secondary radiator, the ionization produced by the primary in a given space was diminished by « per cent. and the ionization produced by the secondary diminished by y per cent. Thus by plotting per- centage reduction of the ionizing power of the primary as absciss, and consequent reduction of the ionizing power of 418 Dr. Barkla and Mr. Sadler on Secondary the secondary radiation as ordinates, curves were obtained for the radiation trem each element. A gradual change of gradient was noticed with an increase in the atomic weight of the radiator. The gradient of the curve obtained for nickel lay between those for cobalt and copper. Although the experimental error was too large to make the results of one series of experiments absolutely conclusive, this position was maintained in the several series taken, again indicating a strong probability of the atcmic weight given above being approximately correct. [Later experiments have shown that it is possible that this result is not really independent evidence on the point in question. | Since performing the experiments, the results of which are described above, we have noticed that Prof. J. J. Thomson * in experimenting on the easily absorbed corpuscular rays emitted by elements subject to x-rays, found that “in every case except nickel an increase in atomic weight is accompanied by an increase in the streara of radiant energy,” proceeding from the element. On examining the relative values of the ionizations found in these experiments it is evident that if we assign to nickel the atomic weight given above, it falls into order and the law becomes general. : Again, in experiments on the absorption of primary #-rays by elementary substances, the same irregularity occurs. From Benoist’s results connecting the transparency of substances to z-rays and the atomic weights of those substances, his method does not appear sufficiently delicate in this region of atomic weights to indicate such an irregularity, but Hébert and Reynard + found the opacity of nickel to a-rays to be greater than that of cobalt, while in all other cases examined by them an increase in opacity accompanied an increase in atomic weight of the substance examined. This is not an isolated record of such an irregularity, for Blythswood and Marchant { found that contrary to the general grouping of elements of neighbouring atomic weights as preducing approximately the same absorption, cobalt behaves like iron, whilst nickel approximates to copper and zinc in its absorp- tive powers. Though with certain Réntgen beams it appears that an increase in the atomic weight of the absorbing substance may be accompanied by a slight decrease in opacity, the change is invariably a gradual one, and quite unlike the irregularity exhibited by nickel. This irregularity would * Proc. of Camb. Phil. Soc. xiv. pp. 109-114, Nov. 1906. t Comptes Rendus, cxxxii. pp. 408-409 (1901). t Proc. of Royal Society, Ixv. p. 4138. \ X-Rays and the Atomic Weight of Nickel. 419 disappear if we assumed for the atomic weight the value given above. The results of experiments on «-rays which are of interest as bearing on the atomic weight of nickel are briefly stated below :— (1) Curves connecting the atomic weight of an element subject to x-rays and the general penetrating power of the secondary z-rays emitted by it (various absorbing substances being used) indicate for nickel an atomic weight of about 61:4. (2) Many experiments show that the secondary z-radiation from an element is specially penetrating to that element, and to a less extent, to elements of neighbouring atomic weights— the special power being a measure of the proximity. Experi- ments show the proximity of nickel to copper and of cobalt to iron. (3) Curves exhibiting the efficiency of different constituents of a primary beam in producing secondary #-rays, change in character with the atomic weight of the radiator. The curve for nickel appears to lie between those for cobalt and copper. (This method is not at all sensitive, and the experiments are not absolutely conclusive.) (4) Experiments by J. J. Thomson on the total ionization produced by the easily absorbed corpuscular secondary rays emitted by elements subject to v-rays, give for nickela result which with the usually accepted atomic weight is the only exception to the rule of increase of ionization with increase in atomic weight of radiator. If we accept the atomic weight given above it becomes perfectly regular. (5) The relation between the atomic weight of an element and the absorption of x-rays it produces is shown by a con- tinuous curve exhibiting no clearly marked irregularities if we except nickel. When a position between cobalt and copper is assigned to nickel, it becomes quite normal in its behaviour. In discussing these experiments we may dismiss at once the possibility of the abnormal effects being due to impurities, for in the first place the amount of impurity necessary to produce such a change in the character of the secondary radiation is absurdly large. Indeed, as the impurity could not differ much in atomic weight from that of nickel itself— a fact proved by the curves shown in fig. 5—the quantity would have to be enormous. Again, the various specimens, differing considerably in _ purity, when subject to #-rays emitted secondary rays which were almost identical in character, within the limits of experimental error. A420 Dr. Barkla and Mr. Sadler on Secondary Many proofs might be given of the same thing, but further discussion of this point does not appear necessary. . Of the results themselves there can be no question. [We see from a note in ‘ Nature’ that Prof. Walter has verified: the observations made on the special penetrating power of the secondary rays. | There are also so many experiments, the results of which are so directly dependent on the structure of the atom and which furnish numerical data (of varying degrees of accuracy) pointing in independent ways to the same conclusion, that we cannot but recognize the strength of the evidence that the true atomic weight of nickel is approximately mid-way between those of cobalt and copper. If the atomic weight of nickel were the usually accepted value 58-7, we should from the first series of experiments be compelled to conclude that the difference between atoms of neighbouring atomic weights was in this case an exceptional one ; in fact that the relation between atoms of nearly equal weight was, so far as is known, in this case quite unique. The fact that the position obtained by interpolation is between cobalt and copper might be regarded as accidental. But the special power of ne rays it emits of penetrating vertain substances shows that nickel behaves as a perfectly normal substanee with an atomic weight between those of cobalt and copper. If the structure of the atom were an abnormal one, we should expect the behaviour of the atom to be like that of an atom of one weight in one property and that of another weight in another property. To be more precise, if we con- sidered the possibility of the accepted atomic weight of nickel being correct, we should have to conclude that its constitution is an irregular one, but that it behaves in all the ways dis- cussed as an imaginary atom, built up in a perfectly regular way, and possessing an atomic weight of about 61:4, whereas we should have expected inconsistencies in the values indi- cated by different experiments. We cannot conceive of two different systems—a real and an imaginary one—possessing so many properties, identical in quantity as well as quality. For these properties— the. definite power of absorbing #-rays, of emitting under x-ray stimulus corpuscular radiation of definite ionizing power, of emitting under g#-ray stimulus secondary w-rays of definite properties (the general and special properties referred to) and the property of being susceptible to a definite extent to w-rays of various penetrating { dependent on the number, arrangement, and velocity of the \ X-Rays and the Atomic Weight of Nickel. A21. constituent electrons, factors we conceive of as governing the atomic weight. We cannot, however, by any such physical methods take the question beyond the region of extreme probability. But it appears to us that these experiments furnish very strong evidence to support us in the conviction that the true atomic weight of nickel is approximately mid-way between those of cobalt and copper—very probably about 61:4. The principal points of interest in connexion with the theory of secondary radiation brought out during these experiments are the ‘following :— The periodic relation between absorbability of the secondary rays and the atomic weight of the radiator obtained by experi- ments with aluminium as the absorber, is a true relation between the general absorbability of the radiation emitted by different atoms and their weight, for the variation in the penetrating power of the secondary radiation with variation in atomic weight of the radiator is practically the same with all absorbing substances used, except in the case of special relations existing between the radiator and absorber. The secondary y a-rays emitted by certain substances are remarkably homogeneous in character, though the primary radiation producing them is very heterogeneous. This, how- ever, is not true of the z-radiations proceeding from all elements even among those which emit a radiation differing considerably from the primary in character. Change in the penetrating power of the primary beam has not been found to affect the penetrating power of the secondary from these substances, within certain limits in the character of the primary. The fact that after transmission through plates of absorb- ing substances the penetrating power of the secondary beams from certain elements is not changed, shows that transmission through substances does not modify the transmitted radiation in any way. It has frequently been suggested that the chauge observed in the penetrating power of x-radiation after transmission through absorbing substances is due to trans- formation. We have found. however, that when these apparently homogeneous beams are passed through any substance not only is the general penetrating power un- altered, but there is no special power of penetrating further layers of the substance traversed. There appears then to be little support for the theory that the special penetrating powers are due to some specific property of the substance traver sed, other than that of exercising a selective absorption. It should be noticed that what we have shown to be practically 422 Mr. 8. H. Burbury on the Work which may a homogeneous beam of secondary z-rays may not be strictly homogeneous, for a little consideration will show that the method is not a very sensitive one for detecting the different constituents. It is certain, however, that the secondary beams from certain substances are remarkably homogenéous in comparison with the primary. A fuller discussion of some of the experimental results briefly referred. to in this paper will be given in a paper dealing more exclusively with the theory of secondary rays when experiments which we are now engaged npon have been completed. | Note, Aug. 21, 1907.—Parker and Sexton have recently announced (‘ Nature,’ Aug. 1, 1907) that, acting upon the suggestion of Prof. J. J. Thomson that the accepted atomic weight of cobalt was too high, they have determined it electro- lytically, and have obtained as the mean of fifteen deter- minations the value 57:7. At the time that the suggestion was made by Prof. Thomson only a short preliminary notice of these results had been published, so that the published evidence was insufficient to distinguish between the possi- bilities of cobalt or nickel being wrongly placed. It must, however, be concluded that the first two series of experiments described in this paper point very markedly to the probability of the accepted atomic weight of nickel as being much too low. The value 59 has consequently been accepted for cobalt. (See figs. 3 and 4.) XXXVITI. On the Work which may be gained during the Mixture of Gases. ByS. H. Bursury, /.A.S.* N reference to my paper in the July number of this Magazine, Lord Rayleigh calls my attention to a paper of his in Phil. Mag. ser. 4, vol. xlix. (1875) p. 311, with the above title. He there seeks to prove the law enunciated on p- 125 of Professor Bryan’s recent work. The problem may be stated thus :—In a horizontal tube is. a mixture of two gases, say oxygen and hydrogen, the pressure of the combined gases, and also the temperature, being uniform throughout the tube. Consistently with these conditions the gases may be (1) mixed in the same relative proportions atall points in the tube, or (2) wholly or partially separated, oxygen being in greater relative density towards one end, hydrogen towards the other. Rayleigh and Bryan maintain that to bring the mixture * Communicated by the Author. \ be gained during the Mixture of Gases. 423 from state (1) to state (2) work would have on the whole to be spent. Let then my, be the mass of a molecule of oxygen, mz that of hydrogen. And let u,? be the mean square of the velocity of a molecule for oxygen, ux for hydrogen. Then if in an element of the tube of yee v, there be 7, “molecules of oxygen, n, of hydrogen, the total pressure, which is uniform 22 14M, U,? + Nomoto” : for all elements, is — BT But since, on Lord Rayleigh’s authority, myw2=mw,”, the total pressure is independent of the ratio m,/n, so long as ny +7 is unchanged. From this I think it follows that we might, without doing any work, cause the hydrogen and oxygen ‘molecules to exchange their positions by pairs in such way as to bring the mixture from state (1) to state (2). For the pressure being uniform and the tube horizontal, no forces act on the mole- cules, and therefore no work is fle upon them, by reason of the exchanges. And the pressures are not altered by the to} exchanges. The process may be effected as slowly as we please. This may be an operation which with our clumsy fingers we cannot perform, but it is not an operation which essentially requires work to be spent. I then put forward the statement that in a complete cycle of operations at the end of which, as at the beginning, the tube containing the gases is horizontal and in the same position, and the total pressure p uniform, but at the beginning the gases are uniformly mixed, at the end partially separated, no work is done. It is necessary now to consider whether Lord Rayleigh has proved anything which is inconsistent with this statement. I think he has not. At p. 314 he supposes the two gases uniformly mixed in a reservoir, the partial pressures being P, for oxygen, P, for hydrogen. At the top of this reservoir is a vertical tube, in which the same two gases are in equilibrium in vertical column, the pressure of the combined gases at the base being ep. as in the reservoir. The partial pressures diminish as we ascend the tube, for oxygen more rapidly than for hydrogen. There is thus a partial separation of the gases, in addition to condensation of both gases towards the base. He then takes an element at the top, and compresses the gases in it till they have the combined pressure of the base, P;+P.. Then he brings the compressed element to the level of the base. It is proved that the work spent in the compression exceeds that gained from gravity in the descent of the element by an amount which we may call dW. When the same operation has been performed on every element of the tube, 424. The Work gained during the Mixture of Gases. the quondam vertical column now occupies a horizontal position, in which the combined pressure of the gases 1s P,4+ P, at every point, but oxygen is relatively denser at the end of the tube which was the base of the column. There has been effected a partial separation of the gases. And work W has been spent on the whole. I understand Lord Rayleigh to mean that-this work W has been spent in the separation of the gases. Itis understood that, as he suggests, we may suppose movable pistons interpolated to prevent diffusion for as long as we please. This operation of Lord Rayleigh’s is the second half of a complete cycle of which I will now supply the first half. The gases to begin with are uniformly mixed in a horizontal tube AB, and their combined pressure is P,;+P, at every point. Divide the tube into N elements each containing the same number of molecules and numbered consecutively 1...N from A. Set upa model vertical column A'B' containing the same number of molecules of each gasas AB, but in which the gases have attained the state of equilibrium, with P, +P, the total pressure at the base. Divide the column into N elements each containing the same total number of molecules and numbered consecutively 1...N from the base A’. To every element of the tube now corresponds an element of the column, and each contains the same number of molecules—but the proportions in which the gases are mixed are not the same in the one element as the other, nor are the volumes the same. Then, Process (1), interchange molecules of oxygen and hydrogen in the horizontal tube until each element contains the same number of molecules of either gas as the corre- sponding element of the column. In that process the pressure is not altered at any point, and (as I say) no work is done. Process (2), let each element of the tube expand until it has the same volume and the same pressure as the corresponding element of the column. ‘The horizontal tube is now a jac- simile of the vertical column, and may be set vertical without further disarrangement of the gases. It is in fact, when so set up, exactly Lord Rayleigh’s vertical column, p. 314, and shall be dealt with in the way that he describes. My processes (1) and (2) constitute together the first operation of a cycle of which Lord Rayleigh performs the second. Hvidently, since both my expansion and his compression take place after Process (1), the work gained in expansion 1s exactly equal to that spent in compression. Also since the centre of gravity of the molecules in the tube is at the end on the same level as at the beginning, no work on the whole has been done by or against gravity. Therefore, on the whole no work has been gained or spent unless it is spent in \ On the Ionization Curve of Methane. 425 Process (1). Buta partial separation of the gases has been effected. What Lord Rayleigh proves is therefore, if you complete the cycle, not inconsistent with the truth of my state- ment. What he says happens in the operation which he performs does in fact happen, but the work which, as he says, is spent was gained in the first operation of the cycle, of which he makes no mention. No work is done in the com- plete cycle, unless in Process (1), which consists in the passage of molecules along a level surface from the same pressure to the same pressure. XXXIX. The Ionization Curve of Methane. By W. H. Brace, V.A., F.RS., Elder Professor of Mathematics and Physics in the Univ ersity of ’ Adelaide, and W.T. C ooKE, D).Sc* T has been shown by one of us (Bragg, Phil. Mag. April 1907) that the loss of energy experienced by the a par- ticle in crossing an atom depends, in some cases at least, on the speed of the particle. When the atom is a heavy one there is rather more loss of energy at the higher speeds. This is true of aluminium, tin, silver, “and gold, in comparison with each other and with air. It was of some importance to determine whether the prin- ciple extended to gases also, and the great difference between the weights of the N and O atoms, on the one hand, and the H atom on the other, seemed likely to furnish a good oppor- tunity of settling the question. The ranges of ‘the various a particles in hydr ogen itself were too long for the apparatus at our disposal. W ‘e therefore prepared some methane (CH,) since this gas contains a large proportion of hydrogen, a has a convenient stopping-power. The details of the prepa- ration are given below. The accompanying figure shows the curve which was obtained as the result of the experiment. An air curve is also drawn in the figure so as to make it easy to compare the various ranges in the two gases. The pressure and tem- perature of the air were adjusted so that the ranges of the a particle from radium itself were the same in both. It will be seen that the ranges of the other three « particles do not quite correspond. The more energetic particles go further in methane than in air: thus showing that the ratio of the stopping-power of methane to that of air increases somewhat as the speed of the particle diminishes. In other words, fast « particles are less stopped by methane than slow ones, if air is taken as the standard of comparison. This * Communicated by the Authors. From ‘Transacticns of the Royal Society of South Australia,’ vol, xxxi. 1907, 426 Prof. Bragg and Dr. Cooke on the result agrees with, and is an extension of, the principle established in the paper already quoted. It is interesting to see that, as a consequence, the four steps of the ionization curve are more clearly shown in methane than in air; in particular, the portions due to RaA and the emanation are very well separated. The stopping-power of methane, compared to air, is *860 for Ra€ and °880 for RaA. This seems to show that the stopping-power of H is rather lower than the value previously given; but the exact determination depends on the value adopted for the carbon atom, which is at present the subject of investigation. The total ionization in methane was found to be 1°165 times greater than in air. Initial recombination effects were small, probably less than in air: experiments on this point are not yet complete. Preparation of the Methane. The gas was prepared by acting on an aluminium-mercury couple with a mixture of methyl alcohol and methyl iodide, following the directions of Bone and Wheeler (J. C.8. Trans. 1902, p. 541). These authors freed the methane from the hydrogen present as an impurity by passing the gases over “oxidized” palladium warmed to 100° C. Charitschkaff, however, states (J. C.S., A 1. 1903, p. 186) that when a mixture of hydrogen and methane is passed over palladinized asbestos not only does the hydrogen burn, but also some methane. In our experiment the gases issuing from the generator were passed first through two vessels immersed in alcohol which had been cooled to its freezing-point, roughly 160° T. This cooling served to condense the vapours of iodide and alcohol, and to remove also any higher hydrocarbons which might have been formed. The mixture of methane and hydrogen passed secondly through two vessels cooled in liquid air. In these vessels the methane condensed to a colourless liquid, while the hydrogen passed on and was neglected. After sufficient methane had liquefied communication between the first and second pair of cooling vessels was cut off, and the methane allowed to evaporate into a mercury gas- holder. The methane was then recondensed as far as possible by again cooling the vessels in liquid air. Part of the methane was then allowed to evaporate into the gasholder, and the gas coming off was pumped away. This partial evaporation was repeated, and a second portion of gas re- moved. In this way the hydrogen remaining in the con- Tonization Curve of Methane. 427 necting tubes, or dissolved in the methane, was removed. The methane remaining showed a vapour pressure of about 150 mm. of mercury. “As far as can be gathered from the figures available, this pressure corresponds to that given by methane at the temperature of liquid air, say 90° T. UPPER CURVE---Methane (CH,) at 18°5°C. and 64°3 cm. Hg. 17.5 .02. LOWER CURVE---Air at 15°5°C. and 57°0 cm, Hy. -Evidently the gas was quite pure. A determination of its density gave the value *552, taking air as unity. This figure is almost identical with the calculated value, which is °553. XL. Intelligence and Miscellaneous Articles. THE PHOTANTHISTAN : A NEW INSTRUMENT FOR THE COM- PARISON OF LUMINOUS INTENSITIES AND ABSORPTION CO- EFFICIENTS. BY J. J. TAUDIN CHABOT. KNOWN method of showing the sensitiveness to light of selenium consists in illuminating a so-called selenium cell intermittently by means of a rotating opaque disk provided with slits, light from a suitable source alternately passing through the slits in the disk and being cut off. The conductivity of the selenium is found to undergo fluctuations, which—if a constant potential difference be maintained across the terminals of the cell— result in fluctuations in the current. In the case just considered, the selenium is exposed alternately to the luminous radiation from a source of given intensity, and a source of zerointensity. This consideration suggests the construc- tion of the very useful instrument which forms the subject of this article. We may, instead of using a second source of zero intensity, allow two sources, the intensity of neither of which is zero, to illuminate the selenium cell. In general, fluctuations will in this case also take place in the current traversing the selenium cell, with the exception of the special case in which the illumina- tions due to the two sources are equal. The selenium then behaves as if it were subject to a constant illumination—it bas a corresponding constant resistance. ‘This special case forms the principle of action of the photanthistan. In this instrument, the luminous radiations from the two sources under comparison are, by the use of a slotted rotating disk, allowed to fall alternately on the selenium cell. An Hinthoven string galvanometer in the circuit of the selenium cell indicates by its vibrations when the illuminations are unequal ; these vibrations give place to a steady deflexion when the distances of the sources are to one another in the ratio of the square roots of their intensities—assuming equal absorptions of all the media traversed. Exceptional sensitiveness is attained by making the frequency of the alternate illuminations correspond to the natural frequency of vibration of the galvano- meter, resonance conditions being thereby obtained, and very slight differences in the illuminations being sufficient to call into play vibrations of the galvanometer. Thus it is possible by the simplest geometro-mechanical method to compare the luminous intensities of sources of equal and different wave-lengths, and the absorption coefficients of media interposed in the path of the radiations. Degerloch (Wttbe.), May 28, 1607. LONDON, EDINBURGH, ayn DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. (SIXTH SERIES.] OCT O EE Te W907. XLI. On the Properties and Natures of various Electric ianzotons. by W. HH. Brace, M.A., PRS. Elder Professor of Mathematics and Physics in the University of Adelaide *. W* are now aware of the existence of a number of different types of radiation, each of which is able to ionize a gas, to act on a photographic plate, and to excite phosphorescence in certain materials. Of these the « and canal rays consist of positively charged particles of atomic magnitude; the cathode and 6 rays are negative rays, and consist of electrons ; the X and vy rays are supposed to be zether pulses ; and ultra-violet light consists of short ether waves. The 6 rays stand by themselves, for, though they consist of negative electrons like the cathode and 8 rays, they have so small a velocity that they possess no appreciable ionizing powers. The present paper contains, in the first place, an attempt to find whether there is anything to be learnt from a com- parison of the properties of the various rays; and, in the second place, a discussion of the possibility that the y and X rays may be of a material nature. * Communicated by the Author. Read before the Royal Society of South Australia in two parts; the first on May 7, 1907, the second on June 4, 1907. Phil. Mag. 8. 6. Vol. 14. No. 82. Oct. 1907. ZG 430 Prof. W. H. Bragg on the Properties and It appears to me to be a first deduction from such a comparison that in all cases the bulk of the ionization which the rays effect is of the same character, and consists in the displacement of slow-moving electrons, or 6 rays, from the atoms of the gas or other substance which they traverse. Let us consider the various rays in turn. In the case of the cathode rays this principle has been clearly established by Lenard in the course of his long series of beautiful experiments. He has shown that cathode rays of the most varied speeds, impinging on bodies of various kinds, or traversing different gases, cause the liberation of slow-speed electrons from the atoms of the solid or gas. The speed of the electrons is in every case that due to the fall through less than ten volts. This is in no way a contradic- tion of the fact that cathode rays of high speed are also liberated from a solid surface struck by primary cathode rays ; or from the atoms of a gas through which the primary rays pass. But, whether these high-speed secondary rays are scattered primary rays, or are true secondary rays, they must in their turn produce electrons of slow speed in the gas through which they pass ; and so, directly or indirectly, by primary or secondary or tertiary or rays still more trans- formed, eventually the great majority of the electrons set free in one ionization-chamber of or dinary experiment are of the slow-speed type. In the case of the e rays there is abundant evidence that their impact on, or emergence from, solid surfaces causes the ejection of slow-speed electrons (J. J. Thomson, Cambridge Phil. Soc. Trans., February 190d ; Rutherford, ‘Nature March 2, 1905 ; Logeman, Proc. Roy. Soc., September 1906). Now, it is venerally characteristic of all these electric radia- tions that they are concerned with the individual atoms and molecules, and that they do not recognize any difference between the atom in the solid and the atom in the gaseous condition. Consequently, there is every reason to suppose that the heavy ionization caused by an « particle in traversing a gas consists in the production of the same slow-speed alee ons as are set free from a solid, and indeed no trace of faster-moving electrons has ever been found. . The slow- speed electrons originated by « rays have been called 8 rays, and the term may be applied to all such slow-speed electrons as we are now considering. eal it has been shown by Fuchtbauer (Phys. Zeit., No ob 1906) that 6 rays are emitted from a metal surface str ae ‘by canal rays ; and here also there is every reason to suppose that gas molecules struck by such rays emit the \ Natures of various Electric Radiations. 431 same 6 particles. The same author has shown by a direct eomparison that the velocity of these particles is the same as that of the § rays displaced by cathode rays, i.e., about 3°3'x 10° ‘em. ae or the velocity due to about 20 volts, a velocity only s lightly larger than that found by Lenard. As regards 8 and y rays, it is true that it has not been definitely proved that most ot the ionization which they cause is of the 6 type. But this may be inferred from well-known experiments, such as those of Durack (Phil. Mag., May 1903), or McClelland (Trans. Roy. Dub. Soc., February 1906). When a pencil of @ radiation is allowed a cross an ape tion-chamber normally, and fall upon the opposite wall, it gives rise to a secondary ionization, less in quantity, but not much less in speed than the primary. A tertiary radiation is caused by the secondary rays if they impinge on the walls of the chamber, and there will doubtiess be still further derivations. But it appears that the quantity of the derived radiations dies away much more quickly than the speed. Thus the chamber is crossed and re-crossed (a few times) by electrons of high speed, able to traverse an average path of about 100 cm. in air at atmospheric pressure. If the chamber is first exhausted and air gradually admitted, it is found that the number of ions produced by the @ rays is proportional to the pressure. The paths of the @ rays will not be appreciably affected by the introduction of the air; and so the experimental results are consistent with the simple hypothesis that the @ particle (primary or secondary) makes slow-speed ions in proportion to the number of gas atoms traversed. Nor does any other hypothesis seem to be con- sistent with the facts. It cannot be supposed that the bulk of the ionization which is caused in the ionization-chamber consists of high-speed secondary rays, though, of course, these are originated when the primary rays strike the metal surface of the chamber, and to a small extent when they strike gas molecules. or if all the negative electrons set free by the 8 rays were of high velocity we should expect certain effects, as may be seen from the following considera- tions, and none of these effects have been observed. Rutherford has shown (‘ Radioactivity,’ 2nd edition, p. 434) that the « particle of Ra makes. about 86,000 ions in air ; that one 8 particle is emitted from Ra for every four « par- ticles; and that the ionization due to @ particles is of the order of 1 per cent. of that due to & particles in the ease of Ra in equilibrium. Thus the @ particle of Ra produces some thousands of ions. This is also evident from the ex- periments of Durack (Phil. aS , May 1903), who has shown 2 A32 Prof. W. H. Bragg on the Properties and that the B particle produces about 130 ions per cm. in air at atmospheric pressure. Now, the @ particle runs a course in the open air of an average length of 100 cm. This leads to an estimate of its ionization even greater than that obtained by Rutherford. If all the electrons, so liberated, had a high velocity, the energy set free would be out of all proportion to that of the original 8 particle. Yet if we are to ascribe a high velocity to the electrons set free, it must be a very high one, for it has been shown by Allen (Phys. Review, August 1906), that the secondary radiation of @ rays consists of electrons moving with a speed approximating to that of the primary. We cannot suppose that all these electrons are of this high-speed type. Moreover, if this were the ease, the free path of such electrons would become comparable with the dimensions of the ionization-chamber, when the air pressure was only moderately reduced, and the electrons would then be beyond the control of the electric field. Thus the ionization would not be proportional to the air pressure, as was found by Durack and McClelland. The difficulty as to the energy is not obviated by supposing each primary 8 particle to set free only a few secondary electrons of high speed, each of these to become in turn the originator of a few more, and so on. For if that were the case, a reduction of gas pressure would imply, not only that each primary electron set free fewer secondary electrons, but that each of the latter set free fewer tertiaries, and so on, so that the ionization would fall at a far greater rate than the pressure as soon as the free path of the electrons became comparable with the dimensions of the chamber. And, again, the @ rays differ only in speed from cathode rays, which produce quantities of slow-speed electrons, even where their own velocity is great. For these reasons I think it must be concluded that the B particle (and any high-speed secondary) produces slow- speed electrons along its path, in very much the same way as the « particle does, though not in such great numbers. The high-speed secondary rays, studied by McClelland, Allen, and others, are but few in number compared to the slow- speed electrons, though their greater energy puts them more in evidence. McClelland concludes from his experiment that the 8 rays do not produce any slow-speed electrons, when they strike a metal surface, which are comparable in number with the electrons displaced in the gas through which they have passed. This is quite consistent with what has been said above. There must be a few, but the number to be expected is quite small, for the 6 electrons dive so deep into \ Natures of various Electric Leadiations. 433 the metal which they strike, and ionize so few of the mole- cules through which they pass, that very few of the slow- speed, highly-absorbable electrons can be discharged from the surface of the plate. ven in the case of the « particle these electrons are not readily observed ; in the case of the 8 particle the difhculty must be much greater. As regards X rays, we have no such accurate measure- ments of the velocities of the electrons which are ejected from the molecules of a gas traversed by the rays, as we have in the case of the cathode rays, so far as I am aware. But a very large amount of labour has been spent on the investigation of “the secondary radiation caused by the X-rays, from which we may gather much indirect evidence on the-point. Perrin (Ann. Chim. Phys. xi. p. 496, 1897), has shown that the rate of production of ions per ce. by rays of given intensity is proportional to the pressure of the gas. Again, we know from the investigations of Curie and Sagnac, Townsend, and Barkla, that metals struck by X rays return a secondary radiation, which, in the case of the low atomic weights, may be considered to consist principally of scattered primary radiation, and in the case of the high atomic weights to contain both X rays more absorbable than the primary and cathode rays. Dorn has shown that the latter have speeds averaging about 5 x 10° cm., so that they must produce considerable ionization, consisting of 6 rays, in the few millimetres of air close to the metal. The free path of electrons having this speed is about one millimetre in air at atmospheric pressure. Since the X rays do not appear to produce cathode rays of any speed from the air molecules, which they traverse, or from the molecules of any gas con- sisting of atoms of small weight, and since they produce much ionization in some way or other, we may conclude fairly that they produce slow-speed ions themselves. Thus, whether they act directly or indirectly through cathode rays, the result is the same. The principal effect appears to be due rather to secondary than primary. As Sagnac remarks (Ann. Chim. Phys. xxii. p. 196): “The transformation of X rays, by increasing the activity at any point, permits the detection there of very penetrating X rays, which would otherwise have passed unperceived.” In the case of the y rays, such evidence as we have is also in favour of the existence of slow-speed ions, as the result of their action. - It is known that 8 rays of high speed originate where they strike the molecules of a solid body (Eve, Phil. ~Mag., December 1904); such an action may, therefore, be expected in the vase of gas molecules also. It is possible, 434 Prof. W. H. Bragg on the Properties and however, that there may be a differential effect in respect to heavy and light atoms, as in the case of the X rays, The 8 rays will produce 6 rays in their turn; and if, asis probably the case, the y rays are themselves able to ionize, the product will consist of 8 rays, a conclusion which may be safely adopted from the analogies of the cathode rays on the one hand and the X rays and ultra-violet light on the other. As in the case of the hard X rays, the existence of y rays is often made clear by the secondary effects which they produce, as has been shown by Becquerel. To sum up what has been said, the ionization which we measure in the ionization-chamber is almost wholly due to the emission of slow-speed electrons from ihe atoms of the gas contained in the chamber, or of. the chamber-walls ; and this is true for all forms of radiation. Moreover, there is some evidence to show that the speed of the 6 rays is almost independent of the cause and manner of their production. As has already been said, Fuchtbauer found the velocity of the 6 rays, caused by anne rays, to be about 33x 10°, and the same in the case of cathode rays. Logeman found the velocity of the 8 rays, emitted from a plate struck by a rays, to be such that they were deflected by a weak magnetic field. Ewers found (Phys. Zeit. March 1906) the Sy rays of polonium to possess a speed of 3°25 x 10°. With these may be compared Lenard’s estimate, viz. 10°, of the speed with which the ions leave a plate struck by ultra- violet light. It seems probable that we have here a critical speed for the electron. Below this, it is not able to leave the parent atom. If its velocity exceeds the critical amount it possesses powers of penetration and of causing ionization, the extent of these powers depending on the excess. The existence of a common speed for all 6 rays may, of course, imply that the ejection is not directly effected by the lonizing agent, but that the latter simply precipitates the discharge. A man running through a battery might pull the triggers of some or all of the guns which it contained, and the velocity of the shot would not depend on the str ength of the man, nor the rate at which he ran, nor how much energy he spent in the transit. And so it may be understood why 6 rays are projected at a speed which is independent of the nature of the agent, as has been said above. So also it appears to be independent of the intensity of the agent’s action. Fuchtbauer found the velocity of the 6 rays produced by canal rays to be independent ot the intensity of the primary rays: Lenard found the same for ultra-violet light. Natures of various Electric Radiations. 435 In my own experiments on the a rays (Phil. Mag., March 1907), I have brought forward evidence to show that the amount of ionization produced in an atom is proportional to the volume of the atom approximately. Taking this in conjunction with the rule that the ionization produced i in a gas is nearly proportional to the inverse of the speed, we have the very simple, if approximate, law, that the ionization produced by an @ particle in any atom ‘under any circum- stances is inversely proportional to the time spent inside the atom. This appears to point to the ionization as purely a trigger effect. Not that the « particle spends no energy in the atom ; itis clear it must do so, since its speed is oradually reduced, but there is not a direct connexion between the energy spent and the number of ions produced. But what- ever energy the ionizing agent may spend, or in whatever way it spends it, it seems likely that the issue of the 6 particle is the result of some disruption in the atom, or sub-atom, which is the same for all atoms and under all circumstances. If we turn our attention now to all secondary radiation other than the 6 rays, it seems to \be, in general, a rough reflexion or scattering of the primary. Allen has shown that there is only a little less velocity in the secondary rays than in the primary 8 rays, or in the tertiary than in the secondary. McClelland has measured the total ionization produced by the secondary as compared with the primary 8 radiation; and since he used a small ionization-chamber with which he explored the whole space traversed by the secondary rays, which chamber the secondary rays would, as a rule, completely cross if they entered it, it may be taken that he really compared the number of @ particles in the secondary beam with the number of those in the primary. The numbers which he obtained varied from 15 per cent. to 50 per cent., according to the substance, which is the order of things we should expect if the secondary were simply scat- tered primary radiation. Again, the loss of velocity of the cathode particles, which is found to occur on scattering ata plate, presuming the secondary radiation to be scattered primary, is just what we should expect. In the case of the a rays no secondary radiation other than 6 rays has been found ; but a small reflexion of canal rays has been observed, e.g.. by Fuchtbauer (Phys. Zeit. March 1, 1906). Barkla has shown that the secondary radiation me oduced by X rays consists in part of scattered primary radiation, especially when the surface struck is of material whose atomic weight islow. The only cases in which a secondary radiation appears 436 Prot aye: Brage on the Properties and that is neither 6 radiation nor reflected primary rays, are those in which 8 rays are produced at the impact of X or y rays, and in which X rays are produced by cathode rays. It.is remarkable that in the tormer of these cases there is very great difficulty in accounting for the high speed which is possessed by the secondary radiation, caused by X rays and y rays (Wien, Ann. d. Phys., December 28,1905). It may well be that further research will bring these cases into better agreement with the rest. The next question which it is interesting to consider in relation to the various types of radiation, is that of the law of absorption in passing through matter. Absorption in the case of the material radiations appears to be due to two main causes: loss of energy, which causes a gradual loss of speed ; and scattering, which means a diminu- tion in the number of particles in the primary beam. There is a possibility of a third, viz., absorption of the flying particle by an atom which it is traver sing. In the case of the « particle, I have shown that the first of these causes operates alone, so that the particle pursues a rectilinear course throughout its career (Australasian Asso- ciation for the Advancement of Science, January 1904 ; Phil. Mag., December 1904). It is the absence of any effective amount of scattering that makes the study of the motion of an individual « particle comparatively simple. The loss of energy in traversing an atom, or more exactly the probable loss In crossing a given space ‘occupied by an atom, is nearly proportional to the square root of the atomic weight, and the effects appear to be exactly additive. On the other hand, if we consider a stream of 8 particles projected into matter, and attempt to find the history of their motion, we are faced with a problem of great complexity. If we look for an answer expressed statistically , we must find the number of particles in each unit volume of the absorbing matter as a function of the time, the velocity, and the direc- tion of motion. If, on the other hand, we try to follow the motion of any one particle, we must find the chance that the particle considered has any particular position, velocity, and direction of motion at any given time; which is really equivalent to finding the function just mentioned. Moreover, the data are very uncertain. We know go little of the interior of the atom that we are unable to say with what forces the electrons will be influenced when it penetrates within ; whether, for example, we may neglect the action of the positive electricity of the atom, and consider only the electrons \ Natures of various Electric Radiations. 43 as repelling the @ particle with a force varying as the inverse square of the distance, or whether we are to consider positives and negatives arranged in doublets, whose moment will be the i important power, and whose law “oh attraction will not be that of the inverse square. It is a certain simplification to suppose that scattering is mainly responsible for the fading away of a stream of 8 particles. The experiments of Allen, Mc(elland, and others show that the secondary radiation has a velocity not much less than that of the primary ; and, therefore, that this simplification is justifiable ; though, clearly, it cannot be pushed too far. This Allin us to concentrate our attention on the deflexions of the particles only ; but even then the difficulties are still immense. It is not like any problem in the kinetic theory of gases, for there we deal with established conditions; here with a gradual development from initial conditions *. But if we turn from the theoretical to the experimental investigation we find a much more encouraging prospect. ‘The experiments of Lenard are practically a complete graph- ical solution of the question. (See Taf. iv., Wied. Ain. Bd. 51.) We know that an assemblage of atoms behaves just the same in respect to these radiations, when it is con- densed in a solid or spread out as a gas. Thus the sketches which Lenard gives us showing the way in which the cathode rays diverge from a small window and scatter in going through various gases at different densities, must: be “quite applicable to solids also. * In Ins ‘Conduction of Electricity through Gases,’ 2nd edition, p. 376, Professor Thomson investigates the motion of a stream of B par ticles through an absorbing layer. It appears to me—I say it with very great diffidence—that the solution does not take a true account of the facts. The solution may be stated briefly thus :—Taking w, v, w as the components of the velocity V of the moving corpuscle, an expression is found for the probable change in w at the next encounter. Calling this change du, we have 6u=— uk, say, where K is a function of the mass of the corpuscle, the effective mass of the electron of the absorbing body, the velocity V of the corpuscle, which is taken as constant, the ‘atomic charge, and the shortest distance between two corpuscles and the atom. Kis then multiplied by the probable number of encounters in moving a distance 62 along the axis of x, from which follows an exponential law for win terms of x. It seems to me, lii the first place, that, assuming such a multiplication to have any meaning, the proper factor should have been greater than that adopted in the “proportion of V to u, for in advancing a distance O62 along the axis of x the corpuscle moves a distance Véa'/u, not dx. If this change is made, the exponential form disappears from the answer. But, apart from this, it does not seem that the step is justifiable at all. It is tantamount to putting the corpuscle back in its old track after each encounter, and is equivalent to neglecting the existence of the function mentioned aboy e, and the absolute necessity of finding it. 438 Prof. W. H. Bragg on the Properties and Lenard found that his results could be accounted for on the supposition that there was an absorption according to an exponential law, over and above the weakening due to spreading from a centre. If a B particle or cathode particle were liable to complete absorption by an atom which it entered, such an exponential law would result at once. Asa matter of fact, it looks as if several violent deflexions might take place before the final disappearance of the particle’s activity. It looks, also, I think, as if deflexions were usually not at all great during the progress of the particle through the atom, but were apt to be severe when they did happen, as if, in fact, the field of force which deflected the particle was strong but circumscribed. This would happen if the positives and negatives were arranged in doublets. When a particle is deflected from a beam crossing a thin plate, it starts off on a new path which leads much less directly to the open air, and its velocity is somewhat diminished. It may be, therefore, that the infrequency but severity of the particle’s encounters makes it possible to look upon each encounter as an abso- lute, or at least a definite, loss to the stream, so that an exponential law results. Certainly the application of this law to the interpretation of experiments has had very great success, both in respect to cathode and to Band y rays. As examples of the latter we may take Rutherford’s determination of the absorption of the 8 rays of uranium, and Godlewski’s similar determination for actinium (Jahrbuch der Rad. und Hlek. Bd. ui. Heft 2, p- 159). In experiments of this kind the radiating material is spread evenly on a level surface, and sheets of absorbing material are placed upon it. The ionization produced in the space above the sheets 1s compared with the thickness of the sheets ; and the two variables are found to be connected together more or less exactly by an exponential law. There is some difficulty whether such measurements give more nearly the number or the energy of the stream of particles which emerges from the plate, as Rutherford (‘ Radioactivity,’ 2nd ed. p. 184) and Thomson (‘ Conduction through Gases,’ 2nd ed. p. 375) have pointed out. The point was also dis- cussed in my address to Section A of the Austr. Assoc. for the Adv. of Science, Dunedin, 1904, p. 69. There is also an uncertainty due to the application of a formula to radia- tion from an assemblage of points which is really only appli- cable to a plane wave, or a stream moving normally to the plate. If a point source of radiation is placed below an absorbing plate of thickness d, and there is a true coefficient Natures of various Electric Radiations. 439 of absorption }, the fraction that emerges from the further side of the plate is not e*“; much of the radiation passes obliquely through the plate and is absorbed to a greater degree than that which passes normally. This has often been pointed out, ¢.g., by N. R. Campbell (Phil. Mag. April 1905, p. 041), who also gives some figures from which the proper curve of absorption may be drawn. I am not aware, how- ever, that it has been noticed that the form of the absorption eurve, which is far from an exponential curve for a thin radiating layer, approximates much more closely to it for a thick radiating layer: And it is interesting to find that the experimental curves which are most nearly exponential are those for which the layers of radioactive material were thick compared to the penetration of the rays under investigation. As examples, we may take those of uranium and actinium already mentioned. On the other hand, the curve which HW. Schmidt (Ann. d. Phys. Bd. xxi. 1906, p. 651) has obtained for the 8 rays of RaC, the radioactive material being deposited in a very thin layer on metal foil, shows just about the amouut of departure frem the exponential form which is to be expected if the absorption is truly exponential, and there is only one absorption coefficient, not two, as Schmidt has suggested. The following figures give the proportional amount of the original radiation which passes through a plate of thickness n/X, where ) is the absorption coefficient : ‘Cy kor a) than layer ; (2) for a thick layer. The figures are also given, for the sake of comparison, for the case of a plane wave, or a pencil of rays passing through the plate normally :— ” Radiation from Radiation from Plane wave (purely ‘ thin layer. thick layer. exponential). So 1-000 1-000 1-000 1 een 123 “834 ‘905 C2) a ee "O13 "702 “819 0) 467 “600 ‘742 [22 7, seme 387 “O10 O71 Cl eheae Seam 323 437 607 SOM es «3% "274 378 ‘548 eae a ee °235 328 "498 Oe at a. oer aes -200 -283 450 SPRL TITER: sip "248 “405 ORIN e IG “145 ‘214 *368 The absorption of a material used in a thin sheet naturally appears greater than the absorption when the thickness of material is increased, because the rays which are moving obliquely are Babsorbed first. 440) Prot. W. H. Bragg on the Properties and The absorption of y and X rays appears to follow a purely exponential law so far as experiment has been made. The 6 rays are absorbed by molecules immediately on their production. Having thus discussed certain properties of the various rays which do exist, it seems interesting to make an attempt at the estimation of the properties of some rays which might exist, though the fact has not been proved as yet. Radio- active substances emit both positive and negative particles. It does not seem at all out of place to consider the possibility of the emission of neutral particles, such as, for example, a pair consisting of one @ or positive particle and one 8 or negative particle. The recent additions to our knowledge of the laws of absorption of « and 8 particles give us some grounds on which we may attempt to found an estimate of the properties of such pairs. We know that the « particle moves in a rectilinear course throughout its whole range, and passes through the atoms which it encounters without deflexion. It does not pursue a course which is straight on the whole, but zigzag in detail ; the direction and ‘amount of a particle i in motion are the whole characteristics of that motion at any instant, and no memory of any previous motion exists. If, therefore, a particle pursues a straight line in its motion as a whole, it must keep to that line entirely and make no excursions from side to side. We must, therefore, suppose that an atom, or at least an @ particle, endowed with sufficient speed, can pass directly through another atom without appreciable deflexion. The « particle loses speed as it penetrates atoms in this way ; and there can be little doubt that its charge, that is to say, the field which is about it, is a main cause of this loss of energy. But if a @ particle is associated with the a particle so that the tubes of induction pass from one particle to the other, and the field is greatly contracted, it would seem that the chief cause of the stopping of the a particle has been removed”. The penetrating power ot a pair might be very great indeed, and its ionizing power connec poem medical = for, although there does not seem to be a direct connexion between energy spent and ionization produced, there can be no doubt that the two are simultaneous. The limitation of the field of the pair would depend on its moment; if the latter were small, that is to say, if the positive e and negative were close together, the field would be co) more circumscribed. It is, therefore, possible to provide for * See also Rutherford’s ‘ Radioactive Transformations,’ p. 272. Natures of various Electric Radiations. AAT pairs to have varying penetrating and ionizing powers; a pair of small moment being a good penetrater but a bad ionizer. Such a pair would be incapable of deflexion by magnetic or electric fields, and would show no refraction. It is conceivable that it might show a one-sided or polarization effect, for if it were e] jected from a rotating atom it would itself possess an axis of rotation. When X-rays were first investigated, and again when y rays were discovered, it was often sug cested, in each case, that the radiation might consist of material particles. Réntgen himself proposed in the third of his memoirs a theory of this nature. But it was always felt that the difficulty of accounting for the great penetration of these radiations was insuperable. It seems now that this difficulty was quite exaggerated, and even imaginary. It does not appear out of place, therefore, to reconsider the position in the light of the more recent knowledge. Assumin 2, then, that the neutral pair has great penetr ating, but weak ionizing powers, is uninfluenced by magnetic or electric fields, and shows no refraction, it does so far conform to the properties of the y ray. And, ‘further, if it has any moment at all, and therefore any external field, it may at last suffer some violent encounter which will resolve it into a positive and a negative, ana and a @ particle. Of these the 8 particle would be the one possessed of much the greater velocity, and would appear as a secondary ray. Thus, in the neighbourhood of the point of impact, an ionization would appear of much greater intensity than anything pro- duced along the track of the pair itself. So Becquerel has found the action of the y rays on a photographic plate to be almost entirely due to the secondary rays which they produce. On this view the appearance of the 8 secondar y ray would be really a scattering of the incident ray ; and this would make the y ray fall into line with other radiations whose secondary radiations are either scattered primary or 6 rays. If the gradual disappearance of a stream of y radiation were caused by collision in this way, the number disappearing in any unit of length of the course would be pr oportional to the total number in the stream, so that an exponential law would result. It appears, therefore, that all the known properties of the y rays are satisfied on the hypothesis that they consist of neutral pairs. Ifthe y ray is material and contains an « particle, this fact must be considered in reckoning the number and magnitude of the steps from the atomic weight of radium to that of lead. 442 Prof. W. H. Bragg on the Properties and It has been suggested to me by'my colleague Dr. Rennie that the rayless changes of Ra may really be accompanied by the emission of neutral pairs of very small moment. This adds another unknown factor to the calculation. The energy in- volved in such emissions might be quite small, and, moreover, if pairs can be taken up into atoms, so as to form new atoms, the whole of the energy may not appear as heat. It is interesting to carry the speculation a little further and to observe that a pair possessing a very circumscribed field might cause little or no ionization, and be capable of very great penetration. Its end might be incorporation with an atom traversed: Professor Rutherford has suggested to me that such a fate may befall the & particle at the end of its range. On this view it would be possible for a portion of a disintegrating atom to break away, to pass over an appreciable distance, and finally to become part of another atom, the atornic weight of which would be thereby increased. Internal atomic energy might be transferred at the same time. [or if we suppose that it is possible for some of the internal energy of an atom to be set free, and recent dis- coveries seem to compel the supposition, then we must also consider it possible for atoms to withdraw energy from circulation and add it to their internal store. If, therefore, the handing of neutral pairs from one atcm to another is a process which actually occurs, then matter and energy may be continually transferred from atom to atom without our being aware of it: the whole operation may take place in a world apart. We cannot follow it bv radioactive tests, for the ionization may be so feeble ; nor chemically, because the quantity of atomic change may be so slow ; nor thermally, because the energies appear at no stage in tangible form. Since the properties of y rays are amongst the properties — of X rays, an hypothesis which will suit one form of radiation will also so far suit the other. But we know much more about the latter form of radiation than we do about the former. It is of interest, therefore, to consider the extent to which our additional knowledge can be fitted to a neutral pair hypothesis. It is true, of course, that the ether pulse theory has been most ably developed, and is now widely accepted. Nevertheless the evidence for it is all indirect : and indeed some of it is, I think, a little over-rated. It is quite possible that ether pulses may not, after all, constitute the bulk of Réntgen radiation. If, therefore, there is any- thing to be said in favour of any other hypothesis, it seems 2) e e right that it should be said and considered. Natures of various Electrie Radiations. 