pee feats ie ty f b ‘ tei : iM fi A tay see bf | a { o } i P } f ah Abd shane UY Para yt : i raid Obert bad bu chatod |) eh 89 rd us , i ' ey Ht A) Ae a tit ut AT ian nt lad (De ae I aM wt erate pyre ee ris . f; + #) ag) ite , etd sans Shae es ” Ay ° ya he Foe seat OF J wp t Pye? * fue ) as ah a Pes at bi ar SoBe abe 4 OF r+ oe Soper! mais “ae ea 4: = } “er ¥ r - . ae ae ide-ye, 4 2 Webra hie : tr py erat : ait y inte? oe “4 4g alist go “a : } ae he Me aL at : ree it F pk: eb ath. it toons ie as i, N A : , ivi ur fn Crates Ma 7 P ¥ a 7 bse Uae ARE a MA news *, TRE CHa Ceaet ee eee edt hg rirrath ate RR eR a. yey Pies peat ty Rt tae ee ee a Ee DIAL bE, < pa). al Ceol te AORN yO peal Ph eau S) ek tah abcde . HOY Restyte. Vue ae lo id ‘ PyhanM eek tie ie frre) f fv ft iGf ide wures ee - Li tiobet yrs | 8 : B renin weeps UC Pte oes a Wstent n Wrlg ary ty a iicaep nd Spats bites FS WAG Ole su RGU ELE Cte feneenl Lote a> Oo Pid Pia MN) i) hs et Be eryin' ry alt ty eee ies REC tn ory ie | Te ee rth } iy hoe . : if ; ' : > ¢ , ~ > nd ould ok RL ubrana re pe acat a it" Hts at att ' ° t deh ROT ow hk, Ree : ah wp TESS te ' ~ : * : m3 . J , ~* - ya AE weet bi . - SE nated ail NS eed i 4 at 2 | Se le : +) i - et Oe , ’ , be hee a4 \ : , - ’ me ‘ - , : #8 - ‘ - \ ; : ~~ CY m “T 2 26% ZF 7 THE LONDON, EDINBURGH, aynp DUBLIN PHILOSOPHICAL MAGAZINE JA oid AND Seal JOURNAL OF SCIENCE. CONDUCTED BY LORD KELVIN, G.C.V.O. D.C.L. LL.D. F.R.S. &e. JOHN JOLY, M.A. D.Sc. F.R.S. F.GS. AND WILLIAM FRANCIS, F.L.S. | “Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster vilior quia ex alienis libamus ut apes.’’s Just. Lres. Polit. lib. i. cap. 1. Not. O39) 5 p * ae) ae erly Io» ye A } x ) > =: 55 NY ee ie a VOL: Phe SiR, SERIES. "2 « SANUARY—JUNE. 1906. ri P 4 O ‘ < Ta ra) by ) LONDON: TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET. SOLD BY SIMPKIN, MARSHALL, HAMILTON, KENT, AND CO., LD.—T. AND T. CLARK, er , EDINBURGH ;— SMITH AND SON, GLASGOW ;— HODGES, FIGGIS, AND CO., DUBLIN ;——YEUVE J. BOYVERAU, PARTS ;—AND ASUER AND CO,, BERLIN. QJ mE. Co eb t: “‘Meditationis est perscrutari occulia; contemplationis est admirari: perspicua .... Admiratio generat questionem, queestio investigationem, inyestigatio inventionem.”— Hugo de S. Victore. : : “Cur spirent venti, cur terra dehiscat, Cur mare turgescat, pelago cur tantus amaror, Cur caput obscura Phoebus ferrugine condat, Quid toties diros cogat flagrare cometas, Quid pariat nubes, veniant cur fulmina ccelo, Quo micet igne Iris, superos quis conciat orbes Tam vario motu.” J. B. Pinelli ad Mazonium. ¢ ACERE | FLAMMAM. é on an Expeditious Practical Method of rae monic > Analysis. (Ela Feeley e sists See ae Lia rere oe Mr. L. R. Ingersoll on the Faraday and Kerr Effects in the imi KeU MS PC CHUM ays) F ls hie. Lo a NS ot Mr. V. H. Veley on a Modified Form of Apparatus for the Determination of the Dielectric Constants of Non- Romimenme Iniquids 20 70. PAI es te alow tds os Dr. W. E. Sumpner on the Theory of Phasemeters ........ Prof. J. Perry on Winding Ropes in Mines. (Plate II.).... Lord Rayleigh on Electrical Vibrations and the Constitution DIC’ HINGE Oe PRM end OMe a ae Sn At eee A Pang a Lord Rayleigh on the Constitution of Natural Radiation.... Lord Rayleigh on an Instrument for Compounding Vibrations, with application to the drawing of Curves such as might represent Whiterlioht. (Plate UIl.).... 252.05. ... 2.4. Mr. hk. K. McClung on the Absorption of a Rays ........ Dr. H. L. Bronson on the Effect of High Temperatures on the Rate of Decay of the Active Deposit from Radium Mr. A. B. Porter on the Diffraction Theory of Microscopic BUS OUN sayin cay eians «oie, cod: «a: opera mee Tes REMI MEI RY Prof. E. Rutherford on some Properties of the a Rays from uaa (Ceate EVs) a. Aer once tie hen Ge x ass #8, es Prof. H. N. McCoy on the Relation between the Radio- activity and the Composition of Uranium Compounds .... Notices respecting New Books :— Transactions of the International Electrical Congress, UO US eck cet a aac cre, hemi w ays aattsis cab 6.99 5 oA von Neumayer’s Anleitung zu wissenschaftlichen Beo- MSMINIU EMAIL TNGISGI fcc dc Ge aysle « ooqys sapiens des ols MMe moun LAM LGOG: on ee ote eae ces eit Guten Proceedings of the Geological Society :— Prof. E. H. L. Schwarz on the Coast-Ledges in the South-West of the Cape Colony ..........c.. eens lv CONTENTS OF VOL. XI.—SIXTH SERIES. Page Mr. T. F. Jamieson on the Glacial Period in Aberdeen- shire and the Southern Border of the Moray Firth .. 189 Dr. J. W. Evans on the Rocks of the Cataracts of the River Madeira and the adjoining portions of the Beni and Mamore ...:-...>..0 <2 emeee eee. ee 190 Dr. C. Davison on the Doncaster Earthquake of April Zord, 1905. 2... ss. ok aes peel ose eee 190 Prof. E. Hull on the Physical History of the Great Pleistocene Lake of Portugal |....../. 22. eee 191 Mr. A. Harker on the Geological Structure of the Sgurr OL DISS ass ces ee Nea CORE ee tie eb 192 NUMBER LXII.—FEBRUARY. Mr. J. W. Nicholson on the Diffraction of Short Waves by a hicid Spheres. /.2. 0.2) he .G on. od 193 Mr. N.R. Campbell on the Radiation from Ordinary Materials. Plate V..) ios bo cs Pele RE eine 206 Mr. J. Stevenson on the Chemical and Geological History of the Atmosphere’ ..... s¢it.. 7. ea Mela eee 226 Mr. A. Russell on the Dielectric Strength of Air.......... 237 Mr, E. L. Hancock: Preliminary Report on the Effect of Combined Stresses on the Elastic Properties of Steel. GPlate VIi). 2.2). 2. needle 2 ee 276 Lord Rayleigh on the Production of Vibrations by Forces of Relatively Long Duration, with Application to the Theory ot: Collisions .... «a. ¢. su. eteeelee a eee ee 283 Lord Rayleigh: Note to “ Electrical Vibrations and the Constitution of the Atom’ ....98.. =2.-45 3... eee 292 Prof. H. A. Bumstead on the Heating Effects produced by Rontgen Rays in different Metals, and their Relation to the Question of Change in the Atom... .-- 2-22 eeeeeee 292 Mr. S. A. Shorter on the Surface Elasticity of Saponine DOMMDIONS 2... oe ele diese bie Se er 317 Notices respecting New Books :— Prof. O. D. Chwolson’s Lehrbuch der Physik ........ 328 NUMBER LXIII.—MARCH. Dr. P. G. Gundry on the Asymmetrical Action of an Alternating Current on a Polarizable Electrode ........ 329 VErs) J: Morrow on the Lateral Vibration of Loaded and Winloaded: Bars t. o.6405 ws. sa we be ee eee 354 Mr. R. F. Gwyther on the Range of Stokes’s Deep- Water DNANGS: acetone es eis ate ApS 2 ee ee 374 CONTENTS OF VOL. XI.—-SIXTH SERIES. v Page Mr. A. P. Chattock on a Non-leaking Glass Tap .......... 379 Prof. A. Morley and Mr. G. A. ‘Tomlinson on Tensile Over- strain and Recovery of Aluminium, Copper, and Aluminium- SDI (CLEA eye Ud ES PS o> ee 380 Mr. Rk. L. Mond and Dr. Meyer Wilderman on a New Improved Type of Chronograph. (Plate VIII.) ........ 393 Mr. D. Owen on the Comparison of Electric Fields by means oan Oscillating Hlectrie Needle: (sei. ee.2. 2.55 st 402 Mr. H. Morris-Airey on the Resolving Power of Spectro- CLT DSS), ENS Seah eR em ele ee rrae ONL ie Fee CURE) Pee PAS eae 414 Mr. P. Blackman on the Quantitative Relation between Pectin COMGUGHY Mesa ..s6 jicyaet eels lees ¥: my Sueded > veh =| a. 416 Notices respecting New Books :— Messrs. H. Abraham & P. Langevin’s Ions, Electrons, Wor MS CmMles AINE ee oe gina ieg ys) oe CoP Chay iy es aos gaia ba) 418 D. Korda’s La Séparation Electromagnetique et Electro- Siamignne) des Witmer als: Ne Le) aan alsin Wd aig 2) alle! a Pavanels 419 Prot. H. Bouasse’s Essais des Matériaux ............ 419 Prof. Dr. J. Ritter von Geitler’s Elektromagnetische Penwineuncen umd: Welllemy 4.2 .\a stata. 2c crease si 6 420 Medel rick’s Physikalische Mecknik ..62.).0< 240 Ha. 420 Proceedings of the Geological Society : Miss G. L. Elles and Miss I. L. Slater on the Highest Silurian Roeks of the Iudlow District, ...........-: 42] Mr. C. A. Matley on the Carboniferous Rocks at Rush (CORE ADT O Tce yen Sue eRe ee Re aetne es er rene 429 Mr. A. J. Jukes-Browne on the Clay-with-Flints: its Oniera and) Distributron si .tgioiie seer tet es 2) cae sye =e 423 NUMBER LXIV.—APRIL. Mr. E. F. Burton on the Properties of Electrically Prepared Pollordalesolutions isc eRe s ee tsb des ne wee 8 wee 425 Mr. A. O. Rankine on the Decay of Torsional Stress in Bolmiomsnot Gelatiite | Sci: neces cw h cis b omy sla ge vac 447 Mr. 8. H. Burbury on the H Theorem and Professor J. H. Heane's. Dynamical Theory of Gases . 4.50. ascci. ss. d 455 Prof. W. H. Bragg and Mr. R. D. Kleeman on the Recom- bination of Ions in Air and other Gases................ 466 Prof. H. A. Wilson and Mr. E. Gold on the Electrical Con- ductivity of Flames containing Salt Vapours for Rapidly PSU AL IC A UMPOMES A latnels 4 Givin wicks Gam dys wae Ga ss die ae 484 Dr. F. Horton on the Electrical Conductivity of Metallic as “oc ye uh Re A TERROR CATES AO a 505 Mirek \\alner On Ualbot § ined: \iicis see ee Skee wears 531 Mn id EK. Hurst : Genesis of lons by Collision and Sparking- Potentials in Carbon dioxide and Nitrogen ............ 535 vi CONTENTS OF VOL. XI.——-SIXTH SERIES. Prof. E. Rutherford on the Retardation of the Velocity of the a Particles in passing through Matter.............. Prof. A. W. Porter on the Inversion-Points for a Fluid passing through a Porous Plug and their use in Testing Eroposed’tquations of State’ let... 4.°-... Mr. R. Hargreaves on some Ellipsoidal Potentials, Aolo- propicand. [SOtrOpic? .\... . sor! eee ae ee Mr. A. 8. Eve on the Absorption of the y Rays of Radio- aebkive OuDStANICeS . 2... 5) Gg ee) eee ee Mr. P. 8. Barlow on the Osmotic Pressures of Alcoholic Solambtoms: ee on oe Prof. J. H. Jeans on the Constitution of the Atom ........ Profs. Willner and Wien on the Dielectric Strain along telimes ‘of Morce 2200 ic 52 le accel Gee Mr. R. Chartres on “ Minimum Deviation through a Prism.” Notices respecting New Books :— Mr. W. C. D. Whetham’s The Theory of Experimental Hlectrietty: 2. oes aby ep aaedenss se ae er Prof. A. Righi’s La Théorie Moderne des Phénomenes Physiques: Radioactivité, Ions, Electrons.......... Prof. Ossian Aschan’s Chemie der Alicyklischen Verbind- MASON cs. 6 soe OS A Prot. B.C. C. Baly’s' Spectroscopy a>.) = 42.. eeee he Science Year-Boolow ia eae. Sal. 2s ee eee Prof. Dr. H. Kobold’s Der Bau des Fixsternsystems.... Dr. G. F. Lipps’s Die Psychischen Massmethoden Mr. I. A. Black’s Terrestrial Magnetism and its Causes. Messrs. C. R. Mann and G. R. Twiss’s Physics ...... Proceedings of the Geological Society : — Messrs. T. C. Cantrill and H. H. Thomas on the Igneous and Associated Sedimentary Rocks of Llangvnog.... Mr. k. H. Rastall on the Buttermere and Hnnerdale Granophyre |... -e. te eee ee ee Prof. 8. H. Reynolds on the Igneous Rocks of the astern Mendips.....2... 2 sles: +s 0 rr NUMBER LXV.—MAY. Prot. W. H. Bragg on the Ionization of Various Gases by thera Particles of Radium ........022.2.,..). =. soe Mr. W. Hawthorne and Prof. W. B. Morton on the Deflexions caused by a Break in an Overhead Wire carried on Poles.. Mr. J. K. H. Inglis on the Isothermal Distillation of Nitro- gen and Oxygen and of Argon and Oxygen ............ Prof. J. A. Fleming on the Construction and Use of Oscilla- tion Valves for lectifying High-Frequency Electric Winentss Ye ete sh te els. eee ee Mr. G. B. Dyke on the Use of the Cymometer for the De- termination of Kesonance-Curves ee aeeee ss » oe 617 632 640 659 CONTENTS OF VOL. XI.—SIXTH SERIES. Mr. E. Buckingham: Elementary Notes on Thermody- MNCS 7) COMO MIN SLIMOME 9 23.02 lo nlas ie dive weide.ns sess Lord Rayleigh on some Measurements of Wave- Lengths misnea: Moduited PA pparats: 5.14 a aeeu eee tte to ois v2 «0 Mr. J. W. Nicholson on the Symmetrical Vibrations of Con- duetineSuttaces: of Revolution. .7 apes ae ae... 2 Prof. H. Becquerel on some Properties of the a Rays emitted by Radium and by Bodies rendered Active by the Radium tian naerAal OID ye stepta ge ro teuisaarras esa elho aay etaniee, Site one wheal eo ie “eler'gi ote. laa wit Notices respecting New Books :— Dr. Hans Witte’s Ueber den gegenwirtigen Stand der Frage nach einer mechanischen Erkliirung der elek- MGISEMC LESCMCUMM OCI whe tris 4 Menai. la J) las a. Intelligence and Miscellaneous Articles :— On a Mercury-sealed Tap, by A. P. Chattock.......... NUMBER LXVI.—JUNE. Prof. J. S. Townsend on the Field of Force in a Discharge berwecn earallelnblares: +. ae soe. leo. Rok Dr. H. 8S. Johonnott on the Black Spot in Thin Liquid Films 7 Prof. W. H. Bragg on the a Particles of Uranium and Thorium Prof. J. J. Thomson on the Number of Corpuscles in an Atom Prot. R. W. Wood on Fluorescence and Lambert’s Law .... Prof. A. Anderson on the Focometry of Concave Lenses and Moves VINEE ORG Mab. p eis ya's esr MS Ge meus Oe e te hee mine Prof. H. A. Wilson on the Velocities of the Ions of Alkali Balt Vapours at Idioh Temperatures, ...-4........:.... Dr. O. Hahn on some Properties of the a Rays from Radio- PAM OpISUUT TIN ae Mea tice. Ska a oss Se yeep cs a. be Se Dr. H. L. Bronson on the Ionization produced by a Rays Dr. C. G. Barkla on Secondary Réntgen Radiation ..... Mr. A. A.C. Swinton on an Experiment with the Electric Are 82 Notices respecting New Books :— Cambridge Tracts in Mathematics and Mathematical ENV SIC SONOS oN Qo aii tipla wecpera nin oag Sew hv wy ol how Prof. Carslaw’s Introduction to the Infinitesimal Cal- culus; and A. H. Angus’s Preliminary Course in Differential and Integral Carculuse se oes ee KE. Picard’s Gfuvres de fellas Isha Dr. O. Biermann’s Vorlesungen iiber Mathematische INGINORINCUMO@GRIN) Soa cee crew owe cle y oc cs we W. B. Frankland’s The First Book of Euclid’s E leer Dr. Hudson’s Kummer’s Quartic Surface............ J. Guillaume’s Notions @’ Hlectrltate Ae Na danas vil Page 678 OO ———— PLATES. I. Illustrative of Prof. T. R. Lyle’s Paper on an Expeditious Practical Method of Harmonic Analysis. II. Illustrative of Prof. J. Perry’s Paper on Winding Ropes in Mines. II. Illustrative of Lord Rayleigh’s Paper on an Instrument for Compounding Vibrations. IV. Illustrative of Prof. E. Rutherford’s Paper on some Properties of the # Rays from Radium. Y. Illustrative of Mr. N. R. Campbell’s Paper on the Radiation from Ordinary Materials. VI. Illustrative of Mr. E. L. Hancock’s Paper on the Effect of Combined Stresses on the Elastic Properties of Steel. VI. Illustrative of Prof. A. Morley and Mr. G. A. Tomlinson’s Paper on the Tensile Overstrain and Recovery of Aluminium, Copper, and Aluminium-Bronze. VIII. Illustrative of Mr. R. L. Mond and Dr. M. Wilderman’s Paper on a New Improved Type of Chronograph. a\ i‘ A. Deep Sea Ship-Waves*. (Continued from Phil. Mag:; PIED te aes LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. . [SIXTH SERIES.] Dah 7 é AVI ANE: 906 tae ue “ae id June 1905.) By Lord Ketvin. § 65. Ee we to § 63, we must, for the present, as time presses, leave detailed interpretation of the eurves of fig. 17: merely remarking that, according to § 44, io, (which means that J is an integ ger), the disturbance, d, is infinitely great ; of which the dynamical meaning is clear in (70) of § 39. § 66. Let us now find the depression of the water at distance w from the origin, when the disturbance is due to a single forcive, expressed by the formula fT kh? I(a Dao a w+ bh? travelling uniformly with any velocity v. nt this forcive were applied steadily to the surface of water at rest it would WEIR produce a steady depression FG :), a8 we are taking the density of the water, unity. Thus the forcive II(v) would shape the water to an “infinitely long trough, of cross-section shown in fig. 25, representing z= kb (a 2 + 3) on the seale of = 10 cms. “and eal em. ry . i “x a ~ > 7 Taking 4 da of (95) we find tan-!(/b).bk%. Hence the Io * Communicated by the Author; having been read before the Royal Society of Edinburgh, July 17, 1905. 7 What is denoted by a in this and following expressions, is the (w—vt) of §§36....40; the origin of co-ordinates being now fixed relatively to the tray elling ak Ae Phil. Mag. 8. 6. Vol. 11. Now 61. Jan. 1906: B 2 Lord Kelvin on Pics 2b, e\< e~ Deep Sea Ship- Waves. area of fig. 25 is 2tan—!8.bk, or Hee .whk, and the total 180° area of the diagram extended to infinity on each side is mbk. Hence the area of fig. 25 is A or *92, of the total area. This total area, wbk, I call, for brevity, the forcive- area ; and a), I call the mean breadth of the forcive-area. The breadth of the forcive where z=-8k (as shown by the dotted line B B in the diagram) is 0. § 67. Now let the forcive be suddenly set in motion, and kept moving uniformly with any velocity v in the rightward direction of our diagrams. This will produce a oreat com- motion, settling ultimately into more and more nearly steady motion ‘through greater and greater distances from O. The investigation of §§ 1-10 (Phil. Mag. June 1904), and particularly the results described in §§ 5, 6, and illustrated in figs. 2, 3, show that in our present case the commotion, however violent, even if including splashes*, divides itself into two parts which travel away in the two directions from O, ultimately at wave-speed increasing in proportion to square root of distance (according to the law of falling bodies); and leaving in their rears, through ever broadening spaces, what would be more and more nearly absolute quiescence if the forcive were suddenly to cease after having acted for any time, long or short. § 68. But if the forcive continues acting, and travelling rightwards with constant speed, v, according to § 67, the travelling away of the two parts of the initial commotion in the two directions from O (itself merely a point of reference, moving uniformly rightwards), leaves the water, as shown by fig. 26, in a state of more and more nearly quite steady motion ‘through an ever broadening space on the rear side of O,. and through a small space in advance of O; provided certain moderating conditions are fulfilled in respect to KD, v. § 69. To illustrate and prove § 68 ; first suppose v infinitely small. The water will be infinitely little disturbed from the static forcive-curve shown in fig. 25, and described in § 66. Small enough velocities will make very small Hatitbares with any finite value of k/b. § 70. But now go to the other extreme and let v be very great. It is clear, on dynamical principles without calcula- tion, that v may be great enough to make but very little * However sudden and great the commotion is, the motion of the liquid is, and continues to be, irrotational throughout, B2 Lord Kelvin on KG, eX Aus i- Wp KG. ‘0G “OLY Deep Sea Ship- Waves. b disturbance of the water-surface, however steep be the static forcive curve. A “skipping stone” and a ricochetting cannon shot, illustrate the application of the same dynamical principle in three-dimensional hydrokinetics. By mathe- matical calculation ($ 79 below) we shall see that, when v is great enough, we have PevT d ae sili A 4 a - : e - (7), where / denotes the height of crests above mean water-level in the train of sinusoidal free waves left in the rear of the travelling forcive; A denotes the area of the forcive-curve (fig. 25) ; being given in § 66 by the equation GSS TRUE va ash ee | aia DO): and Xr, given [§ 39, (71)] by | Ne ZU Ge! eae es 5, VSI (OOY: denotes the wave-length of free waves travelling with velocity v. § 71. A very important theorem in respect to ship-waves is expressed by (97). Without calculation we see that, i/ A as very great In comparison with sb, (the “ mean breadth” of the forcive-curve according to S68), h must be simply proportional to A, for different foreives travelling at the same speed. This we see because, for the same value of 0, h/k is the same, and because superposition of different forcives within any breadth small in comparison with 2, gives for h the sum of the values which they would give separately. *arther without calculation, we can see, by imagining altered the scale of our diagrams, that hA/A must be constant. But without calculation I do not see how we could find the factor 47 of (97), as in § 79 below. § 72. The effect of the condition prescribed in §71 is illustrated and explained by considering cases in which it is not fulfilled. For example, let two forcives be superposed with their middles at distance 3X; they will give h=0, that is to say no train of waves. The displaced water surface for this case is represented in fig. 27. Or let their distance be 4r or 3X3 the two will give the same value of / as that given by one only. Or let the two be at distance X; they will make h twice as great as one foreive makes it. § 73. In figs. 26, 27, 29, 30, representing results of the calculations of $$ 78, 79 below, the abscissas are all marked according to wave-length. The seale of ordinates corre- ban Lord Kelvin on sponds, in each of figs. 26, 27, 29, to k=243°89, and mb=1:0251.10-3.2. This makes by (98) and (97) A=A, and h=. Fig. 30 represents the curve of fig. 29 at the maximum, in the neighbourhood of O, on a greatly magnified scale: about 1720 times for the abscissas, and 39 times for the ordinates. § 74. Fig. 26 shows, on the right-hand side, the water slightly heaped up in front of the travelling forcive, which is a distribution of downward pressure whose middle is at O. On the left side of O, we see the water surface not differing perceptibly from a curve of sines beyond half a wave-length rearwards from O. A small portion of a wave-length of true curve of sines in the diagram shows how little the water’s surface differs from the curve of sines at even so small a distance from O as a quarter wave-length. It must be remembered that in reality the water surface is everywhere very nearly level; and in considering, as we shall haye to do later, the work done by the forcive, we must interpret properly the enormous exaggeration of slopes shown in the diagrams. It is interesting to remark that the static depression, k, which the forcive if at rest would produce, is about 87 times the elevation actually produced above O by the forcive, travelling at the speed at which free waves, of the wave-length shown in the diagrams, travel. It is interesting also to remark that the limitation to very small slopes is not binding on the static forcive curve. Thus for example, a distribution of static pressure, everywhere perpendicular to the free surface, producing static depression exactly agreeing with fig. 25, would, if caused to travel ata speed for which the free-wave-length is very large in com- parison with 6, produce a disturbance, represented by fig. 26 with waves of moderate slopes: and, as said in § 69 above, would produce no disturbance at allif the speed of travelling were infinitely great. : § 75. Fig. 27 is interesting as showing the waveless dis- turbance produced by two equal and similar forcives with their middles at distance equal to half the wave-length. This disturbance is essentially symmetrical in front and rear of the middle between the two torcives. By dynamical con- siderations of the equilibrium of downward pressures, we see that the area of fig. 27 (portion above line of abscissas being reckoned as negative) must be exactly equal to 2 A, the sum of the areas of the two forcives, representing their integral amount of downward pressure. This area, being 2erbk, with the numerical data of §73, is numerically 32; that is to say a rectangle whose length is $d, and breadth Deep Sea Ship- Waves. 16 ‘PUT 8 Lord Kelvin on the unit of our vertical scale. Approximate mensuration, with a very rough estimate of the area beyond the range of the diagram, continued to infinity on the two sides, verifies this conclusion. §76. Fig. 28 is designed on the same plan as fig. 27 but with eleven half-wave-lengths as the distance between the two forcives instead of one half-wave-length. Like fig. 27, it is symmetrical on the two sides of the middle of the diagram; but, instead of being waveless, as is fig. 27, it shows four anda half waves, all very approximately sinusoidal, with two depressional halves of waves at their two ends, and elevations coming asymptotically to zero beyond the two ends of the diagram. The curve represented by fig. 26 is very accurately the right-hand extreme of fig. 28: and the same figure, turned right to left, is the left-hand extreme of fig. 28. If we commence with the water wholly at rest, and start the forcives at the proper speed, with force gradually (or somewhat suddenly) increasing up to the prescribed amount, the motion produced will be that represented by fig. 28, with, superimposed upon it, a disturbance quickly disappearing in ever lengthening waves of diminishing amplitude, travelling away in both directions from our field. If now, with the regular régime represented by fig. 28, we suddenly cease to applv the forcives, we have left a free procession of four and a half very approximately sinusoidal waves, between a front and a rear deviating from sinusoidality as shown in the diagram. Jrom the instant of being lett free, the front of this procession and its rear will rapidly become modified ; whde for three periods the central part of the procession will have travelled three wave-lengths, with very little deviation from sinusoidality. But, after four or five periods from the instant of being left tree, the whole procession will have gotinto confusion. After twenty or thirty or forty periods, the water will be sensibly quiescent, not only through the space where the procession was, but through a considerable part of the space ever which it would have travelled if its front and rear had been kept guarded by the continued action of the two travelling forcives. At no time after the cessation of the forcives can we reasonably or conveniently assign a “group velocity” to the group or procession of waves with which we are concerned. A prevalent idea is, I believe, that such a group of deep sea waves could be regarded as travelling with half the “ wave- velocity ”’ of waves of the length given in the original group. In § 30 above, reasons are given for accepting the theory of “ group velocity ” only for the case of mutually supporting or) ‘tayIvuh uo 0} poonpad SopVUIPIO Jo oTRog sone pedal! —2) 2G “STA ee )p a P Deep Sea Ship- Waves. 10 Lord Kelvin on groups, given by Stokes in his Smith’s Prize examination paper, published in the Cambridge University Calendar for 1876: and for rejecting it for the case of any single group of waves. In reality the front of a group, left to itself, travels with accelerated velocity exceeding the velocity of periodic waves of the given wave-length, instead of with half that velocity. §77. Fig. 29 shows the steady motion, symmetrical in front and rear of a single travelling forcive, which is a solution of our problem; but it is an unstable solution (as probably are the solutions of the problem of § 45 above, shown in figs. 18, 14, 15). If any large finite portion of the water is given in motion according to fig. 29, say, for example, 50 waves preceding O (the forcive) and 50 waves following O, the front of the whole procession, to the right of O, will become dissipated into non-periodic waves travelling rightwards and leftwards with increasing wave- lengths and increasing velocities; and the approximately steady periodic portion of it will shrink backwards relatively to the forcive. Thus before the forcive has travelled fifty wave-lengths, the periodic waves in front of it are all gone: but there is still irregular disturbance both before and behind it. After the forcive has travelled a hundred wave-lengths, the whole motion in advance of it, and the motion for perhaps 30 wave-lengths or more in its rear, will have settled to nearly the condition represented by fig. 26, in which there is a small regular elevation in advance of the forcive, and a regular train of approximately sinusoidal waves in its rear ; these waves being of double the wave-height given originally. {his motion, as said above in § 68, will go on, leaving behind the forcive a train of steady periodic waves, increasing in number ; and behind these an irregular train of waves, shorter and shorter, and less and less high the farther rear- ward we look for them (see R in fig. 10 of §§ 26, 27 above). It is an interesting, but not at all an easy problem, to in- vestigate the extreme rear (with practically motionless water behind it) of the train of waves in the wake of a forcive travelling uniformly for ever. I hope to return to this subject when we come to consider the work done by the travelling forcive. § 78. Pass now to the investigation of the formulas by the calculation of which figs. 26, 27, 28, 29, 30 have been drawn, and the theorem of (97) proved. Go back to the problem of $41 above: but instead of taking c=-9, as in §§ 46-61, 2:3812 Deep Sea Ship- Waves. re oid | Ly Fia. 29. il Lord Kelvin on 12 ‘(O)p—@)p ‘0 “ST Deep Sea Ship- Waves. 13 take e=1—10-‘; and o=1/(%+ By Dy) (66) and) (37) er § 45 we have the following solution eerie ey vice | 23 ( 100) where 4 1g S=elt® fs sin (7 +4)0 tani 2 14+2Vecoss@+e —icos(j+3 )? logs — TV en Ones (101) and Pus if ecos@ e?cos 20 Nee =—1 a ———————- Toocees + ¢/ s70 - 102 - Sf a ies Pe tin 3 SS e] COS] (102) ‘ fe) Fig. 29 has been calculated by putting pe nae and taking 7=20. The explanation is that, as we al see by (78) of §43 above, (100), (101), (102), express the water disturbance due to an infinite row of forcives at consecutive distances each equal to (203); the expression for each forcive being aT + (e—na)? - (103), where n is zero or any positive or negative integer ; and by (79) we have PAs OU) ee, b= ———_—— . . . . (104). 20 Thus we see that the pressure at O due to each of the forcives next to O, on the two sides, is 1/{1+(27.10*)?} of the pressure due to the forcive whose centre is QO. ‘Thus we see that the pressures due to all the forcives, except the last mentioned, may be neglected through several wave- lengths on each side of O: and we conclude that (100), (101), (102 2) express, to a very high degree of approximation, the disturbance produced in the water by the single travelling Gk whose centre is at O. 79. To prove (97) take @=180° im (100), (101), (102); we ad find (—1)/d(180°) =¢ 15 5) fe t ane ae +1— 7 ++ ais a os 14 Lord Kelvin on Instead now of taking e=1—10-4, as we took in our caleu- lations for (0), let us take e=1. This reduces (105) to aa ihe (—1)/d(180°)=T+1—3 45. gE CC) ee 23 —1 Ps Te Lastly take 7 an inamtely g great odd or even integer, and we find q(180)\=(— 1) cae Now fig. 26 is, as we have seen, found by superimposing on the motion represented by fig. 29 an infinite train of periodic oor waves represented by —4h.sin = and therefore h=7, which proves (97). § 80. To pass now from the two-dimensional problein of canal-ship-waves to the three-dimensional problem of sea- ship-waves, we shall use a synthetic method given by Rayleigh at the end of his paper on ‘‘ The form of standing waves on the surface of running water,’ communicated to the London Mathematical Society in December 1883 *. In an infinite plane expanse of water, consider two or more forcives, such as that represented by (95) of § 66, with their horizontal medial generating lines in different directions through one point O, travelling with uniform velocity, v, in any direction. The superposition of these forcives, and of the disturbances of the water which they produce, each calculated by an application of (100), (101), (102), gives us the solution of a a ee wave problem ; which becomes the ship-wave-problem if we make the constituents infinitely small and infinitely numerous. Rayleigh took each constituent forcive as confined to an infinitely” narrow space, and combated the consequent troublesome infinity by introducing a resistance to be annulled in interpretation of resuits for points not infinitely near to O. I escape from the trouble in the two-dimensional system of waves, by taking (95) to express the distribution of pressure in the forcive, and making } as small as we please. Thus, as indicated in §§ 79, 73, 76, by taking b=104A/(10*.7) we calculated a finite value for d(0). But for values of «, considerably * Proc. L.M.S., 1883; republished in Rayleigh’s Scientific Papers, vol. ii. art. 109. Deep Sea Ship- Waves. 15 greater than half a wave-length, we were able to simplify the calculations by taking b=0. § 81. For the three-dimensional system let, in fig. 31, be the inclination to 0 X of the rearward wave-normal of one of the constituent systems of waves. This is also the incli- nation to O Y of the medial line of the travelling forcive to which that set of waves is due. Take now for the forcive obtained by the superposition of an infinite number of ies oly _ constituents, as described in § 80, ] b?h ate ml Y [Ge cos p+ y sin p40" where k may be a function of yy, and 6 is the same for all values of ap. For the case of a circular forcive svstem we must take & constant ; and we find il awbk = ar NO ae aS RIS i 9); H)= Ju? +0) where 7” =a" + y (109) . (108), 16 Lord Kelvin on § 82. Let now the forcive, whether circuiar or not, be kept travelling in the direction of x negative * with velocity vw: and let % denote the corresponding free wave-length given by the formula 27v?/g. This is the wave-length of the constituent train of waves corresponding to y=0. For the y-constituent, the component velocity perpendicular to the front is vcosy, and the wave-length is cos? p. Looking now to fig. 26, with X cos’ instead of 2; and to fig. 31 ; and to equations (97), (98) ; we see that the portion of the depression at (wv, y) due to the constituent of forcive shown under the integral in (108) is Ambkdwy . zZr(ecoswt+ysinw) ae sin Wer - age provided x cosw+ysin yr is considerably greater than 3 cos*y. Hence for the depression at (a, y) due to the whole travelling forcive, we have Aig) Ach? kd. 2r(excosh+ysinw) | (7, y) =4a coe aveane ~ i. “O-9) § 83. The reason for choosing the limits ~(F -8) to LER e e e e e e e > 1s that each constituent forcive gives a train of sinusoidal 2 waves in its rear, and no perceptible disturbance in its front at distances from it exceeding half a wave-length. Look now to fig. 31, and consider the infinite number of medial lines of the forcives included in the integrals (108), (111) ; all as lines passing through O. Four examples, QP, Y’' Y, LK, X X! of these lines are shown in the diagram: corre- sponding respectively to v=-(F-9), y=0, a= any positive acute angle, —— On each of the first three of these lines RR indicates the rear. The fourth, X X’, is in the direction of the motion, and has neither front nor rear. ‘The integral (111) must include all, and only ali, the medial lines which have rears towards P. Hence @ P is one limit of y in (111) because it passes through P; X X’ is the other limit because it has neither front or rear. Thus all the lines included in the integral, lie in the obtuse angle * This is opposite to the direction of the motion of the forcive in fiy. 26. Deep Sea Ship- Waves. 17 POX’. Thus the integral (111) expresses the depression at P(w, y) due to the joint action of all the constituent forcives, because none except those whose medial lines lie in the angle P O X', contribute anything to the disturbance of the waiter at P. § 84. For interpreting and approximately evaluating the definite integral, we may conveniently put Car C5 gi10), a de oe a Cos? and write (111) as follows: (2, y)=47°b meek), 2 kde. Janu : sin d cos? nN aan) Now if we suppose r/A very great, there will be exceedingly rapid transitions between equal positive and negative values of sin (2arru/d), which will cause cancelling of all portions of the integral except those, if any there are, for which du/dy vanishes. We shall see presently that there are two such values, Y,, W2, both real if tan 0<,/g; wv being a maximum (u,) for one of them, and a minimum (w,) for the other ; and that, when @ has any value between tan~',/} and 27—tan—,/3, the values of Wi, 2 are both imaginary. Consideration of this last-mentioned case shows that, in the whole area of sea in advance of two lines through the centre of the travelling forcive inclined at equal angles of tan~' y 4, (or 19° 28’) on each side of the mid-wake, there is no perceptible disturbance at distances of much more than a half wave-length from the centre of the forcive. The main disturbance by ship-waves, therefore, lies in the rearward angular space between these two lines. It is illustrated by fig. 32, as we now proceed to prove by the proper interpre- tation of (113). Expanding the argument of the sin in (113) by Taylor’s theorem for values of y differing from yy, by small fractions of a radian, we find QU. Arr du 5 ‘ ore ar at 3 (Fas), WW)! Jana? - (114), where Darr (eH ca aed — wi Pac Sal | eens ) Pe a and =gy=(Ww—-wW) _ ( ok (115), Phil, Mag. 8. 6. Vol. 11. No. 61. Jan. 1906, 3 Deep Sea Ship- Waves. 19 From the second of (115) we find dp=dq;/(@8,/7), where oy ea ae on 9 CLIGY, Dealing similarly in respect to ww, and values of My differing but little from it, we take +4,” instead of the —gq,’ of (114), and (d’u/dyp”) 5 instead of the —(Pu/dyp’), of (115) ; because u, 1s the maximum and u, the minimum. Calling i ky the values of & corresponding to Y,, W., and using these ex- pressions properly in (113), we find, for the depression of the water at (av, 7), Laer ea eae ae Laan), sine kg Ue be + aaa). dqg Sin (a+ Jo )| Cul), The limits «7, —« are assigned to the integrations relatively to g, and gq, because the greatness of 7/d in (115) and corresponding formula relative to Ww. makes g, and q2 each very great, (positive or negative,) for moderate properly small positive or negative values of w—v, and W—yYy. Now as discovered by Huler or Laplace (see Gregory’s Examples, p. 479), we have | agsing? = | dq cos q? = V 7/2, and using these in (117) we find d(x, y)= 92 : \ es 2/7 297d [= (sin @,—cosa,) — &,(sin y+ COS tts aD (118). r 8 cos? Wy o Bz Cos” Yo Substituting for ,, #2, values by (115) we find Anh ky em r 2) = Ss aa LBs cont ap x (? Hon ) ky : 2a r : + Bay Sn a (Tet 5 118)’. RUT sin (: Ug + 5) (118) 85. To determine the quantities denoted by §,, 8; in (116) .... (118)’, we write (112) as follows :— rus (a yt) / LEP, +é, wheret=tan y. . . (119), C2 20 Lord Kelvin on Hence, by differentiation on the supposition of 2, y, r constant, we find ae [acty(i+2r)|VIFE . . . (120). 2 ae Tyee [@ +28) +464 60) VTP . (120). By (120) we find fort,, which makes u a maximum or minimum, xt, ty(i+2¢,)=0. . . = =e, mm a quadratic equation which, when (y/x)? < }, has real roots as follows,— oh Pi a) =i heea2 / (G)=3 3 a=— 9 4/ [(@) PG Mary e iy) ~ 3 | (128). And substituting t,,, (either of these,) for ¢ in (121) we find D7 Ree a (Tp) m [2 #) +2yt,, | 132, ee or with simplification by (119), d?u Zee =2ru,, —2(1+#2)9?. . . (124). Eliminating ¢?, from the first factor of (124) by (122) we find (Fur _ [ae ee ‘5 1 eS [= + ty ( 2y +5,) Vite BG bs which, with m=1, and m=2, gives 8, and B, by (116). § 86. Using (123) we see that (d’u/dy"),, vanishes when x=y,/8, and that it is negative for ¢,, and positive for to, whenx>yV/8. Hence ft, makes d,u/dw? negative. There- fore u, is the maximum; and ¢, makes it positive. Therefore uw, is the minimum ; and (119) gives for these maximum and minimum values ruy=(at yt) VIFt2, rug=(atyte)V1+t2. (125). By (122), (123) we see that when y/x7=0, we have —}=+, - and —t,=0. If we increase y trom 0 to +2/,/8, —t, falls continuously from # to ,/3%, and —t, rises continuously from 0to,/4. Thus —t, and —¢, become, each of them, v4; which is the tangent of 35° 16’. Deep Sea Slip- Waves. 21 § 87. Geometrical digression on a system of autotomic, monoparametric co-ordinates *, §§ 87-90. In (119) put Ranh wishin Pane she se CLOG} where a denotes the parameter OW of the curve OCC, fig. 32, which we are about to describe; being the curve given intrinsically by (119) and (122) with suffix ‘m’ omitted from t. In the present paper these curves may be called isophasals, because the argument of the sine in (130) below is the same for all points on any one of them. Solving (119) and (122) for w and y, we find gan —¢ ) L=AH (+ 0)32? J~@ + PB (127). The largest of the eight curves shown in fig. 32 has been described according to values of «, y calculated from these two equations, by giving to —t¢ values tan 0°, tan 10°, tan 20°, .... tan 90°. The seven other isophasals partially shown in fio. 32, all similar to the largest, have been drawn to corre- spond to seven equidifferent smaller values, 19A, 18X.... 13d, of the parameter a, if we make the largest equal to 20d. § 88. It is seen in the diagram that every two of these isophasals cut one another in two points, at equal distances on the two sides of OW. If we continue the system down to parameter 0, every point within the angle COC is the intersection of two and only two of the curves given by (127), with two ditferent values of the parameter a. If we are to complete each curve algebraically, we must duplicate our diagram by an equal and similar pattern on the left of O: and the doubled pattern, thus obtained, would show a system of waves, equal and similar in the front and rear, which (§ 77 above) is possible but instable. We are, how- ever, at present only concerned with the stable ship-waves contained in the angle + 19° 28’ on the two sides of the mid-wake ; and we leave the algebraic extension with only the remark that all points in the angle COO of the diagram, and the opposite angle leftward of O, can be specified by real values of the parameter a: while imaginary values of it would specify real points in the two obtuse angles. * Of this kind of co-ordinates in a plane, we have a well-known case in the elliptic co-ordinates consisting of confocal ellipses and hyperbolas. BACS | G bo Z Lord Kelvin on § 89. By differentiation of (127), we find dx : aa (=—tana . 22 8 2 ae which proves that tan—'¢ is the angle measured anti-clockwise from O Y to the tangent to the curve at any point (2, y), in the lower half of the diagram. Elimination of ¢ between the two equations of (127) gives, as the cartesian equation of our curve, (2? +47) + a?(8y4 — 2027y?— at) + 16aty?=0 . (129). But the implicit equations (127) are much more convenient for all our uses. It is interesting to verify (129) for the case —t=+,/$% in (127), corresponding to either of the two cusps shown in the diagram. § 90. Going back now to $86 and the continuous varia- tions considered in it, we see that —¢, and —¢, are re- spectively the tangents of the inclinations, reckoned from OY clockwise, of portions of the long are OC and of the © short arc W CO, in the upper half of the diagram. Thus, if we carry a point from O to C in the long arc, and from C to W in the short arc, we have the change of inclinations to O Y represented continuously by the decrease ot tan—\( —é,) from 90° to 35° 16’, while y increases from 0 to #8; and the farther decrease of tan-1(—?,) from 35° 16’ to 0°, while y diminishes from w/8 to 0 again. The inclination to O Y of the two branches meeting in the cusp, OC, is 35° 16! (or tan-1,/$). For any point in the short are CWC of the curve u or cos (Ww—@)/cos? wv, is a minimum. In each of the long arcs wis a maximum. At every point of the curve the value of u, whether minimum or maximum, is a/r. Hence for different points of the curve, u is inversely proportional to the radius vector from O. § 91. Going back to (118)! we now see that for all points on any one of our curves, rw, and 7u, have both the same value, being the parameter OW of the curve. The first part of (118)’ is one constituent of the depression at any point on either of the long arcs; and the second part of (118)! is one constituent of the depression at any point on the short are. Taking for example the largest of the curves shown in fig. 32, we now see that for any point of either of its long ares, the second constituent of the depression of the water is to be calculated from the second part of (118)’; while for any point of its short arc, the second constituent of the depression is to be calculated from the first part of (118). | Deep Sea Ship- Waves. 23 § 92. Explaining quite similarly the determination of d(w, y) for every point of each of the smaller curves which we see in the diagram cutting the longer arcs of the largest curve, we arrive at the following conclusions as the complete solution of our problem. The whole system of standing waves in the wake of the travelling forcive is given by the su perposition of constituents calculated according tO (127), with greater and smaller values of the parameter a with infinitely small successive differences. Hence, what we see in looking at the waves from above is exactly a system of crossing hills and valieys, with ridges and beds of hollows, all shaped according to the isophasal curves shown in fig. 32. Looking at any one of the short are-ridges and following it through the cusps, we find it becoming the middle line of a valley in each of the long arcs of the curve. And following a short are mid-valley through the cusps, we find, in the continuation of the curve, two long ridges. Hvery ridge, long or short, is furrowed by valleys All the curved ridges and valleys are parts of one cnesa system of curves, illustrated by fig. 32 and expressed by the algebraic equation (129). With these explanations we may write (118)’ as follows. : Anbk see Ne r d (2, y)= rB sin = ~ 5 (ru) #1 = Gro0 k where B= aioe =) isl eden ied wa GE oeL § 93. An important, perhaps the most important, feature of the wave-system which we actually see on the two sides of the mid-wake of a steamer travelling through smooth water at sea, or of a duckling * swimming as fast as 1t can in a pond, is the steepness of the waves in ‘two lines which we know to be inclined at 19° 28/ to the mid-wake. The theory of this feature is expressed by the coefticient of the sine in (130), and is well illustrated by the calculation of \/<- “a a for eleven points. of any one of the curves of fig. 32, “ie results of which are shown in column 6 of the “following table. They express the depression below, and elevation * In the ease of even the highest speed attained by a duckling, this angle is perhaps perceptibly ¢ ereater than 19° 28’, because of the dynamic effect of the capillary surface | tension of water. See * Baltimore Lectures, p. 593 (letter to Professor Tait, of date 25rd Aug. 1871) and pp. 600, GOL (letter to William Froude, reprinted from ‘Nature’ of 26th Cet. 1871). Z4 On Deep Sea Ship- Waves. above mid-level, due to one constituent of the system of crossing hills and valleys described in §92. Column 1 is —r. Columns 2, 3 are z/a and y/a, calculated from (127). Column 4 is u, calculated by (126) from columns 2, 3. Column 5 is = du/day’, calculated from (124) and columns 2 2, 4. Column 6 is av 2, calculated from columns 1,6. wu, bein g,as we have seen, a maximum for values of —v from 0 to 35° 16’, and a minimum for values from this to 90°, we see that the proper suffix in columns 4, 6, for the first four lines of each column is 1, and for the last six Jines is 2. i age 1. | Col. 2. | Col. 8. | Col. 4. | Col.5. | CoL 6. | | | Melia 2 y s rau a seep | fs Daeg a a addy? | A, Sea | 0° 1:0000 0:0000 1-00000 1:00000' —- 10000 | | 10° 10145 | = -1685 97239 ‘93782| 11-0647 | 20° 10497 | -3201 ‘Q1587 73497| 13210 30° 10825 | -3750 ‘87290 | -33333) 23094 | 35° 16’ | 1-:0887 | 3849 -86602 | 0-00000_ S | | 40° 10826 | -3773 87225 |— 40830, 26660 | 50° 1:0201 3166 93624 |— 1:84070| 17839 | | 60° ‘8750 | 2165 1:10941 |— 500003 —«:1-7888 | 70° 6441 | 1100 | 1:53041 |—14-0987 | 2:2793 80° | -B421 | 0297 | 291922 |-63-3341 | 41672 | s0° | 00000 | 0-000 0 gale 20 i § 94. In (130), & is generally a function of y; but if the forcive is circular, (§ 81 above) & is a constant, and for points on one of the isophasal curves (a=constant) the only variable coefficients of the sine are sec’, and B-!. But for different isophasal curves the coefficient in (130) expressing the magnitude of the range above and below mean level, varies inversely as fa. For mid-wake (W=0) a is simply the distance from the forcive: and we conclude, not merely for our point-forcive, but for a great ship, that the waves at a very large number of wave-lengths right astern, are smaller in height inversely as the square root of the distance from the foreive or from the middle of the ship. § 95. The infinity for ~=+35° 16’ represents a feature analogous to a caustic in optics. There is in nature no infinity for either case, if the source is finite and distributed, not infinitely intense and confined to an infinitely small space. According to the methods followed in §§ 1-72 above, we Practical Method of Harmonic Analysis. aa have in every case a finite intensity of source, or of forcive, except in § 80 where we have supposed b infinitely small, in comparison with A, we avoid the infinity shown in column 6: and can, by great labour, calculate a table of mitigated numbers, rising to a very large maximum at y= +35° 16’; but not to infinity; and so arrive mathematically at an expression for the very high waves seen on the two bounding lines of the wave-disturbance, inclined at 19° 28! to the mid- wake. But it is interesting to remember that we see in reality a considerable number of white-capped waves (would- be infinities) before the well-known large glassy waves which form so interesting a feature of the wave-disturbances. $§ 80-95 of the present paper is merely a working out of the simple problem of purely gravitational waves with no surface-tension on the principle given by Rayleigh * in 1883 for the much more complex problem of capillary waves in front, in which surface-tension is the chief constituent of the forcive, and waves in the rear, in which the chief constituent of the forcive is gravitational. In all the work arithmetical, algebraic, graphic of $§ 32-95 above, I have had much valuable assistance from Mr. J. de Graaff Hunter ; who has just now been appointed to a post in the National Physical Laboratory. II. On an Eexpeditious Practical Method of Harmonic Analysis t. By THomas R. Lyin, M.A., Professor of Natural Philosophy in the University of Melbourne. [Plate 1.] 1. LAOURIBR has shown that if any function f(t) (=y say) of a variable ¢ be such that FO=f E+) =f/E +21) = ke., where 7 is a constant, that is, if f(t) be periodic in ¢, of period 7, then /(¢) can be expressed as the sum of a constant and a series of terms called harmonics, each of the form a, sin p(wt—6,), where p has the values 1, 2, 3, 4, &., and @ = 2t/T. * Proc. Lond. Math. Soc. xv. pp. 69-78, 1883; reprinted in Lord Rayleigh’s ‘ Scientific Papers,’ vol. ii. pp. 258-267. +t Appendix to the papers: “ Preliminary Account of a Wave-Tracer and Analyser,” Phil. Mag. Nov. 1908, and “Investigation of the Variations of Magnetic Hysteresis with Frequency,’ Phil. Mag. Jun. 1905. Reprinted from a separate copy, communicated by the Author, of the RPhceceliin of the Royal Society of Victoria, vol. xvii. (list) pt. 2, Feb, 1006, (© | 26 Prof. T. R. Lyle on an Hxpeditious The number p is called the order of the harmonic, a, its amplitude, and @, its phase. If, in addition, /(¢) be such that FY = —f+7/2), then it is easy to see, by substituting ¢+7/2 for t, i.e. of +7 for wt in y = a+ Xa, sin p(@t—96,), that in order for 7, to be =—Yy,, 195 ij=0; 250) Aa — Oe Hence in this case the constant term vanishes and the harmonies, of which /(¢) is the sum, are all of odd order. When such is the case, f(t) is called an odd _ periodic function. This is the type generally met with in alternating electric-current investigations. 2. If we define the nth component (C, say) of a periodic function f(t) of period 7 as the periodic function which is the sum of those harmonics of f(¢) whose orders are n, dn, dn, Tn, &e., then nO, =fO-f (t+ HF (#4255 )- ++ —7(¢+m-1Z), . nn For if we represent the expression on the right of the above equation by w(t), we find by substituting successively for t, ¢+7/2n, and ¢+7/n in it, that - TNS T WO=-¥ (14 Z)=v(e+ 7), Hence y(t) is an odd periodic function of period t/n, thai. is to say, if f 2) =a%— Xa, sin p(at—6,), where p=1, 2, 3, 4, &., then y(¢) is of the form W(d)= Xb, sin gn(wt—B,), mineredg— 1.3, .5, 1; 9: ce. In evaluating y(¢), therefore, only those harmonics whose arguments are not, 3not, Snot, Xc., need be considered. Neglecting all other harmonics in the different f functions that make up W(t), we find that the remainders in the 2n terms OF -f(t+), p(t425), &e, Practical Method of Harmonic Analysis. 27 are all equal, and that each remainder is the nth component of ; hen BR 4G) 200, 3. If f(é) itself contain only odd harmonics as in the case of alternate-current periodic functions, then f(O=-f(¢+ 5) and equation I., § 2, reduces to nC, =fO-f(t+ 2) + baat +f(ten=1y, \ Wai) The operation on f(¢) mathematically represented on the right-hand side of equations I. or II. is practically performed on alternate-current waves by the wave-tracer and analyser * designed by the author. In the simplest case, when n=1, the wave-tracer gives the first component of the periodic quantity operated on, which in the case of alternating electric currents is the full wave. By the movement of two pairs of brushes n can be made 8, or 5, or 7, in which cases the analyser will give the 3rd, 5th, or 7th components of the wave respectively. Now, in practical investigations with this apparatus on alternating-current waves whose harmonic expressions were required, it was found much better to obtain by its means only the full wave-trace, and then by an arithmetical process identical with the action of the analyser and indicated by equation II. above, to obtain the 3rd and higher components of the wave, and thence to deduce its harmonics. This method of harmonic analysis was drawn attention to in the paper already quoted, and though based on a different formula to that of Wedmoref, is practically similar to his. It is more suitable, however, for waves containing only odd harmonics; and as I have had considerable experience in its use during the last two years and have found it both expe- ditious and accurate, it is possible that a short account may be of value to those interested in alternating-current work. 4, In wave graphs it is more convenient to use angular abscissee w where peas cep ors Making this substitution in the equation y= /(d), it becomes y= g(wv) say, where | g(x) =9 (e+ 2m), * Lyle, “ Preliminary Account of a Wave-Tracer and Analyser,” Phil. Mag., Nov. 1908, } Wedmore, ‘Journal Inst. Elect. Engineers,’ vol. xxv. p. 224 (1896). 28 Prof. T. R. Lyle on an EHupeditious and if f(¢) is an odd periodic function as in the case of alternate-current waves which we are now considering, g (@)=—9 (e+e) =9 (et 2r). Substituting g(w) for f(¢) in equation IT., it becomes nC, =9(2)—g (w+ an) +9 (e+ 2n/n) — - +y(a@+ n—1 7/1), from which we conclude that, if Y09, Yasy Ys 8) see = Ue be m equi-spaced ordinates that exactly include half the wave, i. €. ordinates corresponding to the abscissx w, wt+m/n, e+27/n,.....24+n—1n]n respectively, and called e.s. ordinates in the sequel ; and if Naa ee SGN be the ordinates of the nth component C, whose abscissze are the same as those of Yoo Yip Ya9e 0 2 2 Yn n—l respectively, then Yor—Yityo— -.- +Y,_;=2Ny=—nNi=nN,= =nN,, when n is an odd number, and Yo Yi da = ee when n is an even number, as we are now considering odd periodic functions only. Thus from n e.s. ordinates of the original half-wave we obtain only one ordinate per half-wave of U,, so that in order to obtain m e.s. ordinates per half-wave of C, it is necessary to have mn e.s. ordinates of the original half-wave. For instance, to obtain 3 e.s. ordinates of C, we must measure 3n e.s. ordinates of g(x). Let these be Y0s. Ga) 25 Ge ee and let the corresponding ordinates of C, be No, Ny. Ne, Nees 3n—1) then Yost Yo— +++ FYsqn-3=2Ny= —nN;=n2N,= =2N,,_5, Weg oa» +Yy oN; = —oNy—nN,— | a Yo-Yo tYa= 00+ FY g,-p=NNe=—aNs=nNzs= =nN,_,. Practical Method of Harmone Analysis. 29 Subtracting now the ordinates of CU, so obtained from the corresponding y ordinates, we obtain a new set of 3nez.s. ordinates which are those of the original half-wave with its nth component removed. 5. In practice it will generally be sufficient to determine the Ist, 3rd, 5th, 7th, and 9th harmonics (H, H; H; H, H, say). This can be done with considerable accuracy when 15 e.s. ordinates of the original half-wave are given. Thus if these be Yos Vy Y25 OW CO 0 Yi4y corresponding to the angular abscissee where Dike Lg = in Oi — ee a = ae and if Zp, <1, ¢2) 23, <4 be 5 e.s. ordinates of the half-wave of C3, then 32) =Yo—Ys + Y10= — 325 = 3210; 821 =Y1— Yo + Y= — 926 = 821, 324=Ys— Yo t+ Y= — 3829= 3214, and if uw, 3, Us be 3 e.s. ordinates of the half-wave of C;, then Uo =Yo—Y3tYo—Yo +Yi2= —5U3=duUg= —Iuly =O, Uy =49 Yet y7—-Yr ty = — Dig = 9Uz = — OU = Olja, DUa=Y2—Yst Ys—Yut Yu= — OU; = 0lg= — OU = Sug, the figures subscribed to each ordinate indicating the abscissa to which it. corresponds. Now the full wave C,=H,+H3;+H;+H,+H,4+ &e., and C= Joe se iat: = H; + His; so that if Hy; be neglected, and the sums of the corresponding ordinates of C3; and C; be subtracted from those of C,, the fifteen remainders are ordinates of H,+H,+..., i.e. of Hy, if we neglect H,. If Hj; cannot be neglected it ean at once be removed from C; before subtracting from C), for as it is (g.p.) the 3rd 30 Prof. T. R. Lyle on Ui Hapeditious component of C;, of which we have 3 e.s. ordinates wo, wy, Ue, its three corresponding ordinates are iy, —%, 79, where AW) = Up — Uy + Up. Hence H; will be completely given by Co) C1) Ca, Where Cy ie C) = Uy +1, C7 = Ug — 1g. H,; can now be taken from C;, thus 2j— 19, Zick). 22 8G ee tae ete are the 5 e.s. ordinates of H;+ Hy. In order to determine H; and H, it will now be necessary to plot the 5 ordinates of H;+ Hs, measure off 6 e.s. ordinates from the smooth curve drawn through them, and from these determine their first component, that is 2 e.s. ordinates of Hy. These will completely determine H, it H,, &. be neglected, and by subtracting them from the corresponding ordinates of H;+ Hy 6 e.s. ordinates of Hs are obtained. If H, cannot be neglected it will be necessary (if the original wave-trace is not available) to plot the 15 ordinates of H,+H, obtained above, and from the smooth curve drawn through them to measure off 14 e.s. ordinates. From these, 2 e.s. ordinates of the half-wave of H,, which deter- mine H,;, can be obtained. By subtracting these from the corresponding ones of H,+H,, 14 corrected ordinates of H, are obtained. 6. It now remains to determine the amplitudes and phases of the harmonics of C, from their ordinates which we have obtained. It is easy to show that =f sin? @ 4- sin? (¢+=) +sin? (9+ =) 7 nr 7 + sin? (o+2—1 =)t = il, from which we conclude that the square root of twice the mean of the squares of n e.s. ordinates of half a sine wave is equal to its amplitude. Hence, with the help of a table of squares or of the quarter squares given in most sets of tables, the amplitudes of H,, H;, &c. can be quickly determined. [The rule that the amplitude is equal to 7/2 x mean of the ordinates is only sufficiently accurate when a large number of ordinates is taken. | If a, 4, Gs,» ~~ Gig be the ordinates we have found for H, corresponding to the angular abscisse 2, @, @o, +... Lu; Practical Method of Harmonic Analysis. dl respectively, and if f,,a be the amplitude and phase of H,, or in other words if H,=h, sin (wt—a), then any of the equations sin (t—a) =a //y, sin (¢,—«)=a,/h,, sin (t2—a) =ay/hy, Ke. would determine a, provided the ordinates a), a1, dz, &c. are exactly those of a sine wave. In practice, however, small upper harmonics will invariably be Jeft in a, a, a, &e. [it may not have been thought worth while to remove H,]|, and though their amplitudes may be negligibly small, yet they might cause considerable error in the value of « when determined from only one of the above equations. Hence it is advisable to obtain four values of « from the first four ordinates on the rising side of the wave and four from the last four ordinates on the falling side, and take the mean of the eight. In this way we can to a great extent eliminate any error that might arise through an har- monic even as low as the seventh not having been removed. In a similar way the phases of H;, H;, &. can be deter- mined, but it must be remembered that if, for instance, H;=h; sin 3 (wt—B), and if by, b),....64 are the ordinates of H; corresponding to the abscisse x, #1,--+. ¢ v4, then sin 3 (wy —B) =bo/hs, Xe. 3 similarly, if H,=h; sin 5 (@t—y), with ordinates ¢), ¢1, C2, then sin 5 (a —y) = Co/hs- 7. The wave to be analysed may be given in either of two ways. We may have the complete trace of it obtained by the author’s wave-tracer by the photographic method, or by any form of oscillograph that gives a trace of the wave form; or we may have the values of a definite number only of ordinates per half-wave, such as would be obtained by the author’s wave-tracer by the galvanometer and scale method. From the wave-trace the complete harmonic expression can theoretically be obtained, but the impossibility of aceu- rately measuring on the. photograph, without elaborate apparatus, the different ordinates required leads to great inaccuracy in the result. 32 Prof. T. R. Lyle on an Expeditious From a given number of e.s. ordinates only an approxi- mate analysis can be obtained, more approximate, of course, as the number of ordinates is greater. When, however, each individual ordinate has been obtained with the accuracy of which the galvanometer and scale method is susceptible, the analysis obtained from fifteen such ordinates is much more reliable, as far as the harmonics up to the 9th are concerned, than that determined from any photographic trace. I will therefore illustrate the method by applying it in full detail to the analysis of the wave whose 15 e.s. ordinates are given in row 5 of Table I. (Pl. 1.). Every figure necessary in the calculation will be given. The first row of figures in Table I. are the abscisse x, 2, &e., to which the given ordinates correspond. Space for three rows of figures is left, and then the 15 given ordinates are written down. These are divided into three sets of five each, and the numbers of the middle set are subtracted in order from the sums of first and last set, giving five numbers which are the corresponding ordinates of 3C3. Space for two or more rows is left, and the given ordinates are now written down as in the table, in two rows of six each and one row of three, in order. The columns formed are added and the last three of the sums are subtracted from the first three, giving three ordinates of 5C;. The first of these minus the second, plus the third, gives one ordinate of 15C,;, whose other ordinates are got by alternating the sign. Subtracting 5C,; from 5C; we obtain 5H;. Having obtained C,; we now subtract 3C,; from 3C3 and obtain 3 (H;+ H,). Above the given ordinates write those of C3 with signs changed (row 4), and above these write those of H; with sions changed (row 3). Add rows 3, 4, and 5 to get row 2, in which are the ordinates of H,+H,+Hy &. Neglecting H,, Hy, &e., as is done in the analysis in Table I., we may consider the figures in row 2 as the ordinates of H,, and neglecting Hl, we may consider the figures in row 11 as the ordinates of 3Hs3. The first 15 numbers under Amp. H, are the quarter squares of the ordinates of H,. ‘Twice the sum of these is divided by 15, the number of ordinates, and the quotient is found to be the quarter square of 987. Hence h,, the amplitude of Hy, is 987. Similarly for the amplitudes of H; and H;. Under the heading “Phase of Hy,’ in the first column under sines, are the quotients got by dividing the first four ordinates on the rising side of H, and the last four on the falling side of H; by 4,; in the second column under angles are the corresponding angles, and in the third column are Neer Practical Method of Harmonie Analysis. Di the eight values of 12°—a deduced. The mean of these 2° 2' when subtracted from 12° gives the crossing-point or phase of H, as 9° 58’. Similarly for the phases of H, and H;. It will be noticed that at the crossing-point determined for H3, H3 crosses down, which is expressed analytically by writing its amplitude negative. 8. It will be noticed in the determination of the phase of H, in Table I., that the eight values of 12°—.« differ consider- ably from each other, indicating the presence in what we there take for H, of a considerable upper harmonic, pro- bably H,;. In order to determine H,, fourteen e.s. ordinates of the half-wave are required. If the wave-trace were given these could be measured off from it, but if, as in the case we are considering, only 15 original ordinates are given, it is necessary to plot the 15 ordinates of H,+H, obtained in Table I., and from the smooth curve drawn through them to measure off 14 e.s. ordinates. This has been done and the values obtained are given in row 4, Table II., as well as the calculation necessary for the determination of H, and its elimination from H,+ Hy. What is called the amplitude of H,in Table I. is really /2 RMS. (H,+H,). To get amp. H, it is better to remove the effect of H, by treating it as a correction, thus avoiding error that might be introduced in the plotting. This is easily done, since fi ene 2 M.S (H,+H,) ao al Te ‘ hence A, (corrected) = wh Amp. (H,+ H,?—hZ, = /h? (uncorrected) —h;? In Table II. the corrected crossing-point of H, is deter- mined, and it is seen to differ in phase only by 2 minutes from the value obtained in Table I. The differences between the four values of 3 (24°—8) when determining the crossing-point of H; in Table I. point to the presence of a ninth harmonic, which exists as a third com- ponent in H;+Hp . Hy can, if desired, be determined by plotting the five ordinates obtained in Table I., measuring off from the curve six e.s, ordinates, and proceeding as before. It will be found that H)=3 sin 9 (wf—13°). 9. In Table ILI. is given most of the work required for the determination of the first six harmonics of a complete wave that contains harmonics both of odd and even orders. T'wenty-four e.s. ordinates of the full wave are taken. This Phil. Mag. 8. 6. Vol. 11. No. 61. Jan. 1906. D \ » ¢ } 34 Prof. T. R. Lyle on an Expeditious number is specially suitable, as it enables us to determine directly C,, C., C3, Cy, and C,. To determine C;, replotting will have to be resorted to if the full wave-trace be not available. At the top of Table IIT. are written the 24 given ordinates under their corresponding abscisse. J rom these ordinates the constant term of f(t) has been removed. This can be done by aid of the formula S(O +f (t4+7/n) +f(¢+2t/n)+.... +f (t-+-n—I1t/n) =n[a,+a, sinn (wf—6,)+a,, sin 2n(wi —6,,,) +a,, sindn(ot—@,,)+&e.|, 12.) 2) a which can be easily established by the method used in § 2. From this formula we see that the mean of n e.s. ordinates embracing one period of a periodic function is equal to its constant term, if its nth, 2nth, &. narmonics are neglected. Returning to Table III., we add the second twelve ordi- nates with their signs changed to the first twelve, in order, and obtain 12 e.s. ordinates of 2C,, i.e. of 27H, + H;+H;+&e.]. (See equation I., § 2.) Subtracting these from twice the given ordinates, those of 2[H,+H,+H,+&c.] are left, and the remainder of the work proceeds as in Table |. 2(H,+H,+H,+ &ce.] could be obtained directly from the 24 given ordinates by adding the second 12 to the first 12 of them, in order. (See formula III., § 9.) The amplitudes and phases of the different harmonics were determined as in Table I., but the figures necessary in their calculation are not given. The following are interesting applications of the above method to more general harmonic analysis. To obtain the harmonic expression for the odd periodic function whose graph for half a period is the sides of an isosceles triangle of altitude h. (See fig. 1.) Taking 0 and w as the abscissee of the extremities of the base, relative values of any number of e.s. ordinates can be written down, and any component at once obtained. Thus, 30 e.s. ordinates would be 0, 1,2, 3,.. .14, 15,14, ... 2, 1, and these correspond to an altitude 15. It will be found that all the components (2. e. 3rd, 5th, &e. in this case) are the sides of isosceles triangles passing through the origin, and that the altitudes are —h/3?, h/5°, —h/i*, &. respectively. (See fig. 1.) (The same can be quickly arrived at geometrically.) Practical Method of Harmonic Analysis. 35 Bigs Wr. Hence, if the full wave or C, be represented by C,=q, sin(wt—6,) +43 sin 3(@t— 63) +a; sin 5(wt —9;) + &e., its third component C; is =— i [a sin(8@¢—0,) +a; sin 3(3@¢— 83) +a sin 5(3et—O6;) + &e. |, and its fifth component C; is . [a,sin(Set—9;) +a38in 3(5at — 3) +45 sin5(5a¢—6;) + Ke.], and so on; but by definition C3 and C; are also given by C,=a3 sin 8(@t—O@3) +d sin 9(@t— Oy) +... C;=as; sin D(@f—6;) +.a)5 sin 15(@t— 65) +... Hence, identifying the expressions for the same components, we find that @, = —3*a,= 57a, = —Ta,=Ke., Gi 36s 0Gs-= COn= Ke., so that C,=a, | sin (wt—0,) — SutAC LLMs) 4 sin(S@t— 61) — ke. 3” 5A D2 | | 36 Prof. T. R. Lyle on an HLaxpeditious But C,=0 when wf=0, therefore 0;=0; and C,=/ when wt=7/2; therefore h=a,[14+1/3?4+1/5? + 1/7? + &.] =a,7°/8. Hence a,=8h/r’, and the Fourier series required is sin 3wf sin dat — ke. | SAT. C.= a [ sin at— 32 53 = AN (ot) say. If the left extremity of the base were at a distance a from the origin instead of coinciding with it, then C,=AN (wt—a). Let us eall the function 4N(#t—«) an isosceles function, and the series of isosceles triangles which is the graph of hN(wt—a) an isosceles wave specified by A its altitude, and a its phase. 11. Any wave containing only odd harmonics whose form is polygonal, with n vertices per half-wave, can be resolved into n isosceles waves of the same period, and hence can be analytically represented by a sum of n isosceles functions. A vertex may or may not occur where the wave crosses the axis of abscissee. In the latter case the base angles of the polygon will be equal. For the sake of definiteness let us consider the case when the polygon has 4 vertices per half-wave, and let it be specified by my, mg, m3, m4, ms (M;= —m}), the tangents of the angles its sides, taken in the positive direction, make with the axis of z, and by the abscisse wx, 223, X34, X45, Of its vertices. In the first place let us determine the form of the wave got by adding to the above the isosceles wave L=AN(@t—a) specified in the above manner by M, —M, and X, so that h=M7/2 and a+7/2=X. In general the new wave will have 5 vertices, the abscissa of the one introduced being X, while the abscissee of the others are unchanged, and if X lie say between x23 and 34, and the tangents of the slopes of the sides of the new polygon be mm, mo, m3, 73, 24, —%4, then, remembering that the equations of the different sides are of the form Y=Me+tk, we see that m=my+M, m=m,+M, n3=m;,+M, n3 =m,—M, m=m,—M. Practical Method of Harmonic Analysis. 37 Hence Ny — Ny = My— Mo, Ny— Nz = M,y—Ms, N3—n; = 2M, Ns! — N= Nz — M4, Ny— Ns = M,— Ms. Thus, if we call m,— mz, the function of the vertex Z1., we see that by addition of J to the given wave a new vertex is introduced whose function is equal to that of J(=2M), while the functions of all the other vertices are unchanged. It is easy to see that the function of the vertex of —TJ is —2M, so that if J be subtracted from the given wave a new vertex is introduced whose function is —2M. If the abscissa X of the vertex of correspond with that of one of the vertices of the given polygon 23, say, then no new vertex will be introduced by the addition (or subtrac- tion) of J, and | Ny — Ny = Ny — Mz, Ny—N3 = My—m3+2M, N3—N, = M3— M4, Ng— Ns = Mg— Ms. If, in addition, 2M=m,—m,, then ny—n;=0 and the vertex or break at a 3 is removed. Thus, by subtracting from the polygonal wave an isosceles wave whose vertex has the same function and abscissa as a vertex of the given polygon, this vertex of the polygonal wave is removed, while the functions of its remaining vertices are unchanged. To remove each vertex therefore a definite isosceles wave is required, and since, when all vertives are removed the axis of abscisse or y=0 remains, we see that the sum of the several isosceles waves required to extinguish the given wave is equal to the latter. In the general case, therefore, of a polygonal wave with n vertices, the vertex m,, M,.1) 2, 11 will be removed by Pineting the isosceles wave [= AN (ae ey where Me My =2M = Aha, > —_— Rie eotcs 9. Ge rtd — X =at+a/2; and the complete wave will be fully represented by the sum of the n isosceles functions given by qr vant | | 4 > y —m,.)) N(@t—e, 4. +7 2) ; remembering that m,,,=— my. 38 Prof. T. R. Lyle on an Expeditious The following are examples of the preceding method :— 12(a). Wave-form a trapezium with equal base angles. This is the sum of two equal isosceles waves. Take the left extremity of the base of the trapezium as the origin of the abscisse, and let it be specified by mMm=mM, Mm=0, mM=—mM, Ayp=p, Aeg=T— p, so that its altitude t=m. By $11 the expression for the wave is = [N(@t—w+7/2)+N(ot +p—7/2)] sin 3(@t—w+7/2) Qn. Le os = [sin (@t— w+ 1/2) — 32 + &e. + sin (ot jar) ae BAe ee +&e.] 1 oe ; sin 3u sin 3ot | = a sin b sin of + 33 in Sw sin } ie sin ee Jot +é&e.], which is Fourier’s expansion for a wave of this form. 12(6). Wave-form a triangle. This is the difference of two isosceles waves when the vertex of one lies on a side of the other. Take the left extremity of the base of the triangle as the origin of abscisse, and let it be specified by | Mm=M, M=—N, M=—M, A=", A3=T, so that its altitude h=ym=(z—p)n, and m,n are the tangents of its base angles. By §11 its expansion in isosceles functions is T + i Lon +n) N(wt—pw+7/2)+ (m—n) N(ot—7/2)] 7 1 = = [N(@t—#+2/2) +N(@t—7/2)] | +“ [N@t—n+7/2)-N(ot—7/2)], which is 3 sin Me 9 sin 3(@t —p/2) 3? . Aan IT 2 he. | ae sin 5 sin (wt—p/2) + + &e. | du : cos—5- cos 3(wt — p./2) 32 Aas | Ss a jess 7 008 (wt —p/2) + +&e.| where mp=n(r7—p)=h. Practical Method of Haurmone Analysis. 39 When »=120° the above expression for the triangle reduces to a {sin (wt—8)— pu daa) ve ) pene) —be.} 8) 6 + 5% {cos 30 aes Het ene cae \, if where faigy Avila 3V3 12(¢). Wave-form a polygon with n vertices per half-wave and such that the functions of its vertices are all equal and also the projections of its sides on the axis of «. Let G= MM —Mz=M,—M3=M3—M,= Ke. =m, +m, and let the abscissa of its vertices be a, a+m/n, a+2mn,....at+(n—l1)a/n; then by § 11 the expression for the wave is 2 .N(wt+7/2—[a+rm/n]), where 7 has all values from 0 to n—1. Substituting for the N functions their equivalent harmonic series, summing the terms that have the same arguments and rememberi ing that ng=2m,, the expression for the polygonal wave under moncilenarion becomes 4m if 1 sl a {- ce sin (@t—a-+/2n) + Sir apiek ee mesa [2 SIN 5 3° sin on PAY) iL) ii + are gon 5(wt—a-+ m/2n) + &e. \ ‘ de sing 12(d). If in example (c) x become infinite, the polygon be- comes a smooth curve satisfying the following conditions :— a” J =GOnst., ge" dy dx y=0 when #=0 and when w=7. =m, when c=0, and = —m, when v=7, 40) Practical Method of Harmonie Analysis. This curve is the parabola i My 2 7 <> ee CR y 1 or ? whose axis is v=7/2 and vertex e=7/2, y=m7/4; and the harmonic expression for the wave of which it is the type is obtained by making n==0 and «=O in the expression in (c), and is | ue | ee aoe a oe +h. } 13. To find the harmonic expression for the complete periodic function whose graph for one period is made up of the sides of two equal and similar triangles ABC and A’BC’ so placed that A’ and C’ lie in AB and CB produced respec- tively. Take A as origin, then the abscissz of B and A’ will be w and 2a respectively ; and let the abscissa of C=p, hence that of C/=27—n. By geometrical construction the different components of this wave can be easily obtained if we remember formulal,. § 1. Thus, to get the 2nd component we cut the wave in four portions by ordinates at 7/2, 7, 37/2, 27, invert the second and fourth portions, superpose them and the third portion on the first, add the corresponding ordinates, divide each sum by four, and the plot of the results will be a half-wave, which gives the 2nd component. It will be found for the wave under consideration that all the components are, in general, trapeziums of the type treated in §12(a); and if the trapezium which is the 7th component be specified as in §$12(a) by m, and mw, measured on the original scale of abscissze, it will be found that iy tan A+ tan B 27 mM = - (i.e., that 27” times the function of its vertex is equal to + the function of the vertex of the triangle) ; and that sin 7m, = +sin rp, the same signs being taken together. It is to be noted that as the base of the rth component is a/r, the altitudes of its isosceles elements are each T a MY OS a 2r Ager ee Faraday and Kerr Effects in the Infra-red Spectrum. 41 its expression in isosceles functions is Yr(ot— jt, + x) +Nr(ot+4,— nh ; and its harmonic expression is 7m, ey caine: sin dr, sin drat a. 4m, a ‘| YT ats, Pye ath he Hence the rth component 2(tan A+tan B fh ; sin 3ru sin 3rat C= ZI a sin ru sin rot + SS sin Ne 5Srot +4. } tid as + If h be the altitude of either of the given triangles, then h=p tan A= (7—yp) tan B, and the oo for the complete wave is sin 2u sin 2wt AG) = Cea = { sin pe sin wt + 32 os sin Soi 30t +80. } ’ III. On the Faraday and Kerr Effects in the Infra-red Spectrum. By L. R. IncERsout *. Introduction. HE aim of the present work is a study of electromagnetic rotatory dispersion, particularly in the infra-red spectr um. Because of the important bearing of the phenomenon of magnetic rotation of the plane of polarization of light in the field of electro-optics, the subject has been investigated i in all its various aspects by many observers during the last half- century, and the effects of the different factors which govern the rotation, such as strength of magnetic field, an rele of incidence, and temperature, carefully determined. The most important factor of all, however, if one considers the place it must have in any explanation of the phenomenon—the depend- ence of the magnetic rotation on wave-length, or magnetic rotatory dispersion—has been studied only over a very limited range of spectrum. Thus while the rotatory dispersion in * Thesis submitted for the Ph.D. degree, University of Wisconsin, 1905, Communicated by Prof. C. E. Mendenhall. 49 Mr. L. R. Ingersoll on the Faraday and the visible spectrum may be considered as accurately known for many typical substances, measurements in the ultra- violet and infra-red have been scanty, and, especially in the latter, the broader and more important field, far from satisfactory. As a reason for this lack of attention to the infra-red, it may be urged that the problem of measuring rotations in this part of the spectrum is one of rather peculiar difficulty, necessitating as it does magnetic and electrical complications in spectrobolometric work which requires the highest order of sensibility. But even if an accuracy equal to that of visual measurements cannot be expected, the extension of the work into this field is nevertheless a matter to which con- siderable interest attaches ; for it is there that evidence must be sought in support of rotatory dispersion formule, which cannot as yet be considered as generally established, because of the narrow range of spectrum only over which they have been tested. The effect of absorption-bands on rotation must also be considered in this region, and whether or not their action may be accounted for by a type of dispersion formula analogous to the Ketteler-Helmholtz. It is in the infra-red, too, that one must seek for an explanation of the anomalous character of the rotatory dispersion shown by magnetic metals, and question whether the rotation continues to increase with increasing wave-length throughout the infra-red spec- trum, and therefore perhaps be very considerable for electro- magnetic waves metres long. It was in the hope of throwing a little more light on these and similar questions, that the present work was attempted. The two distinct cases which arise will be treated separately. They are (1) Faraday rotation, or rotation suffered by the plane of polarization of light transmitted through some sub- stance in a magnetic field; and (2) the Kerr effect, or rotation due to reflexion at the polished pole-face of a magnet, or at a paramagnetic mirror in a magnetic field. Parr I. FARADAY ROTATION. That radiant heat as well as light may show Faraday rotation was first proved by Wartmann *, and measurements of the rotation for a number of different substances were later made by De la Provostaye and Desainst and by * Compt. Rend. xxii. p. 745 (1846). + Ann. Chim. Phys. [3] xxvii. p. 232 (1849). Kerr Effects in the Infra-red Spectrum. 43 L. Grunmach*. None of these experimenters, however, made any attempt to obtain radiations of uniform and known wave-leneth fur their work; and G. Moreau ft seems to be the only one who has heretofore done this and so obtained measurements of magnetic rotatory dispersion in the infra- red. He determined the rotation in a tube of carbon bisulphide, placed in a powerful magnetizing solenoid, for wave-lengths ranging from 0°79 w to 1:42 wu. A beam of sunlight was passed in turn through a polarizer, carbon- bisulphide tube, and analyser, and its intensity after disper- sion by a prism of flint glass was measured by a thermopile placed in the spectrum. The method of observation, in brief, consisted in determining the azimuth of the plane of polarization of the light emerging from the carbon bisulphide by two observations of the intensity of radiation for two positions of the analyser 90° different in azimuth. By repeating this when the current was passing in the solenoid, the rotation due to the magnetic field could readily be calculated. Measurements by ordinary polarimetric means allowed the calculation of the field-strengths by the use of known data, and the effect of this field at the galvanometer was annulled by placing near by a small secondary spool in shunt with the main solenoid. He found rotations amount- ing in general to several degrees, being at X=0°79 w equal to 52 per cent. of the rotation for sodium light, and at N=1'42 pw, 32 per cent., with an estimated maximum error averaging about 10 per cent. In the present work the magnetic rotation has been measured for thirty wave-lengths between X=0°58 w and 4-3 4; carbon bisulphide, the substance generally used in magnetic polarimetry, being chosen for the test, because of its high rotatory power, combined with transparency in the infra-red. A powerful electromagnet was used, instead of a solenoid, to furnish the magnetic field; for the gain in field-strength allowed the use of a shorter carbon-bisulphide tube without sensible loss of rotation, and with the great added advantage of less absorption of radiation in the infra- red. To simplify the problem, all other conditions upon which the rotation depends, such as field-strength, length of carbon-bisulphide tube, and temperature,—save the wave- length of the light used,—were kept as nearly as possible the same throughout all the measurements, and hence need not be accurately known, since, being constant, they could in no way affect the form of the dispersion-curve, the determination of which was the desired end of the experiment. * Wied. Ann. xiv. p. 85 (1881). T Ann. Chim. Phys. [7] 1. p. 227 (1894). id Mr. L. R. Ingersoll on the Faraday and INspersion Formule. It is not the intention to enter into a discussion of the various theories of magneto-optic phenomena which have been proposed by Maxwell, Lorentz, Goldhammer, Drude, and others, but rather to test, over a much wider range of spectrum than has heretofore been possible, the various rotatory-dispersion formule deduced on the basis of each, and thus perhaps to furnish more evidence in favour of some one of them, or a modification. Among such formulze may be mentioned that due to Maxwell and formulated by Moreau*, ‘Ln dn (1 oes Ace MER ee and the very similar one of Van Schaik f, ey dn)\ (Cy -) o=An {nr h(a lr x! 5 also that due to Joubin f, Hy: LD oS 4n-Ong |. To these must be added the formulee given by Drude §, oe a be o=Nn {5 ze oars? deduced on the hypothesis of molecular currents ; and val 19a" Cea } Tin et ea Ie deduced on the hypothesis of the Hall etfect, X, being in each case the wave-length of an ultra-violet absorption-band. With the data hitherto obtained, it is impossible to decide definitely in favour of any one of these, for over the limited range of spectrum over which they have been satisfactorily tested—barely half a micron—it is possible, by properly choosing the constants, to make any one of them fit the facts sufficiently well. Moreau’s work in the infra-red points ina general way to the formula of Joubin, although this is hardly as satisfactory as the others in the visible; but, as will be seen later, the points he obtained do not lie at all ona regular curve, and it is possible that his experimental error is larger than estimated. * Ann. Chim. Phys. [7] i. p. 841 (1894). + Arch, Néer. xvii. (1882) and xxi. (1886). t Ann. Chim. Phys. [6] xvi. p. 78 (1889). § Lehrbuch der Optik, pp. 896 & 408. Kerr liffects in the Infra-red Spectrum. 45 Method. The method adopted has some points in common both with the one due to De la Provostaye and Desains * and that used by Moreau*. A beam of light after passing in turn through a polarizer, rotating substance between the poles of an electromagnet, and analyser, was dispersed and formed into a spectrum in which was placed the strip of a bolometer. Any rotation of the plane of polarization such as would be caused by exciting the magnet, would then cause an increase or diminution of intensity of the beam transmitted by the analyser, which effect could be measured for any desired wave-length by the bolometer and the rotation calculated accordingly. If the principal planes of the tees and analyser make an angle a, the intensity at any chosen wave-length as measured by the bolometer may be represented by a= hi cosa; _where I’ is the intensity of this radiation incident on the analyser, and & takes account of absorption. Then any small rotation 8 of the plane of polarization, produced either by turning the polarizer, or by the action of the magnetic field, will produce a change in I, disregarding signs, dl = 26kl’ sin cosa, or, dividing by I and solving for 6, sa cot « radians, or as © cot a degrees. As pointed out by De la Provostaye and Desains, dI will evidently be greatest for «=45°, which is accordingly the angle chosen. For any rotation the value of 8 may be obtained, if a=45°, from di =k’ \cos? (45° + 6) —cos? 45°! = +3 sin 26. AI’, or dl Tr In this way the magnetic rotation for any chosen wave- jength may be determined by a measurement of the intensity | of that wave-length in the spectrum, and of the change in intensity dI when the magnet is excited, or better, when it is reversed, since this gives a doubled effect. Both I and dl are determined as oalvanometer-deflexions, and from their Bh pee ees 6 = 4 sin * Loe. cit. 46 Mr. L. R. Ingersoll on the Faraday and ratio the rotation is at once calculated. This method as so far described has about the same possibilities of sensibility as that of Moreau,—with the advantage, however, that the rotation is obtained almost directly, instead of as the differ- ence between two large angles; but its ability to measure small rotations may be greatly increased by the following simple scheme. Suppose it is possible, after measuring the intensity I, to increase the bolometer sensibility in a known ratio, say twenty times, and at the same time to shift the zero of the galvanometer so that the reading, which the radiation I in connexion with the greatly increased sensibility would otherwise throw far off the scale, may still be brought within the field of vision. In this way, the change of inten- sity dl, which is in general only a small fraction of I, may be effectively magnified and made to produce a galvanometer deflexion of the same order as the latter, with a corresponding increase in the possible accuracy of measurement, for the change of sensibility may be readily effected by cutting out resistance in series with the galvanometer, and the shift of the zero by simply adjusting the balance of the bolometer. Description of Apparatus. Before describing the apparatus in detail, certain special requirements of the problem should be noticed. Since rota- tion appears as a change of perhaps only a few per cent. in the energy at any wave-length, it is evident that for accurate measurement a very intense spectrum is demanded. This must be formed moreover of light which has been polarized, transmitted down the axis of the magnet, analysed, and which has suffered a number of other losses by reflexion and absorp- tion ; hence the necessity for a very brilliant source. It is clear, too, that this source must be exceptionally constant, for changes of intensity might be falsely interpreted as rotations. ; These requirements have been met by the use of a Nernst glower, with special protective covering, asa source. The formation of a parallel beam, as is generally used in polari- metry, which should be of sufficient intensity, and of small enough cross-section to suit the necessarily small apertures in the poles of the magnet, was found impracticable: a conical beam was therefore used, which converged to a focus at the only points where small aperture was demanded,—between the poles of the magnet and on the slit of the spectrometer. The latter instrument had short-focus mirrors, and was designed to give as intense a spectrum as possible without Kerr Kfects in the Infra-red Spectrum. A7 the sacrifice of purity to the extent of causing a dispropor- tionately large error in the measurement of wave-length. As to the actual intensity of the spectrum, it may be stated that with the arrangement used, galvanometer-deflexions were not uncommon, measured with reduced sensibility, which would correspond, on the basis of full sensibility, to 1500 centimetres on the scale. The general arrangement of apparatus may be seen from fig. 1 (p. 48). Light from the Nernst glower G, was polarized by reflexion at the pul of thin glass plates P, mudi atientecdexion at M, formed a real image of the olower between the poles of the magnet, and again on the slit, after reflexion at M, and from the pile of analyser-plates A. This was drawn out into a spectrum at the bolometer-strip B by a 60° rock-salt prism. The latter had the customary Wadsworth minimum deviation mounting, the plane mirror being a Brashear flat 4x10c¢em. The prism itself had faces 4 x5 em., polished by Brashear, and was protected by an enclosure, not shown in the diagram, mounted on the spectrometer-table and con- taining sulphuric acid. The table was rotated by a micro- meter-screw connected with a steel strap pulling tangentially over a lever arm. One division of the micrometer-head corresponded to a rotation of 0:06 minute of are. The mirrors M,, M,, M; were each 40 cms. in local length, while M, was 30 cms. They were mounted, together with the other parts of the spectrometer, on heavy slabs of slate. The broken lines represent various adjustments which, by means of cords, could be conveniently made by the observer without moving from his position in front of the galvano- meter scale. (1) Could be used to rotate the polarizer ; (2) allowed the carbon-bisulphide tube to be thrown in or out of the path of the beam; (3) operated a shutter in front of the slit; (4) rotated the mirror M, and hence shifted the image of the glower on the slit. Neither bolometer nor galvanometer present any especial novelty of construction, save that the latter was made as compact as possible to allow effectual shielding. It was of the type described by Mendenhall and Waidner * and had four coils of twenty ohms each, measuring 16 mms. outside and 2 mms. inside diameter. The system, which had of course quartz-fibre suspension, weighed something less than 2 mg. and had a mirror 1 mm. square. Deflexions of the image of a fine wire in front of a Nernst glower Gy were observed on a scale a metre and a half distant. Fairly good magnetic shielding was secured by surrounding it with six concentric * Amer, Journ. Sei. xii. p. 249 (Oct. 1901). Mr. L. R. Ingersoll on the Furaday and 48 ‘snqe Iv ddy jo juowesueviy— [ “oy Kerr Ejjects in the Infra-red Spectrum. AY sections of annealed steel pipe. This arrangement could be made to give a sensibility of 4x 10—" for 5 ohms resistance, but considerations of steadiness and of proportionality of deflexions led to reducing this ‘to about 2x 10-!° amp. per mm. with 10 sec. period, for ordinary usage. The bolometer used in most of the work had strips } mm. wide and 8 mms. long. Heavy copper leads connected it with the balancin o-bridge, and switches, Sw, which permitted reversal of galv Somer connexions and also changes of sensibility in ihe approximate ratios—3°5, 9, and 28 times respectively. At highest sensibility a candle at a metre’ distance gave a deflexion corresponding to 200 Snsinss on the valvanometer-scale. The magnet was designed to give the greatest field-streneth over ranges of several centimetres, onli the smallest external field possible. 'The pole-pieces were of Swedish iron 9 ems. in diameter, and were bored with conical holes narrowing from 5 cms. diam. at the outside ends, to a slit 5 mms. wide and 16 mms. high at the conical ends. The advantages of a rectangular opening over a circular one are obvious, con- sidering the shape of the glower used as a source, When excited with about 100, 000 ampere-turns, it gave fields a high as 26,000 lines per cm. over an area of a few ee millimetres, using pointed pole-pieces. It will be noted that this is not as oreat as the fields which may be obtained with the du Bois ring type of magnet ; but it may be remarked that in the present work the air- gap was never in practice much less than 3 ems., with, of course, a necessarily great loss of field-strength : therefore, since the ring type depends for its powerful fields, not on an excessive number of ampere- turns, but on the low reluctance of its magnetic circuit, it is doubtful whether its performance under the same circum- stances would excel that of the present type. Moreover, the varied adjustments of which it must admit would be impossible ina magnet of the ring type,—at least without very great modification. The external field was small and its effect at the galvano- meter was pal ets od for by a secondary coil of high resistance, placed near the latter instrument and connected in shunt with one el ie main magnet-coils. When run at full power there was necessarily considerable heating about the magnet, and to protect the neighbouring apparatus from this , the whole magnet was enclosed in a large wooden box (not shown in diagr: am) whose sides were water-jacketed. Analyser and pol iizer were each made up of a number of plates of microscopic cover-glass 3°5 x5 ems. and 0:2 mm. Phil. Mag. 8.6. Vol. 11. No. 61. Jan. 1906. D i 50 Mr. L. R. Ingersoll on the Faraday and thick. Reflexion from thin glass plates, while by no means free from objection, seemed to be the or ily practical scheme of obtaining polarized radiations for this work ; for the use of a polarizing grating would involve too much loss of energy, and the absorption of any doubly-refracting substance makes its use prohibitive beyond about ~A=2°5 w. The polarizer carried a divided circle and was so mounted that it could be rotated about the axis of the beam. The glower was arranged to rotate with the polarizer, and at the same time to turn about an axis of its own, so as to keep its image on the slit always vertical. The analyser also had a number of possible adjustments, and carried with and parallel to it a plane silver surface, by reflexion at which, after passing the polarizer, the beam would be brought out parallel to its original direction. Because of its rather exceptional performance as regards briliancy and constancy, the glower and its mounting are worthy of special mention. When unprotected and in the open air, a Nernst glower may suffer variations of intensity of upwards of one or two per cent., even when supphed with a perfectly constant H.M.F. This is doubtless due to irregularities of convection ; and at the suggestion of Prof. Mendenhall it was tried inside an enclosure made of plaster- of-Paris or cement. This gave a much greater constancy, and as the objections to the plaster enclosure, which was soon destroyed by the heat, have since been removed by making it of firebrick, it leaves little to be desired as a souree fomaumes red work. Specimen curves have been obtained, using 96-volt direct-current glowers made by the Nernst Lamp Company of Pittsburg, and furnishing the current with a storage battery, e hich show a maximum variation of inten- sity of less than ,), per cent. for several minutes at a time. Some of the special adjustments may be mentioned. The analyser and polarizer piles of plates were set with the aid of a nicol at the angle of incidence which gave most completely polarized reflected light. It might be supposed that this setting would have to be changed to suit the different wave- lengths used; but asa matter of fact, as will be pointed out in a discussion of the sources of error, it was not a sensitive adjustment, and might be made once for all with sufficient accuracy for all wave-lengths within the range over which it was possible to work. The angle between the principal planes of the polarizer and analy ser was determined by placing a large nicol with divided circle at N, and setting so as to extinguish, first, by crossing with the principal plane of the polarizery, and, eaconds with that of the analyser. In Kerr Effects in the Infra-red Spectrum. a1 general this angle was made 45°. When ready to take a set of readings, “the small compensating-coil was adjusted in position till the galvanometer-zero was unchanged by the action of the magnet. Because of the greater freedom from magnetic as well as mechanical vibrations, the observations were all made at night. With the spectrometer set at the desired wave-length, the total ener gy I was first measured with reduced sensibility. Then, with the slit still open, the sensibility was increased step by step, the bolometer at the same time being balanced to keep the reading on the scale. When the magnet was excited the galvanometer showed a deflexion, indicating either an increase or decrease of intensity dL. The magnet- current was then reversed, the new deflexion observed, and the operation repeated so as to give usually five readings in either direction. The galvanometer connexions were then reversed, and the process repeated; for in this way, it will be observed, any small outstanding effect dueto the direct action of the magnet on the galvanometer would be eliminated, while at the same time a second set of readings was obtained which served to forma very good check on the first. An occasional set of readings with the carbon-bisulphide cell removed served to show if any other cause was also acting to produce rotation. The mean difference of the galvanometer readings when the magnet-field was direct, and when it was reversed, gave 2 d1, and the first measurement of the total intensity gave I, and their ratio, on the basis of the same sensibility, ~ deter- mined the angle of rotation. The method of computing the mean dl was mainly graphical and need not be described in detail, but it wiil serve to remark that it was designed to render as ineffective as possible errors due to bolometer drift and variations of the source, as well as to eliminate completely any chance of personal bias as to any one or more observations. Sources of Error. It is to be particularly noted at the outset, that only those errors are of first importance which are selective in action, and hence affect the determinations for different wave-lengths unequally. or, while it is of course desirable to know the absolute magnitudes of the rotations, for convenience in checking the results by other methods, if the error can be shown to be a constant one which applies equally to all wave-lengths it can have no effect on the correctness of the results aimed at, ze. the form of the rotatory dispersion K 2 | | a2 Mr. L. R. Ingersoll on the Faraday and curve, and hence need be only approximately determined. This point will be mentioned again in connexion with certain of the errors to be considered. Errors may otherwise be conveniently grouped into two general classes : those incidental to the measurement of the ratio dI/I, and those occurring in the interpretation of this result as rotation for radiations of a definite wave-length. Those of the first class will in the main .be somewhat com- pensating, and their effect may be best observed by plotting from the above table dI/I with wave-length, and noting how closely the points follow a regular curve. Those of the second class may be systematic, and their effect is more diff- cult to estimate directly. As sources of errors of the first kind may be mentioned :-— Variations in brilliancy of the Nernst glower. Disturbing effect of magnet on calvanometer. Bolometer unsteadiness and drift. Changes of temperature due to heating of magnet. Inaccurate determination of the sensibility reduction ratios. Considering them briefly in the order given,—the variations of the glower, as explained above, were ‘small, and their eftect was eliminated by taking the average of several deflexions in each direction, in rapid succession. The graphical method of computing this av erage was especially useful in enabling one to detect and allow for such accidental variations. It was impossible to eliminate entirely the effect of the magnet on the galvanometer even with the most careful shielding and with the aid of the small compensating solenoid, because of the unequal heating effects in the different coils. However, by frequently adjusting this solenoid, by altering its distance from the galvanometer, the effect might be made small; and by reversing the galv: anometer connexions and averaging the two sets of readings, it was practically eliminated. The matter of bolometer drift was rather troublesome, and would seem to be due partly to the high sensibility which was demanded of the instrument, and partly to the fact that the method of observation necessitated frequent changes of balance. However, the effect of drift was far less disturbing in this than in most spectrobolometric problems, and, like errors due to the variations of the glower, it was largely eliminated from a series of readings by taking the graphical mean. reating of the magnet doubtless gave rise to slight changes Kerr Liffects in the Infra-red Spectrum. a) of field-strength, although determinations with a small test- coil showed the effect to be small. But any possibility of this error being selective was removed by so choosing the suecession of wave-lengths to be tested, that the rotation for the same or neighbouring parts of the spectrum might be measured at different times under very different heating o con- ditions. The temperature of the carbon bisulphide was kept constant to within one or two degrees by a water-jacket around the containing tube, hence the error from this source would be less than one per cent. Sensibility ratios were determined by measurements of the same intensity of radiation with the two sensibilities, the ratio of which was desired. Although the discrepancy between successive determinations made in this manner was some- times as much as three or four per cent., so many tests were made that the probable error of the accepted values was very much smaller. Judging from the agreement in different results, for the same or neighbouring the errors of this class is to produce an uncertainty of probably less than two or three per cent. over the greater range of spectrum studied, although at the ends it is considerably increased. To be certain that this rotation was not in part due to some other cause than the Faraday effect in the earbon-bisulphide, the cell containing the latter was removed and a number of tests made, which, as may be seen from the table of results, showed that such spurious rotation was too small to be definitely detected. The rotation due to the thin glass ends of the cell was entirely negligible, being only about one-fifth of one per cent. of the other. As causes of the second sort of errors may be mentioned:— Inability of the pile of plates to polarize completely. The use of a non-parallel beam of light. Impurity of spectrum due to stray light and to the use of a broad bolometer strip and slit. Regarding the first source of error, it is evident that the light would he incident on the polarizer. plates over quite a range of angle, because of the appreciable size, as well as nearness of the ‘glower, which was only about 10 ems. distant; hence complete. polarization could not be expected in the reflected light. Then, since the formula used to reduce the quantity dl/I to a rotation thr ‘ough a certain angle was deduced on the supposition of completely polarized light, the results obtained with it must be subject to a correction which will now be ecaleulated. go wave-lengths, the cumulative effect of ————eEeEeEeEeEeEeEeEeEeEeEeEeEeEeeeeeeeeee ee ee Eee eee 54 Mr. L. R. Ingersoll on the / araday and Let I’ represent the intensity, for any chosen wave-length, of the beam of natural light incident on the polarizer. Then the reflected beam will be made up of two parts,— IK, V’ (polarized in the plane of incidence) ; and } aK, V (polarized perpendicular to the plane of incidence), where K, is a factor which takes account of the percentage of light reflected by the surfaces, and a is a constant to be determined later. On emerging from the analyser, whose plane of incidence makes an angle e with that of the polarizer, the intensity is I=3K,K.V cos?a+3K,K, 1’ sin’? +3K,K, Va sin?a+43K,K,I' ab cos? a, where l and Ky, are constants for the analyser corresponding to a and K, for the polarizer. In general a and 6 will be small and their product may be neglected ; hence, dropping the last term and collecting, I=} K,K, I f{cos?’a2+(a+b) sin? }. A small rotation 6 will cause a change, di= —6 K,K, I' (1—a—)) sina cosa. Solving, dl cos?a+(a+6) sin? a a= Peay (L—a—b) sin 2a ’ Orie — 45°. ; dl 1l+atbh oe iio 2k The constants a and b are seen to represent the ratios of intensities of the light polarized perpendicular to and in the plane of incidence, for both polarizer and analyser. They may be determined with the aid of a nicol or other com- pletely polarizing agent placed at N, fig. 1. If its principal plane is turned at right angles to that of the polarizer, the intensity of the light on emerging from the analyser will be I,=3aK,K,K; V sin?a+ab K, KK; I’ cos’ a, where K; allows for absorption in the nicol. If crossed with the analyser instead it will be o=4 b KKK; id sin? a+ s atl K,K,K, ie cos” a. Kerr Hiffects in the Infra-red Spectrum. Do When set with principal plane parallel to that of polarizer or analyser, respectively, the intensity will be given by I,=4 K,K,K; I’ (cos? «+6 sin? a), I,=1K,K,K; I’ (cos?a@+a sin? a). Making «=45°, and dropping the second terms of the four equations, as they may be neglected with respect to the first, a and b become on solving, a=L/l;=L/l,, 6=1,/1;=1,/L, and hence may be readily measured as the ratio of two intensities. It might reasonably be expected, since the plates were set at the same angle for all wave-lengths, that « and b would depend largely on the wave-length tested. Such, however, has not been found to be the case, at least to any appreciable extent, over the range of spectrum for which a nicol was transparent enough to be used in measuring them, say as far AS; N= 2") pl. Then, s since from there to X=4°3 w the varia- tion in the reaches index of glass, and hence of the polarizing angle, is small, a and } could be regarded as con- stant, within the limits of accuracy required i in ane work, over the whole range of spectrum for which it was possible to measure rotations. This was undoubtedly because the varia- tion of the angle of conn lee polarization with wave-length was much smaller than the wnavoidable variation of the angle of incidence over the surface of the plates. The tests gave the value of a as ‘025 and 6 as *035, making a correction of 12°8 per cent. to be applied to the rotations as determined by the expressions }dI/lor }sin-! dI/1; for while the correction has been calculated only Hon emalll angles of rotation, it may be applied to any rotation actually measured, with sufficient accuracy. With regard to the magnitude of the correction, it may be noted too that, so long as it applies equally to all wave-lengths, its actual alue is a matter of secondary importance. The use of non- parallel light resulted in the edges of the beam being polarized in slightly different planes from that of the centre. This would cause an effective variation of a for different parts of the beam, but such small uncertainty would be less than that of the determination of « itself. Fortu- nately such errors, as well as those incidental to the setting of the polarizer and analyser, were also of secondary importance, being non-selective in character. To be free from elliptical polarization which might result from reflexion at the mirrors or a ——————,S—~—CS 56 Mr. L. R. Ingersoll on the Faraday and M,and M,, the polarizer was in general set so that its plane of incidence was parallel and perpendicular respectively to the planes of incidence on these two mirrors. It should be noted that the elliptical polarization which would inevitably be introduced by the oblique reflexion at the silver surface, immediately after passing the analyser, as well as the polariza- tion which would occur at the faces of the prism, could have no disturbing effect, since after the radiation had once passed the analyser its state of polarization was of no moment. Purity of the spectrum was tested by double dispersion, and although, as might be expected, considerable impurity due to overlapping slit-i images was found, only a trace of stray radiation could be discovered. To take account of the error due to impurity, correction was made for the width of slit and bolometer-strip. The 5 mm. strip subtended an angle of 5’, corresponding to from ‘02 to £m in the rock-salt spectrum. The slit was even wider asa rule, and it might be thought that such an arrangement, while necessary to secure sufficient energy for the measurements, would involve such a large correction as would seriously prejudice the accuracy of the work. But, while by no means negligible, the corrections in the present case prove to be much smaller than in most other spectrobolometric problems involving a like amount of impurity, because they are of a differential nature; for the rotations were determined, not by a single measurement of energy at any point of the spectrum, but by the ratio of the two quantities dI/I, and hence only the difference of the separate corrections to dI and I need be applied. These separate corrections were determined for each of the curves of dl and I plotted with wave- length (the curve of dJ, while not an energy-curve in the ordinary sense, is exactly analagous to one and may be treated in a similar manner) by the simple method of correc- tion for slit-width due to Lord Rayleigh, and outlined in Preston’s ‘ Heat,’ p. 606 (last edition). The difference, or resultant correction, varied from 2 per cent.at A=lp —4 per cent. at 38y. That the correction should be small was indicated by measurements of rotation for the same wave-length, with different slit-widths, which gave results in good agreement. Results. Table 1. 1s a synopsis of the principal results. Rotations are given for forty-two points of the spectrum (including duplicates), as produced by carbon bisulphide in a tube Kerr iiffects in the Infra-red Spectrum. 57 TABLE I, | | | = ._ | Wave- : Mean W2ghi yon Corrected peries, length. Sa aaa ae rallye halle & 2 sin ‘es Rotation. | | | | | p em cm. cm cme | o c cpa ee 0°58 Sa Sr ano Oty Graoy | ea ie 1451 * 16°50 ( apie 0:69 ATA | 33:6 | 336 | 336 | -710 1040 | * 11°82 etot AAC, 0°78 Bee ileal Nese GO |W 1486 MO Pee * 7-98 eee Sere 0:81 | 180 800 | 842) 821 | -456 658 * 7-49 ees .| 12 oan 72) jain) Sars Hem el ely Lee ll OER By (poe Sais ee" | 669 >| V2 146" 149 223 312 358 fe eee G2 MAMAN 1aD VA 4) 15425 “135 1-93 220 ee 635 88:0 | 875 | 87:75 | -136 1:95 LO, Se 220 | 1065 VCE ND Thera Mcrae Ore 1:07 1:19 ee POM Ose Son 46, | 8485. | 064 ‘92 1°02 pie | 2:50 | 744 435 | 42:5 | 43:0 058 | “83 91 eth 38% i280) saz 50 lO Se lelG 9) oh VO51e.| 72 72 Mtge Pe S00l 09D Pol Soo 52) 9 048 || 69 i) ih Melon MOBS GO 1 5:2) (5:6 044 63 69 ite. Pes SO MOSM RO Sev Sie 14-8 046 67 72 Were b.. ee 0 eS oan 22 2) O55) | 044s 63 68 eee Bite Onl econ aaesal eGo ym Os4ua| ‘48 33 We SOUR aol 0) LO hme [oy OBO | "43 47 ae BOOM INaty 164 | 161 | 15-75 046 | ‘66 72 aly bees <3 Sol jas SONI Gils ine: 0 042 60 65 a POM OOM Ai hs Ou a 4 Topi ucO42 60 65 ees... OS econ! (Oi) | Soule 125 041 58 63 0 a SA Brie een 2k) I eSiOelh 2-90ne 035 50 4 A: | aoe 390 | 86:0 2:9 |) 3:0 |) 2:95.) 034. | 49 3 ae £05) | (6D. 8: Bee lise 043 | 61 67 Be gree, #16) |= 45:1) | 6 20 es) 040 57 63 Bere AS coe Wes hehe eka 7) \he Leos | see, 68 “75 ce 0°63 MSs OOS lellco ye Mehes 949 14:16 16:10 oe... O70) (9532-9) | 024-4 124-9) ie 948 738 10-83 12:33 1 wae 0:84 | 158 192" 197 | 7945 508 C27 8:25 cha IO SGhE S| 17S 76755 284 4-08 4-65 ak 140) 1140s, | 213.) 208 BOI 1S F184) ) 264 +00 pee 1:64 |1465 /198 |190 |191°5 die Oi A gdeees Gers 2-12 esl 180-1 1490' | 157 bo) a6) 3) 105 1-51 1-79 pasts 210 |1370 | 1125 |112-5 1125 | -082 117 1:30 MRR. 2:40 |1180 | 774) 747 | 7605 | -064 92 1-01 Peas: 2-68 | 618 34:0; || 38°8. |. 33:9 055 | 78 85 a ee 3:00 | 228 10°6 | 10:3 |"10'45 |, -046 66 72 ih gee 380 | OSS 47) 494 948% | 5049 70 i ae be TORR yi OH © 0) ay Bal O52 74 S1 ee i, G00 Salto oily, asec, ee 044 | 63 69 Sika 4038 | 544) 2 SE ee Oa ‘58 ‘G4 as 0-78 AAD WHEE | inate —5 —0138 | esi Ss 1:02 270 Oa aso POs bees leue o| reve ee) SOCO Pe Tk. 7 001 See) 300 | 165 —1 ) 00 | —05 | —-0003 | Serer eo u) 200 146, nb OOret ecO5 ‘OOOL | e) 416 |. 75 | —2 2 | 00 |00 * Probably several per cent. too low, for reasons which will be mentioned. 28 Mr. L. R. Ingersoll on the Faraday and 4125 cms. long and at a temperature of 29°C. The field- strength was approximately 6000 c.a.s. units, and was given by a " magnet-current of 18°7 amp. The columns marked 2dl, and ‘Qdl, give the means of the several galvanometer- deflexions as explained above, the second column being made with the galvanometer-connexions reversed. All deflexions are stated in terms of the highest sensibility, and have galvanometer-proportionality corrections applied in all cases: but because of a certain amount of unsteadiness which is unavoidable—due mainly to small variations of the source— readings are given only to the nearest millimetre, and in some cases—where a large reading is obtained from one which is actually very much smaller, by reducing to a con- stent sensibility as a basis—only to the nearest centimetre. The considerable differences which are seen to occur, in the values of I in separate determinations on the sailie Wave: length, are due to different slit-widths, or to different brilliancies of the glower on the two occasions. The last column has been obtained from the previous one by the application of the correction factors previously de- duced, necessitated by the existence of partially polarized light and by impurity of the spectrum. These results have been plotted in fig. 2, the circles representing the points of series a; the crosses, hiss of ); and the triangles, those of e. The small circles connected by dotted lines represent the determinations of Moreau, plotted, for comparison’s sake, to the same scale, so that the rotation at A="79 w shall be the same in each case. From the nature of the problem it is impossible to do more than estimate the probable error of the results, but, as pre- viously mentioned, it is believed that the best idea of it may be gained by noting the variation of the points from the mean curve. Tor, since the points were all determined independently and. with many different adjustments and changes of slit-width, &c., it is difficult to see how any systematic error could remain undetected, save perhaps one which applied equally to all wave-lengths, and this would only alter the scale of the diagram. The probable error of some points is much less than of others. Thus, in making measurements on the shorter wave-lengths of series ¢, a water-cell was interposed in the path of the beam, to absorb the slight amount of stray infra-red radiation, ‘which was thought to have caused too low values in the corresponding points of series a, so these points in series c are accordingly given greater weight in drawing the curve. Other things being equal, those ‘points, for the determination of which the Kerr Kffects in the Infra-red Spectrum. a9 greatest amount of energy was available as shown in the I column in Table I., are the more accurate; hence the probable error increases considerably at the ends, especially at the infra-red end, where both rotating-power and energy Fig. 2 Variation of the Faraday Effect with wave-length; constant field. Y = 18 16 4 le FPOTATION 10 8 GREES ws 6 9 WAVELENGTH Present work. oh ae Moreau’s results. are rapidly decreasing. A check on the general accuracy of the work has been furnished by visual meéacurements with a half-shade polariscope using sodium Hae These gave a rotation of 17°9 as against perhaps 17° taken from the curve, which is a consider ‘ably closer Peomant than might be expected, the discrepancy, indeed, being no greater than the uncertainty in reading a point from the curve. Table IL. is a comparison of the results obt: ained by experi- ment, including those of Moreau, with rotations cale ulated by means of the four principal batenules mentioned above, all 60 Mr. L. R. Ingersoli on the Faraday and results, for the sake of comparison, being brought to the same scale by letting the rotation for the D line equal unity. The figures for the ‘formule of Joubin and Maxwell are taken from a table given by Moreau*. The formula is, as given by this writer, $=0, + +C'> , where m=—2X ae Log C=1:29814 and log C'=2°43254, if X is expressed in terms of hundredth microns. In the formula of Maxwell, sa fn eh Wehr? p nF log k=2°87687, and log k'=4:11114. The figures given by Moreau have been seas Oe which, if the writer's knowledge is correct, is as far as the sae ac index of carbon bisulphide is accurately known, The formula of van Schaik gives almost identical results with this of Maxwell in the infra- red, and hence need not be further mentioned. The formule of Drude without modification are inadequate, for the presence of the carbon-bisulphide absorption-band at A='212 w will be of little effect in the infra-red, and will be entirely insufficient to cause the singular flatness of the curve in the Hog ema utoed of 3°5 wu. However, carbon bisulphide has also a well-marked absorption-band at 8:05 w+, and by adding a term which shall take account of this in the same way that the second term does the ultra-violet band, it is possible to fit the formule more closely to the facts. Accordingly they are written where a=—0°0136: b= +0°1530; -c==—0°2370 C= 045 3 eo 8; and ee eee f Rion take a= O2—r~2ye ee ee where GC 116d: 6 = 025198 ¢ = a tee * Loc. cit. + Angstrém places this band at A=84 yp (Kayser’s ‘Spectroscopie,’ Ba. iii.p. 871), which value would serve the purpose almost as well as the above with a slightly different choice of constants. Kerr lffects in the Infra-red Spectrum. 