oF a bh arere ae be te hare et ow wh oho we wo Bay Bao Be *~ ; . > "I , 2 nee a ‘ nee mond i= eats ’ ues o try ‘ BP PPL hel aare he at orale ee Pgroceoie: e of protete « A pe ‘ wens wens ernie a - eres: - verses revere Ki etre Pier rtyemelnr rare aie Oe ee we rer ecree® we oe eo Aa Mewar m ve che oie oo Oo w) es % 9 i 20% SX 11—8625 AAs % UNITED STATES PATENT OFFICE % SBELF Wwe CASE ay ot) mee GOVDPRNMENT PRINTING OFTIOn AMMMMMMVMVBVBwAAAcMKKYZ ~aSB x : > ~ < Oe om =! O Lu. - im LJ O WY) RS) /@ i’ THE LONDON, EDINBURGH, ayv DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. CONDUCTED BY | LORD KELVIN, G.C.V.0. D.C.L. LL.D. F-B.S. &e. JOHN JOLY, WA. D.Sc. E.RS. F.G.S. AND WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.0.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. ee Ups ee a VOL. IV.—SIXTH SERIES. JULY—DECEMBER, 1902. LONDON: TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, SOLD 3Y SIMPKIN, MARSHALL, HAMILTON, KENT, AND CO., LD.—T. AND T, CLARK, ‘ EDINBURGH ;—SMITH AND SON, GLASGOW ;—HODGES, FIGGIS, AND €O., DUBLIN ;—-PUTNAM, NEW YORE ;—-YEUVE J. BOYVRHAU, PARIS ;—AND ASHER AND CO,, BERLIN, GS435 " fea Megiitationts est perserutari occulta : cciteaplaiell -perspicua .... Admiratio generat ee queestio 7 inve investigatio en ’—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 ccelo, Quo micet igne Iris, superos quis conciat orbes Tam vario motu.” J. B. Piet ee CONTENTS OF VOL.AWS~ (SIXTH SERIES). // NUMBER XIX.—JULY 1902. Prof. E. Rutherford and Miss H. T. Brooks on the Com aS of the Radiations from Radioactive Substances .........- Prof. C. Barus on the Sizes of the Water Particles producing the Coronal and the Axial Colours of Cloudy Condensation. fered d. E. -Durackon Lenard Rays... ...e.5 6) fied oe Prof. H. Nagaoka and Mr. K. Honda on the Magnétostriction of Steel, Nickel, Cobalt, and Nickel-Steels.............. Mr. Will. C. Baker on the Hall Effect in Gold for Weak ERINSIIC. HIGIER Ry nites oo 3 oS FoR IES BE ~ Dr. W.N. Hartley on the Composition of Brittle Platinum. . Prof. W. Voigt on the Behaviour of Pleochroitic Crystals along Directions in the Neighbourhood of an Optic Axis. . Hon. Rk. J. Strutt on the Discharge of Positive Electrification pe terehtlsts criy ss es... fale ae BUS AE: Dr. J. H. Vincent on a General Numerical Connexion between the Atomic Weights. (Plates I. & IL.) ........ Prof. J. P. Kuenen and Mr. W.G. Robson on Mixtures with Maximum or Minimum Vapour-Pressure .............. M. W. de Nicolaicve on a New Reaction between Electro- static Tubes and Insulators, and on the Electrostatie Field round an Electric Current, and the Theory of Professor REALITIES gh RS 5 iu crags 2s Mate eee ee ee he ae ees Lord Kelvin on Molecular Dynamics of a Crystal..... Prof. John Trowbridge on Spectra arising from the Dis- sociation of Water V apour and the Presence of Dark Lines mGasecous spectra, WP DL) i. ee Dr. H. 8. Carslaw on a Problem in Conduction of Heat .... Prof. J. D. Everett: Contributions to the Theory of the eesolving Pawer of Objcétives: 6 i2es 6 lo fe i Notices respecting New Books :— C. Wolf's Histoire de l’Observatoire de Paris de sa POUa nae MP LU Li ee cd ee ioe ces W. G. Rhodes’s Elementary Treatise on Alternating PGETCES neh ee ee i ee ee CLR wees | é> Wy A 1V CONTENTS OF VOL. 1V.—SIXTH SERIES. Page Proceedings of the Geological Society :— Mr. P. F. Kendall on a System of Glacier-Lakes in the Cleveland Hulls J....0.2..9. .3-..a¢22- > eer 174 Mr. A. R. Dwerryhouse on the Glaciation of Teesdale, Weardale, and the Tyne Valley, and their Tributary Walley” o's = viens bole ee ne vs p HD 176 NUMBER XX.—AUGUST. itord Kelvin on the Weights of Atoms .....<.. ..:. 22mm 177 Dr. Giuseppe Zettwuch: Researches on the Blue Colour of PAIS SSIEV 3): RU Sw pos Bharat alae oie ss hag en 199 Mr. A. M. Herbert on the Effect of the Presence of Hydrogen on the Intensity of the Lines of the Carbon Spectrum.... 202 Mr. H. A. Wilson on the Laws of Electrolysis of Alkali Balb-VApOUrs... bth. biawnis dd ek vege eae ee ee 207 Lord Rayleigh: Is Rotatory Polarization influenced by the arth’s Motion? ..2.::.).4 ee ssu.2> eerie er 215 Prof. R. Straubel: Experiments on the Electro-thermal Effect i ‘Tourmaline, .*.'.4/.is.(- Seppo poke eee ee 220 Mr. F. J. Jervis-Smith on a High Pressure Spark-Gap used in connexion with the Tesla Coil... .........0.-..-.. ¢ Jee 224 Mr. J. W. Peck on the Steady Temperatures of a Thin Rod.. 226 Mr. T. H. Blakesley on a Method of mechanically ob btaining 6 from the Hyperbolic Trigonometrical Functions of @.... 238 Mr. G. J. Parks on the Heat Evolved or Absorbed when a Liquid is brought in Contact with a Finely Divided Solid.. 240 Prof. J. J. Thomson on some of the Consequences of the Emission of Negatively Electrified Corpuscles by Hot Bodies. 253 Prof. C. Barus on Spontaneous Nucleation, and on Nuclei produced by Skaking Solutions ..........5-. +...) 262 Dr. Meyer Wilderman on the Velocity of Reaction before Complete Equilibrium and the Point of Transition are reached, &c.— Part. HE ...). |. 4.) Haken hee 270 Notices respecting New Books :— Sir George G. Stokes’s Mathematical and Physical Papers, Vol. tide 0: jn. =» eitipsl ele. rye a ee 277 Prof. H. Geitel’s Ueber die Anwendung der J.ehre von den Gasionen auf die Erscheinungen der atmosphar- ischen Hlektricititic. S. ci Sets as ets oes ES 278 J. M. Pernter’s Meteorologische Oplik ;2m....- 4. Ree 278 P. Barbarin’s La Géométrie Non Euchdienne ........ 278 W. R. Cooper’s Primary Batteries, their Theory, Con- struction, and Use ..... Tale A ett 5 S|. 278 E. Lemoine’s poomelrogpipiip ou Art des Constructions Geomeiriques:.iie.<') isda i. © eae. : ee 280 H. Andoyer’s Théorie de la LANE > so s+ 3s « PS 280 CONTENTS OF VOL. IV.—SIXTH SERIES. NUMBER XXI.—SEPTEM BER. merd Kelyinom the Weichts of Atoms ¢...)..-. 6... 6....: Prot. W. B. Morton on the Forms of the Lines of Electric Force and of Energy Flux in the neighbourhood of Wires Paden PleCUmies WaneSs «ain 2 raeits os Fee Ges Me ae Prof. E. Rutherford and Mr. A.G. Grier on Deviable Rays. of RrAGive SUDSLaEeS: + 62% 04 Sk bass cae Coen eis ete Mr. T. C. Porter on the Ebullition of Rotating Water.—A MEELIS. PIM PERVMICT YAU ie hank Pe Ree aie olan Wate eter es : Prof. J. D. Everett on the Comparison of Vapour-Temperatures SORE od Soho Se a a a de Messrs. K. Honda and 8. Shimizu on the Change of Length ot Ferromagnetic Wires under Constant Tension by eMC ett ashes aes ele Die sg eee eiae tare : Messrs. Edwin Edser and Edgar Senior on the Diffraction of Light from a Dense to a Rarer Medium, when the Angle peancidence exceeds its Critical Value: oo... 0... ee Piof. J. J. Thomson: Experiments on Induced-Radioactivity in Air, and on the Electrical Conductivity produced in Gases when they pass through Water. .............-.. ‘ Prof. J. Larmor on the Influence of Convection on Optical Peeuorye Olamiaahion ls Eee ee Pe Eh «Prof. E. Rutherford and Mr. F. Soddy on the Cause and Piature.o: Kadioictivity._Part Pie ioe oe oe Ae Prof. R. W. Wood on a Remarkable Case of Uneven Distri- bution of Light in a Diffraction Grating Spectrum ...... Prof. W. Cassie on the Measurement of Young’s Modulus .. Dr. G. Johnstone Stoney on the Law of Atomic Weights. OEE LS ae > a gee TE eee oat EE a Notices respecting New Books :— Bee Ree AMStTACUS. 62>) «soy aifcehior at LEAN deerme hus ts Proceedings of the Geological Society :— Prof. 8S. H. Reynoldsand Mr. C. I. Gardiner on the Fos- siliferous Silurian Beds of the Clogher Head District. . Prof. W. J. Sollas on a Process for the Mineral Analysis aS te he tae eaten ee we Peg, Rey. E. Hill on the Matrix of the Suffolk Chalky OUT 2s ed Gee AS 0 eee en a ae Re ea a Prof. T. G. Bonney on the Relation of certain Breccias to the Physical Geography ctf their Age...... ROE. Mr. E. A. Walford on some Gaps in the Lias ........ Mr. A. Strahan on the Origin of the River-System of CTL PNT eae GU age ale Seach aa en Mr. A. K. Coomaraswimy on the Crystalline Limestones Oe Fos Ma Cale ly ie i a ae ede ee a Rey. J. F. Blake on a remarkable Inlier among the Jurgssie Rocks of Subwerlandy i 2. 0. cg Pkwy 5 0s Mr. A. J. Jukes-Browne on a Deep Boring at Lyme ere tes hae Se a Perea a is ose cic eee alae ove V v1 CONTENTS OF VOL. IV.—-SIXTH SERIES. NUMBER XXII.—OCTOBER. Prof. R. W. Wood on the Electrical Resonance of Metal Particles for Light-Waves (Second Communication) .... Mr. W. E. Williams on the Magnetic Change of Length and Mlectrical Resistance in Nickel .. ...42...4 age eee Mr. John Stevenson on the Chemical:and Geological History Sijthe Atmosphere ||... 0........) @ ae Mr. W. Rosenhain on an Improved Form of Coal-Calorimeter. Messrs. K. Honda, 8. Shimizu, and 8. Kusakabe on the Change of the Modulus of Elasticity of Ferromagnetic Substances by, Mapnetivation <6... .¢ Asset es yg pe 4) Dr. Meyer Wilderman on the Velocity of Reaction before Complete Equilibrium and the Point of Transition are meached, dc. Part Lh. foo. ne ke 228 Prof. Clarence A. Skinner on Conditions controlling the Drop of Potential at the Electrodes in Vacuum-tube Discharge. (eecond Paper). .\.%. gay tie 5 ge aie ee ee Dr. G. Johnstone Stoney on the Law of Atomic Weights .. Mr. J.J. Taudin Chabot on a Rotating Earth-Inductor without midi Contacts: | a. i «jure Ae ehjece ds islets coe lila oe ee Dr. Thomas Muir on the Jacobian of the Primary Minors of an Axisymmetric Determinant with reference to the cor- responding elements of the latter Notices respecting New Books :— The Scientific Writings of the late George Francis Fitz- Gerald ‘5... aj. not ve SR ee MS 3 ancien Dr. F.-E. Blaise’s A travers La Matiére et L’Rnergie .. Proceedings of the Geological Society :— Dr. C. Davison on the Carlisle Earthquakes of July 9th & 11th, 1901, and on the Inverness Earthquake of September 18th, 1901 :..... .......0 0s i a Mr. F. P. Mennell on the Wood’s Point Dyke, Victoria (Australia)... [ign 8 0 LE vss he acl a Mr. E. Greenly on the Origin and Associations of the Jaspers of South-eastern Anglesey ................ Mr. H. H. Thomas on the Mineralogical Constitution of the Finer Material of the Bunter Pebble-Bed in the West of Eneland |. ..:. .:.si(-4..5 0) eee Dr. C. 8. Du Riche Preller on Pliocene Glacio-Fluviatile Conglomerates in Subalpine France and Switzerland.. 5 Mr. F. A. Steart on Overthrusts and other Disturbances in the Braysdown Colliery (Somerset) 516 CONTENTS OF VOL. LV.—SIXTH SERIES. NUMBER XXIII.—NOV EMBER. Lord Rayleigh on the Distillation of Binary Mixtures ...... Messrs. K. Honda, 8. Shimizu, and 8S. Kusakabe on the Change of the Modulus of Rigidity of Ferromagnetic Substances Ra AEPTRCLIAARIOT DS fe cos OE SU gens Legs BS ev aa punt wig ees Mr. F. B. Jewett on a new Method of determining the Vapour-Density of Metallic Vapours, and an Experi- - mental Application to the Cases of Sodium and Mercury.. 5 Mr. G. C. Simpson on the Electrical Resistance of Bismuth to Alternating Currents in a Magnetic Field............ Dr. J. T. Bottomley on Radiation of Heat and Light from Heated Solid Bodies. (Plates V. & VI.) .............. Prof. E. Rutherford and Mr. F. Soddy on the Cause and Wature of Radioactivity. —Part L.. 0... 2... eee ese ees Mr. J. H. Jeans on the Conditions necessary for’ Equipartition MERE RS ay tse sis 5s Seater Hon. ht. J. Strutt on the Electrical Conductivity of Metals SME ITS Vet OUTS co O's hs aia apts Se ere Se itn Vat ones a Prof. R. W. Wood on the Clayden Effect and Reversal of TEESE Cd TS Senin ea oF me 29S Sie tS SR Pa ee eee Dr. H. A. Wilson on the Current-Density at the Cathode in ena tilectrie Discharseiin. Air... Jee. D2 22 Bae a. 8 wo Ee . Notices respecting New Books :— Dr. E. B. Wilson’s Vector Analysis, a Text-book for the use of Students of Mathematics and Physics, founded upon the Lectures of Professor J. Willard Gibbs .... Mrs Aviom a. ne. Woectric, Are’ ayo. ote sets se as Eugene Néculcéa’s Le Phénoméne de Kerr et les Phé- noménes Electro-Optiques CS OR Be a aa aw Jee Pe eh) eee ey Pe ew NUMBER XXIV.—DECEMBER. Mr. William Sutherland on the Electric Origin of Molecular ESTE CT Se ie eee Ome a) Gi. benaran Ca omere ge.” is MUn anata Messrs. K. Honda and 8. Shimizu on the Vibration of Ferro- magnetic Wires placed in a Varying Magnetizing Field . Prof. J. Patterson on the Electrical Properties of Thin Metal IER oh ere eu See) ¥¢ ae < Abe I. Comparison of the Radiations from Radioactive Substance s Ay By E. RutuerrorD, IA., D.Sc., Macdonald ‘Professor. of Physics, and Miss H. T. Brooks, M.A., McGill University, Montreal *. ’* LL the radioactive substances possess in common the power of acting on a photographic plate and of ionizing the gas in their immediate neighbourhood. ‘The intensity of the radiations may be compared by means of the photograpbic or electrical action ; and in the case of the strongly radio- active substances by the power of lighting up a fluorescent screen. Such comparisons, however, do not throw any light on the question whether the radiations are of the same or of different kinds. It is well known that such different types of radiation as the short waves of ultra-violet light, Rontgen and cathode rays all possess the property of producing ions throughout the volume of the gas, lighting up a fluorescent screen and acting on a photographic plate. None of the radiations from the various radioactive substances show any trace of regular reflexion, refraction, or polarization t. There are two general methods of differentiating to some extent between the various types of radiations. (1) By observing whether the rays are appreciably deviated by a magnetic field. ; (2) By comparing the relative absorption of the rays by solids and gases. * Communicated by the Authors. + A very complete and admirable account of radioactive substances by Henri Becquerel and P. & Mme Curie is given in vol. iii. of the Reports of the Congrés International de Physique held at Paris, 1900. Phil. Mag. 8. 6. Vol. 4. No. 19. July 1902. B ff be if 2 Prof. Rutherford and Miss Brooks: Comparison of The first method has been utilized by Giesel, Becquerel *, Curie, and others. Of the radioactive substances which have been most closely examined, viz. uranium, thorium, polonium, and radium, the latter has been shown by many observers to give out rays deflectable by a magnet. Debierne + states that the radioactive substance which he has termed actinium also gives out some rays deflectable bya magnet. In all cases these deflectable rays are similar in every respect to cathode-rays, and are thus probably streams of negatively charged particles moving with very great velocities. Becquerel{ has shown that the ratio = of the charge to the mass of these nega- tively charged carriers is about 10*, which is about the same value observed for the cathode-rays produced in a vacuum- tube. Radium, in addition to the deflectable rays, also emits non- ‘deviable rays. The ionizing and fluorescent action of radium rays in air at atmospheric pressure, at a distance of from 5 or 6 cms. from the surface of the radium, is very largely due to the rays deflected by a magnetic field. For distances less than this, the ionization is partly due to the deflectable rays and partly to rays which are not acted on by a magnet. Close to the surface of the radium the ionization due to the non- deviable rays greatly preponderates over that due to the deviable rays. This is due to the fact that the non-deflectable rays are very largely absorbed in passing through a few centimetres of air at ordinary pressure. Action of a Magnetic Field on Uranium Rays. Becquerel has examined the rays of uranium in a magnetic field by the photographic method, and found that some of them are deflectable. We have confirmed these observations by the electrical method, and found that only the penetrating | rays of uranium are deviable. One of us § has shown several years ago that the radiation from uranium was complex, and could be divided into two types of radiation, which were called for convenience the a and 8 radiations. The @ radiation is far more penetrating in character than the @ radiation, but is difficult to examine accurately on account of the small conductivity produced by it in the gas, compared with that due to the a radiation. In * Paris Report, 1900. + Comptes Rendus, cxxix. (1899), & cxxx. (1900). t Loe. cit. § E. Rutherford, Phil. Maz. Jan. 1899. the Radiations from Radioactive Substances. 3 order to measure with certainty the very small rate of leak involved, a very sensitive electrometer was employed. The instrument is described by Dolezalek* in a recent paper, and was constructed by Herr Bartels of Gottingen. It was of the usual quadrant type, but was provided with a very light needle suspended by a fine quartz fibre. When the needle was charged to 200 volts it gave a deflexion corre- sponding to 1500 mms., with the telescope and scale at a distance of about 150 cms, for 1 volt between the quadrants. For the special purpose for which it was employed, it was found necessary to improve the insulation of the quadrants and to alter the quadrant connexions. The instrument was easy to work and gave accurate results. It has been employed recently by one of ust to measure the small spontaneous ionization produced in the air, which has been shown by the experiments of Hlster and Geitel t and C. T. R. Wilson § who used specially designed electroscopes for that purpose. In the experiments on the action of a magnetic field on uranium radiation (fig. 1) a thick layer of uranium oxide was Fig. 1. placed on the bottom of a rectangular lead box 5-7 cms. long, 1:8 em. wide, and 4:0 ems. deep, which was placed between the flat pole-pieces of a large electromagnet. The rays, after passing out of the lead box, passed between two parallel insulated plates A and B. One of these plates A was charged to a P.D. of 50 volts above the earth by means of a battery. The other plate B was connected to one pair of quadrants of an electrometer in the usual manner. * Verh. d. D. Physik. Ges. iii. (1901). + Rutherford and Allen, Phys. Zeit. No. 11, 1902. t Phys. Zeit. Nov. 24, 1900. § Proc. Roy. Soc. March, 1901. B2 t Prof. Rutherford and Miss Brooks : Comparison of Hlectrostatic disturbances were completely eliminated by covering the electromagnet and wires leading to it with tinfoil connected to earth. There was always a small current observed between the plates on account of the spontaneous ionization of the air in the testing vessel when the uranium oxide was removed to a distance. The layer of uranium oxide was covered with several thin layers of aluminium of sufficient thickness to completely absorb all the a radiation. The open end of the lead vessel was covered with thin aluminium-foil. In that case the rate of leak of the electrometer was due to ionization produced between the plates by the 6 radiation together with the ions spontaneously produced by the air itself. The latter was accurately determined before the lead vessel containing the oxide was placed between the poles of the electromagnet. As the magnetic field was increased, the rate of leak observed by the electrometer steadily diminished, until with a strong field the rate of leak was reduced almost to that due to the spontaneous ionization of air. This diminution of the rate of leak between A and B is due to the curvature of the path of the rays by the magnetic field before they reach the testing vessel. Since the rate of leak, due to the action of the @ radiation, with a strong magnetic field is reduced to a small fraction of its value when no magnetic field is acting, we may conclude that the 8 radiation is composed almost entirely of rays deviable by a magnetic field. A comparison experiment with radium showed that the 8 rays of uranium were deflected to about the same extent as the radium rays for the same strength of field. No action of a magnetic field on the @ radiation of uranium was observed. Both radium and uranium resemble one another in emitting two types of radiation, one of which is deviated in a magnetic field, and the other not. Absorption of the B Radiation by Substances. Since the 8 radiation of uranium is acted on by a magnetic field to almost the same extent as radium rays, we may conclude that the deviable rays are due to negatively charged particles emitted with high velocities ; for Becquerel has shown that some of the radium rays move with a velocity of at least 1°6 x 10’° cms. per second. The penetrating power of the 8 rays is greater than that of the similar radiation for radium in our possession. It readily passes through 2 mms. of glass before complete absorption. Lenard, in his well-known experiments on cathode-rays, the Radiations from Radioactive Substances. D has shown that the absorption of cathode-rays in substances depends only on the density of the material through which they pass, and is approximately independent of its chemical constitution. On account of the constancy of the uranium rays, it is possible to determine their absorption in different media with accuracy. A few experiments were consequently made to see how closely the absorption varied with the density for the high- velocity particles emitted by uranium. The experimental arrangement is shown in fig. 2, where the dotted lines represent insulators. LARTH. 300 V4). {i a ia ; EARL, A thick layer of uranium was uniformly spread over a shallow rectangular groove 6 cms. square in lower plate A. The plate A was charged to 300 volts by a battery of small accumulators, the other pole of which was to earth. The current was observed between the plates A and B by means of the sensitive Dolezalek electrometer previously described, with, if necessary, a suitable capacity in parallel. In order to completely absorb the « radiation an aluminium plate ‘003 cm. in thickness was fastened tightly over the layer of uranium. The P.D. of 300 volts between A and B (6 cms. apart) was sufficient to carry over all the ions to the electrodes before appreciable recombination occurred. The rate of movement of the electrometer-needle was observed, for different layers of material of uniform thickness successively placed over the uranium. If X is the coefficient of absorption of the radiation in a material, the intensity I of the radiation after passing through a thickness d is given by =e", where I, is the intensity of the radiation at the surface before 6 Prof. Rutherford and Miss Brooks: Comparison of the plate was applied. The absorption of the radiation in a layer of air is negligible compared with that of an equal thickness of solid matter. The maximum current* beiween the plates is proportional to the intensity of the radiation. Preliminary experiments showed that the current dimi- nished very approximately in G.P. with the distance of material traversed, so that the value of > determined was independent of the thickness of the plate. This shows that most of the rays emitted have approxi- mately the same penetrating power. The rays of radium, examined in a similar manner, did not fall off regularly, showing that the rays emitted consist of particles having a wide range of velocities, and consequently a wide range of penetrating power. This is clearly shown by Becquerel, who examined (by the photographic method) the amount of de- flexion of the rays in a magnetic field after passing through different thicknesses of various metals. The following table represents the results obtained. | Substance. r. Density. | Density | RAR Bethe ey TCR, eee 14:0 2°45 57 ITSO ai 1s. csi ten k eaten 14:2 2°78 5:1 HB WOMILO |. ..cesagrewsn suees 6'°5 1°14 7 GOOG Disc. of onemncwees 2°16 “40 5°4 Cardboard............... 37 ‘70 53 MUP ONY eRe scene cack Backus 44 78 5°6 itcgaiina No baci 140 2-60 B4i ie OPEN hehe =e enue 60 8°6 70 RIVE occ ccesceoceacemives iti 10°5 fiat LD ECC IN aN Ed i lw 122 145 10°8 BPN beets SEER 96 73 13°23 It will be observed that the value of the coefficient of absorption divided by the density is very approximately the same for such different substances as glass, mica, ebonite, wood, iron, and aluminium. The divergences from the law are, however, great for the other metals examined, viz. copper, silver, lead, and tin. In tin the value of X divided by the density is 2°5 times its value for iron and aluminium. These differences show that the law of the absorption of cathode-rays depending only on the density, is not true for all substances. Hxperiments are at present in progress to see whether there is any simple numerical connexion between the values of A divided by density for different metals, and to extend the * Rutherford, Phil. Mag. Jan. 1899. the Radiations from Radioactive Substances. 7 results so as to include a variety of substances in the solid and liquid state. Absorption of the Rays by Solids and Gases. The rays not acted on by a magnetic field can be dis- tinguished from each other by their power of penetrating through thin layers of metal, and their absorption in gases. If, on examination, the penetrating power of two types of radiation proves to be the same in each case for all sub- stances, it is extremely probable that the two radiations are © identical. By examining the diminution of intensity of the radiation when sheets of metal of the same thickness are placed over the radioactive substance, the homogeneity or complexity of the radiations can be tested. If the intensity I of the radiation after passing through a distance of metal is given by I,e~**, where J) is the original intensity and A the coefficient of absorption, we can conclude that the radiation is homogeneous in character. If this condition is not fulfilled the radiation is complex. One of us* has at different times given results for the absorption of some of the different radiations in solids and gases. In this paper we have extended the results and ‘compared the different types of radiation under, as far as possible, the same conditions. In the case of both uranium~* and thorium it has been shown that the absorption of the radiation is the same for all the different compounds of each element examined. When the types of radiation are complex, the relative amount of rays of different types may vary for different compounds, but so far there is no evidence that the actual radiations themselves are altered. It is only necessary therefore to examine one compound of each element for the purpose of comparison of the types of rays emitted. The following substances have been employed in the experiments :-— Uranium Oxide & Thorium Oxide.—Two different samples of each obtained from Schuchart of Germany and Himer and Amend of New York gave similar results. Polonium.—This substance was kindly prepared for me by Dr. Walker of McGill University from pitchblende, after the method described in Curie’s first paper. Since that time the intensity of the radiation given off has steadily diminished ; but the type of radiation has been unaltered. * E. Rutherford, Phil. Mag. Jan. 1899, Feb. and March 1900, + Owens, Phil. Mag. Oct. 1900. 8 Prof. Rutherford and Miss Brooks : Comparison of Radium.—Two different specimens were employed. One was of impure radium chloride kindly presented to me by Hlster and Geitel two years ago; this did not give off any emanation and only a small proportion of de- flectable rays. The other, from P. de Haen, Hannover, was not very strong in deflectable rays, but gave out a large amount of emanation when slightly heated. In the course of the es shall examine the following types of radiation. A. Uranium. (1) The @ or early absorbed radiation. (2) The £8 or deflectable rays. B. Thorium radiations. (3) The simple radiation given out by a thin layer. (4) The radiation from the “ emanation.” (5) The excited radiation. C. Polonium. (6) Simple radiation. D. Radium. (7 ) Radiation not affected by a magnetic field. (8) Radiation from the emanation. (9) Excited radiation. (10) Magnetically deflected rays. Absorption of Radiation by Metals. In examining the absorption of the radiation by metal-foil and other substances, the apparatus shown in fig. 2 was employed. The active compound in the form of fine powder was uniformly spread over a shallow depression 6°5 em. square in a large lead plate. This corresponds to plate A in fig. 2. The rate of leak was observed by. means of an elec- trometer between plates A and B with, if necessary, a suitable capacity in parallel. The plate A was connected to one pole of a battery of 300 volts, the other pole of which was earthed. Preliminary experiments showed that with this voltage the maximum or saturation current between the plates was obtained for all the radioactive substances. examined. In most of the experiments described in this paper an Ayrton electrometer was used. In some of the later experi- ments, however, the White pattern of Kelvin electrometer wasused. ‘he former electrometer could be readily arranged to give 200 mm. divisions for 1 volt P.D. between the the Radiations from Ltadioactive Substances. G quadrants. As most of the experiments were carried out during the very dry Canadian winter, it was very essential to screen the electrometer and connexions with testing appa- ratus by wire gauze. Unless precautions of this kind were taken, every movement of the observer produced sufficient frictional electrification to disturb the electrometer. For the same reason and also for convenience the quadrants were separated by a cord connected to a suitable key and operated at a distance. The method of observing the rate of leak was as follows: — A seconds-pendulum was placed before the observer. At the instant of passing the middle point of its swing the quadrants were separated by a sudden pull of the cord. After ten or more swings the connexion between testing- apparatus and the electrometer was broken by means of an insulated key, operated by a second cord. The deflexion of the electrometer-needle when it came to rest was then observed. The number of scale-divisions passed over, divided by the time between the separation of the two keys, was taken as a measure of the rate of leak. This method is more accurate than the usual one of observing the time the electrometer- needle takes to pass over say 100 divisions of the scale. The final deflexion is independent of the amount of dawping and of any oscillation or irregularity in the movement of the electrometer-needle. In experiments with uranium, thorium, and polonium a very thin layer of the material was employed. This is essential in the case of thorium oxide, in order that the rate of leak due to the emanation from it may be negligible compared with the rate of leak produced by the ordinary radiation. Jn dealing with radium a very small amount of material was dusted by means of a gauze as uniformly as possible over a platinum plate. For the specimen of radium employed the rate of leak due to the emanation and rays deviable by a magnet was in this way rendered negligible compared with the rate of leak due to nondeviable radiation. Suitable capacity was, if necessary, placed in parallel with the electrometer to reduce the rate of leak. In figs. 3and 4 (p. 10) curves are given for the absorption of the different radiations by thin aluminium foil and Dutch-metal respectively. In order to plot the curves on the same scale the rate of leak for the bare radioactive plate is in each case taken as 100. The average thickness of aluminium-foil was ‘00036 cm., and of Dutch-metal ‘00012 cm. The curves are given for two specimens of radium, marked C and HE, which 10 Prof. Rutherford and Miss Brooks : Comparison of corresponded to two specimens of radium from P. de Haen, marked “concentrated”? and “einfach”? respectively. ‘The Fig. 3. a i PR 2 OE ite ~Aelyrtayersocore nck |_| 0 ! é 3 4 5 6 7 8 ) 70 curve for the specimen sent by Herrn Elster and Geitel was not very different from the two shown. Curves obtained from specimens of the minerals “thorite” and “ orangite” gave practically the same curves as for thoria. The radiations may be arranged in the following order as regards the power of penetration, beginning with the most penetrating. Excited radiations due to Thorium and Radium : : Thorium Radium Polonium Uranium. The same order of penetration is observed for all the the Radiations from Radioactive Substances. Td substances examined, viz. aluminium and Dutch-metal, tin- foil, and paper. The same order, as will be shown later, holds also for the penetrating power of radiations in air. Absorption of the Radiation in Air. The method employed of determining the absorption of the radiation in air was similar to that explained in a previous paper (Phil. Mag. Jan. 1899, p. 124). Two insulated parallel plates kept a fixed distance of 2 cm. apart, could be moved by means of a screw to different distances from the parallel radioactive surface. The radia- tion from the active surface passed through a circular opening in the lower plate, covered with thin aluminium-foil, and was stopped by the upper plate. The current. between the two fixed plates for a voltage sufficient in all cases to give the maximum or saturation current, was determined for different distances from the radioactive plate. If the radius ‘of the active surface is large compared with the distance of the lower of the pair of plates from it, the current between two fixed plates for a distance # of the lower plate from the radioactive surface, can be readily shown from the theory of ionization (loc. cit.) to vary as e~, where 2 is the coefficient of absorption of the radiation in the gas. The results of the experiments are given in curves fig. 9. For each radiation the maximum rate of leak between the plates at a distance of about 2 mm. from the active surface is taken as 100, for the purpose of comparison. It will be : 4 mire. 2) 6 & [OPN “IG SIBy FeO ey ees) Fe4 eG: - cB) 30). 22. 54 36 38 40 42 observed that the rate of leak, which is a measure of the intensity of the radiation, falls off, approximately in G. P. 12 Prof. Rutherford and Miss Brooks: Comparison of with the distance. The thickness of air through which each radiation passes before the intensity of the radiation falls to half its original value, is given in the following table. | Radiations. Distance in ems. | | Excited radiation from radium and thorium. 1°65 | UPA OWIIL, 0)5a dogdcaek sc ears ee oe ee ee eee 1:0 | PRAaU WG, BF. Aescoabiods. ina ttc wold deans eee eames dara wk) . AO ret MCE” 2 week es ak cane apes See ee eee Sere ‘45 The penetrating power of the different radiations in air thus follows the same order as metals and solid substances. Connexion between Absorption and Density. From the curves of absorption of the radiations in metals and air, the coefficient of absorption » can be readily deter- mined. The following table gives the value of A for aluminium and air for the different radiations. | | Radiation. | dX for aluminium. r for air. Excited radiation......... 830 ‘42 MVAOTUETI he Current, amps. x5'2.107°, - 20 The curves III. have been drawn to show the saturation- currents for different discharge-tube and bell-jar pressures, as indicated in the following table :— came, | yall, | Babe re b +64* 52 b’ — 64 ” ¢ ee Ev 9'5 fy yeas : | 4110 10-7 d' —110 % * A + field indicates that the plate was charged positively. 40 Mr. J. J. HE. Durack on Lenard Rays. - The curves have only been carried up to the point where the Lenard rays reach a maximum, past this the presence of . Réntgen rays prevents one from giving a proper interpreta- ‘tion to the values of the saturation-currents. We can now find a, for any type of radiation (indicated by the pressure in the discharge-tube). I have selected the type given out when the pressure was 195 x:0002 mm., as this is well removed from the point where Réntgen rays are given off, and is considered likely to be most accurate. Calculating a, in this way we get the following numbers:— Pressure mm. ap. ap p. Oy ol “48 9°4 4:0 43 o'2 2:0 “39 The mean of these three values of @,/p is 43, that is the number of pairs of ions one Lenard-ray ion makes in travelling 1 cm. of air at a pressure of 1 mm. of mercury is °43. Professor Townsend* in his experiments found 21 for the number of ionizing collisions one ion (produced in air by Réntgen rays) makes under the same conditions, or about 50 times the number obtained here. This difference I was unable to account for by any experi- mental errors, but before seeking an explanation it was thought desirable to confirm the result. 1 therefore carried out further experiments, using a D’Arsonval galvanometer instead of an electrometer to measure the currents. The arrangement was very simple; the cells, plates, and galvanometer were connected in series and the window always to earth. Measurements of the Lenard-ray current were first made by pumping the bell-jar down to a pressure of about ‘01 mm. It was found to make no difference whether a field + 10°5, — 10:5, or 0 volts per cm. was applied to the gas; the variation of the current was also in agreement with the electrometer observations. a, was next determined from. the same forrhula as before for two pressures, as shown in the table :— Bell-jar Field. pressure, mm. Volts per cm. at Lp|P- Os 4 Fe 500 Td “V7 iG 625 15°5 6 * Townsend, Phil. Mag. Feb. 1901. Mr. J.J. E. Durack on Lenard Rays. Al The five values of a, taken from these two series have been plotted in curve IV. It will be seen that four of them lie Curve IV. Pressure, mm. on a straight line; this line does not pass through the _origin. This may be due to an error in setting the zero of “the McLeod gauge or in measuring the ratio of volumes. These figures justified one in believing the correctness of former results obtained for a,/p ; they are larger than those obtained in the former series, probably because larger E.M.F.’s were applied to the gas. To avoid the trouble of taking current-E.M.F. curves in -all cases and yet be sure the gas was saturated, an H.M.F. was applied to the gas which was a little less than sufficient to give a free fall of 1 volt between collisions of the ions with molecules of air as these ions move towards the plate. This 1 volt free fall has been shown by Prof. Townsend * to give the ions just sufficient velocity to produce others by collisions. This was the plan adopted in working with the galvanometer, and I think it is probable some additional ionization due to the Townsend effect has come in to make a, too large. This conclusion that we have come to, viz., that very fast moving ions are less efficient ionizers than slower ones, is In agreement with the discovery of Becquerel, viz., that of all the deflectable Becquerel rays the slower ones are most easily absorbed. But it has been shown by several observers that ionization is proportional to absorption : hence we would expect the slow Becquerel rays to be more efficient ionizers than the fast ones. As an explanation of this the following theory was proposed * Townsend, Joc. cit. 42 Mr. J. J. BE. Durack on Lenard Rays. by Prof. J. J. Thomson some time ago at a meeting of the Cavendish Physical Society. Suppose a force to act between an ion and a molecule when the former approaches the latter, the force varying inversely as the square of the distance. Let 7 be the radius of the sphere of action of a molecule, that is, an ionizing collision will just occur when an ion comes within this distance from its centre. Let an ion carrying a charge e and of mass m be projected from an infinite distance with velocity v in the direction of the molecule. The initial kinetic energy of the ion is 1 2 dmv’. The work done by the forces when the ion is distant 7 from 2 the centre of the molecule is 2 Now the projected ion will just have sufficient energy to produce a pair of ions when 2 2 é —_—_ , e Hence collisions just occur when Pi r= —. mv? But the number of collisions in unit distance is propor- tional to r’. 4 Hence ey cal aos mv OF @p varies inversely as the fourth power of the velocity. On comparison of my experiments with those of Prof. Townsend, a, does not appear to decrease so fast as is given by the inverse fourth power of velocity. However, this depends on the law of force assumed to act between an ion and a molecule; the argument is the same if we assume (as Maxwell did for the law of force between molecules) the inverse fifth power, in which case a, varies inversely as . the velocity. As far as one can estimate from Townsend’s results and my own, this seems not improbable. I have tried to give an explanation of the variation of a, with velocity based on the consideration of the induced charge on a molecule when an ion passes close to it. Let us assume that.a molecule is a sphere, capable of having a charge induced on it. Mr. J. J. E. Durack on Lenard Rays. 43 When an ion approaches the molecule there will be an attraction between them owing to the induced charge on the molecule. If the mass of the ion is small compared with that of the molecule the force will be directed to the centre of the molecule, and at a distance r is equal to ee 2 =a" ——— aaa ORL 7 (7 Eis a”) Z where a is the radius of the molecule, and ¢ is the charge on . theion. The potential at the point r is therefore Tr 9 2 V=ea* | ——5 7 @ ae yp eat. 2027? — a)" Let an ion be projected from an infinite distance with a velocity which is large in comparison with the velocity of translation of the molecules; let p be the perpendicular from the centre of the molecule to the direction of the initial velocity. Let r = the length of the apse, v= the velocity at the apse. Then ze 2 oS F ea 1 ee | J2 ma —— SIL, . 3 a Bee on 2 2 27? (7? a*) where m is the mass of the ion. Also vp=v'r ; hence : vp e7u3 Dio cno¥ amv? = $m—— — 55 -5—s r rig Uicterad ep or ea it id ies eect Eye mv* 7?—a _ Let p, be the value of p for which a collision just occurs, 2. e. when p=P, the ion is drawn inside the sphere of action by the attracting forces. Also let 7, be the radius of the sphere of action, N the number of molecules in 1 ¢.c. of the gas. We have the mean free path of the ion 1 ERE eee Se ERE eee PE or a=mNp,?, but ea 1 pee 2 9 24 a) _—_ Tr | ° Pi mr 74?—a A4 Mr. J.J. E. Durack on Lenard Rays. Hence Pathe ce eee Oe ap = aN] 9,2 T rae roa If we suppose, as is very frequently done, that the radius of the molecule and of the sphere of action are identical, i. e. that actual contact takes place at a collision, the formula for a, becomes 3 See a,=mN E + move om e, where p is the radius of an ion. The experimental evidence available is not sufficient to test the truth of this formula, but we can make a rough estimate of p from the values of a, obtained by Professor Townsend and myself. BY pe ee 1) ee er )/ (1 32m10® ) Taking the velocity giving Townsend 2=21 as 3.108 cm. per sec, and the velocity in the case of the Lenard rays as 4.10%. | From this we get p=10-" em. From the values of e/m for cathode rays and for hydrogen in electrolysis we know that m the mass of an ion is approx. 10-3 times the mass of an atom of hydrogen, and so if the densities are equal the radius of an ion would be of the order 10-° em. ; but on Prof. Thomson’s view of an atom, viz. that it is made up of ions, the density of an atom would be much less than the density of an ion; hence 10-° is too large for the radius of the ion. Also we know that: the radius of the ion must be greater than 10-18, for it has been shown by J. J. Thomson fF, and also by Searle {, that the inertia due to a moving charge e on a sphere of radius p is p when the velocity is small compared with that of light, * It was pointed out to me that this form A+ = is the same as that 2 deduced by Sutherland in calculating the influence of cohesion on the free path (v. Meyer, Kinetic Theory of Gases, p. 425), and hence it is nut necessary to assume any more than that the force is central. However, I have assumed Jess than this, having merely supposed a charge could be induced on the molecule, that the force is central, and the actual law of force follows from electrostatics; moreover, we deduce a definite form for a in terms of quantities which may be experimentally determined, and thus we can test the theory. + J. J. Thomson, Ree. Researches, p. 21. t Searle, Phil. Mag. xliv. 1897. & Magnetostriction of Steel, Nickel, Cobalt, and Nickel-Steels. 45 e being expressed in electromagnetic units. As the velocity’ increases m, increases ; hence , what is usually taken to be the mass of an ion consisting of the ordinary mechanical mass together with the apparent mass due to the moving charge, is greater than m,. 2 {2 Hence AS 3p t. @. 2 la i 4 Sa —13 3 10 The value therefore that we have calculated for o lies between the limits that can be assigned to it in other ways. The experiments described in this paper were carried out in the Cavendish Laboratory, and I have much pleasure in expressing my gratitude and best thanks to Professor Thomson for many suggestions and kindly advice given _during the progress of the work. IV. On the Magnetostriction of Steel, Nickel, Cobalt, and Nickel-Steels. By H. Nacaoxa, Professor of Physics, and K. Honpa, Lecturer in Physics, Imperial University, Tukyd*. § 1. Introduction. § 2. Magnetization of Steel, Nickel, Cobalt, and Nickel-Steels. -§ 3. Change of Length by Magnetization in (a) Steel ovoid, (0) Nickel ovoid, (c) Cobalt (cast and annealed) ovoids, (d) Reversible Nickel ovoids containing 46, 36, 29, 25 per cent. of Nickel, (e) Reversible Nickel-Steel wires containing 46, 35 per cent. of Nickel in low fields. § 4. Effect of Mechanically Elongating Cobalt and Nickel-Steels on Magnetization, and the reciprocal relations with the change of length. § 5. Change of Volume by Magnetization in Steel, Nickel, Cobalt, and Nickel-Steel ovoids. § 6. Wiedemann Effect in Iron, Nickel, and Nickel-Steel wires. (a) Twist produced by the interaction of circular and longitu- dinal magnetizations, (6) circular magnetization produced by twisting a longitudinally magnetized wire, (c) longi- tudinal magnetization produced by twisting a circularly magnetized wire, (d@) application of Kirchhoff’s theory to Wiedemann effect and reciprocal relations. § 7. Summary of the Results. § 1. Iytropuction. N the course of our researches on the magnetostriction of different ferromagnetic bodies, questions of various cha- racter presented themselves, both with regard to the method * Communicated by the Authors. 46 Prof. Nagaoka and K. Honda on Magnetostriction of measurement and the nature of the sample. The minute- ness of the effect necessitated precautions against diverse sources of error, such as the non-homogeneity of the mag- netizing field, and the non-uniformity of temperature. All these different sources of error, however intricate they may at first sight appear, can, by properly arranging the measuring apparatus, be eliminated. In the present investigation we have used the method of observing the change of length and of volume already described in our former papers*, with slight modifications. Apart from these instrumentalities, the diversity in the character of magnetostriction with different samples is hardly to be avoided. Experiments by Rhoadst with rolled and stretched sheets of iron sufficiently prove that the treatment of ferromagnetic bodies has great influence on the change of length accompanying the magnetization. In our former ex- periments on the magnetostriction of iron, steel, and nickel, the soft iron was what may be practically considered homo- geneous, but the nickel ovoid was turned into shape from a thick plate. It thus seemed advisable to repeat the experi- ments with more homogeneous metals. In addition to this, our investigation did not include the magnetostriction in. cobalt, the only specimen hitherto examined being an ovoid, which was broken in two pieces, and firmly fixed together by wrapping thick paper over the broken edgef. Unlike other experimenters, we tested cobalt in the present investigation in the cast and annealed states, and found an extraordinary difference in the change of length. The curious property of irreversible nickel-steel as regards ¥ g magnetization has been known for a long time by the experi- ment of Hopkinson. The question of magnetostriction in reversible nickel-steel was a tempting subject of investigation, especiaily in connexion with the remarkable small thermal ex- pansion possessed by the metal, and its practical utility in the construction of scales and other instruments, which will not be affected by the variation of temperature. Moreover it was very interesting to examine the nature of the magnetostriction in nickel-steel, as itis composed of two substances, whose length- change by magnetization is of opposite character in weak fields, but similar in strong. A simple conjecture may suggest that the changes produced by magnetization are according * Nagaoka, Phil. Mag. Jan. 1894; Wied. Amn. liii. p. 487 (1894) ; Nagaoka & Honda, Phil. Mag. Sept. 1898, April 1900; Nagaoka, Rapports presentés au Congrés International de Physique, Paris, ii. p. 536 (1900). For literature on magnetostriction see Rapports. +t Rhoads, Phys. Rev. vii. p. 65 (1898); Phil. Mag. Nov. 1901. { Nagaoka, Wied. Anm. lil. p. 487 (1894). of Steel, Nickel, Cobalt, and Nickel-Steels. 47 to the relative proportion of the magnetostriction of the con- stituents, but the phenomena are of a very complex nature. Associated with the change of length and of volume comes the Wiedemann effect, which is measured by the amount of torsion caused by the interaction of circular and longitudinal magnetizations. The measurement in cobalt must at present be postponed, as the metal cannot be brought to a geome- trical shape suitable for experiment on account of its brittle- ness. Investigation of the effect in nickel-steel of different percentages presents the phenomenon in the same aspect as for the length-change, and the sense of twist 1s determined by that of iron in weak fields. A singular characteristic of magnetostriction is its re- ciprocity. with the effect of stress on the magnetization of different ferromagnetic substances. In the present instance, we haye specially turned our attention to cobalt.and nickel- steels. As will be expected from the nature of the length- change, the former metal is characterized by the existence of a amore point closely analogous to that bearing the name f Villari for iron, while with the latter the effect of the Retadinal pull always results in the diminution of. mag- netization. The parallel statements giving the correlation between the magnetization and the effect of torsion, first noticed by G. Wiedemann, can thus be extended to other effects of stress and the strain resulting from the magnetization. § 2. Intensity oF MAGNETIZATION IN STEEL, NICKEL, CoBALT, AND NICKEL-STEEL OvoIps. In all of our experiments we noticed the change of dimen- sions by magnetization and the strength of ‘the field S (H=H'— _—NS, where "1 is the external field, N the demag- netizing factor, and $ the intensity of magnetization). It will therefore be a out of place to make a digression on the magnetization of the ferromagnetic substances here ex- amined, in order to enable us to examine the various changes, considered as functions of the intensity of magnetization. The following table gives the dimensions as well as the Metal. a (em.). | ¢ (em.).|v (c.em.).| — p. N. Le UAE BORO aE Ie) ses a 0:493 10-00 10-40 | 7°85 | 0:0886 LE A Sealine 0:493 10-00 10°40 8°87 | 00836 Sate OU Ge eac ss cdeves manacu men 0°493 10-00 10°38 8:26 | 00836 Annealed Cobalt ...............-.. 0°495 10:02 10°52 | 8:20 | 0:08386 | Nickel- Steel (46 p. cent. Ni) ...| 0°494 10°01 10°45 8:15 | 00836 - », (36 p. cent. Ni) ...| 0°496 10°01 10 48 811 | 0:0836 he », (29 p. cent. Ni) ...| 0°492 10°01 10°43 8'12 |0:0835 9 », (20 p. cent. Ni) ..,| 0-494 10°02 10°40 8:05 | 0:0836 Va 4 48 Prof. Nagaoka and K. Honda on Magnetostriction demagnetizing factor N of the ovoids examined in the present experiments. a, semi-minor axis of ovoid; c, semi-axis of rotation of ovoid; v, volume; p, density, determined by hydrostatic balance. The difference in the volume of ovoids is to be attributed to the slight deviation from exact geometrical shape. As most specimens of cobalt contain more or less quantities of nickel, the cast and annealed samples were chemically analy ‘sed by Mr. Y. Suzuki, student in chemistry, with the following result :—Cast cobalt, Co. 93°36, Ni 5°05, Fe 1-20;9ame 38, Si 0°39, Cu 0°17, Mn 0: 12; ‘Annealed cobalt, Go 92° 7A, Ni 4-07, Fe 1:07, CG 1-64, Si 0:28, Cu 0°15, Mn 0:04. The magnetization was determined magnetometrically * given in the following table :— Cast Steel. Nickel. Cobalt (cast). | 0:8 44 10 14 27 30 13 13 aT 76 56 83 16 319 55 139 14:7 274 31 633 78 198 19°4 340 74 878 FLY. 252 30:0 467 23°0 1122 18:2 314 44-7 572 140 14383 3o'3 O17 89°8 778 302 1555 59°9 426 256 984 511 1627 116 459 474 1080 597 1644 482 484 643 1119 672 1648 796 486 720 1136 Cobalt Nickel-Steel Nickel-Steel Nickel-Steel (annealed), (46 p. cent. Ni). || (86 p. cent.). (29 p. cent.). a 36 4 0:9 ao fi ete 38 12 24 do: 22 24 102334) 4Afa8 134 26 81 22-4. 38 42 241 9-4 352 6-4 139 426 90 6:2 465 14:6 524 ite 188 Ti) 188 169 926 || 304 720 247° | 195 367 35°5 LLO8: 4, ees 900 46:2 243 281 439 120 1274. |, 150 934 688 949 364 AQ7 231 1308 | 262 953 140 | 256 461 568 || 380 1323 || 367 962 || 325 264 617 633 557 1333 soto) S71 AYE 273 788 699 778 1345 | 818 992 893 280 * The magnetizing coil had the following constants ; a eS =380cm. diam. of the core = 3-2 em. » Ann=3197, ‘resistance =0°63 ohm. The ovoid was placed axially, so that the extr emities of the axis were at 5 cms, distance from the ends of the coil, thus insuring the uniformity of the field. a. , of Steel, Nickel, Cobalt, and Nickel-Steels. . 49. The curves of magnetization are represented in fig. 1. The most magnetic of the metals here examined is cast steel, | Fig. 1. F.C) & m ‘ rs} \% > rm 0 100 200 300 ©«6=6480 500 600 700 are 1000 whose magnetization comes very near to that se soft iron. Of the two kinds of cobalt the cast specimen lies between steel and nickel ; but with the annealed specimen the suscepti- bility is small in weak fields, and less than in nickel, and the differential susceptibility (3) is greater in the strong, SO that the intensity of magnetization becomes greater than in nickel. Of the three kinds of reversible nickel-steels the 46 per cent. Ni specimen approaches steel, the 36 per cent. Ni lies near cast cobalt, and the 29 per cent. Ni is less magnetic than pure nickel. The magnetization reaches asymptotic value in fields less than those for steel or cobalt. The 25 per cent. Ni specimen is only feebly magnetic, so that its magnetization is scarcely to be detected by the magnetometer. Here we notice a singular fact, that the intensity of mag- netization in nickel-steel is not proportional to that of the constituent metals. § 3. Cuance or Lencru py MAGNETIZATION. (a) Cast Steel (fig. 2). Dr. H. du Bois was kind enough to give us a piece of cast steel which was regarded as the most homogeneous specimen Phil. Mag. 8. 6. Vol. 4. No. 19. July 1902. E 50 Prof. Nagaoka and K. Honda on Magnetostriction at present obtainable. The rod was turned into an ovoid, and its change of length measured in the manner already described in our former paper. _In low fields the ovoid elongates and reaches a maximum, whence it gradually diminishes, till it indicates no elongation. The decrease goes on steadily, but the rate of change becomes gradually less, and ultimately assumes an asymptotic value. As will be seen from the curve of the length-change (see fig. 2), the general feature resembles that of iron, with slight difference in quantitative details. (b) Nickel (fig. 2). The nickel ovoid which we formerly used for the measure- ment of length and volume changes was prepared from a thick plate of the same metal. ‘Although the ovoid was heated in a charcoal fire for several days lack of homo- geneity was undeniable. To guard against such mischances we have tested a new specimen supplied by Johnson and Matthey, shaped into an ovoid from a cylindrical rod. — The nature of the change does not materially vary from the former specimen. In weak fields the contraction takes place at first slowly, but gradually at an increased rate. Between fields 5 and 100 the rate of diminution is very rapid, -10 2 Siem IS but the change becomes at last sphistne when it amounts to about 38x 10-§ It appears from the curve (see fig. 2) of Steel, Nickel, Cobalt, and Nickel-Steels.- iL that the further diminution of length will be but slight, even if the field be increased to several thousand units. (c) Cobalt (fig. 2). One of us has already examined the iiat of laaatit in a cobalt ovoid, which unfortunately was broken in two. pleces. The result was notwithstanding in close conformity with that already discovered by Bidwell. Rods of cobalt, obtained from Johnson and Matthey, were turned- into ovoids of the same dimensions as for the two former metals. One of the ovoids was examined in the state just as it issued from the lathe, while the other was annealed in a charcoal fire for about four hours, after carefully wrapping it with asbestos paper. As the change of length by magneti- zation and the intensity of magnetization were characterized by a remarkable difference in ‘character, it would be well to describe the phenomena separately for cobalt ovoids which underwent different treatments. Cast Cobalt.—The behaviour of cast cobalt, as regards the length-change, is similar to that of nickel in weak fields, Instead of reaching an asymptotic value, as in nickel, the contraction of cobalt reaches a maximum at about A= 160, from which the metal gradually recovers with increase of field-strength, till it attains its initial length in §=740. The metal, however, goes on elongating but at a less rapid rate up to $= 2000, which is the strongest field employed in the present “experiment. Representing ‘the change of length by means of a curve (see fig. 2) we notice a singular trend, somewhat resembling the inyerted form of the curve showing the same change for iron and steel. If the existence of the maximum elongation in iron warrants the existence of the Villari point, a point of opposite character will exist in cobalt if the metal be subjected to loading. Annealed Cobalt.—The cast cobalt has a silver y hue, similar to nickel only lacking the yellowish lustre of the latter. By annealing cobalt the “surface-colour turns ashy grey, and the permeability of the metal diminishes (see § 1) ina remarkable degree, as will be seen from the curves of magnetization (tig. 1). The change of length by magnetization takes place at first slowly, but goes on steadily i increasing till it amounts to nearly 25 x 10-° for H=2000. The curve (see fig. 2) re- presenting the change is therefore very simple, approximating to a straight line. As will be found later on, we found the reciprocity between the strain caused by magnetization and the effect of stress on the magnetization again established, since the longitudinal pull only produces diminution of magnetization. 2 52 Prof. Nagaoka and K. Honda on Magnetostriction (d) Reversisie Nickel-Steels. Through the kindness of Messrs. Ch. Ed. Guillaume and Dumas, who supplied us with the different samples of reversible nickel-steels, manufactured by Commentry-Fourchambault at Decazeville, we were enabled to examine the magneto- striction of reversible nickel-steels in its various aspects. The samples to be tested were either turned into ovoids of the same dimensions as for the other metals, or used in the form of wires. ‘These two sets of metal of different shape do not show serious discrepancies in the observed results, which are given below for specimens containing different percentages of nickel, either in the form of ovoids or wires. It is to be remarked that the annealing of nickel-steel was conducted in a glass tube, through which hydrogen was kept in constant circulation, and heated to 500° C. upwards for more than three hours. | The curves of the length-change are plotted in fig. 3. All the nickel-steels indicate increase of length in fields up to about H=2000. The character of the change for 46 per cent. Ni resembles that for nickel with opposite sign, inas- much as the curve of elongation in the former has great resemblance to that of contraction in the latter, and is similar to that for the intensity of magnetization. The elongation in very weak fields takes place slowly, but in fields of about 30 units the rate of change is most rapid, and soon reaches an inflexion-point, whence to increase in length very slowly and finally in an asymptotic manner. Fig. 3. Se. A cc ee Wa 20 x10 200 400 600 800 1000 1200 1400 1600 1800 7000 § a=nickel-steel ovoid (46 p. c. Ni). freee ot ky (30 pee. ING). C= yh oF BS (29 p-c. Ni). a'=nickel-steel wire (46 p.c. Ni) annealed. SO Aa he pe 7 eae unannealed, bi'= , » 3 (35p.c. Ni) annealed. Nip te Ae es m e * unannealed, | With the 36 per cent. Ni we observe similar features in the curve of elongation. ‘The inflexion-point lies in higher of Steel, Nickel, Cobalt, and Nickel-Steels. 53 fields, but the elongation is less than in 46 per cent. Ni. After this stage is over the ovoid goes on elongating at an almost constant rate, which is greater than for the 46 per cent. Ni. Although the field at which the curves for 46 per cent. and 36 per cent. Ni intersect has not yet been reached, we can easily infer that if the field be sufficiently increased, the elongation in 36 per cent. Ni*, which is the least expan- sible by rise of temperature, will exceed that for 46 per cent. Ni. The contrast between 46 per cent. and 36 per cent. Ni is similar to that between 386 per cent. and 29 per cent., so that what has just been remarked with respect to the two former alloys equally applies to the relation between the two latter. It is also remarkable to observe that the 29 per cent. Ni, which will apparently indicate the largest increase of length if the field be made sufficiently strong, is the least susceptible of the three nickel-steels. With the 25 per cent. Ni we could not detect any change which is within the scope of measurement now attainable with the present arrangement. _ The nickel-steel wires in the annealed state present similar enanges of length to the ovoids. In the hard drawn state the change is decidedly less than for the annealed. The curves of the length-change in iren or nickel, placed side by side with those in nickel-steel, present a singular contrast. As is well known, nickel contracts instead of elongating like iron, the amount of contraction being several times that of iron. The feature here presented by nickel- steel is similar to nickel as regards the amount and the character of the change, but as to the sense of elongation it is similar to iron in weak fields, increasing instead of diminish- ing as in nickel. It thus appears that the length-change by magnetization is not of a simple nature, and not to be easily determined from the percentages of the constituent metals. (e) Nickel-Steel wires in low fields. Urged by the question of the practical utility of the metal we made special investigation into the change of length in low fields, such as may habitually occur in the neighbourhood of electric installations or in the terrestrial magnetic field. The question will be of great importance in deciding the effect of the terrestrial field; as one instance, we may mention that in using Jaderin’s wire of nickel-steel in geodetic measure- ments. One may suspect, from what has already been described, that the effect of the magnetic field will not be * The expansion-coefficients a for nickel-steel are as follows :— For 29 per cent. Ni: a=0-000010. » 26 per cent. Ni: a=0-C00001. ,, 46 per cent. Ni: a=9-000009. 54 Prof. Nagaoka and K. Honda on Magnetostriction of the same magnitude as that of thermal expansion, which, ‘as is well known, is of very minute amount. Experiments in low fields show that the magnetostriction plays no important part in the use of nickel-steel scales; only in measurements of extreme accuracy it will be necessary to add a very small correction to the measured values, according as the scale is placed in the magnetic meridian or perpendicular to it. As will be seen from the curves of elongation (fig. 4) the difference in a metre will generally be less than ;/, » for measurements made in the said directions. Q bu ' a’ =nickel-steel wire (45 p. cent. Ni) 4’!=nickel-steel wire (35 p. cent. Ni) annealed. annealed. a" =Ditto, unannealed. 6"=Ditto, unannealed. One distinct feature in the curves of elongation is the effect of annealing. In both 45 and 35 per cent. Ni the wire elongates much more in the annealed than in the hard drawn state, so that in cases where the change caused by mag- netization is to be feared we shall be able to eliminate the errors due to magnetostriction in a considerable degree by using the unannealed metal. §4. Errecr or Mecnanicatty ELoncatine CoBar AND NICKEL-STEELS. A remarkable feature in the magnetostriction is the re- ciprocal relation between the strain caused by magnetization and the effect of stress on magnetization. We have already examined the different changes from this standpoint for iron and nickel. In the present experiment we made special examination into the effect of longitudinal pull on the mag- netization of cobalt and nickel-steels in the same light. Magnetometric measurement of the change of magnetiza- tion of a cast cobalt cylinder by loading shows decrease in low fields (see fig. 5). As the field strength is increased the amount of the decrease reaches a maximum and then gradually lessens. Ultimately the field at which the longitudinal pull does not affect the magnetization is reached. When this ~ stage is over the magnetization increases by loading, so that of Steel, Nickel, Cobalt, and Nickel-Steels. 55 the effect is reversed. The existence of a critical point in cobalt, analogous to that of Villari in iron, is thus established (see fig. 5). With annealed cobalt the effect is simpler. As will be seen from the curves in fig. 6 the longitudinal pull Fig. 5. ~ Hig. G aN 7 N Poss 21 a always causes diminution of magnetization which increases with the field. Thus the behaviour of cast and annealed cobalt stands in correlation with the change of length caused by magnetization. Loading nickel-steel wires always results in the increase of magnetization, as will be seen from fig. 7. The following Fig. 7. ie Pe i ee HERE noe COS Le PN hel a deeds EM Sigs Ke, ASS aia peed: peeale de | SN N 2000 10° parallel statements will clearly show the reciprocity between the change of length due to magnetization and that of magnetization wrought by the mechanical stretching. 56 Prof. Nagaoka and K. Honda on Magnetostrictien ; Cast Cobalt. Magnetization produces diminu- tion of length in low fields, which, after reaching a maximum, gra- dually decreases, and finally in- Mechanical elongation produces diminution of magnetization in low fields, which, after reaching a maxi- mum, gradually decreases, and finally becomes an increase in strong crease of length is produced in strong fields. fields. Annealed Cobait. Magnetization produces diminu- tion of length, which gradually in- creases with the strength of the field. Mechanical elongation produces diminution of magnetization, which eradually increases with the strength of the field. Vickel- Steel. Magnetization produces increase Mechanical elongation produces of length. increase of magnetization. § 5. CHANGE oF VOLUME By MAGNETIZATION. It was suggested by Rhoads that the change of volume by magnetization may, in a great measure, be due to the hetero- geneity in the material under examination, while in some ex- periments the arrangement was not free from errors, which, though very small, are sufficient to disguise the minute effect. One serious drawback in these experiments was the use of a disproportionately large mass of iron, which, had the ratio of dimensions been sufticiently great, would not have been altogether objectionable, but as it mostly happened to be, did not give the expected result. Non-uniformity of the field is another source of error, which unfortunately has too often been neglected ; the result obtained in fields which are not uniform will indeed be difficult of interpretation. If the material under test be not placed axially in the direction of magnetization and the mechanical force urging the magnetic substance in one or other direction comes into existence, the change of shape of the volumenometer will in some cases be of such amount that it not only deteriorates the measured change, but screens the desired effect. These various sources of error may, by proper construction of the volumenometer, be easily eliminated. The arrangement of the volumenometer has already been described in our former researches, so that it would be super- fluous to enter anew into the details of the apparatus ; suffice it to say that the axis of the ovoid coincided with that of the magnetizing coil, which was all the while waterjacketed. . As announced by Quincke *, change of volume in the liquid * Quincke, Sitzb. d. Berliner Akad. d. Wass. xx. p. 391 (1900). of Steel, Nickel, Cobalt, and Nickel-Steels. - 57 filling the volumenometer may be caused by the pressure in the magnetic field. To guard against this source of error we have specially examined the volumenometer readings by simply filling it with water or ferric chloride. The result was in the negative within the range of field used in the present experiment, as will be easily expected, since the pressure is proportional to the square of the field strength, (a) Cast Steel (fig. 8). The metal shows increase of volume in fields up to = 2000. In weak fields the change is very small, but the rate is tolerably large; as the field increases the curve reaches an inflexion-point. The change goes on somewhat slowly for fields amounting to a few ‘hundred units ; ; 1t again reaches an inflexion-point, whence to increase steadily and almost at a constant rate as the field is farther increased, (b) Nickel (fig. 8). In our two former experiments we noticed a discrepancy ia the nature of the volume-change in this metal. With a bar of square section we noticed a diminution, while an ovoid showed an increase. That this may be easily accounted for we have already discussed in our former paper, so that it would be unnecessary to enter into the subject anew. With the present specimen, which may be considered as more homogeneous, we noticed a slight increase of volume, which is about the same in amount as that observed in the former experiment. The character of the change is similar to that in steel, the curve of the change presenting two 58 Prof. Nagaoka and K. Honda on Magnetostriction inflexional points. These points do not appear in such a remarkable degree as in steel, but their whereabouts can be ascertained at a glance. (c) Cobalt (fig. 8). Just as we have noticed a difference in the length-change and the intensity of magnetization in the cast and annealed metals, we notice a difference in the volume-change for these two bodies. The results of observation are plotted in curves (fig. 8). The behaviour of cobalt is unlike other ferromag- netic substances—instead of showing increase the magnetiza- tion causes diminution of volume, which in the annealed state bears close resemblance to the character possessed by nickel, indicating glimpses of two inflexion-points in the curve of volume-change. With the cast specimen the feature is still more different from the other ferromagnetic substances.- The diminution of volume takes place quite rapidly in weak fields, so that the curve soon reaches an inflexion-point. The rate of diminution after passing this point is very small, the curve passing on almost parallel to the axis of the field. This state continues for a large range of fields, but the curve, instead of showing another inflexion-point, reaches a point of maxi- mum diminution of volume. The course of the curve turns and proceeds in the same direction so far as the present ex- periment goes. This character is possessed by cast cobalt only among the numerous specimens of ferromagnetic sub- stances hitherto experimented upon. Further, we may notice that the amount of the change is, to a certain extent, greater in cobalt than in iron, steel, or nickel. (d) Nickel-Steel (fig. 9). The volume-change in nickel-steel is simple but extremely ea eT eer Ce oe A eer TT sre4e ed fie dull (eee 200 400 600 800 1000 1200 1400 1600 2000 large compared to other ferromagnetic substances. The common feature of the change, as will bé seen from the —a CC of Steel, Nickel, Cobalt, and Nickel-Steels. 59. graphical representation, is the approximate proportionality of the effect to the magnetizing force. The magnitude of the change is, however, not directly proportional to the intensity of magnetization, as the 46 per cent. Ni shows a smaller effect than the 29 per cent. Ni, which is the least magnetizable among the specimens with the exception of 25 per cent. Ni, whose magnetization is scarcely to be detected by ordinary means. In fields of 1600 c.a.s. units the change amounts to 2 = 3:8x 10-$ for 46 per cent. Ni. “seen i10-- 56.» ” 2459 M10-*),, 29 3 +3 = 2x10 5, 25 3 st =3 1-2 10-* ~... “Soit iron. The difference between steels containing different per- centages of nickel is indeed remarkable, as the changes here noted far exceed that hitherto observed in simple ferro- magnetic substances. The change in 29 per cent. Ni is nearly 40 times greater than in soft iron; in fact, the motion of the capillary meniscus can be easily followed by the naked eye, as the displacement, which takes place almost instan- taneously with the making of the current, is nearly 5 mm. in the capillary tube of 0-4 mm. diameter in the strongest field at our disposal. Even the 25 per cent. Ni shows a volume-change which, in spite of the minute magnetizability, is distinctly visible with a microscope. From the above result, it follows that there is a certain alloy, whose percentage content will lie somewhere between 25 per cent. and 36 per cent., that will indicate greatest change of volume ; the change will indeed be the greatest that we can observe in the ferromagnetic substances of common occurrence. When we consider that the alloys of nickel and iron show increase of volume, we at once perceive that the sense of the change is not common to both the constituent metals. When we further consider the magnitude of the change and compare it with that observed in iron or nickel, we are struck with the immensity of the effect, which is not shared in such an extraurdinary degree by either of the constituents of the alloy. Asimilar remark applies to the magnetizability of the different specimens ; that the alloy of two strongly magnetic substances should give rise to an almost neutral body is in no way a matter for surprise, when considered in the same light 60 Prof. Nagaoka and K. Honda on Magnetostriction as the enormous effect of magnetization on the bulk of the alloy. In the present instance, we are at a loss to find which of the two metals plays a predominating part in the magneto- striction of nickel-steel; perhaps a complete study: of the subject from the lowest percentage to the pure nickel, and the comparative investigation of the phenomena in the succeeding stages, will reveal to us the groupings of the constituent metals while entering into an alloy, and the part played by them in the magnetization and the various phenomena attending it. It may at first sight appear that the smallness of thermal expansion in nickel-steel necessarily entails the minuteness of the change of length and of volume by magnetization, but no connexion. seems to exist between the magnetostriction and the deformation due to temperature variation, as illustrated in the preceding experiments. § 6, WiEDEMANN Errscr In Iron, NICKEL, AND NiIcKEL-STEEL WIREs. (a) Twist produced by the interaction of circular and longi- tudinal magnetizations. | The subject was first studied by G. Wiedemann, who established remarkable reciprocal relations with the longi- tudinal magnetization produced by twisting a circularly magnetized wire. Dr. Knott found that the direction of twist in iron is opposite to that in nickel; Bidwell afterwards discovered that the twist in iron is reversed in high fields. Unfortunately some of these experiments were undertaken with wires which were longer than that of the coil, so that the magnetization was far from being uniform. The twist produced by longitudinal magnetization of a circularly magnetized wire was measured in the following way ~ (fig. 10). To the extremities of a ferromagnetic wire (/) 21 cm. long were brazed stout brass wires (0, >), and a light plane mirror (m) was attached to the lower one. The end of the lower brass wire dipped in a mercury pool, while the upper brass wire was clamped to a small tripod (2), which rested on the top of a magnetizing coil, provided with hole-, slot-, and plane-arrangement. One end of the accumulator was connected with the tripod, while the other was led to a mercury pool. The wire hung vertically in the axial line of the coil, which was used for all the preceding experiments. The yertical component of the terrestrial magnetic field was of Steel, Nickel, Cobalt, and Nickel-Steels. 61. compensated by placing another coil in the interior of the magnetizing coil. The lower part of the wire to be tested was protected against air-currents by inclosing it in a wide brass tube with a small window, just where. the reflecting Fie. 10. SS = te tt tatish mirror was attached. The twist was measured by scale and telescope method, by which the deflexion of 0”-3 per cm. was easily read. The current was measured by Kelvin graded amperemeters, whose constants were from time to time checked by means of an ampere balance. Before each experiment, care was taken to demagnetize the wire completely, either longitudinally or circularly, by passing an alternate eurrent of gradually diminishing intensity. Twist by varying the longitudinal field.—The direction of twist in iron, so long as the longitudinal magnetizing field is not strong, is such that if the current is passed down the wire from the fixed to the free end and the wire is magnetized with north pole downwards, the free end, as seen from above, twists in the direction of the hands of a watch. By keeping the circular field constant, the amount of twist increases at first, till it reaches a maximum in a field of about 20 units (fig. 11) ; itthen goes on diminishing till it ultimately changes direction and continues to twist in the opposite direction with increasing fields. The field at which the twist is reversed increases with the circularly magnetizing field. In nickel, the direction of twist is opposite to that in iron, but the general feature is similar to iron, the only difference being that even in strong longitudinal fields the twist is not reversed. For wires of equal thickness, the amount of twist in nickel is greater than in iron—the maximum twist in iron wire 62 Prof. Nagaoka and K. Honda on Magnetostriction of 1 mm. diam. by passing 6 amperes through it amounts — to about 28” per cm., while with nickel wire of 0°83 mm. diam. under similar conditions, the maximum twist amounts to about 200”, Fig. 11. JRON Wire Atam = 0-938 mr Net Y Load ay Se fi RE a dO DO ( Leet IN Three different kinds of nickel-steel wires, for which our thanks are due to Dr. Ch. Ed. Guillaume, were tested. The results of the measurements are shown in fig. 12. The sense in which a nickel-steel wire twists is the same as for iron. The amount of twist increases with the magnetic field, but it soon reaches a maximum, to decrease afterwards quite slowly as the field becomes stronger ; and the twist is generally reversed in high fields. With the specimens tested, the twist increases with the percentage of nickel. The 23°6 per cent. Ni and 39°2 per cent. Ni were examined in ui hard drawn state; but the 45°2 per cent. Ni wire was examined after annealing it in hydrogen, as already described. Twist by varying the circular field—In iron the twist increases with the strength of the circular field if the longi- tudinal field remains constant. Such is also the case with nickel in moderate and strong fields. In low longitudinal ‘of Steel, Nickel, Cobalt, and Nickel-Steels, 63 fields, however, the twist does not continue to increase with the circular, but we notice a maximum as will be clear in the Fig. 12. Ree SSR Ree tO Bie 40) 0 ) D( 190 figure (see fig. 13). There is great experimental difficulty in increasing the circular field, inasmuch as the wire becomes heated and the result is materially affected. 64 ‘ProtyN agaoka and K. Honda on Magnetostriction The hysteresis accompanying the cyclical change of the circular magnetization deserves special notice. If the longitudinal field be such that with the increase of the circularly magnetizing force, the twist reaches a maximum, the curve of twist goes below its former course on weakening the circular magnetization. The twist, however, goes on slowly increasing, till it crosses the on-curve.and then reaches a& maximum, whence it gradually diminishes and ultimately vanishes in a negative field. The course after passing this point is exactly the reverse of that already described. ‘The character of twist is exactly the same for iron as for nickel, when we take the opposite character of twist into account. The nature of the hysteresis is nearly the same when the longitudinal magnetizing field is made to vary while the circular field remains constant. ) The results are in accordance with the experiments of Wiedemann and Dr. Knott, with the discrepancy in the position of maximum twist in nickel, which occurs in a ‘tolerably strong field according to Dr. Knott. (b) Circular magnetization’ produced by twisting a longi- ‘tudinally magnetized wire. . By twisting a longitudinally magnetized wire, circular magnetization is developed which is measured by the transient current at the moment when the twist is applied. One * of us found. that the current due to twisting was opposite in direction in these two metals, and that it reached a maximum in moderate fields, As the magnetizing current was not very strong, no conclusive measurements were made as regards a) i = the nature of the transient current in strony fields. In order co) to clear this point and see if any intimate relation with the Wiedemann effect could be traced, fresh experiments were undertaken by the same method as before. We have to notice that the ferromagnetic wire was so placed in the axial line of the magnetizing coil that it lay in a nearly uniform field. The measurements of the transient current for iron and nickel wires are shown graphically in fig. 14. The current for constant amount of twist increases with the strength of the longitudinal field ; it, however, soon reaches a maximum, whence it gradually dimimishes. In nickel the transient current attains asymptotic values in strong fields without changing its direction, while in iron it is reversed in a field of about 200 ¢c.a@s. units, when the twist is small. The increase after the reversal is not pronounced, but becomes finally asymptotic. | * Nagaoka, Phil. Mag. Feb., 1889. of Steel, Nickel, Cobalt, and Nickel-Steels. 65 (c) Longitudinal magnetization produced by twisting a circularly magnetized wire. The longitudinal magnetization produced by twisting a circularly magnetized wire presents the same character as the Fig. 14. transient current above described. The experiment is very difficult on account of the heating of the wires. To avoid the rise of temperature, the iron and the nickel wires were covered with urushi (Japan lac) which has the special property of being a very good insulator while, at the same time, the melting temperature is comparatively high. The wire thus insulated was stretched in the axial line of a secondary coil, whose diameter was 1°5 cm. and whose total number of turns was 540,-and a current of cold water was kept flowing about it to keep the temperature of the wire uniform. Thus maintaining the electric current in the wire constant, it was twisted and the induced current in the secondary circuit due to the longitudinal magnetization thereby developed was measured by the ballistic method. As will be seen from the curve (fig. 15, p.66), the longitudinal magnetization developed by twisting a circularly magnetized iron wire attains a maximum when the mean circular field is about 10. It then decreases, but in spite of the constant stream of water, the heating due to electric current prevented the experiment from being pushed to the point where the direction of the current is reversed. To judge from the course of the curve, the tendency is such that there is a reversal. In nickel Phil. Mag. 8. 6. Vol. 4. No. 19. July 1902. r 66 Prof. Nagaoka and K. Honda on Magnetostriction the direction of the induced current is opposite to that in iron, and the total quantity of the current attains a maximum, whence it continually diminishes, but not to such an extent that the current ultimately changes its direction. Fig. 15, Se ——: : These experiments show ‘that the twist produced by the combined action of the longitudinal and circular magneti- zations, the circular magnetization produced by twisting a longitudinally magnetized wire, and the longitudinal mag- netization caused by twisting a circularly magnetized wire, are characterized by having various peculiarities, which are common to all of them. ‘This cannot be a mere chance coincidence; we shall have to ascribe these allied phenomena to the same common cause. In these experiments we were assisted by Mr. 8. Shimizu, a post-graduate in physics, to whom our best thanks are due. (d) Application of Kirchhoff’s Theory to Wiedemann fect. In our last paper on magnetostriction, we noticed that Kirchhoff’s theory can be extended to the study of the relation between torsion and magnetization, exactly in the same manner as was done by Maxwell and Chrystal to explain the Wiedemann effect. There we found that the mean circular magnetization called into play by twisting a ferromagnetic wire of radius R through an angle » amounts to —Iolifiow oyu | ~~ = e —~~— —————— OO alli = OE —————— of Steel, Nickel, Cobalt, and. Nickel-Steels. 67 in field 5, and that the mean longitudinal magnetization caused by twisting a ferromagnetic wire carrying an electric current C amounts to eae oe eS CB) The reciprocal relation between these two phenomena is. thus apparent at a glance. We shall next show how the same phenomena are reciprocally related with torsion produced by the interaction of the longitudinal and circular magneti- zations. The stress-components in a magnetic medium as given by Kirchhoff are as follows :—- eee +h+ =) 2,1 iL pd gt (a? + B? 2 oo e . a es ) Wier 1 i 2 et - Y,=— (= +kh+— = e+ 5 (qe tt k) @ 4 +0’), > “~ ae “2 — y Iv iV 2 2? 4? Y,=Z,=— ce XY wen -( oe 1 hf! = Y,;=> — ({ — + k Xy=Ve=— (jo +k+ 3) 28. Taking the axis of 2 in the axial line of the wire, and two other axes in the plane perpendicular to it, we see that the component magnetic forces in a longitudinally magnetized wire traversed by an electric current are a=-—hsiné, B=hcos@, y=, where h denotes circular field given by | 2Ur a ee © being the current, 7 the distance of the point from the axis of the wire, R the radius, and @ the anyle between 7 and the axis of «. The stress-components in a ferromagnetic medium acted KF 2 . a 68 ~=Prof. Nagaoka and K. Honda on Magnetostriction upon by the forces above specified are given by X.=— her +k+— ay sin? 045 (42 +h— i) (2+ h’), Yj=— (+445) cost 41 (1 re a v) (G+7), Z,= (x ides +3GGeth (G+ 28), 1 Y,=Z,=-— +k+— = ) hi 08 8, a (& a aib 5) AB sin 6, Be pi! cg Et = X,= Y¥,= (= +k+ =) h? sin @ cos 6. The moment about the axis of the wire is given by n={ (Zyz — Ly )dx dy, --\\(z $45 ) AGr dx dy, ~ te (qe tht ae dr dO, a=-0(E “ea S 5 COR. The moment just outside the wire amounts to es 1 2 ee —7(;- +h) CHR’. Thus the effective couple is equal to _ RCH 2 x Cross section. . . . (C) Since the amount of torsion of a cylindrical wire by a given couple is inversely proportional to the fourth power of its radius, it is evident that for given longitudinal current and field the angle of twist is inversely proportional to the square of the radius. This inference was approximately verified in the present experiments. of Steel, Nickel, Cobalt, and Nickel=Steels. 69 In deducing the three formule (A), (B), (C), we cannot, strictly speaking, put k” outside the sign of integration, because the strain coefficient depends on the field strength, which is not uniform in a wire traversed by an electric current. Hence we shall have to use a mean value to obtain a close approximation. | In order to test the consequences of the theory as regards the twist produced by the joint action of circular and longi- tudinal magnetizations, we have calculated the twist by assuming the values of k" calculated from the changes of volume and of length in iron and nickel ovoids. Graphically represented (fig. 16), the fields of maximum twist by Fig. 16. a & a': obs. & calc. transient currents in 107° C.G.S. units for iron. A&A': i a 53 - 3 for nickel. 5 & 5': obs. & cale. Wiedemann effect for iron. B&B: . “f » for nickel. calculation coincide nearly with those given by experiments, and the reversal of twist in iron takes place in low fields as actually found by observation. The quantitative differences are, however, tolerably large in iron, but in nickel the amount of twist is nearly coincident with the experimental values. Calculating in the same manner the quantity of the transient current produced by twisting longitudinally magnetized wires, we find a close coincidence between the experimental and theoretical values in nickel, but the difference is tolerably 70 Prof. Nagaoka and K. Honda on Magnetostriction large iniron. In using the strain coefficients, we must always bear in mind that these values are widely different according to the nature of the specimen ; especially with wires, we are not sure of its being magnetically isotropic. The remarkable qualitative coincidence as regards the existence of maximum twist and its reversal in iren are proofs that the theory, so far as we know at present, admits of connecting various experimental facts in a common bond. The reciprocal relations between the strain caused by magnetization, and the effects of stress on magnetization, as found by actual experiments, will be found to be of paramount importance in arriving at a correct theory of magnetostriction. The strain accompanying the magnetization of ferromagnetic metal will be determined, when we know tle effects of stress on magnetization and wee versd. As regards the relations between twist and magnetization in iron and nickel, we may conveniently place them under the following parallel statements :-— Strain produced by magnetization. Effects of stress on magnetization. (1) A longitudinally (or circularly) (1') Twisting a longitudinally (or magnetized Wire is twisted by circularly) magnetized wire circular (or longitudinal) mag- gives rise to cireular (or longi- netization. tudinal) magnetization. (2) Up to moderate fields, the twist (2') Up to moderate fields, the produced by the longitudinal and circular magnetizations of an iron wire is opposite to that in nickel, In strong fields, the sense of twist is reversed in iron, The twist due to longitudinal magnetization of a_ circularly magnetized iron or nickel wire reaches a maximum in low fields. transient current (or the longi- tudinal magnetization) produced by twisting a longitudinally (or circularly) magnetized wire, is opposite to that in nickel. In strong fields, the direction of the transient ‘curred is reversed in iron. The transient current in iron or nickel wire reaches a maximum in low fields. § 7. SuMMARY. The results obtained in the present investigation can be summarized in the following statements :— Magnetization. (1) The magnetization of cast cobalt is nearly double that of the annealed metal. The magnetization of annealed cobalt is characterized by its high differential susceptibility. (2) The magnetization of 46 per cent. reversible nickel- stéel is between iron and cobalt (cast), while that of 36 per — cent. Ni is nearly the same as in cobalt. The 29 per cent. Ni is nearly half as magnetizable as nickel, and 25 per cent. Ni is of Steel, Nickel, Cobalt, and. Nickel-Steels. 71 only feebly magnetic. The course of the magnetization curve of nickel-steel resembles that of nickel. (3) (a) In cast cobalt, mechanical elongation in the direction of magnetization produces diminution of magneti- zation in low fields, which gradually lessens as the field strength is increased. Ultimately there is increase of magnetization by elongation. Thus, there is a critical point in cobalt which is opposite in character to the Villari point in iron. (5) In annealed cobalt, mechanical elongation in the direction of magnetization produces diminution of magneti- zation, which increases with the field. (4) Mechanical elongation in the direction of magnetization produces increase of magnetization in nickel-steel. Change of Length by Magnetization. 1. In cobalt, the character of the change is different in the cast and in the annealed state. (a) Cast cobalt contracts in low fields and assumes minimum length in =130, whence it returns to its former length in = -740, and goes on elongating at a slower rate as the field is increased (result already obtained by Bidwell with cobalt rod). This stands in reciprocal relation with the effect of mechanically elongating cast cobalt on its magnetization. (6) Annealed cobalt contracts without showing maximum up to H= 1800. The character of the change is similar to that in iron (after passing the maximum elon gation). The effect of mechanically elongating annealed cobalt is reciprocal to the change of length by magnetization. 2. Nickel-steel elongates by magnetization. The character of the change is similar to that in nickel, but the sense is dl a= different. The rate of change | 5 y in high fields is greater ie ~ in 29 per cent. Ni than in 36 per cent. Ni, in which it is again greater than in 46 per cent. Ni. Nickel-steel elongates to a greater degree in the annealed than in the hard- drawn state. The elongation of nickel-steel in very low fields (comparable with the terrestrial magnetic field) is generally less than 10-7. Change of Volume by Magnetization. 1. Iron, steel, nickel, and nickel-steel increase in volume by magnetization, but cobalt shows contraction. 2. (a) Cast cobalt contracts at a rapid rate in low fields, 72 Mr. W. C. Baker on the Hall Effect in. but above = 100 the rate becomes less and the contraction reaches a maximum in §=900, whence to return gradually with further increase of the field. (6) Annealed cobalt contracts at a steady rate as the field is increased. The contraction becomes ultimately greater than in cast cobalt, 3. The increase of volume in 46 per cent. Ni, 36 per cent. Ni, 29 per cent. Ni steels takes place almost in proportion to the strength of the field. The amount of the increase becomes greater as the percentage of nickel becomes less. The volume change in 29 per cent. Ni is the greatest that has ever been observed, and is nearly 40 times that in iron, in strong fields. Wiedemann Hfect. The twist produced by the combined action of circular and Jongitudinal magnetization in iron, nickel, and _ nickel-steel increases with the longitudinal field-strength, and reaches a maximum whence it decreases gradually as the field is further increased. The sense of twist in iron and nickel-steel is opposite to that in nickel. The transient current produced by twisting a longitudinally magnetized wire and _ the longitudinal magnetization caused by twisting a circularly magnetized wire are reciprocally related to the twist produced by longitudinal and circular magnetizations. Physical Laboratory, Imperial University, Toky6, March 1902. V. On the Hall Effect in Gold for Weak Magnetic Fields. By Win. C. Baker, M.A., 1851 Exhibition Scholar from Queen’s University, Kingston, Ontario, Canada, Non-Col- legiate Student, Cambridge *. ON ETTINGSHAUSEN and Nernstf found that the Hall coefficient in certain bismuth-tin alloys depended on the strength of the magnetic fieldemployed. This change extending, in some cases, even to a reversal of the sign of the effect. Kundt{, in his work on the Hal} effect in iron, — cobalt, and nickel, showed incidentally that the coefficients for gold and silver remained constant even to fields of 21500 C.G.8. units. In view of the above, Professor J. J. Thomson suggested that it would be of interest to examine the behaviour of pure * Communicated by Prof. J. J. Thomson. + Wied. Ann. xxxiil. p. 474 (1886). t Jad, xlix. p. 264 (1893). ee ee es Gold for Weak Magnetic Fields. 73 metals in very weak magnetic fields, to see if there existed, in that region, any change similar to the one quoted above for bismuth-tin alloys. The method employed in this investigation was a slight modification of that given by Dr. A. Lebret*. It is repre- sented diagrammatically in fig. 1. The current from a Fig. 1. storage-cell B passed in turn through the reversing key K ; a small resistance S (about 0-02 ohm), and through the plate of metal to be experimented upon, shown at A. This current is spoken of below as the primary current. From the ends of the small resistance S a shunt current was led through the resistance-box R, and then through one set of coils (G,) of the differential galvanometer. This circuit is referred to below as the shunt circuit. The current from the “ Hall electrodes”? H, and H, was sent through the second set of coils (G,) of the galvanometer, and is called the secondary current. In order to prevent changes in the strength of the magnetic field from acting inductively on that part of the secondary circuit that lay between the magnet poles, the device of S. Bidwell+ was adopted. This consists in branching part of the circuit as shown at H,P. Now as a change in the magnetic field acts in opposite senses on the partial circuits H, H, 9, P and H, Hy g, P, these effects may be made to neutralize one another simply by bending one of the wires (q or q2) so as to equalize the magnetic flux through the two * Dr. A. Lebret: “A New Method of Measuring the Hall Effect, especially with reference to Variation of Temperature.” Communica- tions from the Physical Laboratory of the University of Leiden, No. 19. (Translated from Verslagen en Medeelingen van die Kon. Acad. van Wetenschappen van 18 April, 1895, p. 284.) + Phil. Mag. vol. xvii. (April 1884); see also Lebret (doc. cit.). 74 Mr. W. C. Baker on the Hall Effect in ‘‘areas.” A was placed between the poles of a magnet and the current set up in the secondary circuit, due to the action of the magnet on the primary current, was balanced against the current in the shunt-circuit, by altering the resistance R until the galvanometer eee remained at rest on closing the key K. The advantage of this arr angemeut i is that as the key K is closed only for a small fraction of a second, it permits the galvanometer to indicate at once whether the shunt-current is greater or less than that in the secondary, but the primary current is stopped again before the complicated thermo- magnetic effects of von Ettingshausen and Nernst * have had time to rise to significant proportions. By thus obtaining the value of the compensating current in the shunt-circuit for both directions of the primary current and for both directions of the magnetic flux in each case, all effects but the one here sought are eliminated in the mean fF. Gold was chosen to work with chiefly because it could be obtained of a standard purity, in thin sheets, much more readily than other metals. The foil was procured from a local dentist, and its thickness was determined from its mass, area, and the density of beaten gold (19°367, Watts’ ‘ Dic- tionary of Chemistry’). These sheets were found to vary in thickness, even for different parts of the same piece ; so in the final determination of the absolute value of the effect, the portion extending from one secondary electrode to the other was cut out, and its thickness determined after it had been thoroughly cleaned, first in alcohol, to remove the shellac, and then in strong nitric acid. Much trouble was experienced in obtaining a successful connexion to the gold. Attempts to solder it to brass strips failed completely, as the thin foil dissolved in the hot solder, and, by its surface-tension, the alloy drew away from the gold, leaving absolutely no contact. Systems of clamps, such as Hallt used in his original investigation, and the various modifications that were tried, all proved to be too variable to be used with the small resistances employed. The method finally adopted is shown in fig. 2, Two comb-shaped bits of copper (D D) were screwed to a piece of ebonite about 12 cms. square and 5 mms. thick, the copper “teeth” being previously well tinned. The gold-foil A (10 ems. square) could just lie flat on the ebonite between * Wied. Ann. xxix. p, 344. + For a full discussion of how each separate effect is eliminated by taking the mean of these four readings, see Lebret’s paper, Joc. cit. ¢ Phil. Mag. vol. x. p. 301 (1880). = jes es = ete mia — Gold for Weak Magnetic Fields. 75 the two rows of teeth. Small drops of solder were let fall from a_ hot soldering-bolt so that they formed a connexion between the gold and the copper points. The solder dissolved Fig. 2. t PRIMARY FAIMARY CURRENT : + CurRENT Lege * 3 AREA OF Coll | FOR- DETERMINA sl lor STRENGTH | OF MAGNETIC \ AREA OF MAGNET CORE GAP 3cms. some of the gold as before, but as the hot drops were already more or less spherical they did not draw away from the gold before they were cooled by conduction of heat into the copper. This gave a perfect connexion. The secondary electrodes—wires soldered to screws driven into the ebonite— were similarly attached to the gold. a,>a, and 6,>6,>8,. . 2°) 2. It is known that in the case of transparent crystals most characteristic properties correspond to those two direc- tions A, and A, which, lying in the plane of the greatest and the least tensors a, and a3, make an angle 3 with the latter defined by the equations ge . a Sun eee cos? J= : a) — U3 a — a3 d2— a3 ve These directions are also of special importance in absorbing crystals, and are also called optic awes in this case, although on account of their altered properties they would be more correctly denoted by some other term (e. g. polarization axes). Corresponding to the optic axes, we may conveniently consider as absorption axes the directions B,, B, which, lying in the plane of the greatest and least tensors ), and b3, make an angle 6 with the latter defined by the equations . b= b —b ALANS sata | 2 9) 2 3 sin oF et b,’ cos ry, i —T: (3) * A summary of the results contained in a paper presented on Feb. 8, 1902, to the Kel. Gesellschaft der Wissenschaften zu Gottingen (Géztt, Nachr. 1902, Heft 1). + Communicated by Lord Kelvin. ee ea eS ee Behaviour of Pleochroitie Crystals along Optic Aves. 91 The relative position of the two pairs A,, A, and B,, By of axes is In general as impossible to assign as that of the tensor- triplets a, a2, a3 and 6;, by, 63. It is only when the crystal possesses special symmetry that it becomes possible to say something more or less definite. Fig. 1 gives some idea Fig. 1. regarding the general position of these axes ; all the charac- ter eee lines are deaern through the centre of a sphere, and their aie with the spherical surface indicated. . The fundamental formule in the theory of plane wave Be agation are obtained most simply by introducing a system of coordinate axes 2, y, z, of which z coincides mih the direction of propagation. If, then, we denote the com- ponents of the two tensor- triplets along these axes by ay), do., 33, Moz, A315 Ayq ANd Dy, bo9, bs3, bo3, Se b,.*, and if we write shortly One + Oak = Chks e ee tte . (4) where i= —1, then (ci - ey (Cee ee ers i Me). (5) 2 ff (11775 Sor 2 => et ete ha cc, o> CO Di Co Sf f (6) where v stands for the so-called complex velocity, g/f for the ratio of the complex amplitudes for Neumann’s vibration- vector along the y and « axes respectively. Expressed in * If an, Br, yr are the direction-cosines of the triplet a, a,, a3 rela- tively to the axes 2, y, =, then 41, =4,0,° +442 2La,a Bayete A.3=OB iy, T 42Bo2y2 + A833) a 92 Prof. W. Voigt on the Behaviour of Pleochroitic terms of the real velocity w and the absorption-index «, 9) a he a 1—2k’ and if G, F denote the real amplitudes, and R their relative retardation, = Gy, = pre eg ce 4 The formule (5) and (6) express the fact that in every direction there are propagated two elliptically polarized waves with, in general, different velocities and ditterent rates of damping. 4. Of special ee are those crystals in which absorp- tion is so weak that x? may be neglected in comparison with unity, so that we may write v=o (1+2ic).). 4. Se Such crystals produce no appreciable absorption in a thickness corresponding to a few wave-lengths, and are the only ones exhibiting the remarkable phenomena whose ex- planation forms the subject of the present paper. We have in the first place to consider the effects obtained within a small region in the neighbourhood of the optic axes defined by equations (2); in this region the variation of @ is, as may be shown, very slight, and the quantity 2«w?=k hasa variation corresponding almost exactly to that of the analo- gous function «/w characteristic for absorption. The two complex equations (5) and (6) thus define, within the region now considered, the real and imaginary parts of the two unknown quantities v and g/f, as well as the real velocity of propagation , the paraiweter of absorption , the ratio G/F of the real amplitudes, and the relative retard- ation R.’ 5. Regarding these four quantities it must here suffice to state four propositions which, though only qualitative, are easily understood and extr emely helpful towards an explan- ation of the effects considered. These propositions follow from the equations (5) and (6). In order to arrive at them, consider once more all the directions as passing through the centre of a sphere, and defined by their intersections with the spherical surface. The region surrounding an optic axis A, may then be approximately represented by a plane, as shown in fig.2. We here have, besides the direction of the optic axis, represented by the point A,, and that of the wave normal, represented by the point Z, also the plane A, A, of the optic axes ; A, being inclosed in brackets in order to Ss i » Crystals in the Neighbourhood of an Optic Axis. 93 indicate the fact that the direction A, is not capable of being represented in the figure itself. The straight line A, Q further represents a plane through the optic axis A, obtained Fig. 2. as follows :—Let a plane be drawn through the axes A, B,, and another through the axes A, B,; let the angle between them be J; Then A,Q is the trace of the plane bisecting the angle J,; let the angle made by this plane with the direction A, Az be denoted by K. ' 6. From the formule (5) and (6) it follows that the phenomena under consideration in the neighbourhood of the axis A, are symmetrical with respect to the £n system of coordinates (also shown in the figure), the angle made by the — &-axis with the direction A, A, being equal to 2K. Such being the case, the plane A,y contains two directions, ’ C, and C,’ (see fig. 3), making the same angle 6 with A,, and which are highly characteristic of the behaviour of the erystal, and may be termed singular axes. The angle @ is deterniined by the tensors aj, ag, a3 and 8), bs, bs; which are characteristic of the crystal, and is most simply expressed in the form __(b;—63) sin Vy; sin Vay 4 WV (ay— ag) (42—as) wherein V,, stands for the angle between A, and B,, and V., for that between A,and B,. The angle @ thus determined is in all practically important cases extraordinarily small. 7. The four propositions referred to above follow from the formule (5) and (6), and, using the representation in the En plane, may be stated as follows :— (2) The difference of the squares of the velocities of pro- pagation, @;"—w@,", of the two waves (corresponding to each direction Z)—and hence also, on account of the small difference between , and , in the region considered, the difference BD HeRTTO) 94 Prof. W. Voigt on the Behaviour of Pleochroitic itself w;—@, approximately—is constant over ellipses having the points C, and ©,’ for foci. This difference vanishes along the straight line C,C,’, and increases as the ellipse opens out. (The mean square of the velocity, $(@,*+,”), on the other hand, is constant along straight lines perpendicular to the direction A, Ay.) (b) The parameters £, and k,, which determine the absorp- tion of the two waves (corresponding to the same direction Z), are constant along hyperbolas having their foci at C, and C,'.. They have the same value k, along the straight lines obtained by producing C, C,' both ways, and along any hyperbola have values which differ from /;, by equal amounts ‘ opposite sign, the maximum difference occurring along the “AXIS. (c) The vibration-ellipses of the two waves (corresponding to the same direction Z) have constant ratios of axes along circles whose centres lie on the straight lines obtained by producing C, C,’ both ways, and whose radii are such that all the circles cut the circle described on (©, C,’ as diameter orthogonally. The ellipses degenerate into circles at the points C, and (©,’, and become straight lines in the &-axis. The direction of vibration is of opposite sense on the two sides of the &-axis, but is everywhere the same for the two waves. (d) The principal axes of the vibration-ellipses of the two waves are crossed ; their position is constant along equilateral hyperbolas whose vertices lie on the lemniscate having ©, C,’ for axis, and which pass through the points C, and C,’. The coordinate-axes £ and 7 are special cases of these hyperbolas. In order to determine the positions of the axes of the ellipses corresponding to these hyperbolas, it is most convenient to use the well-known theoretical result according to which in the case of weak absorption the vibrations, within a certain distance from the optic axes, differ only imperceptibly from those taking place in transparent crystals, and are therefore nearly rectilinear along directions determined by the famous construction due to Fresnel. According to this construction we have to draw planes through the axes Z and A,, and Z and A, and to bisect the angle I between them ; the ordinary wave is then polarized in a direction parallel, and the extraordinary one in a direction normal, to this bisecting plane. In fig. 3 are shown the curves corresponding to propo- sitions (c) and (d); in addition to this the double-headed arrows arranged round the circumference of a circle indicate the directions of polarization of the ordinary waves when the ee ee ee ee ee > “ieee onl Cw ae os Crystals in the Neighbourhood of an Optic Axis. 95 absorption is vanishingly small. In accordance with what has been said above, these arrows also give the directions of the axes majores for the ordinary, and of the axes minores for the extraordinary waves on the neighbouring branches of the hyperbolas. It will be seen that these directions are not constant along the entire hyperbolic branches, but that they become rotated through 45° during the passage through the points C, and Cy’ of circular polarization. It is evident that in all these propositions the singular axes play an extremely important part—they uniquely deter- mine, from the qualitative point of view, the effects con- sidered. 8. Now as regards the appearances which may be noticed in the neighbourhood of an optic axis, these present them- selves in looking through a plate which has been cut in a direction approximately normal to an optic axis. It is easy to deduce the formule for the intensities with a degree of approximation corresponding to that of the experimental observations—for a given incident light—made either with the naked eye or by means of an inserted analyser. The formule are without exception very complicated, but may be simplified for distances from the singular axes C, and C,' such that the terms containing the squares of the ratios ¢ of 96 Prof. W. Voigt on the Behaviour of Pleochroitie the minor to the major axis of the vibration-ellipse as factors may be neglected. The region within which the simplified formulze are not applicable is in general extraordinarily ‘small. In this way an explanation is very easily obtained of the dark pencils—first noticed by Brewster—which make their appearance when a natural source of light of sufficient dimensions is viewed through the crystal, without the use of any polarizer. The distribution of intensity is such that the hyperbolas mentioned in proposition (6) represent curves of constant absorption. The ellipticity of the vibrations in the plate need not in the case of this phenomenon—to the degree of approximation considered—be taken into account. Ac- cording to the strictly correct formule the distribution of the intensity is somewhat modified in the neighbourhood of the singular axes. 9. The ellipticity of the vibrations has, on the other hand, a marked effect on the appearances presented when a single polarizer is used—whether it be that natural light is allowed to fall on the plate and is examined by means of an analyser, or that plane polarized light is after transmission examined by the unaided eye. Here an opportunity presents itself for testing in a simple manner one of the most remarkable consequences. of theory. If the experiment be carried out in the manner indicated with a plate of an ordinary or an active transparent crystal, whereby two linear or two elliptic similar but crossed vibrations of oppositely directed sense are propagated through the erystal, then according to theory there should be no interference- rings visible around the optic axis. Should, on the other hand, the vibrations be propagated through a pleochroitic crystal whereby the two elliptic vibrations have the same sense of rotation, then theory demands the presence of such rings. Experiment is completely in accord with this, and thus proves the existence, hitherto not established, of these pairs of waves with vibrations of the kind described. The existence of the rings is easily proved in many pleo- chroitic crystals. Frequently it is possible to see them by looking with the unaided eye through the crystal plate at the sky when the light from the latter is strongly polarized; they have in this case been known for some time, but only now has a theoretical explanation been furnished. That the ex- planation given above, which is based on the peculiar nature of the vibrations in the waves traversing the plate, is the correct one, follows especially from the changes which come over the appearance presented when the plane of polarization J, eee ee oe Deep _ — —— Crystals in the Ne ighbourhood of an Optie Axis. Tie of the incident light is rotated— changes which take place precisely in the manner indicated by the formule. When natural incident light is used, then according to the strictly correct formule, the rings are not entirely ‘absent, but, de- pending as they do on e?, are faintly outlined only in the immediate neighbourhood of the singular axes. As a matter of fact there is in this case visible nothing beyond a mere trace, which appears as a dark spot, of the first minimum within the Brewster’s pencils. 10. Although, in accordance with what has been said _ above, the interference rings observable with only a single polarizer (idiophanic rings) prove the propagation of two similarly rotating elliptic waves, they do not exhibit the change in the direction of rotation during the passage through the £-axis, referred to in the fourth proposition. A supplementary experiment thus appears desirable, and the following arrangement would appear to meet all requirements. If instead of plane polarized we use elliptically polarized incident light, and view it with the naked eye, then according to theory, and as is otherwise evident, the phenomenon to be observed must assume a certain dissymmetr y, which was non- existent with plane polarized incident light. Now this want of symmetry is, as a matter of fact, very marked. If we use, say, a plate of rhombic andalusite (whereby the plane A,€ coincides with the plane of optic axes A, A.) in white or, perhaps better, blue light, and if the plane of the polarizer be normal to that of the optic axes of the crystal, then we obtain a nearly circular system of rings, crossed by a dark band which lies in the plane of the optic axes, a pheno- menon with two mutually normal lines of symmetry. If between the polarizer and the crystal we insert a quarter- wave plate, then as the latter is rotated from the position of vanishing effect, the appearance becomes entirely asymmetric, and in a manner which agrees with the predictions of theory. The dissymmetry is particularly striking when ge light incident on the plate is right or left-handed czr reularl 'y polar ized light. In this case there appears on one side of the plane of the optic axis (the &-axis in fig. 3) a strongly marked dark spot, and on the other a briglit spot, and these spots change places if the direction of rotation is reversed. This observation proves in the simplest manner possible that the waves propagated through the crystal on the two sides of the £-axis have opposite directions of rotation, thus furnishing the desired and necessary completion of the proof of the theory. Gottingen, March 1902. Phil. Mag. 8. 6. Vol. 4. No. 19. July 1902. it er oe VILL. The Discharge of Positive Electrification by Hot Metals. By the Hon. R. J. Srrurtr, Fellow of Trinity College, Cambridge *. T was first observed by Guthrie (Phil. Mag. [4] xlvi. p. 273) that red-hot metals were able to discharge posi- tive electrification, and that white-hot metals were able, in addition, to discharge negative electrification. The experiments described in the present paper were undertaken with a view to determine at what temperature the discharge of positive electrification became sensible, and how far this temperature was dependent on the conditions of . the experiment, namely, the state of the metallic surface and the nature and condition of the surrounding gas. It may be well to say at once that I have been able to detect the effect at temperatures of about 270° C., and that it increases with extraordinary rapidity when the temperature is raised. The temperature at which the effect becomes sensible does” not appear to depend very largely on the nature of the metallic surface, or on the surrounding gas, but it alters nearly as much from slight changes in the condition of the surface of the metal, produced by continued heating, as it does when an entirely different metal is substituted. With this preface I will explain the method of experi- menting adopted. When it is desired to measure a very small electrostatic leakage there are two alternative methods. Hither a very’ sensitive instrument must be used, the time of leakage being short, or, on the other hand, a less sensitive instrument may be employ red, the leakage being allowed to proceed for a longer period. The quadrant electrometer may be arranged so that it vill detect a very small electromotive force ; on the other hand, its capacity is large, and its zero seldom remains so fixed in position as not to wander very appreciably in, say, one hour. Further, it is necessary to use long connecting wires to the instrument, and these in any case involve loss of insulation, owing to the conductivity existing normally in air (C. T. R. Wilson, Proc. Roy. Soc. Ixvili. p. 151). If gas flames are in use at the same time there is all the more chance of leakage from the high-potential connecting wires, because of the conductivity of the gases from the foie A gold-leaf electroscope, read by a microscope with a micrometer eyepiece, is free from the objections of large _* Communicated by the Author. ) | | | wt el Discharge of Positive Electrisication by Hot Metals. 99 capacity and shifting of the zero, and can be arranged for the proposed experiment (as I shall explain) so that no con- necting wires need be exposed to the air. It can be insu- lated by means of fused quartz in the form of rod and tube. In this way there is practically no limit to the time during which the leak may be allowed to proceed. It would be quite practicable, if desired, to measure a leakage from a charged wire at 100 volts not exceeding 10—'§ ampere. Fig. 1 (p.100) represents the apparatus. ais the high-poten- tial wire carried by the brass cap 0, which in its turn is cemented into the quartz tube d. d forms a prolongation of the neck of the glass vessel c, which incloses the high-poten- tial wire a@ and the thermometer &. The further end of a is supported by a quartz rod g, carrying a cup on the end in which the wire rests. The glass vessel ¢ is silvered inside, and connected to earth through a platinum wire 7. The brass cap b presses against the brass strip p, which carries the gold-leaf 0. This strip and gold-leaf are inclosed in a glass vessel very thinly silvered inside to make it conducting, and dried by phosphorie anhydride contained in m. This vessel can be exhausted, as shown in the figure. The arrangement of the electroscope is very similar to that employed by Wilson (oc. cit.). The brass strip p is supported by a quartz rod g, and this quartz by a brass rod s passing out through the indiarubber cork ¢. p and s can be brought into temporary metallic contact by means of the iron wire 7, movable by an external magnet. ‘To charge the wire a and the electroscape it is merely necessary to give a suitable charge to s (this charge being adjusted to a convenient value by means of an auxiliary electroscope), and then to make contact with p by means of the iron wire 7. When a suitable charge has been given the magnet is removed and the contact thus broken. s is then touched to discharge it. When ¢ and the electroscope were exhausted insulation was so good that the potential of the system did not sink more than a fraction of a volt in 24 hours when initially charged to about 100 volts. In order to raise the temperature of the wire a, the vessel c was inclosed in a metal oven heated by a gas-burner. In this oven was also placed an elongated glass bulb containing air. This worked a temperature-regulator in the ordinary way, cutting off the gas by its expansion when the tempe- rature rose too high. The neck f of the vessei was long enough to prevent the electroscope getting Aiea heated by the radiation from 2 a 100 = = Hon. R. J. Strutt on the Discharge of the gas-burner when screens were interposed. As, however, the electroscope was exhausted, to improve the insulation, the CNY SWH)aS OL 70 AUXILIARY ELE CTROSCOPE gold-leaf was liable to show radiometer effects. These could be greatly mitigated by not pushing the exhaustion of the electroscope too far. Positive Electrification by Hot Metals. 101 The electroscope was observed with a microscope provided with a scale in its eyepiece. It was found, on comparing the scale of the electroscope with a multicellular voltmeter, that the divi- sions were of approximately equal value throughout the scale, very nearly one volt per division. The scale had 50 divisions. When the apparatus was filled with air at atmospheric pressure a leak was observed at ordinary temperatures. This effect is quite distinct from the effect discovered by Guthrie, since it is observed equally whether the charge is + or — (Wilson, Joc. cit.), whereas Guthrie’s effect is only obtained with a + charge, unless the temperature is above a red heat. To make this effect insensible the pressure was reduced to 1 cm. of mercury. The Guthrie effect is not apparently much affected by moderate reduction of pressure, whereas the effect investigated by Wilson is diminished nearly in the same proportion as the pressure. The first experiments were made with a pure silver wire in air at 1 cm. pressure. This was heated to successively increasing temperatures, and the corresponding rates of leak determined. These were practically uniform for different parts of the electroscope scale. The results were :— Temperature.. 15° 202° 236° 265° 277° 287° 2 14 09 2°70 65 13°d 30°0 Fig. 2. Rate of leak, scale-div. per hour. fo) 100° 200° 300 Temperature, centigrade. These results are plotted on the appended diagram (fig. 2). 102. Discharge of Positive Electrification by Hot Metals. The temperatures are given in degrees centigrade, the rates of leak in scale-divisions per hour. By interpolation it was found that the rate of 10 div. per hour was attained at 270°. The same wire was again taken up the scale of temperature without removing it from the apparatus. Temperature. o, dee 194 B10?" B70 8979 a ee deals en cex 5 ws 1:34 1:96 9) 6:7 456 The rate was 10 div. per hour at 250°, 20 degrees lower than before. This change in the temperature at which an assigned rate of leak (10 per hour) was attained is, of course, far beyond the uncertainties of experiment, and must be attributed to a change in the state of the silver surface. Further heating did not alter it much more. The apparatus was exhausted, filled with pure hydrogen, and the pressure reduced to 1 cm. Temperature.. 15° 175° 183° 210° 225° 223° Lenk. 2 Sees “2 6 10 25 6°] 148 10 div. per hour at 228°. Thus the leakage set in in hydrogen at a somewhat lower temperature than in air. The next experiments were made with a copper wire sub- stituted for a silver one. This wire was cleaned with emery paper before it was put in ; in the course of the experiment it became oxidized. This oxidizing process did not appa- rently facilitate the escape of positive electrification since the leakage was not so soon apparent as in the case of the silver wire. The results were :— Temperature.. 167° 226° 258° 271° 289° 308° 326° 331° Rate of Leak . +1 32 05 29 12:0 380 2040 3400 Thus the rate of leak was 10 div. per hour at about 287°. A repetition of the experiment gave a very similar result. The copper wire was taken out and thoroughly oxidized in a blowpipe flame. It was then replaced. The raies of leak were as follows :— Temperature .... 255° 259° 272° 283 Rate of Leak .... ‘7 311 15:0 83:2 Here the rate of leak was 10 div. per hour at 266°. St ten Numerical Connexion between Atomic Weights. 103. Finally, a well oxidized copper wire was tried in hydrogen. Temperature .... 267° 287° 307° 316° Rate of Leak .... 1°05 1-4 6:0 21:4 10 div. per hour at 310°. These experiments fall into two classes. (1) Those cases where chemical action was occurring between the electrified surface and the surrounding gas. (2) Those cases where there was no such action. To summarize the results: under the first head we have—- Copper inair . . . 10 div. of leak per hour at 287° Copper oxide in hydrogen ae - fe at 310° under the second— Silver in air. . 10 div. leak per hour at 250° Silver in hydrogen a Phen ‘ 228° Copper oxide in air : Fi a 266° So far as the experiments go they suggest that chemical action is rather unfavourable than otherwise to the escape of. positive electrification. The result of most interest in the present investigation is that the discharge of positive electrification by hot metals can be detected at much lower temperature than has hitherto been supposed, becoming apparent very far below a red heat, and increasing rapidly with the temperature. 1X. Ona General Numerical Connexion between the Atomic Weights. By J. H. Vincent, D.Sc., B.A.* [Plates 1. & IL] HISTORICAL. M ANY relationships have been made out between the atomic weights of the elements when these are con- sidered in small groups: and there are a few formule which have been proposed to express the connexion between the atomic weight of an element and the order in which it stands in a list of elements of ascending atomic weights. Mills (Phil. Mag. [5] xviii. p. 393 & xxi. p. 151) states that ‘it is probable that the equation y=p.15—15(-9375)* * Communicated by Prof. J. J. Thomson, F.R.S. 104 Dr. J. H. Vincent ona Numerical includes the numerics of all known elements excepting hydro- gen,” a numeric being an atomic weight y. He arranged all the atomic weights in ascending order of magnitude, and without altering the order, these were divided into sixteen groups by trial. The number pis the same integer for each group. The value of « was obtained by arithmetic for each element. Mills restricted himself only by having 2 always either an integer or infinity, and then chose its value so that the caleu- lated atomic weight should be as near as possible to the expe- rimental value. An example of a group is given below to illustrate the method. Group III. y= 45 — 13(-9375)”. Blais wa ae eee , ovis! Jengilia te 31-98 31-82 | Olaciee inca: 7 30°37 35°45 . Ke ae retest 39-02 38:92 Cad. dena eee 17 39:90 39:99 j SO cathe eeee 42 43°98 | 44-00 | | When we consider the large amount of choice involved in . the compilation of such a table, it is not at all surprising that the numbers in the last two columns of the above table agree closely ; indeed there seems no reason to doubt that | by some such arbitrary process the numbers in the last two i columns could be made to agree to any required degree of accuracy. . To find the atomic weight of an element by this method one would require to know the group in which the element had been placed, the value of x assigned to the element, as well as the constants occurring in the equation. 2 While regarding the work as leading to the conclusion that there might be an infinite number of elements having atomic weights less than about 240, Mills considered that this value was the upper limit. The formule are subsequently derive] by the contemplation of a hot nebular mass of primitive substance which, while cooling freely in space, gives birth to polymers of this ee Se - Connexion between the Atomic Weights. 105 primitive material. ‘‘ But on account of the evolution of heat when a polymer is formed, there will ensue, as a physical consequence, the inversion of more or less of the cooling, and therefore of the polymerization.” Incidentally this theory is used to explain the phenomena of variable stars. The important point about Mills’ work is that it may be considered as indicating the existence of an upper limit for atomic weights. The weak point is that the number of elements below this limit may be infinite. On this latter question Mendeléeff (‘Principles of Chemistry,’ English translation, 1891 ed. p. 19) expresses himself with great clearness. “The actual periodic law does not correspond with a continuous change of properties, with a continuous variation of atomic weights—in a word it does not express an uninterrupted function.” In conclusion, Mills uses his formule to classify the elements with some degree of success. Stoney (Proc. Roy. Soc. 1888, p. 115, and Circular issued to members of B. A. at Bath, 1888) plots as ordinates the cube roots of the atomic weights referred to hydrogen as unit, the abscissxz being successive integers. “ A curve ym =k log (ma), where log k=0°785, and | log a=1:986, threads its way through the positions plotted down from the observations.” Having obtained an expression of this form, Stoney inves- tigated subsequent terms which should include deviations from the formula. Finaily a spiral was constructed and so arranged that it not only showed the periodic classification of the elements, but also gave by inspection the atomic weights. It should be noted that according to Stoney’s formula elements of less atomic weight than hydrogen and also of greater atomic weight than uranium may exist. Three elements lighter than hydrogen and six between hydrogen and lithium were predicted ; a vacant “ sesqui-radius ” in the spiral was left, across which the transition from electro- positive to electro-negative elements was abrupt. This “is not arbitrarily introduced into the diagram, but has a real existence in nature.” This “ sesqui-radius ” is now occupied by the new gases, and thus the prophecy of Stoney has been fulfilled in a most remarkable way. 106 Dr. J. H. Vincent on a Numerical This is a very strong argument in favour of the formula with which Stoney worked, but it is perhaps a stronger argument in favour of the treatment of the periodic law by graphic methods. The prejudice against such methods enter- tained by Mendeleéetf is very surprising. In his book already referred to, he says he has never expressed, “ and will never express, the periodic relations of the elements by any geome- trical figures.” Carnelley (Phil. Mag. [5] xxix. p. 97) founded his method of computing the atomic weights on the periodic law. He mentions that he had made frequent attempts to finda simple numerical expression for the periodic ]aw during seventeen years previous to the publication of this paper, but without marked success. The atomic weight A is given by the formula A=6'6(m+ Vv), where m is a constant for each of Mendeléeff’s “ serics,” while v is equal to the order of each element in its series. The values chosen for m were 0, 24, 5, 84, and thence by differences of 34 to 33, for the successive series II., II1.,... XII. Thus ‘ for any element in series LV. or upwards A=6'6(3°'5a—9 + Vv), where a=the number of series to which the element belongs, and v the numerical order of the element in its own series.” A table of determined and computed atomic weights with their differences is given, from which it is at once evident that the rule is capable of calculating the atomic weights with a considerable degree of accuracy. The greatest varia- tion is for iodine, in which the computed atomic weight falls short of the real atomic weight by 6°7 units. The difference in the same direction for tellurium is given as 6°5; but if we substitute the value now accepted for the atomic weight of tellurium, the difference becomes greater. The mean difter- ence for the 54 elements considered is only 1°9. If, on the other hand, we examine the results from a percentage point of view, they do not appear so satisfactory. Thus the computed value for the atomic weight of carbon is 10 per cent. too high, that of selenium is 82 per cent. too low, that of lithium is 5°7 per cent. too low, and that of nitrogen is 5°7 per cent. too high. The nearness of the constant 6°6 to the 6-4 of Dulong and - Connexion between the Atomic Weights. 107 Petit’s law suggested to Carnelley the trial of the rule | 1 ie teas Rear es oak Wi and he found “ that in almost all cases the numbers agree very closely with the experimental specific heats.” A New Rutz ror Computing Atomic WEIGHTS. If a list of all the atomic weights in ascending order of magnitude be taken and the order in this list be called n, then the nth atomic weight, from n=3 to n=60, is given by the equation W =(n+2)!7!, In the table (p. 108) headed “Augmented List of the Elements,” the numbers standing under n give the actual order of the elements in such a list as the above. The deter- mined atomic weights are given under w, the computed atomic weights under W. The atomic weights are Clarke’s with hydrogen as unit (Journ. Am. Chem. Soc. March 1902). The difference between the determined and the calculated atomic weight is given in another column. Confining our attention for the present to that part of the table from lithium to samarium inclosed by the large bracket, we see that fer the 58 elements considered, the difference between the expe- rimentally determined atomic weight and that calculated by the rule is less than unity in 36 cases. It is greater than 1 and less than 2 in 13 cases; is between 2 and 3 in 7 cases; while in only two cases does the computed value differ from the determined value by more than three units, in both of which the difference is Jess than 4. The mean difference for the whole of the 58 elements with which we are now dealing is about 1°01. The percentage differences are given also in the table. In 19 instances the difference is less than 1 per cent., in 19 it is either 1 per cent. or greater than 1 per cent. and less than 2 per cent.; in 11 cases it is greater than 2 but less than 3, and in 6it is either equal to or greater than 3 and less than 4, in two instances the percentage difference exceeds 4, and in one case the error is 5°8 per cent. The mean percentage error for the 58 elements is about 1°6. 108 Dr. J. H. Vincent on a Numerical - AUGMENTED List OF THE ELEMENTS. — n. IN: w. WwW. w—W. Ti Hydrogen ......'54. 1 1 (by definition)) 1 0:00 BE eb cicia's on hie sic a nea'e Zi Sask 2313 ree oe Gh 3 3:93 3°780 | +0715 88 | 81:15 81-57 | —0°42 Be AUWDIIMIM, 05.5..50c00 39 | 84°75 84:17 | +0°97 Noo. strontium .........3.. 40 | 86:95 86°79 | -+0°16 Lok MGuo a 41 | 883 89°43, | —113 40. Zirconium ............ 42 | 89:7 92:07 | —2°37 41. Columbium ......... 43 | 93:0 94:74 |—174 42. Molybdenum ......... 44 | 95°3 4°40 ..) —210 43. Ruthenium............ 45 | 100°9 100°) +0°8 Be REOGAUMA) Shs. ccs slew 46 | 102-2 102°8 —06 Ao, Pallagiuin .....3..0-st. 47 | 106-2 1 105°5 +0°7 PPO UUMION acces stm saneinne as 148 | 107-11 108-2 —11 Eyesonarmum fos... es.8 5. | 49 | 111-55 1109 | +07 BS, PV MGNUM. cise si.k aha S10 aca i Bt 113-7 | —06 ht orn 51 | 1181 1165 | +16 Connexion between the Atomie Weights. nN. N. 50. Antimony ............ 52 SU ESMINTAS ©. 5s cane nensaes nw | 53 Se. Tellurium .........,.. + | 54 SS ee il BD S42, Cesium ............... » | 56 ee. Barium ............00- | 57 56. Lanthanum ......... 58 re 59 58. Praseodymium ...... 60 59. Neodymium ......... | 61 60. Samarium ............ | 62 i Pou ngieabensvaveceeasscsicecnce ; 63 Tae 2 abet SSS 64 61. Gadolinium ......... 65 OS OS ee 66 ee 67 a 68 a a 69 Sra SRNMIFE: .¢.2<.......~. 70 fe Y erieum |. ........... ae Le a {2 c,h nie ............ 73 Ree emeaLen ............ 74 ys cannceee- 75d ee VanONNITY <-2........-.0- 76 SE ee Li Ua 78 ee 13 Pe METEMry ........+. 52.2. 80 (BO 81 ee 82 i Eannths ...... -....... 83 LL ee 84 NS Ns ae wwianis s- 85 dw ce anes 86 i 87 de ae 28 ey ee 8 88 oe oe 89 SPE TEIOATY! oo 2050200 00c 90 LE ee 91 0 ST ee 92 TABLE (continued). i | w. eoctesscs eeresaseos eer esese eeesecace eS eee Oe 119-2 122-0 | 1248 1276 _.180°4 133°2 18671 138°9 141°8 1446 147-5 150-4 1D3'5 156-2 159-1 162-0 164:9 167-9 170°8 173°8 176'8 179°7 182-7 185°7 188-8 191-7 194:7 197°8 200°8 203°8 206°9 209°9 213°0 21671 219-2 222°2 99353 228°4 Doms) 234-7 287'8 w—W. +03 +39 +13 —0°6 +15 +32 +15 --0-9 —2-4 —21 aed —10 —0'3 -02 —l4 —1°9 418 ri 109 +0°3 eat +1:0 —0'D +1:1 42:3 at] <] =F 25) —1°5 +11 _O6 02 _O1 _08 ZAey 41-0 0-1 + (4 0-0 ay ay 12 =6 Sy, —16 ~ii3 0-0 We may add this statement to the rule: that if the atomic weights are from Clarke’s 1902 list with hydrogen as uuit, then the greatest difference between the computed and the determined value will not exceed 4 units, nor will the per- centage difference be greater than 6; while in 36 cases the result will not be a unit wrong, and in 19 cases will not be 1 per cent. wrong. ee 110 Dr. J. H. Vincent on a Numerical Deviations from the Formula. The elements deviating most from the formula, judging from the differences, between the computed and experlineheys values, are :— w—W. RDEMWC) oe. coi..fn see eee +3°9 Tarra +.* marks the most probable atomic weiglt of a predicted element. Pl. L. is drawn. on ordinary squared paper, and is thus suited to show the differences between the computed and the expe- rimentally found numbers. | q ——— _ —_ ) pone ~~ de Oi th tee ae a, ee Connexion between the Atomic Weights. 113 Pl. Ii. is drawn on paper ruled logarithmically. The graph of an equation of the form y=a™ is astraight line on this paper, so that all the computed points lie on a straight line. The actual distances of the points (@) showing the experimentally determined values above or below the straight line, are proportional to the percentage differences between the computed and the experimental numbers. It will be seen that the actual values of the atomic weights lie very close to the straight line in Pl. II, - An equally good straight line would of course be obtained by plotting the cube roots of w instead of w. Thus the formula is of a different type to Stoney’s, from which it would follow that the actual values (not the logarithms) of the cube roots of the atomic weights plotted against the logarithm of the order would give a straight line. On the Determination of the Power Constant and the Use of the Rule. The whole of the preceding leads to the conclusion that a relationship of the form W=N!. expresses to a close degree of accuracy some fundamental connexion which exists between the masses of different kinds of atoms. | The equation has been thrown into the form WwW ime Niet in the previous pages so as to render the whole as definite as possible. But no claim is madeas to 1°21 being the best value to give tog. The value of g should be obtained from the list of elements from lithium to samarium, augmented or not as may appear most just to anyone who wishes to redetermine the value of g. If there is any truth in the views explained in this paper, the constant ¢ is of primary importance, and its exact determination becomes a matter of interest. The value which will be obtained depends on whether or not an element analogous to manganese is to be assumed between molybdenum and ruthenium; g will be slightly less or greater according as a gap is or is not left. The method might, however, be used to test this point. By considering only elements as far as molybdenum the best value of g could be found, and then the sum of the deviations Phil. Mag. 8. 6. Vol. 4. No. 19. July 1902. i 114 Dr, J. H. Vincent on a Numerical with this value of g could be found 1st when no oe was left,. 2nd with the gap. If the second arrangement gave a smaller mean difference: than the first, then this would justify the prediction of an element in the place under discussion. It may well be, however, that the result of such an inves gation would be different according as one regarded percentage. differences or the differences themselves as of more importance. If the latter, then the mean error is less when no gap is left between molybdenum and ruthenium. Thus if we regard any atomic weight wy as giving usa value of g, we have a series of equations like wy=N‘, or log wy=q log N. Using the atomic weights of all the elements up to and including molybdenum, we have log 3:93= q log 3, log 6°97=q log 5, log 9°0 =q log 6, log 95°3=q log 44. The value of g given by > log w ae > log N will be such that the percentage errors will be least. This. equation may be written > log w Ae log |44 |44.— —log 8’ from which g may be found readily by using a table of the- logarithms of factorials. The value obtained is g=1:209. Similarly g may be computed, when no gap is left between molybdenum and ruthenium, from the atomic weights of the Connexion between the Atomic Weights. 