443, Let us therefore for the moment suppose the X rays to consist mainly of a stream of neutral pairs. We have at once an explanation of the absence of deflexion in electric and magnetic fields, and of regular reflexion and refraction. There should be great penetration, whose amount might vary with the moments of the pairs, or the velocity, if the latter were a variable. We can understand that a pair which struck a light and yielding atom might be returned unchanged : yet if it struck a heavier and more resisting atom it might be disarranged so as to acquire a gre ater moment, and thus to become a better ionizer, but more readily absorbed. Or it might be shattered altogether, giving rise to a secondary ray of the cathode type. ‘The softer the ray, ?.e. the greater the moment of the pair, the more readily might this be done, and the lighter the atom that would do it. (See J.J. Thomson on Bar! kla’s researches, ‘ Electrician,’ April 5, 1907.) In order to explain these known effects on the ether-pulse theory it is necessary to suppose that in light atoms the corpuscles are not appreciably acted on by forces due to other corpuscles, but that in heavy atoms there is a strong influence of this kind. In the former case, the thickness of the secondary pulse is the same as that of the primary : in the latter itis not. It is also necessary to suppose that when the atom is heavy enough to cause a modification of the primary radiation, it differs from a light atom in such a way that the pulse can cause cathode particles to be ejected at a speed due to thousands of volts: whereas this is impossible with light atoms. If the cathode particles in the X-ray tube so affect the motion of an atom which they strike as to make it throw off a pair, then the plane of rotation of the pair will be the same as that of the atom from which it has come, and will contain the direction of the translatory motion of the pair. The pair will therefore be able to show polarization effects. And if such a pair falls upon a reflecting surface, it is not unreason- able to suppose that it is lable to be taken up only by an atom revolving in. the same plane, and sometimes to be ejected again. Thus its subsequent rotation and translation will continue to take place in the one plane. The tertiary ray will therefore be strongest when it is in the same plane as the primary and secondary; and this is Barkla’s polarization effect. If the X ray is an ether pulse, it is difficult to understand why the spreading pulse affects so few of the atoms ee over (‘ Conduction of Hlectricity through Gases,’ pp. 294— 297), why the high-speed secondary cathode rays are ejected AAA. Prof. W. H. Bragg on the Properties and with a velocity which is independent of the intensity of the pulse, and why it should be able to exercise ionizing powers when its energy is distributed over so wide a surface as that of a sphere of say 10 or 20 feet radius. All these pheno- mena are more simply explained if we suppose the ray to be a neutral pair which has only a local action, i.e. can only affect the molecules on its path, which can penetrate to great distances in air, losing little speed as it goes, and which gives rise to a cathode ray when it is broken by impact. It seems to me that the material-nature hypothesis shows to advantage when we consider the secondary radiation of the X rays. ‘The rays cause the emission of cathode rays whose speed averages about 5x 10° (Dorn). We have no experience of any ‘ether wave causing the emission of any but 6 rays, 7. ¢., electrons with a speed ‘of about 108. It can hardly be said that differences in intensity of the eether pulse can account for this remarkable contrast. or the speed of the 6 rays caused by ultra-violet light has been shown by Lenard to be independent of the intensity of the light; and the velocity of the X-ray secondary radiation does not depend on the intensity of the X rays. It may be argued that the breadth of the pulse is the prime factor, on the grounds that Lenard found the velocity of the 6 rays due to ultra-violet light to depend somewhat on the nature of the light ; but it is hard to believe that a diminution of the width of the pulse, no matter how extreme, can increase the energy of the ejected electron about a thousand times. But if we regard the secondary radiation as the result of the break-up of a neutral pair, the high velocity of the ejected electron (5 x 10°) may be more re eadily explained. The action must be entirely different from that of ultra-violet light. It is difficult to found any arguments for or against either theory on considerations of the relative energies of the original cathode stream, the X rays, and the secondary rays. lor if the energies of any transformation do not balance, it is easy to square the account by postulating either some release of the internal energy of the atom, or the reverse, viz. the absorption of energy by the atom involving a dis- appearance of the visible energy. On the neutral-pair hypo- thesis the cathode rays would probably have a trigger action, and the pairs would draw their energy from that internal to the atom: it might not be necessary to invoke the aid of internal atomic energy in order to account for the energy of the secondary radiation. In the case of the sether-pulse theory it is necessary to suppose that the secondary radiation derives its energy from the atom’s store (‘ Conduction of \ Natures of various Electric Radiations. 445 Hlectricity through Gases,’ p. 321). It is not clear whether such a call must also be made at the transformation of cathode into X rays. The whole question, taken into conjunction with the ditfraction experiments of Haga and Wind, has lately been under discussion by Wien (Ann. d. Phys. xviil. p- 991, 1905 ; and xxii. p. 793, 1907) and van der Waals, Jr. (Ann. d. Phys. xxii. p. 603, 1907) : but no definite conclusion is reached. It is not easy to see how the irregular stoppage of the cathode particles can give rise to pulses of sufficient definition and uniformity to show diffraction. It would be easier to explain such an effect as the result of uniform disturbances arising when pairs of uniform nature are torn from the atoms of the anode. On the zther-pulse theory hard X rays are supposed to be thin pulses, soft rays to be thick pulses. Swift cathode particles are supposed to take less time in deflecting and stopping than siower particles, and therefore to give rise to thinner pulses. On the other theory we must suppose that the rays are hard when the moments of the pairs are small: or possibly that hardness is due to high velocity. If the former is the case, it may be that fast cathode particles spend less time within the anode atoms than the slow ones do, and therefore disarrange the pairs less before they are ejected. There is another entirely different argument, which seems to support the neutral-pair hypothesis. The «, 8, and y rays all ionize the gases which they tra- verse. It has just been shown by Kleeman ™* that the ionization per atom due to Band y rays is nearly propor- tional to the ionization per atom due to @ rays (and, there- fore, approximately proportional to the volume as I have shown, Proc. Roy. Soc. of S. A., Oct. 1906; Phil. Mag. March 1907). ‘The figures for the heavier atoms are rather larger for the 8 than the e rays, and still larger for the yxays. It is known that the ionizations due to X rays differ considerably from those due to y rays when the X rays are soft; but approximate to them when the X rays are hard. All this fits in excellently with the theory that all four types of rays are material. Take the « particle first, since its circumstances are the most simple. It moves directly through the atoms, without scattering or transformation. * Mr. Kleeman has been good enough to inform me of his results by letter; but I believe Iam at liberty to quote them, since he has, [ under- stand, recently read a paper on the subject before the Royal Society. Phil, Mag. S. 6. Vol. 14. No. 82. Océ. 1907. 2H 446 Prot. W. H. Bragg on the Properties and aD It liberates ions in the form of d-rays as it goes, approxi- mately according to the volume law. The 8 ray is also a charged particle, and it is readily to be supposed that it would, if its whole motion were rectilinear, liberate ions according to the same law (comparing atom with atom) as the « particle, though the numbers would be less. But the 8 particle is liable to scattering, and each act of scattering generally implies an increase in the length of the particle in the gas, and increased ionizing power since its speed is a little diminished. Now, scattering is proportional to the atomic weight, whilst the ionization 1s more nearly propor- tional to the square root of the atomic weight. Thus a heavy atom is the cause of more than its proper amount of jonization ; and so we find in Kleeman’s table that the ionizations of the atoms Cl, Br, and I are rather higher than in the case of the a particle. Again, the y particle is liable to resolution into its elements, with a relatively large amount of ionization. Since this transformation is chiefly effected by impact with heavy atoms, these latter will be the cause of a disproportion- ately large ionization, as compared with the a rays ; and this is also shown by Kleeman’ s figures. Pussing on to X rays, we find a further illustration of this effect, until we come to very soft rays, when we find that the heavy atoms are the occasion of exceedingly large ionization (‘ Conduction of Hlectricity through Gases,’ 2nd ed. p. 300). ‘There is a good continuity in all these phenomena, with gradual diver- gences just where we should expect them. The a, 8, y, and aK rays all produce the same primary ionization, comparing atom with atom, and differ only in the effects dite to scatter- ing and transformation ; that is to say, differ only as regards their production of secondary ionization. Now, the « and @ rays are certainly material particles, possessing electric fields. There is, therefore, a reasonable argument that the and X rays are also material, and possess electric fields. This is the case if they are pairs, and the smaller the moments are the more circumscribed are the fields and the less the ionization and the loss of energy. If the X rays contain ether pulses only, it is difficult to see why their effects should run so exactly in parallel with those of the « and # rays. It has been announced by Marx, as the result of a most ingenious experiment (Phys. Zeit. 1905, p. 268), that Rontgen rays move with the velocity of hght. It is extremely 1m- probable that material particles can possess such a velocity and the experiment of Marx might seem at first sight to be strongly against any material nature of the X rays. But it Natures of various Electric Radiations. 447 is not clear that Marx really measured the velocity of a radiation causing the emission of high-speed electrons, which is the characteristic feature of X rays: all that he showed was that the bundle of X rays contained radiation capable of exciting dé rays. To see this it is necessary to consider briefly the details of the experiment. An electric pulse is made to travel along a wire, W, as shown in the accompanying sketch. When it reaches the ZLARTH cathode, C, cathode rays are driven against the anode, A, and X rays are given out, some of which travel towards the saucer-shaped electrode, B. At the tocus of B is a small Faraday cylinder, F, connected to an electrometer, H. A small impulse is derived from the wire, W, by electrostatic induction at D, and travels down to B. If the various distances and wire-lengths are properly adjusted, so that the X rays arrive at B at the same moment as the derived im- pulse, electrons are liberated at B by the rays, and guided by the impulse into the cylinder, F', and thence to the elec- trometer. If now the distance of the X-ray bulb from B is altered, say, by an increase of 10 em., the wire from D to B has to be lengthened by 10cm. Thus, according to Marx, the X rays travel with the same velocity as the impulse in the wire, and therefore with the velocity of light. But it is to be remembered that the electrons which are liberated by X rays have an initial velocity averaging about 22 448 Prof. W. H. Brage on the Properties and 5x 10° per sec., 2. e., a speed due to thousands of volts, and are scattered in all directions from the surface on which the rays fall. Neither the weak impulse applied to B by the wave coming along the wire, DB, nor the peculiar form of the surface, B, could have any sensible effect in the way of guiding these fast-moving electrons into the cylinder, F. Only slow-moving electrons or 6 rays could be “guided by such means. Itis no doubt true that X rays do liberate a certain number of 6 rays, but it is clear that the experiment of Marx is quite consistent with the hypothesis that the X rays are complex, and consist in part of ether pulses tra- velling with the velocity of light, and producing 6 rays, and in part of material particles, cr pairs, travelling at a speed as yet undetermined, and exciting high-speed cathode rays. It would be reasonable to expect that a stream of pairs should be accompanied by ether pulses which had their origin at the time and place where the pairs broke away. It is possible that the example of the @ particle shows that a pair cannot possess a velocity greater than 10°, since at a higher speed it would be stripped of an electron, and become an « particle. J. J. Thomson has suggested that at this critical speed the e particle becomes electrically neutralized by the attachment of an electron. Presumably such a pair would then go on asayray. No such consequence has been observed ; and on the present hypothesis it would be better to suppose that the & particle ends its career by being taken up by an atom, as Rutherford has suggested. There is no reason to suppose the y ray or X ray to possess any great speed, so as to give it enough penetrating power. ‘The latter might depend rather on the limitation of the field of the pair; and a sufficient range for the velocity can be found between the minimum speed of the & particle and the maxi- mum speed necessary for penetration, which appears to be | about 10° for a charged particle, but may be less for ene without charge. A moderate speed would account for the reflexion or scattering of the X ray, and would indeed be necessary for this purpose. To sum up, it is clear that a stream of X rays contains some xther pulses, but it is not. easy to explain all the pro- perties of X rays on the sether-pulse theory. The explanations are easier if the rays are supposed to consist mainly of neutral pairs ; and the existence of such pairs is not improbable a priorr. \ Natures of various Electric Radiations. 449 Added July 18.—Since this was written several important papers have appeared, with which the outlined theory seems to me to be in harmony, I have supposed it possible for positive electrons to be detached from atoms of matter in the X-ray tube, and to be sent out in company with negative electrons, one of each going to the formation of a neutral pair. Now J.J. Thomson has just shown (Phil. Mag. May 1907) that the canal-rays consist of positive electrons, which may be H or H, or He, according to circumstances ; and that these appear no matter what the material is,in the tube. It will be remembered that Villard (Zons, Electrons, C orpuscules, p. 1022) was so impressed with the continual presence of hydrogen in vacuum- tubes, that he supposed the cathode particles to consist of hydrogen, until accurate measurements of the mass and velocity of the particles were made. He was largely influ- enced by the reducing action of the rays. After all, ‘it may be that H is produced where they ste, and! that Villard’: observations can be explained in this way. Sir William Ramsay (Journ. Chem. Soc. May 1907) has shown that there is an excess of hydrogen in water decomposed by radium emanation ; but the circumstances are too complicated to make the connexion more than a possibility at present. H. W. Schmidt has arrived at the conclusion (Phys. Zeit. June 1907) that the “ secondary ” radiation caused by # rays striking aluminium consists of scattered primary rays: this is In agreement with the argument stated above. He has also shown that undeflected 8 particles lose no speed in passing through a metal plate. This implies either that the energy required to produce ions does not come froin the 8 particle or that the @ particle does not produce ions until it is deflected. There seem several difficulties in the way of the latter supposition : though it is of course a possibility. It seems to me probable that the @ particle rarely produces more than one ion from a traversed molecule, but that an « particle may produce many: and that initial recombination is to be explained in this way. Kleeman has pointed out, in his Royal Society paper, that an « particle which has lost several ions has not yet been observed ; but it is to be remembered that such a molecule would probably dissociate at once, and it is well known that the a particie does produce dissociation. [) 450«4 XLII. On the Production of Statical Llectricity by the Action of Heat and Light. By Prof. G. MELANDER”*. iT F_\HE problems of atmospheric electricity were among the first to occupy the attention of investigators of elec- trical phenomena. Since the classical exper iment of Franklin in 1751, several physicists have shown that there exists an electrical field over the surface of the earth in clear as well as in cloudy weather. Experiments on atmospheric elec- tricity were at first carried out by means of kites, which occasionally reached considerable heights and_ collected electricity from the clouds. Afterwards balloons were em- ployed and observations were made on the ionization of the air. These experiments showed that the air is nearly always electrically charged, and that in fine weather the air is positively, and the earth negatively charged. That a connexion exists between the intensity of sunshine and the phenomena of terrestrial magnetism, appears to me probable from my experiments on illuminated magnets, and the question arises whether the rays of the sun might not be the indirect cause of the magnetism of the earth, 7.e. whether the earth-currents might not be the effect of sunshine. In order to investigate this question I procured a Dolezalek quadrant electrometer. This electrometer is so sensitive that by using sufficiently fine quartz fibres a deflexion of 17 mm. per millivolt may ie obtained, but it is not advisable to use fibres of smaller diameter than -004 mm., as then the needle, owing to the friction of the air, takes a very long time to come to rest. The needle, which is of silvered paper, was charged to a potential of 89 volts by means of a water-battery. The charge was led to the needle through the quartz fibre, which was rendered conducting by dipping it in a solution of chloride of magnesium. One pair o quadrants was connected to earth, and the other to a small piece of brass, which was hung free in the air with an insulated wire. The charge on a body may be easily measured by bringing it near the brass piece and observing the de- flexion. of the electrometer, and the sign of the charge may be determined in the usual way. In order to avoid all external disturbances the apparatus was completely enclosed in a cage of fine wire gauze. The arrangement of the appa- ratus is shown in the accompanying figure. The cage and the zinc plate ZZ on which it was placed were connected to earth. The door TT allows the body whose electrification is * Communicated by the Author. \ Production of Statical Electricity by Heat and Light. 451 to be measured to be introduced into the cage and placed on a plate PP, which could be raised so as to bring the body near the plate V connected to the electrometer. The deflexion of the electrometer when P is raised will be proportional to the charge of the body on it. 470 ELECTROMETER / 4 24 ” 2] re SSL RRR SY SC} OO] er eT a) SOR CRXY RN ote nee 5 xs 6 ey stat CA e, 0, x "sre7Ss PSEA SS SRE SS SOP TROIS rave As in fine weather the air is positively and the earth negatively charged, I thought it desirable, as mentioned above, to investigate what was the influence of sunshine on the charge of bodies exposed to its action. For this purpose plates of different substances were exposed in sunshine, and their electrical charge before and after exposure measured. In making the experiments I observed that a piece of paraffin wax and a sheet of gutta-percha which had lain in the dark for at least a year, showed even before exposure a negative charge; a stick of sealing-wax which had lain in the ordinary light of a room showed also a slight negative charge ; while the charge on an old ebonite plate and on a glass rod were scarcely perceptible. After exposure to sun- light all these bodies were charged : the paraffin, gutta-percha, and sealing-wax were highly charged, the charge on all three being of negative sign. The ebonite plate showed a slight negative, and the glass rod a strong positive charge. 452 Prot. G. Melander on the Production of Statical One half of the glass rod was ground and the other half smooth, but both parts were by exposure positively charged. Experiments on the electrification of metals by exposure are attended with very great difficulties, as is also the case with electrification by friction. The metal must be held by means of some insulator, and it is difficult to distinguish between the charge on the metal and that on the insulator. A few experiments with brass spheres showed that brass is negatively charged by heating. Other metals were perhaps _ positively charged, but the effect is much smaller than in the case of insulators. The action of sunshine seemed even in summer to depend on the degree of cloudiness of the sky, and as in autumn the altitude of the sun began to decrease, the charge pro- duced also diminished, and in some cases it was observed that in the morning the lower sides of the paraffin plates were positive, though in the course of the day they became negative again. Later on in the year pieces of paraftin which were kept in the darker places about the laboratory showed a constant positive charge ; this was never observed in summer, paraffin wax being “then, as mentioned before, always more or less negatively charged. It was also re- marked that during two very sunny weeks from the Ist to the 15th October all the paraffin plates, even those in the darker parts of the room, showed a negative charge. As in winter the action of daylight became continually weaker, I tried to obtain a source of artificial ight which would serve to charge the plates. A Bunsen flame, whether luminous or not, has not the slightest influence on paraffin, even when near enough to melt it, but if the plate is previously charged its charge is diminished by the heating. Plates exposed for a long time to strong are light showed a slight negative charge, but it is doubtful whether this might not be due to the direct influence of the potential of the arc terminals. Opportunity was also obtained of trying a powerful Finsen lamp, and a mercury-vapour lamp with a quartz tube, but no appreciable effect was observed. The active rays are specially strong in sunlight and are not stopped by a glass window. I have tried to find out whether the plates after exposure gave signs of radioactivity. The experiments were made w ith an electroscope of the Société centrale des produits chimiques of Paris, which is specially constructed for investigations on radioactive bodies. The apparatus was, however, not sensitive enough for this purpose, \ Hlectricity by the Action of Heat and Light. 453 and I have not yet been able to make the experiment with the quadrant electrometer. These experiments may perhaps furnish an explanation of the negative charge of the earth. It appears to be due to the direct action of sunshine. It has already been assumed that the negative charge of the earth should produce by influence a positive charge i in the upper layers of the atmosphere. It has also been de- finitely shown, that the normal electrical charge of the atmo- sphere has a maximum in summer and a minimum in winter. But the difference between summer and winter is generaily assumed to be due to the difference in the humidity of the air in summer and winter ; and this assumption is confirmed by recent observations carried out in different climates, and observations on the daily change of atmospheric electricity show also that it usually varies inversely as the temper ature and humidity of the air. The excitation of electricity by friction is one of the oldest electrical phenomena known, but the question as to which bodies are negatively and Giich positively electrified has not yet been “completely solved. It is known that it depends partly on the nature of the material and partly on the quality of the surface of a body, and hence it is difficult to say how a body will behave in this respect. The bodies which are electrified by friction have often been arranged in so-called potential series, in which each body should be negatively electrified by rubbing with bodies standing before it in the series, and ‘positiv ely elec- trified by rubbing with bodies coming after it. These series, though agreeing with each other in their general arrange- ment, differ greatly in detail. Hence it is evident that other factors, such as the quality of the surface and the tempe- rature of the body, have an influence on the phenomena. It was suggested to me by Prof. Wiener that the electri- fication observed might perhaps be due to the friction of air-currents, possibly « carrying dust, produced by the heating effect of ‘lhe sunshine ; and ng fncner suggested that he experiment should be tried with a glass plate placed over the paraffin. On making the experiment, I found that the electrification when exposed under a glass plate was consider- ably smaller than before ; but afterwards, on separating the glass and paraffin, I found that the olass plate was itself positively charged, and that the negative “char ge on the paraftin was as high as when exposed without the glass. The diminu- tion in the effect shown by the electrometer was therefore due to the condenser action of the two opposite charges. I also made an experiment to find whether currents of air and dust 454 Production of Statical Hlectricity by Heat and Light. passing over a paraffin plate could appreciably electrify it. For this purpose a cylindrical plate of paraffin was placed under a similar piece of wood, the air space between the two being about 1 mm. deep. In the middle of the wooden disk was a hole which could be connected through a glass tube to « water-suction pump. When the pump is in action a strong current of air is drawn over the surface of the paraffin, and the current is similar to the one which might be induced by the heating during exposure to sunshine. No charge what- ever could be detected on the paratiin after this treatment. It has until now been generally held, that it is only through friction and similar mechanical operations that a body may acquire an electrical charge, but the thermo- and pyroelectric properties of the so called hemimorphous crystals indicate that the temperature of a body has an influence on its charge, and the experiments described above show that radiant as well as mechanical energy is able to produce electrostatic charges on bodies exposed to its action. The actual amount of electrification is difficult to deter- mine. Several experiments have given discordant results, so that there must be some disturbing causes. Especially the action of internal friction seems very strong. The electrification by friction has therefore been the subject of my last investigation. The experiments made show, that when two pieces of paraftin, which have the same temperature, were rubbed one with the other, both pieces were negatively charged, but by keeping the temper ature of one piece of paraffin higher than the temperature of the other, the warmer piece shows after rubbing a positive charge and the colder a negative charge. I have made other experiments of similar nature. c. Obs. It is clear that this method will enable us to find the potential due to a circular current in any system of harmonics, provided we choose the equivalent shell appropriate to these harmonics. 6. To find the solid angle subtended at a point P by a circular wire in spher waar harmonics (zonal). Let the axis of the zonal harmonics be the axis of revolution of a spheroid having the plane of the circle as one of its plane-sections, and centre, the origin. Then } i o=| dS. = zi But from the theory of confocals, since r=constant is a Induction in Spheroids. 459 series of confocal spheroids, we have imdp—ade, (c=the major axis) She rar. where p is the perpendicular on the tangent plane at any point from the centre, and api ans me Bac BG, (1 = {as her dr (\). — Cn -++ IL) IE, (2) P,(e) Q; (7) Qn ("), + terms depending on ¢, But where 7’, ’ refer to the point P. Also il 1 [sin? 6 a ye pe he Let 1 eer ~ A2(72 —1),? ‘a es, ; hr»/ peal —cos? 0 and dS =f? /72—cos? 6 V7/727—1. sin Odd. dé ‘ 2 F ; S ! / d(),(1’) OQ Ay (> — 1) sin 6 dé D(C + 1) P,.(«) Ge Qn (7 ae ; remembering that @ terms disappear on integration between limits 0 to 27. Finally, since AQ) _ iL ieee ie oa a! an 1) ! ! ay, ay ‘ v= 2 Qo(z )(u- Iie 2 a ea Ene )'Q.0') du e flit (DU wy Or the potential due to a current ? circulating in the wire is o Y =2nil Qolr')(w—1) +E ae enone ! rst a) ab, dQ), tL menaie) ce na—eys 2 dye dr 7. To calculate the potential due to several turns of wire, 460 Prof. D. N. Mallik on Magnetic we have in the first place to find the mean value of V, 2. €. calculate ii Wie da \V deda OU olen) ae —~dr d Ve : | where c=distance of any winding of wire from the origin, and a=radius of the winding =hyPal Vip. 8. We shall suppose the meridian section of the coil to be a curvilinear area bounded by confocal ellipses (r=constant) and confocal hyperbolas (@=constant), so that + and w may be treated as independent variables. This will enable us to obtain an approximate solution of the problem of induction in a soft iron rod in the form of a very prolate spheroid, due to a coil of small depth. Now | O(a) TOcHoe oe 02 (7) Or’ OH OM” OF ee Je — I —1 leh be era eae — ae Ve ol, . the potential Oa m ps pe— 1 _ vin“ ar eae Jar dp \\ de da aS iin sas i /re—t LON 1p? a , = AY ( nil Qu) mu (el reer: — pn" Thy sa a A © Intl fh n =| D +e Sys a Pale Qu(r Nie [a- go ae +(1— 2)? — 18 | j dvdp. | 242 ee: at oe = —2mrmi Roe SS et cosh! r—r vail vee a 3) 2 2 +. i aPx dQ, If MGs NE eT ae a] Df oF : — w?)3(7? — 1)z ae 5s = n(n+ 1) Pr(w') Qr(a We . dr il (1 Bb HG 1) +(1—p?)2(2—1)8 } drdw ] 5 where m = total number of windings in the coil and i) de da = «. Induction in Spheroids. 461 r ps “(1 —p?)idp= Pipe 3 Vu Vip? 5 Pre) But since (1_—u? e =nP,1—npP», (= (nya = \ nP,1V/ 1 -p?du— \npP,, V/ te da ae From (1) and (2), we have meee 1 pw du=P,(1—p?)? +3) V1 — pt. Paid. (A) 7 Similarly, n+3 a "(r2@—1)? dr=Qu(? = 13-3) QaV/7? 1 dr, (B) fae 1s ole a “ fer (L-y?)Fdu = Pa/l- ‘al and n+1 ee EEA aks. eas ea (Qua ly D ms es Foes te eihe (Oy Vv if 4) oe io Tei 2 ye ( ) It is, therefore, necessary to evaluate the following integrals :— (1) Pa VAN —1 du = tl. 12 2 SS d= ils, (2) r Air ag 1 “VEO B} ee 1 ( ) {2 (4) | me Vr —ldr. 1) 3 a. dP, ] Pa/ =I —ldp= a | (w— ~\vie= Ee du “des 1 j 3 ‘4 ie poy aya Wall ] Sy EE sae, n(r+1) ee) dj \( alin ) hs Phil. Mag. 8. 6. Vol. 14. No. 82.. Oct. 1907. 21 Prof. D. N. Mallik on Magnetic i 2 3 dP, Hees ~ 2a Ue at HD) | (u TaLete ae = ae Vw =Tdp | 1 2 3 nN eee TIL oe mae ee : i we 1dp | a Paes n(n¢2) Ta = WDE. ST? = 2n—3) Tana 2 3 dP, 2 w. (n—2)n Tne (vw —1)?. oan —(2n—7) i I,-4- ks Subtracting, we get n(rn+ 2) 1,=(" — 1): . (Qn—1). P,-1+(n—1) Ce ee =(p?—1)8| 2n— 2,4 CD) Oe dq =(uU ( n—1 n(n— 2) b n-3 i (r.vimae a aS Cease bal (m a ae a = aad) [ (@x-D)P,at we 5)2, ice 4 =,L, ae (1—p*)?du=(1—p)tP,+311,-1 from A _—nt+3 : Ta sll, (say). 2) ae see Sorel A Meee Meee Fe ae ae |i Fe | ue i! 2 ae dP as du reer sete “du + [(uP. + j \x Vw—1d ln Nae aul —. abn (eo fc (1-4) Jk nee) [ Vw—l. te a le oe ee ae 7 ili ime VN) ae pe. We cd te Daas ech . me . (n—2)/)? gees | ban 2— Nv pe’ ie aa a pe els 4c Induction in Spheroids. 463 .. Subtracting, n?_l,= Vw—1. aca: ee ot. — Vu? —1 | @n—1) Prat ¢ om (2n—5) P,-3+. oe | (n = jee He d= — ja "ES cae BORN 8 n-1)? | =— /1—p? { @n—1)Phart =) 2n—5)P nat. ‘ } =n’ iln (say). aes { (1—p)ldu=P, Vina? + da from (C) n db =i tsay)) :. n oer | Dia = pe — Ps joa t\ eS! [pap Patt, het eee r9y — =F: soot 7a" — — Sill gataictony, | i adr — Te 5 ml log —> + tft hs _ 4 (Qn—1)P eel n—l 2n—1 + _ (2n— D) Peck. . = |= _yln-it | Sieg ;+ [Qn- ID) les Aa ecd ar 6 = 2n — — a +... ]. (where the argument of the I’s is r and not ,). ba (1 de a) = dr =Q,/7—1 Pe dy from (D) gtk 1 } ip Ss : 2 2 wae — [teat ° fs =X, (say). 1.(n—1) 464 Prof. D. N. Malhk on Magnetic For n=1, 2 (a J/P—1dr=Q/r—-1- Ve dr ‘ — Gt f) =Q, /r—1— ae .ar al 8 (r— (r—1)° =(), 777 a —; + oh a 1rA 3A ea cies rf Ges aa gickniees Each 1+5[-2+ tt |. where , 2n—2 (2n = 1)A,= 2 | Pas + 5 at esta tere | and (1 — x”) 21+ pow" + put’ +. Similarly, (vei dr = 1 fr log = V72—1ar 2n— rs qe -\[ i Py-it...+ ve dr £ r+1 il = 4 hilnlog— a cae CED) | (22-1) iln-1 +. + sl i Ta Feo se | and 2 fave dr=2 vr=1—2{ QvF=1 dr ie Qo _ Jee 2 | tt dr r/o jl 3 1Qn 3 (145 a *(2—1)! = Q(r?—1) 3) dillon me +E eas 5) -[@n-B that + =| Li rs = 51) (Lio qe eet ll from (B) a = oN, GO Induction in Spheroids. 465 We have also de da = —i? Vi-w cena |i a | dr dw /r—1 ae = 5 faV/1= pcos” ‘ptr Vr —1 sin 'w} =a (say) taken between limits. 10. The potential, therefore, becomes 2 ipa om _ 2mmi| Qu(r’) 1} + [at Bs fue cos hor —r 7? — 1] satel \ Wee +1, + % Grey Pale) Qale') {Me alla + Te Xf taken between limits. 11. Calling this V and changing 7 into r and wp’ into uw and vice versa, let V = Op Qo(r) + Gi Pile) Qi(r) +... +. And V, being the potential inside the magnetic substance, and V, that outside, let Vi = AotAi Pie) Pir) + V. = B, Qo(r) + By Pi(e) Qi(r) +... +... and . 3 ] es e e Then, since V;= V. at r=R=-, where e is the eccentricity é of the spheroid, Ay = By Q(R), A, P,(R) = B, Q,(R), A, P,() = B, Q.(R), &e 12. Again from the equation of the flux, Mb Bes 2 OV —(1+4a nh) oo cae ~ ahs = ()). but since h2 dn =— rdr, P we have oF V 7 (iG DRAans i222 Ack ot — ()) Boe or 466 Prof. D. N. Mallik on Magnetic From these the constants can be determined, viz., = Ao Bo = —ArkCy = @,(Ry’ —A,(1 bdme a «—4rkC,) oe = 0, P»(B) -dQn, dy AQn or A Ow ake +E) gg j= ame since A, P,(R) = B, Q,(R). 13. For a very prolate spheroid, R is very nearly equal to 1. In this case the effect of all but the first term is negligible in the present problem (of induction). To prove this, we notice that AarkC dQn nv dk PCR) AQn ) Oa2) gh a a ees Hence if M, = the part of magnetic induction due to the A, = Q, term, Mo Ute) OU, joi OR 3 I where U=U,+Ui+... = V+V,. 1+ 4k dP c,! ; ~ ‘bt dR +C : in) Pale) ee QR Gaye ak ae aR ee (u) Te Ae R 4 FT IS | But a ae u r+1 2n—1 Qu(r) = 5P, log” 24 -(-= Aa a | dQn _ 1dP, Pag i Pr aS Nee ] [era SL) Ea ae |: Ny ae 2 — 5 ae dr y—] l—n "dr P, AQn Lia dP, iB [A= (P, dPa—1 4 |; Induction in Spheroids. 467 When r=R=1 very nearly, the left-hand side is large, Or oy 5 oa dn Q,(R) aR 3 large compared with TR" Also Ma = F(R? 1)" de I rane pearl RPS Lee ant Fit4e k)Cn— ae i ey) 7p? nearly. peep eae Which is therefore evidently small in comparison with M) (M,, M,... being of decreasing magnitudes) ; for one —_— = al + i and it can be proved, as is also @ prior: evident, that the C’s are of decreasing magnitudes. Now 24/2 fg NN, Wa) RI C= —2nmi} 1+ie| * =e cosh r'—7' vr? =1| Ae ; ; a taken between limits. In order to simplify this, we shall assume that the wire is wrapped round the whole of one-half of the spheroid. This amounts to taking yw between the limits 1 and 0. In this case T a= 4 (aC —ac), 3 3 h? GY + a, 2 and (Oe ami 1 + F, log wana =|) where a, c, are axes of the outer confocal. If now J be the total depth of the layers of wire, since ay = at+n, 468 Mr. J. Russell on the Superposition of a? also ayc;:—ac = a(i+e “:)- (A 2etelog(1+™) | re w\ « | ia C 15. The magnetic induction at any point of the surface is — theretore x =a 2 N 2e%e log( 1+ ) 2 — cr | | =F (1+4ak) 2nmi | 14+— ) |: | bmd(1 ats 2 4 Patna College, Bengal, India. XLIV. The Superposition of Mechanical Vibrations (Electric Oscillations) upon Magnetization and conversely, in Lron, Steel, and Nickel. By Jamues Russe, /R.SL* [Plate XI.] | agen mechanical vibrations affect magnetism has been known since the time of Gilbert. About twenty years ago Ewing published investigations upon the effects of vibrations upon magnetization f. It is also recognized that disturbances other than mechanical produce magnetic effects essentially vibratory. —(B eos" 0 a = ts wher ia A= (Teig2oe and B= ( p Fy (ea. By putting r=R and @=0 in the expression for V3 we find that the potential at the end of the polar radius 4 AS), 2B = 5X1 5s And by putting r=R(1+.e) [e being the value of e at the earth’s surface] and = = the value of ithe potential at the earth’s surface on the equator is found to be 3°") Rd +e) SR +e)? Lhe Es a my Te Eee Since B already contains the first power of ¢ we do not need to retain «B &e. The potential of centrifugal force at the equator, due to the earth’s rotation, is 3R7(1+6¢)’o or $R’o? (w being the earth’s angular velocity of rotation) provided we assume, as in the case of attractions, that the space variation of potential gives the force on unit mass, and not the negative of this force as is usual. Since the earth’s sur- face is a level surface the whole potential at the equator is equal to the whole potential at the pole. Hence 3B 1 | aK {eqa Sit = 5 Re Now 4 = Now gTA= (eo galg 78°) dp -. ==, the earth’s mass. -_ 486 Mr. J. Prescott on the Also 55, =g, the acceleration due to gravity at Re? , the earth’s surface. Thus we get 4 OB uals ie eRg— 3 Krs Re = ak @’, or g 4 ou ib 1 €Ro? 3875 Rip 9° ° ° ° © (a) If p is constant then e may be considered constant and B=peR*. Then our equation would give eae SS “Re? 5 Reo? 2° But g —/ _ = 289, Ro? ~ Hence 1 _ 991. It is certain, however, that e is not constant. We cannot find ¢ therefore without knowing the value of the coefficient R B. Now this coefficient is given in terms of ( pedp, a ¢ quantity which does not contain e, by the theory of the precession of the earth’s axis. By assuming a reasonable law for p we can then find B, and thence determine e. Fig. 2. LARTHS ANS The potential of the earth at an external point P (fig. 2) is GA ANB x } =; Kr {=— = Boos 6—1)¢. The force exerted by the earth perpendicular to OP on Ligure of the Earth. 487 unit mass at P is ous rQd- : Acton's | The moment of this force about O is or. Now the re- action of the unit mass on the earth is exactly the opposite of the earth’s action on the unit mass. Consequently the moment about O of the couple exerted by the unit mass on the earth is ay in the direction tending to increase the angle 6 up toa right angle. If the sun is at P, the couple exerted by the sun, whose mass is 8, is OD eae Fain 0. foley Me If n is the angular velocity of the earth in its orbit — = Tn’. Fe: Thus the couple exerted by the sun on the earth becomes 87Bn? sin @ cos 6. Fig. 3. POLE OF ECLIPTIC EARTHS FOLE Referring to figure 3, by spherical trigonometry, cos 9 = sin asin ¢. 488 Mr. J. Prescott on-the Therefore sin 0 =,/{1—sin’ « sin? $} = 1—t4sin’a sin? 6+ sin‘ asin’ nearly, since sina = sin 234°='4 about, so that the terms ignored are small. Hence the couple exerted by the sun = 8 7Bn’ sin asin 6{1—4 sin? a sin? h+ 2 sin‘ asin‘ dh}. The axis of this couple is OQ, perpendicular to the plane containing the earth’s axis and the sun. The only effective component in precession is that parallel to OP, the inter- section of the plane of the equator and the ecliptic. The other component causes nutation. Hence the effective couple for precession _ = moment of couple x cos w. By spherical trigonometry i sin d ea s/ (1+ tan? a cos? ) = sin d(1—4 tan’ acos’¢ + 3 tan’ acos’ ¢). Thus the effective couple is i L= au Bn? sin « sin? d{1—4 sin’ a sin? d —4 tan? a cos’ + 2sin‘ asin’ d+ tan? « sin’ @ sin’ d cos’ + tan’ aces’ d}. Now a =n. Therefore df= ah . Hence the moment of momentum generated by the sun’s couple action in one year =|" (ee 0 nv > : tte Ob Lee 1h a = 7 Bum sina. 7 {t= asin aH 7-972 6 tan He Teg:2 3 Deol: IL . ees) ~sinta—=.—...24+ -tan’ Gig ey oe + be Mea D: + {tan @ SU 3 I 3, oh which becomes, on putting 233° for a, 8 Deron re {AUR | Y g Baz? sin oh} oa Figure of the Earth. 489 This is the sun’s effect. The moon’s effect must be added to this. The mean place of the moon is in the ecliptic, and if the action of the moon be taken to be the same as that of a similar body always in the ecliptic at the moon’s distance the error. will be small. Let S, E, M denote the sun’s, earth’s, and moon’s masses 3 d,, dy, the sun’s and moon’s distances from the earth: then M | | aa Moon’s effect M Sun’s effect iy ds K+M neg Ml dy ~M+E 8 ds iL _ 1 (Moon’s Period)? mew i (Harth’s Period)? =o Z 7 Se NAS = 2°13 about. Hence the effective moment of momentum created by the combined action of the sun and moon , = 3°18 xX 87’Bnsin (-931) : If L is the moment of inertia of the earth and a, as before, its angular velocity of pou hol this effect turns the earth’s AXIS ih ough 3°18 x 8 w’nB sin @(°931) lo But the earth’s axis describes a cone of semi-vertical angle a in 26,000 years. Hence the angle turned through by the earth’s axis in one year is radians. 27r sin a@ 26000 ° Therefore 931Lx318X8a’Bnsine 2rsine | Iw PET - A90 Mr. J. Presectt on the Whence Be 2x5 @y 26000 x °931x3°18x 87r'n 10 3654 al. ’ = 96000-x -93ix 318x871 3), 5 ee al. Bid. If p were constant, in which case we could consider e constant also, this would give ie alo: which does not agree with the result found by assuming p to be constant in the equation obtained by considering the equilibrium shape of a liquid earth. We shall now have to assume an expression for p in terms of the radius which shall agree with all known facts, and give a density decreasing from the centre outwards. We know that, the density of water being taken as the unit, the mean density of the earth is about 5: 5 ‘and the surface density is 3 or 2°05. Also it is quite certain that p decreases from the centre outwards. These facts tell us that | pB*dB>2°5x1R and <53 xi R’*. The first of these conclusions is easily seen ; for at every point in the earth pB' > 2583) R i pB'dB > 25x Re. 0 The second statement can be proved thus :— We know that R i pB2dB=5'5 x 1 RP. Therefore and therefore Figure of the Earth. 491 Hence aan pB'dp=~, ae ” pds — a pRdB = Lew - 1 (Rip'—8) Bag ~-! ("eae—oy hen Now o is always negative and the remaining factors under the integral sign are positive. Thus ae R “= R =|. pB'd8+a positive quantity, which proves the second statement. A law of density which gives roughly the type of variation to be expected is by git ey p=C—D(5 To make p=3 at the surface we get 3=C—D. C is the density at the centre and can be given any arbitrary value. By making the mean density 5:5, n is determined thus :— bate p83 Bug. This gives pital jy ae ae But also C—D=3. Therefore . Wes yk) Pet een OC 11 Let m denote the value of \ pB'd8 Ol DN R | gdp 0 499 Mr. J. Prescott on the Then 5 3 Tet ong on substituting for x and D. Now the densest materials we know in the earth’s crust nave specific gravities only about 22 or 23. It is highly probable then that the density at the earth’s centre is not more than 30. The fact that we find in the earth’s crust matter so dense as platinum and osmium mingled with much lghter substances, rather indicates that the density at the centre is not nearly so great as 30. For, if substances of such dif- ferent densities are to, be found within a few feet of the earth’s surface, it is very likely that lighter matter will be mingled with the denser in the interior. But at the same time there must be a gradual increase of density from the surface towards the centre. When we have determined m the value of B can be calculated from the equation Substituting for B in equation («), obtained from the rotation of the earth, we find MO m R if Rat 5" 316 Roa? * 2 Le, Lo) on KR a. il RUS WH he Ae Yo dye ob Ne tl BBG ne oe Now Chae Bae 200 Hence 3m Auevall = BiG sco tO Osun Ligure of the Earth. 493 The following table gives the calculated values of e, using the value of m obtained by assuming 7 pas-a(f | | Density at the | Density at the Mean liver | surface. centre. density. | a 3 | 30 5D | ete 3 | 75) Dio | = 308 3 20 D5 302 3 15 a) 300 3 3 lie) 300 5) 12 NN) 299 3 10 Dd nO Dae) 30 DD 310 29 25 a) 309 25 20) Sn) 307 2:5 15 a5 306 2-5 10 5d 299 It appears from the above table that the value assumed for the density at the centre does not greatly affect the result. I believe that any assumption concerning the density, which makes it decrease as the radius increases and which gives approximately the known mean and surface densities, cannot give a value of e differing much from those in the table. I tried another completely differe1it formula for the density to see what result it led to. The formula is yt han EE PY (64K) To make the surface-density 3 and the mean density 5:5, T found that H and K must be 16°35R° and -76R respectively. These values make the density at the centre very large, namely 37:2. The value tound for m is 4°68. This gives The value I consider most probable from my calculations 18 € Phil. Mag. S. 6. Vol. 14. No. 82:Ocer'19070 7-2 Ey fe ON aire XLVI. On the Measurement of Mutual Inductance by the Aid of a Vibration Galvanometer. By ALBERT CAMPBELL, B.A* (From the National Physical Laboratory.) [Plate XII] CoNTENTS. . Introductory. Theory of Modified Carey Foster Method. . Vibration Galvanometer. . Moving Coil Vibration Galvanometer. 5. Practical Working of Galvanometer and Hughes-Rayleigh Method adapted to Measuring Frequency. 6. Results obtained by Carey Foster Method. Hs 0o KO ~ 1. Introductory. TYXHE determination of a self inductance by comparing it with a condenser by means of Anderson’s Method can be made with ease and accuracy, as the two adjustments are independent. The use of a vibration galvanometer in this method as carried out by Rosa and Grover (Bulletin of the Bureau of Standards, vol. i. p. 291, 1905) greatly increases the ease of manipulation and the sensitivity of reading. For several years past we have tested our standards of mutual inductance against the B.A. Standard Air Condensers (as well as Mica Standards) which have been standardized by Maxwell’s Commutator Method. For this purpose I have used Carey Foster’s Method t, in which (as in Anderson’s Method) the adjustments are easy and the formula simple. The connexions are shown in fig. 1. icoaele R is a non-inductive resistance (capable of carrying a fair amount of current); M is the mutual inductance to be * Communicated by the Physical Society: read May 24, 1907. + Phil. Mag. [5] vol. xxiii, p. 121, Feb. 1887, ol Measurement of Mutual Inductanee. fo5 measured, its secondary coil being in series with an ad- justable resistance in the branch AyF ; K is a condenser, and G a ballistic galvanometer. When there is no throw on G on reversing the battery then M=10-*KRr, where M is in henries and K in microfarads, and r is the resistance of the branch AyF. To increase the sensitivity a secohmmeter arrangement was sometimes used. Knowing the value of the vibration galvanometer in other cases, [ attempted to apply it to this one, but found that the methed had to be modified in order to make it applicable. I found later that the modification I had introduced had been already suggested by Rowland*. As the use of the vibration galvanometer, however, is a great advantage (and novel in this method, so far as I know), I think it will be of interest to describe the complete method. 2. Theory of Modified Carey Foster Method. In fig. 2 let Q be a source of alternating current and G a vibration galvanometer or its equivalent. The necessary modification consists in adding a resistance S in series with the condenser K. Let the resistances of the other branches be R and 7, and let the instantaneous values of the currents be 7, 21, and 2 as marked. Let the instantaneous potentials on the terminals of the galvanometer G be 0 and Q, so that there is no deflexion (2. e. the condition of balance is to hold at every instant). Let v be the instantaneous value of the potential at D, and q¢ the charge in the condenser. * Phil. Mag. [5] vol. xlv. pp. 65-85 (1898), - ae. [gee 496 Mr. A. Campbell on the Measurement of Mutual Then — —11—le and V=26 +L aM@ ee dt nay ° di, Se diy dis =ur +L, M, -M-. * 5 : (1) Also == ality q=K(v—2z,8), Se eg eed Se oo Si ; dy K +85; dt’ So iR=v= const. + ie dt+SKi, ; therefore : dis di, | Haei K e489. Substituting in (1) we have a a MS) di, i? TER) + (L- M— ae =o. Now, as will be shown below, we may assume all the currents to be sinusoidal, i. e. RG sin pt, and hence MS r—M/RK=0 and L-M——,°=0. Thus for a balance we must have the following two conditions satisfied, viz. : M=-10-°KRr, | 2. | ee and bauet®, i. ae where K isin microfarads. When S=0, L=M-; and this is therefore the minimum permissible value for L. When L is less than M in the pair of coils under test, a third inductive coil must be inserted in the branch OrO to bring the value of Li up to at least M, otherwise no balance can be obtained. It will be noticed (a) that if R be kept constant the con- ditions (2) and (3) can be satisfied by zndependent adjustments Inductance by the Aid of a Vibration Galvanometer. 497 of K or rand $8; (0) that the adjustments are independent ot the frequency. Accordingly a balance can always be obtained with great facility *. 3. Vibration Galvanometers. Since Vibration Galvanometer methods are familiar to very few experimenters in this country, I think the following general description will be of interest. — By a Vibration Galvanometer is meant one in which the natural vibration frequency of the moving part can be ad- justed to be the same as the frequency of the source of alternating or pulsating current used. The two main ad- vantages in using a tuned galvanometer or other instrument are as follows :—(a) when the instrument is in tune with the source of current the vibratory motion of the moving part is enormously increased, due to resonance; thus a_ high sensitivity is obtained, usually about 100 times greater than that without tuning. () Since the sensitivity is so very much greater for the proper frequency than for others, when the wave form is other than a sine curve the instrument, if tuned to the fundamental frequency, responds to this, and is practically unaffected by the harmonics ; if the instrument is tuned to one of the harmonics instead, all but this com- ponent is practically ignored by it. For this reason the theory of each method in which a tuned instrument is used can be worked out on the assumption that the wave forms of voltage and current are all pure sine curves. The deflexion is usually proportional to the amplitude. This use of a tuned instrument in null methods is, I believe, * The above investigation can be carried out more readily by the use of the operators i= —1 and 1/Kp¥ —1, but to some readers the method given will be clearer. Equation (1) becomes (r-+Lp¥ —1—Mp¥ --1),=Mp¥ -1.4; and the next equations give —Ri,= (S— ae Kp Hence rt RG+Lp ov —1—Mp¥ —1)=MpvV —1 (s- No ). Separating the real and imaginary parts we have | M=KRr R and ie as before. 498 Mr. A. Campbell on the Measurement of Mutual _ due to Max Wien%, in one of whose papers ( Wied. Ann. xliv. p- 689, 1891) will be found a very complete discussion of a number of his methods of measuring inductance and capacity. In all his earlier experiments the tuned instrument was an ‘ Optical Telephone,” in which the motion of the diaphragm was magnified by the use of a small mirror with light spot and scale. The sensitivity of this was 3 x 10-7 amp. per mm. at 1 m. In 1896 Rubens’s Vibration Galvanometer appeared t ; it consists of a series of very small magnets or soft-iron needles fastened to the middle of a tightly str ung torsion wire and in a field due to two strong permanent magnets, round whose pole-pieces are coils carrying the alternating current to be measured. The tuning is effected by altering the effective length of the clamped torsion wire and by adjustment of the magnets, and the sensitivity obtained is said to be four times greater than that of the optical telephone. Some years later | M. Wien brought out a more boner form, in which the small magnet system is between the poles of a small electromagnet magnetized entirely by the current to be measured. 4, Moving Coil Vibration Galvanometer. After using an instrument of ihe Rubens type for some time, I designed another of moving coil type, which I have found more convenient. It consists of an electromagnet (or permanent magnet) with a rather narrow air gap in which is suspended a very light and small coil with bifilar control, which can be regu- lated by altering the tension by means of an adjustable spring or welght (as in some oscillographs). Fig. 3. g ay MONTE Lapa — ee Coie SPRING MRROR O/H THREADS BIFILARS In fig. 3 is shown one arrangement of the suspended system which I have used (shown horizontally for convenience of printing). * Max Wien, Wied. Ann. xiii. p. 598 (1891); xliv. p. 681 (1891) ; xliv. p. 689 (1891); lvii. p. 249 (1896); lviii. p. 853 (1898). See also Ki. Orlich, Elektrotechn. Zeitschi. vol. xxvi. (1908). tT Rubens, Wied. Ann. lvi. p. 27 (1895). { M. Wien, Ann, der Physik; iv. p. 425 (1901). \ Inductance by the Aid of a Vibration Galvanometer. 