61 The constants a and b, a’ and 0’, are those given by Drude for the formule as applied to rotatory dispersion in the visible spectrum. candc’ have been determined for wave-length 3y. Their presence has practically no effect on the formule as applied to the visible spectrum, so the validity in that region has not been sacrificed. The values of x beyond A\=2 wu used in calculations with these two formule have been obtained by prolonging the dispersion-curve already known. Unless the ordinary dispersion of carbon bisulphide between 2 wand 4 wis very anomalous, which is unlikely, the values so obtained are more than sufficiently accurate for the purpose. As may be seen, both the formulz of Drude, as modified, fit the case much better than the others. As to distinguishing between them, throughout the greater range of spectr um tested neither hasa decided advantage, although the first may show a slightly better agreement. But beyond rN=8'90 p, where the curve is very flat, and indeed appears to take a slight upward turn, the ‘state of affairs is much better repre- sented by the second formula, which is the one deduced on the supposition of the Hall effect. The points calculated by this formula have been plotted in fig. 2, each being denoted by the apex of an inverted letter V. | AMNieaera Ue Formule of ke we al Wore Prenhin: "Maxwell. ae | eee ite | eee : a ie D89 1:00 1-00 1-00 1-00 1:00 | 1-00 FCC | EUR PE ie OR AVC ea tea 675 | 670 945 302 48 44 35 995) faye 1 O76 272 “44 38 28 271 | 265 1126 | -248 37 35 25 | -245 | 242 1170 | -231 88 82 22 299 | 995 1419 | 158 3 28 TeU, egg) |, “152 1:80 AUIS al) ile OV >. Pe 098 | -095 2:00 “FAS Ha eae Ura ‘OG ‘O81 | ‘O78 2°50 Ue addy ite la ea tar ee ‘O55 O53 3°00 TE SIU PR ae ee ae eek PR O+1 | ‘O41 My 0) OSE tine teex it oreme | On eee 052 | ‘037 4:00 OBA Ricken fh ARs MMR 2 ‘028 ‘03558 WSO, OMa! | es! WM RSKra Pe: 026 O41 62 Mr. L. R. Ingersoll on the Faraday and PAgr aa: THe Kerr EFFECT *. Du Bois + has shown that, for the visible spectrum, the rotation in the Kerr effect in general increases with longer wave-length in the light used. This is notably true in the ease of iron or steel, while cobalt and nickel exhibit weakly defined minima in the green and yellow respectively, and magnetite appears to reach a maximum in the yellow. Inasmuch as this is entirely different from the magnetic dispersion shown by most substances—e. g. carbon mais —and is not satisfactorily accounted for by theory, it is matter of considerable interest to determine whether this anomalous nature persists throughout the whole spectrum, or is merely characteristic of the limited region studied, which includes less than °3 p. This necessitates infra-red measurements, and accordingly, when it was found in connexion with the work on the Faraday effect that rotations of the order of a degree could be measured, the apparatus was modified to suit the case of reflexion, and the effect found to be measurable. The results so far obtained show fairly good agreement among themselves, indicating as great an accuracy as might reason- ably be expected, in view of the difficulties of the problem. Since, however, they are of quite an unexpected character and point to certain rather important conclusions, it would seem most desirable to verify them, with apparatus modified to secure greater sensibility, and with more perfect surfaces, and thus to explain or remove, if possible, inconsistencies which must now detract from their certainty. To re-model the apparatus, however, and to make a more complete study of the problem, including the important case of rotation by co) transmission through thin films of magnetic metals, may require considerable time, so the first stage of the work is here presented, and is not intended to be regarded as final and complete, but rather in the light of a preliminary report. Method. The rotation was produced by reflexion at the surfaces of two small mirrors of the metal to be tested, mounted near the ends of the pole-pieces of the magnet. ‘To double the effect for greater facility of measurement, and at the same * Read in part before meeting of American Physical Society, Chicago, April 1905, + Wied. Ann. xxxix. p. 25 (1890); Phil. Mag. [5] xxix. p. 253 (1890). Kerr Liffects in the Infra-red Spectrum. 63 time to bring the beam out parallel to its original direction, and hence permit the use of the already existing apparatus with the smallest possible change, double reflexion was resorted to, the two magnetic mirrors being held in a small brass frame mounted between the pole-pieces of the magnet. These had an air-gap of about 3 ems., and were slightly shifted out of line to allow the passage of the beam through them as before. To avoid as much as possible the many complications of the problem of both magnetic and optical character, such as elliptical polarization, the incidence was made as nearly normal as possible, or about 8° at each mirror. While this is somewhat larger than that used by du Bois in his work in the visible spectrum, it is well within the limit of 15° for which the effect, as shown by Righi%, is practically the same as for normal incidence. The method of making observations and their reduction was essentially the same as that already described, and the sources of error were also largely identical, although their relative importance was very different. Thus, errors of adjustment, of impurity of spectrum, and the like, the effect of which was previously shown to be a matter of only a few per cent., were not worth considering here in view of the mececcarily large errors of observation, while the question of deformation of apparatus, due to magnetic traction, which was entirely negligible before, became of capital importance, for it was almost impossible to mount the mirrors so that they would not be warped or shilted by the magnet-field. How- ever, since the mirrors possessed no magnetic polarity, this effect, which in general gave rise to an increase or decrease of intensity of the radiation measured, did not change sign on reversing the magnet, and hence readily separated itself from the true Kerr effect. There is a certain amount of elliptical polarization connected with the rotation in the Kerr phenomenon, even for small angles of incidence, and it might be thought that this would give rise to an error, but it can readily be shown that such error would be only of the second order, and since direct visual tests showed the amount of elliptical polarization to be actually very small, its effect was considered entirely negligible. The apparatus was that used for the Faraday tests, with the modifications already mentioned and some minor changes such as the increase of the number of polarizer and analy: ser plates from six to twelve. The substances tested were steel (hardened), cobalt, nickel, magnetite, Heusler’s metal, and silver, in the form of little polished plates each 6 by 16 mms. * Ann. Chim, Phys. [G] ix. p, 182 (1886). 64 Mr. L. R. Ingersoll on the Faraday and and about 8 mms. thick. Silver was included in the tests to indicate if any external cause was acting to produce rotation, and hence give rise to a spurious effect. The matter of polish * was rather troublesome, save in the case of steel; so, to avoid as much as possible any error due to poor surfaces, several different specimens of each metal were generally tested, and those re-polished several times. Results. The results are shown in the curves of figs. 3-6. It has not been thought necessary to give detailed tables of galvanometer-deflexions, but it may be remarked that, by increasing the slit-width and brilliancy of the glower, these Fig. 5.—Variation of Kerr Effect with wave-length. Constant field. Glass-plate polarizing apparatus, 100 Cicrad es ern a eaE UT | fb (>) \ ine) 12) FOTATION (MINUTES) +20 +40 ee Bras 4 WAVELENGTH : were in most cases made large enough to be perfectly definite, amounting for some of the points in the steel curves to as much as 30 cms. for values of 2dI, although in the case of nickel they were rarely more than 4 or 5 cms. It * Just whether surface impurities have any appreciable effect on the dispersion in the Kerr rotation has not been determined. Micheli (Drude’s Ann. i. p.565, 1900) found that surface impurities tend to lessen the “critical angle” as observed for equatorial magnetization, but nu conclusions can be drawn from that to apply to the present case. Kerr Effects in the Infra-red Spectrum. 69 should be stated, however, that, because of unavoidable un- steadiness, points determined by deflexions of less than 10 mms. must be regarded as uncertain, and this applies particularly to those points near the limits of the spectral region covered. In the curves, the rotations given, measured in minutes of arc, are as determined for the two surfaces— unless otherwise specified; and for reversal of the magnet, and hence to be put on the ordinary basis for the measure- ment of the Kerr effect, should be halved so as to obtain the Fig. 4.— Variation of Kerr Effect with wave-leneth. Constant field. Double-refracting polarizing apparatus. _ eee ita Uns a aie ea eee pe ee -80 2 Pia we 3 SS) am 4BaNOans & FOTATION Poe See ip teenie ie eke \~ Ae 3ée WAVELENGTH rotation for a single surface. On the same basis as the results on the Faraday rotation, they are really fourfold, since the rotations in the former case were stated for only a single throw of the magnet. As is customary, the sense of the rotation is taken as negative, being opposite in direction to current in the magnet-coils. To check the results with as lar ge a change as possible in the apparatus, the curves were all repeated “with the olass- plate polarizer and analyser replaced by a double-image prism Phil. Mag. 8. 6. Vol. 11. No. 61. Jan. 1906. i) 66 Mr. L. R. Ingersoll on the Faraday and and nicol. They allowed measurement as far as X=2°4 w in the infra-red, and this was almost as far as dependable results could be obtained with the use of the plates. While certain characteristic differences appear between the curves obtained with the two different polarizing arrangements,—both in the Fig. 5.—Variation of Kerr Effect with wave-length. Constant field. Glass-plate polarizing apparatns. CLASS SCS alle ° FOTATION (HUIMUTES) m chy Oo oO sh, | : a +] 0 te +20 0 \e wy ge a4 WAVELENGTH matter of form, which may be due to errors arising from oblique incidence at the surface of the nicol, and as regards absolute magnitude, which appears somewhat greater when measured with the pile of plates,—the results are on the whole consistent. The curves of fig. 4 and 6 were made with the doubly refracting arrangement. The first striking feature which appeared in the results was the marked diminution of rotation with increase of wave- length, as is shown in the curves, instead of the reverse effect which was to be expected from the results of observations on the visible part of the spectrum. This indicated the existence of maxima which, in the cases of the three magnetic metals, appeared to lie somewhat to the left of 1, but did not prove easy to obtain because dependent on points just beyond the range of the visible and not far enough into the infra-red for accurate measurement, because of lack of energy. However, in several cases the maxima were clearly indicated, while , Kerr Effects in the Infra-red Spectrum. 67 they are especially well brought out in fig. 4, which shows the results of a more detailed study of steel. Although the magnetic and otber conditions were considerably different for the two curves, they still agree very well. Those points for Fig. 6.—Variation of Kerr Effect with wave-leneth. Constant field. Double-refracting polarizing apparatus. (Magnetite curve drawn by comparison with fig. 3.) -70 + | -6C TES) & hon 710M (MING rT) (=) 410 WAVELENGTH which the two sets of readings—which, as previously explained, were always made for each point—agreed most closely, were coo) regarded as having the least probable error and have been weighted accordingly in drawing the curves. They are plotted as circles, and the others as crosses, while the curves to which certain ambiguous points belong are indicated by small arrows. To show that the slope on the short wave- length side agrees with that of du Bois’ dispersion-curve of iron, made for the Kerr effect in the visible spectrum, the latter curve has been plotted to such scale that it joins on to the lower of the given curves at ‘67 yw, the points being represented by triangles. Cobalt gave results similar to stecl and possesses no especial F2 68 Mr. L. R. Ingersoll on the Faraday and interest; but nickel, curiously enough, appeared to reverse the direction of rotation at about 1:4 yu. This, being such an unexpected result, was for a time regarded as spurious, but as repeated trials on three different samples verified it in all cases where the sensibility was high enough, it is now believed to be genuine. The samples tested were (1) nickel plated on polished brass (points plotted as crosses) ; (2) cast-nickel of supposedly exceptional purity from a magnetic standpoint, although still containing a trace of iron (plotted as circles) ; and (3) commercial rolled nickel (plotted as triangles). As may be seen, there is considerable discrepancy between the various nickel curves. Thus, in fig. 3, this curve, which was made with a rolled-nickel specimen, is unlike its counterparts in the other two sets, while the different curves of fig. 5 seem to show considerable separation after crossing the axis. Whether these differences are real and characteristic of the different specimens tested, or whether they are spurious, can- not yet be stated. Although the measurements on nickel were attended with more difficulty than in most of the other cases, and the probable error of any point is therefore large, it can hardly account for the consistent differences which appear between the curves. In view of this disagreement it is rather odd that all the curves should cross the axis at nearly the same point, as they seem to at about 14 w. Magnetite proved very difficult to test, and the different curves show poor agreement. Because of its low reflecting- power only a single surface could be advantageously used, the place of the other being taken by silver; so the results in the curves of figs. 5 and 6 are for this single surface only, although they have been doubled in fig. 3, partly to put them on the same basis as the others for comparison’s sake, and partly to avoid confusion. The most noticeable feature of the curve for this substance is that, for a good share of the infra- red at any rate, the rotation is in the same sense as for steel, although the positive part of the curve, which would agree with the positive results found in the visibie spectrum by du Bois, is well indicated. The second reversal, as found in fig. 3, could not be verified in later observations. The points on the silver curves were determined with the use of two surfaces of silver plated on brass, and in this way the zero from which the other rotations are to be reckoned was obtained. The curve shows the characteristic Faraday dispersion form, and in the proper, that is positive, sense. It is doubtless due to the effect of the weak field in the neigh- bourhood of the analyser and polarizer, for its magnitude eould be altered and even made to disappear, as is seen in Kerr Effects in the Infra-red Spectrum. 69 figs. 5 and 6, by a proper arrangement of the exciting coils of the magnet. In the latter two sets of curves the pole- coils only were excited, while in the set of fig. 3 one field-coil was added. It was also largely dependent on whether the pile of plates or doubly-refracting substance was used as polarizing agent. The points in the set of fig. 3 have all been corrected by the use of the silver curve, although this has not seemed necessary in the last two sets. Unfortunately no silver correetion-curve was made for the steel curves of fig. 4, its importance not being realized at the time; hence there is some doubt as to whether they correctly represent the position and shape of the maximum, although it 1s pro- bable that the correction in this case would be small, from the fact that a single determination at A=1°34 with the steel covered with silvered glass surfaces gave no effect. The silver points have been plotted by somewhat smaller, and the magnetite by larger, circles than the others, to avoid confusion. Asa further check on the accuracy of the results, some direct visual observations were attempted. The method was rather crude, for the use of a half-shade apparatus and monochromatic light failed to give sufficient illumination with the existing arrangement of apparatus; but it was found that fairly good settings for extinction could be made on the polarized image of the glower itself, and the rotations so determined have been plotted in fig. 6 by the letter V. This use of white light would of course give the integral of the effect for the whole visible spectrum; but the range, save in the case of steel, is small, and in any case it is assumed to correspond to the rotation for some wave-length near the maximum of visibility, or, nearly enough, for sodium light. The agreement with more careful measurements by other observers 1s good, considering the necessary uncertainty of field-strength in the present case, for while measurements with a test flip-coil indicated about 10,000 c.a.s. units, it would vary considerably over the surface of the specimen, which had to have an appreciable area to meet the other requirements of the problem. These points in the visible spectrum have been conveniently used to connect the du Bois rotatory dispersion-curves with those of fig. 6, the former results being plotted to such a scale that the rotation for the sodium line shall be the same as in the present case. ‘The curves join together fairly well, save in the case of magnetite, where, the visible spectrum measurements being indecisive, the scale is arbitrarily chosen. Rather curiously, Heusler’s metal gave entirely negative 70 Mr. L. R. Ingersoll on the Faraday and results, both in visual and infra-red observations, and while the existing arrangement could not be considered as very suitable for the detection of minute rotations, still it may be stated with reasonable certainty that the effect, if it exists at all, is less than a tenth of the rotation for steel. Interpretation of Results. | As to the physical interpretation of the curves, not as certain conclusions can be drawn now as, it is hoped, may be possible after the work has been extended as already men- tioned, bat certain points may be considered. The most evident feature is the striking similarity between the com- pleted curves as given in fig. 6 and a typical dispersion-curve running through an absorption-band. Now the general theory of magnetic rotation calls for an anomalous character of the rotatory dispersion-curve in the neighbourhood of an absorption-band, very similar in fact to the case of ordinary dispersion, and indeed intimately connected with it in theory. Whether the curve should have oppositely directed branches on the two sides of the band, or not, depends on whether the hypothesis of molecular currents, or of the Hall effect, be admitted in forming the equations. (See Drude’s ‘ Opties.’) The latter condition is now well known to occur in the case of sodium vapour, while curves of the former type have been obtained by Schmauss*, and quite recently by Wood t, who worked with a saturated solution of praseodymium chloride. In view of this, the most natural conclusion to be drawn from the curves above given is that the magnetic metals present a case of anomalous rotatory dispersion similar to that found in certain absorbing solutions, with the difference that the region of resonance-absorption, if such it be, instead of being very limited in extent, covers nearly the whole visible spectrum as well asa small part of the infra-red ; in the case of steel it may even extend into the ultra-violet. This might be con- strued as evidence pointing to the existence of free resonance periods in metals, although the definite vibration time charac- teristic of common cases of resonance would seem to be lacking. This general view is somewhat strengthened by the fact that the magnetic metals show an increase of refractive index, as well as of magnetic rotation, towards the red, in the visible spectrum; and while the dispersion-curves as given by du Bois and Rubens{ show a regular rise without maxima * Ann. der Phys. ii. p. 281 (1900), and also several later papers in this publication. + Phil. Mag. May 1905. t Wied. .4an. xli, p. 522 (1890). Kerr Effects in the Infra-red Spectrum. 71 or minima as in the present case, it is not unlikely that, could they be extended on each side of the visible spectrum, more of a resemblance to the rot: tery dispersion-curves would appear. The preceding explanation canes to interpret the magnetic rotation of the Kerr effect as a characteristic property of the metal itself, having the same physical significance as the simpler case of magnetic rotation jn transparent substances. Another point of view may be obtained following the sugges- tion made by Voigt * some years ago, and later dev eloped by du Bois ft. The observations of Kundt iapamo mater |-ot Lobach §, on rotation by transmission throagh thin films of magnetic metal in a magnetic field, have suggested the explanation of the Kerr effect as a special case of rotation by transmission, with reflexion below the surface of the metal. This is the now commonly accepted explanation, but it does not account for the fact that the rotations in the two cases are opposite in sign; and to explain this Voigt and du Bois suggest that one “of the circularly-polarized com- ponents may in general penetrate deeper into the metal than the other, and hence introduce a difference of phase which may give any sort of a rotation positive or. negative. A point in favour of this argument is the peculiar reversal effect which was found in nickel, and which may most easily be explained on this basis, although as regards the negative rotation, it is of interest to note that the Hall effect in nickel is Opposite in sense to what it is in iron and cobalt; and on the basis of the Hall effect as an explanation of the Kerr phenomenon, nickel should show a negative rotation. But even if this view of Voigt and du Bois on the nature of the Kerr effect be accepted, it dues not necessarily mean that the rotation dispersion-curves, as found, are without physical significance, but merely that certain effects which have been attributed to the property of magnetic rotation would then be considered as caused by this, which might be called the differential reflecting-power of the metal, which causes the reflexion of the two circularly polarized com- ponents at different meandepths. For it is not unreasonable to suppose that this, if it exists at all, is just as characteristic a property of the metal, and as intimately related to other gptical properties, as the power of magnetic rotation by transmission itself. The negative results given by Heusler’s metal are quite remarkable, for, to the best of the writer’s knowledge, this is the only case in which this peculiar metal has failed to * Wied. Ann. xxiii. p. 493 (1884). + Ibid, xxxix, p. 25 (1890). { Ibid. xxiii. p. 236 (1884). § Ibid, xxxix. p. 347 (1890). 72 Faraday and Kerr Effects in the Infra-red Spectrum. exhibit its magnetic properties. If more careful tests on it, as well as on the non-magnetic alloys of nickel, can show that the Kerr effect is — entirely dependent on magnetic properties, a considerable advance will be made towards the explanation of the phenomena. Summar OE 1. The electromagnetic rotatory dispersion of carbon bisulphide has been “measured by infra-red methods over a range of spectrum extending from the sodium lines to a: 3, and found to be correctly represented by a formula which takes account of the absorption-band beyond 8 yp, E Gains that an infra-red alsoupH ON, band may affect the rotatory dispersion, much as it does ordinar y dispersion, over a considerable range of spectrum. 2. The magnetic metals and magnetite show, after wave- length 1 w in the infra-red, a decrease of the Kerr rotation, with increase of wave-length. The complete rotatory disper- slon-curves, made by supplementing the results for the infra- red by existing observations for the visible spectrum, show a ee resemblance to a typical dispersion-curve in the region of an absorption-band, indicating the existence in metals of something analogous to a region of resonance- absorption, extending over the visible spectrum. 3. The particular cases of nickel and magnetite are notable, for the rotation appears to vanish for a particular waye- length in each case, and then change in sign. The Kerr rotation for the magnetic alloy, Heusler’s metal, if it exists at all, is less than one tenth of that for iron or steel, although the magnetic properties of the metal are quite comparable. 4, Although the results do not allow of definite conclusions as to whether the hypothesis of molecular currents, or of the Hall effect, should be accepted in explaining magnetic rota- tion, the indications are that the latter theory holds for carbon bisulphide—z. e. it presents a case analogous to that of sodium vapour ; while the curves of the magnetic metals require the former explanation, although the reversal of nickel might perhaps be considered as evidence for the Hall effect. In conclusion, I wish to express my sincere thanks to Prof. B. W. Snow for his kindness in furnishing apparatus and supplies; to Prof. A. Trowbridge for assistance in pro- curing certain specimens of metals ; and especially to Prof. C. I. Mendenhall, at whose suggestion the work was under- taken, and whose ‘aalvice throughout its progress has been of the greatest service. Physical Laboratory, University of Wisconsin. July, 1905. IV. A Modified Form of Apparatus for the Determination of the Dnelectric Constants of Non-Conducting Liquids. By Wee Vince FS." XV ITHIN recent years the determination of the dielectric constants of liquids has attracted considerable atten- tion, partly on account of the simplification of the methods, and partly with a view of ascertaining the validity of the Maxwell equation (2 — 1M /(u? +2)d=(K-1) M[(K42)4,. . (1) or that of Clausius and Mosotti Sezai ee SA ee (2) As regards the latter point the determinations have led to no satisfactory conclusion ; but as regards the former, the application ot the bridge method, the substitution of the telephone for the galvanometer or electrometer, of liquid resistances (Nernstt) for many yards of wire (Paluzt) or Fics I, Ot high-resistance coils, have all served to simplify and render more accurate determinations based upon the conditions of balance according to the principle represented by the diagram (ae. 1) * Communicated by the Author. + Zevts. f. phys. Chem. xiv. p. 622 (1894), { Jowrn. de Phys. |2| v. p. 270 (1885). 74 Mr. Veley on an Apparatus for Determination Herein, if C and C’ are two condensers, R and R’ two capacity free resistances, then a balance is attained when R:B=¢:- cc... ae The general method of working has been to keep one resistance and one capacity constant, and to vary the other resistance concomitantly with the other capacity so as to restore the balance. ‘The method to be described differs only from the above in keeping both resistances constant, and varying one capacity concomitantly with the other, as also to measure the capacities in terms of a length according to the principle that ceterzs paribus the capacity of a condenser varies inversely with the distance between the metallic plates, provided that such distance is small relatively to the area of the plates. Before passing on to a description of the apparatus, it seems desirable to discuss the method worked out by Nernst (cf. supra) and certain of his pupils in Germany, and in this country by Sir James Dewar and Prof. Fleming*. The disad- vantage of this method appears to consist in the fact that the dielectric constant is determined indirectly, since an air-con- denser is not balanced simultaneously against a condenser containing the liquid under investigation; on the other hand, its advantages are (1) the substitution of a small induction-coil instead of a rapidly alternating commutator, and (2) the substitution of liquid resistances instead of bobbins. As regards the latter improvement, I might mention that for some of my earlier experiments Herr Wolff of Berlin wound for me two 10,000 (international) ohm coils of man- ganin according to Chaperon’s method; these coils were placed in the same box and provided with connecting screws so that either one coil could be placed in each of the two arms of the bridge, or both coils could be put into the same arm. But these coils were discarded as self-induction was not avoided, and consequently it was impossible to determine the point of minimum sound of the telephone owing to the consequent and irritating after-tone. However, by using liquid resistances the above difficulty was overcome. My apparatus, as stated above, consisted of two condensers, two liquid resistances, telephone, and induc- tion-coil with actuating battery ; the only point of novelty consists of the first named, while of the remainder various forms were tried with a view of obtaining more satisfactory results. * Proc. Roy. Soc. lx. p. 250 (1898). of Inelectric Constants of Non-conducting Liquids. rs) Description of Condensers. These were constructed for me by Mr. Pye of Cambridge, according to the specifications of the Rev. F. Jervis-Smith, F.R.S., who kindly assisted me in working out the principle of measuring capacities and hence dielectric constants in terms of lengths. Hach condenser consisted essentially of a gilt nickel dish 46 mms. deep (A in sketch) and 70 mms. internal diameter, provided with a binding-screw 8; within each there was a moveable gilt disk B about 58 mms. diameter (actually 29°62 mms. for one, and 57°87 mms. for the other) and 5 mms. thick, provided with a vertical metal spindle 56 mms. long, C, at the end of which was a binding-screw S’ and a metallic T-piece, in the hollow of the horizontil arm of which a glass Fig, 2. rod D was cemented in. This form of condenser is so far similar to that described by Cohn and Arons*, except that the position of the disk is variable, and the capacity of the condenser thereby alterable. The following device was adopted for moving the disk vertically up and down, as also for ensuring that its lower surface remained strictly parallel with the upper surface of Wied: Ann exviily 9. 461 (1886), 76 Mr. Veley on an Apparatus for Determination the bottom of the dish. The above mentioned glass rod passed through a metal collar in which it could be rigidly fixed by a screw; the collar was connected with a sliding piece working upon two upright struts, F, F’, one smooth and the other provided with V-groove ; at the upper end of the sliding piece was fixed a micrometer-screw, the head of which, divided into 50, revolved once for each *5 millimetre on a vertical scale, so that ‘01 mm. could be read directly and less than half that amount by estimation ; the vertical play of the screw amounted to 31 mms. The glass rod could be fixed rigidly in any desired position by a clamping screw. The vertical struts were fixed upon a white marble slab by three levelling-screws (two G, G’ shown) arranged in a triangle; at the other end of the slab was placed the gilt nickel dish kept in position by three ebonite knobs (two H, H’ shown) let into the slab. The corrections for the zero point and the graduation errors of the vertical scale were determined by taking away the dish, placing the apparatus in a horizontal position, and measuring the displacement of the edge of the rim of the disk by a Hilger travelling microscope. A table of correc- tions for each condenser was drawn out once for all. One of these condensers was throughout kept as an air- condenser, while the other was used to contain the liquid dielectric; during working, each condenser was closed with an ebonite plate cut into half and with a small semicircular piece cut out of each half for the spindle to pass through ; these plates served to exclude dust. The two dishes were regarded as the outer, and the two disks with their spindles as the inner plates of a pair of diagrammatic condensers. The major portion of the capacity* of such a condenser (or leyden) is made up of three terms: (a) that due to the area of the lower surface of the disk and the corresponding area of the dish, (5) that due to the area of rim of the disk and likewise, (c) that due to the area of spindle and likewise. Of these, (a) varies with the distance and nature of dielectric, (6) is constant according to the method of working adopted, (c) varies according to the length of spindle immersed within the dish. In actual working, the alteration of capacity due to (c) varied about 1 per cent. on anaverage; as the maximum * The total capacity of such a condenser is a very complex matter, and could only be solved by the method of conjugate functions as dis- cussed by Clerk Maxwell, ‘ Electricity and Magnetism,’ Articles 195 e¢ seg., and J. J. Thomson, ‘ Recent Researches in Electricity and Mag- netism,’ pp. 208-250 (Clarendon Press, 1893), of Dielectrie Constants of Non-conducting Liquids. 77 variations in readings amounted to 1 per cent., the correction to be applied would be of the second order. Liquid Resistances. In earlier experiments these consisted of electrolytic cells of the H-bottle shape (Kohlrausch type) filled with redistilled water; the electrodes were platinized in the usual way. One cell was put into each of the two arms of the bridge, the two cells being immersed side by side in a beaker of cold water to eliminate effects of temperature. The resistance introduced into each arm was approximately 9000 ohms, which was found sufficient-for air or liquids of low dielectric constant. In later experiments, liquid resistance-tubes of the Nernst type were used, filled with Manganini’s (mannite- boracic acid) solution ; these were found to be more suitable for liquids of relatively higher dielectric constant. Inductoria. Two forms of inductorium were used, namely, that of Ostwald-Luther and the wire form (Saiten-unterbrecher). My experience was to the effect that the latter gave the sharper note, and consequently a more distinct minimum in the telephone, but was more liable to break down in the course of work, but this might be due to some slight mechanical defect in the particular instrument. My observations were in complete accordance with those of Nernst*, that a more decided minimum is produced in the telephone when the inductorium gives a buzzing, rather than a humming or singing sound. The inductoria were actuated by a smal] chromic-acid battery or accumulator. Telephone. The form of telephone used was that of Mix and Genest (resistance about 130 ohms) with an insulating handie ; it was found preferable to hang up the telephone on a glass rod ; when the wire inductorium was used, the note of the telephone, except at or about the minimum point, could be heard some feet away, so that the initial adjustments of the micrometer-screws could be made with comfort and con- venience. The whole apparatus (namely, liquid resistances, condensers, connecting wires) was disposed symmetrically as far as possible, and each of the two former pairs was placed together. * Nernst (doc. cit. supra) writes: “Ich habe oft beobachtet dass das Minimum leidet, wenn die Saite summt oder singt, anstatt rasselt ; ich vermag dies nicht sicher zu erkliren.” 78 Mr. Veley on an Apparatus for Determination Method of Working. Virstly, an observation was made with both condensers with air as dielectric, the disk of one (on the right hand, called R) being clamped in a fixed position, and the distance of the disk of the other (on the left hand, called L) from the upper surface of the dish being varied by the micrometer- screw, until the minimum sound in the telephone was attained. Secondly, the liquid to be experimented with was then introduced into the R condenser by means of a pipette (the dish being slightly tilted to avoid the inclusion of air-bubbles) to the point at which the surface of liquid was level with the bottom of the rim of the disk, when the dish was replaced in a vertical position. Superfluous liquid accidentally intro- duced was removed by the pipette or blotting-paper. The distance of the disk from the dish in the L condenser was varied by the micrometer-screw until the minimum sound was again attained. The ratio of the distance of the disk in the second observation to that in the first is the ratio of the dielectric constant of the liquid to that of air (=1). Hence, therefore, as explained above, the(dielectric constants can be determined in terms of a length, measured by one micrometer-screw. Two sets of observations of the first operation are quoted to show the degree of accuracy :— First Set. L (Air) condenser. R (Air) condenser fixed at Scale Readings. _7615 mm. on scale. 8650 8°645 8°645 3°710 8681 The mean value of the readings of the L condenser is 8°666 +0086. Second Set. L (Air) condenser. R (Air) condenser fixed at Scale Readings. 12°:595 mms. 14:05 uel 14°13 ee: 14°12 Eas) 14°12 Mean 14°12 of Dielectric Constants of Non-conducting Liquids. 79 It will be seen from the above that the results are approxi- mately within an error of 1 per cent. The dielectric constants of certain organic liquids were determined to test the accuracy of the method. Benzene. The sample (thiophene free) was purchased of Kahlbaum, and subsequently purified by freezing and distilling over sodium ; the foliowing results were cbtained :— Temperature 17°. L (Air). R (Air) condenser fixed at 77680 mms. 7°615 mms. L (readings). Benzene introduced. 3°3 3°4 Mean 3°384 : mre Coxe - Dielectric constant K= 3334 = ate Nernst * gives 2°258 for carefully dried benzene, Thwing + 2310 as a mean of nine observers ; the value given above is approximately the mean of these two values. Another set of observations, probably less accurate, was made in the reverse manner, namely, by varying the benzene condenser and keeping the air-condenser constant ; the mean value of nine concordant observations gave K=2:267, which differs from the above approximately in the ratio 1/600. Carbon Tetrachloride. Purchased of Kahlbaum, purified by fractional distillation, the portion coming over between 76°59 and 76°99 being col- lected. Mean boiling-point 76°79 at Bar. 750°4 (corr.). Density 4/4=1°62611 (corr. to vacuum). Thorpe{ gives the values for B.P.=76°°76 at 755:4, and D. 0/4=1-63195. Young § for B.P.=76°'75 at 750°1. These several values are concordant. * Loe. cit. supra, p. 608. } Zerts. Ff. physikal. Chem. xiv. p. 800 (1894). en Trans. 1894 (A), p. 494, and Journ. Chem. Soc. 1880, Trans. . Od. § Journ. Chem. Soc. 1891, Trans. p. 912. 80 Dielectric Constants of Non-conducting Liquids. The following values for K were obtained in three sets of observations (temp.=12°5) :— Set (1) of 5 observations ...... Mean=2:071 See Qort 2 = 8027 Set (3) of 5 53 ene » =20e9 Total Mean = 2-049 Drude* gives the value K=2718 at 17°; Turner+, K=2°20 at 14°; but neither of these observers purified their samples or give physical data as criteria of purity. Ethylene Chloride. Purchased of Kahlbaum, portion on distillation at boiling- point 83°°71+°15 at Bar. 757:1 (corr.) collected; D. 4/4= 127536 (corr). Thorpet gives the values B.P.=83°°5 at Bar. 753-9 and D. 4/4=1:27432 (corr.) One set of five observations gave the value of K=11°29 at 17°. Turnerf gives K=10°98, but no details of purification or physical data. Monochlorobenzene. Purchased of Kahlbaum, portion on distillation at boiling- point 131°°55 + :2 at Bar. 736-97 collected ; D. 4/4 =1-12355. Ramsay and Young§ give the value B.P.=132° at Bar. 798°8, Young || D. 0/O=1°12786. One set of seven observations gave the value of K=10°95 at 10°°8 ; a previous observation for this substance does not appear to have been recorded. The necessity for purifying halogen organic compounds before determining their dielectric constants appears to have been overlooked ; most of such compounds decompose slowly, though slightly, in the presence of sunlight with liberation of traces of the halogen acid, which would impart a conduc- tivity to the liquid, and thereby render useless determinations of the dielectric constant, except possibly by the method of Nernst. Thus, to select an example, the constant for chloro- form has been determined by three observers, none of whom * Zerts. f. physikal. Chem. xxiii. p. 809 (1897). + Ibid, xxxv. p. 428 (1909). { Journ. Chem. Soc. 1880, Trans. p. 182. § Lbid. 1885, Trans. p. 604. || Zbed. 1889, Trans. p. 488. The Theory of Phasemeters. 81 purified the sample used, and one definitely states that he used a “ commercial preparation”’; this would, without doubt, contain both moisture and hydrochloric acid, namely, a con- centrated solution of the latter, the amount of which would increase with time and other conditions. Personally I experienced such difficulty in purifying a sample of ethylene dibromide (though of correct melting- and boiling-point) so as to be fit for a determination of the dielectric constant, that the attempt was for a time abandoned. Turner* gives a value 4°865 for this substance, but makes no allusion to such difficulty. It is hoped to proceed with further determinations with this form of apparatus and method of working; meanwhile it is thought that they possess sufficient novelty and give sufficiently accurate results to merit description. V. The Theory of Phasemeters. By W. KH. Sumpner, D.Sc. | eee are instruments of the dynamometer type for indicating the phase relations of the currents and potentials in alternating-current circuits. With few exceptions they are made for use on multiphase circuits. Single phase instruments have been constructed, but they are not very satisfactory, as their calibration alters with both frequency and wave-form. Such instruments consist essentially of two sets of coils, of which one set is fixed and the other forms a single moving system which is not provided with any form of control. The currents in one set of coils are determined by the voltages of the main circuits; while those in the other set are pro- duced by the circuit currents. The total number of coils used in the two systems must be at least three, and as a rule actual instruments only contain this minimum number of coils: the fixed system usually consists of a single coil conveying one of the line currents, while the moving system consists of two independent but relatively fixed coils, traversed by currents produced, through suitable non-inductive re- sistances, by two of the voltages of the multiphase circuit. There is one instrument made commercially for three-phase circuits which is of a more elaborate construction, and contains three fixed coils for the currents, and a moving system—also of three coils—for the voltages. Such an * Loc. cit. supra. + Communicated by the Physical Society: read October 27, 1905, Phil. Mag. 8. 6. Vol. 11. No. 61. Jan. 1906. G 82 Dr. W. E. Sumpner on the instrument is more complicated to make and to connect to the circuit, but it possesses certain advantages as will be shown later. With rare exceptions the magnetic circuits of phasemeters are air circuits, containing no iron, so that the magnetic fields associated with them are weak, and the instruments in consequence are of somewhat delicate con- struction. There, however, appears to be no reason why the use of iron should be avoided in these instruments, and in what follows the writer proposes to show, that the theory of these instruments is the same whether they contain iron or not, and however the coils may be arranged ; that they can be calibrated by direct current methods although for use on alternating current circuits; and that a new type of instru- ment, containing iron, conforms to the theory given. An investigation will also be made of their action when the circuit currents are of unequal magnitude. The study of these instruments really resolves itself into an examination of the behaviour of multiple magnetic circuits when actuated by independent currents. Theory of Four-Circuit Phasemeters. We shall first consider the case of a three-phase instrument having three fixed coils for the circuit currents, and one movable coil, in series with a non-inductive resistance, traversed by a current produced by one of the eienit voltages. In all cases, it will be assumed (i.) that the indeetee density at any point due to the current A in a fixed coil is represented by AF’, where A is the instantaneous value of the current A, and F isa quantity dependent merely on the coil and the position of the point considered ; and (i1.) that the principle of superposition holds, viz. : B= A, + A,F, + A:Fs, where A,, A,, A; are the currents in the three fixed coils and the quantities Ff are functions of the position of the point corresponding to these fixed coils. The addition must be made vectorially if the subsidiary fluxes are differently directed. There is of course no doubt about either of these assump- tions if the magnetic circuits associated with the fixed coils pass wholly through non-magnetic and non-conducting media such as air. When the path of the lines of force lies partly through (suitably laminated) iron it is necessary, however, to consider the effects of varying permeability and hysteresis. But any magnetic circuit with which the moving coil is Theory of Phasemeters. 83 concerned must necessarily contain an air-gap to permit the movement of this coil, and for all dimensions suitable for instruments this air-gap must be such that the reluctance of the iron path is negligibly small compared with that of the gap. The flux densities in the iron under these circum- stances can only reach moderate values for which the per- meability is fairly constant, while even a considerable change in the permeability will not appreciably affect the magnetic reluctance of the circuit. Similar considerations show that hysteresis cannot produce any sensible effect in magnetic circuits the reluctance of which is almost entirely that of an air path. 7 We may therefore assume that, however unsymmetrical the windings of the three fixed coils may be, the induction density B at any point on the conductors * of the moving coil for any deflexion 2 foliows the law B — A,F, -+ AF, + A3F,, ° ° ° e (1) where F,, F., F; are three quantities dependent only on x and quite independent of time, while A,, A,, and A; are the instantaneous values of the currents in the three coils. If the current in the moving coil is denoted by V, the product BV represents the momentary vaiue of the force per unit length acting on the portion of the coil considered. It will also be seen that we can regard the quantities F as line averages for the whole moving coil (for the deflexion x) and that the turning moment acting on the latter may be written (BV A+ hy A eae, 05 ps a) where, if the currents are constant AV denotes the product of the corresponding quantities after taking account of their sign, while if the currents are periodic the expression repre- sents the average value of such product. Now as the moving coil is not provided with control, if the above quantity is not equal to zero the coil will turn until this is the case. Such a position must exist, since if the coil be turned through i80 degrees in either direction, the torque acting on the coil will be reversed in sign, and thus, as the coil turns, must pass through a zero value in either case. One of these corresponds with a stable, and the other with an unstable, position of equilibrium. ff the second member of (2) be equated to zero, we get an equation for the deflexion 2, the solution of which must be independent of the absolute, though not of the relative, * Strictly speaking B is the component of the flux density perpen- dicular to both the conductor and the direction of motion. 84 Dr. W. E. Sumpner on the magnitudes of the currents A, and which must also be unaffected by the magnitude of V. For alternating currents the position of balance can only depend on the phase dif- ferences of the currents A with regard to the voltage V, and on the relative magnitudes of these load currents. For direct currents the equilibrium value of x can only depend on the ratios between A,, Ay, and As. Now in the theory of phasemeters as hitherto given, the following assumptions are made :— (1) That the currents and voltages vary with time accord- ing to the sine law. (ii) That the functions F are of equal magnitude and vary with the defiexion x according to the sine law. (iii) That the load currents are balanced between the phases, that is to say, the magnitudes of the currents Ay, A,, and Az; are equal. It is well known that assumptions (i) and (i) are only true in praciice under most exceptional circumstances, while assumption (ii) is only true when the moving coil is of very small dimensions compared with those of the fixed coils and is placed at their common centre. This cannot be the case in an actual instrument. in what follows, we shall not find it necessary to make any of these assumptions, but we shall confine ourselves at present to the case of balanced loads for which the magnitudes of A,, Aj, and A; are equal. By the magnitude A, of any cyclic function A, of a variable ¢ and of period P, we understand that quantity whose square is equal to . A? = p( Ata. P Yo It follows from the foregoing that with balanced loads the condition of equilibrium at the deflexion 2 is F,A,\V+F,A4,V+F,A;V=0,. . . - (8) and is such that the coefficients of F,, F,, F3; are proportional to quantities which merely depend on the phase differences between the currents and the voltage V, and also that if we pass steady currents through all the coils and adjust those through the fixed coils till they are proportional respectively to A,V, A.V, A;V, we shall get the same deflexion « A given deflexion thus always corresponds with a particular power factor of the load ; and in order to calibrate the instru- ment by means of direct-current tests, it remains to show how to calculate the power factor from the ratios of the direct currents used in order to produce the corresponding deflexion of the instrument. Theory of Phasemeters. 8) Now however the instrument may be calibrated, its readings will only be correct when its coils are all connected to the circuit in the particular manner corresponding with the calibration. We must thus adopt for each fixed coil one direction as positive, and, if we distinguish the ends of the coil as positive and negative respectively, we shall under- stand by a positive current through the coil a current flowing from its positive to its negative end. Moreover, if we consider a current in the mains as positive when flowing in a particular direction along the mains, we have the following equation true at every instant, whatever the law of variation of the alternating currents may be: ieee ea On Poms at a (A) From this it follows that the mean products forming the coefficients in equation (3) must be connected by the relation BO Ae On et) aa yey etal 1/(3) That is to say, in the calibration by means of direct currents we must use three steady currents through the fixed coils such that their algebraic sum is always zero. This can easily be arranged by connecting together all the negative ends of the coils, and afterwards putting two of the coils in parallel through variable resistances, and in series with the third. The two selected for parallel connexion may of course be varied if necessary to calibrate the instrument throughout the scale. But there is another consequence of (4) the truth of which is also quite independent of any assumption in regard to the variation of the currents with time. Hquation (4) can be regarded as a vector equation such that if three vectors are drawn forming a triangle the sides of which are respectively proportional to the magnitudes of the three currents, the angles of this triangle will perfectly represent the phase relations of these three currents. It is also possible to find another vector representing the voltage V in both magnitude and phase so that the mean product of any two of the quan- tities considered is accurately equal to the scalar product of the corresponding vectors *. In all ordinary cases the vector V can be regarded as in the same plane as the current vectors, even if the currents vary in a manner widely de- parting from the sine law; but, in any case, if V, is the perpendicular projection of the vector V on the plane of * See “The Vector Properties of Alternating Currents and other Periodic Quantities,” Proceedings Royal Society, 1897, vol. Ixi. p. 455. 86 Dr. W. E. Sumpner on the the current vectors, we have from elementary vector con- siderations the following relations between scalar products: VA,=V,Ay VA, =VpA, VA; =VpAs. We also have cos d =cos a COS dp, where ¢ is the phase-angle between V and any current A, yp is the phase-angle between V, and the same current A, and a is the angle between the vectors V and Vy. Hence, it will be apparent that in any such equation as (3) or (5) we can regard the vectors V and V, as interchangeable, and also that if we may neglect the square of the small angle a, we can regard cos ¢ and cos ¢, as identical. Now the vector figure will be as represented in fig. 1. In the case considered the load currents are equal, hence the vectors A will be of equal magnitude, and it follows that any two will differ in phase by 120°. If therefore ¢ is the angle between the vectors V and A,, and if we denote by Fig. 1. A g 3 A neaee ba V and A the magnitudes of the voltage and current vectors, we have V,4,=VA cos ¢, VA, =VA cos (120+¢)=—VA cos (60—4), VA; =VA cos (240+¢) =-- VA cos (60+¢). Substituting in (3) we have for balance the condition : I’, cos $= F, cos (60—¢) + F;3 cos (60+). . . (6) If now in the direct-current test we make the steady currents such that —A,=A,+ As, and A, __ cos (60—¢) _ 1+3?tang 7 A; — cos(60+ 6) 1—3?tand’ °° * (7) Theory of Phasemeters. 87 the position of balance will be the same as in the correspond- ing alternating current test, when the phase ef the current through the moving coil differs from that of the current A, by ¢. From (7) we have 1 A,—As tan $= 3 Gite OM) Nic (8) from which & and cos¢ can be found. If cos ¢ so found is to represent the power-factor of the alternate current load, all that is necessary is to select for the voltage V that between the main conductor carrying the current x and the neutral point of the system, and to apply it through a non-inductive resistance to the moving coil. If, however, instead of this resistance a condenser be used, the voltage selected should be that between the lines carrying A, and A, since the effect of the condenser will be to cause the moving coil current to be in quadrature with the voltage producing it. The shape of the curve connecting the deflexion « with ¢ or cos @ will depend on the nature of the functions F in (6), and these are deter- mined by the structure of the instrument. With actual phasemeters the coils are arranged with the object of making the quantities F of equal magnitude, and as nearly as possible sinuous functions of the deflexion w; and the angle between the planes of any two coils is made equal to the angle representing the phase difference of the currents passing through the coils. Such assumptions are equivalent to putting : Fi=fsnz2; EF,=fsin(#—120); F;=/fsin (¢ +120); and if we substitute these expressions In (6) and reduce, we easily find sin (6 +x) =0, or the deflexion x in degrees is equal to ¢ when measured from an appropriate zero. But the accuracy of the instrument as a phasemeter in no way depends upon the fulfilment of these conditions of construction. The introduction of iron into the magnetic circuits, and the use of unsymmetrical winding in the coils, will affect the shape of the curve connecting w and ¢, but will not prevent « from being an accurate indication of ¢. Nor is it even desirable that x should be proportional to ¢. It would be much more useful to arrange to make «& fairly proportional to cos¢. Phasemeters are wanted to measure not $, but cos ¢, or the power-factor, and this for load currents which in practice are always lag ging. By making w proportional to @ the scale-readings for different power- factors are widely separated where least wanted, that is 88 Dr. W. E. Sumpner on the between power-factors 0°9 and 1:0, and are close together for the values most wanted, for power-factors between 0°6 and 0.8, the values of @ for which only differ by 16 degrees. The result is to produce an instrument having a scale the greater portion of which is hardly ever used, while the portion which is most used is small, and the readings un- desirably crowded. Assuming bilateral symmetry in the moving coils, a change in z of 180 degrees must necessarily correspond with a reversal of the currents, or with a change in @ of 180 degrees, but there is no need for the range of z for leading currents to be as great as that for lagging currents, and it is advantageous to get a large range of « for the values of cos @ most needed. Tests on Phasemeters having [ron Cores. The foregoing theory has been fully tested by the writer in reference to three new instruments each provided with Fig. 2. P ; Tal A ie my ! 2 > ; I O Go A\3 ; X Al of e A; Yo S; gh OF S fa\ “ A fe) 8 = 6 2 AL iron-cored magnetic circuits. The structure of one of these is sufficiently indicated in fig. 2. The iron parts are built up of thin circular stampings arranged in two fixed cylindrical coaxial blocks 8) and 8; The outer ones So are provided with twelve slots on their inner periphery arranged sym- metrically at angular intervals of 30°. In each pair of diametrically opposite slots a coil of 8 turns is wound, and adjoining coils are series connected in pairs to form the three fixed coils A,, A,, Az. When positive currents are sent through the coils the currents flow downwards through the slots 1, 2, 5, 6, 9,and 10, and upwards through the remaining slots. This is indicated in the figure by the use of full signs and corresponding outline signs. The moving coil is rect- angular in shape and turns with its sides in the circular air-gap about the common axis of the system. To this Theory of Phasemeters. 89 moving coil a pointer P is attached, which reads on a fixed scale of degrees. For any given values of the currents in the fixed coils, the space distribution of induction-density in the gap tends to vary rapidly at the slots and to be nearly uniform in the space between one slot and the next. To overcome this effect, which was foreseen, successive stumpings had been slightly sheared circumferentially, so that the line of centres for any slot, instead of being quite parallel to the axis, was slightly spiral in reference to it. The stepped nature of the curve connecting x and ¢ shows that the effect in question was only partially neutralized. But this tends Fig. 3 150 ge eeereeeerPEEE srenresuenatse NI Y vo EERE oe jauane endl Pinks lt ees ce "TS a ea led el bel calvanle oala ie Cee | 4 ‘ ceeecotartars . i Mee les a See | boli ES | 30 ERE Peper cH : qa e + Tnosanee ee ee 40 50 60 70 80 90 100 (10 120 150 lise 150 160 aa to make the correspondence of the direct-current and alter- nating-current tests the more convincing. It will be noted that the angular period of the steps in the curve is 30°, the same as the angular interval betw een successive slots. The results are all set forth in fig. 8. The direct current 80 Dr. W. E. Sumpner on the | tests were 83 in number, and are indicated on the curve by | delta signs. About 40 tests were taken with alternating % currents, half of them with a non-inductive resistance in series with a moving coil, and the rest with a condenser | substituted for this resistance. These tests are separately marked on the curve with rings and crosses. The observations | are not all plotted, as several of the points were too close to | be distinguishable, but a fair selection is given. | A few typical observations with direct currents are given in Table I. and will be sufficient to show the conditions of the test. The currents A,, A; are in amperes, @ is the observed deflexion of the pointer in degrees, and @ is calculated from formula (8). TABLE I ths 499/411 | +-49/ —-5 |-28 (5:2 62) -83 93-95 [A | o7] yol 72 | 745 76 109 | 72| 82! 43] 05 |x i 30 | 40 | 50 | 605 | 70 80 iS 119-7 130 161 [ a 1573 1530 46-7 (1289 1217 (ord 85-9 53 | 32:6 The value of ¢ so calculated corresponds in the alternating tests with the phase difference between the current A, through the first fixed coil, and the moving coil current. For both the direct and alternating current tests, the deflexion « of the instrument could be read to, and appeared reliable to, one-tenth of a degree. The value of ¢ was determined with almost equal accuracy for the direct current tests, the conditions for which were simple and could easily be kept constant, while the value of ¢ depended merely on the ratio of the readings of two excellent instruments of the permanent magnet type. But ¢ could not be determined with such accuracy in the alternating-current tests, for several reasons. The testing conditions with running machinery involved cannot easily be kept very constant; alternating-current instruments are not so reliable as those for direct currents ; while ¢ has to be determined from the readings of three instruments instead of from those of two. The alternator used was provided with six terminals arranged for the supply of two-phase and three-phase current. The three-phase terminals were connected to the positive ends of the fixed coils through ammeters and banks of lamps, the negative ends being connected together to form the neutral point. The currents were adjusted to approximate equality, but only Theory of Phasemeters. 91 one good hot-wire ammeter of the range required was available, and this was put in the A, circuit. At first the wattmeter method of testing ¢ was used, a Mather-Duddell instrument being utilized, with its current-coil placed in the A, circuit. The pressure circuit of this instrument was put in parallel with the moving-coil circuit of the phasemeter, and with a Weston dynamometer voltmeter. The current circuits were not altered during the tests. The six terminals of the alternator, together with the neutral point, formed seven points, any two of which could be selected for appli- cation to the pressure circuits. In this way many different values of @ could be obtained, and a new set of tests could be made with a condenser substituted for the non-inductive resistance in series with the moving coil of the phasemeter. Of course, when interpreting the results in the latter case, the value of ¢@ as deduced from the wattmeter readings had to be changed by 90 degrees to get the corresponding phase- difference between the moving coil current and the current A,. The wattmeter tests were made on the instrument shown in fig. 3, but not with the particular arrangement of coils there indicated; and the results found were in close agreement with the curve between w and ¢ as determined by the direct-current method. The wattmeter method proved laborious when a large number of tests were needed; and it was found sufficiently accurate, and much quicker and simpler, to assume that the six terminals of the alternator gave voltages in the precise phase relation indicated by the geometrical properties of fig. 4, in which the points Ay, Ag, Fig. 4. A, Az Ap P A; are 120° apart and correspond with the current circuits, while the points A,;P and QR are the extremities of two perpendicular diameters. The centre of the circle, N, denotes the neutral point. The current vectors are NA,, 92 Dr. W. E. Sumpner on the NA;, and NA; The vector NA, represents zero phase, while the angle between NA, and the vector joining the two points selected for the voltage applied to the moving coil circuit is ¢; the phase of this voltage. When a non-inductive resistance was used with the moving coil, ¢, was the same as ¢ the phase of the moving coil current ; but when a condenser was used, it was found that ¢, had to be diminished by 90°, or increased by 270°, in order to get ¢ the value to plot with x. A few of the observations taken are given in Table Il. Particulars are given in the column V of the voltage points chosen for the pressure circuits. g, was not a measured quantity, but one calculated on certain assumptions from fig. 4. Any error in these assumptions may serve to explain the slight divergence of some of the points obtained with the alternating-current tests from the curve deduced from the direct-current measurements, but the general agreement observed between the two sets of tests can only be made closer by putting any such error right. TaBLeE II. With Resistance. | With Condenser. Tae ¢,=¢. lic, Me dy. :) | pete AA, | 150 Gott seal =h 40 180 27 RP 135 672i © Nay —120 150 555 | NA, 120 87 | CA YAS —150 120 /| “eee RA, 105 94:5 || RA, 165 75 125 A,Q 75 124 || A,P 120 30 | 158-7 | I | Another complete set of tests was made on this instrument with one of the coils, A, reversed, so as to make the instru- ment unsymmetrical. The end of the coil A,, formerly considered positive, was thus made negative. The direct- current test yielded a curve between 2 and @ of a most extraordinary character, yet a number of tests made by the alternating-current wattmeter method yielded points which plotted perfectly on the curve so found. The other two instruments referred to were also thoroughly tested, and with equally satisfactory results. Their structure differed from that indicated in fig. 2 merely in the arrangement and number of the fixed coils. There were three such coils in each case. In one instrument these were wound through six holes, stamped in the laminations of the outer stator So, and arranged symmetrically at angular intervals of 60°. In the Theory of Phasemeters. 93 other instrument, the coils were wound in six slots stamped symmetrically in the periphery of the inner stator 8; In either case, the curve found between a and ¢ was of the same general character as that shown in fig. 3, except that, as the windings were in these instruments 60 degrees apart, 1t was found that the flat parts of the curve covered a greater angular range, and that the angular period of the steps was 60° instead of 30°. In each instrument the direct and alternating current tests were found to be in close agreement, and the direct-current calibration of one of them was found to coincide with a large number of alternating-current tests taken on the same instrument more than eight months previously. It therefore appears clear, both from theory and experiment, that the accuracy of these instruments on balanced loads in no way depends upon the structure of the coils, or upon the presence or absence of iron, or upon the mode of variation of the currents. The theory given of the four-circuit instru- ment described will be seen to be equally applicable whichever of the two systems of coils is fixed, so that if the fixed system consists of a single coil and the movable system consists of three relatively fixed coils, the same theory applies. Three-Circuit and Monophase Instruments. If the three-coil system is reduced to a two-coil system, as in most actual phasemeters, only a slight modification of the theory is required, and the instrument can still be tested by direct-current methods. All that is needed is to put F,=0 in equations 1, 2, 3, and 6. LHquations 4, 5, 7, and 8 still hold good, and in the direct-current calibration there are only two currents to consider, and these may have any values. For a single-phase instrument, which merely differs from a multi-phase instrument in that its two-coil system is parallel connected, and the branch circuits made of different inductive properties, a similar theory applies. For a fixed frequency and wave form there will be a constant ratio between P and Q, the two alternating currents in the two- coil system, and a constant phase difference a between these currents. If, then, @ is the phase difference between the alternating current in the single-coil system and that through P, the corresponding direct currents through the coils P and Q which will produce the same deflexion will be A,=P cos , A3;=Q cos (@—2z). If therefore a and the ratio P: Q are known, it is possible to determine @ for any ratio A,:A,; of the currents pro- ducing the observed deflexion. 94 Dr. W. E. Sumpner on the Power-factor for Unbalanced Loads. It has been assumed throughout the foregoing theory that the load currents are balanced ; a most desirable condition in practice, but one rarely attained. So far as the writer is aware, the behaviour of phasemeters on unbalanced loads has not previously been investigated. There is a fairly general impression that they are inaccurate under these circumstances, and for this phasemeters have been blamed ; though the fault rather lies with those who assume that an instrument, which is only affected by a few of the con- ditions of a circuit, can be reasonably expected to measure the average of such conditions. Now, in the first place, there is not even any generally accepted definition of the power-factor of a three-phase circuit when the load currents are unbalanced. There are really three circuits, consisting of each line current and the voltage between this line and the neutral point. There are thus three power-factors, one for each circuit. Fortunately the voltages, being fixed by the generator, can always be regarded as equal and in symmetrical phase relation; other- wise the definition of the average power-factor of the load would be most complicated. But we shall take the following definition of cos ¢ for unbalanced loads :— _ Aj cos d; + Ag cos hy + Az Cos ds | OO egret ° (9) where A;, A,, A; are the magnitudes of the three load currents, and ¢, dz, 3 are the phase angles between these currents and the corresponding voltages to the neutral point. This formula for cos¢ merely amounts to defining the volt- amperes of an unbalanced three-phase circuit as being the product of the voltage to the neutral point and the sum of the three- Fig. 5. line currents. The relations of the different quantities are indicated in fig. 5, in which the voltage vectors are supposed to be of equal mag- nitude and symmetrically spaced. If this were not the case, we could still determine a neutral point such that the voltages between it and each line would be equal; and the definition (9) would still hold good provided the phase angles ¢y, do, p3; were reckoned from the corresponding voltages to the neutral point so determined. Theory of Phasemeters. 95 Symmetrical Six-Circuit Phasemeter. Now the most likely form of phasemeter to be accurate on three-phase circuits with unbalanced loads, is naturally one in which each system of coils consists of three similar and symmetrically arranged coils, having a common line of sym- metry, and with their planes fixed at 120 degrees from each other. One of these sets of coils must be actuated by the load currents, and the other set by the line voltages. With such an instrument, we must have three equations like (1) for the induction densities at the three moving coils, or we have :— Bo =A Pig + Agl og + Ag 30 B; = Ay Fy3-+ Ag} y3 + As l's3 where in the quantities F the first suffix refers to the fixed coil, assumed to take one of the load currents, and the second suffix to the moving coil. Thus I; means the line average effective induction density due to a unit current in the second fixed coil at the conductors of the third moving coil when the deflexion of the pointer is «. Now under the symmetrical conditions assumed we have :— Fy = Fo F33= P | ligne ll ee ld pee) 3 ° © e e (11) Pe,= FP, =Fy=R but Q and R are not necessarily the same. Hence we have: B,=A,P+A,R+ AQ B=A,Q+AP+A;3R 7; . . . . (12) B; =A,R + AQ -+ ‘AV is Now if the three moving coils are star connected, and their three free ends joined through three equal non-inductive resistances to the three mains, the currents through the three coils will be represented by Vj, Vs, V3, the voltages between the neutral point and the corresponding mains. The condition for balance constituting an equation for x is: V,B, + VB, + V;B;=0, B, =A + AF. =“ AzF's, ; ; = (LO) or PSV,A,+ QS V,A;+ RSV|A,=0. Now referring to fig. 5, and remembering that the voltage vectors are of equal magnitude, and are symmetrically spaced, 96 Dr. W. E. Sumpner on the we have for the different angles required :— rN EX YN V,A,= d,, V,A,= ¢,4+ 120, V,A;=63+ 240, &c., &e. If we substitute in the above equations, using such relations as ed BOS, iN VA; = VA; COs VAs, and divide out by V we get, PA, cos 6; + QSA; cos (fb; + 240) + RSA, cos ($,+120) = e (13) or PZA, cos ¢, = QEA, cos (¢, + 60) + REA, cos (60 —d;) Let us define two quantities C and S such that C= Aj, cos ¢,+ A, cos d2 + A; cos bs) (14) S=A, sin ¢,+ A, sin ¢,+ A; sin bs) hy) We then find on expanding (13) that C—328 C+338 OO ae +R wee but from (14) we get C24 $2?=A,?+A,?+ A3;?+ 22 A,A3 cos (d.—d3) . (16) Now we only propose to consider the case of a moderate want of balance for which the angles ¢,, 2, $3 differ from their mean value by only small amounts whose squares and products can be neglected compared with unity. Under these conditions, the cosine of the difference of any two of these angles can be considered unity, and (16) reduces to :— C?+8$?=(A,+A,+A3)?, but from (9) and (14) C=(A,+ A,+As) cos a hot. S=(A,+A,+A;) sind If now we substitute in (15) and simplify we obtain : Pcos@=Q cos (60+) +Reos(60—¢), . (18) and substituting from (11) P= hn. Oates R= Fa, we have F,, cos @ = Fa cos (60—¢) + Fs: cos (60+) ; an equation exactly similar to (6) and showing that the deflexion is the same as on a balanced load of power-factor cos. Also it appears that for balanced loads only one of Theory of Phasemeters. Sif the moving coils need be used if it is connected to its appro- priate voltage. The deflexion will be the same whichever moving coil is connected to the circuit. For unbalanced loads it is, however, necessary to have all the coils so con- nected if the instrument is to read cos ¢ as defined in (9). To calibrate such an instrument by the direct-current method, the process already described may be applied, the three coils of one system, but only one coil from the second, being used for the test. To confirm this, tests were made on a commercial instru- ment of the symmetrical six-circuit type, manufactured by Messrs. Everett, Edgcumbe & Co. The moving system consisted of three star-connected coils designed for shunt connexion with the mains. A constant current was passed through one of the three fixed coils, various small measured currents were passed through the moving coils in accordance with the method above described, and the value of ¢ corre- sponding with each observed deflexion « was calculated by means of formula (8). The scale of the instrument was so constructed that with alternating currents the deflexion x was. a direct measure of the phase angle. The observed value of «x was found to agree with @ when a particular fixed coil was used for the current circuit. Two additional sets of tests were taken using the remaining fixed coils in succession. In one of these cases ¢ had to be increased by 120 degrees, and in the other diminished by the same amount, to make the converted value of @ agree with w. The tests made were comprehensive, each set consisting of about 35 determinations ranging over the whole scale. The three curves obtained by plotting the (converted) value of @ with « were nearly straight lmes, and were nearly the same; but they were by no means absolutely so, and the differences amounted in some cases to as much as ten degrees. The arrangement of the coils was thus not symmetrical in the mathematical sense assumed in the above proof, and it is difficult to estimate to what extent the indications of the instrument are dependent upon the balance, or lack of balance, of the load currents. To test such an instrument thor oughly with alternating cur- rents on unbalanced loads would be so complicated and laborious that it is unlikely that such a test ever has, or will be, made. There would be needed no fewer than nine elec- trical instruments (three ammeters, three voltmeters, and three wattmeters) besides a number of troublesome adjust- ments and subsequent calculations. The labour of the nine or more observers would be of no avail unless all the readings for each test were taken accurately and simultaneously. Ey iiwliag. ©. 6. Vol. 1h. No: GL: Jan: 1906. H 98 Dr. W. H. Sumpner on the Symmetrical Five-Cirewt Phasemeter. Before leaving the consideration of symmetrical instruments, it may be well here to state the result of an examination of the case of one having five coils instead of six. If the first coil of the moving system is omitted, making F., = Fy = Fs, =0 in equations (10), (11), and (12), it will be found on making the changes which necessarily follow that equation (13) becomes O—388 2 P[C—A, cos ¢;] = Q) — A; cos (¢3+ 60) | (4 23g +h E igs — A, cos ($.—60) |; now in the above equation the coefficient of P is equal to the sum of the coefficients of Q and R (see (21) and (22) below), and we can thus always find an angle y such that P cosy = Qcos (60+7)+Reos (y—60), and hence by (18) the reading of the phasemeter will be that due to a balanced load of power-factor cos x. With the help of (17) and relations proved below (21), (22), and (25), it will be found that dA cos@—AygcosA 3Acos (6 +60) —Ay cos (2+ 60) COs ¥ cos (y+ 60) _ 3A cos (6—60) —Ay cos (?—60) ep cos (y—60) and assuming that @ and y exceed ¢ by small amounts 6 and Xo respectively, it will be found that the above equations involve the relation Xo — 10, e Fy ° ° e ° (19) or the phasemeter on an unbalanced load will read, instead of the true power-factor cos ¢, the value cos (P+ 3%), where @) has the value given by (31) below. Phase Error due to Unbalanced Loads. If the instrument is unsymmetrical and of less complicated construction than those just considered, the next best form will be one having a three-circuit system for the currents, and a single-circuit system for the volts, like the one first described. Referring to equation (3) and assuming that the Theory of Phasemeters. 99 load currents are no longer balanced, we see that instead of equation (6) we shall have as the condition for balance : FA, cos ¢,= FA, cos (60 — 2) + F3A3 cos (60+¢3). (20) Now the vectors of fig. 5 are the same as those of fig. 6, in which latter the current vectors, and also the voltage vectors, Fie. 6. are drawn so as to form closed triangles. Bearing in mind that the voltage triangle is equilateral, it is readily seen that A, cos d; =A, cos (60—¢2) + As cos (60+¢3); . (21) and as we have, whatever 4 may be, cos 0 = cos (60—4) + cos (60+8), we see that we can always determine an angle § from the consistent equations ie __ A, cos¢, _ A,cos(60—¢,) _ A; cos (60+ 43) 99 wip) cosy )* cos (G00), AWeos(60426)0 * ee) and that for such value of @ we have from (20) F, cos 0=F, cos (60—@) + F3;cos(60+6). . (23) If we compare this equation with (6), we see that if the instrument has been correctly calibrated for power-factor on balanced loads, the reading of the instrument will, for the H 2 100 Dr. W. E. Sumpner on the unbalanced load assumed, be cos @ as determined from (22), and that this value is absolutely independent of the quantities F resulting from a particular structure of the instrument. In other words, if a number of such phasemeters be connected to the mains in precisely the same manner, and if these instruments have all been calibrated for balanced loads, each of the instruments will indicate the same reading whatever the nature of the load, and however different the various instruments may be as regards internal structure. But it does not follow that this common reading correctly gives the power-factor of the load. There are certain relations between A,, As, As, ¢1, bo, Ps, resulting from the geometrical properties of fig. 6, but it cannot in general be true that the value of cos @ determined from (22) is the same as that of cos@ as defined in (9). This can readily be seen by putting A; = 0, in which case 0 must be 30 degrees while ¢ may have any value. It may all the same be the fact for small divergences of the load: currents from A their mean value, that cos @ and cos @ differ but very slightly. We thus want to find @) where G6=o+ 4%, since if 6) is small, the error, considered as a fraction of the true power-factor, made in taking cos@ (the reading) to represent cos d (the true power-factor) will be: § dcoosd cos@ do and 6 will correspond with the phase error of an ordinary wattmeter due to inductance in its pressure-coil. For equal phase errors the two instruments will read erroneously by precisely the same percentage on loads of the same power- factor. The question to determine is whether @, for a moderately unbalanced load, is sufficiently great to render the phasemeter unsatisfactory. While @ is small the instrument remains a phasemeter, but when 6) becomes large the instrument tends to indicate the want of balance of the currents, rather than the average power-factor of the load. If we put each of the ratios in (22) equal to Ay and con- sider fig. 6, it will be noticed that Ag is the length of each of the sides of an equilateral triangle drawn so that these sides make angles @ with the sides of the triangle representing the voltages, and so that the vertices lie on lines perpendicular to the voltage V,, and passing through the angular points of the current triangle. For balanced loads the Ag triangle. =(—O) tang, . .' 0. ee Theory of Phasemeters. 101 must coincide with the current triangle, and for moderate variations from balance we may put :— Ay=A(1+e,), As=A(1l+e), A3;=A (1+¢;), Ap=A (1+ 6), where A is the mean value of the ioad currents, so that €; tegte,=0, and where we may regard all the quantities e« as small fractions whose squares and products may be neglected compared with unity. Since when the load currents are equal 6,=¢.=¢3, the above assumptions necessarily imply that if oy=y¥+ 0, do=xKX + Fs, p3= V+ 03, where y is the mean value of the quantities ¢, so that 0, “4 G;, =F G= 0. we may also neglect the squares and products of the quantities 0. Now, if we substitute in (9) and simplify, neglecting squares and products of small quantities, we easily find 3 cos 6=3 cos ¥+ (e+ +¢€3) cos y—(A,+0,+ 03) sin x, or, using the above relations, we have cos @ = COS YX, or @ is the mean value of dy, do, o3. Collecting formule we thus have gi=ot+h, do=h4+ A, ds= $+ 03, | A,=A(1+e), Az=AC +e), As=ACA +63) ; (25) O6=$+ A, 0,+0,+0;=0, ° | ae Ayp=A(1+ 69), Ej tegte=O0. 8 Now certain relations can be found between the quantities e and @ for the current triangle shown in fig. 6, by equating the ratios of the sides to the sines of the opposite angles and reducing. These relations prove to be 3? € = 0,—03, — 33 0; = €9 =" Es, | 32 €9 = O;—0;, —3? 0) = €:—€), 26) 3? 65 = 0,— 8, — 3? 0; = €,—&, 102 ' Dr. W. E. Sumpner on the From these equations it can be shown, with the help of the last relations of (25) and equivalent relations such as 2 €2€3= €;” —€)” — € 3”, that e+ 0 =6,4 6,,=e, +6, =2 neh ae (27) where 3 Pe) +e" +3"; or ¢ is the square root of mean square of the quantities €1, €9, €s, and may be said to measure the extent to which the load-currents are “out of balance.” For small values, ¢ is essentially the same as the arithmetic mean of ¢,, &, and €3. Since algebraically the sum of these quantities 1s zero, it follows that the greatest is equal numerically to the sum of the other two, and thus ¢ is two thirds of the greatest of the quantities €,, €, €3. Now, if we equate to Ay each of the three ratios of (22) and multiply up and reduce, we obtain the three equations €&) cos b—O, sin dh = €, cos H— OM, sin g, €) cos(p— 60) — A sin(d — 60) = «€, cos(d—60) — 4, ae. | (28) €, cos(d + 60) — 4% sin(d + 60) =e; cos(b + 60) — 8; sin(p + 60). If we subtract the third of these equations from the second and simplify with the aid of (25) and (26), we get €) Sin 6+4) cosd=—[e, sin@d+6, cosd]. . . (29) By squaring this equation and adding the square of the first of (28) we get Eo" + Ce + ao 2 a by (27) 3 e ° e (30) or @ is necessarily less than €23. If we choose two angles ®) and 8, such that ep—0, tan By. . £0; tan Bye we can use (30), the first equation of (28), and (29) to prove sin (89>—¢) = sin (8,—9), cos (89>—) = — cos (8,—9) ; these simultaneous equations involve the relation Bo—-O+f,-G=7 or Bo=7+2 o6—8£;. Theory of Phasemeters. 103 But from the above we have G,=€22 cos 8p; or O)= —e2? cos (26—8)), ano) or Q.= -—-[0, cos2h+e, sin 2], and the fractional error made in reading cos ¢, which by (24) is —@, tan d, becomes A cos cos b in which the quantities e and @, are determined solely by the divergences of the load-currents A,, Aj, A; from their arith- metical mean value. The same formula can be obtained by equating any two of the ratios (22) without bringing the quantities A, and e, into the equations, but the working is not any shorter and the information yielded is less. It will be apparent, on inspection of the error formula (32), that the phasemeter may give very erroneous readings when the load-currents are badly out of balance. This can be seen best by considering a numerical case. Suppose the three load-currents are 21,22,and 17 amperes. The mean current is 20, and the errors «1, €, €; from the mean are 5, 10, and 15 per cent. respectively. It follows that ¢ is 10°8 per cent. and ¢22 is 15:3 per cent. Disregarding for the moment the factor cos (2@—,), the above error has to be multiplied by tan ¢ to get the percentage error in reading cosd. The error will thus be much reduced on circuits of high-power factor, but for power-factors below 0°71 the value of tang becomes greater than unity, and the percentage error in reading cos will be correspondingly increased, though it must be noted that if the scale is graduated to read cos ¢ the absolute error of the reading in the case assumed is never greater than 0°153 sin d. Now, a circuit having three currents proportional to those assumed would be considered badly out of balance, and as a rule a much better state of things obtains, yet the conditions instanced are quite possible in practice. The influence of the factor (cos 2—,) must also be considered. This factor, though it must always decrease the magnitude of the error, can alter its value in a striking manner, and is the quantity =e2? cos (2—£,) tang, . . . (32) 104 Dr. W. E. Sumpner on the which determines whether the instrument reads high or low. The quantity e in (32) depends merely on the average square of the fractional divergences €, €, €,; of the load-currents Ay, Az, Az; from their mean value. The quantity 8,, on the other hand, does not depend upon ¢e but upon the ratios between €;; €, €;. Whatever the value of e, 8, may have any value in accordance with these ratios, so that cos (26—/;) varies sinuously with @, and will be numerically equal to unity for a particular relation between 8; and d. Hven for the same three currents in the mains, @, may have no less than six values, since we can select any of the three currents for the line A,, and after this selection is made we may choose either of the two remaining currents for the line Ag. The six possible values of , for the currents assumed in the above case can be shown to be +19°, +41°, and +79°, and the percentage errors for these values of 6, and for a value of e equal to 10 per cent. are shown in Table III. for loads of different power-factor. Another column is added for the case 8,=0, and in the last column the maximum error eZ2 tan @ 1s shown. TasLe II].—Percentage Error of Phasemeters (for a load 10 per cent. out of balance). Values of 6, in degrees. fastor. + a9. || Lai. | 790... 440.) aan | LO 0 0 0 0 0 0 0 0 Ou 61 |, BF 57 4-2 99) — 3) 44 8 ...| 106 | 8-9 61 30| — 5 | —45 | —9-0)tele 7...) 141 | 9:2 43 |.— 8 1],—50 |, —96.| 142 Ne de eGue. 4), 3169! |) BO 8 | —53 |—10-9 | —16-:0 | —189 | 189 | 5...) 184 | 46 |=—46 |=122 | --18-4 | —23:1 | —28:6 | 945 It will be seen that the error may be quite serious. Thus a 14 per cent. error on a load of power-factor 0°7 means that the instrument may read either 0:8 or 0°6 according as the error increases or decreases the reading. Of course it must be remembered that the error is always proportional to e, which may be called the “ out-of-balance”’ of the load ; so that if this out-of-balance is 2 per cent. instead of 10 per cent., all the above numbers must be divided by 5. In all cases the reading for a power-factor cos ¢ fluctuates, according Theory of Phasemeters. 105 to the way the load is out of balance, between the values cos + 22 sin d, so that for a load 2 per cent. out of balance the reading of the power-factor cannot vary from the true value by more than +°028 as extreme limits. The above formula applies to an instrument having three coils in one system and a single coil in the other and the error is independent of the structure oftheinstrument. The error is largely controlled by the value of tang, where @ is the angle which we have assumed to represent both the pow er-factor, and the phase-difference of the moving-coil current, in reference to the current in one of the fixed coils. As any voltage of the multi-phase system may be chosen for the moving coil, provided the instrument has been correspondingly calibrated, it might at first sight appear possible to select such a voltage for the moving system as {o make the value of tan @ small for the particular power-factors the instrument is most required to read, and thus render the error under practical conditions negligible on unbalanced loads. A careful examination will, however, show that this is not the case. As already shown, an instrument having three current- coils and three voltage-coils, all symmetrically arranged, will read correctly whether the load-currents are balanced or not. But such perfect symmetry is easier to assume in a mathe- matical investigation than to ensure in the structure of so cowplicated an instrument. Jf one of the moving coils is dispensed with, as in the other symmetrical case considered, the instrument is simpler to construct and its symmetry easier to secure. Such a five-circuit instrument is not quite accurate on unbalanced loads; but (19) shows that the error is only one-third as great as in the four-circuit instrument to which Table III. applies; and it will be seen that for all load-currents such as are likely to occur in practice, the error is small enovgh in this case to be neglected. The six-circuit instrument consists essentially of three single-phase instru- ments combined into one. The best solution of the phase- meter problem would no doubt consist of three single-phase instruments used one on each circuit. There are difficulties, not yet overcome, in constructing good instruments for single- phase circuits. But such instruments, even if they existed, would at present be used mostly on multi- phase cireuits, and on such circuits no difficulty arises. All that is needed is for the instrument to have one of its systems of coils arranged multi-phase for two or mure of the voltages, and to have its other system single-phase for the current whose power-factor 106 The Theory of Phasemeters. is required. The fixed phase relation of the voltages will be unaffected by the variation of the load-currents, and thus the instrument wiil indicate the true power-factor of the particular current chosen. Indeed, most actual phasemeters are con- structed and used in precisely this manner, and the error on unbalanced loads is given by a formula like (24) with 0; substituted for 6). Reference to (30) and (31) will show that the error made in assuming that the reading indicates the average power-factor of the load is essentially the same as in the case considered, and to which Table ILI. applies. In conclusion, the main results of the foregoing investiga- tion may be thus summarised :— Summary. 1. Phasemeters for multi-phase circuits are all equally accurate on balanced loads provided they have been correctly calibrated and possess no faults due to purely mechanical causes. Their accuracy is not affected by variations in wave- form or in current-frequency. The calibration of the scale is affected by the number of coils used in the instrument, by the ratios of the ampere-turns used with these coils, by the distribution of the windings, and by the magnetic nature and properties of the magnetic circuits, especially if these contain iron ; but the accuracy of the indications is not dependent upon any of these considerations. 2. Phasemeters can be simply and accurately calibrated for balanced loads by means of a direct-current method of test. 3. The error of phasemeters on unbalanced circuits is generally serious for loads which are badly out of balance. The error, like that of a wattmeter, increases rapidly as the power-factor of the load diminishes. It can only be reduced at the expense of complication in the instrument, by in- creasing the number of coils used in the fixed and moving systems, and by arranging the coils and magnetic circuits to be symmetrical in regard to one another. If the true power- factor of the load is cos d, the reading of the instrument is cos +4 sin g, where @ is the phase error due not to the instrument but to the unbalanced load, and is the product of two factors one of which is the maximum value of 6 determined by the amount the load is out of balance, and the other may have any value between +1 and —1 and is the factor which determines whether the instrument reads high or low. The maximum value of @ is as follows :— Winding Ropes in Mines. 107 G) For an instrument consisting of a single coil for one- coil system, and of either two or three coils for the other system, al = GUE. Gi) For a symmetrical instrument containing three coils in one system and two in the other, C= Lede. Gi) Fora mathematically symmetrical six-coil instrument e=0, where ¢ is the square root of mean square of the fractions €, €, €; by which the three load-currents differ from their mean value. It is also very approximately the arithmetical mean of the quan- titles €,, €:, €; or two-thirds of the greatest of these three quantities, so that 22 is essentially the same as the greatest of the quantities €, €, and 3. i aaa a a r VI. Winding Ropes in Mines. . By Professor JoHN PERRY™. [Plate II.] N Section G I have just read a short paper in which I give a practical formula for the strength of a winding rope. I point out the difficulty of dealing mathematically with the real problem—“ When a cage is descending and the upper end of the rope is stopped, what occurs in the rope ?” The problem taken up in this paper assumes no internal friction in the rope, and it is only towards the end that I refer to the effect of a yielding in the attachments at its upper or lower ends. The solution of the present problem was given me by Dr. Love ; I have gone over his work; one of my students, Mr. A. R. Richardson, has carried the work a good deal further than was done in Dr. Love’s hasty lettertome. Mr. Richard- son has taken a practical example and drawn curves to show how the pull alters at the two ends of the rope and how the speed of the cage alters, and on the same sheets we have what pull and speed would be if motions were simple har- monic, all parts of the rope moving in the same phase. It will be seen, therefore, that my part of the credit of producing this paper is very small. * Communicated by the Author. Read in Section A at the British Association Meeting, Johannesburg, 1905, Ses vo 108 Prof. J. Perry on We assume that the rope with its attached cage is moving downwards with a velocity V when the upper end of it is suddenly stopped and held fixed. Let —w be the displacement downwards of a point in the rope distant z from its lower end, a the area of cross section of the rope, M the mass of cage, p the density of the rope, 1 the length of the rope, E Young’s Modulus. Then equating the mass-acceleration of a small element of the rope to the difference of the pulls on its two ends we get Oe ee Ot poe’ or putting E wi, p 3 oo) eo” 0? 02? ) of which the solution is o=j(at—z)+Fa@tt2).. . 3 Again, equating the mass-acceleration of the cage to the pull in the rope at its lower end, we obtain oe =Hae”, when es zZ or using (1) | Ea f" (at) +E" (at)= 7°; {E\(at)—f" (at)}, or putting Way octal h ___ Mass of Cage Ma? mio “7°T® ™ Mass of Rope’ f(at) +" (at) = at ( at)—f'(at)}. . . (2) The conditions of the problem show that for all values of t<0 we may put f(at—z)= —3¥(:-) O00 f(at—1) + Flat 4D) =0 t>0, t€., H(y)=—fty—2l) WLI EVER (4) Consider the Interval 0 l oo F'(att+2)= 3, ad /(at-)= ~y, ZA Ce Tea oi WN 62.0. a: Hence a waveof extension sets out from the upperend. When the wave reaches a point the point comes to rest and the extension of the rope at the point is a [+z : This state continues so long as t< ms , that is until the return wave from the cage reaches the point. 1 . fo When AS ie bu i cS and Vab-e aol, K’ (at + 2) = . Via ON Res ba oer GE) =e ae ie mca 0@ ae ‘ 4 esis ora) ar 4 1=2¢ L } ClO) NR Gite) _—_ = —@é mb These results show a wave running back from the cage. Hivery point as the wave reaches it starts to move downwards with the velocity V, but its velocity rapidly diminishes. The extension of the rope at a point when the wave reaches it becomes ae but this also rapidly diminishes. In this manner we may interpret our results from the values of f'(y) and F'(y). qu oF epgtet (i — 2) ~A)] eft) © ‘ ( me [tet (04 A)qug, ~ A 8 1b : oq — ny > mg_|_m ~ [date 9 Mug — sag—Ag | ee? — ines N= i — Nel Ol) | 3 Gs— A) IN ees Wo ea yu 0 Se D7 Bien mu (g-f) Ge A) AF Gah) ae Cm Ee ee en Bee 2S oe Le aaa . que a | aw H(ag— —h)pug = 9¢— fe |e es o uu es p) cz 6 (9g—A) @ qem- (SF) AP ae ™M—" yz sare Co, (g—A) — AG A py 2 ry) Dz giao) UE OMG? Goa Re Sy aE ie 7 in Si: a — aes) SS eS ae eee 2 n WA DyUt D » ° qu 8 —~-+ = © au CF Hi es = ee ie AE mone CE OAy | eg We A ee ee ee oS ee i%6 p= oe ULL —— — eS h > aa i-5 — Ae hee rae = wr 2G A ee 0 ONY S <5, Sa ee ae ee eee ee 7 SS = a (A), f *[VALOFUT 113 Vines. in J Winding Ropes C) a | tat + (70 —79 = ) | lel? € ( = = = RL oT - alee pp D 0 w | afgt)-+ (79 — 90) [UZ —2(79 —1Y)Z B= Gp Jip = Mea a ae eee E : a AY ae NGS ezine NV aN (19—79) NV G=ae ym 9 (2p - 1) ol, —— pu rodd 9, qv [Nd D INS) (Ry I A NS = Geese IMIR AM ei te Gay) NIN D A IPUe D UL a Fea G9 — JD) [WZ —.(79 Sie 70) z| die AP 7 0 (ir = ) ae Eas 7 i= Ar ceo ae [01> > 18 1S > >19 19> M>1F 1p >? >16 1Z>M>0 "[BALOJUT Pits Vag. S. 6. Vol. ll. No. 61. Jan. 1906. vo ~ i Prot. J. Perry on 114 | ete +L ~Aetgtt9 + 32 — A) pug — 91 — 4) re AB g Ez ee Aye | le g Ez + (9¢—") Z| *70 = [Ue + \ 7 : yu a4 net (ie —A)e Tilo ea lle SS ING ie Ae Ge=~ AG UH ; a alg 1 0 41 a Ge set Nz Ts is gue LONG mek NC. Gein Ee ad put (ie hg | AGT A Ww mG iin Ve eis AG @-4) Solis IAC A (7-4) = =f 0A = e8vy Jo AyoI0 A. 16 >>) 1L> A> pe 1G > A> I *[BALOUL Is Ines. Ve CU CneL Winding Ropes Vu (Gyo) Gann z | sfe"e —(1L—M)efQtQT + pug’) —70)} 81 —.()) 7) | Su) eae A 6 WD _? | et + (19) 46 = (19-2) z | ee ree preg —19)z \ a : (a) | Ngee seer ia (1¢ cs 1D) )NE— (is we yg | te le she yt = a J Jiu —()¢ >— 10 )z [DU - Ge—w) AQ Gaa- m9 {r= (ag — jg (9-7) J AZ ete ; aut =m) D —— = UNG a == By TeMO'T 4V [NT | 2 + Pei Gest as fs [L>1>1¢ Gaye ale 1g >>] 1>10>(0 "[VsAdOUT 116 Winding Ropes in Mines. The values of f’(y) and F’(y) have been calculated so far as the interval 71 diminishes exponentially with the time but increases exponentially with the distance 7. The case is not mended if we start with e+”, Instead of (15) we then find Ae Ges 1 1 (10y. So Wo = is e(at+r)/c e ° . ° (20), increasing exponentially with » as before and now also with f. It does not appear that any solution exists of the kind * “Theory of Sound,’ § 325, 122. Electrical Vibrations and Constitution of the Atom. sought, unless we introduce another reflecting surface. For the enclosed space thus defined, we find of course undissipated vibrations, and p becomes wholly real. In the calculation of frequencies given above for a cloud of electrons the undisturbed condition is one of equilibrium, and the frequencies of radiation are those of vibration about this condition of equilibrium. Almost every theory of this kind is open to the objection that I put forward some years ago*, viz. that p’, and not p, is given in the first instance. Itis difficult to explain on this basis the simple expressions found for p, and the constant differences manifested in the formulee of Rydberg and of Kayser and Runge. ‘Thereare, of course, particular cases where the square root can be taken without complication, and Ritz+ has derived a differential equation leading to a formula of this description and capable of being identified with that of Rydberg. Apart from the question whether it corresponds with anything mechanically possible, this theory has too artificial an appearance to inspire much confidence. A partial escape from these difficulties might be found in regarding actual spectrum lines as due to difference tones arising from primaries of much higher pitch,—a suggestion already put forward in a somewhat different form by Julius. In recent years theories of atomic structure have found favour in which the electrons are regarded as describing orbits, probably with great rapidity. If the electrons are sufficiently numerous, there may be an approach to steady motion. In case of disturbance, oscillations about this steady motion may ensue, and these oscillations are regarded as the origin of luminous waves of the same frequency. But in view of the discrete character of electrons such a motion can never be fully steady, and the system must tend to radiate even when undisturbedt. In particular cases, such as some con- sidered by Prof. Thomson, the radiation in the undisturbed state may be very feeble. After disturbance oscillations about the normal motion will ensue, but it does not follow that the frequencies of these oscil!ations will be manifested in the spectrum of the radiation. The spectrum may rather be due to the upsetting of the balance by which before dis- turbance radiation was prevented, and the frequencies will coriespond (with modification) rather to the original dis- tribution of electrons than to the oscillations. for example, * Phil. Mae. xliv. p. 362, 1897; ‘Scientific Papers,’ iv. p. 240. + Drude, Ann. Bd. xii. p. 264, 1903. { Confer Larmor, ‘ Matter and A«ther,’ On the Constitution of Natural Radiation. 123 if four equaily spaced electrons revolve in a ring, the radiation is feeble and its frequency is four times that of revolution. If the disposition of equal spacing be disturbed, there must be a tendency to recovery and to oscillations about this dis- position. These oscillations may be extremely slow; but nevertheless frequencies will enter into the radiation ‘once, twice, and thrice as great as that of revolution, and with intensities which may be much greater than the original radiation of fourfold frequency. An apparently formidable difficulty, emphasised by Jeans, stands in the way of all theories of this character. How can the atom have the definiteness which the spectroscope demands? It would seem that variations must exist in (say) hydrogen atoms which would be fatal to the sharpness of the observed radiation; and indeed the gradual change of an atom is directly contempiated in view of the phenomena of radioactivity. It seems an absolute necessity that the large majority of hydrogen atoms should be alike in a very high degree. Hither the number undergoing change must be very small or else the changes must be sudden, so that at any time only a few deviate from one or more definite conditions. It is possible, however, that the conditions of stability or of exemption from radiation may after all really demand this definiteness, notwithstanding that in the comparatively simple cases treated by Thomson the angular velocity is open to variation. According to this view the frequencies observed in the spectrum may not be frequencies of disturbance or of oscillations in the ordinary sense at all, but rather form an essential part of the original constitution of the atom as determined by conditions of stability. Terling Place, Witham, Nov. 8. VILL. On the Constitution of Natural Radiation. By Lord Rayurien, 0.0, F.R.S.* ae expression of Prof. Larmor’s views in his paper f “On the Constitution of Natural Radiation” is very welcome. Although it may be true that there has been no direct contradiction, public and private communications have given me an uneasy feeling that our views are not wholly in harmony; nor is this impression even now removed. It may conduce to a better understanding of some of these 1m- oOo : portant and difficult questions if without dogmatism I * Communicated by the Author. + Phil, Mag. vol. x, p. 574 (1905), 124 Lord Rayleigh on the endeavour to define more clearly the position which I am disposed to favour on one or two of the matters concerned. On p. 580, in comparing white light and Réntgen radiation, Prof. Larmor writes: “ Both kinds of disturbance are resolvable by lourier’s principle into trains of simple waves. But if we consider the constituent train having wave-length variable between > and 7+), 7. e. varying irregularly from part to part of the train within these limits, a difference exists between the two cases. In the case of the white light the vibration-curve of this approximately simple train is in appearance steady ; it is a curve of practically constant amplitude, but of wave- length slightly erratic within the limits 6X and therefore of phase at each point entirely erratic. In the Fourier analysis of the Rontgen radiation the ampli- tude is not regular, but on the contrary may be as erratic as the phase.’ This raises the question as to the general Pegade of the resultant of a large number of simple trains of approximately equal wave-length. In what manner will the resultant amplitude and phase vary? In several papers * I have considered particular cases of approximately simple waves, showing how they may be resolved into absolutely simple trains of approximately equal wave-leneths. But now the question presents itself in the converse form. What are we to expect from the composition of simple trains, severally represented by a,cos{(n+dn)tte} . . . - . (I), where 6n,; is small, while the amplitude a, and the initial phase e, vary from one train to another ? In virtue of the smallness of 62, we may appropriately regard (1) as a vibration of speed n and of phase e,+dnjt, variable therefore with the time. The amplitude and phase may be represented in the usual way by the polar coordinates of a point; and the point representing (1) accordingly lies on the circle of radius a, and revolves uniformly with small angular velocity. For the present at any rate | suppose that the amplitudes a, a, &e. are all equal (1),in which case the points le all upon the same circle. — The radius from the centre O to any of the points P upon the circumference is a vector fully representative of the vibration, and the resultant of the vectors represents the resultant of the vibrations. Atter the lapse of a time ¢ the pcints have moved from their initial positions P to other positions Q, and the aggre- gate of the vectors OP is replaced by the aggregate of OQ. * See especially Phil. Mag. vol. 1. p. 135 (1900). Constetution of Natural Radiation. 125 The difference is the aggregate of PQ. Now we suppose that t is so related to the greatest dn that all the arcs PQ are small fractions of the quadrant, and the question before us is the amount of the ditference between the resultants of the OP’s and the OQ’s, z.e. of the PQ’s. There are certain cases where we can say at once that the difference of resultants is small, small that is relatively to the whole. This happens when all the P’s are rather close together, 2 e. when the component vibrations have initially nearly the same phase. It is then certain that at the end of the time ¢ the amplitude and phase are but little altered from what they were at the beginning. Over this range the vibration is approximately simple, and the range is inversely as the greatest departure from the mean frequency vn. But in general the distribution of initial phases e causes fhe reculiant to be much less than if the phases were in agreement, and it may even happen that the initial resultant is zero. At the end of the time ¢ the resultant will probably not be zero, so that in this case the change is relatively large. The proposition that small changes in the phases of the components can lead only to relatively small changes in the resultant is thus not universally true ; and we must inquire further as to the conditions under which the conclusion is probable. The most important case for our purpose is when the initial phases are distributed at random, as they would presumably be when Réntgen radiation is concerned. If the components are very numerous (and of equal amplitude unity), the problem is one which I have considered on former oceasions * [t appears that the probability ofa resuitant amplitude lying between r and r+dr is 2 —72/Mar ar ¢ eC TCL Rme ences algerie on sez) where m is the number of components. Or the probability of an amplitude exceeding r is e7"/". The mean intensity (when the phases are redistributed at random a great many times) is m, corresponding to the amplitude ,/m. When r is great compared with ,/m, the probability of an amplitude exceeding r becomes vanishingly small. When on the other hand 7 is small, the probability of a resultant less than 7 is approximately Elba It appears that rake chance of the resultant lying outside the range from say },/m to co) 2,/m is comparatively small. %* Phil. Mag. vol. x. p. 73 (1830); ‘Scientific Papers,’ vol. i. p. 491 ; ‘Theory of Sound,’ 2nd ed, vol. i. § 42 a 8465 | 126 The Constitution of Natural Iadiation. We have next to consider the resultant of the components PQ. Here again the phases are distributed in all directions. The amplitudes, however, are no Jonger equal, but they are small relatively to unity. Although the contrary is not’ impossible, it would seem that in all probability the resultant amplitude of the P’s is small in comparison with that of the UP’s, from which it follows that, exceptional cases apart, the amplitude and phase of the resultant remain but little changed at the end of a time ¢, such that the changes of phase of the individual components are small. From the above discussion Iam disposed to infer that a Fourier element of radiation necessarily possesses in large degree the characteristic which (if 1 rightly understand him) Prof. Larmor associates with white light in contrast to Roéntgen radiation. Of course, after the lapse of a sufficient time the final phases of the components lose all simple relation to the initial phases. The final phase of the resultant is then without relation to the initial phase, and the amplitudes may differ finitely, but in all probability within somewhat restricted limits. From this variation 1t seems to me white light cannot be exempt. In the above and, so far as J remember, in what I have written previously, the question is purely kinematical. In saying that Fourier’s theorem is competent to answer any question that may be raised respecting the action of a dis- persive medium, I take for granted that the law of dispersion is given in its entirety. I quite admit that if there are any wave-lengths for which the behaviour of the medium is unknown, a corresponding uncertainty must attach to the fate of any aggregate in which these are included. Doubt- less a complete statement of the law of dispersion may involve the case of wave-lengths for which the medium is not trans- parent. As regards the passage quoted from Sir G. Stokes, his object was, | think, to explain the absence of refraction when Rontgen rays traverse matter. Taking light of ordinary and absolutely detinite wave-length incident upon transparent matter, he contemplates the lapse of 10,000 periods before harmony is established between the etherial and molecular vibrations, that is,as I understand it, before regular refraction is possible. At this rate the light from a soda flame would be incapable of regular refraction, tor the vibrations are certainly not regular for more than 500 periods. indeed Stokes’s argument appears better adapted to prove that Rontgen rays could not traverse material media at all in a reoular manner, than that they would do so without change of waye-velocity. On an Instrument for Compounding Vibrations. 127 I must confess that I have never fully understood Stokes’s position in this matter. A medium is non-refractive and nearly transparent for the pulses constituting Réntgen rays. What reception would it give to simple waves of halt wave-length equal to the thickness of the pulses? I should suppose that it would be non-refractive and transparent for these also, but Stokes’s argument seems to imply the contrary. The paradox would then have to be met that the medium treats simple waves less simply than compound ones. Nov. 16, 1905. LX. On an Instrument for Compounding Vibrations, with application to the drawing of Curves such as might represent White Light. By Lord Rayuuien, OM., FRS.* [ Plate III] N discussions respecting the character of the curve by which the vibrations of white light may be expressed, I have often felt the want of some ready, even if rough, method of compounding several prescribed simple harmonic motions. Any number of points on the resultant can of course always be calculated and laid down as ordinates ; but the labour involved in this process is considerable. The arrangement about to be described was exhibited early in the year during lectures at the Royal Institution. As it is inexpensive to construct and easily visible to an audience, I have thought that such a description might be useful, accom- panied with a few specimens of curves actually drawn with its aid. A wooden batten say 1 inch square and 5 feet long is so mounted horizontally as to be capable of movement only along its length. For this purpose it suffices to connect two points near the two ends, each by means of two thin metallic wires, with four points symmetrically situated in the roof overhead. This mounting, involving four constraints only, allows also of a rotatory or rolling motion, which could be excluded, if necessary, by means of a fifth wire attached to a lateral arm. In practice, however, this provision was not used or needed. The movement of the batten along its length is controlled by a piece of spring-steel against which the pointed extremity ot the batten is held by rubber bands. Any force acting in * Communicated by the Author. 128 Lord Rayleigh on an Instrument the direction of the length of the batten produces a displace- ment proportional to the force*. The tracing point, by which the movements are recorded, is at the other end, as nearly as possible in the line joining the two points of attachment of the four suspending wires. The longitudinal forces are due to the vibrations of pen- dulums hanging from horizontal cross-pieces attached to the batten at ghee Contre: The two ends of a wire or cord are attached to the extremities of a cross-piece, the bob of the pendulum being a mass ot lead (perhaps halt a pound) carried at ime mmmebla ae ane com’. ben see swinging the move- ments of the pendulums are thus parallel to the batten and tend to displace it along its tena In my apparatus the length of the longest pendulum is 34 feet. iva ler the cnetemce of one pendulum the tracing point describes a small simple harmonic motion along the ‘length of the batten. In order to draw a curve of sines the deed vlass destined to receive the record should move vertically in its own plane. I found it more convenient and sufficient for my purpose to substitute a movement of rotation. A disk (like the face-plate of a lathe) revolves freely in a vertical plane rounda horizontalaxis. To this disk a piece of smoked glass is cemented and the tracing is taken near the circum- ference, the axis of rotation being at the same level as the tracing point, so that the movement of vibration is radial. The disk must be made to revolve slowly and with uniform angular velocity. To effect this I employed a sand-clock, a device which works better than would be expected f. The sand, carefully sifted and dried, is contained in a vertical metal tube of about 1 inch diameter, and escapes below through a small aperture of size to be determined by trial. On the sand rests a weight, of such diameter as to fit the tube ea-il fe and this in its descent rotates the disk by means of a thread, of which the free part is vertical while the remainder engages a circumferential groove. The descent of the weight is practically independent of the quantity of sand remaining at any time t. It isscarcely necessary to say that the rey olving parts must be so weighted as to keep the thread tight. The advantages cf the apparatus depend of course upon the facility with wluch a number of vibratory movements % In strictness this presupposes the fulfilment of a condition involving the period of the force and that of free vibration under the influence of tne spring, which it is scarcely necessary to enter upon. + [t was used by H. Draper to drive an equatorially mounted telescope. i See Note at end of paper, for Compounding Vibrations. 