115 elements from ruthenium to samarium. In this case A: Slog w log |}62—log [44 == 21), If, however, we leave the gap, we have fe > log w 4 log |63—log 45 == 15200. Thus the g when we leave no gap is nearer to the first value (g =1:209) than is the value of g obtained when we leave the gap. This leads to the conclusion that no element of atomic weight about 101 with properties analogous to manganese is to be predicted. The mean value of g can now be calculated from i erly OR ee 1 Tog |62 —log |8” which gives g= 1°210. When the value of g has been determined as accurately as possible, then the formula may be employed to determine what empty places in the periodic table are to be filled by predicted elements, in the same way as has been already done above on the assumption that g=1°21. e CONCLUSION. The consequence which follows from the assumption that WH), where N is a + integer and ga positive number whose actual value approximates to 1°21, is that the list of atomic weights starts abruptly at hydrogen but has no end. , The fact that for many years all the elements that have been discovered have atomic weights greater than that of hydrogen and less than that of uranium would point to the conclusion that any law for the connexion between the masses ‘of different kinds of atoms should lead to the list of elements being limited at both the beginning and end. Cavendish Laboratory, Cambridge. 12 PS 6] X. Observations on Mixtures with Maximum or Minimum Vapour-Pressure. By J.P. Kunnen and W. G. Ropson*. [* previous papers + an account was given of the properties of certain mixtures which have a maximum in their vapour-pressures at a given temperature and a minimum in their critical temperatures; and more recently { a case was investigated in which a minimum in the vapour-pressures went hand in hand with a maximum critical temperature. This combination of corresponding properties follows as a result from van der Waals’ theory of mixtures, if the mix- tures are assumed to have the simple characteristic equation similar to van der Waals’ well-known equation for simple substances. This assumption involves the more general one that the mixtures are normal, 2. e. without association of molecules, although the two suppositions are by no means identical ; a simple substance may disobey van der Waals’ law (as it invariably does) and still be normal, as testified by its obeying the law of corresponding states. It will be convenient to briefly restate the theoretical conclusions on the above assumption. For mixtures which have a maximum vapour-pressure for a given composition at a low temperature, the maximum shifts towards the component with the higher vapour-pres- sures, and may either disappear or remain up to the critical condition. These mixtures have at the same time a minimum in their “ hypothetical ”’ critical temperatures—z. e. the eritical temperatures which they would:have if they did not split up into mixtures of different composition but remained homo- geneous,—at a composition coinciding with the composition of maximum vapour-pressure at low temperatures, and have accordingly a tendency towards a minimum in their real critical temperatures. If there is a minimum vapour-pressure at a low tempera- ture, the minimum shifts towards the component with the lower vapour-pressures, and may disappear or remain up to the critical point. These mixtures have a maximum critical temperature at a composition near that of the minimum yapour-pressure at low temperatures. If the mixtures are abnormal either because one or both the components are so, or because of mutual association of the two kinds of molecules, the above rules cannot be ex- pected to hold good. A maximum vapour-pressure may be due not to the low mutual attraction of the two substances, * Communicated by the Authors. + Phil. Mag. [5] xl. p. 178; xliv. p. 174. t Ibid. [6] i. p. 593. Mixtures with Maximum or Minimum Vapour-Pressure. 117 as is the cause of a maximum with normal mixtures, but to the association at low temperatures of the molecules of the component which has the higher vapour-pressures at high temperatures, and the abnormally low vapour-pressure exerted by this substance in consequence. This abnormality naturally makes the vapour-pressures of the mixtures appear relatively high, and may even produce a maximum. In that case there would be no reason to expect a minimum critical temperature. Other exceptional cases due to association will naturally suggest themselves, and instances will be discussed below. The above conclusions for normal substances are, to a certain extent, confirmed by the results contained in former papers, to which the reader may here be referred. The ex- periments described in this paper were undertaken with a view to completing the comparison with theory, and obtain- ing further information on the behaviour of similar mixtures. Three different combinations were examined and will be taken up successively. 1. Propyl Alcohol and Water. In this mixture it was our object to follow the maximum in the vapour-pressure discovered by Konowalow * up to the critical point, to ascertain whether the maximum shifts to any extent to mixtures of different composition, whether it disappears or not, and finally whether the critical tempera- tures showed a minimum or not. | The propyl alcohol obtained from Kahlbaum was found to be sufficiently pure to be used without further purification. Three mixtures were investigated, the first containing ap- proximately 24 per cent. of water (mixture 1); the second and third both approximately 25 per cent. (mixtures 2 and 3). This is approximately the maximum mixture at the boiling- point. Some of our results are shown in Tables I.—V. (p. 118), and the diagram (fig. 1). Aswe could not observe the beginning of the condensation of the mixtures in our tubes, we always took the pressure at a small volume near the end of conden- sation: the figure thus gives condensation lines instead of narrow loops. The vapour-pressures of water used in the figure are due to Batellit; at temperatures above 250° the values are somewhat higher than those found by Cailletet and Colardeau f. Our value for the critical temperature of propyl alcohol agrees well with that found by Ramsay and Young §, viz., * Wied. Anz. xiv. p. 34. + Ann. Chimie et Phys. [7] iii. p. 412. t Ibid. [6] xxv. p. 527. § Phil. Trans. clxxx. p. 137. 118 Prof. Kuenen and Mr. Robson on Mixtures with TaBLE J.—Vapour-pressures Tapie I].—Vapour-pressures of Propy! Alcohol. of Mixture 1. | Temperature, Pressure. Temperature. Pressure. 96:0 0:96 95°15 1:04 98°45 1:06 98-0 A ty 105:1 1:37 105°05 1:52 128°3 2:97 116°8 2°25 h A811 3-23 1308 3:54 1499 563 145°4 5°57 * 160°2 Tau 160°2 7-99 1669 | 8-47 183-1 ) 1835 183°3 12°20 | 216°8 25°12 2283 28°71 227°8 30°61 PAD * 36°35 2451 40°14 248:2 39°76 2546 47°42 © 2506 | 41:36 | 264-9 55:94 Plait- 264:0— 51:51 Critical | point. point. . Tas eE III. Tasie LV. Vapour-pressures of Vapour-pressures of Mixture 2. Mixture 3. Temperature. Pressure. | | Temperature. Pressure. Bees eS ee te | bea Ag ag iia NL Yh 166°9 ai read after | 85:2 0°91 179°1 14°56 the higher, 7°6 1-00 182-7 15-76 | tempera- | 92:2 1-17 215°7 30°57 } tures. 94:15 1°26 224°6 35° 105°1 1°89 24135 | 47° 116'8 2°81 250°2 56" - 323°65 3°50 261°38 | _ 67°33 | 131°1 4:37 275°85 83°81 Plaitpoint. | 1458 6-74 e | 160°15 9:88 | 170°9 12°48 183-4 16°34 245715 50°16 260°1 64:42 275°1 82:04 2105 846 Plait- point. TABLE V.—Critical Constants. Temperature. Pressure. Propyl alcohol......... "264-0 51°5 webrsbures ly: £5. Josie. ie 264-9 55°9 Mixture 2 ..........:. ae 275°85 83°8 i) Mbixtave 3 cc Xi: J BIS 846 Maximum or Minimum Vapour-Pressure. 119 262°-7, but our pressures are all a little higher than theirs, the difference increasing with the temperature up to the critical point, where we find 51:51, their value being 50°16. Fig. 1. | ak N RE RE de ot ni 2 e py [3 a = | < : | | | TEMPERATURE so 250° 260° 270° 2E0°C This difference is probably due to a trace of water in our alcohol (see below). It will be seen (1) that the maximum vapour-pressure remains up to the critical point, and (2) that the critical temperatures have no minimum. The very small difference in the critical temperatures of pure propyl alcohol and of the first mixture leaves some doubt as to whether there might not actually be a small minimum close to propyl alcohol (especially since readings were taken with different thermometers, one having been broken). But even if it did exist, which is very unlikely, the minimum would be very little pronounced, and would not belong to the mixture of maximum vapour-pressure at low temperatures. The fact that Ramsay and Young found a lower critical temperature for water-free propyl alcohol supports the conclusion that there is no minimum. This deviation from the normal case, as deduced from the theory and as realized by mixtures of ethane and carbon dioxide (see above), makes it probable that the maximum ‘apour-pressure in the combination of propyl alcohol and water is not due to a small attraction between the two kinds of molecules, but to association of molecules. The chief cause is probably the very high association of the water molecules amongst themselves. ‘hat this association has begun even at high temperatures appears from the fact that the vapour-pressure curve of water, which is considerably below the curve of propyl alcohol at low temperatures, approaches the latter as the temperature rises, so that it looks as if they 120 Prof. Kuenen and Mr. Robson on Miztures with would intersect, if the propyl-alcohol curve were a little longer. This irregularity would not occur with normal sub- stances, and is due to the very high abnormality of water, which reduces its pressure abnormally as the temperature falls. This low vapour-pressure of the water makes those of the mixtures appear relatively high. In a somewhat crude form our explanation is this: if the water molecules did not associate, water would have higher vapour-pressures than propyl alcohol. Adding water to propyl alcohol, therefore, raises the vapour-pressure until, when the density of the water in the mixture becomes suf- ficiently high, the association begins to make itself felt, and the vapour-pressure passes through a maximum and falls. towards the pressure of water itself. It is thus unnecessary to assume a specially small mutual attraction between the two kinds of molecules, and there is no reason to expect the critical temperature to fall when water is added to propyl alcohol. : As regards the shifting of the maximum, our experiments, as far as they go, do not seem to show a considerable change in the composition of the maximum mixture. On the con- trary, the almost perfect parallelism of the vapour-pressure curves for the two mixtures, 2 and 8, seems to show that the change is very small, and it looks altogether as if the 25 per cent. mixture was still approximately the maximum mixture in the critical region *. It follows, from the position of the critical curve in the diagram, that all the mixtures between propyl! alcohol and the maximum mixture ought to show retrograde condensation of the second kind. It was impossible to confirm this completely in the experiments, but what was observed is in accordance with the theoretical conclusion. When the mixture 1 was in the critical condition, 2. e. at its plaitpoint, compression invariably brought back the liquid surface, and made the liquid increase until it filled the tube. This phenomenon shows that the plaitpoint in the volume-composition diagram is placed on the side of the large volumes; and this agrees with the theory and with the existence of retrograde conden- sation of the second kind, which, owing to gravitation and slight impurities, could not itself be observed. We did not consider it worth while repeating our experi- ments with purified alcohol, as a special experimental diffi- culty prevented us from obtaining accurate results or going into the various questions more thoroughly. We refer to the action of water on glass, which we observed in 1898 +, and * Compare Ramsay and Young, Phil. Trans. clxxx. p. 157. + Phil. Mag. (5] xlviii. p. 188. Maximum or Minimum Vapour-Pressure. 1oF which has been fully investigated by Barus*. A mixture kept at a temperature above 200° C. is constantly losing water which is absorbed by the glass ; the tube gradually becomes quite opaque. The ‘composition ‘of the mixture is thus alw ays changing, and it is obviously impossible, under these circum-- stances, to make accurate measurements about the relation between vapour-pressure and composition. We had, therefore, to content ourselves with the results obtained. 2. Acetone and Chloroform. According to v. Zawidski } mixtures of these two substances. have a minimum vapour-pressure at ordinary and low pres- sures. As our success with mixtures of hydrochloric acid and methyl ether {, which also have a minimum vapour- pressure, had been only partial, owing to chemical action at high temperatures, we ‘resolved to undertake the investigation of these mixtures in the neighbourhood of the critical point. We began by testing v. Zawidski’s observations, and found them confirmed. In our first experiments at high tempera- tures, we inclosed the substances in the usual way in a high- pressure tube of a Ducretet apparatus above mercury §, but unfortunately it appeared that at high temperatures a che- mical action takes place between the chloroform and the mereury. We then carefully dried the chloroform (Schering’s chloral chloroform) with calcium chloride, but were unable to reduce the action to any extent. The nature of the action is such as to generate a gas which reduces the critical temperature and raises the pressure. It is so rapid, that in a short time the tube becomes opaque and useless. The acetone (obtained from Kahlbaum, made from the bisulphite compound) gave no difficulty. The results obtained by this method are contained in the following table (VI.) (p. 122). Lhe table only contains the earlier observations of each series, which are naturally more trustworthy than the later ones, although even these show that the chloroform is gradually changing into a mixture. From the vapour- pressures at 251°°3 and the critical data, we find by inter- polation the following vapour-pressures :— Temperature. Pressure. Chloroform. Mixture. 257°6 50°1 51°4 259-6 515 53°3 Comparing these, it appears that the pressure of the mixture * Phil. Mag. xlvii. pp. 104,461. + Zettschr. physik. Chemie, xxxv. p. 129. ¢ Phil. Mag. [6] i. p. 593. § Phil. Mag. [5] xlviii. p. 187. 122 ~—— Prof. Kuenen and Mr. Robson on Miztures with TABLE VI.—Vapour-pressures of Chloroform, Acetone, | ; -and Mixture. | { | Temperature. Pressure. | Chloroform. 244-5 42-7 2513 45-0 = 45°6 Later. , — 48:4 After prolonged heating. 262°9 | 93°8 Critical point. 262°55 Deo 5» later. Acetone. 195:0 | 25°44 204°9 | 29°97 2148 Berti 224-75 | 40-79 — | 40°84 $ At different volumes, — ' 40-80 233-65 | 46°76 Critical point. SE hg 46°78 a - Mixture. | 2 ore 493 At different volumes. 257°6 514 259°6 53°3 Plaitpoint. 259-4 | 54:6 " » later. is higher than the pressure of the chloroform at the same temperature. Again, drawing a straight line between the critical points of acetone and chloroform in the pressure- temperature diagram, it appears that the critical pressure of the mixture, 53°26, is slightly higher than the pressure on this straight line at the same temperature, 53°03. With a tolerable degree of certainty we may therefore consider the following facts to have been established :— (1) The minimum vapour-pressure which exists at low temperatures has disappeared at the critical point; and (2) There is no maximum critical temperature, and the eritical curve connects the two critical points in the normal manner, with a slight convexity towards the high pressures. In order to confirm the results obtained, as far as pos- sible, by a better method we repeated the determination of the critical temperatures of chloroform and of two mixtures— one containing a very small and the other a somewhat Maximum or Minimum Vapouv-Pressure. 123 larger quantity of acetone, in a closed tube without mer- eury. These tubes were closed at one end, provided with a small bulb at the top and drawn out. They were filled by exhaustion and boiling at the air-pump, and then sealed. In order to obtain the critical phenomena about the middle of the tube, we found that the tubes had to contain as nearly as possible two-fifths of their volume of liquid at the ordinary temperature *. The following values were obtained: — Chloroform .. . 262° 65 Tar anxtare 1) °".: 2 ae Vil MINGUre «4 /. OO Our previous results were thus confirmed as regards the temperatures, and there is no reason to doubt the | accuracy of the above conclusions. In chloroform and acetone we have therefore a combi- nation which has no maximum or minimum in the critical temperature or in the Vapour-pressures in the critical re- gion, but in which a minimum vapour-pressure appears at low temperatures. This cannot be accounted for by the probable but certainly only sight abnormality of acetone. On the contrary, this abnormality would tend to make the vapour-pressures of the mixtures appear higher. The low pressures of the mixtures might indicate a strong attrac- tion of the two substances; but according to theory this attraction would have produced a maximum in the critical temperatures. As such a maximum does not appear, we are led to the conclusion that the low vapour-pressures at low temperatures are due to an abnormal increase in the mutual attraction of the two substances at lower tempera- tures, and therefore probably to mutual association of the two kinds of molecules. Of course this conclusion is only legitimate on the assumption that the equation used by van der Waals is a sufficiently correct test of normality or abnormality. The non-existence of a maximum critical temperature thus suggests the probability of mutual association. With methyl ether and hydrochloric acid, where a maximum critical temperature exists, as pointed out in the paper on these mixtures fT, we had no means of distinguishing between association and mutual attraction. But a great deal more evidence will be required before this distinction is capable of being clearly drawn. * In Ostwald’s ‘ Physico-chemical Measurements’ (1894, p. 114) the prescription is te fill the tubes to two-thirds of their volume. This quantity is much too large, at least with an air-free liquid. The correct amount is given by Nadejdine, E2ner’s Repertoriwm, xxiii. (1887) p. 617. } Pail. Mag. [6] i. p. 597. 124 ~= Prof. Kuenen and Mr. Robson on Miatures with 3. Carbon Dioxide and Ethane at Low Temperatures. These mixtures, as was discovered before *, have a mini- mum critical temperature and a maximum vapour-pressure,,. but had only been examined at temperatures above 0° C. In extending the investigation towards low temperatures, we wanted to trace the maximum vapour-pressure more fully than could be done in the small range between 0° C. and the critical region, and to ascertain whether the maxi- mum was in any way connected with a splitting into two liquids at low temperatures. We have found that no such separation takes place up to the region where solidification sets in. This solidification of the carbon dioxide afforded an opportunity for the study of the influence of the second substance on the phenomenon. The minimum critical temperature belongs to a mixture containing 45 per cent. of ethane; the maximum vapour- pressure, near the critical point, toa mixture containing 30 per cent. According to the theory, the maximum at low temperatures ought to belong to the 45 per cent. mixtures. This point was tested in the following manner :—Two strong glass tubes closed at the bottom were connected with each other at the top by means of flexible high-pressure piping, and with the two supply vessels containing the purified carbon dioxide and ethane. A mixture was let into one of the tubes cooled for the purpose to —50°C., and then dis- tilled into the second tube, and so on backwards and forwards. The last portion in every distillation was not caught in the glass tube, but was blown off and collected over mercury and analysed. From the theory of mixtures of maximum vapour-pressure, it follows that the mixture coming over must gradually approach the maximum mixture at the temperature of the liquid. The pressure will therefore gradually increase. This appeared to be actually the case. The initial pressure was 7°8 atmospheres, and after successive distillations the readings were 8°5, 8°8, 8°5, 8°6, the temperature being kept roughly constant. The analysis of two samples after theithird and the last distillations gave as the compositions 42 and 44 per cent. ethane respectively. The mixture has approached and practically reached the theoretical value of 45 per cent. The predictions of the theory had thus been completely verified. We then proceeded to measure vapour-pressures of two different mixtures by the accurate method described for pure carbon dioxide and ethane in a former paperf. The change of the vapour-pressure with volume is comparatively small for both mixtures, owing to the narrowness of the conden- * Phil. Mag. [5] xliv. p. 187. + Ibid. [67 iii. p. 149. Maximum or Minimum Vapour-Pressure. 125 sation loops*, so that we could with safety apply the method. The vapour-pressures contained in the table are thus inter- mediate values between the smallest and largest, but much nearer the latter, as the greater part of the mixture was liquid. One of the mixtures selected is the maximum mixture at the critical point, mixture A (30 per cent.) ; the other one, B, we had intended to be the 45 per cent.. mixture, but by mis- take we prepared a 50 per cent. one. It will be seen from the tables (VIL. & VIII.) that the pressures of mixture A are TasLeE VII. Vapour-pressures of mixture of equal volumes of Carbon Dioxide and Ethane. Temperature. Pressure, 417-8 56°17 | | 148 aera! | 0 / 37°21 — 948 ) 29-42 20°83 . 21°85 32°22 ; 15°75 32°90 / 15:29 Larger Volume. — ) 15°39 Small os | 40°94 11°66 ) 47°48 ) 9-60 56°80 ) 6-90 58°61 | 6:44 60°54. | SOT 62°69 5-488 65°17 ) 4-950 68°11 | 4°332 Solid and Liquid. 69°39 +066 ,, S 78°38 | PT i2t | TaBLeE VIJI.—Vapour-pressures of mixture of three yolumes of Ethane to seven volumes of Carbon Dioxide. Temperature. | Pressure, | | ++:18°85 60°54 | 38-93 | | 9°26 30°76 20:80 (22-41 32°15 16-02 | 32°75 15:37 41°15 11-92 | 47°60 | 9°56 | 56°32 | 695 | 60°54 597 | 62°65 5-426 | 62°79 5°25 Solid & Liquid (large volume). | 64°63 5058." ;, Md (small volume). | 68°07 4337 ” 39 ” ” / 78:17 2-657 | 39 39 39 39 * Phil. Mag. [5] xliv. p. 188. 126 ~=Prof. Kuenen and Mr. Robson on Miztures with considerably higher than those of mixture B at ordinary temperatures ; as the temperature falls in accordance with the previous experiments, the two curves approach each other (fig. 2), and ultimately the pressures of B are higher than those of A. This would naturally have shown even better if we had used the maximum mixture of 45 per cent. ethane instead of 50 per cent. TEMPERATURE a a a 65 -60° =55° -50°% The plaitpoint of mixture A appeared to be at 18°85 C. and 60°54 atmospheres, as against 18°77 C. and 61°3 atmo- spheres obtained before for the same mixture*. The other mixture B had its plaitpoint at 17°°8 C. and 56:17 atmospheres, as compared with 17°75 C. and 57:2 found before. The temperatures agree very well: the difference in the pressures | is due to the uncertainty of the high-pressure gauges used in the earlier experiments, as explained in our paper on the vapour-pressures of carbon dioxide and ethane. The two curves (fig. 2) practically coincide for such a long distance that the exact point of intersection cannot be ascer- tained ; but this is of minor importance. The curve TOMN is the solidification or three-phase curve : starting from T the triple point of carbon dioxide it rises slightly, attains a maximum at O, and then gradually falls, passing through M, where the curve for the maximum mixture reaches and touches the three-phase curve. From the point of view of the separation of solid carbon dioxide, the mixtures fall into two groups. The mixtures of one group contain less ethane * Phil, Mag. [5] sliv. p. 187. -70° -65° Maximum or Minimum Vapour-Pressure. 197 than the maximum mixture (45 per cent.), and solidify at: points between M and T ; the mixtures of the second group contain more than 45 per cent. of ethane, and solidify at points beyond M. It will be seen from Table VII. that the 50 per cent. mixture belongs to the second group, as it has not solidified at —65°°17 C.: its pressure is at this tempera- ture a little below the three-phase pressure, although the scale of the diagram is too small to show this. The 30 per cent. mixture, on the other hand, belongs to the first group, and the maximum mixture must lie between the two as we we have seen it actually does. The difference between the pressures on the three-phase curve obtained with the two mixtures at the lowest temperature, the boiling-point of solid carbon dioxide, is due to the considerable slowness with which the proper equilibrium sets in; the stirrer which we had inside the tube having become quite immovable in the solid. In figs. 3 and 4 (p. 128) we give ona larger scale diagrams of the relative positions of the three-phase curve and the con- densation curves for mixtures belonging to the first and second groups respectively. These diagrams can only be properly understood by simultaneous consultation of “figs. 5 and 6, which are intended to give an idea of the nature of the volume-composition diagram at two different temperatures, fig. 5 above and fig. 6 below the temperature corresponding to the point M in fig. 2. Figs. 5 and 6 contain the projection of the vapour-liquid plait with the maximum M. A part of this plait is cut off (i.e. is made metastable) by the solidification figure. This figure consists of (1) the vapour-solid plait which reduces to a fan-shaped projection owing to the very small change of volume of the solid; (2) the three-phase triangle SLV ; and (8) the solid-liquid plait, beyond SL, the properties of which are unknown. The three-phase triangle leaves the maximum free in fig. 5, and covers it in fig. 6, so that in this latter case the maximum belongs to the unrealizable (metastable) part. The metastable curves, as far as shown, are dotted. It is now easily seen what condensation phenomena may be expected at the various temperatures with the various mixtures. As an instance, we point out that the mixture « in fig. 5 will, on compression, first begin to solidify at a, then liquid will appear at 6: there are now three phases, and the pressure becomes constant. On further diminution of volume the solid will diminish and disappear at ¢, and ultimately the vapour will all go at d,and the mixture will be completely liquid. The corresponding points a, 6, c, and d arealso shown a ae 5 ee PRE A PP Fe Ey Ly eae ce et Oe es ee 7 ‘ \ } i . i J Br 7 x i ’ | h 5 ‘ wt a 1 ’ 4 "4 ; ee z oo 128 ‘Prof. Kuenen and Mr. Robson on Mixtures BAF : a oS in fig. 3. We were able to confirm this somewhat complex series of changes with the 30 per cent. mixture at a tem- perature of about —63°C. We may leave it to the reader Fig. 3. z & to deduce the phenomena in other cases from the figures, and to ascertain that the p-¢ figures (3 and 4) are in accordance with the v-# figures (5 and 6). Muzimum or Minimum Vapour-Pressure. 129 Further consideration of the pressure-temperature diagram leads to some important results. On the three-phase curve the gaseous mixture is in equilibrium both with the liquid mixture and with the solid phase; te. with pure solid carbon dioxide. It follows that the partial pressure of carbon dioxide in the vapour must be approximately the yapour-pressure of the solid at each temperature. As this -quantity is known, the composition of the vapour-phase may be deduced from the pressures. We may test this conclusion -at the point M, where the maximum curve reaches the three- phase curve, considering that for the maximum mixture the composition of the vapour is the same as for the liquid, and thus the same as the composition of the mixture as a whole. The pressure at M is 4°94 atmospheres ; the pressure of solid carbon dioxide at the same temperature (—65°15) being 2°72 atmospheres : : the maximum mixture thus contains 2°72/4-94=°55 parts of carbon dioxide, which is in exact accordance with our former results. We are thus enabled to determine by the same method the composition of the gas-phase all along the three-phase curve. In this manner we find at O, the top of the curve, 3°85/5°33='72 parts of carbon dioxide and °28 parts of ethane. In our experiments we were not able to observe the temperature and pressure at which the gas was in equilibrium with a trace of liquid and of solid, so that we do not know where the gas curve for the mixture *30 cuts the three-phase curve. We cannot therefore compare the result about the point O with experiment. An approximate value for the volume of the vapour may now be found from the composition and the pressure by applying the gas laws, and we are thus enabled to determine the heat of transformation of the mixture on the thr ee-phase -curve from the formula d H= =i J) yan Saray. (4) where V represents the change of volume of the transforma- tion corresponding to the heat H. The value of H is of special interest at M, where, as we saw, vapour and liquid have the same composition ; the trans- formation at this point thus consists of the evaporation of the liquid mixture as a whole, the solid taking no part in the transformation. H in this case is simply the latent heat of evaporation of the mixture, and V the difference between vapour and liquid volumes, precisely as with pure substances. It is clear that we might apply the same calculation to any other point of the maximum curve. Phil. Mag. 8. 6. Vol. 4. No. 19. July 1902. K 130 ok Kuenen and Mr.. Robson on Mixtures with For = at M we find :209: the volume of one gramme of the gas calculated by the gas laws is 91 ¢. c.: subtracting from this the approximate volume of the liquid, and allowing for a small deviation from the gas law we find for H per eramme of the mixture 89 calories ; the latent heat of carbon dioxide and of ethane at the same temperature being 95 and 114 respectively. If we subtract from the latent heat the external work, we obtain the internal latent heat which should give us a more accurate measure of the relative values of the internal energies. The value of this quantity for the mixture is 79 calories, and for the components 86 and 100. Moreover, we ought to compare not a gramme of the mixture with a gramme of the components, but with the sum of the quantities actually contained in the mixture ; in this way we find 91 calories compared with 79 for the mixture. In whichever way we make the comparison, the latent heat of the mixture appears to be small, as might have been expected: for the maximum i ea is characterized by a comparatively small mutual attraction between the component substances, on which attraction the latent heat doubtlessly to a large extent depends. On the theory of van der Waals the internal latent heat is equal to (= ~ ~) where a is the L wv. attraction-constant and 7 and v are the volumes of liquid and vapour**. As v;, the volume to which the vapour con- tracts on condensation, depends on the volume-constant 6 in the equation of condition, we see that in general the latent heat depends on both constants, but we know from previous results} that ) for mixtures of carbon dioxide and ethane has the normal value, and that the maximum vapour-pressure 1s due to a small aj, the mutual attraction constant. Without actually, calculating the value of the heat of transformation at other points on the three-phase curve, we can see how the value of H/V gradually diminishes at teen peratures beyond M, becomes zero at O where dp/dt=0, and is negative between ‘O and T where dpldt<0. The meaning of these changes is the following:—If we take V positive, i.e. 1f we increase the volume in which the mixture in its three phases is contained, the transformation (fig. 5) consists in an evaporation of the liquid mixture, L. This mixture contains more carbon dioxide than the vapour * Bakker, Dissertation, Schiedam 1888, Tt Kuenen, Phil. Mag. [5] xliy. p. 195. a Maximum or Minimum Vapour-Pressure. 131 V, and during the transformation part of its carbon dioxide will thus be condensed into solid. The evaporation requires heat, but the formation of solid yields heat. As the difference CARBON DIOXIDE _-y THANE os in composition between liquid and vapour increases, the heat of solidification also increases, and at O the two have become equal. Beyond O up to T the heat developed is larger than the heat absorbed, and H becomes negative. Fig. 6. CAPBONW Diox1oE WN The following gives an answer to the question, on what conditions the sign of the heat of transformation at and near the triple point depends. If z, and 2, are the amounts of ethane contained in a gramme of the liquid and the vapour respectively, the evaporation of one gramme of the liquid 132. Mixtures with Maximum or Minimum Vapour-Pressure. gives 2, grammes of gaseous ethane: this quantity requires Me. ; . e — (1—w,) grammes of carbon dioxide, so that i) } ; v Vg hy 1 mee eae ye) = oe grammes will be solidified. We thus find for the heat absorbed, and the corresponding increase of volume near T, Ug Xy hs os Lee = Ly, Lyg + Li . 2 V=v,—vi— Sei v= “1 (W%—vs) —V1+Us. (8) Lo ce At T itself we must take for L,, the heat of sublimation, and for L,, the heat of evaporation of carbon dioxide, and > Ls =e The value of this fraction for carbon dioxide is 43°8/129°9 ="34. The amount of ethane in the vapour is thus found to be more the sign of H thus depends upon whether than three times the amount in the liquid. The value of - at TT is about —:10 atmosphere per degree. By means of the expression for H (1) combined with (2) and (8) we can now calculate both z,/%, and H. The result is x,/7,=*26, and H=— 9°9 calories. If we apply the above formula (2) for H to the condition at QO where H=0, we can obtain an approximate value for the ratio a/a, at that poimt. Taking for L,, 129 calories, and Lz, 88 calories, we find #,/a,=°32. According to this calculation, which however is only very approximate, the ratio of the compositions of the liquid and vapour, which according to Henry’s law would be a constant within certain limits, has only come up from ‘26 at T to 32 at O. At M, as we saw before, its value reaches unity. The direction of the three-phase curve at T agrees with that found by Stortenbeker* for mixtures of iodine and chlorine. Bakhuis Roozeboom and van der Waalst were the first to discuss the properties of such curves from a general thermo- dynamical point of view. We hope that the above will be found to contain a not unimportant addition to our knowledge of the subject. University College, Dundee. * Stortenbeker, Zevt. phys. Chem. iil. p. 19. + Roozeboom, Zezt. phys. Chem. ii. p. 462. ie bea XI. On a New Reaction between Electrostatic Tubes and Insulators, and on the Electrostatic Field round an Electric Current, and the Theory of Professor Poynting. by M. W. pDE NIcoLAlEvVE*. OV e new reaction between electrostatic tubes and insulators.— This special reaction is observed in the electrostatic field which the author has shown to exist in electrolysis during the passage of the current. The tubes of force of this field coincide with the lines of current, and so insulating matter which is dielectric for tubes of the ordinary field behaves in an electrolyte like a perfect dia-electric deprived of electric permeability. First Experiment.—Place in distilled water a system of two vertical plates perpendicular to a third, AB, fig. 1, all insulat- Fig, I. ing, the horizontal section having an H-form. In the compartments formed by this plate immerse two strips of tin 15 to 20 ems. long with horizontal sections represented by K and L. When the strips are - connected up to a source of cur- rent they diverge under the influ- ence of tubes of the kind represented by K D BC L, as repre- sented in elevation in fig. 2. If they are connected up to the Fig. 2. terminals of a 300-volt transformer their extremities are dis- placed as much as 20 mms. outwards. The set of tubes like K D BCL can only exist through the action of the diaphragm * From the Comptes Rendus, 30th December, 1901, and 6th January, 1902, with some additions by the Author. Communicated by Prof. J. H. Poynting. 134 M. W. de Nicolaiéve on a New Reaction upon them, and these tubes will have a reaction tending to compress the diaphragm. ) Second Experiment—Two strips K and L (fig. 3) are sus- pended in water and separated from _ each other by a glass partition, A B. The electrostatic tubes of the kind LAK displace the strips into the positions K! and L’, so that the two bodies under their mutual actions are displaced in the same direction, which is contrary to the fundamental law of Action and Reaction. The only plausible explanation is that the edge A reacts upon the tubes LAK which act like stretched elastic threads pressing against the edge and pulling B the strips. Third Experiment.—Metallic wires or strips K and L (fig. 4) are immersed in water and are fixed. The mica Fig 4. NY Q x NS S S Ss NS N S S 2 SSSessssssss Sr eer ae al a aa ae oe > (See Be ee eee Pomme er em mee ee Le Se -—_— = ‘ partition, A B, floated by a cork, is movable. When in the position A Bit moves from A towards B, in the opposite direction to the movement of the strips in the second experi- ment. The moving force is the difference of the pulls of the tubes LA K and LB K (fig.3). When the edge A has passed the line of the electrodes KL the tubes issuing from the other faces of the electrodes act still in the same direction. When the mica is parallel to the plane through K L it retreats from them, a movement which is produced by the pressures between Electrostatic Tubes and Insulators. 135 of the tubes. Such pressures should be experienced by the walls of vessels containing electrolytes. To confirm the ex- periment and to be assured that the movements are not due to currents of liquid, two electrolytes were placed in series, both consisting of distilled water. After the mica had moved in one, a small quantity of chloride of sodium was dissolved in it. The current became stronger, but the electro- static field became weaker and the mica showed hardly any trace of movement. ‘Tinfoil floating in the water and replac- ing the mica behaved in the opposite way. The author intends to make the third experiment in rarefied gases, where by ionization the electrostatic tubes may also coincide with the tubes of current, but where the influence of the statical lines upon the walls will also come into account. Fourth Experiment.—A mica pendulum (fig. 5) movable round a light axis of glass is placed between the terminals of a Holtz machine with the axis parallel to the line joining the Fig 5. Fig. 6. Be ew tee, et 770) a ie = terminals. If this line passes through the plate and the spark is obliged to turn from the most direct route, the pendulum retreats from the terminals. If the air 1s ionized by the discharges the effect may be attributed to the reactions ot the electrostatic tubes on the edge of the mica, but if not, we cannot so explain the motion. The two faces of the mica may perhaps be electrified by charges of the same sign respectively as those in the points A and B, and the aisplace- ment to the right may be due to repulsion of like charges. 5 1 * lt would be necessary to put a flame under the points and 136 M. W. de Nicolaiéve on a New Reaction the mica to take away the charges from the latter and to facilitate the ionization of the air, but the illness of the author has interrupted this experiment. He has made the following experiment. A disk of mica K (fig. 6) is suspended excen-- trically to one side of the line of two-pointed terminals con-- nected to a Holtz machine. When the flame F is lighted the disk K is displaced to the right by the current of hot air. But when the electric machine is in action, the disk is. displaced at least twice as much. On the Electrostatic Field round an Electric Current. Apparatus.—In a large glass tube placed vertically are sus-- pended two loops, A HC and BF D (fig. 7), parallel to each other, 4to 5 mmm. apart, and consisting of two strips of tinfoil, 3mm. wide, hanging down to a depth of 50cm. The greater this depth the more marked is the effect. The free ends, ABCD, are fixed in a card placed on the top of the tube. The points A and B of the loops are connected up to the terminals of a battery of 100 volts. The points C and D are either insulated or are connected through a rheostat of glow- lamps. In the first case the loops are charged to the potentials of the battery terminals; in the second case a constant current flows through the two loops in opposite directions so that the electromagnetic forces tend to make them repel each other. First Eaperiment.—The battery is unconnected, and the loops are at rest. Then the battery is joined up and the locps move towards each other. The attraction is produced by the system of electrostatic tubes from the one loop to the other. . Second Experiment.—The battery circuit is completed by ——— * between Electrostatic Tubes and Insulators. 137 a rheostat of 900 ohms. The movement towards each other persists and differs little from that on open circuit. The repulsive electromagnetic action exists, but does not manifest itself owing to the feebleness of the current (O-11.amp.). There is only one probable explanation. The electrostatic tubes join the two loops in the same way as in the statical case, and the mechanical effect remains nearly the same, because on the one hand through the small fall of potential the tubes have nearly the same strength, and on the other the electromagnetic repulsion is very small. In the statical condition the ditference of potential be- tween the two ends of each tube is the same and the system of tubes is in equilibrium. In the dynamical condition the differences of potential diminish from 100 volts to zero, and the equilibrium of the tubes is disturbed. The transversal pressures diminish gradually, and the tubes are displaced perpendicularly to their axes, sliding along the conductors and sweeping through the dielectric medium. The fall of potential along the circuit shows that each tube, after an infinitely small displacement, will have a less difference of potential between its ends, an effect which may be set down to the destructive discharge of the end-cellules in the body of the conductors. We see that the experiment leads to results exactly agreeing with the theory of Professor Poynting, and that it confirms that theory. When the inserted resistance is diminished to 200 ohms the attraction changes to electro- magnetic repulsion. As the electrostatic action is inversely proportional to the squares of the distances, and the electro- magnetic action is inversely proportional to the distances, we can make either prevail by varying the distance. Third Lapertment.—In naphtha the attraction increases. Fourth Experiment.—Cutting out the rheostat and im- mersing the loops in distilled water the attraction becomes very powerful and is manifested at a distance of 4 or 5 cm. To get rid of the small liquid currents, and to be sure of the electric character of the attraction, the author put on an alternating current from a transformer and observed the attraction while he dissolved larger and larger quantities of some salt ; the current and the electrolysis went on gradually increasing, but the difference of potential between the loops decreased, and at the same time the attraction decreased down to zero. In this experiment the electrostatic tubes .are propagated in the water transversely to the conducting loop ; they are destroyed in the liquid itself by means of an inter- molecular discharge (by the aid of ions), and the lines of current are directed along the electrostatic tubes. As the tensions of these tubes are, before destruction, several times 138 New Reaction between Electrostatic Tubes and Insulators. greater than in air, a more powerful attraction is observed than in air. Fifth Experiment.—Two vertical strips of tinfoil, par allel to each other 4 or 5 mm. apart, are immersed in water, a plate of glass or of mica a little wider than the strips is interposed, and while the current is on, a repulsion of the strips is observed. The electrostatic tubes coincide with the lines of electrolytic current, and as the plate deviates the tubes uniting the interior and opposite faces, the resultant of the attractions becomes smaller than that of the repul- sions due to the tubes applied to the Fig. 8. exterior faces. To direct the Faraday tubes so as to give preponderance to those which pull the strips apart, it is SSG necessary to arrange as in fig. 8, that is, to fix to the diaphragm two perpen- dicular plates which do not allow the tubes (and lines of current) to scatter laterally ; the divergence of the leaves is thus inctenien several fold. Siath Experiment.—Two vertical strips of tinfoil are immersed in water (fig. 9). They are Fic ae tio, 9, parallel, and as near each other as is ? possible consistent with not being drawn + together by capillarity. The pair of strips constitutes one electrode, while the other is a vertical metallic wire, placed in the plane of the first electrode, and 3 em, distant from it. On the passage of the current, the strips move a little towards the wire, and at the same time diverge from each other just as if they were in air before an electrified conductor. The 4th, 5th, and 6th experiments show the existence of the electrostatic field inside an electrolyte. Seventh Experiment.—It the two linear conductors in Herz’s experiment are replaced by two flexible loops 15 or 20 cm. apart, they attract each other power fully. Here the tubes are in motion between the linear conductors along which they slide by their extremities, and this is the cause of the equality of velocity of propagation in the medium and in conductors. Physical Laboratory of the Academy of Sciences, St. Petersburg. . ) pries XU. Molecular Dynamics of a Crystal. By Lord Kevin *. § 1. | aS object of this communication is to partially realise the hope expressed at the end-of my paper of July 1 and July 15, 1889, on the “Molecular Constitution of Matter ¢ ’:— “The ene investigation must be deferred for a future communication, when ig hope to give it with some further Ts The italics are of present date. Following the ideas and weiaerplas suggested in $$ 14-20 of that paper (referred to henceforth for ‘prev ity as M.C.M.), let us first find the work required to separate all the atoms of a homogeneous assemblage of a great number n of molecules to infinite distances from one another. Each molecule may be a single atom, or it may be a group of 7 atoms (similar to one another or dissimilar, as the case may be) which makes the whole assemblage a group of 7 assemblages, each of n single atoms. § 2. Remove now one molecule from its place in the assemblage to an infinite distance, keeping unchanged the configuration of its constituent atoms, and keeping unmoved every atom remaining in the assemblage. Let W be the work required todo so. This is the same for all the molecules within the assemblage, except the negligible number of those (§ 30 below) which are within influential distance of the surface. Hence 3nW is the total work required to separate all the x molecules of the assemblage to infinite distances from one another. Add to this n times the work required to separate the z atoms of one of the molecules to infinite distances from one another, and we have the whole work required to separate all the in atoms of the given assemblage. Another procedure, sometimes more convenient, is as follows :—Remove any one atom from the assemblage, keeping all the others unmoved. Let w be the work required to do so, and let Sw denote the sum of the amounts of work required to do this for every atom separately of the whole assemblage. The total amount of work required to separate all the atoms to infinite distances from one another is $20. This (not subject to any limitation such as that stated for the former procedure) is rigorously true for any assemblage whatever of any number of atoms, small or large. It is, in fact, the well-known theorem of potential energy in the * a the Proceedings of the Royal Society of Edinburgh for 1901-2, communicated by the Author. + Dae Roy. Soe. Edin., and vol. iii. of Mathematical and Physical Papers, art. Xcvii. 140 Lord Kelvin on dynamics of a system of mutually attracting or repelling particles ; and from it we easily demonstrate the item 4nW in the former procedure. § 3. In the present communication we shall consider only atoms of identical quality, and only two kinds of assemblage. I. A homogeneous assemblage of N single atoms, in which the twelve nearest neighbours of each atom are equidistant from it. This, for brevity, I call an equilateral assemblage. It is fully described in M.C. M., §§ 46,50... 57. II. Two simple homogeneous assemblages of $N single atoms, placed together so that one atom of each assemblage is at the centre of a quartet of nearest neighbours of the others. | For assemblage I1., as well as for assemblage I., w is the same for all the atoms, except the negligible number of those within influential distance of the boundary. Neglecting these, we therefore have Zw=Nw, and therefore the whole work required to separate all the atoms to infinite distances is— tNw. oo. 4 ee § 4. Let ¢(D) be the work required to increase the distance between two atoms from D to » ; and let f(D) be the attraction between them at distance D. We have d : f(D) =—- 7p??? 0" 7 For either assemblage I. or assemblage II. we have w=o(D) + 6(D'!)+¢(D”)+ete. . . . (3)5 where D, D’, D’, etc., denote the distances from any one atom of all neighbours, including the farthest in the assem- blage, which exercise any force upon it. § 5. To find as many as we desire of these distances for assemblage I. look at figs. 1 and 2. Fig. 1 shows an atom A, and neighbours in one plane in circles of nearest, next-nearest, next-next-nearest, etc. Fig. 2 shows an equilateral triangle of three nearest neighbours, and concentric circles of neigh- bours in the same plane round it. The circles corresponding to r, and rz of § 7 below, are not drawn in fig. 2. In all that follows the side of each of the equilateral triangles is denoted by 2X. § 6. All the neighbours in assemblage I. are found by aid of the diagrams as follows :— (a) The atoms of the net shown in fig. 1. The plane of this net we shall call our “middle plane.” Let lines be Molecular Dynamics of a Crystal. 141 drawn perpendicular to it through the atom A, and the points marked 0b, ¢, to guide the placing of nets of atoms in parallel planes on its two sides. (6) Two nets of atoms at equal distances 4/2 on the two sides of the “middle plane.’ These nets are so placed that an atom of one of them, say the near one as we look at the diagram, is in the guide line }; and an atom of the far one is in the guide line «. Fig. 1. (c) Iwo parallel nets of atoms at equal distances, 2X v2, on the two sides of the “middle plane,” so placed that an atom of the near one is in the guide line ¢, and an atom of the far one is in the guide line D. (d) A third pair of parallel planes at equal distances, dW, trom the “middle plane,” and each of them having an atom in guide line A. > (2) Successive triplets of parallel nets with their atoms cyclically arranged Abc Abc .. at greater and greater distances from A on the near side of the paper, and Acb Ach . . at greater and greater distances on the far side. § 7. Let m%, 72, g; . . . be the radii of the circles shown in fig. 1, and 7, 72, 7; . . . be the radii of the circles shown in 142 Lord Kelvin on fig. 2; and for brevity denote X”/2 by «. The distances from A of all the neighbours around it are :— In our “ middle plane” : 6 each equal to q,; 6, g2; 6, 9s; Direngate O..Gest. = as In the two parallel nets at distances « from middle: 6 each equal to /(«?+747) ; 6, / («?+727); 12, Wl? +757) ; 12,V(P+r7); 6, / (+257); 12, V(eP +76") 6, He? +777). In the two parallel nets at distances 2« from middle: the same as (B) altered by taking 2« everywhere in place of «. Fig. 2. In the two parallel nets at distances 3« from centre: the same as (A) altered by taking /(9«7+ 9:7), V(9«?+ q.?), ete., in place of 91, qo, etc. | In nets at distances on each side greater than 3«: distances of atoms from A, found as above, according to the cycle of atomic configuration described in (e) of § 6. 4 § 8. By geometry we find | Q=A3 G= V8A=1°732A; g,=2A; g,= VTA=2°646A ; g;=3A: | (4) T= NZA=D77A 5 72 =2 NEA=11540; vg= VEA=L‘H270; 7,= V¥21BA=—2Z-0822; r,=4 VZA=2°308A ; rg= VIPA=DOSITA; 7-=—5 VEA=QDBV7DA. Molecular Dynamics of a Crystal. 143 § 9. Denoting now, for assemblage I., distances from atom A of its nearest neighbours, its next-nearests, its next-next- nearests, etc., by D,, D., Ds, etc., and their numbers by Sis J 925 etc., = find by §§ 7, 8 for distances up to 2d, for use in § 12 below, ~D,=2, °° D,=1-414a, D;=1-732a, D,=2n, A=12; p=; ja=18; jx=6. § 10. Look back now to $5, and proceed similarly in respect to assemblage II., to find ‘distances from any atom A to a limited number of its neighbours. Consider first only the neighbours forming with A a single equilateral assemblage: we have the same set of distances as we had in § 9. Consider next the neighbours which belong to the other equilateral assemblage. Of these, the four nearest (being the corners of a tetrahedron having A at its centre) are each at distance 34/2X, and these are “A’s nearest neighbours of all the double assemblage II. Three of these four are situated in a net whose plane is at the distance 4/2 on one side of our “middle plane” through A, and having one of its atoms on either of the guide lines b or c. The distances from A of all the atoms in this net are, according to fig. 2, Wate tire le Gee BPs )y ete: 4 5. (5): The remaining one of the four nearests is on a net at distance 2/22 from our “middle plane,” having one of its atoms on fies guide line through A. The distances from A of all the atoms in this net are, according to fig. 1, VBA, JG +9017), AK’ +927), etc. . . (6). All the other atoms of the equilateral assemblage to which A does not belong lie in nets at successive distances «, 2«, 3x, etc., beyond the two nets we have already considered on ‘the two. sides of our “ middle plane” ; the atoms of each net placed of course according to the cyclical law described in (e) of § 6. é 11. Working out for the double assemblage II. for A’s nearest neighbours according to § 10, we find four nearest neighbours at equal distances 3/2X='6132r; twelve next- nearests at equal distances X; and twelve next-next-nearests at equal distances / }ZA=1-° 173r. These suffice for § 12 below. It is easy and tedious, and not at present useful, to work out for D,, D;, Dg, ete. 144 Lord Kelvin on § 12. Using now §§ 9, 11 in (3) of § 4 we find,— for assemblage L., w=12(d) + 6p(1'414d) + 186(1°732A) + 6(2d) + . for assemblage IT. w= 4h(-6132) + 12$(d) + 126(1-173A) + These formulas prepare us for working out in detail the practical dynamics of each assemblage, guided by the following statements taken from §§ 18, 16 of M. C. M. § 13. Livery infinite homogeneous assemblage of Boscovich atoms is in equilibrium. So, therefore, is every finite homo- geneous assemblage, provided that extraneous forces be applied to all within influential distance of the frontier, equal (7). to the forces which a homogeneous continuation of the — assemblage through influential distance beyond the frontier would exert on them. The investigation of these extraneous forces for any given homogeneous assemblage of single atoms— or groups of atoms as explained above (§ 1)—constitutes the Boscovich equilibrium-theory of elastic solids. Fig. 3. It is wonderful how much towards explaining the crystallo- graphy and elasticity of solids, and the thermo-elastic properties of solids, liquids, and gases, we find; without assuming, in the Boscovichian law of force, more than one transition from attraction to repulsion. Suppose, for instance, that the mutual force between two atoms is zero for all distances exceeding a certain distance I, which we shall call the diameter of the sphere of influence ; is repulsive when the distance between them is <&; zero when the distance is =€; and attractive when the distance is >f and 47 "(a) (ue + Ursa) +f" (2a) [ (uy FUP + Cia +442) 7] +f" (3a) [ (u;_, HU, HU)? + (Un + Yige + U1)" + etc. etc. ete. etc.} (13) 5 where = denotes summation for all values of 7,-except those corresponding to the small numbers of atoms ($$ 28, 29 below) within influential distances of the two ends of the row. § 26. Hence the equilibrium is stable if f’ (a), 7” (2a), 7’ (3a), ete., are all positive ; but it can be stable with some of them negative. ‘hus, according to the Boscovich diagram, a condition ensuring stability is that the position of each atom be on an up-slope of the curve showing attractions at increasing distances. We see that each of the atoms in each of our three equilibriums for fig. 6 fulfils this condition. § 27. Fig. 7 shows a simple Boscovich curve drawn arbi- trarily to fulfil the condition of § 13 above, and with the further simplification for our present purpose, of limiting the sphere of influence so as not to extend beyond the next-nearest neighbours in a row of equidistant particles in equilibrium, with repulsions between nearests and attractions between next-nearests. The distance, a, between nearests is deter- mined by ah aoa 4 hoe 2 (14 being what (9) of § 24 becomes when there is no mutual force except between nearests and next-nearests. There is obviously one stable solution of this equation in which one atom is at the zero of the scale of abscissas (not shown in the diagram) and its nearest neighbour on the right is at A, the point of zero force with attraction for greater distances and repulsion for less distances. The only other configuration of stable equilibrium is found by solution of (14) according to the plan described in § 24, which gives a=°680. It is shown on fig. 7 by A,, A;,,, as consecutive atoms in the row. § 28. Consider now the equilibrium in the neighbourhood of either end of a rectilinear row of a very large number of atoms which, beyond influential distance from either end, are at equal consecutive distances a satisfying § 27 (14). We shall take for simplicity the case ot equilibrium in which there is no extraneous force applied to any of the atoms, and no mutual force between any two atoms except the positive or negative attraction 7(D). But suppose first that ties or struts 154 Lord Kelvin on are placed between consecutive atoms near each end of the row so as to keep all their consecutive distances exactly equal toa. For brevity we shall call them ties, though in ordinary language any one of them would be called a strut if its force is push instead of pull on the atoms to which it is applied. Calling A,, A,, A3,...the atoms at one end of the row, suppose the tie between A, and , 13, ... . 1%, give a first approximation to the devi- ations from equality of distance for complete equilibrium. Repeat the process of removing the ties in order and replacing each one by the altered lenoth as in the first set of approxi- mations, and we find a second set ay olds oh ba cS Ores similarly to a third, fourth, fifth, sixth .... approximation till we find no change by a repetition of the process. Thus, by a process essentially convergent if the equilibrium with which we started is stable, we find the deviations from equality of consecutive distances required for equilibrium when the system is left free in the neighbourhood of each end, and all through the row (except always the constraint to remain in a straight line). By this proceeding applied to the curve of fig. 7 and the case of equilibrium a=°680, the following successive approximations were found :— ) | | i OZ x, x; 2, | Ly } | | “Ist Approximation . |+ 018 —-009 +-004) --002 |-+-001 |— 001 000 2nd : . +026 —-014 +-007 |—-003 | +002 3rd y . +031 |—-018 +:009 | —-005 | +-003 | 4th . +034 —-020 +-011 | —-006 | Sth m . +:036 —-022 +-012 |—-007 | | 6th i 4-037 —-023 +:013 | | 7th 5 . |+°038 —-024 | | | &th a . | +°039 Thus our finai solution, with ~=*680, is “St “039; l=: —°024, Od +013, Oe — 007, 43 = +- "003, v= — 001, z-="000. § 29. It is exceedingly interesting to remark that the deviations of the successive distances from a are alter rnately positive and negative, and that they only become less than one-seventh per cent. of a for the distance between A, and Ag. Thus, if we agree to neglect anything less than one-seventh per cent. in the distance ‘between atom and atom, the influential distance from either end is 7a, although the mutual for ce between atom and atom is null at all distances exceeding 2°2a. § 30. If, instead of f(D) denoting the force between two atoms in a rectilinear row, it denotes the mutual force between two parallel plane nets in a Bravais homogeneous assemblage i Ou om Prof. J. Trowbridge on Spectra arising of single atoms, the work of §§ 27, 28 remains valid; and thus we arrive at the very important and interesting conclusion that when there is repulsion between nearest nets, attraction between next-nearests, and no force between next-next- nearests or any farther, the disturbance from homogeneous- ness in the neighbourhood of the bounding plane consists in alternate diminutions and augmentations of density becoming less and less as we travel inwards, but remaining sensible at distances from the boundary amounting to several times the distance from net to net. XII. On Spectra arising from the Dissociation of Water Vapour and the Presence of Dark Lines in Gaseous Spectra. By Joun TROWBRIDGE *. | (Plate III.] ia passing from the study of the light emitted by gases under the effect of electrical discharges to the investi- gation of the light produced by discharges of great quantity, one enters a new field of research. In previous papers on the spectra of hydrogen I have stated my convictions of the importance of the role played by water-vapour in glass — spectrum-tubes. The results of further study emphasize these convictions. With powerful discharges in hydrogen, oxygen, and rarefied air, even when these gases are dried with the utmost care, I always obtain the same spectrum, which | regard as that arising from the dissociation of water-vapour which is always present in glass tubes. The bright-line spectrum, moreover, at high temperatures is accompanied by a faint continuous spectrum on which are dark lines which indicate a selective reversibility in the silver salt. This re- versibility, it seems to me, is of great significance in the application of photography to astrophysics. It has long been recognized that spectrum analysis is an extremely delicate method of recognizing the presence of a gas or the vapour of a metal under the excitation of heat ; and when the improvements in photography enabled us to obtain permanent records of the spectra of gases, 1t was sup- posed that we had a means of escaping from the fallacies of eye-observations which arose from personal idiosyncracies. If the photographic plate were a perfect instrument for recording the infinite number of vibrations which light can communicate to atoms of matter, we should certainly feel that we had made a great advance in physical science. When * Communicated by the Author. from the Dissociation of Water Vapour. 157 we reflect, however, on the supposition that emulsions con- taining silver salts are capable of responding and giving a permanent record of all waves of light, even in the portion of the spectrum considered most actinic, when the waves exceed a certain intensity, we are conscious that we rely without proof upon an infinite range of photochemical action; and indeed I show in this paper the existence of a selective rever-. sibility produced on the photographic plate by powerful discharges producing light of great intensity. Realizing the importance of studying the behaviour of gases under different forms of excitation, I have collected in the rooms devoted to spectrum analysis in this laboratory e three forms of apparatus: an induction-coil actuated by a very efficient liquid break, giving a spark of 30 inches in air ; a step-up transformer, excited by an alternating current, pro- ducing with glass condensers of about *3 microfarad dis-- charges of an inch in length of great body; and a storage- battery of twenty thousand cells. A plant of this nature I conceive to be necessary in the present stage of spectrum analysis ; for molecular motions excited in rarefied gases vary greatly with the kind of electrical discharge. In the appli- eation of photography to spectrum analysis one is immediately confronted with the necessity of submitting the gas to a com- paratively long electrical stimulus in order to obtain a negative. Eyen with a concave grating of short focus several discharges. are necessary with a narrow slit. Hach discharge is capable of modifying the condition of the gas. This fact is well recognized by taking successive photographs upon the same plate with different strengths of current. A simple form of plate-holder enables this to be done. One obtains a striking example of the instability of a spectrum-tube filled, apparently, with dry hydrogen when one subjects it first to very powerful discharges from a glass condenser of *6 microfarad charged by a storage-battery of twenty thousand cells, with practically no self-induction in the circuit, and follows this excitation by an alternating current of much less quantity. The powerful discharge gives what I term the spectrum arising from the dissociation of water-vapour; and the alternating current gives the spectra of argon. This results, J suppose, from the oxidization of traces of air in the tube under the action of the dissociation of the water-vapour. The presence of hydrogen is concealed. On cooling, the tube again shows. the four-line spectrum of hydrogen. The period of the con-. denser-discharges which I have employed varied from one five-hundred thousandth of a second to one millionth. The practically instantaneous current, therefore, varied from five 158 Prof. J. Trowbridge on Spectra arising thousand amperes to ten thousand. The revolving-mirror method showed that the pilot spark was mainly effective, and that the subsidiary oscillations were feeble. The spectrum- tube speedily became milk-white from the sodium set free from the glass. Lord Rayleigh has shown how to demonstrate the presence of argon from very small quantities of air (Phil. Mag. [6] vol. i. p. 108, 1901). My method is substantially his, except that | employ very powerful discharges which set free a sufficient amount of sodium-vapour from the oelass : and the oxygen is supplied from the dissociation of water- vapour which is alwaysin evidence when powerful discharges are employed. ‘The production of argon under these cireum- stances I regard as a striking proof that I am dealing in this investigation with the spectra arising from the dissociation of water-vapour. From the same tube one can, by modifying the strength and character of the electrical discharges, obtain what is generally termed the four-line spectrum of hydrogen, the spectrum of sodium, the spectra of argon, and the spectrum arising from the dissociation of water-vapour. Doubtless one could recognize also the spectrum of helium; I am not yet sufficiently familiar with it. In the course of the study of the water-vapour spectrum one is naturally led to photograph the spectrum of the electric spark under water. It is possible to obtain powerful dis- charges of any suitable length under distilled water by inclosing the spark terminals in glass tubes, allowing only a small portion of the platinum terminals to project from the ends of the tubes. If the terminals are immersed more than one inch under the water, the resulting explosion is apt to break the glass containing-vessel. The light of these dis- charges under distilled water is white and extraordinarily briliant to the eye. When itis examined by the spectroscope one sees a continuous spectrum; and one obtains a continuous spectrum by photography even in the most actinic portion of the spectrum. On bringing the spark terminals to the surface of the water, one immediately obtains the four-line spectrum ot hydrogen or water-vapour. To whatis due the continuous spectrum under water? Does it result from the production of the dissociation-spectrum of water-vapour under great pressure? That there is great pressure is shown by the sudden explosion, which is sufficient to blow the small tamping of water out of both ends of the containing tube. If the water is covered with a thin film of oil, this oil is immediately disseminated through the water, making a milky white emulsion which remains for days. When we turn to powerful discharges through Pliicker or jrom the Dissociation of Water Vapour. 159 Geissler tubes filled with hydrogen which has been dried with care, we also obtain a faint continuous spectrum on which are bright lines and dark lines. Moreover, what are apparently the strongest bright lines of the dissociation- spectrum of water-vapour are not reversed. There is a selective reversibility which arises at high temperatures. This fact seems to me of great importance in the appli- cation of photography to the study of celestial phenomena, Reversal of spectrum-lines does not necessarily indicate re- versing layers of cooler gases, and in certain cases may arise from photochemical action of the silver salt. One imme- diately thinks in this connexion of the phenomenon of dark lightning or the Clayden effect, and of the interesting expe- riments of Professor Nipher *. Spectrum analysis, however, reveals a selective reversibility which must be carefully studied before we can properly interpret the records of photography. There are doubtless many states of vibration, even in the actinic portion of the spectrum, which are not recorded by the silver salt : for this selective reversibility may obliterate or prevent a permanent record. I have obtained this reversing action with different emulsions on glass and also on celluloid films. The strongest reversals are approxi- mately at wave-lengths 4227, 3930, 3965. ‘There is alsoa faint reversal at wave- length 3953. Reversals are often seen on the negative which disappear in the fixing-bath. In this investigation ten thousand cells were employed to charge a glass condenser of °6 microfarad. The charge was sent thr ough Geissler tubes with practically no self-induction in the discharge- -circuit. The bore of the capillary tubes was 1 mm., and the tubes were filled with apparently dry hy drogen at a pressure of approximately ‘1 mm. The tubes were also filled with oxygen and also with rarefied air at the same pressure. I have reached a limit in subjecting glass tubes to powerful discharges, and am now turning my attention to obtaining quar tz tubes in the hope of securing a more resisting mater ‘al. In a previous papert I expressed my conviction that the four-line spectrum observed in the protuberances of the sun is an evidence of the presence of water-vapour in the sun’s atmosphere, and an evidence, therefore, of the presence of oxygen. In the spectrum (Plate ATE fig. 7, B) one sees on the negative two reversed lines which coincide with the great H, H lines of the solar spectrum. These are seen bright in * “On Certain Properties of Light-Struck Plates,” Trans. Academy of St. Lonis, Mo. U.S. vol. x. No. 6. Tt Phil. Mag. [5] vol. 1. p. 338 (1900). 160 Prof. J. Trowbridge on Spectra arising B, fig. 4. One also sees a strong reversed line at approxi- mately wave-length 4227; and there is a reversed band coinciding with the solar region of reversed lines between wave-lengths 4315-4285. These regions in the sun are doubt- less composite photographs of reversals of many elements. I believe that there is a basis of reversal due to the disso- ciation of water-vapour. _ The nomenclature of the stars in regard to their types of spectra may need revision. The higher temperature I get the more dark lines I obtain. An excess of dissociation of water-vapour may suffice to give at a comparatively low temperature the bright-line spectrum of hydrogen. At higher temperature the disso- ciation of this vapour in the presence of atmospheric air may give dark lines. The intense light due to the dissociation of water-vapour under the effect of powerful discharges is the nearest approach to sunlight which I have been able to produce. Its actinic effect is greater than that of magnesium, zine, or aluminium. It may be.that the variability of certain stars is due to a variability in the amount of water-vapour which is being dissociated; and one is led to conjecture whether the light of the sun’s atmosphere may not be due to an electrical dissociation. ‘The selective reversibility of the silver salts seems to me, therefore, of great interest in the subject of astrophysics; for we can have reversible effects on the photographic plates which are not due to the reversing effect of colder layers of gases. In other words, we have actions recorded which are on the plates and not in the heavens. The intense light due to the dissociation of water- vapour may entirely mask the fainter light of the metallic lines in stars which show only gaseous spectra, especially when we consider the varying distances of the stars. I have employed electrodes of platinum, copper, silver, aluminium, iron, and found no trace of the lines of their vapour in the spectrum of the dissociation of water-vapour. Even when caustic soda is present in the tubes, although it fills the tube with a brilliant yellow light with comparatively low discharges, no trace is seen of it when the tube is excited with powerful discharges. Then we have the brilliant white light of the water-vapour spectrum. | The silver salt, therefore, does not respond to all rates of vibration ; or if it does respond, the molecular action is unstable and there is no resultant reaction which is evidenced by a photographic image. There may be spectra at very high instantaneous temperatures which we cannot photograph. It oe From the Dissociation of Water Vapour. 161 seems reasonable to suppose that the silver molecule is limited in its rate of vibrations, and that the photographic plate as well as the human eye is a limited instrument of research. On Plate LIL, A represents the normal solar spectrum in the neighbourhood of the great H, H lines. B represents the gaseous spectra. The photographs were taken witha Rowland concave grating, and are not enlarged or touched in any way. Unfortunately the reproductions ‘do not give many of the reversals, and some of the bright lines do not appear. This is especially the case in fig. 5. Figs. 1 and 2, B, are spectra of oxygen and traces of rarefied air taken with comparatively low current and voltage at a pressure of 1 millimetre. Fig. 3 is a spectrum of hydrogen under the same conditions. Fig. 4is the spectrum arising from the dissociation of water-vapour with very powerful discharges. Fig. 5 shows a line of selective reversibility at wave-length 4227. On the negative the two brilliant lines (fig. 4) which closely coincide with the great H, H lines of the solar spectrum are seen to be revers ed, and therefore appear as dark lines. This reversal is shown in fig. 7. The gaseous spectrum B of fig. 7 closely resembles in general features the solar spectrum photographed with a wide a slit in order to give the general distribution of darkness and light. My conclusions are as follows :— _ Dissociation of water-vapour takes place in the atmosphere of the sun. Oxygen, therefore, must be present. From a careful study of my negatives I regard the evidence for the presence of this vapour as conclusive as that generally accepted for the presence of sodium in the sun. The dissociation of water-vapour by powerful electric dis- charges in the presence of small amounts of atmospheric air results in the production of argon even in tubes presumably filled with hydrogen. Dark lines occur in the spectra of gases which increase with the intensity of the light, and are photochemical in their origin. The great brilliancy of the dissociation spectrum of water- vapour, which obscures the presence of metallic spectra, and the presence of dark lines due to photochemical reversals, makes one cautious in accepting photographic evidence in regard to the states of development of stars. Piil. Mag. 8. 6. Vol. 4. No. 19. July 1902. M XIV. A Problemin Conduction of Heat. By H.S8. CaRsLaw, AMLA,, D.Sc. (Lecturer in Mathematics in the University of Glasgow) *. ao problem of the Linear Flow of Heat in a solid . extending to infinity on one side of an infinite plane, while radiation takes place across that plane into a medium at zero temperature, was discussed by Riemann (Partielle Differential-Gleichungen, § 69). His solution depends upon that for the more general problem of the sphere, and is obtained by making the radius of the sphere increase in- definitely. Another solution was given by Bryan + by the synthetical method, and in Weber’s new edition of Riemann’s book { a third discussion of this problem is to be found. In the following pages another discussion of this problem is given, in which use is made of Cauchy’s Theorem in Contour Integration. The equations which the temperature has to satisfy are as follows :— £>0, . 2 V—=/ (2 tos. a iba E Opes ~ . . . (3) | ‘We begin with the solution for a source in an infinite solid, 1 _. @=2z) Pie alerden a. (+) This may be expressed by the integral, | ra) on eakert eut-2')] a, —® Figs, to} O The path P in a-plane. We transform this into the integral over the path (P) of * Communicated by Prof. A. Gray, F.R.S. + “On an Application of the Method of Images to the Conduction of Heat,” Proc. Lond. Math. Soc. vol. xxii. t Weber-Riemann,: Partielle Differential-Gleichungen, Bd. ii. § 38. oie A Problem in Conduction of Heat. 163 fig. 1, and we take the expressions “a ea kart eia(x—2z’) da, 27 and a e— kart e7ia(z—2') da, 27 according as @ am. The path (P) must have the argument of @ at infinity on the right hand between 0 and =. and on the left between T E : ri and 7, so that e-*** may vanish there: and for the same reason we have chosen the different expressions for the : = integral as # 7 a’, Associate with this solution 1 F Ae ee da. 2er over the same path (P). a The quantity A is determined by the surface condition (8), and is given by ‘ We have thus obtained a solution of (1) and (3) in the form of the sum of two complex integrals, and we proceed to show that this solution corresponds to a source at (.x’) in our solid. Our solution is given by the equation 0a hf (etter da [emrenernt taal, (6 2a i U——-1a@ the integrals being taken over the path (P), and the first integral being altered when «>.2’, as explained above. This may be written £ y ! hh a 2 eia(z+2') ar e—kart g—ta(z—z') Ja 4 i e—ket pia(z+2') J — da ohare i ATM 2a T a+ tle Fig. 2. ‘a Y 4 eeees Vinge ‘ / Mt \ : i es The a-plane. Since there is no pole of any of these integrals within the closed circuit of fig. 2, and the parts contributed by the M 2 da. (7) 164 Dr. H.S. Carslaw : A Problem circular arcs vanish in the limit, these complex integrals. may be replaced by integrals along the real axis of a. The first two become | Lite i S e—kart p—ia(r—2') Joy + ep { e—hart pia(z+z’') da, 60) = whether z is greater or less than 2’. These may be replaced by 1 te a | ee Akt 4kt |. 2 / okt E aaPte We have therefore only to show that the third integral of (7). vanishes in the limit when ¢ diminishes indefinitely. This is best done by considering the complex integral eta(r+2') — kat d. é = a | atih over the path (P).. This integral converges to its value for t=0, ast converges. to zero. When we take the value for t=0, namely eia(ztz’) BAe EO i +ih : and consider the integral taken over the closed circuit of fig. 3, since the integrand vanishes at infinity in the upper "cy: Fig. v- Nea RE Si - —_ - ies SSC ~ oor es 7 N ” x 6 4 XN A XN 00) Sa +0 The a-plane. part of the a-plane, and there are no poles inside the circuit, we see that fa mee ( atith over the path (P) is zero. in Conduction ef Heat. 165 Our solution in (7) therefore satisfies the initial condition tor the source at the point z’, and the surface conditions were fulfilled by the choice of A in (5). We now replace the third integral of (7) by the equivalent integral over the real axis in the a-plane, and obtain our solution for the source in the form hl: .. G2 _ (eta? ———_-— | @ Akt +e Akt | 2 vV wilt [ a |, a +h : Since \ ‘ e-"€ cos aEdé == ee ; a” + h, and { e—" sin x€dE = — rs j a? +h” e this may be changed to its final form, | _@-2)? _ (@t2')? _ @t2'+8? eS | Ss) ee e dkt HOP ( eat 4kt | 9 which agrees with that given by Bryan. The solution for the initial distribution v=/ (2) follows in the usual way by integration, and is given by the equation 1 ie ( se (REP — @t2')? SS 1 Akt Akt | — = a'\\e e dx n(x _ (242482 — 21) \ Gee aN Be f (waka! |. (10) 0 Jo The result for the case of constant initial temperature is of interest, as Riemann’s original problem was to obtain the distribution in this case after a considerable time had elapsed. Put f(v)=v) and integrate: the second integral of (10) simplifies after integration by parts and we obtain 1 pee ce seed cz) g : ey =o 5 andy [ CS ee eM da EO ere ie da’ | ; 2 /mkt LJo te the form in which Weber gives the solution of this problem. Riemann’s result may be at once deduced. Toe 8 XV. Contributions to the Theory of the Resolving Power of Oljectives. By Professor J. D. Everett, /.RS* : high class objectives, both of telescopes and microscopes, the practical limit to the power of separating close points (called resolving power or separating power) depends upon the blurring due to diffraction. Owing to diffraction, the image formed of a bright point is not a point, but a spot, brightest in the central part, and falling off without any discontinuity from the centre to the margin. In favourable circumstances this spot is surrounded by a succession of bright rings. The phenomenon is seen ia “its greatest perfection when small aperture is combined with good definition. Blocking out the central portion of the objective makes the spot smaller and the surrounding rings relatively brighter. Dawes (Mem. R. Ast. Soc. xxxv. p- 158) made very elaborate observations on double stars for the purpose of investigating the separating power of telescopes ; and arrived at the conclusion that the angular distance between the two components, when they are nearly equal in magnitude, and are just separated, is given by the formula 4-56 seconds, divided by diameter of objective in inches. The first calculation of the relative brightness at different points of the spot and rings, which constitute the diffraction image of a point formed by a lens symmetrical round an axis, was published by Airy in 1836 (Camb. Trans. vy. p. 283), in a very clear and readable paper. His basis of procedure is the very direct and intelligible one of considering the concave wave-front which advances from the objective to the focus, and computing, for its initial position, the “ disturbance” which it produces (according to Huygens’ principle) at any given small distance measured laterally from the geometrical focus. Another principle of calculation, less “obviously correct but leading to precisely the same result, is employed in Mascart’s Optique and in Preston’s Light. Both methods of procedure lead to one and the same infinite series for the “ disturbance” at given lateral distance from the geometrical focus; and this series is a Bessel’s function of the first order. It is in fact man? m denoting 27 R Ry distance, and 2» wave-length. The calculation assumes identity of disturbance both in degree and in kind at all points of the wave-front. = Communicated by the Physical Society ; read Feb. 28, 1902. _ 6, where R is radius of aperture, 7 food lenge 6 lateral Theory of the Resolving Power of Objectives. 167 A simple calculation (given at p. 277 of my Deschanel, Part iv.) shows that the extreme difference of optical path, for disturbances coming from different points of a concave wave-front to a point = lateral distance 6 from the geo- metrical focus (the centre of the sphere to which the wave- front belongs), is 2b sina, « denoting the angular radius of the wave- fr ont as seen from the focus. When the extreme difference of path is X, we have therefore r IE hd oe eel Seg aS Ysine Comparison with observation shows that this value of } represents with fair accuracy the limit of separation. The angle subtended by the distance 6 at the second nodal point of the objective, which is identical with the angle subtended by the corresponding distance in the object, as seen from ihe first nodal point, is E 2fsina D? SS See 7 being the focal length, and D the diameter of the objective. "This - ears r/D tor the least distance between the com- ponents of a double star, agrees with Dawes’s value above quoted, if we put A=°000022 inch= °56 micron. The wave- length for the brightest rays is usually taken as ‘55 micron, which is as good an agreement as could be desired. Passirg now to the case of the microscope, and supposing the same fc»mula for the minimum distance é in the image to be still applicable, we may conveniently transform it by means of the equatio1. (which we shall discuss later) pry yy sit Oj pg Ys si Oy) 8) OPE (3) applicable to any optical system which gives sharp flat images. In this equation, y, Yo denote the distances of a point of the object, and the corresponding point of the image, from the axis of the system ; fy fy the indices of the firstaad last iiedia : §, 0, the angles made with the axis by any ‘incident ray and the corresponding emergent ray. The ratio (~, sin ,)/(m sin 9) is equal to the magnification y2[yi, and is therefore the same for all values of 9. This constancy is called by Abbe the sine condition. In the present case @2 is a, yy is b, wis 1; andif a, denote the obliquity of an extreme incident ray, the equation gives My, ¥, Sin @4,;=0 sing, sin a } sin a rN r are. Ae —iine is: a an os a ee Se 4 Ji fy SIN & fysina,"2sna 2u,sine, Zsina, , 168 Prof. J. D. Everett on the Theory of r, denoting the wave-length in the first medium which corresponds to > in air. This value for y;, the distance between points or lines which can be barely separated, has been extensively adopted. Helmholtz in the Jubelband of Pogg. Ann. 1874, p. 557 adopts it in the form last written. Abbe calis p, sina, the. numerical aperture of the objective, and adopts the formula wave-length divided by twice the numerical aperture. Drude (Lehrbuch der Optik) adopts it as the limiting distance for oblique illumination, and its double as the limiting distance for direct illumination. Microscopic test-objects are not self-luminous like double stars, but are viewed by transmitted light. If no condensing arrangement i is employed, the pencil of light sent by a point of the object to the objective consists of rays from different parts of the source, that is, in effect, from different sources. An orthogonal section of such a pencil does not possess the characteristic properties of a wave-front. Different portions of it have no definite relation of phase, and are incapable of mutual interference. Our formule are therefore no longer applicable. Practically we may regard such an orthogonal section as made up of a number of small parts, each of which is a wave-front, giving by reason of its smallness a very large diffraction image of a point of the object. These separate images of the same point overlap without inter- ference, and as they do not exactly coincide, compose a larger and more blurred image of the point represented. The cure for this evil is furnished by employing a con- denser of high quality, to throw upon the part of the object under examination a very sharp image of the source of illumination. If the image were perfectly sharp, each point of the object would get its light from its own special point of the source, and the effect would be to make the object act as if it were self-luminous. Lach point of the object would send to the objective a pencil whose orthogonal sections would be true wave-fronts, to which our previous reasoning would be applicable ; so that the diffraction spot which represents a point would have the small size due to the largeness of the entire aperture. This appears to me to be the chief benefit conferred by sharply focussing the source on the object ; but it has not so far as I am aware been pointed out by any writer on the microscope hitherto. Abbe in his great paper on microscopic perception (Archiv fiir mikr. Anat. ix. p. 413, 1873) regards the condenser merely from the point of view of geometrical optics, and recommends the use of one which is not achromatic. Microscopic observers long ago ascertained, as an empirical fact, that achromatic condensers gave better results than non- the Resolving Power of Objectives. 169 achromatic ; while mathematicians refused to believe them, and maintained that achromatism could be of no advantage, seeing that the sole purpose of a condenser was to give w ide pencils of strong light. There is another advantage from sharp focussing by the condenser, which may be regarded as the complement of that above indicated. If the focussing were perfectly sharp, the waves from one point of the object could not interfere with waves from another point. Such interference gives rise to spurious diffraction patterns, liable to be mistaken for structures existing in the object. The two components of a double star exhibit no mutual interference in a telescope ; and different points of a microscopic object cannot produce mutual inter- ference if they send light which has come from completely distinct sources. Lord Rayleigh (Phil. Mag. xli. 1896) was, I believe, the first to indicate this advantage. Abbe, in his paper on microscopic perception, makes no allusion either to the focussing of the source on the object, or to the finite size of the spot which (with its surrounding rings) is the diff- raction image of a single isolated point. The following explanation of the advantage of oblique illumination is, TL believ e, new. Perfect sharpness of focussing by a condenser is un- attainable ; and two points of the object which are not further apart than twice the limiting distance of separability will inevitably have a portion of the source in common, as regards their illumination. Let @ denote the obliquity of the illumination, the two object-points in question being supposed to be in a plane which contains the illuminating rays and the axis of the objective. The difference of optical path for rays coming from the same point of the source to the two object- points is ssinB, s denoting the distance between the two points. The best condition for separation is, that this dif- ference of path shall be half a wave-length in the medium in which the object is immersed (say 432,), for this gives the most complete extinction in the overlapping portion of the two diffraction spots which are the images of the two points. Putting then BiSUEe = alg) i eg t ics 1a hey 2 ae iga 9 (DB) and assigning to s the value ),/sin a, which being doubie of the accepted minimum value may be taken as representing an ordinary test, we deduce BUR fo OM ite a ats) ey? COD If we put s equal to the accepted minimum itself, we obtain ciate el Pe 2A a a a aaa These conclusions agree with the received view among 170 Theory of the Resolving Power of Objectives. microscopists, that the obliquity of illumination should be rather less than the obliquity of the extreme rays of the. incident pencil. Note on Hockin’s proof of the Sine Condition. Various proofs have been given of the sine condition expressed by equation (3), which must be fulfilled in every ease in which a sharp image, in a plane perpendicular to the axis of the instrument, is formed of a small flat object whose plane is perpendicular to the axis. By far the simplest is that given in an article “On the Estimation of Aperture in the Microscope,” published after the author’s death in the Journal of the Royal Microscopical Society (1881, ser. 2, iv. p. 3387), where he is described as the late Mr. Charles Hockin, junr., an electrician and mathematician of repute. Appreciative notes by Abbe are inserted in the article. Strange to say, the proof does not seem to have been reproduced in any English publication, though it is to be found, modified for the worse, in German optical treatises. In Miiller-Pouillet it is erroneously described, and the author’s name is givenas John Hockin. These circumstances, in conjunction with the great importance of the theorem itself, are my reasons for reproducing it. I have corrected a clerical error of — for + in the two principal equations. Let PP’ in the figure represent the axis of an optical system which gives the linear image P’Q' of the small object- line PQ, both the lines PQ and P’Q! being perpendicular to the axis. The incident pencils may be of large angle ; and the image is supposed to be aplanatic, that is to say, all rays sent by P pass through P’, and all rays sent from Q pass through Q'. Let PS be any one of the rays sent from P, and QS a ray from Q intersecting it at 8S. Since PQ is small, the angle PSQ is small, and the plane pencil bounded by PS, QS will give an emergent pencil bounded by P’S’, Q'S’, the optical path from 8 to 8’ having the same value for all the rays of the pencil ; denote this value by (SN’). Then, if » be the index of the first and pw’ that of the last medium, the optical path from P to P’ is 2. PSE Rey ee, Notices respecting New Books. 17k and is constant for all rays that go from P to P’. Similarly the optical path from Q to Q' is 2». QS+(88)—p'. Q'S, and is constant. Subtracting, and denoting the difference of the two constants by ¢, we aye p(PS—QS)—p'(P'S'— Q'S) = or (calling the obliquities @, 6’), ».PQsin §—p'P’Q’ sin &’ =c. But § and @ vanish together, therefore ¢ is zero: and we have pnb Ocm 0 = or PAY st 0 si ok set a The ratio of wsin @ to pw’ sin 6’ has therefore the constant value P’Q’/PQ for all the rays by which the image is formed. The present paper has been framed with a view to sup- plementing two papers by Lord Rayleigh, one of them (in two parts) in the Phil. Mag. for the second half of 187 1) and the other (which has been alr eady quoted) in Phil. Mag. vol. xlii. 1896. They contain a much fuller treatment of the theory of resolution than I have met with elsewhere. 11 poe Road, Ealing, W. XVI. ee e ae oe. gee Histoire de VObservatoire de Paris de sa fondation a 1793. Par C. Wotr, Membre de UInstitut, Astronome Honoraire de PObservatoire. Paris: Gauthier-Villars, Imprimeur-Libraire. fg is the first part of a work in which it is proposed to give a history, not of the astronomical observations and results which have been accomplished at the famous Observatory of Paris, which was founded about eight years earlier than that at Greenwich, but of its buildings, instruments, and the personnel composing its staff, with the successive modifications and additions in these. It is well known that the Paris Observatory, for more than the first century and a quarter of its existence, was directed by four generations of the family of Cassini, the first of whom was invited from Italy by Colbert, and eventually appointed to take charge of the new establishment. The fourth, also J. D. Cassini, was in charge at the time when the great Revolution transformed not only the rule of the Observatory, but that of all France. Before leaving his post, Cassini formed the project of writing a complete history of the establishment, and requested of the Director of the royal buildings that a search should be made in the public archives for the documents relating to the foundation of the Observatory and its carly annals. Though the answer gave him very little encourage- ment in his scheme, he took the trouble to gather together all the accessible papers which were left by his ancestors, particularly his great-grandfather : these he presented in 1811 to the Bureau des Longitudes, and they form one of the principal sources of information s IES Notices respecting New Books. made use of in the work before us. As its title shows, it carries © the history down to the year 1793: the subsequent period will form the subject of a second volume. The foundation of the Observatory resulted directly and im- mediately from the creation of the Academy of Sciences in 1666. This was at first called the New Academy, and was installed in the buildings of a house in the Rue Vivien belonging to one of Colbert’s sons. In the garden of this house, those members of the Academy who were astronomers—Picard, Auzout, and others— made observations of the stars. But long before this the idea of a regular observatory had heen started. Morin in 1634 had pro- posed that one should be erected on Mont Valérien; and in 1665, Auzout, in dedicating to the King his ephemerides of the comet of 1664, strongly urged the desirability of establishing a building for the express purpose of astronomical observations. It was in 1667 that the observatory was commenced, the architect being Perrault ; only the first story was completed when Cassini arrived in Paris in 1669. Although, as M. Wolf points out, it was impossible at that time to foresee what the progress of astronomy would shortly require in regard to methods of observation, Cassini did himself contend for considerable modifications in the original plan. M. Wolf takes a view of his appointment and work very different from that with which we are familiar in the pages of Delambre, and much more favourable to him. A native of the county ot Nice when it was included in the dominions of Savoy, his first appointment was at Bologna; when Colbert invited him (and many other learned men) to Paris he came intending to make, like Huygens, only a temporary stay, but ultimately was induced to remain, and, though he never spoke the French language with fluency, became naturalized and married a French lady. When he died in 1712 (three years before Louis XIV., in whose name he had been invited to France) he was in the eighty-eighth year of his age, but had been for some time totally blind. His eldest son was killed at the battle of La Hogue in 1692; it was the second, Jacques, who succeeded his father at the Observatory, and during a visit to England become acquainted with Newton and Flamsteed. (Halley, it will be remembered, had visited Paris in 1680 and observed there, in company with the elder Cassini, the great comet of that year, in regard to which Newton first applied his principle of universal gravitation to comets.) The third Cassini (César Francois) took the title of de Thury from an estate acquired by his father ; and his son the fourth (named like his great ancestor J. D. Cassini) 1s commonly called the Count de Thury. We have already mentioned his intention to write a history of the Observatory, and the trouble that he took to collect the documents which haye so greatly aided our present author in the first part of his noble work, very interesting to all astronomers. . Cassini IV. formed schemes for greatly improving the buildings and instruments of the Observatory ; but the great; Revolution in France upset scientific as well as all other arrangements, and led to his resignation in 1793, though he did not die till 1845, in the ninety-eighth year of Notices respecting New Books. 173 his age. With his retirement M. Wolf’s first volume ends: we shall look forward with interest to the appearance of the second, and its proposed account of the suvsequent developments of the Paris Observatory, particularly under Le Verrier, whose directorship (during which the writer of this notice paid his only visit to the establishment) was interrupted and resumed atter the death of Delaunay. Two directors, Arago and Mouchez, were natives of Spain. The present eminent head of the Paris Observatory M. Loewy, is a Viennese, and was invited to Paris by Le Verrier; he is also editor of the Connaissance des Temps. Astonishment has sometimes been expressed that Picard, its founder, was not, instead of Cassini, appointed the first director of the Paris Observatory, but M. Wolf gives reasons why the former preferred the arrangement actually made. The work is illustrated, and has for a frontispiece a representation of a visit by Louis XIV. to the Observatory. W. T. Lynn. An Elementary Treatise on Alternating Currents. By W. G. Ruopves, W.Sc. Pp. xii+212. London: Longmans, Green & Co. 1902. Tue literature of alternating currents is growing apace, and the next few years will probably witness a considerable number of additions to the text-books on this highly important subject. Since the recognition of the fact that alternating currents offer the only satisfactory solution of the problem of power transmission over very long distances, engineers have taken a keen interest in this branch of applied science, and the demand for suitable text-books appears to have been considerable. The book before us is evidently intended for readers possessing a fair knowledge of elementary mathematics, including the elements. ot differentiation and integration, and should prove especially useful to students in technical colleges. We fully share the author's view that the elements of vector algebra should form part of the curriculum of every technical school. In the first eight chapters, which contain a brief account of alternating-current theory, the author is at his best. The numerical examples given at the end of each chapter should prove of great, assistance to the student. Chapter IX. calls for some criticism. In dealing with a Fourier series, most modern writers agree in calling the “ fundamental” the jist harmonic term, its “ octave ” the second harmonic, and so on (this, for instance, is the method adopted by J. J. Thomson and Poynting in their text-book on Sound). ‘The author begins by adopting the old and now generally abandoned method of regarding the first term as the fundamental, and calling the remaining terms the Ist, 2nd, &c. harmonics. Immediately afterwards, however, he states (p. 67) that “ even harmonics are generally absent from the curves representing alternating currents ”—when it is clear that he means odd har- monics, if his own nomenclature be adopted. This point is likely 1o occasion considerable confusion in the mind of the student. The account of methods of testing transformers given in 174 Geological Society :— Chapter XII. deserves severe criticism. It seems a pity that the author did not make a more exhaustive study of this subject before proceeding to write on it. Many standard methods which have given excellent results are omitted, while Mr. Mordey’s “ thermo- meter” method is duly mentioned. The section on polyphase induction motors appears capable of considerable improvements. The Heyland diagram for the in- duction motor, which is so freely used by almost every continental writer on the subject, is not even mentioned, and in place of it we have purely analytical investigations which are not likely to appeal to the reader. Altogether, the second half of the book is much less satisfactory than the first, and we hope that in a future edition the blemishes which we have pointed out will be removed. There is ample room for a book of this kind, and we believe that, in spite of its defects, it will prove extremely useful to a large circle of readers. XVII. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from vol. ili. p. 554.] January 8th,.1902.—J. J. H. Teall, Esq., M.A., V.P.R.S., President, in the Chair. HE following communications were read :-— 1. ‘ A System of Glacier-Lakes in the Cleveland Hills.” By Perey Fry Kendall, Esq., F.G.S., Lecturer in Geology at the York- shire College, Leeds. After referring to existing ‘extra-morainic’ lakes, such as the Mirjelen See and those of the Chaix Hills, the author proceeds to deal with the criteria for the recognition of such lakes. These include beaches, deltas, floor-deposits, and overflow-channels. Shore- scarps are common in Cleveland, but beaches are rare or absent, the reason being in part that stability was rarely secured owing to the overflows being over soft Jurassic strata. Deltas also are not common. The floor-deposit of lakes may be distinguished from river-alluvia by the fact that the lamination is close and regular, but, being parallel to the subjacent surface, it may be highly inclined. On the other hand, alluvia are laid down on horizontal surfaces, but rarely show good lamination. Overflow-channels are grouped into four main types: ‘ direct overflows,’ which trench the main watershed of a country; ‘ severed spurs,’ across the spurs of the main watershed ; ‘ marginal overflows,’ at first merely a shelf cut in the hillside, but subsequently developed into an actual gorge ; and ‘in-and-out channels,’ or crescentic valleys excavated in the face of a hill by water flowing round a lobe of ice. Such overflows are independent of the natural drainage; they have at first a slight and then a steep fall, and in section they have steep sides and flat floors. ‘The meanders of the valleys and the run of the contouring also possess special features, and the valleys rarely or never receive any considerable tributaries. On Glacier Lakes in the Cleveland Hills. 175 Evidence from borings and Drift-filled channels is given to show that during or before the Glacial Period the land was considerably above its present level. The Glacial deposits are described in detail from sections and borings, some of them carried out by the author, and the assemblages of boulders are identified and classified into three chief groups—a Western group, from the Solway, Vale of Eden, Stainmoor Pass, and the Tees; a Northern group, from the l'weed and Cheviots and from Eastern Durham; and an Eastern group, from the Christiania region, the Gulf of Bothnia, and Denmark or the North Sea. The author has been unable to detect any signs of the presence of the sea in this area at any time during the Glacial Period. Three main ice-masses appear to have been concerned in producing the deposits: one from the Southern Uplands and the Solway, joined by the local ice of the Tees; a second originating in the Tweed Valley, and driven southward round the Cheviots by the pressure of the third, or Scandinavian, ice-mass. The general order of events is supposed to have been:—(1) the unobstructed passage of the Teesdale glacier to the coast, (2) the arrival of the Scandinavian ice, and (3) the invasion of the Scottish ice. The first of the extra-morainic lakes described is that of the Vale of Pickering, the lowest of the sequence, which for a long period received all the drainage of the district except that of the western margin, and the outflow from which into Lake Humber was that now occupied by the River Derwent. Newton Dale was the outflow of the lake-series of the Eskdale country. The Eskdale system comprises a series of lakes connected by an ‘aligned sequence’ of overflows ; and here it is possible to trace the consequences of the shrinkage of the ice-masses and to follow out the low-level phases of the lake. The ice pressing upon the northern face of the Cleve- Jand Hills gave rise to a series of lakelets, connected with which are the following set of overflows :—Scugdale and Scarth Nick, Bilsdale, Kildale, Ewe Crag Beck, Tranmire, and Egton Moor. Jburndale contained a lakelet overflowing eastward. Behind a narrow coast- strip of country, extending from Robin Hood’s Ray to Hunmanby, there runs a gorge which receives all the drainage of the ‘ hinter- land’ and carries it into the Vale of Pickering. In the production of this arrangement the effects of an ice-sheet shutting the seaward ends of the valleys is traceable ; the position of the main overflows was stable, and the drainage was permanently deflected. In dealing with the sequence of the ice-movements, evidence is brought forward to prove that the Teesdale ice was the first on the ground in question, but none of the lake-phenomena have been correlated with this first phase. The second phase was the complete diversion of this ice into the Vale of York, brought about by the growth of the Scandinavian ice-sheet. The third is the invasion of Seottish-Northumbrian ice, which may have passed out to sea and been driven inland again, carrying flints and smashed sea-shells with it, and may have extended as far as Lincolnshire on the south and Whorlton on the west. i 176 Geological Society. 2. ‘The Glaciation of Teesdale, Weardale, and the Tyne Valley, and their Tributary Valleys.’ By Arthur Richard Dwerryhouse, Esq., B.Sc., E.G.S. After an account of the topographical solid geology of Teesdale, the author describes the four distinct types of Drift in the area:as follows :— (a) A sandy reddish-brown clay, with a large number of well-scratched stones ; (0) A black loamy or peaty clay ; (c) A coarse gravelly deposit, with many waterworn and a few scratched stones; (2) A stiff blue Boulder-Clay. The first class is the most widely distributed ; it occurs in elon- gated ridges, and is the direct product of ice-action on the rocks of the upper part of the Dale. The black loamy clay is characteristic of areas occupied by ice-dammed lakes. The third class occurs in long esker-like ridges, and is particularly plentiful in the country formerly occupied by the Stainmoor glacier. The dark-blue clay is mainly derived from Carboniferous rocks, A detailed description of the Glacial deposits, boulders, and striz is next given; and from this the following conclusions are deduced :—Upper Teesdale was heavily glaciated by local ice from the eastern slope of the Cross Fell Range; this part of the Dale was not invaded by any other ice, and the higher peaks stood out as nunataks. At the period of maximum glaciation a number of lakes were formed, owing to the obstruction of the drainage of lateral tributary-valleys by the ice of the main glaciers. Lunedale was occupied by ice (the Stainmoor glacier) which came from the drainage-basin of the Irish Sea, joined the Teesdale glacier about Middleton-in-Teesdale, and by its thrust deflected the Teesdale ice into the Valley of the Wear. During the retreat of the ice there was a lengthened period of ‘constant level,’ when well-marked drainage-channels were formed. and after this the ice was removed with great rapidity. A tongue of ice flowed from Upper Teesdale by Yad Moss to the Valley of the South Tyne. Similar evidence with regard to Weardale and the Tyne Valley is given, and the following conclusions are drawn among others :—Ice from ‘leesdale and the tributaries of the South Tyne occupied the valley of the latter nearly as far as Lambley, where it was joined by a large glacier which crossed the northern end of the Pennine Chain. This glacier was continuous in a northerly direction with the ice of the Southern Uplands and the glacier of the North Tyne, and, when at its maximum, deflected the last north-eastward, causing a movement in that direction along the southern flanks of the Cheviot Range. But at the beginning and end of the glaciation the ice in the V alley of the North Tyne flowed south-eastward. The southern margin of the South Tyne glacier passed across the heads of Allendale and Devil’s Water into the Wear Valley ; and along this margin were a series of ice-dammed lakes with a corresponding series of overflow-channels, many of which are now streamless. Weardale was mainly occupied by its own ice, but the lower part of the valley was invaded by the Tyne ice from the north and that of the Tees from the south. There were no lakes strictly connected with the last system. me 100 Phil.Mag.S.6.Vol.4. 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Fy 4 4 pi) Skea oS en ae ee < * “ ee eet a Bie Rect FO) el ag. ater ME, om Mi, = im Kr 9 PS, re '# i " © t go-oR Cl ai rey di Nes ty oe t De SER es “gM hs ‘ r F | C aid Pe Ps : : pe? ‘ et saee 2 pet i oe 2h be , 5 vee ; ee fen ae Beramte oe a ee ta was ee ae Sea a gee ee, ee AS ey de pein J ! o “| 7 ar Nght atts rei is seine cal ida 4 ' edema seralie PEE) RE SASS RT OS ee ee ele me 1 ‘ -: : ha \ ; A. Las, 0 ER nly ca ee oe i] ‘ , ’ ‘ ee ‘ ; ey E } s ie At / = ay Ou ‘ ; % 7 ‘ 5 at ' © iy ah a 4 a 2 ee INDE YET), THE LONDON, EDINBURGH, anp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE= f if [SIXTH SERIES.] | AUGUST 1902. XVIII. On the Weights of Atoms *. By Lord Ketviy, G.C.V.0.T § 23. Pe in all our views we have seen nothing of absolute dimensions in molecular structure, and have been satisfied to consider the distance between neighbouring molecules in gases, or liquids, or crystals, or non-crystalline solids to be very small in comparison with the shortest wave-length of light with which we have been concerned. Even in respect to dispersion, that is to say, difference of propagational velocity for different wave-lengths, it has not been necessary for us to accept Cauchy’s doctrine that the spheres of molecular action are comparable with the wave-length. We have seen that dispersion can be, and probably in fact is, truly explained by the periods of our waves of light being not infinitely great in comparison with some of the periods of molecular vibration ; and, with this _ view, the dimensions of molecular structure might, so far as dispersion is concerned, be as small as we please to imagine them, in comparison with wave-lengths of light. Never- theless it is exceedingly interesting and important for in- telligent study of molecular structures and the dynamics of light, to have some well-founded understanding in respect to probable distances between centres of neighbouring molecules in all kinds of ponderable matter, while for the present at all * This is Lecture XVII. of my Baltimore Lectures, as now extended and prepared for press. For convenience of reference the sectional numbers have been retained as in the volume of Lectures. + Communicated by the Author. Phil. Mag. 8. 6. Vol. 4. No. 20. Aug. 1902. N 1 EE ee ee ee ee ee ee . oe 178 Lord Kelvin on events we regard ether as utterly continuous and structureless. It may be found in some future time that ether too has a molecular structure, perhaps much finer than any structure of ponderable matter ; but at present we neither see nor imagine any reason for believing ether to be other than continuous and homogeneous through infinitely small con- tiguous portions of space void of other matter than ether. § 24. The first suggestion, so far as we now know, for estimating the dimensions of molecular structure in ordinary matter was given in 1805 by Thomas Young™*, as derived from his own and Laplace’s substantially identical theories of capillary attraction. In this purely dynamical theory he found that the range of the attractive force of cohesion is equal to 387/K; where YZ denotes the now well-known Young’s tension of the free surface of a liquid, and AK denotes a multiple integral which appears in Laplace’s formulas and is commonly now referred to as Laplace’s K, as to the meaning of which there has been much controversy in the columns of ‘ Nature’ and elsewhere, Lord Rayleigh in his article of 1890, “ On the Theory of Surface Forces f,” gives the following very interesting statement in respect to Young’s estimate of molecular dimensions :— § 25. “One of the most remarkable features of Young’s ‘treatise is his estimate of the range a of the attractive force ‘‘on the basis of the relation T=lak. Never once have “T seen it alluded to ; and it is, I believe, generally supposed “that the first attempt of the kind is not more than twent ‘“vears old. Hstimating K at 23000 atmospheres, and 7’ at “3 grains per inch, Young finds that ‘the extent of the ‘** cohesive force must be limited to about the 250 millionth ““* of an inch [10-* em. |’? ; and he continues, ‘ nor is it very _“‘probable that any error in the suppositions adopted can ‘possibly have so far invalidated this result as to have made “ ‘it very many times greater or less than the truth’.... ‘Young continues :—‘ Within similar limits of uncertainty, ‘““¢ we may obtain something like a conjectural estimate of “. Thus “two molecules in collision will exercise ‘fa mutual repulsion in virtue of which the distance between “their centres, after being diminished to a minimum, will “begin to increase as the molecules leave one another, “This minimum distance would be equal to the sum of the “ radii, if the molecules were infinitely hard elastic spheres ; “but in reality we must suppose it to be very different in “ ditterent collisions.” § 31. The essential quality of a gas is that the straight line of uniform motion of each molecule between collisions, called the free path, is long in comparison with distances between centres during collision. In an ideal perfect gas the free path would be infinitely Jong in comparison with distances between centres during collision, but infinitely short in comparison with any length directly perceptible to our senses; a condition which requires the number of molecules in any 184 — Lord Kelvin 6n perceptible volume to be exceedingly great. We shall see that in gases which at ordinary pressures and temperatures approximate most closely, in respect to compressibility, expansion by heat, and specific heats, to the ideal perfect eas, as, for example, hydrogen, oxygen, nitrogen, carbon- monoxide, the free path is probably not more than about one hundred times the distance between centres during col- lisions, and is little short of 10—° em. in absolute magnitude. Although these moderate proportions suffice for the well- known exceedingly close agreement with the ideal gaseous laws presented by those real gases, we shall see that large deviations from the gaseous laws are presented with con- densations sufficient to reduce the free paths to two or three times the diameter of the molecule, or to annul the free paths altogether. § 32. It is by experimental determinations of diffusivity that the kinetic theory of gases affords its best means for estimating the sizes of atoms or molecules and the number of molecules in a cubic centimetre of gas at any stated density. Let us therefore now consider carefully the kinetic theory of these actions, and with them also, the properties of thermal conductivity and viscosity closely related to them, as first discovered and splendidly developed by Clausius and Clerk Maxwell. § 33. According to their beautiful theory, we have three kinds of diffusion; diffusion of molecules, diffusion of energy, and diffusion of momentum. ven in solids, such as gold and lead, Roberts-Austen has discovered molecular diffusion of gold into lead and lead into gold between two pieces of the metals when pressed together. But the rate of diffusion shown by this admirable discovery is so excessively slow that. for most purposes, scientific and practical, we may disregard wandering of any molecule in any ordinary solid to places beyond direct influence of its immediate neighbours. In an elastic solid we have diffusion of momentum by wave motion, and diffusion of energy constituting the conduction of heat through it. These diffusions are effected solely by the com- munication of energy from molecule to molecule and are practically not helped at all by the diffusion of molecules. In liquids also, although there is thorough molecular diffus- ivity, it is excessively slow in comparison with the two other diffusivities, so slow that the conduction of heat and the diffusion of momentum according to viscosity are not prac- tically helped by molecular diffusion. Thus, for example, the the Weights of Atoms. 185 thermal diffusivity * of water (002, according to J. T. Bot- tomley’s first investigation, or about ‘0015 f according to jater experimenters) is several hundred times, and the ditfus- ivity for momentum is from one to two thousand times, the diffusivity of water for common salt, and other salts such as sulphates, chlorides, bromides, and iodides. § 34. We may regard the two motional diffusivities of a liquid as being each almost entirely due to communication of motion from one molecule to another. This is because every molecule is always under the influence of its neighbours and has no free path. When a liquid is rarefied, either gradually as in Andrews’ experiments showing the continuity of the liquid and gaseous states, or suddenly as in evaporation, the molecules become less crowded and each molecule gains more and more of freedom. When the density is so ‘small that the straight free paths are great in comparison with the diameters of molecules, the two motional diffusivities are certainly due, one of them to carriage of energy, and the other to carriage of momentum, chiefly by the free rectilinear motion of the molecules between collisions. Interchange of energy or of momentum between two molecules during collision will undoubtedly to some degree modify the results of mere transport ; and we might expect on this account the motional diffusivities to be approximately equal to, but each somewhat greater than, the molecular diffusivity. If this view were correct, it would follow that, in a homogeneous gas when the free paths are long in comparison with the diameters of molecules, the viscosity is equal to the molecular diffusivity multiplied by the density, and the thermal con- ductivity is equal to the molecular diffusivity multiplied by the thermal capacity per unit bulk, pressure constant: and that whatever deviation from exactness of these equalities there may be, would be in the direction of the motional diffusivities being somewhat greater than the molecular diffusivity. But alas, we shall see, § 45 below, that hitherto experiment does not confirm these conclusions: on the contrary the laminar diffusivities (or diffusivities of momentum) of the only four gases of which molecular diffusivities have been determined by experiment, instead of being greater than, or at least equal to, the density multiplied by the molecular diffusivity, are each somewhat less than three-fourths of the amount thus calculated. * * Math. and Phys. Papers,’ vol. iii. p. 226. For explanation re- garding diffusivity and viscosity see same volume, pp. 428-435. + See a paper by Milner and Chattock, Phil. Mag. vol. xlviii. 1899. i a) are ee A tage Vs q 186 Lord Kelvin on { !§ 35. I see no explanation of this deviation from what seems thoroughly correct theory. Accurate experimental determinations of viscosities, whether of gases or liquids, are easy by Graham’s transpirational method. On the other hand even roughly approximate experimental determinations of thermal diffusivities are exceedingly difficult, and I believe none, on correct experimental principles, have really been made * ; certainly none unvitiated by currents of the gas experimented upon, or accurate enough to give any good test of the theoretical relation between thermal and material diffusivities, expressed by the following equation, derived from the preceding verbal statement regarding the three diffusivities of a gas, 0=Kpr Sek pe eons where @ denotes the thermal conductivity, « the viscosity, p the density, Kp the thermal capacity per unit bulk pressure constant, A the thermal capacity per unit mass pressure constant, ¢ the thermal capacity per unit mass volume con- stant, and & the ratio of the thermal capacity pressure constant to the thermal capacity volume constant. It is interesting to remark how nearly theoretical investigators + have come to the relation O=kew; Clausius gave 0=5cu; O. HE. Meyer, §=1°6027 cu, and Maxwell, 9=3cu. Maxwell’s in fact is §=kcp for the case of a monatomic gas. § 36. To understand exactly what is meant by molecular diffusivity consider a homogeneous gas between two infinite parallel planes, GGG and ARR, distance a apart, and let it be initially given in equilibrium ; that is to say, with equal numbers of molecules and equal total kinetic energies in equal volumes, and with integral of component momentum in any and every direction, null. Let V be the number of molecules per unit volume. Let every one of the molecules be marked either green or red, and whenever a red molecule strikes the plane GGG, let its marking be. altered to green, and, when- ever a green molecule strikes RRR, let its marking be altered to red. These markings are not to alter in the slightest * So far as I know, all attempts hitherto made to determine the thermal conductivities of gases have been founded on observations of rate of communication of heat between a thermometer-bulb, or a stretched metallic wire constituting an electric resistance thermometer, and the walls of the vessel enclosing it and the gas experimented upon. See Wiedemann’s Annalen (1888), vol. xxxiv. p. 623, and 1891, vol. xliv. p. 177. For other references, see O. E. Meyer, § 107. + See the last, ten lines of O. E. Meyer's book. the Weights of Atoms. 187 degree the mass or shape or elastic quality of the molecules, and they do not disturb the equilibrium of the gas or alter the motion of any one of its particles; they are merely to give us a means of tracing ideally the history of any one molecule, or set of molecules, moving about and colliding with other molecules according to the kinetic nature of a gas. § 37. Whatever may have been the initial distribution of the greens and reds, it is clear that ultimately there must be a regular transition from all greens at the plane GGG and all reds at the plane RRR, according to the law a—w& a (1), where g and 7 denote respectively the number of green molecules and of red molecules per unit volume at distance wv from the plane RRR. In this condition of statistical equili- brium, the total number of molecules crossing any inter- mediate parallel plane from the direction GGG towards RRA will be equal to the number crossing from RRA towards GGG in the same time ; but a larger number of green mole- cules will cross towards RRA than towards GGG, and, by an equal difference, a larger number of red molecules will cross towards GGG than towards RR#. If we denote this difference per unit area per unit time by QJ, we have for what I call the material diffusivity (called by Maxwell, “ co- efficient of diffusion ”’), + g=N- y=N Pe ag ge asa Yo at Ce We may regard this equation as the definition of diffusivity. Remark that Q is of dimensions LZ T—, because it is a number per unit of area per unit of time (which is of dimensions L~?T-') divided by NV, a number per unit of bulk (dimen- sions L-*), Hence the dimensions of a diffusivity are L’? 7-1; and practically we reckon it in square centimetres per second. § 38. Hitherto we have supposed the G and the £ particles to be of exactly the same quality in every respect, and the diffusivity which we have denoted by D is the inter-diffusivity of the molecules of a homogeneous gas. But we may suppose G and F& to be molecules of different qualities; and assem- blages of G molecules and of R molecules to be two different gases. Everything described above will apply to the inter- diffusions of these two gases ; except that the two differences which are equal when the red and green molecules are of the same quality are now not equal or, at all events, must 188 Lord Kelvin on not without proof be assumed to be equal. Let us therefore denote by Q,N the excess of the number of G molecules crossing any intermediate plane towards RRR over the number crossing towards GGG, and by Q,N the excess of the number of & molecules crossing towards GGG above that crossing towards RRR. We have now two different diffusivities of which the mean values through the whole range between the bounding planes are given by the equations Dj= Qo 3 Dre= Oa: one of them, D,, the diffusivity of the green molecules, and the other, D,, the diffusivity of the red molecules through the heterogeneous mixture in the circumstances explained in § 37. We must not now assume the gradients of density of the two gases to be uniform as expressed by (1) of § 37, because the homogeneousness' on which these equations depend no longer exists. § 39. To explain all this practically*, let in the diagram the planes GGG, and RAK, be exceedingly thin plates of dry porous material such as the fine unglazed earthenware of Graham’s experiments. Instead of our green and red marked molecules of the same kind, let us have two gases, which we shall call G and R, supplied in abundance at the middles of the two ends of a non-porous tube of glass or metal, and guided to flow away radially in contact with the end-plates as indicated in the diagram. If the two axial supply-streams of the two pure gases are sufficiéntly abundant, the spaces GGG, RRR, close to the inner sides of the porous end-plates will be occupied by the gases G and £&, somewhat nearly pure. They could not be rigorously pure even if the velocities of the scouring gases on the outer sides of the porous end-plates were com- parable with the molecular velocities in the gases, and if the porous plates were so thin as to have only two or three . * For a practical experiment it might be necessary to allow for the difference of the proportions of the G gas on the two sides of the RRR plate and of the & gas on the two sides of the GGG plate. This would be exceedingly difficult, though not impossible, in practice. The difficulty is analogous to that of allowing for the electric resistances of the connexions at the ends of a stout bar of metal of which it is desired to measure the electric resistance. But the simple and accurate ‘potential method” by which the difficulty is easily and thoroughly overcome in the electric case is not available here. Ido not, however, put forward the arrangement described in the text as an eligible plan for measuring’ the inter-diffusivity of two gases. Even if there were no other difficulty, the quantities of the two pure gases required to realize it would be impracticably great. the Weights of Atoms. 189 molecules of solid matter in their thickness. The gases in contact with the near faces of the porous plates would how- ever, probably be somewhat approximately pure in practice with a practically realisable thinness of the porous plates, if a, the distance between the two plates, is not less than five or six centimetres and the scouring velocities moderately, but not impracticably, great. According to the notation of § 37, 190 ’ Lord Kelvin on Q, is the quantity of the G gas entering across GGG and leaving across ARR per sec. of time per sq. cm. of area; Q, is the quantity of the R gas entering across RRR and leaving across GGG per sec. of time per sq. cm. of area ; the unit quantity of either gas being that which occupies a cubic centimetre in its entry tube. The equations a a AMR TERETE is dg where g and r are the proportions of the G gas at R and of the R gas at G, define the average diffusivities of the two gases in the circumstances in which they exist in the different parts of the length a between the end-plates. This statement is cautiously worded to avoid assuming either equal values of the diffusivities of the two gases or equality of the diffusivity of either gas throughout the space between the end-plates. So far as I know difference of diffusivity of the two gases has not been hitherto suggested by any writer on the subject. What is really given by Loschmidt’s experiments, § 48 below, is the arithmetic mean of the two diffusivities D, and D,. § 40. In 1877 O. E. Meyer expressed the opinion on theo- retical grounds, which seem to me perfectly valid, that the inter-dittusivity of two gases varies according to the pro- portions of the two gases in the mixture. In the 1899 edition of his ‘ Kinetic Theory of Gases’* he recalls attention to this view and quotes results of various experimenters, Loschmidt, . Obermayer, Waitz, seeming to support it, but, as he says, not quite conclusively. On the other hand, Maxwell’s theory ($ 41 below) gives inter-diffusivity as independent of the proportions of the two gases ; and only a single expression for diffusivity, which seems to imply that the two diffusivities are equal according to his theory. The subject is of extreme difficulty and of extreme interest, theoretical and practical ; and thorough experimental investigation is greatly to be desired. § 41. In 1873 Maxwell f gave, as a result of a theoretical investigation, the following formula which expresses the inter- diffusivity (D2) of two gases independently of the proportion of the two gases in any part of the mixture: each gas being supposed to consist of spherical Boscovich atoms mutually acting according to the law, force zero for all distances exceeding the sum of the radii (denoted by s,,) and infinite repulsion when the distance between their centres is infinitely * Baynes’ translation, p. 264. * “On Loschmidt’s Experiments on Diffusion in relation to the Kinetic Theory of Gases,” Nature, Aug. 1873 ; Scientific Papers, vol. i. pp. 343— 300. the Weights of Atoms. 191 little less than this distance: ie Da 5 ewe ta Wy w: = ; : Pires (1), where w,, w, are the masses of the see in the two gases in terms of that of hydrogen called unity ; V is the square root of the mean of the squares of the velocities of the mole- cules in hydrogen at 0° C.; and WN is the number of molecules in a cubic centimetre of a gas (the same for all gases according to Avogadro’s law) at 0° C. and standard atmospheric pressure. I find the following simpler formula more convenient i 2 Vv 62 Stes where V.? are the mean Fe cae es of the molecular velocities ae the two gases at 0° C., being the values of 3 p/p for the two gases, or three times the squares of their Newtonian velocities of sound, at that temperature. For brevity, we shall call mean molecular velocity the square root of the mean of the squares of the velocities of the molecules. The same formula is, of course, applicable to the molecular diffusivity ofa single gas by taking V,=V,=V its mean molecular velocity, and s;.=s the diameter of its molecules ; so that we have ah VG? Oe Wor as) tas a eds (eee ye Pelee Ve } a = 9 /3qr Ns? ar tS Lee (3). § 42. It is impossible by any direct experiment to find the molecular diffusivity of a single gas as we have no means of marking its particles in the manner explained in $ 37 above; but + abohars theory gives us, In a most interesting manner, the means of calculating the diffusivity of each of three sepa- rate | gases from three experiments determining the inter- diffusivities of their pairs. From the inter- EA pee of each pair determined by experiment we find, by (2) § 41, a value of s)V (2 V 37N) ‘for each pair, and we have sy=4(s,+ s2)*, whence $1 = Sy9 + $13 — 8933 Sg=Sjo + So3— $)33 $3=843+523—S12 . (1). Calculating thus the three values of sy (2V37N), and using them in (3) § 41, we find the molecular diffusivities of the three separate gases. § 43. In two communications T to the Academy of Science * This agrees with Maxwell’s equation (4), but shows his equation (6) to be incorrect. + “ Experimental-Untersuchungen iiber die Diffusion von Gasen ohne ordse Scheidewiande,” Sitz. d. k. Akad. d. Wissensch., March 10 and May 12, 1870. 192 Lord Kelvin on of Vienna in 1870, Loschmidt describes experimental deter- minations of the inter-diffusivities of ten pairs of gases made, by a well-devised method, with great care to secure accuracy. In each case the inter-diffusivity determined by the experi- ment would be, at all events, somewhat approximately the mean of the two diffusivities, § 39 above, if these are unequal. The results reduced to 0° C. and standard atmospheric pres- sure, and multiplied by 2°78 to reduce from Loschmidt’s square metres per hour to the now usual square centimetres per second, are as follows :— TABLE OF INTER-DIFFUSIVITIES D. Pairs of Gases. in sq. a per sec. aie O, ‘7214 | Ha eo "6422 | a ee: 5558 | 0, CO 1802 | O,. Od, ‘1409 CO, CO, ‘1406 | CO,, Air | "1425 | CO,, NO | “0984 CO,, CH, "1587 SO.,, iH, -4809 | r In the first six of these, each of the four gases H, O2, CO, CO, occurs three times and we have four sets of three inter- diffusivities giving in all three determinations of the diffusivity of each gas as follows :— ( Pairs of gases. Di. Pairs of gases. TS, | (12, 13, 28)......131 (12, 13; 23) | (12, d 424). 1°44 (12, 14, 24)ccee "190 | (155) Eee 1°22 (23, 24, 54) ae "182 — os 7 Gases. | Mean 1°32 Mean ‘188 6. Desa 2 oa a Te aes Coes 43) Dy, D,. es: Pt G2: 13. BB). das "168 (12, 14, 24)..0...°107 (13,14, 34).0..0be (13, 14, 34). | (23.94, 34).).. Ia. (23, 24, 34) Sa 1a ue | Mean ‘172 Mean °110 ks as es per ae De eid the Weights of Atoms. 193 Considering the great difficulty of the experimental investigation, we may regard the agreements of the three results for each separate gas as, on the whole, very satisfactory, both in respect to the accuracy of Loschmidt’s experiments and the correctness of Maxwell’s theory. It certainly is a very remarkable achievement of theory and experiment to have found in the four means of the sets of three deter- ninations, what must certainly be somewhat close approxi- mations to the absolute values for the four gases, hydrogen, oxygen, carbon-monoxide, and carbon-dioxide, of something seemingly so much outside the range of experimental obser- vation as the inter-diffusivity of the molecules of a separate gas. § 44. Maxwell, in his theoretical writings of different dates, gave two very distinct views of the inner dynamics of viscosity in a single gas, both interesting, and each, no doubt, valid. In one*, viscous action is shown as a subsidence from’ an “instantaneous rigidity of a gas.” In the other +, viscosity is shown as a diffusion of momentum: and in p. 347, ot his article quoted in § 41 above he gives as from “the theory,” but without demonstration, a formula (5), which, taken in conjunction with (1), makes iv Sate Bays iat tk os ee PA ot ad a > (1) p denoting the density, yw the viscosity, and D the molecular diffusivity, of any single gas. On the other hand, in his 1866 paper he had given formulas making t¢ | = 48D Ce Dake § 45. Viewing viscosity as explained by diffusion of mo- mentum we may, it has always seemed to me (§ 34 above), regard (1) as approximately true for any gas, monatomic, diatomic, or polyatomic, provided only that the mean free * Trans. Roy. Soc., May 1866 ; Scientific Papers, vol. ii. p. 70. t “ Molecules,” a lecture delivered before the Brit. Assoc. at Bradford, Scientific Papers, vol. ii. p. 378. See also O. E. Meyer’s ‘Kinetic Theory of Gases,’ (Baynes’ trans. 1899), §§ 74-76. t The formula for viscosity (Sci. Papers, vol. ii. p. 68) taken with the formula for molecular diffusivity of a single gas, derived from the formula oe Mia A : of inter-diffusivity of two gases of equal densities, gives SD = 3A) which is equal to 648 according to the values of A, and A, shown in p. 42 of vol. 11. Sci. Papers. Phil. Mag. 8. 6. Vol. 4. No. 20. Aug. 1902. O 194 Lord Kelvin on path is large in comparison with the sum of the durations of the collisions. Unfortunately for this view, however, com- parisons of Loschmidt’s excellent experimental determinations of diffusivity with undoubtedly accurate determinations of viscosity from Graham’s original experiments on transpiration, and more recent experiments of Obermeyer and _ other accurate observers, show large deviations from (1) and are much more nearly in agreement with (2). Thus taking "0000900, 001430, 001234, °001974 as the standard densities of the four gases, hydrogen, oxygen, carbon-monoxide, and carbon-dioxide, and multiplying these respectively by the diffusivities from Loschmidt’s experiments and Maxwell’s theory, we have the following comparison with Obermeyer’s viscosities at 0° C. and standard pressure, which shows the discrepance from experiment and seeming theory referred to in § 34. Col. 1. Col. 2. Col. 3. Col. 4, Viscosity calculated | by Maxwell’s theory; y-_. +: : Ratio of values in Gas, from Loschmidt’s ce Col. 2 to those diffusivities yy in Col. 2, p=pD. 1a ‘000119 "0000822 691 0, "000269 "0001873 “695 CO ‘000212 *0001630 . “769 co, 000218 ‘0001414 | 649 § 46. Leaving this discrepance unexplained, and elimi- nating D between (1) of § 44 and (3) of § 41, we find as Maxwell’s latest expression of the theoretical relation between number of molecules per cubic centimetre, diameter of the molecules, molecular velocity, density, and viscosity of a single gas, | end IMP mit, 55" V/P Ns oles a 1629 2 (1). The number of grammes and the number of molecules in a cubic centimetre being respectively p and N, p/N is the mass of one molecule in grammes; and therefore, denoting this by m, we have : f M=2WV Bar 4; = 6140-7 3 le Ae Pd A he the Weights of Atoms. 195 In these formulas, as originally investigated by Maxwell for the case of an ideal gas composed of hard spherical atoms, s is definitely the diameter of the atom, and is the same at all temperatures and densities of the gas. When we apply the formulas to diatomie or polyatomic gases, or to a mon- atomic gas consisting of spherical atoms whose spheres of action may overlap more or less in collision according to the severity of the impact, s may be defined as the diameter which an ideal hard spherical atom, equal in mass to the actual molecule, must have to give the same viscosity as the real gas, at any particular temperature. This being the rigorous definition of s, we may call it the proper mean shortest distance of inertial centres of the molecules in collision to give the true viscosity ; a name or expression which helps us to understand the thing defined. § 47. For the ideal gas of hard spherical atoms, remem- bering that V is independent of the veer | and varies as @ (¢ denoting absolute temperature), § 46 (2) proves that the viscosity is Independent of the density oa varies approxi- mately as #@. Rayleigh’s experimental determinations of the viscosity of argon at different temperatures show that for this monatomic gas the viscosity varies as t®; hence § 46 (2) shows that s? varies as ¢~*!