499 Below the coil is a fastening of one or more silk threads c. The range of frequency obtainable depends on the moment of inertia of the moving part, the tension, width of bifilars, &c. In one specimen the ordinary range (from 50 to 100 ~ per sec.) can be obtained by simply tightening or loosening the spring by the screw adjustment, while by placing an adjustable bridge } (fig. 3) under the bifilars the range can be extended to 700 or 800 ~ per sec. The readiness with which the frequency can be adjusted appears to be one of the advantages in the bifilar type. As the frequency is raised the sensitivity decreases in the inverse ratio. With given magnetic field, in normal use (i. e. with resonance) the sensitivity only depends on the damping moment, which is both mechanical and electrical. For example, if the moment of inertia and the control torque be both increased in the same proportion without altering the damping, then both the frequency and the sensitivity remain unchanged. It is of importance, therefore, to keep the damping small. For many purposes, at frequencies of 20 to 200 ~ per second, sufficient sensitivity can be obtained even when using a fairly large mirror (1 em. diameter), but for higher frequencies it is advisable to reduce this size considerably. The control torque is usually strong, the tension being of the order of 0°5 to 1 kom. 0. Practical Working of Galvanometer and Lughes-Rayleigh Method. The best type of current to use is a nearly pure sine-curve alternating current of very steady frequency (see Rosa and Grover above), but an interrupted current can be used with good accuracy. It is desirable to be able to set the frequency of the current by gradual and fine adjustment for the exact tuning, and for this purpose a wire interrupter like that of Wien is effective. It is merely a monochord solidly supported with fine adjustment of tension and maintained electrically with a mercury break as tuning-forks are. When the galvanometer is in resonance (which is known by the maximum elongation of the spot of light with a given current), it does not follow that it is responding to the fundamental frequency given by the wire * ; it may be in resonance with one of the harmonics. In order to determine the actual frequency to which it is answering, a usual method is to test it by a * It is a curious fact that a Rubens Galvanometer with given control sometimes has two points of resonance near one another, e. gy. 40 and 43 —~ per second in one specimen. (See also Rosa and Grover, loc. cit.) 500» Mr:-A. Campbell on the Measurcment oj Mutual condenser and a variable self-inductance brought to resonance. Another method which J have found very convenient for the same purpose is that of Hughes’s In- . ductance Bridge * as developed by Lord Rayleigh +, in which a mutual inductance is compared sgainst an independent self- inductance. The connexions are shown in fig, 4, where M is a variable mutual inductance; L a self-inductance of resistance P ; Q, R, and §8 non-inductive resistances; Hi a source of alternating or intermittent current of steady frequency, and G the vibration galvanometer. R+8 is kept constant, Z being a slider by which 8, which is entirely a slide-wire, can be gradually varied down to zero. As Lord Rayleigh has shown, the conditions for a balance are : QR—SP: = ML oa ee M(P+04R48)=Sh, 2. 4): eee where p=27n, n being the frequency. Let Q as well as R+S8 have a fixed value. For good sensitivity the resistance P usually will have a temperature coefiicient not negligible, as the whole or part of the arm may be of copper- T'wo cases arise according as we consider P (1) known and constant, or (2) only approximately known and variable. Case 1.—lLet P be constant, and hence P+Q+R+S = const. =a (say) ; also R+8 = 0. and Let L also be constant and known, and let a balance be obtained by varying M and the position of Z. Then we have (Gai) = pie (4-2) 28 Ma, QO>s) 5a * Tir 6 Pt vealed Thus n is expressed in terms of the single variable 8, and the slide-wire may be marked directly with the values of the frequency deduced from (6). If wide range of frequencies is to be dealt with, various * Prof. E. D. Hughes, Jour. Inst. Elect. Eng: xv. p. 6. Jan. 1886. 7 Lord Rayleigh, Phil. Mag. Dec. 1886, \ Inductance by the Aid of a Vibration Galvanometer. 5OL values may be given to L. Thus, if L be changed to some sub-multiple L/q, the scale readings for n will merely have to be multiplied by q throughout, provided that P is kept constant. Perhaps a better way is to keep L unchanged, and alter P+Q and R+S8 each in the ratio 1:q, the alterations being made in P' and R only, leaving Q and 8 as before ; from formula (6) it will be seen that, for the same. scale reading, n will become gr. The value of the variable M does not require to be known. The following example, giving values which I have actually used, may be of practical interest. P=25 ohms, Q=5 ohms, R+S=4 ohms, L=0°1066 henry. The graduation of the slide-wire corresponds to Table I. TABiE el: Temperature- | i: 8. coefficient of 7. —~ per sec. ohm. °/, per degree C. 10 0642 —0°43 15 0-608 —0°32 20 0-562 —0-21 30 0-471 | —0:08° | 40 0392 —0-01 | 50 0:320 | +004 | 60 0-260 +0:08 | 70 0-213 +0:°09 80 0-175 | +0:10 90 0-147 | +011 100 0:126 +0:11 110 0107 +0:12 120 0-090 +0°12 Since M=0:0031358, its range of variation will be from about 2 millihenries at n=O down to about 0°28 millihenry aie 20) : This case is usually sufficient to discriminate the actual frequency to which the galvanometer is responding, the exact frequency of the source being determined by com- parison with a standard fork or stroboscopically. Case 2.—If P be. not exactly known, a temperature cor- rection may be applied to the scale readings. Thus in the above example, in which P was entirely of copper, the temperature coefficients of 2 at various points of the scale are shown.in the third column of Table I. It will be noticed that the correction may become large only below 80~ per second. If the variable M has been accurately calibrated, p may be obtained by the equation » _ (Q+8)(R+8) ( Ss :: = a VT ML @ 502 Measurement of Mutual Inductance. For example, the interrupter was tuned to unison with a standard fork which gave 119°9~ per sec.: with L= 0°1000 henry the method gave n=120°0 and 119°8 ~ per sec. in two observations. Although I have described this method as used for deter- mining the frequency to a first approximation, it can be used, with an accurately known frequency, to determine L and M in terms of P, Q, R, 8, and »; and the use of the vibration galvanometer avoids the difficulty of obtaining a pure sibe-curve current. 6. Results obtained by Modified Carey Foster Method. A series (A) of careful tests were made by this method on a standard mutual inductance of nominal value 0:05 henry. This standard consists of a pair of coils of silk-covered wire wound in two deep channels turned on a cylinder of marble, the whole being soaked in hot paraffin wax after winding. It is illustrated in Plate XII. i a It was originally adjusted by Carey Foster’s method, using a ballistic galvanometer with an air condenser as standard. A series (B) of tests were made on it, using Carey Foster’s Method with a secohmmeter commutator. It was also tested (C) by a quite independent method, viz., Kirchhoff’s Absolute Method with a ballistic galvanometer *. In Table II. are shown some of the results of these sets of tests. TasueE II, | M Greatest Set. | Condenser. K. R. £ re error from | ON ets mean of set. ae mfd. Parts in 10,000.) hes eae Nheaies.e 0:9994 100°U0 0:05009 | | | Ng eso cee 0°8003 Ws 0:05008 | $ 0:05009 2 eee SUNOS 0°5003 005010 | J V Beret Wate) Mae iia 004165 | 20 005008 Viica, aes: 0°3000 00 0:05013 pe eee 05000 50 | 0-05013. | ¢ 205010 6 | bieeahc dene he 0:5000 20 | 0-05008 | Osea seems beter BOVEIN est 005019) | | 0-05013 | 0:05014 | 0:05011 4 0-:05014 10 | 0-05013 | | | 005015 | | | 005016 | ) | * Maxwell’s Elect. & Mag. vol.ii. § 759; Kirchhoff, Poge. Ann. Ixxvi. April 1849 ; and Glazebrook, Sargant, & Dodds, Phil. Trans. pp. 223-268 (1883). Lloyd's Fringes for Internal Reflexion. 503 In sets (A) and (B) the frequency was of the order of 40 and 100 ~ per second respectively. The agreement of sets (A) and (B) appears satisfactory ; while the slightly higher result given by (C) is probably within the limits of possible error of the method as used *, The readings in (A) were sensitive to 2 or 3 in 10,000. The resistance R was specially wound to avoid capacity and inductance. An inductance of 0°1000 henry was added in the branch OrO. The tetal self-inductance of this branch by comparison with our standard inductances was 0 765 henry. Hence, by (3), 765 x 100 M = L(gas)=— [5955 = 0-05/)1 henry, which is good agreement with the results given by the formula M=10KRr. Thus we infer that in the mica condenser used there is no appreciable apparent series resistance such as Rowland and other experimenters found in some cases. I would remark that, after using method (A), I feel confident that it is still "capable of much higher accuracy than that shown above. In conclusion I would express my best thanks to Dr. Glaze- brook for most valued advice and help. XLVIII. Lloyd's Fringes for Internal Reflexion, and the Change of Phase of Ordinarily Reflected Light. By P. V. Bevan, M.A., Fellow of Trinity ‘College, Unicersity Demonstrator in Experimental Physics, Cambridget. [Plate XIII.] T is generally assumed that when light is reflected ex- ternally, as in the applications of the wave theory to Newton’s rings, there is a loss of half an undulation. ‘The evidence for this is the single mirror fringes obtained by Lloyd, and experiments with the three mirrors of Fresnel made by Jamin. In the first case we have interference of * The main probable errors in (C) seem to be due to three causes, namely: the variations (natural and other) in the earth’s horizontal magnetic field: some uncertainty in the time measurements: and the magnetizing effect of the current on the galvanometer needles, not necessarily the same for a steady current and a sudden rush. + Communicated by the Author. 504 Mr. P. V Bevan on Lloyd’s two pencils of light, one of which has suffered a reflexion ; in the second one pencil of light has suffered one reflexion and the other two reflexions. The Lloyd fringes give us evidence only as to grazing incidence. From the Jamin experiments it appears that when light polarized perpendicu- larly to the plane of incidence is reflected at an angle of incidence between the normal and the principal incidence there is not the loss of the half undulation. It appears also that when light is reflected near the principal incidence, there is a difference of phase introduced in the two components polarized in and perpendicularly to the plane of incidence, giving rise to elliptic polarization in the reflected perce due to an incident plane-polarized pencil. We can easily prove that if there be a loss of half an undu- Jation at grazing incidence for the case of all light (the result of Lloyd’s experiment), there must be in the case of light polarized either in or perpendicularly to the plane ~ of incidence a change somewhere between the grazing incidence and normal incidence. It is natural to assume that the light polarized in the plane of incidence suffers no change of this kind, but we should expect at the polarizing angle a change in the character of the reflected beam for light polarized perpendicularly fo the plane of incidence. In fig. 1 let P repre- sent the electric vector for incidence nearly grazing, then Q directed in the opposite direction to P as a result of the loss of half an undulation will represent the vector for the netlected light. When we diminish the angle of incidence we reach the polarizing angle when Q is zero. If now we diminish the angle still the vector Q must appear on the other side of Fringes for Internal Reflexion. 505 the ray—opposite to the side on which it appeared Just before the principal incidence, for otherwise when we reach normal incidence the two vectors P and Q would be on the same side of the normal, as in fig. 2. But in the case of a ‘Fig. 2. AY REFLECTEY ft | WSOEN Te pencil polarized in the other way, the two vectors appear on opposite sides of the normal; and in the case of normal incidence the plane of polarization is of course immaterial for ordinary reflexion. The complete results follow from the Fresnel reflexion formulee ; from these it appears that the amplitude does change sign as we pass through the principal incidence. The Jamin experiments are in accordance with the Fresnel formulee, and the phenomena of the elliptic polarization near the principal incidence are in agreement with the Cauchy extension of the Fresnel formule, which take into account a transition layer at the surface. It is hardly necessary to remark that these formulz follow as results of the electro- magnetic theory. There is, however, as yet no evidence for the actual phase changes which reflected light undergoes when the reflexion is internal. There is evidence for the difference of phase changes between light polarized in and perpendicularly to the plane of incidence. Such instruments as the Fresnel Rhomb depend on this difference, but as to the actual value in either case as yet there is no evidence. The Stokes 506 Mr. P. V. Bevan on Lloyd's investigation shows that there is a difference of phase of half an undulation in the cases of internal and external reflexion, but this investigation only applies to the case of incidence internally at an angle less than the critical angle. The experiment of this paper shows that at grazing incidence in internal reflexion there is a loss of phase of half a period in the case of both kinds of light just as in the case of external reflexion. The experiment is of the same kind as Lloyd’s, and is only of interest in that it affords further confirmation of the applicability of the Fresnel formule. Lloyd * concluded that the successive distances of the dark fringes from the centre of the system, obtained by the single mirror, were in accordance with the assumption that a loss of half an undulation took place at the reflexion, in other words that the geometrical centre of the fringe system was a dark fringe. This result is quite clear if the fringes be observed with an eyepiece close up to the mirror, so that the fringes seen have their centre actually on the mirror. — The dark fringes appear clearly at distances from the edge of the mirror in the ratios of their numbers 1, 2, 3, 4, &c., MOC TOG 10 was seMMOS I Bh Hy CWO, 2S Pond he then Gee were a half undulation not lost at the reflexion. Fringes of the same type as Lloyd’s can easily be obtained by means of a reflecting surface of water and internal reflexion. A trough of about 20 em. length was made with glass ends, so that light from a slit could be observed through water in the trough directly and after reflexion at the surface. In this way two pencils of light can be obtained which are in the condition for interference. ‘The water meniscus gives no trouble as the glass is wetted, and so the surface is turned upwards at the ends of the trough and a large perfectly plane mirror is formed. The fringes can he seen on a screen, or with an eyepiece or microscope in the ordinary way. "A fine slit was used illuminated by an are-lamp. If the microscope be near enough to the water-trough a line of the surface will appear in focus, and this will be the centre of the fringe system. With a travelling microscope measurements of the distances of the dark fringes from the centre of the system can easily be made. It was found that these distances were in the ratios 1, 2, 3, &., showing that the centre of the system is a dark fringe, The position of the surface can be determined very * Lloyd ¢ Papers,’ p. 149, Fringes for Internal Reflexion. 907 accurately by scattering a little dust—lycopodium powder— on the surface. If the part of the surface seen in the microscope be illuminated, these specks of dust and their images in the surface can be easily seen. They and the images form a symmetrical figure, and the line of symmetry determines the surtace very accurately. For photographing the fringes a brass tube was fitted to an ordinary camera and the lens placed at the end of the tube, a distance of about 120 cm. being thus secured between the lens and the plate. Fringes formed in the trough at the appropriate distance were thus automatically focussed on the plate and an exposure was made. The photographs 1 and 2 in Plate XIII. were ob- tained in this way. In the photographs the surface is not very definitely shown, as the specks of dust were continually moving, and long exposures had to be given to obtain the fringes. The photographs 3 and 4 are of Lloyd’s fringes, obtained in a similar way with a single mirror of black glass. These are given for comparison. It is clear that the two sets of fringes are of the same type, and indicate that in each case there is the loss of half an undulation on reflexion. The use of polarized light made no difference to the fringes, so that whatever be the plane of polarization for grazing incidencg there is a loss of half an undulation. The width of the fringes can easily be altered by adjusting the position of the sht. The glass ends of the trough make no difference to the fringes, as the direct and reflected pencils both pass through the same glass path, so that, provided the glass is fairly good, clear fringes are obtained. If we now consider the Fresnel formule for the changes of phase on reflexion in conjunction with the Stokes proposi- tion concerning amplitudes we can see that these results are in agreement with the results for external reflexion. We have two cases to consider :—Light polarized in the plane of incidence and light polarized perpendicularly to this plane. Let the angle of incidence be d, then for incidence at an angle greater than the critical angle «, we have in each type of light a change of phase on reflexion. Let y, and yp be the changes ot phase for light polarized in and perpendicular to the plain of incidence respectively. Then 2 cos @ /sin? db—sin? « cos 2+s1n’ a ‘ tan y= 2 cos @ sin? a,/ sin? @—sin? « tan i=) meeaon ET. Re Or eS ae ¥ cos’*sin'a—sin?d+sin’a * 308 Lloyd’ s ieee for Internal Reflexicn. Both these tangents vanish at o= 5 and therefore the change of phase at this incidence—grazing incidence—is 0 or 7. As decreases each tangent increases in magnitude, changes sign on passing through infinity, and becomes zero again at — Hach change of phase therefore changes by the value 7 corresponding to half an undulation. From the ‘eritical angle as @ increases, the formule for reflexion involve no further change of phase except when we reach the incidence corresponding to the polarizing angle for external reflexion, when the light polarized perpendicularly to the plane of incidence gives, “just as in the ease of external reflexion, a zero amplitude for the reflected light—there is then a change of phase again of 2, in other words the ampli- tude of the reflected hght changes sign. From this incidence there is no change up to normal tne eines. Now from the character of the fringes it appears that at grazing incidence the values of ry, ‘and yp are both 7, as there is the loss of half an undulation in both cases. Thenetere at the critical incidence the values of y, and y, are 27 or equiva- lent to 0. Now at this incidence the Stokes investigation applies, and therefore the corresponding external reflexions must involve a loss of phase v, and these reflexions are of course those at grazing incidence. This result is in agree- ment with the Lloyd experiment, and therefore our results are consistent. Hor incidences between this critical incidence and normal incidenee the Stokes Jaw still holds, and the results are again in complete agreement. | We have not taken account of the modifications neces sary, if we assume the transition layer at the surface and not a sudden discontinuity, but these only affect the question of the light polarized perpendicularly to the plane of incidence oo incidence very near the principal ineidence. The modification makes in each ecase—internal and external reflexion—a continuous change in the change of phase and not a sudden alteration of 7. But this does not affect the general argument, which is to connect up the complete system aE changes and ve show that the experimental verification of the reflexion formule for the case of grazing internal incidence enables us to consider all the phenomena as one connected whole. r 509 J Ay & XULIX. On the Theory of erie! Hortes: Th. By G. Bakker *.. ’ , § 1. Observations of Isaac Newton. ie films of liquids, such as oil-films on water or films of a solution of soap in water, become continually thinner and thinner, there appear suddenly, as every one knows, on the thinnest places of the brilliant surface circular black spots. These spots gradually enlarge so that the surface of the film seems to be perforated with holes. This observation was made first by Isaac Newton. I will demonstrate how this phenomenon can be explained in a theory of surface-forces, in which the capillary layer is considered as a gradual transition cf the liquid phase to the vapour phase, such as those of Lord Rayleigh} by means of the properties of the theoretical isotherms of James Thomson and van der Waals. Reinold and Riicker{t have made the very important dis- covery that the black spot, always formed before an undis- turbed film of soap solution breaks, has a uniform or nearly uniform thickness of about eleven or twelve micro-millimetres, while the thickness of the remaining parts of the film exceeds fifty micro-millimetres. The sharp boundary of the black spots is also a consequence -of the relative great difference between the thickness of the spots and the remaining parts of the film. Let us now consider a liquid membrane, the breadth being equal to the unit, lying between two solid strips supported on the right and the left by cords stretched in a vessel containing nothing but water vapour (see fig. 1). Hyio 7 ie Bi Bie A F a ee The liquid film cannot be in equilibrium unless the strips are bound to the walls of the vessel§. When thus the thickness of the film exceeds sufficiently twofold the thickness of the capillary layer, the tensions in the strings, which bind the strips * Communicated by the Author. + “On the Theory of Surface Forces, II.” Phil. Mag. Feb. 1892, p. 209. { Proc. Roy. Soc. June 21, 1877; and Trans, Roy. Soc. April 19, 1883. § Phil. Mag. for December 1906, p. 563. Phil. Mag. 8. 6. Vol. 14. No. 82. Oct. 1907, 2M 510 Dr. G. Bakker on- the to the walls of the vessel, are twofold the surface-tension H of the theory of Laplace. (Fig. 2 presents a part of the liquid film of fig. 1 on an enlarged scale.) , Fig. 2. vapour. B Vapour Tf the film is thick enough we have between the capillary layers AB and A,B, liquid, while we have between A and B as well between A, and B, a gradual transition of the density. Above B, as well below B we have saturated vapour. If we gradually draw out the film it becomes thinner and thinner. If there is still sufficient liquid between A and Ay, we have thus, in supposing a gradual variation of the density between A and B as well as between A, and B,, all the densities of the theoretical isotherms of James Thomson between A and Bas well between A, and B, of fig. 3, and Fig. 3. thus likewise the densities of the phases, which would be unstable if they were isolated. The liquid layers CD and Cay Chie.22))imane thus in equilibrium with the aid of the matter between C, and C, the matter above D, and the matter below D. If we continue to thin the film (fig. 2) the densities C and C,, which correspond with the unstable phases C and C, (fig. 3) of the theoretical isotherm, will finally Theory of Surface Forces. d11 touch each other in forming a new state of equilibrium, and because the new film, not containing the densities between C—D and C,—D, is not complete, it becomes suddenly thinner. Although it is possible that the two layers AD and A,D, precipitate in each other sooner than we have supposed, I believe I have demonstrated that the observation of Newton may be predicted by a theory of the capillary layer, such as the theory of Rayleigh or the theory of van der Waals, where the layer is considered as a continual transition of the liquid- density to the vapouar-density. In his popular Lectures and Addresses, vol. 1. pp. 8 & 9 (1891), Sir William Thomson (Lord Kelvin) says :—‘* The abrupt commencement and the permanent stability of the black film demonstrate a proposition of fundamental im- portance in the molecular theory :—The tension of the film, which is sensibly constant when the thickness exceeds fifty micro-millimetres, diminishes to a minimum, and begins to increase again when the thickness is diminished to ten micro- millimetres. It seems not possible to explain this fact by any imaginable law of force between the different portions of the film supposed homogeneous, and we are forced to the conclusion that it depends upon molecular heterogencousness.”’ Whereas my considerations are very well applicable to a theory of the capillary layer in which the forces of cohesion are considered as the attractive forces between the elements of volume of the liquid, it seems that the conclusion of Lord Kelvin, where he says that the abrupt commencement and the permanent stability of the black film depend upon molecular heterogeneousness, is not indispensable. Further, the author continues (J. ¢.): mine When the homogeneous inlay theory is thus disproved by observation, and its assumption of a law of attraction augmenting more ‘vapidly than accord- ing to the Newtonian law when the distance becomes less than fifty micro-millimetres is proved to be insufficient, may we not go farther and say that it is unnecessary to assume any deviation from the Newtonian law of force varying inversely as the square of the distance, continuously from the millionth of a micro-millimetre to the distance of the remotest star or remotest piece of matter in the universe; and, until we see how gravity itself is to be explained, as Newton and Faraday thought it must be explained, by some continuous action of intervening or surrounding matter, may we not be temporarily satisfied to explain capillary attraction merely as Newtonian attraction intensified in virtue of intensely dense molecules movable among one another, of which the ageregate constitutes a mass, of liquid or solid.” 2M 2 Pil? Dr. G. Bakker on-the Though I cannot comprehend that the phenomenon, dis- cussed by Lord Kelvin, requires the molecular heterogene- ousness of matter, I have nevertheless always considered the idea, whereby capillary attraction is explained as merely Newtonian attraction of dense molecules (Laplace, Secchi, Kelvin), as a magnificent idea, that is not to be rejected before the contrary is proved. So | have found* for a medium the following formula for the potential function d(r) of the forces between their elements, accepting the Newtonian law of forces between the molecules and assuming the law of dispersion of Boltzmann : ; A b(n) oe r+D ie RT the volume of the medium; R=constant of the gas; T=absolute temperature; D-=diameter of the molecules ; f=constant of the gravitation ; ~=weight of one molecule. The meaning is that the potential energy of the elements of the homogeneous medium should be the same as that of the molecules of the gas. oe If p is sufficiently large, the influence of the factor e”*” may be important. Because » is varying inversely as the absolute. temperature, we see that for our medium at a sufficiently elevated temperature the potential function approaches to where A= and r=distance between the elements of r+D SS eer and when, moreover, the medium is sufficiently rarefied the function becomes : 7 so that the cohesion becomes practically null. We find also, in accordance with the consideration of Lord Kelvin, in his popular Lectures and Addresses (vol. i. p. 59, 1891), that the Newtonian law of attraction between the molecules may be very well in harmony with the properties of the forces between the volume elements ot the homogeneous medium, considered in the ordinary capillary theory. If my consideration upon the abrupt commencement and the permanent stability of the black spot is exact, the twofold thickness of the complete capillary layer of soap-solution at * Ann. der Phys. 4¢ Folge (1903) p. 216. Theory of Surface Forces. O13 ordinary temperature is, in virtue of the measurements of Reinold and Riicker, inferior to 50 wp, while twofold the in- complete capillary layer of the black spot is more than 10 pp. Putting / for the thickness of the (complete) capillary layer of a soap-solution, we have also: 50 wp > 2h> 10 py AD TESS SY 1) a Ns Gl) Observation—That we may have in the black spots the same tension as in the complete capillary layer may very well be in accordance with the expression which I have found for the surface-tension H of Laplace; 7. e.: iL (pa? H= |, (cr) IAW eee AR GOs f denotes the constant in the used potential function for the pF forces of cohesion: — ies ‘ and dh is the differential of the Yi nermal to the surface of the layer. The order of greatness of H is also: 1 (V.—V,) iy h Sire SMe tee 56,6 GLa) ah where h denotes the thickness of the capillary layer and Vz and V, are successively the potentials in the vapour and liquid phase. For a black spot we must change V, into the potential of a point in equal distances of the two planes which limit the black film, and just as / is smaller for a black spot than for a complete capiliary layer, so alsothe difference between the potential in the vapour phase V, and the potential in the point at equal distances from the two planes which limit the black film is smaller than the difference V.— Vj, for the * G. Bakker, ““On the Theory of Surface Forces,” Phil. Mag. Dec. 1906, p. 562. + If a denotes the coefficient of the well-known expression of Laplace for the so-called molecular pressure ap”, Gauss and van der Waals have found for the potential of the forces between the volume-elements of a homogeneous phase —2ap, where p denotes the density. Formula (I1.) becomes therefore 1 @(,—p.)? ap h : In this paper I find in § 3 [see formula (17)] for H the formula Le OO Spe — Saf h 51 Dr. G. Bakker ov the complete capillary layer. The surface-tension in the black spot can also be very well equal to the tension H in the complete capillary layer. It may not be superfluous to remark that, though the surface-tension in the black spots may have the same value as in the complete capillary layer, the tension is nevertheless a quantity of somewhat other signification, the ordinary constant of Laplace being the surface-tension in a complete eapillary layer. § 2. The Hydrostatic Pressure-in the Capillary Layer and in the Black Spot. If we consider again the liquid-film of fig. 1, we may easily demonstrate that for low temperatures, for instance near the melting-point, the pressure parallel to the surfaces, which limit the film, may be large and negative. Indeed the part of the film to the right of the plane BB, (perpendicular on AA,) is in equilibrium firstly with an external force at A,, which we measure as twofold the surface-tension, and secondly with the influence of the part of the film to the left of BB, on the considered part. Between the two capillary layers which limit the film the matter is in the ordinary homogeneous liquid state, and therefore the pressure is equal to the exterior pressure or the vapour-pressure. As near the melting-point the vapour-pressure may be neglected, the pressure between the capillary layers of the liquid may be considered as null. The cohesion and thermic pressure in the terior of the film (between the capillary layers) are therefore nearly equal. On the contrary, in the capillary layers which limit the considered film we must have a force directed to the left, which is in equilibrium with half the force in the strings which bind the strips to the walls of the vessel. The value of this force is therefore the constant of Laplace, H. This force, being outward relative to the con- sidered part (between BB, and A), must be reckoned as a negative pressure, which means that the cohesion in the capillary layer parallel to their surface is at low coe larger than the the thermie pressure. If p, denotes the pressure in a direction parallel to the surface, dh denoting the differential of the normal to the surface, the condition of the equilibrium demands: ave. . 2s podh + 20. 2 eae) ; my ‘ 2 Putting il ’ h \ Podh= p, Theory of Surface Forces. d15 where / denotes the thickness of the capillary layer, and p the average pressure in the direction of the surface, we have paid oso woe eons For water the surface-tension being H=76 (dyne pro cm. or erg pro cm.”), and adopting in connexion witk the in- vestigations of Reinold and Riicker, h=10 wy, we find for water at ordinary temperature : P=—73= —76.10° or nearly —76 atmospheres. Whereas the black spots may be in equilibrium with the complete capillary layer, and the thickness of the black spots may be less than 5 pw (Reinold and Riicker), the absolute value of the negative pressure in the black spots of a film of soap- solution may be larger than 150 atmospheres. That the pressure perpendicular to the surface of the capillary layer must be equal to the vapour-pressure, we see in considering the well-known statement of the theory of elastic forces: ae ODIO Mee ete (is de * oy t Oz when we choose the z-axis normal to the surface. The gradient of the properties of the capillary layer being normal to its surface : OP Op = ==, 3%=0; Ox oY baa es Abeer a 5 > Sahat In the homogeneous phases of the liquid and the vapour adjacent to the capillary layer, the pressure being the vapour- pressure, we have: Pzz= Vapour-pressure =, putting p,;=vapour-pressure. § 3. The average value p of the Pressure py parallel to the surface of the Capillary Layer and the Theoretical Isotherm of James Thomson and van der Waals. When we may not neglect the vapour-pressure p; we must complete the equation (2a) to 2 2 i podh—22pyh+2H=0. 1 * Gravitation is not considered. 516 Dr CBaikerontthe Hence H h — =, Pi— P We will now demonstrate that, if F (fig. 4) is the ae on the theoretical isotherm such that surface NHGMLN =surface LFGM, we can put pain Ht Fig. 4. spxp-d Axis F is the point where a vdp=0, and where also the thermo- dynamical potential has the same value as in the homogeneous liquid and vapour phase. If w, is this value, we put generally \, cdp=p—/y. If p denotes the pressure in a homogeneous phase having the same density as in a point of the capillary layer, we shall have p=9—ap? or dp=d0—2apdp, where @ designs the thermic pressure. If V denotes further — the potential of the forces of cohesion, we have: dd=—pdV. Hliminating d@ between these differential equations : vdp +2ade=—dV. Integrating: i vdp +2a(p—p;)=VW,—V, . ~. (3) where the index belongs to the liquid phase. Now for this phase we have V,=—2ap, (Gauss and van der Waals) and equation (3) becomes: V+ 2ap = Py M. «nel. te oa (4) Theory of Surface Forces. 517 For the potential V of the forces of cohesion I have found * dV Vs = V + 2ap. - Fs : Oh oO (5) Hence 2 al == 1-1 ae a eee (5) The member on the right being for a point on the theoretical isotherm nothing but the integral —|, vdp, is given by the superficies (for the point F for instance): —NHGM+LFCM. The member on the right becomes also null in the three points eR end VK. and therefore we have for these points equally: a =(. t The curve, which presents the potential of the forces of cohesion V as function of h must, therefore, be asymptote to two straight lines belonging to the potentials of the homo- geneous liquid and vapour phase; moreover, this curve must have a point of inflexion Q (fig. 5). C uP Ss’ ce : The value of a is also at this point a maximum. This value of the strength of the force may be calculated in the following manner :— The hydrostatic pressure perpendicular to the surface of the capillary layer is equal to the vapour-pressure, and can be considered as the difference between the thermic pressure 6 and the cohesion in the same direction. Now I have found * Phil. Mag. for Dec. 1906, p. 565, equation (11). 518 Dr. G. Bakker on the for this cohesion * ee Ds (ORE CONTR e= TEN ie the potential function of the forces of cohesion being—/ oa e r We have also: _ es ee aes BY = (7) aa 8a fr? rs an dh); wat ; Remarking that Zi = fi, NaN Vv? alga) aD! te ee ‘ ook hits (8) f) For the point of inflexion Q, we have ot =0; hence Vit 2Zap=0.) 20 eee . (9) See equation (5). Moreover if p denotes the pressure in a homogeneous phase with a density equal to the density in the considered point of the capillary layer, we have p=b—ap’. | UN SeeGEDy Hliminating @ and V between (7), (9), and (10), we get us a) syed ular en pe or dV 2fa ,——_. yom fo pimp being denoted by the distance SF in fig. (4). Although in a theory of capillary attraction, where use is made of a potential function of the form ie e* TT re the thickness of the capillary layer becomes infinite and the V-curve of fig. 5 is asymptote to BB’ and CC’, we have practically considered the capillary layer only as a layer for which the gradient of the potential V cannot be neglected in * Phil. Mag. for Dec. 1906, p. 564. t Loe. cit. p. 561. Theory of Surface Forces. 519 calculating the value of the capillary tension : (<;) erable dh, and we may write: ee WaNae ae sia al os. ae 2 Atle Ca ie where the indices refer to the points where the phases may be considered practically as homogeneous (liquid- and vapour- phase). For the same reason the curve PQS in fig. 5 is considered as being touched respectively in the points S and P by the straight lines CO’ and BB’*. The consideration of fig. 5 gives for the curve, which ah presents in function of h, the curve in fig. 6. Fig. 6. 7 SUX - D, Game h-Axis ME & Ye The points V and W in fig. (6) correspond respectively with the points G and P in fig. (4). * The superficies PSTP’ =" Vdh in fig. 5 has a simple signification. 1 Hevea, in integrating the two members of the equation (5), remarking | that os is null for the homogeneous phases, we get N “| ah=\" Vah+2a\ pdh=0, Now, i pdh denotes the mass of the capillary layer per unit of superficies ; hence Superficies PSTP’ = —2am. This equation is.independent of the potential function used. Indeed, the equation (3) in the theory of ‘surface-forces of Rayleigh (Phil. Mag. Febr. 1892) gives immediately : {° Vah=2K * pdh=2Km, 1 1 520 Dr. G. Bakker on the Practically, we consider the curve LVQWM, where VL and WM are the tangents at the points V and W and calculate the superficies between that curve and LM as parabolic segments. Hence Superficies LVQWML= a a dh=V.— V,=2a(p1— pz) =2LM x QS=4LM V2af Vp,—p. . (18) QS being the maximum value of ae given by equation 11. The distance between the centre of gravity and LM is, in virtue of the equations (12) and (9), expressed by dV iN ae an (an) dh if Th 2mfH:2a(pi—pe), . (14) and equally by 2QS=2 .2 V2af V,— slay The expressions (14) and (15) give ey 16 J Pi—P P Ba/ 23 le ae ae ( ) Hliminating respectively ,/p,—p and ape.) between the equations (16) and (13), we have for LM : in 0 a’(p;—ps)? 15 H ee oa aI 6p 7 ee (17) where p is denoted by the distance RF in fig. (4). Practically, J put also for the thickness of the capillary layer : H jhe Further I have found * for the capillary tension : re2 Jal =| (p1 —po)dh. 1 This equation and (18) give: i (18) prh ei poth=pyh —ph 1 or Les tale, ays Pah, podh=p=RF in fig. 4. * Phil. Mag. for December 1906, p. 563. Theory of Surface Forces. 521 That is to say: The average value p of the pressure pz parallel to the surface of the capillary layer may be considered as equal to the pressure of the theoretical isotherm in the point F (fig. 4), where the thermodynamic potential is equal to their value in the homo- geneous phases H and K. The equation 6 at(pi—p2) 7 Si APN seq; 1 ogi? geen) may be written Wc Ta ia kL —p=p,—-Pp= ——}. l7a (eo omen 2 We | (17a) In this formula for the difference between the pressure p, resp. perpendicular and the (average) pressure parallel to the surface of the capillary layer, 7 denotes the constant of the used potential function : while a is the coefficient of the expression ap? of Laplace for the so-called molecular pressure or the function a in the equation of state of van der Waals. Although a is a function of the temperature, we will, as a first approximation, consider a and fas constants ; & being a new constant, we have also ay Hi i —p—k ——_ P1— P2 Now 1—f2 capillary tube and therefore proportional to T;—T™*, where T; is the critical temperature and T the temperature of observation. We have also (when the liquid wets the walls of the tube) : is proportional to the rise of a liquid in a T\2 pi- p= “(1-7 )- ere a being a constant. * E. C. de Vries, Inaugural-dissertation, and Arch. Néerl. Science, xxviii. pp. 210-219 (1894), and J. E. Verschaffelt, Koninkl. Akad. v. Wetensch. at Amsterdam, April 1896. 22 Dr. G. Bakker on the If the pressure is expressed in atmospheres, I have found for ether * : On aa T=absol. temp., ke and for the temperature at which the (average) pressure ? parallel to the surface of the capillary layer is null: For this temperature (110°-7 Cels.) the point F in fig. 4 hes thus on the volume-axis, which is in accordance with the calculation of van der Waals, which shows (a conceived as a constant) that-at the temperature T=0°344 T, the volume- axis is a tangent to the theoretical isotherm+t. For the temperature T=0°82 T;, » being null, we have for the thickness of the capillary layer : . pi—p= 238 (1— H © surface-tension pi vapour-tension’ = which gives for ether, h= S Omm. At 110°7 Cels., I find thus for the thickness of the capillary layer of ether a value of the same order of great- ness as the thickness of the capillary layer of a solution of soap in water at ordinary temperatures according to the measurements of Reinold and Ricker. § 4. The Gradient of py and the Relation between the Pressure pe and the Density p for a Point in the Capillary Layer. While the pressure », perpendicular to the surface of the capillary layer is a constant and equal to the vapour-pressure (see above, the end of § 2; we continue to consider the capillary layer as plane), the pressure p, parallel to their surface has a gradient. We will demonstrate how one can ; 1 find the relation between /, and the reciprocal value vy = — of the density in a point of the capillary layer. For ae cohesions resp. in the direction of the lines of force (that is to say in the direction normal to the surface of the capillary layer) and perpendicular to the lines of force (and therefore * Zeitschr. f. phys. Chem. li. p. 358 (1905). + van der Waals, Continuite:t der gas en vloerstoftoestand. a a De ase ee Theory of Surface Forces. 523 parallel to the surface of the capillary layer) I have found", the potential function of the forces of cohesion being a —f—: 4/0 Bea cathy a) = (a) ae _ 1 pqavy vy ee cay The hydrostatic pressure being, in every direction, the difference between the thermic pressure @ and the cohesion, and we have % pyle - 9 9 EV) ae Ian ial 2 ira enn sar(an) }. eed 2 We 1 “dV. ie P= O—) gona earl an) \. ee and therefore ) peel aN? 9 ie An Ca) 5 (22) Now the pressures p, and p, are respectively the maximal and minimal value of the hydrostatic pressure in any direc- tion in the considered point and the eyuation (22) shows therefore that :— | Lhe departure from the law of Pascal in a point of the capillary layer ts proportional to the square of the intensity of the force of cohesion. Differentiating the equation (22), p, being a constant, we find: dpi Ld a Vi (23) QIN renal ke VV yaoi tks Now we have found [see above, equation (6)] adi Dee uah ty ©) where # is the thermodynamic potential for the considered point in the capillary layer and yw, its value in the liquid- and vapour-phase. We have therefore yO ee CANS : dh — lap Wh (uy —p). c ° . . (24) * Phil. Mae. for Dec. 1906, p. 564. 524 Dr. G. Bakker on the In three points of the theoretical isotherm (fig. 4) the thermodynamic potential has the same value 2. e., in the points H, K, and F; H and K are the points where the physical isotherm (HK) cuts the theoretical, while we have for the point I’: - surface NHGM = surface LFGM. Between H and F, w,>; in the point F, p=p,; and between F and K, w>p,. Now I have demonstrated that IN og ae eae : Eee is always positive in the capillary layer ; Be has therefore in the equation (24) the same sign as w—py. If we therefore denote a point in the capillary layer by the corresponding point + of the theoretical isotherm, we have: between H and F, dps <(Q% l in F, dpe ==(() € between F and K, aps >0. The hydrostatic pressure p, parallel to the surface of the capillary layer diminishes therefore between H arid F, has a GH Vapour. h-Axis minimum value in I’, and increases between F and K. The curve which presents p, as a function of h has therefore a shape as in fig. 7. AB is the thickness of the capillary layer. * Zeitschr. f. Phys. Chem. xii. p. 71 (1902). + That is to say, that this point corresponds with the same density as the density in the considered point of the capillary layer. Theory of Surface Forces. 525 The surface of RDQESR is given by \" (p1—p2)dh and presents the value of the constant of Laplace. Now (see above) the pressure p for the point F at which p=, a : has the same value as the average pressure p= i p2dh in the capillary layer. Hence Wh surface RDQESR = (pi;—p)h, . . . (29) where / denotes the thickness of the capillary layer. The equations (20) and (21) give further by addition : fae sigs, Us 26 2 = yay oe a A ae (26) Now for the point Q in fig. 7, which corresponds with the point F in fig. 4, we have w=, and the eqnation (4) gives therefore for the point Q in fig. 7, V= — Jap. If p denotes the pressure of the isotherm in the point F, we have : 0=p-+ap’. The equation (26) becomes therefore for the point F in fig. 4 or the point Q in fig. 7: D1 + po 4a?? Boe i ad 4 Smfr e~ 9 x 9) OF Further, 27f\?=a™*; hence p= Be By substitution of this value of p in the equation (25), we find : surface RDQESR=4(p,—p.)h=4 surface RUVSR. If, however, we would bring the properties of the theoretical isotherm into connexion with those of the capillary layer, we a) e i .! must find the relation between py and v (= a: Therefore we depart from the equation (26) and make use of the equation of state-of van der Waals, which gives for the thermic pressure: iba mr TQ ===, and thus Bian s He ms a0 tae) UV—D y o—D Aa a= * Phil. Mag. for December 1906, p. 564. Phil. Mag. 8. 6. Vol. 14. No. 82. Oct. 1907. 2N 526 Dr. G. Bakker on the Now d0=—pdV ; aE ay eG ne ee v—b Integrating, V—V,=RT log" — RT ae where the index corresponds to the liquid state. Further, 2a Ve —20p = —_— ve (Gauss and van der Waals)”. By substitution in (27), ee Bay ee poze ome : RT log =j +RIb eee a (28) Since the hydrostatic pressure p, is nothing but the vapour- pressure and thus at a definite temperature a constant, the equation (28) may be considered as the relation between p, and v. For the point H in fig. 4, v=, and p;=p.; the equation (28) properly becomes therefore for the point H: RT il 4a RT a a Sab Naa oe Wee By the aid of the well-known relation Up b 1 1 ; =, =a( = + pi(v2—%), we find easily that for the point K in fig. 4 the equation (28) properly becomes | RT log RT a (= eee re penoe As, however, the equation (28) is not easily to be discussed, we start immediately from equation (24) dpy= a dVe yes Now, d0=—pdV or dV=—vd®, and, still ever adopting * Hence it has often been wrongly concluded that the potential energy of the forces between the molecules should be — ap. Theory of Surface Forces. 527 the formula 0= ET of van der Waals, the equation (24) v—b becomes | dps RT = Gap EY: ° e . ° (29) / My-----" |! ERGFPK-theor Looth. * oS ee IEG pee Cerne & wy waste" _ SurfaceN H RGM N- SLFGMUL § SF-FW 5 i S SS VvAxis In the points of the capillary layer which respectively correspond with the points H, F, and K in fig. 8, and where w=, we have thus dpa _ ee and in the points H, W, and K of the curve HUWVK, which presents the relation between p, and v (the p.—v curve) the tangent is thus parallel to the v-axis. Because“ v has the same sign as the difference 4—y, (see equation 29), , diminishes between H and W and increases between W and K. Further we have, in differentiating (29), ap, _ v" Le ye lnk Bee0 qe Gea) Gee eae For the points of the capillary layer which correspond respectively with the points Gand P of fig. 8, the equation . 2N2 528 Messrs. Owen and Hughes on Condensation Nuclei (30) gives therefore d? RT(v+ 6 = ay aa (41—}). In the point’U just beneath the point G, 4,—w>0 and the ».—v curve turns therefore the convex side to the volume-axis. Because at the point H the tangent is parallel to the volume-axis, the p,—v curve has a point of flexion between H and U. In the same manner we find that the po—v curve HUWVK has also a point of flexion between W and V, where V is the point just beneath P. The curve HUWVK gives therefore together with the empiric isotherm HK a complete image of the relation between the hydrostatic pressures (p,; and p,) and the reciprocal value v = Z of the density in a point of the capillary layer, whereas the state of every point of the capil- lary is completely described by these three things. L. Condensation Nuclei produced by Cooling Gases to Low Temperatures. By Gwitym OwEN, B.A., MSc., Assistant Lecturer and Demonstrator in Physics in the University of Liverpool, and A. Lu. Hucues, B.Sc.* We have recently examined the condition in which air is evolved from charcoal after absorption in a dry and dust-free state at the temperature of liquid air, in order to determine whether it remains dust-free when liberated by warming the charcoal to atmospheric temperature. The char- coal was contained in the bend of a small glass U-tube connected to the cloud chamber of a Wilson’s expansion apparatus ; and, after the liquid air used for the cooling was removed and a sufficient time was allowed for the evolved air to regain the temperature of the atmosphere, a sample of the air was admitted through a glass tap into the cloud chamber. It was at once found that the evolved air contained large numbers of nuclei, sufficient, in fact, to produce dense showers ; but when a control experiment was performed without any charcoal in the U-tube, a similar number of nuclei appeared. The experiments therefore were indecisive as to whether the escape of the absorbed air caused disintegration of the char- coal, but they raised the very interesting question as to the cause of the showers obtained in the expansion chamber when air which had merely passed through a process of cooling * Oommunicated by Prof. L. R. Wilberforce, M.A. ‘ produced by Cooling Gases to Low Temperatures. 529 was admitted. This peculiar effect we have investigated ina series of experiments extending over several months, and the present communication contains an account of the main results obtained hitherto. It was at once found that it was not necessary to cool air to a temperature so low as that of liquid air in order to produce these condensation nuclei. Different gases have been tried ; and with all those experimented upon (except hydrogen) we have found that there is a more or less definite critical temperature below which each gas has to be cooled before the production of these nuclei can be detected. Further, the smaller the pressure of the gas while undergoing cooling, the lower is this critical temperature. The investiga- tion thus resolved itself into an attempt to determine these critical temperatures for various gases at different pressures, and thereby possibly to obtain some information regarding the origin of the nuclei. Q e TO EXPANSION APPARATUS =aD) % ASPIRATOR- ws —— TO ASPIRATOR B E ae 1w) The final form of the apparatus used is represented in the figure. Q is the cloud chamber of a Wilson’s expansion 530 Messrs. Owen and Hughes on Condensation Nuclei apparatus * which, together with its accompanying gauge and mercury reservoir for adjusting the expansion, is omitted from the figure. The cooling was produced by immersing the bend of the glass tube C always to the same depth in petroleum ether previously cooled by stirring with a test-tube containing liquid air. We find it convenient to give the name “‘tester” to the part of the apparatus immersed in the cooling liquid. The internal volume of the “tester” was about 3 cub. centims. The volume of the space ABCDE with the mercury in B at a fixed mark P was about 80 cub. cms. At the commencement of a test experiment this space was filled with the gas at a pressure of 80 cms. By raising or lowering the mercury in B, the pressure of the gas in the ‘‘ tester ” could be increased to nearly two atmospheres or reduced to less than half an atmosphere. The gas was admitted through A and could be withdrawn through E or D by means of an aspirator. The tap E was found useful in rendering it possible to exhaust the apparatus to a low pressure in order to remove the gas lodging in the gauge G. Also by means of it a slow stream of gas would be drawn through the apparatus without there being any danger of water-vapour diffusing back into the “tester,” as might conceivably happen when the gas was drawn through the cloud chamber wa D. As a matter of fact, this fear proved to be groundless, the results obtained being independent of the path along which the gas was swept out of the “tester.” The method of making a test was as follows :— With the mercury at the top of the tube B, the gas was allowed to stream through the apparatus for several minutes in order to remove any nuclei produced by the previous test. The taps D and E were then shut and the mercury lowered in B. By shutting A off at a suitable moment, it could be so arranged that the pressure was 80 cms. when the mercury was at the fixed mark P. In this way the same volume of gas was always experimented upon. ‘The level of the mercury in B was now adjusted until the pressure was that proposed to use. One observer then surrounded the “ tester” with the cooling liquid for 40 seconds, noting (by means of a pentane thermometer reading to —200° C.) the temperature of the liquid at the beginning and end of the cooling process. The mean of these two readings was taken to be temperature which the gas in the “tester” attained. During the cooling the pressure of the gas was maintained constant by the second observer. The tester was now surrounded by water at a temperature of about 15° C. for one and a half minutes. At * C. T. R. Wilson, Phil. Trans. A. vol. clxxxix. p. 265 (1897). \ produced by Cooling Gases to Low Temperatures. 531 the end of this interval the mercury was again brought to the fixed mark P (so that the gas was once more ata pressure of 80 centims.). The tap D was now opened and the mercury quickly raised to a second fixed mark near the top of the tube, thereby driving into the cloud chamber practically the whole of the gas which had undergone the cooling. D was then closed and an expansion of about 1:10 made, completing the test. Between every test, whether nuclei had been produced or not, a stream of fresh gas was drawn through the apparatus for several minutes. At frequent intervals control tests were performed identical with that described above omitting the cooling process only. Reasons are given below for selecting the stated duration of the cooling operation, the time allowed for the gas to warm up, and the value ot the expansion used. It remains to add that always whenever the apparatus required resetting-up, it was first washed with caustic potash, nitric acid, and, after rinsing several times with clean water, thoroughly dried. General Results. The following facts in regard to the nuclei are general in that they apply to all the gases in which the nuclei were obtained. (1) After passing below the “ critical temperature” * the number of nuclei produced increases rapidly with the degree of cooling, the maximum effect being obtained when the cooling is sufficient to cause some of the gas to turn (or to be on the point of turning) into the liquid state. At this stage the number of nuclei produced is generally large enough tu cause coloured clouds. (2) The number of nuclei produced is independent of the time of cooling provided the time is long enough to allow the gas in the tester to fall to the temperature of the cooling liquid. This time was about 25 seconds with liquid air as the cooling agent. We allowed, however, a little margin, and in all the experiments described below the time of cooling was 40 seconds. (3) The nuclei show a remarkable persistency. If an interval of 10 minutes be allowed to elapse between the removal of the cooling mixture and the passage of the gas into the cloud chamber, the shower obtained is almost as dense as it is when the warming-up process takes only one * The term “ critical temperature” in this paper means always that temperature to which a gas has to be cooled before the production of nuclei can be detected. 532 Messrs. Owen and Hughes on Condensation Nuclei minute. When the number of nuclei produced is large, as is the case when the gas is cooled well below its “ critical temperature,” some nuclei can be detected quite half-an-hour after their formation. Jn all the experiments to be described we adopted a uniform interval of 90 seconds for the warming- up process, this interval being considered sufficiently long for the gas to acquire normal temperature and yet not long enough for an appreciable number of the nuclei to have disappeared. | (4) The number of nuclei “caught” is independent of the value of the expansion used. On using large expansions (greater even than an expansion of 1°25 which causes con- densation on ions) no nuclei were detected in addition to the ordinary Wilson effect, where none had been detected with small expansions. On many occasions it was _ noticed that the nuclei caused condensation in consequence of the very slight supersaturation produced when adjusting the pressure-drop in the expansion apparatus preparatory to making an expansion. The small degree of supersaturation thus required to cause condensation on the nuclei proves them to be of considerable size. It is therefore unimportant what expansion is employed. We found it convenient to use a small expansion of 1:10 corresponding to a pressure-drop of 7 centims., and this was used throughout all the experi- ments described below. Determination of the “ Critical Temperature.” In contradistinction to the results given above, the follow- ing depend upon the nature and pressure of the gas cooled. The values of the ‘critical temperatures” given represent the mean estimates arrived at after a large number of experi- ments. The gases tried were ordinary air, air from boiling ‘iquid air, hydrogen, oxygen, nitrogen, and carbon dioxide. Air from Boiling Liquid Air. Liquid air was poured through two thicknesses of filter- paper into the reservoir R (fig. 1) until the latter was half-. full. The mouth of the reservoir was then closed by a small rubber stopper. When the tap A was closed the air as it boiled away escaped through the mercury at M. The rate of boiling was regulated by surrounding R with a tall Dewar vessel also containing liquid air. Before commencing the experiment, the air escaping from R was allowed to stream for half an hour or longer through the apparatus escaping through D and E into the aspirator. While this was going \ produced by Cooling Gases to Low Temperatures. 