129 can be combined*, It is as easy to record the effect of a number of pendulums as of a single one, the contribution in each case being proportional to the amplitude of vibration. In my instrument there are six pendulums, the shortest of such length as to vibrate about twice as quickly as the longest. The frequencies are in fact somewhat as the numbers 5, 6, 7, 8, 9, 10. No precise adjustment was attempted, the object being in fact rather to avoid anything specially simple. The lengths of the pendulums were chosen so as to afford an illustration of the vibrations constituting white light. Of course a complete physical representation of light from the sun or from the electric arc would need a much larger range of frequency. But we may suppose this light filtered through media capable of sensibly absorbing the ultra-red and ultra- violet, while still remaining white so far as the eye could tell, even with the aid of a prism. The range of an octave, for which provision is made, then amply suffices. The number of pendulums may seem, and perhapsis, rather small. The frequency, e.g. 7, given by one of the pendulums must be taken to represent a range from 64 to 74, with an error therefore up to 1 in 14. Such an error will be serious after 7 vibrations, but not so for 3 or 4 vibrations. Hence if we limit ourselves to sequences of 3 or 4 waves, the repre- sentation is about good enough. | Connected with the above is the question what amplitudes of vibration are to be assigned to the various pendulums. — It would not be difficult to give effect to an assigned law of spectrum intensity whether suggested by theory or found in observation. It is to be remembered, however, that such laws relate to averages, and do not give the relative ampli- tudes at any particular time, which will indeed vary fortuitously over a rather large range. I thought it therefore unnecessary to be very particular in this respect. The vibrations of the shorter pendulums die down more rapidly than the slower ones. By giving the former an advantage at starting a some- what wide range is covered. The tracings presented no general features that might not have been anticipated. A few specimens are reproduced— one showing the operation of the longest and shortest pen- dulums alone, the others the effect of all the pendulums. * The principle of mechanical addition is employed in an instrument devised by Michelson. Phil. Mag. 8. 6. Vol. 11. No. 61. Jan. 1906. K 130 = On an Instrument for Compounding Vibrations. Note on the Principle of the Sand- Clock. The difficulty of propelling a column of sand, occupying a tube, by forces pushing at one end is well known ; but I do not remember to have seen any discussion of the question on mechanical principles. A similar phenomenon occurs in the storage of grain, the weight of which, when contained in tall bins, is found to be taken mainly on the sides and but little on the bottom of the bin *. The unexpectedness of these effects depends upon a half unconscious comparison with fluids which in a state of rest are exempt from friction. Jn the present case, when the sand is moving, the tangential force at the wall is reckoned at w times the normal force. We may suppose, as a rough approximation, that there is something like a fluid pressure p. If a be the radius of the tube and dz an element of length along the axis, the tangential force acting upon the surface 2radz is pp.27a.dx. This is to be equated to the difference of the forces upon the two faces of the slice, viz. —za?dp. Accordingly dp __ 7 P 1 a ; or p = poe 7/4, the pressure diminishing as a increases. Hence a powerful pressure at =0 is unable to overcome a very feeble one acting in the opposite direction at a section many diameters away. ‘The case is similar to that of a rope coiled round a post, as used to check the motion of steamers coming up to a ler. ; As regards numbers, it will not be out of the way to suppose p=. When c=10a, p/pp=e-?="14. Noy. 22, 1905. * I. Roberts, Proc. Roy. Soc. vol. xxxvi. p. 226, 1884. “In any cell which has parallel sides, the pressure of wheat upon the bottom ceases when it is charged up to twice the diameter of the inscribed circle.” get a X. The Absorption of « Rays. By R. K. MoCuune, M.A., Senior Demonstrator in Physics, McGill University, Montreal *. ee question of the absorption of the a rays from radium by matter has been discussed theoretically in a most admirable manner by Prof. Bragg in a paper which appeared in a recent number of the Philosophical Magazinet. The theoretical considerations put forward in that paper were also verified experimentally by Bragg and Kleeman {. From the results set forth in these papers it was deduced that the absorption of the a rays in air is mainly due to the fact that their energy is used up in producing ionization, and it was shown that these rays possess the power of ionizing the gas only within a limited distance from the ionizing source. This limiting distance was shown to be fairly sharply defined, and was found to depend upon the nature of the source from which the rays. came. The source from which Bragg and Kleeman obtained their @ rays was a very thin layer ot radium obtained by crystalli- zation from solution. This crystalline layer was, as they clearly pointed out, not a single homogeneous source of a rays, but contained several transformation products of radium, each of which gave out a particles and some of which gave out @ and y rays as well. In addition to this, although the layer of radiating matter was very thin, still the velocity of the rays proceeding from the lower parts of the layer would be appreciably decreased by absorption before emerging into the air, and consequently the source would be giving out rays of different velocities. As the source was not homogeneous the curves which they obtained, as they clearly show, were somewhat more com- plicated than if a single homogeneous source had been used. Prof. Bragg suggested in his paper that polonium, which gives out only « rays, might have been used if it had been available. It was therefore suggested by Prof. Rutherford that it would be of interest to investigate this question, using as the source of @ radiation the radioactive matter deposited on a wire which had been suspended in a vessel containing the emanation from radium. Although the deposit on the wire contains the three products radium A, B, and (, still the * Communicated by Prof. E. Rutherford, F.R.S, 7 Phil. Mag. p. 719, Dec. 1904. } Phil. Mag, p. 726, Dec. 1904. K 2 132 Mr. R. K. McClung on the radium A disappears in a short time after removal from the emanation, and radium B does not give out any rays at all. We have therefore practically a single homogeneous source of radiation in radium C. Another advantage in using this source of radiation is that the layer of radiating material is infinitely thin, and conse- quently there is no absorption by the radiating matter itself. In addition, the source of radiation can be made as small as desired simply by using a very thin wire on which to con- centrate the excited activity. This source of radiation has proved very satisfactory, and the results which have been obtained are quite in accordance with those obtained by Bragg and Kleeman. Although there are several advantages in using the excited activity as a source of radiation, there is one obvious disad- vantage in its use, namely, that the activity dies away with time. However, in all the experiments described in this paper the rate at which the excited activity decayed was measured at the same time as the other observations were made, and the necessary corrections were easily made for the decrease in the activity of the source. This decay of the activity was therefore not at all a serious difficulty. The method of experiment and arrangement of apparatus employed was very similar to that used by Bragg and Kleeman. A diagram showing the arrangement and details of the apparatus is given in fig. 1. Description of Apparatus. A BC D was a metal box which inclosed the plates between which the ionization was to be measured and also the source of the ionization. i was a zinc plate counected to one pair of quadrants of a Dolezalek electrometer in the usual way and was surrounded by a guard-ring, F F, which was con- nected to earth, HH wasa wire gauze which was about -5 cm. distant from the plate EH, and was connected to one pole of a battery of accumulators, the other pole being to earth. K was a brass block made in two sections and contained the source of radiation. The lower half was a solid piece of brass in the centre of the upper surface of which was cuta narrow groove about ‘5 mm. in depth. The upper half con- sisted of a similar solid brass block about 5 mm. in thickness, having a hole 2-1 mm. in diameter passing vertically through the centre. The faces of these blocks were made true so as to fit tightly together. The wire on which was deposited the Absorption of a Rays. 133 excited activity was laid in the groove in the lower section of the block, and the upper half was then placed over it so that the radiations from the wire could only emerge through the hole in the upper block. A well-defined cone of rays was Bigs. 4 EARTH thus obtained. This brass block was placed in a definite position on an upright support, P, which could be adjusted vertically and the amount of adjustment measured on a fixed scale. The plate E was made sufficiently large to include the entire cross-section of the cone of rays throughout the whole range of the adjustment of K. Method of Observation. The wire on which the radioactive matter was deposited was a thin copper one about 0°5 mm, in diameter. About an inch of this wire was attached to the negative pole of a battery of 400 volts, and suspended in the emanation from about 20 milligrams of radium bromide and allowed to remain there for a couple of hours, or longer, so as to get the maximum amount of excited activity upon it. It was then removed from the emanation and cut into short pieces and placed in the groove K. The rate of leak produced between the plates EK and H was then measured for different distances of the source from the gauze H H. 134 Mr. R. K. McClung on the During the time taken to make these measurements, the activity of the excited wire gradually decreased. It takes radium ©, as has been shown by Rutherford, about 55 minutes to fall to half its maximum value after a long exposure in the emanation. This falling off in intensity of the source was corrected for as follows. The first observation after placing the excited wire in position was made at a definite distance of the source from the gauze, and the time carefully noted at which the observation was made. Then three or four observations were made at other distances, noting carefully the time at which each one was made, and then the source was replaced at the original position and the rate of leak measured again, noting the time. Then, after three or four more observations at various distances, the source was again brought back to the original position; and this routine was followed throughout the whole series of observations. The time at which each observation was made was carefully noted. By thus observing the amount of ionization at intervals when the radioactive matter was placed at the fixed position, a decay curve, extending over the whole time of the series of observations, could be plotted. By observing the time at which each measurement was made at the other distances, the necessary correction could easily be made by referring to the corresponding time on the decay curve. The amount of ionization produced for each position of the source was thus obtained for a constant source. Absorption of a Rays by Air. The absorption of the « rays by air at atmospheric pressure was first investigated, and curves were obtained showing the amount of ionization produced for different distances of the source from the electrode HH. These curves were found to be quite in agreement with the results obtained by Bragg and Kleeman. One of these curves is shown in fig. 2, where the ordinates represent the distance in millimetres of the upper surface of the radiating wire from the lower surface of the wire gauze HH. ‘The abscisse represent the ionization as measured by the rate of leak in arbitrary scale-divisions per second. This curve shows the same characteristics as were pointed out by the previous experimenters. Jt shows that, as the source recedes from the electrode, there is a very slow increase in the ionization until a distance of about 4 cms. is reached. Beyond this distance the ionization increases quite rapidly until a maximum is reached ata distance of about 5°8 cms. Absorption of a Rays. 139 thus showing, as Bragg has pointed out, that as the « particle moves farther from the source within a certain limit it becomes a better ionizer, although the velocity has become less after passing through a certain thickness of air. Bie y2. SSRGEEEnETA TIE 100 90 80 70 oe 10 co 50 60 70 30 40 SONIZATION. O/STANCE FROM SOURCE /N mms m oS 10 0 After the maximum point is reached and the distance increased, the ionization falls off extremely rapidly for a small increase in the distance until a distance of about 6°8 cms. is reached, when the ionization ceases altogether. The part of the curve which rises rapidly from this point is due almost entirely to the natural leak of the vessel and the 8 and y ray effects which are present. The range in air over which the a ray is capable of pro- ducing ionization is therefore about 6-8 ems. This agrees very well with the result obtained by Bragg and Kleeman, who obtained a distance of 6°7 cms 136 Mr. R. K. McClung on the Rutherford, in a recent paper in the Phil. Mag.*, has also investigated the question of the distance at which the photo- graphic and phosphorescent actions of the a rays cease; and he has found almost the same distances in those cases as the author found for the ionizing action. ‘The results shown by this curve indicate that as the velocity of the a particle from radium C decreases, the ionizing power of the particle very slowly increases over a certain range; then for a further decrease in the velocity the efficiency of the « particle as an ionizer increases quite rapidly until a maximum ionization is reached. When the velocity decreases beyond this point, the ionizing power of the & particle falls off extremely rapidly and very soon ceases altogether. Rutherford (loc. cit.), in investigating this question of the velocity of the @ particle from a photographic and phospho- rescent point of view, has shown that when both the photo- graphic and phosphorescent actions of the a rays cease, the particles still possess a considerable proportion of their ori iginal velocity of projection, and consequently quite a large amount of their kinetic energy. He also showed that the distance from the source at which these actions ceased corresponded very closely with the distances obtained by Bragg and by the writer for the cessation of the ionizing effect. These results therefore ail appear to indicate that the « particle is not capable of producing either ionization, nor photographic nor phosphorescent effects when its velocity falls below a certain definite amount. This limiting velocity appears to be very well defined for the rays produced by a definite type of radioactive product. We should expect from this point of view that when the point, at which the maximum ionization takes place, is reached a further increase of the distance between the source and the electrode should cause the ionization to cease abruptly. The curve, a ever, beyond the maximum point shows a decided upw ard sl ope instead of being quite horizontal. This upward slope of the curve is at least partly due no doubt to the fact that the angle of the cone of rays is of considerable size. When the distance between the source of the rays and the electrode is gradually increased, the air between the electrodes gets beyond the range of the extreme rays of the cone before it gets beyond the range of the central rays, as the extreme rays have to travel slightly farther, before reaching the electrodes, than the central rays. Therefore, as soon as this volume of air gets beyond the range of the extreme outside rays of the cone, the ionization will fall off, due to the fact that the width of the jonizing cone is decreasing and the volume of air acted upon is decreased. * Phil. Mag. July 1908 Absorption of « Rays. 137 Absorption of «a Rays by Aluminium. The absorption produced by thin aluminium-foil was also investigated. The foil used was about 0°00031 cm. in thickness. The absorption of different thicknesses of alu- minium was determined by measuring, in a manner similar to that for air, the ionization produced by thea rays after Fig. 3. 70 50 So lea ppp Saas ee Sanne eel a SS eee a ee nk Pad A ST de) Tae de ee ea Cro le «feos EES ERISA ee Il Lee ae, p oO LYSTANCE FROM SOURCE IN mms. CN (=) Las) a> Ue PEON eS GON Meena G Mam veg eet ene seb) FieB 30h Se SONIZATION passing through a definite number of layers of the thin foil. Separate curves corresponding to the curve for air were obtained when various thicknesses of aluminium were placed in the path of the rays. These curves are shown in figs. 3, 4, 138 Mr. R. K. McClung on the 5,and 6. As will be observed, they are all exactly similar in character to the one for air. MEGREE=""as CSCC re CCC CERRO CCE ae CCECCCEAC ee COE COC EC CE ee CECE ELCC Cee CHEE CECE CE CCl Er CCC EC SacaSenEe ee: CUO CCE Se COPS CCC sie a Bs es 0 i0 20 30 40 50 .60 .760 80 90 100. 110 Ie VisGize JON/IZATION 50 40 30 DISTANCE FROM SOVRCE /N mrs 20 10 In each of these curves, as in the case of air, there are two characteristic points, namely, that at which the maximum ionization occurs and that at which the @ particles cease to ionize. The range for each of these points is, of course, less than for the corresponding points for air, and the range naturally decreases the greater the absorbing thickness of aluminium. The distances at which the maximum ionization Absorption of « Rays. 139 occurs and at which the ionization ceases for different thick- nesses of aluminium are given in Table I.. Fig. 5. iI TE sa a es ee DISTANCE FROM SOURCE 1/N mms. Co eee oO es OM uiche TA eaiGm aloe ecOre veer cates: eB 0 /ONIZATION TABLE I. Miickncceor Drs: between Distance between ae Source and Gauze | Source and Gauze Aluminium at which maximu at which ionization Gi layer=-O003l em. hls ce. Saka 1onization occurs. ceases. 2 layers. 4°5 cms. 5'8 cms. 4 3” 3°6 bb) 4-8 99 6 »” 2:7 99 39 > 8 9 15 ” 2°6 ” 140 Mr. R. K, McClung on the As seen from the diagram, only a very small portion of the curve below the maximum point can be obtained for a thickness of aluminium greater than eight layers, since the maximum point for a thickness beyond this occurs so close to Fig. 6. 60 50 40 AOE Cae Sel LCC CCC ae COOOL sae CCC CCE ee CCE CECE CCC CEC PL Se ae JONMIZATION. DISTANCE FROM SOURCE IN 777s. 10 0 the gauze. Itis not practicable to place the source of activity closer to the gauze than about 6 mm., as the hole through which the rays emerge must beat least about 5 mm. in depth “ order that the angle of the cone of rays may not be too arge. Comparison of the Absorption by Aluminium and Air. From these curves for air and aluminium the absorption of the a rays by these substances can easily be compared by Absorption of « Lays. 141 considering either the point of maximum ionization, or the point at which the ionization ceases. Consider, for instance, the point at which the ionization ceases in the case of air and in the case when the rays pass through two layers of aluminium. The distance between the source and the gauze at which the ionization ceases is decreased in the second instance. ‘This, of course, is due to the simple fact that when the rays emerge from the aluminium their velocity has already been reduced to such an extent by absorption that they do not now require to travel so far in air before their velocity is reduced to the point at which they cease to ionize. The differences in the air-spaces in the two cases must be equi- valent to the two layers of aluminium in absorbing-power. Referring to the curves in figs. 2 and 3, the maximum ranges in the two cases are 6°8 cms. and 5°8 cms. respectively. A thickness of air of 1:0 em. must therefore absorb as much of the a rays as two layers of aluminium. Therefore, assuming that each layer produces the same amount of absorption, one layer of aluminium ‘00031 em. in thickness absorbs as much a radiation as ‘dD cm. of air. The same result ought to be obtained if we consider the point of maximum ionization in the two cases. This point in air is at a distance of about 5°8 cms., while when two layers of aluminium are interposed the maximum point is at a distance of 4°8 cms. The difference in the two cases divided by 2 is °5, which agrees with the result obtained from con- sidering the point at which the ionization ceases. Similar results are obtained when the other curves for the various thicknesses of aluminium are considered. ‘These results are given in Tables II. and III. Tasue II. Thickness of Air | Thickness of Air Absorbing Distance at which | corresponding to | corresponding to Medium. Ionization ceases. | given thickness of | one layer of Aluminium. Aluminium. ANTI RR 6°8 ems. 2 layers of Al. ... Das 1:0 cm. ‘50 cm. Be i sini ere bra: 48 ,, 2:0 ems. 50 ,, Gy Psy Ses Ses; PS) ae aS, en); tiie DiGi 73 4°24, OZ s, 142 The Absorption of a Rays. Tasxe IIT. | Disieee Thickness of Air | Thickness of Air Absorbing which maximum | Co'responding to | corresponding to Medium. Lonivation enon ee thickness of/ one layer of uminium. Aluminium. ONES. eee Et aot e 8 58 cms. 2 layers of Al. ... 43 ,, 1:0 cm. °50 cm. Art AY. . ie 3°65, 2:2 cms. ‘Os Oa ka je rane is, Salen, 3) By os; ees 1d 5; 4:3 ,, "Dora From these curves we see that we can readily compare the absorptive power of aluminium with that of air, and obtain the thickness of air which is equivalent in absorbing- power to any given thickness of aluminium. These results are in very fair agreement with those obtained by Rutherford, using the photographic and the phospho- rescent-screen methods. He used specimens of aluminium- foil similar to those used by the writer, and therefore the results of the two investigations may be compared. He found by the photographic and the phosphorescent-screen methods that one layer of aluminium-foil was equal in absorbing-power to ‘54 cm. of air. He obtained this result by measuring the distance from the source at which the a particle ceased to affect a photographic plate or a phos- phorescent screen after passing through various thicknesses of aluminium. The close agreement of the results obtained in the two separate investigations is an indirect confirmation of the hypothesis put forward by Rutherford in his paper (loc. crt.) in regard to the nature of the action produced by the a rays from radium on a photographic plate or a phosphorescent screen. These two sets of results taken together appear to point strongly to the conclusion that the ionizing, photographic, and phosphorescent effects of thea rays from radium are all due to the same cause, and it is very probable that in each case the effect produced is primarily one of ionization. In conclusion | wish to express my indebtedness to Prof. Rutherford, at whose suggestion the subject of this research was undertaken, for his valuable suggestions during the progress of the investigation. McDonald Physics Building, McGill University, Montreal, July 21st, 1905. eye XI. The Effect of High Temperatures on the Rate of Decay of the Active Deposit from Radium. By Howarp L. Bronson, Ph.D.* PRELIMINARY account of the method and some of the results obtained have already been given in the American Journal of Science for February and July 1905. As the method is new and has proved very satisfactory in obtaining the decay curves of radioactive substances, it is here given in some detail. Apparatus and Method. In the ordinary method of comparing ionization currents by an electrometer, the rate of movement of the needle is taken as a measure of the current. In doing this, it is assumed that the capacity of the system and the lag of the needle behind the potential is the same for different rates. These assumptions may, in some cases, be warranted, but they certainly are not when the currents compared differ greatly in magnitude, or when the needle is moving rapidly. In the latter case capacities may be added in parallel, which reduces the rate of movement, but creates the difficulty of comparing capacities. This takes time and is never entirely satisfactory. A still greater difficulty is experienced with the “rate” method, when rapidly changing ionization cur- rents are to be measured, because, from the nature of the method, the observations can be neither instantaneous nor taken in rapid succession. The desirability, therefore, of a more direct and rapid method of measurement is evident. The following method, suggested by Professor Rutherford, has been found by the writer to be very convenient and satisfactory for all radioactive measurements thus far attempted. The theory of the method is as follows :— The arrangement of the apparatus, as seen in fig. 1 (p. 144), differs only from that ordinarily used in having one pair of quadrants of the electrometer connected not only to the testing vessel, but also to earth through a very high resistance. It is evident in this case that, when the key is closed, the ioniza- tion current from the testing vessel will continue to increase the potential-difference of the quadrants until the conduction current through the high resistance becomes equal to the ionization current. Since this conduction current is propor- tional to the potential-difference, it follows that, when equi- librium is reached, the ionization current also will be pro- portional to it. If the electrometer is well adjusted, the * Communicated by Prof. KE. Rutherford, F.R.S, 144 Dr. H. L. Bronson: Eject of High Temperatures deflexions, when small, will be proportional to the same potential-difference of the quadrants, This makes a simple direct-reading instrument. Fig. 1. (| Electrometer Earth Resistances of the order of 10" ohms made of amy] alcohol and carbon on glass were tried, and gave results which com- pared favourably with those obtained by the “ rate’? method. The results, however, were not satisfactory, because the re- sistances did not remain sufficiently constant. This was probably due in one case to polarization, and in the other to temperature changes. Professor Rutherford then suggested the possibility of using an ionization current in place of the conduction current through a high resistance. The possi- bility of doing this is due to the fact that the ionization current through a gas, subject to a constant source of ioniza- tion, is proportional to the potential-difference between the plates when this potential-difference is small. Any strongly radioactive substance which will remain approximately con- stant during the time of a single experiment can be used as the source of ionization. In the present case a very radio- active bismuth plate from Dr. Sthamer of Hamburg was used. The activity of this plate was due to a deposit of the so-called radio-tellurium of Marckwald, and has the advantage of not giving out any penetrating rays. If, for example, radium had been used, it would have been necessary to sur- round the vessel in which it was placed with a shield of lead of considerable thickness, in order to prevent any disturbance by the penetrating rays. Rate of Decay of Active Deposit from Radium. 145 The advantages of this “ constant deflexion’’ method are obvious: deflexions are independent of the capacity, and testing vessels may therefore be interchanged without error, measurements can be made over a wide range without any difficulty, and observations can be taken instantaneously and in as rapid succession as desirable. In some cases they were taken at five-second intervals. The precision of an individual measurement is, however, limited by a slight osciilation of the needle. Repeated attempts have been made to eliminate this by better shielding from external electrostatic action, and by careful attention to contacts, but all to no purpose. The most probable ex- planation seems to be that it is due to exceedingly small and rapid changes in the ionization current itself. This difficulty, however, is not serious, for it seldom causes an error in a single observation of as much as one per cent. In the actual carrying out of the experiments the following arrangement of apparatus was found to be the most convenient and satisfactory :— Testing Vessel. The electrometer was of the ordinary quadrant type, except that it was fitted with a very light needle of silvered mica, suspended by a fine phosphor-bronze wire. ‘The needle was permanently connected to a battery of small accumulators, which kept its potentiai constant. As ordinarily used the needle was kept at a potential of 85 volts, and gave a deflexion of 15 cm. for a potential-difference of 1 volt Pin Mags. 6. Vol. Il. No. 61. Jan. 1906. L 146 Dr. H. L. Bronson: Effect of High Temperatures on between the quadrants. By the use of a finer suspension- wire and a higher voltage on the needle, it was possible to increase this sensitiveness nearly one-hundred fold. The scale was 100 cm. in length and only 180 cm. from the electrometer, but it was possible, by turning it at a slight angle, to make the deflexions over its whole length propor- tional to the potential-difference of the quadrants, with a maximum error of not more than one half of L per cent. In case the current to be measured produced a deflexion larger than 100 em., a modification of this arrangement was adopted. By means of the battery B and the two resistances R, and Re, the potential of the radio-tellurium plate was brought below that of the earth. This reduces the potential-difference between the quadrants by the same amount, and thus makes the deflexions measurable on the scale. In this way ionization currents large enough to produce a deflexion of 150 em. could be measured. At this point a limit was reached, because larger currents than this through the radio-tellurium vessel were not proportional to the potential-difference between the plates. No doubt with a more active substance, such as radium bromide, the currents would remain proportional through a still larger range. Both the radio-tellurium and the plate M above it were covered with very thin aluminium-foil, to eliminate as far as possible any coniact potential-difference ; and the whole was enclosed in a metallic vessel to prevent electrostatic or air dis- turbances. In order to correct for the small contact potential- difference, which always remained, an extra key was introduced between the testing vessel and the electrometer. When both keys were closed the testing vessel and all four quadrants of the electrometer were connected to earth ; when key 2 was open the earth connexion was broken and the testing vessel was connected with the electrometer ;- when key 1 was open the earth connexion of quadrants AA was broken, and the reading then obtained was the true zero, and eliminated any error due to contact potential-differences. The entire apparatus was carefully surrounded by a metallic screen to eliminate any electrostatic disturbance, the keys being mechanically worked from without. Results obtained by Curie and Lanne. In the course of a careful investigation of the rate of decay of the active deposit from radium, an attempt was made to see whether it was permanently changed by hightemperatures. The conclusion arrived at, contrary to that of Curie and Danne%, * Comptes Rendus, exxxviil. p. 748 (1904). Rate of Decay of Active Deposit from Radium. 147 is that temperatures between 700° and 1100° C. do not permanently alter the rate of decay of the active deposit. Miss Gates * showed that when a platinum wire covered with the active deposit from radium is raised to a white heat, the active matter is removed from the platinum wire and deposited on cooler bodies in the neighbourhood. Curie and Danne still further extended our knowledge by showing that the constituents of the active deposit were not equally volatile. In addition, they also found that the rate of decay had apparently been permanently altered by the high temperature. The following table gives some of their results :-— t. 0. 630° 29°3 830 24-6 ~ 1000 21-0 1100 20°3 1250 24-1 1300 ; Disp Here ¢ is the temperature in degrees centigrade to which the active deposit was raised, and @ is the “period,” that is the time in minutes required for the activity to fall to halt value. Curie and Danne also state that the curves were all exponential. They conclude from this that the rate of decay has been permanently altered, and that, as the temperature is raised, the period reaches a minimum, at about 1100° C., and then begins to increase again. It was not unnatural to expect that high temperatures should decrease the period of the active deposit, but it seemed very remarkable that the period should reach a minimum and then increase again when still higher temperatures were used. Results of the present Research. It seemed possible that all the results of Curie and Danne might be accounted for by the difference in volatility of the constituents of the active deposit. In order to see whether this were the case, a copper wire on which the active matter had been deposited was sealed in a piece of glass combustion- tubing, which entirely prevented the escape of any volatile products. By exhausting the tube before sealing, it was found that it would stand temperatures high enough to melt the copper wire inside, that is, temperatures of at least HOO*-C- In all cases where high temperatures were employed the * Physical Review, May 1903. Oey 148 Dr. H. L. Bronson: Effect of High Temperatures on wires were heated in a small electric furnace, made by Dr.C. A. Timme of Berlin. Rate of Decay of Active Deposit from Radium. — 153 deposit, and that the periods of these are twenty-six and nineteen minutes respectively. | Long Exposure. | Short Exposure. Time. | Observed | Calculated Observed Caleulated Value. | Value. Value. | Value. 50 52°9 Soil Son 3°61 60 43-4 43°7 3:19 Syl i Su) BOT 2-75 2°73 80 289 28°8 2°31 2:29 100 185 18°5 1:56 | 1-54 120 116 11:6 101 1:00 140 72 [2 | 64 63 160 4-4 4:3 395 393 180 | 2°63 2°63 | 241 242 200 1°59 1°58 "148 147 220 95 | ‘95 ‘089 089 240 56 CS 57 054 054 260 [Oo ao 032 032 280 19 20 ‘0186 O191 The early part of the curve, which is especially affected by the first rapid change in the active deposit, is still under investigation. When this is completed it may be found necessary to take a value for the period of radium C slightly smaller than nineteen minutes, in order to make the theoretical agree as well as possible with the experimental curve. In any case, the above close agreement between the experimental and theoretical curves, added to the separate measurement of both periods, would seem to furnish conclusive evidence that twenty-six and nineteen minutes are approximately the correct values for the periods of radium B and C respectively. Conclusions. The above experiments would seem to prove :— (1) That temperatures between 700° and 1100°C. do not permanently affect the rate of decay of the active deposit from radium. (2) That radium B, and not radium GC, has the longer decay period. (3) That the previous values of twenty-eight and twenty- one minutes are both too large for the decay periods of radium B and C respectively, and that twenty-six and nineteen minutes are much closer to the true values. In conclusion, I take pleasure in expressing my indebted- ness to Professor Ruthertord for his many valuable suggestions and kind supervision of this work. Macdonald Physics Building, McGill University, Montreal, Sept. 25, 1905. foe bay XII. On the Diffraction Theory of Microscopic Vision. By AtBert B. Porter *. 1. LTHOUGH thirty-two years have passed since Professor Ernst Abbe t proposed his diffraction theory of microscopic vision, it is still to some extent a matter of controversy among microscopists {, and is perhaps less familiar to physicists than its importance warrants. The theory inay be briefly stated in the following form. If a lens 1s to produce a truthful image of an illuminated object, it must have an aperture sufficient to transmit the whole of the diffraction pattern produced by the object ; if but part of this diffraction pattern is transmitted, the image will not truthfully represent the object, but will correspond to another (virtual) object whose whole diffraction pattern is identical with that portion which passes through the lens ; if the structure of the object is so fine, or if the aperture of the lens is so narrow, that no part of the diffraction pattern due to the structure is transmitted by the lens, then the structure will be invisible no matter what magnification is used. Abbe and others have devised a number of interesting experiments § to illustrate the theory, but the complete mathematical development has never been published ||. 2. The particular case in which the object is a transmission erating consisting of alternate opaque and transparent lines may, however, be treated by means of a simple application ot Fourier’s theorem. let a and b be respectively the widths of the transparent and opaque lines on the gratings, and let A be the amplitude of the (monochromatic) light which will be assumed to fall upon the grating at perpendicular incidence ; then the distribution of amplitude in the light passing through the grating will be as shown in fig. 1. The function repre- sented by this curve may be developed in a cosine series by means of the formula MTEL ; aale 27H ee) — Sho — b, Cos Rime? +- b; COS + ef @ -- Din COs i — eeee Cc C , ; One MTEL in which bn = ‘ f(a) cos — dx. * Read before the American Physical Society, April 22, 1905. Com- municated by the Author. + Archiv fiir mkroskopische Anatomie, ix. pp. 418-468 (1837) ; Gesam- melte Abhandlungen, i. pp. 45-100 (1904). t+ Gage on The Microscope, 9th edition, p. 21 (1904). § Mueller-Pouillet’s Lehrbuch der Physik, 9th edition, II, 1. p. 712; Lewis Wright's ‘ Light,’ 2nd edition, p. 198. || Mueller-Pouillet, ¢d., p. 703. The Diffraction Theory of Microscopic Vision. 155 Fig. 1. | ‘4 Amplitude Distance along gratin at reght angles Lo the dines. In the case under consideration : a fe) — A trom 2— O00 o— a a =0 from v= 5stow=,5 +, =A from v#= — 5 +e tov=atb, amd 6a. Hence a+b MTL MTL pe “a cos Ha Oe Wee age da | +b oth a+b 2 INTE 2A. mere TPG aL Bal gee Bi ye an +6 It follows that 1 9Aa aN ain TO QA Dara & (1) = ) = —— SII ie ah eG fl aR Doyiye 2 Dar QO and LNG TR Ta Ts 2Ag ia 2ira Qira = —— sin - . COS a) 6 COS) 4 +6 - oT ath Qe bi ar wab ath gee mira MTL SE eh . cos —— + MT ath ath >) 156 Mr. A. B. Porter on the Now the ordinary theory of the transmission grating shows that, in the case under consideration, the amplitude of the light in the central image is Aa 9 R A = 5) e ° e . e (3) a+b and that the amplitude in the mth spectrum is Ae ey aa! mar A comparison of (2) with (3) and (4) shows that the first term in (2) represents the amplitude in the central image, while the coefficient of the cosine in each succeeding term represents the sum of the amplitudes in the two spectra of corresponding order. It thus appears that a diffraction- grating performs a double process of harmonic analysis. In the first place it analyses the incident radiation according to wave-length in the well-known manner, distributing the coiours in order in each spectrum ; in the second place, as shown in equations (2), (3), and: (4), it analyses the distribution of wave-amplitude in its own plane, distributing the Fourier components of the amplitude curve in order among the successive spectra. 3. We may also look at the matter from another point of view. The curve drawn in fig. 1 not only represents the distribution of wave-amplitude in the plane of the grating, but is also the curve which shows the distribution of transparency over the surface of the grating itself, the axis of w representing zero transparency, 7. e. complete opacity, and the height A perfect transparency. (To avoid cireum- locution, transparency is defined throughout this paper in terms of the amplitude of the transmitted light, not in terms of intensity.) Hquation (2) is evidently the development of this transparency curve as a series of harmonic distributions of transparency. The non-periodic term corresponds to a surface of uniform, but imperfect, transparency ; while each periodic term represents a surface covered with equidistant parallel bands of varying transparency. Supposing these bands to run perpendicular to the plane of the paper, the distribution of transparency in them wiil be indicated by the ordinates in fig. 2, where the axis of w again represents perfect opacity, the ordinate 6 a certain degree of transparency, and the ordinate — B represents an equal degree of what we may term negative transparency, 2. é., transparency coupled with a half- period change of phase in the transmitted light. . These results were obtained by directly comparing the deflexion of the rays from an active wire under exactly the same conditions as in the radium experiment. The results obtained are thus in general agreement with those to be expected on the views held by Bragg and myself. There can be no doubt that the « rays from radium are complex, and consist of « particles which are unequally deflected in a magnetic field *. Explanation of M. Becquerel’s Experiment. We are now in a position to explain why the trace of the a rays from radium in a strong magnetic field is not altered when the radium is covered with layers of aluminium-foil. * This br oadening of the pencil of rays ina magnetic field has been also experimentally ‘observed ina recent, paper by Mackenzie (Phil. Mag, Nov. 1905). Properties of the a Rays from Radium. 173 First, consider the experiments with an uncovered thick layer of radium. The outside edge of the traces obtained on the plate by reversal of the field will be due to the most deflected rays which are just able to produce a photographic impression on the plate. The inner edge of the traces will correspond to the rays which are least detlectable, 2. e. which are expelled with the greatest speed. Now suppose the radium is covered with any thickness of foil, provided it is less than that required to cut off completely the photographic effect of the « rays. All the a particles will be reduced in speed, and the more slowly moving ones willlose their photographic effect. The edge of the deflected trace will, however, be due as before to the most deflected rays which are just able to produce an appreciable photo- graphic effect. ‘These rays will have exactly the same velocity as the corresponding rays in the first experiment, and conse- quently the outside edge of the photographic traces will be continuations of that observed in the first experiment. This holds equally well whether the experiments are made in air or in a vacuum. Since, however, the more penetrating rays are reduced in velocity by their passage through aluminium, the inside edge of the photographic traces will be displaced outwards. This effect will be extremely difficult to detect unless a very narrow beam of rays is employed. In addition, the un- doubted scattering of the rays in air (which will be discussed later) will tend to obliterate this etfect in experiments similar to those of M. Becquerel, which were made in air at atmospheric pressure. it is thus seen that the interesting experiment recorded by M. Becquerel is satisfactorily explained on the view that the particles decrease in velocity in passing through matter; and, taken in conjunction with my own experiments on the reduction of speed of the rays from radium C in passing through matter, affords an indirect but striking proof of the general correctness of the theory of the absorption of « rays put forward by Bragg. It is not possible to take the position that the rays, emitted from an active wire coated with radium C, do not exist in radium in equilibrivm; for apart from other evidence, McClung (supra, p. 131) has shown that the range of ionization of the rays from an active wire coated with radium C is identical with the range of the corresponding rays in radium measured by Bragg and Kleeman. 174 Prof. E. Rutherford on some Increase of the Radius of Curvature of the Path of the Rays in Air. We have seen that M. Becquerel early drew attention to the fact that the radius of curvature of the trace of the a rays obtained in air increased with increase of distance from the source. Assuming that the rays were homogeneous, he suggested as an explanation that the mass of the @ particle increased as it passed through the air. Proceeding on these assumptions, it is seen that the « rays from each product present in radium must increase in curvature with the distance of air traversed. In order to test this point definitely, 1 made the following experiment, with an active wire coated with radium C as a source of rays. Using the same apparatus employed to obtain the photograph in fig. 1, the part of the active wire on one side of the mica screen was covered with a sheet of metal of sufficient thickness to absorb all the a rays. The apparatus was filled with air at atmospheric pressure, and the trace of the rays obtained in a uniform magnetic field is seen in fig. 3 (PI. IV.). After 40 minutes, the metal sheet was transferred to the other side of the screen and the apparatus was then exhausted. The trace of the rays then obtained in a vacuum is shown by the two narrower lines in the same figure. There is a striking difference between the two pairs of lines obtained in air and in vacuum. The air-bands are more deflected than the latter and in addition are broader. This experiment conclusively shows that the a rays from the active wire decrease in radius of curvature and" consequently in velocity after passing through air. The greater width and lack of definition of the air-lines have been noticed in all other experiments, and show evidence of an undoubted scattering of the rays in their passage through air. The slight shift of the vacuum-lines in the figure, relative to the air-lines, was due to an accidental displacement of the plate in transferring the metal sheets in the middle of the experiment. Experiments are in progress to see whether this scattering also occurs in the passage of the rays through a solid substance. This scattering of the rays probably also occurs with aluminium, but it would not be evident in the experiments where the layers of foil are placed over the active wire between the source and the slit. Since the rays from the other products of radium imall probability behave in the same way as the rays from radium C, we see that this result of the decrease of the radius of Properties of thea Rays from Radium. BLS, curvature of the path of the rays in air is in contradiction to the hypothesis of M. Becquerel that the value of e/m decreases with distance from the source. We have seen, however, that this conclusion of M. Becquerel is based on the incorrect assumption that the rays are homo- geneous. Taking into account the complexity of the « rays from radium, the results observed by M. Becquerel receive a simple explanation without the necessity of assuming that the value of e/m either increases or decreases with distance. An explanation along these lines was given last year by Bragg and Kleeman. Without entering into intricate calcu- lations, the general reason of the increase of the radius of curvature of the path of the rays with distauce of air traversed can easily be seen. At a distance of 2 cms. from the source, for example, the outside edge of the trace is due to the most slowly moving particles, which are just able to produce a photographic impression after traversing 2 cms. of air. The inside edge is due to the most penetrating rays, viz. those from radium O, whose velocity has been reduced somewhat by passing through the 2 cms. of air. Suppose we consider the trace of the rays distant 3 cms. from the source. As before, the outside edge of the trace is due to particles which are just able to produce a photographic effect after traversing 3 cms. of air. These particles are thus projected initially with a greater velocity than those which were only able to affect a plate for a distance of 2 cms. The average velocity of the « particle along its path is consequently greater than for the corresponding case for a distance of 2 cms. The outside edge of the trace will therefore be deflected through a smaller distance than would be expected if the average velocity were the same in the two cases. The radius of curvature of the outside edge of the path will consequently increase with increasing distance. Quite a contrary effect should be observed on the inside edge of the trace, which is produced by the @ particles of greatest velocity escaping fromthe radium. This velocity is, as we have seen, reduced by the passage through air, and consequently the average velocity of the a particles, which traverse the path of 3 cms.,is less than for the path of 2 cms. The inside trace should theoretically show evidence of de- creasing radius of curvature. This would have the effect of contracting the natural width of the trace unless the scattering of the raysin air masks it experimentally. Quite apart from 176 Prof. McCoy on the Relation between Radioactivity this, it can easily be shown, from calculations based on the numbers given in my last paper on the retardation of velocity of the @ particles in their passage through air, that the decrease of curvature of the outside trace more than com- pensates for the increase of curvature of the inside trace. The net result of these two opposing processes is to increase the radius of curvature of the path, deduced from measure- ments on both edges of the trace, to about the extent observed by M. Becquerel. Summary of Results. The following points have been brought out in this paper:— (1) The rays from radium in radioactive equilibrium are complex and consist of « particles projected with different velocities. (2) The @ particles decrease in velocity in their passage through air and through aluminium. (3) The absence of increased deflexion of the rays from a thick layer of radium after passing through alu- minium, observed by M. Becquerel, is a necessary consequence of the complexity of the rays. (4) The decreasing curvature of the path of the rays in air, observed by M. Becquerel, is also a necessary consequence of the complexity of the rays. (5) There is evidence of a distinct scattering of the rays from radium C in their passage through air. A full discussion of the connexion between the ionizing, phosphorescent, and photographic actions of the a rays will be reserved for a later paper. Macdonald Physics Building, McGill University, Montreal, Nov. 15, 1905. XIV. The Relation between the Radioactivity and the Compo- sition of Uranium Compounds. By HERBERT N. McCoy, Asst. Prof. of Chemistry, University of Chicago™. f ere early determinations + of the radioactivity of pure uranium compounds showed but a roughly approximate proportionality between the activity and the percentage of uranium. The methods used did not take into account the absorption of the alpha rays, to which ionization is almost * Communicated by the Author. Read before the Amer. Phys. Soc., Chicago, April 21, 1905; Abstract, Phys. Rev. xx. p. 381 (1905). + Mme. Curie, Thése, Paris, 1903; also Chem. News, lxxxviil. p. 98 (1903). McCoy, Ber. d. Chem. Ges. xxxvii. p. 2641 (1904). and Composition of Uranium Compounds. 177 wholly due, by the uranium compound itself. If this absorption occurs according to the simple absorption law, it is readily shown* that 2°303 s 1 ee w Jog 1—@ where /, is the absorption coefficient for unit weight ou unit area ; wv is the ratio of the observed activity of any very thin film of a uranium compound to that of a film of the same substance sufficiently thick to be of maximum activity ; s Is the common area of the films ; and w is the weight a the thinner film. ‘he films were from ‘001 to *04 mm, in thickness, the thicker films showing maximum activity. hk, is a good constant for any pure uranium compound. If the observed radioactivity of one sq.cm. of any film of maximum activity is called « it is shown 7 that = == 2ha a. where hy is the total activity of 1 g. of the uranium compound. The ratio, K, of the total activity, so determined, to the uranium content of the compound is a constant, w ‘ithin the limit of error of + 1 per cent., and represents the total alpha ray activity of 1 g. of pure uranium, independently of its form of chemical combination. If @ is taken as unity for pure U207 & is equal to 791. This means that the total activity of 1 g. of pure uranium is 791 times that of 1 sq. cm. of a layer of pure U;QOg sutticiently thick to be of maximum activity. Preparation of a Standard of Radioactivity. The above results were obtained by means of compounds prepared directly from “ chemically pure ” uranium nitrate as furnished by the firm of CU. A. F. Kahlbaum. Since all uranium ores contain radium f, it was necessary to determine with certainty whether the material used was free from radium in amounts sufficient to appreciably alter its activity. This was done by starting with a uranium ore, which of course contained the maximum of such impurities, and con- tinuing the process of purification until no further change of activity occurred. The activity of the U,O, so prepared did not differ by a measurable amount from that of my old “ standard ” oxide, which had been made by direct ignition of Kahlbaum’s nitrate. The measurements of the activ ity were made electrically in the manner previously described. The error of comparison was about 0°2 per cent. * McCoy, J. Amer. Chem. Soe. xxvii, p. 391 (1905). T McCoy, doc. cit. t McCoy, Ber. d. chem. Ges. xxxvil. p. 2641 (1904). Boltwood, Am. J. Sci. xviii. p. 97 (1904); Phil. Mag. [6] ix, p. 599 (1905). Phils Mag 36. Vol. 11. No: 61. Jans 1906. N 178 Prof. McCoy on the Relation between Radioactivity The details of the process were as follows :—29 @. of pitch- blende (from the Wood Mine, Colorado), containing 60 per cent. of uranium, and being about 25 times as active as pure U;O0., were thse in nitric acid and the solution evaporated to dryness. The residue was taken up in water and filtered, and the filtrate added to an excess of ammonium carbonate solution. The solution was boiled and filtered from the pre- cipitate containing iron, &e. Copper, lead, &c. were removed from the filtrate by treatment with ammonium sulphide. The uranium was precipitated from a small portion of the filtrate by prolonged boiling. Ignition of the precipitate of ammonium uranate gave U,O; which was 4°9 per cent. more active than the standard oxide. The treatment up to this point had therefore removed all but about 2 per cent. of the radioactive impurities originally present in the ore. To the main portion of the solution was added a solution of 2 g. of barium chloride. The solution was heated to boiling and a slight excess of ammonium sulphate added. The barium sulphate, so formed, was filtered out. It was freed from traces of uranium by treatment with hydrochloric acid. It was still about as active as uraniumoxide. That the activity of the barium sulphate was due chiefly to radium and not to UX was shown by the facts, first, that the rays were almost wholly absorbed by a thin sheet of aluminium, and second that the activity increased in intensity with time. The treat- ment of the solution with barium chloride and ammonium sulphate was repeated twice. The second lot of barium sulphate was but 0°05 as active as the first, while the third lot was practically inactive. The U;Os prepared from the solution after the third precipitation differ ed in activity from the old standard U;O, by only 0-15 per cent. This difference is just about the limit of accuracy of the method of com- parison. Further treatments with barium salts did not lower the activity of the uranium oxide. These results show that radium and other active bodies occurring in uranium ores are easily removed. There is therefore no doubt that the uranium oxide finally obtained was free from such active impurities, in appreciable quantities. In addition it is established that the material previously used * in deter- mining the absorption coefficients and activities of uranium compounds was also of the same high degree of purity fF. * McCoy, J. Amer. Chem. Soc. xxvii. p. 391 (1805). + The work on absorption coefficients of pure uranium compounds is being greatly extended by Mr. H. M. Goettsch, working in this laboratory ; the results previously announced are being fully confirmed. Attempts by Mr. Goettsch to lower the activity of the Kahlbaum uranium nitrate, used in the preparation of the standard oxide, by treatment with barium salts, were without effect. and Composition of Uranium Compounds. 179 Many persons have used a definite portion of uranium oxide as an empirical standard of radioactivity. I believe it is now possible to accurately define a standard of activity that may readily be reproduced with an accuracy of at least a few tenths of one per cent. ‘To do this, ordinary uranium salts are first to be purified by successive treatments with ammonium carbonate, ammonium sulphide, and barium salts in the manner described. In converting the precipitated ammonium uranate into the oxide, LOM iG 1s necessary to ignite in a stream of oxygen, since Zimmermann has shown * that ignition in air causes slow loss of oxygen and finally the formation of a lower oxide. The standard film of oxide is prepared by grinding in an agate mortar 0°8 to 1°0 g. of the substance with a little freshly distilled chloroform until the former is reduced to an impalpable powder. This is then stirred up with about 15 c.c. more of chloroform and poured into a shaliow metal dish about 7 em. in diameter +. The dish is covered until the solid has settled. The chloroform is then allowed to evaporate spontaneously. The U3Qgis left as a very uniform black film, which adheres well to the dish. Such films may be used daily con months without deterioration. They must obviously be protected from dust when not in actual use. The total activity of 1 g. of uranium is, as has been said, 791 times the observed or “surface activity of each sq. cm. of such a film. I have shown { that the total activity, 4,, of any uranium compound can be found in a second way which does not involve the determination of the absorption coefficient. The ratio of the activities of two films is the inverse of the ratio of their respective times of discharge of the same electroscope through the same range cf the scale ; corrected, of course, for the small natural leak. If a is this ratio for any thin film compared with a standard film of U3Qg of equal area s, and of sufficient thickness to be of maximum activity, and if the activity of 1 sq. cm. of the standard film be taken as unity, then the observed activity of the first film will be sa. If the first film be infinitely thin, there would be no absorption, and therefore sa= 4 kw or Ww J Se a * Ann. Chem. (Liebig), cexxxii. p. 276 (1885). + I have used tinned lids intended for jelly glasses. These were cheaply obtained in large quantities; after being used once, they were discarded to avoid the effect of excited activity which could not be easily removed. t J. Amer. Chem, Soc. xxvii. p. 402 (1905). NGS ~_ b> tH 180 Prof. McCoy on the Relation between Radioactivity The theoretical value of = for an infinitely thin film may be re eadily found by plotting the values of this ratio for thin films of various weights and finding, by a small graphical extra- polation, the zero value. This value may be designated w on & ’ a7 9 f au Therefore k= a (G : 0) The values of k; as found by this second method agreed well, in the case of pure uranium compounds, with those as deter- mined by the first method. The Radioactivity of Uranium Ores. Having found satisfactory methods of determining accu- rately the total radioactivity of pure uranium compounds, these methods have now been applied to the further study of uranium ores. The theory that radium is a disintegration product of uranium demands that all uranium compounds sufficiently old should contain radium in amounts directly proportional to their uranium content. It should therefore be found that the total radioactivity of any uranium ore should be directly proportional to its percentage of uranium. This was, in fact, found to be approximately true for twelve ores from widely different localities *. The average deviation from the mean value of the ratio of activity to percentage of uranium was 7‘1 percent. The determinations of the activity, in the above cases, were made upon equal weights of ore without due allowance being made for difference of absorption. The method of determining total activity, which depends upon a determination of the absorption coefficient of the substance, can he applied only to those substances for which the absorption coefficient is a true constant. This condition will obviously be fulfilled only by substances the radiations of which are homogeneous. If we disregard the beta rays, the ionizing effect of which is negligible, the radiation of every pure uranium compound is homogeneous. For every such compound the absorption coefficient is a constant. Uranium ores all contain radium and'its numerous active transformation products. The alpha rays of these bodies have quite different penetrating powers. It was actually found, as anticipated, that the absorption coefficient of ores was not constant, but varied with the thickness of the film. While * McCoy, Ber. d. chem. Ges. xxxvil. p. 2654 (1905). and Composition of Uranium Compounds. 181 the first method of calculating the total activity was therefore excluded, in the case of ores, there was, on the other hand, no theoretical objection to the application of the second method. Only the purest minerals are perfectly homogeneous. Since the ordinary method of powdering might involve a loss of some dust of greater or less activity than the average for the ore, the crushed samples were moistened with pure redis- tilled aleohol and ground in an agate mortar toa very smooth paste, The alcohol was then allowed to evaporate. The powder so obtained was finer and more uniform than could be obtained by dry grinding. The films were prepared in the manner previously described. As suspending liquids I used for pitchblende, chloroform ; for gummite, alcohol; and for carnotite, water. The uranium in pitchblende and gummite was determined as previously described *, by tre eating the nitric-acid solution of the ore with an excess of sodium carbonate and precipitating the uranium from the neutralized filtrate by means of sodium hydroxide Tf. The sulphuric acid solution of the uranium precipitate was reduced with zine and titrated with perman- ganate. In the analysis of carnotite, vanadium was first removed by treating the dry sample repeatedly with dry hydrogen chloride gas t. Duplicate analyses were made in each case. Five different ores have been studied as follows :— TABLE ie ee Mineral. Teoenlian ees 1. Pitchblende. Colorado. oll 2. Pitchblende. Bohemia. 40°5 3. Pitchblende. Unknown. 61:1 lo 4. Gummite. North Carolina. 04-7 | 5. Carnotite. Colorado. 39°9 | None of these ores contained more than traces of thorium. * Ber, d. chem. Ges. xxxvil. p. 2641 (1904). 7 Brearley, Analytical Chemistry of Uranium, 1903, states that uranium is not completely precipitated by sodium hy droxide. This is true only when the latter contains carbonate, as it invariably does unless special precautions are taken. I have used sodium hydroxide from which the small amount of carbonate originally contained was removed by the addition of a little calcium chloride solution. { Hillebrand, Amer. J. Sci. x. p, 135 (1900), 182. Prof. McCoy on the Relation between Radioactivity The results are given in Tables II. to VI. Column two gives the weight, w, of the film; column three gives the ratio, a, of the ¢ activity of the film of the mineral to that of the standard film of pure U;O, of equal area. The fourth column contains the values of = The accompanying curve represents Table II. and illustrates the method of determining ~) graphically. a/o orp oe LTE PL CO 0-05|__ a Ar i eS i Ree 0-03 Ee ae 002 Le Rey a 0-01 $$} w Ol 0-2 03 Or4 TABLE [1.—Pitchblende, No. 1. | | | Meng W. a | oon | | H | OC | | | | z ag Sala | | | EaBlieg ater ce | 3922 2:27 1887 | [DEAS Meee 3443 2-818 1294 : (peso bey mae 2458 2-504 0982 | Zee aa 1640 2:140 0766 i eel ee. 1135 1-730 0656 Boy etc ustae: 0943 he 83 0615 Peg S-restaete! 0741 1-276 0581 SF evista gaa ‘0523 | “976 "0536 OF Saar | 0466 | "860 | 0542 | | | (“) = 472 | | | | aso and Composition of Uranium Compounds. 183. TaBLE [L1.—Pitchblende,:No. 2. A Ww. a. = i a se ee 3056 2-126 | “1438 A ah, ©. | 3026 2:220 1363 i Be eee 2412 2-130 11383 eee | 1488 1673 | “0889 ) es hear a | “1346 | 1-616 | 0833 HGH dete. | ‘0837 1-170 ‘0716 SG Se | ‘0657 | -938 ‘0701 SS eee | ‘0631 | -937 | ‘0673 te i eg 0470 | 725 | 0648 1110) ae eee ‘0407 ‘637 | 0638 | (*) — 0594 | aso Taste L[V.—Pitchblende, No. 3 *. w W. a, ae a etre... ‘9060 2-924 | “3099 (2 Doan D007 2-920 1715 Be oe: 2207 2-675 | 0825 ae... es 1559 | 2-275 ‘0685 CYS, -:.,... “0835 | 1-582 ‘0541 Cee... ‘0706 1°343 0526 | ae ‘0618 1-235 ‘0501 ee | ‘0580 | 1135 ‘0511 0 eer ‘0360 ‘B15 "0442 10 en | (0382 ‘714 ‘0465 = | 0273 | 584 | ‘0467 | (*) —-0400 a/0 TaBLE V.—Gummite, No. 4. | | | | u ad. | bi | a | i\ CARS ee ee) 2764 2-318 | "1192 Le “1810 1-958 | 0924 | 2 AREA! ‘0704 1-173 | ‘0600 AL, Je ‘0686 1-143 ‘0600 Deere: 0654 1-099 "0595 Cope ‘0570 ‘965 0591 fe ee ei: 0472 "862 | 0548 | (‘") — 0446 | ajo * The activity measurements represented by Table IV. were made by Miss Emma Carr, to whom I wish here to express my thanks. 184. Prof. McCoy on the Relation between Radioactivity TABLE VI.—Carnotite, No. 5, | w | Ww. a — | | a alee oe ‘3704 - 1:829 | 2025 Ora aay ae. | 2634 1-765 | 1493 BL hms all ‘0949 1-094 | ‘0868 1 ls ee | 0477 644 | (O74 ae Be jace he bees | “0423 “574 | ‘0736 Base aloe ‘0172 279 ‘0631 | ey, 0612 | | a Table VI. yy ere the ‘otal activity of unit mass of the mineral as calculated from / fw ky — 2s fh 2) © a /0 The area, s, was equal to 39°82 sq.cm. Pis the weight of uranium in 1 g. of ore. TABLE VII. w 10a EEC cok a a aa Pr es | ; (Fa seer 04 | 1687 ayn | 330 re ee 0594 1341 403 332 Die 0400 | 1990 611 326 tek | 0446 1786 ‘DAT | 397 D hese: | 0612, | 1301 | 399 | 326 | | | | Mean 328 The value of Pp 1S very nearly constant and is equal to 3280 for uranium minerals. The corresponding constant for pure uranium compounds is 791. The ratio of these two quantities is 4:15. That is, for equal uranium content the ores are 4°15 times as active as the pure compounds. If radium and all of the other radioactive substances in uranium ores are genetically related to uranium, it should be found that the amounts of each such substance in the ore, and therefore also the total radioactivity, should be directly proportional to the uranium content, provided the mineral is sufficiently old to have reached the equilibrium condition. The results just described seem, therefore, to confirm the and Composition of Uranium Compounds. 185 conclusions drawn from my preliminary experiments, viz. that uranium is the parent not only of radium, but also of ail the other active substances which accompany it. Apparently the experimental error of the present work is about + 1 per cent. ; but it may be somewhat greater. In consequence there may be comparatively small amounts of active bodies (polonium, actinium, &c.) which are not derivatives of uranium. But as far as radium and its known products are concerned, the case is clear ; for, in ate to the evidence I have presented, it has been shown by Boltwood* that the quantity of radium emanation obtained ‘from various uranium ores is strictly proportional te the weight of uranium in the sample. In addition Soddy fT has finally obtained radium emanation from a quantity of pure uranium nitrate which two years previous had been entirely freed from radium and its products. It is true, however, that the amount of emanation so obtained was much smaller than one should expect if radium is produced directly from uranium Xf. It is possible to calculate, from data here presented, the relative activity of radium and uranium, on the assump- tion that all of the excess activity of uranium ores is due to radium, together with its products. These bodies, collectively, are 4°15—1 or 3°15 times as active as that mass of uranium with which they are associated. Now Rutherford and Boltwood § have shown that one part of radium is in equi- librium with 1°35 x 10° parts of uranium in ores. Therefore mois: (with its products) 1s 3°15 x 1-35 x 10°= 4-25 x 108 times as active as uranium. ‘The value usually accepted is only half as great as this. This ratio may also be calculated from other data. Rutherford and McClung || have found the maximum saturation current due to 1 sq. cm. of a thick layer of U;0, to be about 455 x 10-® ampere. Therefore the total current due to 1 g. of uranium is 791 x 4°5 x 1078 = o°6 xX 107“! ampere]. The total current due to 1g. of radium (plus products) is 1:2 x 10-3 ampere **. From these results it follows that radium is 3°3 x 10° times as active as uranium yt. This estimate may be too caelae. cu. + Phil. Mag. [6] ix. p. 768 (1905). i Ore Boltwood, Amer. J. Sci. xx. p. 239 (1905). é Amer, J. Sci. xx. p. 55 (1905). || Phil. Trans. A, 1901, p. 25. {| McCoy, J. Amer. Chem. Soc. xxvil. p. 402 (1905). ** Rutherford, * Radioactivity,’ 1904, p. 156. +t The direct comparison of the activity of a thick film of pure U,O with that of a minute (Imown) quantity of a pure radium salt will doubt- less give a more reliable result. 5 186 | Notices respecting New Books. low, since the activity of the radium, as given above, pro- bably does not include that due to the slowly changing products radium E and radium F. On the other hand, the estimate of 4°25 x 10°, made by the first method, may be too high owing to the presence of one or more other radioactive bodies intermediate between uranium and radium, in the series of uranium transformation products. The existence of such intermediate substances has been suggested by Soddy * in explanation of the slowness with which radium emanation is produced by uranium. Possibly emanium and its product + actinium are among these supposed intermediate substances. Chicago, August 1905. XV. Notices respecting New Books. Transactions of the International Hlectrical Congress, St. Louis, 1904. Published under the care of the General Secretary and the Treasurer. Printed by J. B. Lyon Company, Albany, N.Y., 1905. Vol. I. pp. 879; Vol. IL. pp. 984; Vol. IIL. pp. 9380: XHESE handsome volumes, embodying the work of the Inter- national Electrical Congress at St. Louis, will form a valuable reference book ake for the pure physicist and the electrical engineer. The scope of the Congress’s activity was a very wide one, as may be gathered from the following list of Sections :— (A) General theory (including mathematical and experimental papers): (B) General applications; (C) Electro-chemistry ; (D) Electric power transmission ; (E) Electric lighting and distri- bution ; (F) Electric transportation ; (G) Electric communication ; (H) Electrotherapeutics. As might have been expected, the papers contributed vary a good deal as regards both length and importance, some being little better than brief general notes, while others are very thorough investigations of permanent value to the scientific worker and engineer. Vol. I., which contains the papers contributed to Sections A and B, should strongly appeal to the pure physicist. It opens with a highly interesting paper by Prof. H. T. Barnes on the Mechanical Equivalent of Heat, and contains a large number of contributions to the ionic theory by leading workers in this branch of science. The papers in Section B are rather more technical, there being, in addition to some which deal with hysteresis, magnetic viscosity, electrolytic rectifiers &c., others devoted to alternators, induction motors and single-phase commutator motors. Volume II. contains the Transactions of Sections C, D, and HE. In Section C, we have valuable papers on * Loc. cut. + Marckwald, Ber. d. chem. Ges. xxxvill. p. 2264 (1905). Notices respecting New Books. 187 electrochemical theory, including one by Prof. T. W. Richards, “The Relation of the Hypothesis of Compressible Atoms to Electro-Chemistry,’ and others on electrolysis and various practical applications of electro-chemistry. The papers in Section D will be of great interest to engineers having to deal with high-voltage plants and transmission lines, as this subject is very fully discussed by many leading authorities. Section E is, perhaps, not quite up to the standard of those already noticed, as although it contains a few papers of real merit, there are others which deal in vague generalities without conveying any solid information. Vol. III. embraces Sections Ff, G,and H. In Section F, the problem of railway electrification naturally claims the first place, and the single-phase system comes in for a good deai of discussion. In Section G, we have papers on high-speed telegraphy, wireless telegraphy, and modern telephone exchanges. Section H will appeal to medical men: it contains papers on the uses of X-rays, photo-therapy and radio-therapy. Although the work as a whole is well printed and illustrated, it seems a pity that the discussions on the various papers should have been put into very small type, so small as to make it some- what trymg to the eyes; the larger type used for the papers might have been retained without unduly swelling the size of the volumes, and it would certainly have been less trying to the reader. Anleitung zu wissenschaftlichen Beobachtungen auf Reisen. Heraus- gegeben von Professor Dr. G. von Neumayer. Dritte Auflage. Tieferungen 1 & 2. Hannover: M. Janecke, 1905. THe first two parts of the third edition of the above work contain articles on the determination of latitude and longitude (by L. Ambronn), on topographical survey work (by P. Vogel), and on anthropology and ethnography (by F. vy. Luschan). The last-named article contains many useful suggestions and is very explicit in its directions to the would-be explorer. The work is to be completed in about 12 parts. Annuaire pour VAn 1906. Publié par le Bureau des Longitudes. Avec des Notices scientifiques. Paris: Gauthier-Villars. Prix: Lfr.50¢. Pp. iv+712+ 4.1614 B.184+C08+D.41. THis wonderful little annual contains, in addition to the usual astronomical, physcal, and physico-chemical tables, a special illustrated article by M. G. Bigourdan, entitled “Solar Eclipses. Brief instractions regarding the observations which may be made during them.” Jn view of the interest manifested in the recent solar eclipse, the article is a timely and simple exposition of the subject with which it deals. Casey XVI. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from vol. x. p. 707. | November 8th, 1905.—J. E. Marr, 8c.D., F.R.S., President, in the Chair. (Ee following communications were read :— 1. ‘The Coast-Ledges in the South-West of the Cape Colony. By Prof. Ernest Hubert Lewis Schwarz, A.R.C.S., F.G.S. The following coast-shelves have been recognized by the author in Cape Colony :— Name of shelf. Wester, Midlands. Eastern. Native Territories. Feet. Feet. Feet. Feet. Cyphergat ...... 5000-6000 ? 5000-6000 ? 5450 ? — Sterkstroom ... 3500-4000 ? 4000 ? 4406 ? 4500 ? Kentani snes a lestceces 8) ow we cane 2500 2500 DerWViluet. 2 i. 1500 1000 1500 1500 | Uplands se: >. 2 700 463 467 600 Bamboes Bay... 50-100 200 151 50-200 Sea-level......... — — — — A Conhas it~ esex as 600 The most striking of these is the Upland sheif, which extends from Caledon to Port Elizabeth. It is cut by deep gorges into narrow ridges or ‘ruggens, but at a height the level tops of these ridges can be observed. The surface is in places covered with superficial deposits, cemented boulder - deposits, gravels, and sandy clays, hardened at the surface into ironstone or freshwater quartzite. The author considers that this shelf cannot have been formed as a peneplain, but by marine denudation. On the 150-to-200-foot plateau there are deposits with marine shells, and in a depression on its top the evaporation of rain-water produces a large quantity of salt. The rock-shelf under the Cape Flats appears also to have been cut by the sea. The Agulhas Bank seems to consist of a succession of ledges, but it is not known whether further shelves extend beyond its margin. Taking the ledges together, the continent would appear to have been subject to lifts of 600 or 700 feet, with intermediate halts and setbacks. The author introduces the term ‘absolute base-level of erosion’ ‘to express the ocean-floor, including the shelf or level of erosion cut by the surf and off-shore currents that came near the water’s edge when the depression of the present land- masses commenced.’ The author compares the shelves of Cape Colony with those described on the European and American sides of the North Atlantic, and he places the ‘absolute base-level of erosion’ at 12,000 feet in North America, 8000 feet in Europe, and 1200 feet Geological Socvety. 189 in South Africa. With these varying heights he correlates the topography of the bordering continents—the sharp divides, open river-valleys, permanent rivers and deltas, of Kurope and America, where the movement has been downward and has almost reached bottom, in contrast with the flat undenuded divides, the steep, narrow gorges, the waterfalls, and the rocky river-gates, of South Africa, which is on the upgrade and probably near the top. 2. *The Glacial Period in Aberdeenshire and the Southern Border of the Moray Firth. By Thomas F. Jamieson, F.G.S. One of the most interesting features in the Glacial geology of Aberdeenshire is the Red Clay found along the eastern coast of the county. It consists of red sediment brought by ice flowing along the coast from south to north, which also carried rocks from the coast between Montrose and Lunan Bay. The clay is some- times finely laminated ; at other times it is mixed with stones; and at times, again, contains esker-like mounds of gravel. It includes fragments of Crag-shells and of Mesozoic limestone. The purer masses of clay seem to have formed in a sheet of water lying in front of the ice, between it and the land, during the retreat of the Aberdeenshire ice, and at a time when the coast was submerged beneath water to a level exceeding 300 feet above the present coast-line. Evidence of the northward motion of the ice is given from striz, the transport and removal of flints, and the bending-over of the edges of folia of gneiss. ‘The red clay is underlain by a grey clay, and sometimes covered by a similar one. ‘The author has recently discovered remains of a still older, dark indigo in colour, and containing small fragments of sea-shells. This has, however, been swept away in most places by subsequent ice-movement. In Banffshire a fine dark clay seems to have been formed under the same circumstances as the Red Clay of Aberdeenshire. The only evidence of warm intervals in this part of Scotland is that inferred from the melting-away of the masses of ice, which preceded and followed the deposition of the Red Clay and the shell- beds of Clava. Gn the southern border of the Moray Firth the author gives examples of Glacial marking on the rocks, and refers to the transport of boulders, including a huge mass of Oolitic rocks 40 feet thick, a mass of clay once considered to be an outlier of lias, ‘pipe-rock,’ and the fossiliferous Greensand débris at Moreseat, now considered to have been transported by ice. The ice appears to have been 4000 to 5002 feet thick about Inverness, in order to reach to and overflow Mormond in North-Eastern Aberdeenshire. The terraces of gravel tound at decreasing heights on the Spey, near Rothes, seem to have been formed during stops in the retreat of the ice. Arctic shells of deep-water type, found 190 Geological Society :— in silt-beds south of Rattray Head, give evidence of a period of considerable submergence; but the recurrence of an ice-sheet appears to have destroyed most of this evidence, as is seen in a section at King Edward. November 22nd.—J. E. Marr, Se.D., F.R.S., President, in the Chair. The following communications were read :— 1. ‘Ona New Specimen of the Chimeroid Fish, J/yriacanthus paradoxus, Ag., from the Lower Lias of Lyme Regis (Dorset).’ By Arthur Smith Woodward, LL.D., F.R.S., F.L.S., F.G.S. 2. *The Rocks of the Cataracts of the River Madeira and the adjoining portions of the Beni and Mamoré.” By John William Evans, D.Sc., LL.B., F.G.S. The crystalline rocks of the cataracts of the River Madeira and the lower waters of its tributaries are part of a ridge with a north- westerly and south-easterly strike, similar to that of the Andes in the same latitudes. This strike is especially prevalent in Equatorial regions. With the exception of comparatively-recent alluvial deposits and a few pebbles of chert, pronounced by Dr. G. J. Hinde to be of marine origin but uncertain date, only crystalline rocks are met with in the falls. They all appear to be igneous, and are mostly massive in character, though some dyke-rocks occur. In places they are typical gneisses, and they are often banded, but in some eases they show no signs of foliation. ‘The prevailing type is acid, with a considerable proportion of alkalies, especially soda; but some of the rocks are distinctly basic in character. Analyses of several of these rocks, made by Mr. G.S. Blake, are tabulated ; and in one case the chemical analysis is compared with one made from the propor- tion of minerals washed out from the thin sections. Accounts of the megascopic and microscopic characters of all the rocks encountered are given. ‘The more acid rocks are usually fine in grain, and are often granulitic in structure. In most cases the quartz seems to have crystallized out before the felspar. The occurrence of andalu- site of chiastolitic type and of sillimanite as inclusions in a felspar is referred to, as well as the presence in one rock of an unusual type of allanite. An altered basalt is described, which contains minute concentric structures allied to those of a pyromeride. Above and below the region of the cataracts is a wide expanse of country covered with alluvium, either of recent or later Tertiary date. 3. ‘The Doncaster Earthquake of April 23rd, 1905.’ By Charles Davison, Se.D., F.G.S. The Doncaster earthquake of 1905 was a twin, with its principal The Doncaster ELarthguake of 1905. OME epicentre half a mile north of Bawtry, and the other about 4 miles east of Crowle and close to the centre of the disturbed area of the Hessle earthquake of April 15th, 1902. ‘The distance between the two epicentres is about 17 miles. The disturbed area contains about 17,000 square miles, including the whole of the counties of Lincoln, Nottingham, Derby, Stafford, Leicester, and Rutland, the greater part of Yorkshire, and portions of Lancashire, Cheshire, Shropshire, Worcestershire, Warwickshire, Northamptonshire, Cam- bridgeshire, and Norfolk. The originating fault runs from about E. 38° N. to W. 38° S., and appears to be nearly vertical within the south-western focus and inclined to the south-east in the north- eastern focus. ‘The first and stronger movement took place within the south-western focus. A twin-earthquake is probably due to the differential growth of a crust-fold along a fault which intersects it transversely, the first movement as a rule being one of rotation of the middle limb, accompanied by the almost simultaneous slip of tke two arches, and followed soon afterwards by a shift of the middle limb. ‘The movements, in which the Doncaster earthquake originated, presented a slight variation in this order. They con- sisted of successive, but continuous, displacements, first of the south-western arch, then of the middle limb, and finally of the north-eastern arch. December 6th.—J. E. Marr, Se.D., F.R.S., President, in the Chair. The following communications were read :— 1. ‘The Physical History of the Great Pleistocene Lake of Portugal.’ By Prof. Edward Hull, LL.D., F.R.S., F.G.S. The formations bordering the lower banks of the Tagus near Lisbon are arranged by the author in the following order of succession :— 6. Recent & Quaternary. Alluvia of the Tagus, Maris with Lymnea (Lacustre superior). is L ‘ 7 5. LAcusTRINE. R | Sands and gravel. 4. Post-PriocenE & { Not represented, unless by some land-glacial PLIOCENE. | beds due to elevation. 3. MIoceNE. ‘Almada Beds.’ Caleareous marls and lime- stones. with marine fossils. 2. Eocene (?). Unfossiliferous sands and gravels (Lacustre inferior). 1. Upper CRETACEOUS. Hippurite-Limestone. A description is given of the Lacustre superior; the Almada Beds are considered to be Miocene, and as the Pliocene is not represented, except possibly by certain glacial deposits, the author considers that that period was one of great uplitt. when the suboceanic gorge, 192 Geological Society. an extension of the present course of the River Tagus, was exca- vated. The margin of the lake was probably formed by the granite of Das Vargans and Cunheira. There is evidence that the general level of the lake-bed was nearly that of the outer sea, and that the sea-waters gained occasional access to the lake during the earlier stage of its formation. The lake was eventually drained by the channel cut by the Tagus at the harbour of Lisbon, upon the elevation of the land to about its present level. 2. ‘The Geological Structure of the Sgirr of Figg.’ By Alfred Harker, M.A., F.R.S., F.G.S. The pitchstone which forms the Sgurr of Higg is a massive sheet, some 400 feet thick, reposing with discordance upon the succession of alternating basalts and dolerites which make up the greater part of the island. The lower surface of the pitchstone is irregularly undulating, and in two places fragmental accumulations are seen immediately beneath it. The generally-received interpretation regards the pitchstone as a lava-flow, or series of flows, occupying an old river-valley excavated in the basalts, aud the fragmental deposits have been regarded as river-gravels ot the pitchstone-age. This is the view put forward by Sir Archibald Geikie. After a detailed survey of the ground, the author finds it impossible to accept this view, and he gives reasons for considering the pitchstone to be intrusive. ‘The form of its base, as mapped out, does not seem to be reconcilable with that of a river-valley, and its character is that of an intrusive Junction rather than an erosion-surface. The fragmental deposits are believed to be of volcanic origin and of the basalt-age. The one exposed at the seaward termination of the ridge is a volcanic agglomerate, probably | filing a small vent. The other, seen at the southerly base of the : Sgurr, is a bedded agglomerate, partly rearranged by water-action. : The Torridonian and Oolitic sandstone-blocks which are abundant in it are held to have been brought up from below, and fossil wood of Oolitic age has been brought up in the same manner. The absence of fragments of the sill-dolerites (themselves younger than the lavas, but cut off by the pitchstone) in both accumulations seems to assign them unequivocally to the age of the basalt, and their conjunction with the pitchstone must then be considered accidental. The conclusions arrived at bring the rock of the Sgurr of Higg into relation with the other British Tertiary pitchstones, which are all intrusive. Thus also is avoided the difficulty of assuming a great erosion in inter-volcanic times, a hypothesis for which the supposed river-valley was.the sole evidence. Phil) Mac. Sex: 6; Vol. 1), Pl. 1. (l= s90usel—(3 OSS |¢ +(.8b Seyrussh-+borgeyews bh— (s-ypyeus ISI Ge) 148 ObS = (4) 4 G6 RSE l8i¢ [bea eG [e111 0801/26 S89 lI82. lise V.22] (Su+'H Ye [bZ—lebieei—ge— [+2 [evi | sat ies = spar ec-| Hs TF EEO (RBBB ESEII HQ _ Gormemshl- =H ; 68! |06S |180L (81) UIS OFS = H ica lexi hee lo. [ssor[esat goat | rier] es ida Sy +2y+Hye Bi eater Sy 62 |OlélveSleZy | LSSiveS|29¢F/ SIF 205 |Chl ey | Zier nae |e eb] 2 | Gt mews = ee zits . g- ati ie “He (CERT) az TS26 068) S[sGs21eq ~ 24347: f= 987 (Ge Jable IL. WF VEPT MOSS 065 65-4°| 76:3°| 877° | 102° borrecled mp. H, 2179) 2259) 2174) 2182 PhaseH,= 8 sin 7(12-8) = Yar 702-3) = 5°43) $= 1/728° Salle IL Abscissa ae (ist) 4 i 795°| perpesteecksseree 50015/5 ae Gaon oncls FE =3e{-153|-159}-2021-37-o6-720-459] 495-313-156 2(H+Hst Het 2 CHAHS+ Hot Hy 2(H3+H3+H 4 (Hat Her) 4CH.4+ Hy +He) 4H, 40) $24, b> He —19 sin6@ol-14) 105 > Heil sina Got 55) 1208] 1295] 1058| 708 $20] 189| 25] T Td Tl 1A 9 0g Se TYG Phil. Mag. Ser. 6, Vol. 11, Pl. Il. Phil. Mag. Ser. 6, Vol. 11, Pl. III. ‘ x = > v ; as m A . . Y i» % ‘ + 4 i a : i 3 e S * ‘ : n f 4 ‘ . . reek Boy. oes es gee a , uN . ‘3 ; + i +. "1 r ; fr t ¢ i ie. ‘< an y 1 i . ’ . 7 ~ : F rey ui) . ay ee _ bd * - 7 . t as te 7 ee 6 RQ Wb 2) a Hee Pere ee : % x : eee ao st , = te A = Ae ~ ae 443.0 Phil. Mag. Ser. 6, Vol. 11, Pl. IV. Fi@. 1. —> 8 layers of foil. —> bare. Magnification 1:4. Fia. 2. fo A B Magnification 1:4, Fie. 3. 7#— air bands. "> vacuum bands. Magnification 1:4. yo «+ F ERT THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SIXTH SERIES.] ES hy Are FEC. XVII. On the Diffraction of Short Waves by a Rigid Sphere. By J.W. Nicuoxson, B.A., M.Sc., Scholar of Trinity College, Cambridge*. HE effect of a rigid sphere upon incident plane sound- waves has been examined by Lord Rayleigh+, who has obtained a complete solution of the case in which the waves have a length great in comparison with the dimensions of the sphere. In the more general case, Lord Rayleigh has expressed the disturbed motion in the form of an infinite series, whose terms consist of products of surface zonal harmonies and functions derived from Bessel functions. The summation of this series cannot be effected; but, as ~ Lord Rayleigh has shown, when the waves are very long, it practically reduces to its first two terms. In this paper, a close approximation to the diffracted waves will be obtained when the waves are very short in comparison with the radius of the spherical obstacle. The method adopted, before the intro- duction of the approximations, is that used by Lord Rayleigh. The final result appears in the form of a definite integral which may be evaluated to the same order of approximation. The motion external to the sphere, whether due to the passage of sound, or to the presence of small waves in a frictionless fluid, is supposed to possess a velocity potential. * Communicated by the Author. + ‘Theory of Sound,’ 1896, § 334; Proc. Lond. Math. Soe. 1872. Phil. Mag. S. 6. Vol. 11. No. 62. Feb. 1906. O 194 Mr. J. W. Nicholson on the Diffraction of Taking the centre of the sphere as origin of polar coor- dinates, and putting cos @=y, then the velocity potential in an incident plane wave travelling along w may be expressed as i ee Omitting the time factor, this may be written* b=Ayt+AryP(u)+A,Po(w)+...+A,Pa(u) +... - (2) nonere An=(2n+1) 0 ye) Inicio eee The diffractive effect is derived from a velocity potential vp, where (V+ R)y=0, or 0 (ee A 8 in QO) A eee ar" Or eae sa( sm ae) teats since wr must, like , be a function of zonal character. We deduce at once v=, alps (x), = . . . . e (4) where ; oO n.n+1° as : Soy) + (BHT, =0. G) This is satisfied by the Bessel function Yr=7*Jn+2(k7), but, for the present purpose, we require a solution finite at infinity, corresponding to a very large value of k. The ordinary asymptotic expansions for Bessel functions cannot be used, as they take no account of the cases in which 2 is very large. Make the substitution f rp, = erg, os ie ne (6) where (@, @,) are functions of rand rn. _ Substituting in the differential equation, and equating terms of different order in k separately to zero, Cao Ve S ¢-(1--3, )). hy? r Wwe o=| (1- ue) dr. e = ° (8) where a term @,’’ has been neglected in comparison with &. The last equation gives ho = (12 —n .n+1)?—(n.n+1)? cos—* & on =! (2) fey? * Lord Rayleigh, loc. ett. + Webb, Proc. Roy. Soe. vol. xxiv. p. 315 (1904). Short Waves by a Rigid Sphere. 195 The general solution of (5) is of the form ane Ne kw 4 Bo—kw (re een. n+1)# We now proceed to determine the values of A and B making this identical with Jn+y(kr) f (kr)® By Lommel’s theorem, when ¢ is large, we have 2 \3 7 “6 Se eae a ee ale dx(2) = sl eos(=—7 a) ‘ ite 21 (82)? —-+-+., i 2\:. ol, ple ere on bac we i whence, retaining only lowest powers of = , our solution Zz must be identical with Jn42(kr) 2) n—L. mond ne?) S Ll (=a (kr)? =) cos Pog eertl oe 3) ee 8(kr)? i) 2\3 = (2). sin(er—n ga.’ a) ae ae Since ih = 414 MD 6 tel ? (ert —n + Dt (kr (kr)? SU Oar saan | and 1 7S Ih n nti k. SS ee 4 (1 a }idr= ee Therefore tikw = Auer fy ntl Ney e —TA pat 2 Jor Wal ah he whence on substitution ie iets _ Bay /2 es ear ain and finally, when kr is large, and no restriction is laid upon the value of n, except that it be less than kr, 5 2 (n.n+ 1)2 T ue 2 Vip yea hl a i (er) -(2 y cos | ( (k?77? —n .m + 1)2?—(n + 4) a | i | ra i (kr)? { (49?) (kK? — n+ 1) hs O 2 196 Mr. J. W. Nicholson on the Diffraction of If x be neglected in comparison with kr, we get the well- known asymptotic expansion of the Bessel function. For the diffracted waves diverging from the sphere, the appropriate solution is CG etka af a —- sy 6 You (kh? .k?r?—n .n+1)% ae Let c be the radius of the obstacle. Since there cannot be motion normal to it, C, is determined by & (A, +y,) =0 when 7=c; . . 27a be p~thwe sy | (2n + De(s = Js ie (he) | = me Tonal oF Peon oe \. Since cos (ke, =2) ce J Ina le os (Rc? —n. m+1)3 by and O(kw.) _ (Pe —n.n+1)3 Dlke) Ee by (2), we obtain cos( te = Z| : — thw, er ore) be ee EE 2 at : : O(ke) (HE. Pen. n+ 1a) | O(ke) (Pe. Re—n.n+ Ie Writing w for kc, and H for P2@—n.n+1, the denominator becomes i W2 e—tku , He = ae on ey ED = = wr z— T H-2w }, or e—tkwe w? ik | — ——; /~ +— 4+:H?$. w: H+ 1 2 2 ++ f The numerator has the value — (2n +1)” Raa Nese are * Le pee gf peer 2 LEE (= HE) sin( kw, a ee . COS ( 7) t ; Short Waves by a Rigid Sphere. 1s) 7) or, if 6, be the argument of the trigonometric functions, the numerator is +(2n+1)e 2w:H# and therefore, returning to the old notation, {(H+w?) cos 0, ++H:? sin 6}; Qh’c?—n .n+1) cos 0, + 6(K7c?— 7. n+ 1)? sin A, 2 n pgttkwe (2n+1). we Sy ean n+h+e(ke e—n(n+1))3 and the velocity potential of the diffracted waves is SV, Eee) 0 or One e—thw PAC (1) = as 0 (kr? . Teatro lye. 7 (16) at the point defined by (7, w) referred to the centre of the sphere as origin, and the direction of the incident waves as initial line. The approximate formule above are only strictly true if ke is infinite, but are very accurate if ke is only a fairly large - quantity. The summation with respect to from zero to infinity may with great accuracy be replaced by a summation from zero to an integer close to the quantity ke. Owing to the fact that kc has been really treated as an infinite quantity, all the values of », which can give rise to an appreciable effect in the diffracted wave, will be included in the new range from zero to ke. Terms near n=ke are reserved for future treatment. Now n(n+1)=(n+3)?— 1 e n+ 5) } e ° ee Denoting = by a, we note that # is a quantity rising ke e iti ile e . by increments i from Dhe to 1, or, to a sufficient order of approximation, from zero to unity. Accordingly we write ne a4 (42) lo We ke au ke ~ £hec? Di Bee es to a sufficient order. he (15) 198 Mr. J. W. Nicholson on the Diffraction of Also pa ET (aa ae ag Mesex0s ( thea aig Or (0? ag Cu? — 69 COS = 1 = w,=¢(1—2”)2—ew cos", | and : ft lie : | 2— a?) cos 6, + eke(1 — «7)2 sin | a ly 1 Ca aa a | n 2— a7 + tke —2”)® 5 7 é i | xe 4.exp.the\(l—a")z + esi et iG | here ‘ 7 a Q=het (l—a*)i—2@ costa aie (18) Now the sum of a finite series }S(a) of the type (16) may be shown to be given by * =s (a) + >+~R= ke ( ste | ae. Se) . lbyclae, where kc is large, and the large integer less than kc is 7, where r=ke(1—e), in which eis small. L denotes the principal value of log iy) ie ==) 55 €). R is a residue of S(z) at any pole which it may have in the contour C, a unit circle round the origin. But the poles of S(z) in this case are all complex, being the roots of the equation 2—a?+.eke(1—a’?)?=0. The | corresponding residues cannot contain a factor of the form exp. (kcp), where @¢ is real and positive, from the form of | the integral and from physical considerations. The imaginary portion of the root corresponding to a pole will therefore | introduce a real exponential factor of large negative argument - | into R, which may accordingly be neglected. | Thus the velocity potential of the secondary disturbance is | ke = ied epee) r) Dept te peu ! Maar e Aely pale x”) cos 0, + tke(1—z”)$ sin O, P ) | ome, has ih 2— 2 -+ke( L—a?)2 fae | r TX ie : CH i xX exp. tee 4 (Ao 2 COSm ae (4 a} +H COS iin Ve Cie {| iF Fa, & a * This theorem was given by the author in a paper read before the l London Mathematical Society on Noy. 9th. It is proved by the | application of contour integration to the function Short Waves by a Rigid Sphere. 199 where 1 b= =, 08 x/(va—1+e). This formula is of most interest in the case of points lying along the axis of #, for the Legendre function then takes the values (-+1)”. For a point at a great distance 7 on the side from which the incident waves come, expanding the terms containing 7, 3(—)\ etete { (2—2”) cos 0, + tke(1—2?)? sin 0, C ea aoe et 2— x7 + ke(1—2x?)2 Sexuckc (U2) 2 COsmivanamin|) . 1 (20) ff On the opposite side, P (uw) =(—)” —3+her =€ Pay See 2 — a. cos 0, + tke(1—2")3 sin 6 Oe. Dat ace of C oan 1 di YP ee oat cO)h x exp. tkes (l—a*)s—a Coleen te. (2) Round the circumference of the sphere the integral takes a much simpler form, but is invalid..: Returning to the formula (19), we note that, using the polar angle ¢ as variable (w=e'%), the contour is traced by making range from zero to 27, « takes the value unity a both limits (whilst its logarithm has the values zero and 27 respectively). But the value «=1 corresponds to a large value of the integer n= —3+ hex. We therefore, with great accuracy, may write the asym- ptotic value 2 4 if 7 Pack (SS Sec Lee diy ee eas 9¢ Puw)=( aarp) s(t we=7). . 22) throughout the range. In terms of w, 2 2 T P =(z 7-9) cos(ten0—Z). erin me ser ( an 2) (23) Therefore at a point (7, @) not close to the axis of « Q UT 1 : 9\3_° Ske? ) a i Leda (2— ww?) cos 0; + tke(1—.2?)2 sin 6; ) é ae lig ees oy Oa an 2a + uke(1— 2%) | iia ” 1 TT ‘ Tw rs aa x COs (Kev — a)° eXp tke { (1 — x?)2—« cos~'x + —> i = °) = Gr CL : \ : (24) + 2'COS, > — ? 200 Mr. J. W. Nicholson on the Diffraction of and if 7 is great compared with dimensions of obstacle 1 Skee \= 8F (e-kry ’ T v= z ne A ( ) LP(z) . &@ COS (Kea — = asin 6 7 A x exp. tke{(1—2?)i—wcosw+em}dr, . . (29) where P(«) denotes the function (2—.) cos 0, + eke(1—a”)® sin 0, 2—«a? + tke(1--27)2 : (26) which always lies between positive and negative unity. To obtain an integral formula, free from the zonal harmonic term, and suitable for the case of points near the axis of 2, we note that the asymptotic expansions of P,(cos @) and of Jo(z) are respectively 2 ii T cs = — = costn+i. o—7) and \/ 2 008 (2-7) ae sin @ ( 2 aD i Te Ap? 2 (cos ) = 0 Att Sl ) vhs e ° e e (2 ) We therefore, under the integral sign in (19), merely replace r ‘ Q ee by To( Zea sin 5) to obtain a simpler form. On the harmonic terms for which n is greater than ke. The quantity #, now becomes imaginary, and the expo- nentials ef the previous investigation become those of real quantities. Since yw cannot be infinite at great distance, the exponential of positive argument cannot be present. The remaining one of order e—* appears as a multiplier in W, and the portion of yr due to terms for which z is greater than ke, is therefore vanishingly small in comparison with the portion previously found. ‘This supplies the justification for taking the limits of # as zero and unity in the summation. The terms near n=ke are not accounted. Short Waves by a Rigid Sphere. 201 Evaluation of the Integrals. The form of y given in (24) may be written a eee I a a ae (28) where WL Ijee 1) Ue * J 2- maw) hae eC 4 X exp. che} 2/1 — a? —2x cos-! wv ee 2 l7r og L)=e" | dee” * {2-08 ke(1 0")! f exp. ke (« cose — ae i ae ERS 7). (0) The quantity U ae 2khex \2 eLe IL a fe) ars ee opie (i- : ) {2-0 uke(l—ayat 7 } ld Now consider the integral a) =| UG OL de Sa arma 37) Cc where (wv, v) are functions of « occurring in any of the four integrals above. If accents denote differentiations with respect to x, Vv = u MEAL ean ub d we ther] a, See Laweke dt a In each of the four cases above, the latter integral may be shown to vanish in comparison with unity *. Thus rey vhkev 22 l= es 17 € \ Si al teewsn abo oe) * Integrals of this class are considered in the paper quoted in the previous footnote. 202 Mr. J. W. Nicholson on the Diffraction of For the integral |, anne TL 7 Cz bey (ae tec a, As ae 2+ @ COS ae bx and Ca vy =O+ 5 a age ee 4A Thus at both limits e=1, «=e, Pea AG vy, =7+0—sin“->» | 4h similarly, : y vo =a —O—sin fe \ r (34) vs =m —sin7}~ +8, | Gf ee ar Ties ha = 7) Sl — 0, J Moreover, a orb 2k. 3 4 ae 2 oe) ce a! een mr sin @) { et OF 2 N eae l= t/ 1 espe 2ke? 7 Cae (35) = 5 . A ¢ = c e . . . o ar sin 0 (1 G2\4 ye Again, a6 at a 2. exp. eee = eal —1} at both limits ; 4 | ue ek — exp, —eke {@—7+ sin7 — + —l , Cc er Cc = e4 2arkr? sin @ @\z il ae A Cc a —Q— sin-!- 7 . C fia exp.--tke| —7—O+sin7t- + —+—l r OF i¢ 7 — @— sin— uaa tke (m +0— ee) 1¢ 7 4-9 — sie ea —the( 8— a + sin—! - a fe 1) ieee sin-1" ih —- (37) w hie. holds except close to the axis of «, where the asymptotic expansion of the spherical harmonies is not valid. At a great distance, v=- (a C Pe ai -e).f abit oe @) , exp. dee) | (38) aki? sin a) The more general formula reduces to t AC exp. the (w+ 0—sin-* “Vi ay ¢ i (=: sin ») 3 C2 i Ji =) tole RG sin exp. the (7—0-sin-1¢ 2 ih 5 -1)} AL é . (ean a—6—sin— 2 | r A For points on the positive side of the axis of «, Jas (1) aT 1, whereas the asymptotic expansion gives oe heme sin @ AD: a 204 Mr. J. W. Nicholson on the Diffraction of We must therefore multiply the previous result by Ae ker sin @. Thus along this direction, fa exp. tke e(7— i — ve) ¥= (=a): (1 a = 2 Soe sin— ee Bi Mle a = ii sin iets —the( — We aesiilis = OY ia sin tb exp. ite a T— es see ee = See (40) 1 — sin)” r and at a great distance, p—r 2Q4¢ == vexpliker <= |. . ee ie - (41) becoming extremely great in comparison with the effect at the end of the perpendicular axis given by (38) with 0= = Along the other side of the axis of w, P,(#)=(—1)” and 6=7. vw in this case is given by (19), which leads to wy = L + I,, where, 2° (i ee aes STL fie et { U exp. tke {7v Vi 228 COS i es 2 c a Shy os +x cos} A) dz. . 44a} ae Cx Pr , 3qre I,=e4 | U exp. tke 5 xcos-!— — ag © home } da (43) fe dis j = where ow kere ea e if I =— eee . AT “ oO 3 SOE r (1 Cae ) © ¢-—lte 20° 2—a*+tke(1—«’)2 “72 and Bi A te exp. —the( — —27+ Vos sin’) I=—-[U],- : ¥ tke B C ~— 27+ sin7*— Y ke( —20-+ sin-1o + ee) exp. —tke{ —27+ sin7!- a C ] P NG Fe = ey ay c2\x- C ; = >) p= Rin 2 i= g/0 Similarly, eae C, y2 exp. tke| 2ar— sin7?- — =—-1 C iL ip C i= aoe, as ° C 4 ¢ C ° (1 — =) 2a — sin7!- es 40 Thus on the negative portion of the axis of «, ; 1 exp. tke exp. the (2ar—sin-¥ i a ae an at) - Cea L 2n—sin7 1 pe uke (Qa — sin 1 — f-Ver! 2ar— sin-1© r f and at a great distance along this axis, —é i 3 Nae ] —wkr —_ ~—— e@ 2mike 4 perme ai az | y me e- *(kr— =) =e OS OKC Te Se RE bale CAE The values of yw here given, with a time factor e~“V added, correspond in each case to an incident disturbance p= exp. tk(w— V2). The greatest diffractive effect occurs in the directions, on either side, which lie in the line of the incident disturbance, and the effect near the axis of the disturbance is of a higher order than that at other inclinations. The formule are not true close to the sphere, as the asymptotic expansions are not valid there. They give the effect of all harmonic terms not close to n=he. i e200. 98 XVIII. The Radiation from Ordinary Materials. By NORMAN R. Campsew, B.A., Fellow of Trinity College, Cambridge*. ‘Plate V.] Haperimental. § 1. ce following experiments are an extension of those described in a paper bearing the same title in the Phil. Mag. for April 1905. They have the same object—to determine the nature of the ionizing radiation from ordinary materials, and they follow the same method. But expert- mental improvements enabled greater accuracy to be attained and the results interpreted with greater certainty. The observations consisted, as before, in determining the relation between the ionization and the volume of a rectan- gular vessel with two parallel sliding sides. It was pointed out on page 538 of the former paper that difficulties arose in Fig. 1. LELECTRODE TZZF7ZILZZ ZLLL7 TZLPLIL LILI ILA LLL ILA LIL ALL PL LAA LALLA ANDI TS) = (SSSASSSSSSS LLLILILTIL ITT LITT LT LLDPE TLV TF WIRE GAUZE CAGE the subsequent calculation of the penetration from the in- fluence of the corners of the box. This disturbance has been obviated by a guard-ring device. § 2. A sketch of the vessel employed is given in fig. 1. * Communicated by the Author. The Radiation from Ordinary Materials. 207 The dimensions of the box are 32 x 32 x35 cms.; the front side, which is hinged, is supposed to be removed in order to show the interior arrangements. A rectangular cylinder of coarse wire gauze 1s fastened to the ends A and B of the box, A being covered with the material under investigation. A plate (C) < carrying the same material could slide on the gauze, always parallel to the ends. An electrode of wire netting was supported, through a slit in the gauze, inside the wire-gauze cage by a stiff, wire, of which all parts out- side the cage were shielded by earthed tubes (not shown). Now when a large difference of potential is established between the wire gauze and the electrode, only the ions inside the cage can carry the current; but rays from outside the cage can pass through the interstices and ionize the air inside as if it were a portion of an infinite volume. The sides of the box parallel to the wire gauze were 8 cms. distant therefrom and covered with aluminium. We shall see that this distance is sufficient to cause the total absorption of the rays from the edges of A or C or from the sides of the box before they reached the cage, and so to prevent them from having any influence on the ionization inside the cage. The dimensions of the cage were 18 x 18 x 32 cms. Thus, so far as easily absorbable radiation is concerned, the ionization inside the wire-gauze cage will be the same as that in a volume of air of identical dimensions enclosed between two infinite plates of the material covering A and B, tor the area of the wire in the gauze is so small that the rays from it produce no considerable effect. § 3. For the measurement of the ionization the method described in a recent note* was adopted. The saturation current is measured by balancing it against the known eurrent through a vessel, containing uranium, in which the pressure of the air could be varied at will. The capacity of the compensating vessel was measured by comparing it with that of a small guard-ring condenser, of which the capacity could be calculated, by the method described by McCleilandy. Throughout the paper the currents are expressed in ab- solute electrostatic units, unless the contrary is expressly stated. § 4. Two series of curves were drawn. In the first the box was surrounded by thick screens of lead in order to cut off the external radiation; in the second the screens were removed. The following metals were investigated :—Lead (1, Commercial sheet), Lead (2. Pure foil for assay); Copper * Proc. Camb. Phil. Soc., May 1905. + Roy. Dublin Soc. Proc, x. 18, p, 167, 208 Mr. N. R. Campbell on the (1. Commercial sheet), Copper (2. Purest electrolytic copper specially rolled); Aluminium, Zinc, Iron, Platinum* (all com- mercial sheet), Tin (Tin-plate), Silver and Gold* (‘* chemically pure”), The surfaces of all the materials except the gold, platinum and pure copper were cleaned with sandpaper before use, in order to remove any surface radioactivity. In the three cases excepted the metals were newly rolled and might be expected to be clean. §5. A word should be said as to the variations in the ionization which were described on p. 534 of the former paper. Much less trouble than formerly arose from the sudden discontinuous changes; on a few occasions “ jumps” were noticed, but I think it is probable that they are due to ex- perimental defects. However, | am unable to explain their origin or to prevent their occurrence; the observations were simply suspended until the normal state of affairs was re- established. The irregular points, often more than 50 per cent. from the curve, are not plotted. But the slow continuous variations are still in evidence. They appear to be periodic in some multiple of 24 hours, but my experiments were, of course, not suitable to a detailed investigation of the phenomenon. It is probable that they are due to changes in the intensity of the external radiation. That their magnitude was not sufficient to incommode the work seriously will be seen from the nearness of the experi- mental points to the curve drawn through them. It may be mentioned that the observations on Lead (1) were interrupted for a period of eight weeks. On resuming after that time, the observations agreed perfectly with those taken before the interval. The resulting experimental curves are shown in figs. 2-12 (Pl. V.), where the abscissee give the distance apart of the sides A and C, and the ordinates the currents x 10”. § 6. The curves can be interpreted on the same principles as those applied in the earlier paper. Let us consider first the case where the external radiation is cut off. We have then as possible ionizing agents (1) the easily absorbable radiation from the ends of the box ; (2) the more penetrating radiation from the same; (3) the radiation from the wire-gauze cage. Let the dimensions of the cage be ax bx w, x being, per- pendicular to the sliding side. * T have to acknowledge again the generosity of Messrs. Johnson & Matthey in lending me sufficient quantities of these metals. Radiation from Ordinary Materials. 209 (2) will give an ionization proportional to the volume, say vabe. (8) will give an ionization proportional to the area of the wire gauze “exposed, Say pa. The ionization due to (1) is more complicated. In the former paper it was calculated on the assumption that the rays were absorbed according to an exponential law; but lately our conception of the ‘absorption of a rays has ‘been completely altered by the important paper of Prof. Bragg*. The calculation must now be based on the theory pr opounded therein, which is fortunately amenable to mathematical treatment. § 7. According to this theory an @ particle travels a dis- tance @ in air producing approximately the same number of ions per unit length at all points of its path; when the distance a is reached it produces no more ions and may be said to be totally absorbed. If it traverses a thickness ¢ of some other substance than air, its path in air will be curtailed by ot, where p is the density of the substance referred to aga, Let A be the number of ions produced by the rays from unit mass of the material when those rays are wholly absorbed in air. Then dA will be the number of ions produced by the rays from unit volume, where d is the density of the substance referred to water=1. It is con- venient to introduce a quantity I, such that Ido is the number of ions produced in unit volume of the surrounding air at unit distance by the rays from an element of volume do of the material, so that the ionization in an element of volume dv at a distance + from the radiating element is ae ee dv I, is connected with A by the following equation :— {va {" dr {* 40 see SMG =o. . (1) AcI,ado=dA . do, poo Anta d Now consider an element at O of volume dS.di in an infinite slab of the material distant / from the plane surtace * Phil. Mag. December 1904. Pil. Mag. 8. 6. Vol. 11. No. 62. Feb. 1906. B 210 Mr. N. R. Campbell on the AB of the slab (fig. 13). Take O as pole and ON, the normal, as axis, of polar coordinates. The rays from this Fig. 13. A SLAB . es e . if es element will cause ionization —$d8 . dl dy in any small volume 7 of air dv, distant » from O, so long as r—/ sec @ is not greater than a—plsec @*; if rv is greater than this there will be no ionization. Now, in an element of volume 2° sin 6dr dé dd there will be ionization I, sin @drd@dgdSdl. This has to be integrated within the limits indicated. @ can range from . Oto 27, @ from 0 to the value given by a—plsec @=0, or y ses ry from dsec? to a—(p—1)lsec 6; hence the ionization is ol ta—(p—1)/ sec 0 teos—l gy ; ar d@sin@.dS dl 0 Qa To dd 2 0 “ [sec @ ? Spee =a | 4 (a—pl sec 9) sin § dO dS dl 0 ‘ ) =2nl, dS al { a—pl+pllog, +. eee To get the effect of the whole slab we must integrate this with regard to 8, the surface, and /, the depth. We thus find as the whole effect a ae area Wey pe a 2718 i (a—pl+pl log = )dl=Ty 278 x 452 (3) for if pl is greater than a, no rays emerge from the surface. * It is assumed here that the rays are emitted with equal intensities in all directions. This seems the most probable distribution, but Brage inserts an obliquity factor cos @. I am unable to find a justification for such a procedure. ee _— Bg Tatas Radiation from Ordinary Materiais. 211 If p is the ionization due to a surface 8 of an infinite slab of the material, then waz da p= 1,5 a — Sp AS. 2 . . . . (4) But d=-0013p, .. p='00016aAS8. We shall write s We Ss. We have now to consider the effect of placing another similar slab parallel to AB and distant 2 from it. Both slabs will emit rays, but all the rays will not produce their full effect before they strike the opposite slab and are ab- sorbed. By drawing the figure (fig. 14) we see that the for Fig. 14, SLAB limits within which we have to integrate for an element distant / from the surface of either slab are :— b=0 to 27, r=l sec 0 to a—(p—1) L sec 8, l l for @=cos“!” to gost ee a a and h=0 to 27, r= lI sec 6 to (x +1) sec O, “et a @ to 0. for @=cos—! Hence the effect due to the single element for which Oe ee p pl 7 t@—(p—71) / sec 8 *cos—] 7 - , T,dSdl dd \ dr sin 6d0 e 0 5 z 7 sec 0 ~ eos—1 el a roll ! 2a (a+) sec 0 * cos =1- * : Daas | ue a \ sin 6 dé 20 e Z sec @ e0 etol b E =2nl, {a4 pllog. FP — —elog* 1% basal tO) P2 D2 Mr. N. R. Campbell on the For the whole slabs we have a—x arts l “tpl 2p,=4n1,S p (o-+p! Oe a —wv log — jar A p ol +418 («- pl+ pllog® Jal . - ame a p for when the depth 7 is so great that none of the rays from the element strike the opposite slab, we must return to the previous case. 2718 : E — 3x Ta 5 | le but p= la 4a fafa aes A is When x=a this becomes p; for «>a the formula breaks. down owing to certain assumptions made implicitly above. From the nature of the physical problem it is easy to see that for «>a p,=p. Hence, summing up the three sources of ionization, the curve representing the relation between the ionization (y). and the distance of the sliding side from the end () is Ax a LE, ive 2 Da = +7 log + —e@, y=p Le = log | +vabi+pu. . . (8) This curve near the origin is concave to the axis of w, but after the point «=a becomes identical with the straight line y=ptvabei+px. Thus p is the intercept of the straight line on the axis of y, and tang@=vab+p, where @ is the inclination of the straight line to the axis of «. § 8. If the screens are removed we shall have to add the effects of (4), the external penetrating radiation (5), the penetrating secondary radiation excited by it, and (6) the easily absorbable radiation excited by it. (4) and (5) will give terms proportional io the volume; let their sum be v'abe; (6) will give a relation between ionization and volume analogous to that given by (1). It does not follow, however, that the absorption of the secondary rays will follow Bragg’s law, for analogy leads us to expect that the easily absorbable secondary rays will be negatively charged, slow-moving, cathode rays, which are absorbed according to an exponential Jaw. In fact, we may anticipate and say that it was actually Radiation from Ordinary Materials. 