°, and therefore s varies as ¢—}6. Experimental determinations by Obermayer* of viscosities and their rates of variation with temperature for carbonic acid, ethylene, ethylene-chloride, and nitrous oxide, show that for these the viscosity is somewhat nearly in simpie proportion to the absolute temperature: hence for them s? varies nearly as ¢—°. His determinations for the five molecularly simpler. gases, air, hydrogen, carbonic oxide, nitrogen, and oxygen show that the increases of mw, and therefore of s~?, with temperature are, as might be expected, considerably smaller than for the more complex of the gases on which he experimented. Taking his viscosities at 0° Cent., for carbonic acid and for the four other simple gases named above, and Rayleigh’s s for argon, with the known 1 densities of all the six gases at 0°C. and standard atmospheric pressure, we have the following table (p. 196) of the values concerned in § 46 (1). § 48. The meaning of “ss,” the diameter, as defined in § 46, is simpler for the monatomic gas, argon, than for any of the others ; and happily we know for argon the density, * Obermayer, Wien. Akad. 1876, Mar. 16th, vol.:73, p. 433. O 2 Col. 1. Gas. 196 Lord Kelvin on not only in the gaseous state (001781) but also in the liquid state (1'212)*. The latter of these is 681 times the former. Now, all things considered, it seems probable that the crowd of atoms in the liquid may be slightly less dense than an assemblage of globes of diameter s just touching one another in cubic order; but, to make no hypothesis in the first place, let gs be the distance from centre to centre of a cubic arrange- ment of the molecules 681 times denser than the gas at 0° C. and standard atmospheric pressure; g will be greater than unity if the liquid is Jess dense, or less than unity if the liquid is denser, than the cubic arrangement with molecules, ! regarded as spherical of diameter s, Just touching. We have re 681N=1/(gs% . . s.r and for argon we have by § 46 (1), Ns?=57700 . ret Eliminating s between these equations we find N=681? . 57700%q°=8-9.10. 99. . . (5). If the atoms of argon were ideal hard globes, acting on one another with no force except at contact, we should almost certainly have g = 1 (because with closer packing than that of * See Ramsay and Travers, Proc. R. 8., Nov. 1900, p. 331. + Maxwell’s Collected Papers, vol. ii. p. 348, eqn. (7). The formula as printed in this paper contains a very embarrassing mistake, Jn for 42.7. tes vii Col. 2. Col. 3. Col. 4..| Col. 5. Col. 6. Col. 7: Col. 8. Col. 9. i: Mean free Ratio @. paths ac- | volume oc- Hence taking cording to | cupied by W=10°0 ($ 50)) Taking Maxwell’s | molecules tc p Mh V Ns? we have N=1020, formulat j|whole volum in terms of in terms in terms | in terms | s at 0° Cent. Mm i) ee grammes per| of dynes of centi- | of (centi- | in terms of | in terms of |= 2. 1s? Nes. cubic centi- | per square | metres per| metre)—!. | centimetres.| grammes. : 2 metre. centimetre. | second. in terms of centimetres. ‘001974 "0001414 | 389200 | 89500 | 2°99.10-* |19-74. 10-74) 2-52 .10-* | 1-340.10- 0000900 | ‘0000822 | 184200 | 32900 | 1°81 ,, 050% 3 6°84. ,, Sli: ., "001234 0001630 | 49600 | 61300 | 248 ,, {12:34 ,, | 362 ,, ct 001257 0001635 | 49000 | 61600 | 248 ,, |12°57 ,, 3°64 ,, A ‘00143 0001873 | 46100 | 57500 | 240 ,, {143 ,, oo Tat ,, ‘001781 0002083 | 41400 | 57700 | 240 ,, {17-81 ,, 3°89. - 4 "724 the Weights of Atoms. 197 cubic order it seems not possible that the assemblage could have sufficient relative mobility of its parts to give it fluidity) and therefore N would be = 8-9 . 10". § 49. For carbonic acid, hydrogen, nitrogen, and oxygen, we have experimental determinations of their densities in the solid or liquid state; and dealing with them as we have dealt with argon, irrespectively of their not being monatomic gases, we find results for the five gases as shown in the following table : | Col. 1, Col. 2. Col. 3. Col. 4. Col. 5 hehe ae Ratio of | Values e sae § 48) solid or | Number of according to | liquid | molecules per | qg-§='89 for argon | Gas. Solid or liquid density. density to) cubic centimetre | (liquid compared standard | of gas at standard | with gas at 0° and gaseous | density. atmospheric density. pressure). N 1 eS ee 1°58 800 | 45°99 .10'°. 9° ‘776 H, liquid at 17° absolute... 090 | 1000 ue + Ss 1-188 N liquid PER io OF 833 | 16-2 S ‘923 = TES ee 1400} 1114 | 290 __,. ‘837 nO, liquid at its freezing pt. 1:27 88s 150 ‘ "935 x. on LAT i ere ae eae 1-212 681 89 ad 1:020 ) 8 solid at 86° absolute... 1°396x| 784 | 12°8 ty ‘960 In this table, g denotes the ratio to s of the distance from centre to centre of nearest molecules in an ideal cubic assemblage of the same density as the solid or liquid, as indicated in cols. 3 and 2. § 50. According to Avogadro’s doctrine, the number of molecules per cubic centimetre is the same for all “ perfect ” gases at the same temperature and pressure; avd even carbonic acid is nearly enough a “ perfect gas” for our present considerations. Hence the actual values of g® are inversely proportional to the numbers by which they are multiplied in col. 3 of the preceding table. Now, as said in § 48, all things considered, it seems probable that for argon, liquid at density 1-212, g may be somewhat greater, but not much greater, than unity. If it were exactly unity, N would be 8-9 10, and I have chosen g=(‘89)~* or 1°020, to make N the round number 10”. Col. 6, in the table of § 47 * From information communicated by Prof. W, Ramsay, July 23, 1901. 198 Lord Kelvin on the Weights of Atoms. above, is calculated with this value of WV; but it is not improbable that the true value of V may be considerably greater than 10?°*. § 51. As compared with the value for argon, monatomic, the smaller values of g for the diatomic gases, nitrogen and oxygen, and the still smaller values for carbonic acid, triatomie, are quite as might be expected without any special considera- tion of law of force at different distances between atoms. It seems that the diatomic molecules of nitrogen and oxygen and still more so the triatomic molecule of carbonic acid, are effectively larger when moving freely in the gaseous condition, than when closely packed in liquid or solid assemblage. But the largeness of g for the diatomic hydrogen is not so easily explained: and is a most interesting subject for molecular speculation, though it or any other truth in nature is to be explained by a proper law of force according to the Boscovichian doctrine which we all now accept (many of us without knowing that we do so) as the fundamental hypothesis of physics and chemistry. I hope to return to this question az to hydrogen in a crystallographic appendix. I am deeply indebted to Professor Dewar. for information regarding the density of liquid hydrogen, and the densities of other gases, liquefied or frozen, which he has given me at __yarious times within the last three years. [To be continued. ] * Maxwell, judging from ‘‘ molecular volumes ” of chemical elements estimated by Lorentz, Meyer and Kopp, unguided by what we now know of the densities of liquid oxygen and liquid hydrogen and of the liquid of the then undiscovered gas argon, estimated V=‘19.10°° (Maxwell’s Collected Papers, vol. ii. p. 350) which is rather less than one-fifth of my estimate 102°, On the same page of his paper is given a table of estimated diameters of molecules which are about 32 or 3'3 times larger than my estimates in col. 6 of the table in § 47. In a previous part of his paper (p. 348) Maxwell gives estimates of free paths for the same gases, from which by his formula (7), corrected as in col. 8 of my table in § 47, I find values of N ranging from 6:05 . 10'* to 6:96 . 10'8 or about one-third of ‘19. 202°, His uncorrected formula #/2z (instead of 4/2 . 7) gives values of N which are 7 times, or 1'77 times as great, which are still far short of his final estimate. The discrepance is therefore not accounted for by the error in the formula as printed, and I see no explanation ofit. The free paths as given by Maxwell are about 1°3 or 1-4 times as large as mine. i yres | XIX. Researches on the Blue Colour of the Sky. Extracts from a Thesis for the Doctor of Science degree of the — sity of Rome. Sy GiusEPPE ZETTWU cH*, R. ZETTWUCH’S paper, from which the extracts given below are selected, is divided into three parts. In Part I. the author givesa ‘connected historical account of the various theories which have been propounded to account for the blue colour of the sky; Part II. deals with the present state of the problem; and Part III. contains an account of the author’s experimental researches on the subject. These researches were directed mainly towards the verification of Lord Rayleigh’s theory, according to which the intensity of the various radiatious due to particles small in comparison with wave-lengths which constitute part of the light of the sky is inversely proportional to the fourth power of the wave-length. The apparatus consisted of a Kriiss spectroscope fitted with a Vierordt double-slit collimator, which enabled it to be used as a spectrophotometer. “Results of the Observations.—The observations are referred to the true mean time at which they were taken, and to the distance of the sun from the zenith at the same time. More- over, as the results calculated as explained in an earlier part of the paper varied with the hour at which the observations were taken and according to local conditions, it was thought more instructive to calculate the value of n which would satisfy an assumed law & instead of 5; L ;, and all the series of observations are oo by a bie description of the state of the sky.” The author next gives a long table of results, and then follow his “Conelustons.—1. From the general nature of the obser- vations and the table of results it is clearly evident that we have to deal with a highly variable phenomenon, as the light reflected from the sky, and coming from the same point of it, is of variable composition. All the observations, no ninth what the state of the sky, show that the predominant radia- tions are those of short wave-length. But their proportion is os even approximately constant. “The divergence presented by the different series of obser- vations is not surprising, as it occurs even in the same series of observations when taken with a variable state of the sky. * Comiuunicated by Lord Kelvin. Translated from the Italian. 200 Mr. G. Zettwuch on the it is thus easy to understand how under such circumstances no general law is capable of representing the phenomenon. “‘T wish further to draw attention to the fact that even with an apparently serene and immutable sky different values have been obtained for n in the same set of observations, and the differences appear to exceed the limits of errors of observation. ‘2. Considering merely the results obtained on clear days, such as those on July 11, 16, and 17, and on October 6, it is seen that the value of n increases continuously with the zenithal distance of the sun; its minimum appears to coincide with the minimum daily zenithal distance. The variations are best seen by constructing a curve whose abscissee represent zenithal distances and ordinates the calcu- lated values of n. JE she such curves, corresponding to July 17 and October 6, are given. | “3. These curves show that for large zenithal distances, between 70° and 90°, 2 increases fairly ‘rapidly. “4, The composition of the zenithal light cannot be repre- sented by a single general formula. In rare instances the results approximate to Rayleigh’s law; however, it is clearly seen that, for zenithal distances in the neighbourhood of 90°, they show no great divergence from it, and tend towards it rapidly. It is further also seen at a glance that it is not at the zenith that the blue has the maximum degree of satu- ration; but that this always occurs at an angular distance of 90° from the sun, a result which also follows from Wild’s observations. ““T have as yet been unable to take observations with a very deep-blue sky ; even on the days when the highest values of n were obtained, the sky did not appear to me to be of an intense and deep blue. “According to my results it appears that the blue of the sky at Rome is less pronounced than in England, Germany, and France. “This conclusion may, however, be somewhat premature. It is necessary to wait for the collection of a larger number of observations, made ata more favourable time than was possible to myself—since the past year has been an excep- tionally rainy one. Moreover, it becomes necessary to consider the small altitude of the observation-station above sea-level (60 m.), and its surroundings. “5. The perturbing cause which in most cases produces variations in the composition of the diffused light is un- doubtedly to be found in the clouds; which, though small in numbers and very thin, disturbed the relative intensity of the two spectra in a surprising manner as they approached the \ iS ™~ Blue Colour of the Sky. 201 zenith; as they passed the zenith, they rendered any adjust- ment impossible by reason of the variations in the intensity which occurred while the observations were being taken. When the movement of the clouds took place between the horizon and the zenith, the values found for x from different readings of the same series of observations were markedly discordant, as is shown by the table. “6. A curious result is obtained by comparing the values found for 2 with the relative humidity u. This comparison shows that to a high value of wu there also corresponds in general a high value of xn. This parallelism does not appear tome to have any clear significance, since 7 hasa larger value in the morning than evening, and the relative humidity in the neighbourhood of the soil is then also greater than at any other time in the course of a fine day. The conclusion, therefore, cannot be regarded as reliable. ‘When ultimately analysed, the results obtained do not admit of an absolutely definite conclusion that at no time does the composition of the diffuse light of the sky coming from the zenith satisfy Rayleigh’s law. It must be stated that under certain circumstances, in a perfectly transparent atmo- sphere and at a suitable angular distance from the sun, the value corresponding to Rayleigh’s law is undoubtedly con- tinuously approached, and in certain cases surpassed. ‘‘ But if the observations on the diffuse light of the sky have in the case of every observer given variable and complex results, those on the blue light emitted laterally by a suitable turbid medium, and in particular on the artificial sky-blue of Bock, have yielded reliable and uniform results. This will be clearly seen from the values which I have calculated for n from the observations of Bock [referred to above] ; the caleu- lation being conducted ina manner similar to that used in my own experiments. Blue of the Sky. Blue of Vapour Jet. N yellow= 2°49 3°99 n green = 4°08 3-99 Gis. —1a Oo aoe Tt at == 4°26 4:00 “ On the one hand, for the blue of the sky the values of n corresponding to the same series of observations exhibit a considerable amount of divergence ; on the other, the values found for the vapour-jet are in perfect accord, and yield the value for n required by Rayleigh’s theory. “From the fact that, on account of the variations taking 202. Mr. A. M. Herbert on the Effect of Hydrogen on place at different times of the day and under different atmo- spheric conditions, and thus escaping the notice of even an expert observer, Rayleigh’s formula regarding the composition of the diffuse light of the sky is not verified numerically, it does not follow that Rayleigh’s theory is not to be retained as furnishing the best explanation of the colour of the atmosphere. Variations in the number and size of the par- ticles which give rise to the turbidity of the atmosphere, and in what is still more irregular—equally invisible strata of water-vapour in the lower regions—explain sufficiently, in accerdance with Rayleigh’s theory, the discrepancies among the complex results which have been obtained in the strata just above the surface of the soil—strata forming ‘ atmo- spheric mud.’ ‘“‘At the present time, the controversial choice lies between the colour proper of the air and Rayleigh’s theory. This theory has an energetic and staunch supporter in Prof. Pernter, who, as we have seen, has several times replied to Spring, combating the latter’s views. In the present state of science, Rayleigh’s theory is the only one capable of explaining satis- factorily certain observed facts of special importance in con- nexion with the colour of the atmosphere, of which the principal one is that at an angle of 90° we get the maximum of polarization by the atmosphere, and of light reflected by a turbid medium—a fact which, according to Pernter, ‘is the expertmentum crucis with regard to the theory of the blue colour of the sky.’ “‘} shall conclude by quoting Pernter :— “¢ ¢The turbid medium called air is that which gives rise to the blue colour of the sky. The weak colour proper of the air—if it exists—contributes nothing towards it.’ ” XX. The Hffect of the Presence of Hydrogen on the Intensity of the Lines of the Carbon Spectrum. By Artour M. Hersert, B.A.* N a paper “On the Spectra of some of the Chemical Elements,” in the Philosophical Transactions for 1864, Sir William Huggins remarks that ‘‘ when carbon is sub- jected to the induction-spark in the presence of hydrogen the strong line in the red (a little less refrangible than the hydrogen red line corresponding to Fraunhofer’s C in the solar spectrum) is not seen.”” This peculiarity is referred to by him once again in connexion with certain cometary spectra * Communicated by Prof. Arthur Schuster, F.R.S. the Intensity of the Lines of the Carbon Spectrum. 203 in a later paper (Phil. Trans. 1868), so that apparently he considered the result to be unquestioned. As no details of the experiments were given, and in fact no further reference to this particular question could be found anywhere, the following experiments were undertaken at Professor Schuster’s suggestion, whose constant advice I had the advantage of in the conduct of them. The red line of carbon is a double one ( x eae ), the more refrangible one being the stronger. When the slightest trace of hydrogen was present along with the carbonic acid gas, in which the spark was taken in the first instance, the red line of hydrogen (\ 6562) appeared; as more and more hydrogen was admitted it was found that the carbon red line very rapidly diminished in brightness, so that with a compa- ratively small proportion of hydrogen in the mixture the carbon line appeared very faint. The other principal line of carbon seen when the spark is taken in carbonic acid is a broad one in the violet (\ 4266). The behaviour of this line in the presence of hydrogen was quite different; as the relative proportion of hydrogen was increased this line merely suffered a gradual diminution in brightness (along with several oxygen lines in its neighbour- hood), but it never disappeared, being quite distinct when the amount of hydrogen present was far in excess of the carbonic acid ; indeed it was quite recognizable with an ex- ceedingly small proportion of carbonic acid in the mixture, and seemed, if anything, to be more persistent than the oxygen lines near it in the violet. Two other carbon lines were examined (X 5640 and dX 5145); they apparently suffered merely a gradual weaken- ing as the proportion of hydrogen was increased, but as they are much fainter than the two principal lines they were not attended to in the subsequent experiments, which were directed solely to investigating the difference in behaviour of the two strong lines. Thus it appeared from these initial experiments that the red line of carbon seen under these conditions is affected by the presence of hydrogen in a totally different way from the other carbon lines. After these few preliminary experiments, in which Sir William Huggins’s observations were generally confirmed, several series of experiments were made with mixtures of carbonic acid and hydrogen in known proportions by volume. The gases, supplied by two Kipp’s apparatus, were passed into an aspirator which was graduated so that definite volumes of each gas could be admitted ; from the aspirator Me re 204 Mr. A. M. Herbert on the Effect of Hydrogen on the gas, or mixed gases, was forced through the discharge- tube, after bubbling through strong sulphuric acid to get rid of most of the moisture present. A slow current of gas was maintained so as to prevent the accumulation in the discharge-tube of any products of chemical decomposition due to the passage of the spark. The spark passed between platinum-iridium electrodes which were about 3 mm. apart; these were fused into the bulb of the discharge-tube, the diameter of the bulb being One of Apps’s induction-coils was used which gave a spark of about 3 inches between its terminals in air, when four Tudor cells (2 volts each) supplied the primary about 4 em. current. A small leyden-jar, the outer tinfoil area being about 280 sq. cm., was included in the circuit. In all the experi- menis the spark was taken at atmospheric pressure. The following results were obtained, each set of experi- ments being repeated several times with similar results ; the effects upon the two red lines are noted :— A. Spark in miuture of Carbonic Acid Gas and Hydrogen. (i.) 24 parts H in 24 parts mixture=10 per cent. H. [Hydrogen line stronger than ons (iii.) 5 ‘ rie ha (v.) 1 3 25 af 14 20 carbon line.] =20 per cent. H. [Hydrogen line strong, carbon line faint. ] =30 per cent. H. [Hydrogen line very strong, (approx.) carbon line very faint. ] =50 per cent. H. [Carbon line hardly distin- guishable. } = 5 percent. H. [Lines about equally strong; hydrogen, if anything, slightly stronger. | A second set of experiments gave the following results :— (i.) 23 parts H in 25 parts mixture=10 per cent. H. [Hydrogen line slightly the (Gii.) 6 * iii.) 10 i CIV lee: (v.) 3 ” ‘Coen! fe 99 stronger. ] =30 per cent. H. [Hydrogen line very strong, carbon line very faint. ] =40 per cent. H. [Carbon line hardly distin- guishable. | =50 per cent. H. [Carbon line hardly visible. | = 1 percent. H. [Carbon line very strong ; hydrogen line very faint, but quite distinct. | = 5yper cent. H. [Lines about equally strong; carbon, if anything, slightly stronger. ] The percentages given do not, of course, pretend to any great accuracy ; thus there did not seem to be much dif- ference in the etfects between 40 per cent. and 50 per cent. of hydrogen. the Intensity of the Lines of the Carbon Spectrum. 205 It will be noticed that in the first set of experiments the hydrogen liae appeared slightly the stronger with 5 per cent. hydrogen in the mixture, whereas in the second set the carbon line was slightly the stronger with the same per- centage. This is probably due to the fact that the vessel containing sulphuric acid through which the gas bubbled was, after each experiment, left full of the mixture just used, so that this contaminated, especially at first, the next mixture. In the first case 5 per cent. hydrogen was tried immediately after 50 per cent. hydrogen, so that probably the hydrogen was somewhat in excess of 5 per cent. during most of the time. In the second case the preceding mixture contained mostly carbonic acid, so that in this case the hydrogen would pro- bably be slightly less than 5 per cent. in the mixture during most of the time. Itis likely, therefore, that with 5 per cent. hydrogen in the mixture the two lines are about equally strong. As before stated, the violet strong line of carbon is not affected to this extent ; it was examined in each experiment, and it merely suffered a natural weakening as the proportion of carbonic acid diminished, but it was quite distinct with 90 per cent. of hydrogen in the mixture, and easily visible with still more hydrogen. Before proceeding any further the effect of nitrogen (or rather, air) was tried ; this simply weakened both carbon lines more or less equally ; with 80 per cent. of air, for example, both carbon lines were quite distinct and fairly bright. The experiments were now repeated, using higher disper- sion so as to separate the two red lines still further. Two prisms of dense glass were used, and a small screen was fixed in the eyepiece, which could be moved along horizontally by means of a screw-head so as to cover up the hydrogen line, and hence to eliminate all possibility of optical illusion due to contrast effects. The results were substantially the same as before ; it appeared that with 50 per cent. of hydrogen the carbon red line is still faintly visible but not readily dis- tinguishable—it seemed to flash in and out faintly rather than to be faintly persistent. At times I thought it was present, at other times I was sure it was not, so that its presence seemed to depend upon very unstable conditions. B. Spark in mixture of Carbon Monoxide and Hydrogen. (i.) 19 parts H in 38 parts mixture=50 per cent. H. [Hydrogen line very strong; carbon line hardly visible. | (ii.) 1 Pe 20 ss = 5 percent. H. [Lines about equal.] (iii.) 9 9 32 5 =28 percent. H. [Hydrogen line strong, car- bon line faint. | (iv.) 22 a 44 - =00 per cent, H. [Carbon line hardly distin- guishable. | Se , ae sn Py 206 Effect of Hydrogen on the Lines of the Carbon Spectrum. Several other series of experiments with mixtures of car- bonic oxide and hydrogen were made, and the results agreed together, and with the corresponding results obtained with mixtures of carbonic acid and hydrogen so far as could be estimated by the conditions of the experiments. C. Spark in Coal-gas. The spark in coal-gas showed the red hydrogen line strongly--the other hydrogen lines were not attended to— the violet carbon line well, but the red carbon line was hardly visible, Taken as a whole, the appearance of these three lines was much the same as in a mixture of carbonic acid and hydrogen containing 50 per cent. of hydrogen. . The effect of mixing coal-gas with carbonic acid was then tried with the following results :— (i.) 5 per cent. coal-gas in the mixture. [Carbon red line slightly the stronger.] (ii.) 10 - a (Hydrogen line slightly the stronger. | iii.) 33 Hs “. [Carbon red line faint, but quite distin- . guisnable. | {iv.) 50 ‘ ‘. [Carbon line very faint, but more readily seen than with 50 per cent. hydrogen. | It will be seen that the red line of carbon is more per- sistent than in the case of corresponding mixtures of carbonic acid and hydrogen; this is only to be expected, as the coal- gas brings carbon as well as hydrogen into the mixture. ' From these experiments the conclusion seems certain that though the red carbon line may not be completely destroyed by the presence of hydrogen—at any rate when the propor- tion of hydrogen does not exceed 50 per cent.—yet it is influenced in a way totally different from the other strong line of carbon in the violet, whereby it suffers a very rapid quenching, as the proportion of hydrogen is increased, to which the violet line is not subject. It might, perhaps, be thought that the effects observed are due to the faint carbon line being rendered invisible owing to the strong glare of the hydrogen red line in its neigh- bourhood. But this possible objection is, I think, completely met by the consideration of the following facts, Firstly, the two lines were well separated by the instrament used, and the screen fixed in the eyepiece enabled either one of them to be covered up; secondly, when a mixture con- taining a mere trace of hydrogen was examined the very faint persistent hydrogen line was seen without any difficulty by the side of the very bright carbon line; and, lastly, when, with 50 per cent. hydrogen, the carbon red line appeared to flash On the Laws of Electrolysis of Alkali Salt-Vapours. 207 in and out, it was quite distinctly seen when it flashed in, and its flashing out was equally distinct. It has been suggested to me by Professor Schuster that the experiments seem to show that the red and violet carbon lines must belong to different spectra of carbon, the particular molecular combination which gives rise to the red line being destroyed by the presence of hydrogen. The fact that the two interfering lines lie near each other in the spectrum is probably accidental. I have to thank Professor Schuster also for many other suggestions made during the course of the experiments. XXI. The Laws of Electrolysis of Alkali Salt-Vapours. By Harotp A. Witson, D.Sc., W.Se., B.A., Clerk-Maxwell Student, Fellow of Trinity College, Cambridge*. N 1891 Arrhenius (Wied. Ann. xl. p. 18, 1891) pub- lished the results of an investigation on the passage of electricity through flames containing salt-vapours, and pro- posed the theory that the salts dissociate into ions in the flame in the same way that salts are ionized in aqueous solutions. Arrhenius’ results were confirmed and extended in 1899 in a research initiated by Prof. A. Smithells and carried out in conjunction with Dr. H. M. Dawson and the writer (Phil. Trans. A. 1899). Since then the writer has published (Phil. Trans. A. 1899 and 1901) the results of further work which seem to show conclusively that conduction through salt-vapours is accomplished by means of ions of some kind, and is therefore to this extent at least analogous to con- duction through solutions. The experiments now to be described were undertaken with the object of determining the relative conductivities of different alkali salt-vapours at various temperatures. Many of the results obtained have been published in a_ paper on the ‘‘ Electrical Conductivity of Air and of Salt-Vapours,” read to the Royal Society this year. in aqueous solutions a salt such as KCl dissociates into two ions +K and —Cl, so that the most likely supposition is that in salt-vapours the ions are of the same nature. However, determinations of the velocities of the various ions in salt-vapours show that the ions generally behave as if they were much heavier than single atoms, and that the positive ion always moves more slowly than the negative ion, * Communicated by the Author, (A paper read to the British Association, Glasgow, 1901.) 208 Dr. H. A. Wilson on the Laws of Under these circumstances it does not seem to be justifiable to make the simple supposition mentioned above, at least not without further experimental evidence in its favour, The experiments now to be described show conclusively that above 1300° C. there is a very close analogy between salt- -vapours and liquid electrolytes. In fact it is shown that Faraday’s laws of electrolysis are strictly applicable to salt- vapours just as to salt-solutions. It is probable that the gaseous ions attract neutral mole- cules to themselves, which accounts for their small velocities ; and apparently the positive ions condense many more mole- cules in this way than the negative ions, so that the negative lions move much the faster. But this ~condenseciaie which appears to be peculiar to ions in the gaseous state, need not affect the number of ions produced by the dissociation of one salt molecule or the charges which they carry. It will be shown below that a salt in the state of vapour gives rise to the same number of ions carrying the same charges as a salt in an aqueous solution, in other words, the capacity of a salt-vapour for transporting electricity is the same as the capacity of an equal amount of salt in the state of solution. The apparatus used is shown in the accompanying figure. ——“a AIR aes GEE GO ae us Re <_<. SOLUTION ate It consisted of a platinum tube TT’ 40 centims. long and 0°75 centim. fir diameter, having a flange FF 6 centims. in diameter joined on at one end. This tube was supported horizontally in a Fletcher’s tube furnace. The flange served to keep the furnace gases from the open end of the tube. An electrode HE, consisting of a platinum tube 12 centims, long and 0°3 centim. in diameter, was supported, on an ad- justable ne stand, along ‘the axis of the tube TT’. Electrolysis of Alkali Salt- Vapours. 209 The end of this electrode was closed by a conical platinum cap which was about 9 centims, down the tube TT’. | At T’ the platinum tube was fitted tightly into a glass tube through which air charged with spray of a salt-solution entered. The spray was produced by a Gouy sprayer S, which projected the spray into a glass bulb G, about 8 centims. in diameter, from which the air and spray were led through an inverted U-tube, in which'the coarser spray settled. The salt-solution was contained in a reservoir, the level of the surface being 30 centims. above the nozzle of the sprayer. The greater part of the spray settled in the bulb and first half of the U-tube, and was returned to the reservoir through a tube up which the liquid was forced by compressed air. The supply of compressed air used was obtained by means of two water-injector pumps similar to the one used in the previous work on the conductivity of flames. Some of the air was allowed to escape by bubbling through mercury which served to keep its pressure nearly constant, and the rest was passed through a large carboy to smooth out small oscillations in the pressure. | | The air-pressure at the sprayer was measured by means of a water manometer, and was kept constant at 50 centims. This arrangement gave enough air to work the sprayer and also the furnace, except at temperatures above about 1100° C., when the air-supply to the furnace was supplemented by oxygen from a cylinder, by means of which a temperature of 1400° C. could be obtained. The temperature of the tube was measured by means of a platinum platinum-rhodium thermo-couple, which was simply connected through a resistance-box and commutator to an Ayrton-Mather dead-beat galvanometer G, of about 500 ohms resistance. The platinum wire served to support the tube, and the Pt/Rh wire was fused on to the tube at a point on its upper surface so that the tube itself formed one of the elements of the couple. The couple was standardized by determining the galvanometer deflexion corresponding to the melting- point of K,SO,, which melts, according to Heycock and Neville, at 1066° C. The K,SO, was introduced into the tube on a small platinum spatula, and the temperature gradually increased until it was seen to melt, and the cor- responding deflexion noted. Then by maintaining the tube at a series of constant temperatures near the M.Pt. and find- ing at which the K,SO, melted, it was possible to obtain two temperatures very near together, at one of which the K,SO, melted and at the other remained solid. The mean of the Phil. Mag. 8. 6. Vol. 4. No. 20. Aug. 1902. big oe SS ped RAs) = ‘ >» i 210 Dr. H. A. Wilson on the Laws of two galvanometer deflexions was taken as corresponding to 1066° C., and the temperature corresponding to any other deflexion was first calculated on the assumption that the deflexion was proportional to the difference between the temperatures of the two junctions. The “ platinum tempe- ratures ’’ thus obtained have been corrected to the 2entigrade scale by means of the table of corrections given by Callendar (Phil. Mag. Dec. 1899, p. 534), This method of getting the temperature was quite suf- ficiently accurate for the purposes of the present investiga- tion, for which it was useless to aim at a greater accuracy than 5 or 10 degrees, and according to Callendar the cor- rections are much more accurate than this near 1000°, while even at 300° the error is not more than 10°. The Pt and Pt/Rh wires dipped into mercury cups kept in a water-bath at a known temperature from which copper wires led to the galvanometer. The gas supplied to the furnace was kept at a constant pressure by means of a gasometer, and the air and oxygen supply-tube was provided with a water manometer, by means of which the pressure of the supply could be maintained con- stant, if necessary, for any length of time. In this way, the tube could be maintained constantly at any desired tempera- ture within 5° C, without difficulty. The current through the air and salt between the electrode KE and the tube TT’ due to various potential-differences between them was measured by means of an Ayrton-Mather galvanometer G;. The P.D. was obtained from a battery of small accumulators B, and was measured by means of a Braun’s electrostatic voltmeter reading from 50 to 1500 volts. Two commutators served to reverse the current through the galvanometer only or through the whole apparatus. | Fig. 2 shows the way in which the current with a constant E.M.F. (840 volts) varies with the temperature when solutions of one gram in a litre are sprayed. It will be seen that in each case the current at first rises rapidly to a nearly constant value which in the case of KI is maintained over a wide range of temperature. Near 1200° the current again begins to rise rapidly, and then somewhere above 1300° suddenly attains a nearly constant value. It is this nearly constant value with which the present paper is mainly concerned. It appears to be the maximum current which the amount of salt passing through the tube can carry, . for it is very little affected by increasing either the tempe- rature or H.M.F. Of course it is possible that with higher temperatures and ere he Electrolysis of Alkali Salt- Vapours. 211 H.M.F.’s than those which it was possible to use in these experiments a further increase in the current might occur ; Fig, 2. 5x io [= I hah iS nee ok, nat Pe 3 CURRENT 0 600 700 600 900 (000 ~—«*H00 i200 1300 ‘1400 but in the absence of any evidence to the contrary, this approximately constant value of the current will be regarded in what follows as the maximum current which the amount of salt used can carry. This current may be conveniently termed the “ saturation ”’ current for the particular salt used. In the following table (p. 212) the values of this maximum current observed with a number of different salt-solutions are given under the heading current (C). The electrochemical equivalent (EH) and the value of the product EC are also given for each solution. The temperature in each case was about 1350° C., and the E.M.F. used 840 volts. It is clear from these results that the saturation current is inversely proportional to the electrochemical equivalent of the salt. The mean value 2°67 x 10-? of the product EC for solutions of 1 gram in a litre is also very approximately one-tenth of the value 2°65 x 10-1 obtained with solutions con- taining 10 grams in a litre, which shows that the saturation oa ee 3 (=e ee al ? 212 Dr. H. A. Wilson on the Laws of current is proportional to the concentration of the solution sprayed. ices | Grams chemical Current, aoe per litre. | Equivalent. C. se | ioe | CE 6: ame He es, 10 168 1511074 | 2:54~1071 Bol i: 0808 10 212 13:5 ,, 285 ikon ee 10 | 166 164 ,, 2728 Ae Nal Eon 10 150 Lavan 2°46 ,, CsCl 2 1 168 1:61, 2-70 x 107? Gs5CO. tie 1 163 161 ,, ye fa ee Bbit.4 takes t 212 1:25 ,, 2°65: |, Bole val 121 2-94 ., 271 te Bb:CO. Vie: 1 115 2-44 ,, 2:30 ,, Wel te 1 166 1-66 ,, 275. b fbr Awe! 1 119 Cae bee 2 S| me ep ae il | 58 AAD ats ae OO Widens. 1 69 4:00 ,, 276 5, Pt OO i Cae 1 150 1-82 ,, 2473... NaBr ........- 1 103 244. ,, PEP. ACL es, 1 59 4°73 ., o7Gi as Wa, CO, 0c 1 53 4:73 ,, sy bee 1 SF Cm ete 1 134 2:03 ,, 272 i LiBr wiireve italia! iL | 87 o12 ? 2°72 ” RN coaceee 1 43 6:25 ,, 2°69 ,, THR@O, 's. see 1 37 748 ,, 27 Te When an electrolyte is decomposed by the passage of a current, then according to Faraday’s well-known laws of electrolysis the amount of salt decomposed is proportional (1) to the amount of electricity carried, and (2) to the che- mical equivalent of the salt. Thus we see that the above results, which show (1) that the maximum amount of elec- tricity transported by a salt-vapour is proportional to the amount of salt passing between the electrodes, and (2) that the saturation current with a definite amount of any salt passing between the electrodes is inversely as the chemical equivalent of the salt, amount to a proof that Faraday’s laws of electrolysis apply also to the saturation current carried by a salt-vapour. To show that the analogy between salt-vapours and electro- lytes is complete, it remains to show that the factor of propor- tionality in the second law is the same for both. ‘To decide Electrolysis of Alkali Salt- Vapours. 213 this it was necessary to make an estimate of the amount of salt passing between the electrodes when a solution of known strength was being sprayed. _ The amount of salt passing through the tube was determined by a modification of the method originally employed by Arrhenius to determine the amount of salt supplied by a sprayer to a flame. A solution containing 40 grams of lithium chloride per litre was sprayed and the air and spray mixed with coal-gas and the mixture then burnt from a brass tube so as to forma Bunsen flame. A Bunsen burner was adjusted so as to give another sensibly equal and similar flame which was placed close beside the first. A weighed bead of fused LiCl was held in the axis of the second flame on a platinum-wire loop and its height in the flame adjusted till the tips of the two flames appeared equally brightly coloured. Under these circumstances the rate of supply of salt to the two flames must be nearly the same, so that the loss of weight of the bead of LiCl measures the rate at which LiCl is supplied by the sprayer. The loss of weight of the LiCl bead was found to be 7 milligrams in ten minutes in one experiment, and 6 milli- grams in ten minutes in another experiment. This gives for the number of milligrams of salt passing through the platinum tube per second when a solution containing 1 gram in a litre is being sprayed :— 6°5 600 x 40 For this amount of any salt we have found experimentally HOS PCC OF, Hence the amount of salt per second of electrochemical equivalent unity which would correspond to a current of 1 ampere is rah Spa ai 2°67 x 107-2 Now 1 ampere in one second liberates in electrolysis 1:04 10-* milligram of hydrogen, so that it appears that the factor of proportionality is nearly the same for salt-vapours as for electrolytes. It is evident that these results prove that Faraday’s laws for the passage of electricity through liquids apply also to =2-7x 10-4. =1°01 x 10~? milligram. (214 = ©The Laws of Electrolysis of Alkali Salt- Vapours. alkali salts in the state of vapour. This must be regarded as very conclusive evidence in favour of the theory that the passage of electricity through salt-vapours is a process very analogous to the electrolysis of salt-solutions. In a dilute solution of such a salt as KCl each molecule of the salt is believed to dissociate into two ions + K and —Cl. According to the corpuscular theory of electricity, if we denote a corpuscle by a, then these ions are K—a and Cl+a. The results described in this paper prove that the amount of electricity which can be transported by salt in the form of vapour isequal to the amount required to electrolyse the ‘same amount of salt in a solution. | | This can be explained on the corpuscular theory in two ways, the first of which involves electrolysis of the salt, whereas the second does not. According to the first the molecules of the salt-vapour dissociate into ions K—a and Cl+« exactly as in a solution. These ions then move to the electrodes and give up their charges, so becoming K and Cl, the K being at the negative electrode and the Cl at the positive electrode. According to the other explanation a molecule of the salt- vapour loses a corpuscle, thus forming two ions, KCl—a and a. Then the KCl—«a goes to the negative electrode and only corpuscles go to the positive electrode, so that no separation of the two constituent atoms of the molecule takes place. The high velocity of the negative ions compared with that of the positive ions seems to favour the latter view; but the known cases in which separation of the elements of a com- pound by electrolysis in gases appears to take place strongly support the view that, the ions are similar to those existing in solutions. | | The present experiments do not show what happens to the ions after they have discharged on the electrodes, except that apparently they do not participate any further in the trans- port of the electricity. Itis hoped that future experiments will throw more light on this question. These experiments were done in the Cavendish Laboratory, and Iam greatly indebted to Prof. J. J. Thomson for his advice and encouragement throughout the course of the work. : get ee i} } XXII. Is Rotatory Polarization influenced by the Earth’s Motion? By Lord Rayueien, /.R.S.* pee question whether the rotation of the plane of polari- zation of light propagated along the axis of a quartz crystal is picked: by the direction of this axis relatively to that of the earth’s orbital motion, is of considerable theoretical importance. According to an investigation of Lorentz, an effect of the first order might be looked for. Such an effect would be rendered apparent by comparing the rotations when the direction of propagation of the light i is parallel to that of the earth’s “hes and in the reverse direction, and it might amount to =,1.. of the whole rotation f. According to Larmor’s theoryt there should be no effect of the first order. The question was examined experimentally many years ago by Mascart §, who came to the conclusion = the reversal of the ray left the rotation unchanged to - Soong part. In most of the experiments, however, the accuracy was insufficient to lend support to the above conclusion. Dr. Larmor (J. c. p. 220) having expressed the opinion that it might be deaths to re-examine the question, I have made some observations which carry the test as far as can readily be done. It appears that the rotation is certainly not altered by s5go00 part, and probably not by the half of this, when the direction of propagation of the light is altered from that of the earth’s motion to the opposite direction. I should scarcely have been able to carry the test to so satisfactory a point, had it not been for the kindness of Prof. MacGregor, who allowed me the use of certain valuable quartz. crystals belonging to the Edinburgh collection of apparatus. These crystals, five in number, are all right-handed, and measure about 50 mm. each in the direction of the optical axis, to which the polished faces are approximately perpen- dicular. They were prepared for Prof. Tait, and were em- ployed by him for his “rotatory polarization spectroscope of great dispersion” ||. For the most part they are nearly free from blemish, and well adapted to the purpose in view. In principle the experiment is very simple, scarcely differing * Communicated by the Author. + This fraction representing approximately the ratio of the velocity of the earth in its orbit to the velocity of light, { ‘AXther and Matter,’ Cambridge, 1900. § Annales de ? Ecole Normale, vol. i. p. 157 (1872) || Nature, vol. xxii. 1880; Tait’s ‘ Scientific Papers,’ vol. i. p. 425, syawe rs Mai i ¥ = from ordinary polarimetry, as, for example, in determining the rotation due to sugar and other active bodies. But the apparatus needs to be specially mounted upon a long stiff board, itself supported upon a point, so that the absolute direction of the light may be reversed without danger of even the slightest relative displacement of the parts. The board swings round in the horizontal plane ; and if its length is directed from east to west, or from west to east, observations taken at noon (in June) correspond pretty accurately to pro- pagation of the light with or against the earth’s motion in its orbit. Similar comparisons at 6 o’clock are nearly inde- pendent of the earth’s motion. In another respect the experiment is peculiar on account of the enormous amount of the rotation to be dealt with. For sodium light the rotation is 22° per millimetre of quartz, so that the whole rotation is 5500°, or more than 15 complete revo- lutions. In the preliminary experiments, with one of the crystals only, sodium light was employed; but the observations were unsatisfactory, even although the light was resolved into a spectrum. If the flame was well supplied with salt, the extinction of the D-iine by suitable adjustment of the nicol still left the neighbouring region of the spectrum so bright as to prejudice the observation by lessening the sensitiveness of the eye. This effect, which is quite distinct from what is ordinarily called the broadening of the D-lines and can be made still more pronounced by stimulating the flame with oxygen, does not appear to present itself in any other method of observation, and is of interest in connexion with the theory of luminous emission. A very moderate rotation of the nicol revives the D-lines sufficiently to extinguish the neighbouring spectrum, just as the first glimpse of the limb of the sun after a total eclipse extinguishes the corona *. When all five quartzes were brought into use it was hopeless to expect good results from a soda-flame. From the fact that the rotation is as A~? we see that there must be 11° difference of rotation for the two D-lines, so that a satisfactory extinction is out of the question. For the observations about to be recorded a so-called vacuum-tube, charged with helium, was employed, the yellow line (situated close to the D-lines) 216 Lord Rayleigh: Js Rotatory Polarization * July 6.—A doubt having suggested itself as to whether this effect might not be due to an actual whitening of the Bunsen flame, such as sometimes occurs rather unexpectedly, the experiment was repeated with a flame of pure hydrogen. The region of the spectrum in the neigh- bourhood of D was even brigliter than before. Anattempt to produce an analogous effect with lithiwm was a failure, apparently in consequence of insufficient brightness of the flame. — injluenced by the Earth's Motion ? 217 being chosen. It was actuated by a Ruhmkorff coil and four Grove cells, situated at some distance away. The various parts, all mounted upon the pivoted board, will now be specified in order. First came the helium tube with capillary vertical, then at a distance of 25 cm. a collimating spectacle-lens, followed by the polarizing nicol. The field of view presented by this nicol was contracted to a circular aperture 7 mm. in diameter, and was further divided into two parts by a “sugar-cell.” This cell was the same as that formerly used in a cognate research on the rotation of the plane of polarization in bisulphide of carbon under magnetic force *. ‘The polarimeter employed is on the principle of Laurent, but according to a suggestion of Poynting (Phil. Mag. July 1880) the half-wave plate of quartz is replaced by acell containing syrup, so arranged that the two halves of the field of view are subjected to small rotations differing by about 2°. The difference of thickness necessary is best obtained by introducing into the cell a piece of thick glass, the upper edge of which divides the field into two parts. The upper half of the field is then rotated by a thickness of syrup equal to the entire width of the cell (say 4 inch), but in the lower half of the field part of the thickness of syrup is replaced by glass, and the rotation is correspondingly less. With a pretty strong syrup a difference of 2° may be obtained with a glass 3°; inch [inch =2°54 cm.] thick. For the best results the operating boundary should be a true plane perpendicular to the face. The pieces used by me, however, were not worked, being simply cut with a diamond from thick plate glass ; and there was usually no difficulty in finding a part of the edge sufficiently flat for the purpose, 2. e. capable of exhibiting a field of view sharply divided into two parts. . By this use of sugar, half-shade polarimeters may be made of large dimensions at short notice and at very little cost. The syrup should be filtered (hot) through paper, and the cell must be closed to prevent evaporation.” The light next traversed the quartz crystals, each mounted upon a small stand admitting of adjustment in azimuth and level so as to bring the optical axis into parallelism with the line of vision. The analysing nicol, mounted near the end of the board, was distant 102 cm. from the polarizer. After passing the nicol the light traversed in succession a direct- vision prism of sufficient aperture and a small opera-glass focussed upon the sugar-cell. The aperture limiting the field had been so chosen that, as seen through the spectroscope, the * Phil. Trans. clxxvi. p. 343 (1885) ; ‘ Scientific Papers,’ vol. ii. p. 363. 218 Lord Rayleigh: Zs Rotatory Polarization yellow image under observation was sufficiently separated from the neighbouring red and green images corresponding to other spectral lines of helium. The position of the analysing nicol was read with a vernier to tenths of a degree—an ac- curacy which just sufficed, and the setting could be made by causing the two halves of the field of view afforded by the sugar-cell to appear equally dark. A good deal of time was spent in preliminary experiment before the best procedure was hit upon. It is necessary that the optic axes of the crystals be adjusted pretty accu- rately to the line of vision, and this in several cases involved considerable obliquity of the terminal faces. In these adjust- ments the sugar-cell and its diaphragm are best dispensed with, the crystals being turned until the rotation required to darken the field is a minimum and the darkness itself satisfactory. When the first crystal has been adjusted, a second is introduced and adjusted in its turn, and so on. In some cases a further shift of the crystal parallel to itself was required in order to remove an imperfection from the part of the field to be utilized. In the end a fairly satistactory darkness was attained, but decidedly inferior to that obtainable when the quartzes were removed. Fart of the residual light may have been due to want of adjustment; but more seemed to originate in imperfections in the quartzes themselves. In my former experiments upon bisulphide of carbon advantage was found from a device for rocking the plane of polarization through a small constant angle*. During the observations now under discussion this effect was obtained by the introduction of a second sugar-cell, not divided into two parts or seen in focus, just in front of the analysing nicol. The cell was mounted so that it could slide horizontally in and out up to fixed stops. The thickness of the cell being sufficient, the strength of the syrup was adjusted to the desired point. Thus when the nicol was correctly set, the upper half of the field was just distinctly the brighter when the cell was zn, and the lower half with equal distinctness the brighter when the cell was out, the object to be aimed at in the setting of the nicol being the equality of these small differences. For the results now to be given the setting of the nicol was by myself and the reading of the vernier was by Mr. Gordon. A second observer is a distinct advantage. As aspecimen, chosen at random, I will give in full all the * Loe. eit. ; ‘Scientific Papers,’ vol. il. p. 366. 9) tS nd influenced by the Earth's Motion ? 219 readings made in the neighbourhood of noon on June 19. Five readings were taken in each position and then the board was reversed. The headings “ Hast” and “ West” indicate the end at which the observer was sitting; “ Hast” therefore meaning that the course of the light was from West to Hast. TaBLeE I. Time 115 30™,|Time 115 50™,) Time 12" 5™, |Time 125 15™,/Time 122 25™. Temp. 17°-4. | Temp. 17°-7. | Temp. 17°9. | Temp. 17°°9.| Temp. 17°°9. | Sore) | West. | Seon ee East. Betis) wnat 45°6 - 45:9 460 | 45°5 45-9 48 | 457 | 464 | 45°5 45-4 455 | 459 461 | | 456 45°7 456 | 457 46:0 | 456 457 | 457 45:8) AGO | | 45°58 45°62 | sue | 4580 | 4604 | } The mean of the three “ Hasts ” is 45°75, and of the two “Wests” is 45°71; so that H-—W= +:04°. All these numbers are in decimals of a degree. The pro- gressive alteration in the readings corresponds to the rise of temperature. It would appear that, as was natural, the quartzes lagged somewhat behind the thermometer. Taste [I.—Noon. | | | / Date. | K-—W. H | June RE a Sa 4-03 Poe eer, paahe G —'05 i Nae! Moa cs aun Breieas +04 Bean wis. 2 d5,82. | +007 Three sets of observations were taken at noon, and the results are recorded in Table II, In two other sets taken 220 R. Straubel: Haperiments on the about 65 the differences E—W were even less. The com- parison of the two hours serves to check possible errors, é. g. of a magnetic character, such as might be caused by the magnetism of the Ruhmkorff coil, if insufficiently distant. _ It seems certain that at neither hour does the difference K—W actually amount to 3; of a degree, 7. e. to =p a5 of the whole rotation. In all probability the influence of the reversal is much less, if indeed it exists at all. P.S.—-Since the above observations were made, I see from the Amsterdam Proceedings (May 28, 1902) that Lorentz maintains his opinion against the criticism of Larmor. Lorentz’s theoretical result contains an unknown quantity which might be adjusted so as to make the influence of the earth’s motion evanescent; but for this special adjustment there appears to be no theoretical reason. I hope that the above experimental demonstration of the absence of effect, to a high order of accuracy, will be found all the more interesting. XXIII. Hxperiments on the Electro-thermal Effect in Tourmaline. By R. STRAUBEL*. S was first shown by W. Thomson in 1877, from thermo- dynamical considerations, there corresponds to the pyro-electric phenomenon—2. e. the electrification produced by a uniform rise of temperature—a reverse effect, namely, a temperature change due to a variation of the electric state. If a pyro-electric crystal be brought into an electric field so that the lines of force run from the analogous to the anti- logous pole, it will be heated ; if the orientation of the crystal in the field is reversed, a cooling will take place. On the effect so predicted by theory 1 carried out some experiments about two years ago, using a Brazilian tourma- line. These experiments, though only qualitative, will be briefly described in what follows. Four plates, each 0°2 cm. thick, were cut from the tour- maline crystal in a direction normal to its axis. The plates were then arranged in two pairs, in one of which the ana- logous poles, and in the other the antilogous poles, were uppermost. Between the plates of .each pair was introduced one set of junctions of a home-made thermopile of ten elements, made of fine wires of constantan and iron. The _ * Translated from the Nachrichten der K. Gesellschaft der Wissen- schaften zu Gottingen, Mathematisch-physikalische Klasse. 1902. Heft 2. sO Electro-thermal Effect in Tourmaline. 221 thermopile was flattened by being placed between two plane hardened steel plates which were subjected to hydraulic pressure ; it was coated with a thin layer of shellac to obtain insulation between neighbouring wires. The plates and thermopile were fitted between the two horizontal plates of a condenser in a vulcanite box 1 cm. bigh and 12 cm. in diameter, the end-wires of the thermopile being brought out through the curved surface of the box. With the d’Arsonval galvanometer employed, one scale- division corresponded to 1°83x10-® ampere, or, since the resistance of the galvanometer and thermopile amounted to 8°59 ohms, to 1°57 x 10-7 volt. If we take the thermoelectric power of the iron-constantan combination to be 53x 10—* volt, then one scale-division represents a temperature-dif- ference between the two sets of junctions of 0°3x10-* degree C. | The small single-plate influence-machine used in the ex- periments had its circuit either open or closed by a cylinder of wood. Between the influence-machine and the plates of the condenser was inserted a paraffin commutator, which also allowed of the short-circuiting of the condenser. The poten- tial-difference between the plates of the condenser—which were placed 1°35 cm. apart—was maintained as high as was consistent with steadiness; in the majority of the experiments it was estimated at some 30,000 volts; it might, however, have departed appreciably from this value, as the estimate was based on the spark-length between spheres of 2 cm. diameter, and determinations of this could only be made before and after the actual observations. The observations were made as follows:—As soon as the electric field was established, the galvanometer gave a de- flexion whose direction depended on that of the field. This deflexion reached a maximum in about half a minute, and then fell to zero in about four minutes. As soon as this hap- pened, 7. é.as soon as no appreciable movement of the spot of light could be noticed, the field was reversed, the maximum deflexion to the other side of zero observed, and so on. The following is such a series of observations; the scale-divisions were 2 mm. ones (p. 222). The extreme two columns on the right are obtained by subtracting the immediately preceding zero reading from the maximum elongation. Such a set of observations having been obtained, one or other of the two pairs of plates was reversed, so that now all the plates had their analogous poles pointing in the same direction. Under these conditions no deflexion was observable ae te ae ae 222 ~R. Straubel: Experiments on the . Zero | Elongation, reading, Elongation. | Maximum deflexion, in scale-divisions, 239°4 245 +56 289°4 235 —4°4 239 243°6 +4°6 | 232°7 —53 236°3 . 240°6 +4:3 236°6 231°7 —4°9 235 +5°7 240°7 | 237 —4:9 23271 +43 237 241-4 ae —- Mean —4'9 +49 on establishing a field, since the same temperature change occurred at both sets of junctions. The following set of observations was obtained immediately after the set given above :— Zero Elongation. reading. Elongation. | Maximum defiexion, in scale-divisions, 234 2344 +04 233°7 234 +0°3 234 234-2 +0°2 234 233°7 —03 234 . 2345 +0°5 234-4 234°6 +02 2348 2348 +00 234 . 234 0:0 234'8 | 2343 —05 2346 235 +04 Mean +0'1 +0:1 Similar results were obtained by inclining the vulcanite box, thereby displacing the plates so that the junctions of the thermopile were no longer between the plates. ‘This was more convenient, as it did away with the necessity of touch- ing the plates, and it was unnecessary to wait a long time before thermal equilibrium was established. Electro-thermal Effect in Tourmaline. 223 As regards the interpretation of the observations, I should like to offer the following remarks:—There seems to me to be no doubt that we really have to deal here with the electro- thermal effect sought for. In support of this view we have in the first place the regularity with which the effect changes its sign with a reversal of the field. In none of the observa- tions has this change of sign failed to take place. Further, where no effects were to be expected, none occurred, or only insignificant and irregular ones. Lastly, the magnitudes are, for fields of approximately equal intensity, equal. Three more extended series of observations, which were compara- tively free from disturbance—z. e. from considerable changes in the zero—gave the mean vaiues 4°3, 4°5, and 4°1 scale- divisions (2 mm. ones). The slow falling-off in the deflexion which takes place with . a constant P.D. between the condenser-plates is evidently to be accounted for in the following way, which is also in accord with other considerations. With the establishment of an electric field there occur the temperature changes in the two pairs of plates, there being a rise of temperature in one pair and a fall in the other. The junctions begin to respond to the temperature changes in their surroundings, and the galvanometer gives a deflexion. But the electrical conduc- tion along the tourmaline surface comes into play the instant the field is established, and by the formation of surface charges neutralizes the electrical action of the field on the tourmaline. In proportion to the amount of this action, however, the temperature-change will, of course, be reversed. The greater part of the actually occurring temperature- equalization is thus probably brought about by a decrease of electrical excitation rather than by radiation or conduction (although the metallic connexion of the two pairs of plates by the thermopile might produce a perceptible effect). As regards the amount of the observed electric change of temperature, it may be remarked, in conclusion, that since the d’Arsonval galvanometer was damped so as to be aperiodic, it will be sufficient for the purpose in hand to multiply its deflexions by half the value of the constant given above for the degree value of a scale-division. This gives, in the ex- ample considered, a temperature change of 0°74 x 10-3 deg. ©, for each pair of plates, a number which, so far as the order of magnitude is concerned, is in sufficiently good agreement with the value demanded by theory. Jena, February 20, 1902. Aha: 9 XXIV. A High Pressure Spark-Gap used in connecion with the Tesla Coil. By ¥, J. Jervis-Suitu, W.A., FR.S.* N October 1896 I showed that an 2#-ray-photo could be produced by means of an exhausted bulb having no terminals, and in January 1897 the relationship between the position of maximum activity at the bulb and the dis- charge from a Tesla inductor was described. The references are p. 994, vol. liv. and p. 294, vol. lv. ‘ Nature.’ Again returning to experiments with exhausted bulbs having no terminals, I wished to improve the Tesla inductor formerly used by me. When a spark-gap is employed in air at normal or less than normal pressure, the sparks often leap from ball to ball, not by the nearest path, but through a rather long one of curved form [the ends of the curved path often terminating in the equatorial regions of the two balls], the discharge from the secondary coil at the same time being somewhat reduced. With this before one it seemed highly probable that far better results would be obtained if the spark-gap were subjected to pressure. In order to put this to the testa spark-gap was constructed as shown in fig. 1, where B is a glass vessel closed with a A 8 ae i FIGS: wy ) edt JBo Fic.é A “ills ee } F163 Fic. /. Co | Vv metal lid L, provided with a stuffing-box through which a screwed rod can be moved by means of a micrometer head M; the rod carries the upper ball, the lower ball is attached to a rod which passes through a plug in the bottom of the vessel; a tube T and a pressure-gauge G are attached to the lid, and also to an air force-pump (not shown) ; one end of the pri- — mary coil P is attached ‘to the lid and the other end to the condenser C. The two sides of the condenser are connected to the secondary of an induction-coil, by the wires J, I. 8 is * Communicated by the Author. On a High Pressure Spark-Gap. 225 the secondary of the Tesla inductor, and the discharge takes place at D. In one experiment the balls in B were placed 0°3 em. apart, and the distance between the terminals at D was 70 cm. The pressure was normal. When the induction-coil was started only a luminous brush of very thin sparks crossed at D. The distances remaining the same in B and at D the pressure in B was raised to 75 em. of mercury ; shortly before this pressure was reached, a torrent of thick sparks passed at D, at the same time the sparks in B became compact and exceedingly bright. On removing the pressure the discharge returned to its former condition. Some of the effects produced by the discharge, though by no means of great length in air, were as follows: — A vuléanite tube 0°45 cm. thick in the wall was placed in paraffin oil, a wire from one terminal being placed within it, and outside it was placed a wire from the other terminal; on putting on the current the vulcanite was instantly perforated by the discharge. Next a piece > of plate-glass 0: 4 em. thick was placed in the oil, the terminals being placed face to face on either side of it. The instant the current was put on the glass was perforated without being cracked. On replacing the thick glass by a sheet of half the thickness, and repeating the experiment, a nearly round hole (0:2 cm. in diameter) was made by the discharge. In each case the conductor in contact with the glass was pointed. A thick piece of plate-glass was also cut through and divided into two parts by means of the discharge. The sheet of glass was placed on a sheet of tinfoil in a flat vessel, such as a photographic developing dish, and covered to the depth of about 2 em. with oil, the foil was connected to one terminal, then on ruling a line with the other terminal on the plate-glass as rapidly as the hand could move it, the glass was found to be cut through under along the path of the terminal. The discharge so produced, by the addition of the high pressure spark-gap, i is very effective when used to excite the Rontgen effects in exhausted tubes and bulbs having no ter- minals. A bulb (fig. 2) was placed in the line of discharge, the distance between B and C being so arranged that but little discharge passed before the introduction of the bulb ; when the apparatus was in action a vivid green glow was produced on the lower side of the bulb at A. In my early experiments in 1896 I used bulbsiof about 4 cm. in diameter, The pictures were fairly good. I now find that in order to obtain sharp definition the bulb should be small, about 1:5 em. Phil. Mag, 8. 6. Vol. 4. No. 20. Aug. 1902. Q 226 Mr. J. W. Peck on the Steady in diameter, and placed about 17 cm. above the object to be a-ray-graphed. [Time of exposure two to three minutes. | Another way (fig. 3) of exciting the effects is to place a flat spiral of wire S above the bulb, the spiral forming a portion of the secondary circuit of the Tesla inductor, pro- vided with a spark-gap having spherical terminals. If a long exhausted tube (fig. 4) (30 em. long, 1°5 cm. diam.) be excited in any of the ways mentioned, at A, anda conductor be placed close to or in contact with the tube at B, then the 2-ray effect will be found opposite to B, acting approximately in the direction C. The apparatus here described is now being reconstructed so that much greater pressures may be used in the spark-gap . vessel, but even with the pressures already reached the dis- charge from the secondary of the Tesla-coil is enormously increased. June 18, 1902, P.S.—I also find that the high-pressure spark-gap, when placed in the secondary of an ordinary induction-coil, increases its effects considerably when used as a generator of Hertz waves. A exp(—A,2)Jo(A.7), + 6 « (9) where the constants A, must satisfy the equation MSE Behe) i eit le do illieChey V being the constant temperature of the hot end, and As a root of the transcendental equation pore 1, ha) 05g de, Gd Now | i er | Jo(Ar) =1— ye T pag ed . e (12) and hence to approximate, suppose Ar so small that second and higher powers may be neglected. The justification of this hypothesis will be shown later. We have therefore trae 2 The surface equation therefore becomes J(Ar)=1 - oro) | ae — ah oie (13) 2 pis +e=0), * Théorie Analytique, chapter vi. 230 Mr. J. W. Peck on the Steady giving — If we oki this value of in the solution, take Ji 0 E(e = ae choose the negative sign so as to make v a when x =f infinite, we get BO ae v=Vexp(—24 ze ee 18) asa first. approximation. This. result is the same as the Fourier solution. The condition of this approximation is that Aa (and hence Ar) should be so small that x and higher pore may be & neglected. By (14) we therefore must have = 9 ay ° ro J small. From this, or from a consideration of the inne of the quantities, it is evident that the ratio k/e has the dimensions of alength. This Jength has of course no connexion with the dimensions of any particular piece of the substance under consideration, but is a quantity characterizing the thermal. properties of the material so far as conduction and radiation are concerned. To. this length a definite physical meaning may be given which is of importance in the problem under. consideration. In the first place let a large homogeneous slab of the substance have its parallel plane faces maintained permanently at unit temperature difference. Steady flow of heat will take place along straight lines perpendicular to these faces, and the temperature gradient will be uniform, 2. é. the decreasing temperatures form, for equal space steps, an arithmetical progression. -Let the quantity of heat that passes per sq. cm. per sec. across any isothermal (a plane) be noted. In the second place, let heat radiate from the surface of the substance and let definite conditions as to the coating of the surface, the pressure and nature of the surrounding medium be specified. et also the temperature difference between the surface (supposed an isothermal if more than an elementary part is considered) and the medium be unity, 2. ¢. the same as that between the faces of the slab in the first case. If now the thickness of the slab in the first case be so adjusted that the quantity of heat conducted per sq. cm. per sec. in the first case is the same as that radiated in the second case, then that particular thickness which gives this equality is the length 4/e. This can be easily proved by a consideration of * Temperatures of a Thin Rod. . 231 the elementary equations of conduction and emission, viz.:— U1 a= Vg Fi a G=% ear ce OSe(o,— vu, 0A wtp 405 (16) subject to the conditions above specified. he number thus obtained is a constant for a substance of given conductivity with its radiating surface under definite conditions ; and by its means is expressed the relationship of the conducting and radiating powers necessary in the present problem. This thermal constant will be called, for convenience of reference in this paper, the thermal length modulus of the substance. If we symbolize this length by L, the Fourier result may be stated in the form r=Vexp(—2|4/ 1"), Ua lula (17) ve with the following two restrictions :—(1) the semi-radius of the rod must be small in comparison with the thermal length modulus ; (2) the geometric mean of these two lengths must be small in comparison with the length of the rod. The first restriction is the condition of the approximation from the rigorous solution for the cylinder referred to in equation (9) above. The second is evident if we consider that the practical realization of the infinitely long bar of the problem is that the radiation at the cold end should be a negligible quantity. The following table gives approximate values of the thermal length modulus, in centimetres, for various substances. Two values are given in each case, corresponding to the extreme | Substance. Conductivity.| | Thermal Length Modulus. | 2 5 a eee 1-09 3630 5450 | Copper .....0-..---...0.. ‘98 3270 4900 nates i 2 ELIA) Td. *30 1000 1500 as es ctadaenshdes "26 870 1300 ete ee od as “15 500 750 German silver ......... ga | 370 550 Mone oe) At: 083 280 415 ADHIMIONY gicids sce. .cou 042 140 210 Rose’s Metal .. ......... 038 130 190 Wood's Metal ......... 027 90 135 Bisriteible Nae oe it ‘018 60 90 : | L CRPATR Ee ee oo ae 007 23 | 35 Marble 005 teens | 25 Oak Pitch FA ed oi > 004 13 20 ) Ginga watistodacie... 002 7 10 | Parnigg- se. 0006 2, 3 | Sulplige (ca |....., ‘0004 | 1 2 eee Be SE ass ed is 232 Mr. J. W. Peck on the Steady values of the emissivity 0°0003 and 0:0002 respectively. The temperature difference of radiating surface and medium is here supposed not to exceed a few. degrees, so that the Newtonian law of cooling is applicable. Thus for any substance to which it is proposed to apply the Fourier solution there are four lengths to be taken account of, viz. the semiradius (a/2), the thermal length modulus (L), the geometric mean of these two, and the length of the bar ((). In experiments on a series of these substances a proper pro- portioning of the bars so as to give the ratios a/2: L, and /aL/2:l, the same for all will give the same degree of | approximation in all the cases. Of course it is to be noted that the equations (6) above would not now be applicable, inasmuch as they assume equality of radius of the bars under comparison. “But the modified forms are easily arrived at and are not much more complicated. The next point is the numerical values which should be assigned to these two characteristic ratios. According to Lord Kelvin (incyc. Britann. Article “ Heat,” § 78), for an iron bar the Fourier solution may be applied with safety for all radii up to5 cms. Beyond this the radial temperature- gradient would become perceptible, and therefore the solu- tion inapplicable. Taking this as a basis, the characteristic fraction a/2:L is 1/224. With the refined thermoelectric measure of temperature now available, this value should cer- tainly not be exceeded. As to the second ratio a value of 1/5 is sufficient ; for if the length of the rod is five times the value of “ La/2, the ratio of the cold end temperature to the hot end temperature is 1/148, and therefore the end radiation is negligible for all ordinary experimental methods of heating. It will be seen from the above table that the first criterion is satisfied for most of the metals for bars say up to 5 ems. in radius, though for the metals of inferior conducting power the point would become of importance with refined measure ~ or temperature. It is moreover impossible to diminish the radii of the bars in the same proportion as their thermal length moduli, so that the error becomes increasingly great as we descend the list, and when we come to the non-metals is sufficiently large to vitiate the method altogether. For example, Despretz*, in the account of his experiments, states that the law of the drop of temperature in geometrical pro- gression is not well satisfied for lead and the inferior metals. He used square bars of edge 2°4 cms.,.and. blackened or varnished the surfaces ; so that for bismuth, say (assuming * Ann. de Chimie et de Physique, t. XXXV1. Pe 422 (1827). Temperatures of a Thin Rod. 233 that some characteristic fraction of about the same order of magnitude holds for a square bar), we have the first ratio about 1/100. Despretz also employed the method to deter- mine the conductivity of marble, porcelain, and other non- conductors, but got completely discordant results. The fraction (v,;+13)/v2, which should be constant for the same bar, varied from 10°83 to 3°87 for marble. From the table we see that the characteristic ratio for marble is for the size of bar employed by Despretz about 1/30, a value much too large for the solution to be applicable. The experiments of Wiedemann and Franz* illustrate the need for the second criterion. They used much thinner bars (0°4 to 0°6 cm. in diameter), and the observations were con- fined to metals only, so that for both these reasons the first condition is satisfied. But no attempt seems to have been made to choose appropriate lengths for the different sub- stances. All the bars were made 50 cms. long, so that the second condition is not satisfied. In the account of the ex- periments they state that the expression (v,;+73)/v2 does not, for the highly conducting substances, vary appreciably from 2, and that therefore the values of the conductivity for these substances are not very reliable. This value 2 implies that the curve of temperatures is not logarithmic but rectilinear, the arithmetical progression has taken the place of the geo- metrical progression ; in other words, the lateral radiation is non-ettective, and the end radiation is effective in producing the temperature drop, so that the conditions of the problem are not satisfied. If we work out for the length employed (50 cms.) and for the case of copper (taking the larger value of. the thermal length modulus since in these experiments the bars were plated) we find the characteristic fraction a/ ee : J to be about 1/2, 2. e. the condition is not satisfied. The same holds true in a worse degree for the silver bars employed in these experiments. Of course this method is not now regarded as satisfactory except for the highly conducting substances, and in several places f we find it stated that the conductivity should be large and the cross-section of the bar small. But so far as l can find these two relationships of the four lengths are not given. To say that & is to be large and a small gives an approach to the conditions ; but to get an exact idea of the * Ann. de Chimie et de Physique, t. xli. p. 107 (1854). + Kelvin, Article “‘ Heat,” in Encyc. Britann. §78; Tait, Text-book on Heat, p. 215. . 234 Mr. J. W. Peck on the Steady approximation it is necessary to have a comparison of quan- tities of similar dimensions. This is done here by expressing the k, e relationship in the form of a length, and for a series of rods we have thus a method of proportioning the dimen- sions so.as to get results of the same order of exactitude in all the cases. Since the Fourier solution begins to be inexact when we get down the list say as far as bismuth (on account of the impossibility of thinning down the bars to the proper size) a second approximation becomes desirable. It may be arrived at as follows: taking one additional term in the values of J (Ar) and on , we have | 27? Jo Ar) =1— 4? : 08 0p. Bee (18) Od .(A7) Mr Ar? The surface equation (8) therefore becomes ka’h' — 4a(2k + ea)? + 16e=0, or | _ 2(2k +ea) +2 VAP $e? Q x ka? ; ‘ ea? on 4h+2ea+ (41 ~ OF ai ka ‘es i: | Replacing : by L we have, after some reductions, the two values for A?. | 16L? + 4aL4 a? AaL—da? 27 li? P meee Denoting these by 4”, Ay*, we have as solution AV + To determine the constants A and B we have a 27? ( Neer? V=A( = gee 1-2 ) and, therefore (since this must hold for all values of » when #18 zero) . (20) Pa ed )+B exp (—)s2) ee 7 yeu) v=A exp (—Ayz) (1- Ad Be Ve Ane Bee 0, Temperatures of a Thin. Rod. 235 These give 2 . she ja: AV B= AV Nye — Ne” hea vas and the complete solution on this second approximation is therefore V= saa? aad exp (—A22) pai ) 27? SS cna) (1- - I. . (23) For an axial point at distance z = oe [A exp(—Agr) —A exp(—Ayz)]. « (24) Numerical calculation will show that in most cases A. exp(—A x) is negligible in comparison with 2,7? exp (—A.#) unless # be small. The following table of values is cited in illustration for the case of bismuth bars of two different radii. L is taken as 60 cms. [or substances for which L is greater or a is smaller, the relative magnitude of the two expressions is still smaller. eal ee d,? exp (—A,7). | A,” exp (—A,2). i I D o a, 0:4645 09-0040 | be 1 “ast ieembeain | ),2=0°5085 : 5 03233 |: 000028 d,?=0-0082 ats | black: A,=0°09055..) | 20 | 0-0832 | 0°000000005 = | pay we ) 1 | 6-695 | 0-0019 | d,2=8°0335 | 5 | B23 ~ 000000002 d,?=0-0332 | | x —2-9944...}| 10 | 1299 i ee | X,=0'1822...) | 20 | 0-210 | 00,,8 | | All lengths are expressed in centimetres. The result (23) may therefore be taken : af pr = t= ie [ a2? exp (—Aozx) (1-* — Ver. The family of isothermal suifaces will therefore be given by Ne =a parameter, 236 Mr. J. W. Peck on the Steady or pe ye + . sae Ws ec 2 Saat oo where ¢ is a parameter depending upon the temperature of the isothermal considered. We have, therefore, a family of sinilar coaxial paraboloids of revolution. Their concavities are towards the hot’end, their common axis is the axis of the cylindrical rod, and the distance from focus to vertex (AS) Ber pitch = : 2 This constant of the family, AS or a has by (20) the 2 ° value aLW 2 VW 4al—a?’ Vie eee Jick nl In the diagram these paraboloidal surfaces are shown to scale for the case of a bismuth rod of 4 cms. radius. Close to the origin this form is deviated from because there A,’e—\* becomes comparable with ,"e—%", and at the origin we have the isothermal surface becoming, of course, a plane. The greater L is for a series of bars of substances under similar thermal conditions the greater is the value of the constant AS, and therefore the paraboloids approach more nearly to the planes of the first approximation. or \\ HH , Isothermals y= —44e+C. Lines of Flow y= Ae?/22, In this second approximation the four characteristic lengths are the semi-radius (a/2), the thermal length modulus (L), the distance from focus to vertex of the paraboloidal surface Temperatures of a Thin Rod, 237 (As or x) and the length of the bar J. Similar state- ments as to their ratios must hold as in the first approxi- mation. : The lines of flow (shown in the diagram) are given by the conjugate family of logarithmic curves | YODA NGE A) mS yc.n yee enero) where A is a parameter. The following table gives numerical values for the tem- peratures at the axis and at the surface for bismuth rods of radii 4 cms. and 1 em. respectively. For calculation the formula ite rae [au? exp (—)o) (1 _ xy] is employed, and the results of the preceding table may be used. It will be seen that even for the rod of smaller radius the difference between the surface and axial values is quite appreciable, although the curvature of the isothermals would not show in a diagram of the same scale as that given for the larger radius. The rod is supposed to have its hot end kept at 100°, | P| Axial | Fourier! Surface : 5 value, value. | value. (| 1 | 928 | 913 | 898 jae eos ; | 5 | 646 | 634 | 62:5 Va100°2|| 10 | 411] 401, | 398 | (| 20 | 166 | 161 | 161 | 837 | 833 | 830 }L=60......}| 5 | 404 | 401 | 400 aioe | 10 | 162 | Jel | 361 | (| 20 | 26 26 | 2-6 The only other conductivity measurement of interest in this connexion (beyond these of Despretz and Wiedemann and Franz) is that of Angstrém; for in the Forbes and Tait method, though bars are used, yet the calculation goes direct to the fundamental definitions, and does not employ the Fourier formula, while in the Berget method and several others radiation is avoided altogether. In the periodic method 238 Mr. Blakesley on a Method of obtaining @ from of Angstrém the effect of radiation is minimized by (1) using bright bars, (2) by making the period of the end variation small, (3) by measuring axial temperatures of a fairly thick rod. The radiation can be made negligible while the essence of the method is not affected. In the class ot problems here considered, on the other hand, if we diminish the radiation beyond a certain point we nullify the thermal equation alto- gether, ahd ‘get a° problem requiring a different treatment. The essential point is that the radiation should be small, but not so small as to be ineffective. I have to acknowledge with pleasure kind suggestions and criticisms from Professor Gray in the preparation of this paper. Glasgow University, May 8th, 1902. BP SES, Se $y XXVI. On a Method of mechanically obtaining @ from the Hyperbolic Trigonometrical Functions of 6. By T. H. BuaKEsLeEy, /,A., M.Inst. C.E.* KT ABC bea triangle having a right angle at C; and let a, b,c be the sides opposite the angles A, B, C. Let b be constant. Fig. 1. co The point B is supposed to travel from the point C, and therefore a is the independent variable. D is a point in this line of motion infinitesimally near to B, and B E isia perpen- dicular from B upon the line A D. : Then it is clear that if @ is such a quantity that a=b shin @, it will also be true that c =bh cosh 8, because @—a?=l?, * Communicated by the Author, the Hyperbolic Trigonometrical Functions of 9. 239 d shin @ dé SEM Why Seb cosh BB see 9 3@=bshin 0.30. .69. =bcoshé. 80; Also DB=Sa=0.8shiné=). And the triangle B E D being similar to the triangle A © B, BE _ DB _ 6. cosh gy _ 9 b ¢ ¢ Therefore @ can be obtained by summing such small elements as BH, and dividing the result by 6. BH, in fact, is that component of the motion of B which is at right angles to AB. seein 2, L/NE OF MOTION fruzinGg EOGE Suppose that at the point A there is a circular pin ina drawing-board, but capable of moving round a vertical axis exactly coinciding with the geometrical point A. In the head of this pin is a horizontal slot in which a var slides. This bar is enlarged at one end, as shown in the sketch, so as to carry a small wheel moved, by friction against the board, about an axis exactly coinciding with the centre line of the bar. It will be clear that the movement in arc of a point in the circumference of this wheel will give the quantity >(BE) or 6. if the point of contact of the wheel with the board is carried along CB. If the circumference of the wheel is equal to b, the turns of the wheel will give 0, and these may be given by arrangements (not shown in the sketch) similar to those in Amsler’s planimeter. 240 Mr. G. J. Parks on Heat Evolved or The enlargement necessary to carry the wheel may be conveniently made circular (at least in the portion remote from A) round the point B as centre. In this case it will be avg moved along a ruling-edge set parallel to the motion of B. The bar may be graduated in units of b from the point B as zero, and the slotted pin-head may have a vernier for reading coshé@. Of course CB on the same scale will be shin 0. XXVIL. On the Heat Evolved or Absorbed when a Liquid 1s brought in contact with a Finely Ihvided Solid. By G. J. Pargs*. I. Inrropuction. OUILLET ¢ discovered the fact that when a powder is put into a liquid which does not exert any solvent or chemical action upon it, there is a rise of temperature. In somé of the experiments made by Pouillet with mineral substanées, the rise ‘of temperature varied from °3° to 1° C, This discovery was confirmed by several other investigators, but nearly all the earlier observations were merely thermo- metric, and are therefore of little value for purposes of com- parison, since the rise of temperature must obviously depend on the thermal capacity of the whole mass throughout which the heat is distributed. In fact, by suitably varying the con- ditions of the experiment it has been found possible to obtain any rise of temperature up to 30° C. or more. Junck { found that when sand is placed in water the tem- perature of which is above 4° C. there is a rise of tempera- ture, and when the temperature of the water is below 4° C. a= A . y, i there is a fall of temperature. This is quite in accordance. with what would be expected on the supposition that the Pouillet effect is due to a pressure at the surtace of the powder, and the variation of pressure for a given variation of tem- fs 3 aT, T oie where a is the coefficient of expansion of the liquid at con- stant pressure, p the density, ¢ the specific heat, t the absolute temperature, and J the mechanical equivalent of heat. Meissner § showed that when certain powders are placed perature can be calculated from the equation dp= * Communicated by the Physical Society: read June 20, 1902. + Pouillet, Ann, de Chim. et de Physique, xx. p. 141 (1822). t Junck, Poge. Ann. cxxv. p. 292 (1865). § Meissner, Wied. Ann. xxix, p. 114 (1886), Absorbed on contact of Liquid with Solid. YA1 in water at a temperature below 4° C., a rise of temperature is observed, and he accordingly rejected the physical hypo- thesis of surface pressure, and adopted a chemical or physico- chemical hypothesis which had been advanced by Cantoni*, and which has been more fully developed by Martinit. It has, however, been pointed out that the experiments of Meissner do not disprove the validity of the hypothesis of surface pressure, for as the pressure increases the point of maximum density of water is lowered, and at a pressure of about 200 atmospheres the point of maximum density of water is at or near 0° ©., as shown by Tait, Amagat, Lussana, and others {. Lagergren § has shown that the pressure at the surface cf silica and water would, from the above equation, amount to some thousands of atmospheres. Martini, on the other hand, is unwilling to admit such an enormous pressure at the surface, and he supposes that, just as some solids are dissolved by liquids and thereby become liquid, so liquids are absorbed by powders and thereby become solid, the heat evolved being equivalent to the latent heat which the liquid gives up in solidifying. Other investigators who have made experiments on the Pouillet effect and allied phenomena are Tate ||, Melsens {, Chappuis **, Wiedemann and Liideking +t, Gore tf, Hrco- lini §§, Bellati ||||, and Linebarger . | In Gore’s experiments, a powder such as silica or alumina was dropped from the air into water which contained some soluble salt ; the liquid was not stirred, and the temperature observed was that of the powder which sank to the bottom of the liquid. The object of these experiments was to discover * Cantoni, Rend. del R. Istituto Lombardo, viii. p. 135 (1866). yea Atti del R. Istituto Veneto, viii. (1896); ix. (1897); xii. (1900). { Tait, Proc. R. Soc. of Edinburgh, 1881-82, 1882-83; Marshall, Smith and Omond, Proc. Roy. Soc. Edinburgh, 1881-82; Amagat, Comptes Rendus, cxvi. p. 946 (1893) ; Lussana, Nuovo Cimento (4) ii. p- 233 (1895). § Lagergren, Kongl. Vetenskaps Akademiens, B. 24, Afd. i1., Stockholm, 1899. || Tate, Phil. Mag. [4] xx. p. 508 (1860). §| Melsens, Mémoires de [Academie de Belgique, xxiii. (1873) ; Ann. de Chim. et de Phys. (5| iii. p. 522 (1874). ** Chappuis, Wied. Anz. xix. p. 21 (1883). ++ Wiedemann and Liideking, Wied. Ann. xxv. p. 145 (1885). tf Gore, Phil. Mag. xxxvii. p. 306 (1894); Birm. Phil. Soc. Proc. vol. ix. pt. 1 (1893). §§ Ercolini, Nuovo Cimenti, Serie 4, vol. ix., Feb. 1899. \||| Bellati, Att: del R. Istituto Veneto, Tomo lix. Parte Seconda, 1900. 4/4, Linebarger, Physical Review, vol. xiii. No. 1, July 1901. Phil. Mag. 8. 6. Vol. 4. No. 20. Aug. 1902. R Q42 Mr. G. J. Parks on Heat Evolved or the influence of the substance in solution; and in fact the whole research was the outcome of another investigation in which Dr. Gore showed that a powder has the property of abstracting from a liquid part of the substance in solution. One remark of Dr. Gore bears on the present investigation : having made observations on precipitated silica and sand, he states that the action is purely a surface one, and he suggests that if the relation between the rise of temperature and the area of the surface were known, the method could be employed to obtain the area of the surface of a powder. Prof. FitzGerald* regarded the Pouillet effect as due to a pressure at the surface of the powder and the liquid; he suggested the application of the laws of thermodynamics, and he pointed out the need of further investigation and quanti- tative treatment. Notwithstanding the large number of observations which have been made in connexion with this phenomenon, there are no data by means of which we are enabled to express the quantity of heat evolved as a function of the area of the sur- face. The experiments of Martini, Ercolini, and others show that for the same powder and liquid the quantity of heat evolved is proportional to the mass of the powder used in the experi- ment, but no attempts have been made to calculate the area of the surface exposed to the liquid. The equation used by Ereolini is M+ po—'- k=0, where M is the mass of the water, including the water equivalent of the calorimeter, p is the mass of the powder, and ¢ the specific heat of the powder, @ is the observed rise of temperature, k is a constant and represents the amount of heat evolved on putting one gram of the powder into water. The value of & is, however, not really constant, but di- minishes very slightly as p increases. Martini explains this on the supposition that some of the water is solidified on the powder and its specific heat is thereby reduced to*5. Bellati has, however, shown by direct experiment that this supposi- tion is wrong. Some silica was well dried, and then exposed to aqueous vapour so that it absorbed moisture, the mass of which was determined by weighing the silica before and after its exposure; the specific heat of the water was then found by means of a Bunsen’s ice-calorimeter, an assumed value being taken for the specific heat of silica. The specific heat of the water was found to be much greater than *5, and it did not differ very much from 1. * FitzGerald, ‘ Nature,’ vol. xlix. pp. 293, 316 (1894). va Absorbed on contact of Liquid with Solid. 243 It seems highly probable that the specific heat of the water close to the surface of the silica differs from the specific heat of the water which is farther away from the surface, but any attempt to distinguish clearly between the two must neces- sarily lead to some doubtful assumptions. A consideration of the Pouillet effect is, however, incomplete if the possibility of such a variation in the specific heat of the liquid is not taken into account. ‘There is also another possible source of variation in the quantity of heat evolved, which none of the investigators have considered, namely, the variation of the heat evolved with the temperature. In many of the records of experiments the initial temperature of the calorimeter is not even stated, and in other cases, where the temperatures are recorded, it is impossible to decide whether the variations in the quantity of heat evolved depend upon differences in the initial temperature of the liquid and powder, or upon change of specific heat of the liquid, or upon some cause of error in the experiment. : The objects of the present investigation were to obtain a relation between the quantity of heat evolved and the area of the surface exposed, to find the rate of variation of heat evolved with variation of temperature, and to apply to the results the laws of thermodynamics. The nearest approach to a relation connecting the quantity of heat evolved with area of surface is the state- ment of Mr. Linebarger, that the finer the powder the greater the heat effect, and in the case of water and silica the heat effect is about proportional to the fineness of the powder. This conclusion is based upon a very few experiments with two samples of silica of different degrees of fineness, and it is directly opposed to the views of Martini, who states that the fineness of the powder does not influence the result to any important extent *. IT. On the Relation between the Area of Surface of Silica and the Heat evolved on bringing the Surface in contact with Water. In making any experiment on the Pouillet effect, it is essential that the powder should be perfectly dry and that it should be at exactly the same temperature as the liquid. Very few of the investigators have succeeded in securing these * Martini, Att: del R. Istituto Veneto, Tomo lix. Parte Seconda (1900), p. 622 (Non é dunque la sottigliezza dei granuli della polvere che influisca in modo sostanziale sul fenomeno come te Jo provano le tre qualita di carbonato di calce). 244 Mr. G. J. Parks on Heat Lvolved or conditions, but Mr. Linebarger’s methods seem to leave nothing to be desired, and the experiments now to be described were made in a similar way. The precipitated silica, sand, or other substance to be experimented upon, was heated in an evaporating dish to dull red-heat. A test-tube was drawn out to a narrow neck at about seven or eight centimetres from the closed end, and the tube was then weighed. Some of the powder was now placed in the tube while it was still hot, and the tube was connected to an air-pump, and the air was exhausted as completely as possible, the powder being at the same time heated until the tube showed signs of softening and closing in under the atmospheric pressure. The bulb was now sealed at the narrow neck, and when cold the whole of the tube and the powder were weighed together ; the difference between this weighing and the first weighing gave the mass of the powder, and a third weighing gave the mass of bulb and powder. The calorimeter used in these experiments was a copper vessel, 9 cm. in height and 7°5 em. in diameter ; it weighed 104:605 grammes, and its water equivalent was 9°95 grammes. This was suspended by silken threads inside another copper vessel, this again was placed in a glass beaker containing water, and the glass beaker was placed inside another glass beaker, the space between the two beakers being filled with “ glass wool” or “ cotton silicate,” which is a very bad conductor of heat. The whole apparatus was kept in a cupboard with glass doors. The temperature of the calorimeter could there- fore be kept constant for a considerable time. The thermometers were divided to ‘02° C., and the readings were taken to the tenth of a division, so that there was a possible error in each reading of not more than -002° C. , An instrument was used to serve the purpose of crushing the bulb, thus liberating the powder under the surface of the water, and it also served as a.stirrer to keep the temperature of the water uniform. A piece of brass tubing about an inch in diameter was filed away in the middle, thus leaving two rings at the ends about an inch apart and connected by that part of the tube between them which had not been filed away. A nut was soldered on to the tube between the rings and a screw worked in the nut, the axis of the screw being at right angles to the axis of the tube, so that when the glass bulb was placed in the tube it was held firmly by the screw pressing against it, and a few more turns of the screw were sufficient to break the bulb. The top of the screw was flattened toa sharp edge, which engaged in a split at the end of a stout oD brass wire ; this wire could.thus be used to turn the screw, Absorbed on contact of Liquid with Sold. 245: and then could be immediately removed. A piece of glass tubing was attached to the brass tube so that the screw worked along the axis of the glass tube, which served as a handle of non-conducting material. The water equivalent of this instru- ment was 2°35 grammes, and that of each thermometer was 1°50 grammes. In making an experiment, the bulb containing the powder was placed under the surface of the water in the calorimeter, and allowed to remain there for some hours, generally about twenty-four hours. The temperature was then observed every five minutes, and if several consecutive readings were the same, the bulb was broken, and the temperature again observed until it was constant. The rise of temperature was generally complete in three minutes or less, the liquid being gently stirred together with the powder. The mass of water, M, was always large compared with the mass of the powder, p, and hence the err or, if any, involved in taking the specific heat of the water as a must have been exceedingly small. The temperatures at which the experi- ments were made did not differ very much, and the variation due to these small differences of temperature was neglected ; from theoretical considerations it follows that the variation in the heat evolved is not more than ‘3 per cent. per degree centigrade, and later experiments tend to confirm this. The specific heat of the glass bulb and its contents was taken as ‘19; any error in this assumption could not have affected the results, since the mass of the bulb and its contents was always small compared with the mass of water. The average diameter of the grains of powder was obtained by measuring many hundreds of grains by means of a microscope supplied with stage micrometer and eyepiece micrometer. The microscope was so adjusted that thirty divisions of the eyepiece micrometer exactly corresponded to one tenth of a millimetre on the stage micrometer, so that one division of the eyepiece micrometer represented zap CM. It was found that in the dry state the smaller grains of powder were often joined together, forming larger grains; and it was not easy to distinguish a lump consisting of several small grains from a complete grain; hence any measure- ments of powder in the dry state are likely to make the powder appear much coarser than it really is. When the powder was put in a drop of water on a glass slide under the microscope and stirred with a small brash, the larger pieces of silica were seen to break up into smaller grains ” of fairly uniform size. The average diameter of the grains was 946 - Mr. G. J. Parks on Heat Evolved or found to be ? of a division of the eyepiece micrometer, that is 00025 cm. Suppose now there are n such average grains to a gramme of powder, then, since the specific gravity of the powder is 2°2, we have nx 7 00025)" x22=1 on the assumption that the grains are spherical, and the area of surface is equal to n.7(°00025)?=6 x : s oll) Geen de 2-2 00025 That is, one gramme of the precipitated silica exposed a surface of about 10900 sq. cm. Another variety of silica used in these experiments was examined under the microscope, and the average diameter of the grains was found to be 1:2 divisions or 00040 cm., so that the area of surface per gramme was = 10900 sq. em. Pa abe: Sal Cire Experiments were also made with some fine grey sand of specific gravity 2°6 ; the average diameter of the grains was ‘010 cm., and the area of the surface exposed by one gramme of the sand was therefore 1 1 °X 36 * 01 on the assumption that the grains were spherical. The probable error in estimating the surface of a powder by this method is considerable, because the particles are irregular in shape and size, especially those of the sand. Experiments were therefore made with “ cotton silicate”’ or “ ylass wool,” a kind of glass of specific gravity 2°7, in the form of fine filaments which, when examined under the microscope, are seen to be almost perfect cylinders, of fairly uniform size. The length of each cylindrical filament was very great compared with its diameter, so that in caleu- lating the area of its surface only the curved surface was considered. The average diameter was found to be 00175 em.; hence the area of surface exposed by one gramme of the silicate was 6 = 6820 sq. cm. =231 sq. cm., _/ ee 2°7 x ‘00175 The accompanying table (I.) shows the results of some of the experiments. Other experiments were made, but the results are not shown because they are considered to be = 847 sq. cm. Absorbed on contact of Liquid with Solid. 247 unreliable. In several experiments, there was a slight crack in the bulb before it was placed in the calorimeter, and in these instances the result obtained was far too low, though the crack was not large enough to admit any visible quantity of water ; this shows the oreat importance of keeping the powder dry until the moment of the experiment. Other experiments were rejected because there was a rapid variation in the temperature of the room at the time, so that the final temperature of the calorimeter did not reach a constant value until long after the time usually occupied in making an experiment. The rise of temperature observed in ge experiments with sand and cotton nie silicate was only about 51,° C.,-and hence the results are only given to the second eaten figure. TABLE I. ig Pode = 2 |3 J eo cg Ss | 8a) fees ce = eats So e| = ees = ‘i o =| oS o = 2 . = 3/8 PE ieee pred aed ae ~ ee = Sy ROE SS lo 3 ge | Natureof | $¢ | Z Se Boel ey | | a he - Substance. Si ee iemes| wa apes) a ee as | as] x =) By tenes faces ies Ne seee etn |) 0, = | 22 |B. ms Sixt eml- ob lu lotsa Pes a ee | 2g no Ss oy Se Se. 2Onl are tS (eae oe S| Sri via Pee any dan ae (alo 1 | pe ee =| a aia ie heal =e hey Amt) 2 | @ 3G 7, | A lh 1a = |= 5 eo NS Oo 1. | Silica | f yh i sane 00025 10900 3°749 |3°34| 205°51 (6-334 -208 11:4 |-00105 a » | 9» | 363/855] 210°31 |6:552 | -192 | 11-3 |-00104 3. | is x | ay. | 44691561 | 210-05) |,7-012, | s222, | 11:2 |-00103 4. | - - We | Ay 4-037 |3°53| 239°74 | 7-586 +194 11:5 |-00105! 5.* f is 00040, 6820) 3:940/4:03| 207-26 |7:320 1386 | 7:15/-00105 6. | Sand | 010} 231 |20-050|3°70| 220-03 |5:400 | 022 = -241-0010 ‘a ” * » |20°589 4°57} 240710 | 5-482 | -020 | +23 |-0010 8. 2 53 »- |22°033 [3°81] 252-28 |8320 | -020; -23'-0010 9. > », {207188 |4-14| 255°15 |9°228 | -018 +23 |-0010 10. | Silicate ) ) / | (cylindrical | ) | | filaments) -00175) 847 | 2240 |881| 200-10 | 5-742 | -010 89 0011 11. 99 ” * . | 4006 |3°50| 21093 | 5°722 | :018 “95 O01 12. - _ $9 | .. | 4138 |8-47| 211-75 | 6:052 bid "92 0011 | * See Table IT. for results of other experiments with aa It is considered that these results justify the enunciation of the following law :— “ When silica, sand, or glass, is brought in contact with water, at approximately constant temperature, the heat evolved is pro- portional to the area of the surface exposed by the solid, and the amount of heat developed per square centimetre is approximately ‘00105 calorie when the temperature is near7° C. oo 248 Mr. G. J. Parks on Heat Evolved or Tk Application of the Laws of Thermodynamics. Assuming that the phenomenon of Pouillet is reversible, we may apply the laws of thermodynamics. Let h be the amount of heat developed per square centimetre at the surface of the solid and liquid at constant temperature, let c be the specific heat of the liquid when the surface remains constant, let s be the area of surface of the powder exposed to one gramme of the liquid, the volume of which is supposed to remain constant, let P be the surface-pressure for the given solid and liquid. Then, with the usual notation of thermodynamics, dQ=e.di—h.ds, . . , 7 and dQ=7 . dq, hence T.dp=¢.di—h.ds. .. . | 7 The variation of the internal energy is dU=J .dQ—P.ds=J.c.dt—(J .h+P)ds, (iii) where J represents the mechanical equivalent of heat. Imposing the condition that the variation of the internal energy is a perfect differential, we obtain de , dh dP ime ye eae (iv.) Imposing the condition that the variation of entropy, dq, is a perfect differential, we obtain 2 be i | aged Cs ° ° e e . (v.) dP ens 7 A= ae é or ie: le (vi.) ot dG Tee, and ie. ae (vil. ) Applying these equations to the results obtained for water and silica, we find that the surface-pressure diminishes with rise of temperature, for since heat is evolved when the surface of water and silica is extended, h is positive, and hence from equa- tion (vi) & is negative. Taking h as °00105 when r is 280° Absorbed on contact of Liquid with Solid. 249 157; that is, at-7° C. the and J=4:2~x 10‘, we have iF surface-pressure of water and silica diminishes at the rate of 3 oO 157 dynes per cm. for an increase of temperature of 1° C. From equation (v.) we have is oH oe not» =°0000037 ; ae ads. vmat 280 at a temperature of 7° C. fe dh From equation (v.) it is clear that if either Pear is known, the other can be found, and if both of these could be determined with precision, a value for absolute zero could be obtained, which would be independent of the air-thermo- meter. TV. On the Rate of Variation of the Heat evolved with Change of Temperature. The accompanying Table II. shows the results of experi- ments made to determine, at least approximately, the value of TABLE II. Experiments with precipitated Silica. Average diameter of grains ‘00040 cm. Hstimated area of surface per gramme 6820 sq. cm. . Mass ot water, | M f including water- | Calories | Calories Number itd Mass of | equivalent of | Initial | Rise of per per of Expe- ie carga ie calorimeter, Temp. | Tempe- | gramme _ sq. cm. | riment. = bulb. | powder, bulb, (Cent.). | rature. on een eens _ thermometer, | | powder. surface. | and stirrer. | ° eae: | ee 3940 | 403 | 207-26 7320 "136 715. jp VOWS eee.) 4282 |): a2 190°26 | 7300 164 7:29 | :00107 | o....... | 3760 | 3:55 201°88 | 6930 134 TAD.) “OOLOS Pr Ait. : | 3602 | 3°25 195°71 | 6238 "132 717 =| °00105 | B...:.|) 3721 | 400 196-26 | 6770 136 | 7-17 | -00105 =|. 2 O01 3°32 211-49 | 7-200 ‘122 717 | °00105 7......| 3256 | 358 205°25 7106 | “114 | 719 | -00105 ak) 4166 | 374 214°16 7-502 "138 7°09 | -00104 ae | 4961 | 414 | 197-01 | 23-636 | +164 758 | -00111 | ae | 3950 | 3°92 182°94 | 24-180 | "162 750 | -00110 Aaa | 3657 | - 3°22 202°57 24-410 | "138 764 | -00112 eee ss. | 4789 | 467 206°67 _ 24000 "178 768 | -00115 3 eee 4-417 | 379 21202 | 24060 | -160 7-68 | 0013 PSE AL: 4691 | 3:17 2300 | 24670 | 154 | 7-58 | 00111 i 4003 | 3°84 227-21 23°906 ‘130 7°38 | :00108 BG) Sit,.: 3°829 | 2°99 227-68 24°700 124 7:37 | ‘00108 - 950 Mr. G. J: Parks on Heat Evolved or the term ey which appears in the foregoing theoretical investigation. The same powder was used throughout, and the results are tabulated in calories per gramme as well as in calories per sq. cm., so that the data should be equally useful whatever be the hypothesis advanced. _ The thermometers used in these experiments gave a range of temperature from 5° C. to 25° C.; hence the range over which experiments could be made was rather less than 20° C. It was found necessary to modify the apparatus so that the calorimeter could be kept for some hours at constant tempe- rature above that of the atmosphere. The cylindrical copper vessel in which the calorimeter was suspended was closed by a tightly fitting copper lid, under the rim of which was tightly packed an indiarubber ring which had previously been stretched around the top of the vessel. Into the copper lid, two copper tubes about two inches long were soldered; through one of these tubes the bulb of the thermometer could be put into the calorimeter, and through the other passed the handle cf the crushing instrument. Thus the bulb could be crushed and the liquid stirred and the temperature observed without opening the vessel. The copper vessel was now immersed in several gallons of water, the top of the lid being about an inch below the surface. This water was kept at approximately constant temperature for several hours, during which time the bulb containing the powder was immersed in the water in the calorimeter, so that there could be no doubt about the powder and the water being at the same temperature. This apparatus proved so satisfactory that it was finally . adopted in the later experiments at the lower temperature, instead of the arrangement previously described. In the first eight experiments the mean temperature was about 7°°1 C. and the mean heat evolved was 7°18 calories per gramme, or ‘00105 calorie per sq. cm. In the last eight experiments, the mean temperature was about 24°°3 C. and the mean heat evolved was 7°55 calories per gramme or “00111 calorie per sq. cm. dh °00006 The mean value of a IPF. = 0000035. Ae OOTOSR: The mean value of a BST = 0000037. : dh tae Aes . Hence, roughly speaking, = = : and h varies as T, that is dt the heat evolved is roughly proportional to the absolute temperature. =e a 44 Absorbed on contact of Liquid with Solid. 251 NV; On the Rate of Variation of the Specific Heat of Water with Extension of the Water-Silica Surface. It has been shown that «= : ~ = and hence from the results stated above it follows that a must be very small. If the values of = and : are correct to the second significant figure the value of = is 2x 10-‘*, and this may be taken as indicating the order of magnitude of the term ae ds “igged de : For an accurate determination of aa? experiments would s have to be made over a much wider range of temperature, and it would be advisable also to obtain, if possible, a silica of much finer and more uniform quality than that used in these experiments. It is known that the surface-tension of a liquid in contact with air can be represented approximately as a linear function ; a I of the temperature, and hence, from equation (vii.), a8 s approximately zero. But it cannot be assumed that the surface-pressure of water and silica follows the same law as the surface-tension of a liquid in contact with air. In making any experiment to determine directly the specific heat of water in contact with silica, we are met at once with the difficulty that the specific heat of silica is not accurately known. According to Joly * the specific heat of amorphous silica is -2375, but it has been suggested = that this value is too high, and that the error arose through neglect of the Pouillet effect ; a similar question in regard to the specific heat of earbon has been investigated by Kopp, Wiillner & Bettendorf, and Weber f. Bellati§, in his attempt to determine the specific heat of moisture absorbed by silica, took for the specific heat of the silica the value ‘1993 as the mean of the various values obtained for different forms of silica. The value of as cannot, however, be obtained by direct * Joly, Proc. R. Soc. xli. p. 250 (1886). + Martini, Atti del R. Istituto Veneto, Tomo lix., Parte seconda, p. 637. t Weber, Pogg. Ann. t. 154, pp. 367-423 (1875). § Bellati, Att: del R. Istituto Veneto, Tomo lix., Parte seconda, p. 945. 252 Heat Evolved on contact of Liquid with Solid. experiments such as those made by Bellati. Suppose, for example, p grammes of silica having a specific heat , and w grammes of water, are mixed and raised to a temperature ¢, and the mixture is then put into a Bunsen’s ice calorimeter and cooled to 0° C., the heat given up is de dh h (pk tw+p.sT—p-s. at = (pktw—p.s 2) ie approximately, from equation v. It is necessary, therefore, to distinguish between the true or absolute variation and the apparent variation in the specific heat of water in contact with a solid. ‘lhe true variation in de the specific heat is proportional to dy and is probably very small; but since in any experiment it is impossible to prevent the evolution or absorption of heat at the surface depending hho dh on the term 7, that is, the variation actually observed in any experiment, is dh the apparent variation in the specific heat, : : de proportional to the difference ae the terms Te 2D is, approximately proportional to = Hence the apparent specific heat of water in contact with a solid is approximately (1-2 *) where A is the area of the surface of the water in contact with the solid, and w the mass of the water. For example, in the earlier experi- ments of the present investigation, the mass of water was about 200 grammes and the area of surface exposed by | 4 grammes of powder was 4x 10900=48600 sq. cm., and the value of : was 37 x 1077: hence the apparent specific heat of the water was equal to (1—*388° x 37 x 10-7) =-99919. It is evident that if the mass of water is small compared with the mass of powder, the variation in the apparent specific heat may be very great, so that it is not necessary to assume, as Martini did, that some of the water is solidified on the surface of the powder, in order to account for the apparent variation in the specific heat. VI. Experiments with Mercury. Experiments were made to show a fall of temperature on putting a finely divided solid into mercury. After several fruitless attempts with silica, the following method was adopted. i ai Se ee ee es re int a ~ Emission of Negatively Electrified Corpuscles. 253 About 3000 grammes of mercury were placed in a glass beaker, and some cotton silicate was placed in the same beaker above the mereury ; above the cotton silicate was a cardboard. disk which covered the silicate entirely, except that a space was left for the insertion of the thermometer, and a little space was allowed for the edge of the disk to clear the sides of the beaker. On pressing down the disk the cotton silicate was suddenly immersed in the mercury, and in some experiments there was a fall of temperature amounting to 016°C. But the results were not consistent, for in other experiments there was a slight rise of tempera- ture, caused probably by the cotton silicate being at a higher temperature than the mercury. After leaving the cotton silicate immersed in the mercury for some time, so as to take the same temperature, it was suddenly released, and a rise of temperature was the invariable result. With 11 grammes of cotton silicate the rise of temperature was about ‘02° C., and with 30 grammes of silicate the rise of temperature was about ‘05° C., but the results varied considerably. These experiments do not lend themselves to quantitative measurement, for the surface of the mercury cannot be deter- mined. When the filaments of cotton silicate are put into mercury they tend to cling together in bundles or tufts, and the mercury breaks up into a great number of little globules between the tufts of silicate. The surface exposed by the mercury is thus large and indeterminate. The results show, however, that the sudden contraction of a mercury surface causes an evolution of heat and corresponding rise of tempe- rature, and the effect can be regarded as a modification of the Pouillet effect for a liquid which does not wet, or enter into intimate contact with the solid. H.M. Dockyard School, Portsmouth, March 1902, XXVIII. On some of the Consequences of the Emission of Negatively Electrified Corpuscles by Hot Bodies. By J.J. Toomson, M.A., F.RS., Cavendish Professor of Experi- mental Physics, Cambridge*. T was shown by Elster and Geitelt that an incandescent metal wire in a good vacuum emits negative electricity; in 1899 I showed that the carriers of this negative electricity were “corpuscles,” 7. e. were identical with the carriers of * Communicated by the Author. t Elster and Geitel, Wied. Ann. xxxvii. p. 315.1 254 Prot. J. J. Thomson on the Emussion of negative electricity in the cathode-rays*. Quite recently Mr. O. W. Richardson + has made a series i measurements at the Cavendish Laboratory of the rate at which the electricity escapes at different temperatures. The results of these mea- surements are very interesting ; they show that surprisingly large currents can pass in the best vacua between a negatively electrified incandescent wire and a conductor placed in its neighbourhood ; thus Richardson has shown that the negative electricity streams so fast from carbon ata white heat as to be equivalent to a current of about 1 ampere for each square centimetre of carbon surface. If we suppose that the cor- puscles which carry the negative charge have the same kinetic energy as the same number of molecules of a perfect gas at the same temperature, this stream of corpuscles would oy with them from the metal energy at the rate of about 745 of a calorie per square centimetre of surface per second: the number of corpuscles coming in each second from this area is about. 5x10". The question naturally suggests itself whether this great crowd of corpuscles does not produce other effects besides the electrical ones already mentioned : it is the object of this paper to indicate some of these effects. In the first place, since the corpuscles carry a charge of negative electricity, they will move when acted on by an electric force; so that, assuming the Electromagnetic Theory of Light, they will be set in motion by a wave of light ; they will thus absorb energy from the wave and give out this energy as scattered light. We can easily calculate the energy in the light scattered in this way. The rate at which a small char ged particle, charge e and acceleration f, radiates energy is equal to Bek oN where V is the velocity of light. If the charged particle is acted on by an electric force °X, then | ie m where m is the mass of the particle; hence the rate at which the charged particle is emitting energy is equal to be ae | 3m? V * J. J. Thomson, Phil. Mag. xlviii. p. 547. t+ O. W. Richardson, Proc. “Camb. Phil. Soc. xi. p- 286. . “> =e ee rae Negatively Electrified Corpuscles by Hot Bodies. 255 Now if the electric force is that in a light-wave the mean energy E per unit volume in the wave is equal to the mean value of X?/47V?; hence we see that the mean rate at which’ the particle is emitting energy (this is the rate of emission of the energy of the scattered light) is Ar e arte VE. If there are N corpuscles per unit volume the energy in the scattered light coming from each unit of volume per second is equal to Aq Ne? 3. m? The scattered light will be polarized in the same way as light reflected from small particles. This scattering of the light will cause the medium to absorb light. We can find the co- efficient of absorption as follows :—Suppose the axis of zis the direction of propagation of the light. Let AB and CD be two planes at right angles to z separated by a distance dz, CD being in front. Then if A is the area of either of these planes, the rate at which energy is being scattered by the particles between the planes is equal to | NI_4 ae Nee ge 3. m2 Now when things are in a steady state this energy must be supplied by the excess of the energy flowing into the region between AB and CD through AB, over that flowing out through CD: the average rate at which energy flows across AB is AEV;; the rate at which it flows out across CD is A({E+06E)V: hence we have 4 ASR yes 2 ay Ag. oma or dB toi, deen es 3 dz 3 om? thus _ 4x Net, H=Ce 3 ™ ; 4 and thus the coefficient of absorption is aa Be, 3m? Thus the region round incandescent metals or carbon will, in virtue of the corpuscles coming from these substances, 256 Prof. J. J. Thomson on the Emission of scatter light; and the scattered light will be polarized in the same way as if the light had been reflected from small particles. Since the corpuscles are in rapid motion if the incident light is homogeneous, the spectrum of the scattered light will by Dopler’s principle broaden out into a band. Similarly, if the corpuscles were illuminated by light showing Frauenhofer’s dark lines, these will be obliterated in the scattered light. The most conspicuous example ofa hot body is the sun, the photosphere of which is supposed to contain large quantities of carbon or silicon at a temperature far higher than any we can produce by artificial means. Thus the photosphere must be emitting corpuscles in large quantities, these coming from such hot bodies will be moving with great velocities, and may leave the sun and travel out through the solar system. These corpuscles will scatter the light from the sun; and since the corpuscles are densest close to the sun, we should get a distri- bution of luminosity due to the scattered light which would be most intense close to the sun, and would fade away at greater distances from it. The rate of decay would be fairly rapid; for not only would the intensity of the incident light diminish inversely as the square of the distance, the number of corpuscles per unit volume would also diminish according to the same law ; so that the intensity of the light scattered from the corpuscles would vary inversely as the fourth power of the distance. It seems to me probable that many of the phenomena of the corona may be due to light scattered by corpuscles ejected from the sun. Since cathode-rays produce luminosity when they pass through rarefied gas, the corpuscles ejected from the photosphere would in their passage through the chromosphere cause the gases in the latter to become luminous. The presence of some of the corpuscles throughout the solar system would cause each part of this system to scatter a certain amount of light, so that no part of it would be absolutely dark, nor would’ it be perfectly transparent. T am not aware of the existence of any observations bearing on the absorption of light by interplanetary space. The corpuscles when under the action of a wave or pulse of electric and magnetic force will be pushed forward in the direction in which the wave is travelling; and thus if these waves proceed from the sun, the latter will appear to repel the corpuscles. } To show this, let the direction of propagation of the wave be along the axis of z, let X the electric force in the wave- front be parallel to the axis of #, H the magnetic force parallel to y. Let 2, y, z be the coordinates of the corpuscle. Negatively Electrified Corpuscles by Hot Bodies. 257 Then we have, since X=VH, where V is the velocity of light, a cae z at ng =Xe—HeS =He(V-2)=— Hes, (1) d?y | | SE on BE eC) eee oe, ee OO ee a2 m ae He i’ m 2 —He 7 a a ree where €=z—Ve. Let us first take the case where a pulse of constant electric force is passing over the corpuscle, Thenif xz, z vanish when ¢=0 and uw and w are the initial values of jas and = , we get from (1) and (38) . ‘ z=Vt + ” zt W -cos wt ) pe sin wt, and Mi, 4 =V+usin wf + (o— V) cos of, where w= He/m. Thus if the pulse lasts for a time T, long enough to make oT large, the corpuscle will be set in motion in the direction in which the wave is travelling, and the average velocity of the corpuscle will be that of the wave. Now ~ alT=THe/m=10'.T..H; thus if T the time the pulse takes to pass over the corpuscle is large compared with 1/107H seconds, the corpuscle will be shot forward with great velocity in the direction in which the pulse is travelling. If wT were small, the velocity acquired by a particle starting from rest would be VT”. Let us now take the case of a periodic disturbance; let H be given by the equation 7 H=A ae (Vi—z)=A cos Gy r Equations (1) and (3) become B 2. O. m a5 = — Aecos o% ap = (4) PE Qe, dix ; m aa Ae co cos 6 «a3 Tracey Phil, Mag. 8. 6. Vol. 4, No. 20. Aug. 1902. » 258 _ Prof. J. J. Thomson on the Emission of from (4) we get | gah = — Ae— is ‘n= ie dt Qa “i dx/dt and ¢ vanish simultaneously, substituting in (5), we have Ol. a. ar m a8 Anum * 2 x $=9; or writing @ for au ¢, we have ad’@ ae. Te + ees sin 6=0. The equation of motion oe i. pendulum. Integrating this cibol we find =) Ge) = Tat ¢ where C is he constant of Lae eee for € its value z— Vt, we have 1 (Ar\? dz\? A?e? 3(<)(V-%) = ey coe ~ (Viz), If dz/dé vanish when €=0, we have 1 /47r\? LN her ye 4 iad At J 3(=) liv-5} —V cosy (Vee) 1b If w is the maximum value of its we have v2 A2e? Lee Via ae An? m2 ; hence if bla lee Aq?m? ~ — ” the maximum value of the velocity of the corpuscle will be equal to the velocity of light, If ?A%2?/V?1r?m? is a small quantity, then the maximum value of w is given by the equation TRA a = 9 im V' 3 2A 2,2 Now e/m=10', V=3 x10"; hence TeneV3 =2°5A?710-9, Here A is the maximum value of the magnetic force and X the wave-length. We see that for waves of sunlight To Negatively Electrified Corpuscles by Hot Bodies. 259 A?)? x 10-8 would be very small; so that the maximum velocity acquired by the corpuscles would be very small com- pared with the velocity of light. If, however, the sun gave out Hertzian waves of considerable wave-length, these would communicate to the corpuscles velocities comparable with the velocity of light, so that the sun would appear to repel the corpuscles with great vigour. Thus, for example, if a comet by near approach to the sun got raised to such a high tempe- rature that the corpuscles began to come off, these would be repelled if any Hertzian waves came from the sun, and appear behind the comet as a luminous tail. I now pass on to consider another result of the emission of these negatively electrified corpuscles: we may regard these corpuscles coming out of the metal as evidence for the exist- ence in the metal itself of streams of corpuscles which move freely between the molecules of the metal. Some of these moving at more than a certain speed are able to escape from the attraction of the metal, and produce the stream of nega- tive electricity coming from the metal. These corpuscles moving through the metal constitute streams of cathode-rays, and when they come into collision with the molecules will give rise to pulses of electric and magnetic force analogous to those produced by the stoppage of cathode-rays in a vacuum-tube; inasmuch, however, as the velocity of the corpuscles in a hot body is small compared with that of cathode-rays in a vacuum-tube, the pulses produced by the corpuscles will be very ‘‘ soft’ compared with the Réntgen rays produced in a vacuum-tube, 7. e. the pulses produced in the hot body are very much thicker than those produced in a yacuum-tube. A succession of sufficiently broad pulses would, however, on the electromagnetic theory of light, produce a continuous spectrum of the kind given out by a hot body. Part of the radiation from a hot metal might arise in this way; and this part would have the characteristic property of radiation from a solid of increasing very rapidly with the temperature. For we may regard the corpuscles in the metal as analogous to the molecules of a liquid, and the escape of the corpuscles from the metal as analogous to the evaporation of the liquid. The corpuscles are supposed to be attracted by the metal; so that it is only those escape from the surface which start from near the surface and move so rapidly that their velocity is sufficient to carry them beyond the region of the attraction of the metal. Thus suppose that cis the distance at which the attraction of the metal on the corpuscles is appreciable—c is analogous to the range of molecular attraction in Laplace’s Theory of rsa y eine consider a layer of 2 260 Prof. J. J, Thomson on the Emission of the metal of thickness c next the surface: as soon as a cor- puscle enters this layer it will be acted upon by a force directed away from the surface ; if the corpuscle has only a small amount of kinetic energy it will soon be stopped, and will turn back without ever reaching the surface, one with greater velocity will get nearer to the surface, and those moving above acertain speed will be able to reach the surface and escape from the metal. If the distance c is comparable with the thickness of metal required to absorb the radiation of the type produced by the impact of the molecules against the corpuscles, then the rate of emission of radiation from the metal will depend chiefly upon the more rapidly moving corpuscles. For not only do these possess greater energy, and therefore when in collision produce the more intense pulses, but they travel nearer to the surface so that the radiation which they emit has not to travel through so great a thickness of metal, and is consequently not so much absorbed. | To calculate the rate at which energy is radiated from the. metal by the electromagnetic waves produced by the collisions. between the corpuscles and the molecules, we require to know the attraction exerted by the molecules on the corpuscles ;, for without this knowledge we cannot tell how near to the surface a molecule moving with a given velocity will pene- trate; we also require to know how much of the radiant energy produced by the collision is absorbed in passing from the place of collision to the outside of the metal. In default of information on these points let us calculate the rate of emission of radiant energy on the assumption that only those. corpuscles whose velocity is greater than v, get near enough to the surface for any of their radiation to escape, and that all the radiation from those moving with a velocity greater: than v, escapes without absorption. Assuming Maxwell’s law of distribution, and that the energy in the electromag- netic pulse produced by the collision is proportional to the square of the velocity, we find that the rate at which energy is emitted from the metal is proportional to m as Le @-3 Yet Pe dv, where @ is the absolute temperature. If mv,? is large com- pared with @, this expression increases very rapidly with @. The collision of free corpuscles with the molecules will not be the only source of radiation—indeed if it were only con-. ductors of electricity would radiate—similar radiation will be Negatively Electrified Corpuscles by Hot Bodies. 261 produced by the motion of corpuscles inside molecules from which they never become detached. The electromagnetic effect will evidently be of much the same character, whether the velocity of a corpuscle is reversed by a collision or by swinging round a closed orbit under the action of a central force. If the orbits of the corpuscles in the molecules are circular, the calculation of the amount of energy radiated from them is very simple. A corpuscle moving with an : ; hey? acceleration f emits radiant energy at the rate 3 a , where V is the velocity of light. If the corpuscle moving with a velocity v describes a circle of radius 7, f=- = at if z/r” is the force on the corpuscle divided J} y fo ie by its mass. Un—1 Thus /?= ry and this is proportional to the rate at which the corpuscle is emitting energy. ‘Thus this rate is proportional to the kinetic energy of the particle raised to the power 2n/n—1: and if we assume that the kinetic energy of the corpuscles is pro- portional to the absolute temperature @, the rate of radiation 2n from the corpuscles varies as 97-1. If the force on the corpuscle varies inversely as the square of the distance n=2, the rate of radiation will be proportional to the fourth power of the absolute temperature. To calculate the rate at which energy comes out of the body we require to know the law of absorption ; if the corpuscles are moving with different velocities, the character of the radiation emitted by a cor- puscle will depend upon its velocity; if the absorption does not depend upon the character of the radiation, the rate at which energy is emitted from the body is proportional to the fourth power of the absolute temperature (assuming n=2); but this is not the case if the absorption depends upon the character of the radiation. If, for example, as in the case of Rontgen rays, the greater the velocity of the corpuscles the more penetrating the radiation they originate, a larger pro- portion of the radiation from the quicker corpuscles would emerge from the body than of that from the slower corpuscles, and the rate of escape of the radiation would increase more rapidly than the fourth power of the temperature; while if the law of absorption went the other way it would vary less rapidly. Although the calculation of the amount of radiation 262 . Dr. C. Barus on Spontaneous Nucleation and depends upon a knowledge of the law of absorption which we do not at present possess, it is interesting to find that a collection of corpuscles describing circles under forces varying inversely as the square of the distance in the molecules of a substance which shows no selective absorption would, like the ideal ‘“‘black””? body, radiate at a rate proportional to the fourth power of the absolute temperature. XXIX. On Spontaneous N nib and on Nuclei by Shaking Solutions, By C. Barus *. produced SPoNTANEOUS NUCLEATION. ‘haa ‘Science’ (xv. Jan. 1902, p. 178) I communicated some results which seemed to give evidence of the spontaneous production of nuclei from certain organic liquids. Though my own work is rather more concerned with the diffusion of the nuclei with an ulterior view to their velocity, no matter how the nuclei may be localized, it nevertheless seemed interesting to elucidate the subject incidentally. I therefore made a series of experiments in which condensation was produced by the expansion method in case of gasoline, benzine, petroleum, benzol, carbon bisulphide, and water. Hydrocarbons.—The first three hydrocarbon liquids may be dismissed summarily. The air above them, if carefully freed from nuclei by precipitation, remained free from nuclei indefinitely. The test was made by leaving the receiver without interference for fifteen or more hours, all the cocks being shut off, except the one communicating with the atmosphere through a filter of compressed cotton, half a metre long. A perfect filter is essential throughout. In case of petroleum it is exceedingly difficult to remove the nuclei by precipitation alone; but they vanish in the lapse of time (days), and thereafter the air remains permanently without nucleation. In case of benzol I was for a Jong time erroneously of the opinion that nuclei arise spontaneously out of this liquid, and consistent results leading to this inference were obtained in great number. Doubt was cast on this supposition by the behaviour of the hydrocarbons just mentioned. The true explanation was subsequently found: on removing nuclei by precipitation with the object of obtaining dust-free air, a couche of nuclei is apt to remain. brooding immediately over the surface of the benzol, where it escapes detection. It is * Communicated by the Author. on Nuclei produced by Shaking Solutions. 263 in this couche that the nuclei which subsequently diffuse * into and fill the whole vessel originate. They do not come out of the benzol. To account for these couches, which occur more or less frequently with all hydrocarbons and other volatile liquids, it is necessary to consider the manner in which the nuclei are introduced into the receiver. This is done expeditiously by partially exhausting the receiver and allowing the inflowing air to pass over phosphorus, or glowing charcoal, or near a sulphur flame. In the case of water vapour the nuclei after entrance remain permanently apart. The nucleated air is always homogeneous and the coronas regular. Semi-coronas never occur. This indefinite suspension of nuclei means that they remain small, diffuse relatively fast, and gravitate very slowly. The phenomenon is very similar to the suspension of particles of clay in water. The speed of subsidence is a minimum. In case of the hydrocarbons &c. the occurrences are very different. What goes on while the nuclei are being introduced is not of course visible; but the first exhaustion after nucleation shows a horizontally graded distribution, in which the nuclei are wholly confined to a narrow stratum, usually imme- diately above the liquid, as already stated. The fog stratum may, however, show itself at the top of the vessel, or even between two hemispheres of clear non-nucleated air. Indeed the air is rarely, if ever, nucleated uniformly. The distribution, therefore, is one of density ; and from the relatively insignificant number of nuclei, it may be further supposed that to influence the density of the strata, the nuclei have been loaded on influx, almost without supersaturation, even though the fog particles are small enough to remain invisible. In sucha case it is hardly probable that the nuclei have remained individualized as in the case of water vapour ; it is more probable that they grow by coalescence or cohesion, until they are large enough to condense hydrocarbon vapour with the minimum of supersaturation or none at all. This again is remarkably like the subsidence of clay in hydrocarbon liquids, in which, from the cohesion of particles, the precipi- tation is, relatively speaking, instantaneous. It is not necessary, however, to assume loading. If the nucleus diffuses slowly enough in organic vapours to virtually * The rate of diffusion (roughly, ‘015 centim./sec., upward in benzol vapour, for instance) is the feature of these experiments on which I am now at work. Incidentally one may note that the “ granular” particles in water vapour should diffuse much more rapidly than the “ flocculent ” particles in benzol vapour, the nuclei being otherwise the same. 264 iDr. C. Barus on Spontaneous Nucleation and stick to the layers in question, and if there is any slight differs ence in temperature between the air inside of the receiver and the inflowing air, couches will result from convection. Con- versely, the pare non-occurrence of semi-coronas &c. in case of water vapour is an indication of relatively rapid diffusion, and therefore of nuclei of minimum size. The nucleus depends for tts size, cet. par., on the medium in which it is suspended. Nuclei from the same source will diffuse under otherwise like conditions 100 or 200 times more rapidly in water vapour than in benzol vapour. Under these conditions there would be fewer particles as compared with water vapour for like nucleation, &c., and normal coronas may appear at once in volatile hy drocarbons, whereas they are only reached after many exhaustions in water vapour. Experiment ™ bears this out. Moreover, the particles in the former case being larger require less super- saturation, and are more quickly removed, which is also true of the volatile liquids. Carbon Bisulphide—-The case of carbon bisulphide is peculiar, inasmuch as in addition to the occurrence of couches of the kind just described, this liquid emits nuclei spontaneously. I would not wish to assert this for the fresh and perfectly pure liquid ; but from carbon bisulphide which has been subjected to evaporation and contains sulphur, nuclei are continually evolved at a definite rate. Curiously enough, the addition of nuclei from without, whether coming from sulphur, punk, or atmospheric air (without shaking of the liquid) is almost insignificant. A couche a few centims. high is usually seen on first exhaustion, the remainder of the receiver being clear. After shaking the first. corona is annular, coarse, and normal, the aperture of its white disk s=3°7. The next exhaustion brings out semicircles concave upward or semi- annuli, the succeeding exhaustion quarter-annuli, &c., the colour ‘eventually vanishing in a filmy veil. Left to themselves, these partial nucleations gradually diffuse upward, and full coronas may be again obtained in the lapse of time. The. same result occurs if the air above the liquid has been quite freed of nuclei by repeated precipitation, as the nuclei are now supplied by the liquid itself. These coronas are first partial, then filmy and small but complete. Gradually they become larger and stronger until a limiting aperture and great intensity is reached. In other words, nuclei are emitted by the liquid in the dark, terminating in a state of saturation * Che American Journ, Sci., (4) xiii. pp. 81-94 (1902). on Nucler produced by Shaking Solutions. 