533 on, the glass tube leading from R to the “tester” and the tester itself were well heated with a flame so as to dry them thoroughly. The method of filling the apparatus with the gas preparatory to making a test has already been described. The following table gives the “critical temperature” at different pressures for air obtained as described from boiling liquid air. Pressure in centims. “Critical Temperature ” of Mercury. | (approximate). | 101 | —140° C. 80 —145° C. 41 —160° C. Ordinary Air from outside. The ordinary air was drawn slowly into the apparatus through long tubes containing calcium chloride, solid potash, phosphorus pentoxide, and cotton-wool. The results obtained were practically identical with those tabulated above for air derived from liquid air. Hydrogen. The hydrogen was prepared by the action of KOH on pure aluminium. The gas passed from the generating vessel to the apparatus entirely through glass, no rubber connexions at all being used. On its way the gas was dried and purified by passing through sulphuric acid, calcium chloride, KOH, P,O;, and finally through a glass spiral about 2 feet long immersed in liquid air. A plug of glass-wool was inserted in the tube leading from the spiral to the main apparatus. No nuclei were ever detected in hydrogen until it had been cooled to —175°C. Generally, when hydrogen was cooled by means of liquid air, many nuclei were produced; but on one or two occasions the gas was obtained in such a state (possibly depending on the degree of purity) that no nuclei were formed at this low temperature, the pressure of the gas being approximately atmospheric. The “ critical tem- perature” for hydrogen is therefore uncertain, but it is certainly very much lower than that obtained with all the other gases tried. 534 Messrs. Owen and Hughes on Condensation Nucler Oxygen. Oxygen was generated by heating a Jena-glass tube con- taining pure potassium permanganate. The gas passed through a long U-tube containing soda-lime, and then through a narrow g lass tube 6 feet long bent into a spiral and immersed in liquid “air. The oxygen was then condensed in a tube (similar to R in the figure) by surrounding it with liquid air. Hnough oxygen was condensed to give about 20 litres of the gas. When this quantity of liquid oxygen was obtained the permanganate tube and spiral were cut off by means of a tap. The only piece of rubber used in the whole apparatus was the one connecting the permanganate tube to the tube of soda-lime. The general results were almost identical with those obtained for air, the “critical temperature’? at a pressure of 101 centims. being again about —140°C. At the lower pressure of 41 centims. the critical Heuer ame seemed somewhat lower than in the case of air ; but on cooling by liquid air at this pressure, the oxygen in the tester liquefied and dense coloured showers or clouds were obtained. Nitrogen. Experiments were performed on nitrogen prepared in two ways. One method of preparation was to heat gently a mixture of equal parts of ammonium chloride, sodium nitrite, and potassium bichromate. The gas passed through KOH, H,S0O,, CaCl, P,O;, the long spiral immersed in liquid air and a plug of glass-wool. The joints were all of sealed glass. This method is open to the objection that the nitrogen pre- pared in this way may contain traces of oxides of nitrogen. The other method adopted was to drop ammonium chloride slowly intoa solution of sodium hypobromite. The nitrogen evolved was then passed through sulphuric acid, over hot copper, through wash-bottles containing sulphuric acid, and potash, through calcium chloride and phosphorus pentoxide, the long spiral immersed in liquid air and a plug of cotton- wool. The results for nitrogen are not so consistent as for air and oxygen, probably owing to its being so very difficult to obtain this gas in a pure ‘state. At a pressure of 101 centims. the gas had only to be cooled to about —125° C. to cause the nuclei to appear. At the lower pressure of 41 centims., however, the “critical temperature” is approxi- mately the same as in the case of air. \ produced by Cooling Gases to Low Temperatures. 535 Carbon Dioxide. This gas was prepared from hydrochloric acid and marble and dried by passing through tubes of calcium chloride and phosphorus pentoxide. The results obtained with CQ, are illustrated by those given in the following table :— | ; | | | Pressure in Temperature Effect obtained | : | centims. of cooling. in cloud chamber. | [Seine | f | eins | 35 =a Ce. |) oronlO drops: | 35 —382 | Thin shower. _ Pressure could not ; | { Some of the gas _ be keps constant. } se Culunes alent solidified. ast 80 —67 No effect. 80 — 10) 10 to 15 drops. | 80 = 72 Good shower. Some gas solidified | Poeseticg wgnl o —73 Coloured cloud. Ditto. be kept constant | : 7, --66 | 9 or 6 drops. _ Pressure could not : : Sot |” be kept constant. —68 Very heavy rain. eee solidified. | | We shall now consider certain possible explanations of the production of these nuclei and discuss their validity. (1) By some direct action upon the walls of the cooled tube.— This was disproved at the outset of the investigation by direct experiment, the gas in the tester being air. A double “‘ tester ’? was made consisting of two similar glass U-tubes arranged side by side “in parallel’ and symmetrically placed with respect to the tube B and tap D (see figure). One of the U-tubes contuined a number of glass flakes obtained by breaking up’ a bulb of very thin glass. There was thus in this “‘ tester”? a much larger extent of glass surface, the volume ot the air inside not being appreciably diminished. Cooling tests (by means of liquid air) were performed upon the “testers ” alternately, and it was found that the effects obtained were practically the same ; if anything, the “ tester ” containing the flakes of glass gave a slightly smaller effect. This disproves the explanation that the effect is due to some action at the glass surface. There is also indirect evidence against this view. For, as we have shown, the effects depend in all cases upon the pressure and nature of the gas inside the “tester.’’ Contrast for example the results for CO, and Hydrogen. 236 =©Messrs. Owen and Hughes on Condensation Nuclei (2) Due to traces of water-vapour in the gas-—The im- portance of thoroughiy drying the gas before admitting it into the experimental tube is obvious. Any water-vapour present would be deposited on the cooled walls of the tube in the form of minute particles of ice. On the gas warming up again, these might become detached and float about in the gas in the form of small drops of water, and, consequently, it they did not. evaporate (which, as a matter of fact, we might reasonably expect them to do, the gas in our experi- ments being very dry) they would act as condensation nuclei on admission into the cloud chamber. Against this view that the nuclei are due primarily to traces of water-vapour in the gas, there are several pieces of evidence both direct and indirect. (a) It has already been suggested that any drops of water formed as described above would evaporate on the gas warming up again. To help these supposed droplets to evaporate, on several occasions we surrounded the U-tube with hot glycerine at 120°C. This treatment was ineffectual in removing them. (>) All methods designed to dry the gas before its admission into the apparatus failed to prevent the formation of the nuclei at the temperatures already given. In the case of oxygen and air the gases were derived from boiling liquid oxygen and liquid air. The oxygen was dried before it was liquefied as has been described. The liquid air was poured into the reservoir through two layers of filter-paper in order to remove small particles of ice which necessarily fall into it from the mouth of the Dewar flask in which it was contained. ‘Thus there could hardly have been any appre- ciable amount of ice mixed with the liquid gases ; and even if there were, its partial vapour-pressure at that temperature would be exceedingly small. (This applies equally to any © traces of CO, snow in the liquid gases.) (c) The air from the room was on one occasion treated as follows :—It was drawn through calcium chloride, solid KOH, over a long layer of P,OU;, and finally through a spiral immersed in liquid air containing 17 feet of copper tubing of 1 millim. bore, the last foot being of wider bore packed with cotton-wool; yet after this drastic treatment the air behaved no differently from what has been described above. (d) Indirect evidence against the “ moisture ”’ explanation is afforded by the fact that the “critical temperature” at which the production of the nuclei can be first detected depends so markedly upon the nature of the gas. We might reasonably suppose all the gases tried to contain more \ produced by Cooling Gases to Low Temperatures. 537 or less the same amount of moisture (if any), and yet, as has been shown, the “ critical temperatures” range trom —70° C. to below —175°C. The effects cannot therefore be due primarily to the gases experimented upon not being perfectly dry. Nor can the effects obtained in air and oxygev be due to traces of COs, for we may again reasonably suppose the gases derived from boiling liquid air and liquid oxygen to be as free from CQO, as hydrogen prepared in the way descried, yet the “critical temperature” for hydrogen is much lower than for air and oxygen. This view is strengthened by the fact that the “ critical temperature ” for air mixed with nearly 4 per cent. of CO, was raised only some 20 degrees. (3) It might also be questioned 2f the gas had thoroughly warmed up before admission into the cloud chamber, for the entrance of cold gas into the moist gas in the latter might conceivably of itself produce nuclei. ‘To invalidate this con- tention, it is only necessary to point out that hydrogen cooled to = 150° C. say, would not have had as good a chance to regain atmospheric temperature in the 90 seconds interval allowed as CU, cooled to —80° C.; yet no effect is produced in the former, and dense clouds in the latter case. The fact that showers can be obtained on admitting the gas into the cloud chamber ten minutes after the cooling agent is removed still further disarms this criticism. Discussion of the Results. We are by no means sure as to the correct explanation of the origin of the nuclei produced in a gas, as we have described, by severe cooling. As a possible explanation of the effects obtained in hydrogen, air, oxygen, and nitrogen, we tentatively propose the view that when gases are cooled to a sufficiently low temperature, yet considerably higher than their real liquefying points, the molecules of the gas come together and form aggregations of a considerable size which in some way or other (at present very difficult to under- stand) are able to persist for a long time after the gas has regained its normal temperature. In other words, the effects suggest the interesting tact that what we might call incipient liquefaction occurs in these gases at temperatures well removed from their real liquefying points. It may also be pointed out that, broadly speaking, the lower the real liquefying point of a gas, the lower is its “critical temperature,” and the greater is the temperature-distance between the “critical temperature ”’ and the real liquefying point. The results for nitrogen at a 538 Mr. E. Cunningham on the high pressure show a departure from this rule, possibly owing to unavoidable impurities. In the case of CO, it will be noticed that the effect obtained is much more marked when some of the gas is actually solidified during the cooling process. It might therefore be urged that with CQ, the nuclei are produced not while the gas is approaching the solid state, but while changing from the solid back again into the gaseous condition. This view, how- ever, 1s improbable on the analogy of the results obtained with the other gases. It is further disqualified by a fact which we have not yet mentioned, namely, that the air derived from boiling liquid air is perfectly nuclei-free, so that (as may be seen from the figure) no glass or cotton-wool plug had to be inserted between the reservoir containing the liquid air and the experimental tube. This fact indeed confirms the ordinary view of evaporation, that it is due to the escape of separate molecules from the free surface of the liquid. Evidently then in the case of air the formation of these nuclei is not a “reversible” process. This point was not tested in the case of liquid oxygen as there happened to be a glass- wool plug already in position, but there is no reason for supposing that oxygen would behave differently in this respect from liquid air. The point raised in connexion with the effects in CO, is at present left open ; we hope to investigate it later on among other aspects of the problem. In conclusion we have pleasure in acknowledging our indebtedness to Prof. L. R. Wilberforce for numerous suggestions and for the facilities he so readily placed at our disposal. Our best thanks are also tendered to Professor F. G. Donnan for very helpful advice in regard to the preparation of some of the gases. George Holt Physics Laboratory, The University of Liverpool, August 1, 1907. LI. On the Electromagnetic Mass of a Moving Electron. By BE. Cuxyincuam, St. John’s College, Cambridge *. N his discussion of the electromagnetic mass of a moving electron (Theorie der Hlektrizitdt, i. p. 205), Abraham raises an objection to the Lorentz conception of an electron as having, at rest, a spherical shape, but in motion the shape ofan oblate spheroid the ratio of whose axes is 7~1—v’/¢’, v being the velocity relative to the ether, and c¢ the velocity * Communicated by the Author. Electromagnetic Mass of a Moving Electron. 539 of light. The present paper reconsiders Abraham’s discussion and comes to the conclusion that the objection is not valid. The discussion was suggested by the fact that it has been proved that Maxwell’s equations represent equally well the sequence of electromagnetic phenomena relative to a set of axes moving relative to the ether, as relative to a set of axes fixedin the ether. More explicitly this is stated as follows :— If there are two sets of rectangular axes (A, A’) coinciding at a certain instant, of which A’ is moving relative to A with velocity v in the direction of the axis of x, which is conceived as at rest, and if z, y, z, ¢ be space and time variables associated with A, and 2’, 7’ <',t’ similar variables associated with A’, then the equations 56 bea ioe ail ink i —curl E, transform identically into the equations On is Se pei Sa ia eo the accented and unaccented magnitudes being connected by the relations z' = B(x«—vt), oy ee : B = (1 _— w/c”) 7 E/= (] Ey—cH., E.+vH,), ! inf } Hi Ae H, +E H.—vBy). Further, if p= = div H, and p’= tiv Ki’, the volume integrals taken through corresponding regions 7, 7’, \_ pdr and Se p’dv' are identically equal, giving an exact correspondence as regards distribution of electric charge. Thus the above transformation renders the electromagnetic equations of a system independent of a uniform translation of the whole system through the ether *. * The transformation in question is given by Einstein in a paperin the Annalen der Physik, xvii. (q. v.). It isin substance the same as that given by Larmor in ‘ Aither and Matter,’ chap. xi., though the correlation is only proved to hold as far as the second power of v/c. Prof. Larmor tells me he has known for some time that it was exact. Vide also Lorentz, Amsterdam Proceedings, 1903-4. 540 Mr. KE, Cunningham on the According to this transformation, as a mere geometrical correspondence, the length of a line in the direction of the axis of w moving with the axes A’, as measured in the coordinates w'y'z't’, is greater than its length measured in the coordinates x, y, <, tin the ratio 1 : (1—v?/c?)2, so that Lorentz’s hypothesis of the reduction in the dimensions of a body when it moves relatively to an observer is reduced by this geometrical correspondence to the assumption that in the variables associated with axes moving with it its shape is. unaltered—an assumption suggested by the fact that the electromagnetic equations referred to those variables are independent of the motion through the ether, and by the attempt to form a purely electromagnetic theory of matter. Thus if the single electron at rest has a spherical configura- tion, and there are no other than electromagnetic forces, we should expect it in motion to have a _ Spherical configuration when measured by the variables «'y’s’, which means that as measured by the variables «, y, 2 it will have the spheroidal shape as suggested by Lorentz. The electron as conceived by Abraham, on the other hand, is spherical always as regards the variables #, y, 2, and a prolate spheroid as regards a'y’z’, the ratio of the axes being 1: (L—v?/c?)2 In either case the electromagnetic mass is defined as the ratio of the external mechanical force on the electron to the acceleration of the centre of the electron, and Abraham de- velops two expressions for the jongitudinal mass, 7. e. for the ratio of the force in the direction of motion to the acceleration in the same direction, viz.: oe and - i a for the case of the so-called quasistationary motion, G being the electro- magnetic momentum and W the elon omagnetic energy. lor the latter case these two expressions are proved identical, but for the Lorentz electron they are not equal, and Alene deduces that W cannot be the whole energy of the electron. But the fact is that in this case the mass as above defined is not equal to sepia v dv’ assumption that the electron is “rigid” (Theore der Elek. Wl. pa loo)yalt the change in the shape of the electron with the change in velocity is taken into account, it will be found that the mass as obtained from the change in momentum is identical with the mass as obtained from the change in the energy, as it clearly must be, since a quantity defined in a perfectly definite manner Ca from consistent equations be shown to have two different values. this expression being obtained on the \ Electromagnetic Mass of a Moving Electron. 541 The assumption on which the theory is built is that the forces from sources exterior to the electron balance those due to the electron itself: this is the assumption that there is no inertia other than electromagnetic, and we deduce the equation dw dA Tae Rae: where W is the electromagnetic energy, and A is the work done by the forces due to the electron itself. If w is the velocity of the centre of the electron, v=(v + 0) the velocity of the charge at any point of it, F the mechanical force per unit charge, we have dA | ai = |p(vF)dr, (vF) being the vector product of v and F, If En are the coordinates relative to the centre of the electron of the element of charge whose velocity is v, and «yz of the same element when the electron is at rest, &=(., n=, =z; so that the velocity », of the charge relative to the centre is d& dp IV AVo dt de eB di in the direction of the axis of x. Thus, if F, is the component of F in that direction, dA dB ae =O (pP.dr + [pc a Edt, v = —vyK — we pxl drt, K being the total mechanical force on the electron ; vot = "95 (po (T',)od7o 3 where the suffix 0 in the last integral refers to the corre- sponding quantities when the electron is at rest, so that the region of integration is spherical. For quasistationary motion W is a function of v, only, and therefore ago OW. Ld NV day. a Wy. de Cedex da wi du, = Phil. Mag. 8. 6. Vol. 14. No. 82. Oct. 1907. PAG) 542. | Mr. E. Cunningham on the Hence’ 2 ign | OW f= tk + 2 oye (autre d Uo | and therefore } 1 dW uf a ae er eerG por(F)odry } =k, so that the longitudinal mass is equal to Vd Wi ah i Ge Pot l',)o@ Tp. It is the second term in this expression that is neglected by Abraham, and which he has to account for by assuming the energy of the electron to be made up of W together with a term not electromagnetic in origin. We proceed to evaluate this expression in the two cases (i.) of a sphere with uniform volume density; (ii.) of a sphere with uniform surface charge. Gi.) Volume Distribution. Hence q@ A@ { 1 u2/e2 ac GIN a a Uae Nop la, Gee “Bab 88 tsa cae Me ee = 5 ae Ric ; tg ajor 4 ip { pot(F'z)odTo= po reos @, 3 THPo COS O2a7* sin 0d dr « Ov 0 A et é ) \ Electromagnetic Mass of a Mong Electron. 543 ue dW 1 v, “dy — 2B pot (Fx )odTo perez Ai Oe “i = 5 aap 2 a eee ~ 5 acBe dG ao Gi.) Surface Distribution. ee e” Vo ae 3 ac? B Wee Vo" ee salle as) iG_2 ¢ dvo 3 GG ee Ge Weaiel phe? fs ir ae 3 oo Vy AU, ~ 6 ae’B S In this case the integral \ poa( F,) ¢t) becomes i) oot (F'z)odSo, taken over the da ergs of the sphere of radius a, and F,=270, cos 0. Thus for, \edSp= 477 aay iy cos’ @ sin 8 dé 0 2 = nace == Teo Die 1B aie and 1 dW 1 Pe Ney == Set yea Web les tale Ue" Uo” ‘ ee a a de ee ~ 3 ace? _dG =o 202 544 Mr. H. Cunningham on the Thus in both cases the corrected expression for the longi- tudinal mass as derived from the energy gives the same result as that obtained from the momentum, and no other forces other than electromagnetic come into play. - On the other hand, since from what has been said above it appears that the electron will naturally retain the spherical shape as measured by the variables associated with the moving axes, it appears that some extraneous forces would be required to cause it to retain the spherical shape to an observer remaining at rest. It is perhaps worth noting that ‘‘ the principle of relativity ” propounded by Biicherer in the Phil. Mag. of April 1907 is in essence identical with the statement made in the beginning of this paper. The principle referred to may be stated thus : that in the sequence of electromagnetic pheno- mena the giving of an additional uniform translational velocity v to the whole system of electric and magnetic bodies will not affect the phenomena observed if this velocity v is at the same time given to the observer. ‘The trans- formation of space and time variables mentioned above shows a means of explaining this dependence of the electromagnetic phenomena on relative motion only; and conversely it is a comparatively simple matter to show that it is the only means. [or it is required, among other things, to explain how a light-wave travelling outwards in all directions with velocity UG relative to an observer A, may at the same time be travelling outwards in all directions with the same velocity relative to an observer B moving relative to A with velocity v. This can clearly not be done without some transformation of the space and time variables of the two observers. Suppose two, observers A, B, to be situated momentarily in the same spot, and let B be moving relatively to A’ with velocity v (measured by A in his own system of space and time). Let the direction of motion of B be A’s axis of a, and let the instant of coincidence be A’s time t=0. Suppose axes of Ef to be B’s system of coordinates moving with him with velocity v relative to A’s axes of wy 2, and coinciding with them at t=0. Associated with a given point at a given time as marked by the values (a, y, z, 1) will be unique values of (&, », %, 7), + being B’s measure of the interval elapsed from the time of his coincidence with A, and conversely. There must there- fore be a linear transformation from the variables (2, Yrcenen Lo (Seems) C5 ia Consider now points on the axis of & (or &). Then the \ Electromagnetic Mass of a Moving Electron. 545 transformation must be of the form f= aatb't+e axz+bi+e Male tee ax+bt+e y] Now & will not in general be infinite unless x is infinite, and also when « and ¢ are zero € and rt are also zero. Hence the transformation must be of the simpler form I] PES E=a'xt bit cect or A=(a'b’—Ba""). NT ' eu SG ba20 t=a a+b" i= EASE” the coefficients a’, b', a'’, b'’ being functions of the relative velocity v. | Now if a point starts from A at time ¢=0 and travels with B, its coordinate € is always zero by virtue of the relation «=vé. : Hence b= —a'v, 1. E=a'(x—vt). Now consider what is involved in saying that if a point moves along the axis of w relative to A with the velocity c of light, it also moves with velocity ¢ relative to B. If a point moves from the position a at time ¢ to the position «+ 6x at time ¢+ dt let the corresponding changes in & and t be 6&, 6r. Then | b& = aba 4 b'bt, bt= abut b''St. b& a’ dw =i; bist St ~ aSa4 b" 8 Hence if the point has velocity » in A’s system of ¢o- ordinates and y in that of B a’n +b! ig Gee bur Hence ita particular ik 7 ——-2¢. v=, | ale+£c(b"—a') —b'=0, b! va’ so that bg and @ = = Se - Cc? Ce 546 Electromagnetic Mass of a Moving Electron. Thus E=a'(x—vt), r=a'| — ae +i} 5 If this transformation be reversed we have vaa'(E+ UT), 1 t=al (+ %6 +7) where a’ = ao ¢ , v a (1 = ae and «’ will be the same function of (—v) that a’ is of v. But the transformation shows that if x, x, be two points fixed relative to A and &, & their coordinates in B at any time 7, Lq— a =a!l(E,—&,) ; i.e. a line of length / as seen by A appears to be of length a as seen by B moving relatively to it. But this will be a the same whichever be the direction of B’s motion along the axis of w, so that if «’=/f(v), fw)=f(—»), le. a =o’. uw ; y?\-3 Hence a’*(1— 2) = 1, GG, a= (1- “:) : : Cc Cv/ Thus the transformation is finally £=A(e—vt), Ww 25 r=p(—% +t] where pg =(1-5) ‘ Now let points not on the axis of x be considered. Since the axes of « and & coincide at all time, y and , and.therefore X=1. — Similarly w= 1. The general transformation between wyzt and En fr is therefore | y= 2=4 E= B(«—vt) +ay + dy, eS a(—" +t) + Coy + dec. On Expansion in Bessel’s Functions. 54T. The pe last equations reducing to those ae for y=0 and ui our + hypothesis requires that the equation B47? + 0? = Cr? shall be a result of the equation Beate? = rts This is so if, and only if, ¢,, ¢:, d,, d, are all zero. Thus we have arrived exactly at the transformation as given above, and, as Hinstein has shown (loc. cit.), in order that the electromagnetic equations may be iavariant under this trans- formation the electric and magnetic vectors in the two systems must be correlated in the manner done in this paper. Biicherer in the paper referred to does not take into account this necessary modification of coordinates, and therefore when in the latter part of it he evaluates the electromagnetic mass of the electron on the assumption that it is spherical he is in reality considering the Abraham electron, and so obtains Abraham’s expression for its mass. LI. On Expansion in Bessel’s Functions. By ANDREW STEPHENSON * a the ordinary Fourier expansion in sine series fie => Asim ca, for the range of.# frum 0 to ¢ the determination of the coefficients depends upon the vanishing of the integral °c | sin ape sinae,vrdx when km. I have shown, however, 0 that the coefficients can also be found readily in the more general case when (2@ sin 4,.v sina,,vdv=p sin a; SIN 4&,,¢, e/ 0 where km and p is some constant f. Similarly the cosine exp.insion can be effected if c i COS 4, COS a, vda = p COS 4,€ COS a,,C- 0 * Communicated by the Author + “An Extension of the Fourier method of Expansion in Sine Series,” Messenger of Mathematics, vol. xxxili. pp. 70-77 (1903). A more general discussion is given in a second paper in the same volume. . 548 Mr. A. Stephenson on There is nothing in this method peculiar to the trigono- metric functions, and we now apply it to the Bessel’s expan- sions to obtain a generalization which is essential for the complete solution of a certain type of physical problem. If B,(ur) is a particular solution of au 1 du Npsbns Cad Winsor wat get a then, for wuz, b b (B,u,r)B ap )vdr= a [rf Balae) Bal (or) — waBrl or YB.) a Pe tral! a which is | a mee {0,3 | (ut) B,, 7) aie p,B,,(ay,.0) By (quia) > if Br(pez)) = B,C) = 0; and therefore b { B,(0)B, (ur yrdr = pBn (ura) B, (ue) if the w’s are roots of | B,! 1 3 a arm TPH faye oi oP a) Nee me mG Also from (i.) by approaching the limit #4,=z, we find b 2 (B2Cuer)rdr=3 £ 0°B,!*(u,)) eB, *(uia)— (a= 3) Bs (ua) i. Now consider the problem of expanding a function of 1, for the range between a and 0, in a series of Bessel’s functions of the first order | | Je) =ZA Ber)» \ «4. ee where the w’s are determined by (ii.) and the particular solutions Bo(ur), of Bessel’s equation are so chosen that Bo(ub) =0. Both sides of (ii.) being odd functions of pu, the negative roots are numerically equal to the corresponding positive roots ; and therefore it is sufficient to consider the positive roots alone in the summation. ‘To determine A* multiply Gil.) by rBo(uzr) and integrate between a and 0b: then by the preceding results b i f(r) Bo(uxr) dr =p Bo(u,4)= ABo(ua) +Axh {0?By (u,b) —a®By” (uza) — (a2 + 2p) By?(xa) }5 and therefore, since there is no reason to question the Expansion in Bessel’s Functions. D549 validity of (iii.) in the limit when r=a, b ("7 Buunrdedr ppl Bn =? “ "BP Bo? (web) = By ?(ua) —(@ + 2p) Be? (#42) Through lack of this expansion the solutions of certain problems have hitherto been left incomplete. Consider, for example, the syminetrical motion of a uniformly stretched circular membrane loaded in the middle, z. e. of an annulus to the inner circular boundary of which a load symmetrical about the centre is attached. We have with the usual notation subject to the conditions” 2=0,- when) r=; oye ace oo) T=a 3 c=/(7) 33 t=O; and 2) == eee 0, if the membrane starts from rest. Hence c= Ax cos (uxct) Bo 1 By(1) =Joloer) — gy Kole), My) where and the p’s are determined by B, (ua) a bes a Bo(Ha) met Therefore £ 2 Hs ( f(r) Bo(uar)dr + a — F(a) Bo(uxa) k= wt UBy" (nab) —a°By*(aya)— (a? 2a“ 3) Bur) The small plane oscillations of a unitorm, heavy, flexible, inelastic string hanging freely with a load attached to the end may be investigated similarly. It may be noted that the method employed in obtaining the generalized expansion can be applied to expansions in other functions, if the necessity arises in connexion with any physical problem. June 1907. i HO) LITI. The Rate of Transformation of the Radium Emanation. By G. Rime iy, Ph.D.* PYXHE radium emanation, like all the radioactive products, is transformed according to an exponential law. The ‘“period”’ of the emanation, or the time required for the emanation to be half transformed, is an important physical constant, an accurate knowledge of which is required in many experiments. Although observations of its period have been made by a number of investigators, the results obtained have not been very concordant. The period of the radium emana- tion has been determined by Curie t, Rutherford and Soddy jf, Bumstead and Wheeler §, and Sackur ||; the results obtained by these observers are given below :— Curleseye ance. pale eae 3°99 days Rutherford and Soddy ... 3°77 Bumstead and Wheeler... 3°88 ,, UCI ee ek isc eee Bel) ep Two different methods were used for these determinations. Curie, and Bumstead and Wheeler measured the decay of a quantity of emanation. in a closed testing-vessel; Rutherford and Soddy, as well as Sackur, transferred after different intervals of time into a testing apparatus known volumes of air containing emanation from a large supply which was kept in a gasometer. Since for accurate determinations the measurements have to be extended over several weeks, the first method requires measurements of ionization currents over a wide range of intensity. This is a disadvantage, because the rate of movement of the electrometer-needle, unless very slow, is not accurately proportional to the current, but generally increases more slowly than the latter. The period of the emanation, for this reason, will be found too large. In the second method, this source of error can be | eliminated by putting smaller volumes of emanation-air into the testing vessel at the beginning of the experiment than at the end. The drawback of the second method is the lability of escape of emanation, and also of disturbances of the homo- geneous distribution during the process of transference of the emanation into the testing-vessel. In the following experiments I endeavoured to get measurements of the period of the radium emanation un- affected by both these sources of error. * Communicated by Prof. IE. Rutherford, F.R.S. + Comptes Rendus, exxxv. p. 857 (1902). { Phil. Mag. April 1903. § Amer. Journ. Science, Feb. 1904. || Ber. d. d. chem. Ges. xxxviil. p. 1754 (1908). \ Rate of Transformation of the Radium Emanation. 501 Let two volumes V,, V, communicating with each other be filled with air containing Ra-emanation uniformly dis- tributed. Disconnect them; then, if at the time ¢=0 the smaller volume V,, when passed into an electroscope, produces the current 2,, and at the time? later, the other volume Va, when passed into the same electroscope, gives the effect 2, it ean readily be deduced, that the period T of Ra-emanation calculated from these data is the theory is based on the assumption that the radium emanation decays exponentially with the time. In order to obtain accurate results it is advisable to make ¢ and vs large, and arrange the time ¢ between the two Wa observations so as to make the two currents approximately equal. The electroscope is then used under exactly the same conditions, and no comparison of currents of very different magnitude is needed, ‘To eliminate errors due to changes of pressure and tempe- rature of the air, as well as to possible changes of sensitive- ness of the gold-leaf system, immediately before the emanation is introduced into the electroscope, the latter is standardized by the y-rays from a few milligrams of radium bromide, enclosed in an airtight capsule and placed in a definite position near the electroscope. The readings were not taken immediately after the intro- duction of a quantity of emanation, but three hours later, in order to allow the emanation to reach radioactive equilibrium, when the rate of movement of the gold-leaf is sensibly constant over the time required to make the observations. A quantity of air containing emanation, supplied by boiling some RaBr, solution, was collected into a little gasometer over water and thence passed into a partially exhausted glass vessel of the shape shown in fig. 1. Fig. 1. A The vessel was then sealed off at A and brought into a constant-temperature room tor about two days, to allow the emanation to distribute itself by diffusion uniformly through the air in the vessel, which was generally at a pressure of about half an atmosphere. By means of a small flame, the ——— 552 Rate of Transformation of the Radium Emanation. two vessels were separated at B, care being taken to protect the other parts of the vessels from radiation from the flame. The air in the smaller vessel V, was now transported into the electroscope. The arrangement used is shown in fig. 2. — Fig.2. To PUMP By means of rubber tubing, connexions were made to allow a current of steam to pass through V, into a receiving vessel R containing water, after the narrow ends of the vessel had been opened inside the rubber connexions. The steam was passed through the vessel for some time, in order to completely transfer the emanation into the gasometer R. The electroscope was then exhausted and the collected gas in R allowed to pass in through a tube B containing phos- phorus pentoxide and plugs of cotton-wool. Air was then introduced by means of a stopcock at A, which swept the residual emanation in the tube into the electroscope, and brought the air in the latter to atmospheric pressure. Immediately before the introduction of emanation the natural leak was determined and the leak due to the radium standard. ‘The sensibility of the electroscope used was such that 10—§ gram radium in equilibrium gave about 8 divisions per minute movement of the gold-leaf on the scale of the reading microscope. ‘The actually measured amounts of radium emanation were in most cases 1°5—4 times larger. Three hours after the introduction of the emanation, the readings were taken, and then the emanation removed. The larger vessel V. was dealt with in exactly the same waya suitable time later. ‘The volumes of the glass vessels were determined before the emanation was introduced; the uncertainty due to the sealing off at B (fig. 1) was certainly less than 1/300 of the volume of the smaller vessel. , Notices respecting New Books. D900 The results obtained by this method are given in the following table :—_ No. of VG A Di Ds t Ay experiment. | in c¢.¢.| in e.c.| in div./min. | in div./min. | in days. | in days. Wii Leste in 36:0 | 275 34:2 371 10°60 | 376 ie I te 36°95 | 143 27°0 29-8 6-81 378 1 ee ae 29°6 | 283: 3471 30:7 12°79 375 1 coe an 22D 270-5 53°0 54:4 13-00 O71 WTR sea dei 26:2 | 244 14-40 14:06 11-94 3°80 (FE 543 | 243 44-9 30°8 10:00 3°70 7 gems 24:0 | 272 12:98 11-22 13°96 | 3°76 Shy Gene eae 318 | 14071 42°9 34°0 7:16 372 3°75 Each of the numbers marked in the columns 2, and 2, repre- ‘sents the mean of four readings, which never differed from their mean value more than one per cent. The values 2,, 24, given in the table are corrected for the natural leak, the column 2, also for any slight change of sensitiveness of the electroscope. As it will be seen, the mean of all the experiments, 3°75 days, agrees very closely with the original value obtained by Rutherford and Soddy, 3°77 days. It may be interesting to note that Dr. Bronson in this laboratory recently also deter- mined the period of the radium emanation, using an electro- meter steady-deflexion method. Two decay curves of the emanation obtained by him gave the value of T=3-°71 and 3°73 days. It thus seems certain that the period of the radium emanation is not longer than 3°80 days, and very probable that it is in the neighbourhood of 3°75 days. In conclusion, I desire to express my sincerest thanks to Professor Rutherford, at whose suggestion these experiments were undertaken, for his valuable advice during the progress of this work. Macdonald Physics Building, McGill University, Montreal, May 1907. LIV. Notices especting New Books. Stereochemistry. By A. W. Stewart, D.Sc. Green & Co. 1907. Pp. xx+583. \ E welcome this latest addition to the excellent series at present being issued by Messrs. Longmans under the gevieral title of ‘‘ Text-Books of Physical Chemistry.” The enor- mous amount of research carried out during the last few years in the particular branch of chemistry with which the present work is concerned has rendered the publication of such a volume highly desirable, and it is sure to prove extremely useful to all students London: Longmans, 554 - Notices respecting New Books. of chemistry. The work is divided into two sections, Section I. dealing with stereoisomerism, and Section II. with stereochemical problems into which isomerism does not enter. Section I. is subdivided into two parts, Part I being devoted to optical activity, and Part II. to stereoisomerism without optical activity. The subjects dealt with in Part I. include a general account of the asymmetric carbon atom, of optically inactive and active com- pounds, the determination of configuration, the asymmetric carbon atom as a ring-member, some exceptional cases of optical activity, the quantitative relations between activity and the nature of the asymmetric earbon atom, various active elements other than carbon, and the factors determining the amount of rotation. Part II. deals with cis-trans isomerism in cyclic compounds, geo- metrical isomerism in the ethylene series and in carbon-nitrogen compounds, and stereoisomerism in. the compounds of nitrogen, cobalt, platinum, and chromium. Section II. deals with the phenomena of steric hindrance, the relation between the space formula and the chemical properties, the effects of substitution upon the formation and stability of cyelic compounds, the con- figuration of optically inactive carbon compounds, and the space formula of benzene. There are two appendices, in one of which the author discusses the relations of stereochemistry to physiology, while in the other he gives directions for the construction ot stereochemical models. Enough has been said to give our readers some idea of what they may expect to find in this book. Numerous references are given to original sources of information, and name and subject indexes are provided at the end of the book, which fully maintains the high standard set by its predecessors in the same series. Notions Générales sur La Teélégraphie Sans Fil. Par R. Dp Vauprevuze. Paris: édité par “I’Kclairage Electrique.” 1907. Pp. vi+170. Numerovs books have been published from time to time dealing with the principles of wireless telegraphy, some intended for specialists, others for “‘the man in the street.” Of books of the ~ latter type there has been great profusion, and unfortunately the desire to popularise science has not infrequently led their authors to modes of expression which are neither scientific nor particularly illuminating even from the “popular” standpoint. The art of presenting the facts and theories of physical science in a manner which, while ‘perfectly intelligible to the average well-educated person, retains all the precision characteristic of genuine scientific work, is one possessed by comparatively few writers. ‘To steer a middle course between the technicalities of applied science and the laxity of common parlance is, indeed, no easy matter. We there- fore heartily congratulate the author of the volume under review on having accomplished this extremely difficult task in ® manner which commands admiration. While writing in a way calculated to arouse the interest of the reader, the author never allows himself to depart from those strictly scientific modes of expression without which no really accurate presentation ot facts is possible. The ~ Geological Society. 3) o result is a work which should prove useful and extremely interesting not only to the novice, but also to the specialist. After some introductory chapters dealing with wave-motion, radiation, the general principles of electrostatics and electrodynamics, the generation and transformation of currents, the production of electric oscillations, resonance, and Hertz’s experiments, the author briefly traces the beginnings of wireless telegraphy, and gives an extremely clear account of modern forms of detectors. Then follow methods of obtaining syntony, and finally an account of such practical systems as are actually in use at the present day. We can strongly recommend this excellent little work to all interested in the fascinating subject with which it deals. LV. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from vol. xiii. p. 763. | May 15th, 1907.—Sir Archibald Geikie, D.C.L., Se.D., Sec.R.5., President, in the Chair. ene following communication was read :-—— ©On the Origin of certain Canon-like Valleys associated with Lake-like Areas of Depression.’ By Frederic William Harmer, F.G.S., F.R.Met.8. In glaciated regions, as shown by Prof. P. F. Kendall, the in- vasion of a district by an ice-sheet would tend to obstruct the natural drainage, producing lakes, of which the outflow might take place over the advancing ice, between the ice and the hillsides ; or it might escape laterally, in a direction at right angles to the longest diameter of the lake and to the course of the pre-existing stream. Overflow-channels would assume a gorge-like character, and would present a comparatively-recent appearance. During the Glacial Epoch the North-Sea ice appears to have invaded the plain of the Witham and the valleys of the Welland, Nene, and Ouse, overriding also the higher land separating them; the Tees ice-stream moved up the Trent basin to the vicinity of Derby and thence, immosculating with the Derwent glacier, up the Soar Valley towards Leicester and Rugby ; the Irish-Sea ice passed into the northern part of the basin of the Lower Severn; ice from the Brecknock Beacons passed towards the Bristol Channel and, com- bined with Irish-Sea ice crossing Pembrokeshire from St. David’s Head towards Cardiff, may have caused the accumulation of sedentary ice in the Severn Valley. After considering the case of Lake Pickering and the Maiton Gorge asa typical example, the author passes on to Lake Shrewsbury and the gorge at Iron- bridge. Preglacial drainage of the Upper Severn and Vyrnwy was probably northwards; when a Glacial lake was first formed over the Cheshire plain it may have drained towards the Trent, pos- sibly by Rudyard and Madeley ; when these gaps were closed, the lowest outlet seems to have been towards the south, and the Severn Gorge at Ironbridge was cut. The canon. of the Camlad at. Chirbury, known as Marrington Dingle, appears to have been 556 Geological Socrety. caused by outflow from a Church-Stoke lake which was driven into the Ordovician ground to the north and east. Lake Trow- bridge and the gorges of Clifton and Bradford-on-Avon are next dealt with, the latter being attributed to the overflow of a Glacial lake oceupying the Trowbridge plain, and the former to the blocking of the Flax-Bourton valley byice. ‘The gaps in the Jurassic escarp- ment at Lincoln and Aneaster are explained as overflows from a lake caused by the damming of the Trent outlet towards the Humber. This gave rise at first to the more northern, and later to the southern gorge. Finally, Lake Oxford and the Goring Gap are dealt with in considerable detail. Certain Drift-filled valleys are regarded as excavated by a river flowing from the south-west—the primeval Thames. The distribution of the Chalky Boulder-Clay shows that the advance ef the Great Eastern Glacier from the north- east must have arrested drainage flowing towards the Wash, and caused a lake which may possibly have first overflowed through the Newport valley into that of the Stort, or by the Hitchin valley into the Lea, or later into the Colne by the Leighton-Buzzard valley. When the ice reached Buckingham, such channels were closed and the overflow must have taken place farther to the south-west, over what are now the Tring, Wendover, and Wycombe Gaps, and eventually by the Goring Gap itself. Gravels containing Triassic and drifted flint-pebbles derived from Glacial deposits may be traced from Goring across the Oxford Plain, at an elevation of between 400 and 500 feet, into the Evenlode Valley, and thence into the basin of the Avon. Their occurrence on the higher slopes of the Goring canon indicate that the exeava- tion of the latter did not commence until after the arrival of glacially-derived detritus in the region in question; the Goring Gap is, therefore, of Glacial age. . The author is unable tc reconcile the views here given with those of Prof. W. M. Davis on the valley-erosion of Central England. Any relation which may have existed between the present drainage- system and that of some former period when a peneplain may have extended over the Jurassic and Cretaceous formations alike, and consequent rivers ran out to sea over it, is remote and impossible to trace. With the exception of the Goring gorge, which may be otherwise explained, no connexion whatever exists between the drainage-systems or the topography of the Cotteswolds and the Chilterns, nor does a vestige remain of the peneplain which, at some unknown height above the present surface, is supposed to have united them. ‘The escarpments form two dip-slopes, to which the streams traversing them are respectively conformable. The more important rivers of Central England are longitudinal, following the strike of softer rocks along which the predominant erosion has taken place, the transverse drainage being everywhere subsidiary to that of the plains. The excavation of the latter may have taken place at a comparatively-early period in a direction not vertical, but inclined more or less with the dip of the softer strata, the formation of the dip-slope and the cutting-back of the opposing escarp- ment being contemporaneous; the erosion of valleys in the dip-slope must have been posterior to this, and could not have preceded it. RosskELt. ANNEALED IRON. B.CONDITIONS A.CONDITIONS CURVES !.2.3 WITH VIBRATIONS OF INCREASING INTENSITY. ANNEALED B CONDITIONS. WA 3 . FIG. Vil. NIChWEle QUENCHED A. ann B. CONDITIONS. * Phil. Mag. Ser. 6, Vol. 14, PL‘XI. B CONDITIONS. QUENCHED STEEL | FIG. VIII. 10.000 i mt ee ae “ Sar | a > SS ad eee ee 0 z 4 6 ANNEALED NICKEL SEES PMG VE yee | Bora | ers seen = ef BeeMcHED NICKEL). Looe Bee IG oa pete ee on A —— —__—« —_— ——_ —_ ee E ie Fs 24 R Ben Rigo dente 2 pa oR B 3 A | Me Lea ANNEALED STEEL Sie FUG.IN. 2 | | CAMPBELL. Phil. Mag. Ser. 6, Vol. 14, Pl. XII. BEVAN. N Phil. Mag. Ser. 6, Vol. 14, Pl. XIII Fie. 1. Gero } Fia. 4. THE “LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SIXTH SERIES.] NOVEMBER 1907. LVI. A Theory of the Displacement of Spectral Lines pro- duced by Pressure. By O. W. Ricnarpson, M.A., D.Sc., Professor of Physics in the University of Princeton*. § 1. Introduction. fhe pressure of the surrounding gas or vapour may influence the structure of the lines of emission spectra —and probably also of absorption spectra—in a variety of ways. Increase in the partial pressure of the vapour of the emitting substance generally produces a broadening of the lines, which varies greatly both in quantity and quality with the particular line examined. The lines thus affected lose their sharpness and become diffusely extended: the extension may be more marked towards the region of either longer or shorter wave-length according to the nature of the line in question. This effect depends entirely in the similarity between the surrounding vapour and the centres of emission. Up to the present there is no experimental evidence of a change of frequency of the original line due to this cause, apart from the broadening which has been described. There is, however, another effect of pressure which is not selective. Any gas other than the vapour of the emitting substance affects the lines emitted, if its pressure is high enough. In this case also the pressure impairs the definition of the lines and broadens them out, usually about equally on both sides ; but this broadening is not sufficient to mask a - * Communicated by the Author. Phil. Mag. 8. 6. Vol. 14. No. 83. Nov. 1907. Zeke 558 Prof. O. W. Richardson on a Theory of the well-marked displacement towards the region of longer wave- length. The existence of an effect of this kind was first placed beyond doubt by the work of Humphreys and Mohler*, and we owe most of our knowledge of it to their investigation and the subsequent papers of Humphreyst. The present paper deals with the theory of this second non-selective effect of pressure. Although the calculations which follow do not, on account of the limitations imposed by our ignorance of atomic structure, lead to an exact numerical evaluation of the effects, they, nevertheless, afford results of such a definite nature as to make it extremely probable that the explanation of the phenomena is to be sought along the lines indicated. § 2. Outline of the Method. Briefly stated, the theory to be developed attributes the displacement of spectral lines produced by pressure to the effect of sympathetic vibrations occurring in the surrounding atoms. The fact that an atom A is emitting light shows that it is surrounded by an alternating field of electric force. This alternating eleciric field will produce forced vibrations of equal period and, under certain conditions, of like phase in neighbouring atoms. The electric field due to the forced vibrations will react on the emitting electron in the atom A; and, as will be shown, in such a way as to increase the period of the latter. It will be necessary, then, to calculate the reaction at A due to the forced vibrations set up in an atom at B by a given vibration at A, to sum this up for all the atoms B which occur, and to find.the effect of the resultant reaction on the period of A. §3. The Reaction at A. If we are to arrive at results which can be tested numeri- cally it will be necessary to forego generality to the extent of making some hypothesis about the mechanism of the emitting system in A. We shall suppose that the spectral lines are emitted by a vibrating electric doublet within the atom A, as this hypothesis appears to combine simplicity and general applicability to the greatest extent. To be more precise, we shall assume that the electrons emitting light are oscillating about equilibrium configurations under forces * Astrophys. Journal, vol. 211. p. 114 (18986). + Ibid. vol. iv. p. 249 (1896) ; vol. vi. p. 169 (1897) ; vol. xxii. p. 217 (1905); vol. xxiii. p. 233 (1906). \ Displacement of Spectral Lines produced by Pressure. 559 which, for small displacements, are proportional to their dis- placement from the equilibrium configuration, and that the displacement gives rise to an electric doubiet of moment proportional to it. Whatever may be urged against these hypotheses, it must be conceded that a theory based on a similar set of assumptions gives a fairly satisfactory account of the phenomena of dispersion. We know from the Zeeman effect that the lines of most emission spectra originate with the negative electrons, and it is probable that the value of e/m for the positive electrons is so great compared with the corresponding quantity for the negative, that the positive electricity may be regarded as stationary to a first approximation. Under these conditions the equation of motion for an electron in an isolated atom will take the simple form pe) Sioa see aka 2 (le where & is the displacement from the equilibrium configura- tion, m the mass, and e the charge of the electron. The constant \, depends on the constitution of the atom and the configuration of the electroninit. The time Ty of a complete vibration of this type for an isolated atom is given by ips a vale goer) If the atom were placed in an electric field so that the electric intensity at the electron were equal to X, the equation of motion would become One e nse = eXi— sce aaNet a6) pee up (3) Now if the atom containing the vibrating doublet is sur- rounded by other atoms, even if there is no externally impressed electric field, there will be an electric field due to the doublets induced in the surrounding atoms by the vibrating doublet. The effect is similar to the additional force called into play by dielectric polarization. We shall proceed to calculate the magnitude of this force X, on the assumptions, first of all, (1) that the whole field of force of the vibrating doublet is available outside the atom containing it; and (2) that the induced doublets have the same value as if the exciting field were a static one. The way in which these limitations affect the calculation will be considered later. . We shall suppose that the vibrating electron when in its 2P 2 560 Prof. O. W. Richardson on a Theory of the equilibrium position gives rise to no external force, so that the electrostatic effect of its motion will be equivalent to the creation of an equal and opposite charge at the equilibrium position. Thus when the negative electron has moved a distance & we shall have an electric doublet of moment —eé. Let the coordinates of the undisturbed position of the vibrating electron at A be «’ y’ and those of the displaced position w'+&,y' (see fig. 1). The doublet at A will give rise to Fig, 1. iy’ ) ary! electric force at B in the plane of the figure. Let wy be the- coordinates of the equilibrium position of an electron belonging to an atom which happens to be situated at B. Under the influence of the force in question this electron will move to a point in the plane of the figure whose coordinates may be denoted by +a&,y+a.& An expression for a, and a, may easily be found. Since r= (a—0'P + (y—y!)? 5 4A and rye = (w—a'—&)? +(y—y )? J 6) the potential V,, at ry can be calculated. From equation (3) we have Ve eae = 1, and a aoe Aa AL.) 5 (5) if e is kept positive, the displacements being those of the negative electrons. ds is a coefficient similar to \, of equa- tion (3), the suffix denoting that it is the sth electron which \ Displacement of Spectral Lines produced by Pressure. 561 is displaced. The above cee give a=—"4(1- 3u2 + a bu?) = 2) 6 = = As ( 3uv+ aa du?) ‘g Ze S= = — U — — L ————— 2 ry 2 =) 7 ees anl aye where ee Gye ot. Ty TY Higher terms in /r; have been neglected. The next step is to calculate the reaction on the vibrating electron due to the induced doublet —a,&e, —a,€e, 0 at x, y. The part of the potential at 2'+&, 7/ arising from this cause is evidently V =e(r;'—1, ), where re =(v2—2 —(1—-ap)EP+ (y—y' +a€). . (7) By varying the potential energy we find the force in the direction of x on the negative electron at w'+&,7’' arising from the sth ‘ae in the atom B to be @ {ke D eo airneeh + 1441* —108u') t. r\° In ee this expression pe in & have been retained except in the fnalresult. The force due to all the doublets in the atom at B will be obtained by summing up the above expression for all the electrons that occur. Denoting A, by L, and >A? by L., the extra force on the electron at A due to the doublets induced in the atom at B ae (= Ely ne Beers Ty Tp Lars (L—45u? + 144° — L08u") | (8) This is the effect due to one atom, the effect for the whole of the surrounding gas will be obtained by multiplying this by the number of ‘atoms in the element of volume and inte- grating over all the atoms which occur. If v is the number of atoms in unit volume, we find for the 2 component of the force Saye dry {2 du , a -* 7 (1—15u?) + = (1-45? +1 if — 14 — 1080) 2 Ly =F one?, | 81, +1:26-2 |. hy PAO TET ANN, WOES") 562 Prof. O. W. Richardson on a Theory of the It will be noticed that the forces perpendicular to the #- axis vanish, by symmetry. The lower limit @ of integration with respect to dr, may be taken to represent the radius of the sphere within which it is impossible for the centre of an atom of class B to lie. This interpretation will only be exact provided that each atom contains only one electron, and that placed at its centre. In general vy would have to be replaced by py, where p is the probability that an electron of type s will be found at the point 7,u,¢. The quantity p would then come within the integral which would range from ©,—1 and 27 to 0,+1land0. It will, however, be sufficient for our present purpose to suppose that « represents a kind of average formed in the above way. It is evident that « will be of the order of magnitude of the radius of the atom A and have the sum of the radii of A and B as an upper limit. In carrying out the integration we have assumed that vp the number of molecules per unit volume is constant. This will not be true if the potential energy of B in A’s field of force is comparable with the kinetic energy of B. In this case we should have to replace vp by yye~™R@ inside the in- tegral, where w is the potential energy of a molecule of B of mass m, @ is the absolute temperature, and R the gas constant. This, however, is a refinement which does not seem to be required by the facts at present. So far we have entirely ignored magnetic effects. It is, however, easy to show that, on this wiew of the atom, they are small compared with the electrostatic effects already considered. Let & be the maximum excursion from the equilibrium position of the electron A, then if 7 is its periodic time the maximum velocity is equal to 2a Sait The maximum velocity of B is evidently of the order 20M, *. &)/7. The force on A due to magnetic teria is therefore of order not greater than 160° { 1 Be i “dry where ¢ is the velocity of light. ry The order of the dectt ostatic force is given by the first term of equation (9). The ratio of the latter to the former is z 5 ae Putting r=10—", and 3 x 10—-° and 10-° as superio ae for a and & respectively, the ratio is approximately 2x 10°. The forces of electrostatic are evidently enormous compared with those of electromagnetic origin. The possi- bility of magnetic effects on other views of atomile structure will be considered later. Displacement of Spectral Lines produced by Pressure. 