213 tound that p's (corresponding to ps) was given more accu- rately by the formula oi Om year enti a) CC.) than by Bragg’s formula. | Hence for the unscreened curve we shall have to add to (8) the terms | ti (lene se abe. sy oe (9) This curve is of the same form as (8), and is similarly related to p’ and v’, as regards its straight portion. § 9. From what has been said it should be obvious how to deduce, by working backwards, the quantities p, p’,v, v', a,» from the experimental curves. The matter is slightly com- plicated by the fact that the screens used were only so thick as to cut off two-thirds of the external radiation ; the weight of lead required to cut off all the radiation from a box of the size used was almost prohibitive. Accordingly, observations were treated in the following manner. The values of mw were first ascertained (see § 10), and pa subtracted from the readings recorded before they were plotted in the diagrams from which figs. 2-12 are copied. Smoothed curves were then drawn through the experimental points. In most cases, there was no doubt as to where the curve should lie, but when the points were irregularly dis- tributed it was feared that the drawing of the curve might be influenced by knowledge derived from the former series of experiments. In these cases the help of an unprejudiced friend was invoked; in all cases two independent workers drew substantially the same curve. The “screened curve”? (A) was now subtracted from the “unscreened ’’ (B). The resulting curve (C) gives the effects of (4), (5), and (6), and has the equation Y= =e ae aoe. vas swt) (LO) From the intercept and the inclination of the straight portion we can find p’ and v' at once. Subtracting v’ « from each point of the curve (C) we get the curve (D), which should represent the effects of the easily absorbable secondary radiation, and have the equation jp— Fr — / ie 59 — AX Gi erie (1 ‘ ‘). This is compared with curves drawn from calculation of the formulee (7) and (7') for different values of a and 2X. As stated above, it always agreed best with (7'); the value which gave best agreement between experiment and caleu- 214 Mr. N. R. Campbell on the lation was assigned to the metal under investigation. We now know p’, v’, and X. Fig. 15 shows the nature of the agreement attained, and also the difference between formule (7) and (7'). (7) is the complete line, (7) the dotted line. Fig. 15. re LA (LAA SE eave 2a. De eae ee ee aE a OF RE St A Be Ob.) eS 9 AO i an cee x Since only two-thirds of the external radiation was cut out by the screen, the curve (A) must contain half the effect of the agents (4), (5), and (6), as indicated by curve (C). Hence from each ordinate of (A) half the corresponding ordinate of (C) was subtracted; the resulting curve (E) (equation 8) gives the effect of (1) and (2) only, the intrinsic radiations. From this curve p and v can be found imme- diately, and by subtracting cw all through the curve (F) drawn, whose equation is | Ap ee y=r=v.—) [1 an — glog7) | This was compared graphically with the curves drawn from formula (7) for different values of a; one value was always found to agree fairly well with the experimental results, and was accordingly assigned to the corresponding radiation. We now know », v and a. Fig. 16 shows a case of good agreement, and fig. 17 a Radiation from Ordinary Materials. 215 case of poor agreement. Table I. gives the calculated values of Pz for different values of a and w*. a | . A,B, BA, ° BB, = a — A, As . A, By. We see that the points As, B,; ..-An41, Bn, are con- jugate with respect to the sphere X and the points B,;, Ai; ..- Bn, An, are conjugate with respect to the 248 Mr. A. Russell on the sphere Y. Let AlAs wes and b Baws, then the above equations may be written (d—0) 2! = a? = u.(d—uy) (d—uy)Uy! = a? = u3(d—1zy’) In general, we have (Ct Up SH iy (Oe 1) and thus Unt d—a?]/(d—u,1)} = a UnUn—1— {(a?—a?) |d} un — (a?/d) up =. This form of difference equation is well known* and is readily solved by assuming that u, = vn41/tat+(d’—a’)d. Making this assumption we find that tpi {(C—2a2)/d}rnt (a4/B)en = 0, a linear difference equation with constant coefficients. Hence solving in the ordinary way + we get Un = Aa™(a/d—q)” + Ba*(a/d—1/q)", or where A and B are constants and 29g = dla — d?—Adja,, . . . >. ie and Qq=dla+ Ve—4e2Ja, . . 2 so that Lo Ag dja, 4) ps Re 6) 0 rn and Vo-—q=V8=42/a.. Now when n is unity u,=0, and thus V,[0, = — (P—a?)/d = —a(14 9?+9')/fg(14+97)}- Substituting for v, and v, their values, in terms of A and B, in this equation we find that B=—Ag’*. We thus find on * Boole’s ‘ Finite Differences,’ 3rd ed. p. 233. + Boole’s ‘ Finite Differences,’ chap. xi. { I have called this expression g so as to introduce elliptic function notation. It is a pure number and has nothing to do with an electric charge. Dielectric Strength of Air. 249 substituting for v4; and vp their values and simplifying, that 1 4n—A4 Un = aq i= = . ° ° 5 (5) and An t ==) n ad SS n i 4n—2 SG aay ae Miao s eee eet (0) Let us now suppose that charges Q,, ... Qn, are placed at the points A,,... A, (fig. 2), and that dienes Ore Or are placed at the points B,,...3B,- We shall find the ines of these charges so that the potential of the spherical surface X is V, and that of the spherical surface Y is zero. Consider the potential at a point P’ at a distance a from B. The potential at this point will obviously be Qn Qn’ | (oie a Tee ). If therefore we choose the ratio of Qn to Q,’ so that Qn/Qn' = —P'A,/P'B, = a constant for every point on Y, the potential at P’ will be zero, and therefore also the potential of the spherical surface Y will be zero. Since A, and B, are conjugate points with respect to the sphere Y we have * Gun PD) ERB aay Gin) 1 Pine Fen Tanmen aot) Again, the potential at a point P distant a from A is given by Q; 1 On oa ae mF This will be V,if we make Q,;= V,a and Quer PAns: AvAntr _ _ Uns (8) On aw PIB CN hem (bak hyn Hence if we determine the charges Qn and Q,’ by means of (7) and (8) the potential of the spherical surface X will be V, and that of the spherical surface Y will be zero. From (7) and (8), we have Qn+1 Bi Uns Un On Wee ai cdl iB = q° 5 es l—q*t?? 4n—2 * Russell, ‘ Alternating Currents,’ vol. i. p. 101. ? ‘o) 5) 250 Me UAT Rseell One and thus, since Q, = Via,, we have eee 2n—1 oe nel . oe Hence also Oe ae ee =e , The electric intensity between the two spheres will obviously have its maximum valies! i. ab L and i, and thus, Q, Qs tik Ont Rn a2 © (a—Uy)? eta Ah (a—Un41)? Q, Oy 7 dau)? (V d=e-. ie Now by (8) oy, aus Qn+1 (Un41/a) (d=a—u)? 7 @—tny)* and hence R a ss Qt A+Un+1 4 m (Osten ye Substituting for uns, and Q,4; their values from (5) and (9) we get Vee)? le oe ae l—y 1 (1+ 9%" 3)2 ees g-2. Gly The value of the electric intensity R,,’ at M is given by R (estes Q, t Qn Ta ee Geneseo ie LCL Ne, ge a aay Gh! (Qa eaeam (aaa, )? Noticing that d—u,=a’/u, and that Q,/Qn’ = —a/u,’, we find that io aa Oe eed ao Lew ks gets pl noi! We can write down the valves of R,, and B,,’ when the spheres X and Y are at potentials 0 and V, in a similar manner, Hence by the principle of superposition we find that the electric intensity at L when the spheres are at ho Or — Dielectric Strength of Air. potentials V, and V, is given by Cee lg = a l-g T(1tqr3y! NCSU Se eT cena —_— LUT feat ant wai aad a 1G) > php? ( ) The most important case is when V,=—V.=V/2, and in this case ee eet an — ee = =a ; (ae ae Y) where pr & (1+q9)’2 Lore n—1 F EO eae gay! esicay ahs (15) and w is the minimum distance between the two spheres. It is convenient to tabulate / for various values of w/a. We see that f is the factor which converts the average electric intensity in the line joining the centres of the two spheres into the maximum electric intensity. In measuring dielectric strengths electricians as a rule merely give the average electric intensity, assuming that / is unity whatever may be the shape of the electrodes. Another practical case is when one of the spheres 1s main- tained at zero potential. In this case let us suppose that w— Vs and V¥,—0:. Hence by, (13) VA y= Pcie where ; v al ate g)? oo i A59 Grote Se. = — ei EE E91) meee see = CHG hi a l-—q i (1+ g@-3e4 ? ( ) In practice it is very difficult to make certain that one sphere is at zero potential, and so this method of testing dielectric strengths is not advisable. We may write (13) in the form We EVENS: = — Bist 21 eat) ee Re, 2 Ti x (27 hi) V,-V, PME Nea. 2 . = Fits Pam, Chile Ae (17) wv * Thus if we can calculate the values of / and /, for any given value of w/a we have completely solved the problem. 252 Mr. A. Russell on the When V, is zero or negative we see, since /,—/ is always positive, that for a given value of V;— V2, R,, has its greatest value when V, is zero and has its least value when V,-= — Vj. We shall now give methods and formule for calculating f and f,, and we shall also give tables of their values. 8. Approximate Formule for the Maximum Electric Intensity between Two Equal Spheres. Formula (15) may be written in the form we (l+q)? 1-¢” pone Pe ad (1+)? 1—g?""1 : 129 . (1+ gute! Pieler } : It is easy to see that the (n+1)th term of the series in the brackets equals id een "= Pf tig@tg + 1je 7a (Maqrg—-..tg")" 1g gig" + 1g eee By formula (3) g+1/q=d/a=2+2/a=y (say), patna and thus * n(n—3d) q” 2s 1/q” ==" iB: 0 dla a 7 rn(n—r—1)...(n—2r +1) IZ yt, +=) of ae We can thus easily express f in terms of y. Substituting and simplifying we find that | pa y+ y+y—l i yty?—2y—-1 2 (y¥—-1)? (yv=-y-l)?— (y —? — 2 +1)? yi +y>—3y?—2y4+1 (oy sy tage Le pA Ay By aay (y° —y*—4y? + 3y? + 3y—1)? See it eet ee ree Now y cannot be less than 2. Hence expanding by the binomial theorem and neglecting 1/y° and higher powers of * Todhunter’s ‘Theory of Equations,’ 8rd ed. p. 183. Dielectric Strength of Arr. 1/y, we find that y—2 Me eo oy 83 f=" eee ih ho bo Or ee) 2 y gn eats 6 6441 196i, 252 = Sas aa . (18) It will be seen that the coefficients of 1/y are rapidly getting larger, but it has to be remembered that / must equal unity when y—2 is zero. We therefore alter the above formula so as to make f=1 when y is 2, and yet make the expanded form of the altered formula agree with (18) as far as the coefficient of 1/y%. By this means we secure that the formula (19) gives the correct value of f when y is 2, and again when we can neglect the ninth term in the series formula (15). Expanding y/(y—2) in powers of 1/y as far as the term con- taining the eighth power, and substituting in (18) we get =! {1 US petal BEEZ Las 3 i? ae ee approximately, or De 22) Pen tees 2 — 1/(,,— iz: a ne fay t+ 5 ele Substituting 2+.2/a for y, we get 1 xa ala SS a ete Mey eo Bete) eae) Salama O(a EDP va ala 2a/a a3 2(afa+2)? (a/a+2)’ (a#/a+2)** isu The values of fare easily computed by this formula. For values of w/a less than 0°1 or greater than 0:7 the error is less than 1 in 1000, whilst for values of «/a between 0-1 and 0-7 the error is never as great as 2in 1000. For practical purposes therefore the formula (20) gives the values of f with sufficient accuracy. We could have made it more accurate by taking more terms into account in the expansion (18), but we have not done so, as we have found by actual com- putation that the Kirchhotf-Schuster formula ~ oar, gad ts ae : sums the series with a most gratifying accuracy until v/a gets greater than 0°7. It therefore completely covers the part of the scale of our formula which is slightly inaccurate. The formuls: (20) and (21) therefore give the complete practical 254 Mr. A. Russell on the solution. It is not easy to give a simple proof of (21), but we have found above by elementary considerations the first two terms. If we expand the expression (20) in powers of «la we get el ees io eae ae ell hen? Peles a | 26h a O56 a - The difference between the values of 7 given by (21) and (20) when w/a is small is roughly the hundredth part of 2/a, and as f is greater than unity it will be seen that the per- centage error made by using (22) instead of (21) is small. Tn Table IIT. below the values of the column headed 7 have been found directly from the series-formula (15). In caleu- lating this column I have to acknowledge the help I received from four of my pupils, Messrs. Hewitt, Hoggett, Ritter, and Taylor. In the second column the numbers are calculated by (21), and in the third column by (20). Iam indebted to Mr. Arthur Berry, of King’s College Cambridge, for showing me how the direct calcul. ation can be greatly simplified. The formula i ) may be written (Hee (USE Op pare fl cian yn ge i 2a (1—q) Vg 27 ee ae ae for* Kk A aS gen 1)/2 ina i Lf 97-1: We have used this theorem to check several of our results. For instance, when «v/a is 0°5, g is also 0°5 by formula (1). Also v t ./2kK/7 kK m= 291+ 3q" +n) = 2g ane +¢+q°t+qet...) = 27(1 40:25 +.0:015625 +0°000244+ ...) == 2«(1°26537).. Therefore Gama eae (1:26587)? = 1°1331 Hlso |} 7 & Grn es a —() 0 ON. > (1 + Ga) ( 0 We thus find that f=1:1726, when 2/a=0°5. * A. Enneper, Elliptische Functionen, p. 179. + A. G. Greenhill, ‘ Elliptic Functions,’ p. 303. Dielectric Strength of Avr. 200 Knowing the values of f we can find the values of /, easily by means of an elliptic integral series w ‘hich is quoted in Kirchhoff’s paper. It can be shown that * oO. 2n—1 1—q?- kk K? —])r-1l 2 ae ans + Cae 9 +9232 we Hence it follows from (15) and (16) that ee Cena: (a> aC oafa he Ny ae The values of k, k’, and K can ae be found by well-known formule. Let us suppose, for instance, that we wish to find the value of 7; when z/a is 0°5. We have already found that fis 1:1726 and qg is 0°5. pe | /IKJa=142 59" 1 =1+1+0°125+0:'003906 +0:000031+ .. = Ook We also have se V IRM ]a==14+2> (—)" 9g” 1 =1—1+40°12503—0:00391+... =) led dele Thus k/ =(0°12112/2°1289)? =0:0032369 and k= /1—k?=0°99999., Hence kk K2/7? =0:01662. Thus finally by (16) fr =1:1726 + {9/(4 »/2)$(0:01662) = 11990. This agrees with the value of /, found by direct calculation from (16). * A, Enneper, Elliptische Functionen, p. 180. Tt A.G. Greenhill, ‘Elliptic Functions,’ p. 303, { Greenhill, p. 803. 256 Mr. A. Russell on the For values of x/a greater than unity the values of /, can be computed by the remarkably simple formula i if is tt* Fart * (ela 1)(@/a-2)) Hence it is unnecessary to tabulate the values of 7, when x/ais greater than 4. The first row in the following table is taken from Schuster’s paper, the second row is calculated by the formula 1 Die CE Dap aie: © ve! Te onan (25) and the third row by (24). Tasie I1.—Values of /}. ee boat B Aes dill 8, (Schuster’s valued ...| 4-900 | 6172 | 6144. | ~ 7-196 UP emnnann Py (25), eee! 4200 | 5167 | 6143 | 7125 | sill Fes oe. 421 | S467 | 6143 | 7125 | suit The values of 7, given in the last row are the correct values. TaBLeE I1{.—Values of /. x/a. qby (1). | fby (15). | fby (21). | fby (20). 00 10000 | 1-000 1-0000 1-0000 O-l 0°7298 1:034 1:0336 10343 0-2 0 6417 1-068 1:0676 10686 03 05821 1-102 11020 11032 O-4 05367 113 1°1370 11384 05 0°5000 1173 11/24 11735 06 0:4693 1-208 1-2083 1-2095 Ore 0:4431 1-245 1:2447 1°2460 0-8 04202 1-283 12814 1:2832 0-9 0:4006 1321 13190 13210 10 0°3820 1°359 13594 1S 03139 1-559 15594 2:0 0:2680 1-770 1-704 30 02087 2214 22149 40 0-1716 2°677 26777 50 0:1459 3151 31513 6-0 0°1270 3°632 3°6317 70 01125 4-117 41165 80 0-1010 4-604 46044 9:0 0:0917 5095 50946 10-0 0:0838 5°586 55865 100°0 0:0098 50°51 50°5098 1000:0 0:0012 500°5 500-5010 Dielectric Strength of Air. 257 For values of w/a greater than 1°5 the values of / given in the last column are correct to four decimal figures. We have shown above by direct calculation that the value of / when v/a is 0°5 is 1:1726. The Kirchhoff-Schuster formula makes it 1:1724. This formula is therefore very accurate for values of «/a less than 0°5, and these are the values which it is so laborious to find by direct computation from (15). In the following table for the values of /, the first column is taken from Table III. The next column is calculated by the equation | Ay ee 4a hh Ke Se a 2a 7 and the last column for /; is got by the equation Ji=ft d. Taste [V.—Values of /;. Xa. F from Table IIT. IN: fige 0 1-000 0:00000 1-000 0-1 1:034 0:00001 1:034 0-2 1-0676 : 0-0008 1-068 0:3 1102 ; -0:004 1-106 0-4 1°137- 0-015 1-150 0-5 1173 0-026 Og 0:6 1-208 0-045 1-253 | O-7 1-245 0-068 1313 08 1-283 0-095 1:378 | 0-9 1321 0-125 1-446 1:0 1359 0158 1517 | The values of f; given in this table are in exact agreement with the numbers given by Professor Schuster *. 9. The Disruptive Discharge between Two Spherical Electrodes. The formule and tables given above enable us to find the maximum value R,, of the intensity of the electric field round two spherical electrodes .provided that the electrodes are not enveloped by corone; that is, provided that none of the air surrounding them is broken down. If no corone are formed before the disruptive discharge ensues, then we can calculate R,, at this instant, and so find Ryas. the dielectric strength of the air. As in the case of a concentric main o1 * Phil. Mag. vol. xxix. p. 192. Phil. Mag. 8. 6. Vol. 11. No. 62. Feb. 1906. Ss 258 Mr. A. Russell on the two concentric spheres, it is of importance to know in what cases corone can be formed. The problem is now much more difficult as the coronz are only approximately spherical, the maximum thickness of the stratum of conducting air round each electrode being on the line joining the centre of the two spheres. Si If we make the assumption that the surrounding air is broken down to the same depth at every point on the surface of either electrode, we can find whether the value of R,, in- creases or diminishes with this depth. In the former case a disruptive discharge will certainly ensue, and a fortzora it will ensue in the actual case of two spherical electrodes, as the actual breakdown begins at the centre of the spherical face, raising, as it were, a small blister at that point, and so R,, must be greater owing to the greater curvature. When the distance between the spheres is greater than the radius a, we have, to an accuracy of 1 in a 1000, R = iM §4(1+a/a)+a/(2+2/a)t, 7 where @ is 1:077, provided that v/a is less than 7. Henge eM M 1 2ae Od Oa ae d(d—2a) = we j =a i oe ei CG, G ~a}. and therefore dR, . Voy 20er 2) 1 diam 2 C2 ei when V and d are constants. Hence, for values of d less than a(2+,/2(1+2), that is, for values of d less than 4:O4a, R increases as @ increases, and thus, on our assumption, a disruptive discharge will ensue. If the spheres be not further apart than twice their diameter we should therefore expect a disruptive discharge to ensue the moment R,, became Rnax. For large spheres, experiment shows that this is the case up to a distance apart equal to about three times their diameter. For greater distances apart, the moment R,, attains the value R,,,, the air in the neigh- bourhood of that point is broken down and a partial corona is formed, the value of R,,, at the surface of the corona being less than Ryax- In these cases, as the equipotential surfaces are no longer spheres, we cannot apply our formule. Dielectric Strength of Air. 259 10. The Maximum Llectric Intensity between a Sphere and a Plane. When the plane is at zero potential, we see, by taking the ‘image of the sphere in the plane, that ie = (V/«) Io, . ee : . (26) where 7, is the value of the factor 7 given above correspond- ing to 2x/a; x being the least distance of a point on the sphere from the plane and @ being its radius. 11. The Maximum Hlectric Intensity between two infinitely long parallel Cylinders. Let us consider the value of the electric potential at points between the two cylinders, the sections of which by the plane of the paper are shown in fig. 3. If q and —q be the ‘(CD=d=the distance between the axes of the two parallel cylinders. LM=z=the minimum distance between the cyl-nders. a=the radius of either cylinder. A and B are inverse points. CA CB = Cl-— DAS DB. charges per unit length on the cylinders the axes of which pass through A and D respectively, the potential v at any point P external to them is given by v= —2q log (AP/BP), where A and B are the inverse points of the circular sections. The maximum values R,, of the electric intensity will be at Land M. The potential at any point p on CD will be v= —2¢q log r+ 29 log (e—7), where 7 is Ap and ¢ is the distance AB. Hence Z 2¢ — “ mou c—?r Tf. ~~ 260 Mr. A. Russell on the Now R has its maximum value R,,, when r is Al. ZqC 2q¢ 29 Hence R= AL(e¢e—AL) ~ a(d—2a) ~ ax’ where « is the minimum distance between the cylinders. Now, we have * W I~ Alog 4(d+-c)/2at? og }(d+-c)/2at where V is the potential-difference between the cylinders and @?=d? —Ad?. Hence we have R aN hs UG ze ae ™ « log 4 (d+e)/2a} where y woes bo =| \/ —— : ees log (1+.a/2a+y)’ eee tte ID ~\202 and y = halat (e/2a)? es. Values of 7 are given in the following table :— TABLE V. eo eee ee zla...; 0-01 | 0:02 | 0°03 | oot | 005 | 0:06 | 007 | 0:08 0:09 | — fe wae 1:00 “100 | 1-00 | 1-01 | 1-01 | 1:01 | 1-01 | 1-01 | 1015 | | | | | | | l | | | zja..4 O1 | 02 | 03 |-04 | 05] 06 | 07 | 08 | feame | fesse] 102 | 103 | 1-05 | 1-065] 1-08 | 110 | 141 | 113 | 114 | | | | | | | | | | | | aja...| 1 2 3 4 5 6 i |, 8 4S _—— } —_—_—- Tany 1:16 | 1315] 1-46 | 161 | 1-74 | 188 | 201 | 214 | 994 | | ay cee: | 239 | 3:56 | 462 | 562 | 658 | 11-0 (2p. O | | | | * Russell, ‘ Alternating Currents,’ vol. i. p. 102. zja...| 10 | ‘20 | 30 | 40-| 50°‘| 100-| 1000 | 10000 4 587 Se Se er Dielectric Strength of Air. 261 12. The Disruptive Discharge between Two Parallel Cylinders. It is well known in practice that when we have two parallel wires with a high P.D. between them, then in certain cases coronee envelope the wires. When they are close together, however, this. effect is not produced, a disruptive discharge occurring directly the P.D. attains a certain value. It is important therefore to know what distance apart the wires must be in order that coronz can be formed. If we assume that sec 6=d/2a, we find that mm Nin ing tan? “~ d(1—cos 6) log (tan 6+sec 6)’ Let d be constant and let a vary, then, solving the equation AR»/d?=0, we find that log tan (7/4 + 0/2) = sin 6 sin? G—cos 6° When @ is nearly 70° this equation is SRC, and in this ease d=5'85a nearly. Hence making the assumption that the coronz are sete drical in shape, we see that R,, diminishes as @ increases when d is greater than 5°85a. In practice, therefore, we should not expect coronee to be formed when the wires were at a less distance apart than about three times their diameter. 13. The Application of the Formule to Haperimental Results. I. Wits Dirrcr PRESSURES. | Gi.) Lord Kelvin’s tests with large electrodes. Lord Kelvin * was the first to make accurate tests on the disruptive voltages between electrodes in air. He found that the apparent dielectric strength of a thin stratum of air was much greater than that of a thick one. The apparent dielectric strength in our notation being V//«, we have Vfjie= Rmx. + 0°38 7/2, where V is in kilovolts, and P_ ., the dielectric strength of air, is a constant. In Kelvin’s experiments 7 was practically equal to unity at all distances, and thus V/« increases rapidly as « diminishes. From his experimental results+ Lord Kelvin concludes that a battery of 5510 Daniell cells could produce a spark between two slightly convex electrodes when the minimum * Proc. Roy. Soe. 1860, or eu p. 24, + Proc. Roy. Soe. April 12, 1860, p. 259. 262 Mr. A. Russell on the distance between them was 1/8th of acentimetre. Taking the E.M.F. of a Daniell cell as 1°07 volts, this makes the dielectric strength Ryax, of air to be 40°8 kilovolts per centimetre; a result which is only about 6 per cent. higher than the number we give as the average value of Rmax. (ii.) A. Heydweiller. 5 em. spheres (2°5 cm. radius). In the valuable paper by A. Heydweiller, published in the Annalen der Physik und Chemie, vol. xviii. p. 785 (1893), there are many tables of sparking-distances given both between equal and unequal electrodes. We consider merely the last table he gives, and we choose the 5 centimetre spheres as being likely to give the most accurate results. The height of the barometer was 74°5 cms., and the tempera- ture 18° C. during the test. The columns headed « and V are taken from Heydweiller’s paper, f; is calculated by the formule given above, and Rmax, is found by Rinaz aa { (V— 0°38) /a3fi- We have assumed that the potentials of the spheres are V and 0 at the instant of the discharge. The results seem to indicate that this was not the case when the electrodes were at their greatest distances apart. Taste VI. Heydweiller’s test with 5 cm. spheres (a=2°5). «“=distance apart in ems. V=disruptive pressure in kilovolts. De zla. Ff. (cale.). | V (observed). | RKmax. (cale.). | 1 05 | 02 1068 18-36 37-5 | | O6 | 0:24 1-081 21-60 | 375 t eee: 028 | 1-102 24°54 37°3 | Oo | - 032") 1-116 27°35 37:0 | 09 | O36 | - 1132 | 30-09 | 36-9 | ;. 10 0°40 1150" 3 32°ED 36°9 oe. | 044 | 1169 39°58 37°0 | oe 4S | 1-188 38°31 37°0 ! ees qa “Oroe) || 1-209 41-01 374 | ies], 056, |. 1281 4368 | Sit | amor a (0:60. . | 1°2538 46°23 379 Os 064 | 197 | 48-66 38-2 The mean value of the numbers in the last column is 37°5, and none of them differ from the mean value by as much as 2 per cent. Hence this experiment gives 37°5 kilovolts per centimetre as the dielectric strength of air. Dielectric Strength of Air. 263 (iii.) J. Algermissen. 5 em. spheres (4=2°5 cm). In the following table the values of « and V are taken from Dr. Zenneck’s work ‘ Elektromagnetische Schwingungen und Drahtlose Telegraphie,’ 1905, p. 1011. They are due to J. Algermissen, and are deduced from the average of the values obtained on different days under varying conditions. We have assumed that the potentials of the electrodes were +V/2 and —V/2 respectively at the instant of the discharge. As the results in the last column are very approximately constant our assumption is justified, Tasue VII. J. Algermissen. 5 cm. spheres (a=2°5). zx is measured in ems. and V in kilovolts. x x/a. F(cale.). V (obs.). | Rmax. (calc.). 15 0-6 1-208 46-2 36:6 16 0-64 1-223 Ae6 |) 865 | 17 0:68 1-238 51-0 36°6 | rS.. et O72 1-253 53-4 ae | fo | o%6 1-268 55'S sey | | One) | e070 1-283 58-2 368 2-1 0-84 1:298 60-6 sy 4 2-2 PauOcs 1312 | 62:8 36:9 | 93. | O92 1:326 650 | 37-0 | 2-4. 0-96 1342 67-0 Srey | 25 | 1:00 1-360 69:0 371 | 26 | 41:04 1374 70:8 37-0 27 1:68 1:390 72-6 37-0 | 2-8 1:12 1-406 74-4. 37-0 2-9 1-16 1-421 76-2 370 | 3-0 1:20 1437 73:0 37-0 3:1 1-24 1-452 19-7 37-0 3:2 1-28 1-469 81:3 7-0 3°3 1°32 1-484 83-0 37-0 | 3:4 1:36 1:500 84-7 37-0 3-5 1:40 1515 86-4 37-1 3-6 1:44. 1533 88-0 BVell ath 3:7 1:48 1549 89-6 37-2 3:8 1°52 1566 91-2 73 | 3-9 1:56 1583 92:7 aye a 4:0 1°60 1599 94-2 37-4. Aen ale 1616 | 95-7 37-4 Ae = Ge 1632 | 97-2 37-4 t The mean of the values of Rmax, in the last column gives the dielectric strength of air as 37°0 kilovolts per centimetre, and the greatest difference between any of the calculated numbers and this value is only about one per cent. It will be seen therefore, that the agreement between theory and 264 Mr. A. Russell on the experiment is quite satisfactory. The three final values for Rmax. obtained in this table closely agree with the mean of the values we deduced from Heydweiller’s test. Considerable weight, therefore, must be attached to the results of these experiments in determining the value of Rmax.. (iv.) J. Joubert and G. Carey Foster. 1 em. and 2 em. spheres (a=0°5 & 1). In Foster and Porter’s (Joubert’s) ‘ Electricity and Mag- netism, p. 135, tables of the sparking-distances between 1 centimetre and 2 centimetre spheres are given. ‘The results for the 1 cm. spheres are taken from Joubert’s Traité élémentaire d’électricité (2nd edit.), and those for the 2 cm. spheres were obtained by G. Carey Foster. An analysis of the table for.the 1 centimetre spheres shows that if we cateulate Rmax, for sparking-distances of 5, 10, and 15 oms., on the assumption that the air round the electrodes is not broken down to any appreciable depth before the discharge occurs, the values are much too large. This is in accord with the conclusion of $9. The mean of the values up to a distance of 2 cms. apart makes R,,,;. 42°8. The mean of the values for the 2 cm. spheres makes Ryax, 42°9. (v.) E. Hospitalier. 1 cm. spheres. An analysis of the experimental results given by H. Hos- pitalier in the Formulaire de l Llectricien, 21st year, 1904, p- 289, for the sparking-distances between two electrodes, each one cm. in diameter, shows that the potentials of the spheres arenot + V/2 and — V/2 at the instant of the discharge. The values of Rmax, calculated on this assumption diminish steadily from the maximum value 44°1 when the spheres are 0°6 of a em. apart to 40°0 when they are 2 cms. apart. The values of 7, however, are little affected by the absolute values of the potentials of the electrodes, provided that «/a is not greater than 0°3. Taking, therefore, the mean of the first three results given, we find that Ryax, is 42°2. (vi.) Compagnie de V Industrie Hlectrique. Plate and sphere. | The Compagnie de Industrie Electrique et Mécanique have published tests * on the disruptive voltages between a plate and a ball. * Turner and Hobart, ‘ Insulation of Electric Machines,’ p. 33 (1905). Dielectric Strength of Air. 265 Taste VIII. Compagnie de PIndustrie Electrique. Plate and 2 cm. ball. | ip ala sls (cale. by § 10). | V (obs.). Mees 05 0-5 1-36 i Push lee reiG:s 1:0 1:0 1°77 26 | 44:6 15 15 22 31 | 445 | 2°0 2:0 2-68 35°5 46°5 25 2°5 315 39 48°] 30 30 3°63 42°5 50:4 4:0 4:0 4:60 [PRS Oe ge Baye ee 5-0 5:0 5°59 54:0 | 59:5 | 6:0 6:0 6:57 580 | 62:5 | It will be seen that Rmax. is beginning to increase rapidly (see $9). The mean of the first four values gives 45°6 kilo- volts per centimetre as the dielectric strength of air. In practice the plates used are not large, and so we are only ee in using our formula for f, when the plate and the ball are close together. We do not attach much importance tap) to this test. Il. Wire ALTERNATING PRESSURES. G.) C. P. Stemmetz. 2 inch spheres. In a paper on the * Dielectric Strength of Air,’’ published in the Transactions of the American Institute of Hlectrical Engineers, vol. xv. p. 281, Professor C. P. Steinmetz gives the results of an elaborate and careful research on the dis- ruptive voltages between pointed, spherical, and cylindrical clectrodes. Alter nating voltage was used of frequency 125, and the shape of the wave was practically identical with a sine curve when a particular smooth-core alternator was used. The ratio of the maximum to the effective voltage in all his experiments with this machine was practically “L42. The spherical and cylindrical electrodes were put in nitrate of mercury and then rubbed with a clean cloth. When this was done it was found that the disruptive discharge, tor a given distance apart of the electrodes, always took place e at ‘the same voltage. If the electrodes were merely polished, then at small distances apart the results were very erratic. The accuracy of the results obtained probably lies w ell within 4 per cent. in most cases. In the experiments the barometer varied from 75°2 to 76°2 ems. This variation introduces an uncertainty of about one per cent. The voltmeter readings may be one per cent. out, and there may be a one per cent. 266 Mr. A. Russell on the error in determining the ratio of the maximum to the effective potential-difference. An error is also due to the moisture in the air. This, however, was found to be small. When the electrodes were immersed in “live” steam at atmospheric pressure, the effect of the steam was to zncrease the apparent dielectric strength of the air, a greater voltage being required to produce the disruptive discharge. As pressures up to 160 effective kilovolts were employed, the sparking-distances were large and could be measured with great accuracy. We should expect that, with these high voltages, our formule would apply with considerable accuracy, as the disturbing effect of the cathode glow wouid be small and the field would be approximately symmetrical. In the following table the results of tests when the electrodes were spheres 2 inches in diameter are analysed. The column headed Ryax. gives the values of the dielectric strength in kilovolts per centimetre, calculated by the formula Rinax. = { (1'42V —0°8) /e} fa TABLE LX, C. P. Steinmetz. 2 inch spheres (a=2°54 cms.). ~=125. E/V = 1-42, where H is the maximum and V the effective value of the alternating voltage. | | | ie le: ala. | f(eale.). | V (obs). Bmax. (cale,. | 1] Aa 0318 0-125 1:04 8:95 39-0 Off. ' (8) Py being as before the total pressure between the spheres at any time, and «a, a coefficient of inertia—in this case the simple mass of a sphere. On the other hand, the equations for @, &e. are of the form Cs be + C5 coy) = ee : : : ‘ E (3 * Love, loc. crt. p. 154. + Proc. Lond. Math. Soc. vol, xiii. p, 189 (1882). by Forces of Relatively Long Duration. 287 c, &e. being coefficients of stability to be treated as large. This form applies to all the lower modes, for which the force of collision operating at any moment may be treated as a whole. By equation (1) of Hertz’s theory Po = f, 2:2, but now that we are admitting the possibility of vibrations a must be reckoned no longer from the centre, but from a point which is at once near the surface and yet distant from it by an amount large in comparison with the diameter of the circle of contact. We may write inclusion being made of the coordinates of the lower modes only. The sum of all the coordinates would be zero, since (in the case of equal spheres) the pole does not move. Thus IEG — hey (2g, Lt 25 + neler ° * cC 6 (Gap) In the first approximation c¢, &c. are regarded as infinite, so that dy &e. vanish. Po reduces to hk, (2,)2, and so from (8) Ay dy => iD) (2¢61)2, ° . ° ° ° (12) the solution of which gives ¢, as in Hertz’s theory. If P, be regarded as a known function of the time, @, 1s deter- mined by (9); but it may be well at this stage to ascertain how far Py is modified in a second approximation. Retain- ing for brevity @; only, we have approximately @3 = Po/cs. Hence - 2 3k 2 Ey obs = bo 2g {1 4 2 (241) eae 612) 2 Cy and we infer that P) is changed by a term of the order ¢,~}. We will now pass on to consider the general problem of a vibrator whose natural vibrations are very rapid in comparison with the force which operates. We write (9) in the form db+nid=Pija=P, .. . . (14) where n? = c/a, and is to be treated as very great. If 6 and @ vanish when ¢ = 0, the solution of (14) is * t = “|| sin 7 (t—t’) Day Qi’. : : . (15) 0 * «Theory of Sound,’ § 66. 288 Lord Rayleigh on the Production of Vibrations If the force operates only between ¢ = 0 and ¢=7 and we require the value of @ at a time ¢ greater than 7, that is is after the operation of the force has ceased, we may write co) = al sin n (¢—?’) D;—4) dt’. st eie 5 (16) (De If + be infinitely small, the force reduces to an impulse, and we get @ =n sin nt .\ ® dt ; ell but it is the other extreme which concerns us at present. In many cases, especially when ® = 0 at the limits, we may advys antageously integrate (16) by parts. Thus db = n-* D,_, cos n (t{—T) —277 Dy=0 Cos nt er | eos n aes dt’: is Te dt’ Again iE T att 2 | es n (t—t’ ela —— a =-sin 2 ({—T) ie Ne dt n° il dD, _ @ 9 ] 5 d°>P —— as ae aes SI] at) ae 2 tt; 19 a es ee | sin n (¢—t') de? (19) and so on if required. In this way we obtain a series pro- ceeding by descending powers of n, and thus presumably advantageous when n is great. As an example, let ®=1#, so that d@@/di?=0. The force rises from zero at ¢ = 0 to a greatest value at t=7 and then suddenly drops to zero. From (18), (19) we find g¢ =n" 7Tcosn(t—T) + n?sinn(t—7T) — n-sinnt. (20) Again, take the parabolic law DD) = tr, 3 | ee so that © = 0 at both limits, oO) di noe d® | dt? =—2. From (18), (19) @ =—tn-* sin n t—7)—T n-* sin né + 2n-* cos 1 oat —2n-* cos nt =—2n~*7 cost} nt.sinn(t—37) +4n‘*sindnr.sinn (t—47). . (22) by Forces of Relatively Long Duration. 289 If @ and its differential coefficients up to a high order are continuous within the range of integration and vanish at the limits, the leading term in the development of (16) is of high inverse power in». An extreme case of this kind is considered by Mr. Jeans*, who takes C al mw (+t?) " In this case the solution involves the factor e~”’, smaller when n is great than any inverse power of n. But the force is not here limited to a finite range of time. The application of these results to the problem of the col- lision of equal elastic spheres is not quite so straightforward as had been expected. In (9), ra) = Po / hy = liga! Is a2, ° ; (23) a denoting, as in (4), (5), (6), (7), the approach of the spheres. The terminal values of « and of «: are zero. Again, d 1 da : (ga = ae ei, OS eyes 24. dt (2 ) 2 dt > ( ) so that d ® / dt vanishes at the limits of the range. But SA Ne NRE RGLONS em sree ce de) = 44 (a) ee Se ice hy ae = (201) use being made of (4), (5); and the first part of this becomes infinite at the limits where a = 0. Equations (18), (19) give it Ciel, we ae g=—7| sin n (¢—t') Fay dt’, . eee (20) 0 and in this we have now to consider the two parts sinn (¢—t’) a2 dt’ and | sin n(t—t') a dt’. For the second we get on integration by parts, since 2 vanishes at both limits, 1 da? — — | cos n (t—t’) —— dt! A) ( i at * “Dynamical Theory of Gases,’ Cambridge, 1904, § 241. I should perhaps mention that most of the results of the present paper were obtained before I was acquainted with Mr. Jeans’ work. Phil. Mag. 8. 6. Vol. 11. No. 62. Feb. 1906. U 290 Lord Rayleigh on the Production of Vibrations which is of order n—}, or less. In the first part the relation i . e. between dt’ and da is, as in (7), da az aaa SL : ACTS ao - hy hea ab) . . ° é (27) dt! = Tf we exclude the terminal parts of the range, the integral would be of order n-}, or less, so that it is only the terminal parts that contribute to the leading term. For the beginning we see from (27), or independently, that N= eile 7%... nearly, so that for this terminal region fxm n(t—t!) a-= dt' = = s nt! I S] ! ! — %0 i nt oem NeEy — cos nt = oe x Cane (nt’)2 (nt!) When we suppose 2 very great, the limits of integration may be identified with zero and infinity; and further by a known theorem a 2 7 ain £aa "COS LG ices ey ei hy eras eo are tt) 0 Ve 0 V2 Thus, so far as it depends upon the early part of the collision, ch Be Ee ie oe) aes 4 dayne There will be a similar term due to the end of the collision, derivable from (29) by replacing nt with n (t—7). If, as I think must be the case, (29) gives the leading term in the expression for a vibration, the next question is as to the order of magnitude of the corresponding energy in comparison with the energy before collision, viz. } Mass x a”, or 4 7pr? a”. : The maximum kinetic energy of the vibration is given by by Forces of Relatively Long Duration. Zon and the ratio (R) of this to the energy before collision is 27 ky ao : E? ao WOM aan pr ~ 32 (l— a”)? a, pr R if we introduce the value of k, from (2). The precise value of a, would have to be calculated from Lamb’s theory. It is easy to see that it is decidedly smaller than, but of the same order of magnitude as, the mass of the sphere, viz. 4 pr. The precise value of R would depend also upon oe, but for our purpose it will suffice to make o =4. Thus we take is ee aI NN ren sonny (OA) Dp? n> - ce) tion of the second order in spherical harmonics (¢ = 3) B\ °85 7 i Ve =A/ ie) . WATT: 5 f C c J (32) so that approximately R According to Lamb’s caleulation * for the principal vibra- ae do 50 \/ (B]e): In (33) 7 (E/ p) is the velocity of longitudinal vibrations along a bar of the material in question, and the comparison is between this velocity and the velocity of approach before collision. In steel the velocity of longitudinal vibrations is about 500,000 ems. per second, or about 16 times that of sound in air. It will be seen that in most cases of collision R is an exceedingly small ratio. The general result of our calculation is to show that Hertz’ s theory of collisions has a wider application than might have been supposed, and that under ordinary conditions vibrations should not be generated in appreciable degree. So far as this conclusion holds, the energy of colliding spheres remains translational, and the velocities after impact are governed by Newton’s laws, as deducible from the principles of energy and momentum. Terling Place, Witham, Dec. 22, 1905. (33) * Loc. cit. p. 206, U2 ie 02 XXIII. Note to “Electrical Vibrations and the Constitution of the Atom.” By Lord RayLEIcH™, FIND that the remerk (p. 121) that solutions such as (12), (15), (19), involving a factor et” “cannot apply to a problem where the disturbance is supposed to originate in the neighbourhood of the sphere” needs qualification. That the solutions as they stand cannot be so applied may be admitted ; but Profs. Lambt and Lovet have shown how by limiting them suitably they may be made to express the advance of wayes into a region previously undisturbed. This is a matter of some importance, and I regret that I overlooked the memoirs just cited, in which clear explanations are given. XXIV. The Heating LEjfects produced by Réntgen Rays in different Metals, and their Relation to the Question of Change in the Atom. By H. A. BumsrEap, Ph.D., Asst. Professor of Physics, Yale University §. | ee study of the phenomena of radioactivity during the past five or six years, and, in particular, the brilliant series of experiments and deductions which we owe to Rutherford, have left little room for doubt that a certain proportion of the atoms of radioactive elements are continually breaking up, and that the constant emission of energy by these bodies is a result of this atomic disintegration. This process in any given radioactive body appears to be going on at a fixed and definite rate which is characteristic of the particular substance studied and which is quite un- influenced by any external circumstances whatever. Although radioactive substances have been subjected to the greatest extremes of temperature available in the laboratory, and to great variations in other physical and chemical conditions, no certain results have been obtained (so far as the writer is aware) which point to any corre- sponding change in the rate of decay of the substance. In fact the process of atomic disintegration has appeared to be quite beyond human control ||. * Communicated by the Author. + Proc. Lond. Math. Soc. vol. xxxii. p. 208 (1900). t Proc. Lond. Math. Soe. vol. 11. p. 88 (1804) § Communicated by Prof. J. J. Thomson, F.R.S. || The apparent change (due to high temperature) in the rate of decay of radium-excited activity, discovered by Curie and Danne, has been shown to be due to the fact that the successive products of radium volatilize at different temperatures. Cf. Bronson, Am. Jour. Sci. July 1905. Fleating Effects produced by Réntgen Rays in Metals. 293 On the other hand, all substances when illuminated with Rontgen rays or with Becquerel rays of the y type give out a complex secondary radiation, part of which at least is wholly different in character from the primary radiation. For example, the secondary radiation due to Rontgen rays consists in part of negatively charged corpuscles or électrons which are not present in the primary rays. This suggests that there may be some breaking up of the atoms of the secondary radiator; but it is only a suggestion, for it by no means follows that the presence of 6 rays involves atomic disintegration. The modern theories of electrical conduction imply the existence in conductors (and all bodies are con- ductors to a greater or less extent) of large numbers of corpuscles not closely bound up in the atomic structure ; and it is quite conceivable that some of these may constitute the secondary ® rays, the necessary energy having been, in some way, imparted to them by the primary radiation. The most direct way of discriminating between these two possibilities is to investigate the energy relations when, for example, Réntgen rays are absorbed by matter. If none of the atoms are broken up, then the conservation of energy, in the ordinary sense, will hold: if, on the other hand, some of the atoms are exploded by the Rontgen ays, as dynamite is exploded by a shock, then the total energy after the absorption of the rays may be considerably greater than the energy of the rays themselves. This excess of energy might be expected to manifest itself mainly in the form of heat in the absorbing body; for it is known that a large fraction of the secondary Rontgen rays are very easily absorbed indeed *; and Sagnac found that ter tiary rays were more easily absor bed than secondary rayst. Thus only the secondary rays which are produced very near the surface of the absorber would carry their energy away with them ; those which are set up throughout the mass of the body would be absorbed before reaching the surface, and eventually would warm _ the absorber. _ Assuming for the moment that Roéntgen rays are able to cause atoms to break up, it is very impr obable that the atoms of different substances are equally susceptible to this effect ; and we should expect to find an inequality in the amount of heat produced when Rontgen rays are equally absorbed in different substances. If, on the contrary, there is no atomic disintegration, the quantities of heat should be equal. It was * J. J. Thomson, ‘The Conduction of Electricity through Gases,’ p. 263. Telbidi ps 2 ie. 294 Prof. H. A. Bumstead on the Heating Effects from this point of view that the problem was proposed to me by Professor J. J. Thomson, during my stay in Cambridge last year ; and the experiments which I am about to describe were carried out in the Cavendish Laboratory under his direction, and owe much to his advice and co-operation. In considering the various experimental means by which this problem could be attacked, the radiometer seemed to promise certain advantages over other heat-measuring instruments. For measuring ordinary radiation with this instrument (the development of which is chiefly due to HK. F. Nichols), the usual method is to have opaque vanes with a transparent wall near them upon one side ; when one of the vanes is illuminated, it is heated and the molecular reaction causes it to be repelled from the neighbouring wall. But it is quite possible to reverse this procedure and have the wall opaque and the vanes transparent, and, although the attainable sensitiveness is probably less than in the other case, it has obvious advantages when one is dealing with Roéntgen rays instead of ordinary light. The walls can be made of the metals under investigation, and of suitable thick- ness to absorb a considerable fraction of the rays incident upon them ; while the vanes may be made very transparent to the rays and be thus far less in the way, and be less heated by the rays (independently of the heating of the substances under examination) than would be possible with the thermopile or bolometer. In the construction of the radiometer and its gradual adaption to the present purpose, I was particularly fortunate in having the advice and assistance of Professor K. F. Nichols who was also in Cambridge, and who most ‘S) Kindly put at my disposal the results of his long experience with the radiometer. I wish here to express my thanks to him for a much shorter period of apprenticeship to the instrument than would have been possible without his help. Apparatus. The radiometer and its adjuncts passed through many preliminary and tentative forms before a_ satisfactory arrangement was obtained. The final form which proved fairly sensitive and manageable is here described. r Aa ie i: The vanes were made of aluminium-foil which weighed about 1 mg. per squarecm. Hach vane measured 8 x 10 millimetres with its greatest dimension vertical, and the two pieces of foil were stretched between two very thin horizontal rods of glass at top and bottom, which in turn were kept at the proper distance apart by their attachments to the central rod produced by Rontgen Rays in Different Metals. = 295 of the suspended system. The inner edges of the vanes were 4 mm.apart. The various joints were made by very small drops of alcoholic shellac which were baked on with a hot glass rod. The system was put together on a flat brass table and, after a few trials, it was not difficult to get one in which the aluminium vanes were very fairly smooth, plane, and parallel to the central rod. The mirror, for use with telescope and scale, was attached to the central rod 3 em. above the middle of the vanes ; it was usually about 5 mm. square and was made of specially selected microscope cover- glass. All the mirrors used gave very satisfactory definition. In the final system, the weight of the mirror was 13 milligrams, that of the ‘rest of the suspended system 5 miligrams ; ; the moment of inertia was approximately 0:002 grm.-cm.?,_ The two aluminium vanes were electrically connected by means of a bit of light phosphor-bronze strip. The other details of the suspension are shown in figs. 1 and 2. The working quartz-fibre, His 3.cm. lone, and i is suspended from a glass rod carrying a small magnetic needle, N : as this, in turn, is suspended by a second fibre, F’, it may be caused to rotate by means of the bent magnet outside the case ; it thus serves as a sort of torsion head for controlling the zero of the radiometer. ‘This very elegant device is borrowed from the work of Nichols and Hull on the pressure of radiation. The metals whose heating effects were to be compared were mounted upon an ebonite disk (W, figs. 1 and 2) 6 mm. thick and 7°8 cm. in diameter. Three rectangular holes, 3°6 x 14 cm., were cut in this disk, at an angular distance from each other of 120°. Across these holes strips of the metals under investigation were fastened with a little soft wax ; the strips were 2 cm. long and 1 cm. wide and their inner edges were 4 mm. apart. Up to the present, 1 have had time to compare only two metals, lead and zinc. The lead strips were 0°30 mm. thick and the zine strips 0°82 mm., these thicknesses being chosen because they gave nearly the same absorption of the Rontgen rays used, as will appear later. The thinner lead strips were blocked up from the wheel on small bits of card, so that the surfaces of lead and zinc towards the radiometer vanes were in the same plane. The arrangement of the metal strips on the ebonite disk was g as follows: across one of the rectangular openings, two lead strips were placed; this was for testing the balance of the radiometer when both vanes were influenced by the same metal ; across the second opening «lead and a zine strip were placed side by side, while the third opening also contained a lead and a zine strip but in reversed order. The shaft which Prof. H. A. Bumstead on the Heating Effects 296 GLLEL LAS IN YW Yj A Qiyo» AS? Yy Saas ESS WU i SS} =" CIN Pp 1 ENS 3 As 2 Hy H $ (l UM SS | = rhs meee produced by Rontgen Rays in Different Metals. 297 carried the ebonite disk was provided with a ratchet-wheel with sixty teeth; and the disk could be rotated from one position to another by an electromagnet inside the radio- meter-case. The current for this purpose was led in by means of wires passing through small glass tubes sealed with sealing- wax, into holes in the base-plate of the instrument. Certain marks on the edge of the ebonite disk which could be seen through the observing window enabled one to be sure that the disk was in proper position in any given case. All the metal strips, before being mounted on the disk, were covered on both sides with leaf aluminium which was held by the thinnest possible layer of soft wax, put on when the metal was hot. This was to give both metals the same surface, so that the loss of heat from the surface for a given rise in temperature might be the same in both cases. The ebonite disk was also covered with aluminium leaf to avoid electrostatic effects ; to the same end a small quantity of an impure ania salt was put inside the case in a small open dish. All the metal strips were connected to the shaft of the wheel by thin copper wires ; the shaft in turn was connected to the case and to earth. The portions of the apparatus hitherto described stood upon a brass base-plate turned flat and smooth, which rested on three levelling-screws. Through this plate passed the tube which led to the P,O; bulb, pump, and McLeod gauge. The whole was covered with a heavy, cylindrical, brass casting, 12°5 cm. in internal diameter, 29 em. high, and with walls 1-4 em. thick. This heavy metal case was found to be necessary owing to the sensitiveness of the radiometer to thermal disturbances ; with a blackened glass bell-jar which was first tried, the zero was so unsteady that nothing couid be done with the instrument. As a further protection against thermal disturbance, the cover and base were surrounded with cotton-wool and a felt jacket drawn over the whole. The case was provided with two windows, 2°9 em. in diameter; one of these (A, fig. 1) was covered with sheet aluminium 1°2 mm. thick, and served to admit the beam of Rontgen rays; the other was of glass for observing the deflexions. Both were put on with sealing- wax and the joints covered with soft wax. The inside of the cover was painted with lampblack in alcohol with a little shellac to make it stick. The bottom of the cover was turned flat, and the joint between it and the brass plate was surrounded by a mixture of equal parts by weight of vaseline, paraffin, and rubber which, after being put on, was glazed over with a small gas-flame. When ‘all the joints 298 Prof. H. A. Bumstead on the Heating Effects were carefully made, little difficulty was experienced in maintaining the vacuum for considerable periods; the rise in pressure due to leakage was usually less than 0°002 mm. per day. In the preliminary experiments for testing the working con- ditions of the radiometer, the ebonite wheel and its metal strips were replaced by a light ebonite frame which carried two strips of platinum foil (one opposite each vane), through either of which a known current could be sent. By this means one could readily find the pressure of maximum sensitiveness, and compare different quartz fibres and different forms of the suspended system. The best pressure appeared to be between 0-03 and 0°08 mm., and within this region the variation of sensitiveness with pressure was slow; in the subsequent work a pressure between these two limits was usually employed. From a knowledge of the resistance of the platinum strips and of the current employed, it appeared that a deflexion of one millimetre (scale distance, 196 em.) corresponded to an emission of about 0°04 erg per second from each square centimetre of platinum surface. The deflexions were also found to be proportional to the energy generated in the strips. Of course the radiometer action depends primarily on the temperature of the surface, and with a surface of different emissivity, the deflexion for a given emission of energy will be different. The Rontgen bulb finally employed was a very large one made by Miiller and obtained from Isenthal & Co. The diameter of its spherical portion was 17 em. and the electrodes were big enough to bear a very heavy discharge. The anti- cathode was sealed into the bottom of the water-tube so that it was in direct contact with the water, and I have frequently caused the water in the tube to boil without ser iously heating the rest of the tube. It was provided with an automatic vacuum adjuster which worked well; the focus was sharp and the Réntgen rays obtained were very powerful and fairly steady in intensity and “hardness.”” The bulb was driven by an 18-inch Apps coil and a rotating mercury-jet interrupter. The coil was in an adjoining room and about 6 metres from the radiometer ; its orientation was adjusted so that it produced very little effect upon the magnetic “ torsion head” of the instrument—less than 4 mm. with the largest currents used; this was always in one direction and could be applied as a correction. The secondary leads were gutta-percha covered and supported by silk ribbons ; where they passed from one room to the other, through the wooden frame oyer a door, they were enclosed in long olass tubes. As the rays used were not produced by Réntgen Rays in Different Metals. 299 very hard there was little difficulty with the insulation, though there was often a good deal of brush discharge from the leads. The earthed metallic case of the radiometer ‘protected it com- pletely from any electrostatic disturbance. A lead screen, 2 mm. thick, which hung by a quadrifilar suspension from the ceiling about 2 cm. in front of the aluminium window, per mitted both strips to be exposed to the Réntgen rays, or both screened, or either exposed while the other was screened. A large cardboard screen was kept between the Roéntgen bulb and the radiometer, to diminish the effects upon the instrument due to the heating of the bulb. Measurements of the absorption of the lead and zinc were carried on simultaneously with the radiometer observations. lor this purpose an electroscope was set up 270 cm. from the bulb ; it had an aluminium window 2 cm. in diameter and the Senernder was covered with sheet lead 2 mm. thick. As this did not sufficiently protect it from the rays, a lead wall was built up of blocks two inches thick between the electro- scope and bulb with a hole opposite the window; this gave satisfactory protection when the window was screened. Observations were made with a micrometer-microscope and stop-watch in the usual manner. Eaperiments. The experimental method was based upon the following considerations :—The Rontgen rays absorbed in the strips will generate heat throughout the mass of the metals and a steady state of temperature will be reached when the heat generated per second is equal to the heat lost per second through the two surfaces by radiation and convection. (The possibility of any appreciable loss by conduction through the ebonite support of the strips will be considered later.) The heat lost through any surface is proportional to its emissivity and, for such small temperature differences, to its excess of temperature above its surroundings. The lead and zine strips had the same surface—aluminium leaf—and it is natural to assume that the emissivity is the same in both cases ; this assumption, however, will be justified experimentally. Moreover, it will appear from theoretical considerations that, in the steady state, the difference in temperature between the front and back surfaces of either metal is a small fraction of the excess of its temperature above its surroundings; and this too will be confirmed experimentally. It follows therefore that, very approximately, half the heat generated in either strip is lost through each of its two surfaces, and that the total heat oenerated per second will be proportional to the temperature 300 Prof. H. A. Bumstead on the Heating Effects of either surface in the steady state, and hence to the repulsion of the radiometer vane exposed to that surface. The first step ina series of experiments was to test the balance of the radiometer by exposing the two lead strips simultaneously to the Rontgen rays. The balance was usually found to be fairly good, and could be to some extent adjusted by moving the bulb horizontally before the window; the stand carrying the bulb could be moved by a horizontal screw for thispurpose. In two of the series of experiments (quoted below) it was found impossible to get a good balance by moving the bulb; in these cases the lack of balance was determined and applied as a correction. The wheel was then clicked round to the second position, in which one vane of the radiometer was opposite to a lead strip and the other opposite to a zine strip. This was a somewhat delicate operation as each click caused a violent disturbance of the radiometer (partly magnetic and partly thermal), and it was necessary to get it under control by means of a subsidiary magnet before making another click; otherwise the vanes might have become entangled in the moving wheel and the suspension broken. After the shift from one position to another several hours had to elapse before the radiometer was again fit for use. Several exposures to Réntgen rays were then made in which the zine and lead strips were exposed separately and both together. The wheel was then moved to the third position, in which the zine and lead strips were in reversed order, and similar observations taken. It may be said at once that the reversed position of the lead and zine did not alter the character of the results. The general nature of the results may be most readily set forth by considering a particular experiment as an example. In fig. 3 the results of this experiment are shown graphically ; the abscissee represent time in minutes, the ordinates deflexions of the radiometer in centimetres on the scale; the position of the wheel was such that a positive deflexion means a repulsion by the zinc of its vane, a negative deflexion a repulsion by the lead of its vane. Between 2™ and 5™, the zine strip was exposed to the rays; the rays were then cut off and the zine allowed to cool for 5 minutes (5%-10™), the lead was then exposed for 3 minutes (10™-13™); it, in turn, was allowed to ceol for 5 minutes (18™—-18™) and then both strips exposed simultaneously for 3 minutes (18™-21™), after which the rays were again cut off. It is plain from the figure that neither metal was exposed long enough to the rays for the steady state to be attained; but it is also plain that the great preponderance of the lead over the zinc is not due to this yl- = aS = =~ —N produced by Roéntgen Rays in Different Aletals. Cn iO aN ne | S oa ae aa | SHERHRASRGRORRONGS sth < SEG aS. ao 7 af LA ee ee as CE er Heinen nt | | Cece coe eeee Eee Ceeerr Lee ral CEECeeereeeer eg PEELE TTT CEPCPRREE CECT | i ee HAF AE felch d) sh Ss Ta] +H SEH PPT Pal pie ill is Oh PEEEEEEEE EEC EEL 5 fa | | He lle SUTSUESEED pe || ea ae ’ ' B01 te e 302 Prof. H. A. Bumstead on the Heating Effects cause. In fact we may from these curves get an approximate idea of what the steady deflexions would have been if it had been safe to continue running the bulb at the rate necessary for such large deflexions. If X is the coefficient of absorption of the metal for the rays used, then the energy of the rays at any point in the interior of the strip whose distance is # from the front face is I,e-*" and the energy absorbed in an element of thickness dx is \lje-d«. Jet us assume that the heat generated in the element is proportional to this, say adlye-da. The equation of the flow of heat under these circumstances 1s: IV 2 C a == a + arl,e-™” du? with the boundary conditions dV dV ee = he Ley Aig KS, 2: =e (— ye aes: where V is the temperature (measured above the sur- roundings), ¢ the time, ¢ the specific heat of unit volume, & the conductivity, h the emissivity of the surface, and / the thickness of the strip. The solution of this will have the form V=V,— SAc-"; where V, is the steady value and is the solution of the differential equation with the left-hand member put equal to zero; the successive values of y in the sum are determined by a certain transcendental equation, and the A’s are functions ot z into which y enters. What is observed is the temperature of the surface where v=/. The variation of this temperature with the time is represented fairly well (except at the very beginning) by a single term of the sum of exponcntials, so that we may write as a rough approximation YS Veh ea). The variation of the temperature with the time during cooling will have different values of the A’s and y’s, but (again excepting the initial part) the curves of heating and cooling will have very nearly the same form. ‘This is seen in the figure, and it also appears mathematically that, with the values of the conductivity and emissivity involved, there is a nearly uniform temperature throughout the metal within less than a minute after the rays are turned on. We may therefore, for such accuracy as is needed in this discussion, produced by Réntgen Rays in Different Metals. 303 take the curve of cooling to be represented by y—N cea; the time being eounted from the moment the rays are cut off. In this equation ea Le ehh and one may get rough values of y for lead and for zine by drawing tangents to the curves of cooling. In the following tables are several values found for different points of the curves in fig. 3; the zero for the zinc curve was taken as the mean of the position at 2" and 10™ and, for lead, the mean of 10" and 18”. Zine. Lead. dV dV | Vv. dt i Y: Ve dt A y- b je 2AE Sas ee eae ea ie Ae ae Seis beer ieee || ig ee A Corl 1°8 06 Ge | GB 1:0 2-0 16 0:8 3:0 4:0 Tes Hee 105 0-7 US | TS) 7 08 0:50 06 OSes ales 16 Average .....- 0:68 Average ....-7) 1:4 In order to determine the steady value from the value at the end of three minutes we have yar aee eat oF a ea UE which e1ves, for lead Vj = 13°95, and for zime V, = 7-4. Approximately the same rates of cooling and heating were obtained in all the experiments made upon this point. r, > 20. If we assume as before that one-half of the secondary rays generated in any element are propagated straight back toward the front surface (which will exaggerate the intensity of the secondary rays), we get for the intensity of the secondary rays escaping from the fr ont surface L. |) 707 200m ee | +251 | = 7-90 | +396 | 200, raed Geel aan ane Gee ee e709 | = 2°30.) F689) Yarn ae | — 363 ieaaer eats eo tae 961 |) — S20 sy 8i80 | eee. +985 | —507 | 194 | | | | | | | Sto ye. Re as er Spee soe 1R75” | p64) 1 aS | eaahae 1395 | +74 | 188 | Surface Elasticity of Saponine Solutions. ole It is in no perfunctory spirit that I wish to express my thanks to Professor J. J. Thomson for permission to work in the Cavendish Laboratory and for the help which I con- stantly derived from his advice and suggestions, some of which were vital to the suecess of the experiments. I take pleasure in acknowledging my great indebtedness to him. Conclusions. The present experiments indicate that when Rontgen rays are equally absorbed in lead and in zine, approximately twice as much heat is generated in the lead as in the zine. It does not appear possible to attribute this result to errors in the measurements or in the theory underlying the experi- mental method. To account for this effect the writer has been able to think of only one hypothesis which is not in more or less direct conflict with experimental facts. This hypothesis is that, by means of Réntgen rays, the atoms of certain elements may be artificially broken up and that the energy thus liberated forms a part (and perhaps the greater part) of the energy which appears when the rays are absorbed by matter. New Haven, Conn., U.S.A. Oct. 20, 1905. XXV. On the Surface Elasticity of Saponine Solutions. By S. A. SHorrer, B.Se., Assestant Demonstrator in the Physical Laboratory of the University of Leeds * TYNHE question of the concentration of dissolved substances in the surface-layers of solutions has been the subject of much research since the time of Plateau’s well- Bee experiments on the superficial viscosity of liquids. The present paper deals with the specially interesting example of this phenomenon aftorded by solutions of saponine. The investigation may be divided into three parts :—— (1) Examination of the mechanical properties of the surface-layer by means of the torsion-balance ; (2) Theoretical investigation of the effect of a viscous- elastic medium on the motion of the disk of the torsion-balance ; (3) Absolute measurement of the surface-rigidity. * Communicated by the Author, 318 Mr. S. A. Shorter on the The Mechanical Properties of the Surface ti On examining the surface in the usual way by means of the iereionebalance. it was found that the effect of ae surface on the motion of the disk depends upon the dimensions of the various parts of the apparatus. If a very powerful wire is used, twisting the torsion-head sets up oscillations which are damped by the surface. If a very weak wire is used, a large rotation is required to set up visible motion, and this motion consists of a simple drift towards the position of equilibri ium of the wire. With wires of intermediate strength it is possible to obtain some indication of a temporary position of equilibrium. The disk moves rapidly forward, suddenly comes to rest for an instant, and then moves Corwen’ again. With a wire of suitable torsional moment it is possible to obtain a type of motion which clearly demonstrates the elastic nature of the forces called into play by the shearing of the surface. On twisting the torsion-head the disk moves forward, comes to rest, and then moves back against the torsional couple of the wire, comes to rest, moves forward again, and so on: in this way executing a few rapid oscilla- tions before settling down toa simple drift. These oscillations do not take place about a fixed centre. The motion isa compound of damped oscillatory motion and translational motion in the direction of the initial twist of the wire. It is difficult to obtain these oscillations with a fresh surface. They are more readily obtained after the solution has been standing for some time. If, however, the motion is started by giving the vessel containing the solution a small rapid Pokition: “oscillations are easily obtained provided the moment of inertia of the suspended system is not too great. If the suspending wire has a very small torsional moment, the motion set up is damped oscillatory motion without translation. It is clear that shearing of the surface gives rise to forces of an elastic nature. These forces are not. permanent, so that the surface may be described as viscous-elastic. We will next investigate mathematically the effect of a viscous-elastic eda on the motion of the disk. Mathematical Theory of the Motion. Suppose a circular disk of radius 7, and moment of inertia I to be suspended by a wire of torsional moment e. Let the disk touch centrally the surface of a saponine solution con- tained in a circular vessel of radius 72. Let @ be the angular displacement of the disk from the position of zero torsion of += Surface Elasticity of Saponine Solutions. aly the wire, and let L be the moment of the viscous-elastic forces acting on the disk. Neglecting o the inertia and ordinary v iscosity of the lhquid, the equation “of motion of the disk will be re ae We will assume that the quantity L obeys the equation dT, ae do ih din & Hee Sh where p is related to the absolute coefficient of surface- rigidity by the equation The dimensions of n (which we need not formally define) are of course cre of an ordinary coefficient of rigidity multiplied by a length. Hliminating L between the first two equations, we have Weare Wd) © see und) aate 7 ee ine ake a the solution of which takes one of the forms G=Pe + Qe" Rex” =), or O=Ac~* 1 Be" cos (yt + C), according as ee) ay (eve Se ia eles 0 There are three possible types of motion : (1) when 7 is so small that the above expression is positive ; (2) when the expression is negative; (3) when 7 is so large that the expression is positive. For convenience we shall refer to these as (1) oscillatory motion of the first type ; (2) aperiodic motion; (3) oscillatory motion of the second type. The two types of oscillatory motion are quite distinct. When 7 is very small the disk oscillates under the action of the wire and the surface exercises a damping effect on the motion. When 7 is very large the disk oscillates under the combined action of the elastic forces of the disk and surface. Motion according to the equation O= Ae 4 Be? cos (yt +! ') is not necessarily oscillatory in the ordinary sense of the eA 0) Mr. S. A. Shorter on the term. In the accompanying figure are drawn a number of curves representing various types of motion according to this equation. Curve I. represents the type naturally suggested to the mind by a casual examination of the equation. It may happen, however, that the steady decrease of the term Ae-#? is so rapid as to disguise the oscillatory nature of the motion. Curves IJ., IIT., and IV. illustrate this point, and Fig. 1. \ 7a show the continuity of this motion with the aperiodic motion represented in Curve V. A very dilute solution of saponine affords on standing an example of continuous change from oscillatory motion of the first type to that of the second type. When the surface is fresh the disk may be set into oscillation by twisting the torsion-head. The surface viscosity gradually increases till > CTS Surface Hlasticty of Saponine Solutions. 321 the motion becomes aperiodic (Curve V.). On further stand- ing, the motion changes to oscillatory motion of the second type. The transition is first dicated by a momentary retardation after the rapid initial motion (Curve IV.). This becomes more and more marked till it amounts to an actual stoppage (Curve III.). After this a slight backward motion can be detected. This increases (Curve II.), and soon it becomes possible to obtain two oscillations, then three, and so on; tillontwisting the torsion-head we obtain several, as in Curve I. A study of the above curves will show that it is quite useless to attempt to measure the surtace-rigidity statically by means of the torsion-balance. The temporary position of equilibrium indicated by a stoppage or a backward movement of the disk does not afford any measure of the ratio between the torsional moments of the wire and the surface. In the following investigation, the elasticity has been measured dynamically. Lf the torsional moment of the wire is very small, we have t a GeO aaa (is oe 4 wr? —I] @=A-+ Be 2 Cos Cee +0), provided that Apr? >I. Hence Agr? +r?) I po OPEN) where T is the period and 2 the logarithmic decrement of the oscillations set up by giving the vessel an initial rotation. Measurement of the Surface Rigidity.—Fresh Surfaces. Apparatus.—The disk was made of brass and had a diameter of 710 cms. The upper end of the suspending wire was clamped to a bracket firmly fixed to the wall. The lower end of the wire was clamped centrally to a short piece of brass rod’ whose lower end could be screwed into the centre of the disk. A small mirror was fixed to the rod so as to enable the motion of the disk to be observed by means of a distant telescope and scale. The moment of inertia of the suspended system was 2050 grm.cm.” In all the experiments, the period of oscillation under the action of the wire was very large compared with the period under the action of the surface, so that the torsional moment of the wire was negligible. The vessel for holding the solution was made of Phil. Mag. 8. 6. Vol. 11. No, 62, fed. 1906. 4 322 Mr. S. A. Shorter on the glass, and had a diameter of 15°50 cms. The coefficient of surface-rigidity was calculated from the formula _ (re —7,") 1 nyt ry To ‘|? The omission of the term involving the logarithmic decrement is admissible even when the damping is excessive. The vessel was placed on a graduated turntable, and the disk was set into motion by sharply turning the table through about half adegree. The oscillations were timed by observing the end points since, of course, the centre of oscillation was indeterminate. A stop-watch reading to 3 sec. was used. Method of Experiment.—The disk was cleaned by polishing in the lathe with fine emery and afterwards wiping with a clean cloth. The glass vessel was cleaned by treatment with hot chromic acid, followed by repeated washings with distilled water. The disk was suspended and allowed to attain a state of steady oscillation. The vessel was placed centrally on the turntable and adjusted concentric with the disk. The solu- tion was then run in from a large separating funnel—a little having previously been run to waste in order to ensure a fresh surface—care being taken to avoid the formation of bubbles on the surface. During this operation the motion of the disk was observed through the telescope. Six solutions were used, containing one part of saponine in 10°, 10°, 10*, 10°, 10°, 10" parts of water respectively. In the case of the first three solutions, the slow oscillatory motion was stopped immediately the solution came into con- tact with the disk. Before coming to rest the disk generally executed a few rapid oscillations of small amplitude. These oscillations could be set up by rotating the turntable. In the case of fresh surfaces it was never possible to observe more than four oscillations, so that the time of oscillation could only be measured very roughly. Different experiments carried out with these three solutions gave for the initial period values ranging from 2:2 to 2°5 sec., corresponding to absolute values of the surface-rigidity varying from 83 to 65 dynes per cm. ‘his variability is not surprising when we consider, first, that it is difficult to measure the time of oscillation accurately; and, secondly, that we are dealing not with a perfectly fresh surface, but with one a few seconds old, and during this initial period the elasticity is increasing very rapidly, so that the value obtained will depend upon the exact moment of taking the observation. It is probable, too, that the manner ot formation of the surface has some Surface Elasticity of Saponine Solutions. 323 influence on the initial elasticity. Some of the earlier experi- ments seemed to indicate that the initial elasticity was slightly greater if the liquid was poured out so as to splash and form bubbles on the surface, than if it was poured out with the minimum of mechanical disturbance, but this result was not satisfactorily verified by subsequent experiments. No difference in the initial elasticity between the con- centration limits 1 in 100 and 1 in 10,000 could be detected. Between the concentrations 1 in 10,000 and 1 in 100,000 a rapid change occurs. HWxperiments carried out with solutions of intermediate strengths gave the following results :—— Tase I. | Concentration: 1 part in : T (initial). 15,000 2°5 to 3 sec. 16,000 | & sec to ©. 17,000 | | Motion oscillatory of the first type with exces- 20,000 J sive damping. It does not follow that any specially marked change occurs between the concentrations 1 in 15,000 and 1 in 17,000. The point at which the effect of the surface changes from elastic to viscous depends upon the dimensions of the appa- ratus. Thus, by using a vessel with a diameter of 8 cms., all the above solutions show an initial elastic effect. By using a disk with a very small moment of inertia and having the annular space between the disk and vessel narrow, an initial elastic effect can be obtained with solutions much more dilute than the above. There is a limit, however, in practice to the effectiveness of such arrangements, due to the fact that a certain amount of liquid moves with the disk and surface, so that however light the suspended system there is a lower limit to the inertia of the total moving system. In the case of the 1 in 100,000 solution, it is impossible to obtain an initial elastic effect even with the most favourable arrangements. The surface has, however, a marked initial viscosity. The excessive rapidity of formation of the elastic surface in the case of the stronger solutions is shown by the fact that’ it is impossible to destroy, or even temporarily impair, the elasticity by mechanical means such as stirring the liquid with 324 Mr. S. A. Shorter on the a glass rod. In fact, the only effect of such an operation is to set up oscillations of the second type. In the case of the 1 in 10’ and | in 10° solutions, there was a rapid increase of superficial viscosity on standing, and the surface gradually developed an elastic effect as previously described. The 1 in 10" solution showed no trace of elasticity, or even of marked viscosity, after 24 hours. The properties of elastic surfaces formed after prolonged standing will be next investigated. The Hlastiaty of Long-exposed Surfaces. After prolonged exposure of the surface the elastic forces attain a high degree of permanence. In many cases the disk may be made to oscillate for about 20 seconds. At this stage the surface cannot be described as viscous. For small motions which do not shear it beyond its elastic limit, the surface behaves as an elastic rather than a viscous body. It is only under excessive shear that the surface shows a viscous effect. On measuring the surface elasticity at intervals extending over several days, it was found that after the initial period of rapid increase there were considerable fluctuations during the course of the day. The elasticity was generally greatest in the morning and decreased during the day. ‘These fluctuations were most pronounced if the temperature of the room was much higher during the day than during the night. Further investigation of this point showed that these fluctua- tions were not primarily due to temperature changes. The decreases which occurred during the day were found to be due to the condensation of water-vapour from the air of the room on the surface. Thus the effect was very marked if after a cold night the room was warmed and occupied by a number of persons so that the air became saturated with moisture at a temperature much above that of the solution. In order to eliminate this effect a special form of apparatus was designed. This is shown in the accompanying diagram (fig. 2). A is abell-jar 35 cms. high and 18 cms. in diameter. From a short piece of brass rod passing through the centre of the stopper B was hung, by means of a thin steel wire, the ‘rod carrying the disk and mirror. Cis a wooden base with a circular groove into which the mouth of the bell-jar could be fitted. A steel screw was fixed through the centre of the base. To the upper end of this was fixed a circular piece of wood, D, which served as a platform for the vessel. To the ‘lower end was soldered a horizontal radial arm, E, which ‘projected slightly from under the base which was supported Surface Elasticity of Saponine Solutions. 329 on three levelling-screws. The bell-jar was luted to the base by means of mercury. In the case of long-exposed surfaces, oscillations could be set up by merely pressing in a horizontal direction against the end of the arm E, which was slightly Fig. 2. A ETAT ANAN LAER \ XY Wes RAN NS ERA DDOR — rn - XSSAS AAAS rs ef ee ee ES VAAL \ ae od eo i ISNA SNS f SN \ aah ——— flexible, without, visibly moving it. Owing to the fragility of the surface this method was preferable to actually rotating the platform through a comparatively large angle. The motion was observed by focussing a short-focus telescope on the reflexion of the filament of an incandescent electric lamp. By this means several well-defined lines were obtained, in spite of the thickness and curvature of the glass; and by observing the motion of one of these relative to the dust- particles in the eyepiece of the telescope, the end-points of the oscillations could be quite accurately noted. The condensation of moisture on the surface was prevented by placing a number of shallow vessels containing calcium chloride on the base. A deeper vessel containing a little of the drying agent was suspended by means of a loop of wire from the stopper. 326 Mr. 8S. A. Shorter on the Experiments carried out in this apparatus showed that the continuous evaporation promoted by the calcium chloride had a marked effect. The fluctuations in the density were totally eliminated, the elasticity steadily increasing to a maximum much greater than any value attained when the solution was exposed to the air of the room. In the following table are summarized the results of a number of experiments carried out with solutions of different strengths. TABLE EL. Concentration: 1 part in | | Age of | Surface | | | | | (days). | 100. | 500. 10,000. |100,000.200,000.| 10°. | 107. | 10*. | iW at 332.4) 871) || 535, -| 390 By 364 81 0 Ol see fi oe | ss, | (490 | 464 | 427° | SOO ieee | 393 | 427 | 581 | 556 |° 581 |. 460 ps. a Bae 408 | eee Be oH i - n a ee | 467 | 612 | 630 A 464 es 0 ot eee | 468 626 | 628 Be 465 Be iia epee | 474 | | "629 | 626 |) 538°) 471 9) ies eee A7B oe 648 | sg 200 dF ee 523 | 648 | 1% Ae ae 548 644 516 | peas | 574: TE eae | 595 | DA: ass! | 597 | | BO scee- | 593 | | | The most striking fact illustrated by the above table is that increase of concentration beyond a certain point is unfavourable to the process of surface separation, causing a slight decrease in the maximum value of the surface-rigidity aud a very great decrease in the speed with which the maximum is attained. There is a marked difference in this respect between a 1 per cent. and a ‘0005 per cent. solution. The latter attains a well-defined maximum in three days, while in the case of the strong solution the increase proceeds very sluggishly and irregularly for a period of about three weeks before a maximum is reached. The action of continuous evaporation in causing a higher degree of elasticity to be attained may be partially explained in the following way. When the solution is exposed to the air of a room whose temperature fluctuates, there will be certain periods during which water is evaporating from the surface and other periods when water-vapour is being con- densed on the surface. When the elasticity has reached a stage when the increase is very slow, continued evaporation Surface Elasticity of Saponine Solutions. 327 will have very little effect. On the other hand, the conden- sation of moisture on the surface will have a marked effect in diminishing the surface elasticity, the magnitude of this effect depending on the relation between the rates of forma- tion of the water-film by condensation, and of the separation of the saponine in the new surface-layer thus produced. Hence the effect of alternating periods of evaporation and condensation, even though the amount of evaporation is much greater than the amount of condensation, will be to prevent the surface from ever attaining the degree of elasticity attained when the surface is kept “‘ dry.” This effect was graphically illustrated by an experiment carried out during the cold weather in the early part of January. The above apparatus was used, but no drying agent was employed. The nights were very cold and the room was strongly heated during the day. In the morning the inside of the bell-jar was covered with drops of water, which had distilled over from the solution. During the day the walls gradually dried, the moisture distilling back to the now colder interior portions of the bell-jar, z.e. to the surface. Corresponding to this to-and-fro distillation of moisture were observed fluctuations in the elasticity. A 1 per cent. solution was used, and the value of the coefficient of rigidity fluctuated from about 400 dynes per cm. in the morning to about 350 dynes per cm. in the evening. The experiment was conducted for several days, and there was no progressive increase such as occurs when continuous evaporation is promoted (see Table II.). In the following table are given the values of the coefficient of rigidity attained by different solutions after standing about 24 hours (a) exposed to the air of the room, (b) in the apparatus. TasueE III. | Concentration: 1 part in a. b. | 10,000 A04 5850; | 1,000,000 92 || 390 10,000,000 Ceeiyel 81 It will be seen that the more dilute the solution the greater the effect of continuous and rapidevaporation. Itis probable that in the case of very dilute solutions the effect is more 328 - Notices respecting New Books. direct than that indicated above. The evaporation, if suffi- ciently rapid, may maintain a permanent difference in con- centration between the body of the liquid and the portions near the surface, in spite of the tendency for diffusion, thus giving the equivalent, from the point of view of surface separation, of a stronger solution. This effect will only operate to any large extent when increase of concentration greatly increases the power of forming an elastic surface, 2.e. in the case of very dilute solutions. The University, Leeds, Sept. 5, 1905. XXVI. Notices respecting New Books. Lehrbuch der Physik. Von O. D. Cawotson, Prof. Ord. an der Kaiserl. Universitat zu St. Petersburg. Dritter Band: Die Lehre von der Warme. Uebersetzt von E. Bere. Mit 259 eingedruckten Abbildungen. Braunschweig: F. Vieweg und Sohn. 1905. Pp. xi + 988. HE translation of this excellent and thoroughly up-to-date text- book is nearing completion, and Vol. ILI. is now before us. It is divided into fourteen chapters. After a general introduction, in Chap. I., on heat considered as a form of energy and its relation to other forms, the author deals, in Chap. II., with thermometry, including modern methods of measuring very high and very low temperatures. The next four chapters are devoted to the deter- mination of expansion coeflicients, specific heats, thermo-chemistry, the laws of cooling, and thermal conductivity. So far the treatment follows, more or less, the usual arrangement adopted in standard treatises on the subject. The greatest amount of originality is displayed in the remaining portions of the book, which form more than one-half of the entire volume. Here the author deals (in Chapter VIII.) with the principles of thermo- dynamics (and a more masterly exposition of the subject could not be wished for), with the applications of thermodynamics to various phenomena studied in the earlier chapters, and to changes of physical state (Chaps. IX. to XI). In Chapter XII. we have an account of the properties of saturated vapours and hygrometry. Chapter XIII. deals with unsaturated vapours, the critical state, and the theory of corresponding states. The concluding Chapter XIV. is devoted to the Phase Rule and the theory of solutions. Little need be added to the praise already bestowed upon this comprehensive and remarkably lucid treatise. To the advanced student of physics it is a veritable treasure, and its detailed and careful explanations, with its wealth: of excellent illustrations, particularly fit it for purposes of private study; while its numerous and systematically arranged bibliographical references render it a most valuable work of reference to all interested in physics. Phil. Mag. Ser. 6, Vol. 11, PI. V. CURRENT x 10° — °c oc aa | ONG Since Ee | CLE ho 2 IEE o Cia JESS S S5eRen0a a Ce RE R Soe eae (el ft ls BEGOEE Tememie DI ESS eae oS —_ & 7 ene eae 1” (S300 See : OOS -CEE Ter s oO eo i a a a JERSE SEAS sees JE SSSR ees ese nee RE OL NS «IEE SSE eaiE sae ‘Sse eh eee aes eee Jee Sees betes kee te ein eee eee Ni Ee o\ Ee NE LN et ea ¢2 ~ Gases “DIY Lind © oly) E Dies 2) Te. 3, = 0 LL) ict = SEI A BBP) =} nee Beer | ‘ lm eH re es 1 0. ad 4 ry De ia e TT | sdaehe 1 (_| Ae E wo x q4 1x] ( Py ae 8 Banas e a ed rel S t0| : ee Gia ne [er as ae &p xv & mor Ss S 4 i iar | Sa |_| =| 8 x 2 3 Us a — 2| a6 2 i ae a EEE mya i=) IE J Sal 12345678910 15 20 25 CENTIMETRES 3 | 0 2 1 012345676 9\0 15 20 25 CENTIMETRES: Pie, 5, Fie. 4. lela 3 16 15 45 1a] 4 | 15 15 i2| 2 u " 10 410) +—4 “9 85 2 x z en o 8 3 x9 Ih * S BE Snes a Ss) mga! = Se) S7 p 2 5 e445 |_| S6 ple 4 in 5 a | os CS aia) 2 3 —} 1 A im ie | i} 1 J il O1 2345676910 15 20 25 I) CENTIMETAES 012345678910 15 20 2 CENTIMETRES. Fie. 10. 13 + te Do) > eer == Pe jt = © 10 Al % 58 ee Pelz cr S5 4 Si Z S 2 j || 012345678910 15 20 2 012345678 910 16 20 25 CENTIMETRES» CENTIMETRES. Tie, 12: 12 u 10] | it S | x9 - Telrad y be 7 | Se | S5| aL 3 _ ’ 7 os sh a gn mee ee ne en) i et papgey yee te ‘Sea nant SE Ney cnichenguRRAOH SANT Stee en tine Phil. Mag. Ser. 6, Vol. 11, Pl. VI. re. 2: Chuck & Ball Bearing Elassembly.] a ay Bs so as citer INDEXE LTHE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE [SIXTH SERIES.] MARC H 1906. XXVIII. On the Asymmetrical Action of an Alternating Current on a Polarizable Electrode. By P. G. Gunpry, Ph:D. (Gétt.), B.Sc. (Lond.), Assoc. R.C.Se., late Assist. Lecturer and Demonstrator in Physics at University College, Cardif’*. a.” great advance made by Kohlrausch t in the study of polarization by the use of alternating currents led to an extended series of researches in the subject, of which especially may be mentioned those of Warburg{, E. Neu- mann§, M. Wien||, Kriiger{], aud others. In all these investigations (with the exception of EH. Neumann’s) the so-called initial polarization capacity was considered, and the strength of the alternating current used was kept suf- ficiently small for this condition to be satisfied. There are, however, cases in which it is well-nigh impossible ‘with measurable currents to keep within these limits, and E. Neumann has considered the effect of an extension beyond initial polarization capacity in the Wheatstone bridge. From another side, however, in recent years the con- sideration of the action of an alternating current on a pola- rizable electrode has come into prominence, namely, in the * Communicated by Principal E. H. Griffiths, Se.D., F.R.S. The oreater part of this paper forms part of an Inaug ural-Dissertation in the University of Gottingen. t+ Kohlrausch, Poge. Ann. exlviil. p. 448 (1872). { Warburg, Wied. Ann. xvii. (1899), and earlier papers. § E. Neumann, Wied. Ann. lxvii. P. 500 (1899). || M. Wien, Wied. Ann. lviii. p-. 37 (1896), and others. q F. Kriiger, Zertsch. f. phys. Chemie, xlv. p. 1 (1903). Phil. Mag. 8. 6. Vol. 11. No. 63. March 1906. Z 330 Dr. Gundry on the Asymmetrical Action of an so-called “ Electrolytic Coherer.” This instrument was in- troduced by Fessenden* and Schlémilcht, the latter of whom made the first penetrating investigation in the subject. Schlomilch, as is well known, found that the current thr ough an electrolytic cell, in which a very fine point of platinum formed the anode, and to which an E.M.F. of several volts was laid, was greatly increased by excitation with electric waves. He found a negative result when the point was a cathode. The explanation of Fessenden, that this resulted from a warming of the electrolyte in the immediate neighbourhood of the small electrode, was proved untenable. Later experi- ments (of Rothmund and Lessing) show a coherer and not an anticoherer effect, when the electrolyte (e. g. phosphoric acid and hypophosphorous acid at higher temperatures) has a negative resistance temperature coefficient. The work of Reich {, in which he found a difference when sending a non- oscillating discharge of a Leyden-jar through the cell ac- cording to the direction of the discharge, led him to explain the phenomenon as a depolarization effect. A great addition to the knowledge of the facts was made by Rothmund and Lessng§. In the first place, they showed that the coherer action was even relatively more pronounced when the applied H.M.F’. was under that required for decom- position, and that under these circumstances the very small polarization current was increased when the point was a cathode as well as when it was an anode. ‘The effect of the waves was, however, much greater for an anodically pola- rized point than for a cathodically polarized one. The magnitude of the effect was found to depend in very great measure on the sign and magnitude of the direct-current polarization. It was also shown that the E.M.F. of electric batteries, in which a small point, made of different metals, formed one of the electrodes, was altered by the action of electric waves. On the theoretical side there is, so far as I know, no satisfactory explanation. The idea of the depolarization set forth by Rothmund and Lessing, by which one phase of the alternating current passes easily from electrolyte to electrode owing to oxidation, the other with difficulty, based on a comparison with the aluminium rectifier, appears to help but little to a clear understanding of the question. A satisfactory * Fessenden, Elektrotech. Zeitsch. xxiv. pp. 586 & 1015 (19038). + Schlomilch, cbed. xxiv. p. 959 (1908). t M. Reich, Phys. Zeischr. Vv. p. 838 (1904). § Rothmund and Lessing, Drude Ann. xy. p. 193 (1904). Alternating Current on a Polarizable Electrode. 331 explanation must account for the very marked dependence on the degree of polarization of the electrode. We know, however, very little indeed of the conditions which prevail in an oxygen- or hydrogen-charged platinum electrode, and the hope of obtaining a satisfactory explanation of the above phenomenon seems remote until this gap in our knowledge is filled. The object of the present paper is to show that in a polari- zable electrode in general (and the results obtained for the simplest of all cases, here treated, are applicable in principle to all polarizable electrodes), so soon as we pass beyond the stage of initial capacity, the alternating current gives rise to an asymmetry, which would appear as a coherer effect ana- logous to the above. In order that this asymmetry may be sufficient to account for the coherer effect used in practice, certain conditions must hold (afterwards to be developed), which, though not in antagonism with any known fact, and, indeed, corroborated to some extent by what is known of the conditions, must be proved or disproved by a greater ex- perimental material than I am at present able to bring forward. With this reservation, however, I believe that the application to this practical case is not without interest. The case here considered is that of a mercury electrode. The conditions are much better known than in the case of platinum, and the changes of concentration, taking place as they do, not in the electrode but in the liquid, are easier to follow. Another advantage that mercury offers, is that the electrode can always be set up in a perfectly definite con- dition, and with comparative ease in a pure:state. The experiments, to be atterwards described, consisted essentially in the sending of an alternating current of fre- quency varying between 80~ and 5000~ per second through an electrolyte between two electrodes, of which one was very small, the other more than a thousand times as large, so that the latter may be considered as unpolarizable in comparison with the former. A galvanometer in the circuit showed that che alternating current, before symmetric, was rendered asymmetric by the passage through the electrolytic cell. In other words, there was superposed on the alternating current a direct current, and the production of this direct current involves the existence of an asymmetry in the E.M.F. of the polarization produced by the alternating current. This asymmetry seems, however, to be a natural conse- quence of the osmotic theory of Hlectromotive Force in genera! and its application to polarization in particular. According ZL 2 TO Dr. Gundry on the Asymmetrical Action of an to this theory we arrive at the Nernst formula for the E.M.F. of polarization : oS ee . 7t where R is the gas-constant, @ the absolute temperature, and n the valency Hoke lon concerned. co is the ionic cencentration in the neighbourhood of the. large electrode (which remains practically unaltered), and c the concentration of Hg ions in the layer of electrolyte- immediately overlying the small electrode. If now e oscillates symmetrically about a mean value, the logarithm, being an asymmetrical function, changes. asymmetrically. ‘We have BS Sloe wo n © e+ sin mt in the direction corresponding to a cathodic polarization. Without the alternating current The E.M.F. in this direction will be increased or diminished’ according as jsinmt is negative or positive. It follows, however, from the asymmetry of the function, that ie increase Saher jsin mt is negative has a far oveater effect on the polarization (E.M.F.) than the diminution when jsin mt is positive. This asymmetry falls away naturally when / is so small as compared with ¢ that, in the expansion: of the logarithm in series, only the first term need be re-. tained, 2. e. in the condition of initial capacity. So soon, howeve er, as this condition is passed, the asymmetry comes into play, and this ali the sooner and the more markedly the smaller c¢ is. It follows, therefore, that the mean value. of the H.M.F. is not zero, but that a direct current is pro-- duced, which flows from the small electrode to the large. electrode in the solution. The asymmetry brings with it an effect equivalent to an apparent dilution of the salt in the. neighbourhood of the small electrode, even when the mean Be eontration really remains unalter Aa (or even when the. mean concentration is really increased by the alternating current, as will be shown sometimes to be the case). Phys ically worded, this effect arises because a diminution. from a small initial value of the concentration causes a much . . 299 Alternating Current on a Polarizable Electrode. 335 greater E.M.F. alteration, than the same concentration increase, So soon as the alternating current ceases to flow, the E.M.F. also instantaneously ceases to exist. There is no atter-effect. The quantitative consideration of this effect requires an hypothesis of the mechanism of polarization, and is intimately bound up with the nature of polarization capacity. In an- tagonism to what he called the ‘ Ladungsstromtheorie”’ of Helmholtz, which looks on the action of the alternating cur- rent as the charging and discharging of the condenser-like double-layer, Warburg introduced what he ealled the “ Leitungsstromtheorie,’” which disregards the part played by the double-layer, and recognizes, alone, the changes of ionic concentration which take place in the neighbourhood of the electrode and the diffusion which goes on simul- taneously. These two points of view lead to different results, which may be tested by experiment: viz., according to the Helmholtz view, the polarization-capacity is independent of the frequency ; according to the Warburg view, it varies as i : : ; : 5==——, while at the same time the phase-alteration 1s / Frequency different according to these two theories. Kriiger, taking into account both these elements of polarization capacity, has shown that the one or the other predominates, according to the nature of the electrode and the concentration of the electrolyte. In dealing, however, with the asymmetry, it 1s clear that the Warburg form alone comes into consideration. The double-layer can introduce no asymmetry, and, indeed, the experiments of Kriiger show that, in the cases considered, this part of the polarization capacity is small compared with the other. The method I have here used is as follows :—An alter- nating current of pure sine form passes through the electro- Ilvte. The resulting changes of concentration follow also an harmonic law, and the asymmetry of the resulting polarization, calculated by the Nernst formula, gives an H.M.F. in one direction, which causes the observed direct current. Jt may be objected, that the symmetry of the current and therefore of the concentration changes is disturbed by this very effect. The direct current observed, however, was always a small fraction of the alternating current, and the alteration of the ion-concentration may relatively without error be considered as due to the undisturbed alternating current. Of course a method of successive approximation may be applied; 7. e. from the calculation I have made, a nearer approximation of the d+ Dr. Gundry on the Asymmetrical Action of an actual concentration changes may be calculated, and so the H.M.F. of asymmetry reckoned once more; but this nearer approximation would make no essential alteration and would add seriously to the complication. Following, now, the method of Warburg *, we suppose 29 sin mt the alternating current, Cy the Hg-ion concentration in the neighbourhood of the large electrode (practically unaltered), c the same in the neighbourhood of the small electrode. c changes, partly through diffusion, and partly through the quantity of Hg-ions brought in and out of solution by the alternating current. Let g = area of the small electrode, and ¢ = the charge of electricity on a gramme-ion. For the diffusion, we have : or 0’e PY; =kK pee . 5 : ° : ° (1) where < is measured perpendicular to the small electrode (supposed a small plane), and « is the velocity of diffusion. The boundary conditions are:— where z= 0 ; 2) sin mt - (2) QeK =($" 286 ; and where z=, C= Opetde val |) ee The solution is: c=) + Be-*s cos ( me = ’ ot ¢) where Sy b=" ee Sto — Pest are m 7 4 4 2qgeK A sin d gé A/ Km t Where < = 0, we have c= c+ B eos ( mi — a} 0) The polarization is R9 C (pea oy n Co * Warburg, loc. cit. Alternating Current on a Polarizable Electrode. 335 = ES pod’ volt. i ——=(9 s ° is always less than 1. Co The observed direct current I corresponds with an E.M.F. which is the mean value of p. Q0 1 Ti ft Gas tay ay nanan oe Wa’ Co) 2 9 w.22\ Me Jo where W is the total resistance in circuit. Therefore 2g Xr m B 1/B\? Ti i : eeaaere en 7) s(- ) a =) = any sa dt ‘ 7m cos (mi ae 7h aes cos? { mt + i Now i cia Gi +7 at ar 0 an Be (Dns ; = cas (oil 9 Yak . UPD O41) te 4 2°? p} m 0 where p is any integer. Therefore ey ee PEN ON ee: ae DES i ee (6.5.4 ie LGR OE i Oe a nas a) This series is convergent if = <1. This condition is 0) always fulfilled, as B / ss -, Cos ( me =e i) Se eet, Co 4 Co The series may be summed, but the summation is more easily obtained by direct integration. 336 Dr. Gundry on the Asymmetrical Action of an As may easily be shown, (" log (1 +.a°+ 2a cos @)=90, 0 xY and therefore 2m 27 { log (1+ £ cos @) dé =! log (1+ a?+ 2ucos@)d0—2mlog(1 + a’) V0) 0 —27 log (1 +a’) 2a (where a ae = 2 SE) te eee ) 1+ nN be e e e B 4 Taking once more the series (6), and neglecting ( ~) and higher powers, Co Oa eh Tet AWE hin UMN ha zetiein C42 r de 8a Waqe? c 2( Ke,2) N where N= = is the frequency. Therefore INI ae alata Te = CONSE. aii: ete Tol ans (7) The direct current therefore flows from the small electrode to the large electrode in the electrolyte, and is directly proportional to the square of the strength of the alternating current, and inversely to the frequency. It is clear that the direct current is the greater, the smaller the value of ¢ is. Tt is to be noted that the effect in this case is not a depolarization, but a virtual increase of the polarization. ae Alternating Current on a Polarizable Electrode. 337 Special treatment of the case of the Solution of a Complex Salt. It is necessary to treat of solutions of complex salts separately. The polarization capacity of a mercury electrode has been worked out in this case theoretically and experi- mentally by Kriiger * In the case of complex salts there is a third element which comes into play in addition to the double-layer of Helmholtz and the effect connected with diffusion, considered by Warburg. This is due to the fact that the mercury ions are formed from complex ions by dissociation when the current brings ions out of solution, and the mercury ions, when brought into solution, disappear to form complex ions, and these ionic reactions do not take place with injinete velocity. Kriiger considers three limiting cases :— (1) The concentration of the mercury salt is very small. In this case the double-layer plays the most important part, as the ion quantity supplied by dissociation is small compar ed with that required to form the double-layer. (2) The solution is of medium strength. With increase of concentration, the diffusion and dissociation come into im- portance. The influence of diffusion, especially that of the undissociated complex, is the impor tant factor. (3) The limiting case, where the concentration of the ot is very great. If the velocity of reaction were infinite, the electrode would be unpolarizable. This velocity is, however, even if very great, by no means infinitely oreat, and for frequencies so highas 1000~ to 5000~, probably the velocity of reaction is an Important factor. The three cases are characterized by the theoretical result that the polarization capacity in the first is independent of : 1 : the frequency, in the second is proportional to ——, and in | ~ e it no e e e the third to N Kriiger gives cases in which these three limiting eases are realized or at any rate nearly approached. tn considermg the asymmetrical action in the case of complex salts, we may put aside the first limiting ease as presenting nothing new, being the same as with typical salts of small concentr ition. Also in the second ease, it is clear that the corresponding case with the solution of a typical salt is only so far altered, that the diffusion is that of the complex, and not that of the mercury ion. The finiteness of the velocity of reaction has * Ksriiger, doc. eet. 308 Dr. Gundry on the Asymmetrical Action of an no importance in the case where diffusion plays the chief part; and therefore we may suppose that the mercury ions which come into solution practically all disappear instanta- neously in the form of the undissociated complex, and with the same rapidity, the mercury ions required for the opposite phase of the current (from electrolyte to electrode) are supplied from the complexes. Let us suppose that the equilibrium in a reaction Hg,A, 2 @ wHigt ty. A’ (where A' represents the anion, and Hg,A, the formula of the complex salt) is reached with infinite velocity, and cor- responds to a very small mercury ion concentration. Let c be the mercury ion concentration in the neighbourhood of the small electrode. ey the same in the neighbourhood of the large electrode. v, Vv) the corresponding concentrations of the undissociated complexes. Then V=GCG. Vy= Cy" by the law of mass action, where o is a large constant. The concentration of the anion is considered constant on account of the presence of an indifferent electrolyte with the same anion. The equations now become y "y P OM io ke Pia DAs ett ace.) as), oe iy" ot Os there. ~—0 lg Su wee av u where ==0, ge ns > hn af) Oe Bh gee, The equation (2)’ is arrived at by supposing that each ion which comes into the solution disappears, and « such ions correspond to one complex molecule. As before, we have ROA iC 0d ANC Oe en Sot Bey 8 p=—_ log sl ae ce =~ log ea cos{ me oa ? ; a pS eee ade KS 5 1 = ee Sea | Wael NY) Pd rales ak te am M2 Alternating Current on a Polarizable Electrode. 339 The direct current I in the direction from large to small electrode in the electrolyte is 27 —rB” ile SOT) 4 W e Vo” { BY if we neglect ( =) and higher powers, 0 = My Ls ths Uy AW .y,7y7e2"xm = 82 W.. GPe?a*xv2 N’ NI oy ee SC OMStags wer he Lay os a lle ea) Me , where N= — = the frequency. AT We are, of course, led to the same relation as before. The magnitude of the effect depends upon the smallness of the concentration of the complex substance. With the third case, however, there is a marked difference. If the concentration of the mercury salt is very great, the changes of concentration that take place are negligible. If the velocity of reaction were infinite, there would be no effect —indeed, no polarization would be possible. This is, however, not the case; and changes take place in the concentration of the mercury ions, though not of the undissociated part. Following Kriiger, we take the case of a mercury salt HgA, which is dissociated in very small quantity, according to the equation Ili Agape a it oreo ye Mae gon cs (8) It, now, ¢ is the concentration of the Hg ions and ¢’ that of the undissociated part, then we have the equation of chemical kineties : de Hide =k? —kyc', my varies te tne h Sh) (9) where k,, ky are the velocities in the two respective directions of the reaction. A certain very thin layer of thickness 6 is supposed, in which the polarization phenomena take place. The quantity of Hg ion which is brought into the solution by the alternating current in every moment must be equal to that which disappears according to the equation (9). — where K= 340 = | Dr. Gundry on the Asymmetrical Action of an In this way, Kriiger obtains the formula for the polarization : 00 p= oS a sin mt), a \ ey omni,” where ty sin mt is the alternating current, q the area of the electrode, e the electric charge on a gramme-ion, and c,the concentration of the He ions in the neighbourhood of the large electrode. The asymmetry of F the logarithm gives rise, once more, to a mean E.M.E,, corresponding to a direct current : Me gal iL ANZA k - Ww 12 KS elie) 4 j=— lg : eq . Ow. kyo” The series 1s convergent, because K <1. If the alternating current is so weak that the asymmetry just appears, we can neglect Kt, K°, &e., and I R@ iy i Ne iy” S2W Vey dx . keg? my) ea ‘ee The direct current is, in this case, tndependent of the Jrequency. Insturbing Eject due to the Asymmetry of the Current itself. When the electrolyte was dilute sulphuric acid, it was clear from the experiments that a disturbing effect of a totally different nature was present, and that this masked that pre- viously described. This effect showed itself, nnlike the other, in a permanent increase of the concentration in the neigh- bourhood of the electrode. ‘There was always an after-effect. When the alternating current ceased to flow, the galvano- meter slowly went back to zero. “I attribute this disturbing effect to the following cause. Only a limited number of He i ions are at hand to carry the current from electrolyte to electrode. Ifthe number imme- diately surrounding the electrode does not suffice, it is only by the slow process of diffusion that the defect may be made up. ‘The result is that part of the pulse of the current is carried by hydrogen ions. Before the return pulse of the current eee electrode to electrolyte, some of the hydrogen Alternating Current on a Polarizable Electrode. 341 has been lost by diffusion. More mercury ions are brought into solution during the one phase of the current than were brought out of it in the other. Hence a real increase of the ionic concentration in the nei ighbourhood of the small electrode takes place. It is to be remarked that this effect goes in the opposite direction to the first. Its existence is shown by the presence of an after-effect. Though it is not possible to ‘separate the two effects, it is interesting to note which predominates. I feund, with all the electrolytes that I tried, a certain eataodic direct-current polarization, at which the two effects exactly neutralized each other. For lower cathodic polarization (greater Hg-ion concentration) the first effect predominates, and a current flows from small electrode to lar ge in the electrolyte ; and for cathodic polarization higher “han this “Nullpoint”’ (7. e. with smaller He-ion concentration) the second effect predominates, and the current from the large electrode to the small electrode in the electrolyte is increased by the alternating current. It is clear that both these effects increase as the Hg-ion concentration is diminished, but the second increases more rapidly than the first. I found the Nullpoint with H,SO, saturated with He,SO, at about 0°14 volt; with KCN, on the other hand, at 0°36 volt; with K.S at about 0°62 volt cathodic direct: current polarization. In order to test the results obtained theoretically for the first and more definite effect, it was necessary to use an electrolyte, for which this second effect was inappreciable. Such a case I found to be KCN solution when no direct- current polarization was applied, as was shown by the very small after-effect on shunting out the alternating current. That the second effect is unimportant in this case is to be attributed to the fact that here the mercury salt in solution is a complex one, and the excess of Hg ions brought into solution mostly disappear in the form of complex molecules, and therefore do not to any great extent effect an increase in the Hg-ion concentration. ‘Tt may also in part be accounted for by the fact that the solution is alkaline owing to hydrolysis, and hence hydrogen icns are present only toa very small extent. Experiments made with other electrolytes are described fully inanother place*. I will here only bring forward the results with this electr oly te, to show to what extent the results previously obtained hold. * Zeitschr. f. phys. Chemie, liii. p. 177 (1905). 342 Dr. Gundry on the Asymmetrical Action of an Apparatus and Heperiments. - For the production of the alternating current, I used partly the sine-inductor of Kohlrausch and partly the Dolezalek alternating-current machine, made by Siemens and Halske. In the former, the rotation of a magnet in the form of a small disk inside a coil gives a current of very pure sine form. By use of different weights to drive the clockwork I could obtain currents of frequency 80~ to 120-~ per sec. With the Dolezalek machine, in which the iron circuit of an electromagnet is almost completed and broken 120 times during each revolution of a wheel and a current induced in a secondary wound round the magnet, a current up to 5000~ per sec. (10,000 pole changes) could be obtained. For the measurements of alternating-current strength I used an electrodynamometer of the Kohlrausch type, which gave a double deflexion of 1 mm., read with telescope and scale at a distance of 1 metre, for a current 0°72 x 10-4 amp. For alternating currents too small to measure directly I measured the E.M.F. of the machine, using a measurable current and known resistances, and calculated from the resistances in use at any time the current str ength. The direct currents were measured by galvanometers of moving-coil type. Fig. I. In some cases a direct-reading galva- : nometer of sensitiveness 1 diy. for 5x 10" amp. was used, “and: im EG others a mirror galvanometer of sen- sitiveness 1 mm. (double throw) for | 432% 10~-° amp. | The electrolyte was contained in a | small beaker. A layer of mercury, | covering the bottom, formed the large | electrode. The electrical connexion with Y it was made with a platinum wire sealed in a glass tube in the ordinary way. - Dipping in the solution, there was a / | op capillary tube of the form shown in fig. 1. \ The small limb, about 3 cm. long, had / Z an inner diameter of 2:14 mm. The G47 wider limb had a diam. 14 cm. The mercury meniscus was from 2 to 3 cm. from the open end of the tube. In some experiments the .M.F. between the electrodes was directly measured with a Dolezalek quadrant electro- meter. Its sensitiveness was 1 mm. for 0°0043 volt. Alternating Current on a Polarizable Electrode. 