265 of the air above. The following are typical data; s is the aperture * :— | . Time of Diffu-| 15 min. 30 min. 60 min. {|2h.40min.| 3h. 6h. | . 157g ‘sion, upward. | Cerona ......... Film, 5 cm.| Partial, | Full, faint,} Strong, Strong, Strong | Intense. high. faint. diffuse. S=1O8, | 520-25, | s=oo4. | See If the evaporation is accelerated, after shaking, as in a warm bright room, the saturated condition may be reached in two hours or less. Usually the coronas of the first hour, though full, are too faint for measurement. On successive exhaustions, the intense coronas vanish by passing through three-quarter, half, quarter coronas, &c., in turn. Persistent Liqguip NUCLEI. Hydrocarbons, §¢.—Nuclei obtained by vigorously shaking all the volatile liquids examined above, showed no tendency to vanish until removed by gravity. I will cite special instances at random bearing on this remarkable behaviour. Coronas produced by precipitating gasoline vapour on the nuclei produced by shaking the liquid, were observed with undiminished strength 7 minutes and 30 minutes after shaking, and might have been seen after an indefinitely longer time. The average apertures were s=1°4, corresponding to the. diameter of particle d=‘0029 centim. In petroleum the coronas were observed strongly an hour after shaking; in benzol similarly intense 5 min., 30 min., 44 min., and 60 min. after shaking; they were distinct 3 hours after but absent next day, about 15 hours after.. In carbon bisulphide the coronas due to shaken nuclei coalesce with the coronas due to spontaneous nuclei, so that they persist indefinitely. From the excessively volatile character of these liquids persistence, even beyond a few minutes, would be impossible if the liquids were quite pure. [or the small drops would evaporate and the large drops subside. Consequently the droplets must be solutions obtained by concentrating the impurities throughout the continued evaporation of the liquid by the addition of nuclei, &c. It is difficult to keep these liquids quite pure in an apparatus of which rubber tubing + is an essential part. Apparatus made entirely of glass parts * Source of light and goniometer are on opposite sides of the receiver, each 2°5 metres distant. The aperture s subtends the central white disk _ of its normalcorona. If dis the diameter of particle, d='00144/s centim. nearly. + Rubber tubing through which carbon bisulphide has been passed will furnish nuclei to precipitate water vapour for days after. Fresh tubing must therefore be provided for each new experiment. 266 Dr. C. Barus on Spontaneous Nucleation and fused together would be undesirable for practical reasons. To avoid these dilemmas experiments may be made with water, in which the difficulties mentioned do not occur, , and a definite decision may be reached. Water.—If all precautions be taken to insure clean and. new apparatus and appurtenances and perfect filtration, the air above the water, if free from nuclei, remains so inde- finitely. Spontaneous nucleation does not occur, If a clean vessel free from nuclei is vigorously shaken so as to comminute the water, nuclei are produced in considerable quantity, as is evidenced by the strong coronas seen on ex- haustion. But these coronas are short-lived, as shown by the following table :— Time elapsed after shaking. Corona. min, All but absent. oP) ”? Be] +P] ” oh bs Co C1 1 3) 9? 2 Faint corona, not measurable. Rain. 6 Corona, aperture, s=1°45. None Strong corona lasting 15 seconds. These nuclei are obviously water globules, which speedily evaporate or subside, vanishing in a few minutes. Let a small quantity of sodic carbonate be added to the water ; the result is a phenomenal increase in the persistence of the nuclei produced by shaking, as for instance : Time elapsed after shaking. Corona. 1 hour. Strong. s=1°4 2 5, ” s=1°6 3 5 ” s=0°9 Aor 2, Just visible. 1D Wik Absent. 15 ,, (violent shaking.) Distinct, clear, small. The size and persistence depends on the violence of shaking, the apertures varying from s=1°-4 to s=2°0 correspondingly. In the lapse of time the corona contracts, but may, in favor- able cases, be seen much after 15 hours. The body in solution in this case is solid, and one is liable to conclude that the nucleus in question is the solid residue left after evaporation. This, as will presently be shown, is not necessarily true ; the nucleus is liquid, being a more or less concentrated solution both here and in the above ex- periments with hydrocarbons, &e. To decide the question as to the cause of the indefinite persistence of the nuclei produced by shaking solutions (apart 1 nae on Nuclei — by Shaking Solutions. 267 from gravitation), it is necessary to test a chemically dissolved gas like hydrochloric acid or ammonia. Pure water was first taken and the evanescence of the nuclei (say within 4 minutes) confirmed. Pure hydrochloric acid was then added, and the persistence of the nuclei established, as shown by the following example :— Time elapsed after shaking dilute HCl. Corona. 4 min. Strong. s=1°65 10.3 Strong. 30 55 15 hours. Distinct. Weak. Tested with pure water again, the fleeting coronas per- sisted somewhat longer (vanished in 10 minutes) than before, showing that traces of HCl still lingered in the clean apparatus. On again adding HCl the above results were confirmed. Dilute ammonia was next tested in the same way. Great care had to be taken after the vessel was thoroughly cleaned to remove lingering traces of HCl. When this was done air free from nuclei remained so above dilute ammonia inde- finitely. No nuclei arise spontaneously from the liquid. On shaking the ammonia nucleus behaved like the nucleus of dilute hydrochloric acid, or of sodic carbonate solution, showing indefinite per sistence apart from removal by gravity. With these experiments the indefinite persistence of nuclei produced by shaking solutions, whatever be the original state of aggregation of the solute, may be considered established. It is finally necessary to inquire into the reasons. Cause of Persistence—Inasmuch as the nuclei are equally persistent, no matter whether the solute is gaseous or whether it is liquid or solid, it is not permissible to accentuate \the possible occurrence of solid residues as the cause of per- sistence. At first sight one would be liable to conclude that the persistent nuclei are loose molecular ageregates ; but their size, which probably embraces many thousands of mole- cules, is unfavourable to such an assumption. They cannot owe their condensational activity to ionization, for the effect is equally marked with the most pronounced hydrocarbon and other insulators. [Frictional electricity seems equally negligible; it would not account for the difference of be- haviour of pure water and solutions; for the electric field within the receiver is a closed field. The endeavour must therefore be made to explain the phenomenon in terms of surface-tension. If p, and p, be the vapour-pressures corresponding to radii r and «, T the 268 Dr. C. Barus on Spontaneous Nucleation and surface-tension, p and o the densities of liquid (solution) and vapour, Kelvin’s equation asserts PrP = 2To/pr, nearly, if p replaces (p—c). The present liquid, however, is a solution and its vapour-pres- sure, p,, lies below the normal value for the pure liquid. Furthermore, as the large drops grow at the expense of the smaller, the vapour-pressure for capillary reasons alone would decrease in the former case and increase in the latter case. At the same time, however, the larger drops becoming more dilute, increase their vapour-pressure, while the smaller _drops becoming more concentrated decrease it. correspondingly. The second group of influences therefore tend to counteract the effect of capillarity. It is quite conceivable that a state ofj equilibrium may eventually be reached in which the drops, large and small, will all have the same vapour- pressure (namely, that of the free surface of the liquid), that further evaporation will thereafter cease and the droplets persist, however small. In fact, after the lapse of time the preceding equation will be replaced for a given drop by Pri— Pg = 2V 0 /p'r", since the pressure, tension, size, and density of the droplet of solution have all changed by evaporation. If the more concentrated droplet of radius 7! now persists, P'r/=p,,, the vapour-pressure at the flat surface of the original solution. Hence Pao —P'o = 201" /p'r". For the case in which a solid is dissolved its mass remains © fixed within each suspended drop while the water alone evaporates. When a gas like HCl or H;N is dissolved the same will also probably be true, for the receiver is filled to the full partial pressure with the gas in question. Hence p' may be expressed in terms of p, or if c=7r°/r'"*, p =i +(p—1) - C, whence finally, if 9=p,, —p'.; r' =2o0T’/(1+(p—1) .¢) . Sp. For dilute solutions, p=1, and the last equation is simply e =2aT'/Sp. | Hence the nuclei produced by shaking dilute aqueous gi. — i % ow ei a on Nuclei produced by Shaking Solutions. 269 solutions may be considered as subject to this condition, in which all sizes of. particles are represented. If 7’=a, P' »=P.., the vapour-pressure at the flat surface. Neglecting the factor for electrolytes, if 6p is expressed in terms of Raoult’s law, n/N and n/N’ being the original and final ratios respectively, of the numbers of molecules in solute and solvent, and p the vapour-pressure at the flat surface of the reservoir of solution, 3 Sp =p(n/N’—n/N)/(1+n/N’). Furthermore, if the law discovered empirically by Quincke* (T=83 +187 n/N dynes) be adduced, T= T + 187 (n/N'’—n/N) where T is the initial and T’ the final surface-tension in dynes per centim. Thus, finally, if (n/N’'—n/N)=4, for brevity, n'=20(T + 187k)(1+7/N’)/p. (1+ (e—le)k. Supposing the electrolytic factor supplied, this equation ex- presses the relation of the radius of the droplets in terms of the original and final ratios of the numbers of molecules of solute and solvent in solution. It implies that if the nuclei produced by shaking are originally of different sizes this difference will be accentuated. There is thus a curious dis- crepancy between equation and observation; coronas pro- duced from nuclei due to shaking are always annular on first exhaustion, whatever be the vapour or however long the lapse of time. They eventually vanish annularly, in case of the most volatile hydrocarbon liquid. This can only occur if the shaken nuclei are of about the same size originally, which, in fact, is approximately seen on trial. A reason for it, however, seems difficult to discern. The fact that mere agitation ¢ of the liquid should leave nuclei in its wake so nearly of a size as to produce coronas at all is the essential question, Brown University, Providence, R.I., U.S.A * Winkelmann’s Handbuch, vol. i. p. 466 (Breslau, 1891). An ex- cellent account of the capillary coefficients of solutions will here be found,. due to Prof. F, Braun. t Lenard’s experiments (Wied. Ann. xlvi. p. 584, 1892) on the. electricity of waterfails might be recalled. \p* [2IDy XXX. Onthe Velocity of Reaction before Complete Equilibrium and the Point of Transition are reached, §e.—Part I1.* By Meyer WiLpErRMAN, Ph.D., B.Sc. (Oxon.)t. CONTENTS. I, Velocity of reaction before complete equilibrium, &c., and the theory of real and apparent freezing-points, boiling-points, vapour-pressures, solubility, &c. II. Velocity of reaction before complete equilibrium, &c., and physical geography and meteorology. I. Velocity of Reaction before Complete Equilibrium and the Point of Transition are reached, and the Theory of Real and Apparent Freezing-Points, Boiling-Points, Vapour- Pressures, Solubility, Se. | TFNHE equation for the velocity of ice-melting and ice- separation established in Part I., shows that the equations used in my paper “On the Real and Apparent Freezing- points and the Freezing-point Methods” (Phil. Mag. Dec. 1897) have only to be corrected by the addition of the instability constant in’ order that the theory of real and apparent freezing-points should be placed on a_perfectl eorrect basis. Asis to be seen from Tables I. and II., the values of C which are obtained from the middle part of the curve, when the equation at = Clto—#)(t—tn) instead of _ =O, \¢- ee is used, differ only a little from the correct value of OC, obtained when K is taken into consideration. For this reason the numerical data used for C in the above paper (see the cor- rections in Phil. Mag., January 1898), which were obtained with the sensitive 1/100° mercury-thermometer, do not differ much from those which were obtained later on under much more favourable experimental conditions, and by means of the platinum thermometer. We can therefore safely assume, that the theoretical conclusions and numerical values given in the above paper, for my own method as well as for those used by others, are essentially correct. Among other things we may regard it as finally established, that the difference between the real and apparent freezing-points, as well as the difference between the real and apparent freezing-point de- pressions, are, in the method used by me, only 0°-00002 to 0°-00004, when the convergence temperature is below the freezing temperature. In the same way all the rules given * For Part I. see Phil. Mag. July 1901, p. 50, + Communicated by the Author. - “2. Velocity of Reaction before Complete Equilibrium, 271 in detail in my publications of 1896 (see Proc. of the Royal Society, 1896; Zeitschrift fir physikalische Chemie, January 1896) are essentially necessary for securing reliable results of great accuracy. In the theoretical treatment of the subject of freezing-points, there were some essential differ- ences between Nernst and myself, and as it is now intended to extend the problem to a very much larger field (of vapour- pressures, boiling-points, sublimation-pressures, solubility, &.) it becomes necessary to deal here in a few words with those differences. In his theoretical consideration of the subject of freezing- points Nernst started (see Zeitschr. fiir physik. Chemie, 1896; see also full translation in my paper, Phil. Mag. December 1897) from the experiments of Boguski on the velocity of solution of metals and marble in acids. He there makes the assumption that the velocity of ice-melting repre- sents the same kind of phenomena as those observed by Boguski, and that it consequently has to be expressed by the equation given by Boguski for the above reactions. He further correspondingly assumes that the apparent freezing-point always depends on the velocity of ice-melting, the term C(t,—t) e e,e e e mer having a positive or negative value according as t, (the convergence temperature) is greater or smaller than t' or to, 2. é.,18 above or below the freezing temperature. On the contrary, I thought that between the reactions of Boguski and that of ice-melting there is no analogy whatever, both representing reactions sui generis. My considerations of the theory of the sulject were based on the notion of perfect equili- brium, and the conclusion was arrived at that when the convergence temperature is above the freezing-point the reaction of ice-melting, and when below that of ice separation, is to be taken into account. The two reactions are of opposite kind, must or may have different velocity constants, and have first to be studied and investigated independently. As will be seen later on, this conception proved to be the correct one. Not only does the reaction of Boguski and that of ice-melting prove each to be suz generis, but Boguski’s equation for the velocity of solution of metals and of marble in acids is, in all robability, an incorrect one, contradicting as it does the well-established laws of mass action ; the phenomenon itself represented by Boguski’s reaction has not been (as will be seen later on) even correctly conceived in its true nature, though the misconception was a natural one. Having now arrived at the result that the velocity of all 272 - Dr. Meyer Wilderman on the Velocity of reactions before complete equilibrium follows the same general law — =U(é,—t)(t—t.+K), we are now entitled to regard all those reactions as being of one and the same nature. If it be furtherconsidered that im the establishing of all the different kinds of equilibrium there 1s always a cooling or warming of the system by the surrounding medium, it becomes evident that not only have we to deal with real and apparent freezing-points, but also with real and apparent vapour-pressures, sublimation-pressures, boiling-points, solubilitzes, &c. In all these cases one of the two opposite reactions (evaporation, sublimation, solution, or condensation to liquid or solid, separation of the solid from supersaturated solutions, &c.) comes into consideration according as the convergence temperature is above or below the point of equilibrium. This equation must necessarily be connected with that of cooling or warming of the system by the sur- rounding medium. The general equation is in all cases dt Fy HC (to—t) (t= toy + K) + O(ts 2), when during the reaction the surface of contact of the solid with the liquid or the gas varies (in the case of freezing- points, solubility, &e.); or Awl zy = C"(t,—t) + C(t,—2), when the surface of contact remains constant (vapour-pres- oN dt sures, boiling-points, &c.). When a becomes = 0, we get not the real, but an apparent point of equilibrium. The apparent point of equilibrium is always obtained between the real point of equilibrium and the convergence temperature. It is above or below the real point of equilibrium, according as the con- vergence temperature is, at the given arrangements of the experiment, above or below the real point of equilibrium. The difference between the real and apparent equilibrium, or the error of the observed results, depends upon how far we suc- ceed by the given arrangements of the experiment in keeping the latter fraction as small and as constant as possible in the equation T” (observed apparent point of equilibrium) =T, (the real point of equilibrium) +. C(t,—t) C’ (to— tov + K) nan C(t,—t) g oi! Reaction before Complete Equilibrium. 273 {which gives the value of theexperimentalerror). The difference between the real and apparent lowering of the vapour-pressure or of the rise of boiling-points, §c., is Of) Care) C'(to—to + K) C(t! —ton! + K'Y and the value of the right side of the equation must be kept by the arrangements of the experiment as small as possible, so that their value may be neglected on the side of t,—#/. The present considerations are only of a preliminary nature, and it is hoped in the future to give a full statement of the subject. The boiling-point method gives moderately satisfactory results if very great accuracy is not required. The velocity constant of evaporation OC" is moderately great at the boiling- point, the equilibrium being always reached in a comparatively short time. So also 100 c¢. em. of liquid and an air-bath are the quantities commonly used (Beckmann). Thus C” is great enough and C is not very small. Further improvements on the method will be made by the use of a greater quantity of liquid, and by the arrangement of the convergence tem- perature as near as possible to the boiling-point of the given liquid. With the methods for vapour-pressures we have also been unable up to now to get satisfactory results, even in the case of moderately dilute solutions, where the boiling-point method is already capable of giving satisfactory results. The reason of this is to be found in the fact that the velocity constant C” of evaporation is very small. As is the case with all reactions, the velocity of evaporation becomes smaller with the fall of temperature ; and it is a well-known fact that the time necessary for obtaining the maximum vapour-pressure is, at ordinary temperature, already very considerable. Since the total value of the observed vapour-pressure is at the (! 2") ~(t.—t,/) = : C(t,—# ordinary temperature very small, the values of a and e La—t/) _ C(t —t") ¢ siderable part of the val rae Ga orm a considerable part of the value of T'—T” or of T,—T,’. It was shown (Phil. Mag. Dec. 1897) that even in the freezing-point method, when 100 c. em. of liquid, a liquid-bath of —0°-3, and a quantity of ice at equili- brium =0°'3 are used, the experimental error in the obtained freezing-points and freezing-point depressions becomes already about 20 times greater than in my method, and amounts to several thousandths of a degree. It is clear that the results Phil. Mug. 8. 6. Vol. 4. No. 20. Aug. 1902. fh 274 Dr. Meyer Wilderman on the Velocity. of obtained with the different methods of measuring vapour-pres- sures must be considerably worse than those of the freezing- points. In the first instance the equilibrium in the case of freezing-points is completely reached after about 15 seconds, whilein the caseof vapour-pressuresit takes hours: thereforethe value of C” is in the case of vapour-pressures several hundred times smaller. In the second instance the quantity of the liquid used to the present in these methods is, in comparison with that now used for freezing-points, very small, a liquid jacket is always employed, and the surface of evaporationT,—T,, cannot be increased ad libitum, as in the case of freezing-points. No care we find is also taken for getting the convergence-tem- perature near the point of equilibrium. To this we must add other very serious sources of error, such as the variation of concentration and temperature at the evaporating surface, which cannot be easily avoided, &c. From the above remarks it is clear in what direction, on which lines, and how far the methods for measuring vapour-pressures can be effectually advanced. We cannot change the value of C”, but we can use greater quantities of liquid, try to keep the evaporating surface larger, keeping the liquid rather wide than deep; we can provide the who'e apparatus with an air-bath placed in a liquid- or vapour-bath of a constant temperature, &e., and get the convergence-temperature as near as possible to the point of equilibrium (there is almost an unlimited number of liquids or solutions to choose from, boiling at any desired tempera- ture), so also we have to provide some arrangements for shaking the hquid. It is obvious that the values of C” and of T,—T,, make it in this case very imperative that great effort should be made to get the value of T,—T, very small. The experiments will, because of this, necessarily be very tedious, but it is unavoidable. No doubt the results will always remain less accurate than may be desirable, limited as we are by the nature of the phenomenon itself in our capacity of making progress. It is further to be considered that an error of 0:001 mm. mercury causes for one molecule normal — solution of a nonelectrolyte already an error of 1°2 per cent. in the total value of the observed depression of the vapour- pressure, and 12 per cent. for 0°] mol. normal solution, while im the freezing-point methods even an error of 0°-0015 does not form 0°1 per cent. error in the total observed value of the freezing-point depression of one molecule nermal solution (the aggregate error of my method, however, does not reach _ the value of 0°:0U01-0°:0003). For this reason also much ‘more accurate readings than to 0001 mm. mercury become Reaction before Complete Equilibrium, ye Be necessary, if even moderately dilute solutions should be investi- gated. The present systems of reading the pressure up to 0-001 mm. seem to me also not to be reliable and accurate to the same extent. Passing to the methods of solubility, we have to note in the first instance that the value of C’” in the equation o sO Ait K) is considerab!y smaller in case of separation of the salt from 2 supersaturated solution, than in the case of separation of ice from an aqueous solution. The first reactions last a few minutes, while thei second ones only last from 15° to 30°. The value of C’’ is accordingly (see tables in Part I.) about ten times smaller for the first than for the last. In the different methods in use about 100 c. cm. liquid and a liquid-bath are usually employed, no account being taken of the proper arrangement of the convergence-temperature. On the con- trary, the value of T, ‘T., or the surface of the solid salt in contact with the liquid is usually great, and can be taken even considerably greater than in the case of the freezing- point method. The principles to be followed here for the development of the method are the same as in all other cases: a greater quantity of the liquid in an air-bath, which is placed in a liquid- or vapour-bath of a suitable constant temperature, should be used, and the convergence-temperature should be kept very near the point of equilibrium. A great value of T,—T,, should be provided for so as to compensate for the small value of C”. For this the solid should be present in great quantity and finely divided in the liquid, &c. The method can also be arranged in a way quite analogous to that of freezing-point, and the experiments given above show that the results in this case are very successful. Since C" is not very great here, and all the conditions necessary for securing a successful experiment have to the present not been taken sufficiently into account, there is no wonder that the results obtained by different investigators almost always differ considerably from one another, and that almost all of the results in this region of investigation cannot claim to be of great accuracy. specially at higher temperatures, where the values of C(t,—t), or velocity of cooling by the surround- ing medium, become very great, we find that the results prove to be very much affected by experimental errors, as could be easily illustrated on the run of a great number of curves. Lip eee 276 Velovity of Reaction before Complete Equilibrium. II. Velocity of Reaction, Complete Equilibrium, and Physical Geography and Meteorology. The formation and melting of ice, snow, hail, glaciers, snowfields, &., the evaporation of water (of the atmosphere, of the sea, rivers, &c.), the condens:tion of saturated vapours (to water, clouds, rain, dew, &c.), the solution and carrying away as well as separation of the solid components of the earth, in short, all the most important phenomena which form the main subject of physical geography and of meteorology, follow in their velocity the law given above - =C(t,—t)(t—to + K). From the form of the equation tt follows that all those reactions, even in their pure form, can never reach the point of perfect equilibrium. But, besides, here especially do the phenomena become always more complicated, owing to the interference of other factors, such as the cooling or warming of the surrounding temperature. For this reason always only apparent and never real points of equilibrium are reached in nature, therefore all the phenomena in nature never come to a state of perfect rest, but everything in nature is ina ‘state of eternal reaction. All the above phenomena must therefore henceforth be considered not only in the light of the theoretical points of equilibrium, as it has been up to the present, but alsoin the light of their actual state, in the light of velocity of reaction. This I shall endeavour to doin due course ina future publication. Since the conver- gence-temperature, owing to the continual variations in the surrounding temperature, is continually changing, the appa- rent point of equilibrium of a given system also undergves continuous variations and shiftings. .In considering the above phenomena the importance of the instability constant K must not be overlooked, because zt alone explains how a heterogeneous system can be fornwd from a homogeneous one without having it necessary as a condition for such a trans- forming that the newly-formed part should first be present in the system (e.g. it explains why overcooled water separates ice, not only when an ice-crystal is first introduced, and an unstable heterogeneous system is thus first formed, but also why this separation takes place without such a crystal having been introduced, see Part I.). The instability constant, it. must be remarked, depends upon a series of factors, internal and external. For instance a supercooled liquid or a supersaturated solution begins to crystallize too early if the liquid is shaken, or if a speck of dust has fallen into it; the Notices respecting New Books. 207 same liquid can be much more supercooled in narrow tubes than in wider vessels ; the same liquid can be more super- cooled if the cooling proceeds slowly, and if the temperature is equalized through the whole mass of the liquid, than when this is done rapidly. On the whole, the limit to which a liquid can be supercooled, a solution supersaturated, «c., depends upon the nature of the solvent, of the dissulved ~ substance, and upon the nature of the reaction itself. XXXI. Notices respectiny New Books. Mathematical and Physical Papers. By Sir Grorce GaBrien Stoxss, Bart., M.A., D.C.L., LLD., F.RS., Fellow of Pembroke College and Lucasian Professor of Mathematics in the University of Cambridge. Vol. III. Cambridge: At the University Press, 1901. Pp. vii+415. ee the long interval which has elapsed since Sir G. Gabriel Stokes published Vol. II. of his collected papers, the pr. sent volume will be eagerly welcomed by all students of mathematical physics. The immense convenience of having the papers of our great leaders in science collected in book: form can hardly be overestimated, especially in view of the ever-swelling stream of modern scientific literature, which makes such demands on the time of those eager to keep in touch with recent progress—time that can be ill-spared for the purpose of wading through a mass of bulky volumes in search of some classical paper of much earlier date. We sincerely hope that the author will find time and strength to complete the collection of his papers at an early date. About one-fourth of the present volume is occupied by the important memoir “On the Effect of the Internal Friction of Fluids on the Motion of Pendulums.” Then follows a paper on “the possible effect of the Radiation of Heat on the Pro- pagation of Sound,” and the renamder of the book is taken up with various papers, chiefly on Light—‘“On the Colours of Thick Plates”; “On a New Elliptic Analyser”; “On the Conduction of Heat in Crystals”; “Qn the Total Intensity of Interfering Light”; On the Composition and Resolution of Streams of Polarised Light from different Sources,” and “On the Change of Refrangibility of Light.” In the prefatory note to this volume, the author explains the reason of the long delay in its publication. It had been his intention to enter on * some rather elaborate and in part laborious calculations bearing on two of the papers which appear in the present volume.” This intention had, unfortunately, to be abandoned, and the papers referred to appear in their original furm. = 1 See hey . ' Ucber die Anwendung der Lehre von den Gasionen auf die Erschan- ungen der atmosphirischen Elekiricitit. Von Prof. Dr. Hans GeEITEL. Braunschweig: F.Viewegund Sohn. 1901. Pp.28. In this interesting pamphlet, the distinguished author seeks to explain the phenomenon of atmospheric electricity by the aid of recent researches regarding the discharging effect of air on charged conductors. The theory advanced possesses the merit of great simplicity, and, should subsequent quantitative researches furnish additional evidence in support of it, will mark a distinct step towards the solution of an extremely difficult problem. 278 Notices respecting New Books. Meteorologische Optik. Von J. M. Perntzr. I. Abschnitt. Wien und Leipzig: Wilhelm Braumiiller. 1902. Pp. vili+d4. Tus is the first part of a treatise on meteorological optics, and it deals with such problems as the apparent shape of the heavenly vault, the apparent altitude: of the heavenly bodies, the apparent increase in the size of the sun and moon when near the borizon, &c., a thorough discussion of each problem from a physico-physiologiecal standpoint being given. The treatise is to be completed in four parts. . La Géométrie Non Euclidienne. Par P. BARBARIN. Paris: C. Naud, 1902. Pp. 78. (“Scientia” Series, No. 15.) Evcuip’s celebrated axiom regarding the intersection at some finite distance of two straight lines which meet a third line so as to make the sum of the two interior angles on the same side of it ~ Jess than two right angles, has been the subject of much discussion auiong geometers, and in modern times has given rise to two systems of non-Euclidian geometry, associated with the names of Lobatchewsky and Riemann. The author of the little book before us gives a very thorough and critical exposition of the new geometries, and the work may be recommended to the notice of those interested in the philosophical basis of geometrical reasoning. Primary Batteries. Their Theory, Construction and Use. By W. R. Coorrr, M.A., B.Sc. London: The Electrician Printing and Publishing Company, Limited. Pp. vi+324. NOTWITHSTANDING the numerous forms of primary batteries which have been invented at different times, the theory of the action of such a battery has been one of the most difficult problems confronting the scientific investigator, and one which, after a century of research, is still shrouded in mystery. The chemical changes which go on in a voltaic cell have, of course, been known for a very long time; but the precise way in which the chemical and electrical effects are related to one another, and the mechanism by which they are linked together, are problems of much greater difficulty and complexity. When Nernst boldly advanced his Notices respecting New Books. 279 elegant theory of electrolytic solution pressure and applied it to explain the action of a primary cell, it was thought that at last a satisfactory solution of the problem had been arrived at. Unfor- tunately, some recent work has placed serious obstacles in the way of Nernst’s theory, and the theory of ionization has by no means received unqualified support from physicists. It is probably owing to the somewhat chaotic state of the theory that no writer was found bold enough to write a comprehensive treatise on the primary cell, dealing with it in all its aspects. This task hasnow been accomplished—and accomplished most success- fully——by Mr. W. R. Cooper in the book before us. In the first few chapters we have a brief historical introduction and an account of the actions going on in a simple voltaic cell, including local action and polarization. Exception might be taken to the manner in which some of the terms are defined in these early chapters. Thus, electromotive force is explained to mean “that force which causes the current to flow in any circuit.” This semi-popular method of definition seems somewhat out of place in a book which is not intended for beginners. In chapters IV. and V. we have a very clear and interesting account of the theory of the voltaic ceil ; a-careful perusal of these chapters will probably couvince the reader that the theory of the voltaic cell has by no means reached finality. Chapter VI. deals with non-chemical cells and thermopiles. Some useful hints are contained in the next chapter, on the testing of cells. Then follows a detailed account of various forms of cells, the subdivision into one-fluid, two-fluid, and dry cells being adopted. Standard cells receive special consideration in Chapter XI. Since the introduction of the dynamo as a generator of electrical energy, the field of usefulness of the primary cell has been consi- derably restricted. In all cases, however, in which comparatively small currents are required at intervals, the primary cell has been able to hold its own. As standards of E.M.F., certain forms of cells will always be used. Within recent years, however, numerous attempts have been made by various inventors to produce a pri-. mary cell which should rival the steam-engine and dynamo as a current-generator. Jor this purpose the cell must be arranged to consume a cheap fuel—carbon. To all those who hope for great things from a carbon-consuming cell we earnestly commend the closing chapter of Mr. Cooper’s book, in which the subject of carbon-consuming cells is dealt with in a masterly fashion. The enthusiasts who look for a complete revolution in the cost of pro- ducing electrical energy when the long-wished-for carbon-consuming cell makes its appearance, will be somewhat subered by the clear and critical account of the subject which is to be found in Mr. Cooper's book. Such enthusiasts entirely overlook the fact that the cost of the fuel forms only one item in the total cost of production. Even a carbon-consuming cell would not enable us to obtain electrical energy at an entirely trifling cost. But 280 | Notices respecting New Books. such a cell is very long in making its appearance—so long, in fact, that we may be pardoned for regarding it as we should do the philosopher’s stone or the elixir of life—things highly desirable, perhaps, but impossible of attainment. — Mr. Cooper’s book is certain to appeal to a wide circle of readers, and we have no doubt whatever that it will at once take its place as the standard treatise on the subject. Géoméirographie ou Art des Constructions Géométriques. Par Emitz Lemownr. ©. Naud, 1902. Pp. 87. (“ Scientia” Series, No. 18.) Most problems in geometrical construction admit of more than one solution, butamong them there is generally one which involves the least number of operations, and is therefore the simplest. This simplest solution constitutes the geometrographic construction. The instruments employed consist of a straight-edge, dividers, and set-square. The various operations involved —adjusting the straight-elge so that it passes through one or two given points, drawing a straight line, setting the dividers to a given length, drawing a circle, &e.—are denoted by symbols. The complexity of the solution may then be ascertained from the symbolical expression for the operations involved, and the number of these latter is termed the coefficient of simplicity (as the author properly points out, the coefficient of complexity would be a more appro- priate term). By a careful study of the problem, the author has in many cases succeeded in reducing considerably the coefficient of simplicity. One case is mentioned in which, by the joint efforts of a number of geometers, this coefficient was reduced from 78 (involving the tracing of 17 straight lines and 20 circles) to 35 (7 straight lines and 5 circles). The author gives the solutions of 69 problems, in some cases giving several solutions one of which (the simplest) is the geometrographic one. The construction is first explained, and is then followed by a symbolical formula, the coefficient of simplicity, and the number of straight lines and circles drawn in the course of the construction. Théorie dela Lune. Par H. ANDoynr. Paris: C. Naud, 1902. Pp. 86. (“Scientia” Series, No. 17.) In this little book, the author develops, in the simplest possible form, the principal portions of the lunar theory, without, however, considering the numerical values of the various constants which appear in the equations. On account of the highly abstruse nature of the subject, the book is necessarily intended for specialists, and to them should prove very useful. IAPVEn | THE LONDON, EDINBURGH, anp DUBLIN . PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. wD Af qi." [SIXTH SERIES) AEA SRR iF i Je. ~ BG. § SEPTEMBER 19 SEP te 19, XXXII. On the Weights of Atoms! ENF QFEIS Zs By Lord Ketviy, G.C.V.O. “SSS [Concluded from page 198. ] § 52. A NEW method of finding an inferior limit to the number of molecules in a cubic centimetre of a gas, very different from anything previously thought of, and especially interesting to us In connexion with the wave- theory of light, was given by Lord Rayleigh*, in 1899, as a deduction from the dynamical theory of the blue sky which he had given 18 years earlier. Many previous writers, Newton included, had attributed the light from the sky, whether clear blue, or hazy, or cloudy, or rainy, to fine suspended particles which divert portions of the sunlight from its regular course ; but no one before Rayleigh, so far as I know, had published any idea of how to explain the blueness of the cloudless sky. Stokes, in his celebrated paper on Fluorescence +, had given the true theory of what was known regarding the polarization of the blue sky in the following “ sjonificant remark” as Rayleigh calls it : ‘‘ Now this result ‘appears to me to have no remote bearing on the question of “the directions of the vibrations in polarized light. So long ‘“‘as the suspended particles are large compared with the waves “‘ of light, reflexion takes place as it would from a portion of “the surface of a large solid immersed in the fluid, and no ‘conclusion can be drawn either way. But if the diameter #* Rayleigh, Collected Papers, vol. i. art. vill. p. 87. + “On the Change of Refrangibility of Light,” Phil. Trans. 1852, and Collected Papers, vol. iii. Phil. Mag. 8. 6. Vol. 4. No. 21. Sept. 1902. U 282 Lord Kelvin on ‘‘ of the particles be small compared with the length of a wave “ of light, it seems plain that the vibrations in a reflected ray “cannot be perpendicular to the vibrations in the incident “ray” ; which implies that the light scattered in directions perpendicular to the exciting incident ray has everywhere its. vibrations perpendicular to the plane of the incident ray and the scattered ray ; provided the diameter of the molecule which causes the scattering is very small in comparison with the wave-length of the light. In conversation Stokes told me of this conclusion, and explained to me with perfect clearness and completeness its dynamical foundation ; and applied it to. explain the polarization of the light of a cloudless sky, viewed in a direction at right angles to the direction of the sun. But he did not tell me (though I have no doubt he knew it himself) why the light of the cloudless sky seen in any direc- tion is blue, or I should certainly have remembered it. § 53. Rayleigh explained this thoroughly in his first paper (1871), and gave what is now knownas Rayleigh’s law of the blue sky ; which is, that, provided the diameters of the suspended particles are small in comparison with the wave- lengths, the proportions of scattered light to incident light for different wave-lengths are inversely as the fourth powers of the wave-lengths. Thus, while the scattered light has. the same colour as the incident light when homogeneous, the proportion of scattered light to incident light is seven times. as great for the violet as for the red of the visible spectrum ; which explains the intensely blue or violet colour of the clearest blue sky. § 54, The dynamical theory shows that the part of the light of the blue sky, looked at in a direction perpendicular to the direction of the sun, which is due to sunlight incident on a single particle of diameter very small in comparison with the wave-lengths of the illuminating light, consists of vibrations perpendicular to the plane of these two directions = that is to say, is completely polarized in the plane through the sun. In his 1871 paper *, Rayleigh pointed out that each particle is illuminated, not only by the direct light of the sun, but also by light scattered from other particles, and by earth-— shine, and partly also by suspended particles of dimensions. not small in comparison with the wave-lengths of the actual light ; and he thus explained the observed fact that the polarization of even the clearest blue sky at 90° from the sun is not absolutely complete, though it is very nearly so. * Collected Papers, vol. i. p. 94. the Weights of Atoms. 283 There is very little of polarization in the light from white clouds seen in any direction, or even from a cloudless sky close above the horizon seen at 90° from the sun. This is partly because the particles which give it are not small in comparison with the wave-lengths, and partly because they contribute much to illuminate one another in addition to the sunlight directly incident on them. § 55. For his dynamical foundation, Rayleigh definitely assumed the suspended particles to act as if the ether in their places were denser than undisturbed ether, but otherwise uninfluenced by the matter of the particles themselves. He tacitly assumed throughout that the distance from particle to particle is very great in comparison with the greatest diameter of each particle. He assumed these denser portions of ether to be of the same rigidity as undisturbed ether ; but it is obvious that this last assumption could not largely influence the result, pr ovided the greatest diameter of each particle is very small in comparison “with its distance from next neighbour, and with the wave-lengths of the light: and, in fact, I have found from the investigation of §§ 41, 42 of lecture XIV. for rigid spherical molecules embedded in ether, exactly the same result as Rayleigh’s ; which is as follows 82r°n (D’ ae IY —D Ty? k= (= D 3a) =82672 n( eh alt oO: where A denotes the wave-length of the incident light sup- posed homogeneous ; 7’ the volume of each suspended particle: DP the undisturbed density of the ether ; D’ the mean density of the ether within the particle; 2 the number of particles per cubic centimetre ; and k the proportionate loss of homo- geneous incident light, due to the scattering in all directions by the suspended particles per centimetre “of air traversed, Thus Uke ia ae A rd aa tnn Mii Re a 02) is the loss of light in travelling a distance x (reckoned in centimetres) through ether as disturbed by the suspended particles. It is remarkable that D’ need not be uniform throughout the particle. It is also remarkable that the shape of the volume 7’may be anything, provided only its greatest diameter is very pian in comparison with X. The formula supposes T (D’ —D) the same for all the particles. We shall have to consider cases in which anny of-T and L’ for different 2 84 Lord Kelvin on particles are essential to the result ; and to include these we shall have to use the formula 82°67. -(D!—D) T° bag ee) et Os eo old 9 pee 2 where > [so ] denotes the sum of ae for all the particles in a cubic centimetre. § 56. Supposing now the number of suspended particles per cubic wave-length to be very great, and the greatest diameter of each to be small in comparison with its distance from next neighbour, we see that the virtual density of the ether vibrating among the particles is PART =D) os and therefore, if « and wu’ be the velocities of light in pure ether, and in ether as disturbed by the suspended particles, we have (Lecture VIII. p. 80) . (5). te E 43 a Gosid =) Hence, if w denote the refractive index of the disturbed ether, that of pure ether being 1, we have fist)... and therefore, approximately, T(D'—D) — § 57. In taking an example to illustrate the actual trans- parency of our atmosphere, Rayleigh says* ; “ Perhaps the ‘ * Phil, Mag. April 1899, p. 382. the Weights of Atoms. 285 have ¢—$3000% — -§ ; which gives 1/k=3720000 centimetres= 37°2 kilometres. . § 58. Suppose for a moment the want of perfect trans- parency thus defined to be wholly due to the fact that the ultimate molecules of air are not infinitely small and infinitely numerous, so that the “‘ suspended particles” hitherto spoken of would be merely the molecules N., O, ; and suppose further (D'—D)T to be the same for nitrogen and oxygen. The known refractivity of air (4a—1=-0003), nearly enough the same for all visible light, gives by equation (7) above, with » instead of >, n(D'—D) T A = "0006. Using this in (1) we find 29°76 SD RAPES CS) for what the rate of loss on direct sunlight would be, per centi- metre of air traversed, if the light were all of one wave-length, dX. But we have no such simplicity in Bouguer’s datum regarding transparency for the actual mixture which consti- tutes sunlight : because the formula makes k-! proportional to the fourth power of the wave-length ; and every cloudless sunset and moonset and sunrise and moonrise over the sea, and every cloudless view of sun or moon below the horizon of the eye on a high mountain, proves the transparency to be in reality much greater for red light than for the average un- dimmed light of either luminary, though probably not so much greater as to be proportional to the fourth power of the wave- length. We may, however, feel fairly sure that Bouguer’s estimate of the loss of light in passing vertically through the whole atmosphere is approximately true for the most luminous part of the spectrum corresponding to about the D line, wave- length 5°89 .10-° cm., or (a convenient round number) 6. 10~? as Rayleigh has taken it. With this value for A, and 3°72 . 10 centimetres for £—', (8) gives n=8°54.10'® for atmospheric air at 10° and at standard pressure. Now it is quite certain that a very large part of the loss of light estimated by Bouguer is due to suspended particles ; and therefore it is certain that the number of molecules in a cubic centimetre of gas at standard temperature and pressure is considerably greater than 8°54.10". 286. _ Lord Kelvin on § 59. This conclusion drawn by Rayleigh from his dynami- cal theory of the absorption of light from direct rays through air, giving very decidedly an inferior limit to the number of molecules in a cubic centimetre of gas, is perhaps the most thoroughly well founded of all definite estimates hitherto made regarding sizes or numbers of atoms. We shall see (§§ 73... 79 below) that a much larger inferior limit is found on the same principles by careful consideration of the loss of light due to the ultimate molecules of pure air and to suspended matter undoubtedly existing in all parts of our atmosphere, even where absolutely cloudless, that is to say, warmer than the dew-point, and therefore having none of the liquid spherules of water which constitute cloud or mist. § 60. Go now to the opposite extreme from the tentative hypothesis of $58 and, while assuming, as we know to be true, that the observed refractivity is wholly or almost wholly due to the ultimate molecules of air, suppose the opacity estimated by Bouguer to be wholly due to suspended particles which, for brevity, we shall call dust (whether dry or moist). These particles may be supposed to be generally of very unequal magnitudes : but, for simplicity, let us take a case in which they are all equal, and their number only 1/10000th of the 8°54.10'§, which in §59 we found to give the true refractivity of air, with Bouguer’s degree of opacity for A= 6.10-°. With the same opacity we now find the contribution to refractivity of the particles causing it, to be only 1/100th of the known refractivity of air. The number of particles of dust which we now have is 8°54.10™ per cubic centimetre, or 1107 per cubic wave-length, which we may suppose to be almost large enough or quite large enough to allow the dynamics of § 56 for refractivity to be approximately true. But it seems to me almost certain that 8:54.10" is vastly greater than the greatest number of dust particles per cubic centimetre to which the well-known haziness of the clearest of cloudless air in the lower regions of our atmosphere is due; and that the true numbers, at different times and places, may probably be such as those counted by Aitken * at from 42500 (Hyéres, 4 p.m. April 5, 1892) to 43 (Kingairloch, Argyll- shire, 1 p.m. to 1.30 p.m. July 26, 1891). § 61. Let us, however, find how small the number of par- ticles per cubic centimetre must be to produce Bouguer’s degree of opacity, without the particles themselves being so * Trans. R. 8, E. 1894, vol. xxxvii. part iii. pp. 675, 672 the Weights of Atoms. 287 large in comparison with the wave-length as to exclude the application of Rayleigh’s theory. Try tor example T=10~*.»° (that is to say, the volume of the molecule 1/1000th of the cubic wave-length, or roughly diameter of molecule 1/10th of the wave-length) which seems small enough for fairly approxi- mate application of Rayleigh’s theory ; and suppose, merely to make an example, D” to be the optical density of water, D being that of ether; that is to say, D’/D= (1°3337)* =1°78. Thus we have ()'!—D) T/D=:0007A? : and witha=6 . 10-5, and with £—! =3°72.10°, (1) gives n=1:48.10°, or about one and a half million particles per cubic centimetre. Though this is larger than the largest number for natural air counted by Aitken, it is interesting as showing that Bouguer’s degree of opacity can be accounted for by suspended particles, few enough to give no appreciable contribution to refractivity, and yet not too large for Rayleigh’s theory. But when we look through very clear air by day, and see how far from azure or deep blue is the colour of a few hundred metres, or a few kilometres of air with the mouth of a cave or the darkest shade of mountain or forest for back- ground; and when in fine sunny weather we study the appearance of the grayish haze always, even on the clearest days, notably visible over the scenery among mountains or hills ; and when by night at sea we see a lighthouse light at a distance of 45 or 50 kilometres, and perceive how little of redness it shows; and when we see the setting sun shorn of his brilliance sufficiently to allow us to look direct athis face, and yet only ruddy, rarely what cauld be called ruby red ; it seems to me that we have strong evidence for believing that the want of perfect clearness of the lower regions of our. atmosphere is in the main due to suspended particles, too large to allow approximate fulfilment of Rayleigh’s law of fourth power of wave-length. § 62. But even if they were small enough for Rayleigh’s theory the question would remain, Are they small enough and numerous enough to account for the refractivity of the atmo- sphere? ‘To this we shall presently see we must answer undoubtedly ** No”’; and much less than Bouguer’s degree of opacity, probably not as much as a quarter or a fifth of it, is due to the ultimate molecules of air. In a paper by Mr. (Juirino Majorana in the Transactions of the R. Accademia dei Lincei (of which a translation is published in the Philo- sophical Magazine for May 1901), observations by himself in Sicily, at Catania and on Mount Etna, and by Mr. Gaudenzio Sella, on Monte Rosa in Switzerland, determining the ratio of the brightness of the sun’s surface to the brightness of the’ 3 ‘ - ‘ “S 288 Lord Kelvin on sky seen in any direction, are described. This ratio they denote by 7. One specially notable result of Mr. Majorana’s is that ‘the value of 7 at the crater of Etna is about five times greater than at Catania.”” The barometric pressures were approximately 53°6 and 76 cms. of mercury. Thus the ! atmosphere above Catania was only 1°42 times the atmosphere i above Htna,and yetit gave fivetimes as much scattering of light by its particles, and by the particles suspended init. This at once proves that a great part of the scattering must be due to suspended particles ; and more of them than in proportion to the density in the air below the level of Etna than in the air above it. In Majorana’s observations, it was found that ‘“‘except for regions close to the horizon, the luminosity of the “sky hada sensibly constant value in all directions when ‘“‘viewed from the summit of Htna.” This uniformity was observed even for points in the neighbourhood of the sun, as near to it as he could make the observation without direct light from the sun getting into his instrument. I cannot but think that this apparent uniformity was only partial. It is quite certain that with sunlight shining down from above, and with equal light everywhere shining up from earth or sea or haze, illuminating the higher air, the intensities of the blue light seen in different directions above the crater would be largely different. This is proved by the following investiga- tioa ; which is merely an application of Rayleigh’s theory to the question before us. But from Majorana’s narrative we may at all events assume that, as when observing from Catania, he also on Etna chose the least luminous part of the sky (Phil. Mag., May 1901, p. 561), for the recorded results (p. 562) of his observations. § 63. The diagram, fig. 1 below, is an ideal representation of a single molecule or particle, 7, with sunlight falling on it indicated by parallel lines, and so giving rise to scattered light seen by an eye at E. We suppose the molecule or particle to be so massive relatively to its bulk of ether that it is practically unmoved by the ethereal vibration; and for simplicity at present we suppose the ether to move freely through the volume 7, becoming denser without changing its velocity when it enters this fixed volume, and less dense q when it leaves. Im §§ 41, 42, of Lecture XV. above, and in \ Appendix A, a definite supposition, attributing to ether no other property than elasticity as of an utterly homogeneous perfectly elastic solid, and the exercise of mutual force between itself and ponderable matter occupying the same space, is explained : according to which the ether within the atom will aa the Weights of Atoms. 289 react upon moving ether outside just as it would if our present convenient temporary supposition of magically augmented density within the volume of an absolutely fixed molecule were realized in nature. For our present purpose, we may if we please, following Rayleigh, do away altogether with the ponderable molecule, and merely suppose 7 to be a denser Fig. 1. 8 E portion of the ether. And if its greatest diameter is small enough relatively to a wave-length, it will make no unnegli- gible difference whether we suppose the ether in 7 to have the same rigidity as the surrounding free ether, or suppose it perfectly rigid as in $§ 1—46 of Lecture XIV. dealing with a rigid globe embedded in ether. § 64. Resolving the incident light into two components having semi-ranges of vibration a, p, in the plane of the paper and perpendicular to it ; consider first the component in the plane having vibrations symbolically indicated by the arrow- heads, and expressed by the following formula Qarut A. ? @ sin where wu is the velocity of light, and ’ the wave-length. The greater density of the ether within 7 gives a reactive force 290° — Lord Kelvin on on the surrounding ether outside, in the line of the primary vibration, and against the direction of its acceleration, of which the magnitude is T(P!—D)\a 2mu__— Acrut D Wicces Cidade |. This alternating force produces a train of spherical waves spreading out from 7’ in all directions, of which the displace- ment is, at greatest, very small in comparison with a; and which at any point # at distance r from the centre of 7, large in comparison with the greatest diameter of 7, is given by the following expression * } 2ar 4 E cos (ui 7); | with pag) cos 0 . ., + ann where @ is the angle between the direction of the sun and the line TE. This formula, properly modified to apply it to the other component of the primary vibration, that is, the com- ponent perpendicular to the plane of the paper, gives for the displacement at / due to this component aT (ut r) Eh sedele U ) a 1(D'—D) rw? D ; Hence for the quantity of light falling from T per unit of time, on unit area of a plane at E, perpendicular to FT, reckoned in convenient temporary units, we have | 9 Wh ye - £24 9? — [| (w? cos? O+p?) . (12). § 65. Consider now the scattered light emanating from a large horizontal] plane stratum of air 1 cm. thick. Let 7 of fig. 1 be one of a vast number of particles in a portion of this with =p (11) . Ci oy ee ee * This formula is readily found from §§ 41, 42 of Lecture XIV. The complexity of the formulas in §§ 8-40 is due to the inclusion in the in- i vestigation of forces and displacements at small distances from 7, and to ! the condition imposed that 7 is a rigid spherical figure. The dynamics of §§ 33-36 with c=0,and the details of §§ 37-39 further simplified by taking v=o, lead readily to the formulas (10) and (11) in our present text, the Weights of Atoms. 291 stratum subtending a small solid angle 0 viewed at an angular distance 8 from the zenith by an eye at distance r.- The volume of this portion of the stratum is © sec 87? cubic centimetres ; and therefore, if } denotes summation for all the particles in a cubic centimetre, small enough for applica- tion of Rayleigh’s theory, and g the quantity of light shed by them from the portion 0 sec 8 7? of the stratum, and incident on a square centimetre at /, perpendicular to LZ, we have pote t(D = DP) ae Brey 32 2 y= 3 (SS ] O see B(@’ cos*O+p*). . (13). Summing this expression for the contributions by all the luminous elements of the sun and taking q=Q to denote this summation, we have instead of the factor aw cos 6+), cos’ 6 Ya° + (0 and we have ( =|r=35 By hey shay oar eR aE where S denotes the total quantity of light from the sun falling perpendicularly on unit of area in the particular place of the atmosphere considered. Hence the summation of (13) for all the sunlight incident on the portion Q sec 87° of the stratum, gives | 2 TID! — D7? a jae —] O sec B($ cos'G+4)S . (15). § 66. To define the point of the sky of which the illumina- tion is thus expressed, let ¢ be the zenith distance of the sun, and w the azimuth, reckoned from the sun, of the place of the sky seen along the line ET. This place and the sun and the zenith are at the angles of a spherical triangle SZT, of which ST is equal to 6. Hence we have cos @=cos cos B+sin CsinBcosy . . . (16). Let now, as an example, the sun be vertical : we have €=0, §=B, and (15) becomes 5 T(D’—D)7 é' C= —* Sea 0.4 (cos 8+sec B)S a, ce axae 292 Lord Kelvin on This shows least luminosity of the sky around the sun at the zenith, increasing to « at the horizon (easily interpreted). The law of increase is illustrated in the following table of values of $ (cos 8+sec 8) for every 10° of B from 0° to 90°. B. | 3 (cos 6+sec {). | B. 3 (cos 8+sec B). | ‘000 | 50° 1-099 LS 1 10° | 1-000 60° 50 (San 20° | 1-002 a (708 1632 2 300 1-010 80° 2-966 40° | 103 90° a | § 67. Instead now of considering illumination on a plane perpendicular to the line of vision, consider the illumination by ight from our one-centimetre-thick great* horizontal plane stratum of air, incident on a square centimetre of hori- zontal plane. The quantity of this light per unit of time coming from a portion of sky subtending a small solid angle QO, at zenith distance Bis Qcos B®. Taking Q=sinBdBdy and integrating, we find for the light shed by the one-centi- metre-thick horizontal stratum on a_ horizontal square centimetre of the ground, e pee cosB 47° T(D'—D)7? { in|) dB sin B.Q cere ai = i> | Sa (18). Now each molecule and particle of dust sheds as much light upwards as downwards. Hence (18) doubled expresses the quantity of light lost by direct rays from a vertical sun in crossing the one-centimetre-thick horizontal stratum. It agrees with the expression for £in (1) of § 55, as it ought to do. § 68. The expression (15) is independent of the distance of the stratum above the level of the observer’s eye. Hence if H denote the height above this level, of the upper boundary of an ideal homogeneous atmosphere consisting of all the ultimate molecules and all the dust of the real atmosphere scattered uniformly through it, and if s denote the whole light on unit.area of a plane at # perpendicular to HT, from all the molecules and dust in the solid angle © of the real atmo- * We are neglecting the curvature of the earth, and supposing the density and composition of the air to be the same throughout the plane horizontal stratum to distances from the zenith very great in comparison with its height above the ground. ee — Re Ey Cage the Weights of Atoms. 293 sphere, due to the sun’s direct light incident on them, we have T (D!—D)7? =H sce 8™, S [=F EP") o.4(co+1). . . (19); provided we may, in the cases of application whatever they may be, neglect the diminution of the direct sunlight in its actual course through air, whether to the observer or to the portion of the air of which he observes the luminosity, and neglect the diminution of the scattered light from the air in its course through air to the observer. This proviso we shall see is practically fulfilled in Mr. Majorana’s observations on the crater of Etna for zenith distances of the sun not exceeding 60°, and in Mr. Sella’s observation on Monte Rosa in which the sun’s zenith distance was 50°. But for Majorana’s recorded observation on Etna at 5.50 a.m. when the sun’s zenith distance was 81°71, of which the secant is 6°927, there may have been an important diminution of the sun’s light reaching the air vertically above the observer, anda consider- ably more important diminution of his light as seen direct by the observer. This would tend to make the sunlight reaching the observer less strong relatively to the skylight. than according to (19) ; and might conceivably account for the first number in col. 3 being smaller than the first number in col. 4 of the Table of § 69 ‘below ; but it seems to me more probable that the smallness of the first two numbers in col. 3, showing considerably greater luminosity of sky than accord- ing to (19), may be partly or chiefly due to dust in the air overhead, optically swelled by moisture in the early morning. The largeness of the luminosity of the sky indicated by, the smallness of the last number in hoy 3 (376), in comparison with the last number of col. 4 (460), may conceivably be explained by earthshine from air and volcanic ash and rock and forest and vineyard and sea below the level of the crater adding considerably to the illumination which the sky experi- ences from above by direct sunlight. This addition would be much greater at 11 a.m., when the sun’s zenith distance was 29°-9, than at 9 a.m., when it was 44°-6, § 69. The results of Majorana’s observations from the crater of Etna are shown in the following Table, of which the first and third columns are quoted from the Philosophical Magazine for May 1901, and the second column has been kindly g given to me in a letter by Mr. Majorana. ‘The values of S/s shown in column 4 are calculated from § 68 (19), with the factor of 294 _ Lord Kelvin on sec 8 (cos’@ + 1)taken to make it equal to Majorana’s r for sun’s zenith distance 44°°6, on the supposition that the region of sky observed was in each case (see $ 62 above) in the position of minimum luminosity as given by (19). It is obvious that this position is in a vertical great circle through the sun, and Ratio of Zenith distance Zenith luminosity of S f leext ‘lean Ti distance sun's disc to =. pea ye Veet H+ oP eam: luminosity of “ | oe | sky. sky, | ; Dies | i aaa 550am. | 8b7 | - 2570000 3280000 5D 7 68°0 | 3125000 3550000 14-4 8 56°1 3650000 3600000 21-7 9 446 3930000 3930000 27°8 11 29°9 | 33'6 | 3760000 | 4600000 on the opposite side of the zenith from the sun ; and thus we have 0=€+ 8. Hence (19) becomes T (D'—D)7° SH”, hae Tee, .3.sec B[cos'(€+8) +1] . (20).° To make (20) a minimum we have 2 sin 2 (8+) 3+cos 2 (8 +8) The value of @ satisfying this equation for any given value of € is easily found by trial and error, guided by a short preliminary table of values of 8 for assumed values of 6+. Col. 5 shows values of 8 thus found approximately enough to give the values of S/s shown in col. 4 for the several values of tan 6 = (21). § 70. Confining our attention now to Majorana’s obser- vations at 9 A.M. when the sun’s altitude was about 44°°6; let e be the proportion of the light illuminating the air over the crater of Etna which at that hour was due to air, earth, and water below; and therefore 1—e the proportion of the observed luminosity of the sky which was due to the direct rays of the sun, and expressed by § 68 (19). Thus, for GB=27°8, €=44°-6, and @=72°4, we have S/s=3930000/(1—e), instead . j a - en eet the Weights of Atoms. 295. of the S/s of col. 4, § 69. With this, equation (20) gives [225 i vt(1—e) —§ O Pirie My ci (1) QR 9%__ dH OH | ao, oe aie ot J according as we are dealing with wire or dielectric. 304 Prof. W. B. Morton on the Write the common periodic factor in the form e%™-?), 2 sad | then m= oe +ix, where » is the wave-leneth and « the attenuation-constant. Let 2): ae ae i. where Ay is the wave-length for the same frequency in free space, V the velocity of radiation, n=(Lein/ HP, oa 2 2 C=kP— n= =) iy + ie) . + < | Then the equations are satisfied by the following scheme,. omitting the periodic factor. Inside. Outside. See ae dd (kar), DK, (cr) > am im | ite tae —d Dhar) —D— ~ Kiler) 5) ey 2 Pi dide t. —d.23,( ker), Dag up i( 2?) 1 (cr) | J The J’s and K’s are the cylinder Bai vanishing for zero and infinite arguments respectively, d and D are con- stants. The argument of the J’s should strictly be Wk, ko? — m? —m?.r, but, as Thomson and Sommerfeld have shown, m is in actual cases negligible in comparison with hg. Further, c is a very small quantity, so we can put for the K’s the approximate values K,(cr) Lila ty i Kcr) = a where y is Euler’s constant 1°781. 2? In the case of two wires at distance b apart, if — ja can be neglected in comparison with unity, then, as I have shown in a former paper ™*, the state of affairs inside each wire is unaltered, and, outside, we get the approximate values by superposing two single wire solutions. * Phil. Mag. l. p. 605. Wrong signs appear in the values given for m, k,, R, and H in this paper, but the results arrived at are uot affected. Forms of the Lines of Electric Ferce. 305 Confining our attention to points in the plane of the wires we thus obtain for points between the wires the values b—4 | Pat ime | SG ese) € arene) and for points not between the wires Z=D log ig. 2 | - Y i R= D (> -75) do : . . . e e (7) tk,2/1 r ee te hic) The further discussion of phase-differences and lines of force is a good deal simplified by the fact that the constant 27 . * . . . ; . —, which appears in “Z” for a single wire, goes out in the Y present case. eeppheiaon of the surface conditions leads to the equation for c? . b ky?Jo (koa) ~ ia : “ z e 2 . . o S oacy kadiliey" aca § 3. The Relative Phases of the Components. We shall now investigate the phase-differences existing between the periodic magnitudes ZRH in the dielectric at the surface of a wire. As the expression for Z is real, the arguments of the complex quantities occurring in R and H will give their phase-differences in advance of "Z. Let a and B represent these quantities for RH respectively, so that if at a given point of the wire we have ZL=Z) sin pt, we shall have R=R, sin ( pt+a), H=H, sin ( pt+8). 306 Prot. W. B. Morton on the Then ine —= + arg. m—arg. (c’) : ie (9) g=—F —ag. (°) | Using equation (8) and remembering that arg. (k,@) = z> we have J (koa) Fs BN eae eee aro eZ Ji(kea) 9 a=arg. Tika 4 + arg. m | e ' (11) ae eS. Jy(koa) or ein aie A Ji (koa) It is now necessary to examine the values of ar g. Jo(ka) for different values of the variable, and also arg. m. Taking first J —* we have for small values of kya Jo + =Lhoa, A ie : My eae e argument is re and B=0. For very large values 7 =i, giving o=y 7. To trace the 0 course of the magnitude 8 between these ae we can use the tables of Jo(wi) and J\(wV2), which have been com- puted by Aldis*. His argument w# corresponds to 2an / a ai p and runs between values 0-1 and 6-0; the corresponding values of arg. Ji come out 44° 23’ and 86° 10’. The curve Jo marked @ in fig. 1 is plotted by calculation from Aldis’s tables. * Aldis, Proceedings of Roy. Soe. vol. lxvi. pp. 42, 483 (1899). Forms of the Lines of Electric Force. 307 Fig. 1. cai ASE ae NCES ete ic 2 ease et . Qa Tee. Turning now to arg. m, equation (8) with (4) gives wahtmemit} 1 pe} , log— kot . Sy (hq) ss ag. maha 1 —p eet » hea log= She sad (kya) 308 Prof. W. B. Morton on the To obtain numerical values it 1s necessary to assume a. particular value of a I have taken this as 100, and have a calculated arg. m by aid of Aldis’s tables. The result is shown in the curve marked («— 8) on fig. 1. The addition of the two curves obtained gives the @-curve, showing the phase-difference between R and Z. To form an idea of the position on this diagram of actual experimental cases, we may take those given in Sommerfeld’s. paper as extreme cases in opposite directions. His first case, typical of skin-conduction and very small attenuation, is that of copper wire of 4 mm. diameter with frequency of 10° alternations per sec. This gives 1358 as the value of aun / PTP and so lies far out to the right, where a and & p are both practically 45°. His other extreme case is that of platinum wire of 0-004 mm. diameter and a frequency of 3x 10%. This gives. 0:256 for the determining constant ; a comes on the inner side of the minimum position for a. The quantity (a—8)=arg. m=tan™ = is, for small values at least, proportional to the attenuation with given wave-length. It runs down to zero with increasing develop-- ment of surface-conduction, towards the right in the diagram. Looking now at the state of things just aside the wire we have of course the same phase-difference as before between Hand Z. For R the advance of phase on Z is from equations (5) T J aaa +arg. m—arg. k,+arg. J ie oF ra, & ean = 4 +arg. m—arg. a, =a~—-.. or the radial electric force inside is 90°:behind ‘that outside. §4. Directions of the Lines of Force and-of Energy-flow at the Surface of the Wires. It is easy to see that when Z and KR have opposite signs. the lines of force are tilted backwards ; when H Z are oppo-. site the energy-flow is outward; and when HR are opposite the flow is backward. Taking, then, a half wave-length Forms of the Lines of Electric Force. 309 (from 0 to 7) between points at which the lengthwise electric force Z vanishes, we find the flow of energy Outside. from 0 to (1w—a) forward, in from (7—a) to (7—f) backward, if , (13) from (7—) to 7 forward, out Inside. ~ from 0 to (5 —«) backward, in | from @ —a) to (w—f8) forward, in ( (14) from (7—) to 7 backward, out / The extent of the eddy in the external energy-flow is given by a. Its course as shown by the curve is in accordance with the statement in §1. For the limiting case of mere surface- conduction (k,a large) a=@=45°, the section (7—a) to (7— 8) shrinks to nothing, 7. e. the energy-tlow is everywhere in the direction of propagation of the waves. At the other extreme (f,a small) when a again approaches 45°, 8 becomes zero, and the region of outward flow disappears. § 5. Forms of Eaternal Lines of Force and Flow. We may write for points between the wires Z=log oer e—* sin Eee iy nr = . i Ste: a ee Ses ea ahd Es Cane nn sin Cu +hy) leading to . (ome T hy = log sin i hy + 7) teonst. . + ae and for lines of flow we get my (i? +m?) —hz(2h? +m?) =hm log | (2h? + m?) sin (mz + hy) —m? cos(mz+ hy)}+-const. . . . . (yen : : : 207 In the last equation m is written for ae In fig. 3 these two families of curves are plotted for the simple case m=h=1. It will be seen that all the curves of either family can be got by moving one of them in a direction making an angle of 45° with the negative direction of <. The angles marked on the diagram give the phase-angles of the lengthwise electric force. The magnetic force being A5° in advance of the lengthwise electric vanishes at all points of the straight line of electric force which meets the surface at 135°. The flow of energy is therefore oppositely directed on the two sides of this line, as shown by the arrows on the lines of flow. An inspection of the figure shows that the flow of energy at the surface is backward and inward from 0° to 45°, forward and*inward from 45° to 135°, and backward and outward from 135° to 180°, agreeing with Forms of the Lines of Electric Force. 313 (14) whenta=@6=45°. In the actual case the lines of force are almost’ parallel to the surface. This is seen from (21) Fig. 3. F —_—— > 20 40 10d". 120: 140 i60 180 Bay Aree PARSE Be Ret when we remember that / is by hypothesis very large. Ac- cordingly we have to imagine the straight lines of force in the diagram twisted round so as to meet the boundary at a very small angle instead of at 45°. (6) Case of koa very small, the current diffused through the whole wire. Here we may put unity tor Jo(ker) and i kyr for Jy (ker). Further, as we have seen in § 3, the argument of m approaches 45°, so we may write m= =a ) So we have ize * in (24) Raa av2 sin( a 4 Z Xr 4 It is remarkable that h disappears from the expressions, or in other words, as we approach this limit the properties of the wire cease to have an effect on the distribution of the field inside. Phil. Mag. 8. 6. Vol. 4. No. 21. Sept. 1902. ¥ al4 On the Forms of the Lines of Electric Force. The equation to the lines of force is Dare ar di TV Zz sin ea 7 (25) ee ae an a Ire ¥ } xX 2arz 2S a. por 2 log r= a log sin——— + const. (26) These curves are shown on fig. 4, beginning, in this Fig. 4. eee 20 2 ADS 60 BO 8100) 120 0 eee Fy VD ARIS OF WIRE case, from the awis of the wire. It may be noted that if we plot one line of force the others are got simply by extending proportionally the ordinates measured from the axis. In this case the magnetic force vanishes along with the longitudinal electric. The energy-flow is backward and inward from 0° to 45°, and forward and inward for the . remainder of the half wave-length. The exaggeration of the diagram in this case consists 11 making the radius of the wire much too great in comparison with the wave-length, in order to get room to show the trend of the curves. Queen’s College, Belfast, 20th June, 1902. if eGio, 3 XXXIV. Deviable Rays of Radioactive Substances. By EK. RurserrorD, I.A., D.Sc., Macdonald Professor of Physics, and A. G. Grier, I.Sc., Demonstrator in Physics, McGill University, Montreal *. § 1. ee experiments t of Giesel, Becquerel, Curie, Meyer, and Schweidler have shown that radium gives out some rays deflectable by a magnet. Becquerel, in addition, has shown that uranium, and the excited radioactivity due to radium, also emit rays deviable by a magnetic field: Becquerel has employed the photo- graphic method for detecting deviable rays, while the Curies, Meyer, and Schweidler have used the electrical method for analysis of the deviable rays from radium. Further experiments have shown that these deviable rays are similar in all respects to cathode-rays. Dorn{ showed that they were deflected in an electrostatic field, while the Curies § showed that they carried with them a negative charge. Becquerel determined the velocity of these “ elec- trons” by observing the magnetic and electrostatic deviation of the rays. He found that the rays from radium were complex, and had widely different velocities. Some travelled at more than half the speed of light. The ratio of the charge to the mass < was found to be about the same as for cathode- rays. These results have recently been confirmed by Kauf- mann ||, who has shown that some of these electrons travel with a speed nearly equal to that of light, while the ratio of ee . — is somewhat less than for the comparatively low velocity m F cathode-rays, and appears to decrease with the velocity of the electron. This points to the conclusion that for these high-speed electrons a portion of the effective mass is elec- trical in origin 4. The authors have found that, in addition to uranium and radium, thorium compounds, and also excited radioactivity due to thorium, give out some rays deviable by a magnetic field. * Communicated by the Authors. Communicated to the American Physical Society, April 21, 1902. + See reports on radioactivity by Becquerel and Curie to Congrés International de Physique, 1900, tome iii. t C. R. exxx. p. 1126. § Ibid, exxx. p. 647. || See Heaviside, ‘ Electrician,’ April 4, 1902. @ Gétt. Nach. ii. 1901. Y2 316 Prof. Rutherford and Mr. Grier on Deviable The main object of the investigations described in this paper was to obtain some experimental evidence of the connexion, if any, between the deviable and non-deviable rays emitted by the radioactive substances uranium, thorium, and radium. It is known that cathode-rays striking on a solid body give rise to Roéntgen rays, and also that Rontgen rays impinging on bodies in their turn give rise to a secondary radiation, part of which is composed of rays similar to cathode-rays. It thus appears possible, as Becquerel has suggested, that. the non-deviable rays may be due directly to the action of the deviable rays. A similar suggestion was put forward by one of the authors* to account for the presence of the two types of rays given out by uranium, one of which was far more penetrating than the other. The relation is, however, much more complicated than such simple analogies would suggest. A discussion of the question, with especial reference to the important results on the partial separation of the active products of uranium and thorium, is reserved till the conclusion of this paper. § 2. In these experiments the electric method has been employed throughout. It has many advantages over the photographic method, especially where quantitative com- parisons and rapidity of measurement are required. Fig. 1 shows the general experimental arrangement. The radioactive substance to be investigated was spread uniformly on the bottom of a shallow paper vessel, which fitted inside a lead box 3 cms. square and 2 cms. deep. The paper vessel rested on a wire gauze 1 cm. from bottom of vessel, and, by means of a water-pump, a steady stream of air was drawn downwards through the apparatus. This carried off the radioactive emanation emitted by thorium and radium, the presence of which in the testing-apparatus would seriously interfere with the measurements. The lead box was placed between pole-pieces, 3°2 cms. square, of a large electro- magnet, which were generally placed 3:2 cms. apart. The testing-vessel V was a rectangular zinc vessel, 10°5 cms. square and 30 cms. high. The outside was connected to one pole of a battery of 100 volts. A brass rod formed the inside electrode, which was connected to the electrometer. A guard-ring, connected to earth, ensured that there was no ( natural leak from the charged cylinder to the inside electrode. The testing-vessel was placed on an insulated metal plate, with a hole in the centre 3:2 cms. square, over the air-gap of * I. Rutherford, Phil. Mag. Jan. 1899.. . e Rays of Radioactive Substances. 317 the electromagnet. This was covered over with a layer of aluminium-foil -00034 em. thick. FLECT / VE 4 DSSSASASSSSSSSSSSSSY SSSSSSSSSSSSSSSSSS LIVERS = TAPER abs SAUZE farATH Lerp Box FART 7a HATER FumP Special precautions were taken to completely secure the electrometer and connexions from electrostatic disturbances of all kinds. It is easy to investigate the magnetic deviation of radium- rays in such an apparatus with an ordinary electrometer, as the ionization action of the radium-rays is very large. For uranium and thorium, however, the ionization due to the deviable rays is very small, and a specially sensitive electrometer is required to measure the effects with accuracy. The. Dolezalek electrometer, described in a previous paper by one of us *, was found sufficiently sensitive for this purpose. All the radioactive substances emit non-deviable as well as deviable rays, and generally the ionizing action of the non- deviable rays is much greater than that caused by the * Phys, Zeit. no. 11, p. 225 (1902). 318 Prof. Rutherford and Mr. Grier on Deviable deviable rays. With the bare radioactive substances the ioni- zation in the testing-vessel is chiefly due to the non-deviable rays. In consequence of this a strong magnetic field does not much alter the ionization-current observed in the electro- meter. The non-deviable rays can, however, be completely absorbed by two or more layers of paper, while the deviable rays pass through with very little absorption. The deviable rays consist of rapidly moving electrons, and ionize the air in their passage through it by collision with the molecules. The average deviable rays are so penetrating that they will probably pass through more than a metre of air before the ionizing action is cut down to one half. When a strong magnetic field is applied, the paths of the rays are curved, so that only a small fraction of the rays enter the testing-vessel. In the experiment a magnetic field of 2200 o.G.s. units was generally employed. This usually reduced the ionization current in the testing-vessel to about 20 per cent. of its pre- vious value. By increasing the strength of field the current steadily diminished, showing that the effect in testing was principally due to deviable rays. A small percentage of the amount of ionization in the testing-vessel was due, in the case of radium, to some extremely penetrating non-deviable rays. These rays have been examined by the photographic method by Villard and Becquerel. The difference between the current in testing-vessel with magnet on and off was taken as a measure of the amount of deviable rays. § 3. Variation of Amount of Deviable Rays with Thickness of Radioactive Layer. Different weights of the radioactive substance to be tested were spread over an area of about 9 sq. cms. Four layers of paper over this completely absorbed the @-radiation. The following numbers show the result from uranium and radium. The amount of deviable rays 1s expressed in divisions per sec. of the electrometer-scale, and represents the differ- ence between ionization-current in the testing-vessel with the magnet off and on. URANIUM OXIDE. LADIUM CHLORIDE. Wt. Divns. per sec. Wt. Divas. per. sec. ‘25 ov. ‘AT 25 15 oO "90 25 ao sya 1:26 1 55 2 ‘ 1°70 1) 6°7 i) a 1:96 Rays of Radioactive Substances. 319 In the case of radium a capacity of ‘005 microfarad was in parallel with the electrometer. The results for uranium are in agreement with the view that each portion of the mass is sending out electrons uniformly. The number of electrons which ¢ escape is at first proportional to the thickness, but tends towards a maximum as the electrons from the lower iia are absorbed before reaching the surface. . The table for radium shows, 2 as far as it goes, a similar action, only in that case we did not have a sufficient amount of substance to investigate the effect of thicker layers. In this sample of radium: (from. P. de Haen, Hannover) the deviable rays were 250 times as intense as from an equal weight of uranium oxide. § 4. Deviable Rays from Thorium Compounds. Thorium oxide is much weaker in deviable rays than an equai weight of uranium oxide, although the non-deviable rays are of about the same intensity. Tor this reason the presence of the deviable rays in thorium is more difficult to detect and measure than for uranium. Jn measurements on thorium compounds precautions must be taken that the presence of tbe radioactive emanation and the excited radio- activity produced by it are not responsible for the deviable rays observed. About 5 gr. of the thorium compound was spread uniformly in a rectangular lead vessel 3 cms. long, 2 ems. wide, and 1 cm. deep., and a very thin plate of mica waxed down over the top. This allowed most of the deviable rays to pass through, but absorbed most of the non-deviable rays, and was impervious to the emanation. Observations were taken as soon as possible after the thorium was placed in the vessel, and the difference of current observed with the magnetic field off and on. By means of side-tubes in the lead vessel a slow current of air was then passed over the thorium, carrying away the emanation. The amount of deviable rays was found to be unchanged, showing that the deviable rays (if any) from the emanation did not appreciably affect the result. If the side-tubes of the lead vessel were closed, and the thorium left undisturbed for 24 hours, the amount of deviable rays was considerably increased. This increase was found to be due to the deviable rays given out by the excited radioactivity produced by the emanation on the whole interior of the containing vessel. This was directly tested by re- moving the mica “plate from the thorium’ vessel and placing it between the poles of the electromagnet. It was found to 320 Prof. Rutherford and Mr. Grier on Deviable give out both deviable and non-deviable rays, due to the excited radioactivity produced on it. The amount of deviable rays for equal weights of different thorium compounds was found to vary considerably, as the following table shows :— Compound. Amount of Deviable Rays. Re 2): 1 Deemanated oxide ......... 1°35 Natmaterytk J4u.c 21s Ae "94 Sulphate f2i0%,. ci ae "83 Oscilate tay. cee “G6 In the above table the amount of deviable rays from ordinary thorium oxide is taken as unity, and the others expressed in terms of it. Jor the purpose of comparison the amount of deviable rays from an equal weight of black uranium oxide is added. The comparisons in the above table were not made directly by noting the effect of a magnetic field, but by an indirect method, explained in § 9, which is based on the observed fact that the penetrating rays from thorium as well as uranium are chiefly deviable rays. Four grammes of the compound in the form of powder were uniformly spread in a lead vessel of area 22 sq. ems. A layer of aluminium, thickness ‘006 cm., was waxed down over the top. This absorbed all the non-deviable rays, but allowed most of the deviable rays to pass through. The ionization-current due to these penetrating rays was deter- mined in the usual way, and was taken as a measure of their intensity. The deemanated oxide, 7e. the oxide which had been largely deprived of its power of giving off a radioactive emanation by raising it to a white heat, gives more deviable rays than the ordinary oxide ; while the nitrate is nearly as active as the ordinary oxide, although containing only about half the amount of thorium. It was also found that the increase of deviable rays with time, when the thorium was kept in a closed vessel for 24 hours, varied very considerably for different compounds. The increase was much greater for the ordinary oxide than for the deemanated sample, while thorium carbonate, which gives out five times as much emanation as the oxide, showed still greater differences. This increase of deviable rays with time in a closed vessel | . ’ Rays of Radioactive Substances. d21 is directly proportional to the emanating power of the com- pound, and is due to the deviable rays produced by excited radioactivity on the walls of the vessel. These results point to the conclusion that a portion, at least, of the deviable rays from thorium is due to the presence of excited radioactivity throughout the mass of the compound itself. If the emanation, which is apparently produced by all thorium compounds, is unable to escape rapidly into the air it produces excited radioactivity throughout the compound. In the deemanated oxide consequently more excited radio- activity is produced than in the ordinary oxide, from which more emanation escapes into the air. Since excited radio- activity gives rise to deviable ravs the effect will be greater for the deemanated than the ordinary oxide. § 5. Deviable Rays from Excited Radiations due to Thorium and Radium. A small proportion of the rays emitted by thorium- and radium-excited radiation is deviable by a magnetic field. As these excited radiations decay with the time it was of im- portance to see if the deviable rays decayed at the same rate. A lead wire was made the cathode in a cylindrical closed vessel containing the emanation from radium, which had. been obtained by bubbling air through a solution of radium chloride. The wire was left exposed for one day in order that the excited radiation should have reached a steady value. The lead wire was then bent inio a small spiral and placed between the poles of the electromagnet of fig. 1. Observations were taken at regular intervals, both of the current due to the deviable and non-deviable rays. Fig. 2 (p. 322) shows the results graphically ; Curve I. shows the decay with time of the non-deviable rays, Curve II. the decay with time of the deviable rays. For the purpose of comparison the maximum value of each is taken as 100. Similar observations were made on the excited radio- activity from thoria. An aluminium plate, 3 x 2 ems., was made the cathode in a closed vessel containing about 200 grs. of thoria and left two days. The following table shows the decay of the two types of rays. The initial value of each is taken as unity for comparison :— Non-deviable Deviable Time. rays. rays. 0 1 1 3 hrs. af 2 83 it Oke *38 “Oey 42 ,, "08 ‘O07 522 Prof. Rutherford and Mr. Grier on Deviable The results for both thorium- and radium-excited radiation show that the deviable rays decay at nearly the same rate as Time th Minutes — cy rae a a ay a ee ar ae RE TR the non-deviable. This result shows that there is a very close connexion between the production of these two types of radiation. § 6. Active Products Separated from Thorium and Uranium. In a previous paper (Rutherford and Soddy, Proc. Chem. Soc., Jan., and Trans. Chem. Soc., April 1902) it has been | shown that a very active product can be separated from thorium as a result of the precipitation of thorium nitrate by ammonium hydroxide. If the filtrate, free from thorium, is evaporated down to dryness and the ammonium salts driven off by ignition, a very small residue is obtained intensely active, possessing in some cases 1000 times the activity of thoria. This radioactive fraction has been termed Thorium X. At the same time the radioactivity of the precipitated thoria is diminished in most cases to about °36 of its original value. The investigation on the radioactivity of thoria has been continued by E. Rutherford and F. Soddy, and at the same time parallel experiments have been made on the partial ns Rays of Radioactive Substances. Jao separation of the active products from uranium by the methods of Crookes and Becquerel. The results of these investigations will appear shortly, but the authors of this communication are indebted to Mr. Soddy, of the Chemical Department, for his kindness in making the chemical pre- parations of thorium and uranium which are tested in this paper. On examination it was found that the Th. X. emitted both deviable and non-deviable rays, and also a radioactive emanation. The deviable radiation is complex, as in. the ease of the ordinary thoria, and contains a large fraction of easily absorbed deviable rays. Jf a large number of suc- cessive precipitations are performed the thoria can be almost completely freed from deviable rays, although about 30 per cent. of the non-deviable rays still remain. We thus see that non-deviable rays persist in thoria when the product responsible for deviable rays is completely re- moved. Very similar actions have been observed for the active products separable from uranium hy the methods of Crookes and Becquerel. Crookes* obtained very active residues from uranium by two methods. In one case it was found that if ether was added to uranium nitrate part of the nitrate was soluble in the ether. The part that was insoluble in the ether was far more radioactive than the part which was not. In the other case the nitrate was dissolved in water and an excess of ammonium carbonate added. 1, no value of @ can be found which will satisfy (3), and therefore no refracted ray ean be formed. Hquation (2), however, shows that when psinz>1, a disturbance travels from the surface AC to a small distance within the upper medium. For when d is very small, the numerical value of the second term to the right of (2) may attain an appreciable value, and as this value is subtracted from that of wsinz in the first term, the value of sin@ may be reduced to less than unity. Thus when the angle of incidence exceeds its critical value, the secondary wavelets in the rarer medium reinforce each other only in the space lying very close to the surface of separation, and in this space alone is a resultant disturbance produced. The existence of a superficial disturbance within the rarer medium when the angle of incidence exceeds its critical value is confirmed by a well-known experiment. The hypotenuse face of a right-angled prism is laid upon the convex surface of a lens, and the point of contact is viewed through one of the remaining faces of the prism by means of light incident through the other remaining face. The point of contact is seen to be surrounded by a black spot, generally encircled with coloured rings. When the eye is so placed that the light reaching it is reflected at an angle exceeding the critical angle, the coloured rings disappear, but the black spot remains. The existence of this black spot proves that light reaches the eye not only from the face of the prism, but also from the surface of the lens; and as, at the edge of the black spot, the thickness of the air-film between the prism and the lens amounts to about a quarter wave-length of light, it follows that light must penetrate from the surface of the prism into the air, at least to a distance equal to a quarter wave-length of light. Thus far the theory here developed presents no new feature. But the existence of the secondary wavelets in the rarer medium, even when they do not reinforce each other to produce a refracted wave, entails interesting consequences which have, we believe, heretofore escaped recognition. When the angle of incidence exceeds its critical value, the wavelets originating in the immediate neighbourhood of A (fig. 1) are incapable of arriving in the same phase at any point in the upper medium. Nevertheless it is possible to 350 Messrs. Edser and Senior on the Diffraction of find a position of the point E such that AP+)\=y.DE+EP, where ) is the wave-length of the incident light. In this case the wavelets from A and E reinforce each other at P, their phases differing by 27. If, then, we stop out the rest of the surface, so as to intercept the wavelets which would ordinarily interfere with those from A and H, light will arrive at P. We may go further and stop out portions of the surface AC, leaving a number of clear spaces from which the wavelets arrive at P in phases differing by multiples of 2a. In this case we have virtually described a zone plate on the refracting surface, and light is diffracted into the rarer medium. Since there is only a superficial disturbance in the rarer medium when the surface is free, it follows that the zone plate must be in optical contact with the surface. The particular case which is most readily verified experi- mentally corresponds to the location of the point P at an infinite distance from A. In this instance the zone plate takes the form of an ordinary diffraction-grating, the lines being placed perpendicular to the plane of incidence. If 6 represents the sum of the widths of a space and a ruling, then for the diffracted rays to reinforce each other at infinity, in a direction making an angle @ with the normal to the surface, we must have 5(u sin i—sin 0)=nd, where nv is an integer. Using white light as an illuminant, we shall obtain diffraction spectra similar to those ordinarily observed by the aid of a grating; but when wsini>1, the central undiffracted image (corresponding to n=0) will be absent. Further, for large angles of incidence, the number of lines per centimetre must exceed a certain value, other- wise the smallest possible value for n will correspond to a diffracted spectrum of such high order that the latter will be too faint to be seen; for here, as in the ordinary case, the intensity of a diffraction spectrum varies inversely as the square of the order, to a first approximation. Let the light be incident at an angle of 45° on the grating, and let w=1°5. Then if the 8th diffraction spectrum for } ="00006 cm. is to be seen along the surface (@=90°), we must have _ 8x °00006 ~ 105-1 Thus the grating must possess more than 100 lines per centi- metre, or more than 250 lines to the inch. For the first ='0096 cm. See Le am OS oo ‘ i len a ee > Light from a Dense to a Rarer Medium. 351 diffraction spectrum to be seen in a direction corresponding to €=90°, a grating of more than 2000 lines to the inch is required. : We have been able to realize experimentally the results deduced from theory above. We used a reproduction of a Nobert’s grating, of 3000 lines to the inch, photographed on a very thin collodion film, and afterwards intensified with mercury. ‘The clear side of the glass carrying the grating was cemented with Canada balsam to the hypotenuse face of a right- angled prism, of which the remaining angles were each equal to 45°. The lines of the grating were adjusted to be perpendi- cular to the triangular ends of the prism. The whole was then mounted on the central table of a spectrometer, one of the mutually rectangular faces of the prism being normal to the parallel beam from the collimator, while the lines of the grating were vertical. Brilliant diffraction spectra were seen on looking at the grating surface, either with the unaided eye or through a telescope focussed on infinity. The brightest spectrum was that seen on looking along the surface (@ nearly equal to 90°). In directions corresponding to smaller values of @ spectra of higher orders were seen; the brightness of these spectra decreased as the order increased, but they only became invisible at an angle of diffraction equal to 10° or 15°. On rotating the prism and grating through a small angle the central undiffracted image was brought into view ; this, of course, took the form of a prismatic spectrum, the light having been refracted at the prismatic faces inclined at an angle of 45°. The central image was easily recognized owing to the circumstance that the blue ends of the diffraction spectra on either side of it were turned towards each other. On rotating the prism so as to increase the angle of internal incidence on the grating surface the central image disappeared, but no change occurred in the general appearance of the diffraction spectra. On continuing to rotate the prism in the same direction one after another of the diffraction spectra dis- appeared, but light still emerged when the prism had been rotated through 25° or 30°. A careful examination left no doubt in our minds that the spectra were formed in accordance with the theory sketched out above. | Of course in the present case the light escaped into the air from the surface of the collodion film. But it is easily proved that when the light is incident on the glass-collodion interface at an angle exceeding the critical angle for glass- air, the light refracted into the collodion must fall on the collodion-air surface at an angle exceeding the critical value for collodion-air. The refractive index of Canada balsam is 352 Prof. J. J. Thomson: Huperiments on so nearly equal to that of glass that no appreciable effect is produced by the film of that substance between the face of the prism and the unruled surface of the grating. On looking through the face of the prism which was per- pendicular to that through which the incident light entered, a white image of the slit was seen, together with diffraction spectra on either side of it. Another experiment was performed, using a grating ruled on glass with 300 lines to the inch. The width of a ruling was very small in comparison with that of a space. The grating was of a cheap kind, and the spacing was probably not very regular ; nevertheless phenomena similar to those described above were observed. When the light was inci- dent at an angle of 45° on the grating only a few spectra, of high orders, were seen. When a strip of a screen such as is used for half-tone process work was used as a grating the number of lines to the inch being equal to 135, no diffraction spectra were seen when the angle of incidence was equal to 45°. The probable existence of the diffraction phenomena de- scribed above was, in the first place, deduced by one of us from theoretical considerations; subsequently the experiments described were devised and executed. The singularity of the results obtained entirely vanishes when the point of view chosen is that of the wave theory of light. On the other hand, the failure of light to penetrate a free surface, com- bined with the readiness with which it traverses the same surface when parts are rendered opaque, afford sufficient interest, we hope, to merit this short notice. At an earlier date, when the wave theory was in more need of confirmation than at present, the experiments described might possibly have appeared as of a fairly crucial nature. At present they may at least serve to illustrate, in a striking manner, certain important points in the wave theory of light. XXXIX. Haperiments on Induced-Radioactivity in Air, and on the Electrical Conductivity produced in Gases when they pass through Water. By J. J. THomson, W.A., #.R.S., Cavendish Professor of Experimental Physics, Cambridge*, Le has been shown by Hlster and Geitel f that a wire, if strongly negatively electrified for several hours either in the open air or, as in one of their experiments, in a large * Communicated by the Author. t Phystkalische Zeitschr. 11. p. 588. Induced-Radioactivity in Air. 50 cellar becomes radio-active, z.é., it increases the electrical conductivity of the air in its neighbourhood. The most natural explanation of this phenomenon is that, as Hlster and Geitel suppose, the atmosphere contains some radio-active constituent which is attracted to the negatively electrified surface ;_ this constituent of the atmosphere behaving like the “emanation” from thorium which has been shown by Rutherford * to induce radio-activity in bodies with which it comes in contact and to be attracted to negatively electrified surfaces. I have, however, as the result of the experiments described below come to the conclusion that though the exist- ence of this radio-active substance in the air is possible it is not necessary for the explanation of the effect observed by Elster and Geitel, and that negatively electrified surfaces may become radio-active without the deposition upon them of substances having specific radio-active properties. As long as we have to experiment either in the open air or in large rooms, it is exceedingly difficult to alter the con- ditions sufficiently to afford an adequate test of any proposed explanation ; I have therefore been experimenting with sir contained in a closed vessel of moderate size, and although under normal conditions | have not been able to get any appreciable amount of induced radio-activity, I have found that a negatively electrified wire placed in the vessel acquired, when the gas in the vessel was exposed to R6ntgen rays or had been bubbled through water, properties analogous to those found by Elster and Geitel in wires placed in the open air. The effects with the gas which had bubbled threugh water were very large. The method was as follows :—a large cylindrical zine gas- holder 102 em. long and 75 em. in diameter, was supported on insulating feet, ‘and closed by a lid ey of millboard ; the outer portions of the top and bottom of the lid were put i in metallic connexion with the gas-holder by rings of tinfoil which overlapped the lid and were fastened _ to the cylinder ; circular guard-rings of tinfoil connected with the earth were pasted on 1 the upper and under surfaces of the lid, these pre- SS ibed any leakage of electricity across the lid from the cylinder to a metal rod placed along its axis; this rod, which was connected with the electrometer, passed through a short metal tube in an ebonite disk which occupied the central portion of the lid, a flange on the rod resting on the top of the tube. The current between the rod and the cylinder was measured by an electrometer which was connected with the * Phil. Mag. [6] i. pp. 1 & 161. 1 i 304 Prof. J. J. Thomson: Haperiments on ; rod. This rod before the measurement of the current was con- nected with the earth, and the cylinder with one terminal of a battery of small storage-cells, the other terminal of which was connected with the earth. The battery contained 500 cells; these were found sufficient in all cases to produce the satura- tion-current, when the air was in the normal state a very much smaller number of cells was sufficient to do this. As the rod had to be strongly electrified in order to investigate the induced radio-activity, there was some danger that the ebonite disk with which it was connected might get charged with electricity, and this electrification by leaking back to the rod produce effects which were not due to the conductivity of the air. To avoid this two ebonite disks were used, the one used to support the rod whilst it was electrified was removed before the current through the vessel was measured and replaced by the second, which was carefully kept free from electrification. In the earlier experiments four different rods were used as electrodes, these were pieces of brass tubing of the same length and diameter. The procedure was as follows: in the morning the current through the vessel was measured, using each of the rods as electrode in turn: the deflexion of the electrometer in one minute, which is proportional to the cur- rent through the vessel, rarely differed by more than about one part in 75 for the four rods. During the day these rods were subjected to different treatment; one was put aside to serve as a standard, a second was connected with the negative terminal of a Wimshurst machine, and exposed to the air of the room, the Wimshurst machine was giving sparks about 3 cm. long ; the third rod was often connected with the positive terminal of the machine and exposed to the air, while the fourth rod was kept in the tank and connected in some experiments with the negative terminal of the machine, in others with the positive. The electrical machine was kept going all day long, and tested from time to time to see that its electrification | did not reverse, and at the end of the day the current j through the tank was measured, using each of the rods as electrode. Ifa rod had become radio-active, the current through the tank with this rod as electrode would be greater than it was when the rod was in its normal state, owing to the additional ionization due to the rod. With the air in the tank in its normal state I was never able to detect any change in the rod due to its long negative electrification. The volume of air in the tank, about 440 litres, was too small to produce the radio-active effects observed by Hlster and Geitel. As the current coming up to the rod'in the tank was much ee "fa — Induced-Radioactivity in Air. 390 smaller than if the rod had been electrified in the open air, I tried the effect of increasing the current by ionizing the gas in the tank by means of Réntgen rays: the tube giving out the rays was placed outside the tank, the rays passing into the tank through the millboard cover; this had, of course, the effect of greatly increasing the saturation-current through the tank, and it was found that now prolonged negative electrification of the rod produced an appreciable effect ; the saturation-current, when the rod which had been negatively electrified in the tank was used as electrode, was considerably larger than when the electrode was a rod which had not been so treated. The magnitude of the effect is indicated by the numbers given below, which represent the deflexions of the electrometer in one minute ; these numbers are proportional to the saturation-current:— Current at 11 a.m. with rod (1) aselectrode . . . 74 Current at 5 p.m. after rod (1), which remained in the tank, had been attached to the negative ter- minal of a Wimshurst machine while the gas in the tank was ionized by Réntgen rays. jurrent at 11 a.m. with red (2) aselectrode . . . T4 Current at 5 P.M. with rod (2) as electrode, this ro having been exposed to the air of the room and connected with the negative terminal of a Wims- hurst machine. 4 Current at 11 a.m. with rod (3) as electrode . . . 72 Current at 5 p.M. with rod (3) as electrode, this rod having been exposed to the air of the room and 71 connected with the positive terminal of a Wims- hurst machine. 86 ~l o> The above experiments were made on the same day. We see that with the negatively electrified rod in the tank there was an appreciable increase; in the case of the other rods the changes were too small to allow any conclusions to be drawn. A considerable number of experiments of this type were made: it will be sufficient to give one more example :— Current at 11 a.m. with rod (1) as electrode . . . 77 Current at 5 p.m. with rod (1) as electrode, the rod having been in the tank in the interval, connected 88 with the negative terminal of a Wimshurst machine and the air ionized by Rontgen rays. Current at 11 a.m. with rod (2) as electrode . . . . 76 Current at 5 p.m. with rod (2) as electrode, the rod having been kept in the tank but not electrified | 74 in the interval. hs 356 Prof. J. J. Thomson : Experiments on The rods which had been made active by long negative electrification gradually lost this activity, and after the lapse of about one hour the current with these rods as electrodes sank to about its normal value. When the rod in the gas exposed to the Réntgen rays was either positively electrified or not electrified at all, no change took place in the satura- tion-current sent through the gas before and after the electrification from this wire as electrode, thus in these experiments, as in those of Elster and Geitel, negative electrifi- cation is required to make the rod active. When a rod is in the active state, the current in the direction corresponding to a flow ot positive electricity from the rod is slightly greater than the current in the opposite direction. When the rod is in the normal state the two currents are equal, The effects produced on the rods in the preceding experiments are not very great; but the method described below gives very large effects, exceeding even those produced by electrification in the open air. Properties of Air Bubbled through Water. I made further experiments to see whether the induced radio- activity on negatively electrified bodies could be detected in the space of an ordinary-sized room without artificial ioniza- tion of the air. I endeavoured to produce throughout the air in the room an electric field of greater average intensity than that produced by a negatively-electrified wire. With this object very finely-divided water-spray strongly negatively electrified was projected into the room ; the spray was pro- duced by forcing a jet of water under high pressure through a small hole in a negatively-electrified plate ; the spray as “it fell was collected on filter-paper which, when drenched by the spray, was placed in the tank through which the saturation- current was measured. Very large effects were obtained in this way, so large, indeed, that it ‘seemed unlikely that they were dite to induced radio-activ ity on the negatively-electrified spray. A series of experiments were accor dingly made to see whether wet paper produced any effect when the water had not previously been electrified. Strips of wet filter-paper were wrapped round the rods used as electrodes in the preceding experiments, and much larger saturation-currents were ob- tained with these electrodes than with bare rods. The current was found to vary much with the nature of the paper— filter, blotting, tissue, cartridge, and foolscap papers were tried—and also with the nature of the solution; the results obtained were complex and irregular, and this method of | | ae Daten ee gag SF ce 1 mete Induced-Radioactivity in Air. 300 investigating the action of water was for the time abandoned in favour of the following, which gave quite regular effects. The airin the large tank, previously described, was made to circulate through water. To effect this two tubes were fastened into the tank, through one of these the air was. sucked by a water-pump into a closed vessel, from which it found its way back into the tank through the other tube ; the air got thoroughly mixed up with water during the process of pumping. A plug of glass wool was placed in the return-tube to stop water-spray. The air which had thus been forced through water was found to be a very much better conductor of electricity than air in the normal state, the increase in the conductivity is sur- prisingly large ; thus, after the circulation of the air through water had continued for about two hours, the saturation- current was more than twenty times the value before the circulation commenced. ‘The air, when once it has been modified in this way, retains its new properties for a very long time: thus, if the tank is kept closed so that the air cannot diffuse out, it takes several days after the stoppage of the circulation for the conductivity of the air to fall to its normal value. The following numbers give an idea of the rate at which the modified gas returns to its normal condition. At 5.20 p.m. on Saturday afternoon the current through the tank with the central wire positively charged was 600, with the central wire negatively charged it was 330; at 10 a.m. on Monday, 7.eé., after more than 40 hours, the current with the central wire + was 143, with the central wire — 115. The saturation-current through air in the normal state was 30 whichever way the wire was electrified. The properties of the modified air cannot be explained by the negative electrification which Lord Kelvin has shown to be present in air which has bubbled through distilled water,. nor could they be explained by supposing that the bubbling of the air through the water filled it once for all with a supply of positive as well as of negative ions. In the air moditied by passing through water there must be a continuous production of ions. A gas which contains a mixture of positive and negative ions, but in which no fresh ions are being produced, though it will conduct electricity, will exhibit peculiarities which will distinguish it from a gas in which spontaneous ionization is taking place; the current through a gas in which no fresh ionization is taking place will increase with the electromotive force acting on the gas ; each increase in the electromotive force producing an increase in the current. There will be no approach to the state of 398 Prof. J. J. Thomson: Heperiments on saturation, indeed in many such cases the tendency is for the current to increase more rapidly than the electromotive force. In the gas in which continuous ionization is taking place the current gets saturated, the maximum current being the one which takes out of the gas in one second all the ions which are produced in the gas in that time; the current will not increase beyond this, however much the electromotive force is increased, provided that the electric field does not become so strong that it gives rise to spark or brush discharge. Air which has been modified by passing through water | shows all the peculiarities of a gas in which continuous ionization is taking place; the current gets saturated ; although, as is natural, from the much greater conductivity ; of the gas the electromotive force required to saturate it is much greater than when the gas is in the normal state. Many experiments on the relation between the current through the modified gas and the electromotive force acting upon it were made. ‘The following tables embody the results of two such experiments. } Potential-difference in volts between the central wire pica and the cylinder. wire +. wire —. 40 30 80 66 45 120 80 70 160 107 80 200 122 97 400 150 126 600 200 139 800 220 138 1000 230 150 These results are represented graphically in the curves in fig. 1. These curves clearly show the approach to satura- tion. The following observations were taken with air of considerably smaller conductivity than that used in the preceding experiments :— ; Potential-difference in volts between the central wire Current. and the cylinder. wire +. - wire —. ; 18 ily 80 29 28 120 36 36 200 58 4H) 400 80 78 600 92 85 800 105 95 —1000 110 95 Induced-Radioactivity in Air. 399 Curves representing the results of these experiments are shown in fig. 1. ee rr SS A Sa a a i ER ae eee - 2 Ge ame ane ee a PD, | L CURRENT ee oe ee 400 500 600 700 800 $00 (000 ‘ POTEVITIAL OIF FERENCE (N VOLTE In these experiments the central electrode was not sup- ported by the ebonite plate at the centre of the lid of the vessel containing the modified gas, but was supported above the vessel and passed into the vessel through a hole in the lid which it did not touch. The air when in the modified. state produced by bubbling through water can be transferred from one vessel to another and still retain some, at least, of its conductivity. To show this a second vessel was prepared. This was a large galvanized iron cistern supported on insulating feet, a central wire placed along its axis was kept connected with the electrometer, and the current between this wire and the case of the cistern measured. This vessel, which we shall call B, was connected by a metal pipe about 150 cm. long and 1 em. in diameter with the vessel A, in which the modified gas was stored. When air was blown from A to B the saturation-current through A diminished, while that through B increased. ‘The gas, while passing through the tube between A and B, could easily be subjected to various physical processes, and 360 Prof. J. J. Thomson: Experiments on by observing the rate at which the conductivity in B in- creased—the rate of flow of air through the tube being kept constant—the effect of these processes on the con- ductivity of the modified gas could be determined. Thus a plug of giass-wool was placed in the tube, and it was found that the modified gas could pass through this without losing its conductivity. _ If the conductivity of the modified gas did not arise from some process of continuous ionization, but was due to the presence of ions placed once for all in a gas in which there was no further creation of ions, it should be destroyed like that of gases sucked from flames by passing the gas through a strong electric field. To test this point a long metal tube, about 1 metre long and 1 cm. in diameter, with an insulated wire along its axis, was inserted between the vessels A and B. The modified gas could pass through this tube when there was a potential-difference of 1000 volts between the wire and the tube without losing its conductivity. Thus, in this respect, the modified gas resembles a gas mixed with the “ emanation ” from thorium. Rutherford has shown that in this case the conductivity is not destroyed by a strong electric field. The modified gas passed through a tube filled with wire gauze heated to a dull red heat without losing its conduc- tivity: when, however, the gauze was ata bright red heat the conductivity was destroyed. The conductivity was also destroyed when the gas passed slowly through a spiral tube immersed in a freezing-mixture of ether and solid carbonic acid. The conductivity can be taken out of the gas by passing it slowly through a tube filled with glass beads moistened with sulphuric acid ; if the gas is merely allowed to bubble through sulphuric acid it escapes with a considerable amount of conductivity. Haperiments with a Gouy Sprayer. The water-pump arrangement, although very convenient for testing the effects of water and air, was not suitable for use with other liquids and gases. To test the effect of different liquids air was forced through a Gouy spray. The air, after passing through the sprayer, was found to have a high con- ductivity, and when it passed into either of the testing vessels A or B, the saturation-current through this vessel was increased. By measuring the increase produced after the current of air from the sprayer had passed into the testing vessel for a given time an estimate could be formed of the . . a A liga i St salty Induced-Radioactivity in Air. 361 conductivity given to the gas by passing through the liquid in the sprayer; by changing this liquid the effect of the nature of the liquid on the conductivity communicated to a gas passing through it could easily be determined. The following is an example of some experiments of this kind :—- Vessel B, normal saturation-current be- fore spraying . . wire+16, wire—16 Pure distilled notes in the spray er, he air after passing through the sprayer went into B, duration ‘of experiment 15 minutes, saturation-current . . wire+39, wire—30 Air blown out of B, saturation-current. wire+15, wire—15 Strong solution of NaCl in the sprayer, air passed through sprayer as before for 15 minutes, saturation-current . wire+30, wire—28 Thus there is no clearly-marked difference between the effects of pure water and brine. Solutions of rosaniline, phenol, hydrogen peroxide, and sulphuric acid were tried, and all gave much the same effects as pure water: the amount of electrification given to the air by bubbling through these solutions is very different, so that these experiments afford another proof of the difference between the conductivity communicated to a gas and the amount of electric charge. Another illustration of this is that though when air is first bubbled through distilled water it is strongly negatively electrified, it loses its charge much more rapidly than its conductivity, and after the lapse of an hour or so the charge will be unappreciable while the conductivity will be almost as large as it was at first. Kther, alcohol, and turpentine were placed in the sprayer and air forced through them, but with these liquids no appreciable conductivity was produced. When coal-gas was forced through distilled water in the sprayer the conductivity was much less than when the same volume of air was passed through. Induced Radio- Activity produced on a Negatwwely-Electripied Surface immersed in Modified Gas. The experiments already described have shown that when air is in its normal state the volume of air in the closed vessel A is too small to give the induced radio-activity observed in a negatively electrified wire placed in the open air. We have seen too that when the current of electricity through the vessel is increased by exposing the gas in it to “Rontgen rays, Phil. Mag. 8. 6. Vol. 4. No. 21. Bept. 1902. 2B 362 Prof. J. J. Thomson : Laperiments on a negatively electrified wire acquires the property of ionizing the air around it; this effect is, however, shown to a very much greater ateait by the gas wien it is in the modified state produced by bubbling it through water. To show this the tank A was filled with the modified con- ducting gas, while the air in B was kept in its normal condition, a clean wire electrode was taken and the saturation- current through B with this wire as electrode measured; the wire was then placed in A and kept negatively electrified by a Wimshurst machine for periods ranging from 30 minutes to 7 hours; the wire was then taken out of A and replaced in B, and the current through B again measured with this | wire as electrode: the current was found to be considerably greater than before the electrification of the wire. The following numbers show the magnitude of this effect :— Current through B with a potential- difference of 1000 volts before wire was, cleciriiied . 5. ss . . Wire+24, wire—17 jurrent after wire had been negativ ely electrified in the vessel A for 7 hours wire + 54, wire —54 The conductivity of the air in the tank A was about 10 times normal. In another experiment when the conductivity in A was about 12 times normal, the results were :— Current through B before wire was electrified oh) ove os . . wire+22, wire—17 After 7 hours’ negative electrification of the wire in A the current through B Was Adie eye ilel ie ak Oka) a -ne spi Larger effects were obtained with electrodes having larger surfaces than that of the straight wire. Thus, when a cylinder of copper wire-gauze was used as the electrode, the current through B before the gauze was electrified was: gauze +22,—21. After 7 hours’ electrification in A the i current through B was: gauze +400, — 200. The amount of ionization produced by a wire after negative electrification does not seem to depend to any great extent on the material of which the wire is made. Wires of the same diameter and length made of zine, lead, iron, copper, amalgamated copper, copper covered With a layer of water and oly cerine, copper wet with alcchol, which all gave when used as electrodes equal currents through B before electrifi- cation, gave approximately equal currents (much larger than the previous ones) after negative electrification in A. To ensure that the wires were exposed to similar influences in a all tea Induced-Radioactivity in Arr. 363 the vessel A they were usually tested in pairs, which were connected together and placed in symmetrical positions with respect to the axis of A. The amount of induced radio-activity on negatively electrified surfaces exposed to the emanation from thorium, or placed in the open air, seems also to be independent of the nature of the surface. The ionizing power of the wire is only produced by negative electrification. If the wire when placed in the modified conducting gas in A is positively electrified, or if it is not electrified at all, then no change in the current through B with this wire as electrode is produced by the immersion of the wire in the vessel A. © To show the ionization produced by a wire after negative electrification in A, it is not necessary to use the wire itself as the electrode in measuring the current through B, an independent wire may be used as electrode, and the ionization due io the wire can be detected by the increase in the satura- tion-current which takes place when the wire is put into B after its negative electrification in A: the effect, although very distinct, is not so large as when the electrified body i is itself used as the electrode; ; it is desirable to use a piece of metal of considerable area for the body which is negatively electrified. The ionizing power possessed by the active metal is very easily cut off by thin layers of solids. I have, however, been able to detect that an appreciable effect is produced by the negatively electrified metal even when surrounded by thin aluminium foil or paper. In this connexion it may be mentioned that if the conductivity of air when in the modified state is due to rays given out from centres of ionization, these rays must have very little penetrating power, as I have drawn modified air possessing high conductivity over a photographic plate in the dark for more than four hours without producing an impression on the plate. The active state in which a metal rod is put after being negatively electrified in the modified air is not a permanent one. As soon as the negative electrification stops, the activity of the metal begins to diminish, and after a few hours it entirely disappears : measurements of the rate at which this activity disappeared showed that it fell off rapidly at first and then much more slowly: the time taken for the activity to fall to half its initial value was about 45 minutes. It varied a little in the different experiments. When once a wire has been put into the active state it can stand very rough treatment without losing its ionizing power. 2B2 364 Prof. J. J. Thomson: Lwperiments on Thus, for example, washing the wire with water and drying it by heating with a bunsen does not destroy its activity, nor does heating it ina bunsen to a red heat seem to have much effect upon it ; an amalgamated copper wire was made active and then heated until the mercury was given off, even after this treatment it retained some activity. Theory of the preceding Phenomena. These experiments show, I think, that induced radio- activity caused by negative electrification is not necessarily due to the deposition of a radio-active substance. This hypothesis does not seem admissible in the case of the pre- ceding experiments ; for when the air is put in the modified state by means of the water-pump, only a limited supply of air is used, the volume of which, as we have seen, is too small to give rise to radio-activity when the air is in its normal condition, hence if in these experiments the effects produced by negative electrification are due to the deposition of a radio- active substance, such a substance must have come from the water. In the experiments with the Gouy sprayer, however, the amount of water used was very small: to see whether there was any radio-active substance in it which could produce the observed effects, the water in the sprayer was evaporated to dryness on a metal plate ; the plate, however, after this treat- ment did not show any ionizing power. Again, the amount of air passed through the sprayer was not large enough to pro- duce a supply of radio-active substance large enough to produce the observed effects, for a larger volume of air than that passed through the sprayer was drawn past a negatively- electrified wire without imparting to it any ionizing power. The experiments have led me to the conclusion that the ionizing power imparted to the wire in the preceding experi- ments arises in the following way :—In consequence of the negative electrification of the wire positive ions move up to it een it is placed in the modified gas ; some of these ions do not discharge to the wire, but stick close to it, forming a coating of positive electricity around it. Between this coat- ing and the wire there will be a strong electric field tending to draw negative electricity from the wire. Now there are many phenomena which lead us to the conclusion that a wire, even at ordinary temperatures, contains rapidly-moving negatively-electrified corpuscles which, under ordinary cir- cumstances, remain in the wire because their kinetic energy is not sufficient to carry them beyond the attraction of the metal. When, however, there is a layer of positive electricity just outside the metal, the attraction of this on the negative om am aC HO foe nn eee a a ae Induced-Radioactivity in Air. 365 corpuscles drags the latter from the wire; as the corpuscles move across the space between the coating and the wire they acquire additional kinetic energy, and if the difference of potential between the coating and the wire exceeds a certain value they will emerge from the positive coating with suffi- cient kinetic energy to enable them to ionize the molecules of the gas with which they come into collision; for this to be the case the potential-difference between the positive coating and the wire must exceed 2 volts, as Mr. H. A. Wilson has shown that the energy required to ionize a molecule of a gas is of the order of that given to a charge equal to that ona corpuscle when it moves through a potential-difference of about two volts. Thus, on this view, the ionizing power of the wire is due to a kind of polarization, which produces an electric field which makes the wire into a cathode emitting cathode-rays of feeble penetrating power which ionize the gas in the neighbourhood of the wire. If the wire, when in the conducting gas, had been positively electrified the electric field due to the polarization would have tended to force back the corpuscles into the wire rather than pull them out; there would therefore in this case be no emission of cathode-rays and no ionization of the gas, The amount of polarization seems to depend upon the way the gas in which the negatively-electrified wire is placed is ionized. Thus we have seen that when the gas is made a conductor by bubbling through water the effect on the nega- tively electrified wire is much greater than when the gas is made a conductor by Réntgen rays, although the conductivity of the gas is greater in the latter case than in the former. Again, | made the gas in the vessel a very good conductor by keeping a Bunsen burner burning in the vessel, but in this case I could not detect any ionizing power in a negatively- electrified wire which had been kept in the vessel. Air which has been passed over phosphorus is a conductor of electricity, but I could not detect any ionizing power in a negatively- electrified wire immersed in it. The principle by which we have explained the ionizing power of the negatively electrified wire—the emission of cathode- rays from the wire under the infiuence of a coating of positive electricity close to the surface of the wire—will also, I think, explain the conductivity produced in air when it bubbles through water. We may suppose that by this process very minute drops of water get mixed with the air, these drops must be exceedingly small, otherwise they would not be able to pass through a plug of .glass-wool; the very slow rate 366 Huperiments on Induced-Radioactivity in Arr. at which the conductivity dies away also shows that the drops must settle down exceedingly slowly, so slowly that they take some days to fall through 1 metre ; from this we may con- clude that the diameter of the drop cannot greatly exceed 10-° em. If each little drop gets surrounded by a layer of positive electricity then, just as in the case of the wire, the drop might emit cathode-rays which would ionize the air in its immediate neighbourhood ; thus each little drop would act as a centre of ionization, and thus make the air a con- ductor. The formation of a layer of positive electricity outside the drop is what we should expect if any chemical combination went on between the water of the drop and the oxygen of the air leading to the formation of such a com- pound as H,Q,, for, in forming this compound, the water would combine with a negative oxygen ion and not with a positive one ; thus from the layer of oxygen outside the drop the water would pick out the negative and leave the positive ions, this would lead to the production of the coating of positive electricity round the drop required to make it act as an ionizing agent. The drops of water as well as acting as producers of ions would also act as traps to catch ions moving through the air in which they are suspended ; they thus tend to reduce the conductivity, because when an ion gets attached to one of these drops, it is as it were anchored to it, and only moves with great difficulty ; in some cases the presence of drops of water diminishes the conductivity of the gas instead of increasing it: thus I found that squirting a steam-jet into either of the tanks A or B materially diminished the satura- tion-current through the tank. The ordinary polarization of the electrodes in the electrolysis of liquids is usually explained by the existence of a layer of electrification close to the surface of the electrode, thus the polarized electrode resembles in this respect the electrified wire and the small drop of water on the preceding theory. I there- fore thought it of interest to see whether a polarized electrode, when taken out of the electrolytic cell, would ionize the gas. Two platinum plates or wires were immersed in a solution of sulphuric acid of about the maximum conductivity, and a current of from 1 to 5 amperes sent from one electrode to the other for about an hour ; the electrodes were then taken out, washed with distilled water, and dried with filter-paper ; they were then placed in tank B and the saturation-current through the tank when these were used as electrodes measured. It was found that the one which had been used as the negative electrode (i.e. the one against which the hydrogen was eee Injluence of Convection on Rotatory Polarization. 367 liberated) now gave considerably higher currents than before the electrolysis, in some cases twice the current, while the positive electrode gave the same current as before. On first charging up the negative electrode positively, there was frequently a very large current for a short time, which was not repeated on “the second charging, as if there were some positive ions loosely attached to the electrode which got driven away ; the smaller increase to which I have alluded lasted for about half-an-hour. The amount of the increase varied a good deal; in one or two experiments there was no change in the current. The experiments with liquid electro- lytes are more ambiguous than those with gases, as there is the possibility of some acid adhering to the plate and not getting entirely removed by the washing and drying, and then setting up some chemical action. Against this explana- tion we have the fact that the increase only occurs with one electrode—the negative, not with the positive—so that if it is due to the chemical action it must be caused by something produced at the negative terminal and not at the positive. Hydrogen peroxide seemed to me the most likely substance, so [ immersed a platinum plate in a strong solution of H,0s, and washed and dried itin the same way as the electrodes. I found, however, in this case no change in the current through the tank B. I have much pleasure in thanking my assistant, Mr. E. Everett, for the help he has given me in these experiments. June 1902. XL. On the ie of Convection on Optical Hobateny & Polarization. By J. Larmor * HE postscript (this volume, p. 220) to Land Rayleigh’s account of his decisive determination that the orbital motion of the Harth is without influence on the rotatory pola- rization produced by quartz, has brought to my notice the recent paper by Prof, H. A. Lorentz there quoted. The fundamental character of Lord Rayleigh’s negative result may be illustrated by reference to Prof. Lorentz’s Versuch ener Theorie . . ., p. 119 (1895), where the opposite conclusion is considered as not unlikely in view of the formal possibilities that are open. But the main object of this note is to entirely admit the demur made by Prof. Lorentz, that my criticism (‘ 4ther and Matter, p. 214) of his calculation of rotational effect, there given, is not well founded. The conclusion which I ‘had reached was in fact that for light of given absolute wave-length the optical rotation would “be * Communicated by the Author. 