563 It is now necessary to consider the quantities L, lL, in equation (9). On the assumption we have made in the ealculation that the displacements a,£, a,& of the electron B were due to a steady electric force, it is easy to show that K-1 oe Atrvy of the surrounding medium when there are v) molecules per unit volume. Asa matter of fact, the displacements a1&, as& are produced by a periodic force of time 7. If we neglect the initial disturbance at B of period corresponding to A,, the coefficients a, a, will be given by equation (5) provided X, is replaced by X,/1—72/7*._ Under these circumstances it can easily be shown that , where K is the specific inductive capacity Neb. ope 1—(7,/7 rea S0i> stil Nd, Ce (10) where yp is the refractive index of the medium for light of the wave-length emitted. It seems permissible to disregard the initial disturbance on account of the difference in period. It will only produce a broadening not a shift of the line. The quantity L, is evidently the value of peo taken over the molecule B. Unless 7 is in the neighbourhood of 7; one of the natural periods of the B molecules L, will be of the order L,?/n, where n is the number of mobile electrons in the molecule. The ratio of the two terms in equation (9) is = 1:26L, _ 1:26(u?—1) Sna® 327 nv,2 : (11) Taking the case of air as the surrounding medium we have p?—1=5°9x 10-* when »=4x 10" According to J. J. Thomson’s most recent estimate n will be of the order of twice the ratio of the density of the gas to that of hydrogen. This at any rate can be taken with safety as a lower limit ton. Putting n=29 and taking 1°5 x 107° (half the radius of the sphere of molecular action) for a we find that the ratio is very nearly =2x10-*. In the neighbourhood of an absorption-band of one of the B molecules one of the terins 2 r,/ 1 =) would be great compared with the others. _ In this case a superior limit to the ratio would be obtained by putting n=1 in equation (11). Even in this case the second term is comparatively unimportant. 564 - Prof. O. W. Richardson on a Theory of the In the calculation which led to equation (8) we assumed that the field was propagated instantaneously, 7..e. we assumed that the effect on A of the doublets induced in a molecule B at a distance r from A was determined by the instantaneous state of A. As a matter of fact the induced field at A is determined by the state of B at a time 7/e previously, and again that of B is determined by the state of A ata time r/c earlier still. If we allow for this we find that equation (9) up to the accuracy of the first term would have to be replaced by the real part of AT Qa? * Loametligf e ee, ae Spe On evaluating the integral it does not appear to differ from the first term of equation (9) by more than one part in ten thousand. § 4. Change in Wave-length of the Hmitted Lines. We have seen that the doublets induced in neighbouring atoms give rise to an additional force on a vibrating electron of amount 5 mye? Sy [ 8Ly + 1°26 Ly/a?]. In deducing this formula we have ieft out of account effects due to the motion of the 8 atoms and have also assumed that the full field of force of the various doublets is available out- side the atoms. Admitting the validity of these assumptions tentatively, we are in a position to calculate the change of wave-length of the emitted light. Comparison with equation (3) shows that the equation of motion of the emitting electron now becomes fo 9 of aie) ~2ef{ } 2m il aa If T is the periodic time, X the wave-length in free ether, and ¢ the velocity of light, we have SL, a itis sae ‘as If Xo is the wave-length of the light emitted by A in the Age? Agr 9. & {= » aaeralis ot (PO aes 7) 2 a Vee \ Displacement of Spectral Lines produced by Pressure. 505 absence of other matter, evidently 9 Agr? ¢? e7 =! , 14, No” mr, ( 2) Calling 6X the increase in wave-length produced by the medium, we have On ites Wye ro 5 [ 8Ly _ 2G Lig /a? | . ° : (15) No 12aa*me? Neglecting the second term and replacing L, by “?—1/47, this becomes Choi elas 9, Ni ome mere avert With the exception of « all the quantities in equation (16) are known with considerable accuracy. That « is indefinite has already been pointed out, but there is little doubt that 3x 10-8 may be taken as an upper limit for it (cf. Jeans’s ‘Dynamical Theory of Gases,’ chap. xix.). The theory may now be tested by seeing whether it affords an explanation of the shift of spectral lines observed when they are produced in the are in a gas at high pressures. The only factor in equation (16) which involves the pressure is w#7—1, which is proportional to the pressure. Hence 6r will always be proportional to the pressure. It will also be noticed that 6X is always positive, so that the shift is always towards the side of longer wave-length. Although a number of interesting relationships between the displacements of the different lines have been observed, these two, that the dis- placement is in the direction of greater wave-length and is proportional to the external pressure, appear to have been established experimentally with greater certainty than the others. The next question is as to whether the magnitude of the calculated eftect is great enough to account for the observed displacements. The minimum value of the shift per atmo- sphere for a line of wave-length 7,=4 x 10-° em. on the basis of the preceding theory will be obtained if the following values are substituted for the various constants in equation ie ye x10, c=3 x10", and e=3x 10%. The value of »?—1 is the value of this quantity at the temperature of the are. This has 566 Prof. O. W. Richardson on a Theory of the been taken to be approximately 2730° absolute. These numbers give 6A/Aj=1:07 x 10-5. This is a minimum value because 3 x 10~$cm. is a maximum value for «. Humphreys’* measurements of a large number of iron lines ranging around Ay =4 x 10-° cms. at a pressure of 37 atmospheres give values of 6A/Ay varying between 2x 10-§ and4x10-7. Thus the shift given by formula (16) varies from 5 to 25 times that observed experimentally. If we had taken the more probable value 15 xX 10~* cm. instead of the superior limit 3 x 10-° cm. for a, these factors would have been increased to 40 and 200 respectively. Thus the difficulty on the electrostatic resonance theory is not to account for the existence of the effect, but to explain why it is as small as the experiments show it to be. § 5. Lhe Motion of the Atoms. The fact that the observed displacement is so much smaller than that demanded by the preceding calculation, suggests the advisability of looking further into the assumptions which underlie that calculation. The first point which seems to require attention is the question of the error which has been introduced by neglect of the motion of the atoms. So far the atoms of the gas have been treated as though they were stationary, and effects due to their motion have been left out of consideration. We have supposed that the forced vibrations excited in an atom at any instant were the same as if the atom had remained fixed for an indefinite time in that position; although, as a matter of fact, the atom must, in general, have just moved from a position where the forcing field was either weaker or stronger. It may be suspected that this is the reason for the discrepancy between the observed and calculated values, but the following discussion of a simple case seems to show that, with the values of the physical quantities which occur in nature, the assumption of instantaneous equilibrium gives a close approximation to the truth. The case we shall take as an illustration is the following :— The emitting atom A is supposed to be fixed at the origin of coordinates, and the emitting electron in it to be constrained so that its displacement & at time ¢ is given by =&) cos pt. The moving atom B is supposed to contain one electron which is initially at rest, its subsequent displacement being denoted * Astrophys. Journal, vol. xxii. p. 217 (1905). \ Displacement of Spectral Lines produced by Pressure. 567 by ~. At the instant ¢=0 B is distant r, from A, after which it moves directly towards A with uniform velocity v until a time ¢, has elapsed when it is distant 7, from A. Let r be the coordinate of B at time ¢, and let the direction of & coincide with the line of motion ; then the electric force due to A acting on the electron at B at time ¢= pe so that the equation for yf is a 0! ia 7 where 2X is the coefficient which determines the natural period of yy (see equations 2 and 3). In this the Doppler effect is disregarded as being small, whilst the reaction of Bon A and the decay of £&) with time have been avoided artificially. r is evidently connected with ¢ by the relation TU ees tie 4! ACES) By changing the independent variable from ¢ to v the differ- ential equation (17) can readily be solved, leading to Ov 22& cospt eé a eb, OD / | TSS a Brotyn— (B+ y)r—sin Bro— yr — (B=) dy (19) mS) mv Jr 4 where C=—peand yeti, . . . . © (20) This is the particular integral only ; the complete solution contains in addition the terms C sin y(7,—71) + D cos y(7)—71). These terms represent vibrations of the frequency of the natural vibrations of the electron in the atom B due to the initial impulse and may be left out of account in the present case. The integral (19) may be evaluated by integration by parts. After two successive integrations of the denominator, the unintegrated part contains as a factor one of the integrals sIn u COS U du or ( du. U Uu e/ These can be obtained from tables, but as the object of this investigation is to find the relation between the solutions for the two cases when the atom B is moving and when it is fixed, it 1s more convenient to proceed by integrating the numerator and differentiating the denominator. Integrating 568 . Prof. O. W. Richardson on a Theory of the by parts n—2 times we obtain (aap || /™ x e&o n= Se 1 How ‘er + yi (SE — 5 a (8+ y)"r" ae U n+1 T=, COS Bro—yn —(B—Yy)r ata ory " N—2 yt PY=7o —y) +1 aia cos Bry tyn—(B+y)r+ 7 hr Carr ro 1 cos Bry yr1 — (By) r+ ce Jar p20 as X e&) PS" (n—1)! iL i IL ‘D n+l Ve ra (eq Gaps so 4 z eel Cos WAL aee (1) + le Tin Cty? Te N=3 2 Ton e me (n—1) (= yr ee ni (7 (608 Brotyn—(B+y)r+ come 2 ro ( (B+ ry)" 27241 cos Gryp—yr1 — (B—y)r ee eee ZT) ; 7: — r (8 ey ant ee (22) Confining our attention for the moment to the integrated part of ee — we see that all the terms which involve cos y(7 and therefore represent vibrations of the aoe of oe free vibrations of B, depend only on 7y the initial position of B. The disturbance represented by these terms will therefore rapidly disappear if there is any damping ; whilst even if they persisted their average effect in producing a displacement of the lines emitted by A would be zero on account of the difference in the period and the uncertainty of the phase. The only terms which are of \ Displacement of Spectral Lines produced by Pressure. 569 importance for the present investigation are therefore those aaa n+1 which involve cos B(7, —7,) + ie un The behaviour of series (22) is best illustrated by con- sidering a numerical example such as might occur in nature. The greatest discrepancy between the cases of the fixed and moving atoms will arise when the moving atom is displaced from a distance equal to the free path in a direct line until it is in contact with the fixed atom. The mean free path at the temperature of the arc and a pressure of 10 atmospheres will be about 10-°cm., so that 7»>=10_; cm. 7, is determined by the dimensions of the atom, and is, as we have seen, nearly equal to 3x10-8 cm. We shall take v=10° cms. per sec., which is very near the true value under the conditions described, and, as illustrative numbers, B=5x10! and y=6x10!0, The last two numbers correspond to vibrations of optical wave-length 3°77 x 10~° cm. and 3:14x10-° em. respectively. With these numbers the first series in (22) is equal to Be x 4-05 x 10ss[eos A(ry 11) +0091 sin B(r%>—M) m —'000122 cos B(79—71) — 00000205 sin Bir, —71) + .. .] It remains to consider the unintegrated part of (22). The dotted curve in fig. 2 is supposed to represent the graph of (At y) 9-72 +4 + ALIS Gil y=t+(Bty)?-"r-"-1, The integrand is evidently a sinuous curve bounded by the two dotted lines as shown in the figure. Since the areas below the axis of r are to be reckoned nega- tive, the value of the integral cannot be greater than the 570 Prof. O. W. Richardson on a Theory of the difference between the greatest and the least of the half- periodareas ; and since, in the example under discussion, the smallest area is negligible compared with the greatest, we may take the greatest of the half-period areas as an upper limit to the value of the integral. Proceeding in this way with the integral remaining after four successive integrations by parts, we find that the value of w must lie between b= ay r Boy 4-05 x 10[(1—-000122) cos B(rs—m) NL VU +°0091(1 —-000226) sin B(r, -—1) ] and he af rte x 4:05 x 102 (1 —-000122 4 8-1 x 10-8) cos By—1) +-0091(1—-000226 + 2-1 x 10-7) sin B(ry—7,)]. (23) It is clear that the only terms which are of any importance are retained if we write = oe £0 4.05 x 10”[ cos B(79—71) +0091 sin B(7%—13)]. mv The occurrence of a term containing sin 8(7)—7,) shows that the forced vibration is not in complete agreement with the forcing field, but the smallness of the coefficient of sin B(79>—71) shows that, in this particular instance, the difference of phase is so small as to be of no practical im- portance. In any case the displacement w will be capable of being represented with very close approximation by poon |» 2h us [(1+6) cosB(79>—r1) + € sin B(79—75)], m vr? B?—ry? where 6 and ¢ are constants. We have seen that 6 and e were small compared with unity in the typical example just considered. The only important cases where 6 and e will not remain small are when either 8 is nearly equal to y or the atom B experiences a number of collisions in rapid succession in close proximity to A. There are reasons for believing that these special cases give rise to the broadening of the lines rather than to displacement in any one direction. The point to insist on at present, is rather that these excep- tional cases will not be of such frequent occurrence as to seriously affect the unidirectional shift produced by the more normal case of forced vibrations either in phase with, or in opposite phase to, those of the emitting atom, according as the natural period of the one is greater or less than that of \ Displacement of Spectral Lines produced by Pressure. 571 the other. With these limitations, then, yr will be expressed with close approximation by ae rv 20ek oy pana [28 ee ee If we replace 8 by p/v, y by e/v,/Am=p' /v, and (75—71) by vt, this becomes ¥ 2e°Eq cos pt tf — = - ° mry p—p” This is identical with the solution for the case where the atom B remains fixed at a distance 7; from A. so that the calculated displacement will only be slightly in error on account of our having neglected to take into account the motion of the atoms. It is therefore necessary to seek some other explanation for the discrepancy between the calculated and observed effects. § 6. Causes tending to diminish the effect. In view of the disagreement between theory and experience, the suspicion naturally arises that the view of the structure of the atom which we have used asa working hypothesis is at fault somewhere. We have taken as a fundamental assump- tion that the emitting system can be represented by the linear vibration of an electron. There appear to be at least two reasons why this assumption leads to too big a calculated effect, both of which depend on the probability of an atom having a more complex structure than that we have assumed, In the first place it is possible that the emission of spectral lines is due to perturbations in the motion of electrons rotating in closed orbits within or about the atom. I spectral lines do originate in this way, it is clear that the effect here investigated will be diminished by the variation of phase intro- duced by the rotation. But since this explanation of the origin of spectral lines is a very special and uncertain hypo- thesis which has not hitherto met with much success in explaining the facts, it scarcely seems necessary to pay much attention to it. This position is strengtheued by the fact that the hypothesis of linear oscillators gives a satisfactory account of dispersion phenomena on lines similar to those which have been followed in this paper. It is, however, worthy of remark that when this type of dispersion theory is used to caleulate the number of electrons present in different sub- stances, the values obtained are lower than we should have expected on other grounds, a discrepancy which is in the 572 Prof. O. W. Richardson on a Theory of the same direction as that in the present investigation. This dis- agreement is usually attributed to the existence of undiscovered absorption-bands in the ultraviolet, although, as will be shown below, it is questionable whether any such hypothesis is necessary. The second reason for the discrepancy is one which must be universally operative, and arises from our having neglected the effects of the other electrons in the atom. The preceding theory would be exact. on the supposition that the electrical properties of each atom were due to a single doublet placed at its centre. We have reasons for believing that each atom contains a considerable number of electrons, and consequently of possible doublets. According to J. J. Thomson’s most recent estimate, this number is proportional to the atomic weight of the atom and is of the same order of magnitude. It is thus necessary to take into consideration the way in which the behaviour of any given electron under assigned conditions is affected by the presence of the other electrons in the atom. In developing our theory, we have supposed that a doublet inside an atom A produced the same field of force in the neighbourhood of a distant atom B as if the doublet were immersed in free ether. That this will not in general be the case is seen at once by considering the extreme case where the number of additional doublets in A is indefinitely great. In this case, the atom will behave like a sphere of specific Xs : : inductive capacity c=1 se , where a is the radius of the atom and the summation is extended over all the doublets in it ; so that the electric field due to a doublet at the centre of A will give rise to an external field which is everywhere smaller than the value used on p. 560 in the ratio 3/ck-+2. One way of looking at the question is to regard the other electrons in A as disposing themselves in such a way as to shield external points from the field of the doublet. On account of the finite number of the electrons and their definite geometric arrangement, the above method of looking at the question is only a crude approximation, but it is evident that in any given case the field near B due to the sth doublet in A will be cut down in a certain ratio y, depending on the orientation of the doublet in the atom A. The doublet induced in B wiil also be reduced in a similar manner, since the electric field at a point inside B will be smaller than that outside. It will not, however, be necessary to correct for this, as it can be shown that it nas really been allowed for in the dispersion theory on which formula (10) is based. It may be worth while briefly indicaling the way \ Displacement of Spectral Lines produced by Pressure. 543 in which this point of view affects the ordinary electron theory of dispersion, as given for instance by Drude”. The equation of motion of the sth electron is (ola AOC e UX. 0&; where the term te has been retained for completeness to Bee en Oe. | HO) Ms include cases of absorption. The notation is that previously employed, and is equivalent to that in general usage except that X, is usually put equal to the electric force X outside the atom (see Drude, loc. cit.). Now X, is obviously the electric force at the electron, and in accordance with what has been said will in general be less than X. We may write it X;=y1.X. Proceeding to evaluate the refractive index in the usual way it is found that a factor of type y, multiplies all the terms in the polarization current, and we obtain the refractive index mw and the absorption coefficient « from the equations AsMs 5 Yish ae p2(1 —2”) =14+ 40> aS aes 5 (25) (1 — ) +2r8re p” and G Ns ts ) 2y-2=ArVy> 2 af : (26) AD Says NG aA Ber (1 oo ) As fp € / Here v) is the number of atoms per c.c., the summation extends over each atom, and p is the frequency of the trans- mitted vibrations. If there is no absorption 7;=7,=7,=0, and D Yisrs O77 w=1+4ryH>——, —. SHEN Lic. 7% (27) 1—p?/ps” 9 ree “—J Inspection of this result shows that © Z measures the . TV sum of the moments of the doublets induced in the atom B by a unit force outside. Since the potential at A is deter- mined by the algebraic sum of the moments of the doublets induced in B, no error has been introduced by omission of the yy; factors as far as the atom B is concerned. The procedure outlined would enable us to calculate the * Lehrbuch der Optik, p. 353. Phil. Mag. 8. 6. Vol. 14. No. 83. Nov. 1907, 2Q 574 Prof. Q. W. Richardson on.a Theory of the force outside the atom A due to the doublets in B. By con- siderations similar to those already brought forward, ie force at the sth electron in A will be less than thisi in some ratio y's. Hor the case ot the dielectric sphere y=y'=3/n+2, but there is no reason why this equality should subsist in general. A repetition of the method of calculation of § 3, to the accuracy of the first term in expr ession (s). shows that it is necessary to multiply L, by ysy;’. For this to be the correct explanation of the discrepancy between the calculated and observed values, it is necessary that the average value of ysys’ should be of the order of 1/10 or 1/80 according to which of the values of « on p. 566 we take to be the more reasonable. This would require the specific inductive capacity of the atom to be of order either 7 or 25, the average values of y being 1/3 or 1/9. The experimental results on dispersion do not appear to contradict the possibility of values of y in the neighbourhood of either of the above numbers. It is evident that the coefficient y will depend on the structure of the atom and the orientation of the vibrating electron in it. On this account the pressure-shift for different elements might reasonably be expected to be a periodic function of the atomic weight [as the valency relations require atomic structure in general to be such a function | and also to possess different values for different series of lines of the same element. It will be noticed that a similar periodicity might be expected to arise if the discrepancy were due to the orbital motions of the electrons previously considered. Relations of this kind have been discovered experimentally”, but our present knowledge of atomic structure is too slight to be used to test this hypothesis. It is idle therefore to pursue this part of the subject further, but it is hoped that what has been said is sufficient to show that interference by other electrons is in all probability at least a partial cause of the smallness of the observed shift compared with that calcu- lated on the simpler theory. § 7. An Alternative Theory. A different theory of the pressure shift of spectral lines has been given by Humphreyst, who supposes that the effect is caused by the mutual magnetic perturbations of the atoms. On this view the pressure shift is allied to the Zeeman effect. The following considerations appear to show that the effects * Humphreys, Astrophys. ales ue vi. p. 169 (1897). t Astrophys. Journ. vol. xxiii. p, 2 \ Misplacement of Spectral Lines produced by Pressure. 575 which could arise in this way are much too small to account for the observed facts. Suppose the magnetic fields of the atoms are caused by the motion of some or all of the constituent electrons in closed orbits, which we may take as an approximation to be circular. Although this hypothesis has been criticised by notable authorities, it appears to the writer to have the balance of probabilityin its favour. Ifn is the number of mobile electrons in the atom, o, the radius of the orbit of the sth electron, and T, the time in which it is described, the atom will be equivalent to a magnet of moment A=7-2 o,’/T, electromagnetic units. . . (28) 1 Here e is the charge on an electron in electrostatic units, and ¢ is the velocity of light. This is the maximum value obtained on the supposition that the orbits are all parallel to one another and the rotations all in the same sense. On this view, the maximum intensity of magnetization which an element is capable of is determined by the atomic amperean currents. We shall assume that the magnetic field of any atom is not greater than that which corresponds to saturated iron, us iron is the most intensely magnetic substance of which we have experience. This conclusion is supported by the high value which the magnetic properties of iron indicate. for the number of rotating electrons in the atom. The maximum intensity of magnetization I of soft iron is about 3 x 10* and I=vA, where v is the number of atoms of iron inlec.c. Hliminating A between this equation and equation (28) we can get an estimate for n. Putting i , is now Vibration of Bars treated simply. dd1 given by M=/,e+ f,(7—2-), and is thus dependent on «2, the place of application of the second force. But, as seen from Fig. 2 ¥, - S = 2 7 oe Ss ] re M Q 6) oe x. LYSTANCE ALONG BAP the equation, or the graph as shown in fig. 3, the rate of increase of M is independent of x2, and depends only on the sum of the torces. Fig. 3. = ~< BENO/NG MOMENT LYSTANCE ALONG BAR Thus, for values of « exceeding x2, we have dM/de=j7, +/,, Or, if the angle of the final part of the graph is > with the horizontal, then tan d2.=f, +/>. Hence for any number of isolated forces applied along the eo bar between the origin and x, we have dM /de=fart fos... F, say. . .. , (2) In other words, if the magnitudes of the forces are specified, the space rate of increase of M, the bending moment at any 582 Prof, E. H. Barton on the Lateral point beyond them, is determinate and equals their sum although the actual value of M is unknown unless the positions of all the forces are given also. It is obvious that this sum F of all the forces applied between the free end at the origin and the point «, is also the shearing force on the bar at «. Now suppose forces to be continuously applied between the origin, and w and beyond w also. Then the broken straight- line oraph gives place to a continuous curve, and F becomes the integral of the forces acting between the origin and w. But we still have dM/dz=F; and, since F is now itself a continuous function of w, we may differentiate it and so obtain EM/da®=dF /de=f, say. . . . . (3) Further, this rate of increase of F (per unit length of 2) denoted by f, 1s obviously the value per unit length at 2 of the impressed forces to whose sum that shearing force F is due. Hence, though the bending moment itself depends upon the magnitudes and positions of forces acting elsewhere, and the first derivative of the bending moment at any point equals the sum of all the forces acting up to that point, the second derivative of the bending moment at any point equals the applied force per unit length acting there, and is inde- pendent of all other considerations. This is the relation sought, for the equation of motion is a relation between displacement and acceleration, and the latter is proportional to the force on the element. Thus we need to express the force in terms of the displacement, and by means of the bending moment, this is now possible. Differential Equation of Motion —We have hitherto dealt with a bar at rest and bent by certain impressed forces and the clamp or other arrangement at the opposite end. Hence the element of unit length at « was in equilibrium owing to the ~ applied force f and the difference of the shearing forces at its extremities, which must accordingly have had a re- sultant —7. Now let all the impressed forces be suddenly removed, then at «there must be an acceleration proportional to the remaining force —f. We may thus write wpd'y/di=—f,. . 2) et) where p is the density of the material. Then equations (1), (3), and (4) give dy Ke d‘y ~ Tams OF Fea = 08 i re (5) where b=4/q/p is the speed of longitudinal waves in the bar, Vibration of Bars treated simply. 583 This equation is identical with that obtained by Lord Rayleigh after discarding from the complete equation the terms expressing the rotatory inertia. Thus, inspecting (5) and glancing back over the considerations which led to it, we see that the argument may be expressed briefly as follows. The acceleration of an element of the bar is proportional to the first derivative of the shearing force or the second of the bending moment with respect toz. But the bending moment is itself the second derivative of the displacement with respect to «. Hence the second derivative of the displacement with respect to time is proportional to its fourth derivative with respect to w. Thus equation (5) expressing this relation with the proper coefficients must be satisfied at every point of the bar and at every instant of time. But we need in addition other equations for the ends of the bar which depend on the special conditions there obtaining. Terminal Conditions —The ends may be fixed (2. e. clamped), free, or “supported.” Ata fixed end it is clear that we have, for all values of ¢, displacement and slope each zero. Ata free end, on the other hand, these quantities are arbitrary. But, as there is nothing beyond to produce a couple or transmit force, there can be at the end neither bending moment nor shearing force. By a “ supported” end is to be understood an end at which no displacement is allowed but any slope may be assumed. Thus the only external force added by the constraint is applied at the end, and conse- quently can have no moment there. Accordingly there is no curvature possible. Hence for the three conditions we have the following scheme of equations, shown in Table I. TABLE [.—Terminal Conditions. | Quantities equated to Zero. | State of End. |- | Sidhe ; | Nos. of To dy/dx. | dy/dx. | dy/dx’°. Haunts a WMixed.. . a): | =0 | =0 PAN Nia cieies WM eG) MN Reer tac. ' =0 | =0 (7) | | | im fc ; | "ie . opaeey eres Tea Ts tae Supporteds.. |) —0 Ra: Se (8) | | 584 Prof. EH. H. Barton on the Lateral Since each end of the bar may be of any one of these three types, we have six cases in all. These may be classed as follows :— I, Both ends fixed. IT. Both ends free. III. Both ends supported. IV. One end fixed and one free. V. One end free and one supported. VI. One end supported and one fixed. Thus for any specified bar we have to satisfy (5) for every point and one of the pairs (6) to (8) for one end 2=0, and the same or another pair for the end w=. Solution of Equations —W e now assume, with Lord Rayleigh, that the motion is harmonic. Thus may be written Kl y=ucos( Tmt), . - gy ee elena where / is the length of the bar and m is an abstract number depending on the order of the tone. The substitution of (9) in (5) gives Gi Is aa Suppose u=e is a solution of this. Then, on differ- entiating, we find p’=1, i.e. p= +4/—lor +1. Thus u can be represented as the sum of four terms each involving one of the values of p and an arbitrary coefficient. Hence, after a little transformation, we may write u=A cos mex/l+B sin ma/]+ Cem/?+ De~™/, . (11) This, put in (9), is a solution of (5), and deserves a little notice previous to fitting it to (6)-(8). The simplest case is when the motion is strictly periodic with respect to 2 when C and D vanish. Then, if wave-length, period, and frequency are denoted by 2X, 7, and N respectively, we see that dx ping /l 2T/ N= m/l, or AN=Zarl/ms.. 21). es 2er/r=Kbne2/P, ..or 2a0[cbm?=r2/2mKb,, .. (1B) and ~ Kom . & a ae Sn a / gip. «ss ele = OTe dap ile : Oe We thus have the known relations that :— | (1) Wave-length varies directly as length of the bar and inversely asm. . : (2) The frequency of any given tone in the series of Vibration of Bars treated simply. 585 possible values varies directly as the radius of gyration of cross-section, directly as the square root of Young’s modulus, inversely as the square of the length of the bar, and inversely as the square root of the density. (3) The frequencies of the various tones in the series for a given bar and given terminal conditions vary directly as the square of m. Satisfaction of Terminal Conditions.—Reverting now to equations (6), (7), and (8), if the rod extends from #=0 to x=l, we see that they afford us four equations, two for each end of the rod. To complete the solution, the constants in (11) must satisfy these four equations. We may thus obtain the three ratios A: B: C: D, and have left an equation which must be satisfied by m. And for each value of m so found the corresponding wu is determined in everything save a constant multiplier which must be fixed by the initial state, into which matter we need not further enter. Free-Free Bar.—Beginning the detailed treatment of the bars with one free at each end, let us rewrite equation (11) in the form u=P(cosz'+cosh 2’) + Q(cos x’ —cosh a’) +R(sin #+sinh w')+S(sine’—sinhe’), . (15) where w' denotes mz/l. As Lord Rayleigh points out, this form is advantageous because the four quantities in brackets repeat themselves on differentiation, and vanish with zw’ except the sum of cos and cosh, which equals 2 for «’=0. Thus, for the free end at the origin, we must apply (7) to (15) by differentiating the latter twice to 2, put e=0 and equate the result to zero. Then, for the second part of (7), differentiate (15) thrice to #, put e=0 and equate to zero. These operations give Oa sON arid Fa) ie n="), , 02) te aoy We have now to follow the same method for the other end, where e=/, but can omit to begin with the terms involving Q and 8, which are already known to be zero. Phen we have w= P(cos 2’ + cosh 2')+ R(sin 2’+sinhe’).. . (17) Differ entiatin o@ this twice and thrice r espectively and putting v=l, i. e., =m and equating to zero, we find hae m+ cosh m) +R(—sin m+sinh m)=0, and 2688) P(sin m+sinh m) + R(—cos m+cosh m)=0, These two equations give two expressions for the ratio P: R, I 586 Prof. E. H. Barton on the Lateral and enable us by equating them to find m. Thus, omitting a constant multiplier, we may write, from the second form of (18), u=(cos m—cosh m) (cos 2’ + cosh 2’) + (sin m+sinh m)(sinw’+sinhez’), . . (19) or a corresponding and equivalent expression from the first form of the equation. Series of Tones.—We further derive from the two equations (18) the following relation cos m cosh m=1, or «eh Bye @eenon sec m=cosh m. This may be solved by the aid of tables of hyperbolic cosines, or by a method of expansions and successive approxi- mations as adopted by Lord Rayleigh. Ihe ney also be solved graphically, as shown in the upper part Ober Ei Xen): the method being as follows. Take the second form of equation (20) and plot the graphs y=sec & and y=coshz. Then the values of # at their intersections will give the roots of m sought. It will be seen from the upper half of the figure that, apart from the first value which is zero, the series appr oximates to 3, 5, 7... times 7/2, the approximation becoming closer as we proceed to the higher values. Now the frequencies, as seen from equation (9), are proportional to m’; hence for the higher values they approximate to the squares of the odd numbers. But, since the lowest frequency or prime tone departs distinetly from this simple approximation, the entire series of tones, when expressed as to their relation to the prime, seems disturbed and complicated. Hence the ad-_ vantage of the graphical view of the matter which exhibits the essential simplicity of the whole. The lower part of the diagram (fig. 4) refers to another equation for the fixed-free bar to be dealt with presently. Table II. gives the values of m and the relation of the series of tones for a free-free bar, and, as will be shown later, these apply also to a fixed-fixed bar. The first column of Table II. is from Rayleigh’s values, obtained by computation. The second column follows at once, while the third is derived by logarithmic methods and the fourth expresses the same results in musical notation, the accents representing higher octaves, but the letters do not denote any absolute pitch but are relative only. Vibration of Bars treated simply. TABLE IJ.—Tones for Free-Free or for Fixed-Fixed Bar. D837 Relative Intervals from x ; Values of iz. Frequencies, Prime to each UD a N/N, xm?. Higher Tone. ONES 7i)=O0 | Octaves. Equal | Semitones. FU AAGS, oan. s0as a Pe, oe Oe eee C ee LN. 2756 1 and 5:52 Bg al Miz—AO-996, -..... 5-404 | 2 and 5°23 W | m,=14137 ...... 8933 | Band 191 pie “| m,=17 21 (cs ae ee 13°345 | o and 8 8G Au | | From equation (14) and Table IT., first column, we can obtain the actual frequency of any tone for a given bar. Thus, let the prime tone be required for a free-free bar of steel of rectangular section and of thickness a cm. and length / cm., then k=al,/12, //q/p=b=523,700 em./sec., whence N,=538,400 (a/l*) per second. So if a=1 cm. and /=100 cm., we have N,=53°84 per second. Multiplying this value by the relative frequencies in column 2 of Table IJ., we have the absolute values of the frequencies of the other tones for the same bar. Fixed-Fixed Bar.—On applying the proper conditions, equation (6) in Table I. for a bar fixed at each end, it will be found that the same series of tones is obtained as for one free at each end. Nodes for Free-Free Bar by Theory and Experiment.— By inserting any one value of m in equation (19), the dis- placement curve at any instant may be obtained for that type of vibration. Hence, also, the nodes or points of no displace- ment can be found. The theoretical positions for a thin bar as thus determined by Lord Rayleigh are shown in Table III. in comparison with the actual positions found by the writer's experiments ona steel bar 29 inches long, 14 inch wide, and 4,an inch thick. The actual and theoretical frequencies are also given as a further illustration of how slightly a bar of sensible thickness departs from the behaviour theoretically 288 Prof. E. H. Barton on the Lateral expected on the basis of rotatory inertia being negligible owing to extreme thinness. The bar was supplied by Mr. Joseph Goold of Nottingham, and was excited by Mr. Goold’s synchronized generators. These consist of rods of cane in a massive metal handle, and are adjustable in length to suit the frequency of the tone to be elicited. The bar rests on rubber pads at one pair of nodes. the generator is passed lightly along it between two con- secutive nodes and, when rightly adjusted and handled, the required tone is then powerfully brought forth. The exact positions of the nodes for each tone were indicated by chalk or (preferably) carbonate of magnesia. TasLe ITT.—Actual Free-Free Bar compared with Theory. Frequencies. No. of Distance of Nodes from ene end as fractions of Tone. | | entire length. Absolute. | Relative. (Theoretical Values in brackets.) | per second.| | ali oe 126 1 0-2236, 0-777. | (126-03) | (2249 OL acaneees 350 27777 | 0:134, 504, 8698. | (2756) | (182 (5) | otra ae 686 54444 | 0:095, 359, ‘6506, -909. | (5404) | (0944) (3558) Ie htspltint 1134 90000 | 00759, -2812, 5067, 727, 9282. (8933) | 0734), (C277) (5) Sanat 1696 13-4603 |. :068, +2817, 415, —“59G. suaresenot, (13-345) | (0601) (2265) (-409) | Ggahalte 2366 187777 | 005285, +1951, -351, -505, “658, 812, -950 (0509) (192) (346) (°5) stele 3150 | 25-0000 | 0-046, -168, -306, -4376, -575, ‘706, 837, 956. | | (044) (166) (300) (48) Fixed-Free Bar.—lLet the var be fixed at e=0 and free at w=l. Then we have to determine the constants in equation (15) consistently with (6) in Table I. for e=0 and with (7) for «=. Vibration of Bars treated simply. — 589 Proceeding as before we find P=0 and R=0, and that Q(cosm+coshm) +S(sin m+sinh m)=0 Q(—sin m+sinh m)+S(cos m+ cosh m) =0 From the second of these, omitting a constant multiplier, we find u=(cos m+cosh m)(cos 2’ —cosh 2’) + (sin m—sinh m)(sin 2’—sinhz’). . (22) Further, by equating the two expressions for = aie from (21) we derive an equation to determine m, viz. cos m cosh m+1 29 or J RE sec m= —cosh m, The second of these forms is convenient for the graphical exhibition of the relations of the roots as shown in the lower part of fig. 4. From this it is seen that the higher values of m which satisfy (23) are approximately as the odd values of 7/2, the approximation being very roughly fulfilled for even the second value and showing a serious departure at the first value alone. The frequencies of the possible tones are as the squares of these values form. But as regards the relative frequencies of the overtones to the prime, this de- parture of the first note is vital, and in a statement of these relative frequencies quite obscures the simple relation sub- sisting among the higher overtones which is so clearly seen from the diagram (lower part of fig. 4). The tones fora fixed-free bar are shown in column 2 of Table IV.; these TasLe [V.—Tones for Fixed-Free Bar. ea a “Values of c= Prequendies| pdotervale from | Anprosiuat | Copies | Octaves. Equal AOL Ee tes m,= 187d 1 Semitones.| C Cet ee eazy, | 2 end 777 | | Gy WBA.» bass ea irsoa oui s fala. and 160° |, ., ADa | LICE S 6 Nenkeapis m= 10-996 34:39 | no gand "1-24 DY BSF, nd ook | eats sh 56:85 | 5 and: 9:95 Bh | fe ae | img=17-279 | 84-93 | 6 and 490 mi | Phil. Mag. S. 6. Vol. 14. No. 83. Nov. 1907. ke 590 Lateral Vibration of Bars treated simply. values are taken from Lord Rayleigh’s calculations, but are here given to three places of decimals only. The first column shows the odd values of q/2 for comparison sake. The other columns have been calculated as for the free-free bar in Table II. Nodes for Pixed-Free Bar. 2 positions of the nodes for a fixed-free bar may be found analytically as for the case already cited, and have been calculated by Seebeck and by Donkin. For the early overtones these are as follows :— Second tone, 0:2261 of length from free end. Third tone, 0:1321 and 0°4999 do. do. Fourth tone, 00944, 0°3558, and 0°6439 — do. do. A near approach to a fixed-free bar is made in the behaviour of one prong of a tuning-fork. On fixing the fork with its prongs horizontally one over the other, touching in the neigh- bourhood of the nodes and bowing the end Tor the prong, the higher tones may be elicited and the nodes observed by chalk or other powder. Operating in this way on a large fork of 128 per second, whose length to the inside of the hollow was 1042 Favela! the following observations were made. The second tone (or first overtone) showed a node at 2% inches; or, taking the length of the prong to be 11 inches to the fixed part, 0-216 of its length. This com- pares well with the theoretical value 0:2261. On placing two fingers in the right positions as found by trial and bowing suitably, the third tone was elicited. This showed nodes at 1°5 and 5:5 inches from the freeend. Taking the fractions of the length 11 inches, these give respectively “0136 and 0°5, which again are close to the theoretical! values of 0°1321 and 0°4999. Remaining Cases of Vibrating Bars—A bar vibrating with one end free and the other supported is like half of a free-free bar when vibrating with «a node in the middle. Again, the vibrations of a bar fixed at one end and supported at the other are like those of one half of a rod with both ends fixed and vibrating with a central node. There is now but one case left, namely, that of a bar with both ends supported. Referring to. equation cy and the conditions (8), we find that for c=0, P=OandQ=0. Again, for the end Woh 1, €.,a’=m, we have R—S=0 and sin m=O, iy Os, Ou where n is any integer. Thus equation (15) becomes reduced to a single term involving sina’. We may therefore write, for the bar supported at each end, by eq. (9), ooee y= Kein“ cos (“ ite), a a) l h \ Method of determining Surface-Tension.of Liquids. 591 where K ande are arbitrary constants to be chosen to satisfy the initial conditions. Thus the segments of the bar are like those of a string fixed at the ends. The frequencies of the possible tones are, however, quite different. For, in this case of the bar the frequencies are proportional to n? instead of to n simply as fora string. Thus the frequency of the nth tone is given by ty Nes NE nn University College, Nottingham. May 30, 1907. LVI. The Curvature Method of determining the Surface- Tension of Liquids. By C. V. Raman, M.A.* | | {Plate XV.1 - ee KELVIN, in his lecture on Capillarity (published in his ‘Popular Lectures and Addresses’), describes this method as a practicable one for measuring the surface- tension of liquids. In the following account is described an arrangement by which this method is rendered a convenient and fairly accurate one, and the results of a series of deter- minations made by the method are tabulated. = | FREE SURFACE (OF LIQUID i. ee EUS OF 47 ~The Theory of the Method. Let ADB be the principal section of a drop hanging down from a tube, and p the radius of curvature of ADB at the * Communicated by the Author. 2R2 592 - Mr. C. V. Raman on the Curvature Method point D. If T is the surface-tension, then 2 Daca —=go.CD, p Tae, o being the density of the liquid, since CD is the head at the point D. This is true, provided that the surface of the drop is one of revolution about (CD. p can be determined by measuring the coordinates # and y, of points on the curve ADB. In practice, it is quite sufficient to make the measurements of « and y close to vs vertex for two or more values of 2. The value of the ratio 2 5 at different points close to the vertex varies only very slightly, and any variation shown can be corrected for, by calculating the value of the ratio for the point e=0 from the observed values of the ratio. ‘The reason why the ratio ot varies very little can easily be seen. As we go up Age the surface from the vertex D the head diminishes, and therefore also the sum of the principal curvatures. The section of the surface is therefore nearer being a parabola than a circle, for the sum of the principal curvatures of a paraboloid of revolution dimi- nishes as we recede from the vertex. The measurements of w and y were not made on the drop, but, adopting a more accurate and con- venient method, on a photograph of the surface. The apparatus de- signed for the purpose is shown in fig. Ze A tube 2 cms. diameter is con- nected up with a tube 6 mms. dia- meter by caoutchoue tubing. The arrangement shown in the figure is filled up with the liquid. “The small tube can easily be adjusted so that the liquid bulges out of both tubes, the concavity being in opposite directions in the two. A plumb-line Fig. 2. \ of determining the Surface-Tension of Liquids. 593. hanging between the two gives the direction of the vertical., The apparatus is then photographed in the following manner :— | A horizontal beam of parallel light is produced by an electric spark placed at the focus of an achromatic lens of long focal length (about 1°5 metres), and is thrown on the apparatus. The shadow cast by the tubes is then photo- graphed on a plate held vertically as near to them as possible. The negative is then measured under asliding microscope. It is coupled, film to film, with a “ réseau” plate on which is ruled a set of squares (side = 0°5027 cm.), and placed on an inclined—plane so that it has freedom of up and down move- ment. The microscope, which is capable of motion sideways, has two scales at right angles to each other in its focal plane. The glass plate on which these scales are ruled can be moved in the focal plane by a micrometer-screw. The réseau plate is first adjusted so that the rulings on it are parailel and perpendicular to the shadow of the plumb-line on the plate. By rotating the eyepiece and the photographic plate on the stage, the scales in the focal plane are adjusted parallel to the rules on the réseau plate and to the lines of travel of the microscope and the photographic plate. The objective of the microscope (which is a small one) produces very little magnification, but the eyepiece is a fairly powerful one. The scales in the focal plane (1 division =), mm.) serve only as auxiliaries, for the readings made on them can easily be expressed in terms of the side of the squares on the réseau plate, the absolute value of which is known. The w and y coordinates of any point on the meniscus can thus be measured and reduced to centimetres. What was directly read off was not the y coordinate but 2y. From these measurements the radius of curvature at the vertex of the curve can be deduced in the manner mentioned y above. If the variation of a V4 is not negligible, then a is written equal to ay? a by", since the curve is symmetrical about the axis of # From the observational equations } a“ = ay + by, Ke., two normal equations for the constants a and b can be 594 Mr. C. V. Raman on the Curvature Method deduced and a determined ; and iL oe - Further, by means of the ruling on the réseau plate, the difference of level between the vertices of the two curves can be measured. This gives the pressure corresponding to the observed curvature. In practice, it was found that the curvature of the larger meniscus could not altogether be neglected. It amounted to from 2 to 4 per cent. of the curvature of the smaller. This could be measured and allowed for. IE _ is the I : curvature of the smaller and R that of the larger meniscus, then a eee | om (+ _ we 2a ls a Gert. h being the difference of level between the vertices. The liquid used in the experiments was clean distilled water. Precautions were taken that in transferring the liquid into the apparatus no contamination occurred. That the surface whose tension was measured was free from greasy contamination was ensured by allowing the water to run down from the small tube for some time. The surface of the drop that was finally left hanging was, therefore, an absolutely fresh one, and any oily film originally on the surface would have been reduced in thickness to a very great extent. The parallelism of the beam used to photograph the drop was tested by a telescope adjusted for infinity. To have the photograph as sharp as possible, the plate was held only ‘3 ems. behind the apparatus. It was found that it was necessary to adjust the wide tube so that it might be approxi- mately vertical. If not, there was reason to think that the two principal curvatures at the highest point of the large meniscus would not be equal. This was really the weakest point in the whole work. The writer hopes to repeat the work with a tube so wide that the curvature of the meniscus above it can entirely be neglected. As an illustration of the method, I give a table of the measurements made on one of the plates (see PI. XV.). \ of determining the Surface-Tension of Liguids. 595 Difference of level between the vertices = 44-37 divisions of the microscope scale ; = 0°2826 cm. | Difference 5) ae of level. ve m> &e. ., since the atomic lonizations increase less rapidly with the atomic weight than the values of M,; and M,. This means that the ionizing power of an electron from an atom in a gas composed of the same kind of atoms, decreases with increase of atomic weight of the atoms. This resultis very improbable: and it follows therefore that the values found for M, and M, probably do not represent the primary ionizations. This point will now be considered. If the secondary cathode rays from the various substances have not the same ionizing power in air, the values found for M, and M, will not represent exactly ‘the quantities M, and M, according to the definition. If the ionizing power of the secondary cathode rays increases with increase of atomic weight, this would have the tendency to give values. for M, and M, which increase too rapidly with the atomic weight. Now, although the ionizing power of the secondary cathode rays may vary to some extent with the nature of the substance by which they are emitted, it is very improbable that it varies to such an extent as to account for the above discrepancy. It is more likely that, besides the penetrating rays generated in a substance, more easily absorbable rays are generated which do not get free of the layer, and are therefore not taken into account in the measurements of secondary radiation. If this is the correct explanation it would follow, since the ionization in a gas does not increase so rapidly with increase of atomic weight as the values of M, and M,, that the amount of more easily absorbable radiation produced decreases with increase of atomic weight. Rays emitted by Substances exposed to y Rays. 633 We have seen that if the average velocity of ejection of an electron from a gaseous molecule ionized by 6 or y rays is the same, the ratio of the primary ionization in any particular gas ionized by 8 rays to the primary ionization when the gas is ionized by y rays is constant, and this constant is equal to unity if the primary ionization in any gas is expressed in terms of that in air at the same pressure. If the average velocity of ejection of an electron from a molecule in a substance ionized by @ or ¥ rays is the same, the ratio of the values found for the quantities M, and M, for any particular substance gives, whatever these values may represent, the correct ratio of the quantities M, and M, according to the definition. For, since the radiation from a substance is measured by the ionization it produces in air, and the ionizing power of the radiation is the same for both ionizing agents, the ratio of the number of electrons radiated from the sub- stance to the ionization they produce, is the same with both lonizing agents for any particular substance, and the ratio of the quantities M, and M, therefore in this case independent of the ionizing power of the electrons. Also, the number of electrons that do not get free from the layer of the substance must be in both cases approximately the same fraction of the number of electrons that do get free from the substance, and therefore the ratio of M, and M, for any particular substance also independent of the absorbable radiation pro- duced. Now, the ratios of the values found for M, and M, are approximately equal to unity ; and we therefore conclude that the average velocity of the electrons from molecules ionized by 8 or y rays is approximately the same, and is not influenced by the state of aggregation of the molecules. Tt will be useful to collect the formule expressing the relation between the various quantities involved in the secondary radiation froma layer of a substance exposed to B or ¥ rays. McClelland has shown that the relative value p of the radiation from a layer of a substance exposed to the @ rays of radium is given by bol & It has been shown in this paper that the relative value R, of the radiation with y rays is given by Ky l1—«+ Af ~ w(1—«) en 634 Mr. R. D. Kleeman on the Secondary Cathode The relative amount of radiation emitted per second per c.c. of a substance when exposed to the y rays is independent of pw and «, and therefore given by K, simply. ‘The radiation emitted per ¢.c. when the substance is exposed to the 8 rays is given by Kg=yuxe. The number of electrons ejected per atom is given by — Rywl—«)(2—«£+2 V1 -«) Qe atet= // Si) : iy WLK . in the case of y rays, and by M,=—— in the ease of 8 rays. The ratio of M, to M, is given by My lilo) A= ee 2 V1—«) M, Ki—e+,/1—1«) an equation which does not contain p. M, It remains to describe the method by means of which the radiating power of aluminium was determined corresponding to a difference of 800 ia the radiating powers of lead and aluminium. The adjustable table was removed and also the wire gauze from the bottom of the aluminium chamber. The lead and aluminium plates used as radiators were each of the same dimensions as the plate c. The radiating plate was kept in contact with the edges of the opening of the aluminium box. Fig. 3 shows the modified part of the apparatus. to. <2 Fig, 3. Leaks were taken with the aluminium and the lead plate, and a sheet of thin tissue-paper, used successively as radiators, the tissue-paper being stretched tightly over a metal frame enclosing an area somewhat greater than that enclosed by the edges of the aluminium box. All objects near the opening of the aluminium box were removed, in order to reduce to a minimum (when the tissue-paper was used as radiator), the amount of ionization caused by the secondary radiation from surrounding objects penetrating the tissue-paper and \ Rays enutted by Substances exposed to y Rays. 635 entering the chamber. In this manner the value 330 was obtained for (Al-tissue paper), corresponding to the value 800 for (Pb-Al). The radiation from the tissue-paper must be small in comparison with that from the aluminium plate, and therefore the radiation from aluminium is approximately equal to 330, when the difference in radiation between lead and aluminium is put equal to 800. But some of the radiation from the air and surrounding objects penetrates the tissue-paper and enters the chamber, and therefore the true value for the radiating power of aluminium is larger than the above value. Since the secondary cathode rays possess considerable penetrating power (their velocity being about half that of light), some of the rays that penetrate the tissue-paper have passed over a considerable distance in air, and the amount of radiation received from neighbouring objects is therefore probably of such a magnitude that the ionization produced cannot be neglected. The value obtained for the radiating power of aluminium is therefore only approximate, it may be said to be an inferior limit of the radiating power. Hive has determined the secondary radiation from a number of substances when exposed to y rays. The values that he obtained are given in Table IV. The y rays were passed through a lead screen 6°3 mm. thick. Since the ionizing power of the secondary y rays is small in com- parison with the secondary cathode radiation, the values express the amounts of secondary cathode radiation from the given substances. TABLE LV. Radiator. Secondary Radiation. Wea ias Sie a2 100 Copper s.an ks. 61 BASS o ek deus s Sues < 59 Aluminium ...... 30 (CHIC ire tat ES aS om 30 Parantime sce tre) 4). 