343 The arrangement is shown in fig. 2. Janae 2. M is the alternating current machine. K, electrodynamometer. AB, the solution. A, the small electrode. B, the large electrode. G, the galvanometer. W, a high resistance. R and S are resistances, and e a battery, so that an E.M.F. ee could be included in the circuit. R+S8 was always 10,000 ohms. F, the quadrant electrometer. CD was a resistance-box which amounted to 11,000 ohms. The part CK could be 100, 200, &c. up to 1000 ohms ; or 1000, 2000, &. up to 11,000 ohms. I could in this way obtain a calculable fraction of the E.M.F. of the machine. L was a key, so that the alternating current could be shunted in and out of circuit without stopping the machine. All the resistances were without self-induction. With higher frequencies the resistance W had a very high value (in most cases 100,000 ohms), so that the effective increase of the resistance of the galvanometer and electrodynamometer o44 Dr. Gundry on the Asymmetrical Action of an due to self-induction could be neglected in comparison with the total resistance. The experiments, shown in the following tables, were made with normal KCN solution without any direct-current pola- rization. The direct current observed was always in the direction in the electrolyte from small electrode to large. The deflexions of the galvanometer are shown in the third column. The measurements were made twice for each strength of alternating current, the first series with in- creasing current and the second with decreasing current ; both are given to show the constancy of the effect. In the fourth column the direct current I is obtained from the js mean of the two deflexions. In the last column =, is shown ve with the mean of the values given. 0 The value of the external resistance W was 100,000 ohms. TAB hel, Mieerat Direct | Frequency. Caan t Galvan. | Gusere | = Scr Defi. | Ae | 2o- | Ih | 0 | 10-5 amp. 10-8 amp. | 83 130 | 22:5; 22-1 19:34 1144 | 1-82 36.358 | 31-04 940 & 966 ba 28h 53:2: 52°6 45:8 814 | | igi 1505 ete eset) 06 2796 | DO3 T0150. 141 3) io756 2520 | | P88) W238 26 lmgloc4 ee. ; | 3:59 33:9 : | 29-24 296-4 | | Bas) ab 1 yi ONG ear eee ee) ) be cals 168; 151 | 13°72 1388 | 433.9 | 4-09 26-7: 257 | 226 1352 fe | 508 SiS ental tase Oo e 1268 | 499) |. 0S 10p | TOs Sane B64 90 | | 4°36 1782 07S) |\0) 908) y'< sisienee 564 28:3; 28:0 | 24:80 766 (° * | 7-00 41-0; his pep 724 | Bain <> 696 187: 171 | 15468 | 3184} | 9-00 P84: 281 | 24:30 29:98 | 20-02 11-19 409; 408 | 3526 | 28:29 1028 8-70 13-8; 128 11-50 15-22 12:18 DAD. 24-5 21 30 1440 | 14.99 15°77 39:6; 39-0 33:98 | 13:70 196 | 566; 56-4 48:8 12°72 3100, | 1488 LU eee lay «90 472) it 280 31:8; 302 26S) 10) 470" ae | 335 5452546 | 47-2 420 ( #82 [veer B05 Oe 692) B68 | ee ee Alternating Current on a Polarizable Electrode. d45 All these experiments were done directly after one another. ‘Table II. shows the results of another set of experiments, all done together, but on another occasion. The two sets of results are brought together, and the value NT. of 72 is given in Table III. 0 TasueE II. | | | | Altern. | Direct Frequency. Current Galvan Current we : Defi 4,2 ry | | I 0 BS sh | | | | _______. see 10—5 amp. | 10—8 amp. | 1700 863 | 130; 191 10°82 14:52 | 1431 | 302; 29:3 25 62 12°52 | oq 20°1 56°7; 51:3 466 | 11:56 26:0 | rude Giz 9:96 i 9990 isis | bl - 365 3002 | 11-84 ee | 94 | 77-3. 768 66:40 10:30 60 150 1; 195 17-48 7-76 | 250 48:3; 47-0 41:0 6:56 | 6-66 | 34-9 80°7; 79:7 69-2 5:68 5000 21:8 28:2. 26-7 93-62 4-96 288 45:6; 43-2 38:24. 4°60 | yng 36-1 63°3; 63: 544 LS) pa 50°6 100°7 : 80-4 3:14 TABLE II] | Frequency | yy NI N. Uke Gea 3 966 80200 181 247-8 44800 288 138-2 39800 | 449 80-2 35400 | 587 30-02 17500 1028 14-00 14380 | 3100 | 4-39 13400 1700 1214 20600 | 2290 11-06 25300 | 3260 6:66 21500 5000 4:58 22820 The difference in value for the two sets shows that the condition of the solution is variable. I found in general that results could only be compared when they were obtained on the same day. Phil. Mag. 8. 6. Vol. 11. No. 63. Mareh 1906. QA 346 Dr. Gundry on the Asymmetrical Action of an It is seen that only for high frequencies is the relation I a Sabb Fz const. In any measure satisfied. "The sudden change in the magnitude of the effect between N=400 and N=600 appeared so striking, that I repeated the measurements on a new solution. The esr ly are shown in Tables IV. and V. In this series of experiments, the resistance W was 30,000 ohms. For the sake of comparison, I have reduced the observed current I to the value I’ that it would have if the external resistance were 100, 000 ohms, as in the former experiments. Tape IV. | j | Altern. Direct | rime Altern. Direct | lV Freq | Current | Current Hie Sree | Freq. | Current. | Current | —. Te | sR Pa ra 1! oe T'.. | eae tele Sell |i [eae SR AP ae base 10—4 amp. | 10-8 amp. | 10—4 amp. | | '10—8 amp. | 332 | 0205 5:27. 11251 | | 1362) | 0563 657 | 207 1 0304 |i 11-85 | 1281 | | |' 0685 | 148 Gigie ' 0400 | 159 | 994 || 4) 1099 206 = | 17-08 | Bis | 0268 | 575 | 80 2000 0-689. | 691 |1458 | (0398: |) 4245 | 789 1) 1-02 14:35 | 13°80 | 0°523 1826 | 66-9 | | 1-341 14 =| 11-92 | : | i ) | 523 | 0319 596 | 586 || 2930)' 0835 | 744 |1067 | 0-475 12-45 See | 124°. | Teele i 0°625 189 | 48-4 || 163 | 24:2 aap 758 | 0:399 6:05 | 33-0 || | | | 0-591 138. 1 38a] | 07792] ASI | Seas | 1006 | 0466 | 648 | 298|| 534, O811 675 |70 | 0692 138 | 28844 0-462 13-91 | 65-4 0-91 202 | 24-4 || 0808 202 {547 | TABLE V. | | ! TT! | ee ae 2 a hell to to” % | es = —— »—_- —_ ——. 302 20°6 | 380 | 12600 | 518 79477) 233° | A2300Q08 | 523 569 17°08 8940 | 758 se0) | (114 |) edo 1006 29°34) 88 | 8810 1362 20°9 6:27 | 8550 2000 14-2 AD6 ii:) Wash SBlO 2930 10°9 B20 9550 — ——_ —— | | 5384 Git | 208 10850 | | Alternating Current on a Polarizable Electrode. 347 There is once more to be noticed a sudden change in the neighbourhood of frequency 500. The absence of any approach to agreement for lower frequencies may be in part due to the fact that the disturbing effect is of greater importance when the frequency is low than when it ishigh. Fora given value of the alternating- current strength, the lower the frequency the more mercury ions are required for the current. On this account the asym- metry of the current itself may be an important factor. The following tables show the direct current through 100,000 ohms as observed for different values of i) at low frequencies. TasLeE VI. TABLE V LI, | Frequency 89. Frequency 118. i Altern. Direct i Altern: Direct if Current. Current. dot Current. Current. ie amp. 10-9. | amp. 10—5. amp. 10-5. | amp. 10—5, 0:93 0-038 4400 1-89 a O0a02 846 1°32 0:0506 2900 2°26 | 6:0336 659 2-28 . 00697 | 1340 |) . 2-82 0-0451 567 3°01 0:0936 1034 | 3°74 | 0:0680 | 450 4-65 071195 551 5°54 0:0922 302 580 | 01892 Al4 6-47 01075 | 257 8:37 0:1750 250 729 0:1158 | 218 TasBLe VIII. N=93. | _ Direct I Altern. Current. | Current. in? amp. 10-6. amp. 10—8. 2 34 1950 4-67 4°18 1917 5°25 4-45 1615 61 571 1535 7:0 6°72 1372 8-4 8:05 1141 10°5 10°88 887 From Tables VI. and VII. it appears that the lower the 2A 2 348 Dr. Gundry on the Asymmetrical Action of an frequency the greater is the variation of i with 7%, and ae Table VIII. shows that by making the ps smaller, the variation is greatly reduced. Were it possible to work ‘auth still smaller currents, it may well be that a much nearer approach to constancy of ee at these low frequencies might be found. 40 Finally, Table IX. shows a test for an after-effect. A comparatively strong alternating current (3°05 x 10+ amp.) was run for half an hour through the cell, and readings of the galvanometer deflexion were made every 3 minutes. The alternating current was then shunted out and readings taken every + minute. There was 40,000 ohms in the circuit. TABLE LX. Frequency 680. Altern. current 3°05 x 10-* amp. Readings of Galvanometer. | | | | | | | | | | Time Defiexion. Without With min. | Alt. Cur. Alt. Cur, gt Nie Gigs Se) |Nmeieled Mee Ra lava iinet et eee | ee AT5'5 201'8 ee ee ee ae 485°5 181°8 L owe OK Ey taaere | 478-0 199-3 ee eae i oe 482-9 194-4 [is eo re ee 488-7 1886 | get, gee | 497-6 179°7 I aera (eo Pas" | 507:0 170°3 Bair ee 50771 1702 D7 eRe oe a ee 513-9 163-4 | 30°). Se eee 5147 | =: 1626 | \S0t eae I; 2 MOG Do eae anh be 2 148 Bee 672-7, Coe. 49 | Se ee EA an kel: 23 plug eae PR ye See ae 13 | SIG. scan [Clea ea. 12.00 Site ne tah G76 4a eee 09 | SER ala ar OF 2UGM I sec5k - 21 | | Even after this long subjection to a strong alternating current, very slight after-effect is to be observed. By using a capillary of wider bore | found the value of = - ; to vary inversely as the fourth power of the diameter, wh ae is also in agreement with the theoretical result. Alternating Current on a Polarizable Electrode. 349 The Effect with a Gas-charged Platinum Electrode wn Sulphuric Acd. I was not able to realize with complex salts of mercury the case where the effect, arising from the finiteness of the velocity of reaction, is independent of the frequency. It appears with KCN-solutions, from the approach to constancy of “3 that the velocity of reaction is sufficiently great for 0 the effect due to diffusion to come first into play, even where the solution is comparatively strongly concentrated. In a case where an asymmetrical effect is large at a very high frequency—at which diffusion must cease to play an important part—one is led, inversely, to consider that the effect, if it arises at all in the way above described, can only do so through the finiteness of some velocity of reaction. Such a case is that of the ordinary electrolytic coherer—a small gas-charged Pt electrode in dilute sulphuric acid. In the first place, the effect of the above described asym- metry would be a virtual diminution of the gas charge, 7. e. a depolarization such as is observed. As for evidence of the reaction which takes place, the following work on the solution of hydrogen in palladium and platinum bears on the subject. Hoitsema * found from the pressure-concentration curve of hydrogen in pailadium, that the hydrogen is dissolved at ordinary temperatures in the atomic form and not in the molecular. A. Winkelmann + found that hydrogen diffuses through glowing palladium as H, and not as Hy. The same author { found an exactly analogous result for hydrogen diffusing through hot platinum. More recently, O. W. Richardson, Nicol, and Parnell § have shown that the dissociation of the hydrogen takes place in the platinum, and not outside it. With regard to polarization experiments, it is interesting to note that M. Wien || found for palladium electr odes, covered with Pd-black and strongly charged with hydrogen, Dy the result :—Polarization capacity ’ "Frequency , which * FLoitsema, Zeitsch. f. phys. Chemie, xvii. p. 1 (1895). + A. Winkelmann, Drude Axnalen, vi. p. 104 (1901). { A. Winkelmann, Drude Axnalen, viii. p. 388 (1902). § O. W. Richardson, Nicol, and P: Zc Phil. Mag. vii. (1904). || M. Wien, Drude Annalen, viii. p. 872 2 (190: 2). 350 Dr. Gundry on the Asymmetrical Action of an corresponds with finiteness of velocity of reaction as worked out by Kriiger. With platinized platinum electrodes charged with hydrogen, and with Pd electrodes less strongly charged, the result :— Polarization capacity « which corresponds 1 ,/ Frequency with the case of diffusion, was found. The same result was found by Schonherr* for unplatinized Pt electrodes, which were kept charged by an applied direct-current H.M.F. The evidence, therefore, for the reaction H,=2H taking place with finite velocity, and hence giving rise to polari- zation effects, is affirmative with palladium under certain conditions; butnot so with platinum, where the effect corre- sponding with diffusion seems to hold. It is, however, to be added that, at higher and higher frequencies the diffusion effect becomes of less and less importance ; and the effect due to the finiteness of velocity of reaction, though smaller than the diffusion effect at lower frequencies, would eventually at sufficiently high frequencies outweigh it. Under other conditions with unplatinized platinum elec- trodes, the initial polarization capacity was found inde- pendent of the frequency. This, which corresponds with the Helmholtz double-layer, would introduce no asymmetry. It is thus seen that the nature of the initial polarization capacity may be no safe criterion as to the asymmetry that may arise at higher frequencies. Keperiments with a Platinum Electrode. I have made experiments with platinum electrodes in 3 norm. solution of sulphuric acid of the same nature as those described with mercury electrodes. The large electrode was a piece of platinized platinum foil about 4 sq. cm. in area. A platinum wire 75, mm. diameter was sealed in the end of a tube and then cut off flush with the glass. This formed the small electrode. The arrangement and method were the same as before, except that both cathodic and anodic direct-current polari- zation were used. In order that the state of polarization of the small electrode might be determined, I measured the potential-difference between it and a third electrode of zinc, which dipped in a second beaker. ‘This beaker was filled * Schonherr, Drude Annalen, vi. p. 116 (1901). Alternating Current on a Polarizable Electrode. 351 with the same solution as the first, and an electrical connexion was made between the two solutions by means of an inverted U capillary-tube, also filled with the solution. The E.M.F. measurements were made according to the Poggendorf method. The E.M.F. is given in terms of the H electrode as 0:0 volt. It was found necessary to polarize the electrode half an hour to an hour long before taking readings in order to obtain regular results. It was also found necessary to keep the alternating current small—otherwise the condition of the electrode appeared to be permanently altered. The results are shown in Tables X. to XIII. TABLE .X. ‘Anodic Polarization. E.M.F. of small electrode 1'7 volt. | ) | | | Altern. | Direct i Se Altern, ~ > Direct I 4 Current. | Current. Z2 Pee | Current. Current. ea ‘amp. 20m amp. 10ps". amp. 10~4.| amp. 1077. 1391 1-81 2°55 78 2600 | 2-44 2°45 4-11 | , 2:06 a7 eu 291 4-29 4-99 ees |. £82. | 89 om 4350 2°35 1°63 2-96 aan) 9-97 SB 611 | 3:08 3:90 412 | 258 | 4:58 69 || | 388 6-91 4-6 2020 | 2:26 Me | es NO eee Bale 58 e266 7 5 424> 160) || | 264 |} 4:28 6:07 | iat | TABLE XI. | Anodic Polarization. E.M.F. of small electrode 1°36 volt. oe: | : | 2 Altern, Direct Lae Alters |), Direct I | \ Tees Current. | Current. ig? INE Current. | Current. | 7,” |amp. 10—-*) amp. 107%. amp. 1074) amp. 107!. 2070; 441 | O04 [0-0536|| 3550| 462 0225 | Q-105 | | | 5:3 U:606 | 0-216 2620 | 5:05 | 0242 10-095 | | | I= (( | fale G 2 ed casa ee eg gs 2040, 22 0-156 | 0-08 29990) 54 Pete Tene) Pee Oy 517 | ~0-501° | 0-188] anu on noe Wee +f 5:93 1:93 | 0-549 | | | S840) 50205) (O277 (0107) | 2100 | 1406. |, 0-121 -| 0-074) eno Grin ye Oreos. 0;246) || 449 | 225 | 0-115} 302 Cathodic Polarization. TABLE XII. Dr. Gundry on the Asymmetrical Action of an E.M.F. of small electrode 0:0 volt. Ric Altern. Direct | 4) Current. | Current. amp. 10~4./ amp. 10-7. 1300 1-95 1:29 2°18 2-2 9-44 243 | 1504) 221 |) 4-495 4] 2°50 2°15 1725 2°54 1:87 | 288 | 244 ! 2060 2°66 | 1°53 306 | 2:02 3°46 | 2°88 Jathodic Polarization. ! Eré Altern. | Direct 4} Current. | Current. | amp. 10—4.! amp. 10—“.! | 13880 2°88 1-76 | 1579 2:98 1:75 | 3°30 ole | 1819 3°10 145 | 3°46 2°54 | 2320 aOR 1:24 347 2°34 j 3°93 4:9 | 2780 olZ A! | 3°68 9-99 ay | Freq. % | 3:46 | | 2530 4°59 4:25 3:05 || 2990 3°44 2-90 | 295 | | 3920 216 | 216 || 1400 2°40 | Altern. Current. TaspLe XIII. Direct Current. E ae ooyle oer) OOF Co SS che hee dee Goce) Snle cx BO WAP | | BE.M.F. of small electrode 0°13 volt. 7 _ x | Freq. | % | a. | 2-12 | 3320 1-97 | | Paolo ||| | 3620 1582)5)| 2°18 | | | 1:35 | | 4160 1:94 3:18 | 1:24 | | 1429 1°69 | | Altern. Current. =: amp Omen 2°70 2°99 Direct Current. 1:29 26 Ns appears from these results, that it is only when the electrode is practically saturated with the respective gas that there is any approach to constancy of = 3 fora given frequency, When the electrode is unsaturated, the direct current increases much faster than a quantity proportional to the square of the alternating current. It isalso to be seen that the diminution of the sensitiveness with increase of frequency is less than in the case of mercury. Alternating Current on a Polarizable Electrode. 353 Summary. To summarize the results obtained in this paper :— (1) It is shown that a perfectly symmetrical alternating current acting at a polarizable electrode leads, according to the osmotic theory of polarization, to an asymmetry of the polarization—in other words to a direct current. (2) The case of a mercury electrode being worked out gives as a result that the direct current I satisfies the relation NI —; =const., where N is the frequency and % sin 27N¢t is the 20 alternating current. The direction of the current corresponds with an effective diminution of the concentration in the neighbourhood of the electrode. (3) The same relation should hold when the electrolyte is a solution of a complex salt, provided that diffusion from and to the layer of electrolyte surrounding the electrode plays the important part in the polarization. (4) In cases, however, where the polarization arises (as described by Kriiger) from the finiteness of the velocity of reaction by which mercury ions are supplied from the com- plex molecules, the relation —; =const. holds, being inde- pendent of the frequency. - (5) A disturbing effect which masks, in many cases, the above described one is accounted for, and the reasons assigned why in certein cases this disturbing effect is absent, or nearly SO. (6) Experiments, made with KON solution, show to what extent a =const. is found to hold at high frequencies. At 0 low frequencies the relation is totally departed from, and there appears to exist a critical frequency where a sudden change in the phenomenon takes place. (7) An application to the “electrolytic coherer ”’ is sug- gested on the supposition that the equilibrium in some reaction such as H,=2H is reached with finite velocity, and an effect corresponding with (4) above takes place. (8) Experiments with a Pt electrode, both anodically and eathodically polarized, show that the magnitude of the direct- current effect varies at higher frequencies much less with the frequency than is the case with the mercury electrode. The above work was done in the Institute for Physical Chemistry of the University of Gottingen; and I have the pleasant duty of thanking Prof. Nernst and Dr. Kriiger for placing the facilities at my disposal and for much helpful interest and advice during the work. [eae Se) (ei to. easy XXVIII. On the Lateral Vibration of Loaded and Unloaded Bars. By Joun Morrow, M.Sc. ( Vict.), M.Eng. (Lnver- pool), Lecturer in Engineering, University College, BTUStOl =: CONTENTS. Section I. Introduction. F; II. Unloaded Bars. » ILI. Loaded Bars of Negligible Mass. a TV. Loaded Massive Bars. * V. Practical Formule for Loaded Bars. ., | WI. Correction for Rotatory Inertia. Section I. Jntroduction and Notation. $1. ee METHOD of calculating the frequency of the lateral vibration of bars has been described in a recent paper, “On the Lateral Vibration of Bars of Uniform and Varying Sectional Area” (see Philosophical Magazine, July 1905). It is an important feature of this method that it gives, in a simple form, the equation of the elastic central line of the displaced bar, ‘and thus provides data from which the stresses and strains in all parts may be readily calculated. The method lends itself to many cases of loaded bars which have not hitherto been solved, and the present paper, after dealing with some cases of unloaded bars under different end condi- tions, and bars of negligible mass carrying concentrated loads, gives more par ticularly the solutions for some im- portant problems of loaded bars of appreciable mass. It will be seen that a full consideration of the simpler cases treated first very materially lessens the labour involved in solving the more complex problems in which both the load and the mass of the bar itself are taken into account. These solutions are, in general, obtained by a process of continuous approximation. Each approximation depends on the principle that, at any point in the length of the bar, the curvature is equal to the couple due to the reversed effective forces divided by the flexural rigidity. To estimate the value of the couple a vibration-curve must be assumed. The above principle then gives an expression for the curvature at all points. The process of continuous approximation to the exact solution is based on the fact that the expression for the deflexion, as obtained from that for the curvature, is a much closer approximation to the truth than is that originally assumed for the purpose of calculating the effective forces. * Communicated by the Physical Society: read November 24, 1905. Lateral Vibration of Loaded and Unloaded Bars. 35d A reference should be made here to the important papers by Professor Dunkerley * and by Dr. Chree f on the ‘* Whirl- ing” of Shafts. The relationship of the whirling to the vibrational problem was very clearly brought out by Chree, and under certain circumstances the two problems are identical. §2. The notation used is similar to that of the paper previously cited; « and z are taken parallel, and y perpendi- cular, to the undisturbed position of the axis, bending occurring in the xy plane. E = Young’s Modulus for the material (assumed homo- geneous and isotropic), p = density of material of bar, w@ = sectional area, I = wk? =Geometrical Moment of Inertia of cross- section about the neutral axis, | | = length or span of bar, i rye =Velocity of transmission of longitudinal p vibrations in the bar, yy, &e.= displacements of given points in the length 2 ie of the bar, M, M, = bending couples required to fix the ends. We have also . DanC and for the frequency te on a 2ar Yr The value of N is, however, not always recorded, as it is Paficions to find the expression for « 2 a Section Il. Unloaded Bars. §3. Uniform Bar Clamped at Both Ends.—Taking the origin at one end, the terminal conditions are dy l dy i aa e C= } ——_ — ° i ) e ae da Ota da oe dae y IY» Ge i * Phil. Trans. Roy. Soc. A 1894, p. 279. + Phil. Mag. May 1904, p. 504. 356 Mr. J. Morrow on the Lateral Vibration and hence the equation to be assumed as the first approxima- tion to the type of displacement is = ab(# 2a? = iP le Reaeey The ordinary Euler-Bernoulli theory leads to Cys M om 4 , oY —HI-; = Mo +p Ce) y,dz—lL pox i dx. Substituting as y, integrating, and determining M, by the condition that = =0 when 2=1, we find Hy = SPR 178,571 at 21 Pad +27 a9 238,095, de ve 8 +°059,524 > ON gasp See Y1 pol Similarly, using these values of y and = we arrive ata 1 second approximation, in which 079158 pay, Tie LE 11 12 —-38069 Fa? +-05511 a”°—-03006 = +-00501 ‘F) (-35572 3¢? —°55113 U2? + °49603 l’2® and .- ot Ting gees 1 pol agreeing well with the value of 500°6 obtained for the con- stant by the exact solution. § 4. Clamped-supported Bar.—In this case let y, be the ie at such a distance from the fixed end (taken as origin) that — QO there. The initial type is then dx Yor BW he ei a P +4) of Loaded and Unloaded Bars. aot *"Integrating and determining M) and the arbitrary con- stants by the terminal conditions —y= pees (565476 (Sa? — 744048 Pa +416 Px? —+297619 la” ++059524 28), and tae a 1 A small error in the value of 2 for which y=y, makes no appreciable difference in the final result. The next approximation gives Hy = OE POs (2-36692 D2? 310194 Pat + 157077 Dat ~+88577 Pa? + 08267 Pe! — 03758 le! +-00493 2) ; and putting Tees Ire Ow), oo Y1 pel and 15:42 £U es Wr =F" § 5. Clamped-Free Bar of Circular Section, Diameter vary- ing as distance from Free End.—Taking, as previously in similar cases, the origin at the free end, ENP eee eae ae eae Vl oilers Y. =a (tae ate ») and the diameter d=Az. Then — 94 ae |,” 2(a—2) (1-5 + 5) : | Let ~~ HAZ at [? UD Loar, p : x —y = le Gel -Oara dene 016 40027 77), and Wr BHA? 358 Mr. J. Morrow on the Lateral Vibration In the second approximation, ase Yi pl and in the third approximation, °696176 py, i ‘ 9 2Q TAQ Id Le —y¥ =— aaah poe [8$—-§74742 Px +:957615 2? —*542880 Ba’ +°192,901 Px —:044091 Ix? +:006889 x6 7 8 —-000656", +-000033 al Lie egg eme dgLiN ee yy pl Zin teat Kirchhoff * has obtained the solution for the frequency in this case, and his result may be written 7 2ATD AU: ers ark In the Euler-Bernoulli theory of beams it is assumed that the greatest diameter is small compared with the total effective length. When the diameter varies as the distance from one end, therefore, it is necessary that the variation should be small. In other cases, so far as the mathematical theory is concerned, the solution can only be looked upon as a probable approximation. Section III. Loaded Bars of Negligible Mass. § 6. When the bar carries a load at some point in its length, and the mass of the bar itself is negligible, it is not neces- sary to assume a type of displacement. The method then becomes an exact one, and gives at once the true type and frequency of the vibration, In the following paragraphs, m is the mass with which the bar is loaded, and a is the distance of its centre of gravity from the point chosen as origin. § 7. Clamped-Free Bar.—If the origin be at the load and y, be the displacement there, ay gee ihe ee and the vibration-curve is Nae Nee oe Seer 0) i 2 3h * See Berliner Monatsberichte, 1879, p. 815. of Loaded and Unloaded Bars. 359 where / is the distance between the load and the fixed end. Ch 2 out ye Ga On the other side of the load the bar is straight. §8. Bar supported at Both Ends.—Origin at one end. Mass divides length of bar into segments a ad b. Here, for 2 a, ee =mii,(; 0) 7 e 1). The constants of integration, expressing the inclinations of the bar at its ends, are obtained from the consideration that botl a and y must have the same value in each equation when «=a. ‘The inclinations are, therefore, Re :) a ee (¢ i — Bl He +3 oie ea hig eel Hence bee k y =e : (2° —2ale+a?x), y and Vi a a (a? —2ala+ax’). In either case, gy 2 oR Uh mae § 9. Clamped-Clamped Bar.—With the same notation as in the preveding case. Mt 720, Uv ae b —HiS4 =, i M,)3 — mij, > 5 and if w>a we must add my, (v—a) to the above. By integration we find M,= mi and M, = my, Be 2h Tes (one be and SE lay == Le [(a+3b) #4 3(a— 2b) la? + 30’x— al*). 360 Mr. J. Morrow on the Lateral Vibration In either case, v=a gives ye Ok ( 1\3 qe ah =) ; This result and those of §$ 7 and 8 are identical with the corresponding results obtained, otherwise, by Chree. § 10. Supported Bar with two symmetrically placed Concen- trated Loads——When there are two equal masses, placed at equal distances @ from each end of a bar whose mass is negligible, an exact solution can be obtained in a precisely similar manner. Thus, for a bar supported at each end, or 7 a we must add —my,(e—a) to the above ex- pression. Determining the constants of integration by of Loaded and Unloaded Bars. 363 di a and y when «=a, we get for «a the first term in the brackets is equating the values for a7 (la —wue—ax°—2al?x + dalz’). In either case Ya @ 5 31 FA (—7010119050"a +-016 7a —-00832a° + -00238095la" —-00059524a°). § 16. In the second approximation, for ra, the second pepnession on the right hand must be written pol |" (oe 2) yzde+ i (v— 2)yade | and the term —my,(a@—a) must be added. By the method already indicated we find the inclinations of the ends to be aia): : ( 2 foikeah tel es oe ie —_ = )+ a 00010386pel!! dx mie wey Waal lan ake | asl a) a Ley HOM? 301% GU) a aS Oy 1 at el: dy’ Wi, m a? paP f : of ll ae “(= —_ aoc A { 00010386 pel “7 (- ial, lael?)) alt hd v 490i) 60:04 T BIS) I 2. Bx? 364 Mr. J. Morrow on the Lateral Vibration and the equations of the central line _ Ya mba oP a 3 =r G7 (v? —2la +a?) — pa coll *(— 1:0386/"2 + 1:7085%2 — "84331! a? +°1984P a —-0276 Rx? + 0030124 — 000522) mA an Me i MRO EN hg (© CLG ae (‘ ae lan € a 1) (Oe. Vigo 5 a a “ = . | | aa 30-420 | G0 a 5 =i cs (I= a)(@t— Bla + 08) — PE A | polo — 103860 w + 17085223 — ‘8433 0° +-°19840h 27 ee 0030/2 —-00052”) mA _ oa alu® hye 5) aa” aw 3l a? a’ aR et are 6/ 840 ° 120 (i ot ae “tee ey aoe eg 1 Ca lee oe Lis pa aa a ee te 20 * (a90°~ Got a 315) *~ a0" | tl]: Putting «=a in either of these, we get the followi ing rela- tion between Yq, and Y¥, : an) Ha tomP | (— 1038600 + 1-7085a 8433008 + °1984Pa"— -02762a? + -0030da" — -0005a2) a 4 mar G07 (3392857a! + °517857201L—1-3a4l? + -G07l*— 19047620) i]. l Save fa ce if a= 2 y) . Ee hee iz » and P-t=— = — ‘0i03051pal*; hence Ya ml? 3°306pal + 7:436n ‘| =1 Bae es AR © 39902887 1a 65 1-0497,02 Ue, 48 © 322°U38p@l+ 651°042m ; and further, if the masses of the load and bar be equal, ya _31°379 EI ye me §18. Clamped-Clamped Massive Bar, Load in any position. The end conditions lead to the preliminary assumption Lx 2x° = 77 ay, I, pie fan =z) (« me ey of Loaded and Unloaded Bars. 365 For 2a, add my, (x#—4). By putting «=a, as in previous cases, we find ab? yp, M,= my“ 4.-00357143 ee Loe Ja i eat 3 M,=mi,— - a hear and hence tor «a ine latter portion of the expression is changed to MYa =z 61 “(ale — 2ax’® — 672? + 3ala? + 3Pe—al?). When z=a, either of the above gives — 7? = BLAP, Ya where P-} = © 10-3(1:78572 6 —2°TaP +27 a'?—2°38095 ail =% ae 595240) +2(9) § 19. In the next approximation, for «a: dy! —EI 5 3 =M+(Qh— —M,)> + pol[(" (a—= Syyatet | (o—s)ydey = pony wal {" y(l—ax)da +{ y(l— a)de | = mia —a“+ a) pal =M,+ (th —M,)F + paby. | rs pee l0-"{ — —-33068I"w 4 148809740 — 1:3822° +-4960328—-33068~ + 066147) l [2 m 3.9 @\ .. (@l @l\ ,. Claes ea lap mera oz 2 2 Oe i NEM eae WE Marc (“ (s6"— 39 Sy eros 20 | —MYq rata), Integrating and equating when z=a, we find ole mat a ae a*b? ern 2() 2() iu 2210" My=pooP jn E 000007114502 P+ ek a) | + NYg ss ; rai not, M,=poPj. | 0000071145" oe + aal ‘ot Go 7" ab +. 7 al") | | + Mifa eZ 140 Whence the form of the centre-line is aN 12 Weds tS eee Ag —Hly=poaPy. | e2(-,) L0-*( 3557 Ba? — 551131 a? ef! 12 +4:9603/!a° —3-3069/827 4+ 55112” —-3006 = 3) Fonds (Ba a) = ge) ee Le (al? — — 2q?/? tal) = oa aaa 2Qa* — 35atl? + 52081! — 22070) na " 2 a? pee 4 ab? x? 6? 520 || Ye Veo ge Or ne + (ba'l—14a°? + 210° P— 2207 + 12a7/*) of Loaded and Unloaded Bars. 367 and — Ely’ =poP7, | eo 3) 10-8 (355 73Pat + 5°51130'08 + 4-96031'0" 3306902" 4+-55110"—-30067 +0501 2-4” 4 (a0 208) — = BE Oh: 4p —- ss, aaa as = — i 2 6B “7340 + (a®l—2a?l?) ae + as + (52a7U! — 2207 — 2a? + 7a°l) a po OT 24 840 + (8a — 140°? — 2207? + 1271) RAO P90 eA 17 ee a a ee ie a { (8a7l— 2a") 2? + (3071 — 6a???) a? + 30°Be— a PY. ae Gee” ah ] When «=a these give yy \—L 2 a (*) por [pe 10- *( 8 55T3P—551130'a + 4-96030"« ae soho 49 10 —3°3069/'a° + 5511a*~ 3006 +-0501% ) Gs Vana : Heat PEM een ae Paap (B= Mba + 1lia— 20a —TPat + 5la® =a )] em 32 BL § 20. As a particular case, if the load be at the centre P—!= -0020213 pel! + :0052083mi? and lage ml? — 4*0398pwal + 10°076m 7 ame eae BI 755 2021-3pel + 5208°3m >” If the masses of load and bar be equal we have a further simplification to Li lees) Io ll Ae) a on ee Section V. Practical Formule for Loaded Bars. § 21. The formulse obtained in the last section for the frequency of the lateral vibrations of loaded bars of appreci- able mass are too cumbersome for general use. In every case, however, given the position and mass of the concentrated load and the mass of the bar (assumed uniform throughout Value of f. 97-41 6Q 40 v) 368 Mr. J. Morrow on the Lateral Vibration its length), the frequency is given by a formula of the type te. ae Ya pal* In the following paragraphs the values of @ are given for all positions of the load and for ratios of mass of load to mass of bar varying from zero to 1:0. SS Gee eae BURREGERESEREEEEEEEEEREGETESEEaEaaEaaaaEaaEaaTTeaaaeEeeaaS==o> re eS ECE fafaleietateta Ce scare Ze HAN NSCS eee COONS SSC rey cH PECCOINSSS SEN EEE SSE Li am Hy o Ey Boo a Nicrentnaenes j BESSSSESSS0R95 00000 SSS RESREREESC SCE ECHR AS Ad; 4 TT TT Ast BRS. A 7/2 Peer ee SESEP 4Bee —————— — Receeecen RiSgar emcee EEPEDISESEEE Eee eeScoeeEaER oaannoneoe ‘WAV SEdeeeEe\\veeNen, S SOD EEE EoeoeaSes Sneen5005C050s000500000077GS000 000006 DZannrau ae a’ At ED 4nEEr ea BUF T | Oo a ee PTT ert ee ee ai A it WY een S GEESE wo ¢ eee ‘Aan SEBSECRERAUYNWASK a PALA TT) |_| Bea yea th EERE Ree eee RSE CRRERERSUZBEEEer Al Ava: BE EEE ERBRE POSER SEEESEEBAE eZ Saree baa EESREEZ PTY TTA TIAA A SEESRRES ACNE ES2ean —— a AVF 1 | EEE E EEE vee ! GShSERea000 Prey tat Pe a eee ae a PPT TRS TNA Na i | sEi Tit === Prarie —— eB a4 A AA SEREBESE PV AT A eT AUIATViA Pye Ti Ty yr rrr ZITVI TAY iAA TT Ter TT Ty Pifyyyi Ter yr ity — = LA yVyI Tt BEEBE EEEBE Son SEE EEE Sonn eeee SES COEECUGUUEDe~dEEEE A CN (EE Kt yoy i Zi | =: + ~ ; SESSSS! at as it Been ae aH iB! ot 2 = aaa i [os A i Poa en SY GSERED EER! VAG (GP ARBRE PRESALE PEREERESEL 4 DEESRaEe rl 1 ERELS SE ie Se | oe Ppa yt] a --—— == Ty ea A | PilA TAT TTT) Pr ity SCONE CSS ee et EP 2BRERBESEBRaS SS penne ae ae ees i} t Pep Tae ae a ea ! Baceunnseeeenesseunee=eceeecaae peas) i pet eer TT Pry | eee Pieri ar a FA ee HH Py ry Terry — EGRSSSERSEEREeREe ERS EE eee ewew [Ty 4 SFA REECE EEE EE EEE EEE EEE EEE EEE EEE BEER EEEES PERSE OE EES BEER EERE SREB EERBERACEEeeasS 0 0-1 0:2 0:3 O-+4 05 0-6 O-7 § 22. Bar supported at both ends—lIn this case the values of 8 have been obtained from the last equation of §16. They are given in Table I. and represented graphically in figure i If the ratio of mass of load to that of bar cannot be expressed of Loaded and Unloaded Bars. 369 exactly in tenths, further interpolation 1s required for accuracy. This may easily be obtained graphically by plotting the values of @ given by the curves for the required position of the load. In the tables J is the effective length of the bar, and a the distance of the centre of gravity of the load from either end. The numbers on the curves represent the ratio of mass of load to that of effective length of bar. TasBe I. Values of 8 for Bars Supported at Hach End. | Ratio. Values of 8 for different positions of Load. Mass of Load. l ; | Masson ban | ¢f=—1. | al=2. | ef=s. Gl= AA | Gil oe 0-1 9556 | 9098 | 8591 | 8203 | 79:80 0:2 OSTA ay Mea 2Oe | iG | 70:89 67°73 03 O95 | “80027 |" 69:22") 62:35" | 58/99 O-4 902059) 7oi36 63:01 55°68 52°31 0d 88°69 rata lr’ 5781 50°30 47:03 0-6 86°86 67°39 53°91 45:86 | 42°74 0-7 85°24 | 63°96 49°56 4215 | 39:18 08 83°67 60°84 | 46°25 Bong) | cakes aly) 0-9 82°15 i COe RA oro) 36°27 33°60 10 80:66" 1) 55:39) | A078 33°91 31°38 § 23. Bar Clamped at Both Ends.—The values of B are here found from the last equation of $19. They are given in Table II. and fig. 2. Tasue II. Values of @ for Clamped-Clamped Bar. Ratio. Values of 6 for different positions of Load. Mass of Load Massyot Bar. | @//="1. Gib) | Abas a/l="4. | ajt="d. 0-1 | 499-9 4809 | 443-9 411-2 399-0 0-2 | 497-9 4608 .| 396:7 347-9 3313 03 | 495°9 dates |, Sond ae sOlel 1s, 283-0 0-4 4939 4927°6 1 PO2GGy 7 “2652 247-0 0-5 491:8 404-7 h) | 7 2OGiOR ML 2367" 11) 2190 0-6 CVE esSTS! al soca el mpelas 196-7 0-7 487-3 S719) 9 |e 253:0i 0s 194-8 178°5 0:8 484-9) | 357-0 | ‘2354 | 1789 1633 oe 4826 | 3429 | 2178 | 165-4 1506 480°1 | 3298 | 2064 | 153°7 139°7 370 Mr. J. Morrow on the Lateral Vibration Vij}: iia qaeeeese: ; LLL SRaEaeeer EELe Lp oY See tutmesttasi | ee teesaey cardi // ieabuaseeeeee: | | PBAy ty) eee RRS Seen 4) 408/44 7//SReeseeeeer eee tA COCA E ESC ee CCE Cee A CAE TTR POECEEEEEE CEE CAN RRS i nite i t | os 1} Value of B. Tt T cn Cora Coo Per sane-3 s LAgeL 2 #08) ~ 40 ISSR SESRSESEEe BEER EEE CHEE EEE EEE EEE eee = See ecees ay CeCe COCCI gre a cr EEE EEE EE EEE EEE EE EEE EE oT gE EE PCE COO ee OOOO eels 6 02 0:3 Of -05 06 0% 08 09 1 Section VI. Correction for Rotatory Inertia. § 24, Hitherto the terms depending on the angular motion, both of the concentrated masses and of the sections of the bars themselves, have been neglected. This is equivalent to supposing the inertia of each elemeni, to be concentrated at its centre. The effect of the angular acceleration of the bar is sufficiently small to be neglected in practice, but in the case of a concentrated mass the additional terms may be important. There are various methods of procedure. An important approximate one being to assume in the first place that the type of vibration is unaltered by rotatory inertia and then to find the correction due to this cause. of Loaded and Unloaded Bars. Dah A general method has been given by Lord Rayleigh. 1G is applied to a special case In the next paragraph, in which l’=Moment of Inertia of concentrated mass about an 5 a e E eae 19 AXIS perpendicular to the plane of bending (=mk’*). T and V are the Kinetic and Potential Energies of the system. 95. For a Fixed-Free Massless Bar (cf. Rayleigh’s ‘Sound, Art. 183). Origin at fixed end and mass ™ at free end, the equation of the har 1s 2 3 ? US (yn —16)(7) + (10—2y,)(*) di where 7, and @ are the values of y and = at the point where the load is attached. This equation is deduced from CP Os es B14 = my d—2) +18. Cee nee Integrating, and determining #/, and @ from Be ve Yys=my —-+ O5 | oe. | a tess KI@ = My, > ae ey | \ aed }] we get the desired result. Following Rayleigh’s solution, the equations of motion are / oui my, + (6y,—310) =0 | y lg oe (Bly + 208) <7) | whence a oe MON Oe | Can ale an [2 aN) I+ p ar eee answering to the two different periods. § 26. The solution can be simplified if we assume to start with that the effect of I’ is small. This is usually the case in practice, and the method has been fully investigated by Dr. Chree. Adopting this simpler method (¢7. Chree, /.¢c. p. 511, § 9) ate Mr. J. Morrow on the Lateral Vibration the vibration curve in § 7 can be written and we can take Then, since Oa T=4my,? + +3]! = smi + SE yr ; and | Wes er (“: = de= da* the equation of motion dot _.of , oV dt0I, dy OY EI 9 —3 41 D u bo! Oo becomes ONG: 3E1 mi +5 ahr - -e i — Obs aie a mi? i ve) $27. The same problems worked by the methods of this paper do not involve Lagrange’s Hquations and are as follows :— Taking the origin at the free end, ~ BIG Y =mijya—V6. Whence amTpake min ie | — H16=— my; : +161 I Putting 9m we get Y ml? (yy i 12 BN oy 2) + err 31’ ; 31 a) ilies ¢ = Viel gree res mi? omer ae ne a Se, & — (= 07 Loaded and Unloaded Bars. Shes Or, for an approximate solution, starting with piss =my «—1"0 we may put A= = o - Whence Sin, 1) he ieee ae and ite dHI = 5 Jl mb (142 S| § 28. When the mass of the bar is taken into account, and Rayleigh’s method is used, the kinetic energy is o( &y oe wal + | pride | pet aon 4) av}, where the part in square brackets is to be taken for the position of the load, and those under the integral signs are between the limits. The potential energy of bending is, as before, Wee | BI (5: de. in general the evaluation of these, though perfectly Au = 5 { mi? +V'[ simple, is tedious. The values of y and 2 are taken from earlier parts of this paper, and the energy expressions then used in the Lagrangian Hquation just as in the example already given. § 29. It is, however, simpler merely to add the terms due to Rotatory Inertia to the previous solutions. A general investigation of these terms would occupy too much space, but in a numerical example the work ts not difficult. Referring to § 14 for the case of a en massive bar, the term to be added to the value of =HLe aw ; for the rotatory inertia of m 1s and for an approximate solution we can write a) = a ee fi dx r=0 3 ike at4 Mr. R. F. Gwyther on the Range of Hence the term to be added to — Ely is AN ree a Pee Caen and for a first approximation, ve Bl yy 08194 pol! +3 mB +6 Vl This example is sufficient to indicate the procedure to be adopted in all such cases. University College, Bristol, October 1905. By R. F. GwytHer*. YYNHE waves with which I propose to deal are the waves of finite amplitude of which the investigation was initiated by Sir George Stokest in his paper on the Theory of Oscillatory Waves, and continued in the Supplement to that paper. ‘The object of the paper is to establish the correctness of the opinion expressed in the paper quoted (p. 227) ‘¢ After careful consideration I feel satisfied ... that we may approach as near as we please to the form in which the cur- vature at the vertex becomes infinite, and the vertex becomes a multiple point where the two branches ... enclose an angle of 120°.” The method of the Supplement is adhered to as closely as is convenient. The result is to establish that the velocity in all waves of the series, small as well as great, is represented by a function which possesses poles which as the amplitude increases approach nearer to the fluid surface, and in the limiting form is identical with that mvestigated by Mr. Michell { in his paper on the “ Highest Wave in Water,” in which the poles lie on the water-surface. § 1. Making a change in the notation used by Stokes in the Supplement, in order to make the analytical form of the velocity more obvious, I write _ : ink(o+t) ae De fy Bie G nk where n is an integer, and & is a constant defining the wave- length. Also let ~y»=0 define the free surface of the water. 3 “e+ = * Communicated by the Author. + Mathematical and Physical Papers, vol. i. p. 197, and Supplement, p. 314. { Phil. Mag. November 1893. Stokes’s Deep- Water Waves. By Or Then the velocity is given by E 1 oh é ae. a Ce Cane d(p—wvp) : ink(> +i) (= *)- tg elu: At the free surface we have w=0, and it will be convenient in this case to write, in place of (ee ), C where nko B(“2)=143he ©. PN iy Lois The condition for uniform pressure along the free surface requires that, when yy =0, : 2 gy —s¢ =constant. The determination of the successive values of h, resulting from this condition is only a matter of labour. I have carried the determination to the sixth order, as an extended number of terms is important as the basis of the future argument. Stating results only, I find 2 ke? /g=1+h? + : ete = he, 2 hy= 2h? +ht+ ie h’, i A 18+ ae b= WE OH, y= ed, hex SI, (2) where Ihave written / in place of fy. Also if we write 2a to denote the height of the wave from trough to crest, I find Bae Omi a ka=h+ 3 he + Oa MR Selly (9) 376 Mr. R. F. Gwyther on the Range of If we write out in full the resulting expression for H-*) the successive terms will be seen to show a marked resem- blance to those in the expansion of iko (1— he ¢ ) eal 3 In order to examine this resemblance more closely, I expand ik ,-3 : {x(-*)} on the oe of convergence, and find C ike a eae 2 — (34 +16 ye = Se ee 5 is aga Wt ee i eee +(5"— 4h G +(h — gh )e G + We ¢ ; bike LS. 4 + 3 h®e C e s ° e. e ° . . ) ~ a : “ ™. (4). It is on the greatly increased convergency produced in the series by this step that the argument depends. It is clear that there is a value of w, not very widely different from 3h, ik for which 1—ye © isa factor of the right-hand side of (4). For more precision, write dh= apt By? + yp and determine «, 8, y so that the right-hand side of (4) may iko vanish approximately when 1/ is put in place of e © , 7.e. so as to satisfy pb pe This leads to the equations 1. 4) eee hae oat 54% * gene Ag 2 ey ar) ae Re Ca! s La ee B(1- 73+ — si )=- (a7 * 108" 45747 ) ee ees 29 3) Ae (5778+ sa58" : Stokes’s Deep- Water Waves. og These give approximately on a4 B=—068, UO ee ee) and these values lead to po — 028) 5 sO ie sak ee a) This value of h increases with increasing fractional values of ws, and reaches the value-323 approximately when w=1. Since the hypothesis of convergence holds good for any value of yw finitely less than unity, we may take this to give approximately the greatest admissible value of h. Using the numerical valnes (5) again, we find when p< 1, ike —1 iko\ 4 yale ® =(1-uee) 42 en ly, (20 aatsoatter 1 hour after overstrain. | in in | overstrain. overstrain, es Tons. | / ie | | | | ‘Reading, Diff. Reading.| Diff. | Reading.| Diff. | Reading.| Diff. Gil 20 200 200 0 |. |e 1 Ord Pet 35 236 | 36 236 36 236 36 2 1-0 270 35 278 37 272 36 | 273 3 SOY eed gs 305 39 309 36 308 36 309 36 7 el eee 340 +) 346 37 345 35 345 36 Steed beat 375 | 8d 382 36 380 37. |) bed” eS 6 BO id 402 ed 137 419 | 37 418 | 38 421 | 38 Dials Pw AAD | Sod 456 37 457 | 39 459 38 Boe. 46 486 | 37 496 | 40 496 | 3 497 | 38 eee? | 208 Bo 936 40 536 40 36 39 10. | 50 | 564 | 39 |:.Goneed lagi) 577 4004 | See Id 388 Prof. Morley and Mr. Tomlinson on Tensile Table VII. and in fig. 6, which has been plotted from the table. The readings were taken immediately after the applica- tion of the 4-ton loads, so that little creeping took place. TABLE VII. | Extensometer- | | Time in Minutes. Load in Tons. reais ef | | | 50,000 much units. | nae 0) 200 0 4 502 5 4 A493 28 | 4 483 46 4 482 61 | 4 480 131 | 4 | 476 266 4 47 | | | For this reason the readings are less than for the 4-ton load in the test after overstrain of specimen No. 9. Rate of “ Creeping” during Loading. The early curvature of the load-extension curves for speci- mens Nos. 8 and 9 in their original condition is probably largely due to that part of the extension y hich takes time to develop and which is generally called ‘‘ creeping.” The rate at which “creeping ”’ took place at two different loads, 3 tons and 5°5 tons, was observed both before and after over- straining ; the specimen used (No. 12) was cut from the same bar as Nos. 8 and 9, and was overstrained by a load of 11 tons. The results are given in Tables VIII., IX., X., and XIJ., which are plotted in fig. 7; the broken lines show the rate of creeping before overstrain has taken place, and the full lines show the corresponding rates after overstrain. The extensometer-reading, with no load on the specimen, was 200 in each case, and the extension was measured on a length of 8 inches. On specimen No. 15 an attempt was made to separate, as tar as possible, the plastic extensions due to “‘ creeping,’ from the elastic extensions which develop immediately after. the Joad is applied. For this purpose the jockey weight of the testing-machine was set in succession to the necessary posi- tions before the loads were applied to the specimen by the hydraulic ram. After this the load was very quickly applied, Overstrain and Recovery of Alununium, ete, 389 the extensometer-reading taken, and the pull almost entirely removed again, the total time of application being under 10 seconds. The results of tests of this kind, before and after Tasuie VIII. TABLE IX. Load 8 tons. Before overstrain. Load 3 tons. After overstrain. | : | ae Reading of eatale Reading of | Timein | Extensometer in uns Extensometer in nut es. t ; | “SLEEES x00 inch units. aren sao) inch units. | ae As | 0 414 ) 420 5 494 5 433 | 10 429 10 438 | 29 433 17 441 47 438 25 445 Se 440 30 447 157 445 H 35 449 | doug 450 | 164 469 | ha TABLE X. TABLE XI, Load-5:5 tons. Before overstrain. Load 5:5 tons. After overstrain. : : Reading of : ; | Reading of Time in Extensometer in Time in | Bxtensometer in Minutes. ee Minutes. Ta | 5p,009 Meh units. 50,000 inch units. | P 596 OO Tr eit ene a 610 iL | 639 15 618 | 9) | 653 21 622 10 662 30 629 15 669 35 631 22, | 675 48 637 32 682, Fa u6s 644 37 686 | | 139 662 52 694 | 188 671 167) «| 731 | | 203 673 197 738 | | 230 | 743 overstrain, are shown in Table XII. and are plotted in fig. 8. For convenience in setting the load without loosening the wedge grips which hold the specimen, the load was reduced to 0-1 ton instead of zero. The curve A represents the material before overstrain and the condition immediately after an overstraining load of 11 tons is shown by curve B. In these tests the permanent set (or rather extension, which does not disappear in 10 minutes from the removal of the load) begins 0 -Prof. Morley and Mr. Tomlinson on Tensile to show itself at about 5-tons load. Curve A shows that the material obeys the law of proportionality of strain to stress when the load is applied quickly , Within about the same range. Curve GC, to five times the previous scale, and not ‘ sheared back,” shows the permanent set. From a comparison with fig. 1 and Table I. it appears then, that in sucha material the term ‘‘ limit of elasticity’? cannot be defined without some reference to time, unless it be understood that an indefinitely long time is to be allowed for extension and contraction to take place. | Liffects of Vibration. A eee was overstrained in exactly the same manner as No. 8, and then tested again. It was then subjected to a number of sharp blows from a hammer both endwise and transversely, and immediately tested again. The result showed that the overstrained state was unaltered by the vibration, and subsequent tests showed that this treatment did not in any way affect the rate of recovery from overstrain. — Taste XII.—Specimen No. 15. | Extensometer- | Extensometer- | | Toad in reading before ' Permanent reading after | | Tons. overstrain, Set. overstrain. | ae ia | eee eee —_—- { 0-1 2005 4 ns es, 200 1:0 201s || Me 0 261 she | 1-5 295. | 34 0 297 36 2-0 330 oi 0 336 30° 4 25 365 35 0 376 (2) | =a | 3°0 400 30 ) 41] 3D | 39 437 ou: 0 451 | 40 4-0 A472 35 0 490 39 | | 4-5 506 | 34 O+ 532 42 I 5:0 541 30 O+ 573 4l 55 Sa 39 il 611 | 38 6:0 616 40 2 656 (?): | 45 G5 653 37 4 695 39 7:0 oe | 38 9 738 43 795 (O20) 4? 10 8:0 (gi 38 10 $5 822 51 3 Aluminium-Bronze. A length of 14 inch round bar (specimen No. 2) was turned down to a diameter of 1:118 for a distance of 10 inches and was then tested and overstrained by a load of 37 tons, which Overstrain and Recovery of Aluminium, ete. oul. gave it a permanent strain of ,/, inch and reduced its diameter to 1:109 inches. The specimen was then tested after intervals of 20 minutes, 1 hour, and 5 days; being heated for 3 minutes to 99° C. before the first two tests after the overstrain. The results are shown in Table XIII., from which the broken-line curves in fig. 9 have been plotted in the order A, B, C, D. Examination will show that recovery is complete after the first heat treatment, the materia! showing slightly more hardness than before overstrain. TasBLte XIII.—Specimen No. 2 (Aluminium-Bronze). | | } | 2nd Loading. | 3rd Loading. | ik osdine | After 3 mts. at |After3more mts.) 4th Loading. | Oct. 19. 1905 99°C. and at 99° C, and 5 days after Time | Load | oe ’ | 20 mts. after 1 hour after overstrain. wer in overstrain. overstrain. eee Tons. } | | 'Reading. Diff. |Reading.| Diff. Reading, Diff. | Reading. Diff. 0 0 ZOO! fois: ZOO) Tian ees PAULO A Neen te 2100) Mate ce 1 1 260 | 60 262), |. 162 262 62 | 262), |= 162 2g OR eta 325 | 65 o2n | Ga 328 66 325 3 3 3 Boo) 1 64> f EB9OM RGB ih 892 64 388 63 | 4 4 Ade Wee lt ebay GD 456 64 453 Ghat 5 5 DOO Gm. slo) Wot 522 | 66 518 | 65 | 6 6 Jono i OF 586 67 588 66 585 7 G ie) 655) 68 654 «68 653 | 65 652 87 8 8 724 |) 69 PAN (i 722\ 69 On Laie S) 9 794 | 70 Noor Ne iGs 790 68 ART hi GB 10 10 Soom yall 859 70 SOL ane 857 70 il lial 938 73 | 12 fer OT Wy 7 Sie 0 | | Peas) W087 | 76 | | | 16 37 | | Specimen No. 2 was then again overstrained, by a load of 38 tons, giving a further permanent extension of ,/, inch, and was retested at the same intervals as before, but without heating, with the results given in Table XIV. The full line curves in the order A, B, C, D, fig. 9, have been plotted from Table XIV. in consecutive order. They show that with lapse of time the aluminium-bronze recovers its original properties much more slowly at ordinary atmospheric temperatures than at 99°C. The “shearing back,” in figs. 9 and 10, is at the rate of 5°5 extensometer divisions, 2. e. 0°0011 inch, per ton ot load. Finally, the effect of vibration on overstrained aluminium- bronze was investigated. From results of tests made on a trial 392 Tensile Overstrain and Recovery of Aluminium, ete. specimen which needed considerable hammering to remove it ) from the wedge grips *, it was suspected that vibration had a | similar effect to that of further overstraining. This proved to | be the case, as is obvious from Table XV.and fig. 10, the curves A, B, C, and D of which are from the figures in columns 3, 0, 7, and 9 of the table. The difference between curves B and © shows the effect produced by vigorously tapping the specimen, endwise and transversely, with a hand hammer. TaBLE XITV.—Specimen No. 2 (Aluminium-Bronze). Ist Loading. 2nd Loading. | 3rd Loading. 4th Loading, 20 minutes after) 1 hour after 5 days after } Time | Load Nov. 9, 1905. | overstrain. overstrain. overstrain. 1 in Dias Ws A ag 2 ee ln os ie Ait she RM es Minutes., Tons. | | | | | | Reading. Diff. Reading.) Diff. | Reading. Diff. | Reading.) Diff. | Wess 7 = — — \ 0 0 200 mike 200, ee POON 2: 200) 1 ve 1 if if 259 | 59 262. | 62 262) || 62 262. | 62 | 2 2 S210") 162 329° | 67 331 | 69 3257) Gs 3 3 387(?)| 66(?), 397 66 400 | 69 391 66 | 4 4 |. 448 61 468 au Sj0 | a0 | 458 67 } 5) 5 516 68 DDe1 ee sO > 940) a a7fO 525 68 6. | 6 | 581;-| 65 | 609 | 71 | 611 | 71. | esmiiee i f 650 69 681 72 46824 ear 661 68 8 8 | 718° | 68 | 755' | 74| -754 |- 72 | eee 9 DA ae GS 830 7) 828°) | 74 800: | 69 Oo carl 858 71 905 | 75 901 | 73 871 | gal ie) 3B | | | | TaBLtE XV.—Specimen No. 3 (Aluminium-Bronze). 1st. Loading. 2nd Loading. | 8rd Loading. | 4th Loading. Noy. 16, 1905. 115 minutes after| After vibration, | Nov. 22, 1905, Time | Load | After heating to} overstrain, | aad 30 minutes| after 3 minutes in in | 99° after overstrain. at OO?Res Minutes.| Tons. | . | | | | | Reading. Diff. | Reading.| Diff. | Reading.| Diff. | Reading. Diff. fee eal ee ae ED ess pais | zat 0 | OP i O07)" ae 200 & 200 Hee 200 Pe ieee 2e | 326 °°4" 126 330 130 340 140 326 126 2 | 4.| 465 | 189| 471 | 141| 491 | 141| 4629) 0aeE Smee.) 605) |. 140 615 144 627 146 600 ; 188 + oa 142 761 146 776 149 v4 | a 5 HOS 89D) |) 148 911 150 928 | 152 888 | 147 7 38 | ! | | | | * In obtaining results, shown in Table XIY., the specimen was left untouched in the machine between successive tests. Pages | XXXII. A New Improved Type of Chronograph. By Rospert Lupwic Monp, M.A., F.R.S.E., and MEYER WitbErRMAN, Ph.D., B.Sc.* [Plate VIII] N the course of a physico-chemical investigation we made some years ago a chronograph measuring time to 0°1 second was required. We procured one of the best make with a revolving drum of 60 cm. circumference making one revolution per minute, and subjected it to a careful investi- gation. We found on calibrating it with a clock making electrical contacts automatically every minute, that not only was the absolute value of each revolution not equal to a minute, but that the differences in time between two contacts proved to be very irregular and greatly different. On further comparing four curves obtained successively one after another with the same instrument, the clock having been wound up afresh every time, we found that the form and shape of the succession of the contacts of each spiral was not always the same, so that no correction table could be applied in connexion with the above instrument. Since it is exceedingly difficult to get a large revolving drum to move at the above speed with great regularity, it was evident that unless a simultaneous calibration of the curve is made for every second or two seconds, the above type of instrument cannot be used even for moderately accurate measurements of time. Since no fault could be found with the workmanship of the instrument, it was evident that the reasons for these irregularities had to be looked for in the principle upon which the instrument for high speeds was constructed, This it was not difficult to discover. It is a well-known fact that very little is required to stop a clock, and still less to make its movements irregular. By making a clock drive a drum with a speed of one revolution per minute instead of 24 hours, the clock has to do about 1000 to 1500 times more work, and the solution of the problem for chronographs of higher speed could therefore be only effected if this enormous increase of work of the clock could be correspondingly counterbalanced by a reduction in the work the clock has to do per each revolution. The principles upon which our me Va was worked out can be summarized as follows :—(1) Instead of moving the heavy drum, thick screw, and the one or two carriages * Communicated by the Authors. Phil. Mag. 8. 6. Vol. 11. No. 63. March 1906. 2D 394 Mr. Mond and Dr. Wilderman on a with writing-pens, we keep them all stationary and only move the light spindle with the writing-pen, thus diminishing the load upon the clock arising from the work transmitted by the clock. (2) We reduce the friction of the different parts in motion to that of the moving spindle only, and further reduce that by the use of friction wheels or balls, &. (3) We avoid the reactions of inertia, as far as possible, by a perfect balance of the moving part of the instrument—the spindle. Experiments for several years showed the intricacy and the minuteness of conditions to be carried out simultaneously in the construction of a chronograph for high speeds before a satisfactory result could be obtained. We shall for this reason describe and explain all those details upon which the successful construction and use of our chronograph depends. Figure [. (& Pl. VILL. fig. 1)represents a horizontal type of il Nee et i} i £ Sagar i our chronograph, as made for us by Messrs. Sanger, Shepherd and Co. d is the driving clock, ais the stationary drum 60 em. circumference fixed (in exact horizontal position) to the bracket (C’). The horizontal spindle (7) carrying the pen- arm (h) of the writing-pen (c) and the electromagnet (2) is counterbalanced by the nut (v) which is adjustable on the screw (uw). The horizontal spindle passes at one end through the boss of a pinion wheel (K), driven by the wheel (J) New Improved Type of Chronograph. 395 of the clock, thus describing a circle round the drum. A strip projecting from the spindle forms a long feather, and a corresponding featherway in the boss of the pinion, 2 mm. wide, renders the spindle capable of axial movement with regard to the pinion, caused by the screw of the spindle (/’) and the half-nut (S), fixed to the drum and insulated from the same by means of the ebonite strip. Owing to this double action of the spindle, the writing- -pen describes a spiral on the drum. The instrument shown in fig. I. gives a spiral 50 x 60=3000 cm. long, the circumference of the drum being 60 em. Since the writing pen can easily make one revolution per minute or in 10 seconds, we have 10 mm. or 60 mm. for registration of one second. The line, of our pen being very thin, we can read well to 0:2 mm. or even less, 7. e. 1/50 or 1/300 of a second, provided, however, means are found to make electrical contacts to the same degree of accuracy ; a problem which, it seems to us, will give much trouble if a conscientious scientific investigation should be properly attempted. Since in our type of chronograph the drum is stationary and a great extension in its height and width means only an extension of the length of the arm of the spindle, which means only a small increase of load and almost no increase in the friction or the reaction of inertia, we are thus able to construct instruments with still greater length of spiral and of the same accuracy. The boss of the spindle rests on two little friction wheels (w) fixed to the support (0), and is kept in position by the slight exterior circumferential groove on the boss with which the friction wheels engage; the friction of the spindle at this end is thus reduced to two points only. The screw end of the spindle has only to guide the pen which writes with almost no friction (the spindle must be naturally placed exactly in the centre of the drum). It is made thin for this reason, and the half-nut (s) contains only a little more than a line of the thread just sufficient to move the spindle securely forward. In this manner the friction at this end of the spindle was also reduced to the smallest possible amount. It will be perceived that the wheel (K) is not fixed to the spindle. This enables us to exchange without trouble one pair of wheels for another giving a smaller or greater speed (say one revolution of the spindle in one minute or in ten seconds), so as to get the speed which is most suitable for the investigation of the given physical, physico-chemical, physio- logical or meteorological phenomenon, &e. To allow of the use of the exchange wheels an adjustable fly is provided for the instrument. 2D2 | 396 Mr. Mond and Dr. Wilderman on a Our adjustable fly isan improved type of Breguet governor. Its purpose is a double one: first, to counteract ‘all small irregularities of speed; secondly, to adjust the absolute value of the time of each revolution when different pairs of wheels are used or when the springs in the natural course of time vary in elasticity. As to the first purpose, it should be remarked that only when the irregularities in the movement of the clock independent of the governor are very small, is the governor effective ; . when the variations are too oreat the governor serves no purpose and is a decoration only. The adjustment of the absolute values of the speed of each revo- lution is usually made as follows. When the wheels, &c. of the instrument are properly chosen, the final adjustment is usually effected by employing flexible spirals of a given material and of a certain number of turnings. This adjustment can, however, only be a rough one, and what is still w orse, even if a perfect adjustment is once effected it is certain not to remain perfect after being in use for some time owing to the variation in the flexibility of the springs, to the effect of slow - oxidation, moisture, fatigue, &. So also when exchange- wheels are used, the speed js not in proportion to the number of teeth in the wheel, as is often assumed, because the work to be speht in moving the clock parts and the spindle is not directly proportional to the speed of each revolution; 2. e., each pair of wheels must have its own governor which is to be specially arranged for the given speed. To meet all the above requirements, the springs of the governor are fixed as shown in fig. II. (p. 399), and by turning the screws d’ and d’’ they can be considerably increased or diminished in tension; the adjustment of speed can therefore be carried out with great sensitiveness and without difficulty. At the end of the cross arm (h) a screw (uw) is arranged, which together with the nut (7) forms a balance-weight at the end of the cross arm. This arrangement gives an adjust- able and extremely accurate means for securing an exact balance of all parts of the spindle while in position, which, besides the clock, is the only movable part of the instrument. This is also a point of great consideration in chronographs of great speed, because greater speed does not necessarily mean a corresponding greater accuracy. When a clock moves different parts of an instrument, not only does the clock move those parts, but those parts also move the clock, Since it is exceedingly difficult to get the wall of a hollow cylinder of a uniform thickness throughout, it being a sufficiently difficult task to get its upper surface true alone, the drum is never or almost never completely counterbalanced New Improved Type of Chronograph. oT in all its parts; its movement is, owing to inertia, for this reason not of a uniform character, and this upsets the reeularity of the movement of the clock. In our instrument the parts f and f’ themselves form the axis, and the two cross-pieces (hand h’) with the nut (v) form the arms of a balance carrying the weights to be adjusted to each other by. means of the screw and nut. It is of no little importance for the accuracy of the spiral obtained, that in our instrament this result is produced by one moving part only, while in other instruments it is produced by several moving parts, which in the nature of things can never be made to be absolutely dependent one upon another. We now pass to the description of our improved means for operating and working the writing-pen. After many trials and modifications the following arrangement was adopted. A bell-crank is provided at the end of the cross arm, one of its arms being connected by a rigid link to the armature (A) of the magnet, while the other is connected in a similar manner through the axial hole in the pen-arm to the penholder itself. The end of the pen-arm carries a small cross-head from which two guides (g and 9g’) parallel to the arm project. A cross-piece to the centre of which the operating link is connected slides on these guides, its motion being controlled by light flexible springs (s and s'), and to the cross-plece a flexible stri ip carrying the pen is secured. The pressure with which the pen bears upon the drum is regulated by a small screw (a) acting between the flexible strip and the cross-piece. In our newest type of chronograph arrangements are made to raise the pen from the drum, ‘when the paper is changed, so that the pressure of the pen upon the drum, once adjusted, should always remain absolutely the same. For this purpose a little plate carrying the writing-pen with the screw is hinged to the cross-piece. This arrangement provides a very steady support for the pen, making vibrations of the penholder impossible and keeping the pen inall positions of the spindle at exactly the same distance from the drum (instead of resting on it), and this enables the pen to be brought just so near “to the drum as is necessary to trace a spiral on the same, 7.e. with the least possible friction. To the arm carrying the pen a reservoir containing a considerable quantity of ink may be fixed, from which the ink flows into the pen through a capillar: y tube, or a capillary tube containing a cotton thread. By this means the pen never becomes dry, and there is no necessity for repeated cleaning and filling with ink. The writing-pen is actuated electrically. The current 398 Mr. Mond and Dr. Wilderman on a enters the terminal (T), which is in electrical contact with the base of the instrument, it passes through the support to the friction wheels, driving spindle, electromagnet, the screw, and then, by way of the insulated half-nut, from here it passes by the return wire to the terminal (T’) which is insulated from the base of the instrument. There is another distinctive feature in the arrangement of our pen for registration, and this is that our pen can be used at the same time both for registration and calibration. The Jength of the two guides (¢ and 9’), the greater flexibility of the two flexible springs (s and s‘), allow the pen to slide on the guides long distances, and for this the electromagnet (2) must also be adjusted at its screw (n). By connecting the terminals (T and T’) with a battery, and by using the pendulum of a clock or other suitable calibrating arrange- ments in the circuit for making contacts, we are able by iserting a corresponding resistance to adjust the current passing through the electromagnet so as to get for calibration small deviations of the pen from the normal spiral as desired each second, or better, each half minute or minute. By having the terminals (T and T’) at the same time connected with another battery sending the current in the same direction, and by having the electrical key or the automatic contact of the rain- gauge, anemometer, speed indicator, «c., we can so adjust the voltage and the resistance as to get a greater current through the electromagnet and a corre- spondingly greater deviation of the writing-pen from its normal course, thus registering the observed or recorded phenomenon at the same time. The results obtained for calibration and registration cannot possibly be mistaken for one another even if both contacts should happen to be effected simultaneously, because two intervals of calibration cannot possibly with our instrument be mistaken for one, and the longer line of registration cannot be covered by the shorter one of calibration. Not only does this dispense with a second carriage and pen, but also leads to more accurate results, because we register and calibrate straight on one and the same spiral, not on two separate ones, and we have not subsequently to transfer the calibration from one spiral to the other. For the special purposes, where two different kinds of phenomenon are to be recorded simultaneously, e, g. wind and rain, or where two observers have to record simultaneously the same phenomenon, such as the transit of a star in astronomical work, the instrument can be provided with two ens. | The great regularity and perfection of motion of the spindle New Improved Type of Chronograph. 399 in our chronograph attained in the manner described above is best seen from the fact that not the least sound (except from the fly) can be heard when the instrument is working, while in instruments of the older type of a similar speed harsh sounds both in the clock and in other parts of the instrument are heard, indicative of the irregularity of motion. In figure II. (& Pl. VIII. fig. 2) the vertical type of our chronograph is given. The principles and details are the If hee ae SS o%s L same here as in the horizontal type and are indicated by the same letters. Here the spindle is arranged with its driving end upwards, the weight of the pen-carrying system being taken by the half nut (8) on the drum. A dew of this portion is given in figure III., a hinged 4.00 Mr. Mond and Dr. Wilderman on a clip (y), provided with spring and clamping screw, serving to hold the spindle (7) in operative engagement with the half-nut. The driving is effected through spur-wheels, supported by the bracket (8); the bevel-wheel, as shown in detail in figur es IT., III., and IV., being arranged to run on ball bearings. The arrangements ‘of the pen-carrying system are similar to that described with reference to the horizontal type of instrument, the electrical connexions being also substantially the same. The vertical type isan improvement on the horizontal type, though usually made of a smaller size, since it allows continuous reading of the records on the drum, can stand more knocking about, is easier to be accurately constructed, and gives also better results. When the whole spiral is completed, the instrument stops automatically by itself. In the horizontai type we raise then the spindle (f7”) from the half-nut (s), and push it through the boss of pinion (K) back to its former position, stopping first the governor by means of (y’). In the vertical type, we open clip (vy), release the screw of the spindle from the half-nut, and push it up to its former position. Both types are set into motion or stopped, whenever desired, by stopping or releasing the governor by means of 9. While costly and complicated arrangements for calibration each second are indispensable for instruments with revolving drums, all we require for very accurate work with our instrument where the movement of the pen is very regular is to calibrate it, using an ordinary } sec. or 4); sec. watch and electric key ‘at longer intervals, say each minute (at the same time as we make our research observations}, and in this case we do not even require to exactly adjust the absolute value of a revolution, having only to use afactor. The same or almost the same error in calibration falls upon a minute instead of upon a second, and the results obtained in this manner are much more accurate and satisfactory. Since no work can be done for nothing, any extra work of the pen spent on calibration is not conducive to the accuracy of the resulis obtained, and it is well that we are able to avoid frequent calibration. Up to the present we have tried a great number of arrangements for calibration, some ot them. very complicated and difficult. The great accuracy and regularity in the movement of the w riting-pen, as well as the great ‘length ot the spiral, make our vertical instrument a very handy and easily manageable recording calibrator for other instruments New Lmproved Type of Chronograph. AQ1 with revolving drums, where those have to be used in view of the nature of the research (physiological, physical, &e.) 1 in spite of their mmaccuracy. All that is required for this is to fix to the axis of the revolving drum a suitable wheel with projections making electrical contacts for our chronograph, at as frequent intervals as is desirable, and to calibrate the value of each revolution of the pen of our instrument with an ordinary watch, at a greater time interval. The accuracy of the instrument as a time indicator and the length of the spiral allows of its wide application for all sorts of scientific and technical purposes: e.g. by a corresponding variation in the accessory instruments for more frequent contacts a considerably more accurate anemometer, speed indicator, &c., is easily arranged, allowing a very much greater accuracy than has regen Ma) been pr “anette ll & We shall illustrate this only on the two instruments mentioned, 2.e. on the anemometer and the speed indicator. The anemometer has to indicate the miles of wind in the cage th : unit of time, 7. e. as In the present instrument two clocks are usually used : one moves the drum with the speed of one revolution in 24 hours (this gives ¢); the other raises the writing-pen and allows it to dr op, thus extending the line for contacts several times (this gives F). Since the length of the curve for time is very short, the registration of ¢ is very + defective, — must be defective also. With our instrument the revolving pen makes a contact on our spiral for say each F’ miles of wind. The spiral is about 50 times longer than with ordinary instruments and is used both for the indication of time and for the contacts. The length of line is about 10 times longer for F and about 50 times longer for t. The speed “indicator has to give the number of revolutions (of an electromagnet, dynamo, gas-engine, steam-engine, motor car, &e.) in the unit of time, 7. e. 5 In all present instruments time is given by a revolving drum. The indication of time (¢) is very wrong, especially where large strips of paper are rolled and unrolled from drums and drawn by a clock Gn the first instance on account of enormous friction). The number of revolutions is given by a rising fly—this (s) 1s again wrong, because the rise of the fly is not directly proportional to the ‘speed. Then the pen writes not in straight lines, but in arcs. The result is that we get an idea of the speed, but no quantitative measurement of it, and we have no means of knowing exactly the speed at any given 402 Mr. D. Owen on the Comparison of Electric time owing to the interference of too many sources of error. With our instrument we arrange that a contact should be made by the dynamo, gas-engine, motor car, &e. &e., at eonvenient intervals, say each 1 or 10 or 100 revolutions. The distances between the contacts of the spiral on paper ruled in mm. to indicate the time gives also at a glance the character of the varying speed, but “the same unit divided by the distances between an contacts read In mm., gives at the same time also exactly the speed between the fine intervals indicated on the paper. The greater length of spiral also allows of this variation being observed more frequently and with greater accuracy. London, August 1905. XXXII. Phe Comparison of Llectric Fields by means of an Oscillating Electric Needle. By Davin Owen, B.A. (Camb.), B.Se.(Lond.), Lecturer in Physics, Birkbeck College, London”. XPERIMENTS on fields of force due to electric charges suffer as compared with the corresponding measure- ments in magnetic fields by reason of the impracticahility of obtaining an ‘electric needle’ * corresponding to the oscillating magnetic needle. But while it is true that a permanently electrified needle cannot be obtained, it is possible to have one that has equal charges of opposite sign induced by the field. This paper contains an account ot experiments on the use of such a needle for the measurement of electric fields, steady or alternating, and for the experimental illustration of some of the laws of electrostatics. Theory. Consider a cylindrical needle supported at its centre by a fibre whose torsional control is negligible, placed with its axis horizontal in a uniform horizontal field of strength F. The needle will move so as to set itself parallel to the field. If disturbed from that position a restoring couple will come into play. This couple will be proportional, both to the induced charge, 7. ¢. to the “ ae and to the field. As the foeen is proportional to the latter, it follows that the couple will vary as the square of the field-strength. It will diminish as the angle between the axis of the needle and the direction of the field increases, and will clearly be zero when the two are at right angles. In the-case of an * Communicated by the Physical Society : read June 30, 1905. Fields by Means of an Oscillating Electric Needle. 403 ellipsoid the couple is proportional to the sine of twice the angle 6 between the long axis and the field. Assuming that law to hold for a cylindrical needle, we may write the couple equal to aF? sin 20, where a is some constant. If @ is small we have a Count sy = 2a}? (constant), Angular displacement _ 0 in which case the vibrations of the needle will be isochronous, the time being given by a ee es where [=:moment of inertia of the needle. Werno T= E we may denote the frequency of vibration : Ni oy NE eee ov) elm where } is a constant depending on the form, size, and mass of the needle. Thus it appears that the strengths of uniform fields are directly in proportion to the frequencies of such a needle oscillating in them. Of course if the controlling couple due to the suspending fibre is sufficient to take into account, this may be done by observing the frequency N, when the electric field is nil. Denoting the frequency actually observed in field by N’ we have Nese any ae lens (IL)’ This law was tested by establishing an electric field between a pair of parallel circular plates, each 12 cms. in diameter, kept at a constant distance apart. The difference of potential between them was obtained by means of a Kelvin voltaic pile, whereby any voltage from 400 volts downwards could be applied. The volts were measured by a Kelvin multicellular electrostatic voltmeter reading to 400 volts. The vibrations were observed by the help of a plane mirror placed below the needle, as shown in fig. 1, which represents the apparatus used. The image of the needle in the mirror was viewed through a telescope, in the focal plane of which an image of the needle appears vertical in the position of rest. ‘he vertical cross-wire is set to bisect it. The time of a counted number of oscillations was obtained by means of a stop-watch reading to fifths of seconds, sufficient passages being allowed to admit of the whole period of time measured being from one to two minutes. am in cnt ct i igi A TN A ENTE OLE PELE EAD DORE | ~ A404 Mr. D. Owen on the Comparison of Electric The apparatus was enclosed in a balance-case in order to avoid draughts. Observations were restricted within an amplitude of oscillation of about 5°, in which case the error due to finite amplitude is negligible. The needle used was of copper wire, 1°4 cms. long and 2 mms. in diameter, suspended by a quartz fibre about one- tenth of a mm. in diameter and 8 centimetres long. The plates were ata distance of 3 cms. apart. The results gave as expected a straight-line law connecting V and N. Disturbance of the Field due to the presence of the Needle. The effect of the presence of such a needle in an electric field is in every case to produce a concentration of the field near the needle. Further, if the charged conductor forming one of the boundaries of the field is sufficiently near the needle, the distribution of the charge on that boundary will be altered. This of course prevents the application of the electric needle for the accurate comparison of the electric forces near the surfaces of conductors of different forms and curvatures. It was considered desirable before proceeding 405 further to investigate the nature of the disturbance caused, and to determine its bearing on the applicability of the needle tor exact quantitative measurements of field. A case of importance is that of the field between two parallel metal plates. The question may be put thus: if an electric needle be placed in an infinite uniform field, at what distance does the disturbing influence of the needle cease to be appreciable? I know of no mathematical treatment for the case of a short cylindrical needle such as was used above. The following experiment was therefore performed. The parallel plates already described were used, and the arrangement of apparatus was as in fig. 1. The plates could be moved perpendicular to themselves so as to alter their distance d apart. A constant potential-difference of 400 volts was maintained between them. The needle used was of aluminium, of the following dimensions :— Fields by means of an Oscillating Electric Needle. length =1°526 cms., diameter anh ee and mass = *0329 grams. The distance d was varied between the limits of 6°04 cms. and 1:92 ems., and values of N for these and several inter- mediate vaiues of d weredetermined. The needle, suspended by a quartz fibre, was set centrally between the plates in each case. The results may be tabulated as follows :— i Se80 sees, No. of d os N’ N Nxd exp. in cms, in secs. per sec. |— ./N’?— N,2" NES ee... 6:04 7-20 “1392 -1282 en | Do gee 5:33 6-40 1562 ‘1468 74s a 4-82 5:82 172 163 785 | 2 an 4-40 5:34 1866 178 ‘783 See 4-03 5:00 200 193 Staal Ghee... 3-00 3:69 71 2656 ‘797 Toe. 2-53 3:04 -329 “325 -822 ecole 2325 2-72 -368 "364 844 Ones: 2-07 2:32 -433 ‘430 885 TOR... 1:92 2-04 “490 ‘487 ‘916 | i} { These numbers are represented graphically in fig. 2, where products of frequency x distance apart of plates (Nxd) are plotted against distance apart of plates (d). From this curve it may be seen that beyond d=4:5 cms., or say exceeding three times the length of the needle, the disturbing 406 Mr. D. Owen on the Comparison of Electric effect of the needle is inappreciable, and the product N xd remains constant. This may be seen further by the aid of a Fig, 2. | | | | | Length. of Needle=/526 cms. | \Trameler of Medle= -101 cms. | | | | | | | | | | | { } : = aloes Vl. Delenep pert eee =f 2 a 4 a 6 / og Fo ' ’ ‘ 1 1 1 ‘ ‘ ! ' 1 ‘ i t ‘ ‘ ' 1 ‘ ' ' . diagram (fig. 3) representing the lines of force and the equi- potentials near the needle when the axis of the latter is along the direction of the undisturbed field. Fields by means of an Oscillating Electric Needle. 407 The lines of force are shown as full lines, the equipotentials as broken lines. The equipotentials near the needle are much curved, but the effect diminishes rapidly on going away from the needle, so that the equipotentials PP and P’P’ are practically strai ight. Beyond these the equipotential surfaces are a series of parallel planes, and the field is uniform and of the same value as if the needle were not present. The result suggests the possibility of determining by the use of an electric needle the specific inductive capacity ‘K of . dielectric. For if a pair of parallel plates kept at fixed | difference be used to establish a uniform field, their distance apart well exceeding the limiting distance at which the disturbing effect of the needle is appreciable ; and if between one of the plates and the critical plane a parallel slab of the dielectric be introduced, the effect is to increase the field in the air space by an amount involving K in a simple and well-known way. Of this nothing further will be said in this paper, as careful experiments are being under- taken dealing with the determination of specific inductive capacity by such a method. Iu regard to the disturbance introduced in other cases, it is important to notice that for a given arrangement of conductors and given position of the needle, variations of field due to alteration of potential will be measured by the frequency of the needle, the ratio of frequencies being unaffected by the distortion of the field. For example, in the case of the field between a pair of parallel plates at a distance apart only slightly exceeding the length of the needle; though the frequency of the needle is oreater, as shown above, than in an infinite field of the same strength, yet it increases exactly in proportion to the difference of potential between the bounding plates. The choice of Needles. lt is desirable that the needle should be as small as possible, to reduce the disturbing effect; and sensitive, for the measure- ment of as small fields ¢ as possible. To investigate this latter condition six cylindrical needles were made of aluminium, with dimensions as follows :— Three needles of diam. of 1 mm.; lengths 14 cms., 1 em., °5 cm. M4 ms su POONA Sh beh Gap utp dca? ye ge ak 5 A similar set was afterwards made in brass. These needles were drilled centrally at right-angles to their length with a hole of about *3 mm. in diameter, into which was fitted a suspending wire of the same diameter, and of 2) aT ee | 408 Mr. D. Owen on the Comparison of Electric length varying from 5 to 10 mms. To this wire was cemented a quartz fibre about 4; mm. in diameter, and about 8 cms. long, the upper end of the fibre being cemented to a supporting piece attached to one of the plates. These needles were sup- ported in succession between the plates, which were kept at | the same distance apart and at the same difference cf potential | throughout the experiment. The time of vibration of each | was thus determined :—The dimensions and mass of the needles being known, the moments of inertia could be calcu- lated, and by equation (I) the couple on each when in a specified field could be determined. No high degree of accuracy was to be expected where the moment of inertia of such small needles was involved. The results given below, however, show sufficiently the effect of alteration of length and of diameter. The frequency came out less for the brass than for the aluminium needles, just as calculated from their relative density. The values of the frequency in column 4 are for needles of aluminium. | Dependence of Frequency on Dimensions of Needle. Electric field = 100 volts per cm. | | | Length | Diameter - ae eeu Relative _ Relative (cms.). (ems.) | (dyne-ems.) i N. ) couples. frequencies. 56 | lol | 982 | -197 | 100 100 15108 //MiatO2s a | | Arp rns SapamN, 118 | ‘B10 A} AETO25 9 ah e645 N ere Oi ee Se 140 } 1-500" | {0502 |") 698 4 te pieS37 nue) WenOs5 171 | 1-000 050), ah. e253 6 NY CB eos, 178 | | These numbers show that although the couple on the needle increases rapidly with length and slowly with diameter, yet the effect on frequency is more than counterbalanced by the increase in the moment of inertia. Thus whilst, as the first three rows of numbers above show, the length of needle decreased in the proportion of about 3:1, the couple decreased in the proportion of about 15: 1, whilst the frequency went up in the proportion of only 1: 14. Hence, while as the needle gets smaller the disturbing effect on the field rapidly diminishes, its frequency of v ibration increases, though slowly. This is a favourable circumstance to be borne in mind in experiments such as that suggested above for the determination of specific inductive capacity. Fields by means of an Oscillating Electric Needle. 409 Where the disturbance is not of importance, and it is desired to show the vibrations, either directly or by projection in a lantern, the needle may with advantage be large. Aluminium needles of 14 cms. length and 1 mm. diameter have been found very satisfactory ; brass needles should be of smaller diameter. For strong fields the needles may be still heavier, and the suspension may be of silk threads consisting of several single-fibres. There is thus little danger of breakage of the Suspension, where, as for purposes of lecture demonstration, the needle has to be moved about and may be more or less roughly used. Applications. The electric needle may be regarded as a measurer of electric force, and be applied to test the field-strength due to any arrangement of conductors, effect of alteration of their relative position, or of the potential, &c. In some cases exact results will not be obtained owing to the disturbance introduced by the needle itself. In others the disturbing effect of the needle does not enter. Of the first class the following example may be cited :— Comparison of the electric field at different points on the surface of any conductor. The case of a pear-shaped conductor (fig. 4) was examined. Fig. 4, 3 ane ene ee ee ee ee ee ee end ( ’ ' ' | ! 1 i] ! ea *® ! ' | ' ' i ' ' 6 quater: Four positions on it were chosen, namely, at the pointed end and blunt end, at the equator, and opposite the middle of the flat side (where the curvature is single). The needle used was 14 ems. long. Its nearer end was set in each case Phil, Mag. 8. 6. Vol. 11, No. 63, March 1906, 2 410 Mr. D. Owen on the Comparison of Electric at a distance from the conductor equal to half the length of needle. The results were as follows :— Position. eae pbs Relative frequency. Pointed end ......... | 2-55 Bo | Blusat-end).os.csee: 3:20 8 eC WE0) crenata cane 325 ‘78 | Bint side! 2.5.0. 3:85 66 For a couple of spherical conductors at a distance from other conductors the following numbers were obtained :— Diameter of T Relative Electric force sphere. | i frequencies, (theoretical). 12 ems. | 2°40 sees. if 1 3 9 | 1:23 ” 1:96 4 These comparative numbers indicate the increase of electric force F with carvature. By means of a proof-plane the increase of surface-density o of charge with curvature may be shown. In both cases the numbers suffer in accuracy owing to the disturbance introduced by test needle and proot- plane respectively. Such experiments as the above are best performed by attaching the conductor by a fine wire to the inuer coating of a charged Leyden jar. The potential then changes only very slowly with time. It may be interesting to add that the potential of the pear- shaped conductor, as determined by an electric needle, was 6200 volts in the case to which the numbers above refer. In the following two cases the disturbing effect of the needle is of no significance :— (1) Wherever the variation of electric force with altera- tion of potential is to be found, no motion of the bounding conductors or of position of needle taking place. The electric force as measured by the frequency of the needle is propor-. tional to the difference of the potential. (2) To prove that inside a charged conductor (not enclosing an insulated charged conductor) the electric force is zero. Though this theorem is one of fundamental importance, it is Fields by means of an Oscillating Electric Needle. 411 not easy to demonstrate it experimentally. In the electric needle we have a means of doing this of a simplicity corre- sponding to that which the proof-plane affords for showing that the charge inside the conductor is zero. As the needle is lowered into the conductor, e.g. a metal can or a cylinder of wire netting, the frequency of the needle falls until when well inside its value is the same as when the conductor is discharged. On the Shielding Lffect of Dielectrics. Having mounted a needle within a glass specimen-tube in order to do away with the effects of air-currents, it was observed that even when in the strongest electric fields the needle was quite unaffected. The tube acted as if it were a conductor. As this effect might be due simply to the unclean condition of the surfaces, the experiment was repeated with a carefully cleansed glass lamp-chimney, with the same result. It appears then, that owing to the conductivity of the glass, slight as it is, a closed glass vessel screens electric force from its interior, just as if it were a conductor. The same result was found for a sheet of mica of thickness jy mm. bent into a cylinder. A mica cylinder in ordinary air screens the interior completely (when placed in a steady field, as in fig. 5). If heated over a hot plate and quickly transferred to the field so as to surround a needle swinging in it, there is seen to be electric force at the needle ; but it quickly dies down, and in 20 or 30 seconds the needle once more vibrates in its own natural period, depending on the torsional couple of the quartz suspension. This conductivity of the mica appears to be a_ surface effect, probably due to the deposition of moisture from the atmosphere. Hor if the mica sheet be immersed for some time in melted paraffin-wax at a temperature close on 200° C., then taken out and allowed to cool, the sheet (made into a cylinder as before) is found to be capable of transmitting the field for some time. Bnt even in this case the field within the cylinder falls off with time. Thus in one case a needle within a paraffined mica cylinder gave 12 vibrations in 10 seconds at first, but four minutes later only 8 vibrations were counted in the same time, the fall of frequency being according to the exponential law. Electrical separation has slowly taken place in the mica. If now the plates between which the field was produced be discharged, the cylinder should be left charged, and an electric field should exist in the interior. This is found to be the case. The field dies out with time, as in the experiments in the constant 2H 2 412 Mr. D. Owen on the Comparison of Electric field. Another way of showing this effect of minute con- ductivity is to introduce the cylinder into a steady field, leave it there for some time, and then turn it about its axis through 180°. The field inside the cylinder is seen to be for the moment greater than that of the original field, for on the latter is superposed the field due to the separated charges on the walls of the cylinder. With cylinders of thicker sheets of mica similarly treated with paraffin-wax, the rate of falling off of the interior field is found to be greater. These experiments indicate an appreciable though exceedingly small conductivity in the mica itself. Experiments on the shielding effect of ordinary white paper were made. Cylinders of paper screen the interior completely from the surrounding field. But on heating for a short time over a hot plate the shielding effect vanishes ; in about one minute, however, the frequency of the needle within is found to have fallen considerably, and a minute later is the same practically as in zero field. Dry paper then acts as a perfect insulator. But by the absorption of moisture when exposed to the open air it quickly gains appreciable conductivity. With paraffined paper the shielding power was nil, and remained nil for days in the open air of the room. Of all the materials tried this alone permitted for any length of time the undiminished transmission of electric force. Thus by applying a thin coating of paraffin wax to a sheet of dielectric, and then observing its shielding effect on an electric needle, we have a convenient means of testing the conductivity of the dielectric, which removes all doubts as to surface- action. This effect of the high insulating, non-hygroscopic, quality of paraffin-wax is made use of in the experiments on mica above described. Experiments with alternating fields—As with steady fields glass and mica proved sufficiently conducting to screen off electric effects, experiments were made with these materials, using alternating electric fields. The alternating voltage was obtained by the use of the Musical Arc. Mr. Duddell, I may say here, very kindly advised me as to the conditions for obtaining bigh voltages by this means. The connexions were as shown in fig. 5. The alternating voltage on the self-induction P in the shunt circuit to the arc was found to be about 200 volts. This was transformed up by means of a second coil S, to the terminals of which the parallel plates were connected. In this way any voltage up to 1000 volts could be maintained between the plates. The frequency of alternation of this Fields by means of an Oscillating Electric Needle. 418 voltage was found, by means of a sonometer and standard fork, to be 1700 per second. The needle was allowed to vibrate in the field with (a) glass cylinder surrounding it : ()) cylinder taken away. The time of vibration was found to be the same in each case, namely 1°83 secs. The glass oylinder had a diameter of 5 ems., the thickness of wall being 1-4mm. With such dimensions the weakening of the field inside the cvlinder due purely to the specific inductive capacity effect should only be small. With a cylinder of thicker glass, but diameter only slightly exceeding the length of the needle (1 cm.), the fr ae of vibration was distinctly less in case (a) than in case (b). With mica cylinders the same result was obtained. These experiments emphasise the necessity of using alter- nating fields in all cases where from the measurement of the force “experienced by a mass of a dielectric its specific in- ductive capacity is to be determined. In steady fields, unless the specific conductivity of the material be quite nil, the force will ultimately be the same as for a conductor. This consideration will account for the high values of / obtained in some of the experiments of Boltzmann (see Gray’s Abs. Measmts. vol. 1. p. 465). Use of Hlectric Needle to measure Volts. A pair of insulated parallel metal plates with a needle suspended centrally between them forms a simple means of measuring high voltages. For we have volts across plates=frequency of needle x a constant. The constant may be determined at a low voltage by any voltmeter available. The highest voltage measurable is limited by the difficulty of counting the frequency of the 414 Mr. H. Morris-Airey on the needle if this exceeds 4 or 5 per second. But the range may be extended by opening out the plates; for as already shown the frequency of the needle for constant difference of potential is inversely as the distance apart of the plates, provided that the minimum distance used exceeds three times the length of the needle. The constant & is most simply defined as the volts across the plate required to produce a frequency of oscillation of 1 per sec. for a distance apart of the plates equal to 1 cm. Then if d=distance apart of plates, N =frequency, V=voltage between plates, we have VakdxN. ooo... An instance of this application has been given already Another may be added :-— The difference of potential yielded by a Wimshurst machine was measured by charging a Leyden jar, the outer coating being connected to one pole, the inner to the other pole, the poles being kept well apart. The jar was connected with the pair of parallel plates, which were at a distance of 10°5 ems. apart. The frequency of the needle in the field between them was 2°04 per sec. The needle used had a constant (reduced to d=1 cm.) of 13800 volts. Applying formula II, we haye a x 10°35 x 2°04 27800 volts. The machine, it may be added, was working badly, giving a spark between balls of 2 cms. and 5 cms. diameter respec- tively, Leyden jars being in, of something less than 1 em. length. These experiments were made in the laboratories of the Birkbeck College. I would record. my thanks to the Principal for facilities for carrying them out. XXXIV. On the Resolving Power of Spectroscopes. By H. Morris-Arrey, J/.Se.* HE object of this note is to call attention to a factor which appears to have been neglected in the consi- deration of the resolving power of spectr oscopes. It has been shown by Rayleigh that, using an indefinitely narrow slit, the resolving power of a orating-spectroscope * Communicated by the Author. Resolving Power of Spectroscopes. 415 depends only on the total number of lines on the grating which are utilized. In practice, however, we frequently make use of slits so wide that the theoretical resolving power is far from realized. This case was considered by Schuster, who introduced the idea of “‘ purity ” of spectra. If light containing two homogeneous radiations differing in wave-length by SX falls on the slit of a spectroscope, the condition for resolution of the corresponding lines has been shown by Schuster to be OX 2A+vd Noe ele where d is the width of the slit, R the theoretical resolving power as defined by Rayleigh, and yr is the angle subtended at the slit by the diameter of the collimator ene. This expr esslon ¢ appears to contain no factor depending on the position of the grating or prism; but a simple consider- ation shows that the purity becomes greater as the angle of incidence of the light on the grating increases. When the slit has a finite width we can consider the light falling on the grating to consist of a number of beams of parallel rays s making : slightly different angles with the normal to the grating. Let @ be angle of incidence and 6 the angle which the cor- responding diffracted beam makes with ihe. normal. If ¢ is the grating space, we have the usual relation e(sin ¢@—sin 0) = + ne; from which dO =z © o) pb, cos O and CO a drX 2ecosd The diffracted beams will ne make slightly different angles with the normal, the total variation being dé. This variation can be made as small as we please by i increasing the value of @ so that in the limit when the light falls on ihe grating at grazing incidence the diffracted beams corre- sponding to. any particular wave-length and order all make the same angle with the normal, and will be received in the telescope under nearly the same conditions as if the colli- for any value of p. Gib >: mator-sht had been very narrow. further, oe is also . d increased, so that the total effect is to greatly increase the purity of the spectrum. . oO et 416 Mr. P. Blackman on Quantitative This result is really included in Schuster’s formula when we examine the meaning of the term yp. Hitherto this has always been interpreted to mean in every case the angle subtended by the collimator-lens at the slit. Bat it is clear that by tilting the prism or grating suff- ciently, only part of the beam passing through the lens is effective. Reference to the proof of the formula * shows that in that case it is only the width of the effective portion which should be considered in determining the value of the angle wp. Hence that angle really depends on the position of the prism or grating, and may in the limit be reduced to zero. The smaller y is, the greater is the purity, 'and ultimately by reducing its value the full resolving power is reached with a ereat width of slit. This is confirmed by experiment, and I find that with a small Thorp grating containing between 1300 and 1400 lines it is easily possible to separate the sodium D-lines even when the slit is half a centimetre wide; in fact in most cases the collimator can be entirely omitted. The application of this device is limited by the great loss of light by reflexion at the surface of the grating when large angles of incidence are used. Cases, however, do occur where the principle may be used with advantage. or example, it is very convenient in the photometry of are-lamps when using the Vierordt colour- photometer, where large errors are introduced, notably in the red end of the spectrum, owing to differences in the purity of the two spectra under comparison. Physical Laboratory, Manchester. AXNAV. Quantitative Relation between Molecular Conductivities. By Puttrp BLACKMAN T. HE formation of a salt MX from the acid HX and the base MOH may be represented by the equation H*+X’+ M’4.OH’=M’°+ X’+ HOH. The initial and final electrical states differ by the expres- sion H*+OH’=H.OH; hence, we should expect in the formation of the salt the disappearance of electrical conduc- tivity equivalent to that required by the above equation. This quantity of electrical conductivity will depend on * Kayser, Handbuch der Spectroscopie, vol.i. p. 552. + Communicated by the Author. Relation between Molecular Conductivities. ALT (1) the temperature, (2) the molecular concentration, and (3) the nature of the acid. Supposing these three conditions be fixed, there ought to be a constant quantity for the electrical conductivity corresponding to H*+OH’=H.OH8H. Let penx, Muon, MUu,on, MUu,x, @Um,x, represent the mole- cular conductivities (all measured at the same molecular concentration v, and at the same temperature) of the acid HX, of the bases M,OH and M,OH8, and of the salts M,X 5) Ht 2 ’ 1 and M.X respectively. Then, according to the above, eux + wes, ou=Mew,x + K, MUrx + HUm,on = MUM,x =F Ky where K is a constant. Hence Mux + My, on hx = Mix + PUM, on — MUM, Xe The following values, calculated from the data in the ‘Physikalisch-Chemische Tabellen, von Landolt und Born- stein’ *, illustrate the above: v (at 18°) = 1, 2./ 10, 32. 100. 1000.| 1024. 10,000. pv3H,SO,+pvKOH —pv}K,SO, ... 287) 300/317 418/387) 422 | 468 470 pos H,SO,+pvNaOH — pv d Na, SO,...| 284 297 | 305. 420 381! 413 | 481 | 461 | pUHIO, +vNaOH —poNal0, ......... | | og 4 PERE Is are vi HSO,+pvLiOH —pv} Li,SO, .... 268 | 282/314 419 390 482 poHNO,+p0KOH —pvKNO,......[374| ... |423 492/441) 439 | 485 | 490 | woHNO,+uvNaOH —poNaNO, .../364| ... |411/ 491/428] 429 | 494 | 480 poHNO, +p 2 BaO,H,—po3 BaN,O, .| ... |... | --- [473) ... |... | 481 | wHCl+p~oKOH —peKCl ........., 358) ... |418| 490/439 437 | 489 | 485 | pvHCl+pvNaOH —uNal... 2.2.5. 1308; ... | 408 | 492 |433| 425 | 490 | 479 | pemeiees }Ba0,H, poi Ba, |. |. (470)... /-%. | 490 | PVHCl+ pvLiOH —poliCl ......... Wass] ceo, || ag 493 | 442 are lone oult Gone epKOH —pvKI.............. ee a, Cee poaa ae e UHI +pvNaOH—poNal ............0.. lise see al rh | POLS pOmiOM —pelib..s...scce..) [oe | ATL POHMOe en oKOH —pvKIO,.0... Re el eli | 482 | 481 | pf r e e The last equation, by subtracting the common term peux and then by transposing, becomes | Mey on MUM, on = MUM x MUM xe The equation MU, on — MU, on = MU, x — LUM, , * The table, which was first drawn up from an earlier edition of Landolt-Bornstein, has been corrected by means of the latest (1905) edition recently published, 418 Notices respecting New Books. it will be at once noticed, furnishes a means of calculating the molecular conductivities of (1) insoluble or unstable cases, and (2) insoluble or unstable salts, the molecular conductivities of which cannot be determined by direct measurement. Similarly, it can be shown that eujou~— Memon = KUM, x, — Meu, x, = Um, x, — MUM, x, Hence Mem, x — PUM,x = MUM, x, 7 PUMA X, = Um, x, — HUM,Xx, = UM, x, — PUM, Xs = constant. This final equation, it will be observed, is identical with the hitherto unexplained fact discovered by Kohlrausch (and further extended by Ostwald, see Lehrb. der Alg. Chemie, ii.). Kast London Technical College, London, E. XXXVI. Notices respecting New Books. Ions, Electrons, Corpuscules. Mémoires réunis et publiés par H. Asranam et P. Lancevin. Paris: Gauthier-Villars. 1905. Premier Fascicule, pp. xvi + 512. Second Fascicule, pp. 513-1138. iB any proof were needed of the extent to which the modern theory of electrons dominates physical science, it might, not inappropriately, be regarded as furnished by the publication of the two Jarge volumes under review. The Société Francaise de Physique, which has already done good work in rendering accessible to numerous readers collections of important memoirs on various branches of physics (issued under the title of Collection de Mémoires sur la Physique), has performed another most useful service by collecting all the scattered papers dealing with the rise and development of the electronic idea, and arranging them in a form which renders it an easy matter tolook up the particular contributions towards any branch of the subject made by ditferent iP PRSCTIII CE 0) fa rie ae I LA, Se NK Originally, the work was to have been edited by the Jate M. Alfred Potier (to whose memory it is dedicated), but owing to Notices respecting New Books. 419 his death the editorship passed into the hands of Messrs. Abraham and Langevin—two well-known investigators who have themselves made important contributions to the electronic theory. The arrangement of the matter is alphabetical as regards the authors’ names, and chronological as regards the contributions of each author. At the beginning of the book is provided a table of contents which practically forms a subject index, a separate author index being provided at the end of the book. This arrangement greatly facilitates the task of finding any 1n- formation the reader may be in search of, and enhances the value of the book as a work of reference. It is safe to say that no worker in this most fascinating branch of physics can afford to be without a copy of this timely and important publication. La Séparation Electromagnétique et Electrostatique des Minerais. Par Distri Korpa. Paris: L’Eclairage Electrique. 1905. Pp. 219. Tue subject of electromagnetic separators is one which has not before been treated in a systematic manner, and the present valuable little monograph should prove of considerable interest to mining engineers. The application of purely electrostatic methods to the separation of different kinds of ore is of com- paratively recent origin, and has not as yet attained to anything like the importance which may be claimed for electromagnetic methods. The author devotes a few pages to the electrostatic method, and then gives a detailed account of the practically important electromagnetic separators. Then follow chapters on the magnetic properties of minerals and the theory of magnetic separators ; the treatment of the latter subject is such as to form an elementary treatise on electromagnetism for readers ignorant of the subject, with a view to rendering the book self-contained. A good account is next given of the various magnetic separating plants at present in existence, and of the results obtained with them. The preliminary treatment of the ore before it passes into the separator is then dealt with, and in a concluding theoretical chapter the author gives a brief outline of paramagnetic substances other than iron. Essais des Matériaux. Notions Fondamentales Relatives aux Déformations Elastugues et Permanentes. Par H. Bovuasss, Professeur de Physique 4 Université de Toulouse. Paris: Gauthier-Villars. 1905. Pp. 150. Tnis volume is the first of a series of small text-books to be published under the general title of ‘‘ Biblioth¢que de l’El¢ve Ingenieur.” It deals in a very general manner with the theory of strains and stresses, and with the leading principles which underlie the construction of various testing-machines. It 1s not intended to be a mere laboratory guide, nor is any attempt made to describe the technical details of commercial testing-machines. 420) Notices respecting New Books. The task accomplished by the author is, indeed, a much more formidable one, and much more likely to be useful to the reader than a purely descriptive work. The treatment is characterized by vigour and freshness combined with clearness. To a large extent the author’s method is based on a study of the stress-strain diagram and its characteristics in various cases. No very advanced mathematical methods are used, although the reader is assumed to have a knowledge of the calculus and of the simpler forms of differential equations. The subject is throughout approached from the purely physical rather than technical standpoint, and the rough-and-ready methods of the purely technical man come in for a good deal of severe comment. We could desire no better introduction to the difficult subject of strains and stresses than this masterly exposition, which augurs well for the success of the new series of text-books. Elektromagnetische Schwingungen und Wellen. Von Dr. Joszr Ritter von GEIrLeR, a. o. Professor der Physik an der K.K. Deutschen Universitit, Prag. Mit 86 eingedruckten Abbildungen. Braunschweig: F. Vieweg und Sohn. 1905. Pp. vi + 164. THis monograph forms No. 6 of the series entitled Die Wissenschaft, now in course of publication. The subject of electromagnetic waves has always had a singular fascination for all interested in the development of physical science, and the simple and clear non-mathematical account of it contained in the monograph under review should appeal to a very wide circle of readers. The author deals with the subject in the order of its historical development, beginning with a brief review of the old action-at-a-distance theories, Faraday’s ideas regarding strains and stresses in a medium, Clerk Maxwell’s brilliant theoretical developments of those ideas, and their practical realization in the epoch-making discoveries of Hertz. The remaining half of the volume deals with the methods of detecting electromagnetic waves, with their relation to light waves, and with their practical applications in wireless telegraphy. Dr. J. Fricks Physikalische Technik. Siebente vollkommen umge- arbeitete und stark vermehrte Auflage von Dr. Orro LenMann, Professor der Physik an der technischen Hochschule in Karlsruhe. Erster Band: Zweite Abteilung. Mit 1905 in den Text eingedruckten Abbildungen. Braunschweig: F. Vieweg und Sohn. 1905. Pp. xx+1002. SoME time ago we had occasion to review Part I. of Vol. I. of this valuable work, and now Part II, completing the volume, is before us. The subjects dealt with are measurements of length, mass, and time; various forms of apparatus illustrating the laws of statics ; experiments on the general properties of solids, liquids, and gases; the measurement of temperature and construction of Geological Society. 42] thermemeters; the phenomena connected with the change of physical state ; calorimetry, hygrometry, and heats of combination ; the laws of dynamics; waves and wave-motion; hydrodynamics, the dynamics of gases, and thermodynamics. In a brief review such as the present, it would be impossible to do justice to the wealth of learning contained in this work. Not only are full directions given for the successful carrying out of lecture experiments on a large scale and the construction of various forms of apparatus, but the work abounds in most interesting passages relating to the history of physics and the gradual evolution of different types of instruments. In many instances defects are pointed out in existing forms of apparatus as usually constructed, and suggestions are made for improvements ; the work is thus one which may very profitably be studied by manufacturers of physical apparatus. Special mention must be made of the numerous excellent illustrations which adorn the book. Teachers of physics desiring to become proficient in the art of lecture illustration, or having to prepare estimates of laboratory equipment, would do well to turn to this unique publication for information on these points. XXXVII. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 192. | December 20th, 1905.—J. E. Marr, Sc.D., F.R.S., President, in the Chair. A ere following communications were read :— 1.‘ The Highest Silurian Rocks of the Ludlow District.’ By Miss Gertrude L. Elles, D.Sc., and Miss I. L. Slater, Newnham College, Cambridge. After an introduction dealing with previous work in the district, the authoresses adopt the following classification of the beds :— Treet B. Temeside or Hury- | gn { Zone of Lingula cornea IIT. Temestpe | pterus-Shales. yi 110 to 120 | and Eurypterus. Grover. | A. Downton-Castleor) . x, f Zone of Lingula Yellow Sandstone. { 30 to 50 minima. : B. Upper Whitcliffe | |, {Zone of Chonetes us i. or Chonetes-Flags. I Henle Ue striatella. : A. LowerWhitcliffe or | on { Zone of Rhynchonella Group. | 110 to 120 ahah clit. Ehynchonella-¥lags. | { B. Mocktree or Dayia- xq J Zone of Dayia navi- | 40 to 00. Oia I. AYMESTRY Shales, Group. A. Aymestry or Con- 0 {Zone of Conchidiuir Knightii. | re hom Or ig j Dd to 25 chidium-Limestones. : ——- _——————_—_—. 515 to 850 422 Geological Society :— A brief outline-description of the main subdivisions is first given, as they appear when followed from Ludlow southward to Overton, eastward to Caynham Camp, westward to Downton-on-the-Rock, and northward to Bromfield, and also near Onibury and Norton. The main tectonie features of the district appear to be due to the superposition of Armorican movements in rocks with a Caledonian trend, held by some rigid mass to the north, presumably the Longmynd massif. A detailed description is then given of the succession, as seen at the following localities :— River Teme, Wigmore Road, Deerhouse Bank, Caynham inlier, the ‘Teme and north-east of the Castle at Downton, Downton-Castle inlier, Mocktree, and near Onibury on the Craven-Arms Road, the Onibury-Norton Lane, and at Norton. ‘The paper closes with a detailed list of fossils obtained by the authoresses, supplemented by the collection in the Ludlow Museum. 2. ‘The Carboniferous Rocks at Rush (County Dublin).’ By Charles Alfred Matley, D.Sc., F.G.5. With an Account of the Faunal Succession and Correlation. By Arthur Vaughan, B.A., D.Se., F.G.S. Rocks of the Carboniferous Limestone Series are exposed along 5 miles of coast near Rush, Loughshinny, and Skerries, in County Dublin. The present paper deals only with the beds near Rush, in the southern portion of this tract, where about 2500 teet of the series are exposed, without allowing for gaps in the succession. The upward sequence is (on the whole) from south to north, and the range is from the Upper Zaphrentis- to the Upper Dibunophyllum- Zone. The Rush Slates are the lowest beds, 1380 feet thick, but their base is not visible. They consist.of black and dark-grey, well- cleaved argillaceous, and less perfectly-cleaved calcareous, slates ; and they contain bands and nodules of limestone. The peculiar outcrop of some of the limestone-bands is described, and instances of cataclastic structure are noticed. The characteristic fossil is Zaphrentis aff. Phillipsie. The Rush Conglomerate-Group succeeds the Rush Slates, after a short interval of passage-beds. It is 500 feet thick, and consists of well-bedded alternations of conglomeratic, pebbly, and sandy limestones, with shales and calcareous flaggy beds. Ordo- vician and Silurian rock-fragments abound in them, together with many inclusions of Carboniferous Limestone. The group is shown to be of the same age as the Pendine Syringothyris-conglomerate and the volcanic rocks of Weston-super-Mare, and its existence indicates that the movement and disturbance in Mid-Avonian times extended over a considerable area. The beds above the conglomerates are mainly limestones and calcareous shales. They are thrown into numerous sharp folds, The Carboniferous Rocks at Rush. A423 and are occasionally inverted. The highest beds seen (Oyathawonia- Beds) are correlated with the Eastern Gower or Oystermouth Lime- stone of the South-Western Province; but the fauna agrees still more elosely, and is identical, with that of the highest Avonian beds of the Midlands of England, at Parkhill, Wetton, Thorpe Cloud, etc. The disappearance by solution of a considerable thickness of hmestone is described. A list is given of the fossils from a large number of horizons in the Rush Series (which is divided into the Zaphrentis-, Megastoma-, and Cyathaxonia-Beds), as well as of the fauna of the Curkeen-Hill Limestone, near Loughshinny, the horizon of which is assigned to the Upper Dibunophyllum-Zone, probably below the Cyathaxonia- Beds. The paleontological section deals only with brachiopods and corals. In that part which deals with the brachiopods the inter- relationship of the various members of the more important gentes is discussed in considerable detail. In the part which is devoted to the corals a new subgenus is suggested, and four new species are described. January 10th, 1906.