368 | Prof. J. Larmor on the Influence of independent of the Earth’s motion, if the form of the consti- tutive relation which connects electric polarization with electric force, for the material medium, is not altered by its convection; but, not reflecting that reversal of tke direction of light in a moving medium alters its wave-length, a hasty inference was made that this negative deduction represented the negative experimental result long ago announced as probable by M. Mascart. I understand that Prof. Lorentz assents to, or at any rate admits as probable, the application of the principle (which rests indeed on a development in the molecular direction of his own previous analysis), that uniform convection does not affect the constitution of a permanent material system formed of groups of electrons or material ions that interact by electro- dynamic agency alone; except in so far that, instead of the ordinary time, we must refer the convected system to a new time-variable, the “local time ” of Prof. Lorentz. The con- stitutive relations of a rotational medium, as well as all properties depending on extinction of light, form a case in point. Considering radiation propagated in the direction of the axis of the rotational quality of the medium, say the direction of x, the relation between the material polarization (0, 9’, 4’) and the electric force (0, Q, R) in its undulations is expressed (‘Adther and Matter,’ p. 211) in the form ,_ K-I1 1 6 d I= Ge tt ola gteze)® K-1 1 ey d * = Gee B- gal sqi tag) in which the coefficient €, represents the structural and e, the magnetic type of rotation. When the material medium, instead ot being at rest, is being convected in the direction of x with velocity v, this structural relation should thus remain true when for ¢ is substituted the local time t’ (/oc. cit. p. 168) h’ equal to t— ~ 2, so that every function $(2, t) becomes C ‘ 1 d (2, t— ne) this keeps = unaltered, but changes . vd into (5. =o. 7) gd. Thus the effect of the convection will be to maintain the coefficient of magnetic rotation « di unaltered, but to change the structural coefficient ghar into vd : 1 ae the mixed type ¢, da 7 de: and the equation of electric constitution of the medium being thus modified, the rotation produced by it remains unaltered by convection. This is, in Rk: Convection on Optical Rotatory Polarization. 369 fact, merely a paraphrase of Prof. Lorentz’s argument (Proc. Manse: Acad. April 19, 1902). The conclusion to be drawn from Lord Haglsich? s result may thus be held to stand as before, that in the more complex circumstances of rotational media as well as in ordinary optical propagation in matter, the ions or electrons that form the connexion between the matter and the eether interact in all their relations according to laws of purely electrodynamic type. The single principle that electrification is of atomic cha- racter, with or without a distinct material basis, so that when the medium is convected the ions belonging to it exert the ordinary electrodynamic influence of moving charges, suffices to abolish all first-order effects of uniform convection on the electric and optical properties of material media ; rotational optical phenomena being therein included. It is only when the absence also of second-order effect of uniform convection has to be accounted for that more questionable hypothesis must enter. It appears to be established that, if it could be granted that the molecules of matter are constituted entirely on an electric basis, no second-order effects either electric or optical would arise. Such an electric basis of matter implies that, an ordinary molecule being made up somehow of a group of ultimate atoms describing steady orbits round each other after the manner of a stellar system, the mutual actions of these ultimate atoms, as also their inertia, are wholly electro- dynamic, and are fee really resident in the inter connecting gether in which the atoms constitute mere singular points or centres of strain. If this hypothesis could be admitted,—and no independent reason can be assigned for its validity, except that fundamental presumption of simplicity which we are not unaccustomed to find justified in physical analysis,—the nega- tive second-order optical observation of Michelson and Morley would be explained. Electric effects of the second order would also be absent ; and there appears to be one such (an outcome ofa suggestion of FitzGerald’s) which would otherwise exist, that in Prof. Trouton’s hands will probably furnish an independent experimental test*. Although the constitution of a molecule has not been syste- matically “elucidated on this purely ethereal hypothesis any more than it has on any other, an increasing tendency to con- sider it as a working scheme may be remarked f. And in this connexion it may be noticed that there is no necessity for restricting the singularity in the constitution of the sether to * See Trouton Trans. Roy. Dub. Soc. vii. (1902); also FitzGerald’s ‘Scientific Papers,’ pp. 557, 566, Ixi. + E. g. Planck, Berlin. Sitzunysber ichte, xxiv. p. 486 (1902). 370 Prof, E. Rutherford and Mr. F. Soddy on beamere point; the region of misfit (to borrow an expressive term from Prof, Osborne Reynolds) might, if necessary, have definite extension and structure. Hy potheses of this type are most naturally (indeed, as it seems to me, unavoidably) expressed in terms of an ether which-is only locally disturbed by each moving ion; so that a congeries of connected atoms like the Earth does not push it along bodily and establish any finite flow. But there may be philosophers who prefer not to employ the term ether at all, who are satisfied with a colourless phenomenology, and who manage to escape the consideration of the possibility of an ether whose parts maintain their positions notwithstanding the motion of matter through it, by saying merely that if a certain scheme of formal relations between variables which are symbols of things unknown is altered in a certain formal way, probably originally suggested by the use of dynamical analogies such as have been referred to, the scheme will continue to group the facts under the wider conditions, and they would thus feel freed from any necessity of considering images or models, probably imperfect, of things which being ‘outside ourselves we cannot intrinsically know. Cambridge, August 7, 1902. XL. Phe ae ae uaa of Holcadninen Part Il. By E. Rurnerrorp, M.A., D.Sc., Macdonald Professor o Physics, and F. Soppy, B.A. (Oxon.), Demonstrator in Chenustry, McGill University, Montreal*. CoNnTENTS. I. Introduction. II. Experimental Methods of investigating Radioactivity. III. Separation of a Radioactive Constituent (ThX) from Thorium Compounds. IV. The Rates of Recovery and Decay of Thorium Radioactivity. V. The Chemical Properties of ThX. VI. The Continuous Production of ThX. VII. The Influence of Conditions on the Changes ee a in Thorium. VIII. The Cause and Nature of Radioactivity. IX. The Initial Portions of the Curves of Decay and Recovery. X. The Non-separable Radioactivity of Thorium. XI. The Nature of the Radiations from Thorium and ThX. XII. Summary of Results. XIII. General Theoretical Considerations. I. Introduction. fe following papers give the results of a detailed investigation of the radioactivity of thorium com- pounds which has thrown light on the questions connected * Communicated by the Authors. Accounts of these researches, during the progress of the investigation, have already been given to the London Chemical Society. ee | the Cause and Nature of Radioactivity. 371 with the scurce and maintenance of the energy dissipated by radioactive substances. Radioactivity is shown to be accom- panied by chemical changes in which new types of matter are being continuously produced. These reaction products are at first radioactive, the activity diminishing regularly from the moment of formation. Their continuous production maintains the radioactivity of the matter producing them at a definite equilibrium-value. The conclusion is drawn that these chemical changes must be sub-atomic in character. The present researches had as their starting-point the facts that had come to light with regard to thorium radioactivity (Rutherford, Phil. Mag. 1900, vol. xlix. pp.1 & 161). Besides being radioactive in the same sense as the uranium com- pounds, the compounds of thorium continuously emit into the surrounding atmosphere a gas which possesses _ the property of temporary radioactivity. This ‘‘ emanation,” as it has been named, is the source of rays, whieh 3 icnize gases and darken the photographie film * The most striking property of the thorium emanation is its power of exciting radioactivity on all surfaces with which it comes into contact. A substance after being exposed for some time in the presence of the emanation behaves as if it were covered with an invisible layer of an intensely active material. If the thoria is exposed in a strong electric field, the excited radioactivity is entirely confined to “the negatively charged surface. In this way it is possible to concentrate the excited radioactivity on a very small area. The excited radioactivity can be removed by rubbing or by the action of acids, as, for example, sulphuric, hydrochloric, and hydro- fluoric acids. If the acids be then evaporated, the radio- activity remains on the dish. The emanating power of thorium compounds is independent of the surrounding atmosphere, and the excited activity it produces is independent of the nature of the substance on which it is manifested. These properties made it appear that both phenomena were caused by minute quantities of special kinds of matter in the radioactive state, produced by the thorium compound. The next consideration in regard to these examples of radioactivity, is that the activity in each case diminishes regularly w ‘ith the lapse of time, the intensity of radiation at each instant being proportional to the amount of energy remaining to be radiated. For the emanation a period of * If thorium oxide be exposed to a white heat its power of giving an emanation is to a large extent destroyed. Thoria that has been so treated is referred to throughout as “ de-emanated.” 372 Prof. EK. Rutherford and Mr. F. Soddy on one minute, and for the excited activity a period of eleven hours, causes the activity to fall te half its value. These actions—(1) the production of radioactive material, and (2) the dissipation of its available energy by radiation— which are exhibited by thorium compounds in the secondary effects of emanating power and excited radioactivity, are in reality taking place in all manifestations of radioactivity. The constant radioactivity of the radioactive elements is the result of an equilibrium between these two opposing processes. Il. The Experimental Methods of investigating Radioactivity. Two methods are used tor the measurement of radioactivity, the electrical and the photographic. The photographic method is of a qualitative rather than a quantitative character; its effects are cumulative with time, and as a rule long exposures are necessary when the radioactivity of a feeble agent like thoria is to be demonstrated. In addition, Russell has shown that the darkening of a photographic plate is brought about also by agents of a totally different character from those under consideration, and, moreover, under very general conditions. Sir William Crookes (Proc. Roy. Soe. (1900) Ixvi. p. 409) has sounded a timely note of warning against putting too much confidence in the indications of the photographic method of measuring radioactivity. The un- certainty of an effect produced by cumulative action over long periods of time quite precludes its use for work of anything but a qualitative character. But the most important objection to the photographic method is that certain types of rays from radioactive sub- stances, which ionize gases strongly, produce little if any effect on the sensitive film. In the case of uranium, these protographically inactive rays form by far the greatest part of the total radiation, and much of the previous work on uranium by the photographic method must be interpreted differently (Soddy, Proc. Chem. Soc. 1902, p. 121). On the other hand, it is possible to compare intensities of radiation by the electrical method with greater rapidity and with an error not exceeding 1 or 2 per cent. These methods are based on the property generally possessed by all radiations of the kind in question, of rendering a gas capable of dis- charging both positive and negative electricity. These, as will be shown, are capable of great refinement and certainty. An ordinary quadrant electrometer is capable of detecting and measuring a difference of potential of at least 10—? volts. With special instruments, this sensitiveness may be increased H ; } } ~ * aE Pu ‘ta the Cause and Nature of Radioactivity. 373 a hundredfold. An average value for the capacity of the electrometer and connexions is 8x10-° microfarads; and when this is charged up to 10~? volts, a quantity of elec- tricity corresponding to 3x10-® coulombs is stored up. Now in the electrolysis of water one gram of hydrogen carries a charge of 10? coulombs. Assuming, for the sake of example, that the conduction of electricity in gases is analogous to that in liquids, this amount of electricity corre- sponds to the transport of amass of 3x10- grams of hydrogen ; that is,a quantity of the order of 10~-” times that detected by the balance. For a more delicate instrument, this amount would produce a large effect. The examples of radium in pitchblende and of the thorium- excited radioactivity make it certain that comparatively large ionization effects are produced by quantities of matter beyond the range of the balance or spectroscope. The electrometer also affords the means of recognizing and differentiating between the emanations and radiations of _ different chemical substances. By the rate of decay the emanation from thorium, for example, can be instantly distinguished from that produced by radium; and although a difference in the rate of decay does not of itself argue a fundamental difference of nature, the identity of the rate of decay furnishes at least strong presumption of identity of nature. Radiations, on the other hand, can be compared by means of their penetration powers (Rutherford, Phil. Mag. 1899, vol. xlvii. p. 122). If the rays from various radioactive substances are made to pass through successive layers of aluminium-foil, each additional layer of foil cuts down the radiation to a fraction of its former value, and a curve can be plotted with the thickness of metal penetrated as abscissz, and the intensity of the rays after penetration as ordinates, expressing at a glance the penetration power of the rays under examination. The curves so obtained are quite different for different radioactive substances. The radiations from uranium, radium, thorium, each give distinct and character- istic curves, whilst that of the last-named again is quite different from that given by the excited radioactivity pro- duced by the thorium emanation. It has been recently found (Rutherford and Grier, Phys. Zeit. 1902, p. 385) that thorium compounds, in addition to a type of easily absorbed Roéntgen-rays, non-deviable in the magnetic field, emit also rays of a very penetrating character deviable in the magnetic field. The latter are therefore similar to cathode-rays, which are known to consist of material particles travelling with a ae av4 Prof. E. Rutherford and Mr. F. Soddy en velocity approaching that of light. But thorium, in com- parison with uranium and radium, emits a much smaller proportion of deviable radiation. The determination of the proportion between the deviable and non-deviable rays attords a new means of investigating thorium radioactivity. The electrometer thus supplies the study of radioactivity with methods of quantitative and qualitative investigation, and there is therefore no reason why the cause and nature of the phenomenon should not be the suhject of chemical investigation. Fig. 1 shows the general arrangement. From 0°5 to 0'1 gram of the compound to be tested, reduced to fine powder, is uniformly sifted over a platinum plate 36 sq. cms. in area. - "Furth This plate was placed on a large metal plate connected to one pole of a battery of 300 volts, the other pole of which was earthed. An insulated parallel plate was placed about 6 cm. above it, and the whole apparatus inclosed in a metal box connected to earth, to prevent electrostatic disturbance. The shaded portions in the figure represented insulators. A door was made in the apparatus so that the plate could be rapidly placed in position or removed. Both pairs of quad- rants are first connected to earth. On connecting the one pair with the apparatus, the deflexion of the needle from zero the Cause and Nature of Radioactivity. d75 increases uniformly with time, and the time taken to pass over 100 divisions of the scale is taken by a stop-watch. The rate of movement is a measure of the ionization-current between the plates. The ratio of the currents for different substances is a comparative measure of their radioactivity. With this apparatus -5 gr. of thorium oxide produces a current of 1-Lx 10-! amperes, which, with the electrometer used, working at average sensitiveness, corresponds to 100 divisions of the scale in 36 seconds. In certain cases a special modification of the Dolezalek electrometer was employed which is 100 times more sensitive. With this instrument the radioactivity of 1 milligram of thoria produces a measurable effect. If the substance gives off an emanation, the current between the plates increases with time. Under these conditions, when the thorium compound is exposed in thin layers with a maximum of radiating surface, all but one or two per cent. of the total effect is due to the straight-line radiation. Even when the effect due to the emanation has attained a maximum, this constitutes a very small fraction of the whole. This effect, however, may to a large extent be eliminated by taking the current between the electrodes immediately after the material is placed in the testing- apparatus. It may be completely eliminated by passing a current of air between the electrodes to remove the emanation as fast as it is formed. The current between the plates observed with the electro- meter at first increases with the voltage, but a stage is very soon reached when there is a very small increase for a large additional voltage. A P.D. of 300 volts was sufficient to obtain the maximum current, so that all the ions reached the electrodes before any appreciable recombination occurred. It must, however, at once be pomted out that it is difficult to make any absolute measure of radioactivity. The radiation from thorium is half absorbed by a thickness of aluminium. of ‘0004 cm.; and since thorium oxide is far denser than aluminium, it is probable that the radiation in this case is confined to a surface-layer only ‘0001 cm. deep. It is obvious that different preparations, each containing the same per- centage of thorium but with different densities and different states of division, will not give the same intensity of radiation. In comparing two different specimens of the same compound, it is important that the final steps in their preparation should be the same in each case. Asa rule absolute measurements of this kind have been avoided. It is possible, however, to trace with great accuracy the change of radioactivity of any preparation with time by leaving it undisturbed on its. a 376 Prof. E. Rutherford and Mr. F. Soddy on original plate, and comparing it with a similarly undisturbed constant comparison sample. Most of the investigations have been carried out by this method. Til. The Separation’ of a Radioactive Constituent from Thorium Compounds. During an investigation of the emanating power of thorium compounds, to be described later, evidence was obtained of the separation of an intensely radioactive constituent by chemical methods. It had been noticed that in certain cases thorium hydroxide, precipitated from dilute solutions of thorium nitrate by ammonia, possessed an abnormally low emanating power. This led naturally to an examination being made of the filtrates and washings obtained during the process. It was found that the filtrates invariably possessed emanating power, although from the nature of their pro- duction they are chemically free from thorium. If the filtrate is evaporated to dryness, and the ammonium salts removed by ignition, the small residues obtained exhibit radioactivity also, to an extent very much greater than that possessed by the same weight of thorium. As a rule these residues were of the order of one-thousandth part by weight of the thorium salt originally taken, and were many hundred, in some cases over a thousand, times more active than an equal weight of thoria. The separation of an active con- stituent from thorium by this method is not all dependent on the purity of the salt used. By the kindness of Dr. Knéder, of Berlin, who, in the friendliest manner, presented us with a large specimen of his purest thorium nitrate, we were enabled to test this point. This specimen, which had been purified by a great many processes, did not contain any of the impurities found in the commercial salt before used. But its radioactivity and emanating power were at least as great, and the residues from the filtrates after precipitation by ammonia were no less active than those before obtained. These residues are free from thorium, or at most contain only the merest traces, and when redissolved in nitric acid do not appear to give any characteristic reaction. An examination of the penetrating power of the rays from the radioactive residue, showed that the radiations emitted were in every respect identical with the ordinary thorium radiation. In another experiment the nature of the emanation from a similar intensely active thorium-free residue was submitted to examination. The rate of decay was quite indistinguishable from that of the ordinary thorium emanation; that is, substances chemically free from thorium have been the Cause and Nature of Radioactivity. — oer prepared possessing thorium radioactivity in an_ intense degree. The thorium hydroxide which had been submitted to the above process was found to be less than half as radioactive as the same weight of thorium oxide. It thus appeared that a constituent responsible for the radioactivity of thorium had been obtained, which possessed distinct chemical properties and an activity of the order of at least a thousand times as great as the material from which it had been separated. Sir William Crookes (Proc. Roy. Soc. 1900, Ixvi. p. 409) succeeded in separating a radioactive constituent of great activity and distinct chemical nature from uranium, and gave the name UrX to this substance. For the present, until more is known of its real nature, it will be convenient to name the active constituent of thorium ThX, similarly. Like UrX, however, ThX does not answer to any definite analytical reactions, but makes its appearance with precipi- tates formed in its solution even when no question of insolubility is involved. This accords with the view that it is present in infinitesimal quantity, and possesses correspond- ingly great activity. Even in the case of the most active preparations, these probably are composed of some ThX associated with accidental admixtures large in proportion. These results receive confirmation from observations made on a different method of separating ThX. The experiment was tried of washing thoria with water repeatedly, and seeing if the radioactivity was thereby affected. In this way it was found that the filtered washings, on concentration, deposited small amounts of material with an activity often of the order of a thousand times greater than that of the original sample. In one experiment, 290 grams of thoria were shaken for a long time with nine quantities, each of 2 litres of distilled water. The first washing, containing thorium sulphate present as an impurity, was rejected, the rest concentrated to different stages and filtered at each stage. One of the residues so obtained weighed 6:4 mg., and was equivalent in radioactivity to 11°3 grams of the original thoria, and was therefore no less fhe 1809 times more radioactive. It was examined chemically, and gave, after conversion into sulphate, the characteristic reaction of thorium sulphate, being precipitated from its solution in cold water by war ming. Vo other substance than thorium could be detected by chemical analysis, although of course the quantity was too small for a minute examination. The penetrating power of the radiation from this substance again established its identity with the ordinary thorium radiation. Phil. Mag. 8. 6. Vol. 4. No. 21. Sept. 1902. 2C es a - 378 Prof, E. Rutherford and Mr. F, Soddy on In another experiment, a small quantity of thoria was shaken many times with large quantities of water. In this case, the radioactivity of the residue was examined and found to be about 20 per cent. less radioactive than the original sample. The influence of Time onthe activity of Thorium and ThxX.— The preparations employed in our previous experiments were: allowed to stand over during the Christmas vacation, On examining them about three weeks later it was found that the thorium hydroxide, which had originally possessed. only about 36 per cent. of its normal activity, had almost completely recovered the usual value. The active residues, on the other hand, prepared by both methods, had almost completely lost their original activity. The chemical separa-. tion effected was thus not permanent in character. At this time M. Becquerel’s paper (Comptes Rendus, exxxiil. p. 977,. Dec. 9th, 1901) came to hand, in which he shows that the same phenomena of recovery and decay are presented by uranium after it has been partially separated from its active constituent by chemical treatment. A long series of observations was at once started to. determine— (1) The rate of recovery of the iad of thorium rendered less active by removal of ThX ; (2) The rate of decay of the activity of the separated ThxX ; in order to see how the two processes were connected. The- results led to the view that may at once he stated. The radioactivity of thorium at any time is the resultant of two. opposing processes— (1) The production of fresh radioactive material at a constant rate by the thorium compound ; (2) The decay of the radiating power of the active. material with time. The normal or constant radioactivity possessed by thorium is an equilibrium value, where the rate of increase of radio-. activity due to the production of fresh active material is- balanced by the rate of decay of radioactivity of that already formed, Itis the purpose of the present paper to substantiate and develope this hypothesis, IV. The Rates of Recovery and Decay of Thorium Radioactivity. A quantity of the pure thorium nitrate was separated from: ThX in the manner described by several precipitations with ammonia. The radioactivity of the hydroxide so obtained eal -" :' was tested at regular intervals to determine the rate of recovery of its activity. For this purpose the original speci- men of °5 gram was left undisturbed throughout the whole series of measurements on the plate over which it had been sifted, and was compared always with °d gram of ordinary de-emanated thorium oxide spread similarly on a second plate and also left undisturbed. The emanation from the hydroxide was prevented from interfering with the results by a speeial arrangement for drawing a current of air over it during the measurements. The active filtrate from the preparation was concentrated and made up to 100 c.c. volume. One quarter was evaporated to dryness and the ammonium nitrate expelled by ignition in a platinum dish, and the radioactivity of the residue tested at the same intervals as the hydroxide to determine the rate of decay of its activity. The comparison in this case was a standard sample of uranium oxide kept undisturbed on a metal plate, which repeated work has shown to be a perfectly constant source of radiation. The remainder of the filtrate was used for other experiments. The following table gives an example of one of a numerous series of observations made with different preparations at different times. The maximum value obtained by the hydroxide and the original value of the ThX are taken the Cause and Nature of Radioactivity. a@g as 100 :— Time in days. Activity of Hydroxide. Activity of ThX. 0 t1 100 it at EEG 2 48 100 3 D4 88 - 62 72 D 68 6 ‘a! D3 9) 78 9g i - 29-5 10 83 25°2 13 ge 15°2 15 ane | ea £7 96°5 21 99 28 100 Fig. 2 shows the curves obtained by plotting the radio- activities as ordinates, and the time in days as abscisse. Curve II. illustrates the rate of recovery of the activity of thorium, curve I. the rate of decay of activity of ThX, It 2C 2 as 380 Prof. E. Rutherford and Mr. F. Soddy on will be seen that neither of the curves is regular for the first two days. The activity of the hydroxide at first actually Fig. 2. \ diminished and was at the same value after two days as when first prepared. The activity of the ThX, on the other hand, at first increases and does not begin to fall below the original value till after the lapse of two days (compare section IX.). These results cannot be ascribed to errors of measurement, for they have been regularly observed whenever similar preparations have been tested. The activity of the residue obtained from thorium oxide by the second method of wash- ing decayed very similarly to that of ThX, as shown by the above curve. 4 If for present purposes the initial periods of the curve are disregarded and the later portions only considered, it will be seen at once that the time taken for the hydroxide to recover one half of its lost activity is about equal to the time taken by the ThX to lose half its activity, viz., in each case about 4 days, and speaking generally the percentage proportion of the lost activity regained by the hydroxide over any given interval is approximately equal to the percentage proportion of the activity lost by the ThX during the same interval. If the recovery curve is produced backwards in the normal direction to cut the vertical axis, it will be seen to do so ata the Cause and Nature of Radioactivity. 381 minimum of about 25 per cent., and the above result holds even more accurately if the recovery is assumed to start from this constant minimum, as, indeed, it has been shown to do under suitable conditions (section De , fig. 4). This is brought out by fig. 3, which represents the recovery Fig. 3. eer Mere Pe J eae eee ett as SE ESS Oh a curve of thorium in which the percentage amounts of activity recovered, reckoned from this 25 per cent. minimum, are plotted as ordinates. In the same figure the decay curve after the second day is shown on the same scale. The activity of ThX decreases very approximately in a geometrical progression with the time, 7. e. if I, represent the vied activity and I; the activity after time ¢, I, 0 O Bity ties o/c eee where A is a constant and e the base of natural logarithms. The experimental curve obtained with the hydroxide for the rate of rise of its activity from a minimum to a maximum value will therefore be approximately expressed by the equation where I, represents the amount of activity recovered when the maximum is reached, and I; the activity recovered after time t, X being the same constant as before. 382 Prof. E. Rutherford and Mr. F. Soddy on Now this last equation has been theoretically developed in other places (compare Rutherford, Phil. Mag. 1900, pp. 10 and 181) to express the rise of activity to a constant maxi- mum of a system consisting of radiating particles in which (1) The rate of supply of fresh radiating particles is constant. (2) The activity of each particle dies down geometrically with the time according to equation (1). It therefore follows that if the initial irregularities of the curves are disregarded and the residual activity of thorium is assumed to possess a constant value, the experimental curve obtained for the recovery of activity will be explained if two processes are supposed to be taking ‘place : : (1) That the active constituent ThX is being produced at a constant rate; (2) That the activity of the ThX decays geometrically with time. Without at first going into the difficult questions connected with the initial irregularities and the residual activity, the main result that follows from the curves given can be put to experimental test very simply. The primary conception is that the major part of the radioactivity of thorium is not due to the thorium at all, but to the presence of a non-thorium substance in minute amount which is being continuously produced. V. Chemical Properties of Thx. The fact that thorium on precipitation from its solutions by ammonia leaves the major part of its activity in the filtrate does not of itself prove that a material constituent responsible for this activity has been chemically separated. It is possible that the matter constituting the non-thorium part of the solution is rendered temporarily radioactive by its association with. thorium, and. this property is retained through the processes of precipitation, evaporation, and ignition, and manifests itself finally on the residue remaining. This view, however, can be shown to be quite untenable, for upon it any precipitate capable of removing thorium completely from its solution should yield active residues similar to those obtained from ammonia. ()uite the reverse, however, holds. When thorium nitrate is precipitated by sodium or am- monium carbonate, the residue from the filtrate by evapora- tion and ignition is free from activity, and the thorium carbonate possesses the normal value for its activity. The same holds true when oxalic acid is used as the the Cause and Nature of Radioactivity. 383 precipitant. This reagent even in strongly acid solution precipitates almost all of the thorium. When the filtrate is rendered alkaline by ammonia, filtered, evaporated, and ignited, the residue obtained is inactive. In the case where sodium phosphate is used as the precipi- tant in ordinary acid solution, the part that comes down is more or less free from ThX. On making the solution alkaline with ammonia, the remainder of the thorium is precipitated as phosphate, and carries with it the whole of the active constituent, so that the residue from the filtrate is again inactive. In fact ammonia is the only reagent of those tried capable of separating ThX from thorium. The result of Sir William Crookes with uranium, which we have confirmed working with the electrical method, may be here mentioned. UrX is completely precipitated by am- monia together with uranium, and the residue obtained by the evaporation of the filtrate is quite inactive. There can thus be no question that both ThX and UrX are distinct types of matter with definite chemical properties. Any hypothesis that attempts to account for the recovery of activity of thorium and uranium with time must of necessity start from this primary conception. VI. The Continuous Production of Thx. If the recovery of the activity of thorium with time is due to the production of ThX, it should be possible to obtain experimental evidence of the process. The first point to be ascertained is how far the removal of ThX by the method given reduces the total radioactivity of thorium. A pre- liminary trial showed that the most favourable conditions for the separation are by precipitating in hot dilute solutions by dilute ammonia. A quantity of 5 grams of thorium nitrate, as obtained from the maker, was so precipitated by ammonia, the precipitate being redissolved in nitric acid and re- precipitated under the same conditions successively without lapse of time. The removal of ThX was followed by measuring the activity of the residues obtained from the successive filtrates. The activity of the ThX from the first filtrate was equivalent to 4:25 grams of thoria, from the second to 0°33 gram, and from the third to 0°07 gram. _It will be seen that by two precipitations practically the whole of the ThX is removed. The radioactivity of the separated hydroxide was 48 per cent. of that of the standard de-emanated sample of thoria. 384 Prof. E. Rutherford and Mr. F’. Soddy on Rate of production of ThX.—A quantity of thorium nitrate sation that had been freed from ThX about a month before, was again subjected to the same process, The activity of the residue from the filtrate in an experiment in which 10 grams of this nitrate had been employed was equivalent to 8°3 grams of thorium oxide. This experiment was performed on the same day as the one recorded above, in which 5 grams of new nitrate had been employed, and it will be seen that there is no difference in the activity of the filtrate in the two cases. In one month the activity of the ThX in a thorium com- pound again possesses its maximum value. If a period of 24 hours is allowed to elapse between the- successive precipitations, the activity of the ThX formed during that time corresponds to about one-sixth of the maxi- mum activity of the total thorium employed. In three hours the activity of the amount produced is about one-thirtieth. The rate of production of ThX worked out from those figures well agrees with the form of the curve obtained for the recovery of activity of thorium, if the latter is taken to express the continuous production of ThX at a constant rate and the diminution of the activity of the product in geo- metrical progression with the time. By using “the sensitive electrometer, the course of pro- duction of ThX can be followed after extremely short in-. tervals. Working with 10 grams of thorium nitrate, the amount produced in the minimum time taken to carry out the successive precipitations is as much as can be conveniently measured. If any interval is allowed to lapse the effect is beyond the range of the instrument, unless the sensitiveness is reduced to a fraction of its ordinary value by the intro- duction of capacities into the system. Capacities of -01 and ‘02 microfarad, which reduce the sensitiveness to less than one two-hundredth of the normal, were frequently employ ed in dealing with these active residues. The process of the production of ThX is continuous, and no alteration was observed in the amount produced in a given time after repeated separations. In an experiment carried out for another purpose (section |X.) after 23 successive precipitations extending over 9 days, the amount formed during the last interval was as far as could be judged no less than what occurred at the beginning of the process. The phenomenon of radioactivity, by means of the electro- meter as its measuring instrument, thus enables us to detect and measure changes occurring in matter after a few minutes interval, which have never yet been detected by the balance or suspected of taking place. oer = ee a ae the Cause and Nature of Radioactivity. a8 VII. Influence of Conditions on the Changes occurring in Thorium. It has been shown that in thorium compounds the decay of radioactivity with time is balanced by a continuous pro- duction of fresh active material. The change which produces this material must be chemical in nature, for the products of the action are different in chemical properties from the thorium from which they are produced. The first step in the study of the nature of this change is to examine the effects of conditions upon its rate. Effect of conditions on the rate of decay.—Since the activity of the products affords the means of measuring the amount of change, the influence of conditions on the rate of decay must be first found. It was observed that, like all other types of temporary radioactivity, the rate of decay is unaltered by any known agency. It is unaffected by ignition and chemical treatment, and the material responsible for it can be dissolved in acids and re-obtained by the evaporation of the solution, without affecting the activity. The following experiment shows that the activity decays at the same rate in solutions as in the solid state. The remainder of the solution that had been used to determine the decay curve of ThX (fig. 2) was allowed to stand, and at the end of 12 days a second quarter was evaporated to dryness and ignited, and its activity com- pared with that of the first which had been left since evaporation upon its original platinum dish. The activities of the two specimens so compared with each other were the same, showing that in spite of the very different conditions the two fractions had decayed at equal rates. After 19 days a third quarter was evaporated, and the activity, now very small, was indistinguishable from that of the fraction first evaporated. Re-solution of the residues after the activity had decayed does not at all regenerate it. The activity of ThX thus decays at a rate independent of the chemical and physical condition of the molecule. Thus the rate of recovery of activity under different con- ditions in thorium compounds affords a direct measure of the rate of production of ThX under these conditions. The following experiments were performed :— One part of thorium hydroxide newly separated from ThX was sealed up in a yacuum obtained by a good Topler pump, and the other part exposed to air. On comparing the samples 12 days later no difference could be detected between them either in their radioactivity or emanating power. In the next experiment a quantity of hydroxide freed from 386 Prof. E. Rutherford and Mr. F. Soddy on ThX was divided into two equal parts ; one was exposed for 20 hours to the heat of a Bunsen burner in a platinum crucible, and then compared with the other. No difference in the activities was observed. In a second experiment, one half was ignited for 20 minutes on the blast, and then com- pared with ‘the other with the same result. The difference of temperature and the conversion of thorium hydroxide into oxide thus exercised no influence on the activity. Some experiments that were designed to test in as drastic a manner as possible the effect of the chemical condition of the molecule on the rate of production of ThX brought to light small differences, but these are almost certainly to be accounted for in another way. It will be shown later (section IX.) that about 21 per cent. of the normal radio- activity of thorium oxide under ordinary conditions consists of a secondary activity excited on the mass of the material. This portion is of course a variable, and since it is divided among the total amount of matter present, the conditions of aggregation, &e., will affect the value of this part. This effect of excited radioactivity in thorium makes a certain answer to the question difficult, and on this account the conclusion that the rate of production of ThX is independent of the molecular conditions is not final. The following ex- periment, however, makes it extremely probable. A quantity of thorium nitrate as obtained from the maker was converted into oxide in a platinum crucible by treatment with sulphuric acid and ignition to a white heat. The de- emanated oxide so obtained was spread on a plate, and any change in radioactivity with time, which under these cireum- stances could certainly be detected, was looked for during the first week from preparation. None whatever was observed, whereas if the rate of production of ThX in thorium nitrate is different from that in the oxide, the equilibrium point, at which the decay and increase of activity balance each other, will be altered in consequence. There should have therefore occurred a logarithmic rise or fall from the old to the new value. As, however, the radioactivity remained constant, it appears very probable that the changes involved are independent of the molecular condition. It will be seen that the assumption is here made that the proportion of excited radioactivity in the two compounds is the same, and for this reason compounds were chosen which possess but low emanating power. (Compare section IX. last paragraph. ) ranium is a far simpler example of a radioactive element than thorium, as the phenomena of excited radioactivity and the Cause and Nature of Radioactivity. 387 emanating power are here absent. The separation of UrX and the recovery of the activity of the uranium with time appear, however, analogous to these processes in thorium, and the rate of recovery and decay of uranium activity are at present under investigation. It is proposed to test the influence of conditions on n the rate of change more thoroughly in the case of uranium, as here poGeadar v changes do not interfere. VIII. The Cause and Nature of Radioactivity. The foregoing conclusions enable a great generalization to be made in the “subject of radioactivity. Energy considera- tions require that the intensity of radiation from any source should die down with time unless there is a constant supply of energy to replace that dissipated. This has been found to hold true in the case all known types of radioactivity with the exception of the “naturally” radioactive elements—to take the best established cases, thorium, uranium, and radium. It will be shown later that the radioactivity of the emanation produced by thorium compounds decays geometrically with the time under all conditions, and is not attected by the most drastic chemical and physical treatment. The same has been shown by one of us (Phil. Mag. 1900, p. 161) to hold for the excited radioactivity produced by the thorium emanation. This decays at the same rate whether on the wire on which it is originally deposited, or in solution of hydrochloric or nitric acid. ‘The excited radioactivity produced by the radium emanation appears analogous. All these examples satisfy energy considerations. In the case of the three naturally occurring radioactive elements, however, it is obvious that there must be a continuous replacement of the dissipated energy, and no satisfactory explanation has yet been put forward. ; The nature of the process becomes clear in the light of the foregoing results. The material constituent responsible for the radioactivity, when it is separated from the thorium which produces it, then behaves in the same way as the other types of radioactivity cited. Its activity decays geometrically with the time, and the rate of decay is independent of the mole- cular conditions. The normal radioactivity is, however, maintained at a constant value by a chemical change which produces fresh radioactive material at a rate also independent of the conditions. The energy required to maintain the radiations will be accounted for if we suppose that the energy of the system after the change has occurred is less than it was before. 388 Prof. H. Rutherford and Mr. F. Soddy on The work of Crookes and Becquerel on the separation of UrX and the recovery of the activity of the uranium with time, makes it appear extremely probable that the same explanation holds true for this element. The work of M. and Mme. Curie, the discoverers of radium, goes to show that this body easily suffers a temporary decrease of its activity by chemical treatment, the normal value being regained after the lapse of time, and this can be well interpreted on the new view. All known types of radioactivity can thus be brought under the same cateyory. IX, The Initial Portions of the Curves of Decay and Recovery. The curves of the recovery and decay of the activities of thorium and ThX with time suggested the explanation that the radioactivity of thorium was being maintained by the production of ThX at a constant rate. Before this can be considered rigidly established, two outstanding points remain to be cleared up. 1. What is the meaning of the early portion of the curves? The recovery curve drops before it rises, and the decay curve rises before it drops. 2. Why does not the removal of ThX render thorium completely inactive? , ‘ BS Na Sane ove § % o \2p &é S ia o/h oO. % ww ‘ a \ SI ar inp =) Phil.Mag.S.6 Vol.4.P1.1V (Copy of a diagram circulated at the Bath Meeting of the British Association in 1888. In this copy, the elements, since discovered, that occupy the sesqui- radius which was unoccupied in 1888, are inserted in their proper places. } PLATE Ill. OF A PAPER “ON THE LAW OF ATOMIC WEIGHTS,” READ BEFORE THE ROYAL SOCIETY, APRIL 19, 1888, BY G. JOHNSTONE STONEY, M.A., DSc., F.R.S S S Yop / NN 6 i) See 59 Nt.|Co 59. QUADRANT c. Y ELECTRO POSITIVE. Yf yy QUADRANT B. ELECTRO-NEGATIVE QUADRANT D. ELECTRO- NEGATIVE. QUADRANT A ELECTRO-POSITIVE ey CRIS 2 rss UNoccUPIED Os gs QZ oe SESQUI-RADIUS a4 ' .* id THE IND] 4 EX ED, LONDON, EDINBURGH, ayn DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SIXTH SERIES.) y ft XLVII. On the Electrical Resonance of Metal Particles for Light-Waves—Second Communication. By R. W. Woon, Professor of Experimental Physics, Johns Hopkins aie versity *®. a previous papert I have shown that granular deposits of the alkali metals exhibit brilliant colours by trans- mitted light. These colours were referred provisionally to the electrical resonance of the minute particles for light-waves. At the time of writing this paper, I was not acquainted with Prof. Threlfall’s interesting work on the optical properties of metallic precipitates and his attempts to verify the polariza- tion effects calculated by Prof. Thomson, to which I alluded. I feel sure that the colours observed by Prof. Threlfall, and those which I have observed, are to be referred to the same causes. It was found that the immersion of the particles in a liquid of high dielectric constant produced striking changes in the colour of the transmitted light, the change corre- sponding to a shift in the absorption-band towards the red end of the spectrum. It has been recently shown by Aschkinass and Shaefer{ that the length of electromagnetic waves to which a system of metallic resonators respond, is increased by immersing the resonator system in a liquid of high dielectric constant, which is obviously analogous to the behaviour of the sodium and potassium films. It is also well known that the position of the absorption-band of aniline dyes * Communicated by the Physical Society : read June 20, 1892. 4 + Proc. Physical Society, vol. xviii.; Phil. Mag. April 1902, t Drude’s Annalen der Physik, vol. v. p- 489. Phil. Mag. 8. 6. Vol. 4. No. 22. Oct. 1902. 2 iE OCTOBER 1902. 426 ~=Prof. R. W. Wood on the Electrical Resonance of depends to a certain extent on the dielectric constant of the medium in which the dye is dissolved. Continued investigation along the lines indicated in my previous paper has convinced me that it is impossible to refer the colours either to interference or diffraction, and it remains only to determine whether the resonance of the metal films is molecular, as in the case of the aniline dyes, or whether we are dealing with an electrical vibration of metallic masses, smaller than the light-waves though of the same order of magnitude. At the time of writing my first paper I had been successful in producing coloured films only with sodium, potassium, and lithium. Consequently, the only optical investigations that could be made were such as could be adapted to tilms formed on the walls of exhausted bulbs. Determinations of dispersion were practically impossible under these conditions, except by means of very elaborate apparatus, which it did not seem worth while to construct until further efforts had been made to obtain films of this nature which would be permanent in air, and could be examined with the interferometer. I have since succeeded in producing deposits of gold, which exhibit colours very similar to those shown by the potassium films. The deposit is formed by the discharge from a gold cathode in a moderately high vacuum, the colour depending on the distance of the glass plate from the electrode and the degree of exhaustion. Under certain conditions a green film is deposited, of a tint similar to that of gold leaf, while under other conditions blue, violet, and purple films can be obtained. The colour of the green film is doubtless to be ascribed to the same causes ‘ which operate in the case of gold leaf. The tint of the blue and purple films, however, is changed by moistening the plate with ligroin, precisely as is the case with potassium deposits. The mere approach of a glass rod, moistened with the liquid, is sufficient to produce a change of colour, the film apparently possessing the power of condensing the vapour upon its sur- face. Platinum and other metals in a fine state of division have this same property, consequently it seems extremely probable that the gold deposit is of this nature. Thus far I have only obtained two or three deposits which show this change. Most of the films are but slightly, if at all, affected by lgroin. In the case of the gold films, the particles are too small to be seen under the microscope, with the facilities at my dis- posal ; and I am inclined to the opinion that, in the case of the sodium and potassium films, particles which were actually seen with the microscope were only the moderately large ones, and may not have been instrumental in producing the Metal Particles for Light-Waves. 427 colour. In continuing the work, I plan to make more ex- haustive examinations with the microscope, using- higher powers if possible, employing photography, and ultra-violet light if necessary, for I believe that only in this way can the nature of the resonator be determined. There will be no great difficulty in determining the dispersion, since the gold films are permanent, and can be examined with the inter- ferometer, or they may easily be given a prismatic form. I feel confident that they will show anomalous dispersion, a phenomenon which, if observed, would be almost proof positive that the absorption-band was due to resonance. It would not, however, enable us to decide whether the resonance was within the molecule or not. for prisms built up of tinfoil strips were found by Garbasso and Aschkinass* to refract and disperse electromagnetic waves. Rubens and Nichols have examined the action on heat-waves of resonator systems formed by ruling crossed gratings on thin silver films, and found evidences of a higher reflexion percentage when the length of the resonators “approaches a whole number of half | wave-lengths. Prof. Nichols and I are, at the present time, working in collaboration on the selective reflexion from a number of plates covered with resonators, very much smaller than any that have hitherto been employed. By depositing thin films of gold in vacuo, on glass, and ruling under oil, I have suc- ceeded in producing resonators measuring 0° 8 pw» by llLp, which should resonate in a part of the spectrum where there is plenty of energy. Some of the trial rulings were made on the blue and purple films which I have mentioned, and in examining them under the microscope I have detected numerous minute granules, of about the same size as the sodium particles which I described in my previous paper. Whether these are the particles deposited by the cathode dis- charge, or merely metallic dust cut off by the diamond point, I am unable to s say. The fact that the coloured films of gold are produced when the glass plate is at some distance from the diamond point, seems to indicate that the gold vapour, if we may use the term, has time to condense into minute drops before reaching the plate. These films adhere much less firmly to glass than the green films which are formed when the distance between the cathode and the plate is small. In the latter the deposit is doubtless molecular, and the optical properties are similar to those of gold leaf. I have thus far been unable to obtain coloured deposits of platinum, which is the only other metal I have examined at the present time, which fact makes it seem as if the molecule was in some * Wielemann’s Annalen, vol. liii. p. 534. 2E 2 428 Prof. R. W. Wood on the Electrical Resonance of way concerned with the colour. The variable nature of the colour, however, especially in the case of sodium and potassium, makes it appear improbable that the action is similar to that of aniline dyes; namely, a resonance within the molecule ; for deposits of the same substance can be obtained showing an absorption-band almost anywhere in the visible spectrum, which is not the case with the more common types of coloured media. The colour of the gold deposit varies, as I have said, with the conditions under which the deposition takes place. I have employed gold cathodes of two forms: a flat plate about 3 cms. square, and a thick wire, screening off the radiation from all but the tip with a mica screen. The most interesting deposits were obtained from the small source. In one instance the film showed a brilliant green surface colour, resembling fuchsine, the transmitted light having a purple tint. Owing to the transparency of the film a good deal of white light is mixed with the selectively reflected light ; this can be cut off with a nicol, if the reflexion takes place at the polarizing angle for glass, and the coloured light trom the film which is unpolarized then appears in great purity. One plate showed patches of brilliant carmine red, deep blue, and green, of an intensity and saturation which L have never seen equalled in any interference experiment. The colour of the selectively reflected light depended some- what on the angle of incidence, a phenomenon observed also- in the case of the sodium and potassium films. Increasing the angle of incidence changed the colour from grevn to blue; the period of vibration of the resonator system appears there- fore to be less when the angle of incidence is large. If the glass plate is piaced near the tip of the gold wire, the green deposit, similar to gold leaf in its optical properties, is deposited at the centre. Surrounding this is a film appear- ing light yellow by transmitted light, and bluish by retlecred light. This seems to be what we should expect, for the smallest particles, which will resonate for blue light, will be deposited when the distance from the cathode is a little greater than that at which the molecular deposit occurs. Increasing the distance, we get larger particles, and the point of maximum resonance moves up into the green, giving us a purple film with green surface colour. At a still greater distance we get particles large enough to resonate for red, and the film appears deep blue by transmitted hight. All of these variously coloured films can be changed into the green structureless film by heating. We may regard the change as due to the fusing together of the resonators. If this is the case, the electrical resistance should be less after firing Metal Particles fur Light- Waves. 429 than before. This was found to be the case. The con- ductivity of the films is surprisingly good. A strip of a deep blue film measuring 10 by 5 mms. had a resistance of only a little over 2 ohms, After heating the film its resistance dropped to about half this value. It is even possible to change the colours by heating with- out sending the film over to the gold-leaf stage. I have a yellow film which local heating has changed to blue and purple in spots. A similar temperature change was noticed with the sodium and potassium films, as I mentioned in my previous paper, which I was unable to explain satisfactorily, since it appeared to be the opposite to what we should expect, if it was due to evaporation, which was the only thing that occurred to me at the time. It now seems as if the changes in both instances could be referred to a partial coalescing of the resonators. I find a difficulty in reconciling the assumed resonance of the films with their electrical conductivity, but the matter is perhaps less troublesome than the explanation of why gold- leaf transmits any light at all. Coloured films of a similar nature can be made of silver, by pouring a solution of Carey Lea’s soluble allotropic silver on a glass plate and evaporating it over a flame*. Ten parts of the ferrous sulphate solution are mixed with fourteen parts of the sodic citrate solution, to which is then added ten parts of the silver nitrate. The precipitate is allowed to settle, the liquid decanted, and the residue filtered. Asmall amount of distilled water is next poured into the filter and allowed to run through. More distilled water is now passed through the filter and collected. It will be found to have a very deep red colour, and if a small amount be spread over a clean glass plate and evaporated, it leaves a film which appears deep red, purple, and blue by transmitted light. The reflected light is of a complementary tint, the purple film reflecting green, and the red a greenish blue. Ligroin changes the optical properties of the film, though the change is only to be seen when a nicol is used, and even then it is not very pronounced. I feel pretty certain that I have detected traces of a granular structure in these silver films with the microscope, and hope to confirm the observa- tion as soon as a more perfect objective is at my disposal. An investigation of the dispersion of the films, which I intend to take up next, and a more careful study with polarized light, will doubtless throw further light on the matter. Baltimore, Md., U.S.A., May 30, 1902. * American Journal of Science, vol. xxxvii. p. 476 (1889). ) WS | [ 430 ] XLVIII. On the Magnetic Change of Length and Electrical Resistance in Nickel. By W. HE. Wititams, B.Se.* T is well known that the length of a nickel wire is diminished, while its electrical resistance is increased, by longitudinal magnetization. The first of these effects has. been investigated by Bidwellf, Nagaoka t, and Taylor Jones §, and the second by Tomlinson || and Barlow. If these effects are represented in curves showing the change of length, or resistance, as a function of the magne- tizing field, it will be found that the two curves bear a very striking resemblance to each other. This is well shown by the similarity in form of the hysteresis curves of the two effects given by Nagaoka and Barlow. It was suggested ‘by Prof. Taylor Jones that I should in- vestigate further the relation between these two effects, and the experiments described below were undertaken for that purpose. As both effects vary considerably for different specimens and even for the same specimen at different times, it was thought necessary to measure both changes in the same piece of wire, as nearly as possible at the same time and under the same conditions. Apparatus.— The magnetizing field was furnished by : solenoid 1 metre long, giving a field of 50 c.¢.s. units i ampere, the maximum field used being 420 units. This coil was fixed vertically in a wooden framework. The experiments were made on a nickel wire ‘12 mm. diameter and 80 ems. long. Its ends were soldered to two thick brass rods, the lower of which was firmly clamped to the wooden plank on which the coil rested, the other being held up by means of a lever. The tension of the wire could be altered by placing weights on the other end of this lever. Between the brass rods and the inner tube of the solenoid were placed two brass tubes, which formed the terminals of the copper wire used for comparison of resistance, this wire also being within the solenoid. The coil was provided with a water-jacket through which a current of cold water was kept constantly flowing. The wires were further protected from the heating effect of the current by means of a glass tube, in which they were inclosed. The wires and terminals were, of course, well insulated from each other and from the coil, and * Communicated by Prof. EK. Taylor Jones. + Bidwell, Proc. Roy. Soe. vol Iv. p. 228. af Nagaoka, Phil. Mag. vol. xxxvii. p. 131. § Taylor Jones, Phil. “Trans. 1897. || Tomlinson, ibid. 1883, p. 1. “ Barlow, Proc. Roy, Soc. 1902. \ | a — — Magnetic Change of Length and Resistance in Nickel. 431 care was taken to prevent them touching each other, as this was found to impede the motion of the nickel wire, and to affect the accuracy of the measurement of the change of length. The change of length was measured by the well-known Jever and mirror method, the short arm of the lever pressing upwards against a projecting piece attached to the upper end of the nickel wire. The lever ratio was 15, and the total magnification 18,000. The maximum deflexion obtained on the scale was about 50.cms., which could be easily read to a millimetre. The change of resistance was measured by means of a slide-wire bridge. The bridge-wire was of german-silver, 2°75 mm. diameter, with a resistance of ‘000361 ohm per em. The resistance of the nickel wire was 2°5 ohms, and that of the copper wire used for comparison was 2°6 ohms. The nickel and copper wires were connected in the outer gaps of the bridge, and two auxiliary coils* of german-silver wire of about the same resistance were connected in the inner gaps. These were placed together in an oil-bath in order to maintain them at the same temperature. The connexions were made by thick copper rods, soldered to the brass ter- minals of the wires, except in the case of the free end of the nickel wire, where a short piece of flexible wire was used. The change of resistance in nickel at the highest fields used is about one per cent., and this corresponds to a step of 40 cms. on the bridge. The ends of the nickel wire being at opposite ends of the magnetizing coil the thermoelectric E.M.F. was generally very considerable. It is easily seen, however, that it does not produce an appreciable error in the measured change of resistance (owing to the relatively small value of the effect) provided that the E.M.F. is constant during the time of taking the two readings. In order to secure this it was found necessary to allow the current to flow constantly through the bridge circuit. The error arising from this cause, and also from the heating effect of the magnetizing current, was further diminished by taking the readings rapidly. In ‘order to facilitate this, two sliders were used on the bridge, connected to the galvanometer by a double key, so that either slider could be used at will. One slider was used to balance when the magnetizing current was on, and the other when it was off. In this way it was found possible to arrange so that the zero did not change appreciably during the time of taking a reading. * Cf. Gray and Taylor Jones, Proc. Roy. Soc. vol. lxvii. p. 208. 432 Mr. W. E. Williams on the Magnetic Change of In all the experiments a curve of ascending reversals was first found, and then the residual effect was found separately, and the two added to get the curve of total change of length or resistance. This method has the advantage that the zero reading can be found before and after each separate reading, and it can be ascertained whether it has changed in the in- terval. The residual effect is comparatively small, and the curve is a straight line for the greater part of its length. The magnetic change of resistance was calculated from the formula | dR _ (S+R+100c) dz "ROP aS eda where R is the resistance of nickel wire, S is the resistance of copper wire, o is the resistance of bridge-wire per cm., x is the reading on the bridge. The results obtained are shown in the following tables and the accompanying curves. ‘'aBLE I.—Change of Resistance for Various Loads. dR , a x 104. Load in grammes. H. 0. 50. 100. 300. 500. 700. 10 30 A 1:0 8 3) 0:0 20 10°5 78 6:0 36 D3 *4 30 18°5 157 13°5 75 4°5 8 50 bo 30:0 26°1 15°5 9°6 33 75 45°3 39°6 408 25°8 17-4 72 100 55°2 5dD°5d 53°4 ote ats 14-4 150 69:6 726 72:0 596 47°1 243 200 78:0 83'1 84°7 78:0 66:0 40°2 250 83°7 91°2 92-7 94:9 83°4 55°5 300 88'8 97°7 99-0 102°3 103°3 69°9 350 93°0 102:9 1080 As 1146 84:6 400 96:3 107°4 oad Ks 124°8 101°8 Table I. gives the change of resistance for different loads ranging from 0 to 700 grammes. The corresponding curves are shown in fig. 1, the ordinates being the change of re- sistance a x 10* and the abscisse the magnetizing field in c.G.s. units. It will be noticed that these curves cross each other, which, as is well known, is not the case with the magnetization curves for these loads. ee Lenath and Electrical Resistance in Nickel. 433 Fig. 1. LT a a “G40anee 220 emmae AC FESHOUAL 100» 150 200 ~250, 300 350 400 ---H fon 800 TasBLE II].—Comparison of Change of Length and of Resistance for Various Loads. ; } | | 50 grammes. 100 grms. | S500grms. | 700 grms. | ) Sia | l | | H. | dL. potas dL. totals dL. |dRx3.| dL. | dRx°3. 10 | a neay became: et 0|' 0 90 | 25) 40 | 11 | 20 ily SP Gute 30 | 56/ 70 | 351 48 || 5 | 14 ii| 1 8 | 50 |109 | 125 || 81 {| 104 | 191 80 tea 75 |168 | 185 1185 | 146 || 44) 57 || 10] 241 100 | 219 935 |li7 | 193 || 72) 84 | 18) 36 150 | 295 | 306 || 252 | 263 ||130 145 || 48) 75 200 | 347 | 355 | 305 | 31:2 | 187 203 | 93 120 250 | 87-7 | 377 | 341 | 346 | 25:0 | 25:7 11155 | 167 300 | 41:2 | 412 1365 | 369 || 305 | 303 | 23 | 213 350 433 436 || 385 387 «| 353 346 | 289 262 | 400 |... DA we eae | 885 Bet. Skee i In Table II. the columns headed dL give the change of 434 Magnetic Change of Length and Resistance in Nickel. length in millionths of the length of the wire, and the adja- cent columns headed dR give the change of resistance for the same loads, the numbers of Table.1. being multiplied by a factor, as shown in the table. This factor is chosen so as to bring both changes into agreement for a field of about 300. These results are plotted graphically in fig. 2. The { | i DUAL 50 oe (STANCE | 5 oe wie eee ‘ se LENG TH FlleLD-H- 0) 50 100 150 200 250 30.0 350 400 450 full lines represent the change of length and the dotted lines the change of resistance. The two residual curves are given for a load of 50, and are on the same scale as the correspond- ing curves for the total effect. It will be seen from the diagram that for the loads 50, 100, and 500 the two sets of curves very nearly coincide, and that the discrepancy between them may be regarded as arising almost wholly near the origin. The residual change of resist- ance is considerably greater than the residual change of length, but the general shape of the curves is the same in both cases. Chemical and Geological History of the Atmosphere. 435 It will be noticed, however, that the ratio of the change of resistance to the change of length is different for different loads, so that different factors have to be used in bringing them into agreement, showing that the effect of loading is different in the two cases. This is also seen by comparing the set of resistance-curves in fig. 1 with the length-curves in fig. 2. As may be seen by a comparison of the curves given by Nagaoka and Barlow, there is no similarity between the curves of change of length and change of resistance in iron. The change of length i is in this case different in sign at high and at low fields, being a contraction in the former and an elongation in the latter case. There is no such change of sign in ‘the change of resistance. It may be conjectured that this is in some way connected with the Villari reversal which occurs in iron, and this view is perhaps supported by the fact that there is a similar reversal in nickel at very low fields* where, as mentioned above, the greater part of the disere- pancy shown by the pr esent experiments arises. The experiments were made in the Physical Laboratory of the University College of North Wales, and I desire to express my best thanks to-Prof. Taylor Jones for placing the necessary apparatus at my disposal, and also for many suggestions made in the course of the work. a Bangor, July 1902. XLIX. The Chemical and Geological History of ye the Atmosphere. By JouN STEVENSON, M/.A., FI.C.F y 4 Il.—The Composition and Extent of the Atmosphere in very Primitive Times. | . my former paper (Phil. Mag., Sept. 1900, p. 312, and Oct. 1900, p. 399) it was shown that there was good reason to believe that there was no free oxygen in the primitive atmosphere of the earth, and even that reasons could be given in favour of the view that considerable quantities of hydrogen or of hydrocarbon gases were present in the primitive atmosphere. We estimated that if the crust of the earth contained on the average +1, of 1 per cent. of carbonaceous matter, there would be as much of such oxidizable matter in each half-mile thickness of the crust of the earth belonging to the continental and transitional areas as * Heydweiller, Wied. Ann, vol. lii. p. 228 (1894). T Communicated by the Author. 436 Mr. J. Stevenson on the Chemical and would be equivalent to the whole of our present free oxygen ; and as the continental and transitional areas occupy only about one-half of the surface of the earth, it is obvious that there would be as much carbonaceous matter in each 3-mile thickness of the whole of the earth’s crust (or each shell or layer of the crust } mile thick) as would be equivalent to the whole of our present free oxygen, if the rocks underlying the great oceans should also contain +) per cent. of carbonaceous matter. We know practically nothing on this last point, but as regards the continental and transitional areas it is highly probable that the average percentage of carbonaceous matter is greater than 54,, and that the rocks containing carbonaceous matter have a much greater thickness than $ mile. Further, there is a considerable quantity of sulphide of iron present in many rocks, and this has probably been formed by the reducing action of carbonaceous matter on sulphates. All these circumstances point (as was explained in the paper) to the probable existence of an atmosphere in very ancient times containing much hydrogen or hydrocarbon gases, and if we knew the exact quantity of carbonaceous matter derived from organic remains, and also of sulphide of iron produced by the reducing action of organic remains, we might hope to be able to make some estimate of the ancient atmosphere or of the quantities of hydrogen or hydrocarbon gases present in it. But the above data, even if they were ascertained with a fair degree of completeness, would still be insufficient for our purpose, as the question is complicated by other con- siderations. We must on the one hand allow for free oxygen that has been removed from the atmosphere and absorbed or fixed in the ground through the oxidation or peroxidation of various substances, especially the protoxide and the sulphide of iron; and on the other hand we ought to allow for carbonaceous matter which may have been destroyed in the course of geological history, but in such a way that its former existence would have an important bearing on our inquiry. As regards the quantity of oxygen used up in oxidizing iron compounds, it was calculated by Ebelmen, about 1845, that if all the sesquioxide of iron on the earth was originally protoxide, there must have been at least as much oxygen abstracted: from the atmosphere to effect the peroxidation as there still is of free oxygen in our atmosphere. This estimate is confirmed, and more than confirmed, by Messrs. Clarke and Hillebrand’s series of rock-analyses published in Bulletin 148 of the United States Geological Survey (Washington, 1897), from which Mr. Clarke calculates that the average ae nl Geological History of the Atmosphere. A3T quantity of ferric oxide (sesquioxide of iron) in known rocks is 2°65 per cent. If this were all originally protoxide of iron it would require to effect its peroxidation for each half-mile thickness of the earth’s crust: belonging to the continental and transitional areas, or for each 4-mile thickness of the whole of the earth’s crust, a quantity of oxygen equal to the whole quantity in our present atmosphere. Also it may be noted that the oxygen required to produce 2°65 per cent. sesquioxide of iron from protoxide is very nearly equivalent to 0-1 per cent. of carbon, that is, there would require to be this amount of carbon or carbonaceous matter in the ground to balance the oxygen that has been removed from the atmosphere in the oxidation of the protoxide of iron. Besides peroxide of iron, the binoxide of manganese found in the ground has probably been peroxidized by atmospheric free oxygen, but it may be passed over on account of its comparatively small quantity. But besides peroxides there is a very considerable quantity of sulphates found on the earth, and these have very probably been formed through the oxidation of sulphides by free oxygen. Clarke and Hille- brand ‘estimate the quantity of anhydrous sulphuric acid (SO;) which is found combined with lime and other bases in the crust of the earth at 0°06 per cent. of the total rocks present. The quantity of oxygen (viz. 0°036 per cent.) represented in this percentage, being only about one ninth of that required to produce the sesquioxide of iron (referred to above) from protoxide, may be passed over, but besides the sulphates found in the solid crust of the earth, there is a very considerable quantity found in the sea. Prof. Dittmar (see Encyclopedia Britt., 9th ed.) estimated the sea to contain 2192x 10 tons MgSO, 166610" tons CaSQ,, and 1141 x10! tons K,SO,, which are equivalent to a total quantity of 2994 10! tons SQ; (anhydrous sulphuric acid). The oxygen present in this, viz. 1776x110" tons, is con- siderably greater in amount than the total free oxygen of the atmosphere (viz. 1200 x10! tons). It is no doubt possible that the sulphur present in the above sulphates may have always existed in combination with oxygen, but this is not very probable if there was originally a considerable excess of oxidisable elements relatively to oxygen itself on the earth. For the same reason we may infer that the sulphur of the sulphide of iron which has been formed from sulphates by the reducing action of organic matter has in the course of such a reaction only returned to its original form of com- bination, and should therefore be left out of account in calculations regarding the composition of the primitive > ~*~; re ‘ 438 Mr. J. Stevenson on the Chemical and atmosphere. In any case we must admit that the large quantities of sesquioxide of iron and of sulphates found on the earth form a very formidable counterpoise to the car- bonaceous matter, and therefore weaken to a very considerable extent the position taken up in my first paper regarding the history of free oxygen. But on the other hand there are certain considerations which tend to strengthen the position very materially. It is quite possible that in the treatment of this question allowance should be made for carbonaceous matter which formerly existed on the earth, but which has been destroyed in the course of geological history, for not- withstanding its destruction, its former existence and the mode of its destruction might have an important bearing on the question before us. It is obvious that coal and similar carbonaceous matters would undergo great changes if the strata containing them should become highly heated, and that they would even be destroyed or disappear if they should be highly heated in contact with oxide of iron and certain other metallic oxides. In that event the carbon would be converted into carbonic oxide or carbonic acid, and the metallic oxides would be reduced to the metallic condition, or at any rate to compounds containing a smaller eda of oxygen than before. At first glance one would be inclined to say that this reaction cammot have taken place to any great extent in the course of geological history on account of the comparative rarity of native metallic iron and other free metals, but a little reflection will show that the reaction may quite possibly have taken place on a large scale in very early times, though little or none of the metallic iron then produced may be now visible. It is obvious that when the rocks became heated up to the point at which the metallic oxides present were reduced to the metallic condition the rocks would either be fused or would be not far from the fusing-point, and if reduction should sometimes have taken place before fusion, still the process of heating would probably, in most cases, be continued until fusion also took place, and in that case the metallic iron or other metals produced would sink down through the melted rock-mass. If this melted mass should be very great or deeply-seated within the crust of the earth, the metal might sink to such a depth that it would never afterwards be brought by geological changes sufficiently near the surface of the earth to come within the range of human observation. Fortunately for the purposes of this inquiry there are sufficiently substantial data from which to make some inferences as to the probability of the reaction having taken Geological History of the Atmosphere. TAS9 place in very early times, and even roughly to estimate the extent to which it may have taken place, or at least there are eertain observed facts which may be explained by means of the foregoing theory. These data or facts have reference to the chemical composition of rocks at varying depths of the earth’s crust, or perhaps more properly the composition of very ancient rocks as compared with that of those which are regarded as being more modern. It is well known that the oldest rocks, or those which are regarded as the oldest, are much more basic than comparatively recent rocks, in fact the ancient rocks are frequently called ‘basic,’ and the more recent rocks “‘acidic.””. There is, so far as | am aware, no exact line of demarcation or exact definition of the terms, but, generally speaking, rocks or minerals which, like the supposed ancient rocks, contain about 55 per cent. of bases and only 45 per cent. of silica are called “ basic,” while rocks or minerals which, like the bulk of more recent rocks, contain about 60 per cent. or more of silica and only 40 per cent. or less of bases, are called “acidic.”” Now this difference in the composition of ancient and comparatively recent rocks may quite well have been brought about in the course of geological history. According to the usually accepted theory, the earth was so hot in very early times as to be in the liquid condition, and also according to accepted theories, the tides were very high and energetic in those early times. Under these circumstances, the materials which now constitute the crust of the earth must have been well mixed, and therefore the © composition of the liquid mass’ (at any rate in its upper part, containing as it probably did materials that were mutually miscible or had sufficient chemical affinity to combine with each other and produce compounds that were mutually miscible) must have been fairly uniform throughout. Indeed it should have been quite comparable, as regards uniformity .of composition, with the composition of the sea at the present day. There would therefore be no distinction of basic and acidic rocks at that period. The proportion of silica and of bases would be uniform throughout the mass. But when the earth cooled sufficiently to become solid, or to permit of the formation of a hard crust on the surface, natural operations might very well have brought about the great variety that is now observed in the composition of rocks. The primitive atmosphere, as we shall see in the course of this paper, most likely contained very large quantities of carbonic acid. This carbonic acid, acting along with water or aqueous vapour on the primitive crust, would soon decompose the rocks, forming carbonates, hydrates, and free silica or rock-forming materials 440 Mr. J. Stevenson on the Chemical and containing a much higher proportion of silica than the original rock-mass of the earth. There may also have been a very considerable quantity of hydrochloric acid in the primitive atmosphere or ocean, which of course would also act on the crust with the formation of chlorides ; but as the total quantity of chlorides on the earth is very small in compa- rison with that of carbonates, they may for our present purpose be left out of account. Nowif we were to add to modern acidic rocks the bases (chemically speaking) of the rocks composed of carbonates, oxides, and hydrated oxides that are found inter- spersed with them, or if we were simply to imagine them all to be fused together, the resulting mass of silicate rocks would obviously be less acidic and more basic than it was pre- viously, though possibly it might not be so basic as the deep- seated primordial rocks, which are technically called “ basic.” Indeed, we may be quite sure that it would not, for it is well known that sandstone or free silica is very much more abundant than limestone, and even in the English Oolitic system, which is comparatively rich in limestone, Prof. Phillips estimated that there was three feet of sanstone for one foot of limestone. If then the total limestone of the earth bears such a small proportion to the total sandstone, it is evident that if the materials composing the upper part of the crust of the earth were all fused together the composition of the resulting mass would still be acidic when compared with that of the older or primordial rocks lying lower down. Therefore, if the whole rock-mass of the earth was at one time uniform in composition or homogeneous throuzhout, a portion of the basic constituents must have been abstracted trom the materials which now constitute the upper part of the crust. The principal bases in both basic and acidic rocks are alumina, lime, magnesia, oxide of iron, potash, and soda. Of these, oxide of iron is the base, the deficiency of which in acidic rocks is most pronounced when compared with its percentage in basic rocks. Indeed, it is possible that the other bises being so largely represented by carbonates, chlorides, and sulphates may not be deficient at all, though this is rather doubtful, as we shall see later on ; but in any case there would be required a fuller knowledge of the subject than we at present possess to enable us to answer this part of the question definitely. In the case of iron, however, the difference is very marked. Basic rocks contain from about 5 to 30 per cent. of oxide of iron. the average amount being probably at least 8 per cent., and that princi- pally in the form of protoxide of iron. Acidic rocks, on the other hand, contain on the average only some 2 or 3 per cent. ies Ade 7 Geological History of the Atmosphere. 44] of oxide of iron, and that mostly or very largely in the form of sesquioxide of iron. We may therefore cenclude that basic rocks contain on the average about 6 per cent. more of oxide of iron than the more recent acidic rocks. Now this difference in composition may quite well have been brought about by the action of carbonaceous matter at a high temperature on basic rocks or on the materials derived from them by ordinary disintegration and denudation. The forma- tion of metallic iron by volcanic or plutonic agency is not only conceivable but is very highly probable. The molten or heated materials lying beneath volcanoes no doubt consist in many cases to a large extent of what had been sedimentary rocks, containmg among other things oxide of iron and carbonaceous matter, which, when heated together, would react on each other, forming carbonic acid (or carbonic oxide) and metallic iron. Even if the oxide of iron and the carbonaceous matter should not have been in direct contact with each other at first, they would be brought into contact by the agitation caused in the mass by the evolution of carbonic acid from carbonates, of steam from clays, shales, and other hydrated rocks, and of hydrocarbon gases and carbonic oxide from the carbonaceous matter itself, while in some cases the hydrocarbon gases and carbonic oxide might themselves be able to effect or at least to assist in the reduction of the oxide of iron. The production of metallic iron is therefore just what we might expect as one of the results of volcanic action, and if iron of volcanic origin has not yet been met with, or only to a very insignificant extent, this circumstance may be explained by the sinking of the iron down into inaccessible regions, or by its subsequent oxidation through exposure to the action of atmospheric free oxygen. Native iron in small quantities has been observed in many localities in both Hurope and America, especially in granitic and basaltic rocks. Metallic iron has even been known to be produced in France by a fire in a coal-mine, from which we may infer that if the materials existing in that mine were heated up in a volcano, a considerable quantity of metallic iron would be produced. Further, when we reflect that there must be many coal-bearing regions in the world where the percentage of carbonaceous matter over large tracts of country, and down to very considerable depths, amounts to 1 per cent. and upwards, the reasonableness of our standpoint is quite apparent. In the deep bore at Paruschowitz, in Silesia, which is 2003 metres deep, 83 seams of coal, having a total thickness-of about 90 metres, have been met with. This makes the thickness of the coal 4°5 per Phil. Mog. 8. 6. Vol. 4. No. 22. Oct. 1902. 2G AAD Mr. J. Stevenson on the Chemical and cent, of the total depth, and the weight of the coal about 2°25 per cent. of that of the total rocks present; and of course there might be a large quantity of thinly-disseminated carbonaceous matter in addition to the coal itself. There is, therefore, nothing very fanciful or far-fetched in this theory about the production of metallic iron by volcanic action, but of course the question as to whether the reaction has taken place on a scale sufficiently great to affect the com- position of the whole of the upper crust of the earth to a great extent is a very wide and somewhat difficult one, involving as it does a number of important considerations. In particular the occurrence of the reaction to such an extent would require a truly enormous quantity of coal or carbonaceous matter to effect the reduction of the oxide of iron. Let us suppose that the acidic or upper and altered part of the crust of the earth is on the average 10 miles thick, and that it is composed of rocks having an average specific gravity of 2°6. Its weight in that case would be about 20 x 1018 tons, and if 6 per cent. oxide of iron has been removed from it by reduction with carbonaceous matter, the quantity of oxide removed would be 1:2 x 10!8 tons ; and this would require for its reduction about 0°1 x 1018 tons carbon, or fully 200 times as much as would be required to combine with and use up the total free oxygen of our present atmosphere, It is obvious that such a quantity of carbonaceous matter would take an extremely long time to produce by the growth of vegetation and the deposition of coal or bituminous matter in the ground at anything like the rate at which these natural operations are carried on at present. If the average percentage of carbon- aceous matter in the crust of the earth should be only 75 of 1 per cent., and should have been only 4}, of 1 per cent. during the whole of geological history, it would take a series of sedimentary strata 50 miles in thickness all over the earth to give the amount required. Then if we assume (as is most probable) that the ordinary geological operations of denudation and deposition have been confined to the rocks that lie within a comparatively short distance from the surface of the earth, say a layer or outer crust not exceeding 10 miles in thickness, then the whole of the materials composing this crust would require to be denuded away, redeposited, and heated to fusing-point or thereby no less than five times in the course of geological history. This supposition is hardly credible, but still it is quite possible, not only that the proportion of carbonaceous matter is greater than ;!, per cent. in the present crust of the earth, but also that it was very much greater in very ancient times. Geological History of the Atmosphere. 4A It is generally supposed that there was compuratively little coal deposited in pre-carboniferous epochs, but this is a mistaken idea ; at least there is a great abundance of carbon- aceous or bituminous matter in the rocks of these epochs, though it may not be available for use as coal. In both Devonian and Silurian rocks in certain parts of America there are thick strata of bituminous shale and of limestone rich in bituminous matter and organic remains; and the Laurentian rocks of Canada contain so much graphite that (according to Sir W. Dawson) their average percentage of carbonaceous matter must be at least as high as that of the rocks of the carboniferous epoch. We have therefore no evidence to lead us to suppose that there was less vegetation growing or less coal deposited on the earth in the Laurentian epoch than in subsequent epochs, and we know from the presence of much ferric oxide in the rocks of that period that there must have been free oxygen in the earth’s atmosphere. The conditions therefore as regards the presence of free oxygen on the earth, and (inferentially) the decay or erema- causis of vegetable remains, must have been similar to those of the present day, and probably only a small proportion of the vegetation of that epoch would be preserved in the form of coal or graphite. But, as is evident from Dr. Phipson’s experiment on the growth of plants in various gases, vegeta- tion might quite well have grown on the earth in the periods anterior to the existence of free oxygen. In the absence of free oxygen the remains of the vegetation would not be subject to eremacausis, and would therefore be preserved (for a considerable time at any rate) in the form of coal or graphite or mineral carbonaceous matter of some description. Obviously then it would require a very much shorter time under these conditions to produce 0°1 x 10 tons of coal than it would under modern conditions when probably less than 1 per cent. of vegetable remains is preserved as coal or carbonaceous matter. In fact the time required to produce our 0:1 x 1078 tons of coal would come within quite reasonable or credible limits, for it is surely not unreasonable to suppose that the ordinary geological operations of de- nudation and deposition have been going on for a period at least two or three times as long as the time that has elapsed since the earlier part of the Laurentian epoch, and a period of this extent is probably long enough under the conditions above specified to produce 0°1x10?* tons of coal or other carbonaceous matter as the result of vegetable growth. This quantity is equivalent to about 0°5 per cent. of the weight of the whole crust of the earth for the first ten miles of its thickness. 2G 2 444 Mr. J. Stevenson on the Chemical and But another difficulty in the way of accepting our theory is raised by the question as to whether it is possible or probable that the whole crust of the earth for several miles of its thickness should be heated after its first solidification to a temperature sufficiently high to produce metallic iron from oxides and silicates and other compounds of iron through the reducing action of carbonaceous matter, and also to liquefy the rocks so as to allow the metallic iron to sink down to an inaccessible depth. We know sufficiently well that all through geological history down to the present day certain portions of the crust—the seats of voleanic action—have been heated to this extent, but as regards the area and depth of these portions or regions, and the quantity of material heated in each case, our information is very limited. However, judging from what we may roughly infer regarding the prevalence of voleanic action both in our own times and in past geological history, we should say that the total amount of volcanic action has probably not been sufficient to heat up the whole crust of the earth to the extent required for our theory. At any rate, we should say with a fair degree of certainty that the total voleanic action on the earth, as inferred from geological observation, would not be sufficient to heat up the whole erust of the earth (in portions at a time of course) repeatedly to the fluid condition, as would require to be the case if the amount of carbonaceous matter has always averaged con- siderably less than 4 per cent. But on the other hand it is quite possible that the conditions affecting the prevalence of volcanic action or heating operations were very different in very ancient times from what they have been during known geological epochs. When the surface of the earth first became solid the underlying rocks must have been very hot, perhaps liquid in many places ; but even if they were solid they must have been near the fusing-point, and therefore volcanic eff cts must have been more easily produced then than now. Further, the low degree of conductivity for heat possessed by ordinary rocks has, at this point, an important bearing on the question before us. Lord Kelvin in his essay on the ‘Age of the Earth’ gives expression to the opinion that vegetation or some kind of organic life may quite well have begun very soon after the surface of the earth first became solid, and it is easy to see that any vegetable or other organic remains deposited in those very early epochs would not have much chance of remaining ia a comparatively unaltered condition for a great length of time, as the sedimentary rocks of that epoch would be liable to be heated to a high temperature within a comparatively short period after their deposition. Also we should expect Geological History of the Atmosphere. 445 that the metallic iron produced by the heating of the organic or carbonaceous matter present in those deposits along with oxide of iron and other iron compounds also present would sink deep down—possibly as a rule to inaccessible depths. Jt should also be remembered when discussing the question of the production of the heat necessary for our theory, that the combination of the carbon or organic matter with the oxygen of the iron compounds would probably tend to raise the temperature of the mass to an appreciable extent, and that the long time during which the materials would be heated together, or even the long time during which the iron eompounds would be heated in the presence of reducin gases derived from the destructive distillation of the organic matter, would be in favour of a more thorough reduction of the iron compounds to the metallic condition than we should expect to take place if the very same materials were heated for a short time in a modern blast-furnace. Another point worth noting is that the reduction of oxygenated iron compounds by carbonaceous matter may have taken place, at all epochs and on a very large scale, in the presence of sulphur compounds at quite ordinary temperatures, and it is also possible that a large quantity of the sulphide of iron produced in this way may have sunk down to an inaccessible depth when the rocks containing it were heated to fusion by volcanic action (or the causes which bring about volcanic action). Of course the disappearance of sulphide of iron in this way involves the question of heating up just as much as reduction to tbe metallic state would, but still enough has already been said to show that the question of heating does not, or at least need not, put insuperable difficulties in the way of our theory. Questions regarding the nature of the vegetation or organic life in those very early epochs need not cause any serious difficulty, for organisms of the humblest type, such as diatoms or infusoria, would be sufficient for the purpose. The very obvious difficulty regarding the absence or comparative absence of light at the base of the great atmosphere which we have conjectured, and the probably adverse conditions for the growth of vegetation thereby produced, may be met by asking the question—Why do plants require light to promote their growth? Is it not to decompose carbonic acid and water in order to produce compounds containing a smaller proportion of oxygen? If cumpounds containing less oxygen were already present in the atmosphere and ocean in abund- ance, the conditions would be very different, and in these conditions it is quite possible that vegetable growth or organic growth of some kind might go on in the absence of light. a, NN 9 4q “ap? , e af 446 Mr. J. Stevenson on the Chemical and In addition to the difficulties which have just been discussed, there is one to which reference was made in connexion with the argument drawn from the composition of basic and acidic rocks. We stated that if the acidie rocks of the earth’s crust, containing as they do 60 per cent. or more of silica, have been derived from a primordial basic rock-mass containing only 45 per cent. (or less) of silica, it is not easy to see what has become of all the missing bases. It should be noted that the quantity of missing bases is even greater than one may at first be apt to infer from the above percentage of silica. In basic rocks containing 45 per cent. of silica and 55 per cent. of bases, there will be 122 parts by weight of bases to 100 parts of silica, while in acidic rocks containing 60 per cent. of silica and 40 per cent. of bases, there are only 66 parts by weight of bases for 100 parts of silica, or not much more than half the proportion of base relatively io silica found in the basic rocks. Acidic rocks would thus seem to have lost about half the quantity of base which was originally present. If then they have been derived from primordial basic rocks we should expect to find a very large quantity of carbonates, sulphates, chlorides, and hydrated oxides on the earth, or else we should infer that a very large quantity of oxide of iron has been removed, perhaps several times more than the 6 per cent. already postulated. As regards the ~ amount of carbonates &c. we have already remarked that there seems not to be as much limestone (which is the principal carbonate present) as would be equivalent to the sandstone or free silica alone, while the sulphates, chlorides, and hydrated oxides are comparatively small in quantity. There might no doubt be large quantities of carbonates in the rocks underlying the great oceans and these might be accompanied by a comparatively small quantity of sandstone. It is quite reasonable at any rate to infer that considerable quantities of carbonates exist below the great oceans from observations made regarding the evolution of carbonic acid at the bottom of the sea, or at least the presence of carbonic acid in varying proportions at different places in the sea (see Prof. Dittmar’s figures on this subject in vol. i. p. 219 et seg. (Physics and Chemistry) of the Reports issued in connexion with the ‘Challenger’ Expedition); and at the same time we should reasonably expect that there should not be much sandstone underlying the great oceans, or at any rate the abysmal regions of the great oceans, on account of the very long period during which they are supposed to have been in existence. Also, as regards the quantity of oxide of iron removed from ail Y ig . Geological History of the Atmosphere. AAT the rocks composing the crust of the earth, it is quite possible that it may have been much greater than the 6 per cent. pos- tulated above. If the average composition of the earth as a whole is at all similar to that of the meteorites which fall upon it, and there is some reason to suppose that it is, the percentage of iron present should be very large, and therefore we should not be surprised if the rock-mass forming the earth’s crust originally contained very much more than 8 or 10 per cent. oxide of iron. To postulate a considerable addition to the quantity of oxide of iron originally present would no doubt intensify some of the difficulties discussed in the preceding paragraphs, but it would not necessarily make them insurmountable. However, our information with regard to the various data required, viz., the composition of the primordial basic rocks or rock-mass of the earth, and the average composition and total quantity of the acidic and other derived rocks, is too indefinite to admit of them being used as the basis of a decisive verdict either one way or the other. At the same time, it is worth noting that the total quantities of water and carbonic acid (or carbonates) on the earth, so far as they can be estimated roughly, seem to accord fairly well with the requirements of our theory, at least in so far as the question of whether there is enough carbon and hydrogen on the earth to form the carbonaceous matter necessary for reducing the oxide of iron is concerned. The quantity of carbonic acid on the earth as inferred from Dr. Sterry Hunt’s estimate of the carbonates present, viz. enough to form an atmosphere 200 times greater in extent than our present one, may be taken roughly at 1°4 x 108 tons, which corresponds to about 0°38x 108 tons carbon. As we have already estimated that the quantity of carbonaceous matter which would be required to remove 6 per cent. of oxide of iron from a shell of the earth’s crust ten miles in thickness would be 071 x 1018 tons, it is obvious that there is more than enough carbon on the earth, if it formerly existed in the unoxidized condition, to effect the reduction in question, and indeed that there is enough to remove fully 20 per cent. of oxide of iron from a shell of the earth’s crust ten miles thick even if each particle of carbon took part only once in the reaction. And besides the carbonic acid there is a very large quantity of water on the earth, even larger than the quantity of carbonic acid as estimated above and containing a larger proportion of oxygen. If a large pro- portion of the hydrogen of the water originally existed in the unoxidized condition, either quite free or in combination with carbon or other elements, there would obviously be ee ee 448 Mr. J. Stevenson on the Chemical and ample materials for reducing a very large quantity of oxide of iron to the metallic condition. No doubt we should hardly expect, even if there was a great deficiency of oxygen on the earth relatively to the other elements, that all the carbon and hydrogen would be originally unoxidized, but still after all it is only a comparatively small proportion of the total quantity of these elements that our theory requires to have been present originally in the unoxidized condition, something like + or 3/5 or even considerably less. We need not there- fore go further into detail on this point, but it may be well to state again how we conceive that the hydrogen or other oxidisable gas, present by our hypothesis in the primitive atmosphere, gradually disappeared. We assume that vege- tation or organic life of some description could grow and flourish in such an atmosphere, and that it may possibly even _ have derived nourishment from the hydrogen or hydrocarbon gases or perhaps also carbonic oxide (CO) which may have been present. The coal or carbonaceous matter formed from the remains of these vegetables or organisms would eventually become heated along with materials containing oxide of iron, with the resultant formation of metallic iron and carbonic acid. If the hydrocarbon gases and carbonic oxide of the primitive atmosphere were absorbed directly by vegetation (or the organic life of the time) they would gradually come to be used up and disappear, and after that period carbonic acid alone would supply the carbon required for vegetation or organic growth. The use of carbonic acid would involve the liberation of oxygen, but as long as free hydrogen existed in the atmosphere the oxygen liberated would be taken up by the hydrogen and water formed. If carbonic acid was necessary from the very first for the support of life, there would probably be oxygen evolved from the very earliest period, and this oxygen would for a long time be used up in oxidizing the hydrogen, hydrocarbon gases, and carbonic oxide or whatever oxidisable gases may have been present. Whatever may be thought of the above theory and the arguments adduced in support of it, we may be tolerably sure that if the primitive atmosphere did not contain hydrogen, hydrocarbon gases, or carbonic oxide it must have contained a very large quantity of carbonic acid gas. It is quite obvious that if the rocks composing the crust of the earth were heated until they became liquefied, the limestone and other carbonates which are present in enormous quantities would be decomposed, with the result that silicates would be formed and carbonic acid set free. Similarly we may infer that if the earth was all highly heated and liquid in very os Geological History of the Atmosphere. 449 ancient times, there could not be any carbonates present such as we find now, and therefore the carbonic acid now found in them in the combined condition must have existed at that time in the free condition, unless of course the carbon and oxygen composing it existed in some other forms of chemical combination. The total quantity of these carbonates is very great. Dr. Sterry Hunt, as already referred to, in his papers on the Geological Relations of the Atmosphere, calculated that there was enough CQ, present on the earth in the form of carbonates to form, if set free, an atmosphere 200 times greater in extent than our present atmosphere. Now it is obvious that an atmosphere of CO, of this extent would have a very great influence on many terrestrial phenomena. The terrestrial radiation of heat would be much affected by it, and the temperature of the surface of the earth would be considerably higher than with our present atmosphere. Prof. Arrhenius, of Stockholm, calculates (Phil. Mag. April 1896, p. 268) that if the present small quantity of carbonic acid in the atmosphere (‘03 per cent.) were increased 2°5 to 3 times, the temperature in the arctic regions would rise about 8° or 9° C., an amount sufficient to cause very great climatic changes. And if such a (comparatively) small addition of carbonic acid to the atmosphere is likely to cause such a change in the temperature, what are we to infer regarding the influence of a quantity several hundreds of thousands of times greater? Clearly an atmosphere con- taining such a quantity of carbonic acid or even a considerably less quantity, say one tenth or one hundredth of the above amount, would have a marked effect in retarding the radiation of heat from the earth, and it is therefore quite possible that the rate of the secular cooling of the earth was considerably lower in very early geological times than it is now. Further, an atmosphere containing much carbonic acid must have bad a much more powerful solvent or disin- tegrating action on siliceous rocks than our present one, and therefore the rate of the formation of carbonates and prob- ably also the rate of general denudation must have been much greater than they are now. The rate of denudation would also be increased, as compared with that of modern times, by the much greater rainfall which we should expect to take place as a result of the greater extent of the at- mosphere and the greater quantity of aqueous vapour that it would contain. It is worth noting here, that the formation of carbonates from silicates (which are anhydrous, or nearly so, in the case of igneous and crystalline rocks) is usually accompanied 450 Chemical and Geological History of the Atmosphere. by the formation of hydrated silicates, and so, in taking a general survey of geological history, we shall find that there has been a fixation, not only of much carbonic acid in the crust of the earth, but of a very large quantity of water as well. This quantity is so great as to represent a very considerable proportion of the total water existing on the earth. Taken along with the moisture or uncombined (hygroscopic) water present in the rocks it may amount to as much as 4 or + otf the quantity of water present in the ocean itself. Mr. +. W. Clarke in his recent estimate of the average composition of the rocks forming the crust of the earth gives the water at 1°51 per cent., which for a ten miles’ thickness of the earth’s crust would give a total of about 0° x 101* tons water. As this estimate seems not to include hygroscopic water, it may be well also to note his earlier estimate (which does include hygroscopic water), viz., 1°96 per cent., a percentage which in a ten miles’ thickness of the earth’s crust would give about 0°4.x 10! tons water, or nearly one third of the water present in the ocean (say 1°3 x LO’* tons). It is obvious that if this water present in the rocks has been derived from the atmosphere and the ocean, the ocean must have contained considerably more water in ancient times than it does now, and probably covered a greater area of the earth. It is also worth noting that the combined and hygroscopic water present in rocks may be the real or the principal source of the steam which is evolved in such large quantities during volcanic eruptions. A question of some interest which is naturally suggested here is that regarding the ratio of the quantities of terrestrial hydrogen and carbon to each other. It would be of very considerable interest if the quantities should be found to bear a ratio to each other that could be expressed by such a formula as CH,, or that of some other hydrocarbon compound. However, if we accept Dr. Sterry Hunt’s estimate of the quantity of carbonates on the earth, we shall find that there is not enough carbon to form methane (CH, the hydrocarbon which contains the largest proportion of hydrogen) with the hydrogen of sea-water alone. It is no doubt possible that carbon might be present in large quantities in the internal parts of the earth combined with iron and other metals, but of this we have no definite information, and in any case we would naturally expect, as already stated, that a large pro- portion of the hydrogen and the carbon would be present on the earth in the oxidized condition from an indefinitely early period. In conclusion we may sum up the results of this paper by | | ——— | On an Improved Form of Coal-Calorimeter. 451 saying that the primitive atmosphere was most probably very ‘extensive one, perhaps a hundred or several taadred times greater in extent than our present atmosphere. It may have consisted principally of carbonic acid, or it may have contained, either in addition to or instead of carbonic acid, large quantities of hydrogen, hydrocarbon gases, and carbonic oxide. At present our information regarding the data bearing on this question is not definite enough to decide the point with certainty, but we may reasonably hope that sufficient evidence will sooner or later accumulate to give a fairly decisive verdict. | L. On an Improved Form of Coal-Calorimeter. By WALTER RosEnHAIN, B.A. (Cantab.), B.C.E. (Melbou Ne HE author recently designed a coal-calorimeter for use in a Works laboratory +. In doing so, he was guided in the first instance by an instrument which was shown to. him by the courtesy of Professor T. Hudson Beare t at the Engineering Laboratory of University College, London, and Fee author Te to acknowledge his dene due to ro- fessor Hudson Beare in this matter. The instrument which the author saw at University College had the advantage of great simplicity, but on trial oes the somewhat THe conditions of a Works laboratory certain improvements suggested themselves, and, after a number of intermediate forms, the present instrument was arrived at. The author was greatly aided in this work by the Cambridge Scientific Instrument Co. In the present form of coal-calorimeter the Thomson principle is retained §, and the coal is burnt in a stream of oxygen while inclosed in a chamber immersed in the water of the calorimeter. The calorimeter therefore consists of two essential parts, a vessel for containing the water, and a chamber in which the combustion takes place. The former is a rectangular vessel of sheet-brass, containing about 24 litres of water, while the latter is much smaller, and is finde principally o of glass and provided with a sat of pipes and valves for the admission of the oxygen and the escape of the products of combustion. As the improve- * Communicated by Professor Ewing, I’.R.S. + Of Messrs. Chance Bros. & Co., Ltd. , Glass Works, near Birmingham. t Prof. Hudson Beare states that this instrament was desioned by Mr. Legros, A. M.Inst.C.E § Wm. Thomson, F.R.S., Journal Soc. Chem. Ind., 29th Noy. 1896. 452 Mr. W. Rosenhain on an ments which the author believes he has introduced into the present form of calorimeter are principally connected with the design of the various details of the instrument, a detailed description will be necessary. The calorimeter-vessel is seen in section in fig. 1. The brass vessel is provided with two opposite windows, which allow of a full view of the interior of the vessel, so that the progress of the combustion in the glass combustion-chamber can be observed. When in use the calorimeter-vessel stands in a wooden casing, as a pro- tection against radiation, and this casing is provided with slots to corre- spond with the windows in the vessel itself. On the base of the calorimeter- vessel is a lug which forms part of a _bayonet-joint by which the combustion- chamber can be fixed in its place within the calorimeter. Fig. 2 shows the combustion-chamber in section, as seen in its place within the calorimeter, while fig. 3 is a plan of the same. Fig. 4 shows the combustion- chamber in elevation, placed upon an independent stand when removed from the calorimeter. In fig. 2 (a) is the outer wooden case, (0) the brass calorimeter-vessel, (c) the bayonet-joint. The combustion- chamber itself is formed by a lamp-chimney—in practice a Jena incandescent gaslight chimney is used—which is closed at top and bottom by means of pairs of brass plates. In each case the outer plate is movable, and can be brought near to the other by means of a screw ; a rubber collar is placed between each pair of plates, and this makes a tight joint with the glass when the screws are drawn tight*, These are shown in section at (d d) fig. 2. In each case the fixed inner plate carries the various attachments. These will be best understood by following the course of the oxygen that flows through the chamber when in use. The gas enters ATT EOE TOTO ETON SEL EL EETEILI DE RETESE SODPESITSVELDTED Raat PT AAT AA N R N N 9 ; Ni S N N iS : N N ., S N 4 Ny S Ny SS * It is proper to state that the use of a lamp-glass for this purpose is taken from Prof. Hudson Beare’s instrument, but the author has substi- tuted cylindrical gaslight glasses for the curved lamp-chimneys of the former instrument, as the cylindrical glasses are made of more regular shape. » a] a Improved Form of Coal-Calorimeter. 453, the instrument at the tap (e), and flows down the tube (/') to the small “rose” nozzle (y). After taking part in the-com- bustion of the coal, which is placed at (A), the gas leaves the chamber by the openings (i 2), and flows down the tubes (7 9) to the ball-valve (k). Lifting this valve, the gas enters the small chamber (/), and escapes into the water of the calori- meter by the small holes (m) (see also fig. 4). This continues until the combustion is finished ; then the supply of oxygen ADA Mr. W. Rosenhain on an is cut off, and the tap (n) (figs. 2, 3, and 4) is opened. This _ establishes free communication between the gas in the com- bustion-chamber and the water of the calorimeter through the small pipe (eo). As the water-level in the calorimeter when filled for use is at (p p), the tap (m) is only just above water-level, and the whole of the pipe (0) is immersed in the water ; any gas escaping by this pipe is thus thoroughly cooled. When the tap (mn) is open, the water is only pre- vented from entering the combustion-chamber by the ball- valve (k). Such a valve was found necessary to prevent the water from rushing into the combustion-chamber whenever the combustion slackened. At those times the gases in the combustion-chamber would cool and contract so rapidly that the oxygen supply could not keep up the pressure, and, in the absence of a valve, the water often entered and ex- tinguished the combustion. The presence of the valve, however, necessitates a by-pass, which is provided by means of an opening (q) in one of the tubes (7), which is normally closed by a stopper with a long handle projecting above the water-level. It will be seen that no stirring arrangement is used, as it is found that the vigorous bubbling of the gas from the many small holes (m) stirs the water most efficiently. The combustion is started in the first instance by means of a platinum wire heated electrically. An insulated wire passes down the tube (¢) from the terminal (s) ; the other terminal is formed by the oxygen inlet-tube (f), whose upper end carries the terminal (u). Both the oxygen inlet-tube and the lead-tube (¢) pass through the upper clamping-plates by means of stuffing-boxes which allow the heating-wire to be moved about and also admit of the adjustment of the position of the oxygen inlet. The stand (v) (fig. 4) is provided with a bayonet-joint similar to that on the base of the calorimeter-vessel for the purpose of holding the combustion-chamber when removed from the calorimeter. For the introduction of the sample of coal at the commencement of an experiment, the chamber is placed on this stand and the wing-nut (w) is loosened ; this allows the lamp-glass and its attachments to be lifted off and replaced when the coal has been put in place. The com- bustion-chamber, having been screwed up, is then removed from the stand and put into place within the calorimeter- vessel, the water being only poured in after this has been done. The length of time occupied by a combustion varies with the conditions : with a sample of coal in the shape of a briquette, weighing about 14 grammes, and containing 7 per » i Improved Form of Coal-Calorimeter. 455 cent. ash, the time of a combustion will be about six minutes, and the rise of temperature about 23° C., but as the-com- bustion takes place in full view, it can be readily retarded or accelerated by adjusting the oxygen. In the author’s opinion, the present form of coal-calori- meter has certain special advantages, and these will best appear by comparing it with the well-known Mahler-Ber- thellot “‘bomb”’ calorimeter. Certain chemists have stated that the latter form of instrument, in which the coal is burnt, practically instantaneously, in an atmosphere of oxygen under very high pressure (up to 180 lbs. per sq. in.) is alone reliable, as in their opinion * the combustion of coal in a current of oxygen under atmospheric pressure is never complete. Were it possible or necessary to determine the calorific value of coal to an accuracy of 0°1 per cent., then this objection would be perfectly valid, as such combustion is never perfectly complete, but such accuracy would in any case be merely imaginary, owing to the varying quality of the coal in various “parts of eyen one truck-load, and the author has found that by observing certain precautions, the combustion in the present instrument can be rendered suffici- ently complete for the degree of accuracy required. The most important of the special precautions which must be observed is to provide for a free access of the oxygen to the entire sample of fuel. When the coal is burnt as a powder lying in a platinum crucible, this condition is not fulfilled, as the carbon dioxide formed by the combustion tends to remain in the crucible and to dilute the inflowing oxygen. To avoid this, the author replaces the platinum crucible by a flat tray of porcelain, and uses the sample of coal in the shape of a small cylindrical briquette standing freely on the tray, the briquette being readily formed from the powdered sample by pressure in a mould. The author prefers a porce- lain to a platinum tray on account of the feebler heat- conductivity of the former, which therefore does not cool down the layers of fuel in contact with it so rapidly towards the end of the combustion. The author finds that these modifications reduce the time occupied by a combustion to about one half, and at the same time cause a very nearly complete combustion to take place. The only residue is generally a very thin film of tarry matter deposited upon the porcelain tray close to the specimen. To determine the weight of this unburnt residue the following experiments were made. A series of samples of coal were burnt in the calori- meter under working conditions, except that larger quantities * Hempel, ‘Gas Analysis,’ p. 356, 456 Mr. W. Rosenhain on an of coal were used to render the measurements more exact ; when the combustion itself was over, the sample was in each case removed from the calorimeter without haying been brought into contact with the calorimeter-water ; this “calorimeter ash” was then dried to constant weight at 130° C., and its weight determined ; it was then exposed to oxidation in a muffle, also until constant weight was attained; the difference between the weight before and after the treat- ment in the muffle was taken to represent the weight of the unburnt residue left by the combustion in the calorimeter, and, as the following table will serve to show, this was in all cases found to be small. Weight of | Ash from Ash after Difference | Percentage of coal used. | calorimeter. muffle. | (unburnt). “unburnt residue,” tenets thetic olds of i errr 26019 ‘3651 3572 |. 0079 | *30 per cent. 3°4228 "4854 ‘4790 ' 0064 | 5 ae 25023 3420) 3341 ‘0079 |. So 17865 _ 12848 “2791 ‘0057 | gay i It has also been suggested that in the present form of instrument there is a risk of a small quantity of carbon mon- oxide being formed and escaping unburnt in the gases leaving the calorimeter. To test this point the author made a number of analyses of the gases leaving the calorimeter during a combustion. For this purpose the valve in the base of the instrument was firmly screwed down by means of a piece of indiarubber packing, and the piug in the opening of the lower outlet-tube was rep!aced by a glass tube. The gases, therefore, instead of bubbling up through the water of the calorimeter, passed along this tube and through the apparatus arranged for the analysis. The gases were first passed through solutions of caustic potash, to absorb the carbon dioxide, and then through strong sulphuric acid ; the only gases which would pass through would be oxygen and any carbonic oxide present; tlis mixture was then passed through a long tube filled with palladium asbestos, and kept hot during the experiment. Any monoxide present would be oxidized, and its presence and amount observed by the increase in weight of the soda-lime ab-orption-tubes through which the gases were passed after again drying them. As the entire arrangement was in action before the specimen was ignited, it will be seen that all the gases passed through the apparatus, so that any formation of carbon monoxide, even at the beginning or end of the combustion, would be detected. =P. hl ae + i] Improved Form of Coal-Calorimeter. 457 The result of a number of such tests was entirely in favour of the instrument, as it was found that when the combustion was properly regulated no carbon monoxide whatever could be detected. Only in one case was any real increase of weight in the absorption-tube observed, and in that case the amount of carbon dioxide obtained corresponded to 0°33 per cent. of incompletely burnt carbon ; but in this case the oxygen supply was very badly adjusted, and the combustion was obviously imperfect, a considerable amount of soot being deposited ; the experiment was, however, continued in that way in order to test the efficiency of the analysing arrange- ment, and the result serves to show that the apparatus was quite satisfactory. The author therefore feels justified in stating that any loss of heat due to the escape of partially burnt gases may be disregarded when the combustion is properly conducted *. As compared with the “bomb” type of coal-calorimeter, the present form of instrument has certain obvious advan- tages. One of these is greater simplicity and cheapness ; no high pressures have to be resisted, and no explosions can possibly occur. Further, the combustion takes place in full view, and can be watched and regulated throughout, and the combustion takes place under conditions rather more like those of actual practice than explosive combination under great pressure. The operator has therefore a means of Judging the behaviour of the coal as regards coking and clinkering which is not afforded by the other instrument. But the strongest objection to the ‘* bomb ” instruments is that in them the combustion takes place in a closed vessel having thick walls; the heat must therefore penetrate these walls and be transferred to the water of the calorimeter by con- duction alone, and it is probable that a considerable time must elapse before the water has taken up sensibly the whole of the heat. In the present instrument the water is admitted at the end of the combustion to the interior of the combustion- chamber, and thus has every opportunity of taking up the whole heat quickly. With the large bulk of water and the small rise of tem- perature used in the present instrument, the radiation cor- rection is very slight; with a temperature-difference of 2° C. the rate of cooling is about 0°:001 C. per minute, and the value of the correction can be readily found in any of the * The thanks of the author are due to his senior assistant, Mr. W. J. Rees, for help with these experiments. Phil. Mag. 8. 6. Vol. 4. No. 22. Oct. 1902. 2 458 On an Improved Form of Coal-Calorimeter. usual ways ; it is, however, necessary to ensure the constancy of temperature of the stream of oxygen passing through the instrument. When the supply is taken from a cylinder the gas is apt to be cold, and should be passed through a coil of tubing to attain the temperature of the room, and finally bubbled through a wash-bottle containing a thermo- meter to ascertain its temperature and to saturate it with moisture. A certain amount of heat is introduced into the calorimeter by the electric ignition ; this may be kept constant by always using the same strength of current for the same length of time, and the correction may then be eliminated by using the same current when calibrating the instrument. The author prefers to do this by burning in it a known weight of a substance whose calorific value is known, and deducing the water-equivalent of the whole from the rise of temperature observed ; by slightly adjusting the water-contents the water-equivalent may then be brought to round numbers, thus saving much time in calculations. The substance used by the author is pure carbon, such as obtained from sugar, and the heating value is calculated from an elementary analysis. Cakes of such carbon may refuse to ignite in the instrument, but this can be overcome by adding a small but known weight of some such substance as stearic acid, which ignites readily and starts the combustion of the carbon. It has been suggested to calibrate these instru- ments by the combustion of such organic bodies alone, but the author finds that they will not burn satisfactorily in this instrument. As an alternative method of calibration a known amount of heat may be introduced into the calorimeter by means of the electric ignition device, but the author does not regard this as anything more than a check upon the other calibration. : From the above account of the present instrument it will be seen that no novelty of principle is claimed for it ; but the author believes that the modifications of design and method of use which he has introduced will allow the old principles to be applied to greater advantage, and will render this type of calorimeter more convenient to use and more accurate and certain in its. results. [ 459 j LI. Change of the Modulus of Elasticity of Ferromagnetic Substances by Magnetization. By K. Honpa, Rigakushi, S. Saimizu, Rigakushi, and 8. KusaxaBe, Rigakushi *. . PT has been generally admitted that magnetization - has very little effect upon the elasticity of ferro- magnetic substances. Wertheim first measured with a micrometer the elongation of an iron wire due to tension in the magnetized and in the unmagnetized state with exactly the same result. Guillemin ¢ placed an iron bar horizontally and fixed it at one end and hung a small weight at the other, which was left free. The magnetization of the bar by a coaxial coil produced a small rise of the weight. Wartmann § used Chladni’s figures to investigate the change of elasticity of magnetized iron and steel plates, and also examined the sound accompanying longitudinal and transversal vibrations of magnetized iron wires. No influence of magnetization was observed. Treéves|| set in vibration two tuning-forks having the same period of vibrations. When one of them was placed in a coil and magnetized by a strong electric current, its vibration was accelerated producing beats; but when the current was broken the beats were no more to be heard, and the two notes were in unison. This experiment shows an increase of the modulus of elasticity by mag- netization. H. Tomlinson {| found, on the contrary, that the elongation of an iron wire by loading is independent of magnetization. Bock** found the effect to be smaller than 4 per cent., if there is any. By passing an electric current through a stretched pianoforte-wire, M. G. Noyestf noticed an increase of elasticity, which was less than 1 per cent. Maurain ff also found a small increase of elasticity by means of tuning-forks placed in a very strong magnetic field. Inthe investigation on the effect of tension upon magnetic elongation of a pianoforte-wire, B. Brackett §§ observed a small increase * Communicated by Prof. Nagaoka. + Wertheim, Ann. de Chim. et de Phys. [3] xii. p. 610 (1842). t Guillemin, Comp. Rend. xxii. pp. 246, 432 (1846). § Wartmann, Ann. de Clim. et de Phys. xxiv. p. 360 (1848). || Tréves, Comp. Rend \xvii. p. 321 (1868) ; Archives des Sct. Nat, n. s. xxxiii. p. 74 (1868). { Tomlinson, Proc. Roy. Soc. xl. p. 447 (1886). ohne Wied. Ann. liv. p. 442 (1895); Phil. Mag. [5] xxxix. p. 548 (1895). ‘ ++ M. G. Noyes, Phys. Rev, [4] ii. p. 277 (1895); Phys. Rev. [6] ii. p. 432 (1896). tt Maurain, Comp. Rend. cxxi. p. 248 (1895). §§ B. Brackett, Phys. Rev. [5] v. p. 257 (1897). 2H 2 -< + A Sa nt L 460 K. Honda, 8. Shimizu, and 8. Kusakabe on Change of of elasticity amounting to about 4 per cent. J. 8S. Stevens and H. G. Dorsey* used the method of flexure, and applied the interference-fringes to measure the amount of depression. The effect of magnetization upon a loaded iron and steel bar was found to be very small; it showed a minute increase of the modulus of elasticity by about 34, per cent. for the strongest current used. In the next year, Stevens measured the magnetic elongation of steel wires under several loadings and found an increase of elasticity. Lately, Tangl+ published his results on the same subject. He made use of the prin- ciple that the moment of a bifilar suspension increases with tension applied to its lower end. Besides iron, he also examined nickel wires. In fields ranging from 200 to 480 C.G.8. units the maximum increase of the modulus of elasticity amounted to about 1 per cent. for iron and nickel. All of these experiments show that magnetization increases slightly the modulus of elasticity in iron and nickel, and that the change increases with magnetizing force, but its law is not clearly brought out. 2. The method of measurement in our experiment was similar to that of Stevens and Dorsey, as shown in fig. 1. Fig. 1. Aand B are two magnetizing coils of the same dimensions, which rested horizontally in a coaxial line. FG is a stout brass rod of rectangular section extending between two fulcrums ; it is also supported at the middle point by another fulcrum. The coils can therefore be moved independently of the bar. LM isa rod to be tested placed in the axial line * J. S. Stevens and H. G. Dorsey, Phys. Rev. [2] ix. p. 116 (1899) ; Phys. Rev. [2] xi. p. 95 (1900) ; Zertschr. ii. p. 682 (1900). t+ Tangl, Ann. de Phys. vi. p. 34 (1901). Elasticity of Ferromagnetic Substances by Magnetization. 461 of the coils. It is supported at L and M by two fulcrums ; one of them is an ordinary wedge fixed to the brass rod, while the other consists of a cylinder which can rotate about its own axis. is the weight suspended from the middle of the bar. At the centre of the bar a fine copper wire, whose diameter is about 0°08 mm., is soldered and stretched vertically upwards by means of a weak spring P. This copper wire is wound once round a rotating cylinder to which a reflecting mirror is fixed, and stretched upwards, as used in Hertz’s dynamometer. The rotation of the cylinder is observed by means of a vertical scale and a telescope. The dimensions of each part of our arrangement are as follows :— Length of each coil ............. « -= 39°90 cm: _ Its internal diameter............... = 5°80 cm. UCT et a ne ied ain, EE ae =o9o) Chi. Distance between the coils in} = 2°35 cm. for iron and steel. ALES APY! Side sts vente Beis ihecceei = 20 em. for nickel and cobalt. Distance between two fulcrums] = 59-91 em. for iron and steel. EET hel 1 eh gia ae evn ie ea ge = 21-95 cm. for nickel and cobalt. Diameter of rotating cylinder... = 0°172 cm. Sel (2 VE oh oo ee re =261-3' ‘em: The sensibility of our apparatus was such that a displace- ment of one division of the image of the vertical scale in the field of the telescope corresponded to the change of depression of 1:72 10-° em. at the middle of our ferromagnetic rod. It was necessary to protect the mirror and the thin copper wire from air-currents in order to get rid of minute vibrations of the mirror. . | The measurement was conducted in the following way. The bar to be tested was placed in the axial line of the coils and then loaded by a weight. The tension of the fine copper wire was then suitably adjusted, and the mirror was directed to the observing telescope. This adjustment was performed as in the former experiment. To begin with, the bar was demagnetized and then the initial reading taken. A current was then passed through the coils and the corresponding deflexion noted. These processes were repeated with suc- cessively increasing currents. Since the resistance of the coils did not exceed 3 ohms, no trace of heating effect due to current was observed during the time in which the deflexion was taken; we therefore dis- pensed with a water-jacketing arrangement. The lateral contraction or elongation, which necessarily accompanies the magnetization of a ferromagnetic rod, was at most of the order 2x10-® cm. for iron and 7X10-§ em. for nickel. Hence with our arrangement, the lateral change of dimension 462 K. Honda, 8. Shimizu, and 8. Kusakabe on Change of due to magnetization was within the limit of experimental errors. The disturbance of the results due to magnetic elongation or contraction in the longitudinal direction was eliminated by means of the rotating cylinder which served as. one of the fulcrums. The bar bent slightly downwards if loaded; hence when it was magnetized it would strive to make itself straight. This may cause an apparent increase of elasticity ; but it was con- firmed by direct experiments that the effect was negligibly small, because the reading obtained by inclining two coils with respect to the bar toa degree greater than the actual case was almost the same as in the case when the coils rested in a coaxial line. Since the bar was considerably shorter than the whole length of the coils, it lay nearly ina uniform field except at the middle. The effect of the air-gap between the coils was also studied, varying its width by 1 or 2 cms.; however, such a change had no sensible effect on our results. 3. The dimensions of the specimens used in our experiments and their moduli of elasticity were as follows :— Wee G Cc eee Metals: Soft Iron, Steel. Steel. Nickel. Cobalt. | Length ...... 64:00 cm. | 6400 cm. | 640m. | 24:20 cm. | 27-30 em. “Breadth... 0-903 0920 | 0-948 0510 | Radius “Thickness ...| 0901 | 0913 | 0953 | Ol = 0680 . | Elasticity »--| 2°02 x 10!? | 2:01 x 10!” | 2:05 x 10'? | 1-96 x 107 | 1-7o x= | Z The present arrangement was not suitable for the absolute measurement of the modulus of elasticity, since the yielding effect of several parts of the arrangement disturbs the result. Hence the modulus of elasticity was determined by the ordinary method of flexure with two reflecting mirrors. The intensity of magnetization of the specimens was deter- mined by the magnetometric method. The results are given in fig.2. Ordinates represent the intensity of magnetization, and abscissee the effective field. The magnetic change of length was found to have an intimate relation to the change of elasticity, so that it was measured for each specimen. ‘To each end of the bar a brass rod of the same thickness and 15 cms. long was soldered. The bar was then vertically suspended coaxial with the mag- netizing coil by means of a screw adjustment. From its lower end a weight of 1 or 3 kilogram was hung by a ———- eee |. a al Elasticity of Ferromagnetic Substances by Magnetization. 463 copper wire. The weight was dipped in water so as to avoid its vibratory disturbance. The rotating cylinder with a Es aoe Fig. 2. cae ee eo aM | act if DERAN ee # eed “ H reflecting mirror, deseribed in the preceding paper, was brought in contact with the copper wire under slight pressure to prevent sliding. The magnetizing coil was so long that the bar lay in a nearly uniform field. The results of expe- riment are given in fig. 3. Here H denotes effective field Fig. 3. ope SG a a a AD eS i eae ARE RAR eee and zt the magnetic change of length per cm. We observe that the elasticity of a substance undergoing a large change of length is also similarly atfected by magnetization. 464 K. Honda, 8. Shimizu, and 8. Kusakabe on Change of 4. Soft Iron.—In observing the deflexion from our scale- reading by passing a current through the coils, we were first struck with the large effect contrary to the results of previous experimenters. The largest deflexions for soft iron and Wolfram steel amounted to about 9 cm. with a scale at 2°61 m. distant in a field of 500 c.G.s. units, while for a steel bar it was only one third. Even nickel, for which the distance between the two fulcrums was only 22 em., showed a deflexion of 3 cm. The curves for the change of depression corresponding to different ue gs in soft iron are given in fig. 4. Ordinates ALeECeeee Metal) (OS ei i a PRS GN, Gee RS Se ee a Gas Slick i | ac Ppa Spe Cee eee ee represent in centimetres the amount of the change of depres- sion, taken positive when it indicates an increase of elasticity, and taken negative when it indicates a decrease. Abscisse represent the effective field, and T the suspended weight in grams. The general course of these curves resembles that of mag- netization. In weak fields, however, we notice a minute decrease of elasticity when the load exceeds about 1°5 kilograms. Iron contracts laterally when magnetized by weak currents, and this contraction may produce such an apparent decrease of elasticity; but the actual calculation shows that the initial depression is more than can be accounted for by the lateral contraction. When the field increases beyond this region, the change of depression increases rapidly and soon reaches its asymptotic value, after which the increase takes place quite slowly. As the weight is Increased the change of depression is also increased. The rate of increase is lar ge with small loading and decreases as the load is increased, approaching to an asymptotic value. a Elasticity of Ferromagnetic Substances by Magnetization. 