20 The relative values that he obtained for the metals copper, lead, and aluminium, agree with those of the writer as well 636 Mr. R. D. Kleeman on the Secondary Cathode as can be expected, when it is remembered that the amount of secondary radiation from a substance depends on the nature of the screen placed in the path of the y rays (see next section), and that the relative values of the radiating powers are liable to greater uncertainty than the relative differences. § Il. Tt was found, as has already been mentioned, that the y rays from radium are heterogeneous, and that the different constituent rays give rise to different relative values for the secondary radiation of a set of substances. The constituent rays are selectively absorbed, and a partial separation of different sets of rays from the original bundle could therefore be effected by means of metal screens. © Some slight alterations were made in the apparatus to make it more suitable for the investigation of this pheno- menon. The gauze was removed, and the plate c and the dishes a and } were discarded. The substances which were used as secondary radiators were in the form of plates equal in dimensions to the plate c. The plate under investigation and the plate with which it was compared were placed one on top of the other on the table d, which was then raised by means of the screw e till the top plate or radiator made con- tact with the edges of the aluminium box forming one of its sides (see fig. 38, § L.). The difference in the amount of secondary radiation from a substance and a_ standard substance was, as in the foregoing experiments, compared with that of two standard substances. The above modification of the apparatus increased its sensiliveness, by reason of the larger radiating surface employed, but it restricted the number of substances that could be used as radiators. The substances used as radiators were: carbon (black lead contained in a shallow dish), aluminium, sulphur (a plate of sulphur, the surface of which was made a conductor of electricity by covering it with a thin layer of black lead), iron, copper, nickel, zinc, tin, and lead. Screens of various substances were placed in the path of the y rays. A screen was placed at N, and the differences between the radiating powers of the above substances and aluminium determined, the radiation from the substances being produced by the y rays not absorbed by the screen. A screen of some other substance was then placed at N, and the process repeated, and soon. The screens used were of the following substances: iron, copper, zinc, tin, mercury Rays emitted by Substances exposed toy Rays. 637 lead, and bismuth. The mercury screen consisted of a little box of thin sheet zine filled with mercury, the inside surface of the box being covered with paraffin-wax to prevent the mercury coming into contact with the zinc. The dimensions of the box were: 4°8 cm. long, 1°3 cm. broad, and 5°5 cm. high. That the amount of secondary cathode radiation from a substance depends on the nature of the y rays to which it is exposed, can be conveniently demonstrated as follows :—The difference in the amount of radiation from iron and aluminium, and lead and aluminium, is determined with a screen of copper, and the former difference divided by the latter. A value of this ratio is then found, using a screen of lead. The whole process may be repeated several times and the means taken. Hach ratio can be obtained with ease correct to five per cent. In this way, using screens of copper and lead respectively, 1°8 and 2°4 cm. thick, the writer obtained the corresponding ratios 6°4 and 4:2. It will be well, before stating the principal experimental results obtained, to give some numbers from which an idea of the relative magnitude of the quantities measured, and the probable accuracy of the determinations, can be obtained. When a copper screen 1°8 cm. thick was used (see Table V.), and the radiating substance was aluminium, a leak of 1792 divisions in 40 seconds was obtained, and with lead as the radiating substance a leak of 1850 divisions in 10 seconds TasBie V. | Lead Bismuth | Juead Mereury | Tin Zine | Copper | Iron screen screen screen screen | screen | screen | screen | screen 2mm. 14cm. | Idem. | 14cm. | 13cm. | 20cm. | 18cm, | 2-5 em, thick. thick. thick. thick. thick. thick. thick. thick. Sei 195) 1 196, «| —1a5 | e3-| — 64 | — 62 | = 88 Shean [bet SGM ea? EE sat iteomeit. 98 || 16M hae ae Fe—Al...| 158 BOM | eck 188 160 127 125 122 Mi Ale. | 176 225 227 218 185 156 156 160 Ga Al. , 198 239 263 230 191 158 156 167 Yn—Al...| 216 271 272 270 229 189 185 202 Sn—Al...| 408 465 442 456 389 365 374 408 | Pb—Al...) 800. 800 809 800 800 800 800 800 | - Phil. Mag. 8. 6. Vol. 14. No. 83. Nov. 1907. 2U 638 Mr. R. D. Kleeman on the Secondary Cathode was obtained. The difference in the leaks is 5608 divisions in 40 seconds, which is a measure of the difference of the ionization produced by the secondary cathode rays from aluminium and lead. And since an observation could be repeated any desired number of times and the mean taken, a considerable accuracy could be reached in the determination of the difference in the amount of secondary radiation from any two substances. As a rule, about 64 observations were made in determining the difference in the radiating powers of a given substance and aluminium, in comparison with that of the two standard substances lead and aluminium. The principal results obtained in these experiments are given in Table V. The nature and thickness of the screen used in a set of determinations are given at the top of the column containing these determinations. The difference between the radiating powers of lead and aluminium has in each case been reduced to 800. The results will now be discussed and an endeavour made to draw some conclusions from them. Since the difference in the amount of secondary radiation from any two substances is independent of the intensity of the primary y rays, if the difference of the two standard substances is always reduced to the same figure, the secondary radiation from a given substance with the different screens in the above table should be, obviously, the same if the screens produced a change in intensity only of the y rays. But the figures distinctly show that the y rays that penetrated the various screens differed in their power of producing secondary radiation froma given substance. Therefore the relative differences in each column of the table depend on the nature and thickness of the screen used in their determination. A beam of y rays will probably not change much in nature when sifted through a screen of lead 2 mm. thick only, and therefore the second column of the table gives approxi- mately the differences in the radiating powers of the substances under the influence of the full y radiation emitted by radium in radioactive equilibrium. The screen of lead placed in the path of the y rays served to cut off the 6 rays. In order to be able to draw any conclusions from the effect of the various screens on the relative differences of the radiating powers of the various substances, it is necessary to compare these differences with those in the second column of the table. Thus, it will be seen that the difference (C—Al) is de- creased with a screen of lead, mercury, or bismuth, while the Rays emitted by Substances exposed toy Rays. 639 differences (S—A1),(Fe—Al),(Ni—Al), (Cu—Al), (Zn—Al), (Sn—Al), are increased with these screens. With a screen of iron, copper, zine, or tin, the difference (C—Al) is very much decreased, while the other differences are also nearly always more or less decreased. Thus it seems that the y rays from radium consist principally of two groups of rays, the rays of one of the groups being much better absorbed by a screen of lead, mercury, or bismuth than by a screen of iron, copper, zinc, or tin, the opposite being the case with the rays of the other group. Let us examine more closely the values given in the table. Tt will be convenient to express the radiation from a substance in terms of that from aluminium, so that tor (Pb—Al) we may write (k,—1) Al, and in the case of any substance D write (ka—1)Al for (D—Al). It will also be convenient to denote the group of substances sulphur, iron, nickel, copper, zine, and tin, by the symbol N,,, so that (N,,—AL) stands for (S—Al), (Fe—Al), &e. Now, when the thin lead screen is replaced by the thick screen of lead, we should expect, if we assume that the y rays are heterogeneous, that the radiation from lead would decrease ina greater proportion than that from aluminium, and the value of (4,-1) therefore decrease. Further, if we assume that the radiation from each of the substances N,, is decreased in the same proportion as that from aluminium each of the values of (ka—1) of the differences (Nm—Al) will remain unchanged. Therefore, if we multiply (4,—1)Al and the values of (ka—1)Al by a factor which brings (4,;—1)Al to its previous value, each of the values of (4,—1)Al will become greater than its previous value. This result agrees with that obtained by experiment with the differences (Nia—Al), when the thin lead screen was replaced by the thick screen of lead (see table). The greater decrease of the radiation from lead than that from aluminium and the substances N,,, with increase of thickness of lead screen, shows that the rays that are most efficient in producing secondary radiation from lead. are more easily absorbed by lead, than the rays that are respectively most efficient in producing secondary radiation from aluminium and _ the substances N,,. It appears also that the rays that are respectively most efficient in producing secondary radiation from aluminium and the substances N,, are absorbed to an approximately equal though small extent by lead. Tt will be seen in Table V. that the value of the difference (C—Al) is decreased instead of increased, as the other differences, when the thin lead screen is replaced by the 2U 2 640 Mr. R. D. Kleeman on the Secondary Cathode thick screen of lead. This is explained if the radiation from aluminium is decreased in a greater preportion than that from carbon, an element of smalier atomic weight, when the thin screen is replaced by the thick screen (a similar assump- tion we have seen fits the facts for Pb and Al). For, the numerical value of (k,—1) of (C—Al) is then decreased, since it is negative ; and this decrease may be of sucha magnitude that the value of (k.—1)Al becomes less than its previous value when multiplied by a factor which brings (k,—1)AI to its previous value. It will be observed that it follows from the investigation in the preceding paragraph that this factor tends to increase the value of (C—Al). ‘Thus the greater decrease of the radiation from aluminium than that from carbon, with increase of thickness of lead screen, shows that the rays that are most efficient in producing secondary radiation from carbon are less absorbed by a screen of lead than the rays that are most efficient in producing secondary radiation from aluminium. Since the results obtained with a screen of mercury or bismuth resemble those obtained with the lead screen, the foregoing conclusions hold good for these screens also. Next, let us investigate the results obtained with the screens of ircn, copper, zinc, and tin. We should expect from the foregoing results, and the fact that the differences of the radiating powers obtained with these screens resemble one another, that each of these screens would absorb approximately to the same extent the rays that are respectively most efficient in producing secondary radiation from aluminium and the substances N,, or (S, Fe, Ni, Cu, Zn, Sn). Also, we should expect these rays to be more easily absorbed by these screens than the rays that are most efficient in producing secondary radiation from lead. In this case the radiation from aluminium should decrease in a greater proportion than that from lead, when the thin lead screen is replaced by one of the above-mentioned screens, and the radiation from each of the substances Nm and aluminium decrease in the same proportion. Therefore the value of (£,—1) will be increased, while each value of (4a—1) of the differences (N,,— Al) will remain approximately the same. Therefore, when (4;—1)Al or (Pb—Al) and the values of (4,—1)Al or (N,—Al) are each multiplied by a factor which reduces (Pb—Al) to its previous value, the values of (N,—Al) will become less than their previous value. Now, this result is approximately obtained by experiment with the differences (N,,—A1), when the thin lead screen is replaced by a screen of iron, copper, Rays emitted by Substances exposed to y Rays. 641 zine, or tin, and the supposition made at the beginning of this paragraph therefore true. It will be seen that the differences (N,,—AI) are least affected when the thin screen of lead is replaced by a screen of tin. This is probably due to the fact that the atomic weight of tin lies between that of lead and zine, and there- fore partakes to a greater extent of the properties of lead than the substances zinc, copper, and iron. ‘The effect of a screen of lead, it will be remembered, is to increase these differences. It will also be seen that the difference in the radiating power of aluminium and a substance, when the thin screen of lead is replaced by a screen of this substance, is in nearly all cases decreased to a greater extent than any of the other differences. The magnitude of the decrease of the differences becomes smaller as we pass progressively from this difference to the neighbouring differences. Now, if the radiation from a substance A is decreased in a greater proportion than that from any one of a number of other substances B,,, when the thin Jead screen is replaced by a screen of the substance A, the value of (k,—1) of (A—AlI) will decrease more than its value for any of the differences (B,,—Al). Therefore we conclude that the rays that are most efficient in producing secondary radiation from a substance are most easily absorbed by a screen of the same substance. A further examination of the differences obtained with the screens of copper, iron, zinc, and tin, shows that with these screens the differences (Ni— Al) and (Cu— Al) become approximately equal to one another. Now, if the radiation from copper decreased in a greater proportion than that from nickel, when the thin lead screen is replaced by one of these screens, this would decrease the value of (kg—1) for the difference (Cu—Al) more than its value for the difference (Ni—Al). And since the value of (Cu— Al) is larger than that of (Ni— Al) with the thin lead screen, this would have the tendency of making the values of (k,—1) of these differ- ences more nearly equal. Thus a screen of iron, copper, zinc, or tin, absorbs to a slightly greater extent the rays that are most efficient in producing secondary radiation from copper, than the rays that are most efficient in producing secondary radiation from nickel. The iarge change in the value of the difference (C—Al), when the thin lead screen is replaced by a screen of iron, copper, zine, or tin, remains to be examined. We have seen that the decrease of the differences (N,,—A1), when the thin lead screen is replaced by one of these screens, can be explained 642 Mr. R. D. Kleeman on the Secondary Cathode by assuming that the radiation from aluminium decreases in a greater proportion than that from lead, and the radiation from each of the substances N,, decreases in the same pro- portion as that from aluminium. For in this case these differences decrease when they are multiplied by a factor which makes (Pb—Al) equal to its previous value. But it will be seen that the decrease of the difference (C—Al) is much greater than that of any of the other differences, and cannot therefore be explained altogether in this manner. It is evident that the radiation from carbon does not decrease in the same proportion as that from aluminium, when the thin lead screen is replaced by one of the above-mentioned screens. If we assume that the radiation from carbon decreases in a less proportion than that from aluminium, the value of (f,—1) of the difference (C—AlI) is numerically decreased, since it is negative. In this case the value of (C—Al) or (kg—1)Al would be much more decreased than that of any of the other differences when they are multiplied by a factor which brings (Pb—Al) or (4,—1)Al equal to its previous value. Thus the rays that are most efficient in producing secondary radiation from carbon are less absorbed by a screen of iron, copper, zinc, or tin, than the rays that are most efficient in producing secondary radiation from aluminiuin and the substances N,,. We have seen that the rays that are most efficient in pro- ducing secondary radiation from carbon are also less absorbed by a screen of lead, mercury, or bismuth than the rays that are most efficient in producing secondary radiation from lead. It will be profitable to place some of the foregoing con- clusions side by side for comparison. We have seen that the decrease of (C—AI), when the thin lead screen is replaced by a screen of iron, copper, zine, or tin, is due, firstly, to the radiation from carbon decreasing in a less proportion than that from aluminium, and secondly, to the multiplying of (C—Al) and (Pb—Al) by a factor which brings (Pb—Al) to its previous value. This factor gives rise to the decrease of the other differences, since the radiation from lead is decreased with any one of the above changes of screen, in a less proportion than that from aluminium and the other substances. The decrease of the difference (C—A1), when the thin lead screen is replaced by a screen of lead, mercury, or bismuth, is due to the decrease of (C—Al), produced by the radiation from carbon decreasing in a less proportion than that from aluminium, being greater than the increase pro- duced by multiplying (C—AI) and (Pb—AlI) by a factor Lays emitted by Substances exposed to y Rays. 643 which increases (Pb—Al) to its previous value. This factor gives rise to the increase of the other differences, since the radiation from lead is decreased in a greater proportion than that from aluminium and the other substances. From the foregoing we see why the difference (C—Al), when the thin screen of lead is replaced by a screen of iron, copper, zinc, or tin, is more decreased than in the case when the thin screen of lead is replaced by a screen of lead, mercury, or bismuth. To sum up, the experiments as far as they have gone indicate that the rays from radium consist principally of two groups of rays, the constituent rays of each group differing not much from one another in their properties. The rays of one of the groups are more efficient in producing secondary cathode radiation from aluminium, sulphur, iron, nickel, zinc, and tin, than from lead, and are all more or less easily absorbed by each of these substances excepting lead, the absorption by lead being much less. The rays of the other group are more efficient in producing secondary cathode radiation from lead than fromthe other substances, and are more easily absorbed by lead, mercury, and bismuth, than by any of the other substances. There is also a third—apparently weak group of rays which is most efficient in producing secondary radiation from carbon. This group of rays is less easily absorbed by the above-mentioned substances than either of the other groups. It may be pointed out in passing that according to the foregoing, when it is required to shield a piece of apparatus from the y rays of radium, it is better to use a combined screen of lead and one of the metals iron, zinc, or copper, than a screen composed of one of these metals only. The y rays of radium thus resemble X rays in the absorp- tion by a substance depending on the nature of the rays and that of the absorbing substance. Further, the amount of secondary radiation from a substance exposed to y rays depends on the nature of the rays, and this has been shown to be also the case with X rays. These facts are additional evidence that the general nature of the y and X rays is the same. Both the y and X rays probably consist of electro- magnetic pulses produced by the acceleration of electric charges. Since the @ ray activity due to radium E is small in comparison with that due to radium C, in the case of radium only a few years old, the y rays from radium are principally produced by the acceleration of the electrons ejected by radium C. 644 Mr. J. 8. Dow on a Form of Paschen * has found that the electrons ejected by radium bromide (that is to say, by radium C) possess different velocities, but may be divided into two -groups, the average velocity of the electrons of one of the groups being greater than that of the other group. These two groups of electrons might possibly correspond to the above two principal groups of rays. It sivas me much pleasure to thank Prof. Thomson for his inspiring interest and advice during these experiments. Cavendish Laboratory, Aug. 14, 1907. LXIII. A Form of Cosine Flicker Photometer. By J Ss Dow, AC. Gil se Sem [Plate XVI] “HE illumination of the white surface employed in any I cos 6 d? intensity of the source illuminating the surface, d the distance of this source from the surface, and @ the angle between the rays of light striking the surface and a normal to the surface |. Hence, when measuring the intensity of a source of light, we may either vary ‘“‘d,” in which case we utilize the inverse square law, or @, in which case the cosine law is utilized. While the inverse square law is almost invariably utilized in photometric measurements, this method is inconvenient in one respect. In order to vary ‘‘d”’ the photometer is usually moved to and fro between the two sources of light to be ‘compared. The observer is therefore obliged to be continually moving his head in order to follow the motion of the photo- meter, and this is particularly distracting when theeyeisapplied — to a telescope. In order to avoid this necessity, many workers prefer to keep the photometer stationary and to move one of the sources of light. But in the case of gas-lamps and many other sources of light, this method is obviously unsatisfactory, and, even in the case of glow-lamps, is sometimes Inconvenient. The utilization of the cosine law is advantageous in this respect, for the photometer may then be kept stationary and the illumination of the photometrical surfaces adjusted in the photometer itself. The type of instrument about to be described by the author, and shown in fig. 1 (Pl. XVI.), has this advantage. Indeed, while it is desirable that such a photometer * Paschen, Ann. der Phys. xiv. p. 889 (1904). + Communicated by the Physical Society: read June 28, 1907. photometer is equal to , [where I equals the Cosine Flicker Photometer. 645 should be mounted on a photometrical bench in the usual way for accurate work, the author has used the apparatus shown. in the Plate for many purposes, such as the comparison of the results obtained by the methods of flicker and equality of brightness, without employing a photometrical bench at all. Also it is evident that the convenience of an instrument of this type is independent of the distance between the sources of light, provided the illumination of the photometrical surface is not too low. The general principle of this instrument is shown in fig. 2. Fig. 2. Sive View Front View The two sides of the rectangular Ritchie wedge, W, are illuminated by the two sources A, B. Above the wedge a 45° mirror, M, is placed so that the observer’s eye at E sees an image of the illuminated surfaces reflected in this mirror. The wedge is arranged to rotate about the line of intersection of the photometrical surfaces as a horizontal axis. To the observer, therefore, this line appears stationary as the wedge is rotated. Suppose now that the two sources A, B, are equidistant from the wedge. Then, if the intensities of the two sources are the same, photometrical balance is obtained when the wedge is placed symmetrically about a vertical axis, as shown. If, however, A, say, is the brighter of the two sources, the wedge must be rotated in a clockwise direction, so that the rays from A strike the surface presented towards A more obliquely than before, while, conversely, the rays from B strike the surface presented less obliquely. Hence let « represent the inclination of either surface to the vertical, when the wedge is in its symmetrical position. Let 1, I, represent the intensity of A and B respectively. Icosa The illumination of the surface facing A is then 2B 646 Mr. J. 8. Dow on a Form of Similarly, the illumination of the surface facing B is L — ; hence if I,=I, the surfaces appear equally illu- minated and we obtain photometric balance, with the wedge in its symmetrical position. Suppose now that I, is greater that I,, and that it is therefore necessary to rotate the wedge through an angle @, in a clockwise direction, in order that the illuminated surfaces may appear equally bright. : The illumination of the surface presented to A is now I, cos (2+ 0) 7 , and the illumination of the surface presented to B is I, See, Therefore I, _ cos (a—@) I,” cos (a+6)° | The ratio TL corresponding to each value of 6 is therefore 2 known. In this case the angle « was made 45° for, by so doing, the maximum angular range of photometrical reading is obtained. A lever, rigidly attached to the wedge and utilized by the observer to rotate it, also served as a pointer indicating the I, _ cos (45—6) ie I, cos (45+8@)’ value of @ and the corresponding ratio a scale attached to the instrument. This arrangement is shown in fig. 1. The scale is also diagrammatically exhibited in fig. 3. The most serviceable portion of this scale lies in the neighbourhood of 0:2 to 5-0. Outside this range the values cos (45 —@) cos (45 + @) of 0, for satistactory readings. At the extreme ends of the scale, too, the rays necessarily strike one of the photometric surfaces very obliquely, and therefore emphasize any in- equalities or roughness in texture of the surface and reduce the sensibility of the instrument. At present fine plaster of paris has been used by the author to secure white matt surfaces. Under these conditions, the theoretical readings on the scale deduced from the cosine law agreed very closely with those obtained experimentally and assuming an inverse square law. Between the limits 0°2 to 5 the agreement was within 3 per cent., and probably the substitution of perfectly ground photometric surfaces for those prepared by hand would result in still closer agreement. change too rapidly with increasing values 647 Cosine Flicker Photometer. 40 648 Mr. J. S. Dow on a Form of Beyond these limits, however, the agreement was naturally less satisfactory. Hence it seems desirable, when using an instrument of this type to assign convenient distances to the sources of light and to utilize the most open, central, portion of the scale. When using a photometer with inclined photometric sur- faces such as occur in the Ritchie wedge, attention must be paid to the possibility of “angle-errors,” 2.e. errors introduced by uncertainty as to the exact angle at which the rays of light strike the illuminated surfaces. In this case a consider- able rotation of the photometer, as a whole, about a vertical axis will alter the illumination of both surfaces equally and will, therefore, not affect the photometric result. But if the two sources are not in true alignment with the photometer, or if the photometer is tilted slightly about a horizontal axis, the illumination of the photometric surfaces may be differently influenced thereby, and errors may result. Suppose, for instance, that we are comparing the intensities of two glow-lamps each half a metre distant from the photo- meter. Then, if the centre of illumination of one of these sources is raised say, one centimetre, the angle at which the rays from this source strike the surface presented to it is altered by about 0°6 degrees. This corresponds to an alteration of illumination of about one per cent., when the most open, central portion of the scale is used. It is desirable, therefore, that the sources of light should be distant not less than, say, 1 metre from the photometer. It should then be possible to adjust the alignment of the lamps with sufficient exactitude to avoid appreciable error from this source. Indeed, in making accurate experiments with any photometer, it is desirable that the distance of the sources from the photometer should not be less than this value. Otherwise the inverse square law cannot be rigidly applied owing to the fact that the centres of illumination are rarely correctly located *. A tilt of only one degree of the photometer, as a whole, about a horizontal axis would cause an error of about 4 per cent., even when the most favourable portion of the scale is used. It is, therefore, desirable that no appreciable tilt of this character should be introduced either by inequalities in the level of the bench or undue play in the carriage of the photometer. Yet, it may be pointed out that the “double comparison * ‘Electrician,’ Sept. 14th, 1906, for some notes by the author on this point. Cosine Flicker Photometer. 649 method,” now almost invariably used when careful photo- metric tests are attempted, eliminates all want of photometric symmetry in a stationary photometer and would completely eliminate the above source of error, if the same portion of the scale was used in both experiments. This instrument can be utilized either on the Equality of Brightness or Flicker principle. This is accomplished as follows. Fig. 4. The image of the wedge, as formed by the mirror M, is outside the focal length of the convex lens L,, and this together with the lens L, forms a real image of the illuminated surfaces in the plane of the aperture at A. The eye of the observer applied to the third lens L; sees a magnified image of the aperture and the illuminated surfaces—both simul- taneously in focus. If, now, an observer is comparing, say, a red source with a green one, the field of view appears to him as shown in fig. 5a, when the lens L, is stationary. He then adopts as photometric balance the position of the photometer-wedge in which the red and green fields appear equally bright. The element of flicker may, however, be introduced by modification of the method due to Rood*. The lens, Ly, is mounted on springs and attached to a cord passing over a pin mounted eccentrically on the pulley of a small electric motor. When the motor is caused to rotate the lens oscillates to and fro and the boundary between the photometrical surfaces * Amer. Journal of Science, 1899, p. 194. 650 Mr. J. 8S. Dow on a Form of appears to oscillate with it. A band of flicker is thus pro- duced, and the field of view assumes the appearance shown in fig. 5. Fig. 5. FLICKER (@) (db) | The observer may then judge the position of photometric balance by observing the cessation of flicker in the band. Or he may drive the motor so fast that all flicker disappears and the intermediate band merely assumes a colour intermediate between that present in the two adjacent portions of the field of view. He may then use this intermediate colour to assist him in his decision as to the exact point when all three sections of the field of view appear equally bright. The question may now be raised whether, when using this instrument, the results of using the Equality of Brightness and Flicker methods is the same. The author has found that for widely different colours and for certain portions of the retina this is not the case *. Under the conditions present in this instrument, however, the agree- ment was very close unless the colour difference was very © marked indeed. ‘This is illustrated by the results shown in the following :— Nature of Lights Results by Flicker _ Result by Equality of compared. method. Brightness method. White to White ......... 1:031 1:034 White to Apple-Green . 0911 | 0-906 (impure) | White to deep Green ... 121 | 1:08 White to deep Red ...... | 2°23 2:09 * Proc. Phys. Soc. vol. xx. Cosine Flicker Photometer. 651 When comparing lights of the same colour the sensitiveness of the photometer seemed to be very much the same for both methods, but when the comparison of sources of light ditfering widely in colour was attempted, the Flicker method gave rise to the most consistent results. It seems possible that the sensitiveness of a photometer of this type might be improved by introducing the element of contrast in the manner shown in fig. 6 (Pl. XVI.) Hach of the photometrical surfaces is shown divided into 3 equal and similar portions. The portions 2 and 5 are intended to be as white as possible. The portions 1 and 6 are tinted with a neutral wash of such depth as to reduce the coefficient of reflexion from the surface by say 4 per cent., while 3 and 4 are intended to be intermediate in shade between 1 and 5 and 2 and 6 respectively. Now if the Equality of Brightness method is used, the observer attempts to set the wedge so that 3 and 4 appear equally bright. The contrast in light and shade exhibited between 1 and 2 and 6 and 5 respectively should then be the same. If, now, the wedge is rotated slightly in a clockwise direction, the contrast between 1 and 2 becomes more marked but that between 6 and 5 less marked than before. We have thus a double change such as occurs in the Lummer-Brodhun contrast photometer and a corresponding gain in sensitiveness. If the Flicker method is used a corre- sponding effect wiil exist. The author has endeavoured to facilitate the comparison of heterochromatic sources of light by applying Crova’s method. | As the temperature of an incandescent solid is raised, the luminous radiation in the form of waves of short wave-length increases more rapidly than the luminous radiation of great wave-length. According to the principle discovered by Crova*, however, the luminosity in the spectrum of such a source in the neigh- bourhood of A=0°582y is a measure of the total luminosity of the source. Crova therefore proposed to view the surfaces illuminated by two heterochromatic sources through a solution allowing only rays in this portion of the spectrum to pass. This solution was composed of :— Anhydrous ferric chloride, 22°32 gms. Crystallized nickel chloride, 27:19 gms. Distilled water, 100 ce. * Comptes Rendus, vol. cxix. no. 16, p. 627. 652 On a Form of Cosine Flicker. Photometer. It must be noted, however, that the principle on which Crova’s method depends, only applies rigidly to an incan- descent body yielding a continuous spectrum. In the case of a luminescent vapour yielding a spectrum in which the luminosity is concentrated in isolated bright lines, the method is inapplicable. Yet, since the portion of the spectrum which Crova’s method proposes to utilize is by far the most valuable portion from an illuminating point of view (2. e. the portion which, for a given expenditure of energy, produces the greatest sensation of brightness), the method may prove satisfactory even in many cases of this character. The chief difficulty which the author has found in applying this method lies in the fact that, if a sufficient depth of solution is employed to restrict the light passing to a very narrow region of the spectrum, and hence to render the colours of the two illuminated surfaces identical, the lumi- nosity of the surfaces becomes, as a rule, inconveniently low. The only case, in fact, in whieh the author succeeded in obtaining an apparently perfect colour match without undue loss of illumination, was when comparing an_are lamp against an incandescent mantle. When a flicker was utilized, however, it was found that a depth of 3 millimetres of solution, which, while most trans- parent to yellow rays, actually allowed rays from A=0°52 to =0'68y to pass, rendered the comparison of most sources distinctly easier. The tollowing are a few cases in which this method was applied. Carbon Glow-lamp compared with Nernst lamp. Argand Gas-burner i » Jncandescent Mantle. White Arc-light 5 », Incandescent Mantle. White Arc-lig ht is » Argand Gas-burner. Flame Arc-lamp (Iixcello carbons) compared with Argand Gas-burner. Flame Arc-lamp (Bremer carbons) » Argand Gas-burner. In all these cases the means of a set of photometrical results obtained with and without the Crova screen agreed very closely, in the first two cases within 2 per cent. The unsteady nature of the arc lights rendered very exact comparisons with these lights impossible, but in this case also the difference seemed to be, at any rate, less than 5 per cent. All these sources of light, however, yield a continuous spectrum. It is true that some isolated bright lines, super- imposed over the main spectrum of the arc, serve to increase the efficiency of the flame carbons. Yet the brightest of these lines were congregated in the yellow and orange and Secondary Réntgen Radiation from Gases and Vapours. 653 would, therefore, not seriously affect the applicability of Crova’s method. Quite otherwise were the results obtained when comparing a mercury-vapour lamp against a carbon-filament glow-lamp. The luminosity of this lamp was concentrated in three isolated bright lines in the yellow, green, and violet respectively, practically no red rays being present. It was found that the depth of solution utilized in the experiments described above not only failed to very notice- ably improve the colour difference between the sources but also seriously affected the photometric results obtained. The use of yellow screens in order to facilitate the photo- metric comparison of heterochromatic sources of light is certainly only justifiable in the case of illuminants yielding continuous spectra. Even in this case it is essential that the yellow screen should exhibit absorbing properties similar to those of Crova’s solution, namely minimum absorption in the neighbourhood of A=0°58y, and a uniformly increasing absorption on either side of this point. LXIV. On the Secondary Réntgen Radiation from Gases and Vapours. By J. A. CrowrHer, B.A., late Scholar, St. John’s College, Cambridge ; Open Research Student, Emmanuel College, Cambridge”. Introduction. .... gases through which Réntgen rays are passing give off some secondary rays was first discovered by Réntgen himself +, who noticed that a photographic plate, placed near a beam of X-rays, was gradually affected even though shielded from the direct action of the primary rays. Sagnacf also, during his researches on the secondary radiation from metals, observed a similar effect. The subject has been more thoroughly investigated by Barkla §, who studied very ex- haustively the secondary Roéntgen radiation from air, and also made some experiments on four other gases, hydrogen, carbon dioxide, sulphur dioxide, and hydrogen sulphide. * Communicated by Prof. J. J. Thomson. + Rontgen, Ann. Phys. Chem. ixiv. pp. 18-37 (1898). t Sagnac, Comptes Rendus, cxxvi. pp. 521-523 (1898). § Barkla, Phil. Mag. v. pp. 685-698 (1903); vil. p. 543 (1904). Phil. Mag. 8. 6. Vol. 14. No. 83. Nov. 1907. 2X 654. Mr. J. A. Crowther on the Secondary His conclusions may be briefly summarized as follows :-— (i.) All gases, when subjected to X-rays, are a source of secondary radiation. (ii.) The absorbability of the secondary radiation is, within the limits of experimental error, the same as that of the primary producing it. (iii.) For a given primary radiation, the intensity of the secondary radiation is proportional to the density of the gas from which it proceeds. (iv.) The ratio of the intensities of the primary and secondary beam is independent of the hardness and intensity of the primary rays. In support of the third conclusion he gives the following table :— Relative Intensity Relative Density | of Secondary Radiation. of Gas. le aa aR 1-0 1-0 WALES sioieccsacisalshice tierce | 0-17 ROG, Pe Si paaccecees meer | 1:07 1:18 WOR lek Seckiceees she 1°45 1:53 VSOy oF Gogseshnsensaaess 211 2°19 Barkla’s experiments were carefully performed, and, as far as relates to the five gases upon which he experimented, there can be no doubt that his conclusions are substantially correct. As will appear later, they have, in the main, been confirmed by experiments made on the same substances during the course of the present work. Barkla’s experiments, however, included only a very few gases, and these not of a very varied type. There were no gases of very great density, no gases with a very complex molecule, and no gases containing elements of high, or even moderately high atomic weight. Having regard to the importance of the subject, it seemed desirable that more accurate experiments involving a far greater number and variety of substances should be made before drawing any general or final conclusions. Keperimental. Until some means shall have been devised for maintaining a constant stream of X-rays of a definite character, accurate measurements on X-radiation will only be possible by com- parative or compensation methods. Barkla measured his 655 secondary radiation by comparing the rates of leak of two small gold-leaf electroscopes, the ong exposed to the secondary rays to be measured, the other toa small pencil of the primary rays. 3 For the purpose of comparing the secondary radiation from a number of gases and vapours, however, it seemed to be more desirable that the comparison should be made, not with a small beam of the primary rays, but directly with the secondary radiation from a standard substance, air. In this way it became possible to ensure that the radiation from any gas, and that from the standard gas air, were measured under exactly the same conditions. Moreover, if, as seemed probable (and as was subsequently proved to be the case), the secondary radiation from a given volume of air was proportional to the pressure, it would be easy, by adjusting the pressure of the standard air, to make the radiation from it equal to that from the given gas or vapour. In this way the method could be transformed into a “null” method, thus affording not only much greater convenience in measurement (leaving only one electroscope to be read instead of two), but also a much higher degree of accuracy and sensibility. Preliminary experiments having shown that the assumption as to the proportionality between the pressure of, and the secondary radiation from air was correct, this method was finally adopted. Réntgen Radiation from Gases and Vapours. — S70 EARTH (eH ‘ To FesERvior ; er | ( : a POTENTIOMETER #% \\4 IN ‘EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SIXTH SERIES.] DECEMBER 1907. LXVIII. On Magnetic Oscillators as Radiators in Wireless Telegraphy. By J. A. Furmine, D.Sc., F.RS.* A oscillator of the open or Hertzian type is commonly called an electric oscillator because the effects produced in the external field are to a large extent determined by the potential of the free electric charges which alternately make their appearance on the open ends. If, however, the oscillator consists of a metallic circuit completed by a con- denser, the plates of which are very near together, the effects in the external space are mostly or entirely determined by the current in the circuit and little if at all by the con- denser-plate charges, because these being of opposite sign and near together neutralize each other’s effects in the field. Such a closed or nearly closed circuit is called a magnetic oscillator. In the case of an open oscillator or simple doublet Hertz showed that if @ is the maximum electric moment, or product of the maximum static charge on each end and the distance between them, and if % is the wave-length of the emitted radiation, the energy radiated by the oscillations in ergs per period is given by the expression ee aise kis) Vo sent This expression can be reduced to a more convenient form for practical measurement as follows :— Let C be the capacity in microtfarads of each sphere or * Communicated by the Physical Society: read October 25th, 1907. Phil. Mag. 8. 6. Vol. 14. No. 84. Dec. 1907, aay 678 Dr. J. A. Fleming on Magnetic Oscillators half of the oscillator with respect to the other, and V be their maximum potential difference in volts before discharge, then 9x 10°C V /300=3000C V is the maximum value of the charge in electrostatic units. Hence if / is the length cf the oscillator in cms., we have for the electric moment, & = 3000 CVI) 20) es Let the current at the centre of the oscillator have a maximum value A reckoned in amperes, and let a be the root-mean-square or effective value in amperes as measured _ by a hot-wire ammeter. Then, if the oscillations are sinoidal in form, undamped or persistent, and of frequency N, we have AL27 NO V/10% . eee A anya) e - . O C ° c 0 (4) Hence the energy E radiated per period in ergs is given by iN ; EK=47? 10° N° CM POMC Pcl hc (5) and the power W in watts by ; Pp. W =407? 5 A’. LE oe) Remembering that 7?=9°87 and NX=3 x 10%, we can write the above formule in the convenient form 2 B= 02632 a MN A W : a = 7896 Ga’ 1 enim The value of the ratio 1/2 can be determined experiment- ally for any oscillator. For a simple linear oscillation it approximates in value to 0°'4. Hence for such an oscillator radiating undamped waves, the power radiated in watts is given by the expression W=126a?. Thus, for instance, if the effective value of the current at the centre of the oscillator is 2 amperes, the radiation will be half a kilowatt. If we then consider the case of a perfectly closed oscillation circuit having an area S and traversed by undamped or persistent oscillations which have a maximum value A and R.M.S. value a reckoned in amperes, it can be shown that as Radiators in Wireless Telegraphy. 679 such a closed circuit also radiates energy, and we can derive a similar formula for the radiation to that given by Hertz for the open circuit. The author has shown that if M is the maximum magnetic moment of such a closed circuit *, viz., the product of its area S and the maximum value of the alternating current (reckoned in electromagnet measure) in it; and if A is the wave-length of the radiation emitted by it, and E the radiation in ergs per period, then for the magnetic oscillator we have 167r*M? iD => Aer e e ° e e e (9) But by definition M==AS/10, and if the current is sinoidal a=Al/,/2, hence we have Se Furthermore, if the oscillations are persistent the power in watts W radiated is given by 22 W=31,200 ate A? Vic cee) The formule (8) and (11) can be written in the form W=87 x 10-2 Pat? (open or electric | oscillator), . ra 10s S34 (closed or mienctia | 4 i oscillator). (12) These last two tormulz show us that in the case of the open or electric oscillator the power radiated varies as the square of the current in it, and as the square of the frequency, whereas in the case of the closed or magnetic oscillator it varies as the square of the current but as the fourth power of the frequency. Accordingly, in the case of the magnetic oscillator the radiation is small unless the frequency is very high. For the purposes of theory, it is most convenient to consider a closed oscillatory circuit as made up of a series of Hertzian or dumbbell oscillators placed in series with their electric poles of opposite sign overlapping. We can then easily determine the nature of the electric and magnetic field produced by it by the summation of those due to the elementary oscillators. As the writer has given lately in another place a discussion of the problem and furnished the expressions for the electric and magnetic forces at any point * See ‘ The Electrician,’ vol. lix. p. 936 (1907). A series of articles on ‘«The Elementary Theory of ae ee by J. A. Fleming, ) 6 680 Dr. J. A. Fleming on Magnetic Oscillators in the field of such a closed oscillator and the derivation of the formula (10) for the radiation, it is unnecessary to go over the ground again here. (See ‘ The Electrician,’ vol. 59, p- 936 et seq.) The object of the following experiments was to obtain -some information as to the actual distance-effects of closed oscillators of certain dimensions, and to ascertain whether true radiation was at all influential in producing the inductive action of one closed oscillatory circuit on another at moderate distances, or if the whole of the action could be accounted for by ordinary electromagnetic or Faradaic induction. The following circuits were employed for this purpose :— ‘Two pair of square circuits were constructed by winding a few turns of highly insulated copper wire round a wooden Cross. | . One pair had sides 8 feet in length, each frame carrying two coils of 5 turns of 7/21 stranded insulated copper wire. These will be referred to as the “large square coils.” One pair had sides 2 feet in length, each frame carrying one coil of 8 turns of the same sized wire. These are referred to as the ‘‘ small square coils.” The experiments consisted in setting up continuous or undamped oscillations in one of these coils by means of a Poulsen are and then measuring the current created in the corresponding coil placed at a distance by means of the Author’s oscillation-valve or glow-lamp detector. The two coils were placed at various distances and in various respective positions, The coils themselves were erected or placed in the large quadrangle of University College, London. As the are apparatus had to be placed indoors in the Electrical Laboratory it was necessary to connect the coil used as a transmitter or primary coil with the oscillation-producing apparatus by means of a long pair of insulated parallel copper (7/21) wires 14 cms. apart and 273 feet or 836 cms. long. ) The first step was to measure the inductance of these wires for high frequency currents. Anderson’s bridge method was employed with a commutator as described by the Author”. The inductance of the parallel wires or tails above men-. tioned was found to be 50,910 cms., and that of one large coil of 5 turns on the 8-foot square together with the tail * See J. A. Fleming, “A Note on the Measurement of Small Inductances and Capacities,’ Phil. Mag. May 1904, p. 586. See also J. A. Fleming and W. C. Clinton, “On the Measurement of Small Capacities and Inductances,” Phil. Mag. May 1908, p. 493. as Radiators in Wireless Telegraphy. 681 (L) was 310,740 ems. Hence the inductance of the coil itself of 5 turns was 259,830 cms. ‘The inductance of the two coils each of 5 turns in parallel was 198,350 cms., and in serles 779,300 cms. The inductance of each of the small or 2-foot square coils was in the same manner found to be 116,200 ems. In series with these coils was placed a condenser having a capacity (C) of 0:0026 mfd. and the coil and condenser shunted across a 400-volt Poulsen are. The are current was generally about 8 amperes, the potential difference of the are terminals (V,) 260 volts (continuous). The potential difference (V,) (R.MLS. value) of the condenser terminals was 1580 volts as measured by an electrostatic-voltmeter and the R.M.S. current (a) in the square coil was 4:22 amperes as measured by a hot-wire ammeter. The frequency N of the oscillations is given by the formula N=(5:033 x 10°)/4/CL. Hence if C=0:0026 mfd. and L=310740 cms., we have N=177,100. If the R.M.S. current (a) in the coils were strictly sinoidal in wave- form, the value should be calculable from the formula, Baris a= To CVN where V= VV\?—V,?= /(1580)?—(260)?=1560 volts. Hence we should have HALE 26 a Bee a= 7 x 1010 x 1560 x 177100=4°52 amperes. The actual measured value was 4°22 or 7°3 per cent. less, which may be accounted for by the known fact that the actual wave-form of the current in the coilis not by any means truly sinoidal. The wave-length 2» corresponding to a frequency of 177100 is nearly 169,000 cms., or rather more than 1 mile in length. 7 The total area S of the large coils using the 5-turn circuit is 5 x (243°2)? ems.=295,731 sq. cms., and the value of S’a? is therefore (295731)? x (4°22)?=156 x10". Also (177100)? = 554523 x 101°. For a closed square radiator the energy in ergs radiated per period is given as already men- tioned by the expression 682 Dr. J. A. Fleming on Magnetic Oscillators Hence we have in this case for the power W radiated in ergs per second, ww — 10:4 x 156 x 177000 L593 = 922 (nearly) or about 52 microwatts. This is the energy sent out per second through the surface of a sphere described round the oscillator the radius of which is large compared with the wave-length of the oscil- lator in question. It is evident therefore that the true radiative power of a closed circuit of the above dimensions is extremely small compared with that of an open oscillator of the same order of linear dimensions. Hence when a closed circuit traversed by a high frequency current acts to produce secondary currents in another similar circuit at less than a wave-length distance from it, the chief part of the effect cannot be due to true radiation or detached energy but is the result of ordinary electromagnetic induc- tion, or the creation of secondary currents produced by the ebb and flow or pulsation of the lines of magnetic force per- manently connected with the primary circuit *. Nevertheless experiment shows that such circuits may act appreciably upon one another at very considerable distances, when the primary circuit of one is traversed by a high frequency current, and the circuits are in resonance with each other. The old form of wireless telegraphy based upon such mutual induction between closed coils, as in the arrangement suggested by Trowbridge and Stevenson, or the parallel wire method of Preece, Rathenau and others, “employ ed relatively low frequency currents because the receiver used was the telephone, and the frequency was therefore limited by the ~ range of audition. Hven when the circuits were put in resonance, as by Lodge, the difficulties connected with the disturbance of commercial telephony restricted the possibilities of its use apart from other considerations. One object of the present experiments was to obtain data for an opinion whether such inductive wireless telegraphy could be improved by the use of electric oscillations of high- frequency in completely non-earthed circuits so that no disturbance of telephones or telegraphs could possibly arise * Moreover, just as in the case of the Hertzian oscillator true radiation or detachment of energy only takes place about ¢ or 3 a wave-length from the oscillator, so in the case of the closed or magnetic oscillator true radiation effects can only be produced at a similar distance from it. as Radiators in Wireless Telegraphy. 6383 combined with the use of a suitable oscillation detector. With this end in view, a closed primary-circuit had created In it continuous or undamped electric oscillations, and its inductive and radiative effect upon a similar closed receiving circuit was measured by means of the Oscillation Valve or Glow-Lamp Detector first described by the Author in 1904. It consists of a 12-volt carbon filament glow-lamp with a metal cylinder surrounding the filament sealed into the bulb. The cylinder i is carried on a platinum wire sealed through the glass. The filament is incandesced by a 6-cell secondary battery. If the terminals of a condenser inserted in an oscillatory circuit are connected, one to the cylinder and one to the negative terminal of the lamp filament, and if an ordinary movable coil galvanometer is inserted in this circuit, then when oscillations occur in the condenser the glow-lamp acts as an electrical valve and the galvanometer is traversed by a continuous current which bears a definite relation to the potential SE B 686 Dr. J. A. Fleming on Magnetic Oscillators The dotted lines represent the line joining their centres. The following experiments were then made :— Exp. I. Effect of varying the position of the coils —The two 8-feet coils of 5 turns each were set up with centres 60 feet apart. The transmitter current was 5:4 amperes. The capacity in the transmitter circuit 0°0026 mfd. The receiver was tuned to a frequency of 164,000 in syntony with the transmitter and undamped oscillations were set up in the latter by the arc. The electric arc was adjusted to keep a constant high-frequency current in the transmitter circuit of D4 amperes. ‘The are current itself was 8 amperes and are P.D. from 260 to 320 volts. The transmitter was put successively in positions A, B, and C, and in each case associated with receiver in positions A, B, and C, and the receiver or secondary current in milli- amperes being measured. The results are tabulated in Table I. TABLE I, | Transmitter Receiver Secondary Current | Position. Position. in milliamperes. | A A 24:16 AS B 10°77 re C 20°98 B A | B25 F B 20-45 iy C | 18:10 C A | 6-56 He B | 22°58 My C | 37°00 When the coils were in positien C their planes were 6 inches above the ground. The figures in Table I. show that when both coils were in position C the receiver current exceeded that in any other position, and that although the receiver current was small with the coils in the positions of zero mutual induction, viz. (A.B.), (B.4.), or, (C.A.), at) was not ‘covallieimeine position (A.C.). as Radiators in Wireless Telegraphy. 687 In the case of two small coils placed at a distance large compared with their dimensions the magnetic induction for a steady field should by theory be twice as great in the position (A.A.) as in the position (B.B.), and should be the same in position (C.C.) as in position (B.B). Also zero iG - 6 positions (A.B.), (B.A.), (C.B.), (B.C.), (A.C.), pa. ) But when using the high-frequency primary current the secondary current is still large in the cases (A.C.),( B.C.), and (C.B.), viz., when either the receiver or transmitter coil has its plane parallel to the earth’s surface. Subsequent results showed that the height of the coils above the ground affected this result considerably. Never- theless the exalted effect in position (C.C.) is interesting and convenient because it is easy to construct large circuits out of doors in positions (C.C.) and very much less easy without the aid of tall masts to make them in the positions (A.A.) or (B.B.). Exp. Il. Lect of varying distance. Coils vertical_—The same pair of coils were set up on positions (A.A.) and their distances varied. The receiver circuit was tuned to a frequency of 162,000, and the primary current was 4°7 and 5’4 amperes in two sets of observations respectively. TasLE II.—Coils in position (A.A.). Distance of Centres} Primary Current | Secondary Current in feet. in amperes. in milliamperes. 78:0 54 15:7 123°5 : 6°46 170°5 . 1:17 2370 R 0-12 36°2 BT) 41:9 88°0 5 6:99 123-2 - 3°05 169°7 . 1-01 237°0 mi O11 The results are plotted in the curve in fig. 3. 688 Dr. J. A. Fleming on Magnetic Oscillators The curve shows that the inductive effect decreases at first very rapidly with the distance, less rapidly than the inverse cube but rather more than the inverse square of the distance. : 1] Oo Fig. 3. 