—J. E. Marr, Sc.D., F.R.S., President, : in the Chair. The following communications were read :— 1. ‘The Clay-with-Flints: its Origin and Distribution.’ By Alfred John Jukes-Browne, B.A., F.G.S. Until recently the Clay-with-Flints has been regarded as being, in the main, a residue from the slow solution of the Chalk. This was the explanation proposed by Mr. W. Whitaker in 1864, although he admitted that the deposit included some material derived from the FKocene. Writing in 1865, Mr. T. Codrington thought that an over- lying stratum of clay or loam was essential to the formation of Clay- with-Flints. Lastly, Charles Darwin in 1881 seems to have taken it for granted that it was solely a residue from the Chalk. Of late years, the opinion has been growing that it consists very largely of material derived from the Hocene. The present paper is devoted to an examination of the facts, with the view of ascertaining whether the Clay-with-Flints could possibly be derived from the Chalk, or whether the theory of its derivation from the Kocene is confirmed by more detailed enquiry. The author first describes its composition, noting that unbroken flints are not everywhere abundant, that broken angular flints are common, and green-coated flints are not rare; finally, that if the clay is washed it always yields a residue of sand, composed chiefly of rounded quartz-grains with some of iron-oxide, and both apparently derived from the Eocene sands. The thickness of the accumulation is next discussed, especially 424 Geological Society. with reference to sheets of it that lie on fairly-even floors. In such positions it varies from 2 to 12 feet in depth, and large areas occur where it must have an average depth of 3 or 4 feet. The products resulting from artificial solution of chalk are then considered, and a series of analyses is given, from which the average amount of insoluble residue existing in the four lower zones of the Upper Chalk is deduced. Experiments have been made by Mr. William Hill to determine the relative weights of a cubic foot of Upper Jhalk and a cubie foot of Clay-with-Flints, in order that allowance might be made for the difference in calculating the quantity of clay which would be left by the solution of a given quantity of chalk. The result shows that 100 cubic feet of the Micraster-coranguinum- Chalk will produce only 1:2 cubic feet of clay, and the solution of the Marsupites- and Micraster-coranguinum-Zones to the extent of 200 feet over any part of the area would only yield clay enough to make a layer 2 feet deep. Lastly, it is shown that the quantity of flints in the Upper Chalk is so much greater than the quantity of clay, that the natural residue could not form a clay-with-flints. Thus, solution of 100 feet of JMeraster-cor- anguinum-Chalk would yield a bed of flints about 7 feet thick, and only enough clay to fill up the interstices between the nodules. The next section is devoted to the distribution of the Clay-with- Flints, and its stratigraphical relations to the Chalk on the one hand, and to the Eocene on the other. In dealing with this part of the subject, details are restricted to the areas lying west and north-west of the London Basin and to the wide area between the London and Hampshire Basins. From these several lines of investigation the author concludes :— (1) That the Clay-with-Flints cannot have been formed from mere solution of the Upper Chalk. (2) That all its components, except the unbroken and angular flints, could have been furnished by the Reading Beds. (3) That the positions occupied by it are such that no great thickness of Chalk can have been destroyed to form it, the tracts being seldom more than 80 or 40 feet below the local plane of the Eocene base, or the presumed level of that plane. Finally, an attempt is made to explain the manner in which the Clay-with-Flints was formed ; and the theory adopted is that the outlying Eocene tracts, which were in existence during late Pliocene time, were broken up and spread out by the severe climatic conditions of the Glacial Period. In post-Glacial time little has been added, but much removed by erosion. 2. On Footprints from the Permian of Mansfield (Nottingham- shire).’ By George Hickling, B.Sc. +o ' Phil. Mag. Ser. 6, Vol. 11, PL. VIL. Phil, Mag, Ser. 6, Vol, 11, Pl, VII, in Tons. Load Extensometer readings in saeco inches Tie. 1. Ma. 2. Fra. 3. Fra. 4. ene, rt SE HHS EEEEEEEEEEEEEE EEE aie at F aif ce rH H AUUuSnuRaERGEEEEE euaaa a Hee = f a ae H 7 } H a mam a a Cr Ect Pee perce 4 : L Eee saan aa rye-tpR ate i ae t fe it Hen H i H 8] Ha : t oH cH aague Pos HEE SEH an H EERE Sani Hl tHe it rH if 4 | a Eee tI Cy ite +H sae : BEEEEEE EEE +H tH HH 4 HE aa Ht 4 Ht t a [seggu a a 4 H + t H| a Hen eee a i Geeta i i */ EE C He 7 rt ss HT 7 To : mal 7 aRnnauE He t f H A { . Ett : ae EEE HHH Hie aii rrccstiiit suuiitieacet HEH : EE : + to HH oH + : EHH © age Ha +t fe H 6 t PREE seey oe ct im : EEE sere se eiieoccesstit dure : : H HH oeroutcat aoanee i cre jagaal pestle testedts PEELE EEE +H Hi [SEER 1 H 4 7 EEE nite HH ‘ ¢ F Et S HH { HI acs H saa i EEE iH aa H Ht ciaeae EH i He aa rH ane HH EEE dost jeatesateanttendt See : or aSEECariaet if eH He HEE : HH ; Haeeeeatantraaciey Hero EEE ai : ia | tH fe BREESE HEH ect evans aus avaeal ist 4 ‘ H Peoueenaen noe Ere EH Hy FEY tet ag gaauae 4 oe ee Ee HE ° f tf } tH fee i aes) aa ae 10a i= 3 + Ba t a ey au aie | 20080000 inaBauBa 1 SEH EERE: ia ro i i 4 S A ( i i T tt S He (gr 4b z: & H see da: x cH H s CI Ett H H Ht i - : + 3 i f PEt f : i 3 FLEE it 4 ; ke] y H i age EH ie am t fae t iH H S| Et EEE EEEEEEEEE HTH § Prt Fa § ae iat aaa 6 rite EEE SEEEE PEPE ce 3 i 4 e Suna! +H 4 f “| + ae i aH at - i aa : t Ht = EH face 2 oe te inate Se ffs Seggeuazer! i E = EE ae al HEH [ = ieee aubscenea’ ates ‘i cee eeesee AH EE EEA EEE - flarsuaes/ege EEEEEEEELt PEELE EEE ane ae ue Abe isescesceer it & EEE HEH : aaa HH fH se H Bee H Het ] Bete sy easasuagae! ai esstenr Paettavattasttast HH (Gage dog! Bea EEE AEH FE t BEEEEEEELEEEH age aa f eet Ey BREE EEE EEE EE EEE EEEEEHIEEt HH M EEE EH H cae ace i # susueacautaiiactl Hey H gaa vaaeaaerae) Hee : Beeazaa za sean aEETETTSEE HSE PTT euen /oveuareed be BEJfuostatea nassasseastasteeaas SHSEHzon seas dssanseossseaes estseastecaisiesity 4 aren AX B, cy 2 3 Slee - Ses as explainedi EXTENSIONS - Ghimtiaishiad as @xgelince! EXTENSIONS- diminished as explained EXTENSIONS - ence as SEES Boereiens - Gietised as erence! = Tuni Toe inc Scale=lunit= teseinch) Scale - unit = too inch ¢@ __i iF Scale-lunit = eo inch? ! Scale -lunit = too inch 2 V Fie. 8. ae age i. cy me T Bi ae ma Fic. 9. Bie Hee maa ia] = See E aa HEHE HHH niees He : E 4 i Tia. 10. VIG. . Tie. 6. Fic. 7. a feu EEE EEE oud ae t Ht EEPEEEEEEEEEEEEEEEE EEE EEE aA # He LF He HH | = Ht E a i aaa z i Heit t H | H H Eee t H Bang ama " EEE HH th EeEEr 7 E BESEEctacee eee bet 4 He H H EH tt a Et H H q a Ae caec ee faced | BEER ae EEE | 43 ete EEEEEEEPEHTH Fea H EESEEE H HH pares eafetsencit PEPE EEE : EERE 2 BH EERE EEE eit a Peet SEEcees Se oe ee ee ee = é Ha en i cea ae ee] Baie a “HH Z OLE i ere 8 t 5 cI aune HES Toh t ‘y EH 8 si = 8 Bees 5 A 3 EAE 4 He i He gcse EEE Ht EEE 8 ona 7 3 = " : HH] HH f HH 5 EEEH ALEEEE Beavan i 4 u iia ne oa Fee i E i | EB E H ] 50 100 TER) Ee 750 30 Too a 200 50 2 oon, HH i dee z me A Time in Minutes Time in Minutes. rit q Beet H EXTENSIONS -diminished as CHEE Hl Scale. lunit=ressinch & i : A 3 D : Ht BVTENSIONGS = diminished as explained aaa Scale. lunit = isco inch @ SEES EPEH EEEEEEH| ° ' n Extension Scale llunit=ioco a iy i Phil. Mag. Ser. 6, Vol. 11, Pl, VIII. Se eater es acti lbsnsssisasci sr secascieasialetnsasomiamentoni i sores ~ oe ' . f. oF n i : } , pe = ' —— ‘ INDE 4] aa LONDON, EDINBURGH, axp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [SIXTH SERIES.] AE Rb Wooe. XXXVI. On the Properties of Electrically Prepared Col- loidal Solutions. By HK. ¥. Burton, B.A., 1851 Exhibition Scholar of the University of Toronto, Research Hahibitioner of Emmanuel College, Cambridge*. TL. Introduction. Ae a result of experiments by Professor McLennan + and the writer, it was found that when a cylinder of any metal is enclosed within a second one of the same material, insulated from it, and surrounded by air or other gases, it gradually acquires a negative charge, and after a short time reaches a state of equilibrium at a definite potential below that of the enclosing cylinder. Several different metals were tried and each was found to attain a definite charge. These results led to the conclusion ‘that a process is going on at the surface of the metal, whereby an excess of positively charged particles is being continually emitted,” thus leaving the metal itself with a negative charge. Some time ago Bredig t found that by means of electrical pulverization of metals it is possible to produce so-called colloidal solutions of metals in very pure water. HExperi- ments on these solutions have hitherto pointed to the con- clusion that they consist merely of suspensions of very finely divided metallic particles. The fact that these particles * Communicated by Prof. J. J. Thomson. + Phil. Mag. vol. vi. (Sept. 1908) p. 348. $ Anorganische Fermente, Leipzig (1901). Phil. Mag. 8. 6. Vol. 11. No. 64. April 1906. 2¥F 426 Mr. E. F. Burton on the Properties of were in every case found to be negatively charged, suggested that they become so electrified by the emission of an excess of positively charged particles, as in the case of metals referred to above. The experiments detailed in the present paper were carried out in order to give some indication as to how the particles in such solutions come to be charged. To this end colloidal solutions, or sols, of many different metals were formed in water and other liquids, and attempts made to determine the charge on each particle from the velocity with which they move in a known electric field and the size of the particles. The results of these measurements seem to preclude the idea that the charges arise from merely an emission of charged ions from the particles. A co-ordination of the results ob- tained with different liquid media indicates that the formation of colloidal solutions is due to a chemical reaction between the metal and the solvent. Il. Preparation of Solutions in Water. The method of preparing the solutions was similar to that described by Bredig in the paper referred to above. The terminals (B, fig. 1) of a storage-battery capable of pro- viding any required voltage up to 110 volts, were connected Fig. 1. 3 through a variable liquid resistance (R) and ammeter (A) to two electrodes (Hj, E,) of the metal of which a sol was required. The voltage and current used depended on the metal of which the electrodes consisted ; such details will be found in the tables given. The electrodes were held with their free ends beneath the surface of pure water contained in a clean porcelain evaporating-dish (D) of about 100 c.cs. capacity, and the current was allowed to spark between them. Electrically Prepared Colloidal Soiutions. 497 Clouds of finely divided metal scatter from the cathode during the sparking and remain suspended in the water for a time depending on the nature of the metal. The dish (D) was surrounded by running tap-water in order to counteract the heating effect of the arc. The sparking was continued until the water became so clouded as to he quite opaque. The solutions, which usually contained a little sediment from the pulverization, were then carefully filtered. Using gold, silver, and platinum, the resulting filtrates retained nearly the whole of the metal sputtered from the electrodes and remained con- stant for months. When bismuth, lead, and iron were used, the filtrate still retained a large proportion of the metal, but these solutions were by no means as stable as the preceding ones. After sparking with electrodes of zinc and tin, the clouded solution began at once to clear, and the filtrate failed to retain any of the metal. The water used in the experiments was first distilled through the large laboratory still, a trace of acid potassium sulphate added, and then redistilled through a silver spiral tube ; the specific conductivity of this water was abont act) *. Ill. Properties of these Colloidal Solutions. The properties of such solutions are quite analogous to those of the so-called colloidal solutions of arsenic sulphide, gold, silver, ferric hydroxide, and many organic substances, which have been prepared chemically and carefully in- vestigated by Carey Lea*, Linder and Pictont, Barus and Schneider{, Zsigmondy§, Hardy|| and others. They diffuse in pure water very slowly, and may be separated by dialysis from impurities of various salts. They may be readily filtered through paper filters. When viewed with a microscope of the highest powers, no particles can be detected in the solution ; yet when a beam of lght is passed through a tube containing some of the solution, it is diffused and polarized. Bredig{] points out that these two latter properties fix the upper and lower limits to the size of par- ticles which must be in the solution. The microscope can detect directly a particle of diameter as small as 14 x 10-° ems.; while the fact that the particles diffuse light shows that their diameter is, at least, quite comparable with the wave-length * Amer. Jour. of Science, xxxvii. p. 476 (1889). + Jour. of Chem. Soc. vol. Lxi. p- lis, vol. lxyii. p. 63, vol. Ixxi. p. 568. t Zeits. f. Phys. Chem. vol. viii. p. 278. § Liebig’s Ann. ceci. p. 29 (1898). || Proc. “B oy. Soc. vol. Ixvi. p. 110. q aaa ct. and Drude’s Ann. xi. p. 218 (1903). So HF ¢ bo} 428 Mr. E. F. Burton on the Properties of of light, ¢.e. that the lower limit to the size is 10~° ems. Such particles were first rendered visible by means of a special apparatus described by Zsigmondy and Siedentopf*, referred to later, and were then found to possess the Brownian movement common to all ordinary suspensions of fine par- ticles in water. Again, in perfect analogy with the cases of ordinary suspensions, e.g. soap solutions, the metallic par- ticles are completely precipitated by the addition of small quantities of any aqueous electrolytic solution. Of great interest, from chemical and physiological viewpoint, is the very strong catalytic action the platinum solution shows in bringing about the decomposition of hydrogen peroxide. Probably the most interesting of the properties of these solutions is the movement of the particles under the influence of an electric field; in all the solutions which he prepared Bredig found that if two electrodes were introduced into a tube containing the solution, the particles would move towards the positive electrode, showing that they possessed a negative charge. IV. Determination of the Size of the Particles. The first method devised for rendering such ultra-micro- scopic particles visible is due to Zsigmondy and Siedentopf f. An intense, thin beam of light is focussed in the solution and viewed at right angles to its direction by a high-power micro- scope. The particles in the solution appear as bright points due to the light scattered by them into the microscope. This phenomenon is quite analogous to the very common means by which particles of dust doating in the atmosphere of a darkened room may be made visible by casting a bright beam of light into the room; viewed at right angles to the direction of the beam, the particles of dust appear as bright moving specks. A rather simpler application of this prin- ciple, proposed by Mouton and Cotton {, was used in the present experiment. The apparatus is shown diagram- matically in fig. 2, which somewhat exaggerates the relative size of smaller parts. A drop of the solution to be examined is enclosed beneath a thin cover-glass (C) on a microscopic slide (8S). The plate 8 is placed on a special block of glass A, good optical contact being made by an intervening thin layer of liquid whose refractive index does not differ much from that of the glass. ‘The block A (for which a Fresnel rhomb serves very well) allows the direction of a beam of light to be easily adjusted so that, after being internally reflected at the lower surface of A, the succeeding internal reflexion at the upper surface may be made to take place at * Drude’s Ann. x. p. 1 (1903). + Loc. cit. + Revue Générale des Sciences, xiv. 25, p. 1184 (1903). Electrically Prepared Colloidal Solutions. 429 the critical angle. The proper adjustment of the lens L and block A allows the beam to come to a focus at C just at the Biee 2, [. oe drop of liquid. As the particles in the solution come into the path of the beam, the light striking them is now no longer totally reflected, but is scattered into the microscope M. “As the field of view is otherwise dim, the appearance is that of a sky filled with moving siars—the Brownian movement of the particles being at once recognized. No means is afforded of directly comparing the size or shape of the particles as, im general, the better they are in focus the smaller they appear. An adaptation of the above apparatus was used to count the number of particles in a given volume of a colloidal solution. The difficulty of ¢ determining the volume of liquid Fig. 3. po 0 feet a] ae Ta aoe i Att Bi tsa) : ee mea viewed was overcome by the use of the special Zeiss slide used in counting the number of blood corpuscles ina unit volume of diluted blood. Fig. 3 shows the con- 430 Mr. E. F. Burton on the Properties of struction of the slide. At the centre of a circular piece of glass A an area of 1 sq. mm. is divided into small squares of ;!, mm. side by means of fine lines ruled with a diamond point. The plate B surrounds A so as to leave an annular trough about the central disk. The upper surface of B is exactly ‘1 mm. above that of A, so that when the cover-glass C is placed on B, a layer +!) mm. thick exists between A and C. The surfaces of A, B, and C are of course ground per- fectly plane. When a drop of a sol is placed on A and covered with C, a volume of zj55 cu. mm. can be discerned through the microscope. By raising and lowering the objective very slightly, it is possible to bring all the particles in a layer ;!p mm. thick into view, and so, for very dilute solutions, the number of particles per cu. mm. can be very approximately determined. A microscope which magnified about 350 times was used, and the slide was moved slightly so that the par- ticles corresponding to 400 of the unit volumes (each 4,55 cu. mm.) were counted. The Brownian movement, at any rate in such a thin layer of liquid, did not show any constant dritt of the particles, and was not sufficient to sensibly alter the disposition of the particles during the time (about one hour) taken to count the number in the volume (;/) cu. mm.). If the amount of metalin 1 c.c. of a given colloidal solution can be ascertained, then, assuming that the specific gravity of the metal in this state of fine subdivision retains its ordinary value, an idea of the size of each particle can be obtained from knowing the number of particles in unit volume. Such determinations have been made for the colloidal solutions of platinum, gold, and silver. The weight of metal in a given volume cf the solution was obtained by evaporating the liquid in a previously weighed porcelain crucible, and finding the weight of the residue. A reference to the specific conduc- tivities of the various solutions (Table II.) will show that the weight of dissolved impurity remaining after evaporation would be practically infinitesimal. ‘The following is a sample of such determination, typical as regards method and the magnitude of the quantities involved :-— A silver solution containing 6°8 milligrams of metal per 100 c.cs. was diluted with distilled water to one hundred times its original volume. = aa aK 4 ° . ° . > (3) where K=s.i.c. of the medium between the layers. If V indicates the contact difference of potential between the solid and the liquid, we have =v ko... . substituting this value of e in equation (2) and transposing we get 4a ag V.(=x a all electrical measurements a. made in electrostatic units. This equation, which is similar to one given by Perrin”, * Jour. de Chim. Phys. t. xi. no. 10, p. 607 (1904). Electrically Prepared Colloidal Solutions. A35 will enable us to find values of (v ‘) for any solid and liquid if for known values of X and pw we can observe the corre- sponding values of v. The experiments described in the present paper will supply the corresponding values of v, X, w for a number of cases. VI. Velocities of the Particles of Metal Solutions. The first systematic investigation of the velocities of these particles in an electric field is that afforded by the inter esting experiments recently published by Whitney and Blake* The colloidal solution was contained in tubes such as shown in fig. 4; they were 30-50 ems. long and 2°46-2-75 cms. diameter. The ends were closed with goldbeaters’ skin and platinum elec- trodes placed in water-cells just outside these ends. When A was connected to the negative electrode and B to the positive electrode of a set of storage- cells, a migration of the particles set in down the tube. A reversal of the current in the tube caused the particles to rise again. In this way the authors have deduced the velocities of particles in solution of platinum and gold to be respectively 34 x 107° and A} x 105°em. per see. per volt per em. Various circumstances, unavoidable in the use of a tube of this construction, render the determination of the ab- + solute values of the velocities of the particles under unit electric force somewhat unsatisfactory. The rate with which the surtace of the particles in the solution moves down or up the tube varies in a non-uniform manner with the time. As the writers found, the specific resistance of the clear liquid above the surface otf colloidal particles may be continually changing ; this would naturally affect the potential gradient along the tube. Even when this is corrected for, as Whitney and Blake took pre- cautions to do, still the specific resistance of the upper clear layer of liquid remains always different from that of the solution ; a fact which must tend to affect the movement of the particles at the surface of separation, on account of the Fig. 4. > | * Jour. Amer. Chem. Soe. vol. xxvi. no. 10, p. 1339 (1904). 436 Mr. E. IF’. Burton on the Properties of jump in the value of the electric force, just at the surface. . In addition to this the method consists essentially in a com- pression of the colloid which may change the absolute velocity of the particles. Again, as the authors do not give the temperatures corre- sponding to these velocities of the gold and platinum particles, it is impossible to apply the formula (5), which in- volves the coefficient of viscosity of the liquid. These difficulties are obviated if one uses a velocity tube (fig. 5) similar to that used by Hardy* in his work with colloidal solutions. That used in the present experiment consisted of a U-tube each limb of which was about 12 cms. long and about 1°5 ems. in diameter; the limbs were graduated in mms. throughout their length. Into the bottom of the U-tube is sealed a fine delivery-tube provided with a tap (1') and funnel (fF); this tube is bent around so as to run up behind the limbs and to bring the funnel to the same height as the top of the U-tube. The colloidal solution to be tried was poured into the funnel so as to fill the small tube and funnel around to the tap which was closed; water having a specific conductivity equal to that of the colloid was then poured into the U-tube so as to fill it to a height of about 3 cms. The whole tube was then placed ina large glass water- bath so as to be almost submerged ; this water was kept at a constant temperature during the course of any experiment. At the end of a few minutes the tap (T) was very slightly Fie. F. R - \ J } ' on V/7¢ yO 3 &. 4 6 7 ts) 9. o> aa ZF (| opened, and the colloidal solution allowed to gently force the water up the limbs of the tube to any required height. If care-. fully manipulated, the surface of separation between the clear water and the solution was very distinct, and would remain so for hours. Two electrodes of coiied platinized platinum foil * Journ. of Physiology, vol. xxix. p. 26 (1903). Electrically Prepared Colloidal Solutions. 437 -were supported at a convenient level in the two limbs of the tube and the clear water allowed to rise well above them. The elec- trodes were attached to the terminals of a set of storage-cells of constant voltage, and when the circuit was completed, the surface of separation in one limb would at once begin to rise gradually, while that in the other sank. In practice the connexions were made through a reversing key, and the voltage, usually fixed at about 110 volts, was left on one way for ten minutes and then reversed for twenty minutes. The velocity was reckoned trom the displacement of the surfaces during this final twenty minutes; one half the sum of the displacements in the two tubes was taken as the distance travelled by a particle in the given time. A typical set of observations is given in Table I. (ABE, be. Height of Colloidal | te ha | | | eee Temp. | purlece | Observed | Time. es ie arecccan same | Velocity | | bert | Right. | Im ¢€in./Sec. 37.0} «4-118 «=| 11°C. | 54mm.! 55 mm. Meg ees 6 s 41.50 | Current off | | | | 11-48 | = 18 © yee ©? eu 50 " 11°58 aS 5D 56 96x107° 12-08 —1ig | 11°C. | 5 aa nael aoe | Electrodes at 15 mms. in each limb. It will be seen from the table that there has been an apparent settling of the colloid in the tube while the current was running. ‘This was quite usual, but, as the reckoning was made, it could not affect the rate, since this slight lowering of the surface was uniform in both limbs, so that, while it is added to the velocity in one limb, it is subtracted from the velocity in the other. In order to find the value of the electric force in the tube, it is of course necessary to know the effective distance between the electrodes A and B. In order to do this, the tube was filled with a ‘O01 normal KCl solution, placed in the water- bath, and the resistances taken with the electrodes placed at the successive centimetre marks down the tube. In this way it was found that the resistance of the curved part of the 438 Mr. K. F. Burton on the Properties of tube from 90 in L around to 90 in R was 8°8 times the re- sistance of each cm. length of the single limbs. So that when, as in case cited in Table I., the electrodes were placed at 15 in each tube, the effective distance between the elec- trodes was 23°$ cms., and therefore the strength of the 118 23°8 value of the velocity of the silver particles in water at a temperature of 11° C. would be 19°6x10—° cms. per see. per volt per cm. Such measurements required that the specific resistance of all the solutions should be carefully obtained. The resistance- cell used is shown in fig. 6. Two thick platinum disks (2°5 ems. in diameter) were fused by means of welded platinum wires into Fig, 6. two fine glass tubes which were rigidly fastened into the ebonite lid (L) fitting into the glass vessel G. The disks were thus about ‘75 em. apart. A thermo- meter, T, was supported by the lid so that its bulb reached close to the upper disk. The constant of the vessel was , taken by means of a ‘01 normal KCl solution at suitable intervals during the course of the work. The resist- ances were determined by the ordinary Wheatstone’s bridge method, the effects of polarization being annulled by means of a double commutator as used by Whetham*. Solutions of the metals platinum, gold, silver, bismuth, iron, and lead were formed, and the values of the velocities of the particles under unit electric force determined as given in Table II. As has been found by all experimenters, the particles of the platinum, gold, and silver solutions move toward the positive electrodes, showing that the particles themselves bear a negative charge. On the other hand, the particles of the other solutions named move in the opposite direction, corresponding to a positive charge on the particles, The velocities given have all been determined for a tempe- rature of 18° C. electric field was =4°'9 volts percm. Thus the absolute * Phil. Trans. vol. exciv. A, p. 321 (1900). Electrically Prepared Colloidal Solutions. 439 PARI lal, Metal Pe Specific | ee | Velocity in in Conductivity) ~ 9° | ems. per sec. Sol. | ae ae a of Sol. Partelos weet volt per cm. | Voltage. | Current. Platinum .... 40v. | 7°5 ae DISC Ome’ |} = | 20°3 3% 1072 | Golde 2... PaO Pa, I 10Sx10-8 | = 21:6x 10-5 Silver....-4.. GO Tor oy ol LOS AOS 6 aii tn OSG ali? | Bismuth....... 30v. |65 ,, |~70x10-6 | - + Haale iphtee ells 2. 307. 165 ,, | 150x10-6| + | 1290x1075 ie | 50v. |65 ,, | 94x10-§ | 4 | 19:0x 10-5 | As has been mentioned above, the first three solutions of Table II. are extremely stable, the metals remaining appa- rently uniformly in solution for months, while the solutions of bismuth, lead, and iron would be precipitated in the course of a week or so. The bismuth solution is dark brown in colour, not unlike the silver solution in appearance. The lead solution. is initially dark brown as well, but if left in contact with the air the particles rapidly turn white, doubt- less on account of the formation of a carbonate; but whether in the brown or white state, the particles move to the negative electrode in an electric field. The iron solution always possesses a reddish-brown colour, which points to formation of a hydroxide; this quite agrees with the fact given by Linder and Picton that in chemically prepared colloidal solutions of ferric hydrate the particles move towards the negative electrode. If there are particles of varying sizes present in any one solution, no indication of any difference in velocity of the various particles was evident ; however, this does not justify the assumption that the par ticles are all of the same size, because, according to the theory given by Lamb, the velocityof similar ly constituted particles is independent of the size and sh rape. If particles of different sizes do exist in these electrically prepared solutions the size would probably depend on the violence of the sparking during the preparation of the solution. Three silver solutions were prepared, using varying currents and voltages for producing the spark, all other conditions being the same except the time of sparking. As shown in Table III., the differences in the velocities, which were all determined at 11° C., are all within the limits of error in the experime «t. 440 Mr. H. F. Burton on the Properties of TABLE IITI.—NSilver Solutions. | | No | Voltage. | Current. Tune, of | Velocity im emi/ene, | | | Sparking. per volt per em. ———— | [es ss ee i | es 2 80 volts | 85 amperes. | 10 minutes. 19°75l0se | | | ie | eee) ON ema 207), 19°6 x 10~° : Beall RAO) he un ana 500 0s 19-3 >cl Ome | pt el mee a Since there is no a prior? reason for assuming that all the particles are of a uniform size, these results would confirm Lamb’s theory. We are here dealing with the motion of small charged particles through a liquid, so that, other things being equal, the velocities of those particles shouid depend upon the viscosity of the liquid, and therefore to a large extent upon the temperature of the liquid. A neglect of this influence soon leads to bewildering results. That the dependence on the temperature is quite direct is shown by placing side by side the results given in Table IJ., and the velocity found for the same solution at a different temperature (Table LV.).. Tape Ne Coefficient of : Metal. Temp. Viscosity of Water. , eet ty. op X 10°. ee | (H) vi ee f° Dm CRG: -012822 | 196x107 ‘251 Silver...... | | || eerete! ‘009922 | 25:2510-° -250 VII. Remarks on Velocities in Table I. It will be noticed that while the velocities recorded above are distinctly lower than those given by Whitney and Blake, they are in close agreement with those found by Hardy * for solutions of a similar nature. Although they are of the same order as the velocity of the metallic ions, still the slowest moving ion travels more quickly than the fastest colloidal particle. In considering the results given in Table II., one is struck with the fact that the particles of the more electro-positive, oxidizable metals are all positively charged, while the more * Journ. of Physiol. vol. xxxiil. (Dec. 1905) p. 291. Electrically Prepared Colloidal Solutions. 44] electro-negative, non-oxidizable metals give negatively charged particles. When we recall that the iron in such solution appears to form the hydrate, and that they bear a charge of the same sign as the particles in chemically prepared colloidal solution of ferric hydrate, one is justified in sus- pecting that in the cases of iron, bismuth, and lead there is the formation of the hydrates, in greater or less degree, in the preparation of these electrically prepared solutions. Such an hypothesis at once suggests an analogous action on the part of gold, silver, and platinum, VIZ., an interaction between the metal and hydrogen—a view to which the already known existence of a hydride of platinum would lend some colour. VIII. Colloidal Solutions in other Liquids. The suggestions given by the results for the hydrosols are strengthened by the observations on colloidal solutions in the alcohols. Pure methyl alcohol and pure ethyl alcohol were used in the preparation instead of water. Although repeated trials were made with the metals gold, silver, and platinum, the writer has never succeeded in getting them to remain suspended in either of these alcohols. On the other hand, the metals lead, tin, and zine form solutions in both of the alcohols, while with methyl alcohol solutions were also obtained with bismuth, iron, and copper. In all these solutions the particles moved to the negative electrode in an electric field, z.¢., they are positively charged. The numbers are given in Tables V. and VI. Taste V.—Methyl Alcohol (free from acetone). | Used in Preparation. : mi itv i | Metal. Conductivity Char oa on “per ae a art | Voltage. | Current. | of Solution. Wacken + ge em. Road «....- 30 volts. | 65 amp. | 100x10-§ | = -+ | 2210-5 | Bismuth 30h eae. |) og PAB L078 + | 1021075 | Tron ...... AN i NOS SalOmOliy eee |) Copper'..../: 40 ;, y 6Sx10-6 | + | anes | F | |} very 7 « | D5 —60 ‘ Din ae SU oe. | fs bax 10 + | | slight Hine joss: ah We SOR tOr he | ~ Phil. Mag. Vol. 11. No. 64. April 1906. 2G 442 Mr. E. F. Burton on the Properties of TasLe VI.—Ethyl Alcohol. } ee - x , ic : : | T . . Used in Preparation Sion of +| Velocity in Specific ie Metal, |_——______~_—___-___| Conduchayity | Charge‘on | 3 at nae ‘ of Solution. Particles. | P®™ YO Per Voltage. Current. em. ead | £11! 30 volts. ° G5amp. | 2:3x10-° | =F | 45x 107° MEY : ? Ss” + 36x 107° Zine”... i : ieixaOn® + 28x 107? Viewing these results in the light of the chemical nature of the alcohols, the former suggestion as to the interaction between the liquid medium and the metals is strengthened. Although these alcohols have a neutral reaction, they act like weak bases in combining with acids to form salts, or, in other words, they have an easily replaceable OH- group. Those easily oxidizable metals would thus be able to form at least a surface coat of hydrate, while the metals gold, platinum, silver, whose existence in a colloidal state we have been led to suspect to depend on a replaceable hydtaee in the liquid, cannot form in the alcohols. A still further test of this hypothesis is afforded when one uses as the liquid medium a substance which has a replaceable Hand not anOH. Anhydrous acids might be used, but there is great difficulty in keeping them free from water; and, as is well known, electrolytes containing acids have extremely strong power of coagulating solutions. Kthyl malonate is a liquid which fulfils the condition of having a replaceable H ; the samples used in the present experiment were pure from Kahlbaum. When platinum, gold, and silver were sparked Taste VIT.—Ethyl! Malonate. | Used in Preparation. | Specific | Sign of _ Velocity in Metal. |j—————___ "Conductivity | Charge on ae a Bi of Solution: | Particles, | P°™ Y° ‘o- | Voltage. | Current. em. 0 i Ge aes a — ee Platinum .) 40 volts. | 75amp.| -lx10-§ | — | 23x1075 | | | | : Silmeras..400- ,, eee Ore — * | Ge Golde..| 00 | eaaeelblOe? | | STR Electrically Prepared Colloidal Solutions. A43, underneath this liquid, very stable colloidal solutions were obtained ; those of the first two metals named are apparently as stable as the corresponding hydrosols, while the gold solution coagulates at the end of a month or so. From the velocities which are given in Table VII., it will be seen that these particles all bear a negative charge, similar to those of platinum, silver, and gold in hy drosols. When the other metals, bismuth, lead, zinc, and iron were used, a colloidal BAietion could not be aneteen IX. Theoretical Considerations. There is practical unanimity in the opinion that these particles in colloidal solutions are enclosed by a double electric layer, the electricity of one sign on the surface of the particle being in equilibrium with an equal amount of electricity in the layer of liquid immediately surrounding the particle. It is a matter of doubt as to the means by which this double layer is formed. Linder and Picton first suggested some interaction between the liquid and the particle :—‘ Experiment seems to show that if the solution is basic or tends to break up so as to leave a free base active, the motion is to the negative pole. If the solution is acidic (or tends to break up so as to leave a free ‘H’ active) motion is to the positive pole.” This statement is remarkably confirmed by the deter- minations cited in the present paper for solutions in water, the alcohols, and ethyl malonate. Following the conclusion given by Quincke regarding suspensions “of microscopic particles in liquids, many writers have been contented to view the phenomenon as an effect expressed by the term “ contact electrification ”; the particles become charged by the rubbing of the moving particles of the liquid itself against the suspended particles. The recent work of Perrin * has produced results which throw considerable light on the phenomena of electrification by contact between liquids and solids. By measurements of the electric osmose of liquids through diaphragms of various materials, he is led to announce these two laws :— 1. Electric osmose is only appreciable with ionizing liquids, or, in other words, ionizing liquids are the only ones which give strong electrification by contact. 2. In the absence of polyvalent radicals, all non-metallic substances become positive in liquids which are acidic, and negative in basic liquids. * Loe, ct. A444 Mr. E. F. Burton on the Properties of In explaining these results he suggests the hypothesis that a positive electrification of a wall bathed by an acidie liquid is formed by H* ions situated in the stationary liquid layer immediately contiguous to the wall. Opposed ‘to it at a small distance there will be a corresponding excess of negative ions forming another layer. If the wall assumes a negative charge it is on acconnt of similar action of the OH’ ions. It is found that H and OH ions move much more quickly than other ions; if, then, we explain this high velocity by assuming that they are smaller than other ions, we should expect them to penetrate nearer to the boundary of the liquid and so muster at the limiting layer of-a liquid an excess of electric charges of one sign. Although the analogies between this phenomenon of electric osmose and that of the coagulation of colloidal solutions undoubtedly help in explaining ane latter, the formation of these solutions can hardly be credited to merely physical diffusion of the H™ and OH™ ions. As we have seen from the sign of charges borne by particles in solution, it is those which appear to depend on a replaceable H which are negative while those depending on a replaceable OH are positive. The matter is summed up quite clearly in a recent state- ment of Noyes * :— “In regard to the cause and character of the electrification two assumptions deserve consideration : one, that it is simply an example of contact electricity, the colloid particle assuming a charge of one sign and the surrounding water one of the other. This correlates the phenomena of migration with that of electric endosmose. It does not, however, give an obvious explanation of the facts that the basic colloidal particles become positively charged and the acidic and neutral ones negatively charged. The other assumption accounts for these facts. According to it the phenomenon is simply one of ionization. Thus each ageregate of ferric hydroxide molecules may dissociate into one or more ordinary hydroxyl ions and a residual positively-charged colloidal particle, and each aggregate of silicic or stannic acid molecules into one or more hydrogen ions and a residual negatively-charged colloidal particle. To explain the behaviour of neutral substances like gold and quartz by this hypothesis, it is neces- sary to supplement it by the assumption tbat in these cass it is the water or other electrolyte combined with or adsorbed by the colloidal particles which undergoes ionization. It seems not improbable that there may ‘be truth in each of * Journ. Amer. Chem. Soc. vol. xxvii. No. 2, p. 85. Electrically Prepared Colloidal Solutions. 445 these hypotheses, contact electrification occurring in the case of the coarser suspensions and ionization in the case of those which approximate more nearly to colloidal solutions.”’ Comparing the results given for the sign of the charges borne by the particles in different solutions, we have the following :— 1. Water (H*.OH7) can form two classes of colloids, whose particles are respectively positively and nega- tively charged. 2. Replacing the mobile H* by the groups C,H; and CH; so as to form the alcohols, seems to destroy the power ot forming solutions with negatively-charged particles; while 3. Ethyl malonate, CH,(COOC,H;). which has the mobile H readily forms those solutions containing the nega- tively-char ged particles, and those only. It is thus evident that the formation of the solution depends on the chemical nature of the solvent. This leads to the following theory of the constitution of the solution :— 1. In the case of gold, silver, and platinum in water and ethyl malonate, we have an incomplete chemical com- bination with the liquid: thus for platinum and water we have the equation :— ae, OT Pe) fe OME: We may look upon the platinum-hydrogen aggregate as dissociating slightly so as to form an atmosphere of positively -charg ged hydrogen ions about the negatively- charged colloidal par rticle. 2. With the other metals in water and the alcohols, we have a corresponding formation of the hydroxides, thus : = a+ as a — Oh aE OR = (Ph Onn. + EL: and by slight dissociation of the aggregate (PbrxOH), coke) we obtain a positively-charged colloidal particle, surrounded by a layer of OH” ions in the liquid. In accordance with Helmholtz’s explanation, we may look upon the motion in an electric field as primarily due i: electric endosmose. On this view, in formula (5) (p. 434 l will equal d and K will be the specific inductive i ae of the liquid medium. Values of V for different cases are 446 Properties of Electrically Prepared Colloidal Solutions. recorded in Table VIII. ‘The specific inductive capacity of ethyl malonate was found by Nernst’s** method for slightly conducting liquids. TABLE eee & V in volts. | In Water. [In Ethyl Malonate In Ethyl Alcohol. In Methyl Alcohol. Metal K-33. K=80. K=10:7 K=25 8. Platinum..| —-031 —-054 Gotd 2.0) 5 2503 —-033 Silver ...... er 6 — 040 Lead ...... pee! tte oc + -023 +044 Biaaatlsd |; Saas. wee iin RO 4-022 This table shows a surprisingly close agreement among the differences of potential between the particles and the liquids. Taking into account the wide differences between the specific inductive capacity, say for water and ethyl malonate, we can deduce that the charge of electricity on the particle of a given metal must be much greater in water than in ethyl malonate ; in other words, the interaction between the par- ticle and. the solvent seems to be dependent on what may be defined as the ionizing power of the liquid. It is further interesting to note that these values for the differences of potential between the particles and the liquids are of the same order as the value found by Perrin for the difference of potential between chromium-chloride diaphragm and slightly acidulated water (025 volt), and also agrees in the same way with Helmholtz’s values for the difference of potential between very dilute aqueous solutions and the walls of glass tubes in which they were contained, if corrections are made by introducing the value for the specific inductive capacity of water. X. Conclusion. Summarizing the results here recorded, we have the following :— 1. The size of the diameters of the particles of gold, silver, and platinum in electrically prepared colloidal suspensions has been found to lie between the limits (2—6) x 10-° ems. 2. The electro-negative, non-oxidizable metals, gold, silver, * Zeit. f. phys. Chemie, vol. xiv. p. 622 (1894). Decay of Torsional Stress in Solutions of Gelatine. 447 and platinum give solutions in water and ethyl malonate in which the particles are negatively charged. 3. The electro-positive, oxidizable metals give solutions in water, methylalcohoJ, and ethyl alcohol in which the particles are always positively charged. 4. The velocities of the particles under a known electric force have been determined and the potential differences between the liquid and the particle have been deduced by using the formula Ar pv Pankoxes My best thanks are due to Professor J. J. Thomson for his kindly interest and advice during the course of the experi- ment. I also wish to acknowledge heartily the many helpful suggestions which Mr. W. B. Hardy has kindly given me. Cavendish Laboratory, Sept. 1905. XXXIX. On the Decay of Torsional Stress in Solutions of Gelatine. By A. O. Rankine, B.Sc., Assistant in the Physics Department, University College, London *. Vv HE results of the experiments on the time rate of change of stress in lead wires under constant strain, published in the Phil. Mag. Oct. 1904, suggested an investigation of the laws governing this variation in passing from purely viscous to perfectly elastic bodies. uead exhibits both elastic and viscous properties to a marked extent, but does not obey the mathematically deduced laws of Maxwell for such bodies. The experimental curve of stress against, time when the siress remains constant is not of the form W = W,e-, but is represented fairly accurately by the equation W = W,—a log (pt+1). The question arises, “ Does a similar Jaw hold when the viscous and elastic properties are combined in proportions differing from those in lead ; and, if not, how does the law change in passing from the perfectly elastic to the purely ‘wiscous cases?” Jn order to find an answer experimentally, one must be provided with a series of substances of the same kind possessing elastic and viscous properties combined in different proportions and extending from the purely viscous on the one side to the perfectly elastic on the other. Now solutions of gelatine in water fulfil these conditions. Solu- tions of very low concentration possess no elastic properties, Communicated by Prof, F, T, Trouton, F.R.S 448 Mr. A. O. Rankine on the Decay of and at the same time it is possible with high concentrations to make specimens which are perfectly elastic for fairly large stresses. Intermediate concentrations give elastic and viscous properties in varied proportions. Gelatine was therefore chosen for the investigation of the question proposed above. The consistency of solutions of gelatine in water which have been allowed to congeal is very 1 varied in character. All of these, however, seem to possess, to a greater or less degree, elastic properties. It also appears that any particular spe- cimen has a definite elastic limit provided that none of the conditions which determine its consistency vary. It may be subjected to a stress of less than a certain limiting value, and the resulting strain will be constant with regard to time and it will recover on the removal of tbe stress to its original state. If, however, this limiting stress is exceeded, the strain is no longer constant but increases with time. The removal of the stress does not now produce complete recovery, although it should be noted that if the stress is only applied momen-. tarily the recovery is very nearly complete. Now suppose a specimen of jelly stressed beyond its elastic limit. There will result an immediate strain followed by a gradual increase with time. This increase, however, can be prevented by the gradual removal of the stress, and in order to keep the strain constant this removal must be continued until the remaining stress is equal to the elastic limit of stress for the particular specimen. It was to investigate this change in the special case of the rate of decrease of couple in solutions of gelatine twisted through a constant amount, that the following experiments were carried out. I. Method of Experiment. The method used has been to apply equal torsional stresses to gelatine solutions of different concentrations, to maintain the strain always equal to the initial immediate strain, and to record the rate of falling off of the stress. It was arranged that the removal of the stress should be effected automatically by a method very similar to that used by Professor Trouton and myself in our experiments on lead wires (Phil. Mag. October 1904). The interspace between two concentric glass cylinders is filled with a prepared solution of gelatine which is allowed to set. A torsional stress can then be produced in the jelly by twisting the inner cylinder and retaining the outer one fixed. This inner cylinder forms the lower part A B of figure 1, and is rigidly fixed to the brass piece C D which is itself supported. Torsional Stress tn Solutions of Gelatine. AAG vertically by means of two steel points at C and H. The brass projection F G is perpendicular to the direction of the cylinder and has a platinum point at its end G which, when the cylinder is twisted by means of threads passing round the wheel H, can be brought into contact with a fixed platinum plate, thus completing an electrical circuit through a Post- Office relay. The whole is supported on a stand (figure 2). The threads producing the couple pass over two pulleys K Kk and are attached to one arm of a balance. From this same arm hangs a tin vessel L, containing water with a layer of oil on the top to prevent evaporation. The weight of this vessel and a certain amount of the water it contains is counter- balanced by weights placed on the other pan of the balance so that the tension in the threads at any time is hiee |. equal to the difterence between the two weights. C If necessary, therefore, all the tension may be removed by drawing off sufficient water trom H the vessel L. The water is run off by means of a siphon through the electrically controlled valve M into a second vessel N, which is sus- pended from a spring, and the weight of water in the vessel N at any time is recorded on the revolving drum O by the pen P. The current passing through the platinum point and plate before mentioned is far too small to itself actuate the water valve M, and it is necessary to introduce two relays R, and R, to effect a sufficient increase of current. Contact between the platinum point and plate causes the water valve to open and a small quantity of water leaves L. This, however, reduces the torsional stress in the jelly, a small recovery takes place, contact is broken and the valve closes. By means of this intermittent action the inner glass cylinder which isimbedded in the gelatine is always kept in the same posi- tion, 7. e. the strain remains constant; and the curve drawn on the revolving drum gives the weight removed at any time, and since this weight is proportional to the torsional stress its value may be taken as a measure of the latter. Dimensions :—The total length of the outer cylinder was about 50 ems., and the end of the inner cylinder was about 20 ems. from the bottom of the former. In all cases the length of the inner cylinder imbedded in jelly was the same, viz. ‘about 26 cms. ‘The diameter of 450 Mr, A. O. Rankine on the Decay of the outer cylinder was about 3 ems. and that of the inner 1 em. The diameter of the wheel about which the couple was applied was about 4°5 ems. Experiments were made with 3:4, 4, 4:2, 4-4, and 4:5 per cent. solutions, and in each case the couple was produced by 000 gr. wt. acting round the wheel H. The platinum plate was then adjusted so as to come into contact with the point G, and the action of the valve began. SUSPENSION THKEAD SUSPENSION THREAD The friction of the points C, H and the pulleys K, K was not large, being only equivalent to a couple produced by 5) gr. wt. acting round the wheel H, but in order to obtain a smooth curve it was necessary to eliminate it. If it is not allowed for, the pen draws a-curve consisting of a series of alternate vertical and horizontal lines, each upward step being equivalent to the frictional couple. This difficulty was over- come in the following way:—An iron plate 8 (fig. 2) suspended from the second arm of the balance is adjusted to such a distance from the electromagnet T that when a given current flows in T, 8 is pulled downwards with a force equal to the frictional force. This causes the tension in the strings to be relieved to that extent. The current flows in T whenever the water valve opens. Hence the platinum Torsional Stress in Solutions of Grelatine. 451 point is free to recover without having first to overcome friction. In this way a series of smooth curves was obtained. Another precaution had to be taken. Preliminary experi- ments sufficed to show that the consistency of any specimen of jelly depended largely on the temperature. For purposes of comparison between solutions of different concentrations, therefore, it was necessary to maintain them throughout the experiment as far as possible at equal temperatures. To effect this the outer cylinder containing the jelly was surrounded by a water-jacket which was itself wrapped round and round with felt. It was then possible to keep the temperature of the jelly fairly constant for about three hours. The following table shows the variation of temperature in the actual experiments :— Percentage Picea iniaura| Mean Temperature Experiment. : nS Temperatures. P3 eee of Gelatine. Cleats ; for two hours. entigrade degrees. eee hte ot 16°32— 16°44 16°38 a ee +:0 16:23 —16'59 1641 Sah deans 4:5 16:10 —16°52 16°31 bys 4-2 16°15 — 16°63 | 16°39 Oye ceeeaen sok 16:18—16:76 16°47 Il. Preparation of Solutions. The consistency of any specimen of jeliy does not solely depend on the percentage of gelatine present and _ the temperature. It depends also on the way in which the solution is prepared and the time allowed for setting. Thus, if one solution of gelatine be boiled for some time and another of equal concentration be made simply by dissolving the gelatine in hot water without boiling, then, even if the ‘times of setting are the same, the two have different ecnsistencies. A oradual hardening, Ne. occurs in any jelly even after the temperature of the atmosphere has been reached. In order to compare specimens varying only in con- centration, it was essential to ensure that all the other conditions determining the consistency remained constant. The temperature was kept constant in the way before described. All the solutions were prepared by simply dis- solving the gelatine in water that had just been boiled and making up to the required concentration by the addition of hot water. The liquid (equal volumes in each.case) was then poured into the interspace between the two glass cylinders and allowed to set for a fixed time—224 hours. 452 Mr. A. O. Rankine on the Decay of Ill. Results. The curves shown in figure 3 are copied from the experi- mental curves. The break in the curve, which probably indicates the point at which the elastic limit is reached, will Fie. 3 500. = | SER S : 4.0% S (SeTo abe ee Bale ~ 400 | wert Dates aa ALTE, Q N , : / 3 e | RL S 300 ¥ S 0) | 4 5 TIME 1M HOURS. be noticed in the cases of the 3:4, 4:0. 4°2, and 4:4 per cent. specimens. It was not found practicable to maintain the temperature constant for a sufficient time to obtain such a break in the 4°5 per cent. curve. It will be seen, too, that these points lie on a curve which, from theoretical con- siderations, must pass through the point t=0 W=500. For in the limiting case when the substance possesses no elasticity, it follows that it has no tendency to recover when stress 1s removed; and hence the whole weight would be removed instantaneously, and the curve representing the removal of weight with time would simply consist of the two straight lines at right angles, =0 and W=500. If we suppose that all the curves do break when they meet this dotted curve, then it is obvious from the diagram that the breaking point of the 4°5 per cent. curve must be at a considerably greater time and a considerably less weight than that of the 4°4 per cent. curve. This supposition is to some extent justified by Torsional Stress in Solutions of Gelatine. 453 the curve shown in figure 4, which represents final stress against concentration. This curve in the region 4°4 per cent. concentration is ver y steep, anda small change of concentration makes a comparatively lar ge change 1 in the elastic limit. Returning now to figure 3, it will be seen that the curves are not quite horizontal after the break has been reached ; that is to say, the elasticity still gradually Thntanslnee. | Possibly this may be accounted for by the fact that during each experiment the temperature was slowly rising, which condition would tend to decrease the elastic Jimit of the specimen. No type of equation has been found which will fit all the ‘curves, but an equation of the form W = a log (pt+1) fits the 4°5 per cent. curve with considerable exactness This particular curve is of the same type as those for lead wire treated in a similar manner (‘‘ On the stretching and torsion of lead wire beyond its elastic limit,” Phil. Mag. Oct. 1904), for not only do equations of the same form approximately represent the curves, but both curves show similar departures from those equations. The above equation also satistactorily represents all curves corresponding to higher concentrations than 4°5 per cent.; these are not shown in the diagrain. It is noticeable also that the dotted curve passing through the points of breakage of the four upper curves is of like Fig. 4 50 Es. | 0 oie. | 3 4. GRAMS OF GELATINE PER 100 '"ATER shape, being fairly represented by an equation of the form W = Wo—a log (pt +1). Figure 4 shows the final weight, which is of course FINAL WeleyT tn grams wt Ss SS) 454. Decay of Torsional Stress in Solutions of Gelatine. proportional to the couple, plotted against concentration, and, if we regard each specimen as being elastic to the extent shown, it indicates that as the concentration increases the elastic limit increases more and more rapidly. The elastic limits and the times at which they are reached are shown in the following table :— Concentration, | Elastic Limit. Time baa ot 57 gr. wt. 0-114 hour. 4:0 Me O274 ,, 4:2 SO a 0-496, 4-4 i elOG ) 5 2°160 hours. IV. Conclusions. The following conclusions may be drawn from the results _ of these experiments :— 1. That any specimen, the concentration of which exceeds some fixed limit, is capable of permanently supporting a certain stress. 2. That the nature of the variation of stress for constant strain depends on the amount by which the limiting stress is exceeded. Thus we see that the curves of the 3-4, 4:0, and 4:2 per cent. concentrations differ in kind from that repre- senting the 4:5 per cent. concentration; that is to say, they are not represented by equations of the type W= a log (pt+1). Owing to the smallness of the time scale it is impossible to reasonably fit equations to them, and it is intended to repeat these determinations using a more quickly moving drum, in order to obtain a more open scale. But the 4:4 per cent. curve is not of the same type as the 4°5 per cent. No equation of the form suitable to the latter fits it. It appears to partake of the shape of both upper and lower curves. We conclude, therefore, that for specimens of greater concen- tration, i.e. those in which the elastic preponderates over the viscous, the variation of stress under constant strain follows the logarithm law W = W,—a log (pt+1) just as in the case of lead; on the other hand, if the concentration is low and viscosity is the more prominent property, some other law is followed, and solutions of intermediate strength are governed es a combination of these laws. . That, in some cases at least, the whole of the excess The H Theorem and the Dynamical Theory of Gases. 455 stress is dissipated within a finite time, contrary to what we should expect from theoretical considerations. At any rate, whether or not it is admitted that the breaks in the curves indicate that the elastic limit has been reached, it is certain that at these points a discontinuity occurs, the law on the one side being entirely different from that on the other side. In conclusion I wish to thank Professor Trouton and Professor Porter for the kind interest they have shown in the work, and for the suggestions which have enabled me to surmount many of he Mlifmeulitice which have arisen during the investigation. . XL. The H Theorem and Professor J. H. Jeans’s Dynamical Theory of Gases. by S. HW. Bursury, F.B.S.* im OLTZMANN’S H Theorem professes to prove that whenever the state of a gas 1s other than the normal aii... : sue : state, es negative, and H is a minimum in the normal state. His the function \\\ (flog f—/f)dudv dw; fdudv dw being the number per unit of volume of molecules whose com- ponent velocities le between w and u+du,v and v+dv, wand «+dw. In the normal state as usually understood, fo Re imeeseen), As a consequence of the theorem, H, once minimum, remains minimum for ever, making the process irreversible. Then the objection was made that the : = : , a Theorem, OS, a to be necessarily negative, if not zero, proves too much, hee we have only to reverse all the velocities simultaneously, and the system will retrace its course with H increasing. The question is how to explain the paradox. 2. Professor J. H. Jeans, a very strong mathematician, has dealt with this question in his sone work on the Dynamical Theory of Gases. He gives (art. 11) a definition of the density, v, of a gas at a point Pp: namely, vis the number of molecules in a Salas at P, which volume is very great compared with the mean ete cullen distance, but very small compared with the scale of variation of density of the ous. The definition is free from ambiguity. But it ignores varia- tions of density on the scale of the ‘ntermolecula ar distances. * Communicated by the Author. 456 Mr. 8. H. Burbury on the H Theorem and ‘There seems to be no reason why the density should vary at all on a seale infinitely larger than that of the intermolecular distanees, unless in a Anal Pox tryall Pores such as gravity. Jeans’s definition virtually assumes v to be constant, except as varied by external forces. 3. He then gives the usual proof of the H Theorem on the hypothesis of ‘molecular chaos’? (art. 15). This is the hypothesis which I call condition A, namely, that the chance of a molecule having velocities within assigned limits is in- ‘dependent of the positions of all the other molecules for the time being, and also independent of the velocities of all the other tel eetles for the time being, subject only to the con- stancy of $im(w’+1?+w’), the total kinetic energy. The legitimacy 7 this assumption is, Jeans says, not self-evident, because it is conceiv: able, for cheines. that ible having nearly equal velocities should tend to flock together. He reserves the consideration of this question to later chapters. 4. In Chapter II. he introduces a new notation. Given a system of N molecules, he calls the 3N_ position coordinates ty Yi +» Zn; and the 3N component velocities u,v. . wy, the ‘coordinates of a point ina generalized space of 6N dimen- sions.” very state of the s system i is represented by a point in that space, and the series of states which follow each other in natural motion are represented by a line in that space. This is a change in notation, ady antageous it may be, but still only in notation, And as no new hy pothesis is expressly introduced, the physical relations between the molecules must be understood to remain unaffected. Therefore every pro- position concerning these relations, true in the usual notation, is true in the new notation, and vice versa. Also every pro- position which can be proved by the use of the new notation, can be proved—I do not say proved equally well, but can be proved—by the use of the old notation. If the new method leads, or appears to lead, to any physical results not attainable by the or dinary method, that can only be because along with the new method we have introduced some new hypotheses unawares, 5. Jeans then discusses, arts. 39-54, the “ Partition of the generalized space among the position coordinates.” We are to suppose the three-dimension space Q in which the mole- cules are moving to be divided into » equal cells @, @.. Ons each of volume , so that Q=now. The number of ways in wineh | molecules can be assigned to the n different cells, so that there shall be a, in @, dy in @o, Ke. with a, +d,+..d,=N is ; = ne (equation 60, p. 39). a! a, | eee Prof. Jeans’s Dynamical Theory of Gases. 457 This means that the molecules are scattered at random through the space Q. The most probable distribution 1s found by making @ maximum, and is when Ss=22 >a; log a, is minimum, that is when a, = a,=..=4 s=1 Subsequently (art. 55) he discusses the Partition of the generalized space as regards the velocities. This he says is to be effected in the same way as in the case of the position coordinates. That is, we are to suppose another three- dimension space, or diagram of velocities, and u, v, w are the coordinates in that diagram of points ccattoned a random through it, but they are “to be subject to one new condition, namely, that +m (u? + v? + w*) = constant (equation 98). This new space, Jet us ‘call it ©’, may Be divided into n equal cells, @,' Qi sie Caen) Ol wolmne w',and the number of ways In which N molecules may be distributed through 0’, so that there shall be FIM @y fo 1 ws, Ge.with > pf =n, us N! ? x 7 J ? ze, le one eels fs It is shown that 6’ is maximum when \\\ T log f du dv dw is minimum. So the solution is given by making On Ol = \\\ / log fdu dv dw minimum, given Gis) \\\7 dudvdw = 1 (97), expressing only the fact that | the number of molecules is constant ; (2) i\\ m (uw? + v? + w*) du dv dw = constant (98). The usual method leads to i le Oe ys ea Maxcwells: lary: No mention has been made of any possible relation between velocities and space coordinates, such as that referred to by Jeans’s art. 15. If any such existed it would manifestly vitiate the reasoning. It is therefore assumed by necessary implication (a) that no such relation exists, and therefore that the chance of a molecule having velocities within assigned limits is independent of the positions of all the other molecules for the time being. Further, it is expressly stated that the only relation ex xisting among the Phil. Mag. 8. 6. Vol. 11. No. 64. April 1906. 2H 458 Mr. 8. H. Burbury on the H Theorem and velocities is (98). It is therefore assumed (6) that the chance of a molecule having velocities within assigned limits is, Subject to (98), independent of the velocities of all the other molecules for the time being. Assumptions (a) and (6) together amount to Condition A, or ‘molecular chaos. Jeans has therefore by implication a assumed Condition A. Maxwell’s law distinctly asserts Condition A. If therefore you could prove Maxwell’s law without expressly or by im- plication assuming Condition A, you would prove Condition A to be a physical fact, self- existent I suppose. But Jeans has proved Maxwell’s ey only on the imphed assumption of Condition A. He has pr oved it, that is, on precisely the same assumption as all former writers have done. He has in no way altered the logical position of the Kinetic Theory of Gases. . With regard to the proof contained in arts. 39-54, Jeans proves, as I said, that (is maximum when (=a) .. =dn. And this he shows is equivalent to making v constant on average. And further that, the a’s being very great, 0 becomes infinitely less than its maximum when y differs con- siderably from its constant or mean value, so that v may be regar ded as ev erywhere constant. I think that with infinitely small molecules and no forces acting, this follows from the definition of v. Also, is not the result that all the a’s are equal when @ is maximum evident from the mere inspection of 6? And then may we not write a, = = O5 Vs. And, there- fore. Deeg SS 5 The question occurred to me whether the number of pos- “ible arrangements of the molecules, which Jeans calculates, has any effect on the state of any physical system. Consider, for instance, a vertical column of gas under the earth’s attraction. The number of ways in which the molecules can be assigned to equal elements of the column is immensely greater, according to Jeans’s calculation of 6, when they are distributed with uniform density than when they are distributed according to any other law. ‘Has this fact any influence on the actual distribution ? I think none whatever, if the molecules are, as Jeans assumes (p. 39), infinitely alls IT do not think Jeans would say that it has any. In Jeans’s distribution the chance of a given molecule being in the cell @, is oo and is inde- pendent of the position of the cell. We might say that equal cells have equa! value for the purposes of the distribution. Tn the vertical column the chance of a given molecule being in the elementary cell @ is a e~*#, s being the height of the =i Prof. Jeans’s Dynamical Theory of Gases. 459 cell above the base of the column. We might say that the value of a cell for the purposes of this distribution is propor- tional to e495. On this principle we find that the density at height s is proportional to e—hgs as Boltzmann teaches, and is not affected in any way by Jeans’s law of distribution. 9. In arts. 62-65 Jeans discusses the assumption of molecular chaos. The number of molecules whose space co- ordinates lie between x and # + dz, &c., and their velocities between uw and u + du, &., whatever be the positions and velocities of the other molecules, is denoted by vp. It can evidently be written vp= Nf (uv w) du du dw dex dy dz \\\ GUE Otte bn CUUENCIU 6 Oe in which @; ys 23, &., &e. denote the space coordinates of the molecules not included in v,. Similarly the number whose position coordinates lie between a’ .. a+ da’, &., and their velocities between wu’. . u'+ du’, &., is given by Up= N f (au! v! w’) dul dv! du! da! dy’ dz! \\\ (NEBL RUUD Seale Le Ye, Ke. now denoting the position coordinates of all the molecules except those which are included in vp or vg. y= \\\ de dy dz \\\ dudvdw, over all the molecules, v includes all possible states of the system and means the same thing as the volume of Jeans’s generalized space. And UV U : . , —* represent respectively the chances of a molecule being De) included in v, or in uy. The question is whether these chances are independent of each other. Now the motion being continuous, the velocities and positions of all the molecules at any instant are deter- minate functions of their velocities and positions at the pal instant ¢ seconds ago. Consider two molecules m and m' ; let wu, and u,’ denote their initial velocities. If m and m’ exert no forces on each other during the time ¢, and no thir ‘ body sensibly influences both during the time ¢, and if wu w were initially independent, then at the given instant wu cannot be a function of w. If &(u)du be the chance of uw lying between assigned limits, ¢(u')du’ the same for w, it is 3 oO) — 0. Similarly ACs 0. @(w) and certain that du d (u') are then pean ie chances. Clearly, then, if there be no intermolecular forces at all, the chances are ‘independent. And they may be independent if ¢ be smail enough and the initial distance between m and > D) 460 | Mr. 8. H. Burbury on the H Theorem and uv’ great enough. But if, durimg the time ¢, m and m’ exert aa forces on each other, it is certain that in general the two chances $(u) and (w') are not independent. The question ae on the ree and on nothing else whatever. It cannot be affected by any change in notation. There is indeed an attempted justification of the assumption of mnde- pendence in the latter part of art. 65, p. 57. But it is only by reference to the analysi sis of Chapter TII., tne Partition of the generalized space, in which was assumed by necessary implication that molecular chaos or Condition A exists. It is impossible to prove a physical fact by merely using a new notation. 10. Jeans then, pp. 59, 60, gives an “ Analysis of the H Theorem.”’ He Feri us that to obtain strictly accurate results, the quantities he deals with must not be regarded as applying to a single system, but to the average of all systems satisfying conan Pea ions. These conditions I suppose are that each system consists of the same number N of similar molecules, and has the same mean kinetic ener oy. Then he assumes (art. 68) that the function 7 (art. 1 above) consists of two numerically equal parts, one half containing those molecules whose velocities are uw, v, w, and the other half those whose velocities are —u, —v, —w. IJ£ one of these equal parts corresponds to a direct motion, the other corresponds to the reversed motion (art. 1 above). ‘Whence it follows that, taking both motions into account, = is on average as often positive as negative, is in fact on average Zero aa This argument, it should be noted, does not affect the mathematical correctness of the H Theorem. The theorem is founded on a certain assumption, namely, that the number per unit of time of collisions between pairs of molecules, one from the class F, and other from the class f, the two mole- cules being so situated that after collision they are in the classes I’ and /' respectively, is proportional to Ff, that is to the number of such pairs which exist—and is not generally proportional to E’7’. This assumption, though I deny its legitimacy, justifies, if true, the H Theorem. But if it applies to the direct, it cannot apply to the reversed motion, because the pairs of molecules which in the reversed motion pass from the classes Fand / to the classes I’ and f’, are the identical pairs which in the direct motion passed from F’ and 7’ to F and jf, and their number is therefore by the assumption proportional, not to Ff, but to F’ 7’. Therefore the H Theorem is inapplicable to the revers ue motion by Prof. Jeans’s Dynamical Theory of Gases. 461 failure of the assumption on which it is based. And the mathematical correctness of Boltzmann’s theorem, granted his assumption, is preserved. The doubt is whether the assumption itself is valid. It is proved only in the normal state that w, v, ware as likely to occur as —u, —v, —w. We have then, it may be suid, no right to assume it in an analysis of the H Theorem, because that theorem deals only with systems in abnormal states. I understand, however, Jeans’s meaning to be this. According to the H Theorem the system, given in an abnormal : state, passes into the normal state. But when it 1s normal, 2, v, ware as probable as —w, —v, —w, and therefore, the motion being continuous, tle passage from the abnormal to the normal is just as frequent, and no more so, than the reverse. In this form the ar oument is good against Boltzmann as an argumentum ad hominem. But it makes the continuity of the motion a vital point. For if there be any the least discontinuity in the original motion, caused, say, by some external disturbance, it ceases to be true that the system, starting with velocities —u, —v, —w, will retrace the course of a system which ended with u, v, w. And therefore we f atele cannot prove that on average of both motions ae iS Zero. The discontinuity would be fatal to Jeans’s argument, but not to the H Theorem. 13. I agree with Jeans that as a fact on average of all Heh weal ; systems and of all time, oF =0(0, provided that the motion be AL continuous and protected from external disturbance. I agree with him also that, as a fact, on the average of all systems and all time, the states u,v, w, and —u, —v, —w oceur with equal frequency. I agree further with him that on average of all systems and all ne H is nearly minimum. I expressed that myself in the form that when H ‘differs little al ee dt from its minimum, —— and “ge ure very small, whereas if dt dA Hs ditters much from its minimum 7 may be very great. Q oe SS For by consideration of the direct and reverse motions, we see that the number per unit of time of collisions by which two molecules pass from the classes F and 7 to the classes bY’ and 7’, is proportional, not indeed necessarily to F7 as wigan: assumes, but either to If or else to I”7", ‘and as often to one fhe Gther. But when His nearly minimum F’7’—F/ is in 462 Mr. 8. H. Burbury on the H Theorem and EF general very small, and (F’/’/—F*/) log 8 pie of the second order of small quantities. But a consists of terms either of C a this form or of the form (F/—F'7’) log an sl , and is therefore, fH dt 2D It follows that any given system will remain for very long periods of time with A nearly minimum, though H may occasionally for short periods deviate into higher values. As for each system on average of time, so at each time on average of all systems, H is nearly minimum, which agrees with Jeans’s conclusion. Let us suppose there are N states in which H=H,, and is minimum. Of these N states there are say 7, states, ee of which is the end of a course in which H has fallen from H,, its last maximum, to Hy, and n, in which it has fallen from H,, its last maximum, to H,. And if H.< Hy, m>ny Similarly for each of the N states there is a last maximum of whatever its sign, very small, and so is - n H,and N=2,+7,.+...-+y. Then I should say Ny measures a : : nN the chance of H having the value Hy, N the chance of its having the value H2, and so on; and it may be that nr e e . . . . ., is infinitesimal for all values of H not infinitely near to N H,. That gives Jeans’s result. 1, however, there are in fact as many courses in which H passes from Ho 46 H,, as in which it passes from H, to Ho, it is not true that ie variations of H constitute an irreversible process It is not necessary to assume that the fall from a maximum H, to Ho is always followed by a rise to precisely the same value Hy, as the next maximum, so that the system oscillates. It is sufficient to say, as we ‘have said, that, on average of all systems and all time, motions in one direction happen as frequently as in the other direction. 15. Boltzmann’s own explanation of our pare was that the reversed motion, in which H increases, although possible, is in a very high degree less pr obable than the direct motion in which H diminishes, and on this he founded his doctrine of the connexion between reversibility and proba- bility. Ithink this explanation cannot be reconciled with the theorem; for if Maxwell’s law holds when H is minimum, which the theorem is supposed to prove, the state in which the velocities are typically +u, +v, and +w, and the state in which they are —u, —v, and —w are equally probable Prof. Jeans’s Dynamical Theory of Gases. 463 states. To assert that one is in a high degree more probable than the other, would be contrary to Maxwell’s law. 16. The real defect in the H Theorem, and in every proof yet given of Maxwell’s law, consists in my opinion in this, that it ignores the continuity of the motion altogether. The H Theorem is based wholly on the assumption mentioned in art. (11) above. Now let us suppose that at a given initial instant the state of the system is formed as follows :— One person assigns component velocities wu, v, w to each molecule according to any law he pleases, subject only to the condition that =m(w?+v?+w?) = E. And another person, to whom these assigned velocities are wholly un- known, scatters the molecules through the space 0. In that case Condition A is satisfied at the initial instant, Boltzmann’s assumption art. (11) above is satisfied, andif H is rt: al; : : ae not minimum, aH at that instant negative. But in the supposed distribution, the velocities are just as likely to have all the opposite values —u —v —was u,v, w. Ineither case at the initial instant is negative. If, however, the system were left to itself for a finite time, and then the final velocities were reversed, the system would retrace its course back to the initial state. And immediately before it arrives at that state is evidently positive. But when it has arrived at that state ae becomes discontinuously negative, because then dt the origiaal velocities u, v, w would have become —u —v -- w. aie: bas 3 And, as we have seen, 7 negative in that state as well as mcthe origmal state. —, , if not zero, must be dis- continuous when the system in its reversed course passes through its initial position. 17. That is the history of the initial state formed as I have supposed it to be formed. In dealing with the subse- quent course of the system, to prove the H Theorem, or Maxwell’s law, we assume, and if we are to prove the pro- position we must assume, that the independence of the molecular velocities, or as I call it Condition A, exists at every instant during the motion. But if the motion be continuous, the state of the system at any instant is a determinate function of the initial state and of the time elapsed, and of 464 Mas. Ee Burbury on the H Theorem and nothing else whatever. Now that the velocities of a set of molecules, being functions of the same set of initial variables and of the same time, should be always independent of each other, is, if it is to be taken as an exact statement, a mathe- aoathloa impossibility. There must arise correlation between the velocities, at least of neighbouring molecules, as Jeans suggests in Me eubs os 18. In my unorthodox opinion therefore, neither Maxwell’s law nor the H Theorem are true accur ately, if the motion is continuous. As regards Maxwell’s law, it may be for some important purposes accurate enough. If, for instance, we wish to calculate the theoretical value of the coefficient of diffusion between rare gases for comparison with experiment, approximate numerical results are all we require, and all we can have., And it may well be that Maxwell’s law gives : sufficiently near approximation. This I have never denied But in considering the question of reversibility, the method of approximation is ineffectual. or suppose two states of a_ gas, state Aand state B. In state A the position and velocities of the molecules are denoted respectively by #, y, 2 and u,v, w. In state B they have nearly the same values as in A, and the differences are for some purposes negligible. Nevertheless these differences, however small, may in ae cause the two systems to diverge widely feo each other. One may be asymptotic, H continually approaching its minimum, the other may becycic. The asy mptotic character cannot be established by any approximate reasoning. 19. If I am rightin saying that Maxwell’s law, f founded as it is on the assumption of “Condition A, and asserting as it does the truth of Condition A, cannot in continuous motion be ace surately true, nevenneles the system started as I have supposed in art. 16 above and left to itself to move in continuous motion, must ultimately settle down into stationary motion of some kind, and must then have a normal state of some kind. If it ‘he not Maxwell’s law, what isit? I should answer the question thus—Firstly, im that normal state Condition A must not completely ‘prevail. Secondly, the state in which the velocities of the N molecules are typically wu, v, w, and the state in which they are typically —u, —v, —w, must in the stationary motion be equally probable. Both conditions are satisfied if “The chance of “the N molecules having velocities within assigned limits is Cae Cadi ., 5. A wyy | ame <()—>m (Pr +v?+w?) + >>b(uu' +ev' + ww’), “‘ where U isa function of 7, the distance between the molecules Prof. Jeans’s Dynamical Theory of Gases. 465: * whose velocities are wv wand w’ v w', which is evanescent “ except for small values of 7.’ This does not satisfy Con- dition A. Also the second condition is evidently satisfied because Q is a quadratic function. 20. I suggested myself in ‘Nature,’ February 1895, in aid of the H Theorem, that no material system ever cloes remain for any considerable time in exactly continuous motion, free from external disturbances. Such disturbances: are always happening, and their effect, if they come at hap- hazard without regard to the state of the system for the time being, is pro tanto to renew or to maintain the independence of the molecular motions, 2.e. Condition A, and so to make H diminish. JI think that is true. We may assume that if the disturbances are frequent enough and great enough, oe will be in general negative or zero. But then we must remember that, as regards this disturbed system, it is not true that were all the velocities at any instant reversed the system would retrace its course, because the disturbances are not included in the reversal. I think therefore that the true explanation of the paradox of art. 1 above is as follows :—- The system either is or is not isolated, that is protected throughout the motion from all external disturbances. If we take the first hypothesis, that it is isolated, it is not true that the condition of independence (art. 17) exists. Therefore it is not true that ait is necessarily negative. But it is true that dt on reversal of the velocities the svstem would retrace its course. There isa reversed motion, but there is no H Theorem. It we take the second hypothesis, that disturbances are con- tinually happening, it may be true that ie is generally negative. But it is not true that on reversal of the velocities the system would retrace its course. There isan H Theorem, but there is no reversed motion. The reason why we obtain for the same system first one and then the other of two incon- sistent results, first that a dH dt at is positive, is because we apply to the same system first one and then the other of two inconsistent hypotheses. is negative, secondly that j 466 | XLI. On the Recombination of Ions in Air and other Gases. By W. HH. Brace, IA., Elder Professor of Mathematies and Physics in the University of Adelaide; and R. D. KuEEMAn, B.Sc., Demonstrator*. T is well known that when positive and negative ions are distributed through a given space, a process of com- bination goes on until ions of one sign only are left. Let there be p positive ions, and x negative ions in each cubic centimetre at any instant, and suppose that the relations of any ion to all those of opposite sign are of the same character. Then the chance that an ion, say a positive one, will enter into combination before the end of a short time & is propor- tional to nét; and generally the number of combinations taking place in that time may be denoted by apnét, where « is the “ co-efficient of recombination.”” This has been clearly established by the experiments of Rutherford, Townsend, McClung, Langevin, and others. As a consequence, the current passing between two elec- trodes in a gas in which ions are being formed by external agents depends on the magnitude of the potential gradient or electric force. The relations between current and force have been carefully studied by many workers, and the observed facts have been compared with the results of cal- culation based on theory. The comparison is partly, but not completely, satisfactory. Certain experimental results which we propose to describe in this paper seem to throw light on the reason of the dis- crepancy. They point to the existence of another cause, distinct from that represented by the expression enp, which prevents ions from reaching the electrodes in the gas in which they are formed. This cause appears to be a process of re- combination of newly-formed ions with the atoms from which they have just been separated. The effects of it are propor- tional to the number of ions formed in a c.cm. in unit time, not to the product of the existing numbers of positives and negatives. They are independent of the shape of the ioni- zation chamber, and in this they differ from those of general recombination. ‘They depend directly on pressure, and vary greatly from gas to gas. In order to bring these effects into relief, it is only necessary to reduce the number of ions in a ¢.cm. until the number of those that are lost by general recombination is negligible compared with the number of those that are formed. When * Communicated by the Authors. Frem the ‘Transactions of the Royal Society of South Australia,’ vol. xxix. 1905. Recombination of Ions in Air and other Gases. 467 this is done, it is found that it is still necessary to apply a high potential in order te extract all the ions from the gas. For example, in air at atmospheric pressure an electric force of 25 volts to the em. will only extract about 80 per cent. of the ions which are obtained when the force is increased to 1000. The following example will serve as an illustration :— The width of the ionization chamber is 4 mm., the upper electrode being a metal plate, the lower a sheet of gauze. A thin layer of radium is placed 6°2 cm. below the sheet, and a particles emitted from Ra C cross the chamber and ionize the air, which is at atmospheric pressure. The area of the plate on which the rays fall is about 18 sq.cm. The capacity of the electrometer to which the upper plate is connected 1s about 150 em., and a potential of +125 volt applied direct to the electrometer causes a deflexion of 722 divisions on the scale ; ten divisions = 1mm. When the lower plate is raised to 400 volts positive, so that the electric force is 1000 volts per em., there is a deflexion of 982 divisions in 10 seconds, under the influence of the e rays. When a potential of 10 volts is applied, giving a force of 25 volts per cm., there is a deflexion of 772 in 10 seconds. In the latter case the charge Q received per sq.cm. of electrode in one second, measured in electrostatic units, is— eS SLO OX (225-300 als The number of ions falling on each sq.em. of electrode per second is therefore 1:2 x 10° nearly. The velocity of ions at this potential gradient is nearly 25 x1'5, or 37 cm. per second. Thus, if 2 be the number of ions ina cubic centimetre, mo 2 x 10° and ‘therekore 2 = 3°25<10'. 9 * Hence, the number of recombinations taking place in a second in the space between two opposing square centimetres of the electrodes is equal to «x *4 x (3°2 x 10*)?. Li we take the value of « to be 3400 x 3 x 10—!°, we find this number to be nearly 420. Finally, therefore, the number of ions recom- bining in each second is 420, w ible the number received is Px 10°, and thus only 1/3000 of the ions are lost in this way. But the current at 25 volts is only 772/982, or about 80 per cent. of the current. at 1000 volts. Tt is clear from this example that there is some cause which prevents the current attaining its full value other than general recombination between positiv. e and negative ions. Now, it is possible that ions newly formed might be specially lable to recombine with each other. Such a possi- ==) Pi Oma 468 Prof. W. H. Bragg and Mr. R. D. Kleeman on the bility has been already suggested by Rutherford (‘ Radio- activity, p. 33). An electron, which has just been ejected from an atom by a passing 2 particle, does not go far before encountering a neighbouring atom. The encounter, perhaps, results in a “temporary attachment, for we know that ion- clusters are formed in this way. In any case, it is probable that the electron loses much of its velocity of projection. Now, it is still under the attraction of the atom from which it has. come. Supposing this atom to have only lost one electron, the strength of the electric force which it exerts at the distance of the mean free path is equal to ef? = 3x 10-/10-» = 3 E.8.U., or 900 volts per cm. This is large compared with the usual impressed electric forces of experiment. It is by no means improbable, therefore, that the electron may finally slip back into its old place. ick a possibility is not considered in the equations as usually formed. For all writers begin their arguments by the statement :—‘‘ Let p be the anes of positive ions in a cubic centimetre, and n the number of negative.” In doing so they tacitly assume that the relations of any one lon to slit, others of opposite sion are of the same character. But ifa pair of newly -formed ions ran a special chance of recombination until they got away from each other, then the relations of either of these two to the other would be quite different to its relation to all other ions. Let us, then, for the moment suppose that there is a special form of recombination, which we may call “ initial,” as distin- guished from general Peconbien and let us conser the nature of its effects, in order that we may find means of testing the correctness of the supposition. Now, it is clear that the effects of initial recombination do not depend upon the shape of the ionization chamber, and this at once differentiates them from those - of general recombination. [For the special or initial recom beens concerns only the ion and its parent atom. But general recombination depends on the chance of an ion meeting others of the opposite sign, which chance depends on the number inac.em., and this, again, on the shape of the chamber. It, for example, a particles cross a chamber 3 mm. wide, and a sufficient potential gradient is applied, most of the ions will be carried to the electrodes. If the width of the chamber is increased to 6 mm. the magnitude of the stream of ions is doubled, ee positive meets twice as many hegatives as before, and therefore the chance that any one ion enters into recombination is twice as great. Suppose the saturation eurrent for a 3 mm. chamber were 100, using any arbitrary Recombination of Ions in Air and other Gases. 469 system of units, and the actual current for a moderate potential were 90, then for the 6 mm. chamber, under an equal potential gradient, the current would be 160, not 180; the saturation current being 200. This is recog nized in the usual formule. For example, Langevin finds that— - Rok = 60 (1+ = where () is the saturation current per sq.cm. of electrode, and () is the current when such a potential is applied that o is the density thereby caused to exist on each sq.cm. of the electrode. When Q and Q, are both small compared to o, it follows that :— e() ies Eo EQ,” o o Dion Qn ow () ues elo (Qo De Thus, the relative lack of saturation, viz. (Qo—Q)/Qo, is proportional to Qo, which itself depends on the depth of the chamber. Other formulee show the same dependence. But experiment shows that when the density of the ions is small the depth of the ionization chamber has very little effect on the degree of saturation. This may be illustrated by the following experiments :— Five mmg. of radium bromide were so placed that the a rays passed upwards through an aperture in a lead plate and crossed the gauze of the ‘fouiaeinioen chamber. The rays formed a cone mhose vertical angle was about 20°. The apparatus used was the same as that of the previous experiment described, but the currents were so strong that a capacity of 1070 cms. had to be put in parallel with the electrometer. Determinations were then made of the strengths of the eurrent at various potentials:—(1)When the ionization chamber was 3 mm. wide; (2) when 6 mm. wide ; and (3) when 9 mm. wide. The values obtained were then reduced so that the saturation current in each case was set at the same value. Comparison then showed that the curves were almost identical except at low potentials, and this was in agreement with the hypothesis now put forward. For at all but low potentials en” was so smallas to be negligible. When the potential was very low, one or two volts per centimetre, then the ions moved so slowly that » was larger, and an? was not negligible, and under those circumstances the curve showed: a ‘difference of the right kind. That is to say, the 9 mm. curve was further from being s saturated than the others. The currents were specially made not too weak in order to 470 Prof. W. H. Bragg and Mr. R. D. Kleeman on the bring out this contrast between the effects at low and at se potentials. The figures are given in the following table :— Relation of current to potential gradient for different widths of the ionization chamber, the currents being small ; potential gradients in volts per centimetre: currents in arbitrary units, reduced to common maximum. WiptnH or CHAMBER. oO min. 6 mm. 9 mm. pecs) Current. aie Current. Aaa Current. 1000 400 1000 400 1000 400 34:8 ott Bop 330 36:0 303 11°9 308 at 302 16:4 300 8°65 294 9-47 22 9°83 290 6°6 285 TAT 283 Wok 283 4-66 274 5:00 272 3°83 274: 278 Pa2 2:75 247 ol@ 244 1:92 230 IES, 224 Ros 220 1-30 DAS ‘98 169 1:36 174 1:06 196 ‘Ol 108 84 134 159) 147 3 pe + “O04 68 389 106 -20 47 These figures are plotted, as far as 36 volts per cm., in curves A, B, and C of fig. 1. An open scale is chosen so as to show the separation of the curves at low values of the field, when n is not very small. These figures and curves show that the ratio of the current at any particular strength of field to the saturation current is almost independent of the shape of the ionization chamber, when the current is small. As this seems an important point, we have made many experimental tests of it. We give below the details of one such test, in order to illustrate the methods employed and their degree of accuracy. ‘The arrangements were the same as those just described ; and the special object of the experiment was the deter- mination of the degree of saturation under a certain moderate potential gradient in the case of chambers of two different depths. ‘The depths were reckoned in turns of the screw, which raised the upper from the lower plate of the chamber ; eleven turns = 1cem. ‘The currents were allowed to run into the electrometer for 10 seconds. The electrometer was not dead-beat, and therefore the first and second resting-places on the scale were observed, and the mean taken. For example, the second line, marked +, of the subjoined table, Recombination of Ions in Air and other Gases. Tht QWEBEl0 DBE BEE SRE i Bese FEET FESeHRHEEE ESSERE iil iss HHH 1810 8} a, Pa rit a a line ine jeafoe tite ae | EEE 5B 1 EB UT TY fata] iB jefias} Bs Gee a ae ! a ee ao See A H tt Saturation current = -4-00 4 and current in air. Curves showing relation between potential gradient amperes per sa.cm. of electrode Wf{dth of ionisation chamber in mn, Order of saturation current i J == eacea See (ioe Ho | z Bea [| DI _ 4 D & and F are calculated from the results of serserera: ne VA experiments made by Retschinalry. eee o———4U 9 241n9 sev esecee | =i siiritetteecsrs HERR E Nu TI Volts per ca, ——_> 471 472 . Prof. W. H. Brage and Mr. R. D. Kleeman on the shows that the first deflexion was to 57°47 cm., and then back to 54°92, zero being 4700. The experiment repeated gave 57°42 to 54°92, and again 57-47 to 54:93. The leak was also measured with a metal plate over the radium, and the difference taken as the proper value of the leak for that experiment, a small Ce tion only being due to @ rays. The first measurements relate to a chamber of depth 6 turns— (i.) under a potential gradient of 600 volts for the 6 turns ; (ii.) a gradient of 20 volts for the same distance ; (i1i.) under 600 volts again. The difference between (i.) and (iil), as shown in the table, was due to the variation in sensitiveness of the electrometer. In almost all our experiments this variation has been negligible ; in this special case it was not so, because so large an amount of radium was used, viz., Smme. The y rays penetrated all the metal casings, and caused a leak in the cha urge of the needle. The leak had an exag ae influence on the readings because the capacity of the electrometer was increased by the addition, in parallel, of a plate-condenser of 1000 cm. c apacity. This disturbed - the usual balance of the electrometer, in which leakage of the needle’s charge had little effect on fie deflexion tone given quantity of electricity. To obviate any error from variation of sensibility the results of (i.) and (iii.) were averaged, and compared with the result of (ii.). It will be observed that successive determinations of the same leak were very con- sistent with each other. This implies that almost all the observed effect was due to the radium ; extraneous influences were very small. 6 Lorne.” Zero = 2700. | 600volts | 47/7 | (Metal over Ra). | 47 +600 volts. | 57 | 47 42-27 5 S 2 99 99 2) on mf ao 69 i Mean leak = 67 ees 7 Net leak = 852=I, (say). On volts AT 50 Ane ee (Metal over Ra). 47 : 40 46 I Eee | | : Net leak: = 695 aie 20 volts. 55 | 49 39 49 ae ales 53 | 43: 36 4 | Mean oe \ | 600volts | 47 | 70 69 lntean = 84 ; | (Metal over Ra). | 47 | 61 5 Sy | 7 Net leak = S29) Mean vale of ie = - 840, Value of I’, Noy Recombination of Ions in Air and other Gases. 473 3 TuRNS. 300 volts .| 47 : 53 53 es (Metal over Ra). | 47 ; 44 44 \ Mean = 49 ; >~Net leak = 416=I, (say). - \ Mean = 465 | 3 } 300 volts. 52 $27 3 10 volts 47 41 4: Si || sag See ees (Metal over Ra). | 47 : 34 386 f Mean = 38 | 92 2 9 ame ert h on |e a 37 | Mean = 378 Baars fc) 47. SSL he (Metal over Ra). | 47 : 45 | Mean = 48 300 volts. | ae : DOOM OT ee eee ie | 50 | 83 83 ah Mean oo 445 *. Mean value of I, = 406. Value of I’, = 340. Hence, I,/1', = 1:208, and J3/l'3 = 1-193. A repetition of the experiment, in different order, gave I,/Il; = 1°947, and I',/l’; = 1°897. These agree well. with each other, for we find from the first set that I,I’;/I',l, = 1:018, and from the second that the same fraction = 1°025. The fraction I,/I', is the ratio of the saturation current in a chamber about 6 mm. wide to the current when the potential gradient is about 35 volts per cm.; and I,/I’, is the ratio when the chamber is 3 mm. wide, all other conditions being exactly the same. It ought, perhaps, to be mentioned that the current for the chamber of double width was not quite twice that for the other, because the widening was effected by raising the top plate, and so adding to the chamber a layer of air which was about 3 mm. further away from the radium than the original layer. As a little heap of radium bromide was used, the curve was of the form shown in Plate xviii., Philosophical Magazine, December 1904, so that ionization decreased as distance from the radium increased. These results show clearly the existence of at least one effect which we should expect to find as a result of initial recombination. Again, we ought to find that variation in current strength, caused by altering the power of the ionizing agent, makes little difference to the form of the curve when the current is small. We have made several experiments in this direction also. In fig. 2, curves A and B show the results of experi- ments with currents which were of an order ten times smaller Phil. Mag. 8. 6. Vol. 11. No. 64. April 1906. 2] A474 Prof. W. H. Bragg and Mr. R. D. Kleeman on the EESReeas — 1 Lap eBeReeSleeeese BE eS Sasa eRaeseaRe SE of electrode current in air and amperés per 6q. cm. HEE BRAS DB. of TTT TT TT an ——— =) Bl — ese Bee Bee Volts per cm..~—__» COANE AEE EE EEE EE EEE a —- Bn LN ER ERR ERE SE eeee Pied t ys eis HEH = z s be Prmesee SER Recombination of [ons in Air and other Gases. A75 than those already described ; yet their form is very similar. The curve A shows results with an 8 mm. ionization chamber ; curve B,4 mm. The ionization was due to a thin layer of radium, surmounted by a set of vertical tubes, as described by us in the Philosophical Magazine for September 1905. Other experimental results may be expressed in terms of I,, the saturation current for 4 turns of the screw (rather less than 4 mm.), and I’, the current for a potential gradient of 25 volts per cm., and the same depth of chamber. On one occasion 1 was found that I,/I’, = 1:17: Ix/I’s = 1-21; and on another 1,/I’,= 1:18: I./I’s = 1:23. In these experi- ments the radium was 5:05 cm. trom the gauze. When the distance was 6°25 it was found that I,/I’, = 1:27; I,/I’s = 1°29; and again 1,/1’, = 1:30, I,/I’s = 1°30. In the latter cases the a rays did not all get across the chamber: possibly the small variation of the ratios with distance may, in some way, be due to this fact. Tt might be argued that we ought not to find much variation in the lack of saturation when the current is increased by shooting a greater number of « particles across the chamber co} in one second, on the following grounds :—Each particle as it flies across makes something ‘like 10° ions in a centimetre of its path. If there are only about 10° or 10° ions in a c.cm. at any one time, it is clear that these must be all the work of one particle, and that all the ions it produces are cleared away before the next one comes. Thus, the ions made by one a particle have no chance of combining with those made by another, and recombination cannot be proportional to the square of the number per ¢.c. But this consideration, though no doubt true, cannot furnish an explanation of the fact that the curves are little altered when the chamber is altered in depth. It was, indeed, in view of this argument that we made the experiments with the varying depths of the chamber. — It is very instructive to compare these figures with the results obtained by Retschinsky, and described by him ina paper contained in Drude’s Annalen, No. 8, 1905. Very careful measurements have been made by this observer of the relation between current and potential gradient in the case when the currents are of an order 100 to 1000 times greater than those of the experiments described above. Curves D, E, and F’, in fig. 1, are plotted from the table on page 531 in his paper, being reduced to a saturation value 400, so as to be comparable with the other curves in the same fio ure. It will be seen that in this case the curves for different widths of the ionization chamber differ very widely at low potential 6) [2 =~ _ 476 Prof. W.H. Bragg and Mr. R. D. Kleeman on the gradients, and this is in accordance with the present hypo- thesis. For, when the currents are so large, the value of en? is great, and the effects of general recombination must be considerable, unless the potential gradient is much increased. In fact, the general characteristic of these curves is that the larger the current the higher the potential gradient must be at the point where the effects of altering the depth of the chamber cease to be visible. Several observers have determined the form of the curve connecting current and potential gradient, and have caleu- lated therefrom the recombination coefficient. Let us now consider the result of neglecting the effects of initial recom- bination in these calculations. If the currents are very great, the effects of initial recom- bination may be small as “compared with those of general recombination. But they must always be there, and their effect will be of greater relative importance when the current is made smaller, either by using a weaker source of ionization - or by lessening the width of the ionization chamber. If both effects are ascribed to one cause, whose influence is measured by a, then « must be given a value which is fictitiously large. The smaller the “chamber, the greater the apparent value of « must be; and this is actually the case, as found and remarked upon by Retschinsky. For when the chamber is very small the effects of general “recombination ought to be small ; and if, as is the case, there is still a considerable lack of saturation at moderate voltages, the whole of which is ascribed to general recombination, the value found for « must be very great. It is possible to find any desired value of a in this way, if only the currents are made small enough. This is especially true if we use the first formula employed by Retschinsky, and ascribed by him to Riecke. In this the determination of « depends on the difference between two current-values taken from the upper part of the curve, where the slope is due rather to initial than to general recombination. To make this point clear consider the followi ing determinations of a :— Retschinsky gives the following form of Riecke’s equation where the quantities are expressed in electrostatic units :— Y—e)F2 OSn a= 52x 10-4§ CHOY (12 x a c where , = saturation current per sq.cm. of electrode, = current fora potential gradient Fo, = = depth of chamber. Recombination of Ions in Air and other Gases. AT7 He has found by experiment that when / is 1 cm., and Fy is 151 volts per cm., then Gn amperes) C =8:03 x 10—8/200 (area of electrode ='200 sq.cm.) == 40x 1) 1°, = 3:94 107): Therefore, eS A510, C2 and by substitution in the equation it can be found that ale = 4434 (loc cit. p. 530). Now, in a similar experiment, with far smaller currents, we find that when / is 1 em. and Fy is 150 volts per cm., @ = 473 x I-*, | 2 SS Se Therefore OFS = 22x 101, and substitution in the equation gives a value of «/e about 5000 times greater than Retschinsky’s, or about 2 x 10’. In the second formula (Stark’s) the values of a are more correct, because the current values used are taken, one from the lower part of the curve, and one from the saturation values, so that their difference depends less on the effects of initial recombination. Retschinsky draws attention to these anomalies in his results, but ascribes them to absorption of ions by the electrodes. He argues that in a shallow ionization chamber this effect must be greater than in a deeper one ; and so he accounts for the lack of saturation in the small chamber, a lack which is excessive if attempt is made to explain it as wholly due to general recombination. But we think that a more reasonable explanation is to be found in the hypothesis and results described in this paper, in con- nection with which Retschinsky’s results fall naturally into place. When, therefore, the ionizing agent is feeble, the only part of the curve which can be altered by varying the current is that where the potential gradient is small; the feebler the agent, the smaller the oradient. Let us now consider whether our hypothesis makes it probable that we can alter the shape of the rest of the curve by any variation of the conditions of the experiment. Now, if initial recombination takes place because the 478 Prof. W.H. Bragg and Mr. R. D. Kleeman on the ejected electron does not get far enough away from its parent atom before it is stopped ‘by encountering another atom, then diminution of pressure ought to oe it much easier to saturate. But this is a well-known fact (Rutherford, Philosophical Magazine, vol. xlvii. p. 160). In order to obtain results comparable with those we had already obtained at ordinary pressures, we made several experiments in which all the conditions were the same, except that the pressure was less than that of the atmosphere. Curve C in fig. 2 shows the results of such an experiment. If this is compared. with the other curves in the same figure, it will be clear that alteration has taken place in the very portion of the curve where we should have expected it, and where change in the streneth of the current has small influence, VIZ. abe along o the upper part of the curve up to the high potential end. “The saturation current per sq. cm. was ya 10—? amp. sim further support of our hypothesis it may be pointed out that it gives a ready explanation of an experiment due to Rutherford, and described by him in the Philosephical Magazine, vol. xlvu. p. 148 * He found that the satu- ration value of the current through a gas could be obtained for a much lower potential oradient when the gas was drawn away from the uranium nn ionized it, Ph treated in a separate vessel. This is to be expected when it is considered that under the circumstances of the experiment initial recombination was wholly absent. It is now convenient to consider these phenomena as they are manifested in other gases than air. It is well known that the relations between current and potential in carbon dioxide are in some way abnormal. But the peculiarities of this gas are even intensified in ethyl chloride (C,H;Cl). The fact ix that this effect, which makes it difficult to draw all the ions to the electrodes in the case of air, is far greater in more complex gases, and thus it is extremely difficult to obtain the saturation current unless very high potentials are employed. We find it necessary to use a potential gradient of two to three thousand volis per em. in the case of ethyl chloride at | 60 cm. pressure. In the investigations which were made by us (Philosophical Magazine, September 1905), with regard to the ionization curves in different gases, we found the currents to be unexpectedly small in the case of some gases. We suggested that possibly some of the ions made by the « particles did not get away from their parent atoms. We proposed to make a special investigation of the point, and it * This statement may need amendment. The matter is discussed in a later paper. ~ Recombination of Ions in Air and other Gases. 479 was with this purpose that the work described in this paper was undertaken. It now appears that our suggestion was justified, but it is also clear that we should have obtained larger currents if we had used a higher potential gradient ; 500 volts per cm. was insufficient. Consider the curves in fig. 3. In A is shown the relation between current and potential gradient up to 3000 volts per em. for ethyl chloride at 56 cm. pressure, the saturation current per sq.em. being about 3x 10-. B shows the same relation in the case of air at atmospheric pressure, the saturation current being rather smaller. Comparison of these two shows how much more difficult it is to obtain the full current in the more complex gas. Again, © shows the results of experiments in which the depth of the ionization chamber was varied.. The crosses refer to a 2 mm. chamber, the dots in circles to a4 mm. chamber. The currents were of the 10-'* order. The two sets of observations lie on practically the same curve. This shows that general recombination is not responsible for the lack of saturation, and that the cause is probably similar to that whose effects in the case of air have been described above. Curves D and Ei refer to experiments in which the chamber was maintained at the same depth, 2 mm., but the currents were altered by varying the distance of the radium. In the former curve the saturation current is about 10—!8, in the latter six times as much. In the case of the results shown in C, D, and Ij, the gas contained a certain proportion of air. These results all go to show that the form of the curve for ethyl chloride is almost independent, as in the case of air, of strength of current and depth of ionization chamber, wher the ionization is small. But also, as in the case of air, it depends greatly on the density of the gas. I represents the results of experiments at a pressure of 36 cm., and is to be compared with A. All the conditions, except as regards pressure, were the same for the two curves. We have also carried out experiments, similar to some of those just described, for a mixture of carbon tetrachloride and air, and obtained similar results. Although there was only 5 per cent. (by pressure) of the denser gas in the mixture, yet the current at a potential gradient of 330 volts per cm. was only 82 jer cent. of the saturation value, whils in air under similar conditions it was 93 per cent. It is hardly surprising that initial recombination should be more etfective in a complex gas than in air. For the molecule contains many atoms, each one of which is just as — 480 Prof. W. H. Brage and Mr. R. D. Kleeman on the SEnEnEEEEsssss0555=0000% Sanaa eaens ncEEEESESEEEEETEeeeaeeeae Seas canes = eennneees Soeeeeeeemeeeese Ee) eo vs. era) i Bo Cc a 8 =4 a he ay Vg ~ z 2 = BE fase 2° see Baitec ©. 