465 From the change of depression we may calculate the ratio of the change of elasticity to the modulus itself. The depres- sion due to the suspended weight as weil as to its own weight in an unmagnetized bar is given by the approximate formula * = — “ ——. (T+ 2W),: where /, a, b are the length, breadth, and thickness of the bar, T and W the suspended weight and the weight of the bar itself respectively. d and W refer to the part of the bar lying between two fulcrums. The observed change of de- pression divided by this depression is the ratio in question, that is, ey Some of the results of our calculation are given in the following table. In the calculation the effect of the weak spring stretching the thin copper wire was corrected for. ] a = ; a / T+SW.| 329 er. 829 er. 1349 er. 1849 er. 5869 er. 20 1:64x10—7| 077x10-2| 0:50x 10-2 0:-47x1077| 0-44x10-? 30 2-79 1:47 1:09 1-08 0:88 50 315 1-84 1:35 1-28 1-16 100 | 3:36 1-92 1:48 1:37 1-28 250 | 3-40 | 1-93 1-51 1:40 1:32 (193 1-51 1-40 1-32 400 | 3:40 These numbers show that the value of ee becomes greater iE as the field is increased, and that it becomes less as the weight is increased. ee ee ee = [1918 Ce OE OE RS ae eldok pessesoe : 5. Steel.—The general character of the change of depr ession is similar to that “of soft iron, as given in “fig. 53; but the * Clebsch’s Elasticitat, p. 375; Winkelmann’s Physik, i. p. 266. 466 K. Honda, 8. Shimizu, and 8. Kusakabe on Change of initial decrease is not observed. Some of the values of ok are given in the following table :— —— iD) elasticity. With the present specimen, the value of n/ T+sw. 1251 gr. 2184 gr. 50 0:14x10-2) 0:15x107-?) 100 0:22 0:25 200 0:27 0:33 300 0-28 0:37 400 0:30 0:40 0-17 x 107? 3096 gr. 0:25 8B E under a given field reaches a maximum with a load lying between 1270 and 2200 grams. 6. Wolfram Steel.—The change of depression for Wolfram steel bar by magnetization is similar to that for soft iron, as shown in fig. 6. V tend to become asymptotic. It is still greater, and the curve does not Fig. 6. The initial decrease of elasticity is more marked in the metal than in soft iron and occurs even with the smallest load. The following table contains the values of oli H/T -+ew. ee 70 100 200 300 400 500 for different fields and loadings :— 3058 gr. 1:79 x10—? 2-05 2°55 2:93 326 3°54 1378 er. | 2206 er. | | 1671072, 1:56x107? | 1-79 164 | 2:00 | 1-80 2-10 1:89 2:18 | 1-92 2:23 | 1-97 | Llasticity of Ferromagnetic Substances by Mugnetization. 467 The above table shows that the increase of elasticity under a given field becomes generally less as the load is increased. In weak fields, however, a maximum is observed as in the case of steel. It also increases first rapidly and then slowly as the field is increased. 7. Nickel.—Nickel rod shows an abnormal behaviour as regards the change of elasticity by magnetization. The Eaie oe A eS > q results of observation ure graphically shown In fig. 7, and the values of are given in the following table :— H [o+ew. | 105 gr. 255 ere | bol er yh Kp," p.” eh aes pep”, eiette ast | Nelae eter ae (i1.) 2.€., “the active mass of a solid (or liquid) substance is,” as Guldberg and Waage found empirically, “necessarily con- stant, independent of the quantity of the solid.” Thus, what Guldberg and Waage found empirically, Van’t Hoff explained to be a necessary consequence of the law of action of mass. The mutual chemical action between the solid or liquid and gaseous substances is, however, conceived by Van’t Hoff in the same light as it was by Guld berg and Waage, namely, as of a reciprocal nature (and he extends this even to physical reactions), representing them all as follows: before equili- . . . . e ee brium, when a reaction is still going on, water aqueous > vapour, K (solid substance) ~ cp," (gaseous substance or > SS substances in solution); at equilibrium, water = _ saturated ete =< aqueous vapour, K =cp;"p,”..., 1. e., at equilibrium the two << opposite reactions still continue, but become equal, i. e., just as much (counting in mass or D molecules) of every one of the substances is formed in the unit of time as disappears. No variation in the quantities of the substances is thus taking A470 Dr. Meyer Wilderman on the Velocity of place, but the equilibrium is nevertheless of a dynamic nature. In other words the above equation (ii.) is to be understood in this way: we have partial velocities of each of the two opposite reactions: at dt\! TR. (7, = Keep very (5) = K'p'"'p.' Jee dr the total velocity before equilibrium is : dt Le ht otk de = Kp pe” — K’ps'™ pl™ .- = Z eS dt dt \/ and at equilibrium we have {| — )}=({— ) or a, dtr dtr at a ! i ie = Kp,"p cd. RL K'p,'™'p,!” mene «oa (Iv.) pmpm _ KR aap # buf and Fv ip const.* .. .. eee * I.e., at equilibrium the substances taking part, in the two opposite reactions are all present, as before equilibrium, being regulated by iv. or iv.', and none of the substances can disappear because none of the velocity- constants K or K' equals zero. It should be remarked, reversing the argument, that the same two reactions, which take place a¢ equilibrium, take place before equilibrium, with the same velocity constants K and ead (eo Wie eee ere ee BS pn K, (i) eing either >or— (G) . t equilibrium neither (7)=° dt \/ dt lt\/ ‘ ‘ nor ( 7 ) =0, but | 7 ) ~ be = 0, oe conception can be shown to be true in homogeneous systems, and not to be a mere theoretical (dynamical) concepteon which can just as well be replaced by another one, for the reason that it can be shown to be true in all its details experimentally: in cases of chemical equilibrium in homogeneous systems, each of the two opposite reactions can be isolated and studied separately so as to get the constants K or K’ separately. For this it is enough to start with a system in which the reacting substances of one reaction are in great preponderance over the substances of the opposite reaction, dt dt \/ = : so that (a ) a ees ) can for a sutticient time be taken to be equal to #\/ z) or to ( ms) respectively, and the values K and K’ separately determined. We find then that equilibrium actually takes place just when py py FONE bane say LS fi_f? _ becomes = y= =C, 7, e., the whole conception in all its elements py pyr Ki? from the beginning to the end can be tested (in homogeneous systems) experimentally, and proves to be correct. — et ie ome 5 ol IN lie a het 7 3 Reaction before Complete Equilibrium. 471 The present conceptions of the velocity of chemical reaction in heterogeneous systems, and of chemical equilibrium in heterogeneous systems, can thus be summed up in the follow- ing few general statements : The active mass of a solid (or liquid) substance is, before and at the equilibrium constant (K), independent of the quantities of the solid (or liquid) substance. The velocity with which one or more gases (or substances in solution) combine to form a solid substance is K'p,'™'p.'™..., where py', ps... are the concentrations of the gaseous substances (or of the substances in solution) at the time tT, and ny', ng’ are the number of molecules with which each gaseous substance takes part in the reaction ; this velocity is independent of the quantity of the solid. When both opposite reactions become equal, a dynamic equilibrium as present. In this way we are able to explain or interpret the experi- mental data observed for chemical equilibrium in heterogeneous systems. But on the other hand there are almost no experi- mental observations concerning the velocity of reactions in heterogeneous systems, and we are therefore necessarily com- pelled to be very cautious in drawing conclusions from facts observed at equilibrium for the velocity of reaction in the system before equilibrium has taken place; the more so as the above is not the only interpretation possible. Another, which is more in conformity with the facts concerning the velocity of reaction as far as they are known to the chemist at present, may be formulated thus: The active mass of a solid (or liquid) substance is at the time t before and at the equilibrium directly proportional to its surface =-. The velocity with which one or more gases (or substances in solution) combine to form a solid (or liquid) substance at the time t is K’p,!""p,,/"2' . Xi) 1. €., ts at the time 7 a function of their concentrations as well as of their surface of contact with the solid, which is also >,. The total ey BEFORE A ak is —A Si —K'p, Dy 2. 28K —K! py! p2), — zm AT ee dt Seeks op i Ba ee pen, <.) =2( 5 Se nup,/*4 ) Tyree. Da! =f These general statements explain just as well as those given before all the facts observed at equilibrium of hetero- geneous systems, and give at the same time a more correct form for the equations for the velocity of reaction. It is well known that when an acid solution, for example, is acting upon 472 Dr. Meyer Wilderman on the Velocity of a solid, the reaction is very much quicker when the solid is taken in the form of a powder instead of in big lumps, 7 e., the velocity of chemical reaction in heterogeneous systems is dependent on the surface of the solid substance. In attempt- ing to conceive chemical equilibrium in heterogeneous systems in the same manner as we conceive it in homogeneous systems, 1.é@., a8 two opposite reactions which at equilibrium become constant, the above modification of the existing conceptions becomes a priori inevitable, because we have to view equili- brium here, as we did in homogeneous systems, in the light of velocity of reaction. We shall, however, have first to see more carefully what is the advance made in this manner, and whether it is possible or not on this modified basis to bring all kinds of equilibrium, complete equilibrium, points of transition, and incomplete equilibrium, as well as velocity of reaction in all these regions, under one general law, under one general principle. If this does not prove possible, we shall have to look out for other ways and methods to arrive at such general principles or laws, if possible. B. Let us again consider the equation concerning complete equilibrium as well as the points of transition. The general equations tor the velocity of reaction I found to be Bey Mais on ae ) (J )=e Ota BK)... @ 2. é., the velocity of reaction is, in all cases of complete equili- brium and of the points of transition, directly proportional to the remoteness from the point of equilibrium, T,—T, to the surface of contact of the parts of the heterogeneous system which act one upon another, T—T,,, + the instability con- stant K. Let us start with a supersaturated solution, Equation (a) may in this case be written : dt (= )=4(0,—0,)(@,+ E),"): where C, is the concentration of the solutions at the point of equilibrium, Cr, >, are the concentration of the solution and the surface of contact of the reacting parts at the time ¢. Equation (a’) can be written : = = /C;(S,4+K) eC K); = i Near T K e Tp me (tot) (2 + K) Now let us assume for a while that since the velocity-constants change with temperature, we get for ice ~ water the equation dt dt i K Fe = ello—t) (too + K), or Feel?) (=,+K), because K" is to be put =c(t,—t). Should we assume that 21% 476 Dr. Meyer Wilderman on the Velocity of K" can be put =c(t.—t) we shall get above, below, and at equilibrium (Fe) =e, K) and a =c"(t,—t)(3-+ K) for the partial velocities of ice melting and ice separation, 2. é., we shall get the result that the velocity-constants of each reaction ¢(t,—t), ¢’(t,—t) decrease with rise of temperature below the point of equilibrium, become=, K are quite new and none of them are contained in the equations for the velocity of reaction in homogeneous systems, and the latter cannot be retained and applied for formulating the nature of the phenomena in these regions. We further arrive at the necessary conclusion that when the remoteness from the point of equali!rium becomes equal to zero, no more reaction is taking place, and the complete equilibrium as well as the point of transition are of a STATIC NOT OF A DYNAMIC nature. C. The connexion between the three kinds of equilibrium and between the velocities of reaction in the three kinds of heterogeneous systems. We are thus unable even after the modifications made in the laws of action of mass in heterogeneous systems (by the introduction of the surface of contact of the reacting parts) to connect all kinds of equilibrium and all kinds of velocity of reaction under one general law. At the most we may assume (neglecting even the very probable difference in the values of the velocity constants for solution or separation of salt or ice, &c.) that the only general result arrived at up to the present i in the above manner (by the introduction of the surface of contact into the old conceptions) is that there are in heterogeneous systems two great classes of phenomena, which seem to be essentially different without, however, any apparent reason: complete equilibrium and the point of transition are of a static nature; incomplete equilibrium in heterogeneous systems is of a dynanve nature. In the first only one of the two opposite reactions is taking place, before equilibrium is arrived at, according as the system is abuve or below the point of equilibrium, and non-action occurs at equilibrium ; in the second, on the contrary, two opposite reactions take place simultaneously before equilibrium is arrived at, and both reactions still continue at equilibrium. lt remains now to see whether we cannot succeed in connect- ing all kinds of equilibrium and all kinds of velocities of reaction in heterogeneous systems under one general principle, if we undertake this work of classification anew, putting aside from our present conceptions everything which forms only an interpretation of observed results, and 1 retaining only what 478 Dr. Meyer Wilderman on the Velocity of is sure to be correct. We may safely regard as experimentally verified and correct: (1) That every solid or liquid has a vapour or solubility pressure. (2) That the laws of action of mass are established for homogeneous systems. (8) That the equation dt 4 Fp ae ltot)(t— tow + K) regulates the velocity of reaction and equilibrium in case of perfect equilibrium and the point of transition. If now we make an extended use of the very original and happy idea of Van’t Hoff of taking into account the fact that solids or liquids have a vapour or solution pressure, we can not only bring all three kinds of equilibrium and all kinds of velocities of reaction in heterogeneous systems under one general principle, but for the first time we arrive at the true meaning of chemical equilibrium in heterogeneous systems, and we are at last able to derive the equations for the velocity of chemical reactions in heterogeneous systems, which experi- ments have always failed to elucidate owing to the fact that the phenomena in question are much more complicated than was usually assumed. Let us first write down every chemical reaction and every kind of chemical equilibrium in heterogeneous systems in a scheme. Care should be taken that this is done in a most detailed manner, and that to every part of the scheme the proper attention should be given. Let us start, say, with the ease of decomposition of solid NH,Cl into gaseous NH and HCL: pions gas ~ NH; gas + HCl gas. NH,CI solid. An analogous case to this will be nA, in solution, mB, in sol. + m’C, in sol, hg A, solid (or liquid). We have to consider this kind of scheme not only in ease of equilibrium, but also in case of velocities of reaction. Moreover it is of real importance and use, chiefly for the latter : because in case of equilibrium we are always entitled to consider that the solid NH,Cl, which is in equilibrium with gaseous NH,Cl, is at the same time in equilibrium with NH, and HCl as well; this, properly speaking, is implied by the notion of the equilibrium of a system, but we cannot make the same assumption for the velocity wes Reaction before Complete Equilibrium. 479 of reaction. Giving proper attention to the above, we see at once that what we were always accustomed to con- sider “‘as chemical action between solids (or liquids) and gases (or substances in solution) ” does not exist at all, but that these reactions are of a complicated nature, always con- sisting of two different kinds of reaction. The jirst, solid NH,Cl = gaseous NH,Cl (or A, solid = n’A, in solution), re- presents either the evaporation or solution of a solid, or the condensation of the vapour to the solid or the separation of the salt from an oversaturated solution. The second, gaseous NH,CIZ NH; gas +HCl gas (or nA, in solution= mB, in sol. +m'C, in sol.), represents a chemical reaction in the homo- geneous system (gaseous or in solution). The first kind of reaction is regulated by the equation dt " rs =c(t,—t)(t—t,, + K) as shown above, the second by the law of action of mass. Consequently we have not to deal here with different laws for the different kind of equilibrium in heterogeneous systems, but the equation found for the complete equilibrium and the point of transition forms at the same time the basis of incomplete equilibrium in heterogeneous systems, the basis for the so-called chemical velocity of reaction and chemical equilibrium in heterogeneous systems. We have, therefore, arrived at the following very ciear discrimination :— Chemical action between substances is restricted only to homo- geneous systems. The law of action of mass is the regulating principle here. Two opposite reactions are here taking place simultaneously, since the molecules of each kind have in the vapour-space, or in solution, the same kind of free movement, the same possilility of meeting together and acting one upon another. In the same way the mutual action between different parts of the heterogeneous systems is in all kinds of equilibrium restricted solely to the transportation of the substance (possibly molecular, but no chemical transformation) from one part of the system to the other. This is regulated by the equation dt Tp Ulto—t) (t= tow +K), i.e., the surface of contact of the reacting parts of the system and the remoteness from the point of equilibrium are here the regulating principle. 480 Dr. Meyer Wilderman on the Velocity of II. The true meaning of the equations for chemical equilibrium im heterogeneous systems. The laws of chemical velocity of re- action in heterogeneous systems. We return to the system given above: NH,Cl solid, NH; gas, HCl gas. At equilibrium no reaction takes place between solid NH, Cl and gaseous NH,Cl, as is seen from the equation dt ae =¢(to—t#) (t—toy oF K). This means generally : chemical equilibrium in heterogeneous systems depends only upon the reactions which are taking place in the homogeneous parts, since at equilibrium no further reaction occurs between the different parts of the hetero- geneous system. This also explains the fact why “ chemical equilibrium in heterogeneous systems is independent of the mass of the solid”: — =¢(to—t)(t—to+K) is = 0, when t,—t=0 for all values of t—t..+ K. On the other hand the vapour- pressure of a solid for every temperature is at equilibrium of a definite value, is constant. If the vapour-pressure of the solid NH,Cl at equilibrium is p,, that ot the gaseous NH; or HCl is p, dt 12 noe ee Re ay! mr saan avenge Sia tery P= Bi =i (observations of Horstman in 1877 for the quite analogous case of solid NH,SH~ NH;+SH,.) The constant K'" is therefore not the “ active mass of the solid,’ as assumed, but the ratio of the velocity constants of the two opposite reactions in the homogeneous part. We cannot therefore assume that a phe- nomenon expressed by . ae te at exists where Ki is the active mass of the solid, but we are very well justified in thinking that dt Lael. 21 KW. Sup dar van he Aig <— gives the existing relations at equilibrium where », is the pressure of NH,Cl gas at equilibrium. K'p}—Ki=0 —==_-— Reaction before Complete Equilibrium. 481 Reverting to “ the velocity of chemical reaction in hetero- geneous systems,’ by such an expression we now understand the velocity with which one or more substances of one part of the heterogeneous system transform indirectly (by means of its vapour or dissolved molecules) into other substances of another part of the heterogeneous system. In the above system NH,Cl, NH3, HCl we see two reactions taking place simultaneously: The jist reaction is solid NH,Cl~> or = gase- ous NH,Cl is regulated by the equation (= = c+ (po—pr) ‘we omit for convenience’ sake the insiability constant; we ought in more strict calculations to always write }; + K instead of -), where =; is the surface of the solid NH,Cl, p, is the -vapour-pressure of the solid NH,Cl at the real point of equilibrium, pris the vapour-pressure at the time 7. The second reaction is gaseous NH,Cl— NH; gas+ HCl gas ; it is regulated by the equation dt : ! a if a Teh ek aah where p,’ is the vapour-pressure of NH; HCl gas at the time r. Tf the reaction is now begun, e. g., with solid NH,Cl, a state will soon be urrived at in the system at which in the unit of time as much of the solid NH,Cl is transtormed into NH,Cl gas as the gaseous NH,Cl dissociates into NH; and HCl; because the gaseous NH; and HCl can be formed continuously from gaseous NH,Cl only because gaseous NH,Cl is simultaneously formed from solid NH,Cl. Now the quantity of gaseous NH,Cl which -is transformed in the unit of time into NH, and HCl is given by the total velocity of reaction in the i homogeneous system, 2. e., by (<); therefore gas as well as of AT e( pope) =cpr— eps" and from this ; _ c&rpote"pr”? — aa? SOT Saas I . . e ° . (i.) 1.¢., before equilibrium has been arrived at, the concentration of the gaseous NH,C\1 is of no constant value, as it is a function of the surfuce of the solid NH,Cl and of the concentrations of the gaseous NH; and Hl at the time 7; since these vary during the reaction, pr must also change (as given by i.). pr 482 Dr. Meyer Wilderman on the Velocity of This can be clearly understood also from the following : should at the time 7 more of the gaseous NH,Cl dissociate into NH, and HCl in the unit of, time, than solid NH,Cl transforms into gaseous NH,Cl, p; would become smaller and po—pr greater, 2.¢., the reaction of the dissociation of the gaseous NH,Cl into NH; and HCl would become slower and the reaction of evaporation of the solid NH,Cl quicker. Again, should in the unit of time at the time 7s more of the solid NH,Cl evaporate than of the gaseous. NH,Cl dissociate into NH; and HCl, p; will become greater and the ».—pr smaller, 2. ¢., the reaction of evaporation will become slower and that of dissociation quicker. The vapour- pressure of the solid NH,Cl has thus the function of a regulator which keeps the velocities of the two reactions equal. As to the mode in which the reaction takes place it may be further added that if we start the reaction with solid NH,Cl, pris po and only the re- action of condensation of the gaseous NH,Cl to solid NH,Cl can occur. If we put the above value of p; from equation (i.) into dt ; dt \/ ( ig = CBr (Po— Pr) or into (a) dt we get dt CLirPo + a pr” ) ue —c"pr? ws mPa, Hoa. ee i.e., the velocity with which solid NH,Cl evaporates or gaseous NH; and HCl are indirectly formed from solid NH,Cl ts a function of the surface of the solid NH,Cl (of the surface of contact of reacting parts of the system) and of the concentrations of the gaseous NH3 and HCl. The same is the case with the indirect formation of the sohd NH,Cl from NH; and HCl. If the surface of the solid NH,Cl remain during the whole time of the reaction constant, we have instead of (1.’) “= AM! i = K(p,— ete )=K" Kp: ae i. e., the velocity of reaction is a function of the concentra- tions of NH, and HCl. If one of the products of dissociation be introduced, e. g., if — zl dt dt Reaction before Complete Equilibrium. 483 in the air-space A mol. NH; or HCl are present, and we start the reaction with the solid NH,Cl, then (i.) becomes i CL rDo 35 Cpe (pr + A) Lae c! 5h car and (i.’) becomes Me CXrpot cpl (pe+A)\ (Cpo— cpr (pr + A)\ -- = eae e+cz- Jae b+ c2r 6. 1. e., the velocity of dissociation of solid NH,Cl becomes smaller when one of the products of dissociation ts introduced. As is to be already seen from this comparatively simple case, there is no wonder that to the present the equations for the velocity of chemical reaction in heterogeneous systems could not be found. It is only natural that a simple connexion between the velocity of reaction and the concentrations, or the concentrations and the surface of the solid, has always been sought for; the processes which are taking place here and the remoteness of p; from po escaped the attention of the experimenters, since the equations for the velocity of evapora- tion or condensation, &., were quite unknown to them, and without them there is no possibility of getting to the true equations in this very complicated region of phenomena. As we shall see in some other examples, the equations for the velocity of chemical reaction in heterogeneous systems easily become of a very complicated form; we now know them, nevertheless, with complete certainty, since they follow directly from well-established and known equations, so that the investigation of the former is reduced to the investigation of the latter. Let us now take another system in order that we may further follow up the points which come into consideration in the solution of the problems of this kind :— nA, gas, mB, gas+m'C, gas. } or { or A, solid 3, solid, and nA, in sol — mB, in sol.+m’C, in sol. ¥ or 4 { or 4 A; solid _ B, solid, e. g., the dissociation of CaO; into CaO and CQ,, CaCO; gas CaO gas+CO, gas { or f { or f CaCO, solid CaO solid. soo Dr. Meyer Wilderman on the Velocity of At equilibrium only the reaction in the homogeneous part CaCO; CaQog.+ COy is to be considered, 2. e., dt , if aaa = =O Pa G < dt where p, and p,’ are the vapour-pressure of the solid CaCO, and CaO, p" is the pressure of CO,. We consequently get heey id ‘po p" = 0, i.e.,p" is independent of the quantity CaCO; or CaO taken (observations of Debray, 1867). If CO, be introduced we have a Mesoae Se ee ie 4 fapilt | (fas (J, =p. Po(p' +A)=0, and (p +4) = ee | i.e., the pressure of CQ,, which is ultimately obtained over the solid CaCO; and CaO, will remain the same whether CO, is introduced or not (observations of Debray). For the velocity of decomposition of solid CaCQs into solid CaO +COx., or of the formation of solid CaCO; from CaO and CO, we have For CaCO; solid> or or «CaO solid :— ? i dt"! ee Sal ee the equation (=) =¢!""X_!(po! —pr'). Now just as much of the solid CaCO, transforms in the unit of time into gaseous CaCO; as gaseous CaO and CO, are formed from gaseous CaCQ3. Therefore _ Clrpot ce pr'pr! BOM owl SE 1G 3 9 c == Cir and dt CEPotelpr' pr) _ ss (pot! — cere a =0E-(x, o+cx; )=e2e( e+ ¢>r On the other hand we have that the number of molecules of the solid CaO (if we neglect the quantity of the gaseous CaO) which are formed in the unit of time is equal to the Reaction before Complete Equilibria. 485 number of molecules of the solid CaCQ3 which have disappeared in the same time. Therefore 5 >> far ft a : a) =e3(po— Sabet rh )= ) =c"S-'( po —p), and from this follows :— 0 &rpo— (cl + 6&r)e Sr! po! 2 Sia ce'S pr! — (e +edr) "Sr ’ nae ene xe Cala) and 4 ho ee) (<) aS 3 i. cae +6 Pi (oS. Cd Pesan | dt re Q y: wa o>, Pt cd Spo — (co! +c3r)o"Sr'po! ike ae (ep tas ae ) as —= Ca, Pee Tw sete nail, lean (il ) 1.e., the velocity of decomposition of solid CaCO; into solid CaO and CO, gas is at the time t a function of the surface of the solid CaCO3, of the surface of the formed solid CaO, and of the concentration of the CO, at the time tT. If the evaporating surface of the solid CaCO; be kept con- stant during the whole time of the reaction, we have at\ pila, WON Sf ) dt =K K'pr Goa os? : Let us now take another system :— Gi") . z, . <— . n’ A, gas or in sol. + 7A,, gas or in sol. ~ m'B, gas or in sol.+m!By gas | or f for} [or in sol. Aj, solid. B, solid. e.g. KsCOs in sol. + BaSO, in sol. ~ BaCO; in sol. + K,S0, in sol. { or } } or } BaSO, solid. | BaCOs solid. At equilibrium the reactions BaSO, solid+or or7(po—pr). For CaCO in solution +2HCI in solution~ CaCl, in solution + CO, in solution, as well as for Zn in solution +2HC] in solution ~ ZnCl, in solution +H, in solution, we have :— dt \/ > ae = Opry pK, or if the opposite reaction be neglected :— din! . a =p, 7”. Now just as many molecules Zn in solution (or CaCO; in solution) must in the unit of time transform into ZnCl, (or CaCl,) and H, (CO,) as molecules of the solid Zn (CaCO) 488 Dr. Meyer Wilderman on the Velocity of are passing into the solution ; therefore :— = hae 12, Ciro 555 CBr (Po—Pr) =C'Pr BP" 3 Br= oe os > + ee c d dt vy pays 0 ba ae an v0 Se( po Tyres, ede Pe), . (iii). Cpr? +cat) Ne pl + ede i.@., the velocity of solution of zinc or marble in acids, such as HCl, HBr, NO;H, must be a function of the surface of the solid and of the square of the concentration of the acid. The equation for the velocity of solution of marble or zine in acids belongs to the comparatively very simple cases, but is nevertheless of quite a different form from that which De la Rive or Boguski could, under their circumstances, suppose, since the form and kind of the processes which come into con-. sideration, as well as the laws of evaporation, solution, &c., were not known to them when they carried out their experiments. It must further be remarked that the equations (=) (=) T T Sc., must be taken as they actually are, with all the additional terms for the deviations and abnormalities of whatever kind they may be, should any such complicate or limit the phenomena. For instance, the laws of action of mass are applicable chiefly to dilute solutions or to gases in the dilute state, they cease to hold good as we pass to greater concentra- tions or to higher pressures. Often the products of the reaction influence the velocity of the reaction and complicate the phenomenon. Reactions of a higher order often occur as if they were reactions of a lower order, &c. It may be well to emphasize again that the equations derived here for the velocity of chemical reaction in heterogeneous systems hold good only from the time when the velocities. become equal and they give no information as to the velocity of reaction before this takes place. For this reason it may happen, though under very exceptional conditions, that one or more of the reactions in the system may first have to almost complete themselves before they can become equal to. the rest of the reactions in the system, 7. e¢., that so far as these reactions of great speed are concerned only a small region of their individual curves will be governed by the above equations. III. Onthe real and apparent points of chemical equilibrium in heterogeneous systems. It was shown before (Part IT.) that all physical reactions between the same substance in the different parts of the hetero- geneous system never reach, because of the nature of the Reaction before Complete Equilibrium. ASG equation, the point of equilibrium, and especially that, owing to the interference of external factors such as the surrounding temperature, &c., the obtained points of equilibrium are not the real ones but only apparent points of equilibrium. Jt is evident that chenucal equilibriumin heterogeneous systems has also only one point where it is real, and this is where equilibrium is real for all its constituent reactions. Since now the real point of equilibrium is certainly not reached by the physical reactions, it follows that chemical equilibrium in heterogeneous systems is also.only an apparent one, and the obtained results concerning equilibrium will, according to the arrangements of the experiment, always differ from one another, and always only approximate more or less to those results which are the correct ones. Having, namely, for equilibrium of the physical reactions the equation OF = c(t, —t)(t bye +K)—e (tt) = 0 instead of dt ~ = =c(t,—t) (¢—t,, + K)=0, the values of p;, p-’ at equilibrium will always differ from P., P.’, and, according to the laws of action of mass, there will always be a redistribution between the quantities of each kind of molecules constituting the system in the homogeneous part, so as to correspond to the given values pr, pr’. Look- ing thus away from the form of the equations for velocity of reaction themselves, which show that a system can arrive at its point of real equilibrium only in an infinite time, and giving our attention to the more serious source of error arising from external influences, it is evident that to secure success in this region of research all the steps necessary to secure correct equilibrium for the physical reactions must be taken in the first instance. Only after this is done shall we be able from the equations concerning the velocity of reaction to calculate how far we succeeded in approaching the real point of equilibrium after a given time T,—7,. Should the nature of the phenomenon, or of the problem, on some occasions require very great accuracy in the method employed, we shall have here, as in the case of delicate freezing-points, or of solubility measurements, to make also detailed investigation of the values C, c’, t,-f, t—t. + K, t,—t, &e., as this alone will enable us here as there to discriminate between correct and incorrect results, independently of the assertions of every investigator. Davy Faraday Laboratory, Loyal Institution, May 1902. Phil. Mag. 8, 6. Vol. 4. No. 22. Oct. 1902. 2 i \ A / ‘ a 4 BA a | LP ee Be ome: ; . LILI. On Conditions controlling the Drop of Potential at the | Electrodes in Vacuum-tube Lscharge-—(Second Paper*). By Cuarence. A. SKINNER, Adjunet Sie rare of Physics, University of Nebraskat. HE results of oxparineia described in a’ former com- munication seem to indicate that the drop of potential at the electrodes in vacuum-tube discharge is caused by a resistance to discharge of the gas ion to the metal electr ode, this resistance increasing with the velocity with which the ion impinges on the electrode. To explain this it is con- ceived that the discharging ion must give up its kinetic energy with—or before it can give up—its charge. Different physicists have suggested that at least a momentary chemical combination takes place between the carrier and the electrode. It is very plausible then that the elastic reaction of the ion impinging on the electrode introduces a force resisting dis- charge, the resistance increasing with the velocity of impact. This being true, the ions approaching the electrode will accumulate at its surface until the thereby increased electric intensity becomes sufficient to cause as many to discharge in a given interval as arrive at the electrode during the same interval. From this standpoint the drop of potential will depend on the time required for the discharging ions, arriving with a definite velocity, to come to rest at the electrode—their kinetic energy being first given up by collision with both the neighbouring gas molecules and the electrode. This being a mechanical explanation of the phenomena the laws of mechanics should be applicable in deducing and in predicting experimental results. The complicated nature of the problem, however, presents at present a discouraging barrier to any rigid mathematical discussion, but a simplified case may be considered in order to test the applicability of the view. Suppose perpendicular to the plane of the figure (fig. 1) a | plane electrode OA. Moving /reely in the direction aO per- pendicular to the electrode is a particle of mass m carrying a + Communicated by the Author, having been read before the American Association for the Advancement of Science, June 1902. positive charge e. This particle is supposed to be driven towards the electrode by a uniform field equal to | Vee, OVA Rica * The first paper under this title was published in the Phil. Mag. of | Dec, 1901. } , oe. ~~ = > = F ie al oy- ae On the Drop of Potential in Vacuum-tube Discharge. 491 where V is the fall of potential from @ to QO, and s the dis- tance. The force accelerating the particle is Vv =e Son and the acceleration produced ‘The kinetic energy of the mass when it reaches QO is given by the expression sn? + Ve), where w is the velocity of the particle at a, and Ve the work . done by the field on the charge ¢ in moving from a to O. The energy with which the. particle rebounds is ($ mu? + Ve), where & is the coefficient of restitution*,O A glance at this suffices to suggest that a loss of simplicity may have occurred through specialization; and a little examination of the form of the elements of the derived determinant | pi, | makes clear that the more appropriate and more promising object of investigation is that which is indicated in the title of the present paper. (2) In a general axisymmetric determinant of the nth order there are 4n(n+1) different elements, and the same uumber of different primary minors; consequently the Jacobian of the latter with respect to the former must be a determinant of the order n(n+1). Further, as each primary minor is of the (n—1)th degree in the elements involved in it, its differential-quotient with respect to any one of the latter will be of the (n—2)th degree, and therefore the degree of the Jacobian in question will be not higher than 4n(n+1)(n—2). It will be seen presently that this degree is attained by the Jacobian containing as a factor the 4(n+1)(n—2)th power of the original determinant. (3) For the purposes of proof it is necessary to draw attention to two results regarding determinants of special form. The one, given by Ferrers* about the year 1857, is almost self-evident, viz. : eelgeretigishl 4 yaks Weel | | uN fg es ae i | 1 1 wiretiic l+an | The other is not so easily stated. It concerns a determinant of the order 3n(n+1) whose elements are derivable in a peculiar way from those of a determinant of the nth order, * Ferrers, N. M., “Two Elementary Theorems in Determinants,” Quarterly Journ. of Math. i. p. 364. 1 1 = aya... a 1+ + 4+...4 “4 ay ae) a, si ) a tienes ta teats ee 4 ad Lares | pil lil peat Primary Minors of an Axisymmetric Determinant. 509 every row fy. Ng, i ee of the latter taken along with itself producing the row Bic, Paget ak ee Way Zhe apse ye Diglls of the former, and, taken along with any one a ky, ks, ee ey ky of its fellows, the row hyky, loko, aeyes hk. In—tkn t+ hakn=1, e885 hyka+ hoky 3 and the result in question is that the determinant thus derived is equal to the (n+1)th power of the original. or J 0(4, 4, ¢, fg, 4) where A, B,... denote the signed complementary minors of a,6,.... As first obtained it takes the form ¢ b —27 C ; a a b a — 2h mad : P —a h g —J d ho —b - peer g Des * Brill A., “ Ueber diejenigen Curven eines Biischels,” Math. Annalen, ili. pp. 459-468. 510 Dr. T. Muir on the Jacobian of the Multiplying this columnwise by A‘ in the form Oat ch Gg” eee ga ah ee? fee fh hb 0 Fo Cae eg of 2hg 2hf 2fo be+f? het+fgo hft+bg 2ga 2fh cq het+fgo act+yg’ aft+gh Qah 2hb gf hftbg aftgh ab+ie we obtain 7 | aA—A’ aB aC al aG aH . Pe GA, ub Bea BF. 0G ie cA cB cO—A cE cG cH 27A. 2fB 2FC 27F—A 2fG 2fH | 2gA 29B 29C 2qF 2gG—A 2gH | | QhA 2hB 2hC 2QhE 2nG 2hH—A | : i which, it is evident, equals aA .bB.cC .2fF. 2gG. 2H This last determinant, however (§3), Aé =GA.bB.cC. 2fF . 2gG.2hH ee A consequently we have JAt—A® f oes dig Au A t j qa and therefore (5) In the case of the axisymmetric determinant of the aA +bB+cC +2fF + 29G + 2h \ | Primary Minors of an Axisymmetrie Determinant. 511 fourth order a, as as Us a, bs b, A ih P pee OF A say, ay b, Ca d, the Jacobian o(A;, B, Cs, D,, C4, By Bs, Ay As, Ag) O(a; bo, C35 a4, C4, D4, bs, Qs, 43, a») (where the order of the independent variables deserves notice) is equal to e:d,—c¢ bod,—b/ ¢3d,—¢,7 2 ajd,—a? bod,—b2 ady—aZ . wee 2(a4b,— Gods) | 2 Multiplying this by A? in the form bel ay? as” eats yas / ) Us” (a 6? ateite Als | | 20442 Zab, 2ash, aybs + ash, we obtain aA, - boBy.e;Cy. «22. « 2agAg. 2aeAg A x); 1— 1 ica 1 | aA, : aT : | A att l Som: 1 5 so that we have JAP=AWS y— mA, +beBo+. . .+ 2a.As Latyeo sk A 512 On the Jacobian of the Primary Minors. and as a, Ay+boBot... + 2agAg=a,A, + deA_+ azA3 + aA, + dyA, + b.B,+ 63B3+ 0,B, + a3A3+ b3B3 + ¢303 4+ C404 + a,A,+ 6,B,+¢,0C,+d,D, =4A, the final result is J =A’(1—4). (6) The process, it is not difficult to see, is perfectly general, the fundamental part of it being the multiplication of the Jacobian by A”*! expressed in a particular form, and -the transformation of the product into aimorn(1—™ This gives the equation n& n+1— Agn(n+1) SG ) Jano A (1 a whence there follows J=(1—n)Aiethe-2), Since | Ain | = | ai. | "1, and therefore | [aot | Ped eG the theorem may be more neatly enunciated thus :—// | din | be an axisymmetric determinant, then 0(An, Ago, er Anny An-1n)+ ar) Aj) =(1—n) { Ain | a O(Gity Aaa) + + +) Anny An—1yp 9s a2) | Ain | (7) Putting n=3 we obtain a result in which both Sylvester and Cayley were interested from a totally different point of view*, and which on account of its seemingly unique character has attracted considerable attention since their time. Capetown, South Africa, 16th July, 1902. * Sylvester J. J., ‘‘Examples of the Dialytic Method of Elimination as applied to Ternary Systems of Equations,” Cambridge Math. Journ. ii. pp. 232-236 (1841); Cayley A., “ Note upon a Result of Elimination,’ Phil. Mag. [4] xi. pp. 378-879 (1856). FSi See gi LVII. Notices respecting New Books. The Scientific Writings of the late GEorGE Francis FitzGERALD. Collected and Edited with a Historical Introduction by JosEPH Larmor, Sec. R.S., Fellow of St. John’s College, Cambridge. Dublin: Hodges, Figgis, & Co.; London: Longmans, Green, m Co. 1902. T will be long before the painful impression created by Fitz- Gerald’s early death wears out among his contemporaries. ; oe a Cag: Rigidity of Ferromagnetic Substances by Magnetization: 541: produced torsions proportional tojtheir respective weights, the friction at the pivot does not seem to disturb our results. The examples tested were the same as used in the pre- ceding experiment, except the nickel rod. In the present ex- periments the length of each rod was reduced to 22 cms., and the diameter of the cobalt bar also to 1°082 cm. . The nickel rod used in the last experiment was not sufficiently thick for the torsion experiment, so that another nickel bar, whose diameter was 1°117 cm., was substituted for it. . Our apparatus was not suited for the absolute measurement of the modulus of rigidity, and therefore its determination was carried out in the usual manner: with Prof. Nagaoka’s apparatus above referred to. The results were:— Metals... Softiron. Steel. Wolfram steel. Nickel. Cobalt. Rigidity 7:92 x 10" 7-89 10" 8°57%10" 7-41.10" 6:04 10" _ 4, Soft Iron.—The results of observation are given in fig. 3. Fig. 3. Here ordinates represent the change of twist due to mag- netization given in seconds of arc, taken positive when the change indicates an increase of rigidity and taken negative when it indicates a decrease; abscissze represent the effective field. N is the moment of force expressed in C.G.s. units. From the figure we see that the untwisting of the rod always increases with magnetizing force, its amount increas- ing in the same way as the intensity of magnetization with increasing magnetizing force. As the moment of force in- creases the amount of untwisting increases proportionally, so that the change of rigidity is fairly independent of the twist- ing couple for all magnetizing fields. The form of the curves is similar to that of the curves of depression in the ‘former experiment, except in very weak fields. In the pre- sent case the initial minute depression of the curves was not ‘observed. The angle of torsion, as calculated from the applied couple 542 K. Honda, 8. Shimizu, and 8. Kusakabe on Change of and the rigidity, and the observed change of twish due to magnetization, gives the ratio of the change (8K) to the rigidity (K) itself. BES caveats 20. 60. 100. 200. 400. 600. 800. Te x 10°. . 0-19 0-58 076 096 1:10 118 1-22 These numbers are also plotted against magnetizing force in fig. 4; the course of the curve ‘resembles that of mag- netization, having one inflexion point and approaching to an asymptotic value as the field is increased. Fig. 4 Ba (1) W=|Z.89 x0 ® (2) - =|/4 364/08 (3) - =|20. 87%/0 (4) - =|27.48«/0% OE =/53. 96|x/0 4 mie 0. as That there is untwisting by magnetization forms a re- ciprocal relation to the well-known fact that the magnetization of iron decreases by twisting. The above results for soft iron agree in quality with those of previous experimenters, and the amount of the change nearly coincides with some of Barus’s results. In the ex- periment of Day the change of rigidity was a little smaller than in the present case, and greatly atfected by the amount of twisting couple, in contradiction to our results. Stevens’s experiment gave much greater change of rigidity. A 5 Rigidity of Ferromagnetic Substances by Magnetization. 543 0. Steel. We have seen that in steel the change of elas- ticity due to magnetization is much smaller than in soft iron. So, in the case of rigidity, we also observed comparatively little increase. The results are given in fig. 5. We see Fig. 5. 200 400 600 300 that the form of the curves is similar to that of magnetization in steel. Here again, the change of rigidity is independent of the twisting couple for all magnetizing fields; the values of x for different fields are given in the following table and ASS 60. 200. 400. 600. 890. x X10. O18 22 Ula 20ao.” O's6 The results of previous experimenters fairly agree with those of the present case. The reciprocal relation between torsion and magnetization also holds for steel. : 6. Wolfram Steel.—The change of elasticity in Wolfram steel due to magnetization is nearly the same as that of soft iron both in quality as well asin quantity. This remark also applies to the present case, so that what we have said about the change of rigidity in soft iron equally applies to the case Fig. 6. ec00 400 600 800 H of Wolfram steel, as will be seen from figs. 6 and 4, and the following table :— ED, 5 s9583> 20. 60. 1€0. 200. 400. 600. 800. XU? 015 073 085 0-98 1-10 Vie). ge 544 K. Honda, 8. Shimizu, and 8. Kusakabe on Change of These numbers are very close to the corresponding ones in soft iron, except in weak fields. 7. Cobalt.—As in the case of steel, the effect of magneti- zation on the rigidity of a cobalt bar is very small. The rigidity always increases by magnetization, as shown in figs. 7 and 4, and the following table:— ~~ =~ ~~ ) | HD asesterss 100. 200. 400. 600. 9800. 10°72 0S O12 Oat 23 "aa OK K Thus the course of the curves is less steep in cobalt than in iron or steel; the inflexion point is not so marked in the former metal as in the latter. The change of rigidity is also independent of the applied couple. | So far as we are aware the effect of torsion on the mag- netization of cobalt has not yet been studied; but if the reciprocal relation holds in the case of cobalt the above results show that the effect of torsion on the magnetization of cobalt is the same asin iron. We have seen from the experiment of Prof. Nagaoka and one of us that the behaviour of the cast cobalt as regards magnetostriction is remarkably different from that of annealed cobalt. The present specimen was well annealed, so that the above inference is to be restricted to an annealed cobalt. | 8. Nickel.—The change of rigidity of a nickel bar is so large that it was necessary to reduce the sensibility of the apparatus by using a rotating cylinder of thicker diameter. As in the case of the change of elasticity, we again observe in the metal a singular phenomenon that the change of torsion by magnetization alters its sign as the magnetizing force is increased. The results are graphically drawn in fig, 8. In weak fields the deflexion shows a further twisting of nickel, that is a decrease of rigidity. This decrease reaches a maximum as the field becomes stronger ; it then begins to decrease, and in a field of about 100 c.e.s. units the rigidity returns to its ‘original value. When the field is further increased the rigidity rapidly increases, and then its rate of increase becomes gradually less. Thus the character of the change is quite analogous to that of the change of elasticity. | o al ia Rigidity of Ferromagnetic Substances by Magnetization. 545 Ina given field the change of rigidity is independent of the twisting couple. It is also a proof of the same fact that. the curves corresponding to ‘different couples pass through a point on the axis of the field. The ratio of the change to the modulus itself for different fields is given in the following . table and in fig. 4. 15 ee are 20. 40. 80. 100. 200. 400. 600. 800. = X10?..—0-96 —1:68 —0°67 0°12 2°63 5:32 667 7:48 _ Thus in nickel the change of rigidity is considerably larger compared with other ferromagnetics. The nickel rod used in the preceding experiment was turned into a square rod from a plate, and the mechanical process, which the specimen underwent, hardened it in magnetic quality. If we study the change of elasticity with the present sample the propor- tionally large change would be observed. According to Profs. Nagaoka* and Zehndert the mag- netization of nickel increases by twisting in weak fields; in strong fields, however, it diminishes by twisting. These results are reciprocally related to ours. The change of twist so far described for iron, steel, nickel, and cobalt is independent of the direction of the magnetizing field. 9. In comparing the change of rigidity by magnetization with that of elasticity, we observe one marked difference that the former is independent of the applied stress while the latter is largely affected by it, especially with small stress. * Nagaoka, Journ. Coll. Sci. Tokyo, ii. p. 304 (1888) ; iii. p. 189 1889). + Zehnder, Wied. Ann. ali. p. 210 (1890). 546 Mr. F..B. Jewett on a New Method of It may also be noted that the reciprocal relations between torsion and magnetization, as found by the actual experiments, will be found to be of paramount importance in the theory of magnetostriction. We may conveniently place the results of our experiment with those of previous investigators under the following parallel statements :— , Magnetization to Twist. Twist to Magnetization. (a) The magnetization of iron (a’) The torsion of iron de- decreases by twisting for all mag- creases in all magnetizing fields. netizing fields. (6) The magnetization of nickel (6') The torsion of nickel in- increases by twisting in weak tields. creases in weak fields. (c) The magnetization of nickel (c') The torsion of nickel de- decreases by twisting in strong creases in strong fields, fields, A similar reciprocal relation would probablv exist in the case of cobalt. The actual verification of the relation will be undertaken in the near future. - In conclusion we have to express our best thanks to Prof. H. Nagaoka and also to Prot. A. Tanakadate for many valuable suggestions. LXI. A new Method of determining the Vapour-Density of Metallic Vapours, and an Eaperimental Application to the Cases of Sodium and Mercury. By FRANK B. Jewett *, [* all investigations on the composition and distribution of light in the spectral lines it is of prime importance that the lines themselves be as narrow and sharply defined as possible ; this is especially true in those cases where the analysis is carried on by means of interference phenomena, for here the difference of path over which interference takes place decreases as the width of the line increases. There are in general two causes which may affect the breadth of the lines: (a) motion of the light-producing molecules in the line of sight, and ()) change in the period of the source caused by frequent collisions of the molecules f. To these might be added a third cause, suggested by Lommel f, in which an inhomogeneity is produced in the source by forced changes in the period of ionic vibration, thus putting - an upper limit on the power to produce interference-fringes ; this latter supposition is, however, yet to be verified, and trom the present experimental data it seems probable that any * Communicated by the Author. + Michelson, Phil. Mag. (5) xxxiv. p. 293. { Lommel, Wied. Ann. ii. p. 251; Drude, Lehrbuch der Opteh, p. 498. = —_ >is > ap Pst lglg aliggy a determining the Vapour-Density of Metallic Vapours. 547 effect due to it must be almost if not wholly negligible in comparison with that of (a) and (0). This being the case, the determination of the relative importance of the two factors, pressure and temperature, is the question which at once presents itself for solution. In his very exhaustive article on “The Application of Interference Methods to Spectroscopic Measurements” Professor Michelson has taken up this problem in considerable detail. He finds that in the cases where the density of the vapour is very low tke effect of changing pressure on the width of the spectral lines is almost wholly negligible ; for hydrogen this is true even in the case where the pressure is as high as 2 or 3 mm.; in fact, when the relation between the breadth of the lines and 1/P (pressure) is plotted the influence of P is seen to become vanishingly small at about 5mm. In summing up, Professor Michelson states as follows :—“ It thus appears that in the case of hydrogen—and probably in all other cases—the width of the spectral line diminishes toward a limit as the pressure diminishes, which limit depends upon the substance and its temperature ; and that the excess of width over this limit is simply proportional to the pressure.” As mercury and sodium are both readily usable in vacuum- tubes, the foregoing facts would suggest them at once as the ideal substances for an experiment on the effect of pressure and temperature on the broadening of the spectral lines. As a preliminary to such an experiment a knowledge of the densities of the saturated vapours at various temperatures is of course necessary. Jn addition to making a determination of the densities for such a purpose as the above, there is still another and even more urgent reason, viz., the evident dependence of the change in the lines in the Zeeman effect, and also in some cases the reversal of the same, upon the density of the light-producing vapour. It was particularly with a view to the solution of this latter problem that the following experiment was proposed and undertaken. Apparatus.—The method employed was one suggested by Prof. Michelson, in which the amount of vapour filling a known volume is determined by finding the amount of con- densed metal in the observing flask when the latter is cooled off. The apparatus consisted of three essential parts—the heating-bath, the gas-bulb, and the thermometer. The bath finally found most satisfactory is shown in section in fig. 1 (p. 548); a and 6 are two sheet-iron boxes lined inside and out with heavy sheet-asbestos, and having a 3-inch air-space between them ; the inner box (a) is about 14 inches on a side ; around+the inside and on the bottom of a area number of iron 548 _ Mr. F. B. Jewett on a New Method of © resistance-coils carried on an asbestos-covered iron frame, and ending in two heavy terminal wires cc, which pass out Fig. 1. O O O O O O O O O O O IN NOOO COO TOO through the covers of both boxes ; the bulb d is supported on a metal frame e, and constant circulation is maintained by an electrically-driven fan /; g represents the stem of a platinum thermometer. With this arrangement, and with suitable regulation for the current, the temperature may easily be kept constant at any desired point to within one or two degrees *. The gas-bulb or reservoir (fig. 2) was of hard glass of known cubical content, and had a capacity of about 2000 c.c. ; proceeding from the bulb were two tubes, one a heavy capillary and the other with an internal diameter of about 1 cm. : * In one instance where the bath was used for calibrating a Beckmann thermometer the temperature. was held constant to 0°1 for fifteen minutes. OE — A gine ae PE ee gt determining the Vapour-Density of Metallic Vapours. 549 < The thermometer was of the Callendar platinum-resistance type *, with auxiliary compensating-leads and direct reading Fig. 2. Wheatstone bridge, and was capable of reading to 0005 ; this particular instrument was one of those calibrated at the Kew Observatory. In order to make an observation a tube (a, fig. 2) was sealed to the larger tube (6), and the capillary-tube (c) drawn down at (d); this being done, and both tubes and bulb thoroughly dried, a small piece (0°5-0°7 gm.) of C.P. metallic sodium was introduced into (a), and the latter quickly sealed off at (e), as shown ; (c) was now connected to a Geissler- pump, and the air drawn out to a residual pressure of 0'1~ 0:2 mm., after which the bulb was filled with some inert gas (H or N) and again pumped out and the capillary-tube sealed off at (d). The bulb thus prepared was now introduced into the bath and the temperature raised to any required point ; the apparatus was kept at the desired temperature for fifteen or twenty minutes, thermometer-readings being taken every two minutes ; the cooling had to be done very slowly, as the capsule containing the molten sodium was very liable to erack, and the inrushing air carried the metal into the bulb. Upon removing the latter from the bath, the whole inner surface showed a bright metallic coatmmg of condensed sodium vapour, varying in thickness with the temperature to which the bulb had been subjected. To determine the amount of * E. H, Griffiths, ‘ Nature,’ Noy. 14, 1895. 550 | Mr. F. B. Jewett on a New Method of sodium in this coating, and consequently the amount of saturated vapour that had filled the bulb, the tube (b) was cracked off at some point (m), thus getting rid of the metal remaining in (a); the bulb was then thoroughly washed out with hot water until the washings failed to show an alkaline reaction with phenolphthaline, and the amount of Na present as NaOH in the washings determined by differential titration with standardized N/10: NaOH and N/10* H,SO, solutions ; this amount, together with the corrected volume of the bulb, furnished the requisite data for finding the vapour-density. As this process had to be repeated for every determination, the making of a large number of observations was an ex- ceedingly tedious matter. The above-described method was the one finally chosen for sodium ; a number of methods depending upon the gravi- metric determination of the amount of metal volatilized, while giving good results for those metals which do not oxidize easily at low temperatures, e. g. Cd, proved absolutely useless in the case of sodium on account of the rapid oxidiza- tion of the latter when in contact with the air. A difficulty which it was at first feared might render the determination impossible at the higher temperatures, viz., the action of sodium on glass, was not encountered except when the residual atmosphere contained O or water-vapour, the solvent action being apparently exhibited only for the oxide or hydroxide ; aside from this fact the results obtained in the presence of air were so extremely erratic that all the final determinations were made either in the presence of oxygen or nitrogen. (The majority of the tests were made with hydrogen, and as they gave consistent results the accuracy of the process was not questioned at the time, especially as the hydride, Na,H,, was not supposed to form at pressures so reduced as those employed *. Owing, how- ever, to a peculiar brown metallic appearance of the deposit in some instances, doubt was cast on the validity of this assumption, so that while the great mass of chemical data seems to weigh against the formation of the hydride, there still remains the possibility that the density of the vapour, calculated on the assumption that it consisted of free Na, gave too low a result. This question can be easily settled, however, by the employment of N, since the nitride, NaN3;, is not formed by the direct combination of Na and N f.) Some of the results are given in Table I., and the curve, * Roscoe & Schorlemmer, ‘ Treatise on Chemistry,’ vol. ii. pt. i. p. 107. + Berichte, xxv. p. 2084 (1892); Zert. f. anorg. Ch, vi. p. 38 (1894). determining the Vapour-Density of Metallic Vapours. 551 with temperatures as ordinates and densities as abscisse, 1s * shown in fig. 3 (p. 552); the dotted curve shown is that for Hg __ at temperatures where the density of the vapour corresponds to that of Na; the temperatures for this latter curve are indicated on the curve. TABLE I. Temp. Density. fe) 368 0:00000009 373 0 0000002 376 0-00000035 380 0-00000043 38d 0-00000 L03 387 0°00000135 390 0-0U000160 395 0-00000270 400 0 CO00V0350 406 0 00000480 408 0:00000543 412 0:00000590 418 0:000007 14 420 0-00000750 While the densities were not obtained much below 365°, it will be noticed that at this temperature—which cannot be far from that commonly employed in vacuum-tube work *— the density of the Na vapour increases at about the same rate as that of Hg at 85°, while at points slightly above this the Na curve increases much the more rapidly. This fact, taken together with its low atomic weight, might well account for the peculiarities observed by Professor Michelson. As was stated above, the experiment was undertaken solely to determine the densities within the range between 350° and 450°, and indeed the use of a glass bulb precludes the possibility of anything being done above 500°; with a porcelain bulb it would be comparatively easy to attain any desired temperature below 1700°. The ease with which the temperature of the electric bath could be regulated at once suggested the desirability of making a series of determinations on the vapour-density of Hg, and with the slight alteration in the form of the bulb * Professor Michelson assumes that the temperature of the heating- box, 350°, is that of the vapour also. There appears to be some doubt as to the legitimacy of this assumption, owing to the very considerable heating produced by the discharge itself. yon Mr. F. B. Jewett on a New Method of A EE ALT TT eS ee Re A Ee SECC Hp et CCN i CCLRC a CCECK a SRE SS Sane: CEB CACE a e CLOT R a CCC ACh a Ba sceeen NSe ae ps bod 675 ee ee ae RAS 759 a determining the Vapour-Density of Metallic Vapours. 553 shown in fig. 4, a set of continuous readings 5° apart was obtained. The mercury-reservoir (a, fig. 4) isa long narrow Fie. 4, ay tube of hard glass of known coefficient of expansion, and having a carefully calibrated bore. In making a deter- mination the reservoir is charged with a known weight of mercury, and the bulb exhausted and sealed off as in the case of sodium ; it is then introduced into the bath and supported in such a position that (a) is vertical ; the height of the mercury column is observed through glass windows in the Taste IT. Temp. Density. Regnault & Hertz. | Ramsay & Young. S) 40 0-00000007 000000007 0:00000009 60 00000003 0-0000005 0-0000003 70 0:00000045 00000005 00000005 80 00000007 00000008 0-0000008 90 00000012 0-0000014 0-0000014 100 00000021 00000024 00000023 110 00000046 i CaS eae Oe Ae Ne sro oe 120 0:0000060 00000064 0-0000059 140 0-:0000138 00000147 0 0000137 160 0:0000302 00000323 00000297 180 00000624 0:0000649 00000603 200 00001580 0:0001236 00001152 220 00002020 0:0002271 0:0002077 240 0-:0003754 CONG sg I as 260 0-0005830 Pune yt ce, 270 0:0006528 0:0007257 0 0007310 280 00008645 0-0008994 00009113 300 00015466 0:°V013547 0-0013796 305 | AMM Seine Oe fo Pek ol pared, . 310 | (00016447 0-0016472 OU0I6734 320 O-UOL9879 00019921 00020 180 325 | otake io 5 SARS i ea ale a7 Se ed bet te Phil. Mag. 8. 6. Vol. 4. No. 23. Nov. 1902. | me 6 ) Fan d 504 Mr. G. C. Simpson on the Electrical sides of the bath by means of a cathetometer. The readings thus obtained, together with the known coefficients of ex- pansion of glass and mercury, furnish the requisite data for determining the amount of metal volatilized. A partial series of the results obtained is given in Table II., together with the results calculated from the observed tensions of mercury-vapour as given by Regnault and Hertz; a more complete. set of readings will be published later. In conclusion I desire to express my thanks to Professor Michelson for the encouragement and helpful criticism given throughout the work, and also to Dr. Gale for the assistance so kindly rendered in the work on the density of mercury- vapour. Ryerson Physical Laboratory, March 25, 1902. LXII. On the Electrical Resistance of Bismuth to Alternating Currents in a Magnetic Field. By Grorcs C. Simpson, B.Sc., Fellow of the Victoria University*. N a previous paper (Phil. Mag. 1901, ii. p. 800) I deseribed experiments which showed that the anomalous eftect produced in a bismuth wire carrying an alternating current placed perpendicular to a strong magnetic field can be con- veniently represented by an E.M.F. (called the “ bismuth H.M.F.”) set up in the bismuth itself. It was then found that this bismuth H.M.F’. varies in phase and magnitude with different frequencies of alternating current used—the phase being 100° 13’ behind the applied E.M.F. with a frequency of 3 per second, the lag increasing to 126° 31’ with a fre- quency of 60 per sec. ; the magnitude being a linear function of the frequency and increasing with it. This investigation having given the variations of the bismuth E.M.}'. with frequency, the field being kept con- stant, experiments have since been made to find how the bismuth E.M.F. varies with the field-strength for a given frequency. The investigation again consisted of two parts— determinations of the changes in the angle of lag and in the magnitude. I. The determination of the variation of the angle of lag with different field-strengths, the fi equeney being constant, was made by the same method as that already used and described in the previous paper. The experiments were now more difficult owing to the diminution of the whole effect due to decreasing * Communicated by the Author. -_ Resistance of Bismuth to Alternating Currents. 555 the field-strength, the maximum field at my disposal having been employ ed in the previous experiments. Three sets of experiments were made having frequencies of 30, 20, and 13°3 per sec., and in each set three different field-strengths were used. The results of these experiments plotted according to the theory given in the previous paper are shown in figs. 1, 2, and 3. In these figs. the points Fig. 1. __ SRR sunnesnstsueeneeeeceee Beer po ee BEE HEE Carte fe ee ea) el Jee ARS ees eee se = 0 Z Se a a Pa! Aiba de Fig. 2 So) PSRs _*) SORES ee ae tT | eee ere | | ee LT ee 4° RRS eT A ee _. hE RES {EGRESS SSR cae ee _ GER EST Shee Sea eSe ees JO 6k Foes See eee! ae eal Bees Cane oe Se cea cs 2 0 TUE MO EP where the straight lines cut the abscissa give the cotangents of the angles of lag. In each of the figs. the straight lines for the different field-strengths cut the abscissa in the same point ; hence the experiments ee that the angle of lag is 2 \. & a ; rn Pee Oe d 556 Mr. G. C. Simpson on the Electrical independent of field-strength. Thus the curve already given connecting angle of lag with frequency holds for all field- s trengths. Fig. 3. So jaja LT 1) le ee ot | a Ee Pe aa a ee AT Ea MEE RRRISiti SA Oa a ee eee CEC Ca er Peete ace pe Mee ar is je | Fe 3/4 re Ws Se BP Sea Se =. Ee Sie Sele oe Beeld ECE bef REECE Peed Be als Re kee ce | NL —| II. The variation of the magnitude of the bismuth E.MLF. with different jield-strengths, frequency constant, was calculated from the results obtained in the above determination. These results, with a few more from separate experiments, Fig. 4. -020 - Les Pee AR a || | fe (a a MEP Any. EOC CCC eat FA cane ae pa cof eh eee a i feet | | | a Lit | | ger [otto breencm | | | TT | | 9 10 No 2 13 4 15 16 17) Wea are plotted in fig. 4, in which the value of the bismuth E.M.F. = is plotted against field-strength. The conclusions to be drawn from this fig. are very interesting, showing as they do: Ist, that the magnitude of the bismuth E.M.F. is a linear function of the field-strength ; 2nd, that the bismuth E.M.F. is zero at the same field-streneth for all frequencies ; and Resistance of Bismuth to Alternating Currents. 507 3rd, that this field-strength is considerable—4500 lines per sq. cm. This latter result is also interesting from the fact that Lenard and others, using very high frequencies, have found a negative effect in no field; with the low frequencies used in my experiments the negative effect cam just be detected, but could not be satisfactorily measured. Temperature Variations. Experiments were next undertaken to find the effect of temperature variations on the bismuth E.M.F. In all the previous experiments a Hartmann & Braun bismuth spiral, designed for field-testing, had been used, but this became useless when experiments were made at other than atmospheric temperatures, so it was replaced by a wire ‘3mm. in diameter and about 10 cm. long, bent into the form Fig. 5. SSS of a flat grid and soldered to two thick copper wires (fig. 5). These grids were very easily broken, and a number were used during the experiments; the bismuth wire was supplied by Messrs. Hartmann & Braun. For temperatures above atmospheric a grid was placed in a glass vessel (fig. 6) consisting of an inner vessel having a Fig. 6. is} flat tube joined on at the bottom, into which the bismuth wire projected, surrounded by a similar slightly larger vessel. 598 Mr. G. C. Simpson on the Electrical In the space between the two, water from a thermostat - circulated, so keeping the bismuth (placed in oil) at the required temperature. For temperatures below atmospheric a similar vessel was used, except that the space between the two walls was evacuated, and different freezing-mixtures placed in the inner vessel. Low temperatures were obtained as follows :—Liquid air gave a constant temperature of —185°, a mixture of solid CO, and acetone gave —70°, while —95° was obtained by bubbling air through this mixture; solid CO, in alcohol produced —40°, The bismuth wire having a very low resistance (about 2 ohms at 17°) and the field being comparatively weak, owing to the large separation of the pole-pieces necessitated by the glass vessel, the whole effect to be measured was extremely small, so that it was found convenient to work only with the strongest field to be obtained under the conditions (about 7000 lines) and with a frequency of 30 per sec. With this field and frequency complete experiments were made at —185°, —70°, — 40°, 0°, 17°, 43°, 68°, and 100°, the results of which are given in fig. 7. In this figure it will be seen Fig. 7. eI i ny ed Ha VA Shee a PERE NER REEL is] Sadellnast alc |. | et Ben a Ye See. : S Pace ee ss aa SSaESam a SNe au ai ills ae IN No Ss ie a es ee BY EAN ihe Sea : ae Se 3 ener (eeeicges ANSSSEE AN ACN NC Wier aN [44 an at + + Bi + |: of + fie ye ae that the lines all cross the abscissa in the same point, hence the angle of lag ts independent of temperature. Resistance of Bismuth to Alternating Currents. 559 As the angle of lag has already been found to be. inde- pendent of field-strength, it may now be safely said that the angle of lag is a function of the frequency only. To find the relation between the magnitude of the bismuth EMF. and temperature, the results given in fig. 7 were used; but besides these it was found possible to get a measurement of the magnitude only, every 10° between —90° and 0°, by making use of the fact, just found, that the angle of lag is independent of temperature. Fig. 8 gives the results of these experiments, and shows Fig. 8. -260 -240 -220° -200° -I80 -160° -140 -120° 100" -80 -60 “AO -20. 0 20 40 60 80° 100° that the effect, which is small at —180° and 100°, becomes comparatively large between, reaching a maximum at —70°, where with the small field of 7000 lines and a frequency of 30 per sec. the bismuth E.M.F. is 2°2 per cent. of the H.M.F. applied to the bismuth, being five times greater than its value at ordinary temperatures. This variation of the bismuth E.M.F. with temperature is most important, because it shows that the effect, if not due to the Hall effect, has a close connexion with it, for a very similar variation of the Hall effect with temperature has been demonstrated by Dr. A. Lebret (‘The Hlectrician,’ vol. xxxvi. 1896, p. 785). In conclusion the results of the whole investigation may be briefly stated :— I. The magnitude of the bismuth E.M.F. (a) is proportional to the current in the bismuth; (>) is a linear function of the field-strength ; (c) increases with the frequency ; (d) varies with temperature, having a maximum value about —70°, decreasing rapidly on either side, 560 Dr. J. T. Bottomley on Radiation of At ordinary temperatures its value is given by Fj = (85 + 3°9 n) (H—4500)10-8, where n=frequency, and H=field-strength. Il. The angle of lag of the bismuth E.M.F. behind the current in the bismuth (a) varies with frequency ;_ (>) is independent of temperature and field-strength. Owens College, Manchester. LXIII. On Radiation of Heat and Light from Heated Solid Bodies. By J.T. Borromiey, D.Sc., FRS.* [Plates V. & VI.] ee following paper describes a further instalment of experiments on radiation of heat and light from heated solid bodies, a subject to which I have given attention for a considerable number of years. It is a difficult subject, and it has only been at times that I have been able to make pro- gress in the prosecution of the inquiry. I have treated it from first to last in a purely experimental way. 1 do not feel that there exists at present sufficient experimental in- formation to admit of anything like a complete theory. Indeed the information which we possess is of the scantiest character. My aim has been to determine directly the quantity of heat lost from a given surface under given conditions ; and the method by which I have carried out my experiments has been to put the radiating body into a vacuum as complete as I can obtain, and then to measure the energy lost from it in a given time, noting the circumstances. By adopting this plan J avoid determinations of the value of heat-receptors, such as sooted bolometers or sooted thermojunctions ; and I obtain results in absolute measure. In a paper published in the Transactions of the Royal Society as far back as 1887 I showed that it is possible to obtain with the Sprengel-pump a vacuum so good that the effect of convection on loss of heat from a hot body, in so far as that loss is caused by non-condensable gases, ceases to be of importance in comparison with loss due to pure radiation ; in fact, that increasing the vacuum, as * Communicated by. Lord Kelvin. Heat and Light from Heated Solid Bodies. 561 indicated by the McLeod gauge, beyond a certain point makes no difference to the amount of heat lost. 3 It is not certain that the results would be quite the same could all the mercury vapour, which must undoubtedly exist in the vacuum-chamber, be removed; and this is a question which still requires investigation. Other condensable gases, such as vapour of phosphorus (given off from the drying apparatus) also need consideration. The last mentioned gas I have, however, recently done away with, I hope com- pletely, by using phosphorus pentoxide which I have specially prepared for the purpose. I only desire at present to call attention to one particular part of the general investigation. In 1887, together with Mr. Mortimer Evans, I pointed out the marked difference in emissivity between a_ polished metallic-like surface and a dull sooted surface. I think it is now generally admitted* that such a difference does really exist, but at the time my conclusions were controverted. For example, in his book on ‘ Practical Electrical Measurement,’ Mr. Swinburne has the following passage :— «Mr. Bottomley read a paper at the British Association in 1887 giving an account of some experiments as to colour and temperature. His conclusions are opposed to those generally accepted by physicists, and before they can be accepted a great deal more evidence must be given. Mr. Bottomley, apparently, regards his paper as a mere first notice, and intends to continue his important experiments. At present it may be suggested that his arguments as to Mr. Evans’s experiments are open to criticism. The resistance of a lamp- carbon varies with the temperature in accordance with no evident law, and the colour of the light and radiation depend on the surface temperature of the whole carbon. A carbon of high emissivity would need a higher internal temperature to preserve a given surface temperature than one of low emissivity. The same reason- ing applies to two platinum wires, one of which is blackened. Besides, Mr. Bottomley does not state whether the lampblacked wire was heated to incandescence before the tube was sealed off the pump7; and if it were not, it would be coated with hydrocarbons, * { Note added July 31st, 1902.] in the discussion which followed this paper at the meeting of the British Association, September 1901, one of the speakers expressed the view that incandescent-lamp makers do not find any difference between flashed and unflashed filaments. I venture to think, however, that this is incorrect. Incandescent-lamp makers are naturally reticent as to their experience, but I believe that all first-class makers are now fwly alive to a ditference in economy between a brightly flashed filament and a dull unflashed filament. + The tube is never sealed off the pump. The pump is kept working the whole time to remove occluded gases given off from the platinum, 562 Dr. J. T. Bottomley on Radiation of which would spoil the vacuum in that tube. It is, no doubt, un- likely that one so careful as Mr. Bottomley would make such mistakes ; but, on the other hand, his results are so opposed to those of others that they may be disregarded for the present, and the law that efficiency is a test of surface-temperature, and colour is a test of both, may be taken as true.” I have always desired to examine further the question here referred to,and to come to definite conclusions on the subject, but it is only recently that I have been able to arrange for a set of perfectly conclusive experiments. The apparatus which I use is shown in Pl. V., which will serve to explain the details. The radiating body which I have used recently has been a thin platinum strip heated by an electric current. The strip was rolled for the purpose by Messrs. Johnson and Matthey, to whom I beg to express my thanks for the great trouble they have taken in order to provide me with perfectly uniform material. The way in which it is mounted is shown in the figures. The strip AB is held stretched between two spiral springs in a glass tube: the outer ends of the spiral springs ~ terminate in loops, and two pieces of copper rod are passed into the tubes CC and C’C' so that the springs pull on these rods. These rods pass down through long narrow side tubes into mercury cups, and by means of these the electrie current which heats the platinum strip is passed into it. At the points HE (see elevation) of the platinum strip fine platinum wires are attached by welding, and they are brought out through the sides of the glass envelope. These serve as potential electrodes ; and it is to keep the platinum strip AB in the middle of the tube, and to avoid pulling unduly on the potential electrodes that the two spiral springs, one at each end of the tube, are introduced. Two exactly similar tubes are employed, as shown in Pl. V. (plan). They are connected together at each end, as shown; and by means of a branch tube, attached to one of the two end tubes and connected to a Sprengel-pump, the air is withdrawn from both tubes at the same time. By this arrangement it is provided that the vacuum in the two experimental tubes shall be at all times precisely the same. In one of the tubes the platinum strip is brightly polished and perfectly smooth, just as it came from the makers’ hands. The other tube contains a platinum strip of exactly the same length between the points EH, and cut from the same hank, but with the surface covered with an exceedingly fine coating of lampblack. The arrangements for drying the vacuum consist in (1) a - Heat and Light from Heated Solid Bodies. 563 flask of phosphorus pentoxide attached to the pump bya wide side tube, and so arranged that it does not choke the connexion between the pump and the apparatus; (2) four pockets, two on each experimenting tube, as shown in sketch, each one containing phosphorus pentoxide. These pockets are short side tubes of the same diameter as the main tubes, and they allow free access for diffusion of the water-vapour into the drying material. This method of arranging the drying-tubes seems to me to be far better than the usual plan of putting a good long column of drying material between a pump and the apparatus to be exhausted. The effect of the latter is only to dry the gas that is pumped away, not to dry the gas remaining in the experimental apparatus, except by diffusion. Moreover, such an arrangement must very seriously retard the process of exhaustion at very low pressures, by choking the tube. The vacuum is measured by a modification of the McLeod gauge attached to the second of the end tubes mentioned above (see Pl. V.), so that the experimenting tubes are between the pump and the gauge. By this arrangement it may be safely assumed that the vacuum in the experimenting tubes is at least as good as the vacuum in the gauge, especially as the gauge was so made as to allow a wide tube connexion with the apparatus, in order to assist diffusion and prevent its readings from lagging behind what they should be. The electrical connexions, by means of which the currents of electricity, which heat the strips, are passed into them and are measured, will be easily understood from the figures (PI. V.). The current is supplied by a storage-battery of ten cells. There are two separate circuits, one for each strip. The current sent into each is regulated partly by the number of cells, and partly by a rheostat in circuit ; and an amperemeter in each circuit measures the current passing. A voltmeter can be applied to the working part of either strip by means of the potential electrodes, HE, E’H’, and the double-pole change-over switch indicated in the figure. It will be seen from the elevation on Pl. V. that the electrodes, EE, are attached at some distance from the ends of the strip AB. This is to avoid disturbance from the cooling effect of the end attachments. It is the portion EH which L call the working part of the strip. In a very interesting paper by W. H. Weber, published in the Annalen der Physik und Chemie, vol. xxxii. p. 256, a paper which I think has scarcely received the attention which it deserves, the author traces from the very commence- ment the production of light by a heated solid body. He 564 — Dr. J. T. Bottomley on Radiation of shows that a solid body first becomes luminous at a very much lower temperature than 535° O., which was given by Draper as the temperature of the lowest visible red heat. Weber found traces of luminosity at a temperature as low as 391° C. for platinum, and about 378° C. for iron. He also describes very carefully, and in an extremely in- teresting manner, the dawn of a dusky gray light at these temperatures, and its transformation at higher temperatures into the light of low red heat, and subsequently into bright red light and white light. Following Weber J have commenced by bringing up the platinum strips to the very lowest temperatures at which luminescence could be perceived, and 1 then measured the electrical power required to maintain the temperature of each strip, one of them polished and the other covered with lampblack. This being done, I passed on to very dull red, then to dull red, and subsequently to cherry-red, and to a white heat; and in each case I made similar measurements with the voltmeter and amperemeters, to ascertain the power in watts required in each case. The two strips were matched as to light-giving quality as closely as possible. After some practice my assistant, Mr. W. T. Evans, whose accuracy I cannot sufficiently praise, attained great skill in matching the pairs of strips. The results of our experiments are shown in the following table (p. 565) and in the corre- sponding curves 1, 2, and 3, Plate VI. Column 2 of the table describes the condition of the strips. The specification gray light, dull red, &c. is purely arbitrary, and mainly indicates the opinion of the experimenters, Mr. Hvans and myself, as to the light-giving condition of the surface. The gray light referred to in experiments 1 and 2 is the colourless light of Weber; though in our experiments, at the lowest point of temperature at which he observed the beginnings of light, we could not see anything*. The nearly white light of experiment 13 is not nearly so white as the light produced from an incandescent electric lamp. It has been explained that the two strips were matched in appearance in our experiments, and Column 9 shows approximately the temperature of each strip, inferred from the resistance of the strip which is given in Column 6. The resistance is easily obtained as the ratio of the potential-difference to the current. The current in amperes passing through each strip is shown in Column 4, and the potential-difference in volts between the points HH, in each strip, is shown in Column 5. By multiplying together the amperes and the volts and dividing by JS, the product of Joule’s equivalent J, and S * Doubtless through want of practice. Heat and Light from Heated Solid Bodies. — 565 the surface, in square centimetres, of the strip between the potential leads EH, the absolute amount of energy lost by the strip per square centimetre per second is found. This is equal to AV/4:28, and is shown for all the experiments in Column 10. The figures in Column 10 represent the number of gramme-water-degree-centigrade-units of radiant energy lost per second from each square centimetre of surface of the strips. Table of Results. aay Condition. | Strip. | Amps.| Volts. |Ohms.| Watts. Meee Temp.| AV/JS. _,, (Bright! 19 | 1-01 | 0-592/. 1-922|,... | 435° | 00417 1. | Gray light. fpiock.| 5-351 2:81 | 0525| 15-09 | “® | 452 | 0-397 é Bright, 218] 1175) 0:552| 25 |... | 465 | 00543 : % Black.| 59 | 3:23 | 0547} 19:05 | ‘ 487 | 0-414 3, {| Very dull }[Bright.| 231) 132 | 0572) 805 | ao | 495 | 0:0662 rede isch) | G2. eg4h) 0057 21-4 503 | 0-465 i Bright.| 284) 1-43 | 0611] 331 | gog | 550 | 00727 ns Black. | 625/37 | 0:592| 231 560 | 0-50! : Bright.| 28 | 1-74 | 0622] 4:7 |. | 573 | 0-106 5. |Dullred. fpack. | 7-2 | 432 | 0-600} 31:1 | ° | 573 | 0-676 i Bright, 304] 1-975) 0650] 60 | g1, | 613 | 01802 " Black. | 77 | 477 | 0°620| 36: 607 | 0799 : Bright) 32 |21 | 0656] 672 | goo | 623 | 0-146 i Black.| 80 | 5:05 | 0°632| 40-4 625. | 0-877 it Bright.) 35 | 2:37 |0677| 83 |. | 655 | 0-180 8. |Fairred. [pick | 85 | 5-47 | 0-644| 465 | °° | 643 | 1-01 Bright.| 4:0 | 279 | 0-697; 1115 |, | 685 | 0-242 9. | Good red. fplack. | 9-45] 6:32 | 0670] 597 | 586 | 685 | 1-206 . Bright.| 4-62| 3:35 | 0-724| 15:45 |... | 727. | 0-385 ype red. Wpiaek. |.10-4 | 7-24-|.0;606} 75-2.) 7°% | 7277. lies i [Very bright) Bright.| 53 [41 | 0773) 217 | 6 | 800 | 0-472 a fea. Black. | 11:6 | 8:52 | 0735] 98-9 793 | 2147 x Bright.) 599/48 | 0801] 287 | 42. | 843 | 0623 ‘4 Black. | 12:75| 9:85 | 0-772| 125-6 848 | 2-73 | . [Bright.| 64 | 535 | 0-836] 342 |... | 898 | 0-742 13. | Nearly white. p)ock. | 13-2 |105 | 0-796| 1387 | *°% | 891 | 301 Column 7 gives the power in watts supplied to each strip, i. e. the product of the current into the P.D. between the points EE. Column 8 gives the ratio of the watts used by the dull strip to the watts used by the bright one, both being matched in appearance, and both being practically at the same temperature, as is shown by the numbered experi- mental points on No. 1 curve lying so nearly on the same ordinates as the corresponding points on No. 2 curve. 566 Dr. J. T. Bottomley on Radiation of Curves No. 1 and No. 2 were plotted from the results of measurements of resistance and temperature made on the two strips when dismounted after the radiation experiments. The resistance numbers of Column 6 were then marked on these curves, and the corresponding abscisse gave at once the temperatures shown in Column 9. Tt will be seen by the divergence of Curves 1 and 2 that the increase of resistance with temperature in the dull strip is very slightly lower than that in the bright strip. This is probably due to the conducting power of the thin filament of lampblack which covered the strip. The lampblack would have a slight effect in reducing the resistance of the strip, and it would also have an effect, of minor order, in reducing the rate of increase with temperature of resistance of the coated strip. Curve 3 of the figure shows the watt-ratio for the two strips at the mean of the temperatures given in Column 9. It appears from the table and the curves that the blackened strip consumes energy at a greater rate than the bright strip when the two are at the same temperature, and that at each point when the strips are giving off an equal amount of light the blackened strip is using much more energy per second than the polished strip. It seems also that the ratio between the power used by the two strips is much higher at the commencement of luminescence than at a brighter heat; and it may be that a point would be reached at a very high temperature where this ratio might become constant, or else that at an extremely high temperature the power required to supply the blackened and the bright strips might not be very different in amount. The platinum strips were used in order to give a better comparison by eye than can be got from thin wires of the same electric carrying capacity, but it has been very difficult to obtain platinum strips which would not break at a very moderate temperature. I have tried commercial platinum strip, and also strip of perfectly pure platinum; latterly I tried strip containing 10 per cent. of iridium in order to harden it, but none has been as successful as I hoped. It has been very disappointing that in every case one or other of the strips broke, and my experiments have been stopped before I could reach a really very high temperature. The breaking of the strips is not to be attributed to an over great tension in the spiral springs. The amount of pull in the spiral springs was only so great as to take up the slack due to the expansion of the platinum with heat. I have a very Heat and Light from Heated Solid Bodies. 567 strong feeling, though I am not quite able to prove the assertion, that the platinum wires become excessively brittle, or as it is sometimes called with respect to brass wire, “rotten,” during the long process of heating and pumping which is necessary, as a preliminary to the experiments, in order to remove from the platinum the gases occluded in it*, In a paper which I published in 1900 along with Prof. J. C. Beattie (Royal Society Proceedings, March 1900) +, the radiation from polished and blackened platinum wires was determined in a somewhat different way. The apparatus - used was practically the same as that which I have just now described, but instead of comparing the energy lost by the wires when they presented the same appearance to the eye as to light-giving quality, the comparison was made between pairs of wires at the same temperature, the temperature being known by the resistance of the wires. Three pairs of wires having different diameters were used in these experiments, and it was shown that the thermal energy lost by the sooted wire was from four-to five times as great as that lost by the polished wire, the two being, as I have said, at the same temperature. In one respect the determinations, an account of which is given in the present paper, and in the paper by Dr. Beattie and myself, are not perfectly satisfactory. We have not been able to take account in a proper way of the temperature of the enclosing envelope. In order to be able to see the condition of the wires, and in particular to observe their appearance when they became luminous, glass envelopes were used in these experiments; and owing to the nature of the arrangements and the method of experimenting it was not found possible to immerse the glass envelopes in a cooling bath. Consequently, the glass became more or less heated during the experiment, and the heating was unequal in the cases of the bright wire and the sooted wire. It has already been pointed out (Phil. Trans. A, 1887, p. 450) that the * [| Footnote added Oct 18th, 1902.| In apaper by Dr. Hartley (Phil. Mag. July 1902) it is mentioned that the preseace of carbon and phosphorus render platinum brittle. It is quite possible that some traces of phos- phorus vapour may still find their way into my tubes, although I have made the greatest effort, by preparing the phosphorus pentoxide which I use with every care and every precaution I can think of, to avoid this contamination, of which I have always had a fear. My phosphorus pentoxide, the best I could buy, was most carefully redistilled, by myself, in acurrent of oxygen. The distillation was carried on in special tubes of hard glass, constructed by Mr. Evans, following the method of Shenstone. ¢ Phil. Mag. June 1900, pp. 543-559, ae 568 Ladiation of Heat and Light from Heated Solid Bodies. proportions in which the radiation of longer period and shorter period are present in the total radiation depends on the radiating surface, other things being the same. In the case of the sooted wire, the quantity of long-period radiation is, in proportion, far in excess of that proceeding from a bright metallic polished surface. Consequently, with the same total electric energy supplied to both wires, the glass tube containing the sooted wire becomes very much hotter than the tube containing the bright wire. It has also been pointed out that with a substance like glass, conducting badly and somewhat diathermanous, it is impos- sible to tell how much heat is returned to the radiating wire from the interior skin of the tube, which no doubt rises to a high temperature during the experiment. To a certain ex- tent, therefore, the results which we have recently obtained must be considered as not strictly comparable with those formerly obtained, in which a metallic envelope cooled with water was used. The absolute value of the radiation observed ought to be somewhat lower in amount than would have been found had the enclosing envelope been of metal properly kept cool, and the disturbance from this cause must have been relatively greater in the case of the dull than in the case of the bright wire. I cannot conclude without expressing my warmest thanks to my assistant, Mr. Evans, whose aid has been invaluable. Without the help which he has given me the experiments could not have been carried out at all. The investi- gation is still in progress, indeed, the present paper must be regarded as a description of preliminary trials; I hope before long, however, to obtain further results in the same direction of considerable interest. The temperatures shown on the curves and in the tables have been obtained partly by direct experiment and partly by using the results of other experimenters who have given comparisons between platinum resistances and temperatures. They must only be regarded as approximations, and may possibly require to be corrected. The amount of the correction cannot, how- ‘ever, alter the general conclusion that the polished surface is much more economical for the production of light than the sooted surface; and that as far as our experiments have - gone, the polished platinum surface and the sooted surface are practically at the same temperature when they present a similiar appearance to the eye. [ 569 J LXIV. The Cause and Nature of Radioactivity—Part IT. By EH. Rutuerrord, M.A., ).Sc., Macdonald Professor of Physics, and F. Soppy, B.A. (Ozon.), Demonstrator in Chemistry, McGill University, Montreal *. CONTENTS. I. Introduction. II. Method of Measuring Fmanating Power. Tif. The De-emanation ‘of Thoria ‘and the Regeneration of the Emanating Power. IV. The Effect of Conditions upon Emanating Power. V. The Cause of the Emanating Power of Thorium. VL. The Chemical Nature of the Emanation. VII. The Nature of Emanating Power. VIIL The Excited Radioactivity from Thorium. IX. Further Theoretical Considerations. I. Introduction. HE investigation of the radioactivity of thorium, detailed in the first part of this communicationf, arose out of an examination of the power possessed by thorium compounds of giving outa radioactive emanation. ‘The nature of this property” and its relation to the radioactivity of thorium remain to be considered. A short résumé of what was known at the commencement of the work may be of interest. Thorium radioactivity was discovered by Schmidt and Curie independently 1 in 1893, and Owens in the following year investigated its nature in detail (Phil. Mag. 1899, p. 360). He observed the inconstancy of the radiation and the effect of air currents in reducing its value. The discovery of the thorium emanation which ex- plained these results, and its power of exciting activity on surrounding matter, followed shortly after (Rutherford, Phil. Mag. 1900, pp. 1 & 161). It was shown that the radiation from the emanation decays rapidly, but at a perfectly defined rate, falling to about one- half the original value at the end of one minute. The ema- nation passes unchanged through cotton-wool, weak and strong sulphuric acid, and aluminium and other metals in the form of foil, but not through an extremely thin sheet ct mica. The emanating power of thoria is independent of the surrounding atmosphere, but is destroyed to a large extent by intense ignition, and does not return when the substance is kept. There is a very close connexion between the excited radio- activity produced by thorium compounds and the emanation. * Communicated by the Authors. + For Part I. see Phil. Mag. Sept. 1902. Phil. Mag. 8. 6. Vol. 4. No. 23. Nov. 1902. ria og Ne 570 Prof. H. Rutherford and Mr. F. Soddy on It was shown that the amount of the former produced under various conditions was proportional to the amount of the latter, and if the emanating power of thoria be destroyed by ignition, its power to excite radioactivity correspondingly disappears. Simultaneously with the appearance of the papers referred to, Curie showed that radium also possessed the power of exciting activity-on surrounding objects. Later, Dorn (Abk. der Naturforsch. Ges. fiir Halle-a.-S., 1900) re- peated the work quoted for thoria, and extended it to include two preparations of radioactive barium compounds (radium) prepared by P. de Haen, and a preparation of radioactive bismuth (polonium). He found that radium, but not polo- nium, gave an emanation, especially on warming, and this possessed the power of exciting activity on surrounding objects. Radium and thorium are in this respect completely analogous and different from other radioactive substances, but the phenomena in the two cases are quite different. The emanation from radium retains its activity for many weeks, while the excited radioactivity it produces, on the other hand, decays much more rapidly than that from thorium. One of the most interesting advances in this connexion was made during the progress of the work by Elster and Geitel (Phys. Zeit. 1901, ii. p. 590), who found that it is possible to produce excited radioactivity from the atmosphere, without further agency, by simply exposing a wire highly charged to a negative potential in the air for many hours, and that this also possesses the property of being dissolved off by acids, and of being left behind unchanged on the evaporation of the latter. But here again the rate of decay is different from that of the excited radioactivity produced by thorium. At the commencement of the work the presumption seemed to be in favour of considering emanating power as a separate phenomenon not directly connected with the ordinary radio- activity of thorium. The former could be destroyed in thorium oxide by ignition without reducing the latter. Later many external conditions were found to affect the value of emanating power without influencing the radioactivity. The nature of the phenomenon had been fully examined from this point of view with very puzzling results, but the conclusion was arrived at that emanating power is probably the mani- festation of a change of the nature of a chemical reaction. The discovery of ThX and its continuous production, how- ever, revealed the true interpretation of the results, and © enables a fairly complete explanation of the phenomenon to be given. the Cause and Nature of Radioactivity. 571 Il. Method of Measuring Emanating Power. The emanation from thorium (and from radium) behaves in all respects like a temporarily radioactive gas, and diffuses rapidly through porous substances, as, for example, thick cardboard, which are completely opaque to the straight line radiation. Hach particle of the emanation behaves as if it were a radiating centre, producing charged carriers through- out the gas in its neighbourhood. The emanation passes through plugs of cotton-wool and can be bubbled through liquids without appreciable loss of radioactivity, whereas the charged carriers, produced by the emanation in common with the straight line radiation from radioactive substances, on the contrary, completely disappear on passing through a plug of cotton- or glass-wool, or by bubbling through liquids. The means of eliminating the effects of the straight line radiation and of measuring the amount of the emanation alone thus suggest themselves. Air passed over uranium or other non- emanating radioactive substance will no longer conduct a current after passage through cotton-wool. The conductivity in the case of thorium, however, will persist, and afford a measure of the amount of emanation present. Fig. 1 shows the experimental arrangement for comparing Fig. 1. FROM age “—* the emanating power of substances. These are placed in the form of fine powder in a shallow lead vessel inside the glass cylinder, C, 17 cm. in length and 3°25 em. in diameter, pro- vided with indiarubber corks. A current of air from a large gas-bag, after passing through a tube containing cotton-wool to remove dust particles, bubbled through sulphuric acid in the vessel A. It then passed through a bulb containing tightly packed cotton-wool to prevent any spray being carried over. ‘The emanation mixed with air was carried from the vessel C through a plug of cotton-wool, D, which completely removed all the charged carriers carried with the emanation. The ilatter then passed into a long brass cylinder 75 em. in 2P2 572 Prof. E. Rutherford and Mr. F. Soddy on length and 6 cm. in diameter. The cylinder insulated on paraffin blocks was connected to one pole of a battery of small lead accumulators, the other pole of which was con- nected to earth. Three electrodes H, F, H, of equal length were placed along the axis of the cylinder. The current through the gas was measured by means of a Kelvin electro- meter of the White pattern. The electrometer and con- nexions were suitably screened by means of wire gauze con- nected to earth. An insulating key was arranged so that either of the electrodes EH, F, ‘, or all of them together, could be rapidly connected to one pair of quadrants ‘of the electrometer, the other two being always connected to earth. The measurements were carried out in the usual way by observing the rate of movement of the electrometer-needle after the one pair of quadrants were connected with the electrodes. On placing the emanating substance in C and continuing the air current for several. minutes at a constant rate, the current through the gas due to the emanation attains a steady state. The number of divisions of the seale passed over per second may be taken as a measure of the current. With this apparatus the emanation from 10 grams 7 ordinary thorium oxide produces a current of 33x 10-4 amperes between the three electrodes connected together and the cylinder. With the electrometer working at an average sensitiveness, this corresponded to a deflexion of 100 divisions | of the scale in 12 seconds, so that one-hundredth part of this current could be readily measured—that is, the emanation produced by one-tenth of a gram of thorium oxide. The electrometer one hundred times more sensitive than this failed to detect the presence of an emanation or radioactivity in the oxides of tin, zirconium, and titanium, the other elements. of the same group in the periodic table. Rate of Decay of the Radiation from the Emanation.—The three electrodes EH, F', H, were used to compare the “rates of decay ” of the radiations from the emanations of different substances. In the previous papers quoted, it has been shown that the radiating power of the thoria emanation falls to half its value in about a minute. In consequence of this, the current observed for the electrode E is greater than for the electrode H. Knowing the velocity of the current of air along the cylinder and the respective currents to the elec- . trodes H, F, H, the rate of decay of the radiation can be readily deduced. If, however, we merely require to compare the rate of decay of one emanation with another, it is only necessary to compare the ratio of the currents to the elec- + 4 | 4 d N i i ne apts Ste gai we — a ‘ ne hale wa = a the Cause and Nature of Radioactivity. 573 trodes E, F, H in each case, keeping the current of air constant. If the ratio of the currents is the same. we may conclude that the radiating power of each diminishes at the same rate. The comparison of the emanation is thus rendered qualitative as well as quantitative. In most of the experiments the current to the electrode E was about twice that to the electrode H ; the velocity of the current of air along the cylinder was thus about 0°8 em. a second. Comparison of Emanating Power.—The experiments in all cases on the amount of emanation from different substances are comparative. The standard of comparison was usually a sample of 10 grams of thoria as obtained from the maker, which gave out a conveniently measurable quantity of ema- nation. Preliminary experiments were made to find the connexion between the weight of thoria and the amount of emanation as tested in the cylinder. The following numbers show that the.amount of emanation is within the limits of aecuracy desired directly proportional to the weight of sub- stance :— Divisions of scale Weight of thoria. per second. 2 grams. L-41 rhea 2:43 eget 6-33 AO ve iegs 13:2 Correction for Natural Leakage.—LKven with no emanating material in © the electrometer generally indicates a slight movement on separating the quadrants. This is caused by a small current, chiefly made up of leakage due to conduction over the ebonite, as well as the current produced by the excited radioactivity which has collected on the negative electrode during the course of the day’s experiments. It varies from day to day, and is as a rule negligible; but in case of bodies possessing very low emanating power it is necessary to correct for it. The number ot divisions of the scale per second indicated by the electrometer-needle when no emanating material is present, is subtracted from the number obtained with the specimen being tested. The corrected number indicates the current due to the emanation alone. Alternative Method of Comparing Emanating Power.—The apparatus (fig. 1) described in the first paper (Phil. Mag. Sept. 1902) for the comparison of radiations, can also be quite well employed for a comparison of emanating power. In this case, a thick layer of thoria (several grams) is spread over the plate and covered with two thicknesses of ordinary paper. d74 Prof. E. Rutherford and Mr. F. Soddy on This has been found almost completely to stop the straight line radiation, whilst allowing the emanation to pass through unimpeded. The current is now measured when a steady state has been reached, due to the accumulation of the ema- nation. ‘This takes some time, and draughts of air must be guarded against. For this reason, it is less convenient than that first described, but the results obtained by the two methods are almost exactly the same. Thus asample of “ de- emanated” thoria, which gave 12 per cent. of the emanating power of the comparison sample by the first method, gave 13 per cent. by the second method, whilst a sample of oxide prepared from thorium oxalate gave 37 per cent. and 39 per cent. by the two methods respectively. This close agreement in the values by methods so completely different in character is a proof that the indications of the methods are worthy of a great degree of confidence. Ill. The De-emanation of Thoria and the Regeneration of the Emanating Power. The emanating power of thoria, as has been stated, is destroyed to a large extent by intense ignition. A closer study of this is the first step in the investigation of the phe- nomenon. Previous experiments had not succeeded in com- pletely de-emanating thoria, although a reduction to about 15 per cent. of its original value had béen accomplished. A sample of this preparation which had been kept for two years had not altered from this value. An experiment was performed in which thoria was heated for one hour by means of a powerful gasoline furnace to the highest temperature which could be safely employed with platinum vessels. The temperature was such that the fireclay walls fused, and the pipeclay of a triangle showed signs of having been softened. It was found that the sample retained about 8 per cent. of its original emanating power. In another experiment, a small platinum crucible filled with thoria was heated for half-an- hour in a small furnace by a large blowpipe and powerful pair of bellows. Some asbestos-wool had completely fused on the outside of the crucible, and the temperature was pro- bably but little lower than in the previous experiment. This sample also retained about 8 per cent. of its emanating power. No turther attempt has yet been made to completely destroy the emanating power. A small quantity of thoria heated in a platinum crucible in the open over an ordinary-sized blowpipe and bellows for five minutes retained about 45 per cent. of its emanating power. The effect of time as well as of temperature was a - the Cause and Nature of Radioactivity. D795 studied by heating about equal quantities in a platinum erucible over an ordinary Bunsen burner for different periods. Heated 10 minutes. §Hmanating power=61 per cent. ae 1 hour. a6 hi) ae ze 24 hours. a ARI eee It thus appears that there is a large and practically sudden decrease of emanating power for each temperature above a red heat, followed by a very gradual decrease with time when the temperature is maintained ; thus, five minutes on the blowpipe, whilst much more effective than the same time at the temperature of the Bunsen burner, produced rather less effect than 24 hours at the latter temperature. Eject of Moisture—The next point to be examined was whether the loss of emanating power could be attributed to the loss of water and desiccation of the thoria hy ignition. A sample of de-emanated thoria (retaining about 14 per cent.) was placed in the middle of a Jena glass tube, one end of which was closed and contained water, the other end being drawn out toa jet. This was supported in a powerful tube- furnace in a sloping position, and the part containing the thoria heated to the highest possible temperature, while a slow current of steam from the water at the end was passed over it, escaping by the jet. When all the water was evapor- ated, the jet was drawn off and the tube allowed to cool in an atmosphere of steam free fromair. The thoria, on testing, was found to have been lowered in emanating power to about 7 per cent. The further heating had thus reduced the ema- nating power without the steam having at all regenerated it. In the next experiment, the reverse was tried. Two exactly parallel processes were carried out for ordinary thoria pos- sessing the normal amount of emanating power. In the first, it was heated in a porcelain tube in the tube-furnace for three hours, while about 500 c.c. of water were distilled over it from a retort. In the second, another quantity of thoria was heated in exactly the same way for the same time, only a current of well-dried air was substituted for the steam. The result was conclusive: each sample had had its emanating power reduced to exactly the same amount, that is, about 50 per cent. of the original. These experiments prove that water-vapour exerts no influence either in de-emanating thoria or in effecting a recovery of its lost emanating power. The Regeneration of the Kmanating Power by Chemical Processes.—The task of subjecting de-emanated thoria to a 576 Prof. E. Rutherford and Mr. F. Soddy on series of chemical changes to see if it would recover its lost emanating power was then undertaken. It may first be mentioned that thoria which has been subjected to ignition has changed very materially in chemical and physical properties. The pure white cclour changes at temperatures corresponding to the first stages of de-emanation to a light brown, and after subjection to the very highest temperature to a pure pink. At the same time the solubility of the substance in sulphuric acid is greatly diminished. A part always obstinately refuses to dissolve, even after long and repeated boiling with the concentrated acid, although this part is diminished on each successive treatment, and appears to be in no way different from the rest of the substance. No difference, however, occurs in the readiness with which chlorine attacks it when intimately mixed wiih carbon. The formation of the chloride by this method is the easiest way of dissolving ignited thoria. Preliminary experiments went to show that emanating power is a quantity which varies, not only with the nature of the chemical compound but also for the same compound very materially with its previous history. Thus the exide from the oxalate does not possess as a rule so great a emanating power as that used for comparison. The following two exactly parallel experiments were therefore made, the one with the ordinary, and the other with de-emanated thoria possessing 9 to 10 per cent. of the emanating power of the first. Each was converted to chloride in the ordinar y way, by mixing with sugar solution, carbonising, and igniting the’ mixture of oxide and carbon so obtained in a current of dr y chlorine. Each sample was then treated with water, the thorium precipitated as hydroxide with ammonia, and the hydroxides washed and dried at 110°. The result was conclusive, for each sample showed the same emanating power. For the first few days after preparation this value increased rapidly, but after having been kept a fortnight both specimens showed about 260 per cent. of the emanating power of the thoria used as a comparison sample. Thus the process of de-emanating thoria by ignition does not irretrievably destroy the emanating power, for after solution and reprecipitation no difference whatever exists in the emanating power between ordinary and de-emanated thoria. A fair conclusion from these experiments is that the cause of the emanating power is not removed by ignition, but only rendered for the time being inoperative. Cm Qt o ~] ~! the Cause and Nature of Radioactivity. IV. Egect of Conditions upon Emanating Power. The experiments just described brought out two new points. Thorium hydroxide possessed an emanating power which increased with time since preparation, and when it attained its maximum it was much greater than that of the oxide. Before any further work was undertaken, it was necessary to make a close study of the influence of cadanee upon the emanating power of thorium compounds. Eject of Temperature —The effect of increase of tem- perature on the emanating power of thoria has already been fully investigated by one ‘of us (Phys. Zeit. ii. p. 429, 1901). The results, stated briefly, show that an increase in tem- perature up to a certain limit, in the neighbourhood of a red heat, correspondingly increases the emanating power. At the maximum this is between three and four times that at the ordinary temperature, and is maintained at this increased yalue for several hours without any sign of-diminution with time. When the thoria is allowed to cool, the emanating power then returns to the neighbourhood of the normal value. If, however, the limit of temperature given is exceeded, de-emanation sets in, and even while the high temperature is maintained, the emanating power falls rapidly to a fraction of its former value. On cooling, the substance is found to be more or less de-emanated. Itis of interest that no increase of emanating power is observed when de-emanation commences. These experiments were extended to include the effects of cooling. The platinum tube which contained the thoria was surrounded with a felt jacket containing a mixture of solid carbon dioxide and ether. The emanating power immediately fell to 10 per cent. of its former value. On removing the cooling agent it again rose quickly to nearly the normal. In another experiment some thoria was surrounded in a platinum crucible with a mixture of solid carbon dioxide and ether, and kept in a vacuum for several hours. On removing it, and allowing its temperature to rise, it possessed much the same value as an ordinary sample, and after standing some time in the air it was again tested, and no difference could be detected between the two. Thus changes in temperature produce very marked simul- taneous changes in emanating power, but between the limits of —110° and an incipient red heat no permanent alteration in the value occurs. Effect of Moisture-—Dorn (loc. cit.) had noticed that moisture produced a moderate increase in the power of thoria 578 Prof. E. Rutherford and Mr. F. Soddy on of giving an emanation, and of exciting radioactivity on surrounding surfaces. We have confirmed and extended his results by the following experiments. Two similar samples of thoria left sealed up for a week, the one in a desiccated atmosphere, the other in air saturated with water-vapour, showed an increase and decrease in emanating power respectively. The moist sample possessed nearly twice as much emanating power as the dry. More complete desiccation, by sealing-up the specimens in vacuo with phosphorus pentoxide for a month, did not further reduce the emanating power. Some thoria mixed with concentrated sulphuric acid gave about one half of the usual amount of emanation when vigorously shaken. These experiments show that the presence of water, although producing a marked increase, is not essential for the production of the phenomenon. Other experiments were made on the effect of light and air on emanating power. The most useful result obtained is that thoria does not change in emanating power when kept in closed vessels under different conditions, but when exposed to the air the emanating power varies within comparatively narrow limits. Thorium Hydroxide.—This compound, like the oxide, has its emanating power increased by water-vapour. A similar experiment to that described for the oxide gave as the result an emanating power of 400 per cent. of that of thoria for the moist sample and 300 per cent. for the dry. Exposure to the air for a short time again equalized the two values. Carbon dioxide, which thoriam hydroxide absorbs from the air to the extent of 2 per cent. of its weight, is without influence on the emanating power. Effects of Molecular Condition and State of Aggregation of Lhorium on the Emanating Power.—Unlike the radio- activity, the emanating power of thorium compounds is by no means mainly controlled by the proportion of thorium present. The effect of temperature in de-emanating thoria and the high value of the emanating power of thorium hydroxide illustrate this. Thorium sulphate, oxalate, and nitrate possess but low emanating power, while thorium carbonate has been obtained with a value five times as great as that of thoria. In general a dense crystalline compound in not very fine powder possesses a much higher emanating power than a light floury compound in a much finer state of division. Solution, however, has been found generally to greatly increase the emanating power of soluble thorium salts. In a the Cause and Nature of fadzoactivity. d79 careful determination, using 20 grams of finely-powdered thorium nitrate, this worked out to be only 1°8 per cent. of the emanating power of thoria. Dissolved in water, however, and tested for emanation by bubbling a current of air through the solution, it gives about three times as much emanation as thorium brides That is, solution in water increases the emanating power of thorium nitrate nearly 200 times. The emanating power, as in the case of solids, is proportional to the weight of substance present, and within the limits tried is not much affected by dilution, for a solution of 10 grams made up to 25 c.c. in volume possessed a similar value when diluted four times. V. The Cause of the Emanating Power of Thorium. The separation from thorium of ThX, detailed in the first art of this communication, showed that not only the radio- activity but also the emanating power of thorium is connected with the presence of a non-thorium type of matter, ThX. The solutions from which thorium hydroxide had been pre- cipitated by ammonia possessed, when concentrated, about as much emanating power as the solutions from which they were prepared, while the precipitated hydroxide was more or less completely de-emanated. On allowing these preparations to stand, the emanating power of the filtrates gradually dis- appeared, while that of the hydroxide in most cases rose steadily with time, till at the end of a fortnight they had attained a maximum between three and four times that of ordinary thoria. This recovery of the emanating power in the case of the hydroxide was noticed long before “the similar change of its radioactivity was observed, but the two phenomena admit of a similar explanation. If, in the precipitation by ammonia, care is taken to remove the ThX completely, the ‘thorium hydroxide is at first almost devoid of emanating power. The small fiaction that remains—only a few per cent. of the maximum—can be accounted for by the reproduction of ThX during the time taken to dry the precipitate. The Rate of Recovery and Decay of Emanating Power.— The rate of decay of the emanating power of ThX, and the recovery of this property by the thorium from which it had been separated, were then investigated in parallel with the similar experiments on radioactivity already described. One quarter of the concentrated filtrate used for the latter purpose was taken, and the decrease of its emanating power with time measured. The increase of emanating power of the thorium hydroxide trom which it had been prepared was also 580 Prof. E. Rutherford and My. IF’. Soddy on measured. Fig. 2 expresses the results. The decay-curve is merely approximate, for it is not easy to accurately take the emanating power of a liquid without special arrangements to assure the constancy of the air-current and ‘the shaking of the solution. Fie. 2. PLT) Phat erbe me ee 80 The eee oe only Rs a pr nee Ke acter, bear out the conclusion that emanating power decays and recovers according to the same law and at the same rate as the radioactivity of ThX, and that it is therefore one of the properties of the latter and not of thorium. The decay-curve given, so far as it can be relied upon, shows that the eman- ating power of ThX at any instant is proportional to its radioactivity. VI. The Chemical Nature of the Emanation. The following work has reference to the emanation itself, and not to the material producing it, and was designed to see whether the emanation possesses chemical properties which would identify it with any known kind of matter. It had been noticed at the time of its discovery that it passed unchanged through concentrated sulphuric acid. The same holds true of every reagent that has been investigated. The effect of temperature was first tried. The air con- taining the emanation, obtained in the usual way by passage over thoria, was led through the platinum tube heated - = the Cause and Nature of Radioactivity. 581 electrically to the highest attainable temperature, and also through the tube cooled by solid carbon dioxide and ether. The tube was then filled with platinum-black, and the emanation passed through it in the cold, and with gradually increasing temperatures, until the limit was reached. The effect of the intense heat was to convert the platinum-black completely into platinum-sponge. In another experiment the emanation was passed through a layer of red hot lead- chromate in a glass tube. The current of air was replaced by a current of hydrogen, and the emanation sent through red hot magnesium-powder and red hot palladium- black, and, by using a current of carbon dioxide, through red hot vine-dust. In ey ery case the emanation passed without sensible change in the amount. If anything, a slight in- crease occurred, owing to the time taken for the ae -current tc pass through the tubes when hot being slightly less than when cold, the decay en route being consequently less. It will be noticed that the only known gases capable of passing in unchanged amount through all the reagents employed are the recently-discovered members of the argon family. But another interpretation may he put upon the results. If the emanation were the manifestation of excited radio- activity on the surrounding atmosphere, then since from the nature of the experiments it was necessary to employ in each case, as the atmosphere, a gas not acted on by the reagent employed, the result obtained might be explained. Red hot magnesium would not retain an emanation consisting of radioactive hydrogen, or red hot. zinc-dust an emanation consisting of radioactive carbon dioxide. The correctness of this explanation was tested in the following way. Carbon dioxide was passed over thoria, then through a T-tube, where a current of air met and mixed with it, both passing on to the testing-cylinder. But between this and the T-tube a large soda-lime tube was introduced, and the current of gas thus freed from its admixed carbon dioxide before being tested in the cylinder for emanation. The amount of emana- tion found was quite unchanged, whether carbon dioxide was sent over thoria in the manner described, or whether an equally rapid current of air was substituted for it, keeping the other arrangements as before. The theory ‘that the emanation is an effect of the excited activity on the sur- rounding medium is thus excluded. It is a preort improbable on account of the very different rates of decay of the activity in the two cases. The inter pretation of the above experiments must therefore be that the emanation isa chemically inert gas analogous in nature to the members of the argon family. 582 Prof. E. Rutherford and Mr. F. Soddy on In light of these results, and the view that has already been put forward of the nature of radioactivity, the speculation naturally arises whether the presence of helium in minerals and its invariable association with uranium and thorium may not be connected with their radioactivity. VIL. The Nature of Emanating Power. The foregoing results therefore find their simplest expression on the view that, just as a chemical change is proceeding in thorium whereby a non-thorium material is produced, so the Jatter undergoes a further reaction, giving rise to a gaseous product which in the radioactive state constitutes the emanation. It will be seen at once that this secondary change is of a different kind from the primary, for it is affected apparently by the conditions in a very marked manner. It was shown that moisture, the state of aggregation, and temperature in- fluenced the value of the emanating power. From —80° toa red heat the latter regularly increases in the ratio of 1:40 in the case of thorium oxide, while the ratios between the values for thorium nitrate in the solid state and in solution is as 1:200. The secondary reaction appears therefore at first sight much more nearly allied to ordinary chemical reaction than the primary. It must not be forgotten, however, that the laws controlling the manifestation of the two phenomena— radioactivity and emanating power—are of necessity very different. In the former we deal with the intensity of radiations emitted by a solid, in the latter with the rate of escape of a gas into the surrounding air from either a solid or a liquid. Since this gas is detected by its radioactivity, and this decays extremely rapidly with time, a very slight delay in the rate of its escape will enormously affect the experl- mental value obtained for emanating power. On the other hand, it is now well established by experiment that sometimes thorium compounds de-emanated chemically by removal of ThX do not recover their normal emanating power with time, but remain constant at a lower value. On one occasion a carbonate was prepared which possessed hardly any emanating power until it was again dissolved and preci- pitated. In another experiment two samples of hydroxide prepared from different nitrates were tested together for rise of emanating power. That of the one rose normally to its maximum (as i in fig. 2), which was twenty times the minimum. The other started from the same minimum, but rose to a maximum only one-fourth as great. When the experiment the Cause and Nature of Radioactivity. 583 was repeated under the same conditions, using the same sample of nitrate, the compound behaved normally. It thus appears that the emanation can be almost entirely prevented from escaping in the radioactive state in some cases, and partially prevented in others, where no visible peculiarity of physical condition exists, and where other preparations similarly prepared behave normally. These are outstanding points in the theory which remain to be explained. It is not possible at present to decide whether these variations of emanating power are caused by an alteration in the velocity of the reaction which produces the emanation, or by an alteration in the time taken for the latter to escape. The experiments detailed in the first paper on the augmentation of the proportion of excited activity in compounds de-emanated by ignition appear to favour the view that the change still proceeds, but the emanation does not succeed in escaping. The experiment on the regular variation of emanating power with temperature might be explained quite well by either hypothesis. VILL. The Excited Radioacti vity from Thorium. Since the emanation gives rise to the phenomenon of excited radioactivity, and the latter appears to be caused by an intensely active invisible deposit of matter, it must be supposed that a tertiary change is taking place. The emana- tion, a gaseous product of the secondary reaction, is again changing and giving rise to a third reaction-product causing the excited activity. The fact that it is manifested entirely on the negative electrode in an electric field, points to the positive ion being the means by which it is transported. Without, in the present paper, going further into the con- sideration of excited radioactivity, it may be mentioned that the successive changes occurring in the thorium atom are not yet ended at this stage. The fact that the excited radiation consists in part of cathode-rays may be recalled here. Further, the intensity of excited activity at first increases from the time of its formation, exactly as in the case of ThX newly separated from thorium, the increase reversing the effect of the normal decay. The radium excited activity behaves in a somewhat analogous manner. The matter in this case causing excited activity does not appear to be homogeneous, but behaves in its action towards acids, &c. as if consisting of two different kinds (compare Rutherford, Phys. Zeit. p. 254, 1902). 584 On the Cause and Nature of Radioactivity. IX. Further Theoretical Considerations. Hnough has been brought forward to make it clear that in the radioactivity of thorium, and. by analogy, of radium, we are witnessing the effect of a most complex series of changes, each of which is accompanied by the continuous production of a special kind of active matter. The complexity of the phenomenon gives rise to an important question concerning the fundamental relation between the changes which occur and radioactivity. So far it has been assumed, as the simplest explanation, that the radioactivity is preceded by chemical . change, the products of the latter possessing a certain amount of available energy dissipated in the course of time. A slightly different view is at least open to consideration, and is in some ways preferable. Radioactivity may be an accom- paniment of the change, the amount of the former at any instant being proportional to the amount of the latter. On this view the non-separable radioactivities of thorium and uranium would be caused by the primary change in which ThX and UrX are produced. The activity of ThX would be Ss: ee ee ae eT caused by the secondary change producing the emanation, the activity of the emanation by a tertiary change in which the matter causing the excited activity is produced, the activity of the latter being derived from still further changes. The law of the decay of the activity with time (equation 1 first part) in all cases but the primary then appears as the expression of the simple law of chemical change, in which one substance only alters at a rate proportional to the amount remaining. In the primary change the amount remaining is infinitely great compared with the ‘amount that alters in short time,’ and therefore the velocity of reaction is constant. This view certainly affords an explanation of why the emanating power of ThX is proportional to the radioactivity. So long as the latter is considered a consequence of what has occurred there is no reason why this should be so. But if itis considered the accompaniment of the change in which the emanation is formed the result follows naturally. Further and more exact determinations of the rate of rise and decay of emanating power are therefore called for. In the case of uranium the changes so far as they can be followed by the radioactivity appear to be at an end with that which causes the activity of UrX. It is of interest that this substance gives only cathode-rays, and that it continues to do so for many weeks after its separation from uranium. This gives rise to the question whether any connexion can be established between the nature of the radiation and the kind of change producing it. - we Conditions necessary for Equipartition of Energy. 585 The only consideration which is opposed to this view is the existence of polonium. The radiations of this body resemble closely the non-separable radioactivity of uranium, both in penetrating power and the absence of deviable rays. But all attempts (Soddy, loc. cit.) have so far failed to separate polonium from uranium, and until this is done its existence does not of itself affect the present question. Tt seems as if amore satisfactory explanation of the residual activities common to both uranium and thorium, and of the connexion between the emanating power and radioactivity of ThX, is obtained on the modified view. But further work, both on this latter point and on the nature of polonium, must be awaited before the connexion between radioactivity and chemical change can be considered exactly determined. Macdonald Physics Building, Macdonald Chemistry and Mining Building, McGill University, Montreal. LXV. On the Conditions necessary for Equipartition of Energy. By J. H. Juans, B.A., Isaac Newton Student and Fellow of Trinity College, Cambridge *. Introduction. et: ie object of the present paper is, firstly, to give a proof of Boltzmann’s Theorem on the Equiparti- tion of Energy from a somewhat new point of view ; and, secondly, to examine what are the precise conditions under which equipartition will take place, and whether these con- ditions are such as will occur in an actual gas. At the outset it must be explained that the equations leading to the law of distribution admit of a simple hydro- dynamical interpretation in generalized space of n-dimensions. I have made use of the hydrodynamical analogy for two reasons. In the first place it is easier to think in terms of generalized space than in terms of multiple integrals; and in the second place the terminology and results of hydro- dynamics being ready to hand, a great deal of obscurity and repetition may be saved by starting at once from the hydro- dynamical standpoint. So long as we only use hydrodyna- mical results and conceptions which have a mathematical (as opposed to a physical) basis, there will be no danger of a faulty “argument by analogy.” * Communicated by the Author. Phil. Mag. 8. 6. Vol. 4. No. 23. Nov. 1902. 2Q Tho] Cane Mr. J. H. Jeans on the Conditions The General Dynamical Theorem. § 2. Let us begin by considering the moticn of a very great number of exactly similar dynamical systems, the systems being supposed for the present not to influence the motion of one another. We shall ultimately take such a system to be a molecule of a gas. Let us suppose the configuration of this system determined by n coordinates | Th en ee and let the corresponding momentoids be Pw P25 e 6©« @ @ Pn . . e . . . (2) Now imagine a space of 2n dimensions, these dimensions cor- responding to all possible values of the 2n independent variables G15 q25 AAR Cet dw Pi P25 Se eon Sox ee Pn é 5 . (3) Then the configuration and rate of change of configuration of any system can be represented completely and uniquely in this generalized space by a single representative point *. Instead of saying that a system is in the phase (q1, da, - - - Pry Poy + - +), we shall say that it is at the point (q1, go, - - - ‘Pi; Po, - + -), OL our generalized space. Let us suppose that the number of systems of which the coordinates of the re- presentative points lie between G1, Jo -- + + Pi, Po - +s > and gitdqy, gtdq, - . . » prtdpy pPotdp, .... 1S vACLe G25 Spe AA P15 Pe alike a dq; dq2, Pa ne dpy, dps ~ This is the number of representative points which occupy the element of volume dg, dq, ... dp, dp... of our generalized space. We may, therefore, speak of /(q q..- 1 Po ++.) as the density at the point g, g..., and shall, for ‘ the sake of convenience, denote it by p. $3. If we are given the values of the 2n coordinates of scheme (3) at any instant we shall be able, from a knowledge of the energy-function of the system, to calculate the values * It will tend to clearness of thought to imagine infinite space, so that all the coordinates can range from +o to —o#. If the coordinates are not uniquely defined from the configuration (e.g. if g, is an angle so that for a given configuration g, may have any of the values ¢,, 27+@,, Anx+,... &c.) we may either suppose just sufficient of the space taken to give only one possible value of each coordinate inside the space, or we may suppose one representative point for every possible system of values of the coordinates, so that the arrangement of. points in our generalized Space is periodic. Dv) P} a A necessary for Hguipartition of Energy. 587 of these coordinates at any subsequent instant, so long as the system is not acted upon by any forces which are not included in the energy-function. In this way we find a “ path” in the generalized space which is described by the system in question. In this way we may map out the whole of our generalized space into “stream-lines.” It is obvious that there will be one, and only one, stream-line through every point of this space, and that stream-lines which are adjacent at one point remain adjacent throughout their whole course. The motion of the representative points may, therefore, be replaced by a hydrodynamical motion, this motion being continuous as regards both space and time. Let us denote differentiation with respect to a fixed point in this space by d/dt, that with respect to a moving element by D/Dt. The velocity at any point is, under all circumstances, a function of the coordinates only. The necessary and sufficient condition for a steady state is therefore do From the hydrodynamical equation of continuity, dp _Dp_ & op 0& dt. DA (ane Ob. where £ is any one of the 2n coordinates of scheme (3), and the summation extends to all. Now the molecules which at any given instant occupy the element of volume dg, dq, .. . will be precisely those which at some subsequent instant will occupy some other element dq’ dq.’ . . ., and, by a known theorem, dg dds. MR ea AG. kg ee 3) In terms of our present notation equation (6) may be expressed concisely in the form aren i Dp . ~- =v. . . . . . . . ( i; (7) Hence from equation (5) the condition for a steady state is seen to be = op 0g ( 1n~ —— > = 9). thal (2n) 0& Ot of § 4. Let the total energy of the system, supposed expressed in the Hamiltonian form, be denoted by E. The energy in- cludes the potential and kinetic energies of the system. It 588 Mr. J. H. Jeans on the Conditions may include the potential energy of the system in a perma- nent field of force, if such exists, and it may include electro- static or electrodynamic energies, or any other energies which are such that the equations of motion may be derived from the function E in the Hamiltonian manner. The equations of the system are 27 in number, being of the forms | OVE fold) See Pay a OPr e e 1 <= i 2 ° . . n) (9) Of 3 ee th ap Tyee ay hth Be n) The elimination of ¢ from these equations will give the equations of the stream-lines which determine the paths of the representative points in our generalized space. These equations will be 2n—1 in number, and will be capable of expression in the forms ar,=constant(s=1, 2, .. . 