40 ) Ss 253 a | N 30 5S a * x & 3 S a ‘ % i yg Ns, 25 -3/o on Sa. u e, a 9 Cc xy \y) Wr, 2 R xe @ | x R ’ v —~ . a = re ‘a Bose.) Ns K 9g v K 1090 » | x x =x & 295) ® 0801 «, : = \ z ~ 3 2 Was rr /0 a 2 \ SS \ oe” \ ee e | \ \ 3B 3 a Height of Corl in feel Phil. Mag. 8. 6. Vol. 14. No. 84. Dec. 1907. 3A 694 Dr. J. A. Fleming on Magnetic Oscillator: They show how much the receiver current varies with the height of the coils above the ground, the maximum value being reached when the coils.are about 2 inches above the surface. Also they show that when the coils are laid flat on the ground there is a great increase in the power taken up by the arc. Raising the coils from 6 inches to 6 feet above the ground decreased the secondary currents to one-fifth. xp. VIII. Comparison of coils of different areas.—The two large or 8-feet coils were compared with ihe two small or 2-feet coils. In both cases the distance between primary and secondary was 79 feet, and the coils were parallel to the earth and at 6 inches above the surface. In both cases the primary current was 5:4 amperes. The small coils had 8 turns and were tuned to a frequency of 214,400. The large coils had 5 turns and were tuned to a frequency of 162,000. Tape VIII. Secondary Coils used. BEIGE Frequency. Current in of turns. hy. ‘ milliamperes. | Small. 2 feet in side... 8 214,400 0-082 Large. 8 feet in side... 5 162,000 27'4 The large coil therefore produces 340 times the effect of the small coil. Exe. IX. Comparison of the same coils with different numbers of turns.—The two large coils were wound with two circuits each of 5 turns and they could be joined in series so as to makeacoil of 10 turns. The coils were placed parallel to the earth and at a distance of 6 inches above it. The primary current used in both cases was 5°4 amperes. The inductance of the primary circuit was 380,000 cms., and when 10 turns were used it was 1,000,000 cms. The power taken up in the arc therefore was not the same in the two cases, as Radiators in Wireless Telegraphy. 695 TasueE IX. | Number | Power tuken Frequency Secondary of turns .| upin Arc, | of Current in on Coil, | in watts. Oscillations. | miliiamperes. i) 2495 162,000 Die | HOME ha 1587 99,600 21-4 The increase in the number of turns by increasing the inductance lowers the frequency of the oscillations, and this lowers the power taken up in the arc, and therefore the secondary current is reduced roughly in proportion to the decrease in frequency. In all the above experimenis the Poulsen are was used as a generator of undamped oscillations. it was considered desirable, however, to compare the effects obtained in this case with those when using a spark method of exciting intermittent oscillations. The large square coils were placed vertical and facing each other in positions (A.A.) and at 68 feet apart. They were tuned to a frequency of 162,000. Oscillations were then excited by an arc and a spark and the primary and secondary currents measured and volt amperes given to the generator in each case, as follows :— TABLE X. Volt | Primary Secondary | Generator. | Volts. | Amperes. BAA | Current in | Current in | Day | amperes. milliamperes. Spates. <2... 12:2 2°6 31:7 2°15 0°56 | PNG 2s. sd5 260 80 2080 5°4 ee 0) Roughly speaking, therefore, 70 times more power was being expended on the are than on the induction-coil used to create the spark, but the secondary current only increased some 38 times. This seems to indicate that the intermittent spark method of exciting the oscillations is not inferior but rather superior in efficiency to the arc method, for the particular purpose here considered. The conclusions to be drawn from this preliminary set of 3A 2 696 Magnetic Oscillators as Radiators in Wireless Telegraphy. experiments are that the inductive effects observed between the closed oscillatory circuits used are in the main due to electro- magnetic induction and not to true radiation. Secondly, that the most advantageous position of the coils is with the plane of the coils parallel to the earth’s surface and at a small distance above it. Thirdly, that the increase in the area of the coils is especially advantageous, and that therefore the coils used should consist of single turns of wire enclosing as large an area as possible. Fourthly, that the inductance and capacity of the circuit must be kept low to keep up the frequency. lastly, the spark method of exciting the oscil- lations can be advantageously employed. The best method, therefore, for constructing and using such closed circuit antennze for high-frequency closed circuit wireless telegraphy which seems to be indicated by the foregoing experiments is as follows :-— In some large field set up a number of short wooden posts having telegraphic insulators attached to them. Round these lay a number of wires, which may be bare copper wires, so as to form a closed circuit of one turn of a number of parallel wires, the circuit being say a foot or two from the ground, or if cows, horses, or sheep are kept in the field it may be better to keep it up 7 or 8 feet from the ground. Complete this circuit by a condenser and spark-gap and make provision by a high-tension transformer for exciting oscillations in the circuit. In a similar distant and syntonised circuit include any of the receiving devices now employed in radio-telegraphy, and signals can be transmitted and received without high antenne and without interruption to commercial telephonic circuits. Such closed horizontal receiving circuits will not pick up signals from the vertical antenna transmitters commonly used. 3 The method suggested is in fact the old form of magnetic induction space-telegraphy, but conducted with electric oscillations in place of the low-frequency currents obtained by an ordinary alternator or interrupted battery-current. On the other hand, direct experiment with low-frequency alternating currents of 5:4 amperes passed through the small coils used in these experiments, showed that no inductive effects detectable at more than a few yards at most were apparent when using an ordinary telephone as a receiver. Even if the whole of the inductive effect is due to simple electromagnetic induction, the use of high-frequency currents is a distinct advantage. Hzpansion of Bessel Functions of High Order. 697 The experiments here described are merely a preliminary to large scale experiments in actual closed cireuit telegraphy the writer hopes to be able to try later on. One drawback to the magnetic induction form of telegraphy is the rapid rate at which the effect falls off with the distance. In the case of true radiation at long distances the forces vary inversely as the distance, but a more rapid rate of decay, something between the inverse cube and inverse square, holds good for the inductive effect at least at short distances. Hence the use of magnetic oscillators as transmitters is never likely for this reason alone to rival the electric or open oscillator, but there may be circumstances under which it is possible to use them with advantage. In conclusion the author desires to mention that the actual measurements recorded in this paper were taken by his assistant, Mr. G. B. Dyke, B.Sc., with the kind help of Mr. K. W. McMillan, and to these gentlemen is due an acknowledgement of their share in the work, in making these observations with much intelligence and care. \ LXIX. The Asymptotic Expansion of Bessel Functions of High Order. By J. W. Nicworson, D.Se., B.A., Lsaac Newton Student in the University of Cambridge™. N certain investigations in the theory of diffraction by large obstacles the author recently found it necessary to obtain some approximate formule for the Bessel functions whose order is half an odd integer. The results can be applied to a large number of physical problems, and in fact supply the key to the solution of the majority of problems connected with the bending of waves round large spheres, with which little progress has hitherto been made. The Bessel functions are of several types, determined by the relation between their order and argument. The attention of investigators has been mainly confined to the types in which the order is small in comparison with the argument, which may be of any magnitude. In this paper, expressions will be obtained for functions of large argument, and of order comparable with, but less than that argument. ‘This special problem has received little attention, anda memoir by Lorenz+ appears to furnish the only contribution yet made to the * Communicated by the Author. + Cuovres Scientifiques, i. p. 405 et seq. 698 Dr. J. W. Nicholson on the Asymptotic subject. The results obtained by Lorenz may be sum- marized as follows :— Writing J @= —" S10 Gi. i ai eee 2R\2 5 (=( G7) ot in all cases in which n+4 is less than z, which is large; then, if z—n—4 is of higher order than 2, A [os ee| Os i ane (4) d= (Pat PE) SF + (n +9) sin The formule deduced by Lorenz for higher values of n, more closely equal to, or greater than 2, are not relevant to the present purpose. When = and n are only moderately large, these forms cease to be good approximations, and in this paper it is proposed to generalize them, and to carry the calculation to higher orders. Making, with Lorenz, the substitutions (1) and (2) in the relation ) JJ —J'J=(—)”.—, TZ +—- -+ ‘it appears, after some reduction, that de 1 oR) But for extremely great values of <, in comparison with n, Lommel’s* ordinary formula yields i) Tie, as Thus p=2—"F — (q—2) 4 Jibs PO SRG in the more general case when n is of order 2. The differential equation for the functions J must there- fore be satisfied by the form i R\i “dz fa(=) exp. io ee (7) * E. g., vide Whittaker, Modern Analysis, 1902, p. 294. Expansion of Bessel Functions of High Order. 699 Substituting this expression in the equation ) af 2 df us ae i ayy it appears that RR’ —3 Re4(1-"-4 (oR 9-0) where the accent indicates differentiation with respect to <. If this be again differentiated it becomes linear, and yields BM 4 a 1—* at) gee HS Fs i ln) which may be integrated in series. By reference again to Lommel’s formula”, it appears that when z is very ‘ereat in comparison with n, R takes the value unity. The series solution of (8) satisfying this condition is rae 14” a ate (9) When x is of order z, and z—n is not small, this leads at: once to as proved by Lorenz. The value of ¢ in (4) follows by (6)- We proceed to obtain a definite integral for the function R. Writing m=2n-+1, so that m is an odd integer, sien 212? 1) m?—l? m3" 1.3 mo) Gaye 34. 25 = =| “ 86) dd, TT Jo where OY; m?—12 cos?@ m*—1?. m?—3? /cos?6\2 S(0) = 14 ES + , ( Le) + --- (10) But by a well-known 5 a since m is odd, sinh Tivee ln ; m? — 12. m? —3? SAL by AA ‘she : 3 So ie: Wepre ce eigen ee oF = ae 7 lucas f=: BI sim? te= ane * Loe. cit. tT Vide Chrystal’s Algebra, Part II. p. 180. 700 Dr. J. W. Nicholson on the Asymptotic Thus, 1 i aul nh q : 22 then 2zsinh mt _ , m—1?2 , & 2 meosh | i BY) face: But when s is an integer, lo @) { eX ustl dy = s! 0 Hence 22 Bed tated S(@) == $= e-“ sinh mt du ; m cos 6}, or, since u cos 6 = 22 sinh ¢, Az? = i (0) a e—22 sinh t/cos 8 sinh mt cosh t dé, cos 0), and poe { ? S(0)d0. T Jo Bf The usual rules for the change in the order of integration are satisfied by the presence of the exponential factor, and Se 3 1B = Be i sinh m¢ cosh eat | * sec? 0. dO. eAsee 8, (11) mT ), ; where A= 2z sinh ¢. Let K,(A) be the second solution of Bessel’s equation of order zero, with independent variable i, defined by nK,(0) = | enAeohe dy, . , , (12) 0 Then writing cos @= sechu, T Ir SeCHO » dgiems=ccu =| Cosh w Sui semn coe 0 0 = —7K, (X). oer ( au E Thus R=— = { sinh mé cosh ¢ K,/(2< sinh ¢) dt 0 shed d Bo vies (TR (Oe 6 = {, sinh mt a {K,(2< sinh 2) }dt, R=4: | K,(2zsinht) cosh midi, . . (13) 0 after integration by parts, m still denoting 2x +1. Expansion of Bessel Functions of High Order. 701 As a double integral of reversible type, jp =| { e722 sinht cosh b cosh mt dt dp. ° (14) TT 0 0 First approximation to R. The most significant portion of the integral, with the assumed magnitudes of m and ¢, occurs neart=0. Thus writing sinh t=¢, and integrating over a small range which is itself capable of being regarded as infinite owing to the large argument of the exponentials, 4z (°° ‘ n= i uw Que os ecosh muat. 0 0 vis to the first order of approximation. This leads to TE a i i Re f | T { ap U 22 cosh v—m 1 2z coshy+m § meee d (sinh w) om \) 40%?—m? +42? sinh? yp 22 —— (42 —m?)” e e e ° e ° ° e e ° e (15) in accordance with (3). Approximation of any order to R. We proceed to obtain an expansion of the integral r=( ada Agi v es WL iG) Jo ; pew hae : ; f where > is large, and v’ or ay 18 never zero in the range o integration, v also being everywhere positive. By an in- tegration by parts, © =— 1 —Av ‘ Ve ji —Av Je lose | Ah aah dt. Under the conditions supposed, the second term is of lower order in 2% than the first. Continuing the process, an asymptotic expansion is obtained, each term being of a higher order in = than that immediately preceding. Although not in general convergent, this series may be used for calculating | 702 Dr. J. W. Nicholson on the Asymptotic R to a high order, as in the usual theory of eae ex- pansions. The series is evanescent at the upper limit on account of the exponential, and thus, if 7,=0, T=(4 2d ne v=0 rv! " r2v! dt" v at aa aliaal If E denote the operation emer 1 ie ee t= (1+ 5 ici Cask: ve. {ee TAGE 0 which may be symbolically written T= A= Ep) 2 Go ae where the sign of equality denotes asymptotic equivalence. Now R — = ( (1, +1,) dr, . e ° ° Cie) 0 eg where (ke I,) =| ea sinh ¢ cosh w+mt dt. | 0 If m is of the same order as z, and such that z—m is not of low order, these integrals are of the form treated above. Writing X=22 cosh v, M=Np, he il and denoting I, or I, by I, T= { e-AGinht Fwd |. |, (20) 0 Thus in the above notation, v =sinht + pt, One Vy == ae n™=0, pent) = 1, By help of these results it is readily proved that, if w=v,’, ee ovale 1 on oar an >) St jays ed Noe) ae Te | iL Leon 280 6 SS ee Lie ibe Hy(=) oe Ome) and so on, where w=1+ p, Aw = 22 cosh w+ m. Expansion of Bessel Functions of High Order. 703 Accordingly, ee at, eee Rw r2w2 rdw © re? Dw? ' Aw? ATWO bite which may obviously be expressed in the form BOR i lKor Oe One) oF aes 3! Bzam2 ve 5! com? £ 6! Q22dm! Bu et i 5622 88 | , 280 32 9° a Ozom®” 8! A22Qm*" 9! Anne © che Ww AW where D denotes the operation in brackets. Accordingly by (19), 22 * R= 7 | (1,+1,)dy iL hi aay Bi Le oh Wr aes 22 cosh y+ - i dy z 1 1 aie pf ‘5. cosh rat 9 ~ cosh +m $ dvp, since the integral obviously satisfies all necessary conditions for differentiation. The value of the integral is ae=pas as in (15), and thus Z R=2-{ 1+ <,D,Dj+ 4D.Ds'+ ~VD2Ds+ 5 D,Dy 5623 BNE bey fo) Uetdee here Rage } ul 8! Daa a ee nf 422 =m? ) 0 where D, =52) D, = ; te If 5-=—— = sin @, the second approximation becomes pes, R = sec a— <3 (cos ai sill: @) SCet oy iyi m( 2) 704 Dr. J. W. Nicholson on the Asymptotic Second form for the function R. The formula just proved suggests the existence of an asymptotic series of the form | ; ) RX he ip where w=(42?—m?)? and A,=1. Xd: Ns # y aAieg at ago Le ba i oe See Such a series may be obtained directly from the differential equation. Writing R=2cpw—q>tua® and 2e id 4 ; H b 4 2 SU] SPARS NY a DLL PO PEO Z- LIE exact scale, but the relative proportions as there given are approximate. The principle and arrangement is precisely the same as in the preliminary apparatus, except that all the various parts are made compact and self-contained. In describing the different parts of it I shall make use of the co) e e e same letters as before, so that their functions will be readily for Measuring Ionization. Ge) understocd by referring to the former description. The apparatus was constructed to fit in between the quadrants and the base of a Dolezalek eiectrometer. A represents a rectangular brass box, closed on all sides, and mounted so as to be free to revolve on the base B, its horizontal position being adjustable by means of the levelling screws. On top of this box is fastened the electrometer proper E, one pair of quadrants of which is connected to the electrode t, and the other, d, to the electrode v, and to earth. The electrodes ¢ and v serve as supports to the plate e, which forms the upper plate of the standard 8. The electrode v is insulated from the plate by a piece of ebonite. Below this plate is fastened the standard, insulated from the brass box by ebonite. The cover g of the standard can be moved out and in by means of the ebonite rod h, which runs through a bushing ‘k. The rod is graduated in millimetres, and “the position of the cover of the standard can be read at a glance. Contact between the piaie e and earth is made by means of the key K, which moves up and down in a brass bushing connected to the case A. This key is operated by the aid of a thread running over a small pulley. The testing-vessel X, as here shown, is for use chiefly with penetrating types of radiations, such as 8, y, and Rontgen rays, though it would serve admirably for measuring the excited activity due to radium, thorium, &c. It consists of a cylinder } connected to, and insulated from, the case by means of an ebonite block. The central electrode a passes through this block and is joined to the plate e. Between the rod a and the cylinder b is fastened a small guard-ring + connected to the case by a small screw running through fhe ebonite. Hlectrical contact with the cylinder b is made by means of the binding-post / which passes through the ebonite block. The whole testing-vessel is surrounded by another concentric cylinder n joined to the case. If desired, the testing-vessel can be quickly removed and the parallel-plate vessel substituted in its place. ‘The whole apparatus is so constructed that it can be readily taken apart if necessary. The potential necessary for the operation of the instrument is furnished by two sets of Volta piles, each consisting of 170 elements of zinc and copper disks joined together by moistened blotting-paper. ‘These sets are sealed up in glass tubes and fastened to the sides of the case, one set serving for the standard, and the other for the testing- vessel. The potential of these piles is quite sufficient for saturation with the standard used, being in the neighbourhood of 100 volts 720 Dr. S. J. Allen on a Null Instrument each. One of them is also sufficient for charging the needle of the electrometer. The movement of the needle is observed by means of a spot of light reflected from the concave mirror m onto a scale fastened to the case. ‘the whole apparatus is thus self-contained, and, by simply lowering the needle down onto the quadrants to protect it, can be moved from one place to another, and operated with- out any accessories. Jn making an experiment the case is earthed, thus electrically shielding all the working parts from static influences. It was found that the needle was perfectly steady in its movements, and a steady source of ionization could be balanced to one-tenth of a millimetre, which is about one-tenth of one per cent., though of course the accuracy of the instrument necessarily depends on the correctness of the calibration. I have not as yet had time to make a very exact cali- bration of the instrument, but the curve B in fig. 2 shows one which is correct to one or two per cent. In order to illustrate the working of the instrument, I will give very briefly the results of several well known experiments in radioactivity and Rontgen rays. EXPERIMENT I. Determination of the strength of a small quantity of impure radium bromide.—This experiment was performed with the preliminary apparatus, the radium being placed on the lower plate b of the testing-vessel X. The middle point of the battery was earthed, and the cover of the standard opened until on separating the quadrants from earth there was no movement of the needle, thus showing a balance of the instrument. ‘This balance-point was found to be at 13°8 millimetres on the scale s, which from the cali- bration curve A corresponds to 16 per cent. of that of the standard. The sensitiveness of the electrometer was about 0°80, which multiplied by the 16 percent. vives 12°8 divisions per sec. as the “rate of leak” which ought to be observed tor the standard, using the instrument in the ordinary “ rate of leak” method. This ought of course to be equal and opposite to the “rate of leak” of the ionization-vessel X observed in the same manner. A test of this latter, made by closing the standard and moving the contact m ton, gave a “ rate of leak”? of 12:5 divisions per second, which is in good agreement with that calculated from the balance- -point and the calibration curve The sensitiveness as here expressed represents the quantity by which the ordinates of the calibration curve have to 41 be multiplied in order to give the “rate of leak’’ of the standard. EXPERIMENT II. Balance-point and sersitiveness—In this experiment some uranium oxide was placed in the vessel X and the balance-point obtained for different sensitivenesses of the electrometer. The results expressed in Table I. show that the balance-point is practically independent of the sensi- tiveness of the electrometer. The observations were made on different days and not always under exactly the same conditions, which will account for any considerable variation of the balance-point. ~I for Measuring Ionization. TABLE I. Sensitiveness. Balance-point. |P.D. between plates. 0408 33'8 51 volts. “444 33'5 OT a 690 32°5 41 Ss; 690 338 ims 480 — (848 D2 es, 638 34°1 iy) Pe, 760 34:0 BZ 454 34:0 5 eas 454 26°8 cL Ree 840 34:3 5) an a 840 27°5 bly 220 346 ols 150 34:3 aly VE Experiment III. Decay-curve of the excited activity col- lected from the atmosphere-—In this experiment the active matter present in the atmosphere was collected on a copper wire about 300 feet long suspended 20 feet above the earth. The active deposit on the wire was rubbed off onto a piece of cloth and placed in the vessel X. Readings of the activity were made at different times by both the balarite and the “rate of leak”’ method, and the results are expressed in Table IT. An examination of these shows that the activity does not decay to half value in about 40 to 45 minutes, which is the usual rate, but is much longer, thus undoubtedly showing the presence of some thorium-excited activity as well. EXPERIMENT IV. Test of the penetrating power of Réntgen rays.—This experiment was made with the completed instru- ment, and will serve to illustrate its action. (22 Dr. 8S. J. Allen on a Null. Instrument TABLE IT. Sensitiveness 0°84. Balance Method. “Rate of Leak” Method. _ Time Balance- Intensity. Per | Time | Rate of Fer ‘ln mins. | point. cent. || in mins. Leak. cent. | | 0) 9-1 6-7 100 | ) | 6°66 100 | 54 a oll 46 |, 2 5:45 96 eso 6:7 ig) 27 22 3°90 69 i OS Oe Paley a9 2°34. 41 | 165 iS) | “o) 24 81 1:54 27 105 1:01 18 | 164 60 11 | | ! ; | Note.—-The first of these readings | | was taken about 5 minutes after the | first one by the balance method. The X-ray tube was placed about 88 ems. from the window of the testing-vessel, the axis of this being 45° to the plane of the target. ‘The tube was operated by a 10-inch induction- coil placed about a metre from the instrument. Under these conditions and without any further serena the needle of the electrometer was perfectly steady, and readings could be readily made of the ionization due to the X rays. The opening at the window had to be narrowed down to about 4 millimetres, so that a balance could be made with the present uranium standard. For strong X-ray tubes a much stronger standard would be more convenient. The readings for an absorption test of the X rays are shown in Table III. The results indicate at once the diversity of rays sent out by the tube; the soft rays for the first few layers beirfe cut down to 50 per cent. by about 2 millimetres of aluminium, while the harder kind are only eut down to half value by ¢ about 5 millimetres of iron. The small quantity of rays which penetrated through the case of the electrometer quickly discharged the needle, so that it was necessary to place a thick lead sereen in front of the instrument. For regular work with X rays it would probably be found convenient to use a fine phosphor-bronze suspension, and connect the needle through this permanently to the source of potential. However, as I have shown, a change in the for Measuring Lonization. 723 sensitiveness of the electrometer does not affect the accuracy of the reading. Tape IIT. XX yays: | Per cent. Per cent. oe Peo | et | Unaksorbed Unabsorbed ee : | t Sa Oe qa Rays. Rays. 0 94:0' | 89 a LOO Note.—In these | 1 layeraluminium.| 61:5 eer | 79 observations the Lahde 46°95 58 | 65 layers wereadded Bor 9 3 390 ol | 57 successively, the a ., pe 36°0 47 | a2 | one for brass in- Br, a 31:0 42 47 cluding all the Orns * ye Woe 37 aluminium. as » 20) 1°30 33 ees hy DLAss: LS rater ie 20 100 LLG Sai yopre 14:3 70 We) 39 20» 128 4-5 5-0 25 Ete 1)! 18 11-5 30 3°3 14 ONY ip = 4s HOS yy Mes 2:6 13 Thickness of each aluminium layer °050 centim. 25 5 iron pias 5 ” rs brass » “088 ,, y rays. 0 200° | 220 100 1 layer iron. | 19:4 21°0 95 3 eo? ” | 18:4 17:2 79 6 oe) ” il72il 14:0 64 de a 16:0 IL-5 52 Al) St 14-9 8:2 38 AOR uh 35 141 6:5 30 In Table III. are also shown some results with the y rays of 5 milligrams of pure radium bromide. A comparison of the penetrating power of the two types of rays shows that the softest y rays are about equal in penetrating power to the hardest X rays the tube was capable of giving. The above described instrument on account of being com- pact, portably accurate, and easily manipulated, may commend itself to those engaged in research in radioactivity, or other form of ionization, as a standard instrument. University of Cincinnati, June 1907. ) ede ty LXXII. On the Amount of Radium Emanation in the Atmosphere near the Earth’s Surface. By A. 8. Evz, M.A.* J T has been proved by Elster and Geitel that a negatively- = charged wire, exposed for a few hours in the air, receives a radioactive deposit similar in character to the quick-changing products of radium. Radium is known to be widely dis- tributed among the constituents of the earth’s crust. More- over, there is evidence that the emanation from the radium in the earth escapes into the atmosphere. Irom the emanation arise the active deposits of radium in the atmosphere. The radioactive changes in the air and soil account for the jonization of the air; and important electric and meteoro- logical effects result, the characters of which are at present imperfectly understood. It is, then, important to form an estimate of the amount of emanation in the atmosphere, expressed in terms of the quantity of radium required to keep the supply constant. Throughout this paper the cubic metre, and one-billionth (10-7) gram of pure radium will be adopted as units of measurement. By “pure”? radium is meant that which generates 110 gram-calories per hour per gram of radium. The first attempt to measure the amount of radium emana- tion in the atmosphere was made by the present writer T, by an indirect method, in the following manner :—On the ground in the Campus of McGill University was placed a large zine cylinder, of known volume, with closed ends. Along the axis was a wire, charged negatively to 10,000 volts, on which was collected the active deposit from the air in the cylinder. The activity of this deposit was measured by a gold-leaf electroscope, which was calibrated by means of the active deposit collected on a wire from the emanation obtained from a standard solution of radium of known strength. By this comparative method it was found that a cubic kilometre ot air contained the active deposit which could be obtained from the emanation arising from ‘14 gram of pure radium bromide. In other words, one cubic metre of air near the earth’s surface, at the place of measurement, appeared to contain the emanation from 82 x 10~” grams of pure radium. But there was no definite evidence of the existence of the emanation ; its presence was inferred, not proved. There was also an objection to the method. The active deposit collected on a charged wire fluctuates largely in magnitude ; * Communicated by the Author. < 107% In May 1907, with 660 grams of charcoal. 35x10- In July and August 1907, with 150 grams Ql elieheeoel Ree eyes Ware nee nr, Cana ITS MO These figures, whilst of the same order, are not in satis- factory agreement. I have great confidence in the last large result : every point has been carefully verified, and several months of practice permit of a remarkable degree of accuracy in the measurement of these small quantities—a degree of accuracy which can only be realized by those who have done practical work of this kind. It is, of course, possible that the amount of emanation in the atmosphere may vary in different seasons of the year. During July the weather was moderately warm (65°-70° F.), with S. and W. winds and sun. Every day or two there were thunderstorms with rain. The heavy rain may have forced emanation from the ground in larger quantities than in winter and spring. The active deposits on wires during July were not abnormal. The ionization was not large ; for I found n+ =425, n— = — 830 on a hazy day, n+ =400, n—=450 on a remarkably clear day. It is my intention to continue to measure the emanation in the atmosphere for some months to come, in order to ascertain if there is a variation between summer and winter values. A few notes are added which may save trouble to those who are making experiments similar to these. The emanation is given off from the charcoal in the latter part of the heating ; so that it is necessary to heat thoroughly. With emanation from 10-° or 10~-! gram of radium about 97 per cent. of the total emanation absorbed by the charcoal may be driven off by careful heating with two Bunsen burners. With stronger solutions, of the order 10-‘ gram, only 80 to 85 per cent. can be driven off in this manner by the first heating. Charcoal containing emanation can be partially de-emanated by passing a strong current of air through it. A general principle will be found to hold good in this case, as in most others, that whatever is easily absorbed is easily extracted, and conversely. I venture to recommend the last-described method for the measurement of emanation in the atmosphere. It is well to 732 Radium Emanation in Atmosphere near Earil’s Surface. use three tubes and to add the results obtained, as it tends to minimise the effect of small errors. Great care was taken to make absolutely certain that the emanation was not derived from radium impurities in the apparatus employed. A very slow current of air through the tubes containing charcoal gave nearly the same result as a “rest” experiment. Charcoal does not absorb well if choked with water-vapour. It seemed sufficient to bubble the air through two flasks of strong sulphuric acid. This acid was always renewed after a calibration experiment, in order to remove any radium which might be carried into the acid from the radioactive solution. 1 found that water and sulphuric acid absorbed but little of the emanation passing through them during these experiments. In any case, the method is comparative, and a slight absorption cannot, therefore, vitiate my results. Since Strutt found that one gram of rock, on the average, contained 1-4 x 10-™ gram of radium, and we have seen that 1 cubic metre of the air contains the emanation from about 81x10-” gram, we may conclude that 60 grams of rock would provide the radium emanation in 1 cb.m. of the atmo- sphere, if all the emanation escaped from the rocks. But Boltwood has shown that only 5 to 10 per cent. of the emanation escapes from a mineral ; so that by far the greater part of the emanation in rocks, even near the surface of the earth, must undergo transformation without passing into the air. Hence, if there enters the air 5 per cent. of the total emanation supplied by the rocks and soils extending to a depth of one or two metres, the supply would be sufficient to account for the emanation in the atmosphere extending to a height of 5 kilometres. But radium emanation certainly reaches the atmosphere. from considerable depths. Dr. Ruttan has kindly collected for me the natural gas and the mineral water from Caledonia Springs. The water, temperature 40° F., contains only 2°6X10-% gram of radium per litre; but 1 cb.m. of the gas contains the emanation from 114,000 x 10-” gram of radium,.or about a thousand times as much as a cubic metre of the atmosphere as measured at Montreal. This large output of radium emanation was detected owing to the fact. that the gases bubbled through water. In other cases it might escape to no less extent without detection, no water being present. It may be observed that in the present state of our knowledgs tka amount of radium in the earth near the Production and Origin of Radium. 733 surface; the amount of emanation in the atmosphere; the resulting active deposit ; the penetrating radiation due to all these ; the ionization in the atmosphere: all are of the correct order of magnitude, so that they may be correlated. Result—Vhe emanation in the atmosphere is absorbed by coconut-charcoal: its presence can be proved and its magnitude determined. Four measurements have been made at Montreal, and the results are given in terms of the amount of radium required to maintain the supply per cubic metre constant. The smallest value obtained was 24 x 10-}, the largest 127 x 10-¥. The probable average value is 80x10-'. The amount of emanation is of the correct order to account for the active deposits of radium C, which may be collected on negatively- charged wires from the atmosphere. Now that Professor Ruthertord has left McGill University, I wish to state my indebtedness to him. If my papers have had any merit, it may be attributed, without exaggeration, to his influence or inspiration, and for these I am grateful. McGill University, Montreal, August 1907. LXXITT. The Production and Origin of Radium. By E. RUTHERFORD, /.R.S., Professor of Physics, University of Manchester™. Sul: HE present point of view of regarding radium as a substance which is undergoing slow transforma- tion was first put forward definitely by Rutherford and Soddy in the paper entitled “ Radioactive Change” (Phil. Mag. May 19038, p. 590) in the following terms :—“ In the case of radium, however, the same amount (viz. about 1 milligram) must be changing per gram per year. The ‘life’ of the radium cannot in consequence be more than a few thousand years on this minimum estimate, based on the assumption that each particle produces one ray at each change. ... So that it appears certain that the radium present in a mineral has not been in existence as long as the mineral itself, but is being continuously produced by radioactive change.”’ On this theory, the parent substance which produces radium must always be present in minerals containing radium. Uranium from the first appeared to be the most probable -* Communicated by the Author, having been read before the British Association, Leicester, August 1907. Previous accounts of the results were given in letters to ‘ Nature, Jan. 17 and June 6, 1907. fiat Prof. E. Rutherford: on the parent, since it possessed a life long compared with radium and was always found associated with it. There were two obvious methods of attack to throw light upon this question, one direct and the other indirect. The first consisted in an examination to see whether in course of time radium ap- peared in a solution of uranium initiaJly freed from radium. The second depended upon an examination of the relative amount of radium and uranium in ‘radioactive minerals. According to theory, if uranium is the parent of radium, the ratio of the amount of radium in any mineral to that of uranium should be constant. The constancy of this ratio has been completely substantiated by the independent work of Boltwood* , Strutt, and McCoy {t; and there can be no doubt that anentim and radium are genetically connected. Rutherford and Boltwood§ have found that for every gram of uranium in a mineral, there is present 3°8 x 10—-* gram of radium. The question of the growth of radium in a uranium solu- tion was first attacked ‘by Soddy ||, and later by Boltwood {. Without entering into the details of these important investi- gations, 1t suffices to say that, in carefuily purified uranium solutions ,no growth of vad has been observed, over the space of the few years that observations have been in progress. It radium is produced at all, it is certainly produced at less than 1/1000 of the rate to be expected theoretically. This result is not necessarily inconsistent with the view that radium is a transformation product of uranium, for the absence of observable growth of radium in a limited time is to be expected, if one or more products of slow transformation exist between uranium and radium. In the meantime, Boltwood** bad approached the problem from a different direction. By aspecial method, the actinium was separated from a kilogram of carnotite. A solution of this actinium, initially containing very little radium, was placed aside and examined 120 days afterwards. A notable increase in the amount of radium was observed. In addition, the rate of growth in this interval was about that to be ex- pected if radium were half transformed in about 2000 years a result in conformity with calculations of the probable life of radium. The work of Boltwood marks a definite and ** Boltwood, Phil. Mag. April 1905. * Strutt, Proc. Roy. Soc. March 2, 1905. t McCoy, Ber. d. D. Chem. Ges. No. 11, p. 2641, 1905. § Rutherford and Boltwood, Amer. Journ. Sci. July 1906. || Soddy, Phil. Mag. June 1905, Aug. 1907. € Boltwood, Amer. Journ. Sci. Sept. 1905. ** Boltwood, ‘ Nature,’ Nov. 15, 1906. Production and Origin of Radium. . tao important stage in the attack on this problem, for it clearly shows that radium, as theory predicted, is produced from another substance and that this parent substance is normally present with actinium. Boltwood concluded that actinium was the direct parent of radium and was itseif an intermediate product between uranium and radium. This conclusion was strongly sup- ported by his observation that the amount of actinium in minerals, like the amount of radium, was proportional to the amount of uranium. Since actinium has probably a lite comparable with that of radium, such a conclusion is con- sistent with the observed absence of growth of radium in uranium solutions, for the uranium must first form a con- siderable quantity of actinium before the transformation product of the latter, viz. radium, could be detected in the solution. This question will be discussed later in the paper after the consideration of further experimental results. It will be seen that the problem is more complicated than at first appeared. § 2. Old Experiments. It may be of interest to give a brief account of some ex- periments commenced by myself in 1904 to determine whether radium was continuously produced from actinium. A pre liminary account of this work was given in the Bakerian Lecture (Phil. Trans. A, p. 218, 1904). Two grams of an active preparation, of activity about 250 times that of uranium, obtained trom Giesel, were taken and dissolved in acid. The initial content of radium was determined by the emanation method, and the greater part of it then removed by succes- sive precipitations in the solution of small quantities of barium as sulphate. Measurements were then made of the amount of radium in this solution at intervals over a space of three months, but with no certain evidence of the growth of radium. The amount of radium was estimated by the ema- nation method. The radium emanation, which was allowed to collect in the solution for a known interval, was removed into a large electroscope by aspirating a considerable amount of air through the solution. Later work of Boltwood has shown that this aspiration method is unreliable tor an accu- rate determination of the amount of radium present, but it no doubt serves for comparative measurements under identical conditions. In the light of later knowledge, the methed employed for the separation of the radium present initially in the solution 736 : Prot’ Hy Ruthertord on the was very unsuitable for several reasons. A trace of sul- phuric acid remaining in the solution after the removal of the barium might possibly precipitate the radium as sulphate a form in which it would be very unlikely to release all its emanation by aspiration of the solution. After three months’ observations, this solution was put aside with the intention of testing its radium content at intervals; but the pressure of other work and the recognition of the danger of contaminating the solution in a laboratory in which a large quantity of radium was in use, led to a postponement of further tests for a period of over two and a half years. On the appearance of Boltwood’s paper I imme- diately examined this solution to see whether there had been a growth of radium in this long interval. ai) e112. For the case of a cloud-covered earth the data are very uncertain. Lowell takes t=0:2 of 0°42=0-084, assuming that the atmosphere has already reflected and absorbed 0°58 before the cloud is reached, surely an overestimate, since the cloud-surface is in the higher air. Let us guess that Evaluating the Surfuce- Temperatures of the Planets. 753 t=0°1. The absorption without cloud is according to Lowell about 0°3. With cloud much is reflected back withont reaching the lower and more absorbing regions. Let us guess that a=0°2. Of the radiation from the surface we may suppose perhaps that 0°2 passes through, that 0 7 is reflected, and that 0°l is absorbed. Of the 0:2 passing we may suppose that 0:1 is absorbed and 0-1 goes into space. Mien. == 07.1 and a,=0°2. | With these values we get for the different values of 1 (a) one (b) OS = 1-08: (c) ee These guesses, then, make the temperature under a cloudy sky at least as great as under a clear sky. But this is certainly not true in common experience, where, however, we may have clouds accompanied by cold winds and no approach to the steady state here assumed. The results merely serve to show that with certain absorptions and transmissions clouds might actually raise the surface- temperature, and that for the present it is better to neglect them. , Mars.—Ilf we apply Lowell’s data for Mars we have t=0°64, and a=0°40 x 0°65 =0°26, t;=0°6 and a,=0°4, since R is dark radiation. With these values we get for the different values of n CA ON Cigy Marla dy: Wenge 3 (a) F=099; (DG =102; (9) g=110 Comparison of the Earth and Mars.—WLet us take the temperature of the Harthas 17°C. or 290°A. If it were removed to the distance of Mars its temperature would be inversely as the square root of the distance, which is 1°524 that of the Earth or 290/1:235 = 235°. With the different values of x the temperature of Mars should be 99 (a) 235x Gg = 2tT? A. or —26°C., (b) 235 x ag =e? A. or —31°C.,, (OV 2300x te = 231° A. or —42°C. Of course the data are very uncertain and the formula used is only an approximation. But with these data it is 754 Prot. J. H. Poynting on Prof: Lowell’s Method for hard to see how the temperature of Mars can be raised to anything like the value obtained by Professor Lowell. Perhaps the data are quite wrong. It is conceivable that Mars has a quite peculiar atmosphere practically opaque to radiations from the cold surface. Those who believe that there is good evidence for the existence of intelligent beings on that planet, should find no difticnlty in supposing that they have been sufficiently intelligent to cover the planet with a glass roof or its equivalent. Then we might easily have t+ =0°77 and t,+ - =0°5, and then the temperature might be raised to 281° A. or 8° C. Indeed, if the glass were of such kind as to transmit solar radiation, and if it were quite opaque to dark radiation while still reflecting a con- siderable proportion, the temperature might easily be raised far above this. oe An Attempt to represent the Effect of Day and Night on the Temperature of the Harth. The “greenhouse” formula, which has been used in the foregoing discussion, would hold only if all the conditions were steady. But in reality the alternations of day and night prevent a steady state, and we can only hope that the neglect of these alternations does not greatly affect the ratios of the temperatures found for different planets or for different elevations on the same planet. I shall now attempt to represent the effect of the diurnal variation in the supply of solar heat to the Earth, or rather to an abstract Earth. or even if we could represent the actual conditions we should obtain differential equations so complicated that they would be useless for practical purposes. | To simplify matters, let us suppose that we are dealing with the equatorial region of the earth at the equinox, that the air is still, that the surface is solid and black, and that the sky is clear. The temperature of the air except near the surface can | change but little during 24 hours. For over each square i centimetre at sea-level we have 1000 gms. of air with specific heat 0°2375, and therefore with heat capacity 237°5. Con- | sider a band of the atmosphere | cm. wide round the equator. A stream of solar radiation of length equal to the diameter 2r of the earth enters a band. of air of length equal to half the circumference. If the solar constant is 3 the ayerage Evaluating the Surface- Temperatures of the Planets. 755 27s 28 a8 energy entering a sq. cm. column is on emg cal./min. Then in 12 hours 1375 cal. enter on the average, and if this heat were all absorbed and retained it would raise the temperature on the average about 1375/237:5=5°'8 C. As the absorption is only partial and as radiation takes place from the air, the rise cannot really average nearly as much as this. Again, consider the radiation during the twelve hours of night. If the air were a black body and of temperature 300° A., and these are absurdly exaggerated estimates of its radiating power and of its average temperature, it would only radiate about 1:2 cal./min. per sq. cm. column from its two surfaces, or 864 calories in the twelve hours, and neglecting the radiation from the ground the temperature would only fall about 864/237°5 or 3°°6 C. Obviously, then, the air as a whole cannot undergo much variation in tempe- rature as day alternates with night. It is indeed a flywheel storing the energy of many diurnal revolutions. We may, then, in a rough estimate consider that its temperature and therefore its radiation remain constant during the 24 hours. If the total radiation trom a sq. cm. column per second is A, there will be a stream D downwards and U upwards where D+U=A. We can find an expression for A by equating it to the average absorption. Considering an equatorial band 1 em. wide, the average energy entering it per sq. em. in the 24 hours is ip Let the average amount a é é absorbed be — The value of @ at sea-level varies for Tv e clear sky from perhaps 0°3 with tle. zenith sun to very nearly 1 with the setting sun. Let the average radiation from the surface during the 24 hours be R, of which ak is absurbed by the atmosphere. Then neglecting conduction through the air, the constant temperature assumption gives us as ; A =i +a,R. T : leis : If a fraction — is radiated downwards Tie as aR D =— — + aaah ni n The actual surface temperature depends not only on radia- tion but also on conduction both by ground and air. But: we shall neglect this-conduction and shall suppose that the: 756 Prof. J. H. Poynting on Prof: Lowell’s Method for surface has reached an equilibrium between receipt and ex- penditure of radiation. This is a condition to which the surface tends at or soon after noon by day and before dawn at night. We shall suppose that the low temperature radia- tion trom the surface is either transmitted or absorbed, so that, using the previous notation, ijta,;=1 and 7,=0. Tf Rg is the equilibrium surface radiation reached we suppose about noon See cles R= 4.2 NTT re If R, is the equilibrium surface radiation in the later part of the night we have to omit tS and Roe NT n > To proceed further, we must express R in terms of 8, We can only do this by some assumption. Probably it is not very far from the truth to assume that R=4(R,4+R,), and we shall take this value. It gives us t a — 2° nr ees (by and substituting in the values of day and night radiations we get t a a, 2° wae ( semen R/S = (an seta Mn © a been 7 t a ( Ze ean R/S = — + a, ——— i a ) iL meal n Though these formule are only obtained by making large assumptions, and by neglecting important considerations, they nevertheless show the tendency of the day and night HMvaluating the Surface- Temperatures of the Planets. 707 effect, and it is worth while to apply them to the Harth, taking the best data at our command. At the surface let us take t0°42 and a,-=0°5 as before. For @ we have no trustworthy observations, and I doubt whether a calculation from Langley’ s al eneitete is of any more value than an estimate. Since a varies from perhaps about 0°3. to 1, let us take @=0°628 or 27/10, a value simplifying arithmetic. At the level of Camp Whitney 3550 metres above sea- level, with barometer about 500 mm., and therefore with about 4 of the atmosphere below it, fas may take £=0°6 and G0: ii For @ we must take a value much smaller than that at sea-level. Since the most absorbing third of the atmosphere is below, I do not think it is far wrong to take a as having half the ale at the lower level, and [ therefore put 4= "314, But I have also examined the consequences of putting it equal to 0419, 2. e. 2 of its value at the lower level, and the results are given below to show how much the figures are affected by the variation in the value taken. We have no data for nm. I have therefore calculated the values of Rz and R, in terms of S for successive values of n equal to 1, 3, 4, $,2; corresponding to D equal to A, # A, 3 A, 2 A, and 4 A respectively. In the following tables the values of R,/S and ‘R,,/S are given, and also the mean R/S=4(Rz+R,)S. Then foliow the ratios of the day and night temperatures, 0, and 0, to the temperature @ of a black surface radiating S, and the mean value 6/0. The last column gives the range 0,—@, on the supposition that @=300° A. TABLE I[..- At sea-level. ¢=0°42, a,=0°5, d=0-628. | . Range m. | D/A. | Ra/S..| Rn/S.| BR. | Oa/@. | O@n/@.| 9/8..| about 300° A 1 Mos an ct OsemieLoulocss | 0.05) lm acly 5/4 | 4/5 | 0:83 | 0-41 | 0-62 | 0-95 | 080 | 088 | 51° 4/3 | 3/4 | 079 | 0:37 | 058 | 0:94 | 0-78 | 086 | 56° 3/2 | 2/3 | 0472 | 0:30 | 051 | 092 | ov4 | 0°83 | @5° 2 | 1/2 | 062 | 0:20 | 0-41 | 089 | 067 | 078 | 95° Phil. Mag. 8. 6. Vol. 14. No. 84. Dec. 1907. 3B 758 Prof. J. H. Poynting on Prof: Lowell’s Method for Tas_e II. At 3550 m. above sea-level. Barometer 500 mm. i= 0:6, Gi—0 4 a— 07a n. | D/A. | Ra/S.| Rr/S.| BR. | @a/0. | On/@.| 0/0. | about ff ff tf | 1 I 0971 )0:37 (0:67) 1 90'997 0:78 eee ale d/t | 4/5 | 086 | 0:26 | 0-56 | 096 | O71 | 0-84 89° 4/3 | 3/4 | 0°84 | 0°24 | 054 | 0-96 | 0°70 | 0:83 94° 3/2 | 2/3 | 0°80 | 0:20 | 050 | 0:95 | 0°67 | 081 100° Z 1/2 | O74 | O14 | 0-44 | 0:93 | O61 | O77 | 125° TasuE ITI. At the level of Table II. and with t=0°6, a,=0°4, but with 4=0°419=2/3 of 0°628. at a Range nm. | D/A. | Ra/S.| Rn/S.| Re | 6a/0. | On/0. | 0/8. | about 300° i 1 | 1-02 | 0-42" | O42 | or | ost) oon eee 5/4 | 4/5 | 0:90 | 0:30 | 0-60 | 0:97 | 0-74 | 0-86 | 80° 4/3 | 8/4 | 087 | 0:27 | 057 | 0-97 | 0-72 | 0-85 | 88° 3/2 | 2/3 | 0:83 | 0-23 | 053 | 0-95 | 0°69 | 0:82 | 95° 2 | 1/2 | 076 | 0-16 | 0-46 | 0-93 | 063 | 0-75 | 120° The third table is only given to show that the change in the value of @ does not greatly affect the results. The value of a@ of Table Il. is much more reasonable if that of Table I. is near the truth. We need, therefore, only compare the results given in the first two iiblest If we take the same values of n in each table the value of R is less at the higher level than at the lower in every case except that in which n has the extreme and probably inad- missible value of 2. The value of @ is less at the higher level in every case. But it appears most probable that 1/n or D/A is greater at the lower level than at the higher. For consider a thin layer of air at sea-level. It is r- diating equally up and down, but of the half going upwards a con- siderable fraction ill be intercepted by ‘the superin- cumbent and strongly absorbing layers. Now consider a Wealuating the Surface- Temperatures of the Planets. 799 thin layer close to the surface at the higher level. It, tvo, radiates half up and half down. But of the half going up- wards a less fraction will be intercepted since the superin- cumbent Jayers are now less absorbing. Thus D/A will be greater at the lower than at the higher !evel*. We should, therefore, compare the results for any value of D/A in Table I. with the results in Table II. for a somewhat lower value. We may exclude the extreme cases of n=2 and n=], as the true value is certainly between these, and confine our examination to intermediate values. Suppose, for example, that D/A=4/5 at the lower level, while it is 3/4 at the upper level. Then 0/9=0-88 from Table I. at the lower, while 6/0=0°83 from Table II. at the upper level. Or if D/A=#? at the lower level, while it is 2 at the upper level, 6/0=0°86 below, while 6/@=0°81 above. Or in each case the mean temperature is higher at sea-level by about 5 in 87 or by about 17° in 300°. It is to be observed that the lower mean temperature at a higher level must hold good if the higher level is so much higher that there is practically no atmosphere above. For then t=1 and a,=0, so that Rz=S and R,=0. Therefore 62/9=1 and 0,/9=0 and 6/@=4. The lower mean temperature of elevated parts of the earth’s surface is a well established fact. Perhaps if it were only observed in the case of mountain peaks it might be ascribed to the cold air blowing against them. The fall of temperature in free air as we go upwards tends towards that given by convective equilibrium, though recent observations show that it is not so great as that given by the adiabatic law. ‘Thus for a rise of 3500 metres the adiabatic law would give a fall of about 32° C. if the sea-level temperature were 300° A.; whereas the observations of Teisserene de Bort at Trappes show a mean annual fall of about 16° C. for this rise (Lineyc. Brit. xxx. Meteorology, p. 695). A continual blast of air thus cooled might of course reduce the tempera- ture on the mountain peaks, even if radiation did not tend to any such reduction. But we can hardly account in this way for the equally well established lower temperature of elevated continental plateaus. According to Abbe (loe. cit. * Another consideration leading to the same conclusion is that the atmosphere acts like a plate with its lower surface much warmer than its upper. When we only have the part above an elevated region the difference of temperature between the surfaces is much less than for the whole air, and the radiations up and down are more nearly equal. 3H 2 760 Prof. J. ©. McLennan on the p. 694) 0°-5 C. must be subtracted from sea-level tempera- ture for every 100 metres general elevation of the land surface or about 18° for an elevation of 3500 metres, and this fall may be ascribed to radiation in some such way as that here set forth. It the atmosphere of Mars is comparable with our own _ atmosphere at high levels, and if the effect is of the same general character in the two cases, it appears probable that the surface temperature of Mars is actually lower by many degrees than that which the surface of the Harth would have at the same distance from the Sun. LXXV. On the Radioactivity of Lead and other Metals. By J.C. McLennan, Ph.D., Professor of Physics, University of Toronto”. I. The Relative Activities of Different Metals. iG a paper in the Phil. Mag. of September 1906, Eve states that while investigating the natural ionization of air confined in vessels made of different metals, he found that 24 ions per ¢.c. were generatea per sec. when the receivers were made of copper, zinc, iron, and tinned iron, while 96 ions per c.c. were regularly produced in air per second when the confining vessels were made of lead. The high conductivity of air contained in lead vessels has been frequently noted by other observers ; and from Hve’s results it would appear that lead either contains some active impurity from which other metals are entirely free or else it possesses an intrinsic radiation very much stronger than that exhibited by other metals. The view that lead contains an active impurity is supported by a description in the Phys. Zeit. of November 1906, of some experiments by Elster and Geitel, in which they suc- ceeded in extracting from lead oxide small quantities of an active substance which from its characteristics they were inclined to think was Radium F. In this paper they state that they were unable to obtain any active emanation from the materials treated, and on this account they suggest that possibly the source of the Radium F can be traced to the presence of Radium D in the lead. Since the decay period for Radium D is forty years it would follow, if the high activity of lead is due to the pre- sence of this radium product, that very old lead should * Communicated by Prof. J. J. Thomson, F.R.5. bie ell A v5 \s Radioactivity of Lead and other Metals. 761 exhibit an activity less intense than that which it emitted when freshly mined. Hye does not appear to have tested many different samples of lead, but if the explanation offered by Elster and Geitel of the high activity of lead be correct, one should expect to find that samples of lead selected at random from different localities would exhibit widely differing degrees of activity. Such a difference in the radioactivity of lead obtained from different sources was recently observed by the writer while making some measurements on the conductivity of air contained in metal vessels. In these experiments the metals examined were made up into cylinders 60 cm. long and 24 cm. in diameter, and from measurements with a sensitive quadrant electrometer on the saturation current through the air which they contained, their activities were deduced. The experiments were conducted in a room free from any artificial contamination; and in carrying them out, the cylinders were first carefully cleaned w ith glass paper and then thoroughly washed out. with hydrochloric acid. water, ammonia, and ethyl alcohol, and finally, before making the measurements, air filtered through glass: and cotton-wool was blown through each of them for fifteen or twenty minutes, The results obtained with the different metals examined are contained in Table I. (p. 762). From this table it will be seen that the values of “gq” for aluminium and zine are somewhat less than those found by _Eve for this constant with the same metals. They are, how- ever, in good agreement with H. L. Cooke’s corrected value “ q¢”? =13°6 given by Eve for air confined in a well-cleaned brass vessel. The values found for ‘‘g” in the experiments with lead cylinders, as will be seen from the table, range from 23 to 160 ions per c.c. per second. The lowest value, 23, was obtained with the lead which had been in the laboratory between twenty-five and thirty years, and had probably been avery much longer time away from the mine. With the cylinder No. 4, which was made from an old drain-pipe, the value of ‘g >’ was found to be 78, a somewhat higher value than than obtained with No. 1. Although both of these cylinders were made of comparatively old lead, it is highly probable that No. 4, from the nature of its use, had become contaminated with some active substance. It may possibly too have possessed a higher activity than No. 1 when originally mined. 