3 see sands =e eo #311 © 3S =) 8... OW ets 3“ Gg S Sea S-gF Bis & SRERTRBERL OP Geo 08808 42 #2d0flle ; SUMS HS SRSRREORS Se USLee SS ola ee, ee 2 BHE@s BEPERSSRES GSreD of "Po 8) See oem erate tele taletat per etoretal ian isa eco 2h 5 = ERERB BS ecoliaog 2 .°%oat ah dls Haig SRE Bie DAHA LM ES alia - ~ 2 -] GE BB ee ae = PESHU SE EESBEEDE 6S (NERS Oe es ee a 2 [| (am og oe a = hee Ce maa a a & edo 8 8 oo oS ae mT | {A228 25 oS = 2 oe (Wt heBsas gsi Onbs EB ae) Samm woos 8 Bess Sem | |} fe oe we) = | +S b~ ) ov . 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Perhaps, therefore, the molecule as a whole loses two or three electrons, and its ‘electric field is the more intense. Recombination of this kind must also be easier, the shorter the free path. It will be clear from the foregoing that certain effects occur which are characteristic of a process of initial recom- bination, a process which is « prior? not improbable. The question now arises as to whether any other cause could produce the same effects. When we consider the great increase of current in a complex gas which is caused by an increase in the electric force applied, we cannot but ask whether any of it is due to the production of other ions by those actually made by the particle. Could the electric force aid the freed electron to gather speed sufficient to ionize by collision? Bua ae one BERS SESSeR Rese Bey ee deiteiatasl nln e | Ionisation curves of ethyl chloride at different pressures. Position of standard point } a} Bio} rouse ine of mercury on s0)e10)590 PEREEEH BO LESS OUes see seees ea ope ye Pal SOD Seesaw Sess eeass Cee eaaae i nO ia Fe a [oe a | PECs a Ree Skee eReee ee ar EN npc Ph ot ttt a) Fe a | ie i i fa fa a si a na i a | a | a fo a i i fe | 400 B00 1200 1600 2000 a Distance radium to ionisation chamber. ————> in the following table, where P denotes the pressure, R the range, and I the ionization on an arbitrary scale :— Lthyl Chloride. . R. I, ROE. RCP. 53'8 2 Syl 1140 3260 at 41-0 3°78 860 3260 155 32°35 4°83 666 3220 ayy eA: 6°92 476 3300 tae Air. ace 4°72 546 SY) S00 at2 6°08 432 2620 352 46-9 (oa 340 ENOL) 348 38°8 9:00 283 %540 349 484 Prof. Wilson and Mr. Gold: Electrical Conductivity of These results relate to two gases only ; but so far as they go they show :—(i.) That the range varies inversely as the pres- sure, which result might have ‘been anticipated ; (ii.) that the total number of ions “se free in a gas is independent of the pressure, but is different in different gases. The total ion- ization is greater in ethyl chloride than in air. This is a contrary eect to that which we obtained duri ‘ing our experi- ments on absorption. We were unaware at that time of the enormous force required to saturate the complex gas. Finally, the following | Pep rments may be briefly described:— We have tried the effect of reversing the field on the rela- tion between current and potential, and found a result which was practically negative. We have found a similar result when the a particles were not shot straight across the ion- ization chamber in the direction of the lines of force, but ina slanting direction. These experiments were made in the endeavour to find whether there was any relation between the direction in which electrons were projected and the direction of the applied field. We have also tried to alter the range in air by using different potential gradients, with the ae that it might be possible to obtain ions from an atom traversed by a slower @ particle, if only enough electric force were applied. But a result was the same, no matter whether the force was 20) volts to the em. or 2000 : - and a variation on 2 mm. could hardly have escaped detection. During the progress of this work, one of us (R. D. Klee- man) left Australia for England. We wish to ack with gratitude the assistance of Mr. H. J. Priest, B.Sc., epietine o the observations. XLU. On the Electrical Conductivity a Flames containing Salt Vapours for Rapidly Alternating Currents. By H. A. Witson, M7. A., D.Sc., MSc., Professor of Physics, King’s College, London, Fellow of Trinity College, Cambridge, and E. Goup, B.A., Hutchinson Student, St. John’s College, Cambridge *. HE following paper contains an account of a series of experiments on the electrical conductivity of a Bunsen flame containing various alkali salt vapours, the currents used being alternating ones with frequencies varying from 7-14 x 10' to 6°2 x 10°] per second. The conductivity was measured between two platinum electrodes immersed in the flame, and the variation of the * Communicated by the Physical Society: read November 24, 1905. Flames containing Salt Vapours for Alternating Currents. 485 conductivity with the amount of salt present in the flame and with the nature of the salt was investigated. The variation of the conductivity with the trequency of alter- nation, the maximum electromotive force, and the distance between the electrodes was also examined. The _ results obtained enable a comparison to be made between the con- ductivities of the various alkali salt vapours for alternating currents and their conductivities for steady currents as previously determined * It appears that the relative conductivities for rapidly alternating currents are nearly proportional to the square roots of the corresponding conductivities for steady currents. The flame is found to behave for very rapidly alternating currents more like a dielectric of high specific inductive capacity than like a conducting medium ; and it is shown that this result is in accordance with the ionic theory. The rest of the paper is divided into the following sections :— (1) Description of apparatus used. {2} Variation of the conductivity with the concentration and nature of the salt vapour. (3) Variation of the conductivity with the maximum Feed eanthies sie ‘equency, and the distance between the electrodes. (4) Theory of the conductivity for rapidly alternating currents. (5) Summary of results. (1) Description of Apparatus used. To produce a steady flame containing a definite amount of salt vapour, an apparatus similar to those deseribed in the two papers referred to above was used. The principal parts of the apparatus are shown in fig. 1. A mixtnre of coal-gas and air containing spray of a salt solution was burnt from a glass tube TT tipped with a short thin copper tube 1 cm. in diameter. The mixture was formed in a glass bulb B, from which it passed througli a wide tube AA to the burner. In the bulb and AA the coarser spray settled, and was allowed to escape through the tubes Dand D’ The spray was produced by a * “The Electrical Conductivity and Luminosity of Flames containing Vaporised Salts,’ by A. Smithells, H. M. Dawson, and H. A. W ilson, Phil. Trans. A 193. 1899. ‘On the Electrical Conductivity of Flames containing Salt Vapours,” by HL. A. Wilson, Phil. Trans. A 192. 1899, 486 Prof. Wilson and Mr. Gold: Electrical Conductivity of Gouy sprayer K, worked by compressed air, which was supplied by a rotary blower worked by a EL. motor. The compressed air entered at H, and the salt solution at N. Bie. 1. ow) FF. Flame. 5B. Sprayer-bulb. EE. Electrodes. IX. Sprayer. | SS. Glass tubes. N. Solution-tube and funnel. WW. Wood block. HH". Compressed-air tubes. TY. Flame-tube. M. Gas tube. AA. Wide indiarubber tube. DD’. Solution-overflow tubes. The pressure of the air-supply was indicated by a water- manometer, and was always kept at the same value, about 80 cms. of water. The salt solution was contained ina large funnel, and its level always kept a constant height above the sprayer-nozzle. The amount of gas entering the bulb was measured by a water-meter, and its pressure kept constant by means of a regulator; it did not vary appreciably. The gas and air supplies were so adjusted that a * non- luminous ” flame having a sharply-defined inner cone was obtained. This flame was very steady in appearance, and could be maintained constant for any length of time required. The electrodes used in most of the experiments consisted of two concentric cylinders made of thin platinum, of the following dimensions :— Diameter of outside cylinder. . 2°4 ems. Height gs ae ae | Bt Diameter of inside cylinder EipL owl 2 Height 3 e a One They were supported symmetrically about the axis of the flame at such a height that the inner cone of the flame just reached up to the level of the lower ends of the cylinders. Flames containing Salt Vapours for Alternating Currents. 487 The conductivity between the electrodes was determined by means of a Wheatstone-bridge arrangement, of which the electrodes formed one arm, “and the other ‘three arms consisted of small air-condensers, the capacity of one of which was adjustable. The arrangement is shown in fig. 2. ior 2 Kk. Flame-Electrodes. G. Galvanometer. 1 n C,C,. Air-condensers. » Tesla Coil. rC., Adjustable Air-condenser. J,J,. Leyden jars. D. Detector. S. Spark-gap. Be Cell: I. Induction-coil. An induetion-coil, I, charged up two Leyden-jars, J, Ja, and these discharged ata spark-eap S. The outside coatings of the Jars were connected through the primary of a Tesla coil, T. The primary of this coil consisted of 33 turns wound into a spiral, 29 ems. long and 19:2 cms. in diameter, on a large glass cylinder. The secondar y coil had three turns, and was placed inside the glass cylinder, halfway up it. It was connected to the bridge arrangement at A and B, as shown. An “ electrolytic detector, he aD: was connected to the points M and N of the bridge. Tins dereator consisted of two platinum electrodes dipping into 20 per cent. sulphuric acid. One electrode was a platinum cylinder 3 cms. in diameter and 4 ems. high, while the other was a platinum wire rooo inch in diameter sealed into a glass tube and cut off close to the surface of the glass. The large electrode was contained in a test-tube, which it just fitted, and the glass tube carrying the Aral electrode was supported by a ‘cork fitting the test-tube. The small electrode was just below the surface of the acid at the middle of the tube. The two elec- trodes were connected io a silver-chloride eell B and a 488 Prot. Wilson and Mr. Gold: Electrical Conductivity of moving-coil galvanometer G. The cell B gave about one volt and served to polarize the electrodes. When an alter- nating P.D. was produced between M and N, the detector was depolarized and a current passed through the galvanometer. The deflexion of the galvanometer-coil was read by means of an incandescent lamp and a scale, a current of 10-° ampere giving a deflexion of one scale-division. | The condensers C,, Cy, each consisted of two parallel circular disks 10 ems. in diameter, supported on ebonite rods. The distance between the disks of C, was 0°15 em. and of C, 0°75 em., In most of the experiments. The con- denser UC; consisted of two brass disks 10 cms. in diameter, whose distance apart could be adjusted and measured by means of an accurate micrometer-screw. To determine the conductivity between the flame-electrodes, the rapidly alternating P.D. produced by the Tesla coil was applied at A and B “(fig. 2), and the condenser C3 was ad- justed until the deflexion of the galvanometer was a minimum. On starting the alternating current, the galvanometer de- flexion increased to a maximum alms and then fell off slowly. The alternating current was always kept on for 15 sees. and the maximum deflexion noted, and then atter an interval of 15 secs. the current was turned on again and so on. During the intervals the condenser was adjusted, and the deflexions corresponding toa series of positions of the adjustable condenser-disk were thus obtained. A curve was ~* then drawn on squared paper showing the relation between the galvanometer deflexion and the condenser-screw reading, and so the screw reading for which the deflexion was a minimum was obtained. ‘The observations at each position ot the condenser-disk were repeated several times and the mean taken ; the series of observations was also repeated first in one direction and then in the other, while various intermediate positions were also tried so as to make as certain as possible that the correct relation between the deflexion and the condenser distance was obtained. These precautions were very necessary because the apparatus was sometimes irregular in its action. No great difficulty was experienced in keeping the flame ; sufficiently constant during the experi- ments, but it was not easy to keep the alternating current constant. This was due partly to variations taking place at the spark-gap and partly to irregularity in the action of the induction-coil interrupter. The spark-gap finally adopted consisted of two platinum spheres kept in an atmosphere of hydrogen. In most of the experiments the length of the gap was about 0:2 cm. Flames containing Salt Vapours for Alternating Currents. 489 Several different kinds of interrupters were tried, but finally the ordinary App’s platinum contact-breaker was used. The platinum contacts were always carefully filed smooth before starting an experiment and a 10-inch coil was used with a four-volt battery, the contact-breaker being adjusted so that the coil gave only a short spark when not connected to the Leyden jars. In this way the apparatus was made to work sufficiently steadily to obtain fairly satis- factory observations. The distance between the condenser- ylates corresponding to the minimum galvanometer-deflexion could be obtained within about 5 per cent. of its value. It was only after a long series of attempts extending over nearly a year that the apparatus was got to work well enough to obtain reliable results, and numerous modifications were tried before the form above described was finally adopted. To compare the conductivities due to different salts, the increase in the apparent capacity of the flame-electrodes consequent on introducing each salt was calculated in terms of the capacities of the three condensers. With a bridge arrangement each arm of which is a capacity with negugible self-induction, the condition for a balance is ©,C;=C,C,, a condition independent of the N frequency. It was found that when the ratio = was altered, 1 then C; changed approximately proportionally, so that it appeared justifiable to apply the equation C,C;=C,C,. Let d, be the distance between the plates of the adjustable con- denser at the minimum for the flame free from salt, and d, for the flame containing salt. The capacity of the adjustable , sae : condenser in the first case is Tear + D, where Disa quantity = nearly independent of d, and A the area of each condenser- plate [Clerk Maxwell, ‘ Hlectricity and Magnetism,’ art. 202]. We have therefore Ce Fes + D| = CO. where C, is the apparent capacity of the flame-electrodes with the flame free from salt. Also if C,! is the apparent eapacity with salt in the flame we have A } C = ie } Ub Hd y D) OU Plhul. Mog. 8. 6. Vol. 11. No. 64. April 1906. 2K 490 Prof. Wilson and Mr. Gold: Electrical Conductivity of Hence ie (Z.- z)= C. (CJC) ; so that the change, in the apparent capacity, due to the introduction of the salt is given by the equation CP er s\n iollemeal Oe ele: ee i.) In the experiments we have made, the self-inductions of the arms of the bridge could be neglected i in comparison with the capacities without appreciable error. It was found possible with the bridge arrangement de- scribed to obtain an approximate balance. That is, the minimum galvanometer-current was always small compared with the currents when the adjustable condenser-plate was far from the position which gave the minimum deflexion. This showed that the arm of the bridge containing the flame behaved like a capacity simply, or like a capacity and’ self- induction in series. If the flame had behaved like a capacity and resistance in parallel, then a balance could not have been obtained. The current through the flame with a given maximum P.D. and frequency is proportional to the apparent capacity, so that it is reasonable to regard the apparent capacity as a measure of the conductivity of the flame for the rapidly alternating currents employed. l'o obtain relative values of the apparent capacities, it is. ; 1 therefore sufficient to calculate [= io for each salt solution 9 ay « sprayed. Since the absolute amount of salt in the flame could be only roughly estimated, it was useless to attempt to obtain exact values for the absolute apparent capacities ; so: . . e O that it was unnecessary to know the ratio a exactly. 9 a The value of d,, the minimum position for the flame free: from salt, was About half the value obtained with no flame. 1 : : Consequently — corresponds to twice the capacity of the: dy flame-electrodes with as dielectric. The capacity in this case was 3°6 cms., and : was very nearly } in most of the / 2 experiments described below. Galvanometer Deflexions, Flames containing Salt Vapours for Alternating Currents. 491 (2) Variations of the apparent Capacity with the Concentration and Nature of the Salt Vapour. The salt solutions sprayed were made up with distilled water and pure salts carefully dried. We shall first give a few examples of the curves obtained, showing the relation between the distance apart of the condenser-plates and the galvanometer deflexion, from which curves the position of the minima were deduced. Tig. 3 shows several such eurves. The sharpness of the minimum was usualiy greater 0 1 2 3 tenths of an inch. Distance between plates of Adjustable Condenser. when the conductivity was large and the distance therefore small, than when the converse was the case. The accuracy with which the minimum could be found was consequently nearly the same for large as for small conductivities. During the course of the experiments the ratio of the two condensers, C,, O,, was changed on one or two occasions. When this had been done, some of the observations made before the change were repeated, and the factors required to reduce all the results to the same standard so determined. The following table contains the results obtained, the number of alternations per second being 3:2 x 10°, and d,=3°33 tenths of an inch. Dood 492 Prof. Wilson and Mr. Gold: Electrical Conductivity of | ee ds, | Salt. a ae Gin tenths of ph ile eae an inch). d, dy CSO ke 50 or Oo 12-2 Bonen. Liabe ik) | 0-18 5:26 5 aT Oe 1 | 0 34 2-64 aah ehe ise 0:333 0-48 1-78 PUR ae 0-1 1-10 0°61 | ORCC Ne: O55 0-13 7-40 ieee 255 0-30 3-03 ALi Bi 3 0-26 | 0:59 1-40 Ye. 0-026 | 1-90 0:23 DOM vee AST | 0-22 4-24 ees 96) 97 0-29 B15 igae ee 1°92). 9M 0-41 14 RECO eae 504 ore iee O19 4-96 labs 10 ee0:25 370 agen 1 | 0:50 1-70 KACO ei 100 | 0-062 158 “ir eheae 10 | 0:297 3:07 OL re eas 100 | 0:20 470 RE ese Nike: PO. i), O30) ls 3-03 st ya oe 1 0:50 1:70 NaCl cae 100 0-47 1-83 1G i ae. 102°5 1:3 0:47 | Zz 0 10 20m Fon ao SOM GONE O70) 0) a0 Sons NOONGeapee ee Flames containing Salt Vapours Jor Alternating Currents. 493 — o and the corresponding gq ty strengths of the solutions, are shown graphically: for each salt. ” Fie, 5 shows the steady currents due to an H.M.F. of 0:227 volt, taken from the papers referred to above. In fig. 4 the above values of ao | 30 1) ampere. 20 Current 1 0 ne) 20 GRAMS PER Limoe The amount of salt entering the flame in the present experiments was nearly the same as in the older experiments. ae for cone ds a normal solutions obtained from the curves in fig. 4, and also the steady currents due to 0°227 volt. The following table gives the values of | gl | Steady Current Vara Salt. Oh, WE Salt. i= 1054 ampere). Ratios. sar iaae (x) k') CSO os. | 67 CsCl... 22:2 3 0-70 ZOSeO. ...| Gey) CsNOR 36°6 6:2 1:03 #Rb,CO, ...) 3°7 RbNO,,. 25-9 1:37 RbCl... 32 TROON, Anos 11:3 BB) 1:05 KACO)... 5s, PON) PEE COL... 11-2 1:15 1 (O} IR ee 26 ICON aaa 9°75 | 22, 0:92 The fifth column contains the ratios of the numbers expressing the conductivities for steady currents to the values of Pass In the previous work the conductivities of q ay cesium and rubidium carbonates were not measured: so the values for nitrates are given, since the conductivities of all oxysalts of the same metal were found to be nearly equal for 494 Prof. Wilson and Mr. Gold: Electrical Conductivity of steady currents. It will be seen that, roughly speaking, the relative conductivity for steady currents varies in a similar way to the conductivity for rapidly alternating currents as 1 aig represented by a ae The last column contains the square root of the con- e e . e 1 ductivity for steady currents divided by ino. The Le 1 numbers in this column do not vary much, showing that the conductivity for rapidly alternating currents varies, roughly speaking, as the square root of the conductivity for steady currents. The conductivities of KCl and RbCl were found to vary nearly as the square root of the concentration in the case of steady currents ; so that we should expect them to vary as the fourth root of the concentration for rapidly alternating currents. The following table showsthat this is nearly the case. Grams whe of | ea Salt. per litre. d, a, | kf C. a Oe at ie Cen: Rabe Sf ain Ram a A ll PbO 48° oa Mod Ye AD ieee | O65 bp aecas 7 | IN | 12 oe ey ale 181 Kel. eee 100 | 4°70 1-49 ee | 908 SOS wb oly CAS m se Se 10a lege er gle 170 4 Considering the large variation in C the values of k/,/C are surprisingly constant for these two salts. The following table shows the relative variation of the conductivity CsCl for steady and alternating currents. The numbers are taken from figs. 4 and 5. ; oa paren fee (rae per htre. | (i) | (z') eames |) we. Do eel ee 26 0-70 tage 15: jug are 195 0-69 Sante 10 Sota: Ge 0°68 2A ates 5 Erect ate WY" 7-4 0-66 eG sa 1 26 3-0 0:67 Flames containing Salt Vapours for Alternating Currents. 495 . jee % It is clear from these results that Aid: varles nearly as dg 1 é the square root of the steady current due to a small P.D. (3) The Variation of the Conductivity with the Potential- Difference and Nunber of Alternations per Second. The variation of the conductivity of the flame as measured by : _ = with the maximum P.D. applied to the bridge ee arrangement, was effected by varying the length of the spark- gap in the primary circuit of the Tesla coil. The spark passed between two platinum spheres in air at the ordinary pressure. The following table gives the results obtained when spraying a solution of CsCl containing one gram per litre : | | Spark- PD: ae aae length. (E.S. Units dg. | dy Gita ky /P.D at gap.) | (A). 0:0055 ems.| 260 (25) a eos 655 VOL. ., 36 0°42 | 2:08 3°95 Cte’. 4-7 0°43 | 2:03 4-4 0-028 _,, 6-4 045 0) = G78 et 0044, 88 050) | 170 TO | 0°10 : 16 0°53 | 1:59 63 | 0:20 ,, 27°8 We ORD at Say 72 | | a No Be ies . eae lh The last column contains the products of ha and the de a square root of the corresponding potential-difference as estimated from the spark-length in the primary cireuit of the Tesla coil. The numbers in this column vary between 4 and 7, while the P.D. varies by a factor of 11. Taking into account the roughness of the method used to estimate the P.D. and the large change made in it, we may conclude that a= probably varies approximately inversely as the a ay square root of the maximum P.D. applied. The effect of varying the number of alternations per second was tried by altering the capacity in the primary circuit of the Tesla coil. A solution containing one gram of CsCl per litre was sprayed. The following table gives the results obtained :— 496 Prof. Wilson and Mr. Gold: Electrical Conductivity of | Capacity. | : Self- | Alternations | a ie i | : nduction. | per second. 2 ded 33000 cms. | 136500 cms.) 714x10' | 04 | 21 6400 NY, Sas aee Vian Wt eae 1600; | : | 324x10° | 084 2-6 | 150): yy i | 10°8 x 105 | 0300 3:0 | 150 ,, 4100ems.| 62 x10° | 0°30 50 ae It will be seen that the value of : ~ 2 varies as the 2 number of alternations per second is changed. Untor- tunately it was not found possible to obtain the variation of d, with the frequency very exactly; and all that can be said is that changing the frequency from 7:14x10* to 6°2xX10° per second does not change a by more than 2 ay 25 per cent. of its mean value. es varies as n”, where 7 is the Gs Gy frequency, then the results just given show that z lies between +0°05 and —0°05. For a pure capacity z=0, and for a pure self-induction x=—1; so that it appears that the flame behaves nearly like a pure capacity. That it does not include much con- ductivity in parallel with the capacity is shown by the fact that it could be nearly balanced by three condensers. In the section below, on the theory of conductivity, it is shown that these conclusions from the experiments might have been anticipated. To obtain the apparent specific inductive capacity of a salt vapour, it is only necessary to multiply the numbers for i da apparent specific inductive capacities so obtained vary from about 100 for the strongest solution of K,CO; sprayed to about 4 for the solution of LiCl *. Some experiments were made to find out how the con- ductivity varied with the distance between the electrodes. If we suppose that 7 given above by 2d,=6°66 and add on unity. The * These values of the apparent specific inductive capacity have of course no relation to the true specific inductive capacity, which must be nearly unity. Oe ee eee _—3SO ee Flames containing Salt Vapours for Alternating Currents. 497 Two parallel vertical platinum disks each 1:5 cms. in diameter were used, and it was found that La, was in- dependent of the distance between them when this was less than 3 or 4 millimetres. Nig: oe , When they were 10 millimetres apart alee was about CesT double its value between 0 and 4 mms. This increase in the apparent capacity is no doubt due to the fact that the cross- section of flame acted on by the P.D.is greater when the distance between the electrodes is comparable with their diameter. : opel We may therefore conclude that Fg would be in- g dependent of the distance between the electrodes if they were very large. This is in agreement with the results for constant P.D.’s, for which the current is independent of the distance between the electrodes when they are near together. (4) Theory of the Conductivity of Ionized Gases for rapidly alternating Currents. It will be convenient now to describe an approximate theory of the conductivity of ionized gases for rapidly alternating currents—a theory which affords an explanation of the experimental results obtained in this investigation. Suppose a large parallel plate-condenser filled with a uniformly ionized gas, and let the distance between the plates be D cms. Let the potential-ditterence between the plates be given by the formula V=V sin pé, and let the number of positive or negative ions per c.c. be n, each ion carrying a charge +e. In a Bunsen flame the cms. — for one volt Cc. velocity of the negative ions is about 1000 per em., while the velocity of the positive ions under the same potential gradient is only about 60 = Moreover, the mass of the positive ions is probably very large com- pared with that of the negative ions. Consequently, in a rapidly alternating electric field the amplitude of vibration of the negative ions will be large compared with that of the positive ions. As a first approximation, therefore, we shall assume that the positive ions do not move at all, so that all the current is carried by the negative ions. We shall also suppose that all the negative ions move in the same way with the same velocity, so that the number of negative per e.c. 498 Prof. Wilson and Mr. Gold: Electrical Conductivity of remains 2 except within a distance d of each electrode, d being twice the amplitude of vibration of the negative ions. It is easy to see that on these assumptions the negative ions will practically all be contained in a slab of thickness D—d, which will vibrate between the plates so as just not to touch either of them. For if a new negative ion is formed outside the slab, it will almost immediately strike the electrode near it ; whereas a new negative ion formed in the slab cannot reach either electrode except by diffusion, which we shall neglect. Thus we may regard the whole space between the plates as filled with positive electricity of density +7e, and the vibrating slab of thickness D—d as containing also negative electricity of density —ne. Thus inside the slab the total density is zero and outside is + ne. Let X denote the electric intensity between the plates at a distance x from one of them. Then, inside the slab =0, and outside oN Arne. AL Let A and B be the two plates, and let the slab be repre- sented by the space between the ino dotted lines Shi dhe AB=D; 9s) D cooviee An 1 B=t,, and suppose ane potential of A kept zero while that of B=V. Let the rise of potential | in AE be V,, in EF be V3, and in t | ee FB be V>, In EF Das teh | so de 0), ae X is constant. Let its value be Xj. Then Wa = X,(D —i), where d=t,+¢,. In AE we have av Ae wee where p=ie. From this we get aA =—4A7pv+C and V=—27pc?+Cr+D, where C and D are constants to be determined. When c=0 Vee) and when «=t, Vv ae — Arpt, + C= s Xa Hence = 2mpt)?— Xof Flames containing Salt Vapours jor Alternating Currents. 499 In the same way in FB we have V=—27p2?+C'a4 D’. When w= D—t, ——— — Xp and VN 3 so that we get for V at v=D, V=—X,D+27p(t’?—12,”). Now ¢,+t,=d, so that Vi SGD empd(2t;—d). 2. 3s CL) dt, dt 5) where A is a constant representing the viscous resistance to motion with unit velocity. Let m be the mass of a negative ion; then its equation of motion is The force acting on a negative ion is —X,e—A it —Kye=moet+As’. Sere ah ee CZ)) The current-density inside the slab is given by the equation Pat "Am de? where K is the specific inductive capacity of the medium between the plates in the absence of ions. Thus K is unity, and — dt 1 AXo a? ae WEE EN Si aes Shh) Now in a flame containing a salt vapour the fall of potential nearly all takes place near the electrodes, so that X, is probably very small, even when rapidly alternating : : 1 dX currents are used. Consequently, since p is large, — —° Aq dt E ° . ° dt, - may be neglected in comparison with — Pa Hence (38) ; } dt Oe ee becomes amr: approximately. Substituting in (1) the value of Xp got from (2) we get F mart, A dt V=Vosinpt=D(" S344 oh) + mpd (2). This gives mi at; AD ah ede’ e dé dt at Vo pcos pt = + dorpd 900 Prof. Wilson and Mr. Gold: Electrical Conductivity of Br it Oh Se eres p mD d%i AD di Sa Den Saas et eae Tdi. er The solution of this equation is —— sin ae . ar ree Lraey fa aye ee. pend Pe where ii os Arde ay, Tana —— lita PAD: V = Ve cin pt is Filial to a condenser of capa- city U, the current is given by the equation i=CVpq p cos pé. For the flame, if A and m are both negligible (5) becomes V,p cos pt Aad S= afl per unit area. Now i And 2 is the amplitude of vibration of the negative ions so that dp must be the amount of electricity flowing during a half- vibration. : .) Let i= — = Soria) p= so that the apparent capacity is . ; Sin pt. Then we have, integrating from 0 to 7, ae 27rp T Te ond or d= so that the apparent capacity per unit area is de ee And — S7Vo. If p=0 this makes the capacity gh whereas it should be aX AnD This is due to the omission of —— = ae hich would no be negligible if p were very small. If, however, we take / plsnV, to be not the apparent cas bal the in- crease in the apparent capacity due to the presence of. the ions, then no error will be made even if p be small, The quantity ana which has been determined is pro- ay portional, as we have seen, to the increase in the apparent Flames containing Salt Vapours for Alternating Currents. 501 capacity when salt is ie to the flame. In what follows we shall speak of 4 —7 as the apparent capacity. a) Wy Thus we should expect the apparent capacity per unit area to vary as the square root of the number of ions per c.c., and inversely as the square root of the maximum P.D. applied, but to be independent of the distance between the electrodes. The experimental results are in surprisingly good agreement with these conclusions. Thus we have seen that the : apparent capacity is nearly independent of the number of alternations per sec., and varies as the square root of the steady current conductivity. For small ‘E.M.F.’s the conductiv ity for steady currents is proportional to the number of ions per ¢.¢. and to the velocity of the ions. But it has been shown * that all alkali-salts in flames give ions having the same velocity, so that the conductivity for steady currents should vary nearly as the number of ions per c.c. present. Hence the observed apparent capacity varies nearly as the square root of the number of ions present. The apparent capacity was also independent of the distance between the electrodes, provided this was small compared with their diameters. Further, we have seen that the apparent capacity varies roughly ‘inversely as the square root of the maximum P.D., measured by the length of the spark-gap in the primary coil of the Tesla transformer. It appears, therefore, that the expression 4/p/87V, does represent approximately the ob- served variations of the apparent capacity of the electrodes in the flame containing salt vapour. This expression has been obtained by neglecting the mass of the ions and the resistance to their motion through the flame-gases, so that it appears that the amount of alternating eurrent through the flame is determined merely by the density of the layer of positive charge left in the gas near the electrodes when the negative ions move under the action of the applied field. If a steady P.D. V is applied to two electrodes immersed in an ionized gas, and if the positive ions cannot move, it is easy to see that a current will only pass for the short time required for the accumulation of positive charge near the negative electrode to become sufficient to make the electric force near the positive electrode zero. Thus the two electrodes will behave like a condenser when the P.D.is applied. When a rapidly alternating P.D.is applied it is easy to see that even if the positive ions can move, provided their velocity is small * HH. A, Wilson, Phil. Trans. A. 1899. 902 Prof. Wilson and Mr. Gold: Electrical Conductivity of compared with that of the negative ions, the arrangement will behave like a condenser if the number of ions per ce. 1s very large and the mass of the negative ions very small. Denoting the apparent capacity ie unit area by C, we ae ves Ve S7V, => where K is the apparent specific inductive capacity. Con- VAIS? sequently p = Dar “D 5-7» Lhe length of the spark-gap used in the experiments on the variation of the apparent capacity with the concentration and nature of the salt was about 2 mms. in hydrogen gas at atmospheric pressure. The Tesla coil had 33 turns in its primary coil and 3 turns in its secondary, so that V, was about 400 volts or 1:2 ES. units. D was 0°6 ems., so that for the strongest K,CO; solution sprayed, for which K = 100 (p. 496), we have 1:2 x 10000 — ox Fx 0:62 The charge on one ion is 3x107'° E.S. units, so that the number of ions per ¢.c. was 5400 Doel at! The amount of salt entering the flame was determined by finding the loss of weight of a bead of sodium-chloride placed in an equal Bunsen flame, so that the light emitted by this flame was equal to that emitted by the flame when a solution of NaCl containing 10 grams per litre was sprayed. In this way it was tound that 0°53 milligram entered the flame per minute. Consequently the amount of K,CO; entering the flame per minute with the strongest solution was 5°3 milli- grams. ‘The velocity of the flame-gases was about 200 ems. per second, and the diameter of the flame about 3 ems., so that the amount of salt per c.c. in the flame was about IS, 200 x m(1°5)2 x 60 Hence, taking the mass of an atom of hydrogen as 10-4 gram, the number of salt molecules per c.c. was about 1 LOR ae wy. eRe Poe ee It thus appears that about one molecule in 30 molecules of K,COs; was ionized in the flame. For most of the other salt solutions sprayed the proportion of the molecules ionized in the flame comes out less than one in 30. 5400 E.S. units. = ihe LO: — if XO mullisram. Flames containing Salt Vapours for Alternating Currents. 503 In the paper on the conductivity of flames for steady currents, referred to above, numbers are given which are proportional to the molecular conductivity of all the salts tried, so that it is not necessary here to discuss further the ~ variation of the conductivity with the nature and concen- tration of the salt vapour. Let ¢ be the number of ions produced per c.c. per sec. in the flame and n the number present pere.c. Then qg=2«n’, where a isa constant which has been shown by Langevin to be equal tO. f dmre(ky +h), where 7 is a proper fraction, and 4, kz are the ionic velocities due to unit electric intensity. For the ems. 3 flame we have k,=1000 ae for one volt per cm., or cA cms x 10° - “for one E.S. unit of electric intensity. Hence ie f.3X10- x3 x 10°=11 x 10-8F. Now for the strongest K,CO solution sprayed x= 18 x 10”, hence G=y Illa x ese X N02 = 4 x 10 The number of salt molecules per c.c. is about 5x 10"; so that it appears that each salt molecule is ionized and re- combimes about 10°/ times per second. The value of 7 under ordinary conditions is about 0°2. Probably in the flame it is oe say O'l. Taking the temperature of the flame-gases to be 2000° C., we get “for the number of collisions made by a salt molecule per ‘second in the flame rather less than 5 x 10°. So it appears that the K,CO 3 molecules are ionized once for every 5 collisions with another molecule. It is therefore probable that the cause of the ionization of salt vapours in flames is the shock of molecular collision. The current which could be carried by the 5x 10 ions produced per ¢.c. is about 60 amperes, which is enormously greater than the observed currents per ¢.c. of fame between the electrodes. This result « agrees with the conclusion * that the observed steady currents through flames containing salt vapours are very far from the saturation value. Since each salt molecule is ionized many times per second, the salt would all be carried to the electrodes as ions if the current were sufficiently great. If we suppose that the electrodes absorb the ions which reach them, then the maximum possible current would be equal to that required to electrolyse the same amount of salt ina solution. ‘This has been previously found to be the case for alkali salts vaporised in a current of air ft. A. Wilson, Phil. Mag. October 1905, * + H. A. Wilson, Phil. Mac. Aueust 1902 d04 The Electrical Conductivity of Flames. Equation (5) may be written as —pepVo sin (pt—a) i (mDp? —4a dep)? + A? D? b It is easy to show that the term A*D? is negligible compared with (mDp?—4mdep)?. We have D=0°6 cm. and Xe=Av, where X=electric intensity and v=velocity of negative ions duetoX. IfX=1 ES. unit, v=3x 10° — so that D2, A? scc. 1s equal to Oeoae ed) 6 LS Oe my in (mDp?—4mdep)’ the term 4adep is about 6 x 107° for e=3 107), and 4dp isabout 20. Also when p is say 10°, mDyp? must be small compared with 47dep, because, as we have seen, changing p does not much aftect the apparent capacity. Hence (mDp?—4mdep)?’ is of the order 10-*. The expression for 7 becomes therefore on putting a= — 90°, _ pepV,,cos pt — dadep—mDp =X ee Hence the apparent capacity per unit area is cs aE i 4a dep—mDp*" Therefore if Cy, and C, are values of C corresponding to values 7, Po of p, we have ~ 4idp — = De p Cr 7 ut — fase 4adp 5 Dps C; L il Dies pai 2 — i — =), ae aah oa Also approximately p=S8a7V,)C* when p is small enough for mDp? to be small compared with 47 dep, so that cust Diop) popes 2 cone s7Vo oO =) xi If C,inearly =C, we can put C?=C,C,, and get ele SOP ein, m 87V,(C,—C,) Thus if the variation of C with p were known with sufficient e 2 2 e e ad e accuracy, — for the negative ions could be calculated. It is m hoped that further experiments will enable this to be done for the negative ions of different salts. ee aL The Electrical Conductivity of Metallic Ovides. = 505 Summary of Results. (1) For rapidly alternating currents a flame containing an alkali-salt vapour behaves like an insulating medium having a high specific inductive capacity. (2) The conductivity of different alkali-salt vapours in a flame for rapidly alternating currents as measured by the apparent capacity of platinum electrodes immersed in the flame varies as the square root of the conductivity of the same salt vapours for steady currents. This result confirms the view that the negative ions from all salts have the same velocity. (3) The apparent capacity varies nearly inversely as the square root of the maximum applied P.D. (4) The apparent capacity is nearly independent of the number of alternations per second. (5) The apparent capacity is nearly independent of the distance between the electrodes. (6) The results (1) to (5) are in agreement with the ionic theory of the conductivity of the flame for rapidly alternating currents when the velocity of the positive ions and the inertia and viscous resistance to the motion of the negative ions are neglected in comparison with the effects due to the number of ions per ¢.c. (7) The apparent capacity per sq. cm. area of the electrodes is equal, according to the theory just mentioned, to a/ ne[BxV o, where n is the number of sos ions per ¢.c., e the charge on one ion, and V, the maximum applied P.D: (3) Not more Jud one molecule in 30 salt molecules is ionized at any instant in the flame, but each molecule is probably ionized and recombines several million times per second. (9) The steady currents observed through salt vapours in flames are very far from the maximum possible currents cor- responding to the number of ions produced per second. XUIUI. The Electrical Conductivity of Metallic Oxides. By Ff. Horton, D.Sc., B.A., Pellow of St. John’s College, Cambridge *. Gi hae theory of electrolytic dissociation has furnished a simple explanation of conductivity, in electrolytes, by assuming that the current is carried asa stream of electric charges “by the ions into which a certain proportion of the molecules of an electrolyte are dissociated. Conduction in *k Communicated by Prof. J. J. Thomson, Phil. Mag. 8. 6. Vol. 11. No. 64. April 1906. 21 506 Dr. F. Horton on the Electrical metals is not due to this cause, for we cannot conceive that a molecule of an elementary substance could be split up into two dissimilar atoms, or groups of atoms, having opposite charges ; and experiments have shown that the conduction of electricity through metals is not accompanied by any detectable transportation of matter *. A theory of metallic conduction not involving the trans- portation of matter in the atomic state has been put forward by Professor Thomson+. On this theory metallic conductors owe their conductivity to the dissociation of the atoms of the metal, the products of dissociation arising from a single atom being an extremely small negatively charged corpuscle and the remaining larger portion of the atom which bears an equal positive charge. These negative corpuscles are identically the same in mass and charge from whatever atom they are produced, and they can move about freely in the mass of the metal. When an electric force acts upon them, they travel in a direction opposite to that of the force, and this convection of charges constitutes the electric current. The conductivity of compound bodies may belong to either the metallic or the electrolytic class. The distinction between these two classes is generally based on the sign of the tem- perature coefficient of the conductivity of the conductor in question. If the conductivity decreases with rise of tempera- ture, the conduction is taken to be metallic; if it increases, the conduction is considered to be electrolytic. This, how- ever, cannot be taken as an infallible rule, for, although the conductivity of liquid electrolytes generally increases with the temperature, a series of electrolytic liquids is known which behave in the opposite manner. Such acids as sulphuric and phosphoric, the hydrolytic dissociation of which takes plage exothermically, belong to this series. In these cases an increase of temperature decreases the electro- lytic dissociation, causing a diminution in the conductivity which more than compensates for the increased mobility of the ions. On the other hand, the conductivity of all the metalloids, which cannot be electrolytic on account of the elementary nature of the conductors, increases with rise of temperature, the increase being probably due to changes in the crystalline structure when heated f. It has long been known that many substances which, at the ordinary temperature of the laboratory, may be regarded * KE. Riecke, Phys. Zeitschr. 11. p. 639 (1901). + J. J. Thomson, Rapports présentés au Congrés International de Physique, vol. iii. p. 138 (Paris, 1900). ft Siemens, Pogg. Ann. clix. p. 117 (1876). — a P inal — a ee ee Conductivity of Metallic Oxides. 507 as non-conductors, become conducting when their tempera- ture is raised. The conductivity of such substances was studied by Faraday *, who found that silver sulphide, lead fluoride, corrosive sublimate, and periodide of mercury, all increase very rapidly in conductivity with rise of tempera- ture. Since the time of Faraday this subject has been investigated by many experimenters. It has recently received special attention from Nernst+, who has given it practical application in the Nernst filaments for incandescent lamps. The conduction of electricity through these filaments is considered by Nernst to be electrolytic, but the recent experiments of Streintz{ and of Guinchant$ have shown that a large number of substances which become conducting at high temperatures give no trace of electrolysis. Jhe conduction in these cases must theretore be metallic, and on Professor Thomson’s theory due to the negatively charged corpuscles liberated from the atoms. If this sup- position be true, it follows that either the number of free cor- puscles within these substances, or the mean free path of these corpuscles, increases very rapidly with rise of temperature. Now Wehnelt || has studied the emission of corpuscles from the alkaline earths when they are raised to high temperatures, and has found that the rate of emission increases very rapidly with the temperature, and at 1500° C. is quite enormous. At these high temperatures, therefore, there must be a large number of free corpuscles inside the substance, which probably owes its conductivity to their presence. Such an explanation would account for the great increase in conductivity with rise of temperature observed by Faraday, Streintz, and others, and explain the loss of insulating power of quartz and other non-conductors when raised to high temperatures. The object of the present research was to investigate the variation of electrical conductivity of solid metallic com- pounds with change of temperature, and to ascertain whether the conduction is carried on electrolytically or metallically. For this purpose the metallic oxides seemed to be the most * Faraday, Exp. Res. vol. i. § 482 (1833), § 1840 (1888). t Nernst, Zertschr. Elektrochem. vi. p. 41 (1899); Gessel. Wess. Gottingen, Nachr. Math. - Phys. p. 828 (1900). t Streintz, Ann. d. Physik, ii. p. 1 (1900); Akad. Wiss. Wien. Sitz.- Ber, ii. 2a, p. 845 (1902). § J. Guinchant, Comptes Rendus, exxxiv. IN 1224 (1902). || Wehnelt, Ann. d. Phystk, xiv. p. 425 (1904); Phil. Mag. [6] vol. x. p- 80 (1905). 2 L 2 508 Dr. F. Horton on the Electrical suitable compounds, especially as the emission of corpuscles from a Jarge number of metallic oxides had been studied a Wehnelt. The oxides were used in the form of slabs about 1 sq. em. in area, and from 1 to 2 mms. in thickness. A slab of oxide was placed between two stout platinum plates which were pressed firmly together by means of two porcelain rods 1 cm. in diameter. These rods hada small hole along their axis, and platinum wires from the electrodes passed through them and served to connect to the Wheatstone bridge used for measuring the resistance. The surfaces of the electrodes and of the oxide in contact with them were ground or filed plane so as to make good electrical contact all over. Two types of electric heatin o-furnace were used in these experiments. With the more easily fusible oxides it was necessary to watch the oxide to see that the temperature was not raised above the melting-point. The furnace used to heat these oxides consisted of an iron box lined with asbestos cardboard. The porcelain rods passed vertically through the box, the slab of oxide being in the middle. A strip of platinum foil, 5 cms. wide, passed above and below the oxide, and this was heated by an alternating current from a transformer. The oxide could be seen by opening a small door in the side of the furnace. Ovxides such as lime, magnesia, and quartz, of high melting-point, were heated in an electric furnace consisting of a coil of No.-20 BaWees platinum wire wrapped round a porcelain tube 2°5 cms. in diameter and 13 cms. long. This was placed inside a larger earthenware tube and the space between filled with magnesia. This furnace is shown in section in fig. 1. With both forms of furnace the temperature of the oxide was obtained by means of a thermocouple of wires of platinum and an alloy of platinum with 10 per cent. of rhodium, the junction being close to the oxide. In order to standardize the thermocouple the melting-point of potassium sulphate was taken as the fixed point, and the galvanometer deflexion corresponding to this temperature (1066° C.) was found. The platinum temperatures given by the galvanometer-readings were corrected to degrees centi- grade by means of the curve given by Professor Callendar * The galvanometer deflexion corresponding to the melting- point of platinum was also found and used for standardizing readings up to 1700° C. * Callendar, Phil. Mag. vol. xlvii. p. 519. Conductivity of Metallic Oxides. 509 In some cases the resistance of the oxide was obtained by measuring the current passing through it under a known Vie. 1.—Electric furnace. B CLL, Vie LLM B A A are the leads to the heating-coil; B B are the platinum wires from the electrodes ; C C the thermocouple wires. E.M.F. by means of a delicate d’Arsonval galvanometer ; but more generally the resistance was measured directly by a 510 Dr. F. Horton on the Electrical Wheaistone bridge. With some of the oxides electrolysis was found to accompany the conduction, and with these another method had to be used for obtaining the resistance. Kohlrausch’s method of using an alternating current and a telephone indicator does not work well for resistances over 10,000 ohms, and the resistance to be measured was usually greater than this value. The method of using a rotating commutator to reverse the battery and galvanometer circuits together many times a second requires an exceedingly well- made commutator. Unfortunately the one made for the researches which Mr. Fitzpatrick carried out in this laboratory was in use at the time and not available for this work. Other commutators were tried, but none worked satisfactorily. The method finally adopted was not of great accuracy, but was sufficiently accurate for the object of the present research. It consisted in having the galvanometer per- manently connected up to the Wheatstone bridge without a key in circuit, and noticing the direction of its first kick on momentarily closing the battery circuit. The resistance was connected to a reversing key which was reversed after each “make” of the battery circuit, so that successive momentary currents were sent in opposite directions through the electrolyte. This method worked better than I had expected, and, by taking care not to let a continuous current pass through the oxide, results in very good agreement were obtained. There was sometimes a small thermoelectric force developed on heating the oxide, and consequently the resistance in one direction was slightly greater than in the opposite direction. The mean of these resistances was always taken, and the circuit through the oxide was kept open except just when observations were being made. The voltage used on the battery circuit varied, according to the resistance to be measured, from 1 to 500 volts. The oxides experimented on were lime, baryta, magnesia, bismuth trioxide, plumbic oxide, cupric oxide, sodium peroxide, and quartz. The results obtained will now be given. lume. The piece of lime used was *85 cm. square by :70 mm. thick. Its resistance at the temperature of the laboratory was greater than 100 megohms. The following table contains the resistance, and the conductivity calculated therefrom, at different temperatures :— Se ee eee Conductivity of Metallic Oxides. 51L { | Temperature Resistance in | Conductivity in | | Centigrade. ohms. mhos. | | ey age Pee ry | 763 70,000,000 138 x10 | 879 9,125,000 1:06 x10 - 930 4,175,000 B38) 10) Sai iene: 2,000,000 | 485 x10 | 1105 6v0,000 | 162 x10 | | i175 245,500 | 396 x10. | | 1235 104,100 | 9:38 x10! | 1304 35,100 207 x10 | 1370 DSS aes) Seal tar, : 1448 1 1 90) 101) | | 1466 91:0 | 1-:035x10° | Diagram I.—Showing increase of conductivity of Lime with temperature. CONDUCTIINTY. 700° 800° + 900° 1000" 00° 1200° 1300° |400° 1500° TEMPERATURE CENTIGRADE. The relation between the conductivity and the temperature is shown graphically in diagram I. The ordinates give the value of the conductivity, “the abscissee being temperatures in degrees centigrade. In the first curve, starting from the left, each unit of the ordinates represents 10-° mho; in the 43 512 Dr. F. Horton on the Electrical succeeding curves the value of the ordinate is successively multiplied by ten, so that in the second curve each unit is equal to 10-* mho, in the third 10-® mho, in the fourth 10-% mho, and in the last 10-4 mho. These curves are exactly similar to those obtained by Wehnelt * for the relation between the number of corpuscles given out by lime (measured by the saturation current) and the temperature. Wehnelt found that the number of corpuscles emitted from glowing lime obeyed the law found by O. W. Richardson t and by H. A. Wilson ¢ to hold _ the negative corpuscles from hot platinum, viz., »=A6%¢ 6 where n is the number of corpuscles, @ the absolute temperature, and A and 6 are constants. If the conduction is carried on by the corpuscles set free in the interior of the oxide at high temperatures, we might expect a similar relation to hold between the conductivity and the temperature. Diagram Ii. 4A Oe rere ee BO ® SCALE OF L0G yC- 3 L0G,,0 au 2 ) 0005 *0007 “0009 CALE OF xs In order to ve this we may denote the conductivity by e, and write the equation in the form logy c—$ logy) @=logy, A—*434b 6-1, so that on plotting the values of log,e—4 logy) @ against * Wehnelt, dan. d. Phys. xiv. p. 425 (1904). + O. W. Richardson. Phil. Trans. A. vol. cci. p- 497 (1908). { Hl. A. Wilson, Phil. Trans. A. vol. ccii. p. 2438 (125). Conductivity of Metallic Ovides. aii those of 6—! we ought to obtaina straight line. In diagram LI. the ordinates are the values of log) c—4 logy, @, the abscisse being the corresponding values of g-!, It will be seen that seven points representing the largest values of @—! (7. e. the lowest temperatures) lie very nearly on a straight line. The fact that the points above 1300° C. do not lie on this line is probably due to disturbing causes which affect the resistance to be measured. At these high tempera- tures, the lime would probably have some chemical action on the platinum electrodes, causing, possibly, a decrease in the contact resistances. It was, for instance, always found that the lime was fixed to the electrodes after it had been strongly heated, but not when lower temperatures were used. This explanation would account for the fact that the value found for the conductivity at high temperatures was greater than it should be on the present theory. Diagram Il. may therefore be taken as showing that the increase of con- ductivity of lime with temperature follows the same law as the emission of corpuscles from its surface. When the above series of experiments had been completed, tests were made to see if any polarization could be datected which would show that some part of the conduction through lime was electrolytic. The lme was connected to a battery for a few seconds anda current allowed to pass through it. The battery was then cut out and a delicate d’Arsonval galvanometer substituted. This indicated a small polarization current in the opposite direction to the original current and dying away logarithmically with the time. The polarization current when the lime was at 800° C. was very small, but it increased as the temperature was raised, the increase being no doubt due to the decrease in the resistance of the lime. A battery of 100 volts was next connected up in series with the slab of lime and galvanometer, the latter being shunted for measuring larger currents. The current through the oe meter oradually decreased, and, if the E.M.F. was left oa for a few seconds and the key connected to the lime reversed, a larger deflexion in the opposite direction was obtained which also decreased with time. But if the current was allowed to pass for several minutes in one direction through the lime, the galvanometer deflexion decreased to about a tenth of its original value, and, on reversing the key, the deflexion obtained in the opposite direction was only slightly greater than the small value just before reversing. This increased with time slowly at first, but soon very “rapidly. and then more slowly again as a maximum deflexion was reached. the current then decreased with time, at a gradually 214 Dr. EF. Horton on the Electrical decreasing rate until about the same magnitude as the direct current just before reversing. ‘This behaviour may be explained by supposing that a ‘Jay er of oxygen is formed by electrolysis against the anode, and that this increases the resistance of the circuit in addition to causing the polarization H.M.F, When the circuit is completed for only a short time before the key connected to the lime is reversed, very little gas can have collected at the anode, and this gives a back- H.M.F., but does not greatly increase the resistance. On rever sing, therefore, a large deflexion in the opposite direction is obtained. On the other hand, when time is allowed for much gas to collect at the anode, then, on reversing, the deflexion in the opposite direction is slightly larger than the small value just before reversing, owing to the back-E.M.F. This increases as the oxygen recombines with the calcium which is now formed at that electrode, and the oxygen which is being formed at what is now the anode combines with the calcium already liberated there by the direct current. Thus the resistance @ gradually decreases until all the collected gas is used up; a maximum current then passes and the de- flexion afterwards decreases as oxygen collects against the other electrode. These experimeuts were carried out at about 1000° CC. At higher temperatures the current did not die away to so small a value; and on reversing the key connected to the lime a large deflexion in the opposite direction was obtained which gradually died away, and did not increase even when the direct current had been flowing for a long time. It is pro- bable that this is due to the oxygen escaping more easily from the electrode at the higher temperature and not forming a layer over the anode, and thus increasing the resistance of the circuit as it did in the experiments at 100° €. Several specimens of lime were experimented on and gave results practically identical with those described above, both as regards the variation of conductivity with temperature and the electrolytic effects of the current. It thus appears that the conduction of electricity through heated lime is carried on partly by electrolytic ions as in a liquid electrolyte ; but the fact that the increase of conductivity with temperature corresponds, so closely, with the increase in the rate of emission of electrons, seems to indicate that most of the con- duction is metallic. AMlagnesia. A piece of magnesia °84 cm.x°83 cm. and ‘090 cm. thick was used. ‘The resistance of this at the temperature of the laboratory was too large to be measured by the method Conductivity of Metallic Oxides. used, being over 100 megohms. The values of the resistance at higher temperatures and also of the conductivity calculated from the resistance and dimensions of the slab are given in the following table. ee eee Temperature | Resistance in | Conductivity in Centigrade. ohms. mhos. 471 35,000,000 369x107? 564 | 8,000,000 4-34 1078 630 800,000 1:61 x 10-7 743 | 215,000 6:00 x 1077 828 | 88,000 1-46 10-6 933 | 31,000 416x107 70 | 22.300 579 x 10-8 1055 12,450 1:04 10-5 1191 4,900 2-63 x 107° 1204 6,800 190x107? 1280 12,900 100x107? 1341 | 290,000 445x107! Diagram II]—Showing increase of conductivity of MgO with temperature. CONDUCTIVITY. In diagram ILI. the values of the conductivity given in the above table are plotted against the corresponding | 500° TE MPERE TURE 1000° CENTIGRA LE. ~~ 1500° 516 Dr. F. Horton on the Electrical temperatures. The curves obtained are similar to those given by lime. It will be observed, both from the table and diagram, that after 1200° C. the conductivity suddenly altered its behaviour, and began to decrease with increasing temperature. At these co) temperatures the resistance was not constant, but increased as time went on as well as with increasing temperature. if is, however, well known that the er ystalline structure of magnesia alters when heated to high temperatures, the alter ation being accompa nied bya change i in density. Several specimens of magnesia were experimented on and they all behaved in the same manner, giving a minimum resistance at from 1200° C. to 1250° C. It therefore : appears probable that this sudden change in the conductivity is due to an alteration of the condition of the oxide into a less conducting state, the resistance continually increasing while the change is going on. In order to see whether the increase of conductivity with temperature follows the same law as the emission of corpuscles Diagram IV. =6 ' oo SALE OF LOG jg C ~ F L0G py G. tS | { | “A | 0006 0008 0010 -00l2 ine: SCALE oF 0 from the surface, the values of logy,c—4logio 8 were plotted against those of @-1, as in the case of lime. This is done in Conductivity of Metallie Oxides. 5 lik diagram 1V., which shows that the points lie very nearly indeed on a straight line. Experiments showed that the conduction of electricity through magnesia was accompanied by a little electrolysis ; but all the effects of this were much smaller than in the case of lime. The results obtained with the other oxides experimented on are very similar to those for calcium and magnesium, the temperature-conductivity curves possessing in all cases precisely the same characteristics as those connecting the emission of corpuscles with the temperature of the oxide ‘when used as the cathode ina discharge-tube. The results obtained with these oxides will therefore be given more briefly. Baryta. This was difficult to work with on account of the strong chemical action it has on platinum when heated, and because of the ease with which it absorbs moisture and Serie gas from the air. Also, if heated above a dull red heat, takes up more oxygen from the air and forms the eae, The numbers given in the following table are therefore not so reliable as those given for lime or magnesia. ‘The dimensions of the piece of barium oxide used were *853 cm. by °843 em. and 467 em. . thick. Temperature —s Resistance in Conductivity in Centigrade. | ohins. | mbhos. 307 | 646,000 1-00 x 107% 311 359,000 Tsim? | 312 iy roo ae a7 10m 320 TELCO SES 319 We ESISONO! Vy e298 e105 | B45 | 78,400 8:29 x 10-8 355 | tOwrG0 6-03 x 10° 369 | 6,892 | 943x10-5 386 602 | 1:08 10-3 428 | 357 | 182x10—2 450 24) |) B04 107? 469 | i176 | =3'70x10—2 497 | 1 eee Gh edOr=2 | When the conductivities in the above table are plotted against the corresponding temperatures, curves similar in type to those given by lime and magnesia are obtained ; but 518 Dr. F. Horton on the Electrical the various readings do not fall so well on the curves as in the former case. This is no doubt due to the causes already mentioned, and especially to the action of the baryta on the platinum electrodes. The effect of this could be seen in the blackening of the oxide through some considerable distance from each surface of contact. Much importance cannot, there- fore, be attached to these values of the conductivity of baryta. Experiments showed that, as with lime and magnesia, some electrolysis was caused by the passing of the current. Some experiments were afterwards made to see whether any evoiu- tion of gas at the anode could be detected. These will be described later. Plumbie Oxide. Some lead monoxide was melted in an atmosphere of oxygen (to prevent reduction) and cast into a slab. This was. filed up to ‘758 cm. x°*733 cm. and *158 cm. in thickness. The following table contains the values of the conductivity at various temperatures after the resistance had become small enough to be measured. | | Temperature Resistance in Conductivity in | | Centigrade. ohms. mhos. 384 7,000,000 3:86 x107° 420 2,350,000 1S S107 462 650,000 4:15 x10~ | 504 250,000 1:08 x10-6 539 128,000 Pat 10 © 572 | 72,000 Sb. x10-6 600 45,000 6-00 «10-6 646 | 13,500 2:00 «10-5 687 4,050 667 «10-5 700 | 2,870 9-39 «10-5 757 730 3695 x 10-4 esi | 330 8-175x 10-4 | | The relation between the conductivity and the temperature is shown graphically in diagram V. When a current of ‘001 ampere was sent through this. oxide no sign of electrolysis could be detected, either asa liberation of gas oras a polarization H.M.F. This current is much greater than those used in the determinations of the conductivity of the oxide. On sending a current of -015 Conductivity of Metallic Oxides. 519 ampere through the oxide for a short time, and then con- necting it up to adelicate galvanometer, a feeble polarization current was indicated ; but this was much smaller than those Diagram V.—Showing increase of conductivity of Plumbic Oxtde with temperature. FPLC. Uo) a a 2 Wa aw Gere ean by li ee eae i 2 am 0 Si on at Gee ee aw TEMPERATURE CENT/GRALE.. . observed in the experiments with the oxides of the®alkalire earths. The temperature of the plumbic oxide during these experiments was 780° C.; the polarization was still smaller at lower temperatures. | Bismuth Trioxide. Slabs of bismuth trioxide were prepared ina manner similar to that employed with plumbic oxide. Some pure trioxide was melted in a stream of oxygen and cast into a slab which was filed up to the required size. The sample from which the numbers given in the following table were obtained was “(7 em. X°(7 om..and -202 cm. thick. 520 Dr. F. Horton on the Electrical | Temperature —_—_—‘ Resistance in Conductivity in | Centigrade. | ohms. | mbhos. / | 225 | go000000 | 427 x10-9 261 20,000,000 | 1-71 x1078 315 2,550,000 | 134 x1077 342 | go0ovuo | 427 x1o-7 | 376 | 259,000 132 10m 424 | 49,000 697 10-5 458 | 22.000 155 x10-5 487 | 15,300)" | “228 "scnges 515 | 9,500 | 359 «10-5 535 | 7150) |) 4p l= 566 | 4700 | 7-27 x107° 598 | 3400 | 1040x1074 645 | 2050 | 1:664x10~4 i The above values of the conductivity are plotted against the corresponding temperatures in diagram VI. Diagram VJI.—Showing increase of conductivity of Bismuth Trioxide with temperature. 10 pease | 8 See Th ! S x 6 i : SS pel 95] | | GS | | | ie : | 1p | | vA | e yf Waren yl | Puielamel | ie ae ‘eo J. : i 200° 300° 400° 500° 600° 700° TEMPERRTURE CENTIGBADE. Conductivity of Metaliie Ouides. Beall Electrolysis was more easily detected with this oxide than with plumbic oxide, a small polarization current being obtained even at 200° C. Cupric Oxide. Some pure oxide of copper was melted up by means of the oxy-hydrogen flame, and the melted mass ground into shape on a carborundum wheel. Its dimensions were :—1:006 cm. x °994 em. and 2°179 mms. thick. ‘Two series of experiments were made with this specimen, the first up to 400° C. and the second to over 1000°C. ‘The results obtained in both series are given in the following table :— | Temperature Resistance in | Conductivity in Centigrade. ohms. mhos. 22 462,400 | ari xt00? 59 91,560 [2 238 100° 66 74,560 | DEBS Nee 134 12,360 ee inohclOm | 157 5,930 | BAS<1Oe | 268 5565 | 391x10-4 | | 303 BOO St tj eat xehOme) a | 385 962 | 226x10-3 | 463 363 | 600x10-% | 12 645,100 a ss alOlr | 487 DH 00784 | 564 113 «| =~ -02424 | 618 On T 03711 | 691 2°34 0931 | 733 1-455 1497 | 786 B45 | 258 873 347 “628 944 196 1-111 974 121 1-80 1038 ‘021 10:37 The resistance of copper oxide at high temperatures is so small, that it was necessary to subtract from the measured resistance the resistance of the platinum leads. The resistance of these at various temperatures was found by a preliminary experiment in which the two electrodes were placed in contact Phil. Mag. 8. 6. Vol. 11. No. 64. April 1906. 2M 522 Dr. F. Horton on the Electrical and heated up just as in the experiment proper, The values of the conductivity are plotted against the temperatures in diagram VII. Diagram VII.—Showing increase of conductivity of Cuprie Oxide with temperature. 20 | . oo a : Le Oe eae 17 ae eT 9 TE a ee en Ce oe a CONDUCTIVITY. 0 100 200 300 400 500 600 700 800 900 1000 TEMPERATURE CENTIGRADE. No sign of electrolysis could be found when a current was sent through this oxide at the ordinary laboratory temperature. A current of 1°625 x 10-° ampere was sent through the oxide. This slowly decreased to 1528 x 10~* ampere in 10 minutes, but on cutting out the battery no trace cf polarization current could be observed. The decrease of current was not due to decomposition such as had been observed in the case of lime ; for on reversing the direction of the current through the copper oxide a steady and equal deflexion of the galvanometer in the opposite direction was obtained. Thus we may conclude that the passage of a current of electricity through copper oxide at the ordinary laboratory temperature is not accom- panied by electrolysis. At higher temperatures it was Conductivity of Metallic Oxides. D23 impossible to test for a polarization current because of a thermoelectric effect due to one face of the oxide being sightly warmer than the other. A current of about 25 ampere was sent through the oxide at 700°C. The galvano- meter deflexion remained steady except on one occasion when it decreased slightly. In no case did the current fall off as it had done in the experiments with lime, so that we may con- clude that at high temperatures, also, the conduction of electricity through copper oxide is not accompanied by electrolysis. Sodium Peroxide. The results obtained with this oxide were not very satis- factory on account of the readiness with which it deliquesces when exposed to air. Only a small range of temperature could be used, as the oxide melts at about 300°C. The numbers in the following table refer to a piece of oxide 1 sq. em. in area and 2 mms. thick. Temperature Resistance in | Conductivity in Centigrade. ohms. | mhos. 20 | 5000 | Aci 59 2500 8 x10” 109 | 12001 7) |) ensel0n 198 | 600 Se Ome 24 | 400 Weis xe eles 284 | 200 Po) 0 seioa. Diagram VIII. = /0 who. CONDUCTIVITY. / Hid 0 100° 200° 300° 400° TEMPERATURE CENTIGRADE. The above values of the conductivity are plotted against the corresponding temperatures in diagram VIII, 2M 2 524 Dr. F. Horton on the Electrical Quarts. A rectangular slab of fused quartz was used in these experiments. Its two faces were ground parallel and roughly polished, and the edges were ground square. The area of the slab was °946 x :939 sq. cm. and it was °1514 cm. in thickness. The two faces through which the current was to be passed were platinized by means of a colloidal solution of platinum, and thus good contact over the surfaces was assured. The platinized slab was held between the two platinum electrodes in the heating furnace and its resistance at various temperatures measured. The following values were obtained : Temperature | Resistance in | Conductivity in | . Centigrade. | ohms. | mhos. | 486 | 95,000,000 | *° 1-79x 107 | 580 12,000,000 «1-42 10 | 652 | 3,500,000 | 486x10~ Glee | al 070,000 10810. | 703 | 1,980,000 -| 8s9xl0. | 795 Nh 750,000. 1. 127 al ae 869 | 409,000 | 416x10 / 919) 2) |<), 250,000, 1) 680x105 | i013 =. | 170,000 «| = 00x10. 1093 | 121,000 | = -1-40x10-” | 1288 | 65,200 | 261x 1000 \ { Diagram IX.—Showing increase of conductivity of Quartz with temperature. (Sit Ons Ae foe We} CONDUCTIVITY. mo) wy 5) 0 007 isthe ae TEMPERATURE CENT/GRADE. The'rapid increase of conductivity with rise of temperature is readily seen from diagram IX., in which the above values Conductivity of Metallic Oxides. 525 of the conductivity are plotted against the corresponding temperatures. When the experiments already described had been per- formed, it was thought to be desirable to investigate further the electroly sis which was found to accompany the conduction in the case of some of the oxides, and to apply a more delicate test for it in those cases in which no trace of a polarization current could be detected. The oxides chosen for these experiments were lime, baryta, and cupric oxide ; lime and baryta because they were the oxides with which electrolysis had been most easily detected, and the cupric oxide because it behaved as if its conductivity were entirely metallic. Wehnelt has shown * that if glowing lime (or certain other oxides) be used as a cathode in a discharge-tube, a strong current can be made to pass. If the cathode consists of a strip of platinum covered with lime, the whole of the current must pass through the oxide. If electrolysis takes place, oxygen will be liberated at the free surface of the oxide and calcium next to the platinum strip. The gas pressure in the discharge-tube will thus increase with the passage of the current, and the amount of .gas liberated in a given time will be proportional to the current passing. Wehnelt found in his experiments that there was “no notable increase of pressure,” which seems to indicate that the passage of the current thr ough the oxide was unaccompanied by electrolysis. In the following experiments much larger cathodes and stronger currents were employed, so that if the conduction of electricity is electrolytic, the amount of oxygen evolved would be quite easily detected. A strip of platinum foil 2 cms. long and 3 cm. wide, having a thermocouple of fine platinum and platinum-rhodium wires fixed to its middle point, was covered with lime and used as the cathode in a discharge-tube, the anode being a disk of platinum 2 ems. in diameter placed parallel to the strip and about 2 cms. away from it. The discharge-tube was connected to a mercury-pump and McLeod gauge, and the whole apparatus was pumped down to a low pressure. The platinum strip and lime were heated, by means of the alternat- ing current from a small transformer, to a white heat for several hours. The heating was accompanied by a considerable evolution of gas from the oxide. This was pumped out of the apparatus at intervals, and the heating was continued until the pressure remained fairly constant. The transformer * Ann. der Physik, xiv. pp. 425-468 (1904); Phil. Mag. vi. pp. 80-90 (1905). 526 Dr. F. Horton on the Electrical was then removed and the strip was heated to a lower tem- perature by means of the direct current from a battery of 10 E.P.8. motor cells. The cathode was also connected to the negative pole of a battery of small accumulator-cells, the positive pole of which was connected to the anode through a current-measuring instrument—a Thomson galvanometer for small currents and a milliammeter for larger ones. In making the experiments, the required temperature of the cathode (indicated by the thermocouple) was first obtained by adjusting the resistance in the heating circuit. The pressure of gas in the apparatus was then measured by the McLeod gauge, and the apparatus left for 15 minutes, after which the pressure was again read and the discharge started through the tube. The current was allowed to pass for 15 minutes. It was measured at intervals during this time and the mean value was calculated. ‘The pressure was then read, and the apparatus was left to itself for another 15 minutes. In this way any liberation of gas due merely to the heating of the cathode could be allowed for, the temperature of the cathode being maintained the same throughout the experiments. It was found that the passage of the discharge slightly increased the temperature of the cathode, and at very high temperatures (1400° C.) the arrangement was unstable, for at the higher temperature the lime gives a larger supply of corpuscles for carrying the current, which is increased, and thus still further increases the temperature of the cathode. In order that the current passing through the tube should not become sufficient to raise the temperature of the cathode above the melting- point of platinum, a small fuse cut from a sheet of thin tin- toil was placed in the circuit. The results obtained varied with the length of time during which the oxide had been heated before the observations were made. It was found in one case, when there was still a fair amount of gas being given off on merely heating the cathode, that the extra liberation of gas when a current of 2°66 x 10+ ampere was sent through the tube was within 8 per cent. of that required by Faraday’s law on the supposition that the conduction through the lime was entirely electrolytic*. On heating the cathode to about 1400° C. for several hours longer, there was much more gas given off from it, and on pumping this out and repeating the experiment it was found that the evolution of gas had practically ceased, and that on now sending a discharge through the tube the pressure was altered * It is interesting to note in this connexion that Skinner (Phys. Rev. July 1905) has found that the evolution of hydrogen from a fresh cathode obeys Faraday’s Law. Conductivity of Metallic Oxides. 527 only very slightly, the alteration being in most cases an increase, but ina few cases a decrease. The following numbers serve to illustrate the results obtained :— Temperature of cathode =1100° C. Potential-ditference between the electrodes =40 volts. Time. Pressure in mm. of Hg. Current in amperes. 304 P.M. 0018 Bae ‘00185 nae 4-2] 0021 431, 00224 aa Increase of pressure per minute while discharge was peer ='000014 Mean increase per minute when no discharge was passing .. =*000010 If the conductivity of the lime was entirely electrolytic, the passage of ‘(03 ampere would have liberated oxygen a arate sufficient to increase the pressure of gas in the apparatus by 0803 mm. per minute. So the actual increase of pressure while the discharge is passing is only (4. of what would be expected if the conduction were entirely electrolytic. The experiment may therefore be taken as showing that in the conduction of electricity through heated lime only a very small fraction of the total current is carried by means of electrolytic ions. A result similar to this was obtained by using barium oxide on the cathode in place of lime. Some experiments were also made with a cupric-oxide cathode, and no increase of gas- pressure in the apparatus could be observed when a discharge was allowed to pass. Conclusion. The point of most interest in connexion with the con- duction of electricity through the metallic oxides is the method by which the current is carried. Nernst * has given reasons for supposing the conductivity to be electrolytic, the chief of these being (a) that definite traces of electrolysis were found in some cases ; the chemical composition at the cathode after the current nad been allowed to. flow through the oxide for a long time being found to be different from that at the anode ;- (b) the conductivity of a mixture of oxides was found to be much greater than that of each oxide separately. Nernst states that the products of electrolysis are continually recombining, and so the supply of electr olytic ions is kept up. * Nernst, Zectschr. f. Elektroch. vi. pp. 41-43 (1899). 52& Dr. F. Horton on the Electrical The conclusion from the present experiments is just the opposite of this view, and is that the conductivity of the oxides investigated is mainly metallic. Jt may be that the signs of electrolysis obtained, in some cases, by Nernst corre- spond to the signs of electrolysis found with some of the oxides in the present experiments. With mixtures of oxides it is probable that signs of electrolysis would be more readily given—for instance, the wandering of colour towards the cathode in the case of mixtures containing coloured oxides (e. g. oxide of iron) may be due, as Nernst suggests, to the coloured oxide being in solution in the rest and giving rise to the ordinary phenomena of electrolysis ; but Ido not think it is justifiable to conclude that because such traces of electro- lysis can be detected therefore the whole conductivity is electrolytic. In the present paper it is shown that some oxides (e. g. CuO) show no trace of electrolysis; and [ think that if the conduc- tion of electricity through these oxides is carried on by means of electrolytic ions, some evidence of the liberation of the products of electrolysis would have been obtained in the experiment in which a current was passed through oxide of copper whilst it was heated in a vacuum. The distinction between electrolytic and metallic con- ductivity is generally based on the sign of the temperature coefficient of the conductivity of the conductor in question. If the conductivity decreases with rise of temperature, the conduction is taken to be metallic; if it increases with rise of temperature, the conduction is considered to be electrolytic. This rule is, however, one with so many exceptions (some of which have already been stated at the commencement of this paper) that it is useless for deciding the question. The effect of increased temperature on the conductivity of electrolytes has been studied by many observers. For aqueous solutions the experiments over the largest range of tempe- rature are those by Noyes and Coolidge*. These observers have studied the conductivity of solutions of sodium and potassium chloride up to 306° C. They find that for very dilute solutions (‘0005 normal) the conductivity increases at a rate closely proportional to the increase of temperature. With more concentrated solutions the conductivity curves rise more slowly and attain a maximum, after which increase of temperature decreases the conductivity. The authors show that this is due to a decrease in the number of dissociated * Noyes and Coolidge, Proc. Amer. Acad. of Arts & Sci. vol. xxxix. p. 160 (1903-94). Conductivity of Metallic Oxides. 529 molecules with rise of temperature, which is greater the more concentrated the solution. Hxperiments on the conductivity of solutions in other solvents show similar results. Walden and Centnerschwer ~* have investigated solutions in liquid SO, from —76° C. to the eritical point, 157° C. In all cases it was found that the con- ductivity first increases with rise of temperature and then falls off, following roughly a parabolic formula. An increase of conductivity with rise of temperature is also found in the case of fused salts. The conduction through these is electrolytic, and the amount of the ions liberated by the current has been shown to follow Faraday’s law of electrolysis T; but the increase of conductivity of fused salts with temperature is not nearly so great as that obtained in the case of heated metallic oxides. The increase of con- duetivity with temperature of all the oxides examined in the present paper is much more rapid than in any known case of electrolytic conductivity. On heating aslab of cupric oxide from 12° C. to 385° C., its conductivity increased 5600 times ; and on heating lime from 763° C. to 1466° C. the conductivity increased to nearly 10° times its value at the lower temperature. In cases of electrolytic conductivity the increase of con- ductivity with rise of temperature is due to the increased mobility of the ions at the higher temperature. As the oxides used in these experiments remained solid throughout the observations, it does not seem reasonable to suppose that the mobility of the current-carriers could have increased by the enormous amounts given above. The only alternative explanation is that the number of the carriers is enormously increased, a supposition which is not compatible with the idea that the conductivity is electrolytic ; for in cases of electrolytic conductivity increase of temperature decreases the degree of ionization, the decrease being more rapid the more concentrated the solution. If, on the other hand, we consider the conductivity to be metallic and the current to be carried by the negatively charged corpuscles which are wandering about in the interior of the oxide, formed by the dissociation of the metallic atoms; then the explanation is at once to hand, for Wehnelt’s work has shown that the number of these cor puscles emitted by the oxide (and, therefore, probably the number contained by it) * Walden and Centnerschwer, Zevtschr. phys. Chem. xxxix. p. 518 (1902). + Lorentz, Zevtschr. f. Elektroch. vii. p. 277 (1900); p. 755 (1901). 930) = The Electrical Conductivity of Metallic Oxides. increases rapidly with the temperature. Moreover, in the present paper it has been shown that the conductivity of the oxide increases in the same manner as the rate of emission of corpuscles from its surface. The fact that mixtures of certain oxides conduct better than either of their constituents, is capable of explanation on the corpuscular theory of metallic conduction. For there is ample proof that the ease with which a corpuscle can escape trom an atom depends on its surroundings. In an atom placed by itself and left to its own resources, a corpuscle has nothing to help it to escape except its own velocity; but if it is surrounded by other atoms, the other corpuscles exert forces on it and so help it to eseape. A corpuscle, for instance, might escape from an atom in the solid or liquid state when it could not escape in the gaseous state. Liquid mercury is a good conductor of electricity, and if there are the same number of atoms in mercury vapour as in the liquid we should expect a much higher conductivity in the vapour on account - of the larger free path of the corpuscles; but neither Maxwell nor Hittorf could find any trace of conductivity through hot mercury vapour. Professor Thomson * found that at high temperatures mercury vapour was a better insulator than air under similar conditions; while Strutt t has shown that up to a full red heat the conductivity of saturated mercury vapour is only about one ten-millionth part of that of the liquid. It seems not improbable, therefore, that there might, in certain eases, be many more free corpuscles in a mixture of two oxides than in either oxide separately. Even neglecting this influence of the surroundings on the freedom of tne corpuscles, we should expect to obtain a mixture of better conductivity than either of its constituents by mixing two metallically conducting bodies, one containing a large number of free corpuscles, but in which the mobility of the corpuscles was small, and the other in which the mobility of the corpuscles was very great, but containing only a few. On mixing a little of the first substance with the second a good conducting mixture would be obtained. I do not, therefore, think that Nernst’s reasons for consi- dering the conductivity of heated metallic oxides to be electro- lytic are conclusive. The experiments described in this paper seem to show that by far the greater part of the current is carried by uegatively charged corpuscles, as in metals. In the case of those oxides or mixtures of oxides in which a * J.J. Thomson, Phil. Mag. [5] xxix. p. 364. Y Hon. h. J. Strutt, Phil. Mag. [6] iv. p. 596 (1902). Note on Talbot’s Lines. dbl feeble polarization current or other signs of electrolysis have been observed, we have both metallic and electrolytic con- ductivity associated in the same substance. These experiments were carried out at the Cavendish Laboratory, and I gladly take this opportunity of thanking Professor Thomson for his advice and interest during the investigation. XLIV. A Note on Talbot’s Lines. By James WALKER, J/.A., Owford *. T is sometimes felt that Stokes’s explanation of the ‘polarity ” of Talbot’s lines is mathematical rather than physical, so that those who are unable to follow the anaiysis still require an adequate reason for the fact that the retarding plate must be inserted on the one side of the aperture rather than on the other. Prof. Schuster has indeed supplied this want by considering the source of light to be due to a succession of impulsive velocities ; but there is perhaps still room for an elementary explanation of the phenomenon on the old familiar lines of regarding the light as resolved into a congeries of mono- chromatic constituents. 1. When a stream of monochromatic light, coming from a distant slit, falls upon the object-glass of a telescope that is limited by a rectangular aperture with its sides parallel to the luminous line, it is easily shown that the diffraction- pattern in the focal plane of the telescope is characterised by a series of dark lines, arranged at equal distances on either side of the geometrical image of the slit. When half the aperture is covered by a retarding plate, the minima of an even order retain their former positions, but those of an odd order are displaced towards the side on which the plate is placed by an amount depending upon the retardation introduced by the plate. Let us now suppose that the primitive light is white and that its monochromatic constituents have been separated before reaching the aperture by a prism ora grating, so that the different colours occupy different angular positions in the field of view. The minima of an even order will now disappear ; for on account of the dispersion there will be a gradual shift of the * Communicated by the Physical Society: read February 28, 1906. + An Introduction to the Theory of Optics, p. 329; Phil. Mag. [6] vol. vil. p. 1 (1904). | 532 Mr. J. Walker on Talbot’s Lines. centre of the system and consequently of these minima on passing from one wave-length to the next”. The case of the minima of an odd order is, however, different ; for as the wave-length alters, there is not only a shift due to the dispersion of the light, but also a dispersion due to the varying displacement caused by the change in the retardation introduced by the plate, and if tiese balance one another, the bands corresponding to different wave-lengths will be superposed and will therefore be rendered visible. It is clear then that the plate must be so placed that the dispersion of the bands that it produces must oppose the dispersion of the light introduced by the prism or the grating. Thus the retardation of phase caused by the plate increasing with decreasing wave-length, the plate must be placed over the right or the left half of the aperture, according as the dispers’ sion in the focal plane of the telescope from red to blue is from right to left or from left to right. 2. The following analysis of what takes place may perhaps tend to make the foregoing expianation somewhat clearer. Let us suppose that the light, falling normally upon the aperture, is nearly monochromatic, as is the case when a small portion of the spectrum is considered, and that the slit of a spectroscope is placed in the focal plane of the telescope in a direction perpendicular to the bands of the diffraction pattern. Then the light will be drawn out into a short spectrum, and the aperture being uncovered, this will be traversed by bands running along it, that are nearly straight and parallel to the sides of the spectrum (fig: 1): ig. a: d-SA When half of the aperture is covered by the retarding plate, the bands (a)of an even order will retain their positions, * The slight change in the distance between the minima as the wave- length alters, may be left out of account when a small region of the spectrum is considered. Mr. J. Walker on TValbot’s Lines. 333 but those (>) of an odd order will be shifted, and as the amount of the displacement varies with the wave-length, will be made to slant across the spectrum. Thus the right half being that which is covered, the appearance will be that represented diagrammatically in figure (2). Now the effect of a dispersion of the light will be to move each horizontal line of the spectrum in its own direction by an amount depending upon its distance from the end—in fact to give the figure a kind of shear. If this motion be to the right, the result will be that both sets of bands will slant across the spectrum, but if it be to the left, the bands (a) will be made to slant, while the others (() will be placed more nearly along the spectrum and, the shift being properly adjusted, will become exactly parallel to the sides. Hence in the former case no bands will be seen when the focal plane is viewed directly with an eyepiece, but in the latter case the bands (6) will become visible. 3. The best thickness of the retarding plate for a given part of the spectrum may now be determined. It is obvious that the resultant disturbances in any direction from the two halves of the aperture have the same amplitude, and that their phases are those of the secondary waves emanating from the central elements. Since the source of light is a line parallel to the sides of the aperture, directions perpendicular to these sides alone need be considered, and if 534. Note on Talbot’s Lines. ¢ be the angle of incidence, the disturbance in a direction 6 may be repr resented by A cos (= vt — A) + A cos au {vt—h(sin 6 +sin d)} = 2A cos {Za (sin @+sin }) — . | X cos kK oe —> | 2h being the width of the aperture, 4 the retardation of phase. introduced by the plate, and 0, being regarded as positive when measured on the fale of ihe nor ell on which the plate is inserted. Hence the intensity is 4A? cos? 15 —h(sin 8+sin d) — =) | , and there will be a primary series of minima given by A=0, being those due to a rectangular aperture of width A, and a secondary series of minima in directions given by Xr h(sin @+sin @)= {2+ @n—1) \e. A= 12 ae Let the telescope be directed so that light of wave-iength Ao is incident normally upon the aperture, and let p be the order of the secondary minimum next to the focal point. Then @ being very small, ( r Ae = (a — (2p—1) } 5? and for light of wave-length X,+ dro A A | Ao + Or Ao dA h(@+60+6¢)= ts (2p—1) Lies 4 i r Ay dA EE ash aay Be cl) Sy fis whence ee I SOUS (80+ 86) = 5 vt Sh. Hence for bale of the bands due to the monochromatic constituents Ay and Ay» +6A, we must have d& __ 2rhdd dXo Ao ro ; which gn the best thickness of the plate. Sand { ae must have the same sion: whence AS Also - S pias = e dn being negative, a angle of incidence must increase on the positive side of the normal with decreasing wave-length. eee ssa XLV. Genesis of Ions by Collision and Sparking-Potentials in Carbon dioxide and Nitrogen. By H. HE. Hurst, B.A., B.Sc., Hertford College, Oxford *. a explanation of the theory of ionization by collisions of positive and negative ions with molecules of a gas in a uniform field of force was given in a paper on the “Genesis of Ions in a Gas” (J. S. Townsend, Phil. Mag. Noy. 1903) and the experiments were continued in a further paper (Dec. 1904). The apparatus previously used for these experiments with air and hydrogen has recently been used to verify the theory in the case of nitrogen and carbon dioxide, and the results of these experiments. are recorded in the present paper. A detailed description of the apparatus and of the method of conducting experiments will be found in the first-mentioned paper. Briefly, the apparatus con- sisted of two parallel plate electrodes, one of which was zinc. In the first experiments on nitrogen and those on carbon dioxide, the other electrode was a quartz plate coated on one side with silver. ine lines were ruled on this to allow ultra-violet light, produced by a spark between aluminium terminals, to fall on the zine electrode. In the second set of experiments on nitrogen, a zinc plate with fine slits was substituted for the silvered quartz. These plates can be arranged at distances from ‘1 to 1:2 cm. apart. By means of an electrometer the currents between these plates were measured for different values of the electric intensity between them, their distance apart, and the pressure of the gas in which they were immersed. In the previous experiments the electrometer was kept at. zero potential while the current was passing, by means of a condenser and potentiometer arranged as an induction balance. In the experiments here recorded the same eftect was cbtained by finding the rise of potential during half the time of an experiment, and then starting with the potential of the electrometer and electrode connected to it below zero by this amount. Hence during half the time of an experiment the potential- difference between the electrodes is slightly too large, and during the other half too small by nearly equal amounts. The same precautions with regard to insulation were taken as were described in the previous paper. Tt has been shown that if mp) negative ions are liberated from the zinc plate by the ultra-violet light, and travel through the gas under the action of the electric force between the plates, the number which arrive at the positive electrode * Communicated by Prof. J. 8. Townsend, F.R.S 536 Mr. H. E. Hurst: Genesis of Ions by Collision and is given by (a= Be o™ 2 — Beet? R=No- where « is the number of new ions of one kind, either positive or negative, produced by a negative ion in travelling through 1 centimetre of the gas, 8 is the number produced by a positive ion in travelling through | centimetre, and d is the distance between the parallel plate electrodes. The values of « and @ depend upon the electric intensity X between the plates, and also on the pressure p of the gas. They may be determined for any values of X and p, by _mneasuring the currents for different distances between the electrodes, X and p being kept constant. It was also shown that at a distance d, given by a—Be°"?*—0, sparking takes place when the difference of potential between the plates is Xd, when ultra-violet light falls on the negative electrode. If a is the value of d satisfying this equation | fabs: log a — log = mie : The carbon dioxide used in these experiments was prepared by the action of pure hydrochloric acid on marble. Before entering the drying apparatus it passed through glass wool and over calcium chloride. It was dried by passing through sulpburic acid and standing over phosphorus pentoxide. In the following tables g is proportional to the currents determined experimentally, for fixed values of X and p, and different distances between the plates. The distance d between the plates is given in centimetres, and X the electric intensity in volts per centimetre. a@ and 6 are calculated so that the formula (ean an Bern? shall be in agreement with the currents at three different distances. is taken as unity. Below the tables are given the values of a determined from the equation N= No aes loga —logB Zoned) Xa, and the sparking-potential V determined experimentally. ft will be seen that the theoretical values of n agree with the values of the current g determined experimentally. In some of the tables 8 is too small to be determined with the Sparking-Potentials in Carbon dioxide and Nitrogen. 537 apparatus used. In order to determine # in these cases it would be necessary to have an apparatus which admitted of larger distances between the plates. When £8 is small the formula (a— Byetaa: Foes Bee 4 reduces to n=ne*’. When the sparking-distance a was more than 1°2 cm., it was not possible to determine the sparking-potential, since the plates could not be separated by more than that amount. r= No Carbon dioaide. Pressure 2 mms. ee : GG a: | a0 8:32 70°7 747 | | a ==21-21 i ee al |B = "0085 See ee ee 8°32 alist rt3ys) | a="369. Xa—516. V=517. Pressure 1 mm. ete: 2 3 -4 5 6 Sat (oe B54 | 247 | W381 | 226 | 787 B= oon ee 8-54 | 248 | 738 | 298 790 a=7(36. 0.) lay V=509, Pressure 1 mm. Eden Ree 2 3 4 5 | Sastry. ur ye eee 10°7 36:1 129 643 | asl JERE A Be o1as Pa On 10-7 36 130 G45 | = Ne Xa=500. V=495. Phil. Mag. 8. 6. Vol. 11. No. 64. April 1906. 2 N 038 Mr. H. E. Hurst: Genesis of Lons by Collision and Pressure 1 mm. GR os SAR Re ys is "4 ae pel 13 51 289 | | a =12-68 x0). OQ ee ee ee 13 50'4 278 wees Xa=488. V=49i. Pressure *3 mm. | | {RE OR Vem Beant 3 2 2, “A | 6 | 8 ! X—525 Qos successeeteal aa Os: BRS jaa 303 Jaa eee 3-64 138 | 529 301 a='929 Xa=488. V=485. Pressure *5 mm. | 5a foam bs ie PS CHAS. 3) 3) “4 6 Ke 700" awe ee ee 3-9 78 166 ‘4 | 109-2 Gg Ree ae 39 | 785 | 165 | 373 aly a="706 Xa=494. V=-497. Pressure *5 mm. (FAR 5 BAR 2, 3) | =! “a Kemer hg ex ee 4-58 963 | 232 708 EA) Meee © 458 | 10-14 24-9 71-2 { a='613 Ka=—537 V=530. Sparking-Potentials in Carbon diowide and Nitrogen. 539 Pressure *25 mm. | BLM, Mkes | 2 4 6 8 Sa ees 2-05 4:39 9°82 25-8 | fe — 350. * Hee ote: ae ie : | B —-089 TU arwrcinieininivin sieinieisie | 2°05 4°35 | 9 17 | 26'1 a=1-062. Xa=558. V=564. Pressure 4 mms. | | Bains tee’ ahtee Aide 2 “4 5 6 =) i re | 641 | 162 | 41 108 | 263 | Sa a =9°28 papad yes : 2 / 262 een ment ie Hero sib elle 2a) eal 104 262 Pressure 4 mms. | | oe 2 4 6 SMe iat iid CA eee CA) TO AAT iene 7 | } 2A OC A | : | : A | Z | © seal TOE Bee a 1:64 | 2°69 : 4-41 | G20 | 11:9 | Pressure 2 mms. Emern Re ict D “4 6 | | MOO | Ghent 9-6 95 seg m= Lis CY) Wn 2. 8B small WEE as uccaws' 9-6 92°5 881 r The values of « here obtained for the smaller values of Xx ) agree very closely with those obtained by Prof. Townsend (Phil. Mag. April 1903). Some doubt has been expressed as to the validity of the experiments performed on carbon dioxide, as the gas is electrolysed by spark-discharge into 2 NG 2 940 Mr. H.E. Hurst: Genesis of Ions by Collision and carbon monoxide and oxygen, some of the oxygen being set free as ozone, which would oxidize the zinc plate. In the experiments recorded above, all the currents g were measured before determining any spark-potentials, and if sparking took place during these experiments it was by accident, and was only momentary. The largest currents used were of the order 10—!° ampere, so that if electrolysis takes place before a spark passes, an extremely small amount of gas is electrolysed. Hence the oxidation effect on the electrodes is small, and in the case of the experiments on air the only noticeable effect of oxidation was, that the currents produced by a given intensity of the light were proportionately less. were unaltered. That is to say, oxidation causes less ions to be given off by the zinc plate under the action of ultra-violet light. As to the change of constitution of the gas, the results of the experiments show that the spark-potential can be predicted from measurements of the currents before a spark passes, so obviously it is of no importance whether the gas remains as carbon dioxide or aiter passage of the current contains traces of ozone. If the gas were electrolysed in quantities the last experiments of a series should not be consistent with the first, but no measurable inconsistency was ever noticed. The nitrogen used in the first set of experiments was obtained from air by passing air and ammonia over red-hot copper, the ammonia being in excess of that required to reduce the copper oxide formed. The nitrogen so produced was again passed over red-hot copper, and then over caustic potash into the drying apparatus, where it passed through sulphuric acid, and was finally dried by remaining in contact with phosphorus pentoxide. The following tables give the results of experiments made on gas prepared by this method. Nitrogen prepared by First Method. oe Pressure 4 mms. Bcc 2 st ene genie? 3 4 5 Ts xX=700 GER S s s2 immer: £1 U5) | 858 18:5 | 43°6 | | | | a =7:08 | 1% AQ : 2 | 1 [eS Os | 415 8:58 | 286 44 | a="708. Xa=496. V=494. The ratios of the currents. Sparking-Potentials in Carbon dioxide and Nitrogen. 541 Pressure 4 mms. rive Quer eee eo “4 6 8 pres fg Flt. 246 AG) e110: : 25°7 pas | rae 2-16 473 106 25:4 a=1:236 Xa=649. PRE ee De i ee 4 5 i aemeren Pe gla. se 873 19°7 504 = eee 417 907 | 20 07 ) a="6ls Xa=852. | v= 349. Pressure 2 mms. aes 2 Bch es Sociale | /X=850 Piet hurk pie |e ee ee Be as. The | ae) Ge | 44-7 peaqenn) GRCeu Pressure 1 mm. Denes 2 ro ah wed 7 8 Reas0 ge el eae | eae Sig eats eae saa | ego | ise "| erat. 107 a='88. Xa=308. Wos0ey 042 Mr. H. BE. Hurst: Genesis of Lons by Collision and Pressure 1 mm. RO SS Ae ei 2 3 | : D es ple Vie Me 3°72 7-68 a 16-9 485 | Bee TL Car ea 3°72 755 1695 | 48:1 a—-bOile Xa=316. V3. Pressure ‘5 mm. aes lee fen 2 | “4 | 6 | 10 NE 2G 2D AY. Sactensmnleniniele 1°92 | 3°82 | 761 | 49°5 | | 2a. Og ees 192 | 377 | 768 | 498 T—lA95 Xa=814. Pressure 4 mms. rise ae an tts 2 6 1-0 oes | X=390 G ashes eteoeeees 1°31 2-25 3°85 Aan pet ee , ae 2-25 3:86 | Pressure 8 mms. renee 2 6 1:0 X=350 O) consle cee eee 1:03 112 1:18 Fe Pe ime ce 1-08 1:10 118 Sparking-Potentials in Carbon dioxide and Nitrogen. 543 Pressure 16 mms. | iene eee | ‘| 3 5 =e ee lr dna a aoe rgaTcOnGn vat) «Lok y | | ao EP | ne | | 7 B Seal VU == Cit see auras fare | Os | eth | kG In order to test whether hydrogen was present in the gas in appreciable quantities, some more nitrogen was prepared by the same method, and its specific gravity carefully determined. The mean of two experiments gave ‘971 as its sp. gr., which was probably correct to ‘2 per cent., as an error of 3 milligrams in weighing would only have produced 1 per cent. error in the result. The sp. gr. of pure nitrogen is ‘972. In the following experiments the nitrogen used was prepared by a similar method to that used by Lord Rayleigh for obtaining nitrogen from air. Air was passed through strong ammonia, over hot copper, through dilute sulphuric acid to remove excess of ammonia, then over hot copper oxide to a gas-holder, where it stood over water containing sulphuric acid. This gas was afterwards passed through a solution of caustic potash, and again over heated freshly reduced copper in a long tube, and copper oxide in another long tube. The copper oxide was kept red-hot, and the first portions of nitrogen were used to wash the receiver, which was exhausted each time. After an hour some nitrogen was collected and the receiver sealed. From the receiver the gas passed into the drying apparatus as before. Lord Rayleigh tested the efficacy of this method of removing hydrogen, by allowing a constant stream of hydrogento mix with his gas before it passed over copper oxide, and found no hydrogen in the gas at the finish. In order to avoid difficulties arising from the burning away of the silver on the positive electrode, a zine plate perforated with fine slits was used. The following results were obtained. Pressure 4 mms. iid ba ee 2 3 4 5 | 6 | | = a = — ium fy | x — 700 ee we ee 4-2 886 | 19:2 44-2 | 123 | a pies eee Pua Sees 42 | 885 | 189 | 494 | 123 544 Mr. H.E. Hurst: Genesis of Ions hy Collision and Pressure 2 mms. l Sea RA 2 #35 4 5 NES 2D 0'h Ma raneneccee: | 394 7:95 Ni | ae ine 6:76 ec fp beech, A 3:94 8:05 17-2 41-9 | 8'="08 | a='665. Xa=349. V=344. Pressure 1 mm. RR See Mgt: 2 3 4 5 X29 US ae ES 3°58 TAD 15°9 54°3 a =6'18 S is BY ket NAD aval 3°58 720 16°3 521 | B ='194 | c— We: Xa=304. V— Joe: A satisfactory agreement may be found between these tables and those for the nitrogen which was first used. Besides these experiments a number of determinations of | the spark-potential were made, for different values of the pressure and distance between the plates. | The effect of mixing small quantities of oxygen with the ) gas was also determined. The sparking-potentials were j determined by connecting in series with the parallel plates a battery of small cells, a voltmeter, and a resistance-box. In the experiments on carbon dioxide and the first sample of nitrogen the total external resistance was about 50,000 ohms, but in the later experiments on nitrogen 68,000 or 98,000 ohms. ‘This increase of resistance raised the sparking-potential about 2 volts. In all the determinations the lowest potential which gave a spark when ultra-violet light of small intensity fell on the negative electrode is given, and this is the potential V in the preceding tables. But in some of the experiments the poten- tial required to give a spark without the action of ultra-violet light was also determined. After one determination had been made and a spark had passed, it was found necessary to wait a Sparking-Potentials in Carbon diowide and Nitrogen. 9545 few seconds, and in no case was sparking allowed to be more than momentary. It was found that unless these conditions were complied with, other phenomena occurred which made the determination of the sparking-potential uncertain. These phenomena were especially noticeable in the neighbourhood of the minimum sparking-potential, and at values of pd less than the critical value, p being the pressure and d the distance between the plates. The results of all the experiments are collected in the following tables, in which are given the potentials required to produce sparks with ultra-violet light acting, the potentials required without light, and in some cases the potentials calculated for the distance ya: log z—log 8 . a—B Carbon dioxide. | : | | Distance Calculated Spark potential : : oo between pd. potential. with light. one ee P plates d. Xd. V. We Tape mm. cm. volts. | volts. volts. 2 "369 "738 516 517 1 “736 ‘736 HIG. | 509 | 525 1 "O71 ‘571 500 495 509 1 ‘465 465 | 488 491 a5) "929 "464 488 485 5 706 =| +353 494 497 <6l3 "306 537 530 542 25 | 1-062 "265 508 564 Nitrogen prepared by first method. Spark Dp. d. pd. Xd. eye potential me De) without light. min. cm: volts. volts. volts. 4 ‘708 2°832 496 494 + 1:236 4944 649 2 1:41 2°82 493 2 ‘67 1°34 352 349 1 "88 "88 308 303 305 1 “601 ‘601 316 311 311 5 1-195 “597 314 046 Mr. H. E. Hurst: Genesis of Ions by Collision and Nitrogen prepared by second method. l } Buenas rhe aba: Gi mu ee | p- | f pd. | CARN Bi aeons potentia ae eae without light. 1 alas athe (ae lease eaters (oe ust 512 - ‘708 2832 | 504 504 4 Lies RG i | | 460 464 2 38. | 116 || 332 334 2 | 65 | eee OD 339 343 2 665 1°33 349 344 346 2 "8d 1:70 382 384 | 2 67 1°34 329 345 ] 4 “4 330 336 il a) “5 | 310 314 1 58 58 304 300 304 1 601 ‘601 298 3038 1 868 “868 300 306 1 1:0 1:0 310 314 Mixture of Nitrogen and 11 per cent. of Oxygen. | | | } UN ewe PBS | 516 |. Sle 4 ib eVOSem 62532 a 514 520 | Be) a eg oa 479. | eae ie pa 16 4 355 |}; ee PEN ROD 1:30 | B42) 9 a 2 1) ESS 1-70 392 398 2 |= 4603.2) aleSa0 | 341 | 349 1 | GOI ee cook ae 302 | | Mixture of Nitrogen and 5 per cent. Oxygen. | 1 “4 “4 369 | 371 is ip 5) | 33+ 308 58 58 | | - 820 394 601 GOT pal wi 320 "65 ‘65 316 320 ‘70 ‘70 312 316 8 “80 316 320 268 68 320 324 10 10 | Olt 332 The sparking-potentials for nitrogen do not agree with those obtained by Strutt (Phil. Trans. 193, p. 377, 1900). He found that the sparking-potential of nitrogen varied con- siderably with different samples of gas, although prepared by the same method. This he attributed to the presence of Sparking-Potentials in Carbon dioxide and Nitrogen. 547 traces of oxygen, since if the gas was passed repeatedly through a liquid alloy of sodium and potassium, a constant minimum potential of 251 volts was obtained. The volume of the apparatus used was small, and before determining a sparking-potential the gas was sparked through vigorously. If the apparatus had previously been used for the experiments on hydrogen, it is possible that the sparking would drive out some hydrogen occluded in them, which in a small volume might form an appreciable percentage of the gas present. This would tend to lower the spark-potential and make its determination uncertain. In the determinations of spark- potentials described in this paper it was found that in the neighbourhood of the minimum spark-potential, the spark- potential was sometimes affected to the extent of 6 or 8 volts by the previous passage of a current through the gas, and before the potential could be again determined some time must elapse if the results were to be concordant, so that all potentials were determined without sparking having taken place immediately before. It will be seen by comparison of the tables given for nitrogen prepared by the methods mentioned, that there is not a great difference between the results obtained in both cases. The tables of sparking-potentials show also that a small percentage of oxygen only produces small differences in the sparking-potentials, and that 5 per cent. produces more effect than 1 per cent. These facts seem to show that small quantities of impurities do not produce disproportionate effects. If this be true, the variations in the spark-potential of nitrogen are not produced by minute traces of impurity but are due to other causes. Further experiments in this direction are to be attempted shortly. The accompanying curves, figs. 1 and 2, show the relation between the sparking-potential and the product of the pressure of the gas p and the distance between the plates d, for carbon dioxide and nitrogen. As the spark-potential deter- mined with ultra-violet light falling on the negative electrode was In most cases nearly the same as that determined without the light, one curve only has been drawn in each case, through the points representing the potentials obtained with the light. “The theoretical values of the spark-potential calculated from the formula before given are also indicated. . : ) 548 Mr. H. E. Hurst: Genesis of Ions by Collision and Fig. 1—Carbon dioxide. : aac © Y determined oe ert gerelally © with ultra vio 2 Lighe. t{ S x Theoretical value of Xd. ) S | = 550 zy | | | y i 1} = and | | NY 1p $ Xa | | : 2 | | = | : | | | | Pe \ x i} => 500 j 7 j «xo 0; 10) . I -2 “3 aft 5 “6 7 POX a measured tn centimetres yar - millimetres of Mercury. | Ey | fe Bled | Ze 600 2D Vala a Mics evel Vale ie i a a : 80 + SPARKING POTENTIAL IN VOLTS. 2 3 4 5 7? x @ a meashied in CcerntimelTes P > . micllimetres of Mercury. a Sparking-Potentials in Carbon dioxide and Nitrogen. 549 Fig. 3 shows the curves obtained with the different samples of nitrogen and also the effect of small quantities of oxygen. . Wee SPARK POTENTIAL /N VOLTS. € Curye tit ecated Ly 4 broken Ln cyers to\the f Ai ; 2pst sapiyate of Vilrogere | 1 2:0 3:0 PTCSSUTE X Bislarce faa. Wa IHCASRICA 72? 7777728. Of TerCUTY. a meastizza in cris. The theoretical investigations are intended to apply to cases where the pressure is not less than the critical pressure, and it will be noticed that the effect of smallimpurities is negligible at the higher pressures. The minimum spark-potential for the first nitrogen is about 302 volts, for the second about 295 volts. The gas containing 550 Mr. H.E. Hurst: Genesis of Ions by Collision and 5 per cent. of oxygen gives a minimum spark-potential of about 312 volts. In the tables before given it will be noticed that the theoretical values of n, calculated from the formula (a= pce Nn =N Beebe agree with the values of A current g determined experi- mentally, so that the theory furnishes an explanation of the currents which take place in a gas before sparking occurs. In preceding papers on this subject it was shown that a and , are functions of re and the accompanying curves, figs. 4 and 5, show the relations between these variables. In Fig. 4, 15 l | H 1 e | | “Ne | @ | a iE oe ee | a | | | | ot <4 a) | ye Be . | | | 4 } | | | { 3 = | 4 | | | ohger loifirst 7ett. La ' & ; | or | xheper lo\secona 7 ee | 7 (sale | | | ae Le | | | | } | | 100 200 300 400 500 600 700 sae 2 1000 1100 1200 1300 1400 1500 4600 1700 1800 1900 2000 those for nitrogen, the curves relate to the first set of experi- ments, and the values for the second experiments were put in after the curves were drawn. It will be seen that the discrepancy between the two sets is comparable with the errors of experiment, so that we shall give the following conclusions drawn from the results of the first experiments, since it seems that the presence of small quantities of impurities only produces small errors. The larger values NVp of a can be represented by the formula *=Ne x (J. S. Townsend, Phil. Mag. April 1903), obtained on the assumption that new ions are formed by collision when the colliding ion has a velocity due to a fall of potential ¢V. Sparking-Potentials in Carbon diowde and Nitrogen. 