2n—1), 2) where vy, is a definite function of the 2n coordinates *. There is one further equation which can be derived from equations (9), and this may be expressed in the form *r.,=constant+ f/(7), . -' San where vf, is a function of the 2n coordinates. This last equation determines the motion of the particles along the stream-lines. The 2n equations (10) and (11) are the exact equivalents of the 2 equations (9). Now let us transform coordinates in our generalized space, from the coordinates of scheme (3) to the generalized co- ordinates vr, re, ses PL Won—1; Won- ° . e (12) Transformed into these coordinates equation (8) becomes s=2n Op OV, = =O... Sa 2 oY, ot i For the first (2n—1) values of s (s=1,2,...2n—1) we have Ons Lg ot * From another point of view equations (10) may be regarded as first integrals of the equations of motion. The whole question turns on the ~ fact that the equations are 2n—1 in number. That this is so is evident from the fact that the path of every point must be detinitely and uniquely determined by them. — AS tie : ) necessary for Equipartition of Energy. 589 If we exclude (as we legitimately may) the case of systems which remain permanently at rest in an equilibrium con- figuration, it follows that we must have ON different from zero. Hence equation (13) assumes the form OP. =(, Ovo, 2n and the most general solution is pP=O(Wi, Wa. + + Woe) - + » C4) in which ¢ is the most general function of the (2x — 1) variables. § 5. If the systems are not subject to external disturbance there is little more to be said. Of the 2n—1 quantities Wy, Wo, - - . Yron-1, one (say W,) may, without loss of gene- rality, be taken to be identical with EZ; the remaining (2n—2) ys are necessarily functions of quantities other than H. Thus it appears that although p=$(B), (the solution leading to equipartition of energy), ig a parti- cular solution of the general equations, it is by no means the only solution. In other words, equipartition, although pos- sible, is not necessary. This is as it should be, for Maxwell’s condition of continuity of path is not satisfied. § 6. Maxwell and Rayleigh now suppose that the system is subject to certain external agencies, and postulate that these agencies shall be such that by them each system is made to pass through all phases which are consistent with the conservation of energy. From the point of view of this paper, they postulate that the elements of fluid are moved out of their stream-lines, and this in such a way that every element is made to pass over the whole of the particular surface | EK =constant to which it initially belongs. If this postulate is granted their proof is unassailable, but they do not prove that the postulate is true in the case of any single system, and it seems to the present writer that for a large class of natural systems the postulate cannot possibly be true. Consider, for instance, the case of a particle moving upon a horizontal plane, in which the disturbing influence is supplied by a system of rigid barriers. As a preliminary, suppose these barriers replaced by a continuous field of foree, such that the potential becomes infinite over certain lines a,b,c,... inthe plane. If this potential is included in the 590 ‘Mr. J. H. Jeans on the Conditions energy-function E of § 4 the analysis of §4 must hold, and the system moves only over a single stream-line, not over a complete energy surface. Now suppose the field ‘of force to continuously change so that ultimately the potential is in- finite over the lines a, 6, c..., and is zero over the rest of the plane. This ultimate state is an exact mathematical re- presentation of the case in which the motion is disturbed by rigid boundaries placed over the lines a, b,¢... However near the field of force may be to this ultimate state the argument of § 4 must be admitted to be valid. Hence unless we assume the whole argument in some way to become invalid, when we finally pass to the limit, it would seem that the theorem cannot possibly be true for the case in question. I cannot, for myself, see any reason for treating this limit as an exceptional case, and Lord Kelvin’s recent expe seem to bear out this view. § 7. The same argument will, I think, apply to any, case in which the motion is determined for all time by the state of the system at a given instant. For example, it applies if we try to replace our typical system by amass of gas whether inclosed within rigid boundaries or not. When, however, the subsequent career of the system is in some way fortuitous the objection does not hold, and this class of exceptions iIn- cludes the important case in which the systems are molecules of a gas, in which the disturbance of the path arises from fortuitous collisions with other molecules. Application to Molecules of a Gas. § 8. Let us now suppose the exactly similar dynamical systems of § 2 to be the molecules of a gas. Suppose that each molecule is surrounded by an imaginary sphere, and let it be supposed that these spheres are of such a radius that two molecules exert no action upon one another except when their spheres intersect. When two such spheres intersect an ‘‘ encounter” is said to take place, lasting until the spheres again become clear of one another. Binary Encounters. $9. We shall begin by considering binary encounters only; that is to say, we assume that the event of a sphere being simultaneously intersected by two other spheres is so rare that it may be neglected. We treat this case as follows :—As soon as an encounter * Kelvin, Phil. Mag. [6] ii. p. 1. necessary for Equipartition of Energy. d91 begins between two molecules their existence as single mole- cules is supposed to be abruptly terminated, and their repre- sentative points are removed from our generalized space of 2n dimensions. During the progress of the encounter the two molecules together will be supposed to form a new dynamical system—a double molecule. This system will be specified by 4n independent coordinates, 2n for each constituent mole- cule. Hence any such system can be represented by a point in a space of 4n dimensions, one dimension corresponding to each coordinate. We shall not, however, require the whole of this 4n-dimensional space. If 2, y, 2, x’, y’, 2’ are the co- ordinates of the centres of the two molecules, the condition that an encounter is beginning or ending is (v—a’)?+(y—y')P?+(e-2'yP=4R?. . . (15) In the 4n-dimensional space this equation will be the equation of a certain “surface”? S (of dimensions 4n—1), and the re- . . . . . ~ presentative points of all double molecules will be inside 8. We shall find it convenient to denote each double molecule wo representative points, since the réles of first and secon by ¢ presentative points, since the réles of first and second molecule can be alloted in two different ways. Let o be the density in this new space, then the necessary and sufficient conditions for a steady state are d = =a SN are mee coer ghey dp u dt =(), . e . . . . . (1 7) in the latter of which the change in p includes that caused by the formation and dissolution of double molecules. § 10. Before determining the relation between p and o we must make Boltzmann’s assumption that the gas is in a “ molekular-ungeordnet”. state. Having made this assump- tion we proceed to calculate the number of encounters of a given kind which occur in an interval dt. Equating this to the number of representative points which cross the corre- sponding element of the surface S during the same interval co) we arrive at the equation ep em) ee in which o is the density at any point on 8, and p, p’ the densities at the two points of 2n-dimensional space which are determined by the coordinates of the two encountering molecules. The analysis of § 4 applies (with obvious modifications) to 592 Mr. J. H. Jeans on the Conditions the new space. Hence equation (16) may be replaced by the condition that o shall be constant along a stream-line. Let p, p’ be the densities at points occupied by the repre- sentative points of the two component molecules, at the for- mation of a double molecule, and let p, p’ be the densities at the points representative of the same two molecules at the dissolution of the double molecule. Then pp’ and pp’ are the two values of o at the two ends of a single stream- line in the 4n-dimensional space, and, therefore, by equation (18), ie pe =pp’,' . a the same result as is obtained by Boltzmann’s well-known H-theorem. 3 Since the motion is dynamically reversible we may take p, p. to be the densities at formation, then p, p’ will be the densities at dissolution, and the same result holds. From this it follows that in equation (17) the decrease in p caused by the formation of double molecules of any specified kind is exactly counterbalanced by the increase caused by the dissolution of double molecules of the same kind. Hence in equation (17) dp/dt may be taken to be the change in p caused solely by the continuous motion of the fluid, and may be treated as in § 4. | § 11. To sum up, we have found that the equations of steady motion, on the hypothesis of binary encounters, may be expressed as follows :— (z) Throughout the 2n-dimensional space, p must be con- stant along every stream-line. (8) Throughout the 4n-dimensional space ¢ must be con- stant along every stream-line. (y) At every point on the boundary of the 4n-dimensional space we must have c=pp. To these may be added a fourth condition— (6) At every point on the boundary of the 2n-dimensional space (2. e. at infinity) the flow across the boundary must be nil, or what is the same thing, we must have ae These conditions are necessary and sufficient for steady motion. Ternary and figher Encounters. § 12. By a simple extension of the method already ex- plained the possibility of encounters of ternary and higher — wi necessary for Equipartition of Energy. 593 orders may be considered. For instance, to take ternary encounters into account we imagine systems of triple mole- cules, these being represented in a space of 6n-dimensions. The density in this space being T we have as conditions additional to those given in § 11—- (e) Throughout the 6n-dimensional space 7 must be con- stant along every stream-line. (¢) At every point on the boundary of the 6n-dimensional space we must have T=po. § 13. Encounters of higher orders may be similarly treated. If p; is used to denote the density in the space of 24n-dimen- sions, in which k-ple molecules are represented, the complete system of conditions for steady motion is (i.) Along every stream-line in the 2kn-dimensional space, Ga CONSENT Thiele iiss 0s), Ser ey) Gi.) At every point on the boundary of the 24n-dimensional space rile=y ON) Pmt ee Se te 2's in which p,, ps refer to the two systems of molecules of orders a, 6, of which the encounter results in the particular system of order & which is represented at the point in question (we therefore have always a+ b=hk). If encounters of all orders are to be taken into account these conditions must be satisfied for all values of k from k=1tok=a. In the case of k=1, equation (21) must he interpreted so as to become identical with the condition (6) of § 11. lt will be noticed that if these conditions are satistied for all values up to k=~x, no hypothesis need be made as to the smallness of the radius of molecular action in comparison with the free path. The only assumption now made is that the gas is in a “ molekular-ungeordnet ”’ state. Solution of Equations. § 14. Let y be a quantity, a function of the coordinates a a mclecule or system of molecules, such that throughout the eeeistarbed motion of the molecule or system y maintains a constant value, and such that when two molecules or systen:s combine to form a new sy: stem the y of the new system is equal to the sum of the x’s of the component systems. Speaking loosely we may say that yx is defined as being capable of exchange between molecules at a collision but is indestructible. 594 Mi J. H. Jokes on the eee ee Then a solution of our equations (20) and (21) will be seen to be log pp=V(k=1, 22 2. co). 0 Further, the difference between this value for log pz and the most general solution for log p, which is such as to satisfy equations (20) and (21) must be a quantity satisfying the conditions satisfied by y. ~ In other words, the most general solution of our equations consists of the superposition of solutions of the type of (22). Let 11, yo, xa, - - - %- be inde- pendent quantities, each satisfying tke conditions already postulated for y, and let it be supposed that there are no other such quantities, then the most general solution of the equations of steady motion will be log pr=ArX1+AsxXet . . - HAs, in which A, A,...A, are independent and, so far, arbitrary constants. § 15. The quantities A, A,...A, can be uniquely deter- mined from a knowledge of the values of Xy1, Sx, .-. the sumimation extending throughout the gas, and the various sums accordingly each remaining constant throughout the motion of the gas. Hence for a given mass of gas (the values of Xy1, 2x2. -. being given) there is a unique solu- tion for a steady state, provided that a steady state is possible. § 16. Let us next examine what quantities satisfy the con- ditions assumed for y. Firstly, if we take y,=1 for a single molecule, y,=2 for a double molecule, &e., we see that x satisfies the requisite conditions, and Yy is proportional to the total mass of gas. Again, if we take ~,=2H, where E is the total energy of the molecule or system of molecules (including, if necessary, the potential energy in an external field of force), we see that xy, satisfies these conditions. As other obvious instances we may suppose yx to represent the amounts of translational or rotational momentum. As a final instance we may consider imaginary molecules which are capable of carrying a charge of electricity, and we notice that the amount of this charge would be a possible value for y. For instance, if we have a number of electrically charged spheres each of mass m and capacity C, inclosed in a vessel of which the velocity is (uw, v, wo), the solution will be found to be ma i ((u—atg)2-+ (v—09)2-+ (w—t9)) + = (Q-Qo)" | 5 in which Q, is the mean value of Q, the electric charge. - ays necessary for Equipartition of Energy. 595 § 17. The ideal gas of the kinetic theory may be supposed to be devoid of mass-velocity, both translational and rota- tional, and to be fully defined, in its steady state, by its density and temperature. For such a gas the only y’s which ean occur are the x, and y, of the last section, so that the solution is log p=AyX1 + Ao X2- Changing the constants this becomes a Be etme sta sen ie ew cen. (ey in which A, h are determined uniquely by the values of the density and temperature. For such a gas we have, therefore, proved that there is only one steady state, subject to the hypothesis that the gas is “ molekular-ungeordnet,” and this steady state is that given by the well-known Boltzmann law. To arrive at this result we have found it necessary to suppose that there are only two invariable quantities—the mass and energy of the gas (corresponding to the two varia- bles density and temperature). The result may break down for either of two reasons : G.) It may be that there is some third invariable quantity counected with the coordinates of the gas. If this is so, two samples of a gas having the same temperature and density will not in general possess the same physical properties. The uniformity of the experimental results obtained from different samples of gas, seems to supply an argument of overwhelming strength against supposing this to be the case. (ii.) It may be that the two quantities (=x, and Sy.) which have been supposed to be invariable are not really so. This is certainly the case with the gases of nature, in which the ageregate energy of the molecules is subject to dissipation into the ether. If we admit this latter objection it is at once obvious, on physical grounds, that no steady state is possible. Mathe- matically we are left with a solution in which p is propor- tional to x, and is therefore constant in the 2n-dimensional space. This solution fails because it does not give p=0 at infinity. Conclusion. § 18. To sum up, we have seen that for a gas of which the molecules are of any kind whatever, the solution for the steady state is unique when a steady state is possible. We have found out how to determine this steady state when the structure of the molecules is completely known. For an 596 Hon. R. J. Strutt on the Electrical ideal gas, defined as one in which the aggregate mass and aggregate energy of the molecules remain constant through- out any possible natural motion, and which is such that the physical state of the gas is fully defined by its density and temperature, this steady state is given by the well-known Boltzmann law. ‘These results depend upon the “ molekular- ungeordnet 7” assumption, but are not limited by the hypo- thesis of binary encounters. If the Boltzmann law does not give the steady state there must be some other variables besides the density and tempe- rature, a knowledge of which is necessary to determine the physical properties of a sample of gas. A gas in nature can never attain a steady state on account of the interaction between matter and ether. I have tried to follow out some of the consequences of this in former papers * In a future paper J hope to apply the methods of the present paper to some problems of dissociation and ionization. LXVI. The Electrical Conductivity of Metals and their Vapours. By the Hon. R. J. Srrurt, Fellow of Trinity College, Cambridge. § 1. Introduction. vi is known that mercury vapour, even at very high tem- peratures, is a good insulator ; a better one in fact than air under similar conditions{. Liquid mercury, on the other hand, is of course a good conductor, like other metals. Let us try to form some idea of what the difference in conductivity between the liquid and the saturated vapour amounts to. It is stated in the paper referred to that mercury vapour at atmospheric pressure, even at a yellow heat, allowed a much smaller current to pass than air under similar conditions. With air, contained in a tube 7 x 1 inches, into which the electrodes dipped, a current was observed which was measured by ten scale-divisions on a sensitive galvanometer, when an H.M.F. of 156 volts was applied. We may suppose that one scale- division represented a current of not more than 10—* amperes, and that the mercury vapour gave only 4 the current observed with air. Thus the current would be 2 x 10~° amp. * “The Distribution of Molecular Energy,” Phil. Trans. cxevi. p. 397 ; “The Mechanism of Radiation,” Phil. Mag. [6] 11. p. 421; “The Theo- retical Evolution of y,” Phil. Mag. [6] ii. p. 638. * Communicated by the Author. { J. J. Thomson, Phil. Mag. [5] xxix. p. 364. a i. eh” Conductivity of Metals and ther Vapours. 297 If the electrodes were each 10 x1 cms. in dimensions, and 1 em. apart, the specific resistance would then be no less than as =8 x 10" ohms, roughly. On the other hand, the specific resistance of liquid mercury at ordinary temperatures is about 10-4 ohms. Ata yellow heat, it would not at the most be more than 5 times this amount, according to the experiments which have been made on the variation of its resistance with temperature; this would make the liquid resistance 2X 10-3 ohms. But in all probability it is not more than half as much. Thus, at a yellow heat, so far as can be judged from existing data, the resistance of the vapour, at atmospheric pressure, should be that of the liquid. This stupendous difference of properties is very remarkable. And the question presents itself, what changes do the resist- ance of the liquid and of the vapour respectively undergo. as the critical temperature and pressure are approached ? It must be supposed that, since above that temperature the liquid and the saturated vapour are indistinguishable, they have the same electrical resistance, whether that resist- ance be high or low. In what manner does this wonderful change of electrical properties set in? Is it gradual or is it abrupt, like the change in the magnetic permeability of iron at high temperatures? I have not succeeded in going far towards an answer to this question, but have thought it desirable to record such small progress as I have been able to make. § 2. On the Probable Values of the Critical Temperatures of Metals. There are various methods by which some estimate of the critical temperatures of ordinary liquids may be made in the absence of direct observations. These, however, lead to hopelessly discrepant results when it is attempted to apply them to mercury. One of these methods depends on the temperature coefficient of the surface-tension of the liquid. Since the surface-tension of a liquid is a linear function of the temperature*, it is easy to find by extrapolation the temperature at which the surface-tension would vanish. * There is reason to think that thissurface-tension should be multiplied by the (specific volume)é for the linear relation to hold strictly. But this hardly affects the result in the case of mercury. Tae? ae 598 Hon. R. J. Strutt on the Electrical This gives an approximation to the critical temperature. In the case of mercury the surface-tension for different temperatures is given by Frankenheim*. His results point to a critical temperature of about 750°. Again, in the large majority of cases, the absolute critical temperature bears a fairly constant ratio, about 1°6, to the absolute boiling-point. This holds fairly well through a great range of boiling-points, from liquid hydrogen upwards, This would make the critical temperature about 724°, in fair agreement with the estimate from surface-tension. “If these estimates were anywhere near the mark, there would be no great difficulty in determining the electrical resistance up to the critical temperature. But other methods of estimating this critical temperature unfortunately lead to avery different conclusion. ‘Thorpe and Riicker ft have found that in many cases the absolute critical temperature (@) can be caleulated from the formula _ (¢+278)V,—273 1? 995(V,—1) where V; is the volume at some temperature t, the volume at 0° being taken as unity. If this be applied to mercury, taking tas 100° C., the critical temperature indicated is no less than 2700° C. Let us now consider the matter from the standpoint of density. It is usually found that the critical density of a substance is about one-third the density of the liquid at low temperatures, also that it is about 4°4 times the density which the same substance would have at that temperature and pressure if it behaved like a perfect gas{. (This may be alluded to as the theoretical gas density.) Combining these two generalizations, we see that the theor — gas density under the critical conditions would be about 5 53 the liquid density at low temperature. This latter for mercury is about 13°6. Thus the theoretical gas density for this substance under critical conditions should be very nearly unity. This does not of course in itself determine the value of the other critical data. But if a value be assumed for one of them, the corresponding value for the other can be found. The following are approximate values :-— Assumed critical temperature (°C.) 2738 546 819 1092 1865 1688 1911 Corresponding critical pressure 999 333 444 555 666 777 886 In abmospheres by 2.64 ie): 9G * Poge. Ann, Ixxv. p. 229 (1848). t Chem. Soe. Journ. vol. xly. p. 135 (1884). t Young, Phil. Mag. Feb. 1892, p. 185. Conductivity of Metals and their Vapours. 599 We have, then:— Critical Temperature of Mercury. From temperature coefficient of surface-tension .......... 750° Me IGS: SOOE LRN PONT oho. c ls ole) Leys. o aad ss metas ese see 724° From the thermal expansion at moderate temperature .... 2700° It is evident from this table that the methods which are successful in estimating the critical temperatures of ordinary liquids entirely fail when it is attempted to apply them toa metal. The fundamental difference between mercury and other liquids, so far as critical phenomena are concerned, probably lies in the very great density of the former. Few of the ordinary liquids which have been investigated are so much as 15 times the density of water. Mercury has 14 times that density. Thus the vapour-density has to increase enormously before it can compare with that of the liquid. It is, however, difficult to understand the entire failure of the argument from increase of surface-tension. Probably a careful investigation of the surface-tension of mercury up to the highest temperatures practicable would yield interest- ing results. I have attempted, but without success, to observe the critical phenomena of mercury. The experiment was carried out as follows :— A tube of quartz was built up according to the directions given by Shenstone *. Its length was about 3 cms., internal diameter 1 mm., external diameter about 7 mms. It was provided with a handle of quartz rod, fused on at one end. About two-thirds of the length were filled with mercury, and the end was hermetically sealed, taking care to make the sealed end as strong as the rest. The. tube was then heated in a bunsen-burner, and the appearance. of the mercury watched from behind a thick plate-glass screen. The liquid mercury attained a full red heat, but nothing could be seen in the part of the tube occupied by the vapour. The temperature was further increased by means of a Herapath blowpipe, and subsequently by placing the tube inside a Fletcher’s injector- furnace. At the highest temperatures attained (probably above the melting-point of silver) the vapour in the space above the mercury showed a pale steely-blue tint, which, so far as could be judged, was due to absorption. This tint is probably analogous to the green colour of gold-leaf as seen by transmitted light. The liquid mercury, on the other hand, * ‘Methods of Glass-blowing.’ 600 Hon. R. J. Strutt on the Electrical presented the ordinary appearance of a metal at a yellow, or nearly yellow, heat. When this stage was reached, the tube, which was the strongest I was able to make, burst with a loud explosion. Some of the fragments were examined, and they showed a “conchoidal” fracture, along a diametral plane of the tube. The quartz had ruptured abruptly under the internal pressure. There was no sign of viscous yielding. Of those elements which behave electrically as undoubted metals, mercury is the most volatile. The next is arsenic, and it was thought desirable to try to observe its critical phenomena. Some powdered arsenic was hermetically sealed up ina strong quartz tube, and the tube heated as before. At a dull red heat the arsenic melted to a silvery liquid. As is well known, it will not melt at ordinary pressures, but passes from the solid to the gaseous condition. The vapour began at once to show a strong yellow absorp- tion tint. I satisfied myself that the colour was due to absorption, and not to radiation, by observing it against a background of bright sky. The vapour of arsenic begins to show (selective) absorption of light at a very much lower temperature than does mercury. So that it sooner approaches the opaque quality of the liquid metal. There seemed, therefore, to be a chance that its critical temperature might be reached. This hope was disappointed. The tube con- taining arsenic was heated (all over) in a large blowpipe- flame, and the temperature raised by enriching the air-blast with gradually increasing proportions of oxygen. The liquid and vapour began to look somewhat alike, but with close observation could easily be distinguished. Finally, the quartz began to yield, viscously in this case, and the experiment could be carried no further. § 3. Observations on the Electrical Resistance of Hot Mercury and its Vapour. Although the above experiments made it unlikely that the critical temperature of mercury could be reached in quartz tubes, it remained possible that some indication of the changes which the electrical resistance would undergo at that tem- perature might be got by observations at lower temperatures. To make a tight joint whereby a conducting wire can be led into a quartz tube containing mercury, red hot, and at an enormous pressure, seems at first sight a somewhat formidable mechanical problem, the more so since it is not possible to fuse platinum air-tight into quartz. Conductivity of Metals and their Vapours. 601 Success was attained as follows :— The quartz tube took the form of an inverted Y (a dd, fig. 1). It was constricted toa very small diameter at the parts dd, for a length of about 1 cm. on either side of the joint. The lower parts of the limbs 6d were of much larger diameter. The tube was filled with mercury up to the level ¢, the current being led in and out by iron wires ee, which projected some distance up inside the arms 0d. | The iron wires terminated in brass cups ff, carrying appropriate binding screws. These cups were filled with sealing-wax, which cemented them to the quartz tube. This sealing-wax had been sucked up the limbs while hot for a considerable distance, up to the points gg, so as to fill the space between theiron wires ee and the lower parts of the quartz tube. The tops of the iron wires projected out through the sealing-wax, making contact with the mercury. It may be well to explain that the mercury was introduced through the open end of a by making a vacuum in theapparatus before- hand. a wasthen strongly sealed. The resistance between the Phil. Mag. 8. 6. Vol. 4. No. 23. Nov. 1902. 2R 602 Hon. R. J. Strutt on the Electrical electrodes ff lay mainly in the narrow portion dd, and this alone, with the branch a, was kept hot. The limbs bb were immersed in tanks of water to keep them cold, so as to avoid melting the sealing-wax. It is evident that if the parts dd had alone been heated, the mercury in them would simply have distilled into the branch a. To avoid this, a was kept somewhat hotter, so that the vapour-pressure of the mercury in it effectually pre- vented the thread of mercury in the parts dd from separating. The resistance between the electrodes ff was about} ohm. It was determined by means of a slide-bridge and 1 ohm coil. Though the greater part of the resistance was in the narrow parts dd, the limbs 0d, which were not heated, contributed something. ‘The amount to be allowed could only roughly be guessed, since the temperature of the limbs was uncer- tain, varying from point to point. In fact the experiments made no pretension to accuracy, since the temperature was only estimated without measurement. It was merely attempted to ascertain whether or not the resistance increased enormously. Thus, in an experiment, the bridge balanced at 52:4, wher the mereury was cold, and at 64°7 when it was heated as hot as a bunsen-burner would make it. This makes the re- sistance 17 times as much when hot as when cold. If we make allowance for the fact that the limbs of the tube were not heated, the resistance was probably twice as great at the red heat as at ordinary temperatures. This is something like what might be anticipated from the known temperature coefficient at lower temperatures. The experiments had to be somewhat hastily carried out, since the heat soon travelled down the limbs of the tube by conduction, and made the cement slightly viscous. It then soon yielded to the enormous pressure, and the mereury forced its way out, leaving the top of the tube empty. For this reason it was not possible to go beyond the full red heat attainable in the bunsen flame. The same tube was used to obtain a measurement of the conductivity of saturated mercury vapour at the same temperature. This was easily done. The top branch a of the tube was no longer kept hot. The mercury from the narrow parts dd distilled. into it, leaving these parts filled with vapour. The tube was joined up in series with a battery-ceil (E.M.F. 1°5 volts) and a high-resistance D’Arsonval galvanometer. A de- flexion of about forty scale-divisions was observed, indicating about 4x 10-7 amperes. The resistance was thus about Conductivity of Metals and their Vapours. 603 15 4x10-' that the current really passed altogether through the vapour. Quartz conducts appreciably at such temperatures, especially if it contains the slightest trace of alkali. A special experiment was made in which a current was sent through the hot quartz by means of wires passed up the limbs of the tube, in the absence of mercury. This experi- ment showed that the conduction through the quartz was comparatively insignificant. We have, then, as the resistance of the liquid, in the tube, about -25 ohm, and for that of the vapour, not less than 4 x 10° ohms. The liguid resistance is therefore, at a full red heat, still 10° times that of the saturated vapour. A few experiments were made on arsenic vapour. The procedure was very similar to that adopted in the case of mercury. The inverted Y-tube had, however, to be filled in a special manner ; this was as follows. The two branches were sealed at the ends. The finely powdered arsenic was introduced through a (fig. 2) and =4x10° ohms. It cannot be considered certain Fie. 2. shaken down till it filled the side limbs. a@ was then sealed also. The whole tube was heated so as to melt the arsenic, under pressure. On cooling, the metal solidified in an 2R2 604 Hon. R. J. Strutt on the Electrical ageregate of crystals, which were electrically continuous*. To make contacts with the ends, the sealed extremities of the limbs were ground off obliquely on a grindstone. They were then plunged into a fusible metallic alloy //, contained in the _ brass caps cc shown in the figure. ‘This alloy is the same as that introduced by Mr. E. H. Griffiths, It contracted firmly round the quartz on solidifying, and made good con- tact with the arsenic. On heating the top of the tube the arsenic melted in the parts cc, and liquid portion rested on the solid dd, which acted as a conducting cement. The top part b contained arsenic vapour. This method of leading the current in and out proved quite satisfactory ; the joints remained tight as long as was desired. In an experiment the tube was joined up with the battery- cell and galvanometer previously mentioned. A deflexion of 60 mms. was observed ata bright red heat, the highest temperature attainable in a Herapath blowpipe. The length of the vapour-column was about 3 cms., and its cross-section about 1 mm. square. Thus the specific re- sistance of the saturated vapour ata bright red heat is about 10* ohms. The specific resistance of solid arsenic at 0° is about 3°5X10-> ohms. There are no data for exactly predicting the resistance of the liquid above the melting point, but it must be of the order of 10—° ohms at 1000° C. Thus the resistance of the vapour is 10° times that of the liquid at this temperature. It was thought interesting to determine whether or not the vapour of arsenic obeyed Ohm’s law. For this purpose an E.M.F. of 400 volts was applied to the tube, and the galvanometer shunted in a known manner so as to make the deflexion suitable. The temperature was kept at a bright red heat as before. It was not possible to keep the tempe- rature very steady, but within the limits of accuracy of the experiment the current observed was 200 times as much as before when the #.M.F. was increased two hundred fold. § 4. Conclusion. The results of the preeeding reasoning and experiments may be summarized as follows :— (1) Mercury vapour is an insulator, while liquid mercury © * Finely powdered arsenic appears to insulate perfectly, so far as can be observed by ordinary experiments with a galvanometer. : . : fi yy ‘ ee Conductivity of Metals and their Vapours. 605 is a conductor. Since the liquid and saturated vapour are indistinguishable above the critical temperature, one or both of these must undergo a remarkable change of electrical properties as that temperature is approached. (2) Attempts to predict the critical temperature of mer- cury seem to lead to results altogether inconsistent with one another. (3) Attempis to observe the critical phenomena of mer- eury and arsenic in quartz tubes have failed. In both cases experiment proves that the critical temperature lies above a dull yellow heat. (4) Upto a full red heat the conductivity of saturated mercury vapour remains of quite a different order of magni- tude from that of the liquid, the latter being 10 miilion (107) times as great as the former. But, on the other hand, the conductivity of the saturated vapour is immensely greater than that of the vapour at atmospheric pressure. For the former was found to have a resistance J0’ times that of the liquid, the latter more than 4x10" that of the liquid. Thus the vapour at atmospheric pressure has a resistance about 4 x 10’ times that of the saturated vapour, both ata full red heat. It need scarcely be said that this ratio is of quite a different order from the ratio of the densities of these vapours. It seems likely that as the critical temperature is ap- proached the vapour begins to conduct freely, while the liquid changes its electrical character to a much less extent. -5) The conductivity of saturated arsenic vapour at a bright red heat is of the same order as that of mercury, and obeys Ohm’s law, at all events up to an electromotive intensity of more than 100 volts per cm. I do not think it is likely that the critical phenomena of metals will ever be observed. Ji would, however, be worth while to make more elaborate observations on the re- sistance of mercury as the temperature rises. This could perhaps be best done by heating the mercury electrically, the necessary pressure being applied by means of hydraulic testing machinery. I propose to attempt this as soon as I have command of the necessary appliances. Terling Place, Witham, Sept. 1902. [ 606 ] LXVII. The Clayden Effect and Reversal of Spectrum Lines. © By Prof. R. W. Woop *. ib the July number of the Philosophical Magazine Professor A Trowbridge publishes a series of photographs of the spectra obtained by passing single powerful discharges through Pliicker tubes containing hydrogen. Some of the lines of the spectra appear reversed, which the author explains by supposing a selective reversibility of the silver salts for certain wave-lengths, expressing the opinion that the phe- nomenon is of great significance in the application of photography to astrophysics. ‘One immediately thinks,’ he says, “‘ of the phenomenon of dark lightning or the Clayden effect.” Strong reversals were found at wave-lengths 4227, 3930, and 8965. These are undoubtedly the calcium lines, which almost always appeur in the spectra of heavy discharges. It appears to me that the whole matter can be very easily referred to the Clayden effect ; and I cannot see how the phenomena have any bearing on the interpretation of astro- physical photographic records. It will be remembered that Clayden showed that if the image of a lightning flash or spark was thrown on a photo- graphic plate, which was subsequently illuminated with diffused light, the spark-images were reversed. That this was not ordinary reversal due to extreme brilliancy he proved by reversing the order of the two exposures, in which case there was no reversal. He was unable to obtain the effect with any other source of light than the electric spark, and referred the phenomenon to some peculiarity of the light originating in an electrical disturbance. In repeating and extending the work of Clayden I showed (Nature, Nov. 30, 1899; Science, Nov. 17, 1899) that the re- versing power extended throughout the entire spectrum ; in other words, that it WAS NOT SELECTIVE, and that it could be obtained with the light from the crater of an are-lamp, and from the incandescent lime of the oxy-hydrogen light. It was also shown in the same paper that the time element was the all-important factor, flashes of light of a duration of mow of asecond or longer not reversing under any circumstances. The effect of a ‘ light-shock” of a very brief duration, 1 5 co ue Sep oac say less than gy Sec., is to diminish the sensibility of the * Communicated by the Author. ©. cepa Due 2 Clayden Effect and Reversal of Spectrum Lines. 607 plate, so that a subsequent exposure does not produce so intense an image as it otherwise would. The two things necessary for a Clayden reversal are, first, « light-shock of great intensity and exceedingly brief duration : ; and, secondly, a subsequent illumination by a feebler light of longer duration. It is not difficult, it seems to me, to see how both of these conditions could have been fulfilled in Professor Trowbridge’s experiments. The heavy discharge produced a bright - line spectrum of sufficient intensity and sufficiently brief duration to give the necessary light-shock to those portions of the plate on which the images of the bright lines fell. The heat of the discharge raised the inner wall of the tube to incandescence, superposing a continuous spectrum of much longer duration on the bright-line spectrum already impressed. The bright lines would then come out reversed exactly as they did in the experiment which I described in ‘ Nature.’ Professor Trowbridge showed me some of the tubes used in the experiments, and the badly corroded inner surface indicates that it must have been raised to an exceedingly high temperature. A brief phosphorescence of the gas following the discharge may have helped in the production of the continuous spectrum, though I am inclined to refer it chiefly to the incandescence of the glass surface. I feel confident that a photograph of one of these discharges with a revolying mirror or moving plate would reveal the dual nature of the illumination. One other point requires mention. Professor Trowbridge states that the strongest bright lines are not reversed, and that there is therefore a selective reversibility. That the strongest lines should not appear reversed is precisely what we should expect; for, as I showed in the experiments referred to, if the initial illumination is TOO intense reversal does not take place, 7. e. the light-shock must not be too heavy. By taking a series of photographs of very bright sparks, with different stops in the lens I found that only “the j images obtained with the small and medium stops came out rever sed. It seems probable that the calcium lines in Professor Trow- bridge’s experiments had the requisite intensity for reversal, while the other lines were too bright. If this explanation of these pseudo-reversals be accepted, it does not seem to me that they can have any bearing on stellar photographs, for it is difficult to imagine how the dual illumination could be produced. [ 608 ] LXVITI. The Current-Density at the Cathode in the Electric Discharge in Air. By Haroup A. Wirson, B.A., D.Se. (Lond.), Clerk-Mazwell Student, Fellow of Trinity College, Cambridge *. Te experiments described in this paper were undertaken with the object of measuring the current per square centimetre on the cathode, in the electric discharge in air at low pressures. It is well known that the negative glow at pressures of about one millimetre is confined to a definite area on the cathode, and that this area covered by the glow increases with the current through the tube. Wehnelt (Ann. der Physik, No. 2, 1902) has shown that the discharge from the cathode is confined to the area covered by the glow and that the current-density is uniform throughout this area. So long as the cathode is not entirely covered by the glow the fall of potential between the glow and the cathode remains independent of the current, but when the cathode is entirely covered the “cathode drop” increases with the current. This fact leads one to expect the area covered by the glow to be proportional to the current through the tube, and the experiments now to be described show that this is the ease. The method employed was very simple ; the cathode used consisted of a straight wire fixed along the axis of the dis- charge-tube and the length of the wire covered by the glow was measured and also the current through the tube. The discharge-tube used is shown in the figure. It con- sisted of a glass tube, AB, about 3 cms. in diameter and Fig. 1. 40 PUMP eErc <— A B C 30 cms. long, having an aluminium disk electrode A sealed in at one end, and a narrow tube BC joined on at the other. This narrew tube served to support a glass tube E which carried the cathode WW. The glass tube H was fastened in with sealing-wax at C, so that it could be easily taken out when it was desired to try a new cathode. The discharge-tube was connected to a Toepler pump and McLeod gauge and to bulbs containing phosphorus pentoxide. The discharge was passed from the disk A to the cathode wire, and it was found that the glow appeared on the end of * Communicated by Prof. J. J. Thomson. Ps On the Current-Density at the Cathode. 609 the wire nearest to A and formed a uniform coating over the wire, covering a definite length of it. This length was measured by means of a millimetre-scale placed along the tube and backed by a mirror, so that errors due to parallax could be avoided. The shape of the glow is indicated by the dotted line. It resembled a test-tube. The discharge was produced by means of a battery of small secondary cells, and an adjustable resistance and telephone were included in the circuit. The Crookes’s dark space between the glow and the cathode of course increased in thickness when the pressure was reduced, and ultimately the glow extended to the walls of the tube. When the pressure was so low that this occurred the length of wire covered by the glow was not proportional to the current, and the glow appeared to tend to concentrate itself at the end of the cathode, showing that the walls of the tube impeded it from spreading out uniformly. Measure- ments were therefore only made when the glow did not reach the walls of the discharge-tube. Table I. gives the results obtained Rak a platinum wire TABLE J.—Platinum wire 1:42 mm. in diameter. P l. C C ’ | | lp ies cael ie iq 51 5°35 7°36 0:27 | 39 16 54 031 | 2:58 8-1 5°16 | 0-25 2-04 51 2-63 0-25 “ 7-55 3°72 24 | 1-40 85 2°51 0-21 | “ 76 2-26 0-21 4:5 1-32 0-21 | | 0-96 5°55 1:20 0-23 | ” 92 1°69 0-19 2 3:4 0-70 0-21 | 0-67 4°5 0-69 0:23 2 8-9 131 0-22 i - 91 1:33 0-22 | 3:8 , 0-61 (24 610 Dr. H. A. Wilson on the Current-Density at 1-42 mm. in diameter as cathode. p is the pressure in mms. of mercury, / the length of the glow in cms., and © the current in milliamperes. \] The quantity 5 is approximately independent of the current at any one pressure, which shows that the current per unit-length of cathode covered by the glow is a constant. 8 also nearly independent of the pressure, so that the current per unit-length of the cathode is proportional to the pressure, Tables II. JII. and IV. contain the results obtained with other wires as cathodes. In every case tp is approximately independent of / and p. TABLE IT.—Platinum wire, 0°19 mm. in diameter. | C | p he C. ip ; | | : eats ‘NTE ) 2:93 | 4-4 1:07 0.083 | | 12°8 3°66 0098 i | 13-4 3:76 0-096 | | 5 | 3-4 0:875 0-088 . . 2:18 7-5 1:56 0:095 . i 4-4 0:67 0-070 | 1-475 12-5 1-62 ooss | . £ico5 1-21 0-073 . | | | 1:36 86 | 0-794 0:068 | i 4'8 | 0513 0-079 | | ‘; 4-2 | 0:47 0-082 . a 12-4 1:39 0-082 | | 0-93 7-27 0622 0:092 - 5-4 0:454. 0-090 | 55 8:95 0-75 0-090 0:65 10-1 | 0745 0-110 . ‘ 6:9 | 0-496 0-110 | ae = } | Meu Scene 0:08 If i is divided by zd (d being the diameter of the wire) we get the current-density at the surface of the cathode. Tasie [TT.—Aluminium wire, 2:08 mms. in diameter. the Cathode in the Electric Discharge in Air. 611 p d. C | os : | lp 6-7 15 58 0°58 3-64 53 7-49 . 0:39 3” 1°3 2, 16 0°46 3:13 63 6:96 0:35 2:37 $13 5-78 0:30 Ps | 2-6 | 9-26 0°37 3 | 2-2 1:97 0:3 13-05 11:95 0:39 2-07 7-4 5-96 0:39 9 33 2:49 | 0:37 ” ! 108 9 7 0:43 1:46 12-25 5-46 | 0:31 | 1:16 | TD 2:30 | 0:27 s | 12:25 4-09 0:29 1:13 7-95 2°35 | 0:26 0-975 11:4 3-23 0:29 | 0 4:8 1:18 0:25 | 0-78 31 0:60 0:25 2 8:8 1°63 0:24 | : | 12:3 2-43 0:23 | 0-68 129 2-35 0:27 | 053 | 61 0-68 oleae i“ | 122 1:75 0:27 | 0:45 | 9-2 1:13 0:27 | A 13-0 1:79 0:31 a | 57 063 ! 0:25 | re 0323 | Table V. contains the values of we for each of the wires used. lpnd The current-density for the two thickest wires is nearly the same, but for the smaller wires it is much greater. This suggests that the effective diameters of the wires are really greater than their actual diameters, so that if, in calculating the current-density, a small constant quantity was added to the diameter of each wire, then the current-density would he the same in every case. It was found by trial that if 0°5 mm. is added to the diameters the calculated current- 612 Dr. H. A. Wilson on the Current-Density at Taste [V.—Aluminium wire, diameter 0°61 mm. 4 | C P- Uf. | C. | tp i 8:5 66 8:83 0°16 4-07 131 6:92 0-13 2°87 as 2:30 0:15 ie 5D) 2°36 0-15 is 2-85 1:18 0°14 % 10°45 5:36 0-18 2:43 6°65 2-52 0°16 | 4 58 1:93 0-14 | 1:94 10°9 3:29 0-16 - 5 1:35 0-14 if 3:0 0:81 0-14 | 1:38 475 | 0:67 0-10 | : 6:15 0-97 0-11 | | ‘ 5:85 0-98 0-12 | :. 10°85 2:14 0714 ) 11:95 2:40 0-15 | 0-94 7-4 0:80 012 | : 9-9 101 0-11 | | 0-48 13:9 0-885 0:13 ) 5, Or4 0:57 | 0-13 Mean ..3....:00" 0139 | TABLE V. C o Diamete? - ip k pra’ ipx(d +005) 0-208 em. 0:323 0:50 . 0-403 0-142 ,, 0:236 0°53 0-394 P OOG 2; | 0:139 0°72 | 0-397 Le OLS 5, 0.088 1-47 0-406 density is the same for all four wires. The results of this calculation are given in the last column of Table V. It appears, therefore, that the effective area of a cathode is that of a layer 0°25 mm. thick covering it. At the surface of this layer the current-density is given by the formula t=0°'4p. The above results also show that the current- density is the same for cathodes of platinum as for cathodes | of aluminium. If we suppose that the current at the cathode is entirely za °° =a .—_ ae i $ the Cathode in the Electric Discharge in Air. 613 earried by negative ions produced close to its surface, it is easy to calculate what proportion of the air-molecules which strike the cathode must be ionized to give a current-density of 0:4 p milliamperes per sq. cm. If e is the charge carried by one ion, and 2 the number of molecules striking the surface of the cathode per sq. cm., then if every molecule striking the surface were ionized there the current would be ne. Now n=3NG where N is the number of molecules in a cubic centimetre of the gas, and G the square root of the mean square of their velocities. For air at the ordinary temperature G=5 x 102) Also fora sec. 1 _coulombs. gas at 760 mms. pressure 2Ne=5335 Hence p x5 x 10? 760 x6x2x0°115 = 47°7 p amperes per sq. cm. néeé= The actual current observed is 0°4 p milliamperes per sq. cm. so that the fraction of the molecules striking the cathode which would have to be ionized to carry the current is ee | 47-7 x 1000 120,000" It is therefore clear that the amount of gas present in the tube is amply sufficient to account for the observed current- density at the cathode. J. Stark (Physikalische Zectschrift, 2 Jahrgang, No. 5) has given a formula which represents the variation of the cathode fall of potential with the current- density. This formula is K=K,+ = (C—apf )} where K is the cathode drop, K, the “ normal” drop when the cathode is only partly covered by the glow, p the gas pressure, f the area of the cathode, C the current, and & and « constants. When the cathode is only partly covered, as in the present experiments, K=K,,, so that Stark’s formula becomes C= zpf. This equation becomes identical with that which my experi- 1 ments have led to, viz.,.=0-4p on putting at Stark does not give the value of his constant z and his experiments do not appear to be well adapted for its determination since he was mainly concerned with the variation of the cathode drop with the current-density when the cathode is en- tirely covered by the glow. 614 Notices respecting New Books. Skinner (Phil. Mag. Dec. 1901) has also given a formula for the variation of K with C. Itis K=Kn+ ; (C —a) where b and a are constants. This gives C=a when K=Kz, and is therefore evidently incorrect, for a should certainly depend on p. That Skinner’s formula will not do has been pointed out by Stark (Physikalische Zeitschrift, 3 Jahrgang, No. 13). The results described in this paper therefore confirm Stark’s formula in so far as it applies to the current-density when the cathode is only partially covered by the glow, The fact that the glow only covers a definite area on the cathode is evidently a consequence of the existence of a minimum value for the cathode drop. As the current- density falls the drop falls until it reaches the minimum value. Any further diminution of the current-density would then involve an increase in the drop, so instead of the current- density diminishing, the area of the glow diminishes. In conclusion I wish to say that my best thanks are due to Prof. J. J. Thomson for his kindly interest and advice during the carrying out of these experiments in the Cavendish ee LXIX. Notices respecting New Books. Vector ANALYSIS, a T'eat-book for the use of Students of Mathematics and Physics, founded wpon the Lectures of Professor J. WILLARD Gisss. By Dr. Epwix Bipwert Witson. (New York, Scribner’s ; London, Arnold, 1901.) HIS is one of the Yale Bicentennial Publications, and is in some respects a very remarkable treatise. It is essentially an ex- pansion of a short pamphlet circulated privately by Professor Gibbs some twenty years ago, and forms a goodly volume of fully 400 pages. As in that pamphlet, so in this book, the feature which distin- guishes the vector methods elaborated by ‘Professor Gibbs from the vector methods associated with the names of Hamilton, O’Brien, and Grassmann (to name only the originators of distinct methods) is the treatment of the linear vector function in terms of the so- called ‘‘dyad.” I1t is this which gives significance to the notation adopted for the scalar and vector parts of vector products. So far as these important quantities are concerned, the substitution of a. for —SaGand of ax for Va is a trifle, for which there could be absolutely no excuse unless the dot-cross notation is based upon some fundamental principle more important than anything which occurs in quaternion vector analysis. If then we leave the ‘‘dyad”’ out of account, there seems to be no sufficient reason why the pictorial notation of Hamilton should be discarded in favour of a purely ee a % ee > § a ~ Notices respecting New Books. 615 artificial notation, which is simply a commutation of that used by Hamilton’s brilliant contemporary, O’Brien. On the other hand, if we find that Gibbs’s conception of the “indeterminate product” known as the “dyad” is fundamentally more important than Hamilton’s conception of the quaternion, and that this general indeterminate product is analytically more effective than the quaternion, then we cannot but recognise the value of the nota- tion used by Professor Gibbs. When we have occasion to discuss them we shall speak of these rival notations as the dyadic and quaternion notations respectively. There is a widespread feeling that vector analysis is a growing necessity for physical investigation; and yet some of the most strenucus supporters of this view have protested that the vector analysis developed with great fullness and logical rigour in Hamilton’s quaternions is not what is wanted. These criticisms find a faint echo in the preface to the present volume. It is said that “‘ Heaviside has set forth the claims of vector analysis as against quaternions, and others have expressed similar views.” And again, “‘ As yet, however, no system of vector analysis which makes any claim to completeness has been published.” Now in the first place there is no antagonism between quaternions and vector analysis, since the most completely developed system of the latter is to be found in the former. In the second place, although till now no general treatise called “‘ vector analysis” has been in existence, it is simply against the facts to state that no system which makes any claim to completeness has ever been published: On the contrary it is a fact which it is pure sophistry to deny that in Hamilton’s two great works there is contained a complete system of vector analysis in a highly developed state. The main objection urged against the quaternionic system by Professor Gibbs (see ‘ Nature’ vol. 48, pp. 511—12) is that neither the quaternionic product nor the quaternionic quotient of two vectors can claim a prominent or fundamental place among such fundamental geometrical conceptions as the sum of vectors, the vector product of two vectors, or the scalar product of two vectors. This is perhaps largely a matter of opinion ; and yet after a student has formed a clear conception of the vector as a directed quantity is it not reasonable and natural for him to ask, What is involved in the conception of the quotient a//3 as the operator which changes 6 into a? This is Hamilton’s method, and leads at once to the conception of the quaternion, and the whole system of vector analysis unfolds itself naturally and consistently. Professor Gibbs’s method is very different. He first defines as independent and fundamental conceptions the “direct” and “skew” products of two vectors, the direct: product being Hamilton’s scalar of the product of two vectors with the sign changed, and the skew product being the vector of the same quaternion product. Now these well-known quantities are not factorisable products. They may be taken to be, as the quaternion nomenclature cléarly shows, parts of a real product which can be factorised, in the sense 616 Notices respecting New Books. that if AB=C, then A=C/B. But Professor Gibbs takes no account of the possibility of the existence of such a factorisable product. In a footnote on page 67 the student is promised (if he persevere) the definition of the product of two vectors where neither dot nor cross occurs. This is at last given on page 271, where we read that “the symbolic product formed by the juxta- position of the twa vectors ab without the intervention of a dot or a cross is called the indeterminate product.” Six pages previ- ous we are told that ‘‘an expression g, b formed by the juxtaposition of two vectors without the intervention of a dot ora cross is called a dyad.” The dyad and indeterminate product are thus by definition one and the same thing. Itis called indeterminate because it is neither a scalar nora vector*. Since each vector involves three numbers the most general conceivable product should involve six. The dyad, however, involves only five, since the assumption is made that the product of the tensors of the constituent vectors only is involved. Given the dyad, the directions of both vectors are fully determined, so that equality between two dyads means that the constituent vectors are, in regard to direction, the same in both. It is difficult to see what service such a restricted product is to be in any system of vector algebra, nor do we gain any enlightenment from subsequent parts of the book. In fact this product with its five disposable numbers is indeterminate, does not appear to be factorisable, and has no attachable meaning until it ceases to be itself by being defined anew as an operator in combi- nation with other vectors. The quaterniou involves four numbers, and having therefore what might be called from analogy two degrees of freedom is fitted to play an important réle in vector combinations. It has pleased Professor Gibbs to introduce the one condition that scalar multiplication in vector products is to he associative. Thereby he gets a purely symbolic indeterminate and uninterpreted product. Jt pleased Hamilton to introduce the condition that vector multiplication in products of three or more vectors was to be associative. Thereby he obtained a real determinate and fully interpreted product called the quaternion. It is very difficult to understand the argument that the real quaternion should be disallowed in a vector analysis, but the dyad as a symbolic indeterminate product welcomed with open arms, There are hints throughout the book regarding higher indeterminate products of vectors called triads, tetrads, etc.; but the theory of these is not given, there beg, we are told, no real need for them in physical applications. As a matter of strict logic, there is no real theory given of the dyad as an indeterminate product. * Dr. Heaviside demands that vectors be treated ‘‘vectorially,’ and that a vector analysis be purged of products which are non-vectorial. This is his reason for condemning the quaternion. It is curious that he has expressed intense admiration of the dyad or indeterminate product, which its inventor tells us explicitly is no vector but purely symbolic, and acquires a determinate physical meaning only when used as an operator. Could anything so hope- lessly ‘“‘ unvectorial” be said of the quaternion ? Notices respecting New Books. 617 What then is the use of this indeterminate product? By the simple insertion of a dot or a cross we get the scalar or vector product; «and these are stated to be functions of the indeter- minate product in the seuse that when it is assigned the others are determined. But how can an indeterminate purely symbolic product be assigned in any true and real sense? And what is the functional relationship connecting the indeterminate product with the “dot and cross” products? We know that the quantity aX —a. which is Hamilton’s Va3+SeQ is a quantity which is associative in products and which has a definite geometric meaning. It is in fact the quaternion af. Gibbs’s dyad, written in exactly the same way, has no such useful properties. Out of it the scalar and vector parts of the quaternion product are obtained by the artificial introduction of a dot and a cross; there is no indication that the properties of the scalar and vector parts are in any way connected with the properties of the dyad, viewed as a product complete in itself. There is, however, another use of the dyad, a use which connects it in a very ingenious manner with the linear vector function. The artifice consists iu adding to either side of the dyad a vector with a dot between. We thus get the quantities «.p, p.afs which are in quaternion notation —aS fp, —BSap. If we take the sum of several of these operating dyads we get what is called a dyadic, which then becomes a symbol for Hamilton’s linear vector function. Thus (a,3,+4,0,+ a,,,).p = — aSsp= — op. This is undoubtedly a very neat way of representing the trinomial form of the linear vectcr function, and it has its merits. For example, by merely shifting the operand vector from the one side to the other we pass to the conjugate function. That in itself is, however, of passing moment and seems to have no analytical significance, for writing the dyadic trinomial in the concise form @ Professor Gibbs falls back upon Hamilton’s time-honoured expression and gets absolutely nothing more. The dyadic method leads of course to a special discussion of the proper- ties of the linear vector function, and the usual cubic is deduced. It is then stated on page 321 that “this equation may be called the Hamilton-Cayley equation. Hamilton showed that a quaternion (sic) satisfied an equation analogous to this one and Cayley gave the generalization to matrices..... The analogy between the theory of dyadics and the theory of matrices is very close. In fact a dyadic may be regarded as a matrix of the third order, and conversely a matrix of the third order may be looked upon as a dyadic.” This sentence contains a mis-statement, and to the ignorant reader would convey a very inadequate idea of the great services rendered by Hamilton. The truth is that Hamilton's linear vector function is the matrix of the third order, and the cubic equation first e-tablished by him, five years at least before Pihil. Mag. S. 6. Vol. 4. No. 23 Nov. 1902. 28S 618 Notices respecting New Books. Cayley, is the equation satisfed by the matrix of the third order and by the dyadic viewed as a functional operator. There is in fact identity—no mere analogy. There is, on the other hand, no evidence that the “ indeterminate product” with its five involved numbers, or the dyadic trinomial with its fifteen numbers, satisfies an equation of tiis kind at all. As soon as the dyadic is regarded as an operator of the kind defined, it becomes Hamilton’s linear vector function, and of course satisties the same cubic equation. In fact if, as seems 1o be the ease practically throughout the book, the dyadic exists only as an operator, then the dyad should strictly speaking be written aj. or .a6, just as in working in quaternions we may put the linear vector function in the symbolic form a88,. +4,88,. +4,5),., meaning that the operand i is to follow. Professor Gibbs also defines the “ skew” products of a dyad into a vector. They are (uB) xX y=a(B X ~ aX (By)=(ax f)y That is, the original indeterminate product is split up, and one of the members is joined with the new operand to form a new vector, which with the other member forms a new indeterminate product. This is then to be used as a dvad operator. To find what the relation of this new dyad is to the original dvad, we must let it act upon a vector. Extending to dyadics we find ind quaternion equivalents to be as follows :— (a,8,+a,8,+ ...)Xp.c=—oVoo, o.(a By, +4,3,+ .+. )Xp= Vp¢'e, pik (euS ari. sarees ).o =~ Voga, 6p X(a9,+-..6.) =¢'Vpo, where ? is 2uS., and g' is the conjugate 3GSa. Hence these “skew ” products are equivalent to the quaternion operators oVp., Vpg., which in the quaternionic treatment come naturally to the front when needed without the necessity for new definitions, This constant appeal at every turn to new definitions is certainly not a pleasing feature of Professor Gibbs’s method. The section on Double Multiplication starts as usual from arbi- trary definitions, and seems to us to make serious demands upon the memorizing power of the student. Its value is not very apparent ; for its chief if not only use in the treatise seems to be tu arrive at the inversion of the linear vector function. Passing it over meanwhile, we shall cunfine our remaining remarks to a description of the dyadic treatment of what corresponds to Hamil- ton’s beautiful operator y. In quaternion vector analysis, y is a differential vector operator of the form id,+jd,+kd, where d, d, d, are differentiations in the directions of the mutually perpendicular unit vectors? j*. From this single definition (or from any other equivalent to it) the properties of y evolve themselves naturally along the lines of the calculus. j ; ‘ 5 - > Notices respecting New Books. 619 It is far otherwise with the dyadic treatment. Professor Gibbs virtually starts with the definitions of what are to him four distinet operators, y operating on a scalar, a.y operating on a vector, v. operating on a vector, and y x operating on a vector. Itis noted, however, that “for practical purposes and for remembering form ule it seems by all means advisable to regard fi tau , rt ¢ Y=" ay TI dy t dz as a symbolic vector differentiator.” Remembering formule! Here again it is difficult to imagine a mind finding rest in such an arbitrarily constructed calculus, when already in Hamilton's and ‘Tait’s works there lav to hand an effective vector analysis in which y was a real vector differentiator. The collocation Ye is defined in chapter vil. as meaning a dyad, and then we read; “The operators y. and yx which were applied to a vector function now become superfluous from a purely analytical stand- point. For they* are nothing more or less than the scalar and vector of the dyadic yw. ‘The analytical advantages of the introduction of the variable dyadic yw are therefore these. In the first place the operator may be applied to a vector function just as to ascalar function. In the second place the two operators y. and yx are reduced to positions as functions of the dyadie. On the other hand, from the standpoint of physics nothing is to be gained and indeed much is lost if the important interpretations of y.w and y x w as the divergence and curl of w be forgotten and their places taken by the analytic idea of the scalar and vector of yw.” With this last statement we are quite in accord if by Vw we understand the purely symbolic indeterminate and uninter- preted product. But it is otherwise with the quaternion quantity vw, towhich a real meaning can be assigned. Y is then a vector operator and the scalar and vector parts of the result of its operation on a vector have analytically and geometrically just those very meanings which make them all-important in physical investigations. To a worker in quaternions these meanings are always in evidence. “Curl” and “Div” are useful descriptively, but they are not analytical working symbols like Sy. and Vy.. When the quaternion method is adopted and the true Y associative with wtself in product combinations is used, everything develops in a perfectly natural manner, and there is no need for the complicated tabulations of the different types of the second order combinations of the dyadic v, so characteristic of the pages of Professor Gibbs’s ‘ Vector Analysis.’ We have not space to discuss the integral functions Pot, New, Lap, and Max f, which are analytically inverse functions of the true y, * This is loose language. v. and vy X are not the scalar and vector of vw. + Thev are discussed at some length ina paper on Lecent [nnovutions in Vector Theory (Proc. R. S. E., xix. pp. 212-237, 1893). 620 Notices respecting New Books. and the necessity for which seems to arise mainly from the neglect of the associative principle in product combinations of y. This particular section, however, 1 is very instructive reading, quite apart from the dyadic system of vector analysis. The collocation v¢ is called a triadic, but its properties (if there be any) are not discussed. The dyadic y x @ and the quantity Vy. are, however, defined. The former is the quaternion operator Vv¢.; hence when realized it means not the more general quantity V.vgz, but the particular case V.v,¢,a, where the suffixes mean that y acts on the constituents of g and not on w. In this respect the dyadic notation is not so general as the quaternion. The quantity y.o corresponds to what McAulay writes in the form 9,V,, meaning dig te Ried ke da? dy OF aes 7) k being the usual rectangular system and the constituents of $ varying with position. If ¢ is written in the form ga =aSiat+BSyat ySka da df dy then Ear dx dy. dz* So far there does not seem to be the least advantage in the ‘‘dyadic” over the ‘‘ quaternion.” It leads to nothing more, gives no greater generality, and is occasionally indeed less general. Passing over various examples which a quaternionist would not need to tabulate as they are perfectly simple transformations in quaternions, we come to the equations among line, surface, and volume integrals. ‘Tait has practically given these; but we owe to McAulay the completely general form which jnelaae all. He shows that if Q be any linear function of a vector JQdp=(JQVday), IQda=\Qvau where da represents the vector area element of the surface, bounded in the first case by the curve (p), and bounding in the second case the volume v, and where it is understood that vy acts on all the varying factors in the expression. Professor Gibbs gives four relations connecting line and surface integrals, namely, \\a at = \dpu, \\da x va=\a Ty cree ee en eee where wu is a scalar function, ‘w a vector, and pa. linear vector function. Notices respecting New Books. 621 In quaternions, the first is Judp =||Vdayu. The second, if regarded from a quaternion standpoint, would be \dpa =(\Vday a. But to find its meaning in dyadics, we must realize the expressions by adding .o or prefixing co. We then get (1) JdpSae = ||VdavSao which is simply a repetition of the first case, or (2) [Sodp.a=(\Soday.a, an equation which is true if o is constant, or if Vyo vanishes. But generally JSdp 0.@ =(\aSdave +|\Seday.a. The third relation given is (\da.v x a= \do.a. This in quater- nion notation is (Sdya = {\sdava. The fourth relation again deals with dyadics. If we consider — the dyadic as representing the linear vector function we find the quaternion relation to be Sdppo = ((Sdaygo where vy acts both on ¢ and o. In the dyadic notation, however, Vv X 9.0 means V.v,9,¢, so that the relation given by Professor Gibbs is [Sdppe=(|Sduy,9,¢ and is true only when o is constant or when Sday,¢o, vanishes. The six relations connecting volume and surface integrals, given on page 400, may be discussed in a similar way, and will be found in no respect more general than the quaternion equivalents, and in some cases less general. One example will suffice, namely, \\\eov x o=(\da xX ¢. By definition da x @ means in quaternion notation — Vdag. if the operand vector follows, and 9' Vda. if the operand vector precedes. Thus in quaternions {WVdapo=(VarVvoe, and \\p'Vdao=\\\dug' Vive, where vy acts on o and on the constituents of the linear vector 622 Notices respecting New Books. function. But in the dyadic notation yx¢.c=Vy,¢,7. Hence the dyadic formula is true only if o is constant or if V.y,9e, vanishes, Because of the great importance of the subject, we have givena fairly full description of the essential parts of Professor Gibbs’s dyadic theory. It certainly gives us nothing more in the way of a practical working vector analysis than we already possess in the Hamiltonian system. The so-called indeterminate product as such is useless. Cayley has said that ‘“‘a product which is not associative has no meaning until the grouping of the faetors is determined.” To such a category evidently belong the triads and tetrads hinted at; and the dyad regarded as a product is so far like unto them. Not till it is used as an operator does the dyad take on a determinate meaning ; and thenit is found to be nothing more than a bit of the linear vector function, one of the most beautiful of Hamilton’s discoveries. The Gibbsian dyad is in fact a kind of Jay figure for decorating with notations. There is, of course, no fundamental reason why vectors should obey the associative law in products; but we have only to try to master the meanings of Professor Gibbs’s combinations of dots and crosses with the vector operator y, to be convinced that the neglect of the associative principle leads to an increased complexity with absolutely no advantage whatever. The one excuse, it seems to us, for elaborating a vector analysis in rivalry to that developed by Hamilton is that a greatly superior thing is being presented. In the dyadic system of vector analysis we find no evidence of superiority. On the contrary, it is demonstrably more arbitrary, more complicated, and less flexible than the quaternionsystem. Had the quaternion system been unknown, the other would have been, asa kind of shorthand notation at any rate, a welcome aid in physical research ; but when we bear in mind that Professor Gibbs deliberately set out to construct a system free from the fancied blemish of the quaternion and yet did not scruple to introduce in its stead an indeterminate product which is without any geometric significance whatever, and when we find on careful comparison that practically the dyadic system is simply a modifica- tion of quaternion methods, in large measure a mere difference of notation, we can find no satisfactory reason for a man of Professor Gibbs’s great powers leaving quaternionic paths to invent new notations, new names for old things, and an indeterminate purely symbolic product to take the place of the determinate real quaternion. Whatever views, however, may be formed as to the merits or demerits of the system, there can be only one opinion as to the zeal, ability, and self-abnegation with which Dr. Wilson has fulfilled his task. Professor Gibbs is indeed to be congratulated in having a pupil so capable of producing in systematic book-form the subject matter of his lectures. C. G. K. Notices respecting New Books. 623 The Electric Arc. By HertHa Ayrton, Member of the Institution of Electrical Engineers. London: ‘“ The Electrician” Printing and Publishing Company, Limited, 1902. Pp. xxvi4+-479. Tue Electric Are is one of those physical phenomena which, although generally known for well-nigh a century, have defied the efforts of the experimenter, and resisted most of the attempts to lift the veil of mystery surrounding them. It is only within recent years that our notions regarding the processes which take place in the electric are have begun to clear ; and this result is in no small measure due to the distinguished writer of the book before us, who by a series of experiments requiring an amount of care and patience that few could command, has succeeded not only in establishing definite laws regarding the phenomenon of the arc, but has also thrown a flood of light on the labours of previous experimenters, and put forward a hypothesis regarding the mechanism of the are which is in striking agreement with the experimental knowledge of the present day. Notwithstanding the striking nature of the phenomenon, and the fascination which it seems at all times to have exerted upon the experimenter, the origin of its discovery seems to be hidden in obscurity. Davy is generally credited with the discovery of the electric arc, but, as Mrs. Ayrton clearly points out in the interesting chapter on the History of the Arc, his claims are by no means as substantial as is generally assumed to be the case. The difference between an ordinary electric spark and an arc does not appear to have been realized in the early days of the are, this latter being regarded simply as a species of spark. lt will be useful here to give a brief outline of the contents of Mrs. Ayrton’s book. Chapter I. contains a very clear description, illustrated by numerous fine diagrams and sketches, of the appear- ance of the arc, and the effects produced by changes in the current and length of arc, and by coring the carbons. In Chapter IL. we have a brief history of the arc, which includes a most useful summary of the researches of Continental physicists. This chapter must have involved an immense amount of labour, and English readers will feel grateful to Mrs. Ayrton for having brought within their reach much information which has up to the present remained inaccessible. Chapters IV., V. and VI. deal with the relations connecting P.D., current, and length of are. The distribution of potential in the arc, and the drop of potential in passing from the are to either carbon, are considered in Chapter VII. The next two Chapters, VIII. and IX., deal with the steadying resistance included in the are circuit, and the power efficiency of the are. Chapter X. contains an account of Mrs. Ayrton’s highly interesting experiments on hissing arcs, and her theory regarding the cause of hissing. Chapters XI. and XII. are concerned with the luminous efficiency of the arc, and include an account of Mrs. Ayrton’s theory regarding the mechanism of the arc, such questions as the a = oo a 624 Notices respecting New Books. existence of a back-E.M.F., and the effect of superposing a small alternating current on the ‘continuous current of the are, being also considered in this connexion. An Appendix which is mainly concerned with the mathematical aspect of photometry, and which also contains a list of the most recent papers on the electric arc, forms the concluding section of the work. A very copious index is also appended. There is little that we have to find fault with in the book, but it may be pointed out that the chapter on the luminous efficiency of the arc emphasizes the need for a thorough revision of our system of photometric units, which at the present time are in a somewhat chaotic condition. Thus, although the useful term “luminous flux” is employed by Mrs. Ayrton, it is used in the same sense as “ quantity of light.” It would seem preferable to restrict this latter term, in accordance with Blondel’s recommenda- tion, to the time-integral of the luminous flux—a quantity which is of importance in photography, and for which “ quantity of light” certainly seems to be the right term. The time seems ripe for the appointment of a Committee of Scientific Experts to deal with the question of nomenclature in photometry. Le Phénoméene de Kerr et les Phénoménes Electro-Optiques. Par Eveine Nuicuncka. Paris: C. Naud, 1902. (“ Scientia” Series, No. 16.) Pp. x+92. . TuE title of this monograph, which forms one of the most recent additions to the excellent “ Scientia ” series now being brought out by Messrs. C. Naud, is somewhat ambiguous, if not misleading. By “ Kerr’s phenomenon” we generally mean the rotation of the plane of polarization due to the reflexion of polarized light from the pole of a magnet. This, however, is not the effect which forms the subject of the present memoir. The author studies another electro-optic effect, also discovered by Kerr—the double refrac- tion produced by electric polarization of the medium. The very existence of this effect has been doubted by some physicists, who attributed the results obtained by Kerr to purely secondary causes, and not to electric polarization of the medium. In the light of more recent experiments, however, there seems to be no room for any further doubt, and the excellent résumé of both the experi- mental and theoretical investigations bearing on this subject contained in the present volume will be found most useful by physicists. The author gives an exhaustive bibliography of the subject, and references to various physical text-books in which it is dealt with. The book itself is divided into three parts: Part I. deals with experiments; Part II. with theory; and Part III. is devoted to theoretical considerations regarding the possible existence of a phenomenon analogous to the Zeeman effect in a magnetic field. Phil. Mag. Ser. 6, Vol. 4, Pl. V. ELEVATION : Ase DE oO ()000% Se er a es ser en 70 PUMP = — TO M°LEOD GAUGE E Phil. Mag. Ser. 6, Vol. 4, Pl. VI. Watt-Ratio. 00? Jo oinjerodurs y, 00 ‘20ULISISOY SWIYO THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND Pe tan JOURNAL OF SCIENCE. Sh —s [SIXTH SERIES.] DECEMBER 1902. ey yO LXX. The Electric Origin of Molecular Attr ‘action. By WitL1AM SUTHERLAND *. Introduction. Y molecular attraction we understand intermolecular forces whose effects are not appreciable at distances of a larger order than molecular, thus excluding ordinary gravi- tation and ordinary electric ‘and magnetic “force. But the law of molecular attraction which I have discussed (Phil. Mag. [5] xxxv., xxxix., and other volumes), namely, that of the inverse fourth power, can be most readily accounted for by tracing it to the electric polarity which the electron theory of chemical valency necessarily ascribes to molecules, because the theory of magnetism familiarizes us with an inverse fourth power force between magnets at distances great com- pared with their lengths. In applying this known magnetic result to account for molecular attraction we are at the outset confronted with the difficulty that in the case of magnets the force is as often repulsive as attractive, the nature of the force depending on the relative direction of polarities in the magnets, whereas the molecular forces required io account for cohesion must be preponderatingly attractive. We have to investigate how, if the electric axes of molecules are distributed at random, and repulsive forces would there- fore seem to be as common as attractive, it is possible for the attractive so to prevail over the repulsive as to leave a final balance of attraction, as if on the average all the forces were * Communicated by the Author, Phil. Mag. 8. 6. Vol. 4. No. 24. Dec. 1902. 2T 626 Mr. W. Sutherland on the attractive. There is this fundamental distinction in the effects of attractive and repulsive forces whose strength decreases with increasing distance, that the attractive forces by their | own operation tend to increase themselves, while the repulsive tend to decrease themselves. Consider, for example, a diatomic gas in which each molecule contains a single electric doublet formed by the opposite electrons holding its two atoms together. If two neighbouring molecules are approaching one another with their electric axes similarly directed in the straight line of relative motion, then the attractive force acts with strength increasing to thé maximum possible value at the instant of collision. If their electric axes were oppositely directed in the line of motion the forces would be repulsive, and could reverse the motion before their maximum possible strength had been attained. In general there is the same tendency for attractive forces to increase their strength and for repulsive to diminish. This causes attraction to pre- ponderate. The idea that molecular polarity might account for the inverse fourth power law of molecular attraction encouraged me when first investigating that law, though I failed to see how the attractive forces due to polarity could on the average be of more importance than the repulsive. It therefore seemed better at that time to work inductively at the accumulating mass of experimental material on molecular force, than to follow out a deductive theory of molecular attraction founded on molecular polarity, of which until re- cently we have had little convincing evidence. But with recent developments of the electron theory, which forces on our con- sideration electric doublets as a prominent feature in molecular structure, it becomes imperative to follow the deductive path. For if with Helmholtz we regard every chemical bond as con- sisting of a # and a electron (Phil. Mag. [6] iii. Feb. 1902) ? we see that every junction of atom to atom involves the existence of an electric doublet ¢), analogous to a magnet and exercising on every other such doublet a force of attraction or repulsion varying inversely as the fourth power of the distance between them. ‘The electron theory supplies us therefore with a true cause of molecular attraction on a very simple basis, namely, the inverse square law of electric force and the existence of the two sorts of electrons in equal numbers. The results to be interpreted in the light of the electron theory are contained in the following communi- cations in the Phil. Mag.: series [5] “A Kinetic Theory of Solids,” vol. xxxii., “ The Laws of Molecular Force,” xxxy.,. “The Viscosity of Gases and Molecular Force,” xxxvi., “The Attraction of Unlike Molecules,” xxxviii., ‘‘ Further Studies on Molecular Force,” xxxix., “The Fundamental Atomic Electric Origin of Molecular Attraction. 627 Laws of Thermochemistry,” xl., “ Molecular Force and the Surface-Tension of Solutions,” xl., ‘The Molecular Consti- tution of Water,” 1.; and series [6] “ Lonization, Ionic Velo- cities, and Atomic Sizes,” iii. The scope of the present paper is outlined in the following Table of Contents :— 1. Statement of the theory, consideration of difficulties, anda short digression on the Maxwell-Faraday stresses in the ether and cohesion of the ether. la. The range of molecular force. 2. Comparison of results with known laws of molecular attraction. . Relation to Helmholiz’s theory of chemical valence. . Period of rotation of an electric doublet. . Electric doublets in different classes of chemical sub- stances. - Molecular couples and gyrostats. Or i Oo or) 1. Statement of the Theory. Briefly it is this :—That the electric doublets in molecules exercise mutual directive actions as do magnets, so that the nearer two neighbours approach the more do their electric axes tend to take the same direction, and therefore on this account they exercise a stronger attraction on one another ; and also because attracting forces varying inversely as the fourth power of the distance produce motion which increases their strength, there are two causes which make the attractive forces amongst a number of moving doublets of more dyna- mical importance than the repulsive. To fix ideas we must look more closely into the system of forces between two magnets. In Maxwell’s ‘ Electricity and Magnetism’ (2nd edit.) art. 887, we have Tait’s results for the forces of magnets on B magnets translated from quaternion into ordinary expressions. Let AB and CD be two magnets of moments m, and m, in Mk oe 628 Mr. W. Sutherland on the different planes with their centres at distance r apart. Through the centre of C D draw ab parallel to A B, and let py, be the cosine of the angle between C D and ad, and X,, A, the cosines of the angles made by A B and C D with 7, then the action of ABon CD consists of forees R, H,, and H, given by the equations ? R = (M42 ar DAqAg) 3M, Mo/ 1, Hy =A_3m,mo/74, H, =A ,3m,m,/7* ; and also of two couples one of which acts in the plane of ab and OD with a moment sin (H,;H,)m,m,/7*, where (H,H,) is the angle between H, and H, which the couple tends to increase, while the second couple acts in the plane of R and H, and tends to diminish the angle between these directions with a moment cos (RH,) sin (RH,)3m,m,/7%. The more important standard case for our present purpose is that in which the two magnetic axes are in the same plane with the join of the middle points of the magnets. This can be further simplified for the discussion of a typical case by assuming the two magnetic axes to be parallel with one another and making an angle @ with the join. Then the forces reduce to a central repulsion — (2 cos? @—sin? 0)3mym,/7*, . 2. Se and a component 2 sin @ cos 8. 3mym,/74 acting at right angles to the join. These latter rotational forces and the couples equilibrate one another if the two magnets are part of a rigid system. We shall neglect them for the present, and confine our attention to the central force. When 0=0 this becomes —6mym,/7r*, the minus sign denoting that it is an attraction; and when 0=7/2 the force is repulsive of amount 3mm,/7*. This well-known case of the attraction in one standard position being double the repulsion in another might lead to an erroneous conception of how attractive force might prepon- derate over repulsive. For example, we might determine the average force acting between two magnets as one moves in a quarter-eircle of radius 7 from 0=0 to 6=7/2, namely, T 2 (23mm, sae 3mm, 1, y i (2 cos? 8 — sin? #)d@= — ee and imagine that, if a number of magnets or electric doublets direct their axes to parallelism, they will exert forces on one another which are preponderatingly attractive. It is im- portant to expose the fallacy of this incomplete reasoning, because in doing so we can touch upon a matter germane to the present inquiry. Electric Origin of Molecular Attraction. 629 If the electric properties of matter are to be explained in. terms of electrons, so also must the electric and magnetic properties of the ether. Ihave proposed to call the molecule of electricity formed in the ether by the union of the atoms = and ) of electricity the neutron, and to denote it by 4. In an electrostatic field we must suppose the electric axes of the neutrons so turned in the direction of the field that each hasa positive component of electric moment in that direction. This acquisition of a common direction by the axes of the neutrons constitutes what is called the polarization of the ether regarded as a dielectric. The amount of the component electric moment is proportional to what Maxwell calls the electric displacement, which we can thus realize as a veritable displacement to be specified by an actual distance, namely, the component of the vector joining the centres of the two electrons in a neutron in the direction of the electric field. We thus come into contact with an important point in the dynamics of the ether bearing also on the subject in hand. We shall therefore glance at the problem: What is the virial of the forcive of a set of doublets uniformly distributed with parallel axes through any space ? Take aspherical shell of radius r and thickness dr, and take the ring cut out by cones whose axis passes through the centre parallel to the axes of the doublets, and whose semivertical angles are @ and @+d@: then if there are n doublets per unit volume, and if R denotes the central force between a doublet at the centre and any doublet in the shell, we have for the part of 42 Rr due to the doublets in the ring and at the centre, using the value of R given by (1), the expression n 3M, Mz 2 Pr and for the whole shell (770 d0=0. Thus the tendency is for the virial} .42=Rr for all the doublets in a large space to vanish. Neither attractive nor repulsive forces predominate in the virial; and thus we see how it wou!d not be correct to argue from elementary con- siderations that in parallei doublets uniformly distributed attractive forces could be assumed to preponderate. Moreover, we see that if to the neutrons of the ther we apply Clausius’s equation of the virial, as in the kinetic theory of matter, the production of an electrostatic field does not cause any variation of the virial of the internal forces. Now (2 cos? @—sin?9)27r? sin 6 d@ dr=f(0) dO, say; 630 _ Mr. W. Sutherland on the the Maxwellian specification of the Faraday stress in the eether, when acting as an electrostatic field of intensity F, is a tension F?/87 along the lines of force, and a pressure of equal amount in every direction at right angles. Thus the change of the external virial for a volume v occupied by neutrons is —vi?/167 on account of the tension, and 2vF*/167 on account of pressure. But by Clausius’s equation, if there are no other forces this must represent the change of the kinetic energy in volume v; so that we find half the energy ¥?/87, which Maxwell considers to be stored in each unit volume of the electrostatic field, is stored there as kinetic energy of the neutrons, if our simple conception of the action of the neutrons is correct. The other half of the energy must be that which has been put into the field in turning the electric axes of the neutrons so that they have all a positive component of moment in the direction of the field. When the ether is not a field of force and the neutrons have their electric axes disposed at random, two cases will arise according as the neutrons have velocities of translation or not. If they have, then on account of the nearer approach of those attracting one another there will be a preponderance of attraction, which will give cohesion to the ether. If, on the other hand, the neutrons have no translatory velocities, but only rotate, then attractions and repulsions will act with the same strength, and there will be no cohesion in the ether on account of its neutrons. Having indicated how the prin- ciples of electric doublets must be applied to the ether as well as to matter, we had better now analyse some of the known laws of molecular force to test, before we proceed farther, whether they are compatible with an origin in the properties of electric doublets. But first to fix ideas we must interpose the following section. la. The Range of Molecular Force. For the central force between two small magnets no range can be assigned, and similarly none can be specified for that between two electric doublets by themselves. But in con- sidering a large number of such doublets we find conditions arise which practically fix the range of molecular attraction as a distance of the same order of magnitude as the average distance between two neighbour molecules. We have seen that there are two reasons for the preponderance of attrac- tions over repulsions, namely, an effect analogous to induc- tion by which two approaching doublets tend to pull one ~ another’s electric axes into the straight line joining their Electric Origin of Molecular Attraction. 631 centres, and an effect due to the large departure from average conditions when a pair of neighbours collide. For example, two molecules A and B, separated by a large number of others, may have their axes so directed that “they have the maximum mutual inductive effect and maximum attraction at that distance, but it will be possible to find near A a molecule C whose effect on B is nearly equal and opposite to that of A, anda molecule D near B which neutralizes the _ effect of Bon A. But if A and B are on the point of col- lision it is not in general possible to find another pair C and D capable of neutralizing the mutual effects of A and B. For molecules whose distance apart is several times the mean molecular interval, the preponderance of the attractive over the repulsive forces diminishes rapidly with increasing dis- tance. To take account of the average effect of this pheno- menon we can replace the perpetually varying actual forces by a fictitious molecular attraction f(7)/r*, in which f(r) can be assigned a form which best represents the average facts, and introduces a fairly definite range beyond which mole- cular attraction is negligible. A speculation of van der Waals (Ann. d. Ph. Beibl. xviii. p. 734) suggests one form that 7(7) might conveniently have assigned to it provisionally. He assumes that molecules attract one another according to Newton’s law of gravitation, but that the lines of force are absorbed by the medium in such a way that the potential energy of two molecules may be written —fe~"*/r, where » is a parameter characteristic of the substance and is equal to H/K, the ratio of Laplace’s two capillary parameters. But we shall see immediately that molecular attraction has no direct connexion with gravitation. Moreover, the absorption of lines of force would be difficult to reconcile with the absence of any known. gravitational property corresponding to the electric one of dielectric capacity. But van der Waals’ factor e~”* becomes intelligible if taken as representing our f(r). In the absence of “knowledge as to the form of f(7) perhaps the simplest way of taking account of it is to remove it and assume that the force Lr: acts from a distance r=y, where vy is of the order of the distance between contiguous molecules, up to a distance r= I and not beyond, L being so chosen that the effects due to distances greater than I. are allowed for by exaggerating the effects up to distance L through treating the function f(r) as 1. This simple method of treating the unknown 7(7) has the temporary advantage of agreeing with that which I have already adopted in investigating the law 1/7* while providing a more definite meaning for L than that formerly suggested. In one place G22 Mr. W. Sutherland on the I proposed that L might mark the linear dimensions ‘of molecular swarms, but according to the present line of reasoning the idea of a molecular swarm gives place to that of a range limited to a small multiple of the average distance between two neighbours. Thus the range for an ordinary vapour would be different from that in its liquid. In steam over boiling water the average distance between neighbour molecules is about twelve times that in the water, but we cannot assert that because steam still shows measurable effects of molecular attraction therefore the range of mole- cular attraction in water extends to at least twelve times the distance between two neighbour molecules. The correct deduction according to the principles under discussion would be that in steam the range of molecular attraction must be taken to be about twelve times as large as in water. In the next section we shall introduce a great simplification by treating the range of molecular attraction as the average distance between two neighbour molecules, thereby express- ing that attractions which eventuate in collisions are by far the most important of the forces we are now considering. 2. Comparison of Results with known Laws of Molecular Attraction. It will now be shown that the laws of force so far dis- covered satisfy the conditions required by the electron theory. In the first place, although the force between two molecules was on the analogy of gravitation written by me in the form 3Am?/r*, it soon appeared from its application to experi- mental data that 3Am? ought to be regarded as a single parameter of molecular force 3a? which had no direct de- pendence on the mass m of a molecule. ‘This marks a strong contrast to the law of gravitation, and satisfies the first con-~ dition of the electron theory, namely, that molecular mass does not enter into the expression for molecular attraction. In the second place it has been proved (xxxviii.) that the force between two unlike molecules 1 and 2 is 3a,a;/7*, ay and a, being characteristic constants of 1 and 2. In the third place an almost direct proof of the electronic origin of molecular attraction is furnished by the law of the parameter a for binary molecules of the type RS, (Phil. Mag. [5] xxxix. pp. 25 & 45), namely, a{n==(p/n+0)", -. 1s 4 p and o being parameters having definite values for each element R and each element S, because, to quote from the Electric Origin of Molecular Attraction. 633 paper just referred to (p. 45), it “ means that the mutual energy of two molecules of this type divided by the number of equivalents in each can be obtained by regarding each equivalent as a separate attracting entity.” For if each pair of electrons forming a chemical bond attracts each other one, then in Clausius’s equation of the virial if, neglecting for the present purpose external pressure, we write INmv?= 4.12 30?r/r4, where the double summation >> is to be effected for all the N molecules, we have really to sum for the electric doublets which produce the molecular attraction. In the first place, then, we have to evaluate %3a’r/r*, where r represents the distance of any one definite molecule from any other, and the summation is to be effected for all molecules within a distance L. Now if there are n doublets in each molecule and a is the value of a appropriate to a doublet, this would take the form n*Xa?r/7*, if each doublet were associated with a molecule entirely its own. But as there are n doublets in each molecule, it is clear that in general the parameter a cannot be equal to na. But there is an important exception to this, namely, when the axes of the doublets are all directed the same way, so that their moments are simply added together and then a=na. We shall see in section 5 that complex molecules show a tendency towards this state of identical direction in the doublets which they contain. But the case of the simpler types of binary compounds is one where considerations of symmetry do not favour the hypo- thesis of similarly directed doublets in the molecule. For example, the structure of CaCl, would be best represented by the formula >Cl#Ca#Cl), where the two doublets are oppo- sitely directed. In the case of SnCl, we should expect the four doublets to be pointing from the centre to the corners of a regular tetrahedron. The collision of molecules carrying doublets directed in such ways as these can be regarded in the following manner. The circumstance chiefly directing the occurrence of attraction between two molecules is that the doublet in one which is nearest to a doublet in the other should have its axis in nearly the same direction as that of the latter. It is true that there are n? ways of arranging two molecules so that they may have a pair of doublets in the most favourable position for attraction. But out of every n chances which the n doublets give a molecule of being attracted by another only one eventuates in attraction, be- cause it happens to be the strongest and ultimately leads to 634 Mr. W. Sutherland on the a collision. Thus on the average the attracting power of molecules containing » symmetrically arranged doublets each is only n?/n=n times that due to a single doublet. Jn this way the remarkable equation (A) may be explained. The attraction of such molecules depends on the number of equivalents in each in a way that points suggestively to the doublet origin of molecular attraction. The most important point now is to determine the definite connexion between the electric properties of doublets and the experimental parameters of molecular attraction. If we write Clausius’s equation of the Virial as adapted for the kinetic theory of N molecules in a volume v we have 3 pv/2=Nmw/2 +4. 453K, where the last term, which is the virial of the internal central forces R (different from Maxwell’s R for magnets), includes the virial of the preponderating attractive force as well as that of the repulsive forces coming into play during mole- cular collisions. These latter give a virial proportional to the kinetic energy, so that the last equation may be cast in the form pu=RTvf(v) +vd(e),. . . se where v¢(v) represents two-thirds of the virial of the attrac- tive forces, and R is now the usual gas constant. Now ac- cording to the law of attraction 3Am*/r’, or better 3a?/r*, I have shown (xxxv.) that if the N molecules form a sphere of radius R (still another signification for R, but the context prevents confusion), and if 6 isa length of the order of the distance between neighbour molecules, 4.4$223307/r* P 2R—b =ban? 4 1(R—2)* log —2R?(R—b) + x log ah. - (3) —3(R—b) where p is the density of the substance formed by the N molecules. But according to what we have stipulated about the origin of our preponderating attraction and the range of molecular force we can evaluate $.32>Rr ina far simpler manner. Let es, and es, be the electric moments of any two doublets, where e is the numerical value of the charge $ orb and s; and s, are the distances between 3 and p in the doublets, then, if » denote the-average distance apart of two neighbours Electric Origin of Molecular Attraction. 635 which have their axes so directed as to attract one another with the maximum force at that distance, we may consider the total attraction in which these two take part at a given instant to be expressed on our magnetic analogy by 6¢’s,s,/7", all other forces in which these two are involved cancelling one another. Thus, as in the theory of the viscosity of gases and molecular force (xxxvi.), we replace the almost intract- able medley of nature by a simple representative pair of molecules. The part contributed to the first summation in the internal virial by this pair is 3¢’s,s,/27°, which stands for 4=Rr, and then . 42 >Rr=3Nes,s2/2r*. In a homogeneous substance s;=s,=s, and we may write 7°=v/N, obtaining for the virial of the attractions BN7e?s?/2v. The expression (3) may be written Gan (N?/v?) (407 R?/3) f (0/R) = 62 f (b/R) a2N?/2, making it evident that a is proportional to es. The simplest way of comparing the results of the two methods of calcu- lating the virial of the attractive forces, namely that which treats the attractions as operating between each molecule and all the rest within a sphere of radius R, and that which treats them as on the average acting only between imme- diate neighbours taken in pairs, is to calculate numerical values for f(b/R) when R/b=2, 10, and 100, namely 0°60, 2°69, and 7°78, which give (3) the three values (0°94, 4:2, and 12°2) a*N?/v. By increasing R from 26 to 1008, that is by increasing the number of molecules included in the first summation of >> from 8 to 100,000, the value of the internal virial of the attractions is increased only 13-fold. This illustrates how the effect of molecular attraction depends mostly on the mutual actions of immediate neighbours, as we indicated in discussing the range of molecular force. In the papers referred to, the internal virial term vd(v) in (2) is proved for the element gases to take the form —l/v, while for compounds at small enough values of v it also takes the form —//2v, passing at larger values of v through a very interesting transition to be discussed in section 5. In these communications values of / have been found for many substances, though mostly given indirectly by the tabulation of M?/, where M is the molecular mass referred to that of the hydrogen atom as 1, and / is given for unit mass of the substance in terms of 10” dynes as unit of force. Then, since / is (2/3) 67 (6/R) N*q? or N%e?s?, and if N refers bole 636 Mr. W. Sutherland on the to unit mass it is 1/m where m is the actual mass of a molecule, ~ and so N=1/MA where fh is the actual mass of an atom of hydrogen, the tabulated values of M?/ are really values of e?s?/h?. But e/h is a standard electrolytic constant. Hence it follows that in investigating the laws of (M’/)3, as in some of the communications referred to, we were really studying the law of s the distance between $ and b in the doublets which form the chemical bonds. The electric theory of molecular attraction leads thus to the simplest possible physical interpretation of the parameters of molecular force, and invests their laws with a more immediate interest. _ The best test to apply to the theory at this stage is to calculate the order of magnitude of s to see whether it is consistent with what we know of molecular sizes. The linear dimensions of molecules are of the order 10—® cm., and of electrons (Phil. Mag. [5| xlvii.) of the order 10—'4, and these are limits for the size of s. Let us take the simplest type of binary molecule such as NaCl, for which the tabulated value of (M2/)? (xxxix.) is 5°6, which is to be multiplied by 10° to give the value when the dyne is the unit of force. Now es/h=(M*l)? and h/e=345x10-", for Neti s= Pao x10. To determine the linear dimensions of the NaCl molecule we can proceed as for that of the Li atom in “ Ionization &.” (Phil. Mag. [6] ili. p. 176) where the radius of the Li atom is found from its ionic velocity in water to be 2x10-*. The volume of the Na atom is 7°4/2 times that of Li, and of Cl is 19/2 times (see Table III. of that paper), so that the mean radius of NaCl will be (26°4/2)* x 2 x 10-°=7°26 x 10-® cm. The diameter d of the NaCl molecule is thus found to be 1:45x 10-8. The fact that we have found s a little larger than d indicates that we have overshot the mark in reducing molecular attraction so that it operates between only imme- diate neighbours at their average distance apart. But from the nature of the case we can expect to obtain only the order of magnitude of s, which is about equal to that of molecular diameters. 3. Relation to Helmholtz’s Electric Theory of Chemical Valence. It is of great importance in chemical dynamics that we should be able to find accurately the ratio of s to d in order to push farther with Helmholtz’s theory that the chemical forces between atoms are identical with the forces between the electric charges constituting their valencies. Richarz ; j i] } Oe imi ae mie or le ED = f “Fe clube wae le Electrie Origin of Molecular Attraction. 637 (Wied. Ann. lii.), to test this theory in the simplest concrete way, treats the dissociation of N,O, into 2NOQ, and of I, into 21 as the performance of work e?/r against electric force for each molecule of N,O, or I, dissociated, 7 being the distance apart of the charges = and ) which hold the two parts of N,O, or I, together. Richarz, assuming 10°° to be the number of molecules in a c.c. of gas at 0° C. and 1 atmo, and 7 to be 10-5, finds for e a value agreeing with that derived from other sources. In order to make his results more definitely comparable with those of this paper, I will carry out his reckoning in the following manner :—ILet w be the mass of lec. of H, at 0° C. and 1 atmo, then the number of mole- cules ina c.c. of any gas under standard conditions is u/2h, and the work of dissociating such a c. c. of NO, is ee a a) Ede ie 2h rT 2 - r 2 i) Mo But if pis the density of the molecule m=47p7r°/3, taking 7 to be its radius, : ,_w(eVls ae aaa) M37P"> W = 25 x 10° ergs, ih 2; p=92/49 (Phil. Mag. [5] xxxix. p. 7). p= "0896 x 10-3, h/e=345 x 10-"". Su. P= MIO} cm, We have followed the method of Richarz in identifying 7, the distance apart of the charges, with the radius ot N,O,. Strictly, according to our reasoning, the electrical work per molecule eé*/7 ought to be written e?/s, and the previous reasoning would give us an equation for r*/s. But the im- portant point at present is that the distance apart of the electric charges forming chemical valencies in molecules is found to be of the same order of magnitude as molecular diameters both from the electric theory of molecular attrac- tion and from the simple cases to which Helmholtz’s electric theory of chemical forces has been applied. Of course Richarz’s simplifying assumptions require that when N,Q, is dissociated into 2NO, the mass of gas should consist of a mixture of NO, ions, namely 2NO, and pNO, evenly mixed and forming a conductor for any difference of potential. In the same way, when iodine is dissociated to the atomic state it ought to be a good conductor of electricity if Richarz’s calculation applies to it. Now J.J. ‘lhomson’s experiments on the passage of electricity through hot gases (Phil. Mag, [5| xxix.) proved that the specific conductivity of gaseous 638 . Mr. W. Sutherland on the iodine at about 1100° C. is about the same as that of glass at 300° C., and enormously less than that of ordinary electrolytic solutions. But the vapour-density measurements of Crafts and Meier show that at this temperature about a quarter of the I, is dissociated into 2I, and therefore if Richarz’s simplifying hypothesis were true for iodine the conductivity ought to have been found enormously greater by J.J. Thomson than it was. Until this difficulty with I, and the corre- sponding one with N,Q, has been cleared up, we do not know what becomes of the electric charges which Richarz assumes to be separated, and are therefore not entitled to write ¢/r or €?/s as the electrical work done in dissociating a molecule such as I, or N,O,. To account for the facts with iodine we shall have to assume a rearrangement of doublets rather than the splitting of them into separate electrons. Moreover, we have in Helmholtz’s theory to take account of changes in | the mutual potential energy of electrons and atoms in any ; change of relative positions caused by rearrangement of doublets. Therefore at present we must not attach too much importance to the agreement in order of magnitude . between ours and Richarz’s r as derived trom Helmholtz’s theory in a form which is the simplest possible and is appa- . rently too simple for the facts of nature. There is obviously room for immediate further experimental and theoretical work in this interesting department. ! ‘ ; ¥ 4 4. Period of Rotation of an Electric Doublet. If we carry out the Richarz simplification to one of its logical consequences we shall consider the two electrons of a molecule like NaCl, when giving the line spectrum of Na, to be revolving round one another with their relative path (perl'aps entirely in the Na atom) a circle of such size that centrifugal force and electric attraction are in equilibrium. Let 2 be the inertia of an electron, then where K is dielectric constant and N index of refraction for . NaCl (preferably perhaps for Na), and for the period of . revolution we have | Qmrs__ YarNs° ti U é rs ‘ with the values s of order 4x10-%, 2/e = 345 x 10-"~500 (J. J. Thomson), e of order 8 x 10-!, and N=1°5, this gives sy lla a el lama eile ae Electric Origin of Molecular Attraction. §39 a period 36x10-17%. It is worth noting that this period corresponds to a frequency 28 x 10"* which is about ten times as large as that of the visible part of the spectrum, and is nearly equal to the 33x10 which in “The Cause of the Structure of Spectra” (Phil. Mag. [6] ti. p. 273) was found to be the value of a fundamental spectral constant denoted by 1/A=VB, where V is the velocity of light in free ether and B the parameter in Balmer’s formula, which Rydberg assumes to be a constant of nature in his modified form of it, namely n=)—Bb/(m+p)?. We shall now resume the study of the Laws of Molecular Force in the light of the electron theory. 5. Electric Doublets tn different classes of Chemical Substances. Before considering in some little detail the laws of (M7J)3, which are those of s, for different chemical types, we must disenss the remarkable contrast shown (xxxv.) between the characteristic equations of element and compound gases. For the element gases H,, N,, O, and also for the compound CH, the equation of van der Waals represents the experi- mental facts down to nearly two-thirds of the critical volume. It can be written k l pe LueeCT EET) ioe i ° . e ° e ° (4) where the terms are respectively two thirds of the following, the virial of the pressure, the kinetic energy, the virial of the collisional forces, and the virial of the molecular attrac- tions. For compound gases in general the type is 2k l Wd eck ° ° e e ° (5) Ethylene was found to have an intermediate form of equation, and probably other substances could be investigated to show different stages of transition from (4) to (5). svidently (5) could be made more general by replacing & in each of the three places where it occurs by a different parameter, but, as in xxxv., we will continue to use it in its more convenient simple form. When we contrast the collisional virial term for element gases RIA/2(v—k/2) with RV2k/(v+hk) for compounds, we see that in the first case v is diminished hy k/2, and in the second v is increased by k. Now, according to the kinetic theory, the —//2 comes in because the mole- cular free path is shortened by an amount depending on the pvu=RT+RT 640 Mr. W. Sutherland on the molecular radius on account of the mutual impenetrability of molecules. According to the kinetic theory k/2 stands for 4 times the volume of the molecules which occupy v. Then in compounds we must regard the v+k, which comes in instead of volume minus 4 times the actual volume of the molecules, to represent a lengthening of the mean free path, that is to say a diminution of the number of collisions. In the case of compounds then a collision is an event which, instead of shortening the interval between two successive ones from what it would be if the molecules could penetrate one another, actually prolongs it, so as not only to neutralize the term (—4 times volume of molecules) but to add on &. In ethylene we meet with a transition case where the negative term is only neutralized, and the collisional virial is KTh/». In compounds in general then, a collision is an entanglement of the parts of the molecules which lasts long enough to produce an appreciable effect on the dynamics of the mole- cules, namely a diminution of the collisional virial below what it would be if the molecules collided like hard spheres. But in the present connexion the contrast between the virials of the attractive forces in element and compound gases is most important. From v= to v=k (nearly) in element gases it is —l/v, and in compounds —//(v+k). For volumes less than & the form for compounds is —J/2v. For com- pounds then we write the virial of the attractions l i! k vtk ov wutk and so see in it the general attractional virial —//v numeri- cally reduced because a repulsional virial, which is a fraction kj(w+k) of it, enters into the equation. When v=& the fraction takes the value 4, which it retains for smaller values of v, the virial then being —l/v+l/2v=—l/2v. Evidently then the entanglement during a collision of two compound molecules, which diminishes the virial of the collisional repulsive forces, introduces the virial (d/v){k/(v+k)} of repulsive forces of electrical origin. - We must briefly inquire into the probable cause of the contrast between the behaviour of element and compound gas-molecules during collision. In an element gas like H, we have # attached to H, and also pb attached to H, whereas in a compound gas like HCl 2 is associated only with H, and p with Cl. We can imagine then that in H, or H Ub it is possible for # and p to change places so as to form pH HZ without displacing the atoms, whereas in the case of HCl Electrie Origin of Molecular Attraction. 641 it is impossible to get the electrons to change places without the atoms doing so also. When NaCl is giving the spectrum of Na perhaps both $ and > are in Na. In a compound molecule, then, an electric doublet has less freedom of motion than in the molecule of an element gas. On this account the collision of molecules of an element gas is a simpler event than that of compounds. Moreover, in all compounds but the simple binary ones there are several doublets in each molecule, and during a collision a variety of possible com- binations of positions of the doublets will succeed one another, causing an alternation of attractions and repulsions, which leave a different average preponderance of attraction at close quarters than at a distance. Thus below volume & the preponderance of attraction is expressed by a virial —/l/2v, and above k by a virial —J/(v+k), which, when v is large, can be identified with the standard form —J/v. Now this contrast between the behaviour of compound and element gas-molecules at close quarters was verified in the Viscosity of Gases &. (xxxvi.), where it was found that at close quarters the mutual potential energy of two compound mole- cules is only half of what it would be if they behaved as the molecules of element gases. In this way I have sought to explain the most important difficulty in the way of the electric theory of molecular attraction, namely that the attractional virial for compounds appears in the form —l/(v+) instead of —J/v, which is required by the general theory. Previously (xxxv.) I sug- gested that this phenomenon in compounds might be due to the pairing of compound molecules. This explanation must be withdrawn to be replaced by that of molecular entangle- ment here suggested, an entanglement being only a temporary sort of pairing. 7 We proceed now with the investigation of the laws of s. In the case of the haloid compounds of the alkaii metals it was shown in “ Further Studies” (xxxix.) that to (M/)3, which is proportional to s, the metallic and halogen atoms contribute parts as follow : eee Na. Ke. RO Ca) BF. OF. Baez eik moo! 26 60 Tae: OF P29 i2e ere For the Li family these can be written 1-2 (2, 3, 4, 5, 6), and for the F family 0°9 (1, 2, 3, 4). With the haloid com- pounds of the dyad metals of the Be family, we must remember that (M*//2)? now consists of a part F, due to the halogen atom as given above, and a part F’,/2 due to the Phil. Mag. S. 6. Vol. 4. No. 24. Dec. 1902. 2U 642 Mr. W. Sutherland on the equivalent of metal, the latter having the values Be. Mg. Ca, Sr. Ba. 2°1 ad 3°2 a7 4°2 which can be written 0°53 (4, 5, 6, 7, 8). | These simple laws for s lead to the foltowing statement in regard to the Periodic Classification of the elements :—In successive columns the valency charges form the arithmetical progression e, 2e, 3e and so on, while in the successive rows the values contributed by atoms to s, which is the other com- ponent factor of electric moment, form arithmetical pro- gressions such as are exemplified above. In conjunction with these simple numerical relationships amongst the elements we must take the corresponding ones demonstrated in “ A New Periodic Property of the Elements” and “ The Cause of the Structure of Spectra” (Phil. Mag. [5] xxx. and [6] ii.). The volumes of the gramme-atom B of the alkali metals as given in “ Further Studies”’ are subject to a simple numerical law, being given by ; 2+ (n—1) n2°7=2°7{ (n—43)? +3} nearly ; where 2 has the values 1, 2, 3 and so on, as the following comparison shows ; i ON ae K. Rb. Cs. | Bfound... 20 74 186 364 | am | i cule. S33 2'C 74 18-2 34°4 56°0 . The volumes of the gramme-atom of the halogens in com- pounds run as 1, 2, 3,4. But in the Be family there is no such simple relation discoverable. Butin ‘“ Further Studies” it was shown that the following relations hold approximately between F and B, namely in the Li family F7=0-9B+4-4, and in the Be family F?/4=0°9B+3:0. From formule just given we see that for the Li family .a more accurate relation is | B=242'7 (F/1:2—1) (F/1:2—2). For the uncombined metals the following results are established by Tables XXIX. and XXX, of “ Further Studies.” First that (M/p)/M*J or B/M?l is the same for the members of one chemical family, and second that for families of different valency n the values of nB/M?l are nearly 2°8, except in the case of the Be family, for which it is 2:0. Thus, then, for the metals we have the relation that e*s* is proportional to the volume of the atom with which the doublet is associated. To assign a simple meaning to this © formula let us assume a doublet in a metallic-atom, and use ," ~ Electric-Origin of Molecular Attraction. 643. for it the formula we used in calculating the period of rotation of #7 in NaCl, namely, awe @ 1 so UNF? e*32 = N*v*s*, ~ Now 7 is constant; and if Nv is constant for the metals, then es? x s*; and if s is equal or proportional to the linear dimension of the atom, the remarkable proportionality between e*s? and volume of atom in the uncombined metals would be accounted for.. It would seem as though the $ andb ina metallic atom moved out till centrifugal force balanced elec- trical attraction, and so determined the linear dimensions of the atom. If we remember that N varies inversely as the velocity of light through the atom, the condition that-Nv is to be constant makes the ratio of v the linear velocity of = or b to that of light through the atom constant, a result already made probable in the 7th section of “The Cause of the Structure of Spectra.” On passing from the simple cases of metals and binary compounds, where we are dealing with only a few regularly arranged doublets in each molecule, to typical organic com- pounds where the atoms are built up to molecules by means of elaborate ramifications of doublets; we must expect to pass through intermediate types, where the simplicity of the binary compounds is lost without being replaced by the other sort of simplicity which we may expect on account of the law of averages coming into play in the complex organic compounds. We had better then study the case of the typical complex organic molecule first. We must expect the doublets in such a molecule to exercise a mutual directive action on one another, so that the whole molecule may be considered to have an electric moment obtained in the following way. It is known that with a uniformly magnetized sphere the external field of force is the same as that of a small magnet at its centre with a magnetic moment equal to the intensity of magnetization multiplied by the volume of the sphere. Therefore for a number of magnetic spheres of different sizes uniformly magnetized with the same intensity the mag- netic moment of each will be proportional to its volume. Now in a complex molecule we must on the average expect the doublets to arrange themselves so as to correspond as nearly as possible to the case of uniform magnetization. For the electric doublet I have already proposed the name neutron, so the proposal we are spas eee might be called that of an 2U 2 644 On the Electric Origin of Molecular Attraction. average uniform neutration in complex molecules or an ap- proximation to it. The electric moment of such a molecule must then be prcportional to its volume. But this is one of the main results obtained in “ Further Studies,” being ex- pressed as follows at the end of section 1:—‘“‘As a subsidiary result, it has been shown that the attracting powers of the atoms of Cl, Br, I, O, 8, N,.and C (C unattached to H) are approximately proportional to their volumes in the combined state.” In the complex organic molecule the different atoms and radicals contribute to the limiting volume of the gramme-mole- cule parts which are,on the average, 10 times the part which they contribute to (M%)?, 7 being the virial parameter ex- pressed for a gramme of the substance with 10” dynes as the unit of force. But the fundamental radical CH, hasa limiting volume whichis 19 times the part it contributes to (M7Jj?. On the other hand, the two terminal hydrogen atoms of the paraffin molecule C,H2,4+2 seem to possess a ratio 4 instead of 10. For the great majority of gaseous compounds such as CO,, SQ,, C.N,, and the simpler volatile liquids the ratio B/(M2/,? is nearly 10. For a few such substances the ratio is small; thus for H,O it is 6, for HS itis 7, and for NH, also 7. Itis worth noticing that these are substances pos- sessing remarkable powers of ionizing electrolytes. This power would thus seem to be due to a high intensity of neutration. In the case of electrolytes of the simplest binary type we have B/(M?l)? ranging from 3°3 for LiF to 73 for RbI. On the other hand, the element gases Ho, Oz, No, and the compound CH, have values for this ratio near 19. Now when dissolved in water these are not electrolytes ; and this fact would seem to be due to their small intensity of neutration. In these gases also the attractional virial is —//v, molecular entanglement during collision is slight. Obviously then intensity of neutration and the related magnitude of electric moment of doublets are important physical properties of substances, requiring detailed study. 6. Molecular Couples and Gyrostats. As to the couples which doublets like magnets exercise on one another, their chief action appears to be that of giving similarity of direction to the electric axes of neighbouring molecules. The question as to whether they may appear in a kinetic theory of solids will require special examination; but as molecular attraction in liquids is of the same order as in solids, and yet the rigidity of liquids is very small indeed, it i ) } } : : | } : | alee a ET Re om dig me oe Vibration of Ferromagnetic Wires ina Magnetizing Field. 645 would appear that molecular couples. do not enter directly into the molecular theory of rigidity. But the existence of similarly directed electric axes in neighbouring molecules is suggestive of the existence of similarly directed axes of rotation in neighbouring molecules; and this would bring in gyrostatic properties of molecules as an element in rigidity. In ““A Kinetic Theory of Solids” (Phil. Mag. [5] xxxii.) the ascription of independent kinetic energies in the directions of three rectangular axes amounts to the same thing as taking account of gyrostatic energy. ; ! It is obvious that a logical deduction from the above prin- ciples must be the formulation of a dynamic theory of dielectric capacity in which electric doublets and molecular gyrostatic properties will play the most important part, and also the systematic development of an electrical theory of thermochemistry on Helmbholtz’s lines. Melbourne, August 1902. LXXI. Note on the Vibration of Ferromagnetic Wires placed ina Varying Magnetizing Field. By K. Honpa and S. Suimizu*. T is well known that ferromagnetic bodies emit an audible sound at the moment of making and breaking the mag- netizing current. Page f first heard the sound in the magnet, when an electric current passed through a copper spiral placed between the poles of a horse-shoe magnet. The sound was more intense at the break than at the make. A similar phe- nomenon was also observed by Delezenne{t. Marrian§ placed iron and steel wires in a coil, and by making and breaking the magnetizing current, he heard a sound due to the longitudinal fundamental vibration of the wires. Matteucci || examined the effect of tension, and found that the pitch of the sound was independent of the tension, but that the intensity was decidedly increased. The investigation with iron bars of different lengths led Wertheim § to the conclusion that each bar vibrated in its fundamental mode. By passing an inter- mittent current through the magnetizing coil, he heard a continuous sound, the pitch of which was the same as that * Communicated by the Authors. + Page, Poge. Ann. vol. xliii. p. 411 (1838) ; Wiedemann’s Electricitat, vol. iii. p. 838, ft Delezenne, Pogg. Ann. vol. lxiii. p. 530 (1838). § Marrian, Phil Mag. vol. xxv. p. 382 (1844). || Matteucci, Archives, vol. v. p. 889 (1845). { Wertheim, Pogs. Ann, vol. Ixxvii. p. 43 (1848). 646 Messrs. K. Honda and 8. Shimizu on the Vibration of of the make or break of the current. The thickness of the bar had no effect on the pitch of the sound. Non-magnetic bodies gave no sound under similar conditions. He then concluded that the vibration of the wire was produced by the magnetic change of length. Beatson* noticed a sound produced in a stretched iron or steel wire carrying an inter- mittent current. De la Rive f tried, not only bars of iron and steel, but also those of lead, zinc, bismuth, tin, antimony, platinum, gold, and silver. He placed these bars between the poles of an electromagnet and passed an intermittent current through them. They all sounded, the ferromagnetic metals producing sound with only the intermittent current through them, although there was no magnetizing field acting. The experiments with fine powders of several metals and powdered coke gave similar results. He ascribed the phenomenon to some molecular transposition. Ferguson } and Ader § noticed similar phenomena with intermittent as well as alternate currents. Trowbridge || found that nickel and cobalt also produced sound under similar conditions. In studying the effect of tension and compression on the intensity of sound produced in iron and nickel bars, Bach- metjew J found that the effect was parallel to that of tension © on the magnetic change of length. He thus concluded that the intensity of the sound is a function of the change of length by magnetization. A short consideration of these results leads us to distinguish three kinds of the sound. The first is the combined effect of the magnetic force and the electric current. The sounds noticed by Page, Delezenne, and De la Rive belong to this category ; they do not depend upon the magnetic property of the substance, but on the mechanical action produced by the magnetic force and the current. | The second kind of sounds accompanies the magnetization or demagnetization of a magnetic substance in making or breaking a magnetizing current. The sounds noticed by Marrian and others belong to this category. The cause of * Beatson, Electr. Mag. April 1846; Arch. de Genéve, vol. ii. p. 118. t De la Rive, Phil. Trans. i. p: 39 (1847); Pogg. Ann. vol. lxxvi. p- 270; Arch. des Sc. phys. et nat. vol. xxv. p. 311 (1866); Poge. Ann, vol, cxxviil. p. 452; Ann. de chim. et de phys. [4} vol. viii. p. 8305 (1866). Lee Proc. Roy. Soc. Edinb, March 6, 1878; Bel. vol. iii, . 205. § Ader, Compt. Rend. vol. lxxxviii. p. 641 (1879); Bezbi. vol. iii. p. 642. || Trowbridge, Bezd?. vol. iii. p. 289 (1879) ; Proc. Amer. Acad. vol. xi. p- 114 (Dec. 1878). i agg at Exner’s Rep. vol. xxvi. p. 187 (1890); Bezbd. vol. xiv, pe Sih : Ferromagnetic Wires in a Magnetizing Field. 647 the sound is probably the change in length by magnetization. When a magnetic substance is suddenly magnetized or demagnetized it elongates or contracts, and attains its initial length, after several oscillatory changes in length have occurred in quick succession. This oscillation will produce a clinking note at the moment of magnetization or demag- netization. This view is favoured by the experiments of Marrian and Wertheim. But Matteucci found that the tension does not affect the pitch of the sound; if his result were true, the vibration would be of more complex nature. The third kind of sounds is one accompanying magnetiza- tion by an intermittent or alternate current of a definite frequency, or one produced when the above-mentioned current is passed directly through the substance. The sound is probably caused by the continuous series of vibrations above referred to. The experiments of Beatson and others will agree with this view. De la Rive and Wiedemann ascribe the phenomenon to the molecular effect, but Wertheim and Bachmetjew to the magnetic change in length. e also consider it highly probable that the change of length is the cause producing the sound belonging to the second and third categories. The present experiment was undertaken to get a clearer insight into the nature of the phenomenon. In all previous experiments, the range of the frequency of an intermittent or alternate current was very limited ; but in our case, a string alternator * was introduced for continuously varying the period of the current. The arrangement is shown in fig. 1. A copper wire is horizontally stretched ; Fig. 1. one of the ends is fixed to a support 8, while the other passing over the pulley Pis attached to a weight Q. The wire is electrically insulated at the centre R, so that the current through the two mercury cups m, and m, flows in the circuit C. The battery currents pass through the two mercury contacts M, and M;. ‘Lhe vibration of the string is * K, Honda and S. Shimizu, Amer. Journ. Sci. vol. x. p. 64 (1900) ; Phys. Zeitsch. 2 Jahrgang, vol. xxv. p. 371 (1901). 648 Messrs. K. Honda and §. Shimizu on the Vibration of maintained constantly oscillating by the electromagnet n ands. If the string is set in vibration with a single node at R, an alternate current is produced in the circuit C ; if only one set of batteries is used, an intermittent current is produced in the same circuit. The frequency of alternation or of inter- ruption can easily be varied by the change of length and of tension of the wire. ©, and C, are two condensers with suitable capacity to diminish the sparks at the mercury contacts M, and M,. For the study of the longitudinal vibration of a ferromag- netic wire under a varying field, we used Professor Nagaoka’s apparatus for the measurement of minute changes of length. In the present experiment, the glass fibre in the slit of the collimator was removed and the fine slit illuminated by a gas flame was used instead. ‘The image of the slit, after reflexion by the revolving mirror and refraction through a converging lens, was formed in the field of a micrometer ocular. If the wire makes a rapid longitudinal vibration, its amplitude can be measured by observing the broadening of the image of the slit. ‘ The wire to be tested was 21 cm. long and 0°150 em. thick. The magnetizing coil was 30 cm. long and wound in 4 layers on a wooden frame, and gave a field of 19°82 c.a.s. units due to a current of one ampere. The coefficient of self-induction of the whole circuit was 5-2x 10° c.¢.s. units and its re- sistance 12°90, so that the time of relaxation was 0°000403 second. The results of experiments may be summarized as follows :— (a) Wires of non-magnetic metals give no sound by an intermittent or alternate field of any frequency up to 200 per second. (6) A ferromagnetic wire emits an audible sound in an intermittent or alternate field. (c) The pitch of the sound is always the same as that of an intermittent or alternate current. | (d) The amplitude of vibration is in general far greater than the change of length produced by a steady field of such strength that it is equal to the maximum value of the intermittent or alternate field. The pitch of the sound was determined by tuning a mono- chord to the period of the current and counting the number of beats. From the results above mentioned, we may safely conclude that the sound emitted by the ferromagnetics is due to the magnetic change in length of the wire. One make or break of the current forces the wire to accomplish a vibration, and a succession of such series constitutes a sound, the pitch Ferromagnetic Wires in a Magnetizing Field. 649 of which is the same as that of the make and break. If this view be true, the pitch of the sound due to an alternate current must be double that of the sound due to an inter- mittent current for the same number of vibrations of the string alternator, because the magnetic change of length is independent of the direction of the field. By an actual experiment analogous to that of Lissajous, we found this inference to be verified. Our experiments also showed that the magnetic change of length occurs so quickly as to follow a rapid change of magnetization of as much as 150 reversals per second. If the frequency be kept constant, the relation between the ‘amplitude of vibration and the maximum field during one complete period of vibration is similar to the relation of the ‘change in length to a steady field. The maximum field used in most of our experiments was 30°3 C.G.8. units. It is also to be observed that if an intermittent or alternate current is passed through a spiral of non-magnetic metals, an audible sound is produced. ‘This is perhaps due to the periodic attraction of the currents flowing through the spiral in the same direction, and is of a quite different nature from the sound just mentioned. Gradually varying the frequency of the intermittent or alternate current while the range of the field is kept constant, we observed the singular phenomenon that the amplitude of vibration passed through several maxima and minima. Two marked maxima and minima were observed in the case of a nickel wire. The phenomenon, which was principally due to the longitudinal vibration of the wire, was, to a certain extent, modified by the resonance of the system consisting of a reflecting mirror and two springs attached to it, and to the periodic vibration of the wire due to the magnetic change of length. The position of the maxima and minima were not, however, materially changed by the length of the wire or the tension of the springs. In the case of iron, the magnetic change of length for the same field strength was small, so that the phenomenon was not marked. To study the phenomenon specially, we used another arrangement ; the apparatus was the same as that used for the measurement of the magnetic change in length under constant tension. The wire to be tested was about 60 cm. ‘long and 0°05 em. thick ; to the extremities of the wire, two copper wires of nearly the same thickness were soldered. It was hung vertically in the axial line of a magnetizing coil 80 cm. long, so as to lie nearly in a uniform field, and to its lower end was attached a weight. Near the same end, a 650 Messrs. K. Honda and S. Shimizu on the Vilowien of thin rotating cylinder carrying a reflecting mirror was placed horizontally, and came in contact with the vertical wire at a suitable pressure. The working of the arrangement was the same as in the case above referred to. The magnetizing coil was wound in 4 layers, and gave a field of 26°0 c.c.s. units due to a current of one ampere. The coefficient of self-induction of the whole circuit was 1°66 x 10’ c.a.s. units and its resistance 18:2 0, so that the time of relaxation was 000091 second. With the above arrangement, we also found two marked maxima in the amplitude of vibration for iron as well as for nickel. The amplitude of vibration is plotted against the frequency of the current in figs. 2 and 3. In both cases, the Fig. 2.—Iron Wire. Length 59°6 cm.; Diam. 0:0405 em. [AHA PER Ci.) 60 100 140 (FREOvENEY) Fig. 8.—Nickel Wire. Length 60°3 cm.; Diam, 0:0396. 140 (emeqvuency) maximum field during one complete period of vibration was 28°5 C.G.S. units, and the weight attached to the lower end of the wire was reduced to the tension per square millimetre. As will be seen from the figures, the amplitude of vibration and the frequency corresponding to the maximum amplitude Ferromagnetic Wires in a Magnetizing Field. 