762 Prof. J. C. McLennan on the TABLE J. J GCS | | ae ee | Thickness | Average No. | | No. | Tenth GO em. | o Sheet | of a ors aes Remarks. | |Diameter 24 em,). 127 ™™- ecuerabe | ‘| per second. i Wea pegie i ied "Fees ce cee 185 | 23 | This sample was taken _ from a sheet of lead: | which had been used as | _ a lining in a case in- stalled in the Univer-) sity over twenty-eight! | | years ago. ieee Pree Hieacleist eee: ee Os tn 160 Commercial English) | sheet lead obtained! from the lead works at | | Toronto. | Woreeee: Meade rece: | 145 | 37 Commercial English. | | sheet lead _ selected’ | | | from a different ship-| | | ; ment from No. 2. | eA. oe Wend), tc... Pe oriclsne m 78 This sample was ob-, | | tained from a_ sheet | rolled from an old pipe which had been used as a drain for 20 or 30 years, and wasafter- | | | | wards melted down. (Ros tete ieadiaetes. one 180 TER 34 | Rolled from a pig of | | lead recently received, | from the smelter at! | | | | | Trail, B.C. Canada. Gace. foead! Reece ee 1-80 5d Rolled from English pig lead; Quirk and | Bartons. hie aA ead yevecn cs | 1502") 61 _Rolled from English) - | | | pig lead. Cookson’s. {xoRaneas PRIN etc aeae 1°62. 15 _ Commercial sheet zinc. Ores Aluminium... “41 15 Commercial sheet alu- | | minium. | t With cylinder No. 5 the value obtained for “gq” was 34 ions perc.c. per second. This lead, we have reason to believe, was mined not more than two or three years ago, and under the circumstances might have been expected to show a much higher activity. Its activity, however, was practically the same as that of No. 3, which was selected at random from a commercial sheet of lead which probably had been on the market for some years. Cylinders No. 6 and No. 7 possessed a moderate activity compared with the others of the same metal. The number of ions per c.c. generated in air per second with them being 59 and 61 respectively. With cylinder No. 2 the greatest ionization was obtained, the value of **q’’ in this case being 160 ions per c.c. per second. Radioactivity of Lead and other Metals. 763 This cylinder was treated precisely the same as the others, but on account of its high activity special measurements were made with it in order to investigate more fully the character of the radiation which it emitted. Measurements on the radiation from this cylinder showed it to be in great measure an easily absorbed one. When aluminium linings 0°73 mm. thick were inserted in cylinders No. 1, No. 2, and No. 38, and measurements made on their saturation currents, the values of ‘‘g” were found to be 12:0, 13°3, and 14:4 respectively. These numbers, it will be seen, are slightly lower than those found for aluminium alone, which is exactly as one would expect owing to the absorption of the penetrating rays from the earth by the lead. | The value for “g” 13°3 found for No. 2 is slightly greater than that ““g”=12 given by No. 1, although this lead cylinder was 2°25 mm. thick, while No. 1 was only 1°85. This would seem to indicate the existence of a penetrating type of radiation issuing from No. 2 which was absent from cylinder No. 1. A second series of measurements was made with cylinder No. 2 to investigate the distribution of the substance which was the cause of its high activity. Readings were taken on the saturation current first with the lead cylinder entirely unscreened, then with one half of the cylindrical surface screened internally with aluminium 0°73 mm. thick, and finally with the whole of the inner cylindrical surface covered with the aluminium. The values are given in Table Il., and from them it will fasin UT. | | . Tonization Weowense Ta | Peel Cylinder No. 2. (Arbitrary nieuae | ; Seale.) Seale) y eel we cesncitee Completely — un- 54°6 SCREENCCA er Famer te aa .ts | | 99.6 Deda cc tease One-half inner 32°4 | | cylindrical sur- | | | TGS SCHESINECl Ny nil Rann edness | 22°57 | , | | Sint res oa ticaieria All inner cyJin- 9:87 Me | drical surface ~ screened. be seen that the decrease in conductivity was the same for each half of the cylindrical surface. This goes to show that the radioactive impurity in the lead was uniformly 764 Prof. J. C. McLennan on the distributed over its surface. It was also very probably distributed in a uniform manner throughout the mass of the cylinder, as repeated scourings with glass-paper failed to remove it. In this connexion it is of interest to note that, during the last six months, measurements have been repeatedly made on the conductivity of air confined in this cylinder, but during that period no indication of a falling off in the intensity of the radiation from it has been observed. : II. On the Ionization produced in Metallic Receivers by the Secondary Rays excited by the Gamma Rays from Radium. From the foregoing results it is abundantly evident that the high activity of lead, which has from time to time been recorded by a number of observers, cannot be ascribed to any intrinsic property ot the metal, ‘but must be connected with the existence in it, in stot: varying with different specimens, of some foreign body of considerable activity. It is known that part of the ionization in a gas confined in metallic vessels must be due to the penetrating radiation emitted by the earth, and part to the secondary rays excited in the substance of the metallic receivers by these penetrating rays. From the results given above, part must also be due, in some cases at least, to active impurities present in the metal. The extremely low value found for the ionization with the lead in cylinder No. 1, coupled with the value for “q” obtained with zine and aluminium receivers, suggests the possibility that the materials out of which thece vessels were made were entirely or very largely free from active impurities, and that the differences observed in the ionizations were due to differences in the intensities of the secondary radiations from the different metals. It is known that the secondary radiation increases with the atomic weight of the metal composing the radiating surface, and it seemed to the writer possible that the difference in the values of “gq” found for lead and aluminium, namely 23 and 15 ions per e.c. per second, might be accounted for entirely on this ground. - With the object of investigating this point an aluminium cylinder was prepared from a thin sheet of the metal 0°41 mm. in thickness, and a series of accurate measurements made on the saturation current through the air which it contained. A small quantity of radium bromide was enclosed in a block of lead about 3 cms. in thickness, and placed at a distance of about one metre from the aluminium cylinder. The saturation current in the aluminium cylinder was again aie Radioactivity of Lead and other Metals. 765 measured, and the difference between its value and that due to the natural conductivity of the air was noted, and recorded as being due to the gamma rays from the radium bromide together with the secondary rays produced by this radiation. Each of the first eight cylinders referred to in Table I. was then used in turn as a screen between the lead block containing the radium and the testing cylinder, and the cor- responding saturation current measured. The differences between these readings and that taken with the radium before the screens were inserted, were taken as a measure of the absorption of the gamma rays by the respective cylinders. From these differences, combined with the lonization produced by the gamma rays impinging directly on the testing cylinder, the absorptive power of each of the cylinders was calculated as a percentage of the intensity of the penetrating rays issuing from the lead block, and these are given in Table III. The absorption of the gamma rays by two sheets of aluminium 0°73 mm. and 1°46 mm. in thick- ness was also determined in the same manner, and these are recorded, together with the others, as Nos. 9 and 10 in Table III. TABLE ITT. BERCC RAE | No. of ions pro- Cylinder} Material. Percentage b fj a duced by natural No. in mm, Reece me oy ionization. | ag ad oe (See ‘lable I.) dL egies Wendy) ene4.. 1°85 15°36 23 DN fae: ee ae 2°25 16°29 160 Opriaatd eh Geet bee 1:45 9°36 37 Soi ae Wee eee 1:85 11:2 78 5) ate SO aE 1:80 12 92 34 Great: Le OAS Ie eee 1:80 10:12 ay) Hood. SHINY Havzak es 1:80 15°23 61 Once s: ZiT ee ae 162 4°62 15 rosa: Aluminiuin 1-43 92 LOW ees. Bal vatscats« 73 “46 \ A set of measurements was next made on the saturation currents in each of the first three cylinders given in Tables I. and III. ‘These were taken (a) with the air under natural ionization; (6) with the cylinder lined with aluminium, but otherwise the same as in (a); (¢) with the radium bromide - in the lead block mentioned andes at a distance of 1 metre from the unlined cylinders; and (d) with all the conditions the same as in ()) excepting that the cylinders were lined with the sheet aluminium. 766 Prof. J. C. McLennan on the Assuming that this lining completely absorbed the secon- dary radiation from the lead walls of the vessels, which is probable as the secondary rays from lead are easily absorbed, and neglecting the absorption of the gamma rays by the aluminium lining, since from the numbers given in Table III. it must necessarily have been less than one half of one per cent., it follows that the difference between the readings “¢” and “a” represents the ionization produced in the unlined lead cylinder by the radium; while the difference between the readings “d” and “ 6” represents the ionization produced in the lined cylinder by the same cause. The excess of this first difference over the second may then be taken without appreciable error as a measure of the excess of the ionization produced by the secondary rays in the respec- tive cylinders when unlined over that produced by the secondary rays with the lining inserted. In other words, it may be taken as proportional to the difference between the ionizing powers, in so far as the air in the cylinders is con- cerned, of the secondary rays excited in lead and aluminium by the penetrating rays which entered the cylinders. Or taking Ij, and I,s as proportional to the ionizations produced in one of the cylinders by the secondary rays excited in lead and aluminium respectively by the gamma rays which entered it, we have Tj; —Ius= (Reading “‘c” — Reading “a”’) = (Reading Oe — Reading “ch 3 ; (i.) Further, it is known from an investigation by Eve* that — the ionizing power of the secondary rays excited in aluminium by a gamma radiation is 28°6 per cent. of that possessed by the secondary rays excited in lead by the same rays. We have then this equation 100 es Ie = 28:6 ° | ae > ° . . ° (il. ) Again, denoting by I, the ionization produced in the lead cylinder under examination by the gamma rays from the radium alone, we have I, +1i,=The difference between readings “c” and “a” with this cylinder. 02 auie) From equations (i.), (ii.), and (iii.) it is possible then to * Inve, Phil. Mag. Dec. 1904. Radioactivity of Lead and other Metals. 767 calculate Ip, I,,, and I,,;, and so deduce a relation between the ionizations produced in a given lead cylinder by the gamma rays which enter it and by the secondary rays excited in the walls of the vessel by these penetrating rays. The averages of a great many pee arements made in this way with the cylinders Nos. 1, 2, and 3 are given in TABLE [V.. | | Combined ioni- | Corainedic eee | "Natural ioni- | Natural ioni-) zations in un- ps Fe AS ee eR te Cylinder zation (Arbi- | zation (Arbi- lined lead eylin- lined eal Seine alae No. trary Scale). | trary Scaie).) der (Arbitrary Nie ae 1 | Scale). | (Arbitrary Scale), | Reading ‘“‘a.”| Reading ‘).”| Reading “ec.” Reading “ d.” | 2 dae 4-02 97°75 5352 | PMO) Bh. | 53-94 4-48 142-44 43:87 3) ee | 12 4:67 113 D797 Table IV.; and in Table V. the numbers corresponding to the reduced vaiues of these observations are recorded. TABLE V. Column 1.) Column 2. | Column 3. | Column 4. | Column 5. | Column 6.} Coluwn 7. | | SCA « SO S a. iuentes Ouicite x 2) a ena les seCueruscky we oS ae (ee eas ei mess |Haeo7 as oS aoa 8 w Es Oy : 3 Seas = =| ee Oa F a os o eee Be oe oo 2 2.5 = + >| 0 S 4 | F a= LTS) [as] Eat oe] : eo ieee Ratio Ratio See S 52 Cylinder |c SRS elo + RBS I T SEs Se : = eH So|e a ouien ls as ae Sse ae s No = 3 OW |= pe = aa) ~ Qwe ene eS ie Sime eels arial) die fee > | ss Lome) a A -_— & = aS Pa ele 2 PE « (calculated) oaleults) easel ah. Scie CH an 8 eons Sas Sic Ses ose EE = S 2658 S 2657) 23 e.5 2g S CS = Ss S| eS — pal aa ~S = 0 no) See 2Sse aes Sa Be S's dae. bake 90°05 49°5 1-74 “49 33°05 390 100 ( ga-ga X 3305, =300 Daa ses? 88°50 44°39 Dro 66 26°7 32°0 OMEEE sie das 101-00 53°3 1:95 910) | . O42 38:0 | | Mean |... 200 BT 31:32 | 363 Applying equations (i.), (ii.), and (iii.) to the measurements with cylinder No. 1, as an example of the manner in which 768 Prof. J. C. McLennan on the the reductions were made, we have Tip. te ltg = 90°03, oe Tp} 13 =49'50) 0 ee and 100 lis = 28-6 ie: A d : c C 5 (vi.) From which we have woos Iie = DOO Pee ==) LOL3, or Hs == IPT) Ils. and Mag vse! EVD: Ine Similar calculations were made on the readings obtained with cylinders Nos. 2 and 3, and the results of the three are recorded in columns 4 and 5 of Table V. From these it will be seen that the ionization produced in the air in a lead cylinder by the gamma rays from radium is only one-half that produced in it by the secondary rays excited in the lead walls by these same rays. On the other hand, with gamma rays of the same intensity entering an aluminium cylinder of the same size as the lead one, the results show that the ionization produced by the penetrating gamma rays 1s ap- proximately twice that produced by the secondary rays excited by these gamma rays. It will also be seen from the numbers given in the above table, that we have sufficient data to calculate the ionization produced by the radium in a cylinder of any material of the same dimensions as those used in this investigation, provided it was placed in the standard position indicated above. For example, Column 6 of Table V. gives the reduced © readings corresponding to the gamma rays alone which entered the respective cylinders. From Table III. the ab- sorption powers of these cylinders are known in percentages; and by means of these numbers values can be calculated for the ionization which would be produced in the same volume of free air by the gamma rays from the radium. Column 7 of Table V. contains the values of Ij) corrected in this way, and the mean of the results is 86°3. This number, it will be seen, represents the ionization which would be produced by the gamma rays from the radium, used in these experiments in a cylinder of any metal 60 cms. high, and 24 ems. in diameter, situated in relation to this radium exactly as the cylinders were in the experiments described above on the Radioactivity of Lead and other Metals. — 769 supposition that no absorption of the rays took place on traversing the walls of the vessel. If absorption did occur, and the absorption constant for the cylinder was known, the value 36°3 could be modified accordingly, and the ionization produced by the gamma rays alone within the cylinder be deduced. Suppose, for example, that the cylinder was an aluminium one (0°73 mm. in thickness, the absorption from Table III. could be neglected, and 36°3 would represent the ionization pro- duced “by the gamma rays in the air which it enclosed. From the results given in Column 5, Table V. the corre esponding ionization due to the secondary radiation excited in the aluminium by the gamma rays would amount to 57 per cent. of 36°3 or 20°7, so that the total ionization within the ihc nisin cylinder due to the gamma rays from the radium and to the secondary rays which they excited, could be represented by (36°3+20°7) or 57 would be the estimated reading. Tn an actual experiment with an aluminium cylinder of the dimensions given above, and situated approximately in the position indicated, the reading 62 was obtained as the mean of a number of observations. This difference between the experimental and the calculated values for the ionization is not more than 8 per cent.; and it is not surprising when it is remembered that no special precautions were taken to place the aluminium cylinder exactly in the position occupied by the lead cylinders with which the measurements were made upon which the present calculations are based. It is possible that the aluminium cylinder may have been as much as a centimetre out from the position it was supposed to occupy during the measurements. rom the agreement pres sented by these measurements, it seems warrantable to conclude that the relation which has been established between the relative amounts of ionization produced by primary and secondary radiations within a mass of air confined in lead or -aluminium cylindrical vessels with the dimensions described above, is a reliable one. U1. On the Character of the Radiation from diferent Metals. From the foregoing discussion it is evident that with the cylinders examined, a definite proportion existed between the ionization produced by the gamma rays and that pro- duced by the secondary rays which they excited. With lead cylinders the amount contributed by the secondary rays was, as we have seen, twice that arising from the passage of the Co gamma rays. But with aluminium cylinders the relation 770 Prof. J. C. McLennan on the was almost exactly the inverse of the preceding, the ioniza- tion due to the primary rays being nearly iuiee that due to. the corresponding secondary radiation. It will be remembered, too, that the radium from which the gamma rays were obtained was surrounded by a block of lead 3 em. in thickness, so that the radiation which issued from it must have been of a very penetrating nature, and therefore similar in its characteristics to the penetrating radiation which has its source in the earth, and contributes to the natural ionization observed in air or other gases con- fined in metallic vessels. : | It seems fair to conclude then, that in natural or spon- taneous lonization in air confined in metallic vessels a pro- portion should hold between the ionization due to the primary and that due to the secondary rays, similar to the one which was found to hold experimentally with the gamma rays from radium, and the secondary rays emitted by them. Assuming this relation to hold, it is possible to establish a connexion between the conductivity of air confined in a vessel of one metal with that of air enclosed by a second of the same dimensions but of different material, provided neither metal contains any radioactive impurities. With this relation established it is possible then to check the results obtained experimentally in particular cases, and by so doing arrive in a measure at a knowledge of the re- lative importance of the different factors which determine the ionization. In Section J. of this paper it has been shown that with the lead cylinder No. 1 there was generated on the average 23 ions per ¢.c. per second. Assuming that no part of this was due to any impurity in the rive eal it follows from the numbers given in Table V. that one- -third of this number was due to the penetrating radiation which entered the_ cylinder, that is 7°67 of the 23 ions were generated by the penetrating radiation which traversed the air in the vessel. Allowing for the absorption by the cylinder of 15°36 per cent. of the penetrating radiation, it follows that 9:06 ions were generated per c.c. per second in free air by the penetrating radiation from the earth. Turning now to the aluminium cylinder No. 10, it is fair to assume, since its absorption of the gamma rays has been shown to ‘be negligible, that 9°06 may be taken, without sensible error, to be the number of ions senerated per c.c. per second by the penetrating radiation ‘bie entered it. The number produced per e.c. per second by the induced secondary radiation would then, according to Table V., be 57 per cent. of this number, that is 5-16, and Radioactivity of Lead and other Metals. (afd therefore 14°22 would be the total number generated per c.c. per second by the combined radiations. In the same manner it can be shown, by taking Hve’s value of 53°7 per cent. as representing the amount of secondary radiation excited in a zine radiating surface compared with that obtained with a lead one, that 17°88 is the number of ions which should be generated by the penetrating radiation from the earth, and by the secondary rays excited by these in each cubic centi- metre of air enclosed in the zine cylinder No. 8. TABLE VI. Column 1. Column 2. Column 3.) Column 4. | Column 5. | Column 6. ae ge Sseeee) 938 ert es c= = bes ore, Glas ot)! Reese es | = = So = S| o 4 O ! Mie ae Ss Shy Shs (a Sl eee | eS 28 CEs Pratt |tue tees a | Ss 2. SCR Be) r: = | | ao n 5 lm os ge © Oo -— | err! Se : | : S a5 25 2 o Cylinder | Metal. | oe ae rot eten or Ole 2 ne x No 2 H~ 5 ey) Sie Sh ce ee «| Ths | o = ° = GP ES a a = oF st liso tart t ane 2s | ~ © 2 | © ¢£ ayer < mM | lf veces Acoso Age eszeo| Seen | Wetese enh (Bu eeee| Sa | Pies \| WS 2eV is ee bos) Ss s | : S | Se Bs | | ‘all =~ a m2 = mae GN Q wm aa hae Pearce. 4| 15°36 23 23 ¢ | | - —. | Ui a ‘Py cme 16°29 | 160 207. | 187-23 | aa 3 ht bh hot inte eh O36" | 37 24°63 9 b.12- 37 | JhkeAioal eter Wo. Wee 2eetD 53:85 | : | | | (ie Pept ote a 12:92 34 23°67 10°33 | (Sap ee eee bec WY ema ts pelo, 5D 24-42 SUFI, el | Waser k nk: hs theetises| 13:23 61 23°58 Se S| PRROR 3 5.243 VA eee AG | 15 17°88 | = } = Per = | Oe Aluminium 23 Le 14:92 | 18 | Calculations similar to the above have been made on the number of ions which, on the basis laid down, should be generated per ¢.c. per second in the air enclosed by each ot the lead cylinders, Nos. 2-7, and the deduced values are all recorded in Column 5 of Table VI. With cylinder No. 9 the calculated value and that found experimentally present a good agreement; but with cylinder No. 8 the calculated is slightly greater than the observed value, and may be due to our making too high an estimate of the ionization produced by the secondar y rays from the zine walls. Eve states in his paper that he found the secondar y radiation came not C12 Prof. J. C. McLennan on. the only from the surface of the different radiators, but from a considerable depth as well; and since the zine used in these experiments was only 1°62 mm. in thickness, it was probably not so thick as the plates used by him. A smaller value should then be assigned to the ionization produced by the secondary radiation "fron the zine walls; and if this were done, the calculated and the observed values for zine would come into better agreement. The argument which has just been used to explain the high ionization calculated for the zine cylinder would apply with still greater force to the secondary rays from aluminium. With this metal Eve found that the secondary radiation came from as great a depth as 3 mm.; and if this condition holds generaily for aluminiam, it follows that we have assigned for this metal also too high a value to the ionization produced by the secondary rays. A cedar should then be made in the calculated value for “gq” of 14:22 ions per c.c. per second, and as this value is already slightly below the observed value of the number of ions generated per c.c. per second in the aluminium cylinder, this Teduction would leave a correspond- ingly greater number of fons $o he) wecoummed for, very probably by the presence of active impurities in the substance of tle receiver. It is of special importance, however, to note the fair agree- ment which exists between the calculated and the observed values, in these experiments, for the ionization produced in air enclosed in cylinders of lead, zinc, and aluminium, as illustrated hy the numbers given in Table VI. for Cylinders Nos. 1, 8, and 9, since it eraphasizes the view that ordinary neal, do not possess any intrinsic radiation, and that when any high conductivity is observed in air Connie in metallic vessels, it must be due to the existence of quantities, more or less considerable, of some foreign radicactive substance in the metals. Examples of such contamination are clearly in evidence in the results givenin Table VI. for the lead cylinders Nos. 2 to7 inclusive; and the numbers given in Column 6 give an estimate of the relative amounts of the active impurities present in the different samples of lead used in their con- struction. In what has preceded in this Section the discussion has rested upon the assumption that the lead in Cylinder No. 1 contained no active impurity; and while the experimental results rather fit in with the deductions which have been made on this hypothesis, there still remains the possibility that some part of the ionization observed with this cylinder Radioactivity of Lead and other Metals. Ha may have been due to traces of some foreign active substance. If one could surround the cylinder with some substanee which would act as a screen, and so cut off entirely the earth’s penetrating rays, and consequently also the induced secondary radiation, any ionization within the cylinder would then be due to active impurities present in the metals. The difficulty, however, is in finding a suitable screen. In some experiments made in this direction by the writer™ in colla- boration with E. F. Burton some years ago, screens of water were used, and with them it was found possible to make a reduction as high as 37 per cent. in the ionization within a closed cylinder. About the same time H. L. Cookef, in studying the conductivity of air enclosed in a brass vessel, was able to reduce the ionization 30 per cent. by sur- rounding the brass with a screen of lead. Later still Elster and Geitel{ observed a fall of 28 per cent. in the con- ductivity of the air enclosed in an aluminium cylinder on removing the apparatus from the surface of the earth to a closed space in a mine surrounded by a wall of rock salt. But in none of these experiments is there clear evidence that the penetrating radiation was entirely cut off. On the other hand, in several of the experiments which have been made with this object in view, it has been found that active im- purities were present in the substances used as screens, and the screens themselves were observed to contribute a pene- trating radiation which masked any falling off in the intensity of the external radiation arising from absorption. Although many of the surface waters of the earth which have been examined, among other substances, by different experimenters, have been shown to contain minute traces of radium, it is possible that such waters as those of the great lakes of Canada might be fairly free from such an impurity, and if so might serve to screen off radiations from an ioniza~ tion chamber immersed in them. Some experiments made a few years ago by the writer failed to show the existence of any measurable amount of the emanation from radium in the water of Lake Ontario; and from this result it would appear that the water of this lake would seem to afford the substance requisite to carry out an experiment such as that just indi- eated. The experimentai difficulties, however, are con- siderable, and it is doubtful if they could be overcome in a * McLennan and Burton, Phys. Rey. no. 3 (1903); Burton, Phys. Rey. no. 3 (1904). + H. I.. Cooke, Phil. Mag. [6] vi. p. 403 (1903). - { Elster and Geitel, Phys. Zeat. Noy. 1, 1905, p. 733. Pel Mag. 3 Gi Vol.-14. No. 84. Dec. 1907, oF 774 Prof. J. C. McLennan on the manner to give satisfactory results. If this water proved to be an efficient screen, it would be interesting to see whether all ionization would disappear from the air confined in a cylinder such as No. 1 of this investigation, if it were immersed to a considerable depth in it; for on the assumption that the material used in the construction of the cylinder contained no active impurity, this is what one should expect to find. IV. On the Rise in Conductivity of Air confined in Metallic Vessels. In the course of the experiments described above, it was repeatedly found when one of the cylinders was filled with fresh air filtered through cotton- and glass-wool, and after- wards sealed up, that the conductivity of the enclosed air steadily rose for a number of days, and finally reached a steady value. This phenomenon, which has been described already by the writer and EH. F. Burton in the paper cited previously, has also been observed by a number of experimenters, including Elster and Geitel*, Hvet, Wood and Campbell{, and others, but up to the present has not received a satisfactory explanation. During the present investigation special observations were made on this effect in connexion with air confined in the lead cylinders Nos. 1 and 2, on account of the great difference observed in the values of the conductivity impressed upon the air introduced into them. j When cylinder No. 1 was thoroughly scoured and cleaned in the manner described in the beginning of this paper, and freshly filtered air blown through it for twenty minutes, a reading of 7:7 divisions per minute, or a number within 1 or 2 per cent. of it, was regularly and repeatedly obtained throughout the period, now nearly six months, during which the observations have been carried on. If the air after being introduced into this cylinder was allowed to remain un- disturbed for some time, and measurements made on its con- ductivity at stated intervals, it was found that the ionization steadily increased, and after a period of a week or ten days reached a value of approximately 11 divisions per minute. If when this stage was reached filtered air was blown through the cylinder for twenty minutes, it was always found that a * Geitel, Phys. Zeit. ii. pp. 560-563 (1901); Elster and Geitel, cbhed. ii. pp. 116-119 (1900). + Eve, Phil. Mag. | 6] xi. p. 189 (1906). } Wocd and Campbell, Phil. Mag. Feb. 1907, p. 25. S$ 8 8 CONDUCTIVITY (Arbitrary Seale) QD Gah Radioactivity of Lead and other Metals. 175 drop in the conductivity occurred to between 8 and 85 divisions per minute. ae: If the air was again left undisturbed in the cylinder, its conductivity rose once more and finally reached the maximum value of approximately 11 divisions per minute. In con- ducting these operations it was not found necessary to draw fresh air through the cylinder for more than twenty minutes in order to lower the conductivity to the minimum value. TaBLE VII. Cylinder No. 1. Conductivity Date. (Arbitrary Scale). NGS 78 ORS eer ae fare Ri Eee Se 9°0) La palin 9-6 CT A iad 8 alg A ae ee 10°32 2 Det ECE on 10°65 ry lini eas oe ena: IUDs) Le eh oe TEL O02 Fresh air blown through cylinder for twenty minutes : Jeep EO le 8°54 AES a A eee 8:91 2 Ty ree 9°83 TAS) ie a ee ae 10°16 SUMMING hp Niet a. etn 10°79 20) tare ear ran lees Fresh air again blown through eylinder for twenty minutes: eM erAS y fama 4 8:1 | a a a a a a a a Ci i | a a a | a a a ar. [4 al | a | a gi a | a a 16 747 18 29 20 24 22 23 24 25 26 27. 28 29 30 Hf DAN te os 4:°°S PEAY SUINE ~ Bd Oe 776 | Prof. J. GC. McLennan on the With cylinder No. 2 thoroughly cleaned in the manner already described, a reading of 54°5 divisions per minute with but slight variations was regularly obtained with freshly filtered air. With this cylinder, too, when the air was un- disturbed in it the conductivity steadily rose, and after a time approached a maximum value. The time required for the steady state to be reached was, however, much sibs than with cylinder No. 1. A set of readings which exhibit this rise are given in Table VIII. and a curve representing them is shown in hie. 2: Tasie VIII. Lead Cylinder No. 2. Conductivity Time. (Arbitrary Scale). see fe) a a D4°6 ee OE Se D8°3 g UAE as 61 TON Mapu a 62 LO ee eon 63°2 () eaeeier a, 64 Filtered air was now blown through cylinder for twenty minutes: June i. 3 0ne Mee 60°6 HS lO Onesie ce 64:4 Di Oka Wiens 67 Viltered air again blown through for twenty minutes: ome 22 e SO Tea ae 62-4. Filtered air blown through for one hour: SMe 2a OUMP. Me ne 62:8 From this it will be seen that when fresh air was intro- duced into the eylinder on June 17 the reading dropped from 64 to 60°6, and again on June 27 the introduction of fresh air was followed by a drop from 67 to 62:4. Air was then drawn through the cylinder for one hour, but no further drop in the conductivity ensued. When similar observations were made on other occasions with this cylinder similar results were obtained. After a rise occurred, the introduc- tion of fresh air was always followed by a. drop in the Radioactivity of Lead and other Metals. CU conductivity, but the initial value of 54°5 divisions was never reached without re-cleaning and washing the inner surtace of the lead. Fig. 2 68 SHS SESH eee eee anes pti =e Si RREEESEHEE Lead toees ordeal ttt stei feast 67 0 OO 0n Ones Cees Seeee Seeee cee @SRGE Ber", or 9 dati gate fee azaees BR ins oe ee ee aeeeer SERRE Reese See rr Efi fase nti iseet Fined netees cons eeeeteces feed ae ae sestaiset aazeet PO paproiee faed sovevacecd ese coont tents | ned tener czens evesanen. cy Sue Peed somes coed Oa betes ane eed beens Peete rns el eee te LTA SOR08 Seni on! mt ae Ree CS og, EES ee S 3 #557 ASEUEE PUREE EnaUs Spunebnaed fEtaT SenrabEaST PET © S, ro I } 4 piper yi Tat SERES 2 | | ? ‘SEG8 See 8 Bowe wi Ty _ LTT Bagged ~ = - HH HEE FREER EEE EEE EEE EH PEE f 4 4-4 He cuaae Be HEE Begeeesese be ani H+ HH a2 a Ft ceetis H PEEP cunaiitn HH uae AH aan Beoeeanane 7 1-|-I 44-44 mt rips Ee fo 54 EEEEEEEESEEEECE EEE eee meg (24 IF 139) IGS (27 23: 25. 27 23 JUNE From these observations 1t would appear that the rise in the conductivity of the air in both cylinders may be divided into two parts and ascribed to different causes; the one being associated with some change in the surface of the metals used in the construction of the cylinders, and the other with some substance which becomes diffused throughout the air, and can be blown out with it. With cylinder No.1 the part due to the first cause was very small, and in no case exceeded 10 or 12 per cent. of the minimum reading obtained for the conductivity. The second part, too, was very definite with this cylinder, and when the maximum conductivity had been reached it corresponded to a.reading of between 2°5 and 3 divisions per minute. With cylinder No. 2 both parts of the rise in conductivity were well marked. But as the numbers in Table VIII. show, both parts exhibited a steady increase during the time: the 778 Radioactivity of Lead and other Metals. conductivity was under observation; and owing to the length of time required for the maximum state to be reached, it is not possible at present to express them as definite percentages of the minimum reading obtained with this vessel. Repeated observations on both cylinders have invariably given the results just described, and as the greatest care was taken throughout the investigation to prevent contamination of the cylinders by foreign active substances except what might be introduced along with the filtered air, it would seem clear that a process is going on in the metals, possibly a diffusion from the interior, whereby the surface becomes coated witha layer of active matter which makes an important contribution to the ionizing power of the metal. From the observations which have been made so far, it has been impossible to decide whether the second part of the rise n the conductivity of the confined air was due, in whole or in j art, to an active substance introduced with the air or to an emanation from the walls of the vessel, but as observations are still being made with the cylinders, itis possible that some additional facts may be obtained which will clear up this difficulty, and also throw light on the nature of the active impurity which has been shown to be present in varying amounts in the different samples of lead examined. ve Summary of Results. 1. The conductivity of air enclosed in lead cylinders has been shown to vary widely with the samples of lead selected. The lowest conductivity observed in air enclosed by this metal corresponded to the production in the air of 23 ions per ¢.c. per second, and the highest to the production of 160 ions per c.c. per second. 2. These wide variations show that the high activity of lead which has been observed generally is due to the presence of active impurities in varying amounts in the lead, and not to a high intrinsic radiation from the metal. 8. Calculations made on the observations show that the differences in the conductivities of air confined in vessels of different metals, including lead, when free from active im- purities, arise from and are due to differences in the secondary radiations from these metals. 4, Experiments made with the gamma rays from radium showed that of the ionization produced by these rays in air enciosed in lead receivers, two-thirds was due to the excited secondary rays and one-third to the gamma radiation itself. A Gas generated from Aluminium Electrodes. 779 With aluminium cylinders on the other hand, the measure- ments show that approximately two-thirds of the ionization was due to the gamma rays, and one-third to the secondary rays excited by this radiation in the metal. 5. Calculations based on observations on the conductivity of air confined in different receivers lead to the conclusion that approximately 9 ions per c.c. per second are generated in free air by the penetrating radiation from the earth. Before concluding I wish to acknowledge my very great indebtedness to Mr. V. E. Pound, for his kindness in repeating and verifying many of the observations described in the first part of this paper. The Physical Laboratory, University of Toronto, July 1, 1907. LXXVI. A Gas generated from Aluminium Electrodes. By kk, v. Hirscu, PhwW., and F. Soppy, W.A.* lie a recent paper (R. v. Hirsch, Phys. Zeit. vol. vil. p. 461, 1907) one of us showed that when cathode rays were generated hy means of an influence machine in pure gases, the relation between the gas pressure p and the discharge potential V could be represented by p’V = constant. This relation holds for the pure gases examined independently of the amount of current fowing through the tube, but does not hold at all for gaseous mixtures. During the passage of the discharge, a gas is continuously evolved from the electrodes if these are of aluminium, which renders the gas initially filling the tube impure, so that the above relation ceases to hold. But if the discharge is passed for some hours, the gas being pamped out as evolved so as to maintain the pressure within the range required for the production of cathode rays without unduly increasing the resistance of the tube, the value of p?V again becomes a constant independent of the nature of the gas initially filling the tube and about one-quarter of the value for hydrogen. | The value of p?V appears to depend in some way on the molecular weight of the gas, for it is almost exactly fourteen * Cummunicated by the Authors. 780 Dr. R. v. Hirsch and Mr. F. Seddy: A Gas times Jess in nitrogen than in hydrogen. In the case of earbon monoxide and oxygen, the values of p?V are about two-thirds that of hydrogen divided by the numbers 16 and 14 respectively. The behaviour of the gas evolved from the electrodes indicates that it is not a mixture but a pure gas and that its molecular weight is 4 or some multiple. In the present paper the nature of this gas is further examined. The first point was to see if the gas was helium. The spectrum was the familiar one always obtained when a new spectrum tube is exhausted and the electrodes heated with a discharge, and consisted of hydrogen and the secondary spectrum of hydrogen together with faint indica- tions of the strongest bands of carbon dioxide. The gas was subjected to the action of calcium volatilized by an electric furnace in the manner recently described by one of us (Soddy, Proc. Roy. Soc. vol. Ixxvui. A. p. 429, 1907), and was found to be completely absorbed leaving no trace of helium, The quantities of the unknown gas obtainable are too small for ordinary analysis, so it was attempted to identify it by its electrical behaviour, taking the values of p’V for a variety of different substances in the hope of finding one giving a value one-fourth that of hydrogen. The experimental arrangement was similar to that used before. The current was obtained from an 8-plate Wimshurst machine producing nearly half a milliampere when at full speed, so that the independence of discharge potential on the current could be verified within a larger range than formerly, in fact up to the point where the tube became per- ceptibly heated. The potentials were measured directly by a Kelvin electrostatic voltmeter. In the search for the unknown gas the most valuable hint given by earlier results is the fact, that for mixtures p?V is not constant, so that pure gases only have to be tried. But it was found advisable again to ascertain this point by trying several mixtures, between the components of which chemical action was excluded, special care being taken that the mixtures did not change during the investigation. ‘The results are given in the following tables :— generated from Aluminium Electrodes. 781 T. 50 parts N,+32 parts Hy. Dp Vi; pV BGM UO. math: 1100 volt. 3449.10° 46 S008) 4020 40 2800 4480 36 3800 5280 39 5600 5732 29 6700 5948 27 8800 6416 26 10400 | 7028 II. 24 parts N,+29 parts Hy. 64 1100 4504 52 2100 5676 44 3300 6388 3 4600 6640 33 8000 838+ 26 12800 8652 III. 16 parts N,+42 parts H.. 84 ). VEZ00 | 8467 66 9300 19020 16 3400 10660 50 4800 12000 46 6000 12696 AD 80L0 14112 IV. 52 parts He+48 parts Hy. 196 1200 46096 158 2450 53704 132 3600 52580 114 4400 57180 110 5OVO §0500 195 6000 65148 92. 9100 77020 80 13200 84480 At the end of series IV. the gas at a pressure of ‘08 mm. was subjected to volatilizing calcium. A residue of ‘042mm, was left, corresponding to 52°5 per cent. of helium, which is very nearly the original composition. ‘To compare with these results, the values given by the unknown gas (taken in another tube) are given within a wider range than previously tested (p. 782). The constancy of p?V here as compared with the in- constancy in the case of mixtures make it extremely probable that the unknown gas is a definite chemical body. : 782 Dr. R. v. Hirsch and Mr. F. Soddy : A Gas Ds | V. pV. : 26 | 15000 10140 | | 28 13000 10192 | | 32 10000 10240 34 8000 9288 | 40 6000 9600 | | 26 | 5000 10180 / 51 | 4000 10404 | Mean! vale” 2-22). 10292 | | Hydrogen value ...... 38120 | The second indication given by earlier results is the probable connexion of the p?V values with the molecular weights. But as this regularity mainly rests on the com- parison of hydrogen and nitrogen, more gases ought to be tested. Unfortunately, the members of the argon family, which seemed best suited for this purpose, show the peculiarity that their behaviour is extremely dependent on very small impurities present (Strutt, Phil. Trans. vol. exciii. p. 377, 1900 ; Soddy, loc. ct.). Helium was tried and gave p?V values much higher than hydrogen. Several compound gases were then tried, choosing such bodies, the occurrence of which seemed possible tor one reason or another. These gases are :— Water vapour, Carbon dioxide, Methane, Acetylene, Cyanogen, Hydrocyanie acid. None of these gases could stand the discharge without changing ; water vapour, methane and hydrocyanic acid split up into their components, the carbon compounds forming a thin carbon deposit on the glass near the cathode. Acety- lene and cyanogen begin by polymerizing, the latter forming paracyanogen, which is deposited on the cathode, the former probably benzene. On the other hand, a partial decomposition sets in, the equilibrium altering with every change of pressure or potential. Carbon dioxide is less quickly decomposed, but is not stable enough to give satisfactory p?V values. Moreover, it shows an anomaly otherwise not observed, the bulb becoming suddenly non-conducting with a small decrease of pressure, so that no readings could be taken above 5000 volts. On the whole, all these gases were found altogether unlike the unknown gas, and small chance seems to be left to find it among the class of chemically compound bodies. generated jrom Aluminium Electrodes. 783 The only posétive indication obtained is the following :-— It was found impossible to obtain any gas out of the bulbs made in England, which always showed a marked absorption under the same conditions as those in which the bulbs obtained in Germany were generating the unknown gas. Comparing this with the fact previously noted, that the effect could not be obtained with copper nor with iron electrodes, it seemed reasonable to attribute this difference in behaviour to a difference in the aluminium employed. This view proved correct. When the electrodes were interchanged, those from the German tube gave gas when remounted in the new English tube. It is therefore probable that this aluminium contains an impurity responsible for the observed effect. Among the admixtures liable to be found in aluminium, the most likely are carbon, nitrogen, and sodium. The two first- mentioned elements suggested the examination of the cyanogen compounds, and to test the latter possibility one of the English aluminium electrodes was alloyed with sodium on its surface. This electrode now showed a behaviour very similar to the one exhibited by the German electrodes. On applying the coil much gas appeared, the cathode showing a marked scintillation. After a short time this action reversed, the induction current now absorbed gas. -But on applying the steady current given by the Wimshurst machine, a continuous slow production set in, gradually ebbing down as in the case of the old electrodes. The p?V values of this gas neither became really constant nor did they reach entirely the quarter of hydrogen value, but they came very near in both these respects. The following table gives a series of final values :— p V. p 28 12000 9408 3l 9600 9224 36 8000 10368 38 7000 10708 44 6000 11616 The hydrogen value of the tube was 53,000. The values obtained in the beginning of the experiments were much lower and showed a much more decided slope. It is con- sidered as consistent with these results, that the electrode alloyed with sodium behaves like the one made of German aluminium, with the difference that it is polluted by sodium carbonate, decomposing under the influence of the electric discharge, so that the unknown gas is only obtained in an impure state. This result, without solving the question as to the nature of this gas, changes the direction of the research in pointing to the electrode metal as a field of investigation. 784 First Linear Spectra of Emission of Mercury. It is improbable that the sodium plays more than an indirect part in the generation of the gas. The following suggestion seems at least probable. The presence of a trace of sodium in aluminium renders it, as is well known, capable of decomposing water, so that an electrode of such metal becomes charged with hydrogen, probably chemically com- bined as hydride, by mere exposure to air. The unknown gas may be a modification ot hydrogen like ozone is of oxygen, capable of withstanding the discharge of an influence machine, but decomposed by the discharge of a coil. This theory is being investigated. The question of the quality of aluminium used for the purposes of electrodes is of great practical importance. Of old, aluminium was manufactured by a process which rendered the presence of sodium unavoidable. A trace of sodium is, however, a very undesirable impurity technically on account of the metal being attacked by moisture, and the most strenuous efforts of recent years have been directed to increasing the purity of the metal for technical purposes, with the result that the aluminium to-day differs entirely from that first made. Itis avery unsuitable material for the construction of electrodes, the discharge passing with difficulty and irregu- larity. Too great purity of the British aluminium may serve. to explain some of the difficulties besetting the X-ray bulb manufacturers in this country. We are indebted to the Garnegie Trust for the provision of the instruments used in this investigation. Physical Chemistry Laboratory, The University, Glasgow. aos LXXVII. Gradual Modification of the First Linear Spectra of Emission of Mercury. Preliminary Note by Prof. ENRIco — CASTELLI *. (Plate X VII. ] HE recent discoveries made by Sir W. Ramsay on the transformation of several elementary substances, which were lately mentioned at the Congress at Parma of the Italian Association for the Progress of Science, have recalled in my mind a fact I observed about a year ago, in studying the luminous spectra of mercury. I had found that in taking (with a Steinheil spectrograph, fitted with three quartz prisms) some spectrophotographs of the electric arc in the vapour of mercury, contained in a Uviol lamp, the spectrum lines (amounting only to 16, on account of the limited dispersion of the apparatus), while remaining constant in position, showed in time a gradual varlation of their photochemical action: the lines corre- * Communicated by Sir Wm. Ramsay, F.R.S. Geological Soctety. 185 sponding to less refrangible monochromatic rays gradually became more intense, and produced on the orthochromatic plates a greater and greater effect ; while the contrary occurred with the more refrangible lines. Having lately made a’ new spectrograph of the light emitted by the above-mentioned lamp, I found that the group of three lines, of the wave-lengths 3663°3, 36549, and 3650°3 Angstrém units, had nearly completely vanished ; while the three lines 5790°49, 5769°45, and 5460°97, which in the first experiments had given a scarcely visible photographic 1m- pression, now produced a much clearer and a more intense impression than any other line! The figure accompanying this note shows the comparison of two spectrographs of the light emitted by the electric are in mercury vapour, the former of which was made when the Uviol lamp was almost new; the latter after the same lamp (always fed by a continuous current of 60 volts and 2 to 3 amperes) had been working during short periods separated by long intervals, for about one hundred hours. As it is now generally believed that the vibration corre- sponding to each line of the spectrum of an element must be considered as due to its positive ions, I think the modi- fication I have noticed in what Prof. Stark calls the first linear spectrum of mercury, must be considered as depending on an alteration in the character of the positive monovalent ions. probably consisting in such a variation of the vibrating mass, that it renders oscillations of a higher frequency im- possible, while the vibrations of less wave-length, due to a state of a smaller capacity for motion, are made easier and therefore intensified. We have still to find out whether this observation as to probable material modification of mercury can be further corroborated, and also whether it can even become permanent, corresponding to a change in the internal constants of mercury; and this I intend to be the subject for further experimental researches. Padua, R. Istituto Technico, October 5th, 1907. LXXVIII. Proceeaings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 676. | June 19th, 1907.—Aubrey Strahan, M.A., F.R.S., Vice-President, in the Chair. RS following communications were read :— 1. ‘ The Inferior Oolite and Contiguous Deposits of the Bath- Doulting District.? By Linsdall Richardson, F.G.S. 2. ‘ The Inferior Oolite and Contiguous Deposits of the District 786 Geological Society :— between the Rissingtons and Burford.’ By Linsdall Richardson, F.G.S. 3. ‘The Flora of the Inferior Oolite of Brora (Sutherland).’ By Miss M. C. Stopes, D.Sc., Ph.D. 4, ‘The Constitution of the Interior of the Earth as revealed by Earthquakes (Second Communication) : Some New Light on the Origin of the Oceans.’ By Richard Dixon Oldham, F.G. S. The attempts, which have been made to account for the oceans and continents, are all subject to an uncertainty, in that we have had no means of knowing whether it is a mere irregularity of form that has to be accounted for, or whether this irregularity is but the expression of a deep-seated difference in the constitution of the earth. The paper is an attempt to clear up this uncertainty by a comparison of the European records of the San Francisco and Colombian earthquakes of April 18th and January 31st, 1906. In the former case the wave-paths to Europe lay under the continent of North America and the continental shelf of the North Atlantic, being typically continental in character; in the latter case they crossed the broadest and deepest part of the Atlantic basin, being essentially oceanic. The absolute rates of propagation cannot be compared, owing to the time of occurrence of the Colombian earth- quake being fain but the interval between the arrival of the first and second phases is found to be longer in the case of this earthquake, by an amount much in excess of any probable error of record or interpretation. This difference indicates that the rate of propagation of the second-phase waves was relatively slower in the case of the Colombian earthquake, and, consequently, a difference in the constitution of the matter through which they were propa- gated. ‘The Japanese records of the San Francisco earthquake also give an interval between the first and second phases which is greater than the average, the wave-paths in this case too being oceanic. From these facts the general conclusion is drawn, that oceans and continents are not mere surface-irregularities of the earth’s form, but are accompanied by, and probably related to, differences in the - constitution of the earth beneath them, which extend to a depth of about one-quarter of the radius. It is not possible to state exactly in what this difference consists, beyond that it causes the rate of propagation of the second-phase waves to be less, in comparison with that of the first-phase waves, under the oceans than under ie continents. >. “The Swansea Earthquake of June 27th, 1906.’ By Charles pest Sc.D., F.G.S. ; With the exception of the Hereford earthquake or 1896, the Swansea earthquake was the strongest which has been felt in this country for more than 20 years. It, disturbed an area of 66,700 square miles, reaching from Rochdale on the north to Penzance on the south, and from beyond Maidenhead on the east to Waterford on the west. The centre of the isoseismal 8-lies about, 3. miles west of Swansea, the longer axis of the curve being directed H. 5° N. aud W.5°S. At Swansea, Neath, etc., the total number of chimneys thrown down or damaged must amount to several hundred. CasTELLI. Phil. Mag. Ser. 6, Vol. 14, Pl. XVII. RS * laa TIS ee ell ce eee f The Swansea Farthquake of 1906. 787 The shock consisted of two distinct parts—the first part being much weaker than the second, except at places within an oval area lying some miles to the east of the Swansea epicentre. ‘The existence of a secondary focus beneath this area is also indicated by the relative positions of the isoseismal lines, the isoseismal 8 being much nearer the isoseismal 7 at the western than at the eastern end. In twin earthquakes, it is difficult to ascertain the position of the focus in which the weaker impulse originated, but, in the Swansea earthquake, observations in mines offer an unexpected help. The shock was felt severely in mines within an area 8 or Y miles in diameter, and as a tremor outside. The centre of this area lies about 1 mile west of Llwynypia, 224 miles east of the Swansea epicentre, and is close to the centre of the area over which the weaker part of the shock was felt. Observations, 538 in number, were obtained from 39 pits, dis- tributed over an area 49 miles in length, from near Kidwelly to ‘near Pontypool. The shock was, as usual, less strongly felt in pits than on the surface; and the sound was more uniform and monotonous underground. Both shock and sound were observed in pits over about the same area. In pits not more than 5 miles from the nearest epicentre, the sound seemed to pass below the workings; in those at a greater distance, it seemed as a rule to pass overhead or to travel along the workings. There is some, though not decisive, evidence for supposing that the fault was felt more severely in the lower than in the upper workings of a pit. The originating fault in the neighbourhood of Swansea must run from E. 5°N. to W. 5°S., hading to the south, and passing not far from the line joining Llenelly to Neath, which is 5 or 6 miles to the north of the great east-and-west fault under Swansea Bay. The first movement occurred in the eastern focus near Llwynypia, and this was followed after a few seconds by a much stronger movement in the western or Swansea focus. The interval between the parts was such that the earlier impulse was felt first all over its disturbed area ; but, as the foci were quite detached, the earth- guake was no doubt a true twin-earthquake. 6. ‘The Ochil Earthquakes of September 1900 to April 1907.’ By Charles Davison, Sc.D., F.G.S. During this interval, a series of slight shocks was felt chiefly in the villages of Blairlogie, Menstrie, Alva, and Tillicoultry, lying between the Ochil Hills and the river Forth. There were four shocks in 1900, one in 1903, ten in 1905, nineteen in 1906, and eight up to the end of April 1907. The strongest shock of the series occurred on September 21st, 1905; its intensity was 6, and it disturbed an area of about 1000 square miles. The originating fault must be directed from about E. 27° N. and W. 27° S., hading to the north, and passing not far from the villages mentioned above. It cannot therefore be identified with the great Ochil Fault, which in the district referred to runs from about E. 13° N. to W. 13°S. and near Dollar hades to the south; although it is possible that some or many of the slighter shocks may have been due to slips along this fault. INDEX to VOL. XIV. ———_