651 increase with tension. By altering the length of the ferro- magnetic wire, the positions of the maxima and minima are imperceptibly affected. These positions of the maxima and minima do not coincide with those in the former experiment, the first maximum occurring ata little higher frequency, and the second at a considerably lower frequency. ‘The first maximum is also of a frequency higher by at least 2°5 times than that calculated on the consideration that the phenomenon is due simply to the elastic vibration of the wire. Instead of attaching a weight to the free end of the wire, the same end was stretched by means of a spiral spring fixed to the stand. Varying the frequency of the intermittent or alternate current, the maxima and minima of the amplitude of vibration were also observed, as shown in figs. 4 and 9. Fig. 4.—Iron Wire. ee, 00 150 50 ! In this case, the first maximum occurred at a frequency of about 75 per second for iron as well as for nickel, and the second at a frequency higher than 160 per second for these 652 Prof. J. Patterson on the Electrical two metals. These positions of maxima and minima were almost independent of the tension and of the length of the spring. Whether these complicated phenomena are capable of being explained simply by the elastic vibration and the magnetic change in length without taking account of the time lag, or whether they prove the existence of the time effect, requires further experimental and theoretical consideration. Our best thanks are due to Professor Nagaoka and also to Professor A. Tanakadate for their kind guidance in carrying out the present experiment. LXXII. On the Electrical Properties of Thin Metal Films. By J. Parrerson, B.A., Professor of Physics, Muir Central College, Allahabad, labor ; 1851 Exhibition Stienee Scholar, Emmanuel College, Cambridge *. Introduction. HIS investigation was suggested by Longden’s Tf experi- ments on the electrical resistance of thin films deposited in vacuo by the cathode discharge. From his experiments he arrived at the following conclusions :— I. It was probable that the product of the resistance and the thickness of the film was not constant, but increased very rapidly with the decrease in thickness. II, The temperature-coefficient of very thin platinum films was negative and within a certain range zero or negligible. ILL. The effect of artificial ageing on the film was propor- tional to the magnitude of the temperature-coefficient. Miss Stone t had previously made some experiments on silver films deposited by the “‘ Rochelle salt process,” and had arrived at the conclusions: That the resistance of very thin films was much greater than the calculated resistance, and - that heat decreased the resistance of the films, the rate of decrease being much greater for the thin films than thick ones. _ Vincent § quite recently has made very careful experiments on the relation between resistance and thickness of silver films deposited from a silver solution. He found that the conductivity varied as the thickness down to 5x 10-° cm., and below this thickness the conductivity decreased very rapidly. * Communicated by Prof. J. J. Thomson. + Physical Review, vol. xi. p. 40 (1900). t Ibid. vol. vi. p. 1 (1898). § Annales de Chemie et de Physique, |7] xix. p. 421 (1900). —-= - wf 4 Properties of Thin Metal Films. 653 Prof. Thomson* has shown that this variation of the re- sistance with the thickness may be explained by the cor- puscular theory of electric conduction in metals. According to this theory the current is carried by negatively charged particles moving with a definite velocity under an applied H.M.F. These particles have the properties of a perfect gas, consequently they have a mean free path. When this mean free path becomes comparable with the thickness of the film it will be decreased, and consequently the resistance of the film will be increased. (This theory will be discussed more fully later.) If, then, the point at which the resistance of the film becomes abnormal can be obtained, this thickness would be an approximate value for A the mean free path. The mean free path of the corpuscles in a number of metals has been determined by the author (Phil. Mag. June 1902) by measuring the change of resistance in the metal, produced by a transverse magnetic field. It was hoped that the present investigation would furnish another and entirely different method of determining the mean free path. Description of Apparatus. The metallic films, which will be called simply films through- out the paper, were obtained by sputtering from a cathode in vacuo on glass strips. ‘These strips were of ordinary glass about 1 mm. thick, 12 mm. wide, and from 4 to 7 em. long. -To ensure good contact between the electrodes and the film the ends of the strips were silvered for about 1 cm. with one of the ordinary silvering solutions. Owing to the surface- tension of the silvering solution the thickness of the silver deposit gradually increased from zero up to its full value. This ensured good contact between the silver and the film. The surface-tension also made the line of contact between the film and the silver curve at the edges, and thus made it difficult to measure the length accurately. This defect was overcome in the later experiments by cutting glass plates about 4 cm. wide and 20 cm. long. The sides were silvered as before, and then the plate was cut into strips of the desired width. Fig. 1 (p. 650) shows the plate with the sides silvered, and the dotted lines denote where it was cut. The two end pieces were rejected, and the others were all of a uniform length and the line of contact between film and silver was * Proc. Camb. Phil. Soc. vol. xi. pt 2, p. 119 (1901). 654 Prof. J. Patterson on the Electrical straight. Before the film was deposited on the glass the silvered ends were carefully polished, Fig. 1. The apparatus used in depositing the films is shown in fig. 2. B consisted of a number of pieces of plate glass of such a height that the glass strip D, which rested on them, was at the proper distance from the cathode. C is a piece of optical glass so adjusted that its surface is in the same plane as that of D, while E is a cover-glass which could be shaken off when the proper conditions were obtained. The cathode was held in a horizontal position by means of the small rod G, which fitted tightly into the brass tube H. All the joints marked F were made air-tight with sealing-wax and were very satisfactory. The glass strips were put in and taken out by removing the base plate. The apparatus was connected to the pump and drying-bulb with compression tubing. This enabled the cover-glass E to be shaken off by tilting the jar. The discharge was produced by an induction-coil with an Apps’ interrupter. The jar was exhausted until the strip was in the negative glow and about 2 mm. from the Crookes’s dark space. The discharge was then allowed to pass for some time and the exhaustion continued until the vacuum became constant. The cover-glass was then shaken off and the film deposited. It usually required from one to two hours to exhaust the bell-jar and deposit the film. The distance of the glass strip from the cathode was usually about 15 or 20mm. ‘This seemed to be the most satisfactory distance, for if greater than this it was difficult to keep the vacuum constant long enough to deposit the film without a great loss of time in letting the discharge pass and exhausting , 655 Properties of Thin Metal Films. | until the vacuum became steady, and then no better results. less than 15 mm. the vacuum was not carried far enough to produce the best results. v If the distance was were obtained. LL ahh hehehe LOTTI. Ue Lh hhh dL 2, E “ ?, < —» To pump g A 4 4 Y A 5 4 sg g ) A OY 4 yj 4 g s g Y g 4 4 A Oo A 4 4 HY ny ies y 5 4 HY Y g 4 y) g y 4 ‘, -. 3 y Mie ; a = IY & WY Yy ] Y S a a N Yj BB ’?'$»vRFB’”»"oh SS Z Y DW A ve ; 656 Prof. J. Patterson on the Electrical Method of Measuring the Thickness of the Film. To determine the specific resistance of the films it was necessary to measure both their resistance and thickness as accurately as possible. As the films were too thin for their thickness to be determined by weighing, Wiener’s * inter- ference method was used. In determining the thickness by this method, the best optical glass had to be used to obtain any accuracy, and, moreover, in measuring the thickness the films had to be spoiled for measurements of resistance, be- sides, putting electrodes on the optical glass would spoil it, hence it was necessary to make two films at the same time, one on the optical glass C (fig. 2) for measuring the thick- ness, and the other on the glass strip D (fig. 2) for the resistance. Since the cathode was at least 6 cm. in diameter, and as the glass strip and optical glass when placed side by side formed a square 25 mm. to a side, and were placed as nearly central as possible, it was assumed that the deposit was uniform over these surfaces. This was tested by depositing films on two pieces of glass and measuring their resistance. The results agreed closely enough to warrant the assumption. The optical glass was about 25 mm. long and 12°5 mm. wide. A strip of very thin mica about 4 mm. wide was placed over the optical g!ass, as shown in fig. 3. This pre- vented the film from depositing on that portion of the glass. Fig. 3. _2 Mica strip When the films were deposited they were taken out of the bell-jar, and the optical glass was then replaced without the mica strip and another film deposited on it. By this means a metallic surface was obtained over the whole surface of the glass (fig. 4), and the part A was thicker than the part B by the thickness of the first film. The metallic surface also ensured that the change of phase of the reflected light would be the same at both parts A and B. A piece of optically plane parallel glass was placed over the metallic surface and *® Wied. Ann. xxxi. p. 629. co os apa aS ee Rene 4 aes Ay os 2 ee a Properties of Thin Metal Films. 657 fastened with a little soft wax at the edges. When a beam of parallel white light was allowed to fall on this, inter fer ence- ae 4. LLL gig litpilplisih LL LLLLILILL DDLELIT OT ETE Eee. YA bands were produced by the thin air-film between the two dlates. As the air-film in one part was thicker than in the other by the thickness of the first film deposited, two sets of inter- ference-bands were produced, one of which was displaced relatively to the other. By measuring the width of each band in the one set and the displacement of the corresponding band in the other set the thickness of the metallic film could be obtained. If D (fig. 5) is the thickness of the thinner Fig. 5. Yf YY ELLER air-flm and D+d the thickness of the other, and A2, An+1, Nm; m+1, the wave-lengths extinguished by interference re- spectively in the thicker and thinner of the adjacent air-films, the indices of the d’s giving the order of the bands, then we have 2(D+d)=nd,=n+ 1 Anyi =ke. 2D =m np=mt IN nai = &e., or from the three following equations which correspond to three interference-bands, 2(D+d)=nnr, —n+l Aet-15 2D=nNn,, from which we have At) ll AECRE aa aM teie , dai rages Stew lahatys SRE Oar tc ID (1) Phil. Mag. 8. 6. Vol. 4. No. 24. Dec. 1902. 2X 658 Prof. J. Patterson on the Hlectrical That is, the number of band-widths 2, is a towards , which the red end of the spectrum, gives a multiple Rae is the thickness required. The displacement of one set of bands ae to the other was measured with the spectrometer. The optical glass was placed in front of the slit of the collimator (fig. 6). Fig. 6. The line of junction of the two lamin was placed so as to be perpendicular to the slit. The light from a Welsbach entered the collimator through an opening A, and part of it was reflected by the glass mirror C through the collimator-slit, and fell at perpendicular inci- dence on the air-film. It was then reflected back through the collimator and glass prism D and viewed by the telescope EK. Two sets of dark bands were thus obtained in the spec- trum, one of which was displaced relatively to the other. By measuring the angular width of each band and the displace- ment of the corresponding band in the other set, the thickness of the metallic film was obtained from formula 1. The spectrometer was calibrated by means of known lines and a curve was drawn connecting wave-lengths and the angles of Fig. 7. EEE. ts VALLI LLL fu VIM. the graduated circle. From this curve the wave-length corre- sponding to any angle could be obtained. The chief difficulty i in measuring the thickness arose from the indefiniteness of the dark bands. By depositing a very thin film of metal on the cover-glass so that the interference- in tet Sel. See? ron Properties of Thin Metal Films. 659 bands were obtained from the arrangement shown in fig. 7, the phase of the light was changed so that, instead of dark bands on a bright background, there were bright bands on a dark background. This gave greater distinctness to the spectrum, and enabled one to measure the thickness with greater accuracy. An example is given in Table I. of a set TABLE I.—Determination of the Thickness of a Film. Vernier readings. t, Fraction of | Wave- Thickness wave-length length of film First set of | Displaced displaced. in py. in em. bands. position. (e) if ie) i bl 53 31 48 ol iT al, 12 5/72 4960 3°44 10—6 30 48 30 44 5/58 5220 4:50 30 23 30 19 4/50 5490 4°39 29 57 29 54 4/52 5800 4:46 29 36 29 33 3/42 6090 4°35 2 AZ oe 3/48 6520 4:08 32 12 32 06 | 31 38 31 32°5 6/68 4800 4-22 al 10 31 06 55/56 5020 4-93 30 44 30 40 4 52 5260 4:05 30 19 30 15°5 4 50 | 5540 4°43 29 56 29 d3 35/46 5820 4°43 29 369 3/39 | 6080 = 60 Mean of 12 readings............ 4:33 10—6. of readings taken to determine the thickness of a film. Not all the measurements of the thickness of the films were as good as this. The greatest error occurred in the very thin films as the displacement was so small that it was exceedingly difficult to measure it. It was impossible to measure less than 2 x 10-® em. by this method. Measurement of Resistance. The resistance was measured with a standard Wheatstone bridge. The resistance of the silvered ends was neglected as it was negligible compared with the resistance of the film itself. The length of the film between the silvered ends was measured with a cathetometer. Several methods of fastening electrodes to the silvered ends were tried. One method was to wind fine copper wire around the silvered end and then deposit 2X 2 660 Prof. J. Patterson on the Electrical copper electrolytically on the silver and copper wire to ensure good contact. This precaution was found to be unnecessary unless the films were to be heated or coated with paraffin. The electrodes represented in figs. 8 and 9 were also used. Fig. 8. Fig. 9. Longitudinal Section. time of deposit. 203 186 140 170 163 179 236 234 176 664 Prof. J. Patterson on the Electmeal resistance of both measured. These films are marked with the suffixes A and B. The greatest difference between the resistance of two films deposited at the same time occurs in 3) A and 35 B, where the difference amounts to 11 per cent. The least difference occurs in 34 A and 34 B, and amounts to 2 per cent. The films are, moreover, very thin, so that the agreement is fairly close. If the specific resistance of the films is constant and the rate of deposition constant, then the resistance per cm. square multiplied by the time of deposit is a constant, and the thick- ness is directly proportional to the time of deposit. As will be seen from the last column in Table V. the product of the resistance per cm. square and the time of deposit varies very much for the thicker films. In the case of the thinner films or those deposited in a minute or less the product is too great to be accounted for by variations in the conditions, but it would seem to be due to a change in the specific resistance. There was no attempt to keep the conditions constant when depositing the film, so that the variation of the product of resistance multiplic ‘d by time of deposit for the thicker films was probably due to changes in the induction-coil, and, moreover, the films were not. deposited in succession, so that this would also make a difference. To obtain a rough approximation of the thickness of the films, which were too thin to be measured by Wiener’s method, the average value of the rate of deposit per minute of the films whose thickness could be measured was taken, and the thickness of the others calculated from that and the time of deposit. The values of the thickness of all the films not marked with an asterisk were calculated on the above assumption. The above results would indicate that the specific resistance is fairly constant for all thicknesses above 10~® ecm., and helow this value the specific resistance changes very rapidly. Another set of platinum films was made, and this time the vonditions were kept as constant as possible. A new cathode 6 cm. in diameter of rolled platinum 1/10 mm. thick was used. The induction-coil, which gave a 6-inch spark, was adjusted to run very steadily. The films were deposited in succession, and the depositing apparatus was never taken off the pump for a longer period than was necessary to change the glass strips. It usually required about one hour to make a film. After the film was removed from the bell-jar in which it was made, it was put into a glass tube and protected from the air and dust. Four films thick enough to be 665 measured by the interference method were made and their thicknesses measured. After the films were all made they were put into a glass vessel. This vessel was exhausted as far as possible and dried ; it was then sealed off and heated for seventy-three hours to a temperature of 110° C. All the films were thus treated exactly alike. The resistance of the films was not measured before ageing in order that they might be handled as little as possible. The values obtained for this set of films are given in Table VI. Properties of Thin Metal Films. TABLE VIJ.— Resistance of Platinum Films. | | | Dimensions of Film in em. | Resistance R E ! | Time of | ae aa ae | deposit | After | per em. | times Length. | Breadth. Thickness. —- ss ee eo |" eu time of | (Shours square. | J 796 | deposit. | to110°C. | 66 | 132 | 1:16 1592x10-6| 10 | 1658 1457/ 86 | 146 757) 132 | 118 |492 Fh DD24 |. 18°09}, 89 | 286 69*| 117 | 116 (295 ,, 5 96605, 2639 | 79 || 132 80*| 1:47 116 (249, 4 3434 | 27:09; 68 | 108 mee ise 1-15 1215, 31 | 3969! 3459] 74 | 121 64 | 1:50 HIS 0-85." 3 5519 | 4231 | 78 127 76 | 1:34 Ph 19-69... 23 50-71 | 45°41 | 77 125 68 | 118 | 116 |153 24 | 5357, 5266] 81 132 72 | 1:19 gt OT | 22 5849 5750} 79 129 65 | 1-41 IO 11-99 -,, 2 T1-72| GObS) | 74") Wee mp too) 114 |108_—C=é, 12 |) 765: | GOON IG ee 71 Py? 1-16 |O9! , 14 88:85 8808) 80 132 mee 4G att 10-77, 13 | 1285 | 97°69} 75 122 67 | 138 | 112 {062 _,, 1 1022 8294] 51 83 7) i151 | 1-14 |046 ~~, 3. | 32907 | 2401 | 111 182 81 | 148 | 107 [038 ,, | 374s8ec.| 5648 | 4083 | 155 255 70 | 118 | 11s jo31 ” | 30 ., | 5793 | 5793 | 179 | 290 Seer 118 | 105 (026 ,, | 25 13325 {11856 | 308 | 494 79 | 1-43 | 109 021 ~ |20 7/3409 |25984 | 546 | 866 The films are numbered in the order in which they were made. As far as possible a thick and a thin film were made alternately. The films whose thicknesses were measured directly are . marked with an asterisk. It will be seen from Table VI. that with the exception of the very thin films the resistance per sq. em. multiplied by the time of deposit is fairly constant. No. 67, however, seems to be a very marked exception to the above, but as the time of deposit is the only means of knowing the thickness, it may be that the film was deposited in 13 min. instead of 666 ~ Prof. J. Patterson on the Electrical 1 min., in which case the result would be in agreement with the others. It was impossible to make another film without making a complete set. The average rate of deposi- tion of the four films whose thickness was measured directly is 0612 10-6 cm. per min. The thickness of all the other films was obtained by multiplying 6°612 x 10-® cm. by the time of deposit. In fig. 10 time multiplied by resistance per cm. square is plotted against the time of deposit, and in fig. 11 the specific Fig. 10. Lage tn I 2 10 MIN, Phe OF DEPO . 600- 400 an 200 (8) 9 ae 27 63x10™ OM, resistance for a given ieee La ae thickness. These results confirm those previously obtained ; that the specific resistance remains constant down to a thickness of less than 10-® em., and that the specific resistance becomes abnormal between T: 7 and 46x 10-7 cm. Below this thick- ness the increase of resistance ae decrease in thickness is very rapid. The effect of heating the films by an electric current was also tried. The current from an’ 8-volt cell was passed through a film 4°38 x 10-6 em. thick, and having an initial resistance of 26°72 ohms per cm. square. After heating the ie eee ee ee Properties of Thin Metal Films. 667 film for some time by the above means the resistance was reduced to 12-06 chms per em. square. The resistanee was not further reduced by heating with the current. Glass, however, would not stand the temperature to which the films were raised, so mica was used instead. The films deposited on mica were heated zn vacuo by the electric current. They were found to stand a current-density from 1:0 to 2°0 x 10° amperes for a few minutes, and then only when the current was gradually increased. Putting the full current on at once destroyed the films instantly. ‘Two films were deposited on mica with resistances of 15°80 and 20°24 ohms respectively. They were heated in vacuo by the electric current, and the following results were obtained :— 1 ampere for 8 hours reduced resistance of 1st from 15-80 to 5°18 ohms. l-2amperes ,, 20 ,, more, resistance became 14°89 ohms. O-4ampere ,, 8 ,, reduced resistance of 2nd from 20°24 to 15:77 ohms. ; as ,, 20 ,, more, resistance became 8°88 ohms. Po) » 24 5 ” ” » 898 ,» The first film had a resistance of 1:79 ohms per cm. square when it was least, and the second 2°62 ohms per em. square. The thickness of these films was not measured, but the specific resistance would be about 30 x 10-® ohms per cm. cube. These results show that the final specific resistance of the films depends on the treatment that they receive. It was impossible to reduce the resistance of the films to that for ordinary platinum. ' These results also show that heating the films with the electric current has a much greater effect than heating in an air-bath. ‘Lhis is most likely due to the higher temperature to which the films are raised in the former case. The temperature-coefficient of a number of the films was also measured. ‘They were heated in an air-bath to about 50° C. or cooled down to 0° C., the temperature of the room being about 15°C. The temperature-coefiicients for a number of the films are recorded in Table VII. Taste VIl.—Temperature-Coefficient of Platinum Films. 2598-4 | 000011 | Number of Thickness in | Resistance per | Temperature- | | film. cm. cm. square. | coefficient. / Z / 66 5°92 10 14:57 / 000049 64 i-Sin'2 5, 42°31 | 0 0005 77 0°46 _,, 242°1 ) 000033 81 OSS x 408°3 | 000024 82 026. ,, 1185-5 | 000027 79 (PEE: | 668 Prof. J. Patterson on the Electrical Longden* found that films having a resistance of 53 ohms per cm. square had a temperatur e-coefticient of —0-0003. This is somewhat smaller than those obtained for films of about the same resistance. In the above table all the co- efficients are positive and too large to be negligible. Longden found, however, that for resistances from about 670 to 14000 ohms per cm. square the temperature-coefticients were negli- . gible or zero, and above this they were negative. Moreover, he found that the artificial ageing of the films depended very much on the temperature-coefficient, and that if the tempe- rature-coefficient was negligible there was very little if any artificial ageing required. From Table V. it will be seen that in the experiments described in this paper, there was a very great decrease in the resistance of the films on heating, and that the greatest decrease occurred in those films which came within the limits of Longden’s results, for no tempera- ture-coefficient and no ageing. Longden used the Wehnelt interrupter on his induction-coil, and it may be that the rapidity with which the films are deposited has a very marked effect on the results. It is more probable, however, that the different results are dué to different degrees of purity of the cathode. It is well known that a very small amount of impurity has a very marked effect on the resistance of plati- num and the temperature-coefficient. Owing to the exceed- ingly small quantity of metal in the films a very small amount of impurity in it could cause all the difference. Besides, the rate at which the impurity is disintegrated from the cathode may be very much greater than for the platinum itself (Recent Researches), and consequently the amount of im- purity in the film would be greater than that in the cathode. Resistance of Silver Films. The silver from which the films were deposited was not chemically pure although the amount of impurity in it was very small. Silver deposits very rapidly in the cathode discharge so ~ that it was very difficult to get a film. The films were often crystalline in appearance or powdery so that they rubbed off the glass ; this was especially true of the thicker films. By letting the induction-coil run very lightly so that the deposit was slow very good films were obtained. The depositing apparatus was exhausted until the dark space was about half way between the cathode and the glass strip. This degree of exhaustion was found to be better for the silver films than exhausting until the dark space just reached the glass strip. * Physical Review, vol. xi. p. 84 (1900). ~ - 7 —s — one nae, - — ————— SE A te om Se, ali RO ae ee apnea Properties of Thn Metal Films. A few films were made and their thickness and resistance measured. They were then heated in vacuo for ninety hours toa temperature of 90° C., and their resistance again measured. The results obtained are given in Table VIII. 669 TaBLE VIIJ.—Resistance of cree Films. | Dimensions of film in em. Resistance | | i fee ee ay wo. f mld i = HOE J iyo 8413 a pate Sie F2hs 4 Z. a a: -| | After | per cm. No. of | Dinad Thick- | Before | heating | percm.| cube | film. Sea ness. | beating. | 90 hours | square. | x 10°. | to 90° C.| 8 | 138 | 107 |57210-6 2339 | 1561 | 1210 | 69 88 189 | 104. | 5°7510-6 3080 | 2:538 13974 | 62 86 | 145 | 106 |89210—-6 2-588 | 1-892 | 1383 (|, (12-0 84 A ee Ae Onc ce i 852 1-410 | 0-791 The specific resistance of film No. 86 appears considerably greater than that for the other films, but this was most pro- bably due to the crystalline structure of the film which was lacking in the others. It will be seen from Table VIII. that heating has a considerable effect on the resistance of the films, although probably not so muchas in the case of platinum. F an No. 85 was heated zn vacuo by the electric current for 43 hours with 0:5 ampere, and then for 2 hours with 0°75 ampere, when the resistance became 2°068 ohms. In this case the electric current increased the resistance instead of diminishing it. These results are sufficient to show that in silver, as well as in platinum and bismuth, the specific resistance is much greater than for silver in bulk, and consequently these experiments were not pursued further. Some thick silver films were also made by depositing the silver from the solution known as Common’s silvering solution™, . The films were thoroughly dried and their resistances measured. They were then heated, one zm vacuo by the electric current, and the other in a hot-air bath, while the third was left exposed totheair. Table LX. (p. 670) exhibits the effect of heat on these films. The resistances were measured at the temperature of the room, and a slight change in that would account for the small difference obtained in the second case. It would seem from * Proc, R. I. vol. xiii. (1890-92). 670 Prof. J. Patterson on the Electrical TABLE | X.—Resistance of Silver Films. | Resistance of Resistance | Treatment of film. film. per emi. square. - Initial resistanee of No. 1.................. 0°3766 0157 Heated zm vacuo 30 hours to 85° C 0°3875 INO; 2 initial wesistamGer: 5 -sicxccnee ssc cose 0°2533 es 4 days without being heated ...... 0°2530 01163 No: BS amitial resistamGeres) woiat.cesess sells . 0:2828 0°1169 Heated in vacuo with electric current for 43 hours with 0'5 ampere, and 2 | 0'3240 hours with 0'7 ampere «..;........... the first two that heating had very little effect on the resistance except that it increased the resistance when heated by the electric current. The thickness of these films was also measured roughly, and showed that their specific resistance would be the same as that obtained by Vincent*, namely, 2°4 x 10—* ohms per cm. cube. These experiments were not pursued further. The Change of Resistance of the Films produced by a Magnetic Freld. The change of resistance produced by a magnetic field on a few films was also measured. ‘The apparatus was the same as that used by the author f in the experiments on the change of the electrical resistance of metals when placed in a mag- netic field. The method is briefly as follows :—Three other resistances nearly equal to the resistance of the film were made, and the four connected in the form of the Wheat- stone-bridge. The bridge was balanced by placing one of the arms in multiple are “with a variable resistance. A ver sensitive D’Arsonval galvanometer was used. ‘The films of bismuth and platinum were made by sputtering from the cathode in vacuo, while the silver films were deposited chemically from Common’s silvering solution. The resistance of the silver films was increased by slotting them. as shown in fig. 12. The platinum films were heated in vacuo until their resistance became constant. They were treated exactly like the films whose resistances were measured. Their thickness was not measured, but they were thick films. The results for the * Annales de Chimie et de pe [7] tome xix. p. 494 (1900). a mae Mag. June 1902. Properties of Thin Metal Films. 671 bismuth films were given in a note communicated to the Cambridge Philosophical Society*, and are given here for completeness. The results are given in Table X. Fig, 12. JQ TaBLE X.—Change of Resistance in Magnetic Field. Thickness Film. cae Resistance. ed = if dis | 1 a ae lial A SH, ay oar | Bismuth ...| 1x10—-5 58-04 26200 27-0 27300 31-0 6x 10—6 103-05 26200 53 27300 59 4x 10—6 968°7 26200 1-0 Platinum ... es vt 24400 0:35 | Bee ks ie i 24400 10 | Comparing these results with thore obtained by the authort for the change of resistance produced by the magnetic field, it will be seen that in platinum and silver the values are slightly greater for the metal than for the film, but they are of the same order in both cases. In bismuth films, however, the change is very small compared with the change in the metal, and the magnitude of the change decreases very rapidiy with the decrease of thickness. Contact-Dijference of Potential. The contact-difference of potential between the film and the cathode from which it was deposited was measured. The film and cathode were each connected to one pair of quadrants of a quadrant electrometer. Ali connecting wires were care- fully screened with conductors connected to earth. The film and cathode were placed about 1 cm. apart, and the air between the plates ionized by Réntgen rays. The electrodes took up the potential-difference in a few seconds, but the rays were left on until the electrometer remained steady. Using the bismuth cathode and a film deposited from it, a contact-differ- ence of potential of 0°034 volt was obtained, the film being * Proc. Camb. Phil. Soc. vol. xi. pt. 2, p. 117. + Phil. Mag. June 1902. 672 Prof. J. Patterson on the Electrical positive to the cathode. In platinum, however, the results varied considerably. The cathode, after being used for some time, was tested against a freshly deposited film and gave a difference of 0-047 volt, the film being positive to the cathode. After carefully polishing the cathode and depositing some more films from it, these were tested against the cathode, and a difference of 0°15 volt was obtained, but this time the cathode was positive to the film. The cathode and film were next put in a weak solution of platinic chloride, and they then gave a difference of 0:09 volt, the cathode being positive to the film. The film, which was at first positive to the cathode, was again tested about a month afterwards with the freshly polished cathode, and this time it was negative to the cathode and gave a difference of 9°015 volt. Photo-Electric Effect and Radiation from Hot Films. Hixperiments were made to see whether there was any difference between the rate at which the cathode and the film deposited from it discharged electricity under the influence of ultra-violet light, but no difference was detected. Experiments were also made to see whether it was possible to get negative radiation from hot platinum films zn vacuo. The films were deposited on mica and electrodes clamped on the ends. The film was heated by a steady current from a number of accumulators which were insulated. The film was charged to a known potential. The leak was observed between the film and an insulated electrode which was placed above it. The electrode was connected to one pair of quadrants of a quadrant-electrometer, the other pair being earthed. It was not possible to heat the film hot enough to get the negative radiation, but the positive radiation was obtained. The positive leak increased very rapidly with the increase of current through the film, but did not reach a maximum when the film broke down. Table XJ. shows the TABLE XI.—Radiation from Hot Pt. Film. ~ Current in amperes Potential on film | Time of 200 div. on | through film. in volts. _ electrometer scale. | 05 +40 | no leak. | 0-6 ” ; 29 0-72 ¥ | 530. sec. 081 3} co) ge 0°93 29 9 ) 1-0 2 83 ” 1 ” 1Z "i > “9 Men mi? Properties of Thin Metal Films. 673 connexion between the current through the film and the positive leak. These experiments were not pursued further since they show that owing to the large radiating surface, the film would not stand temperatures high enough | to give negative radiation. Change of Phase of the Light Reflected from a Platinum Film. Duplicates of the platinum films given in Table VI. were deposited on mica thin enough to give interference-bands in: the spectroscope. One half of the mica was covered with another thin sheet so that no metal could be deposited on that half while it deposited on the other part. This mica was then placed before the slit in a collimator of a spectro- scope with the metal side away from the aperture. Two sets of bands were thus obtained, one due to the reflexion from the mica-air surface, and the other from the mica-metal sur- face. The displacement of the bands due to the change of phase at the mica-metai surface was towards the red end of the spectrum. With the very thin films the displacement was very small, but increased rapidly with the thickness up to its full value and then became fairly constant. Theoretical Considerations. The films of the three metals—platinum, silver, and bis- muth—deposited in vacuo by the cathode discharge, all have their resistance considerably higher than the value calculated from the specific resistance of the metal. A number of films were examined under the microscope but no discontinuity could be observed. Reducing the width of the film did not affect its resistance per cm. square, and, moreover, the eftect of the electric current on the platinum films would tend to increase rather than to diminish any discontinuity that might exist. The experiments would show that the thickness was fairly uniform, and would not vary by more than a small fraction of the average thickness. Small quantities of many different gases are present in a vacuum-tube, hydrogen and mercury vapour being always present unless very special precautions are taken to get rid of them. Most metals absorb gases to a greater or less extent, platinum especially absorbs a good deal of hydrogen. It may be that from the manner in which the films are Phil. Mag. 8. 6. Vol. 4. No. 24. Dee. 1902. 2Y 674 Prof. J. Patterson on the Electrical deposited a good deal of gas is absorbed by them, but the amount is so small that it would be impossible to detect it. Lord Kelvin* has shown that a platinum plate which has absorbed hydrogen is electro-positive to one that has not, while if it has been kept in oxygen for some time it is electro- negative to the standard. In the experiments on the contact- difference of potential the film was positive to the platinum cathode when the cathode was old, but negative when it was polished, so that these experiments would not indicate whether the gas was absorbed by the film or not. It is not known just what effect the gas in the depositing apparatus has on the disintegration of the cathode by the discharge, but that there is some effect is seen from the fact that aluminium which sputters very little in air does so very freely in helium and argon. The condition of the surface of the cathode has also a considerable effect on the rate of deposition, at least, of the film. After the cathode had been used for a long time its surface became dull and spongy in appearance. In this state the rate of deposit was slower than when the surface was freshly polished. It is most probable that part of the difference between the measured resistance and the calculated resistance is due to the manner in which the film is obtained. The film is formed by particles of the metal striking on the glass surface and adhering. These particles are more or less loosely connected, and by heating they settle down into a more and more com- pact mass, and consequently their resistance is decreased. This is also seen from the fact that the rate at which the films are deposited has a great effect on the condition of the film. If the deposit is too rapid the film is powdery and does not adhere to the glass. This phenomenon was very noticeable in depositing the silver films, and Longden (loc. cit.) has also noticed the same effect in platinum when using the Wehnelt interrupter. It was also noticed in the bismuth films, and that after a certain thickness was reached the surface lost its metallic lustre and became dull and powdery in appearance. Another cause of the discrepancy would probably be the impurity in the cathode, as small amounts of impurity pe the resistance of the three metals very much. From the corpuscular theory of electrical conduction in metals we have, if n be the number of corpuscles per unit volume, e the charge on a corpuscle and m its mass, » the mean free path, c the initial velocity, * * Nature’ vol. xxii. o6r. Properties of Thin Metal Films. 675 then the conductivity is given by i ipsa CFP Ws a. Dm, ee This equation holds until the thickness of the film becomes comparable with 2X. When the thickness becomes comparable with » there are three cases to be considered, namely :— When ¢ the thickness is (i.) greater than 2 A, (ii.) between 2 > and A, (il.) less than 2X. Assuming that the corpuscles cannot leave the metal, Prof. Thomson has calculated that for (i.) % becomes vr (1-7); and for (il1.) ) becomes Arie Vi (los; Sf 5) On substituting these values of A in the equation 1 _ nen c Qme we get when f=2% TODD ae? i LEME Tey and when that is, that the resistance of the film has increased one- seventh in the first case and one-third in the last. Hence the resistance of the film does not change very much until it becomes equal to the mean free path of the corpuscle. From the results obtained for platinum films it will be seen that the resistance began to change rapidly between 7°6 and 4x 10-7 cm. The value of A calculated from the change of resistance of the film is 6x10—7 cm. These numbers agree very closely. * J. J. Thomson, Rapports présentés au Congrés International de Physique, vol. iii. p. 138, Paris, 1900. + Proc. Camb. Phil. Soc. vol. xi. pt. 1. p. 119 (1901). 2Y¥2 676 Prof. J. Patterson on the Electrical The average resistance of all the films whose resistances are normal is 82 ohms for a thickness of 10-® cm. and 1 em. square. Using the value 6x10-" for X and 82 for o the relation between specific resistance and thickness given by the above formule is plotted in fig. 14, curve A, where the ordinates represent specific resistance and abscissee thickness. The experimental values are plotted in curve B. Fig. 14. 9 iOA - A=6x1077CM From these two curves it will be seen that the experi- mental values agree very well with the ealculated for films whose thickness is greater than 6x 10-‘ cm., and for those below that thickness the experimental values vary more rapidly. Vincent*, from his experiments on silver films, concluded that at the surface of a metal there exists a thin layer which he called a transition-layer or the range of molecular action. The thickness of a thick film thus consisted of three parts, namely : A transition-layer from air to metal : an intermediate layer of constant specific resistance : a transition-layer from metal to glass. On this theory he obtained the following empirical formula for the conductivity 2 =—A-+ce, o where o is the resistance, ¢ the specific resistance which is constant, and e the thickness, A the correction to be applied tor the two transition-layers. He found that this relationship - held down to 5x10-* cm. and below this the formula no longer held, and consequently the intermediate layer was absent. He concluded from this result that the upper limit for the range of molecular action was half this limiting value or 2°5x10-§ em. Moreaut confirmed these results for silver. He also made nickel films by depositing nickel electrolytically on the silver films. He found that the range of molecular action was 2°2 x 10-° cm. for nickel. * Annales de Chimie et de Physique [7] vol. xix. p. 421 (1900). + Journal de Physique [3] x.-p. 478 (1901). Properties of Thin Metal Films. 677 This view in regard to the transition-layers existing at the surface of a metal is included in the corpuscular theory of electrical conduction in metal films. From the equation Hen ine Le Aas) 52 EM Saha WY ide Gi wee 6) Be ae the specific resistance for a film of thickness X is 4 of the normal specific resistance. This would give a value for > of about 6 x 10-® em. from Vincent’s results. The value calcu- lated from the change of resistance of pure silver in a transverse magnetic field is 1:3 x 10-6 cm.*, and from the silver film itself it is 1:1x10-§ em. The numbers are all of the same order. The specific resistance for a given thickness is plotted against the thickness in curve C, fig. 15, where the upper limit 6x10-® em. is taken for > and the normal specific resistance as 2°65 x 107® ohms per cm. cube, which would be the value given by Vincent’s results from the above formula. The experimental values obtained by Vincent are given in curve D. Fig. 15. “aoe — x S$ 42 3 S % = S = & < —— It will be seen from the above curves that the experimental values also vary more rapidly than the theoretical. At the surface of the metal, in order that equilibrium may be maintained between the air and the metal, there exists a layer of negative corpuscles¢. It is most probable that owing to this layer of negative corpuscles the number of corpuscles per unit volume is not constant throughout the surface-layer A, but that it decreases towards the outside. This would make the resistance vary still more rapidly than the above theoretical equation would indicate. Vincent and Moreau (/oce. citt.) concluded from their obser- vations that the transition-layer was the same thickness for all * Phil. Mag. June 1902, p. 655. + J. J. Thomson, Rapports présentés au Congrés International de Physique, vol. iii. p. 138, Paris, 1900. ae 678 Lord Rayleigh : Does Motion through metals, namely, about 2°5x10-° cm. for the upper limit. The experiments on platinum films, however, would indicate that for platinum films the thickness of the layer is much less. According to the corpuscular theory this transition-layer would be determined by A, the mean free path of the corpuscles, and » has about the same value for a number of the metals*. The thickness at which the specific resistance of the platinum film becomes abnormal cannot be taken as the value of X in the metal itself, owing to the properties of the films being so very different from those of the metal. Summary of Results. (i.) The specific resistance of the films deposited zn vacuo by the cathode discharge is several times greater than the specific resistance of the metal from which they are deposited. | (ii.) The specific resistance of platinum films which have been subjected to the same treatment remains constant above a thickness of about 7x 10-7 cm. Below this thickness the increase of specific resistance with decrease in thickness is very rapid. (iii.) Heat decreases the resistance of both silver and platinum films, and the thinner the film the greater the decrease. In platinum films the greatest decrease is produced by the electric current. (iv.) The values obtained for ), the mean free path of the corpuscle in the metal, are of the same order as those obtained from the change of resistance produced by a transverse magnetic field. In conclusion my most sincere thanks are due to Professor Thomson for his valuable advice and kindly interest through- out the whole course of the investigation described in this _ paper. Cavendish Laboratory, May 12, 1902. LXXIII. Does Motion through the Ather cause Double Refraction 2 By Lord Rayizien, O.M., F. Biers bs Rist well-known negative result of the Michelson-Morley experiment in which interference takes place between two rays, one travelling to and fro in the direction of the earth’s motion, and the other to and fro in a perpendicular direction, is most naturally interpreted as proving that the * Phil. Mag. June 1902, p. 655. + Communicated by the Author. Read before Section A of the British Association at Belfast. the Atther cause Double Refrastion ? 679 zether in the laboratory shares the earth’s motion. But other phenomena, especially stellar aberration, favour the opposite theory ofa stationary ether. The difficulty thus arising has been met by the at first sight startling hypothesis of FitzGerald and Lorentz that solid bodies, such as the stone platform of Michelson’s apparatus, alter their relative dimensions, when rotated, in such a way as to compensate the optical change that might naturally be looked for. Larmor (‘ Aither and Matter,’ Cambridge, 1900) has shown that a good case may be made out for this view. Tt occurred to me that such a deformation of matter when moving through the ether might be accompanied by a sensible double refraction ; and as the beginning of double refraction can be tested with extraordinary delicacy, I thought that even asmall chance of arriving ata positive result justified a careful experiment. Whether the result were positive or negative, it might at least afford further guidance for speculation upon this important and delicate subject. So far as liquids are concerned, the experiment is of no great difficulty, and the conclusion may be stated that there is no double refraction of the order to be expected, that is comparable with 10% of the single refraction*. But the question arises whether experiments upon liquids - really settle the matter. Probably no complete answer can be given, unless in the light of ae particular theory of these relations. But it may be remarked that the liquid condition is no obstacle to the development of double refraction under electric stress, as is shown in Dr. Kerr’s experiments. The apparatus was mounted upon the same revolving board as was employed for somewhat analogous experiments upon the rotation in quartz (Phil. Mag. vol.iv. p. 215, L902). Light, at first from the electric are but later and pr eferably f: om lime heated by an oxyhydrogen jet, after passing a spectacle-lens so held as to form an image of the source upon the analysing nicol, was polarized by the first nicol in a plane inclined to the hori- zontal at 45°. The liquid, held in a horizontal tube closed at the ends by plates of thin glass, was placed, of course, between the nicols. When at 12 o’clock the board stands north and south, the earth’s motion is transverse and the situation is such as to exhibit any double refraction which may ensue. It might be supposed, for instance, that luminous vibra- tions parallel to the earth’s motion, 7 e. east and west, are propagated a little differently from those whose dir ection is transverse to the earth’s motion, z.¢. vertical. But if the * 10-$=(10—4)”, where 10~* is the ratio of the velocity of the earth in its orbit to the velocity of light. 680 Lord Rayleigh: Does Motion through board be turned through a right angle so as to point east and west, both directions of vibration for light passing the tube are transverse to the earth’s motion, and therefore no double refraction could manifest itself. The question is whether turning the board from the north and south position to the east and west position makes any difference. In no case is any effect to be expected from a rotation through 180°, and such effect as a rotation through 90° may entail must be of the second order in the ratio which expresses the velocity of the earth relatively to that of light. It should not be overlooked that according to the theory of a stationary ether, we have to do not only with the motion of the earth in its orbit, but also with that of the sun in space. The latter is supposed to be much the smaller, and to be directed towards the constellation Hercules. In the month of April, when successful experiments were first made, the two motions would approximately conspire. If the saggested double refraction, due to the earth’s motion, were large enough, it would suffice to set the analysing nicol to extinction in one position of the board, and to observe the revival of light consequent on a rotation of the latter through 90°. Buta more delicate method is possible and necessary. Between the polarizing nicol and the liquid column we introduce a strip of glass whose length is horizontal and transverse te the board. This strip, being supported (at two points) near the middle of its length, and being some- what loaded at its ends, is in a condition of strain, and causes a revival of light except in the neighbourhood of a horizontal band along the ‘neutral axis.” Above and below this band the strained condition of the glass produces just such a double refraction as might be caused by the motion of the liquid through the ether, so that the existence of the latter would be evidenced by a displacement of the dark band upwards or downwards. In order the -better to observe a displacement, two horizontal wires are disposed close to the bent glass so as just to inclose the band, and a small opera- class focussed upon these is introduced beyond the analysing nicol. The slightest motion of the band is rendered evident by changes in the feeble iliumination just inside the wires. The board is mounted upon a point so as to revolve with the utmost freedom. The point is carried on the table and faces upwards. The bearing is a small depression in an iron strap, rigidly attached to the board, and raised suthciently to give stability. The gas-leading tubes are connected in such a manner as to giverise to no forces which could appreciably vary as the board turns. the Aither cause Double Refraction ? 681 Observations were made upon bisulphide of carbon in a tube 76 cms. long, and upon water ina tube 734 cms. long. In neither case could the slightest shift of the band be seen on rotation of the board from the north-south position to the east-west position, whether at noon or at 6 p.m. The time required to pass from one observation to the other did not exceed 15 seconds, and the alternate observations were repeated until it was quite certain that nothing could be detected. Of course the significance of this result depends entirely upon the delicacy of the apparatus, and it is worth little without an estimate of the smallest double refraction that would have been detected. It may even be objected that the investigation stands self-condemned. In consequence of the earth’s magnetism there must be a rotation of the plane of polarization when the light traverses the bisulphide of carbon in the north and south position ; and this effect, it may be argued, ought to manifest itself upon rotation of the board. To take the objection first, it is easy to calculate the rotation of the plane of polarization. For one 0.G.s. unit of magnetic Sd ei the rotation in CS, at 18° is 042 minute of angle* In the present case the length is 76 ems. and the earth’s ehomepatal force is °18 ; so that the whole rotation to be expected fF is 76 x°18 x °042=°58'. So small a rotation of the plane, which would show itself, if at all, by a fading and not by a displacement of the band, is below the limit of observation. The delicacy of the apparatus for its purpose may, indeed, be interred indirectly from the rotation of the nicol found necessary to engender a marked revival of light at the darkest part of the band. If @ be this angle, the revived light is sin°@, expressed as a fraction of the maximum obtainable with parallel nicols. In the actual observation the nicols remain accurately crossed, and the question is as to the effect of a double refraction causing e.g. a retardation of vertical vibrations relatively to horizontal ones. If this retardation amounted to $A, X being the wave-length, the effect would be the same as of a rotation of the nicol through 90°. In general, a retardation of phase e, in place of 7, gives a revival of light measured by sin? (Je). If the revivals of light in the two cases be the same, we may equate * Phil. Trans. clxxvi. p. 343 (1885) ; Scientific Papers, vol. ii. p 377. + The difference between astronomical and magnetic north is here neglected. 682 Lord Rayleigh: Does Motion through to $e. Hence if we find that rotation 6 produces a sensible effect in lessening the darkness at the darkest place, we may infer that there is delicacy sufficient to detect a relative retardation of 26 due to double refraction. This comparison would apply if the test for double refraction were made by simple observation of the revival of light. As actually carried out by location of the band, the test must be many times more delicate. It was found that a marked fading of the band attended a rotation of the nicol through 4’, According to this e would be 93 or since a retardation of 4) corresponds to e=a, a retardation amounting to =, x 3A should be perceptible many times over, regard being paid to the superior delicacy of the method in which a band is displaced relatively to fixed marks. _ Another and perhaps more satisfactory method of deter- mining the sensitiveness was by introducing a thin upright strip of glass which could be compressed in the direction of its length by small loads. These loads were applied symmetrically in such a manner as to cause no flexure. The double refraction due to the loads is of exactly the character to be tested for, and accordingly this method affords a very direct check. If the load be given, the effect is independent of the length of the strip and of its thickness along the line of vision, but is inversely as the width. ‘The strip actually employed had a width of 15 mm.; and the application (or removal) of a total of 50 gms. caused a marked shifting of the band, while 25 gms. was just perceptible with certainty. To interpret this we may employ some results of Wertheim (Mascart’s Traeté d’ Optique, t. 11. p. 232), who found that it requires a load of 10 kilograms per millimetre of width to give a relative retardation of 5A, so that with the actnal strip the load would need to be 150 kilograms. The retardation just perceptible is accordingly 4A+6000. This may be con- sidered to agree well with what was expected from the effect of rotating the nicol. We have now only to compare the relative retardation which would be detected with the whole retardation incurred in traversing the 76 ecm. of bisulphide of carbon. In this length there are contained 1,200,000 wave-lengths of yellow light, or 2,400,000 half wave-lengths. The retardation due to the refraction may be reckoned at ‘6 of this, or 1,440,000 half wave-lengths. Thus the double refraction that might be detected, estimated as a fraction of the whole refraction, a lc. the Ather cause Double Refraction ? 683 is 12x 10-1 The effect to be expected is of the order 10-°, so that there is nearly 100 times to spare. The above relates to the bisulphide of carbon. With the water the delicacy of the test was somewhat less. When it is attempted to replace the liquid by solid matter, the difficulties of experiment are greatly increased. The best results that I have been able to obtain were with built up thicknesses of plate-glass. A sufficient thickness in one piece is liable to exhibit too much double refraction from the etfect of internal strains. A number of triangular pieces of plate-glass, no larger than necessary, and about 6 mm. thick, were put together in a trough to a total thickness of about 110 mm. The interstices between the faces being filled up with bisulphide of carbon, the internal reflexions were sufficiently reduced. One difficulty is to get quit of motes and threads which adhere to the glass and become extra- ordinarily conspicuous. Advantage was thought to be derived from shaking up the bisulphide of carbon with strong sulphuric acid. At the best the residual motes and specks in the glass interfere very seriously with the observation, and the loss of light due to imperfect transparency operates in the same direction. The least load upon the upright strip that could be detected with certainty was now 100 grms., so that as compared with the observations upon liquid there was a loss of delicacy of four times. In addition to this, the effect to be expected is reduced in the proportion of 7:1, that being the ratio of lengths traversed by the light. Thus in all we lose 28 times as compared with the liquid. In the latter case we calculated a margin of 100 times, so that here there would remain a margin of about 3 times. A subsequent attempt was made to increase the total thickness of the combined glasses to about 220 mm., but no real advantage was gained. The loss of light and increase of disturbance from motes and residual double refraction prejudiced the delicacy in about the same proportion as the length of path was increased. But although the results of the observations upon solids are very much less satisfactory than in the case of liquids, enough remains to justify us in concluding that even here there is no double refraction (of the order to be expected) due to motion through the ether. Terling Place, Witham, 68474 LXXIV. The Discharge of Electricity through Gases and the Temperature of the Electrodes. By J. A. CUNNINGHAM, B.A. (RUT. & Camb.), A.R.CSeL., 1851 Kahibition Scholar, Cavendish Laboratory, Cambridge *. Introduction. fie conduction of electricity through hot gases and vapours has been the subject of investigations by Becquerel, Blondlot, Grove, Maxwell, and Hittorf. In 1890 Prof. Thomson + reinvestigated the whole subject, and showed that the heating of the electrodes was an essential part of the phenomenon. Recently Dr. H. A. Wilson has investigated the conductivity of air and salt vapours up to about 1300°. His electrodes were, of course, also hot, and from his previous experiments on flames he had concluded that the ionization of the air took place quite close to the hot electrodes. It has long been known that hot bodies possessed the pro- perty of discharging electricity §. _ The experiments of Elster and Geitel || are fundamental, and the subject has been taken - up at the Cavendish Laboratory by Prof. Thomson J, who showed that the carriers were charged particles, Prof. McClel- land **, Mr. O. W. Richardson ++, and Prof. Rutherford tt. The result of all these experiments is to show that a hot metal gives off positive ions at a red heat and negative ions at a white -heat, and that this negative current increases very rapidly with further rise of temperature, the potential- difference being much less than is necessary to produce a discharge in the ordinary sense. When we pass to the discharge in a vacuum-tube the phenomena become more complicated, and the results more difficult to interpret. Hittorf§§ carried out a very extensive series of experiments on the temperature effects at various parts of the discharge. He found that the luminosity in the positive column was extinguished in the neighbourhood of a heated platinum spiral, or if the anode itself were made white hot. On heating up the cathode he found no marked dimi- nution in the total potential-difference until a yellow heat * Communicated by Prof. J. J. Thomson, F.R.8. + Phil. Mag. [5] xxix. pp. 358, 441. t Phil. Trans. excvii. p. 415 (1901). § Guthrie, Phil. Mag. [4] xivi. p. 257 (1873). || Wied. Ann. xxxvill. p. 27 (1889). q Phil. Mag. [5] xliv. p. 203 (1897). . ** Proc. Camb. Phil. Soc. x. p. 241 (1900), and xi. p. 296 (1901). ++ Ibid. xi. p. 286 (1901). tt Phys. Rev. xiii, p. 321 (1901). §§ Wied. Ann. xxi. p. 90 (1884).: On the Discharge of Electricity through Gases. 685 was attained, after which it began to diminish rapidly. The co) differences were more marked at reduced pressures. Hittorf also found that the potential gradient in the positive column was independent of the current, but diminished with the pressure. The “ cathede fall”’ remained practically constant until the cathode was covered with the negative glow, after which it increased with increasing current. It also increased very rapidly with diminishing pressure. Apparatus. The form of vacuum-tube used in the present series of experiments is shown in the diagram (fig. 1). The electrode Fig. 1. \ é “- : Ve => To Tort er PUMP. (KK) consisted of a platinum wire bent backwards and for- wards on itself so as to form a plane grating. Tour strands of wire of the same thickness fused into each of two side 686 Mr. J. A. Cunningham on the tubes served to lead the heating current through the grating without undue heating of the blue-glass joint. The grating could thus be included in the circuit of a carefully insulated secondary wound on a ring transformer. The current for the primary was taken from the Cambridge town (alternating) supply, and was regulated by means of a rheostat. ~~ > The opposite electrode (A) was made of a similar grating, but could not be artificially heated. The three infoniaaeiaae electrodes (H, D, & B) were made of fine platinum wires whose free ends inside the discharge-tube were hammered out flat, and the edges then trimmed off parallel, so that the width of the blade was only about double the diameter of the original wire. They were fused into side tubes perpendicular to the bars of the gratings, and so that the plane of the blade was parallel to the axis of the discharge-tube. Professor Thomson has pointed out that, especially when working at low pressures, an ordinary wire placed in front of the cathode would be subjected to a bombardment of negatively charged corpuscles, from which it would derive a negative charge and acquire a potential which might have nothing much to do with the potential of the surrounding gas. Prof. Thomson’s scheme of using a transverse pencil of cathode particles whose deflexion would measure the electric intensity at the point was not easily applicable in the present case, since when the cathode was at a high temperature the illumination from it would render a phosphorescent spot practically invisible. It was thought that the flat-bladed electrodes here adopted would expose only a very thin edge to particles moving rapidly along the axis of the tube, and a maximum surface to the ionized gas whose potential it was desired to ascertain. This tube was connected by means of a short glass tube with the Tépler-pump, PO; bulb, and McLeod gauge, so that the whole system rapidly came to one uniform pressure. A three-way tap served to admit fresh supplies of air, and by being closed at night prevented an excessive diffusion of mercury-vapour into the dischar ge-tube. The discharges below described always presented : a rich red colour without any apparent traces of the blue due to mercury. The current from a battery of 1000 small secondary cells, used for generating the discharge, passed through two variable liquid resistances, and was measured by means of a low resistance @’Arsonval galvanometer of the Ayrton and Mather type. A telephone in series served to check the steadiness of the discharge. A German voltmeter of simple construction (with an aluminium needle suspended about a horizontal axis a little Discharge of Electricity through Gases. 687 above its centre of gravity} served to measure the total potential-difference between the electrodes, and at very low pressures (Table XIV.) also for the cathode fall. Its scale was carefully calibrated by direct comparison with the Kelvin multicellular voltmeter, which was used for measuring potential - differences between the other electrodes raneing from 250 to 1000 volts. The German instrument was a little sluggish in its movements, and its indications were used mainly as a check on those of the other instruments, except when special precautions were taken to tap it before each reading. For potentials between 100 and 300 volts an Ayrton and Mather direct-reading voltmeter (with vertical cylindrical quadrants) was employed. The temperature of the hot electrode (KK) was measured by means of a platinum platinum-rhodium thermo-couple. The wires (0°1 mm. in diameter) were attached to adjacent bars of the grating. They were fused through the end of a small glass tube at the top of the discharge-tube, and passed over into two glass tubes immersed along side a mercury thermometer in a bottle of water. These “glass tubes were partly filled with mercury, which served to make good con- tact with the copper wires leading to the galvanometer. This was also a d’Arsonval of the Ayrton and Mather type. To reduce the deflexions of the galy anometer to degrees centi- grade use was made of Messrs. Heycock and Neville’s deter- mination of the melting-point of potassium sulphate*. The thermal junction was attached to a strip of platinum. foil which was heated up as in the course of the experiments. The deflexion of the spot of light on the scale was then read off just when the K,SO, began to melt. The observation was repeated with very slow ‘increments of current through the foil. From the final value thus obtained a curve of temperatures against deflexions was plotted in the manner described by Callendar ft, and verified by a determination of the melting-point of sodium sulphate. The deflexions of the spot at all distances of the galvanometer from the scale were readily reduced to this standard distance. There is a little doubt attaching to some of the highest temperatures recorded owing to a sagging of the wire-grating which left the portion to which the thermo-couple wires were attached slightly out of the plane of the grating, and so made them rather cooler than the rest. With this apparatus, where there were only glass joints and there was therefore practically no leak until very high * Chem. Soc. Journal, Ixvii. p. 160 (1895). + Phil. Mag. [5] xl viii, p-. 519 (1899). 688 Mr. J. A. Cunningham on the temperatures were reached, it was often thought desirable to vary the temperature backwards and forwards so as to try and isolate the temperature effect as completely as possible. It was also possible to raise the temperature of the platinum grating by more gradual steps than would actually appear from the numbers recorded in the accompanying tables. Where in such cases a gradual change of temperature was accompanied by a gradual and continuous change in the dis- tribution of potential, it was often thought sufficient to record the measurements of successive maximaand minima. And in nearly all cases plenty of time was allowed to elapse for the instruments to settle down to perfectly steady readings. A few general remarks on some of the appearances observed may not, perhaps, be out of place here before proceeding to a detailed record of the actual measurements made. The temperature of the cathode was observed to rise gradually by the action of the discharge. At moderately high pressures (0°5 to 2mm.) and with small currents, on first starting the discharge the negative glow was seen to wander about in an unsteady manner over the surface of the cathode, accompanied by a noise in the telephone which only ceased after a very considerable lapse of time. This unsettledness was most marked on starting the discharge for the first time with a new wire. When the cathode was now gradually heated up the nega- tive glow was observed to move away from the central hottest portion of the grating and wander up into the side tubes, where the wire was cooler. On further heating the discharge would come back again and proceed from the hottest part of the cathode. This phenomenon is consistent with the measure- ments recorded below, which show a more or less well-marked maximum ‘“‘ cathode fall”? at temperatures below a yellow heat varying with the pressure; and it seems natural to suppose that the discharge will pass where it can do so with the greatest ease. It will be seen at a en from all the tables where the cathode was taken through a cycle of temperature changes that a sort of hysteresis becomes apparent. This may be partly due to an error of observation. The cooling was nearly always more rapid than the heating up. The method of observation adopted was to keep an eye fixed on the volt- meter after each successive reduction of current in the primary of the transformer, and at successive readings of the voltmeter to look up quickly at the corresponding reading on the conveniently placed scale of the galvanometer con- nected with the thermo-couple. Particular attention was paid to recording maxima and minima on the voltmeter with ae ——— a lon mtip~ Discharge of Electricity through Gases. 689 their corresponding temperatures. As in all recorded cases, the potential indicated on the voltmeter was changing but slowly, and as the coil of the d’Arsonval galvanometer was inclosed in a silver cylinder and was very dead beat, it was thought that the error of observation could not really be very great. Some such lag is, after all, only to be expected. Results. In Tables I. to VIII. are shown the measurements of the fall of potential along the discharge at different pressures, the temperature of the cathode being kept constant. ' | : Phil. Mag. 8. 6. Vol. 4. No. 24. Dec. 1902. 2 7, TABLE I. | | Temperature | Potential Difference, | | _ of Cathode. Volts. | Pressure, 2 mm. of | Deflex-| | Mercury. ion. | °C. || K—-A.| K—E. E-A. | K—D. | K-B. | 090 | 35 | 815 S00 pul Glove -S, 665 || 1:18 10:90 | 35 780 TAN. Ne (AO eS: 520 || 088 0-90 | 35 G0 We See te WDOS) uIP k, 500° || 066 090 | 35 || 650 BOR ole (422): ie 396 || O51 095 | 38 || 600 DaOe eos italy. 2) 345 || 0-88 0-90 | 35 538 320 che, 203 340 | (350) || 0-29 090 35 522 352 170 a SMO 090 35 519 370 | 149 a ie 108 065 | 27 558 B00. ules. S053 i. 4 OO 090 35 580 AAS AGI HE ve tie ORLO4 090 | 35 654 ATS) ie ARGC IN ake ie Me OOTS 1095 | 38 | 705 HOB ey OR. Is 38 eet | 0:050 | 095 | 38 1100 rae Ti pets 1) Va Res ae snes OOaE | 1} TaseE II. } Temp. of | Potential Difference Current, ~~ Pressure, Z Cathode. | | 4 | = \Defin., °C.) K—A.| K-E.| E-A.| Defin. [Amp.x10,” ee ee ee Oe ee eee eS Se eee p28 | 820 || 1150 | 293 | 860 660 | 396 | 267 333 | 832|| 960 | 268 | 680 || 740.) 444 | 1:99 333 | 832 || 800 | 292 BIZ. We BBB Wl) SOT | | ae 33:3. | - 832 755 | 290 (465) (86) | (516) | 1:03 1333 | 832] 730 | 2938 (437) || 9-0 5:40 0°76 333 | 832 || 660 | 230? | (430) || 915 | 5-49 0:563 333 | 832 || 625 | 290 (335) sae ASC ape ot oe goa | 832) 580 | 387 |. 181 |) 925 | 555°) O-904 33:3 | 832 || 625 | 480 | 190 || 965 | 5-79 0-210 | 33:3 | . 832 600 | 465. |. 192 |) 845.1) SOT! 1) Oe eaa.| 882) 780° | 587 |. 197 795 477} 2 08 4 33:3 | 8382 || 690 | 482 212 ||. 7-85 471 | 0-079 | 333 | 8321} 730 | 520 255 || 740 | 444 | 0-058 | | | 840 | 527 313 655 | 393 }) 6041 | $33 | 832 || 1070 | 540 | (S30) no b> 0-029 | 690 Mr. J. A. Cunningham on the Tasue IIT. pears! Potential Difference, Current Pressure, Cathode. a : mm. of ©, —---——_}_ Hg. Defin.| °C. || K—A. | K—-H. | E—A. | Defin. |Amp. x10’. 437 | 1040 || 1200 300 900 | 5:45 307 | 270 439 | 1043 | 955 272 682 6°70 4:02 | 1:95 43-9 | 1043 || 810 292 518 7-60 4-56 1-43 43:9 | 1043 || 780 300 490 7-70 4°62 1:35 43-9 | 1043 || (725)?| (200) | (525) § ss 1-00 439 | 1043 | 750 215 os (7-4) (4:5) 0-74 | 43:9 | 1043) 690 260 430 (7-8) Ke 0°53 | 43:9 | 1043 || 565 367 199 83 498 | 0:39 1439 | 1043 | 565 | 377 | 184 || 815 | 489 | 0980 | 404 | 986 | 630 440 201 || 77 462 | 0-196 | 42:7. | 1020 |) 625 432 199 || 7:7 4-62 | 0:196 | 48:3 | 1080 | (680) | (490) | 207 | (73) A 0:143 43-1 | 1028 || 670 468 200 || 76 4:56 | 0-096 | 43-7 | 1040 |} 710 487 226 =| (71) o 0-068 | 43:9 | 1043 | 3800 522 282 | 670 4:02 | 0-054 | 439 | 1043 || 865 502 | (363) || 6-05 363 | 0-042 | 43-9 | 1043 |) 970 464 | (506) | (55) ia 0-031 43:9 | 1043 || 1045 435 | (610) | 5:0 3:00 | 0-027 439 | 1043 || 1340 437 | (900) | 33 1:98 | 0-020 | | TABLE LV. | / cae e Potential Difference. | Current. ie ear | $Y | | Hg. Defln.| °C. || K—A. | K—E. | E-A. || Defin. |Amp.~x 10’. 502 | 1163 || 960 | 275 661 59 3:54 1:90 50:3 | 1165 || 810 | 300 5i2 (6:6) <: 1-40 50°4 | 1167 730 | (817) | 413 71 426 | 1:05 50-4 | 1167 || 730 | 296 | (430) 7-0 420 | O74 50-4 | 1167 || 685 | 285 | (400) | 7-2 4°32 0:55 50-4 | 1167 || 570 | 366 204 75 450 0-40 50-4 | 1167 || 570 | 372 195 7°45 447 | 0:30 50:2 | 1163 || 630 | 426 206 72 4:32 | 0:206 | 50-4 | 1167 680 482 204 (67) | O151 | | 50-4 | 1167 || 780 | 565 290 63 378 | 0108 | 50-4 | 1167 |] 770 | 560 210 6-1 3°66 0:079 50-4 | 1167 || 795 | 508 284 a || 0055 | 504 | 1167 || 900 | 500 | (400) | 54 3:24 0-039 504 | 1167 || 1080 | 690 | (890) || 422 | 252? | 0-037 50-4 | 1167 || 1450 | 950 | (500) et ee 0025 ant =e no Discharge of [lectricity through Gases. 691 TABLE V. i [oS > ra ne | Potential Difference. Current. Ree | | Hg. | Defin. | oC, | SS: K-—E | E-—A. | Defin. | Amp. x10’. 55°4 | 1256 | 1010 | 277 Ta | eae fo ge 215 554 | 1256), 860 | 293 538 61 3°66 153 | 55-4 | 1256 || 790 | (887) | 433 6-4 3-84 110 | 1555 | 1259 | 740 | 300 | (440) || (66) vs 0-82 554 1256 | 660 220 | (440) ea 4 0-60 (554 1256 | 570 | 345 224 (7-2) | 0:43 554 | 1256 | 570 | 350 214 Ne Bi li Be 0-314 | 55-4 | 1256 575 360 196 70 | 420 0:224 554 | 1256 | 640 | 390 241 (eon bot o. 0-171 55-4 | 1256 | 680 | 480 199 ||- (6:3) a 0-130 55-4 | 1256 750 558 196 ae | oe 0:106 554 | 1256 | 780 | (566) | 214 5°75 3-45 0-082 554 | 1256 | 780 | 521 259 (5°65) | 3:39 0-066 554 | 1256 | 810 | 500 -| (810) SYM taste 0-057 554 | 1256 | 880 | 5435 | (335) 51 | 3:06 0-050 55°4 | 1256 | 920 612 | (310) 51 | 3-06 0-054 So4 | 1256 - 1120 715 | (405) bir ea 2 0-037 | 55-4 | 1256 | 1310 | 860 | (450) | 31 | 1:86 0-034 55°3 |1254 | 1420 930 | (490) Set bet 0-029 | Tapae yf. | | | | ae Potential Difference. | Current. heresies | - —||- 7 | | mm, } ig o9, |K—A|/K—E]|E—A.|K—D,| Detn. Ke ee | / et | | 59:8 | 1335 | 1160 | (330) | 830 |(4:5) | .. 210 | 60°3 | 1340 | 960 | (360) | 602 (5-4) | .. 1-40 63°3 | 1394 | 790 | (840) | 450 | 1 (6-0) ncaa 102 | 60°3 | 1340 || 700 | (343) | 357 6% |, 402 | O75.) | 60°3 | 1840 | 665 | (342) | 323 | 68 | 408 | 055 60-4 | 1344 | 575 | 340- | 285 71 | 426 | 039 60-4 | 1344) 565 | 350 | 215 70 420 0-29 60:4 | 1344 | 570 | 370 | 202 | 685 | 411 | 0:22 | | 60-4 | 1344 640 425 | 215 166 | 396 | 0174 | 60-4 | 1344 710 500 | 206 G2). bynes (Olle | 60-4 | 1344 | 770} 573 | 196 | | beak Nae ok ne 60-4 | 1344 | 820 | 563 | 250 | ... |... | ... | 0-065 60-4 | 1344 840 | 580 | 258 | 700 || (5-4) |... | 0:058 60-4 | 1344 = 990) | (590) | (400) | 810 | 45 | 2-70 | 0-041 | 60-4 | 1344 , 1150 | 725 | (425)| 1020 || ... | ... | 0-035 | 60-4 | 1344 | 1220 | 800 | (420)| ... || ... vor. |, OO | 60-4 | 1344 | 1200 | 775 |(425)| ... || 3:55 | 213 | 0-033 | 60-46 1346 | 1300 860 | (440) |. Soha. | 0-032 eC heen ae anaes (tote aN 692 Mr. J. A. Cunningham on the Tasue VII. eae Potential Difference Current Cathode. | i a " | Pressure, : , —____—___—_| mm. of Defin.| °C, |K—A.|K—H) BA) B—D_ D-A_| Defin. | AMPS He. —_— | ee pees — _—- 65°5 | 1432 || 1850 | 360 990 | 280} 720 iss | (2 2-138 65°5 | 1432 || 1020 | 328 692 | 190| 500 o1 | 3:06 1:53 65'3 | 1429 850 | (280) | (570) | 120; 450 ~ Co 1-43 65°5 | 1432 770 | 300 470 100 | 3880 || 59 | 3:54 1:07 65:5 | 1432 650 | 302 348 |< 90 wie es 0604 65°55| 1434 587 | 328 259 ye ahineate - |e 0°431 65:5 | 1482 583 | oc 213 | 38h : 63 | 378°) aa 655 | 1482 || 680) 470 | 210 | |... | (oo) aie 65:5. | 1432 780 | 510 270 tes we ll eo 0-078 | 65°: | 1432.) 1110 | 565 545 |>3810 90 | 39 | 235 0:035 | 65°3 | 1429 || 1480 | 480 | 1050 920 | 150 — ide 0-023 65°5 | 1432 || 2000 vl ee us Sy ) 0 0017 Taste VIII. T c | | Baa ae | Potential Difference. Current. |Pressure, Rigen Bec) | a Desus) 20. 4K =A. K-E EK—A.| K—D.| K—B.|| Defin: ae 69:4 | 1500 | 1650?} 305 |.1190 | (760)| ... 6°09 2°95 69°4 | 1500 | 1220 | 293 | 930; 340; 930 10°54 2°20 69°5 | 1502 | 970 | 283) 670 | 3833) 720) (16-4) 1:60 69-4 | 1500 || 800 | 295 | 490) ... | 610 || (22-0) 1:20 69-4 | 1500 |) 690 | 295 | 380; 3810| 500 || (28-0) 0-71 69-4 | 1500 | 685 | 304 | 326 | 305 | 485 || 27-7 0:66 69°5 | 1502 || 580} 304} 2801 335]... 29:34 | 0-30 69-4 | 1500 || 575 | (385)| 240 | 352 | 472) 3244 | 0-99 69-4 | 1500 || 630/ 420; 203) 508 | 34:44 | 018 69-4 | 1500 || 750 | 554 | | 700 | 3404 | 0-103 69-4 | 1500 || 860| 614) 220) 740) 820) (81-8) 0-078 69'4 | 1500 || 960 | 674 | 262 | 905 | 30°54 | 0:058 69-4 | 1500 || 1080 | 695 | 335! 900; 980) 30-00 | 0-056 | 69°4 | 1500 | 1050 | 700} 3501! 920 | 1010 &% Ou ' py co = oes T i=) f=) | \ At low temperatures of the cathode the “cathode fall” (K—E) shows a well-marked minimum at a pressure of about 0°65 mm. of mercury. At higher temperatures this minimum tends to become less marked, and to occur at a greater pressure. In fact the cathode fall becomes almost independent of pressure above 0° mm. The cathode fall at O >° the highest (1500° C.) and at the lowest (35° C.) are plotted in © ae Discharge of Electricity through Gases. 693 The potential-differences between the fixed electrodes A,B, D, E, and K when the cathode is at a temperature of Pe; ‘500-8 “ Cathode Fall” of Potential.—Volts. -- 200 : ee Se Te IS -0 5 Z0vm 25 Pressure,—mm. of mercury, about 1500° C. are shown in fig. 3 (p.694) and Table VIII. The fall of potential close to the anode (B—A) decreases steadily with diminishing pressure. The potential-gradient in the positive column (D—B) is approximately proportional to | the pressure above 0°5 mm. The gradient at the negative | end of the positive column, and including the Faraday dark | space (E—D), is very much less than anywhere else in the discharge, and seems almost te vanish at a pressure of about 0°65 mm. | | In Tables IX. to XIV. we pass on to the results obtained by pumping down to any required exhaustion and then gradually heating up the cathode, the actual pressure being measured and recorded at intervals. As the volume of the discharge- tube bore but a small ratio to that of the pump eylinder, McLeod gauge, and P,Q; bulb, the heating of the cathode only produced trifling changes of pressure, and it has been shown already that the cathode fall is hardly affected by 694 * Mr. J. A. Cunningham on the slight changes of pressure except at very high exhaustion. At very high temperatures and low pressures the slight leak did, however, produce quite appreciable effects, as is well illustrated by the latter part of Table XIV. Fig. 3.—(Temperature = 1500° C.) 1500 a | = 1300! Ye Potential Difference.—Volts. D S : a SeenON ENE kt OP eee} 2) 5 mim. of Mercury 0 15, 20 25 Pressure. TABLE IX. | ‘ “ i ae a aS | . | poe eae | Potential Difference. Current. | Piepeemad | i re : E—A. | Defin.of Amps. |/Mercury. ' Defin. | °C. | K-A.| K-E. (cjculated)| Galvanr. x 104, | 168 ass || 793 | 386 | 457 25-2 | Bd | 5:8 105. We 320 | wer | 27 102 | 804 324 | 480 252 | Bd | 78 Ws i |... 318 | | | | . 16:3 455 g04 | 380 | ° 474 | | . | 197 Bao AL ea. 340 | . . 20-2 545 337 | ; | 463 1112 “ig 306 26-9 | 8-97 | : | 553 1255 747 302 |. 445 | | . 59:3 1325 752, | 800. |... 452 | | | 673 | 1463 || 793 | 296 | 497 | | | 70°3 1514 | 798 994 | 504 65 S83 | cu | Discharge of Electricity through Gases. 695 TABLE X. f rat f | a, se be ? Potential Difference. | Current. Bancseee mm, of | Defin. | °C. aia K—D. | D—A. || Defin. athe Hg. | 803 | 1681 787 | 350 | 487 19 786 | 1653 798 | 358 | 440 73:4 | 1566 793 | 362 431 533 | 1220 770 | 366 404 52:3 «1202 770 | 360 410 24-8 650 782 | 373 409 19:8 535 ROM age 193 | 594 804 400 404 || 249 | 8-30 10 | 305 815 | 455 360 7 297 is 420 =n EA ye: 410 | | ya} 142 420 | | 28 105 | °450 | 241 | 8:08 | | TaBLe XI. | | | aa | Potential Difference. Current. ks hee! ressure, | | : mm. of Defin,| °C. KA, K-D, D-A|D—B|B—A.| Defn.| 4™P: | He. | 37 | 133] 720] 410 | (310)| 262] (48) || 20:4 | 6-80 | 1-07 174 | 480) 710 | 398 | (812)) 259) (53) | 209 | 6-97 180 | 495 || 700) 390 | (310)| 258] (52) | 21-9 | 7:30 377 | 920) 665 | 368! (297)| 250} (47) | 199 | 663 | 1:14 37°, | 920 || 665 | 368 | (307)| 253] (54) || 23:0 | 7-67 449 1063 | 665 | 365 | (300)| 252} (48) | 19°85, 6-62 520 1196 | 665 365 | (300)| 252 (48) | 19°65) 6-55 538 1230 | 663] 352 | (311)| 262] (49) || 19:90/ 663 | 1-14 561 | 1270 || 660 351 | (309)| 265 (44) | 19:80) 6-60 609 1352 || 660 | 353 | (307)| 271 | (26) || 19°3 | 6-43 679 | 1475 | 665| 357 | (308)| 277] (81) || 185 617 | 1-16 | 71-4 | 1583 || 673 | 362 | (311)|} 282] (29) || 186 | 6-20 | 1:17 72-4 1550 | 675 | 360 (315)| 284| (31) | 19°0 | 638 73:5 | 1570 || 680] 359 | (321)| 287] (34) | 17-5 | 5:87 62:5 | 1880 | 675 | 356 | (319)| 275 | (44) 241 | 635 | 700! 402 | (298)| 273 | (25) || 124 | 418 | 1:12 23-4?| 6107] ... | 412 | | 99-4 597 | 740) 445 (295)| 278 | (17) | | 21-4 | 575 || 742 | 453 | (289)| 279 | (10) |) | | 20-1 | 542 || 785} 434 | (301)| 275 | (26) || 15°7 523 (187 | 510) 742!) 450 | (288)| 278 | (10) || 15:0 | 500 | 1:14 | 29 | 108 eer bia te: | | a4 90 | 525 290) 110 | 367 — | 696 Mr. J. A. Cunningham on the TABLE XIT, rae a Potential Difference. | Current. ane | | . | | mm. | Defin.| °C. ea. K—D. p—A|D—B., Defin. x10%, | 4 | | [ee | 19 | -.75 || 525 | 370| 148| ... || 228 | 7-60 | 0376 95 76 Ne) a a aaa 90.) 280 |... |) 888 | 16°2 9451 Wea) ease Rieti, 192 | 520 || 5385 | 392] 152 1922 || 20:4 | 6:80 21-7 (| 580 \| 535 || 304) 152... | IS7 1enT 24-7'| 648 || 535 | 398] 152] ... || 19°7 | 657 28:0 || 720 || 545 | 395) 153 19-2 | 6-40 40-7 | 980 || (555) | 400 | 155 | 188 | 6:27 41-2 | 990 || (548)| 393 155 18:8 | 6:27 61-7 | 1367 || (545)| 390) 155 | 186 | 6-20 66-4 | 1450 || 545 | 392! 154 | 185 | 617 | 71-4 | 1533 || (553)| 392 | 161 | ... || 183 | 610 | 0-406 71-0 | 1525 || 550 | 392| 160| 128 | | 742 | 1580 || 555 | 394! 158 77-4 | 1684 || (545) 388 | 157 178 | 598 | 79:0 | 1660 || (528)| 375 | 153 18-0 | 6:00 | 81-2 | 1696.|| ...° | 240 | 77-7 | 1638 || (528)| 372 | 151 | 85:0 | 1750 || 320 | 190 | 151 | ... “| 03892 780 | 1642 || 470 | 343| 148 17-2 | 5°73 764 | 1617 || 525 | 389] 150 | 751 | 1594 || 560 | 407 | 150 722 | 1547 || 570 | 415] 150 | 17-0 | 5°67 565 | 420] 150 | -| 53:0 | 1213 || 565 | 412 | 150 34:2, | 850 || 580 | 426] 152 168 | 5:60 24-2 | 637 || (575)! 428 | 152 80 | 250 || (542)! 390! 152 168 | 56 37 | 183 || 560 | 400] 151 19:2 | 64 0:374. 36 | 130 || 565 | 404 | | | | The results of Tables IX. and X. are plotted in fig. 4, eurves E and D respectively. The one was obtained while the cathode was being warmed up, while the other was a cooling curve, which may account for the shifting of the initial minimum and maximum along the axis of temperature. The curve D shows the potential-difference between the cathode and a point in the top of the positive column (K—D). The results obtained at a rather lower pressure (about 1-1 mm.) are given in Table XI. and plotted in fig. 5, where the cathode (K) is supposed to lie along the line of zero-potential below the diagram, and the P.D. between it and each of the electrodes A, B,and D is measured by the ordinate drawn to the respective curve at any given temperature. Here the initial variations (at a temperature below 600° C.) Potential Difference.—-- Volts. a Oo oO a D Discharge of Electricity through Gases. Fig. 4. 450 a 409 250 Cathode Fall of Potential (K—E),—-Volts. 0 70 «OOO i500 2000: Temperature of Cathode, Ix, °C. Fig, 5.—(Pressure= 1°] mm.) ik | eta 500°C 1000 1500 2000 Temperature of Cathode, K, ° C. 695 _ Mr. J. A. Cunningham on the have become less marked though still apparent. The differ- ence of potential between the cathode and the top of the positive column (K—D) shows a distinct tendency to a maximum above 1500°C. The potential-gradient in the positive column (D—B) is pretty nearly constant with a slight minimum about 920°, after which it increases uniformly up to the highest temperature attained. The curves for heating up and cooling down are indicated by the aTTOWS, cooling curves being dotted. In Table XII. and fig. 6 the pressure is still further reduced to0'4 mm. The initial minimum and maximum of potential- difference at the negative end of the discharge have broadened out, so to speak, along the axis of temperature, and contracted parallel to the axis of potential. There is a gentle maximum about 800° C., and a second above 1500° C. before the final very rapid diminution. Table XIII. and fig. 7:—In this series of experiments, made soon after admitting a fresh supply of air, so far from the apparatus showing any tendency to leak, the pressure steadily diminished during the course of the experiments. This could only be accounted for as being due to the constant TaBLE XIII. ae | |} wee | Potential Difference. 4 ‘Current. (Pressure, |b ee mim. of | | Defin. °C, | K- A] K-E, E—A| K—D.| K—B.| Defin.| S92 | Hs. | A _ | ne te an {ee 1-9 74 || 540 | 355 | 187 | 480] 510 | 29:0 1740 0-172 20°5 | 550 | 580) 410 | 185 | 490 | 560 | 321 | 19:22) 0173 286 | 732| 600] 429 | 178| 510! 587 | 332 | 1992| O-171 335 | 887 || 615) 453 | 177 | 530] 602 | 35-6 | 21:36) 0-167 497 | 1153 || 640| 474 | 172| 552) 623] ... |... | O-167 | 60 | 1350 | 670| 515 | 169| 586] 654 | 41-1 | 2466) 0156 | 695 | 1500 || 710 | 542 | 169 | | 705 | 1518 || 705 | (530), 173 | 620 | 42-7 | 25°62 | 71-6 | 1536 | 710 | (546)! 164 | 640 | | 726 | 1552 | 710 | (649)| 161 | 641 ! | 73-3 | 1566 || 710 | (549); 161] 630] ... || 45-0 | 27-00) 73:8 | 1574 || 705 | (550)| 155| 615 | 74-2 | 1580 || 700 | (546)! 154 | 5981 ... |... | 2. | 0-150 | 665 | (515)| 150 | 560 | | 655 | (502)| 153 | 565 Va eee 71-0 | 1526 | 740 | (583)| 157/| 660 | 75-0 | 1593 || 700 | (346)| 154 | 624 | 761 | 1612) 680 | (528)| 152 | 600 767 | 1620 | 670 | (520); 150} 5Y0 74-5 | 1585 | 740 | (585)! 155) 655 | 72-0 | 1540) 760 | 605 | 155) 670 67-5 | 1468 Re ice ef 57-2 | 1290 | 755.) 598 | 157 | 660 | | | 740 | 583° | 157 | 655 385 | 987 | 720! 562 | 158] 687 | 55 | 188] 670, 514 | 156) 573| ... | 576 eee ee 0-140 P] ' . for) ay | i { | 2 ie ari ee 2 3 a N = | . es) 2 Se ae it eater oe es fs ou a os \ Sam oan HST Pt ee a ee Wy on ™_ > E ie) Sg ° 9S a | SH ro a) ° re fo) ne oO = 2 os > ofS oO cone = g5 & SSeS ee 2 eA H sey Ogaa i) ‘3 A i ae oo ae (eB aed o « = D> — \ tan Ay LJ mes \ SS SS SiG 2 eS RQ 3 " ee | 5 Do bh : Ss oa. ‘ tse © & He By 60 ‘ \ a D _ > sae a 38 \ ) Lad S | “ oe ‘ Y\. } QR em Sl See EE Ag Se ey (on) a Pes) ices ne 8 chee ne 2 Se ae eto — ww ‘SJ[OA — ‘ooTadoY YT [BIFW94OT SPO UN OO ORS RCL, Utara tate 700 i Mie aicoke Cunningham on the raising and lowering of the mercury in the McLeod gauge causing a movement of the heated and ionized air to and fro! hemueen the discharge-tube and the P.O; bulb, and so bringing about a more perfect drying which would, perhaps, also partly explain the cathode-fall being so much greater after the cathode had cooled down than it was before heating. We have, however, already noticed a progressive increase of this “lag” as the pressure was diminished. At this low pressure “(0° 15 mm.) the whole curve is, as it were, tilted up and there is only one real maximum value of the cathode- fall a little below 1600°C. The previous maximum is here only represented by a change of curvature. Above 1600° the diminution of cathode-fall becomes very rapid. The potential-gradient in the rest of the tube (E—A) re- mains practically unchanged with temperature. TABLE XIV. ae Potential Difference. | Current. Presi a ne | = Defin.| °C. | K—-A/K—D|D-A|D-B,| Defn. | AMP? Ee 7 | 103 || ... | 1460 < 90 | 104 | 347 | 0-030 See al nO gsm) ABO le 4 Gal 86 | 2:87 152) 430 | 4 ago i 202 | 545 )/ ... | 1490] ,, SGD Sl NGED S| ic ARO 3 96-8.) 1698 |) 3 “1480 17, 49:9 | 1158 |...) 14004) |, 64-2.) TATION 22. 14th. |. G52) 4 De he AD eS on 106 | 3:53 “3:6 |(16ya ce) TOROe, | 707) eral eee TAO en ale ae 106 | 353 79:7 | 1670 1) ee DBO de) eS 100 | 3:33 79°90. | 16754). Oo 80-4 | 1683 Ib 4.) 1510!) 80'7 | 1688 | ... 1500] 100 0-040 80-0 | 1676 | ... 1420] 145 | 80'8 | 1690 | ... | 1410 | 185 80-4 | 1683 || ... | 1880} 240 80-4 | 1683 | ... | 1885 [>310 >310 || 66 | 2:20 | - 80-2. | 1680.1; ... 1250). 901) 2 178 | 593 | 0-052 WAT | 1589 | ca) W200. 19°1 6:37 66:9 | 1458 ||... | 1140], 20-6 | 687 B72) | 1200 th eo eGo) |) 21:5 | 7-17 34:2 |) 850} Led LORD ae | 22-2 | 740 B00 4 oe0DN |) toa. ae | 1997 4) B96 A eh ORgi eae 12) S85 Hh a SEO 10°6 | 320.) 1030); 940) (4) oes. 1 Sa | aces 39 ||) 140.) O85 |) SB0r saa ee ol aay 30 nes oD POO ieee 105 | 3:50 28. |: G05 Hl STOR P70") | eae ee 98 | 3-27 725 | 290] ... 51 1:70 2-2 |: 85 || 1030) ‘720 > S10 20 os | 027 | 0976 ( | | | | OO Ea — oe Discharge of Electricity through Gases. TOL On reducing the pressure to 0°04 mm. (Table XIV.) the potential-gradient becomes so steep that only the German voltmeter was available for measuring the cathode-fall, and even it was working at a very unsensitive part of its scale. The electrode D was right in the middle of the negative glow, and the whole of the rest of the tube was practically dark. But as soon as the cathode became white-hot the pressure began to rise so much that the measurements on cooling down were not strictly comparable. The most interesting part, however, of this table is that which shows the effect of variations of current on the potential-gradient in different parts of the discharge. or all values of the current greater than about 2°5 x 10-* amperes the potential-difference across the whole 83°5 mm. (D—A) at the positive end of the discharge remained too small to be measured by any of the available instruments ; and, as has TaBLe XV. A=Cathode; K=Anode. { : | ne | Potential Difference. | | Current. pueeree| | mm. of | Sadi laeioze las) ey (elie, TAs Dea Amps.| Hg. | C. | A—K.| A—B.| B—D. (cale.) (cale))|| DS 104 |} 18 | 70) 875) 352) 255 607 | 268 |) 242 | 8:07 | | } 181 70| 850| 366] 214) 580| 270 || 245 | 8:17 | IP cont Be ( SkO1> SRO] 2x.) 249° Peso | / | | 850) 366) 231 597 | 253 || 243 | 8-10 | }155 | 438| 780} 367] 194 561 | 229 | 942 | 807-| 1-83 | } 174 | 482 | 775 | 368) 194 562) 213 | | | 181 | 498 || 775| 368| 198 566 | 209 || 24-1 | 803 | . liz-9 | 492) 775| 370] 192 562| 213 | 240 | 8-00 | | | 448 1060 | 770 | 370 | 202) 572} 198 || 239 | 7-97 | | 504 | 1167| 770! 369| 208 577, 193 || 236 | 7-87 | | 60°3 | 1340 | 768! 367 | 213 580| 188 | | 71-4 | 1533 | 765 | 365 | 220 585! 180 || 226 | 7°53 | | 71-4 | 1533 | 768} 358| 230 588 | 180 || 236 | 7:80 | 71-4 | 1533 | 765! 362) 217 | 579 | 186 | 241 | 8:03 77-5 |.1635 | 765 362| 225) 587 | 178 || 23-95] 7-98 | | 824 | 1716 | 770; 370| 232, 602 | 168 || 23:2 | 7-73 | | 370 | 224 594 | 24°5 | 8:17 ) bes | 1725.) -...-|. B75'| 220)\ 595 251 | 837 | 63:4 | 1397 || 793 380 | 208 | 588 | 205 || 249 | 8:30 : 514 | 1185 | 793, 383| 198 581 | 212 || 249° | 8:30 / | 194 525 | 793 | 383) 190 573) 220 | 246 | 8:20 | 176 | 485| 800; 383] 187, 570} 230 | 245 | &17 | 24 | 91] | 383 | 220| 603.| ... || 23:5 | 7-83 . 4 | 91) 845, 383] 207) 590| 255 || 248 | 8-27 23 | 89! 810! 385| 166 551 | 259 || 34-5 111-50 | | | 810 | 383| 160) 543} 267 |) 41-7 /13:90 | 182 | 702 Mr. J, A. Cunningham on the Taste XVI. A=Cathode; K=Anode. 465 | 1093 623| 409] 99] 508 Tae of Potential Difference. ‘| Current. node. | Pp | ressure, | | | B=D.\A=D) | Peed: Defin,) °C. | A-K.) A—B. (cale. | (cale. |D—K.| Defin. | SDS Merely: : . *obs.) | *obs.) | | eae | 0:55 20 | 632! 407 90x, 497 | 185 || 251 | 8:37 0°602* | 0:55 20 | 632 | 410 90x! ... mn 25°3 | 843 * | 055 20 632 | 409 90 | 499 | 133 || 20:1 | 837 117°5 484 | 620! 400 97 497'| 123 || 216 | 720 ere 488 | 623) 410 91 501 | 122 || 25:1 | 8:37 1195-| 530) ... | 418 | | 20-9 562 || 623 | 410 92; 802) 121 || 250 | 83a / 26'8 693 || 623; 410 93 | 505 120 || 25:5" | 6:50 30? ect (62ea- | 4a . | 20°7 | See | gag | | | | 115 || 25-1 | 8:37 | 1525 | 1205 | 623) 408] 99| 507) 116 | 250 | 833 630 | 1890 || 623 | 408] 101 | 509, 114 || 248 | 8:27 73:2 .| 1563 ||, 623°) - 407) 403 | 510) 113 || 248 816 | 409 | ,.. 4 w. |... ||) 251 Seay 176-4 | 1617 || 623} 410] 101) 511 | 412 }| 95-59) 850 ) 80'1 | 1680 |; (680)} 414 | (104)| (618)! 112 || 25:1 | 8:37 1806 | 1685 | 680 | 430; 89] 519 111 || 25:1 | 837 | 81:0 | 1693 || 640! 440/ 90x) 530x) (110)]/ ... ... | Gee 1653. | 1480 || 640 |... ... | 580%) 112 || 25°5 | 8-50 | | (640)} 452) (72) | (524), 116 || 25°5 | 8-50 /53:3 | 1220 | 640 | 452 71 | 523} 117 || 26-5 | 888 640 | 458 60 |} 518 | 122 || 289 | OG 208 560. 2065 555 | 640/ 450| 65] 515! 125 | 247 | 8-28 2 556 | 640) 444| 70] 514. 126 | 235 | 7-83 | o-619 78 | 645 | 446). 64] 510) 135 || 241 | 8-03 0-6 7 | ) 9:0 | 280 || 640 44, 64 510 | 180 | 239) 7a 20 } 1:2 645 447 63 510 135 || 246 | 8:20 a (Je) already been mentioned, the gas in this part of the tube remained quite dark. But on allowing the current to fall gradually below the above value a brilliant yellow positive column began to rise up from the anode, and the potential- gradient in this part of the discharge increased very rapidly. It was at first thought that the tube had begun to leak rapidly until a direct measurement with the McLeod gauge disproved this. The cathode-fall had also only shown a very slight diminution. And on increasing the current the potential- difference (D—A) fell off again instantly to its former immeasurably small value. While confirming the old well-known observation that at . ordinary temperatures the cathode-fall increases with increas- ing current-density, this table also shows that, on the other Discharge of Electricity through Gases. 703 hand, at high temperatures the cathode-fall diminishes with increasing current. The measurements of the fall of potential along the dis- charge at different temperatures of the anode are collected in Tables XV. and XVI. at pressures of 1°83 and 0°63 mm. respectively. The effects of temperatures on the fall of Fig. 8. Potential Difference at Anode (IK—D),—Volts. = Sess =- 0 "ROL 1000 1500 2000 Temperature of Anode, °C. potential close to the anode are shown in fig. 8. This ‘* anode-fall””? (K—D) shows a steady diminution with rising temperature. The changes of potential-gradient near the cathode were probably mainly due to its slow warming up, the amount of which could not, however, be measured. It will be noticed that though the total potential-difference across the electrodes diminishes, yet the “ anode - fall” K—D) increases with increased current at all temperatures of the anode, though, perhaps, less markedly at high tempera- tures. The potential-gradient in the positive column, as we have noticed before, diminishes with increasing current. I am glad of this opportunity to express my indebtedness to Professor Thomson for many encouraging suggestions during the progress of the work. St. John’s College, Cambridge. Maes. LXXV. Excited Radioactivity and Ionization of the Atmosphere. By EH. RurHerrord, M.A., D.Sc., Macdonald Professor of Physics, and 8. J. ALLEN, M.Sc., Demonstrator in Physics, McGill University, Montreal*. Sige’ experiments of Elster and Geitel+ and C. T. R. Wilson{ have shown that a well insulated charged conductor placed inside a closed vessel gradually loses its charge, and that this loss of charge is due to a small spon- taneous ionization of the volume of air inside the closed vessel. Wilson calculated from his results that about 19 ions per c.c. are produced in the air per sec. In a later paper§ Wilson has shown that the ionization in different gases varies approximately as the density and pressure of the gas. These results point to the possibility that the ionization observed in gases may be due, in part at least, to the emission of an ionizing radiation from the walls of the containing vessel. Recently Elster and Geitel || made the interesting discovery that a negatively charged conductor, placed in the open air, becomes temporarily radioactive. This radioactivity decays in the course of a few hours. The phenomena appear to be closely analogous to the ‘ excited” radioactivity produced by the radioactive emanations of thorium and radium. The excited activity from the air can be concentrated on the negative electrode in exactly the same way as one of the authors has shown for thorium-excited activity. In addition Elster and Geitel have shown that the substance responsible for the radioactivity can be removed by solution in acid. On evaporating the solution to dryness an active residue, which decays with time, is left behind in the vessel. This also is in striking agreement with what one of us (lve. et.) had previously shown for thorium-excited activity. In the experiments of Hlster and Geitel, and Wilson, the amount of ionization of air has been determined by observing the rate at which the leaves of a charged electroscope of _ special construction fall together. This method, while very simple and advantageous for some experiments, is, in general, slow, and in many cases does not allow of sufficient variation of experimental conditions. In the present investigation the authors have utilized a * Communicated by the Authors. {Communicated to the American Physical Society, Dec. 27, 1901; Abstract published in the Phys. Zeit. No. 11, 1902. + Phys. Zeit. Noy. 24, 1900, t Proc. Roy. Soc. March 1901. § Ibid. Dec. 1901. || Phys. Zect. ii. p. 76 (1901); xl p. 590 (1901). q; Phil. Mag. Feb. 1900. tate ae | a Raa Sill li ee ee Ae Excited Radioactivity and Ionization of the Atmosphere. 709 sensitive quadrant electrometer for examination both of the ionization and excited radioactivity produced in air. The electrometer employed is a modification of the Dole- zalek electrometer which is described in Instrumente Kunde, Dec. 1901. It is of the ordinary quadrant type, with a very light needle of silver paper suspended by a fine quartz fibre. The apparatus, as constructed by Herr Bartels, of Gottingen, was for determination of small P.Ds. for electro- chemical work. For our purpose it was necessary te com- pletely alter the insulation and method of connexion of the quadrants. In the present experiments the needle was charged at intervals of two days by lightly touching the needle by a fine wire connected to a battery of 200 volts. It was found that the needle did not lose more than 10 per cent. of its charge in 24 hours. The damping of the needle, on account of its lightness, was fairly rapid. and no extra to) damping vane was required. The deflexion was observed by a telescope and scale at a distance of 2 metres. The zero point was found to be very steady. For the first suspension employed the electrometer gave a deflexion of about 1800 mms. of scale corresponding to one volt P.D. between the quadrants, when the needle was charged to 200 volts. This suspension was accidentally broken in the course of the experiments and was replaced by a quartz fibre which gave only about + of this deflexion for the same voltage. When dealing with the very small rate of discharge which is produced by the spontaneous ionization of air, it is very essential that every precaution should be taken to guard against external electro- static disturbances. The electrometer and all the connecting wires were inclosed in gauze cylinders connected to earth. The floor and woodwork in the immediate neighbourhood of the testing apparatus were covered with metal connected to earth. The separation of the quadrants was done by means of a special mercury key operated from a distance by a cord. The insulating substances necessary in experimental arrangements were completely diselectritied by means of flames. Production of Excited Radioactivity. The simplest method of obtaining a large amount of excited radioactivity from the air is to expose a long insulated wire charged to a high negative potential in the open air. After exposure for several hours the wire is removed and wound on a frame, or in the form of a flat helix. The ionization produced by the radioactive wire in the testing vessel is then observed,) by means of the electrometer, in the usual way. Phil. Mag. 8. 6. Voi. 4. No. 24. Dec. 1902. 3A 706 Prof. E. Rutherford and Mr. 8. J. Allen: Hacited Elster and Geitel in their experiments have used an electro- scope to measure the ionization produced. In order to produce a considerable quantity of activity on the conductor it is necessary to charge the wire to a high negative potential. Potentials varying from —5000 to — 100,000 volts have been used in the experiments. A positively charged wire remains quite inactive howeyer long it may be exposed. Decay of Excited Radioactivity. The excited radiation from the air decays with the time in a manner similar to the excited radiation from thorium and radium, but at a different rate. The excited radiation from thorium falls to half value in about 11 hours, while the excited activity from air falls to half value in about 45. minutes for the range of voltages examined. It has been shown * that the excited radiation from radium decays in an irregular manner, the rate of decay depending on the time of exposure. The rate of decay is rapid at first, then nearly stationary for some time, and then a regular decay to zero, falling to half value in about 30 minutes. It is thus seen that the rate of decay of excited activity, due to the atmo- sphere, is more nearly allied to that from radium than to that from thorium. In the experiments detailed below the excited activity was produced on a long insulated copper wire, 15 metres long, suspended outside the laboratory window about 15 feet from the ground. The wire was kept charged by means of a Wimshurst machine driven by a motor. The potential of the wire was measured by means of the sparking-distance between two brass knobs. | In order to regulate the potential of the exposed wire to any desired value a needle-point connected to earth was placed near a small plate connected to the charged wire. The distance between the point and the plate was adjusted until the spark just refused to pass between the knobs. This. method was found to be more satisfactory than varying the speed of the machine. After the wire had been exposed a definite time, it was rapidly removed and wound on a rectangular metal frame 120 ems. long and 10 ems. wide. * Rutherford, Phys. Zeit. xu. p. 254 (1902); and Rutherford and Miss Brooks, Phil, Mag. July 1902. Radioactivity and Ionization of the Atmosphere. 707 The method of winding is shown in fig. 1, where the frame A is seen in position inside the testing cylinder B. The testing cylinder was of metal, about 150 cms. long’ and 30 ems. diameter. The outside cylinder was connected to a Fig. 1. battery of 100 volts. ta order to ensure that there was no conduction current between B and A over the supports the insulator CD was cut into two parts and separated by a metal ring connected to earth. The arrangement can be clearly seen from the figure. 3A 2 708 Prof. E. Rutherford and Mr. 8. J. Allen: Ezcited The radiation from the wire ionized the gas inside the testing cylinder and the current between the ‘electrodes was observed with the sensitive electrometer in the usual way. On account of the weak ionization of the air by the radiation a P.D. of 100 volts was sufficient to remove all the ions to the electrodes before appreciable recombination, and to give the maximum current through the gas. Vig. 2,1 shows the decay-curve for a copper wire exposed UMS) NEEGEEEES 210 minutes inside the en at a P.D. of —26000 volts; fig. 2, 11 the curve for the same wire exposed 270 minutes in the open air at —24000 volts. The ordinates represent divisions per sec. of the electrometer and the abscissee time in minutes. In most of the experiments (especially when the wire was exposed for several hours) it was found necessary to use a condenser in parallel with the electrometer to decrease the rate of movement of the needle. There was always a current (about 2°d divisions per sec.) in the testing vessel when the wire was inactive, due to the spontaneous ionization of the air in the cylinder. Allowing for this it will be seen that the current (which is proportional to the intensity of the radiation) falls off in a geometrical progression with the time, falling to half value for both cases in about 45 minutes. | ha St AO cate ag IN A. ta iy ath it ily Radioactivity and Ionization of the Atmosphere. 709 Fig. 3 is a decay-curve for a lead wire exposed in an attic 190 minutes at — 25000 volts. In this case the lead wire was wound in the form of a flat spiral and placed inside a testing vessel consisting of two parallel plates, one of which Fig. oe Rees = 20 . 40 6O =e) 10 Ro) 140 fo) [e) 12 was connected to the electrometer and the other to the battery. This again falls to half value in about 45 minutes. A large number of curves of decay have been determined under very varying atmospheric conditions, but no certain differences in the rate of decay have been observed, although the amount of excited activity in a given time varies greatly with the weather and amount of wind. The rate of decay was the same for a copper as for a lead wire, and was inde- pendent of the diameter of the wire. The rate of decay for a brass rod charged at — 100,000 volts was about the same as for a lead or copper wire exposed at —5000 volts. The rate of decay for low voltages has not been investigated. We may thus conclude that over the range examined the rate of decay is regular and independent of conditions. In this respect also it resembles the excited radiations produced by thorium and radium. It will be seen, from these results on the rate of decay, that if the intensity of the excited radiation is initially I), the intensity I after a time ¢ is given by I=I,e-*”. 710 ~=Prof. E. Rutherford and Mr. 8. J. Allen: Excited Since tL : I, when ¢=45 mins. rA='00026. If the excited activity produced on the wire is due to a uniform rate of deposit of radioactive material the radiation from which decays with the time according to the above equation, it necessarily follows* that the intensity I after a time of exposure ¢ is given by I=, (1—e-™), where I, is the maximum value of the intensity reached after - a very long exposure. If this result is correct the amount of excited activity in a given wire for a fixed voltage should reach half its final value in 45 minutes. Some experiments have been made on this point with wires exposed in the open air for different times. The amount of excited radioactivity in the air was found, however, to be too variable to test the truth of the equation. The results, how- ever, showed that the amount of activity increased at first roughly in proportion to the time, but after three or four hours’ exposure reached a practical maximum. More accurate ex- periments on this point are at present in progress, using a closed room instead of the open air, when the amount of excited activity is much more constant. The amount of excited radioactivity from the air increased with the voltage of the exposed wire. On account of the variation of the amount of excited radioactivity in the air from hour to hour and day to day no definite results on the variation of the amount of excited radioactivity with the’ voltage were obtained. isffect of Weather Conditions. A large number of experiments were made on the effect of atmospheric conditions on the amount of excited radioactivity from the air. The wire was usually exposed for 30 minutes at a voltage of —25000 volts, outside a laboratory window, at a height of about 15 feet from the ground. ‘The results showed that the amount of excited activity produced from the air varied very greatly with the atmospheric conditions. Other conditions being the same, a bright clear day gave more excited activity than a dull cloudy day. The effect of temperature was not very marked. If anything slightly more activity was obtained on a bright day during the Canadian winter, with a temperature of about —20° C., than * E, Rutherford, Phil. Mag. Feb. 1900, p. 180. Radioactivity and Ionization of the Atmosphere. a11 on a bright warm day in the spring. The most powerful factor in * determining the amount of activity given to the Wire is the presence or absence of wind. A windy day always gave much greater effects than a quiet day, when other conditions were the same. This is true whether the air was cold or warm, or the day bright or dull. Most of the experiments were made during the Canadian winter, when there was about two feet of snow over the ground. The prevailing wind was from the north, and had been carried over snow-covered lands. The fact that the amount of activity was uninfluenced by the presence of snow shows that the excited activity is not likely to be due to any effect arising from vegetation. The amount of water-vapour in the air appears to have little influence on the result, for at —20° C, the air is extremely dry. Penetrating Power of Hucited Radiation. It has been shown in a previous paper* that the penetrating power of the excited radiations of thorium and radium was the same. As the penetrating power is one of the methods of distinguishing between the various radiations a special experiment was made to compare the penetrating power of the excited radiation from the air with that of other known radiations from radioactive substances. Lead wire was employed in these experiments as it could readily be retained in the form of a flat helix. The wire was excited by exposure of two to three hours at —30,000 volts. It was.then wound to form a flat helix and placed between a parallel plate apparatus. The ionization current between the plates was observed for different numbers of sheets of thin aluminium foil placed over the helix. The average thickness of the aluminium foil was ‘00034 cm. The results are shown in Carve I. fig. 4 (p. 712) where the penetrating power of other known. types of radiation are added for comparison. The excited radiation due to air has greater penetrating power than any of the types of radiations, not deviated by a magnetic field, from the radioactive substances uranium, thorium, and radium, and is also more penetrating than the excited radiation produced by radium and thorium. No special experiment has been made to determine the absorption of the excited radiation in its passage through the air, but its approximate amount can be readily deduced from known data. In all the different types of radiations examined * E, Rutherford and Miss H, T. Brooks, Phil. Mag. July 1902. 712 Prof. E. Rutherford and Mr. 8S. J. Allen: Excited it has been generally found that if one radiation is more easily absorbed than another, in aluminium for example, it is also more easily absorbed in air. Since the excited radiation from the air is slightly less absorbed in aluminium than that due to thorium, we can thus conclude that it is slightly less absorbed in air. Ne eeeeEES NCCC | teat TT Now it is known that the fia of the xsd radiation from thorium falls to half value after passing through 1°6 ems. of air. It thus follows that the intensity of the excited © radiation from air falls to half value after passing through about 2 cms. of uir, and is almost completely absorbed in a distance of 10 or 12 cms. From the differences observed for the penetrating power and ratio of decay we can conclude that the excited radiation from air cannot be ascribed to the presence of any known radioactive substance in the atmosphere. Le] Transmission of Eecited Activity. We have seen that the excited radiation from the air is similar in all respects to the known types of excited activity by thorium and radium. In both eases the activity is confined to the: cathode in an electric field, and can be partly removed by rubbing with a cloth or by solution in acid. The differences observed in the rate of decay and pene- trating power of the radiations show that the effects obtained Radioactivity and Ionization of the Atmosphere. 713 cannot be ascribed to the presence of a minute quantity of thorium or radium emanations in the atmosphere. The close resemblance in the phenomena, however, renders it probable that the excited activity from the air is due to a process similar in character to that which produces excited activity from the emanations of thorium and radium. One of the authors* has recently shown that in the case of radioactive substances the excited activity is due to a transmission of positively charged radioactive carriers to the cathode. These carriers travel in an electric field with about the velocity of the positive ions produced in air by Réntgen or Becquerel rays. There seems to be little doubt that the excited activity is due to a deposit of a minute quantity of intensely active radioactive matter. Such an hypothesis is essential to explain the facts of solutions, and that the radioactivity can be trans- ferred from the radioactive body to the cloth by rabbing. The production of excited activity from the air cannot be ascribed to any surface action on the conductor due to the electric field. A wire does not give any appreciable activity if it is confined in a cylinder where the volume of air is small, although the wire is subjected to the same voltage as in the open air. All the evidence obtained up to the present points strongly to the conclusion that the excited activity is derived from the volume of the air surrounding the charged wire. Since the activity is confined to the cathode, the carriers to which the activity is due must possess a positive charge. These carriers may obtain a positive charge either by the condensation of temporary radioactive matter “of some kind round the positive ion already existing in the air, or by the expulsion of a negative electron from the carrier. The latter explanation seems the more probable, for we now know + that all the radioactive substances thorium, radium, and uranium, as well as the excited activity due to thorium and radium, possess the property of spontaneously expelling electrons. There is as yet no definite evidence of the origin or mode of production of these radioactive carriers in the air, but assuming their presence, many of the experimental facts observed receive a simple explanation. | The higher the potential of the wire the greater the distance from which the carriers are conveyed to ‘the cathode. The amount of excited activity on a wire exposed in free space, on this view, should increase rapidly with increase of voltage. * Phys. Zeit. x. p. 210 (1902). + Rutherford and Grier, Phys. Zeit. xvii. p. 385 (1902). 714 Prof. E. Rutherford and Mr. S. J. Allen: Evcited There is strong evidence that a wire charged to a high poten- tial attracts the carriers over a large volume of air. It was experimentally found that the amount of excited activity obtained from a wire charged to — 20,000 volts in a cylin- drical vessel of volume 141,000 cub. cms., when outside air was drawn through it at a rate of 500 ems. per sec., was only a few per cent. of the amount obtained from the same wire in the open air. The increase of exolted activity observed on days on which a strong wind is blowing is, on this view, due to the con- tinued supply of fresh carriers which are brought in the sphere of action of the electric field. Since the exposed wire merely acts as a collector of radioactive carriers under the influence of the electric field the amount and nature of the excited radiation should be independent of the nature of the conductor, and this is found to be the case. It thus appears probable that radioactive carriers are con- tinually produced trom some constituent of the atmosphere, but at a rate depending on atmospheric conditions. Bright clear weather appears to be the most favourable condition. Since the earth is nearly always charged negatively with regard to the upper atmosphere, it follows that these radio- active carriers are being continually deposited over the surface of the earth. We must thus regard the earth as covered with an invisible layer of intense radioactive material which ionizes the air strongly within a few centimetres of the surface. The presence of these carriers in the volume of the air will also cause the production of fresh ions throughout the atmosphere, for each carrier acts as a radiating centre. A hill or mountain peak, or any high mass of rock or land, concentrates the earth’s electric field upon itself and consequently it will receive more excited radioactivity per unit area than the level plain. Elster and Geitel have pointed out that the greater ionization observed in the neighbourhood of projecting “peaks, receives a satisfactory explanation on this view. Spontaneous Ionization of the Air. The experimental arrangement. shown in fig. 9 was employed for determining “the number of ions produced per c.c. per sec. in air and the variation of the ionization current with the strength of the electric field. The current was observed by means of the electrometer between two concentric zinc cylinders A and B, 154 cms. in length, 25°5 and 7°5 cms, in internal diameter. The evlinders were placed vertical and the base of both cylinders closed. q . | 2 f : e Radioactivity and Ionization of the Atmosphere. 715 The large cylinder was closed at the top by a zinc plate, in the centre of which was a circular opening slightly larger than the internal cylinder. A metal flange, fixed round the top of the inner cylinder, rested on an ebonite ring C. Fig. 5. LARTH eT TE RE OTT ree oe et ee ee | SS oten biden taka a al ee el ee ae eee er nt PRAT ERTIES EET PT TIE” PELE ET EE LT PITTED Seen es ee TT eT ee ETE te ae eae Ce Between the ebonite and the zine plate D was placed a ring of thintmetal E, connected to earth, which rested on a similar ring of a partial insulator like eld EY The thin metal ring, connected to earth, served as a guard ring and ensured that even with a large P. D. between the cy linders, no current 716 Prof. E. Rutherford and Mr. 8. J. Allen: Exzetted could leak across the insulator to the inner cylinder, which was connected to the electrometer in the usual way. The outer cylinder was connected to one pole of a battery of small storage-cells, the other pole oftwhich was earthed. - The electrometer needle showed quite a rapid movement due to the ionization current between the electrodes with a P.D. of a few volts between the cylinders. The cylinder was made fairly air-tight and allowed to stand undisturbed. Observations of the current between the cylinders were made at intervals for over a month. In order to avoid correction for the slight variations in sensitiveness of the electrometer from day to day, the ionization current between two paralleled insulated plates due to a standard sample of uranium oxide was observed at the same time. Previous experiments have shown that the uranium oxide is a very constant source of radiation. The following tables show the variation of the current, due to the spontaneous ionization of the air, with the P.D. between the cylinders. Table I.is for air which has stood undisturbed for a month inside the vessel; Table [I. for the ordinary air of the room ‘several hours after it had been introduced into the apparatus. TABLE I. TABLE I. ——_ : | Current in divisions | | Current in divisions | | P.D. in volts. per sec. of P.D. in volts. per sec. of | ) | electrometer. . ) electrometer. ) ae i “Be ae: 04 | 8 “50 EDD) "22 | ad 59 21, ae 82 | 4:2 | 65 a. 6:5 02 | 65 67 | 3 | ‘61 13 “EL 26 ) 65 | 26 “(2 39 . “67 | 52 | 73 52 68 | 1a | } ; The results are expressed graphically in fig. 6, curves I. and II. respectively. The curves are very similar to those observed when the air is ionized by Becquerel or Rontgen rays. The current first increases approximately directly as the voltage, but soon reaches a stage in which large variations of the voltage only cause a slight increase in the current. On account of the very small amount of ionization of the air and consequent slow rate of recombination of the ions, the maximum current is reached for a very small voltage. The current for 50 volts Radioactivity and Ionization of the Atmosphere. 717 isnot very different for the two samples of air, but in Curve I. the current reaches an approximate maximum much earlier than in Curve II. This difference is probably due to the presence of dust particles in the air in the latter case. Some Fie. 6. g ee Ee EST, SR ae E sree pee eS pe ea an i IN Re tia a ae ae Da a Nd é Basins eel fa | Lee bewsilermen iectms | Ll lo 20 30 40 50 of the ions in their slow passage between the cylinders give up their charges to the dust nuclei. This action causes an increase in the rate of combination of the ions and conse- quently a larger electric field is required to produce the maximum current. The capacity of the electrometer, cylinder, and connexions, was 150 Es. units when 1 mm. division of electrometer corresponded to *00182 volt. The average value of the movement of the electrometer needle was 100 divisions in 132 seconds for 50 volts between the cylinders, The current between the cylinders was thus 6°9 10—* E.s. units or 2°3 10—* amperes. The volume of air between the cylinders was 71200 e.c. Taking the value of 6°5 10- E.s. units, found by J. J. Thomson * as the charge on an ion, the number of ions produced per c.c. per second is 15. * Phil. Mag., 1898. 40 -30 718 Prof. E. Rutherford and Mr. 8S. J. Allen: Excited This is not very different from the value of 19 found by Wilson for air inside a silvered glass vessel, using the electroscope method. No certain difference was observed in the current for a period of time extending over one month. The production of excited radioactivity from the air suggested the possibility that a radioactive emanation was present in the air and that this might cause the ionization observed. If this is so, the radiating power decays at an extremely slow rate, or the emanation is being continuously reproduced in the inclosed space. Application of the Ionization Theory. In the spontaneous ionization of air we are dealing with an extremely slow rate of production of ions, and it is of interest to see how far the experimental results are in agree- ment with the ionization theory of gases, which has ‘been previously tested in cases where the ionization is. many thousands of times more intense than the present one. We have already noted that the variation of current with the voltage is ingeneral agreement with the theory. If g is the constant rate of production of ions per sec, and no electric field is acting, the number n of ions per c.c. increases until the rate of production i is equal to the rate of recombination of the ions, or g=an®, where @ is the constant of recombination. Now we have shown that g=15, and McClung * has found from the recombination of ions of Réntgenised air that a =3400 e about, where ¢ is the charge on an ion. Substituting these values, we find n= 2600, 2.é.. when a steady state is reached, the number of ions per c.c. is 173 times the number produced per second. The time T taken for this number of ions to diminish to half, supposing the rate of production stopped, is given by =174 seconds. We can obtain a rough approximation of the agreement with theory of the current voltage curve shown in Curve I. (fig. 6) from the following considerations. The electric field X, at any point distant » from the centre * Phil, Mag, March 1902. Feat — . a _ r - cs < r Radioactivity and. Ionization of the Atmosphere. 719 of two concentric cylinders of radii 6 and a, is given by Vv "82 V FS ARE al ap l : sage = 29 a substituting values of 6 and a of cylinders in fig, 5. Now if N is the maximum number of ions per c.c., the. current ? per unit length of cylinder over any cross-section. when a small P.D. V is applied, is given by = Ber N ce. u aX, where w= sum of velocities of positive and negative ions im unit field. Substituting the value of X ?=1-64LaNeuV. Tf I is the maximum current when all the ions produced reach the electrodes l=qger(b'—a), and ti G4N wa ¥ I g(l’—a’) Now for a P.D. of *36 volt the current 7 is ‘4 of its maximum value (see Table [. p. 716). Now it will be shown later in the paper that the velocity of the ions produced in air is about the same as that of the ions produced by Roéntgen rays. The value of u (the sum of the velocities of the positive e and negative ions) for a gradient of 1 volt per em. is thus about 3-2 cms. per sec. Substituting these values, we obtain = =352. - Taking into consideration that ‘4 of the ions are removed by the current before recombination, it follows that when no. voltage is acting bs aie eae Pokus =53 roughly. Now we have shown that if a has the same value as that obtained for intense ionizations wa ; should equal 174, a value over three times as great. There are, however, several causes at work which tend to - make the observed value less than the theoretical. In the ’ ei ibs: | 720 Prof. KE. Rutherford and Mr. S. J. Allen: Lacited first place, no correction has been made for the disappearance of ions by diffusion to the sides of the vessel. This can be shown to be quite an important factor in causing a low value of —. Curve i (fig. 6) shows what an important influence the presence of dust has on the shape of the current voltage curves. In addition, it has been assumed, for simplicity of calculation, that the potential g oradient is not disturbed by the movement of the ions. Experiment and theory have, how- ever, shown that there is a sudden drop of potential near both _ electrodes and that the electric field some distance from them is less than if no ions were present. All of these three causes act in the same direction and tend to give too low a value N ot + The agreement between theory and experiment is thus as close as could be expected under the experimental conditions. The results show clearly that, when air is kept in a closed vessel and no electric field is applied, the number of ions per unit volume, when equilibrium occurs between the rate of production and dissipation, is more than 50 times the number produced per sec. per unit volume. Velocity of the Lons. Some experiments were made to obtain an approximate estimate of the velocity of the ions which are spontaneously produced in air and at the same time to determine the number of ions per unit volume present in the outside air. For this purpose, the apparatus shown in fig. 7 was employed. Air from the outside of the building was drawn through a zine cylinder, length 200 ems., diameter 30 ems., by means of a fan driven by a motor. The air in its passage through the tube passed through three circular parallel wire gauzes, A, B, C, 2 ems. apart and insulated from each other. The first gauze A was connected to earth, the second B to the electrometer, and the third C to one terminal of a battery of storage-cells, the other terminal of which was to earth. A guard-ring, connected to earth, was arranged between B and C to ensure there was no 5 e conduction leakage across the insulators between B and C. Suppose gauze C is charged positive. The positive ions, carried with he current of air between the gauzes, start i travel up against the current of air, while the negative ions travel to the positive electrode with the current. If the velocity of the positive ions in the electric field is greater - Radivactivity and Ionization of the Atmosphere. 721 than the current of air, they will all reach the gauze B and for a given current of air the current observed with the electrometer will be unaltered when the strength of the electric field is increased. Fig. 7. B CARTH It was experimentally observed that even with a small electric field, there was some current to the gauze B. This amount increased with the voltage to a practical maximum. 5 The experimental results are shown graphically in fig. 8 (p. 722) for velocities of the current of air of 100, 205, and 250 cms. per sec. respectively, when the gauze C was charged positively. Ii will be seen from the curves that, for a velocity of 250 ems. per sec., the maximum current is reached with a P.D. of about 350 volts. Since the gauzes were 2 cms. apart, the velocity K of the positive ions for a potential gradient of 1 volt per cm. is given by 2u 2x 250 RS AEs a0 where u is velocity of current of air and V the smallest P.D. for which the niaximum current is reached. The other two curves also give a value of the positive ion of about 1:4 cms. per sec. It was not found possible to obtain more than an approximate result for the velocity of the ions, on account of the variation in the conductivity of the air drawn through in the course of a series of observations. The curves shown in fig. 8 were obtained on special days when the variation of the conductivity was small. Phil. Mag. 8. 6. Vol. 4. No. 24. Dec. 1902. 3B = ]"4 cms. per sec., 722 Prof. EB. Rutherford and Mr. 8. J. Allen: Eveited Observations made ina similar way, to determine the velocity of the negative ion, were not very definite on account of variations during an experiment. The results showed that ig. 8. 4b if | 4oo 500 Qu: e aphiele ~ 200 300 600 the velocity of the two ions was about the same, but it was not possible to decide whether the negative ions move slightly faster than the positive, as is the case for ions produced by Rontgen and Becquerel rays in air. The results obtained for the velocity of the ions are only approximate in character, but they point to the conclusion that the ions produced spontaneously in the atmosphere travel at about the same rate in the electric field as the ions produced in air by Rontgen and Becquerel rays. In a recent determi- nation Zeleny * has shown that the sum of the velocities of the positive and negative ions, produced by Roéntgen rays in dry air, 1s about 3:2 cms. per sec. Variation of the Number of Lons in the Aur. By noting the maximum current between the gauzes, an estimate can be made of the number of ions per unit volume present in the air drawn through. If A is the area of the cross-section of the cylinder, uv the mean velocity of the current of air, N the number of ions — per unit volume, the maximum current z observed by the electrometer is given by j;-A.y.N.e, where e is the charge on an ion. * Phil, Trans. Roy. Soc. 1900. Radioactivity and Ionization of the Atmosphere. 723 Substituting the observed values of i, A, and w in this equation, the value of N can be deduced. The value ef N was found to be variable both from hour to hour and day to day. The following numbers illustrate a few of the results obtained. Number of ions per Date. unit volume. ee ee, Se ee as 2 AO Re ee ees 30 SANs ATE ME Ta oe Se ro 14 Oe el) ME evil) ate ee ANY Nay cute 16 AME UN SB Res Ske, Ge 13 The temperature of the air in most of these cases was about —12° C, A bright clear day was found to give a greater value of N than a dull day. A very similar apparatus has been employed by H. Ebert * to determine the number of ions present in the air, only in his experiments the air was drawn between concentric cylinders, and an electroscope employed instead of an electrometer. We see from the above results, that the number of ions per unit volume in the air varies considerably, but on three days was almost the same as the number produced per sec. in a closed vessel. This is a surprisingly small number if we consider the outside air to be ionized at the same rate as the air inside the closed vessel ; for we have shown earlier in the paper, that in a closed space the number of ions per c.c. increases to 50 times the number produced per sec. before the rate of recombination is equal to the rate of production. After making due allowance for the causes tending to remove the ions, viz., the presence of dust and other particles in the outside air, and the electric field between the upper atmosphere and the earth, the number per unit volume is far lower than would be expected. It is possible that the spontaneous ionization of the air observed in closed vessels may be due (in part at least) to a radiation continuously emitted from the walls of the vessel. The spontaneous ionization of the outside air may, on this view, be much smaller than that observed in closed vessels, and the number of ions present per unit volume correspondingly less. McGill University, Montreal, June 9th, 1902. * Phys. Zeit. No. 46, 1901, poy Spee LXXVI. Notices respecting New Books. Harper's Scientific Memoirs. Edited by J. 8S. Ams, Ph.D., Professor of Physics in Johns Hopkins University. 15 volumes. New York and London: Harper & Brothers, Publishers. \ i heartily commend the enterprise of the publishers in issuing this most timely series of reprints and translations of classical scientific memoirs. es 15 volumes published include the foilowing :— L. The Free Hapaieon a Baan Memoirs by Gay-Lussac, Joule, and Joule and Thomson. ‘Translated and edited by J. S. Ames, Ph.D. II. Prismatic and Diffraction Spectra. Memoirs by Joseph von Fraunhofer. Translated and edited by J. S. Ames, Ph.D. III. Réntgen Rays. Memoirs by Rontgen, Stokes, and J. J. Thomson. ‘Translated and edited by George F. Barker, LIL.D. IV. The Modern Theory of Solution. Memoirs by Pfeffer, Van’t Hoff, Arrhenius, and Raoult. Translated and edited by Harry C. Jones, Ph.D. V. The Laws of Gases. Memoirs by Robert Boyle and E. H. Amagat. Translated and edited by Carl Barus. VI. The Second Law of Thermodynamics. Memoirs by Carnot, Clausius, and Thomson. ‘Translated and edited by W. F. Magie, PhD: VIL. Lhe Fundamental Laws of Electrolytic Conduction. Me- moirs by Faraday, Hittorf, and F. Kohlrausch. Translated and edited by H. M. Goodwin, Ph.D. VILL. The Lffects of a Magnetic Field on Radiation. Memoirs by Faraday, Kerr, and Zeeman. Edited by E. P. Lewis, Ph.D. IX. The Laws of Gravitation. Memoirs by Newton, Bouguer and Cavendish; together with abstracts of other important memoirs. Translated and edited by A. Stanley Mackenzie, Ph.D. X. The Wave Theory of Light. Memoirs by Huygens, Young, and Fresnel. Edited by Henry Crew, Ph.D. XI. and XIL. The Discovery of Induced Electric Currents. Vol. J.: Memoirs by Jeseph Henry. Vol. II.: Memoirs by Michael Faraday. Edited by J. 8S. Ames, Ph.D. | XIII. Phe Foundations of Stereo-Chemistry. Memoirs by Pasteur, Van’t Hoff, Lebel, and Wislicenus. ‘Translated and edited by George M. ‘Richardson, Ph.D. | XIV. The Expansion of Gases by Heat. Memoirs by Dalton, Gay-Lussac, Regnault and Chappuis. Translated and, edited by Wyatt W. Randall, Ph: i XV. The Laws of Radiation and Absorption. Memoirs by Prévost, Stewart, Kirchhoff, and Kirchhoff and Bunsen. Trans- lated and edited by D. B. Brace, Ph.D. The volumes are arranged on a uniform plan, which consists in having a general preface by the editor on the subject dealt with in Notices respecting New Books. 125 the volume; this is followed by the memoirs, a biographical sketch of the author being appended to each memoir. The bibliography and index at the end of each volume form useful features. In a few cases, where the papers seemed of excessive length, some portions have been left out; such omissions have, however, been indicated in every case, and as a good deal of judgment appears to have been exercised in the matter, the arrangement has not detracted from the valne of the papers. We hope that the publishers will see their way to add to this most useful series of scientific classics. Sichtbare und Unsichthare Bewegungen. Von H. A. Lorenz. Unter Mitwirkung des Verfassers aus dem Holliindischen iibersetzt von G. Srepert. Mit 40 eingedruckten Abbildungen. Braunschweig: F. Vieweg und Sohn. 1902. Pp. 123. Ir is not every distinguished man of science that condescends to write a popular book; and in many cases the attempt when mado_ is hardly asuccess. But there are notable exceptions ; anda perusal of the book before us has convinced us that Professor Lorentz’s gift of clear exposition attains to the same high standard of excellence as that which characterizes his scientific work. The book before us is the outcome of a course of seven lectures which the author was asked to deliver to anon-scientific audience, and forms most interesting reading. After expounding the leading principles of dynamics in the first three lectures, which are entitled respectively ‘‘ Rectilinear Motion,” “‘ Curvilinear Motion,” ‘“* Wave- Motion. Light-Waves,” the author considers, in Lecture IV., the subject of Light in greater detail, especially in connexion with Spectrum Analysis. This is followed in Lecture V. by “‘ Molecular Motion ”—including a sketch otf the kinetic theory of gases. Lecture VI,, on ‘ Electrical Phenomena,” is one of the most interesting in the book, as it contains a simple exposition of the electronic theory and the Zeeman effect. Lecture VII. is intended as a sort of réswmé and expansion of the preceding lectures, con- sidered with special reference to the principle of the Conservation of Energy. The book is one which may be read with pleasure and profit by the advanced student as well as the general reader. Electrochemical Juchiegiey. Vol. I. No.1. $29 Chestnut St., Philadelphia, Pa., U.S.A., September, 1902. THE appearance of a new periodical devoted entirely to the electro- chemical industry is a healthy sign of the development of that industry in the United States. The first number promises well. It contains several interesting articles by well-known experts, one of the most striking of which is ‘“‘ Niagara as an Electro- chemical Centre.” We heartily wish the new periodical every success, mica ~ 726} INDEX to VOL. IV. ——<—>——_ AcrTon E and chloroform, on the vapour-pressures of mixtures of, 121 /Ether, on motion through the, and double refraction, 678. Air, on induced-radioactivity in, 352; on the current-density at the cathode in the electric discharge in, 608, Alkali salt-vapours, on the laws of electrolysis of, 207. Allen (S. J.) on excited radioactivity and ionization of the atmosphere, 704, Alternating currents, on the electrical resistance of bismuth to, 554, Atmosphere, on the chemical and geological history of the, 436; on ionization of the, 704. Atomic weights, on ageneral numeri- cal connexion between the, 103; on the law of, 411, 504, Atoms, on the weights of, 177, 281. Baker (W. C.) on the Hall effect in gold for weak magnetic fields, 72. Barus (Dr. C.) om the sizes of water- particles producing coronal and axial colours in cloudy condensa- tion, 24; on spontaneous nuclea- tion and on nuclei produced by shaking solutions, 262. Bismuth, on the electrical resistance of, to alternating currents, 554 ; on - the resistance of thin films of, 660. Blake (Rey. J. F.) on a remarkable inlier amoung the Jurassic rocks of Sutherland, 423. Blakesley (T. H.) on a method of mechanically obtaining 6 from the hyperbolic trigonometrical func- tions of 6, 238. Blue colour of the sky,on the, 199,281. Bonney (Prof. T. G.) on the relation of certain breccias to the physical geography of their age, 419, Books, new :—Wolf’s Histoire de YObservatoire de Paris, 171; Rhodes’s Elementary Treatise on Alternating Currents, 175; Stokes’s Mathematical and Physical Papers, 277; Geitel’s Ueber die Anwend- ung der Lehre yon den Gasionen auf die Erscheinungen der atmos- pharischen Elektricitat, 278 ; Pern- ter’s Meteorologische Optik, 278 ; Barbarin’s La Géométrie non Kuclidienne, 278; Cooper's Pri- mary Batteries, 278; Lemoine’s Géométrographie, 280; Andoyer’s Théorie de la Lune, 280; Science Abstracts, 416; Larmor’s The Scientific Writings of the late George Francis litzGerald, 515 ; Blaise’s A travers la Matiére et l’Energie, 515; Wilson’s Vector Analysis, 614; Mrs. Ayrton’s The Electric Arc, 623; Néculcéa’s Le Phénoméne de Kerr et les Phénoménes Electro - Optiques, 624; Harper’s Scientific Memoirs, 724; Prof. H. A. Lorentz’s Sicht- bare und Unsichtbare Bewegun- gen, 725; Electrochemical In- dustry, 725. Bottomley (Dr. J. T.) on radiation of heat and light from heated solid bodies, 560. Brooks (Miss H. T.) comparison of the radiations from radioactive substances, 1. Calorimeter, on an improved form of coal-, 451. ‘Carbon dioxide and ethane, on the vapour-pressures of mixtures of, 124, Carbon spectrum, on the effect of the presence of hydrogen on the lines of the, 202. Carslaw (Dr. H. 8.) on a problem in conduction of heat, 162. | } q \ ? Ya Cassie (Prof. W.) @n,the measure- ment of Young’s médulus, 402. Cathode, on the current-dengity- at the, in the electric 608. \ Chabot (J. J. T.) ona rotating earth- inductor without sliding-contacts, | 506. Pe.) Chloroform and acetone, on the vapour-pressures of mixtures of, 121, ‘Clayden effect, on the, 606. Cloudy condensation, on the sizes of water-particles producing coronal and axial colours in, 24. - Coal-calorimeter, on an improved form of, 451. Cobalt, on the magnetostriction of, 45; on the change of rigidity of, by magnetization, 544. Conduction of heat, on a problem in conduction of, 162. Conductivity, on the electrical, pro- duced in gases when they pass through water, 552; on theelectri- cal, of metals and their vapours, 596. Convection, on the on optical rotatory polarization, a. Coomaéraswamy (A. K.) on the crystalline limestones of Ceylon, 421. Corona, on the phenomena of the, 256. Corpuscles, on the emission of nega- tively charged, by hot bodies, 253. Crystals, on the behaviour of a pleochroitic, along directions in the neighbourhood of an optic axis, 90; on the molecular dynamics of a, 139. : Cunningham (J. A.) on the discharge of electricity through gases and the temperature of the electrodes, Current-density at the cathode in the electric discharge in air, on the, 608. Davison (Dr. C.) on the Carlisle earthquakes of 1901, 516; on the Inverness earthquake of 1901, 516. Determinant, on the Jacobian of the primary minors of an axisymmetric, 507. Diffraction of light, on the, 346. discharge in air,/ Oram of a ~ 4 influence of,