901 N is the average number of collisions of a negative ion in moving thr ough a centimetre of gas at 1 mi. pressure. In Fig. 5. woh ofl 8k 8 A a aoe SA Se eee a Oa re a ee a & pt 1 oe Bis eee Be) a ae ctl lhe tical Resales SIE RY - re ea ee , aS eae eee a a ch, EN aa a ST Sn SERS 2 ee a MS = e 4 eA ee eee ee ee [ui ale Vie al Pere bel ho filer ey -020 col [eM] | Scola de lig IMA eal axl tna | 100 200 300 400 500 600 700 foo. a 100 1100 1209 1300 1400 1500 1600 1700 1800 1900 2090 the case of carbon dioxide when N=17°4 and V=18°8 volts, the values of « calculated from the above formula agree with those obtained from the curve for values of s between 2000 and 350. For nitrogen the numbers N=13°6 and V=28°5 give values of 2 agreeing with experiment for es of = hetween 175 and 525. For the smaller values of ; it is necessary to suppose that some new ions are formed ees the velocity on collision is less than that due to the critical fall of potential V. The values of N and V for nitrogen do not differ much from those for air given in the paper previously mentioned, and the curve there given falls between those for nitrogen and carbon dioxide. It is not possible to represent B a) within the range of experiments performed by a formula of NVp the type Ne X . Perhaps, as in the case of the smaller 552 Genesis of Ions by Collision. values of = one could be obtained on the hypothesis that some collisions after velocities less than a critical velocity are productive of new ions. This view obtains some support from the fact that the curves for z are very similar to those A a . portions of the — curves corresponding to the smaller values xX or = ib will be noticed that the values of a for COQ, and nitrogen are of the same order of magnitude, but that 8 is much smaller in CO, than in nitrogen. It has been shown that all ions have the same charge. Now, if we assume that a positive ion is approximately of the same size as the molecules of the gas in which it is formed, and a negative ion very small compared with these, a positive ion in travelling a given distance will make about four times as many collisions as a negative ion in travelling the same distance. Therefore a negative ion in a gas at 1 mm. pressure will make approxi- mately the same number of collisions per centimetre as a positive ion in the same gas at ‘25 mm. pressure. In CQ, at 1 mm. pressure the number of collisions made by a negative ion in going 1 cm. is 17:4, and when the electric intensity is 175, ais 2.4. Now at z mm. pressure 8 is ‘001 for the same force. So that for an equal number of collisions under the same conditions, a negative ion makes about 2400 times as many new ions in CO, as a positive ion. In nitrogen a negative ion weuld make about 17:4 collisions per centimetre at a pressure of 1:28 mms. For the same electric intensity 175, «is 1°28. At 32 mm. pressure the number of collisions of a positive ion in nitrogen would be approximately the same as in the cases already considered, and for intensity 175, B is about ‘058. Under these conditions then, a negative ion in nitrogen produces 22 times as many new ions as a positive ion in going a given distance. Hence the positive ion in nitrogen differs less from the negative ion than does the positive ion in CQ,. Since ali negative ions are the same, this will be the case if negative ions are small compared with positive ions, and positive ions in nitrogen smaller than those in carbon dioxide. There is a considerable difference between the values of @ for nitrogen and those for air, B being larger in nitrogen than in air. From this it would seem that 8 for oxygen is small. In conclusicn, 1 wish to express my thanks to Professor Townsend for his advice and assistance during the course of the experiments, and also to Dr. 4. B. Baker tor his criticism of some points connected with the preparation of the gases. [ obs | XLVI. The Retardation of the Velocity of the a Particles in passing through Matter. To the Editors of the Philosophical Magazine. GENTLEMEN, N the Philosophical Magazine of July 1905, I gave an account of some preliminary experiments on the retar- dation of the velocity of the « particles from radium C in passing through matter. _ Using an active wire coated with radium C as a homo- geneous source of radiation, the velocity of the « particles was found to decrease in passing through aluminium, and the lowest value of the velocity observed was °64Vo, where Vo is the initial velocity of projection of the a particles from the bare wire. I have recently repeated these observations under much better experimental conditions, using more active wires, and with the photographic plate closer to the source of rays. I have, in consequence, been able to measure the velocity of the @ particles after their passage througha greater thickness of aluminium. The lowest value of the velocity which could be measured was ‘43Vo. The photographic effect observed on the plate was very feeble, and certainly less than 4 per cent. of that found for the unscreened wire. The thickness of aluminium in this case was equal in absorbing power to almost 7, cms. of air—the maximum range of the ionization of the a particle from radium C. As I pointed out in my previous paper, such a result suggests that the ionization produced by the a@ particle falls off rapidly when its velocity falls below a certain critical value. The deduction from experiments of this kind are, however, complicated by a scattering of the a rays in their passage through matter. Thisis initially small, but increases with the diminution of the velocity of the @ particle. I have determined the value of e/m for the & particle from radium C after passing through a screen equal in absorbing power to 5°5 cms. of air, and found it the same as for the a particle from the bare wire. This experiment shows that the a particle retains its charge and mass unaltered over a greater part of its range in air. Further experiments are in progress to see if it is possible to detect by special methods the presence of the a@ particles after passing through an absorbing screen equal to 7 ems. of air. It is hoped that, by such methods, it may be possible to Phil. Mag. 8. 6. Vol. 11. No. 64. April 1906. 2 O D904 Prof. A. W. Porter on the Inversion-Points for settle definitely whether this critical velocity of the « particle is only apparent or has a rea] existence. As these experiments will take some time to complete, I have taken this opportunity of stating briefly the results so far obtained. I am, Gentlemen, McGill University, Montreal, Yours faithfully, February 27, 1906. EK. RUTHERFORD. XLVI. On the Inversion-Points for a Fluid passing through a Porous Plug and their use in Testing Proposed Equations of State. By Autrrep W. Porter, B.Sc., Fellow of, and Assistant-Professor of Physics in, University College, London*. i a paper in the Phil. Mag. vol. xlv. p. 227 (1898), Rose- Innes showed that the results obtained by Joule and Kelvin for the change in temperature of a gas in passing irreversibly through a porous plug could be represented as well by the formula ae as by the formula adopted by Joule and Kelvin, viz. : A 72° Rose-Innes’ formula, if a valid empirical formula, would Indicate that a point of inversion must exist; that is to say, that there must exist a temperature below which cooling will occur, while heating takes place if the gas is above this temperature. The fact proved later that by sufficient cooling hydrogen, which heats at ordinary temperatures, cools at lower tem- peratures, demonstrates that for it an inversion-point exists ; and still later (Krakauer Protocolle, 1901 ; Drude’s Annalen, 1902) Olszewski has experimentally shown that hydrogen suffers neither heating nor cooling when the temperature is —80°°5 C. and the pressures on the two sides of the plug are about 113 atmospheres and that of the atmosphere. The object of the present paper is to examine the subject more minutely; and the outcome of it is that it is shown that any of the usually adopted equations of state of a gas require that there shall be not one inversion-point only, but a whole series of such points corresponding to all possible pressures. Instead of dealing with finite changes of pressure we shall * Communicated by Prof. F. T. Trouton, D.Sc., F.R.S. a Fluid passing through a Porous Plug. DID consider the difference of pressure on the twe sides of the plug as being infinitesimal; considerable simplification results from doing this. Of course, it must ke recognized that this condition does not hold good for the circumstances of the Olszewski experiment, the discussion of which is undertaken in section (d). The equation characteristic of the cooling-effect is HE) saa ea where v=specific volume, p=pressure, T=temperature, C, the specific heat at constant pressure, and U the intrinsic energy of the fluid. If no change of temperature takes place for an infinitesimal change of pressure T(2") —v=0; 5 r), Yl)" a relation which is independent of the calorimetric properties of the fluid. For any given equation of state this equation completely determines the inversion-point corresponding to each temperature. We proceed to connect it with van der Waals’s equation and with an equation of Dieterici. (a) Van der Waals’s Equation. We will write the equation in its reduced form, 7. e.,’ pressures, volumes, and temperatures will be expressed as fractions #, 6, and vy of their critical values. The results obtained will then be the same for every fluid obeying this equation owing to the applicability of the law of corresponding states, The reduced equation is (2+ zn) (38—1)=8y, and the equation characteristic of the inversion-points becomes oP co" )—B=0, a p Or Sy 33 — A +o (838—1)=0; whence the inversion temperature is given by the equation _ 888-1)" 48° bo © bo 296 Prof. A. W. Porter on the Inversion-Points for From this and the previous equation y can be eliminated, with the result 9 ye Le = di = pl This formula connects the reduced pressure and volume which correspond to an inversion-point. The simplest mode of calculation is to obtain y for a series of assumed values of 8, and then to calculate « by means of the last equation. The curve obtained by plotting y against # is shown in the following diagram (fig. 1). eee a pers ( Ordinates—Reduced Temperature. / i Abscissee —Reduced Pressure. Ordinates—Reduced Temperature. Dotted curve { Abseissz— Reduced Volume. The form of this curve involves the following consequences: (1) For all pressures from zero to nine times the critical pressure there are two inversion temperatures which range from a little below the critical tem- perature to about 6°7 times the critical value. (2) At pressures higher thamrnine times the critical value there is no inversion-point. The curve separates the regions for which cooling and warming occur from one another. The cooling region is of a Flud passing through a Porous Plug. D957 very limited extent. It corresponds to positive values of pov ———v. ot On the same figure is plotted the reduced temperature against the reduced volume corresponding to the series of Inversion-points ; whence it can be seen that the inversion- point which corresponds to the maximum pressure occurs when the volume is equal to the critical volume, the temperature being three times and the pressure nine times their critical values. Olszewski’s so-called inversion-point is inserted in the same figure (reduced pressure = 8, reduced temperature 5°95). It is obvious from the diagram that in his experiment the gas during its expansion must first of all have risen in temperature and afterwards cooled down to the same value as at first. The point obtained is therefore only a fictitious Inversion-point. We shall return to a consideration of this question later on in this paper. (b) Dieterica’s Equation. In Drude’s Annalen for 1901 (v. p. 51), Dieterici published an equation of state, viz. : —A Ri ae P= ie ne es u—b 5 which fits remarkably well throughout a very wide range both above and below the critical point. Indeed, it is the most satisfactory of all which contain three constants only. The law of corresponding states is true for this equation, and when reduced it becomes The reduced temperature of the inversion-point is given in terms of the reduced volume by the equation eee EN: Touvar Fs and it is given in terms of the reduced pressure by the equation 5y—8 a a=(8—y)e 7 558 ~=Prof. A. W. Porter on the Inversion-Points for The values of « and @ corresponding to various inversion- points are tabulated below :— Reduced temperature | Reduced volume _—sReduced pressure of inversion-point. | of inversion-point. | of inversion-point. O 5) Wenee | 1 Ay i ee a. 2 2/3 Ge? = 9-894 3 | 4/5 Se =1611 4 | de? = 17-93 5 | 4/3 Bet = 16-422 | 6 | 2 Qe © = 19-47 | | 7 | 4 cli 6-89 8 | aD 0 | These numbers are plotted on fig. 2. Fie. 2, Reduced Inversion-points according to Dieterici’s Characteristic mm Ordinates —Reduced Temperature. Abscisszee--Reduced Pressure. Ordinates--Reduced Temperature. Abscissee—Reduced Volume. Continuous curve { Dotted curve { (c) General Discussion. The curves which we have obtained corresponding to different equations of state both exhibit the same general a Flud passing through a Porous Plug. 559 consequences with regard to the series of inversion-points. At the same time they exhibit the extreme sensitiveness of phenomena depending upon the Joule-Kelvin effect in dis- criminating between different equations of state. On each of them are shown the points representing hydrogen (H) under usual conditions (7. e. about 20° C. and a few atmo- spheres pressure). This point for hydrogen is calculated from the values of the critical temperature recently determined by Olszewski, viz., 32°2 absolute (Drude’s Annalen, 1905, x. p. 986). It will be seen that both van der Waals’s and Dieterici’s equations given above indicate a heating of hydro- gen in expanding at ordinary temperatures. The inversion- point corresponding to a few atmospheres’ pressure is about 6°7 times the critical temperature according to van der Waals’s equation, 7. e. at about 216° abs. ; while according to Dieterici’s it is at 8 times the critical temperature, 7. e. at about 258° abs. Thus for moderate pressures, if the latter equation holds good, hydrogen should undergo cooling at temperatures much higher than has hitherto been thought. An accurate determination of this temperature for various pressures will discriminate between these two equations, even at points in the neighbourhood of atmospheric temperature and pressure, in a way which no direct measurements of p, v, and ¢ can ever be expected to do. Dieterici had previously published another equation similar to van der Waals’s, but.in which the molecular pressure term is given by a/v: instead of a/v. This equation holds good near the critical point only, at which point it is very satisfactory. The law of corresponding states applies and the reduced values for the inversion-points are easily shown to be _4(48—1)° ae es UO 2) D raeh The same general conclusions can be derived from these values. The equation does not profess, however, to have an equally general validity as the others, and consequently will not be further discussed. It is a notable fact with regard to each of these equations that the maximum pressure which gives any inversion-point is that for which the volume is the critical volume. A further connexion is shown between any inversion-curve and the corresponding equation of state by the following considerations. 960 Prof. A, W. Porter on the Inversion-Points for Consider any two points A and B in the same vertical on inversion-curves, such as figs. 1 or 2; for these the pressure is the same. They will therefore correspond to two points A’ and B’' ona constant-pressure line upon a v-T diagram. y | But for both A and B, PS, (7) =(. Therefore a curve v=T/f(p), obtained by integrating this equation, passes through A’ and B' on the v-T diagram ; the form of this curve is immaterial to the present argument. That is to say, the two inversion volumes at a given pressure are proportional to the corresponding inversion temperatures, since /() is the same for both ; or A’ and B’ lie on a straight line passing through the origin as shown in fig. 3. For the same reason, if there were m inversion temperatures for the same pressure, the constant-pressure line on a v-T - diagram would be cut times by a line through the origin. Again, in general for any fluid we may write To (a) = lip: ), and F(p, T)=0 for inversion-points. But the maximum pressure for which inversion occurs corresponds to or - 37/8 = a Fluid passing through a Porous Plug. d61 which can only be when on =(), excluding infinite values of ol oF eae Op By ditferentiation we get St ar(™ ar(n)) =P or Hence the maximum inversion-pressure corresponds to 9 Ov Aj . ap = for the corresponding constant-pressure line on a v-T diagram, that is to say, it corresponds to a point of inflexion on such a diagram. (d) Discussion of Olszewski’s Observation. In Olszewski’s determination of his inversion-point for hydrogen a large fall of pressure was used ; and consequently his point does not correspond in definition with those referred to in this paper. The criterion of all points such as his is that the temperature does not fall on the whole in the actual flow, even though the difference of pressure is large, and this corresponds to the condition U + pv = constant, where U is the intrinsic energy of the fluid. If then it is possible to obtain the values of U+ pv for various tempera- tures and plot constant-pressure values against these temperatures, the resulting curves will necessarily intersect one another, the point of intersection of any two constant- pressures lines representing the inversion-point in Olszewski’s sense. The value of pv can be determined for some fluids from Amagat’s determinations ; but the value of U involves calorimetric data as well, and these are very imperfectly known. For a substance obeying van der Waals’s equation auU=d@ —pdv =C,dT + (1 or raed Jee - a = Cra aaah dv, iD) gt and peat a Ov ol" 562 Prof. A. W. Porter on the Inversion-Points for Consequently C, = a function of temperature alone. fi U-U.=/() -2 +4 where v, is conveniently taken as the volume for which T 1s zero, viz. b. Hence for a van der Waals’s fluid U + pv can be calculated, with the exception of a part of it which is a function of temperature alone, without knowing the specific heat at constant volume. Writing the above in terms of critical volume and tem- a B 3) : C . a perature, and adding pv, 2. e. 7Z> we have h U-U,+prv—F(yT.) = (3 == \ Fig. 4. Reduced Temperature g 5 2 y The quantity on the right-hand side (yf) is plotted horizontally against reduced temperature vertically in fig. 4, and the fact is brought out in this diagram that successive constant- a Fluid passing through a Porous Plug. 563 pressure lines do not intersect at one point; all within a certain range must therefore have a caustic curve as envelope, and it should be noted that each one of these meets the caustic twice. The actual calculation of the caustic is cum- brous, and as no particular importance attaches to it the calculation has not been made. In Olszewski’s experiment with hydrogen the initial pressure was eight times the critical pressure, and the final was atmospheric, 7. e. roughly 5!, the critical value. These constant-pressure lines are shown, amongst others, on the diagram; their intersection can be calculated more accurately by successive approximations from the equation. When this calculation is made the point is found to be at about 5:8 times the critical temperature. Now Olszewski’s experimental value is nearly six times the critical temperature. There is thus very good agreement be- tween these two results. Inspection of the diagram (fig. 1) shows that while the gas decreased in pressure as it flowed from one side to the other of the throttle, it must (if van der Waals’s. equation were valid) at first have heated until the pressure had fallen to about three times the critical ; in the subsequent 7? part of the expansion it must have cooled by an equal amount, thus bringing about zero change on the whole. On the other hand, inspection of the curve of inversion- points corresponding to Dieterici’s equation shows no possi- bility of this compensation occurring; for Olszewski’s observed point lies within the cooling region. Thus the evidence afforded by this single experimental value is much more in favour of the validity of van der Waals’s equation zn the region involved than of that of either of the two other equations. (e) Ramsay and Young Fluids. For any fluid obeying Ramsay and Young’s linear law we have p=BT—A, where B and A are functions of the volume alone. All the three equations which we have considered satisfy this law ; it is therefore of interest to find the general equation for the Inversion-points of such a fluid. We at once obtain ey dB, dA pov _ tl Gane hae AU witie Lothi twee dv dv 564 Prof. A. W. Porter on the Inversion-Points for This is zero whenever ce ih di dv fone nik ey a ee Bros = Br) unless T is the critical point at which dB dA _ 0 ni Pookes | Mae ie Another example of a characteristic equation following Ramsay and Young’s law is the five-constant equation ot Rose-Innes. In this equation pee (1- ma SS Aa v vtKk—g/v’ v(u+e) where e, x, g, /are constants, and R is the ordinary gas constant. From these we obtain . poe _ vl(2v+«) "de (v + )2u? and —d(Bu) — — - Re(1+29/%,) dv (w+ K —g/v")?- The inversion-points are therefore given by ie 20 1L+x/2v sad ee Cane See 2 (v+«) . Hence when v is very large the inversion-point approaches the value 21/Re ; while as v diminishes T; at first iereases since «/2v is the dominant small term. Hor isopentane the values of the constants as given by Rose-Innes (Phil. Mag. vol. xliv. p. 81) are | = 54208005) ae 03; 006, Ces qo walo, R = 4/-008158. The critical constants as calculated from these data and as observed by Young are Critical temperature. (-) 2, “191°-7 C., 18i7an@ > “pressure yi. Sees 20200 mam. 5» volume . . « 4°5, -4:266 cm*. pene The value of T; for infinite volume is therefore 1666 absolute, that is about 3°6 times the calculated critical a Flud passing through a Porous Plug. 565 temperature. For temperatures higher than this value it is easy to show that there would be a heating effect. Hence we have in this case a curve of inversion-points whose upper portion rises with increasing pressure instead of diminishing as it would do according to the other equations, and is at the same time much lower if we take the evidence afforded by observations on isopentane. The fact that the slope of the inversion-point curve cor- responding to Rose-Innes’ equation is for large volumes of opposite sign to that of the other equations, suggested the idea that possibly the equation rigorously valid for an actual gas might lead to a curve parallel to the pressure axis; this would imply a single inversion-point for all pressures. It is easy to obtain an equation for which such would be the ease. For, provided that the fluid satisfies Ramsay and Young's linear law, the condition that there shall be one inversion- point only is that dA /d : v re has (By) =constant=T, ; or 7 d( Bw) aye dA dv dv For the sake of illustration we will follow Rose-Innes in taking A= Bey and adapt his value of B to satisfy the above condition ; then p U(r) Carat En ac Ceers| integrating this equation we obtain l K T,Bo=— a i log v—log (v+K)— aie — const. } ; and the equation of state becomes ee vtkK K P= ar | | const. + log : = | = ere u The value of / x const. /«T; is R, the ordinary gas constant. How nearly such an equation, having one inyersion-point only, is capable of representing the behaviour of isopentane is evident from fig. 5, where pv for the critical isotherm is plotted against the cube root of the reciprocal of the volume. he circles represent experimental values, while the dotted line represents the above equation with values of the constants chosen so as nearly to satisfy four of the exverimental values. 566 Prof. A. W. Porter on the Inversion-Points for The equation to this isotherm, with the numerical values of the coefficients inserted, is pv =397930 +3892300 logy, v+1:870 _ 5554710 VU v+1°870 Fig. 5.—Critical Isotherm of Isopentane. Q “25 Crilical ‘S 75 Vos 1-00 Fluid satisfying dotted curve would have one inversion-point only. Observed values ©. The comparison between experimental and calculated values may be more easily made by means of the following table. |! ] | a pv 2 Ss cole 2-4 | -7503 | 117790 3 6931 | 79380 ; 4 6299 | 100080 8 5 189680 20 3684 | 296800 80 ‘2321 | 369120 100 2154 | 375000 observed.\observed. 490&0 26460 25020 23710 14840 4614 3750 p calculated. Porter . |Dieterici. 29627 | 42730 25453 25020 23778 14752 4614 3148 26780 25320 23400 14560 4604 3740 a Fluid passing through a Porous Plug. 567 Thus, from the last two columns, it is seen that this equation, which only indicates one inversion-point, actually fits the experimental values better than Dieterici’s second equation throughout a range from large values of v to values below the critical volume which is 4°266. Below this, however, it is hopelessly out of competition. At the critical volume, however, it is far superior to van der Waals’s equation, as is shown by the cross on the diagram, which gives the value of pe for the critical point as calculated from van der Waals’s. The constant inversion-point comes out as 14 x critical tem- perature for isopentane ; bat it should be noted that the equation does not satisfy the law of corresponding states. (£) General Condition for the uniqueness of the Inversion- Point. We have worked out the special case of a Ramsay and Young fluid. In the general case where no restriction is introduced it must be possible to write Sn) = 0-9/0, D, where /(p, T) is a function of p and T which never vanishes unless when T=«, and which is not infinite when T=k. The constant inversion-point is of course T=k. Integrating this equation, we obtain a(n) hy baby) = (T=) (pHa) + HP) as the most general equation of state which gives a unique inversion-point. In this expression y is restricted to be a function of p and T, whose first two differential coefficients have no zero unless when T= «, and no infinity when T=x. Further, y(p) is any function of p alone. Conclusion. The chief points brought out in this paper are the following :— (1) The value of the inversion temperature of the Jouie- Kelvin effect is probably a function of the pressure ; and even for the same pressure two inversion-points, in general, may exist. er ry es 56 38 (2) Different equations of state, all of which are fair approximations tothe behaviour of a real gas, indicate very different values for these inversion temperatures. (3) The sensitiveness of the positions of these points to change in the characteristic equation of the fluid makes a knowledge of their actual position, as determined experimentally, a very valuable means of discriminating between the relative validity of any proposed equations of state. Mr. R. Hargreaves on some Ellipsoidal In conclusion attention may be drawn to the fact that all the results given in this paper are evact consequences oz the equations of state to which they relate. XLVI. Some Lllipsoidal Potentials, Aolotropic and Isotropic. By R. Hareruaves, J.A.* ie a former paper on Alolotropic Potential, the potential functions corresponding to normal distribution on a conducting ellipsoid and to uniform volume-distribution were treated. The functions are ( ae and. ( a) 2 ; Juve Ji VJ where J is the cubic in X which replaces the isotropic form (P4+A)(U+A)(CP+X), and wa=1 represents the eolian quadrie which replaces a confocal. If the additional factor Ola ao occurs under the integral slgn a vector type 1s given, P which was also considered in the second, but not in the first ease. It is proposed now to deal with the more general types tm dN s s (1 l a : NE [ua > OF, We —wiee-or, (1—2ie and with types in which the factor Se is attached to the several forms. ‘The second and third forms belong to volume distributions with densities depending on powers of u,; the first has also a normal surface-density. The energies attaching to these potentials take the simple form of numerical multiples of that of a conductor. They are obtained by the use of what (in the paper cited) were called wave-forms of the potential. Two theorems are re- quired for the purpose: one to connect the wave-forms with * Communicated by the Author. Potentials, Aolotropic and Isotropic. 569 those written above, and the other to deal with moments and products of inertia of any even order for an ellipsoid. The evaluation of energy turns on a similarity in the forms of the two theorems, and they prove to be closely related. A potential is then considered which is a linear function of members of the second type, namely, é. ; 2 n—l dn Plier cleentln --atle, steel eile, ny) aa vr V/ J The energy is a quadric in the 4’s, persymmetric in form ; while the whole charge is a linear function of the k’s. For any value of n this potential may be determined so as to give a minimum of energy subject to constancy of total charge. The minima have simple values which decrease as n increases, ranging from that for uniform volume-distribution (n=1) to that for normal distribution on a conductor (n=). Thus the potentials form an interesting series of links connecting the two potentials commonly considered with reference to an ellipsoid ; and each potential, with a distribution depending on n constants, in some measure simulates that of a structure containing n parts brought into relation by a minimum condition. To give greater generality the work is written in zeolo- tropic form; but most of the energies evaluated vary as ik and the only difference between isotropic and 1? o AI | seolotropic forms consists in the relation of the constants in the cubic J to the axes of the ellipsoid. § 1. Of the three forms* Be EO ue i aL tua) dr Va Ze Vd : A), al ‘ Wee (" (1 = t,)*dr ae Ja Vd ; = the first will be taken as fundamental, results for U, and V, being directly deducible from those for W,. Since u, may be written =1 when it is not under the sign of integration, we have (1) aA, pan sh S fe ig OMaeea Gon A Wada: A AR Ma Oa Nadi * The notation is that of the previous paper on ‘ Adolotropic Potential’ in Phil. May. April 1905, quoted as At. Phil. Mag. 8.6. Vol. 11. No. 64. April 1906. Paid 570 Mr. R. Hargreaves on some Ellipsoidal Thus the surface-discontinuity or density is the same for all the functions W and is that of wy; while potentials U, and V, containing differences of powers of u, have only a volume-density. A second differentiation gives diye

dr Jdn *)- sp Oa dr diddy = = DV INdedy OS dx dy Aan JoOk “| +2 (" {; Liens: , op ONa OU, “VY Ua +s—1uU, Ou Oy x. When V2; is formed, the sum of terms such as those in the first bracket vanishes, and the total outside the sign of integration is —sp/ /J. Under the sign of integration the bracket gives pes > (pa+ 2p’a!) —4(s—1) Thea Og. or Que? J/J —4(s—1) us *u, quoting AL. (76) and (86). Hence the integral pees i fe) = C0 s—l = i a. Of 2 )\a=so uf eee P|, or v7 Externally the lower limit is variable, and a two terms are cancelled in virtue of u,=1; thus Va~,=0. Internally the lower limit is constant oS 0, and there are no terms outside the neg sign ; since X= 0 makes J=1, u,=w,; thesan= tegral is spuz ", that is V ow =sp us’ and the volume-density is —spu;. The surface-density o dvr, a dp, aoe dy, | sae =—[o Moe eb en(o oath ant vol +p ee 5 oh] =? Oa a ,dr D) _ pa @ being a perpendicular from the centre on a tangent plane and J mn direction-cosines of a normal. dps a, Ob ag Whe ong Ms Since == a AG = an are external dz ax Ox’ ax dx ~ Potentials, Hfolotropic and Isotropic. 571 oYvs potentials, so also is ae It is more convenient to use an v independent notation for the vector type, and we take X.= ‘% ve OVE Tas No) * VJ Since ee: ih STi Rees ee ieee ) ous an oil [aus tsi (ax +y'y + B’2) vik the surface-discontinuity is the same as for x, and the e < GD ° surface-density is a (ax+c'y+b'z). The volume-density is —sp(ax+cly+b’z)us—* as appears from the connexion with wWsi1; or by work following closely the lines of Al. p. 442 we show that lee rant vy 8 2) VI =p ee (an +y": Fett ED) \ an = —sp(au+q'y + B'2)/V/ I + sp uy Nien ils. ope from which Ve X.=0 externally and =sp (aw+¢y+0'z zy ae internally. § 2. We proceed to the formule by which the above are emeterred to wave-forms. In the latter it is more con- venient to work with w=)AA, and A(w)= AJ (A), identity in final results following how dp] VA A(w)=dr/ VJ. The fundamental formula for ranetor ence is ge (cate te ae = ( Ugh pe =| War _ (3) 2a) Ung + peu, ? VW? UNG Take and a particular case is AG ( (etmyt+nz)* do ("uidn. 20 u, Want a ore: the general case applies to external potentials, the particular to internal potentials, the latter specially required for energy. Now io is an immediate integral, with regard to mw, of (le+my+nz)*% da _ Slee cst fe > 1 a (us + pu, )st3? F 25a V A(w) WA(u) , (4) ~ Gs DAW) FFE (3 4) o72 Mr. R. Hargreaves on some Ellipsoidal the particular case with ~=0 being _ 1 ¢ Getmy+nz)* do _ Wa , 3/2 : i 4dr uxt! (254 DAR (40) U, and u, on the right hand have (xyz) for variables, u, and u, onthe left have (Jmn). We shall deduce (4) from =| dw eel LES ' (5) Aa (uy ue,)? — 7 A(p) ee an integral obtained indirectly in the previous paper, and first give an eee proof of (5). The volume integral ( dx di al/2 ae pe 2 ; Al} 7 7 Yy me where the range of integration is the volume contained a by the ellipsoid Ue tace a PA . at Be fe —=1, is well known. Put Gag, 2=r(lim, sy and use a polar element of volume rdrdw, where dw is an element of area,on a unit sphere ; then integrate with regard to 7, the boundary value being: Q 2 1=R(=, i ae 2) The result is 1 [2 Wiz nz i ae ef dw ie eile 62 te ¥? =aby, or Lif 2 24 2\92— a dw/(al? + bm? + cn”) ae If the ellipsoid is referred to general axes, then ug (1, m, n) takes the place of al? + bm? + en®, and abe must be replaced by A,. If again for a we write A+ypp, for a’, A’+ yp’, then A, is replaced by A(y), a determinant with the elements A-+wypp,... and this is (3). The step to (4) is made by using an operator / i 3( 2° - +2 iw) say O. Sul n,n) = 0 Since Win = 2 d Ne we have O.u, (1, m, n)=(la+ my +nz)?. Potentials, Holotropic and Lsotropre. O73 And since l : ad d 2a! A (uu a) =Aly) = As and 7a Aw) = 24 Ci) x ie we have UA(m) ie a Deepen le Also wac.) written at length is Ya? {(BC—A”) + pu(go+rB—2p'A’) + pP} +23 y2{ BIC —AA'+ p(q'O' +7 Bl—pA'—plA) + WP}, and therefore d : FA MAW = (C+ wry? + (B+ wg)? —2 (At wp yz, | ard _ a qA! Maw = (C+ pr ew + (Bi + yg!) yo— (A+ pp)ye— (Al + wp')a’. | When the whole operator is used all terms are cancelled, and we have the three results O .u, (l,m, n) = (le + my +nz)?, O. A(p) =UAu)(2,Y, 2) = al (14) ; 1) Ay? and Orang.) (oy5.2) 0. Hence the operation applied to the first and third members of (4) yields a repetition of (4) with s+1 for s; and (4) follows by repeated use of the operator starting from (5). The formula of transference when ax + y'y+ Q’z appears under the integral sign is got from (4) by use of the operator a do Pa Bae, De= "aK '* 9 aCh* 9 gE for which O, .u,=lU(le+my+nzy, O,'.A(w) =A) (av +ry'y + B'z), ; (8) OF nay Os This gives 1 \ Ile +- my + nz) dew aa (ax +y'y + B'z) 3 oS SS ——— 9 Agr (UF tt): Bel (2s+1)As Vv A(u) ( ) mere with regard to w from mw to » and raise s by 1, then ; =| i(le+ my +nz)s*) do _ i * Us(ax + y'y+ B’c)\dp 10) 2a Up (UA ae fu, 2? 2 WANG) > ( 574 Mr. R. Hargreaves on some Ellipsoidal and in particular As? (ide + my + nz) deo _ ihe (au +r'y + B’2)dp s+3/2 a ey) 0 VA(u) 7a rs Uy UA § 3. The faaddiacgal integral for moments of inertia in an ellipsoid is 1 AA 5 ~)28 3 f ua(Z, m,n) 75 = | (otmy tne) a (2s+1) Qs +3). | (11) The coefficients of like power arrangements in /mn are equal on the two sides, so that all moments and products of inertia of degree 2s are comprised in the formula. A way of expressing the results for individual terms, which also applies to (4), will be given later : but for our main purpose the form (11) and some collateral results are required. In immediate connexion with (11) are i s! 3B UA S = ( (tet my trey” Ua dt= (954 1)(9s +2543) cS (116) and the surtace integral il Be 5) (3) = | (le+ny +02) ods =o TTA ee (11 ¢) where @ is a perpendicular from the centre on a tangent plane. ; Write z,.7,2—7Q. 7p, ), use apolar element of volume 7dr do and integrate to the surface value i? aN, ie, Ve For (11) } (le + my +nz)** dr =|fe (IN + mp + nv)” dr doo 1 me ee | R*s+58 (1X + mp nv) dws for (ii b) ( (ic my +nz)* Un “dt ness u +3 (Bese 1A + pe + nv) uf (A, vdeo ~ 232s! mol 8 (Atm ti)™ deo; and for (11 ¢) i; (lve + my +nz)* adS= (res (N+ mp + nv) do, since a@dS=R* de. Potentials, Afolotropic and LIsotropre. 575 Thus the three forms all depend on one angular oe which, in view of the value of R, and eee a / A "(N+ mp+nv)** do — {uy (1, m,n) ts rea {ug(, 2,V)} 2 7 Os 1)Actie ” This integral is a variant of (4b) got by writing a for A. A modification of (11) by a factor av+¢y+6'z is required oe d d Nes for the y functions. Operate with a Il +o — Fait b Fy OD (ah) and raise s by 1, thus leg = =) (av +c'y +0'z) (le + my +nz)*8*! dr Me 3l UA\ . ~ (2s+3)(2s +5) S pee, lta) then 1 f 7 |) (aetelyt+ biz) let my +12)84 ug dt Be, 0G Ua\” (2s +3) (2s +2 s'+5) (<2) , (124) and ‘ye Doe i al (aw + cy + Uz) (la + my + nz) @ dS By) UA = a= || D) eee eee eo are connected with (12) in the manner shown above for (11 6) and (11). § 4. The evaluation of energy now follows by combining the typical Ses thus :-— alle +my+nz)*sdo = us At eva =z, fu! om Deru, FP by (30) . by (118) Tey 3 2s! ae lone aoe 3h, 9 (Oma (28+ 2s' +3) pupa ite) using @, as in Al. (135) for = aDS is dp Ae MO, Ia we WANG T i) = Vanes We may fi write (13) as ee Sonam et Ua pdt = 7 £(2s41) 2s+20'+ Bago + (13 0) 576 Mr. R. Hargreaves on some Ellipsotdal and the surface integral is SPT .P ig a= SR oe \y.eus Hse eG | oo yore lee) Now the poremael Yor has a surface-density Aete. and a volume-density —s'pw,‘. The term in energy due to the interaction of a, and w,. is therefore E(s, s’) =4)\ paypdS ~ {eeu Ws dt = F(t ihe Ze )= 3p°T Po co) EWS SS | Syma Ore | 8 (2s +2s' +1) The energy due to , alone is 3p?7),/16 (484+ 1), i.e we write s'=s and halve the result. The energy belonging to hab, + ke is ve ks + 2k ks, ayes es |. 6 Ast+t1l 2s+2s'4+1 ° 45/41 but it is tone sufficient to give as in (14) a single compo- site term. The total charge attaching to 1, is | ee en _ 88pT. OPT, 4\ padS — | Spun ah 9 ~9.47> HQs41)- For normal distribution on a conductor s=0, e=3pr,/2, and the energy is e*,/12r,. From (14) may be derived the composite term in the energy of k,U,tkyUs, or of k(rs—Ws41) thsi pss 4i)- For this term we are concerned with the products Ps! We Ps'+1 Vo Psi Wes+1 t Ps'+1 Wort and the application of (14) yields ee E 2 ih ] ; amet ts ini nia ee ae Os 3.) 95 4 Ota Bes ati (15) ~ 9549S +1 Qs+9943 WFIILH? which multiplied ue ks kg 1s the contol tae required. dn VW] I ? p —— ( — s ate To deal with the function V, ox n | > Val (1—w,)’, the two summations for the indices of p and wW may be taken (14) Potentials, Holotropic and Isotropic. a¢7 separately. The first is 3p°T Ho sy siCy _ =; a ] Spiro, 2-4... 2s! and the second is oo tia ope Ao 8 Ry wes le ah so (a ae HOT pice os = Oe oe eB OSLL Dee ORT SLT, _ 3p Th, Dp Ane cy Pay (16) ORO en Ose ON Seal and this quantity multiplied by &, & is the composite term in the energy of k, V,+ky Vs. The summations for (16) are made by a series of steps in which the combination formula C=C + C is used, and the difference of adjoining terms Sip Gall Gp s—l r—1 taken. The densities attaching to U, and V, are respectively p(stluz—su,) and sp(1—u,)*~!, and the corresponding oP sO and on ae oe they 2s+1 2s+3 Ze OMA SET follow from those of y,, or may be got by independent work. The energy formula for U; may be got directly, viz. for the composite term i(s;'s") = \ pv U.dt total charges Ol eee maur(l—u )dr_,. = | p(s’ Fld —s'ul—}) dr. an wal a -» which by (13) __ 8p’ TP | a if 1 if } a=, eee Jt Ih Se 4 ( sear 2s+2s'+3 2s4+3 2s+28'+5 1 1 } ] IS — ——— (aa 2s+2s'+1 2543 254+2s'+3 = 39°7,oo/(2s + 2s’ +1) (284 28'+3)(2s + 28+ 5), in agreement with (15). Moreover, the energy of ws may be calculated from that of U, by treating y, as Us+Us4i+ ... ad inf., and making a double summation of the formula just obtained. Hither U,; or V,fors=0 gives the case of uniform volume distribution e=ptT , and energy =e7y/107>. 578 Mr. R. Hargreaves on some Ellipsoidal § 5. We now give corresponding results for y,. Using the integrals, (10% ) for the first step, and (126) for the second, ui(aat cy + Vs yee pening 0 JJ f s+1 ~\ 28 - x, nalan boy +U'e)ar (2 (le 0 27u, Ua st 32 x = : Aa oy (2s-+3)(2s + 2s’+5) Qari, uy 3” aL, —Os3)\Gsr2s45). °° >: where.Ly as in Ad. (135) stands for ” adr a. A.do wa S omttea es This and the corresponding surface integral may be written 3pT,L a> a us bl = aed fuclartey +i Z)NsAT T2Qs+3)Qs+2s'+5) 7 (17 b) and Meer Ne _8pt,li, Bp f(etey biz) XewdS= z £(2s+3)- (17 c) The surface-density due to x. is = (av-+c'y+b'z), and the volume-density —s'puS—l(ax+e'y+/z) ; thus applying (17 6 and c) the composite term in energy attaching to indices sand s' is 3 25! Den K(s,)= op 1, 2s apr Li 8(2s+3) om 2s+2s'+3 - 8(2s + 2s'+3)° (8) If functions with y/7+fy+e’z and B’7+a'y+yz are also under consideration, the three functions may be distinguished as xs(x), xXs(y), Xs(¢ 2). In the composite term for y,(y) and vs (y), M, appears for L, above, but if a composite term for V<(2) and vs! (y) Is In question N,| appears, viz., N/= Adlmdo _ (‘ ydxr a Za a7 J ° 0 For the density of y, (y) has the factor c’c+oy-+alz ; and if this is taken with y;(x) a factor m is introduced in place of 1 in the second step towards (17), where (12 6) is quoted ; while the contrary arrangement, density of y,(z) with potential Potentials, Aiolotropic and Isotropic. 5G9 x (y), introduces the factor m in the first step where (100) is quoted, with an identical result. For the volume potentials of magnetic ee 2s eee “yp ae (1 u allat+yyt+ ae vi and ip Se Nel ie AN (1—ua)s(ax + y/y + B’2) ap which we may call U,'(#), Vs'(#) the composite terms in energy are respectively 3p°r,L,/(2s+ 2s + 3)(2s-+ 2s" + 5)(2s4+2s'+7) . (19) and 2 2 2s 3e°T Li, DAL Delos! (20) 8 35... aaRe4 3 Tn lieu of total charge in connexion with yy, we may here take a magnetic moment* defined for y.(a) by LOR, = \eputr= 22543)? er rotor Ui(«) ib ig or the function U,'(x) it is SEU IRE correspondence is given between the two types of potential. § 6. We now consider with reference to a potential 2 = EA -- ae, el U =I Thus an exact dx Lt) (ky + katt, + ue+.. SL ee the problem of eos the &’s soas to make the energy H a minimum subject to the constancy of total charge e, Hi and e being given by = ae dp, { tL 2k ko ena Hi a Teeter c |) | . (21) iehtyrdye 3 SoleUaee Bes * In the case of Ad. (117) where these functions are used, it is, however, a question of total charge, and e=38pr,/2 for the conductor (s =0), e=pr, for the uniform volume distribution (s=1). The energies for x, and for x, are then respectively ¢°L,/36r, and e°L,/70r,; thus if we seek the energy of convection currents due to surface charge instead of body charge, we must write in At, (117) c/36V* outside the square bracket. 580 Mr. R: Hargreaves on some Ellipsoidal Ifa similar problem is stated for — ale L—wu,) (ky +hotta + .. hi) (ax + y'y + B’2) ie is replaced by L, and e by mz, and the coefficients open with ly A ea 1 1 ———__ and =—— instead of ane — By writing ie ee 13% 3 me S e Bie c= Ee for each subscript the minimum problem is pre- OPT 0 sented with pure numbers, and we may generalize it by making the series of coefficients start at a different place. Thus using Ap=1/(2p—1)(2p+1)(2p +3) and 6,=1/(2p—1) 2p +1), it is required to find w the minimum value of O.= 9, + Goto t+... 2, Extn E where M= Oph, + Opyibo+.-. Aprn—1Ey | N= Ap p1€ + Opr2ket ..dpynkn | r+ (22) n= Ona nce, «2 Ont one = define the 7’s, and 1=6p&,+Ops18+... Opinriké, J is an equation of condition. From the point of view of potential theory, interest attaches to the value of the minimum, which proves to be _ 2p—-1 n+1 2n4+2p—-1 2 — n 2n+2p+1 in the general case; and to the nature of the distribution which gives the minimum. For p=1 the case of (21), w= (n+1)(2n+1)/2n(2n+3) and EH=é¢,o/67, ; while the density for the potential P is Pas + &(—1+2u,)+&(—2uat 3u2). AE(H—n—lLug ta 1) or (28) 3p [fi —& + 2(&—&)uat 3(B—E,)we t+... +n£ we] aa ) | or say \ (24) | =o UA Let vqu7t+.. + 2,U- ZF | 3T,, a Potentials, Aolotroptic and Isotropic. 581 The conditions of no variation are = 0b, No=Obs,...with L=bpE,+...bptn—1én 5 1. é. Ap Ey ee Apntn—-1 En = ob, | 3 . (25) An+n-1 E, Simin p+ 2n—96 0 = Onin—1 | bn&éy + vee Geen E,=1 )} Write the first as wbp= (FE, — Eo) dy + (2 oy) (a> + p41) aie (&; —£,)(ap>+ Apn+1 af Ay +2) = RINe ete E,(ap os ar KO =) > and note that Ant ap4it .--Aptn—1 =f (, — by 42) a HW ( iL gah: il q 4 ag apes 2p +2n—1 Pees er cae 2p—1 = eat oe ome a 1 an i Be oe 2p—1 Ip+2n—1 2p + I Int In+13° The first cu of (25) is then tpt Ln al an pts +3 Bel pet bs ao Lp Dare ale BOSE ee @ al ; and others of this type are got by increasing p by 1, 2, 3... n 2n—1.2p+2n—1 tion of condition treated in this way becomes Since bp + On+1 Se Ope a — , the equa- Bi 1 Vy ss Nn , [SLA ee SS == 9) oe 92> ei 2p Eo op Loman et? OD The group of equations is then equivalent to Vy Ur 2p + C(29—1 2p+1 2p + 2n 1 gee vy Uy oo gag SL he er Qn +3 ane Qo+2n+1— at Chet 582 Mr. R. Hargreaves on some Ellipsordal together with (26). The first with (26) gives 20 + C(2p—-1) =2p—1, and the right hand of the g+ 1) equation \ ¢ : + =20+C(2p+ 29-1) =2p +29 -l= goog? which if the stated minimum (23) is correct D = (Y= Shits | Ue oa E n(2p+2n+1) The group of equations is then Uy Vo Un 2p+2q41 ei = 2p — 2 a —— [n(2p+2n+1)—2q] . (27) where g has in succession the values 0, 1, 2 ..n; if these are satisfied the original conditions are satisfied and @ has the value in (28). Tf P*(#) is used for the 7th differential coefficient of the zonal harmonic P,(), the solution of (27) is comprised in the statement of the following as an identity, viz. : > 20+ 1 2n+1 20+3 2yn+1Z Zp+3 2p+5 , y+ Lop? . — + agp 2 a 4-0, po? — P Qn i p2te ' (42 ) 2n+p R23) ~ n(Qp+ 2n+1)1. 3... 2p ae The numerical coefficients on the left hand are cleared by an integration a dp, followed by p—1 integrations = \" pidp, and the result is 2n—1) thy ye a Hm 4, 29-+-In—-1 (2p -l pit? . vy pL + vob! aR oe Unf P == n(2p a In+ 1) 2 Ponies b) (29) for p=1, tytayet... =P,,,,/n(2r+3),”, 2 ede and for p=2, ayi+ e+... =3(uP2,,,—Po.42)/n(Qn+5). (29¢) The left-hand member of (27) is got from the left-hand member of (29) by multiplying by petl and integrating from Potentials, Holotropic and Isotropic. 98d #4=0 to 1, 2.e. we require , a! | Pott du=n(2n +3)—29, for p=1, 0 . | i (MPS, 19 a Poeea)e du=n(2n at 5) —2q, for Oe 2, | 0 1 and (30) l Pa LS n(2p+2n+1)—2¢ for the general case. i) Now 1 iL ‘i a SG (1) ia (29 jis 1) | [Ti aT 0) and alt 1 | pee) du= Porat (1) -2y| (een Porat dp 3 0 0 the last term vanishes for g=0, 1, 2....n, but no further, and therefore 1 \ Pog Met du = (n+ 1)(2n +1) — (2g +1) =n(2n +3) —2¢. 0 Again | ‘ ; 1 if (HPont2— Poo dp—P,, 9 )—Cgt 3) | ee Ponto while 1 1 | peat? Po g2dw= Porta (1) — (2g+ ma) Po pod. 0 0 The last integral vanishes for g=0, 1, 2,...n, but no further, and therefore 1 \ (22 sale een) al d= (n a 1) (2n ai 3) ie (29 a 3) ae n( 22+ D) —, 2q. 0 The solution is therefore fully verified for the cases p= 1 and 2, which belong to the two problems stated, the cases of potentials P and Q. For the general case a mode of proot will be briefly indicated. Carry out the operation I by using Pi, —MP,’=(s+1)P; differentiated any number of times, hen in the result J?-!. 1g ttee yields LES ane —(p—1)(2n+2p+ 1) Pee +a residue, | Py 0 be d84 Mr. R. Hargreaves on some Ellipsoidal The residue can be expressed as a linear function of the P’s of odd degree from P3443 to Po op and the multiplication of these by y27+! and integration from 0 to I yields a zero result from g=(0 to q=n. The integral on the left hand of (30) is then A comparison of (296) with (24) shows that the solution gives directly the density. Nowa zonal harmonic has a point of inflexion between each maximum and minimum, therefore #1 P. 4, vanishes for n—1 values of yu”; hence the density vanishes for these values of wu, The distribution is one in which there are n concentric ellipsoidal shells of alternate positive and negative charges. When v is indefinitely increased the charges on all but those for which u, is nearly =1 are indefinitely small, and the case becomes that of a conductor. A simple independent proof for the case of n infinite shows the character of the limit. Since b pe Uncerese age \Ch IC) by - the equation of condition may be written t= E(Gp t+ Gppit...) + &o(Qppitappot-..)+..-=m ++... 2. é. itcan be expressed in terms of the 7’s. But 60=£67,+... subject to O=6y,+5n,4+... makes the é’s all equal ; and it is then easy to show that each =2(2p—1), and that o=(2p—1)/2. The potential P (case p=1) is then Ray OT, ( tu) 4a, Fuad.) = dx e We ay UR VA OT and the potential Q (case p=2) is ters) ee = (ax +y'y + 8’) (L—ua) (1 + Ua ua? +...) Be ow A es ( (avty'y+P'z) ais ‘ VJ ? The higher derived functions which would correspond to higher values of p in the minimum problem are not here constructed. | § 7. In conclusion we return to the general theorem of moments, give an independent proof, and then show how to iu [ Pon -2p—1 —(p—1)Q@nt+2p +1) Dona atel d= (n+p) (2n+ 2p—1) —(2¢+1)—(p—1)(2n4+ 2p +1) =n(2n+4+ 2p +1) —2¢ as required. Potentials, Holotropic and Lsotropic. 585 deal with individual terms. We set out from the sphere, for which e 1 urri2 249-2137 T ce) i R (Cr ("20 [ : , s = — r’ sin @ dr d@ dd (r sin @ cos @)”” (7 sin 6 sind)?” (7 cos 0)?” Maes O 3) 0 <0 2 Speen 9 Syn | 2 San | peer t, 5 8 Ys I I yop ees vg dee Ou ae 2s 1, 1.3... 2y,+2y,+23+3 hence for an ellipsoid referred to principal axes ax? + by” t+e2?= ily with A= be, of L a) — é 227 2 2v2 +273 d 4 . J us —3 (. e y ie Loe L352 — LL. Se. QT hg Bouse ey, UR Ay VA) VA, Therefore, if 2s =2v,+ 2, + 2vs, [2s 12% mn (5 5, 5 5 (le+my+nz)*%dr = >= OD Ee 0 2v1|2v9| 2v3 T, ad : has (— i (= ‘ cer ~ (2841) (28+3) “ly, |vg vy \Aa / Tad A a 3 (= + Bm? + =) s ~ (2s+1) (2s+3) aN Now suppose wy < transformed by a linear substitution to other axes 2, y, 2, which are not principal axes of the ellipsoid, and /mn transformed by the inverse substitution to /jm,n; (cf. Salmon, Higher Algebra, p. 102). The transformation makes la+my+tnz=la;+myy,+n,21, leaves Ac unaltered, and gives Ajly?+ ... + 2A,'mn,... for AP+ Bm?+Cn?. Hence dropping the subscripts we have the general form 1 » Uine\S ae acts: D’D> = ——— me P = \(letmytn ea, Qst1)(ds43) a) (11) In order to deal with specified products of inertia, a mode of writing the coefficients in the expansion of a ternary quadric is required, say {ual e, y, Zi = day 2s K (v1, Va, ¥33 @) with 2s=V, +. +73 Phil. Mag. 8. 6. Vol. 11. No. 64. April 1906. 2Q 586 Mr. A. 8. Eve on the Absorption of Then comparing corresponding terms in the expansion of (11), Sie se L opandt= 2 Bay: es T, (2s+3) |2s+1 A* The particular cases s=1 and 2 were given in M. p. 443 without proof. Making a similar application to the angular integral (3), the type of an individual term is 1 l44.m.n"3sd@ V) Ve vs (° KO, v2, ¥3 3 &) de , SSS SS pi? —_., (83) Lor} Up(Uat Ml)? — 2s As), V/ A(u) The special cases s=1 and 2 were also given in Al. p. 445 and p. 459. The calculation of the coefficients K is facilitated by the use of sequence equations, obtained by differentiation of (31). Thus differentiation with regard to « gives the first of VjK(Y, vo, v3; a) =(4y,+r2+73)[aK (v,—2, v2, v3) +e/K(v,—], »,—1, v5) +b'K(y,—1, v9, v3—-1)] VoK (V1, Voy V3 3 4) =(¥, +¥2+ 3) [KY —1, vo—1, v3) +O KY, ve—2, vs) | +a’'K(m, 2-157 —1)) V3K (V1, V2, ¥3 3 4) = (4 4+¥. +43) [6'K (vy, —1, ve, v3—1) +a’K(y, ve—-1, v3—-1 +cK(v, v2, ¥3—2) |. If in K(y, v2, v3) one of the indices is negative K=0. There is a second group of relations of which the type is A(y+1)K(y4+1, v2, v3; a) +C/ (ve +1) K(%, v.41, v3 3 @) +B'(vr3+ 1) K(y,, v2, v3+1 5 a) = (y,+%+73+1)K(y,—-1, v2, v3; a), got either by inverting the first group, or independently by the use of (Ag =. gue + B’ s) es, | Cie div dy OED Sets eae XLIX. The Absorption of the y Rays of Radioactive Substances. By A. 8. Hvse, M.A., Lecturer in Mathematres, McGill University, Montreaé*. G bisa following investigations were made in order to ascertain whether the y rays could be taken as an accurate measure of the total amount of radioactive matter present in a given substance. It was, therefore, necessary to ascertain whether the y rays of various substances were absorbed to an equal degree under the same conditions. * Communicated by Prof. E. Rutherford, F.R.S. the y Rays of Radioactive Substances. 587 When the activity of a substance is measured by the a or B rays, the effect observed depends on the density of the active substance. In the case of 8 rays it is necessary to cut off the a rays by screens of aluminium or some light material, and these screens absorb the 8 rays of the different active substances to an unequal extent, so that the @ rays are not satisfactory as a test of activity. There seemed good reason to anticipate that the y rays would afford a most satisfactory measure of the total active matter in a given body, because these rays under the ordinary experimental conditions are but slightly absorbed by the matter from which they are emitted. It is possible to measure the rays of the substance in bulk, also, and this is an advantage when considerable quantities of ore are under investigation. Moreover, previous experiments indicated that the y rays from thorium, uranium, and radium were absorbed to an equal extent in passing through the same thicknesses of lead. It was found, however, in the course of these experiments, that radium and thorium do emit y rays which have identical coefficients of absorption, whilst the y rays from uranium are weak and easily absorbed. Thus the y ray method can be employed to great advantage in comparing radium and thorium, but uranium and actinium cannot be compared with them, or with one another. Apparatus.—An electroscope, 380 centimetres high and 20 centimetres in diameter, made of zinc ‘45 mm. thick, contained the usual gold-leaf system on a long insulated central rod. The fall of potential was measured by the movement of the gold-leaf read by a microscope with a graduated scale in the eyepiece. The radioactive substance under examination was placed on a platform about 7 cm. below the electroscope. Layers of lead were introduced between the active body and the electroscope. Corrections were made in the usual manner for the natural leak of the instrument. In every case lead was used as the absorbing material. Substances Investigated. (1) Radium Bromide. (2) Uraninite from Joachimsthal, Bonemia. (1 kilo.) (3) Uranium Nitrate, prepared ‘by Himer and Amend. 1 kilo. ) (4) Thorius Nitrate, prepared by Himer and Amend. (2 kilos.) (5) Radio-thorium, lent to me by the aren euEl. Dr. Hahn, who was working in the McGill Physics Building. (6) Actinium, Giesel’s preparation, activity about 300. 2 2 588 Mr. A. 8S. Eve on the Absorption of (7) Actinium, Debierne’s preparation, activity about 700. This substance, belonging to Sir William Ramsay, was kindly lent to me by Dr. Hahn. Results.——If I) be the intensity of radiation on one side of a lead plate, and I be the intensity on the other side after absorption, we have [=],e-*", where « is the thickness of the plate, and X is the coefficient of absorption. This formula, deduced from a —2I, assumes that the absorption by a thin layer per unit thickness is proportioned to the intensity. Ji, has been found by McClelland, Wigger, and others, that in the case of radium A” is not constant over wide ranges, but the less penetrating y rays are first absorbed, and the subsequent values of X are therefore smaller. In the present experiments, the range of the thicknesses between which the values of X% have been obtained will be stated, without including the minute correction for the air traversed, or for the -45 mm. of zinc which formed the base of the electro- scope, or for the glass vessels, such as test-tubes, in which some substances were placed. Radium.—The results obtained for radium are in fair agreement with those found by McClelland, using the electrometer method (Phil. Mag. July 1904). y rays. ! Thickness of lead X (ems.)~!. in cm. 64 to 1°21] cs, 2 toMesn9 7516) 1-79 to 2°36 AG | OE Py a0) “46 | | McClelland found that > varied from ‘64 to *44 through the same range. The result is shown in fig. 1, where the abscissee denote the thickness of lead traversed, and the ordinates give the logarithms of the intensities as measured by the gold-leaf electroscope. It will be seen that the radium line thus plotted is not straight, and that > has a gradual slight decrease in value. Uraninite—The specimen from Joachimsthal gave values of % almost identical with those obtained from radium bromide, although in one case the radium was concentrated, and in the other was distributed through a kilogram of pitchblende. It will be found later that the y rays from the y Rays of Radioactive Substances. 583 uranium are almost absorbed by °64 cm. of lead, so that the y rays from uraninite are mainly due to radium, and are a measure of the radium present, not more than 20 per cent. being lost by self-absorption. 0 10 *bo 5 LIA ILO Y AL. 5 49 : s2 Thorium.—One kilogram of thorium nitrate was sealed in a flat glass cylinder, 16 cm. in diameter. The values of ® were found to be practically the same as those for radium and for uraninite. Radio-thorium.—lt is important to note that radio-thorium gave values of X almost identical with those for radium and thorium, but initially the rays from radio-thorium appear to be slightly more penetrating, possibly because the self-absorption is less. Dr. Hahn has shown that radio-thorium has produced. Th.X and Th. Emanation, and since radio-thorium gives rays similar to thorium we have another proof, if proof were needed, of the similarity between radio-thorium and thorium. Radio-thorium has not yet been obtained in a pure state, but the eleven milligrams kindly lent me by Dr. Hahn, as measured by the y rays, were equivalent to 1570 grams of thorium nitrate. This result is of the same order as that found by Hahn, when using y rays, so that radio-thorium is 143,000 times more active than thorium nitrate. But it will be seen later that the latter, thorium nitrate, loses about 15 per cent. of its y activity by self-absorption, so that radio-thorium is actually about 12x 10* more active than an equal weight of thorium nitrate. Now radium bromide was found to be about 15x 10° times as active as thorium nitrate, when measured by the y rays; hence the impure radio-thorium had an activity about one-hundredth part of that of pure radium bromide. 590 Mr. A. 8. Eve on the Absorption of It will be convenient to state here the actual figures obtained for the substances which have been considered up to the present point. The differences in the observed intensities are probably within the limits of experimental srror, as it is difficult to place such different substances under precisely similar conditions with respect to the electroscope. y rays. Intensities. Total thickness f lead i “ ae ofdead amen Radium. Uraninite. pt Resin -64 100 100 100 100 1-21 72 73 72 | 15 1:79 52 53 52 | 5D 2:36 40 4] 40 49 3-00 | 29 30 31 31 Uranium.—The y ray effect of uranium was found to be surprisingly small. A kilogram of thorium nitrate gave ten times the effect of a kilogram of uranium nitrate, measured through ‘64 em. of lead. The y rays of uranium were so readily absorbed, that it was not possible to measure » over a wide range, or with great accuracy. The mean of repeated observations between °28 and °57 cm., and also between °64 and °92 cm., gave AX=1'4; so that. the y rays, like the @ rays of this substance, appear to be homogeneous. A specimen of pure uranium gave A=1°6 approximately. In the case of uranium nitrate the loss of y activity by self-absorption must be large. The ratio of the activities of uranium nitrate and thorium nitrate was determined by measurement of the « and 8 ray effect from 12 grams of each substance. a ray 0°6, io ray16:0; whilst for a kilogram of each, y ray Ovl. It will thus be seen that these methods offer no certain test for comparing the total activities of uranium and thorium or of uranium and radium, and the same difficulty will be found in the case of actinium. On the other hand, the eS the y Rays of Radioactive Substances. 591 equality of the absorption of the y rays of thorium and radium makes the y radiation an accurate comparative measure of the joint quantities of these radioactive substances in two given bodies. Actinium.—Dr. Godlewski has published in the Philoso- phical Magazine for September 1905 an account of some penetrating rays of actinium, with a coefficient of absorption equal to 4°5. He experimented with a preparation of Giesel’s actinium, activity about 300, and he was able to take measure- ments for thicknesses ranging up to about 3 mms. of lead. Using a stronger preparation of Debierne’s actinium, activity about 700, it was possible to carry Godlewski’s work further. When the rays passed only through *45 mm. of the zine which formed the base of the clectroscope, the activity was measured by 2°35 scale-divisions per minute. On adding successively *15, °30, -45 mm. of lead, the ob- served activity fell by an ‘exponential law, with A=10°5. These rays probably consist partly of homogeneous B rays, and they are not plotted in the diagram (fig. 2). Further Fig. 2. Loy ‘60 oa i) ra ’ AiiAlLO 7O : ~< Ss ; ° Lead Thickness in mr. sheets of lead, *15 mm. thick, were added, until a total thickness of 2°85 mm. was reached. The results plotted on logarithm paper gave a straight line, so that the rays are homogeneous between these limits. This result confirms Dr. Godlewski’s work with Giesel’s actinium, but he found X=4'5, and in the present case A=4°1.. These values are nearly equal, for A is a sensitive function, and the difference is probably due to experimental conditions. The two pre- parations of actinium have the same emanation and excited activity, and the same coefficients of absorption are therefore to be expected. 12. d92 Mr. A. 8. Eve on the Absorption of When a thickness of 2°85 mm. of lead was reached a fairly well-marked change occurred, and X% became equal to 2°7, and this value was maintained to a thickness of 4°35 mm., or even to 5°7 mm. Beyond that the effects were small and very difficult to measure, but the mean of repeated observa- tions indicated that X% was equal to about 2 between 5°7 and 8°7 mm. The results are shown in fig. 2*, but it may be convenient to state them in tabular form also :— Thickness in mm. | Zine. Lead. A (ems.)—1. A wee 0 2k 10°5 A + 45 | Eee coke 4°] 3 + 2°85 i Lae Poe G + B74 viens Sas 202 =F 8:7 It appears, then, that actinium has two types of 6 rays and one or two of y rays. The two types of 8 rays are both homogeneous and easily, but not equally, absorbed. It is, of course, possible that there is one type of @ rays, and that all the rest are y rays. The question can only be settled by photographs of actinium rays deflected in a magnetic field. This work is under investigation by Dr. Godlewski. It is noteworthy that both uranium and actinium have homogeneous @ rays, and that these substances give rise to easily absorbed yrays. But thorium and radium have hetero- geneous 6 rays, and the resulting y rays are much more penetrating. We may fairly conclude that the high velocity £ particles give rise to the more penetrating y rays, and that low velocity 8 rays generate easily absorbed y rays. And we have here a striking similarity with the generation of Rontgen rays by the cathode rays. For in a “hard” bulb, with a good vacuum, the cathode rays have a high velocity, and when these are abruptly stopped a penetrating type of Rontgen rays arises. But in a “soft” bulb, the low velocity cathode rays generate easily absorbed Réntgen rays. So also the abrupt expulsion of high velocity 8 rays causes * It was not possible to exhibit all the results of this paper in a single diagram. In fig. ] radium and thorium are compared with uranium, and in fig. 2 actinium and uranium are contrasted. The horizontal scales in the two diagrams are not the same. the y Rays of Radioactive Substances. o93 highly penetrating y rays, and the low velocity 6 rays pro- duce weak y rays. In the case of uranium and actinium there appear to be no 6 rays sufficiently swift to cause the most penetrating type of y rays, for the 6 rays are homo- geneous, and have a more or less uniform velocity. Standard of y Ray Measurement, The writer suggests that one kilogram of pure thorium nitrate enclosed and tightly sealed in a thin glass vessel, 16 cms. in diameter, would form a convenient standard for testing the amount of radium or thorium in a given ore in bulk. The y activity could be tested through a centimetre of lead, and the rays of actinium or uranium would then be practically excluded. The results of various experimenters could be readily compared in terms of such a standard. Concentration and Distance. If the distance of an active substance from the bottom of the electroscope is varied, the fall of potential of the gold- leaf also alters. In comparing two substances their centres of mass should be made to coincide relatively to the electro- scope. The measured activity was found, roughly, to vary inversely as the square of the distance from the active substance to the centre of the electroscope. In order to see whether the observed eftect was dependent on the degree of concentration of the substance under investiga- tion, a few pieces of pitchblende were placed, first at the centre, then at the circumference of a glass dish 16 cms. in diameter. The activity observed was three per cent. stronger when the pitchblende was all near the centre of the dish. “If, therefore, the dish were full, the loss owing to the scattering would be about one and a half per cent. This loss is due to the fact that the cone of rays cut by the electroscope is different when an active particle is at the centre, and when it is at the circumference of the glass vessel. Self- Absorption. Two methods were employed to form an estimate of the loss of activity due to selt-absorption by thorium nitrate. In the first case the electroscope was placed on a platform of lead -64 cm. thick. A kilogram of thorium ee was then placed beneath, and the activity measured 2 A small quantity of radium was placed at the centre of the mass, and the total activity was 84°4. Next the activity of the radium O94 Absorption of y Rays of Radioactive Substances. without the thorium was found to be 989. Hence the activity of the radium was reduced from 98°9 to 82-1, by the absorption of half the thickness of the thorium nitrate. But X for thorium and radium has the same value, and in the thorium nitrate the central layers are absorbed to an average extent. Hence the actual reading of the activity of thorium nitrate being 100, the corrected reading would be about 122. A second method of finding the self-absorption was by the measurement of layer after layer, superadded to one another, in a circular dish, 16 cms. in diameter, adjusted so that the centre layer was at a constant distance from the electroscope. The rise of activity was indicated by a straight line when the masses were taken as abscissee and the activities as ordinates. The absorption of a thin layer of 200 grams could not be large, and by successive approximations the self-absorption was found to be about 15 per cent. for 1 kilogram of the material placed beneath 64 cm. of lead. _ These two results are in rough agreement. Moreover, the intensities found for 5 kilogram of thorium nitrate, 1 ale gram of pitchblende, 2 mg. “of radium bromide, and 11 mg. of radio-thorium, followed the same curve for various thick- nesses of lead. It is fair to conclude that the loss of activity of a kilogram of pitchblende, due to self-absorption and to lack of concentration, can be fully corrected by an addition of twenty per cent. to the observed value, when °64 cm. of lead cut off the 6 rays. Summary. (1) Radium, uraninite, thorium, and radio-thorium emit y rays which are absorbed at the same rate bay lead. (2) For thicknesses of lead between °64 and 3:0 cms. the values of X range from ‘57 to ‘46 for all these sub- stances. (3) Uranium nitrate is weak in y rays, and these are readily absorbed ; X=1°4 between 2°8 and 12:1 mm. of lead. (4) Actinium emits four types of rays :— 1. & rays. 2. B rays which are homogeneous. X=163 (Godlewski). . More penetrating rays, either 8 or a ~=4:5 (Godlewski). A=4:1 (Eve), between *45 and 2°8 mm. Oo The Osmotic Pressures of Alcoholic Solutions. 599 4. Most penetrating rays, probably y rays. N=2°7 toh2°0, from 2°38 to:3°7 mm. (5) A kilogram of thorium nitrate sealed in a thin glass vessel 16 cms. in diameter, placed under a layer of lead 1 em. thick, might be adopted as a convenient standard for measuring the quantity of radium or thorium contained in a given mass of ore. (6) The self-absorption of the y rays from 1 kilogram of thorium nitrate in a vessel 16 cms. in diameter and about 3°4 ems. deep, is such that about 18 per cent. should be added to the results actually obtained. When used as a standard no such correction should be made. In conclusion I take pleasure in expressing my gratitude to Professor Rutherford for proposing the experiment, and for his usual kind interest and ever ready assistance. McGill University, Montreal, December 19, 1905. L. The Osmotic Pressures of Alcoholic Solutions. _ By P.S. Bartow, B.A., St. John’s College, Cambridge™. YHE earlier experimental work of this paper dealt with the use of the ordinary copper-ferrocyanide membrane for solutions in which the solvent was ethyl alcohol. Tammann + showed that ethyl alcohol could get through this membrane against the osmotic current, but did not itself seem capable of setting up an osmotic current. As there did not seem to be sufficient evidence on this point to justify the assumption that all copper-ferrocyanide membranes, however prepared, could not be used with alcoholic solutions, it was considered necessary to try the cells which had already been in use. The substance of the membrane is precipitated in the colloidal state ; and the outward passage of the alcohol would appear to point to the absorption, under pressure, of the alcohol by the membrane. A large number of experiments were made. All the results were negative and in agreement with Tam- mann’s work ; but the work done seemed justified by the limited knowledge we have of the detailed properties of colloids. The inevitable small differences of preparation of the mem- branes might very well have produced some change in the * Communicated by Prof. J. J. Thomson. + Annal. Phys. und Chem. Neue Folge, xxxiv. p. 509. 596 Mr. P. S. Barlow on the Osmotic colloid that would modify its behaviour towards alcohol (as observed by Tammann). A considerable time was devoted to this work, a full account of which would be needlessly long ; it need only be said here that the results give fresh negative evidence in “support of the theory that for the osmotic pressure to show itself, the membrane must be able to dissolve the solvent and have a distinct “ attraction of solution ” for it. Every opportunity was allowed as regards time, some of the experiments continuing for several months, and all for more than seven days. The solutions used were of levulose, lithium chloride, lithium sulphate (anhyd), camphor, shellac, methyl oxalate, ferric chloride (anhyd), glycerine. In addition to the cylindrical cell of the usual type, cells were also made of thin porous plates in which the membrane was formed. All the cells worked normally with water. The copper-ferrocyanide membranes being unserviceable, other membranes were tried. Of the vegetable and animal parchments, the bladder membrane was the only one to show any pressure. The cell was made by stretching the prepared bladder across a brass cylinder. The cylinder consisted of two parts which could be joined by means of flanges and screws. The bladder was held between the flanges, thus dividing the interior into two compartments. The side con- nected to the gauge was filled with the solution ; the other side was connected to a small glass reservoir and was filled with the solvent. ‘The bladder was backed on the side of the solvent (the outside) by perforated zinc. The bladder cell (B 11.) was used with solutions of lithium chloride, methyl oxalate, and camphor in absolute alcohol. Of these, the lithium chloride and camphor solutions gave osmotic pressures, The methyl oxalate showed no sign of pressure. No quantitative values were expected from the experiments with bladder, it being a very imperfect semi- permeable membrane. ‘The result, however, was satisfactory after the experiments with the ferrocyanide membrane as showing that, under conditions depending on the membrane, these solutions would give pressures with the solvent. Iam not aware that any quantitative results have been published of experiments made with non-aqueous solutions to measure directly the osmotic pressure. J lusin* has made ‘quantitative measurements of the rate of inflow, using vul- canized indiarubber and bladder. He found that the amount of liquid entering in a given time is proportional to the * Comptes Rendus, cxxxi. p. 1808, Dec. 31, 1900. Pressures of Alcoholic Svlutions. 597 quantity of the liquid absorbed per unit area of the mem- brane. In general, work with non-aqueous solutions seems so far to have been confined to electrical conductivity and the depression of the freezing-point. I turned to pure indiarubber as a possible membrane when it was clear that the ferrocyanide cells were unserviceable. The pure substance I was unable to obtain, so I made use of euttapercha tissue. Separating alcohol and water, this tissue gave a pressure on the side of the water. I shall say here that 1 am not aware that guttapercha has been used for the direct measurement of osmotic pressures, though I think it has been used to show that with it, the osmotic current is towards the water. I may also say in passing, that thin and slightly vulcanized indiarubber tissue has been tried with these solutions, but no pressures were obtained with the samples used. The experiments that remain to be recorded are those in which guttapercha tissue was the membrane. ‘The first series of readings with solutions of lithium chloride was obtained with cell Br. Only three pressures were obtained in three weeks ; that is, including the cleaning of the cell, each reading below took more than a week te obtain. The maximum pressure did not require all that time to be set up, but the cell was left untouched for some time to make certain that a steady value had been reached. | Guttapercha Theoretical | Observed a samete ae membrane. Pressure. Pressure. Berea By Cell B1....... ol2mm. | 4-4 mm. 11°3.C. os 4 ee 937 | 12 1S6 Rd? 6, 0.9.58. 1562 37-6 | 11°-6 ican: Al E1875 | 826 1196 No LiCl could be detected on the outside after the experiments. Plotting the observed pressures as ordinates and the theo- retical ones (which represent the concentrations) as abscisse, we get the following curve (p. 598). The falling away indicated by the pressure given by Bu. is unexpected ; it will be referred to later. Here we need only consider the curve as given by the values for cell Br. The curve produced to the left cuts the y-axis at a point 598 Mr. P. S. Barlow on the Osmotic above the origin ; that is, the pure solvent gives an osmotic pressure—which is impossible. According to the curve, the osmotic pressure in the early stages does not increase as. rapidly as the concentration ; while later, it increases more rapidly. Hence the curve is below the theoretical one for a water solution. Fig. 1.—Curve I, i ECE ER eer Sco Ae OBs° | ae aad ett a The curve can only be taken as a preliminary one. But one thing seems evident: that there is some substance present which produces an osmotic pressure in addition to that due to the lithium chloride. The suggestion that naturally occurs is that the extremely hygroscopic lithium chloride introduced a little water into the solution; and previous experiment has shown that, with the guttapercha membrane, water behaves as the solute. If this explanation is legitimate, the zero of the curve for the lithium chloride will be raised and the curve should touch or cut the z-axis on the right of the origin. In a paper on experiments with alcohols and water (part of which appeared in the Phil. Mag. July 1905) it was suggested that, if the solution of the solvent by the membrane was an essential condition of osmotic phenomena, then the tendency of the membrane to retain the solvent would oppose the dilution of the solution and so cut down the osmotic pressure. The effect of such depression would be most. p Pressures of Alcoholic Solutions. 599 marked for dilute solutions*. On this theory a curve, obtained as the above one, should cut the z-axis at that point which would denote the strength of the solution whose attraction for the solvent would just be balanced by the tendency of the membrane to retain it. A further remark may be made here about the change in form of the curve to which theory would point. Since the attraction of the membrane plays a more important part in cutting down the osmotic pressure of the weaker solutions, the curve (plotted as above) should be convex towards the y-axis. The above curve may therefore be raised in its lower portion by disturbing influences. Hven the assumption of considerable dissociation at this dilution would not account for the slow fall of the curve. These considerations on the above curve showed the necessity for a more careful examination of the osmotic pressures of such solutions. This was undertaken as follows : “ Avsolute ” alcohol was redistilied after having stood over fresh and very good quicklime for three weeks and then over dehydrated copper sulphate for another week. It was dis- tilled on a water-bath directly from the latter. The first and last portions of the liquid were neglected ; the receiving flask was only open to the air through a calcium-chloride tube. The redistilled alcohol was kept in a flask under a desiccator or with the neck of the flask covered tightly with a guitapercha cap. Lvery precaution was taken to avoid absorption of moisture, all measurements, &c., being made as quickly as possible where it was necessary to expose the alcohol to the air. The specific gravity of the alcohol after distilling was *7973 at 12°C., compared with water at the same temperature. That of the alcohol before distillation was ‘7980 at the same temperature. This shows that the alcohol, as supplied to the laboratory, was really very good. I point this out here, because in the last of the next series of experiments I was compelled to use “ absolute alcohol,” owing to having run short unexpectedly of the redistilled liquid. The lithium chloride used was the salt supplied to the laboratory as “ pure ;” the salt used in these experiments was kept for some weeks previously in a weighing tube over phosphorus pentoxide in a small desiccator. Care was taken to expose the salt as little as possible. Arrangements were made for carrying out the experiments * Prof. Kahlenberg, by simultaneous work not yet published, has arrived at the same result (Phil. Mag. Feb. 1905, p. 228). 600 Mr. P. S. Barlow on the Osmotic at 0° C. An ice-chest was made of tin in the form of a double box, the inner box in which the cells were to be placed being about three inches from the walls of the outer on all sides. The top was closed by a deep tray filled with ice. The inner box could thus be surrounded by broken ice. The outside was covered with three or four layers of cotton-wool. By means of a deep groove which was surrounded by the ice, the inner box was connected to the surface of the outer one, and in this groove lay the horizontal glass tube which con- nected the gauge to the cell. The gauge could thus be outside the case. The ice-chest was made so that two experiments could be carried on together, but it was only possible to get cell B m1. to work. Several days were spent in attempts with Br. and But., but without success ; and their use for the purposes of this paper had to be discarded. It was unfortunate to be thus reduced to one cell, as the time at my disposal for the work was limited ; and each reading obtained (for a steady value) required a week’s time. Cell Bum. is the newest type of the brass cells used, and has worked the best. ‘The following isa diagram. The section at right angles to the paper is circular. SoLuTion SOLVENT To GAUGE The opening A was connected to an adjustable mercury- gauge, or was open to the air through a large calcium- chloride tube. B was closed by thick rubber tubing. The membrane stretched between the flanges was backed by perforated zinc. In these experiments A was connected by a long piece of tubing to a calcium-chloride tube which was kept outside the ice-chest, the tubing being brought through the groove connecting the two boxes. A thermometer passing through the ice-tray which formed the lid of the chest was placed so as to be near the osmotic vO a | Pressures of Alcoholic Solutions. 601 cell. By keeping the chest packed with broken ice, the temperature inside remained steady at zero. The temperature near the gauge at the outer surface was very steady at about 11°-5 C. “There was a very small volume of solution above the mercury in the gauge which was above the inside temperature. The conductivity of the solutions was found after the steady value for the pressure was obtained. The liquid was with- drawn from the cell and 5:4 ¢.c. (giving what seemed to be a suitable depth of liquid) were used inasmall electrolytic cell. The electrodes were small platinum plates, platinized and then heated to redness. The commutator and galvanometer method of Fitzpatrick and Whetham was used in finding the electrolytic resistance. The cell was standing in broken ice for at least an hour before readings were taken. The resistance of the cell was found; the battery reversed and the resistance again found. The electrolytic cell was then reversed and two observations of its resistance taken as before. The inverse of the mean of these four values was taken as the conductivity, thus eliminating as far as possible polarization effects in the cell, and thermoelectric effects in the commu- tator. The following table contains all the readings I Haye been able to get during five weeks by means of cell B un, Sneed ree ee ae ey of ressure Observed Pressure Conductivity Gs, Solution. ae ae OC. at 0° C. "144 normal. 2440 min. 195 mm. 0042 089 1660 208 0029 040 690 131 0016 | 020 345 76 00087 The last experiment was made using the ordinary absolute alcohol; these values therefore may not altogether agree with previous values, but it does not seem likely that the use of this alcohol will have greatly affected the readings. The following curves (pp. 602-3) are obtained ‘from the numbers in the above table. The differences in Curves II. and III. are such as are accounted for by the form of Curve IV. The conductivity falls off rather more quickly than the strength. Phil. Mag. 8. 6. Vol. 11. No. 64. April 1906. 2 I ow 602 Mr. P. S. Barlow on the Osmotic Before discussing these curves I must say that in the above experiments, lithium chloride was found in the outer alcohol. Fig. 3.—Curve H. 0 067 ea 1 fly — 3 90 A : 1 2 i "a i | CON DUCTIVIT. ‘0018 | Its amount was distinctly less for the weaker solutions. “ It will be remembered that in the experiments of the first table, no salt was found on the outside: there the pressures set up did not exceed 40 mm. All the pressures in the last table are far below some pressures that have been obtained with Pressures of Alcoholie Solutions. 603 the same tissue, and therefore the presence of lithium chloride outside is not due to a leak in the membrane caused by over- strain. Obviously above a certain pressure the guttapercha ' Fig. 5.—Curve IV. er Ree it ea A ee [re iVITY wo | oe Saen vA ie é 4 067 lew membrane is only imperfectly semi-permeable for the case of lithium chloride. It may be that this membrane is permeable to chlorides as the copper ferrocyanide one is; and, like the latter, vould act more perfectly with sulphates. The general character of Curves I. and III. agrees with theory : the observed pressure decreases more rapidly than the strength of the solution, owing to the counter attraction exerted by the membrane on the solvent. The fall of the curves towards the right is unexpected. (A similar fall was indicated by Curve I.) The permeability of the membrane to hthium chloride will not account for this: at most it could only make that portion of the curve horizontal. The only explanation that seems reasonable, supposing the upper part of the curve is reliable, is that beyond a certain strength of solution there is polymerization of the solute or a more complicated grouping of the solute and solvent molecules. This is supported by the form of Curve LV. Curves II. and III. cut the x-axis at points denoting very weak solutions ; and therefore indicating that the equivalent strength of the membrane, in its attraction for the solvent, 2R2 i, 604 | Prof. J. H. Jeans on the is very small. The curves, however, do not embody the results of a sufficiently large number of experiments ; so that ali that can be said is that, accepting the absorbent action of the membrane, they are in general agreement with theory. The work must at present be left at this point, but the writer hopes it may be of value in having opened up an interesting and profitable line for further research in the theory of solution. At present our knowledge of non-aqueous solutions consists of such various and disconnected data, so often disagreeing among themselves when arrived at by different methods, that further accumulation of experimental results is required before any generalization can be attempted. It has become increasingly evident that the theories of solution based on work with aqueous solutions cannot satisfactorily cover the data obtained where the solvent has been other than water. The problem becomes more complicated as the influence of the solvent is found to be more marked. At the same time this comparatively recent development in experiment may be expected to afford a means of making an advance towards the truth of the matter. All we can say now, Raoult said in summary in the last section of his ‘ Cryoscopie’ :—“... the molecules of a salt (in solution) can be hydrated, polymerized, ionized at the same time, in proportions varying with temperature and con- centration ; and, consequently, produce cryoscopic effects (and among these may be included the parallel osmotic ones) much more complicated than is generally believed.” LI. On the Constitution of the Atom. To the Editors of the Philosophical Magazine. GENTLEMEN,— M** I put forward a suggestion in connexion with a question discussed by Lord Rayleigh in his paper ‘On Hlectrical Vibrations and the Constitution of the Atom ” (Phil. Mag. Jan. 1906) ? Lord Rayleigh states an objection against regarding the atom as a system in steady orbital motion, rather than as one performing small oscillations about a position of statical equilibrium,—namely, that the sharpness of spectral lines indicates a definiteness of structure such as it is difficult to imagine associated with a system of electrons in orbital motion. He goes on to say: “ It is possible, however, that Constitution of the Atom. 605 the conditions of stability or of exemption from radiation may after all really demand this definiteness. .. . The fre- quencies observed in the spectrum may . . . form an essential part of the original constitution of the atom as determined by conditions of stability.” If this were so, these frequencies would depend only on the constituents of the atom and not on the actual type of motion taking place in the atom. Thus if we regard the atom as made up of point-charges influencing one another according to the usual electrodynamical laws, the frequencies could depend only on the number, masses, and charges of the point-charges and on the ether- constant V. What I wish to point out first is that it is impossible, by combining these quantities in any way, to obtain a quantity of the physical dimensions of a frequency. If to the quantities already mentioned we add another, for instance the energy of motion of the atom, it may be possible to obtain frequencies. Here, however, the frequencies will be functions of the energy. And, as ‘Lord Rayleigh says, the energy must change in the course of time, whereas the frequencies, so far as we know, do not. Or, instead of combining the original quantities with the energy, we may combine them with a length, in such a way as to obtain frequencies. ‘Thus Lord Rayleigh obtains fre- quencies in his analysis, but only in virtue of having introduced the radius of the imaginary sphere of positive electrification. If this positive electrification, instead of being limited to an invariable sphere, were supposed free to expand under its self-repulsion, Lord Rayleigh’s py) would be indefinite, as would consequently be the frequencies also. The situation with regard to linear dimensions is precisely the same as that with regard to frequencies. It is impossible to derive a scale of linear dimensions from the quantities permanently associated with point-charges and ether. Thus the atom would have no definite size, but would expand and contract indefinitely under external influences. It seems, then, that we must somehow introduce new quantities—electrons must be regarded as something more complex than point-charges. And when we have once been driven to surrendering the simplicity of the point-charge view of the electron, is there any longer any objection to putting the most obvious interpretation on the line-spectrum, and regarding its frequencies as those of isochronous vibra- tions about a position of statical equilibrium? The main objection felt, as I understand, against this interpretation, lies in its being inconsistent with the point-charge view of an 606 The Constitution of the Atom. electron. Isuggest that the objection applies equally to the ‘‘ orbital motion ”’ interpretation. Lord Rayleigh’s objection to the statical interpretation, that the theoretically calculated spectrum series would be for p? and not for p, and that they would apparently be too complex to agree with the observed facts, remains, and seems, it is true, to be almost insuperable; but is the case any worse than that which might have been made out against the atomic theory a century ago from the fact of the ratios of specific e . ° bad . . heats of gases forming the simple series 1+ 5—, in spite OTN of the enormous complexity of the atomic conception of matter ? Hvidence, which seems to me to have great weight, can be derived from considerations of the par tition of energy. The value of Dulong and Petit’s constant shows that those parts of the energy which vary with the temperature are fully accounted for by the potential and kinetic energies of the atom regarded as a point; and the same is shown by the fact that y for monatomic gases has the value 12. ‘Thus the energies of the degrees of freedom which represent rotation or internal motions of the atom, are either infinitesimal or are incapable of variation under the ordinary interatomic forces. Thus if electrons are describing orbits, the planes of these orbits must remain almost or completely fixed in space. If we rotate a body in the hand the atoms must maintain their directions in space, as indeed, on this view of the atom, would be shown also by the fact of our not experiencing any gyro- static couple. Butif the body isa crystal, its optical constants and axes do not change by rotation all the atoms rotated their planes relatively to the body as a whole—and if the body is a permanent magnet, its magnetic properties and constants do not change. A similar dilemma is soon reached with reference to the velocity of rotation. The Zeeman effect shows that this can be altered even by the fields available in the laboratory, while the value of y would show that it is not altered by the munch more eftective magnetic fields which ought (on the “ orbital motion ’ theory) to be found at collisions of molecules. Finally, may I mention that in the Phil. Mag. for Nov. 1901, I attacked a problem similar in many respects to that which forms the main substance of Lord Rayleigh’s paper? The actual premises upon which I worked were different from those of Lord Rayleigh—his positive sphere being repre- sented, in my work, by a crowd of positive electrons, and the definiteness of structure, which he obtains by regarding as they surely would if The Dielectric Strain along the Lines of Force. 607 this sphere as rigidly fixed, being obtained in my work by using a law more general than ee] /7?. Both papers, however, deal with a spherical atom executing small vibrations: in both the principal vibrations are found to corr espond to sphe- rical harmonies, the order of the harmonic being the 7 of the spectrum series. Lord Rayleigh obtains only a single series, falling off from the head according to the law 1/n, and also a single spectral line. Nothing corresponding to this series appears in my work; but corresponding to the single line I obtained a number of series falling off according to the observed law 1/n®. Given the value of e/m for electrons (or electric fluid) the same relation can be obtained, in either case, between the frequencies and the radius of the atom. Untor ‘tunately the numerical calculation given in § 23 of my paper was inaccurate : corresponding to. frequencies of the order of those of light the radius must be about 3 x 107‘, which is not good as regards agreement with facts, but is perhaps as near to the true value as can be expected in a vague calculation of this kind. ‘My picture of the atom led to a Zeeman effect, consisting of a splitting into three or more sharp and fully polarized lines. Lord Rayleigh’s model would, I believe, do the same. If, however, the atom consisted of electrons in orbital motion, the planes of these orbits making all directions with the lines of magnetic force, it appears as if the Zeeman effect could at best consist of a widening into a continuous band, a point which has, I think, already been made by.Lord Kelvin. Princeton, N. J., J. H. JEANS. Jan. 24th, 1906. Petts f =i = ae \\ LI. The Dielectric Strain along the Lines of Force. ‘\\ To the Editors of the Philosophical Magazine. Vo GENTLEMEN, N the issue of December 1905 you published a paper by Mr. L. T. More, “On the Dielectric Strain along the Lines of Force,” in which our paper ‘* Ueber die Electro- striction des Glases”?* is criticised. We should be much obliged if you would publish the following reply. Our experiments have shown that the expansion of the volume of electrified glass tubes and spheres was in some kinds of glass in agreement with the mechanical pressure of the armatures and the elastic constants of the glass. In other kinds of glass the expansion was found to be too small. These results confirm in general those of Quincke, but are * Ann. d. Physik (4) 1x. p. 1217 1902). 608 The Dielectric Strain aleng the Lines of Force. in opposition to the results of Cantone, who found the expansion greater than the theoretical saline. They do not disagree with those of Mr. More, supposing he has used Thuringian or a similar kind of olass. In the above-mentioned paper Mr. More says:— (1) That our method was “ faulty.” (2) That “we had attempted to show that the real elasticity of glass was greater when obtained from electrical stress than when found by mechanical and acoustical methods.” (3) That we had mistaken the nature of the problem in regarding the effect as being due to a variation of elasticity of electrified and not-clectrified elass, while the effect obtained by us was produced partly by the faults of the method employed, partly by the alteration of the inductive capacity of glass by pressure. As to (1): We have improved the metliod of Quincke until the observations showed sufficient regularity for the same kind of glass. It seems that Mr. More distrusts the exactness. of our method especially for the reason that the results obtained were very different with different kinds of glass. We will show afterwards that, on the contrary, these differ- ences are an indirect proof of the correctness of our statements. Asto (2): Mr. More misunderstood what we called “the coefficient of elasticity by electrostriction.”’ We introduced this coefficient because it enabled us to compare in a simple way our resuits for different forms of tubes and spheres. He has overlooked that we have made some experiments (p. 1258) expressly for the purpose of proving that there is no real change of the coefficient of elasticity by electrification. As to (3): Mr. More has overlooked also that we published some months later a second part of our investigation, entitled “* Ueber die Anderung der Dielectricitats-constante des Glases mit dem Druck”*. In this paper we tried to examine if there was an alteration of the inductive capacity with mechanical pressure in the same glass tubes as we had used in the experiments on electrostriction. The result was, that he same kinds of glass, in which the expansion by elec- srification was found too small, showed an increase of the inductive capacity with pressure. The agreement was not only in sign, but even in value. We are glad to see that in the principal points Mr. More agrees totally with our views, viz., that there exist no other real forces in electrostriction fan the pressure of the armatures. But we think we have donea little more than he. Mr. More has shown that in some cases there was no electrostriction, and suggested, without ascertaining it by experiments, that * Ann. d. Phystk (4) xi. p. 619 (1903). Minimum Deviation through a Prism. 609 all opposite results were faulty. We have proved experi- mentally, that in the cases where the expansion was found too great (Cantone) there were errors in the measurements ; and in the cases where the expansion was found too small (Quincke and Wiillner & Wien), we proved also by experiments, that the variation of the dielectric power agrees in sign and value with the observed discrepancy. Accordingly there remain no observations leading to the conclusion that there are other forces in electrostriction than the pressure of the charged armatures. We are, Gentlemen, Aachen and Danzig, Yours faithful ly, February 1906. — A. WtuLiner ; M. WIEn. LILI. Note on “ Mintmum Deviation through a Prism.” ee By R. CHAaRtTRES *. é+d=minimum. 6'+¢'=constant. Sind=y sin &. Singd=yvsin dg’. Mieke CRB = 0, FBO, then F is to be a maximum, while D is constant. il ; or (1) .. cosF—cosD= Biss (1- Shh will be a minimum. 2xy n : Aen But since wae EE ley sin (0+ ¢) é 1 ; : “. m, as also ( 1—-,), will be a maximum when 6+ ¢@ Vi is a minimum, “. that (1) should be a minimum wy must be a maximum ; SU eee eh") and 0 * Communicated by the Author, being reprinted, with additions, from the Phil. Mag. vol. vi. p. 529 (1903). \\I Rega 2) et LIV. Notices respecting New Books. The Theory of Experimental Electricity. By W.C. D. WHETHAM, M.A., F.BS., Fellow of Trinity College, Cambridge. Cambridge: at the University Press. 1905. Pp. x1+ 334. _ Ete there are countless books in existence dealing with # the subject-matter of the present volume, there is no doubt that this text-book fills a distinct gap, and that it will strongly appeal to all students who look for something more in a text-book than a mere exposition of the leading facts and principles of the science, and who are capable of feeling something of that spirit of enthusiasm which has inspired numerous recent investigators in their epoch- making discoveries. It is owing to these discoveries that a considerable remodelling of our electrical text-books has become not only desirable, but imperative. For, to quote the author’s remarks in his preface, “the great shift in the chief points of interest of experimental electricity, due to recent development in physical science, has changed the proportion of the various branches of the subject, and has put out of date many of the older standard text-books.” We therefore cordially weleome the author’s effort at presenting the subject from a thoroughly modern standpoint and in correct perspective, and congratulate him on the success with which he has accomplished his task. As compared with the older text-books, the work under review is characterized by the relatively large amount of space devoted to electromagnetic waves, electrolysis, the conduction of electricity through gases, and radio-activity. These subjects occupy fully one-third of the volume, and the author’s account of them is both clear and fascinating. The book seems remarkably free from minor blemishes, although we must protest against the author’s use of the expression “the electromotive force between two points,” and against the statement, on p. 111, that “in the science of current-electricity, it is usual to call a difference of potential an electromotive force ”—a statement which is somewhat surprising in a modern text-book on the subject. La Théorte Moderne des Phénomenes Physiques: Radhoactivité, Lons, Alectrons. Par A. Rieu, Professeur 4 l'Université de Bologne. Traduction libre et notes additionnelles par EH. Nscuncna. Préface de G. Lippmann. Paris: “ L’Eclairage Electrique,” 1906. Pp. 25. WHEN reviewing the first Italian edition of Prof. Righi’s little treatise some two years ago, we had occasion to refer to it as one of the most lucid and delightful expositions of a subject of ab- sorbing interest. That the work in question has met with the appreciation which it deserves in other countries is evidenced by the appearance of the present French transiation of the second Italian edition. The translator—M. Néculeéa—has supplied some additional bibliographical and other notes, and a very interesting Notices respecting New Books. 611 preface is contributed by Professor Lippmann. Little need be said in praise of the French edition; the translation is well done, and we can only express the hope that is will serve to make this charming book better known to the English-spzaking public. Chemie der Alicyklischen Verbindungen. Von Osstan ASCHAN, A.O. Professor an der Universitit Helsingfors. Mit vier eingedruckten Abbildungen. Braunschweig: F. Vieweg & Sohn. 1905. Pp. xlv+ 1163. THE enormous growth of organic chemistry during the last two decades has necessitated the subdivision of the subject into a number of branches, of which one—the chemistry of the so-called alicyclic compounds (a term due to HE. Bamberger)—forms the subject of the present exhaustive treatise. This class of organic compounds includes a large number of substances of considerable technical importance, and is of special interest to students of pharmaceutical chemistry. The mere bulk of the volume before us bears ample testimony to the immense amount of material accumulated in this department of organic chemistry ; there are over 5000 references to original sources of information. The necessity of some sort of systematic account of the large amount of work done in this direction is therefore amply evident, and it is fortunate that this extremely laborious task has been undertaken by an author whose scientific activity has contributed to the advance- ment of this particular branch of organic chemistry. The present volume fills a gap and will earn for its author the gratitude of all advanced students of organic chemistry. The work is divided into two parts, Part I. being general, and Part Il. special. Part I. consists of an introduction in which the author defines the limits of his subject, and deals with homology, isomerism and nomenclature; and of four sections, dealing respec- tively with the theoretical development of the chemistry of alicyclic compounds, the effect of the ring structure on the chemical nature of such compounds, its effect on some of their physical characteristics, and the stereo-chemistry of alicyclic com- pounds. Considering next the special Part II., we have in Section I. a systematic account of the modes of formation and preparation of alicyclic compounds, in Section Il. an account of monocyclic, in Section ILL. of bicyclic, and in Section IV. of tri- and poly-cyclic compounds. A copious index closes this most valuable and exhaustive work of reference. Spectroscopy. By H. C. C. Bauy, F.J.C., Lecturer on Spectroscopy and Assistant-Professor of Chemistry, University College, London. With 163 illustrations. London: Lonemans, Green & Co. 1905. Pp. xi+ 568. THE enormous development of spectroscopy and_ spectroscopic methods has for some time past rendered the appearance of a com- prehensive and up-to-date text-book on this subject highly desirable. 612 Notices respecting New Books. This want is now supplied by Mr. Baly’s excellent work, which forms one of the series of Teat-Books of Physical Chemistry now being issued by Messrs. Longmans, under the general editorship of Sir W. Ramsay. After an historical introduction devoted to an account of the rise and progress of spectroscopy, the author deals with the slit, prisms, and lenses, and their combi- nation to form a complete prism-spectroscope. The practical use of this instrumentis then fully dealt with. The diffraction-grating and its practical use are next considered. Then follow chapters dealing with measurements in the infra-red and_ ultra-violet regions, with the application of interference methods to spectro- scopy, the efficiency of the spectroscope, the photography cf the spectrum, the production and nature of spectra, the Zeeman effect, series of lines in spectra, and change of wave-length by pressure and by motion in the line of sight. An interesting feature of the book is the detailed and fully illustrated description of Rowland’s grating ruling-engines given in the concluding chapter. The Appendix contains recipes for silvering-solutions for glass mirrors. An index of names and subjects is provided at the end of the book. In spite of the vast amount of matter dealt with, most of the explanations given are characterized by clearness, and the book contains many valuable practical hints which are the result of the author’s own experience, and for which the reader will feel duly grateful. There are a number of obvious misprints —which is almost inevitable—and occasionally there are lapses from that clearness which characterizes the book as a whole. We would particularly direct the author’s attention to the entirely inadequate if not actually misleading account of the principle of Langley’s bolometer given on p. 229, which should be thoroughly revised in the next edition. The Science Year-Book. With Astronomical, Physical & Chemical Tables, Summaries of Progress in Science, Directory and Diary for 1906. Edited by Major B. F. S. Baprn-Powrtu. London: King, Sell & Olding, Limited. 1906. Pp. 208+ 365 + 27 + vi. TuE scope of this most useful year-book, which is in its second annual issue, is sufficiently described by its title. Compressed within the first 208 pages is a vast amount of information, including brief summaries of scientific progress during the past year. Then follows a diary, with a whole page for every day of the vear. A few additional pages for memoranda &c. follow, and finally an index is provided. It was hardly to be expected that a publication of this kind should be quite free from error. We note, for example, that Prof. Unwin’s name is stil given as that of the Professor of Engineering at the Central Technical College; a number of misprints are almost unavoidable—but these are small blemishes, and do not seriously mar the extreme usefulness of the book as a whole. Notices respecting New Books. 613 Der Bau des Fixsternsystems, mit besonderer Berucksichtigung der photometrischen Resultate. Von Dr. Hurmann Koponp, A. O. Professor an der Universitat und Observator der Sternwarte in Kiel. Mit 19 eingedruckten Abbildungen und 3 Tafeln. Braunscliweig: F. Vieweg und Sohn. 1906. Pp. xi+ 2056. [** Die Wissenschaft,” Heft 11.] THE problems which are considered in the present monograph have long formed the subject of much speculation on the part of astronomers. It is only, however, with the development of the recent powerful methods of research in this field that definite knowledge has taken the place of vague conjecture, and that trust- worthy conclusions have been arrived at. The author divides his admirable account of the present state of the subject into three sections. Section I. deals in a general way with types of imstru- ments and methods of observation. Section II. deals with the results obtained up to the present ; while Section III. contains an account of the conclusions which may be drawn from them. Bibliographical references are given in an appendix. It may be interesting to quote the following sentences from the conclusion, in which the author thus sums up our knowledge regarding the structure of the universe: ‘Throughout a finite space of spherical form are scattered bodies of greatly varying mass and physical state. Besides gaseous nebulas of very low temperature there occur bodies in the state of greatest condensation and highest incandescence. The arrangement of the individual masses is no random or uniform one, but they are collected in heaps around single concentration centres, which, however, are loosely connected with each other and are arranged in the form of a large, many- branched spiral. In the more remote parts of this spiral there predominate the hotter and gaseous stars, while those more closely related to the sun—which is not far removed from the centre of the spiral—also resemble it, on the whole, in their physical state. The sun has a motion of translation—shared by the majority of the nearer stars—towards a point in the milky way, which forms the principal plane of the entire spiral.” Die Psychischen Massmethoden. Von Dr. G. ¥. Lipps, Privatdozent der Philosophie an der Universitat Leipzig. Mit 6 eingedruckten Abbildungen. Braunschweig: F. Vieweg und Sohn. 1906. Pp. vu+ 151. Iv is but seldom that physicists devote much attention to the study of the psychical processes involved in the making of observations. True, they are generally introduced to Fechner’s Law in connection with photometry, but there their psychical studies may be said to begin and end. ‘To those with a metaphysical turn of mind, the monegraph under review, which forms No. 10 of the series known as ‘Die Wissenschaft,” may be recommended as affording a detailed account of the subject and methods of experimental psychology, 614 Geological Society :— Terrestrial Magnetism and its Causes. By F. A. Brack. London: Gall & Inglis. 1905. Pp. 226. AccorpDING to the author's views, the ‘electric waves, or electric displacements in the ether” which are projected from the sun, ‘dash against the surface of the earth, or at least the enveloping atmosphere, and thus come under the influence of the earth’s movements” (p.15). ‘An electric sheet is thus wound around the earth frcm apex to apex in the course of the diurnal rotation..... The sheet may be compared to a great series of electric wires wound around the earth from east to west. It is suggested that this would furnish a simple explanation of the magnetization of the earth ”(p. 20). Having quoted the above extracts, we feel that it is unnecessary to add anything further, as they are quite sufficient to enable our readers to form an idea of what sort of book it is that we are dealing with. Physics. By Cuartes Rrpore Mann, the University of Chicago, and GrorGe Ransom Twiss, the Central High School, Cleveland. Chicago: Scott, Foresman & Co. 1905, Pp. x+453. THe writing of a thoroughly satisfactory elementary book on physics is by no means an easy task, and the authors of the present volume are to be congratulated on having achieved a very considerable amount of success in this difficult undertaking. The book is just of the type that will appeal to youthful minds: it is profusely illustrated, and at every point the principle under discussion is exemplified by reference to some real thing which is already within the sphere of the reader’s experience. The style is easy, and the mode of treatment full of suggestion and likely to stimulate the imagination and awaken the interest of the young student. The summaries, questions, problems and suggestions to students at the ends of the chapters are also admirable features of the book, and must have involved a good deal of time and trouble in their preparation. There is a striking absence of pedantry and dogmatism about the book. We have noticed but few misprints or errors, but would suggest the substitution of “rate of change of motion” for ‘‘ change of motion” in the last line on p. 47. LV. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 424. | January 24th, 1906.—J. E. Marr, Sc.D., F.R.S., President, in the Chair. (fee following communications were read :— 1. ‘On the Igneous and Associated Sedimentary Rocks of Llan- gynog (Caermarthenshire).’ By T. Crosbee Cantrill, B.Sc., and Herbert Henry Thomas, M.A., F.G.8. The sedimentary rocks associated with the various igneous. masses comprise the following :— The Buttermere and Ennerdale Granophiyre. 615 Lower Otp Rep Red marls and sandstones, with cornstones and conglome- SANDSTONE. rates at the base. ( Didymograptus-bifidus Beds. Blue-black shales, with one or Be etc ay | mere thick bands of grit towards the base. _ Giravic). { Tetragraptus-Beds. Black and buff shales with thin grit- : | bands: thick bands of ashy grits and conglomerates | towards the base. These rocks are described in detail. They occur in two main anticlines, overfolded, and complicated by thrusts which cut out a great part of the intervening syncline. They are covered uncon- formably by the lower beds of the Old Red Sandstone. The igneous rocks occur in three well-defined areas, which belong to the same petrographical province, near Coorab, at Capel Bethesda, and at Lambstone. Both interbedded and intrusive rocks are represented, and full petrographical descriptions of all types are given in the paper. The latter include diabases, and the large porphyry-mass of Lambstone. ‘The extrusive rocks have been determined to occur in the following order :—(1) augite-andesites ; (2) rhyolites ; and (3) augite-andesites, with some hornblende-andesite. ‘The ex- trusive rocks are interbedded with fluxion-breccias and with tuffs ; they are associated with the lower members of the Tetragraptus- Beds, and are consequently of Lower Arenig age; while the intrusive rocks have been injected into the extrusive rocks, and have also affected the Tetragraptus-Beds, but at what date exactly it 1s im- possible to say, except that it antedates the Old Red Sandstone. Much of the folding and faulting was accomplished before the Lower Old Red Sandstone was deposited, but certain faults involve this forma- tion, and make it clear that there was an important later movement. 2. ‘The Buttermere and Knnerdale Granophyre.’ By Robert Heron Rastall, B.A., F.G.S. (Christ’s College, Cambridge). This paper embodies the results of field-mapping and micro- scopical study of the large mass of igneous rocks known, collectively, as the Buttermere and Ennerdale Granophyre. From the facts put forward it is concluded that the intrusion is an example of an acid-magma, which has crystallized under the peculiar set of con- ditions that gives rise toa very perfect development of granophyric structure. ‘These conditions are probably, to a certain extent, inter- mediate between those of plutonic and true hypabyssal rocks. The masses appear to be of the ‘cedar-tree’ laccolite-type intrusive about the junction of the Skiddaw Slates and the Borrowdale rocks, but penetrating into the higher rocks. Besides the normal acidic rock, which comprises the bulk of the intrusions, there are some marginal patches of more basic character, showing obvious genetic relationship, and slightly earlier in point of time than the intrusion of the acidic rock. These basic fore-runners afford evidence of differentiation of the magma before intrusion—an example of Prof. Brogger’s deep-magmatic differentiation. Considered as a whole, the character of the magma shows closer affinity to the tonalite- group than to the true granites, although it is somewhat more acid than ithe majority of tonalites. The more basic types include dolerites, quartz-dolerites, and a rock-type intermediate between 616 Greological Society. quartz-dolerites and granophyres, for which no satisfactory name seems to exist. There is also a development of peculiar rock-types as the result of the re-mixing of previously-differentiated partial magmas of an acid and a basic character respectively. A study of the distribution of different types of granophyric structure shows a certain regularity of arrangement, and an attempt is made to reconcile these with known physical laws, especially with reference to eutectics; and it is concluded that the structure is the result of crystallization under conditions intermediate between those which produce typical plutonic and hypabyssal rocks. February 7th.—J. E. Marr, Sc.D., F.R.S., President, in the Chair. The following communications were read :— 1. ‘The Carboniferous Limestone (Avonian) of the Mendip Area (Somerset), with especial reference to the Paleontological Sequence.’ By Thomas Franklin Sibly, B.Sc., F.G.S. 2. ‘The Igneous Rocks of the Eastern Mendips.? By Prof. Sidney Hugh Reynolds, M.A., F.G.S. The igneous rocks associated with the Old Red Sandstone of the Mendips are exposed along the crest of the range from Beacon Hill on the west to near Downhead on the east, a distance of rather more than two miles. Hitherto they have always been regarded as intrusive, hut the opening of some new excavations has shown that they are associated with a considerable thickness of tuffs, and are in all probability contemperaneous lava-flows. The exposures show a division into three sections—those of Beacon Hill, Moon’s Hill, and Downhead; and a large quarry has been opened in the trap in each section. The trap, which can be traced fairly continuously from one end of the area to the other, is very uniform in character, consisting (as already noted by Dr. Teall) of a non-amygdaloidal pyroxene-andesite, which usualiy contains augite in addition to enstatite. A fine section of tuff some 100 feet thick is seen lying with perfect conformity below the trap in the New Quarry near Stoke Lane; and an interesting little exposure of tuff, remarkable for the numerous rounded blocks of trap present, is seen in the excavation for the rifle-butts on Beacon Hill. The tuff here dips under the Old Red Sandstone to the north. Although the tuff is seen in situ only at the above two points, loose pieces have been met with at a number of other spots all along the southern outcrop of the trap, and point clearly to the occurrence of a continuous band underlying it. Though no sedimentary rocks are seen in direct contact with those of the igneous series, outcrops of Old Red Sandstone com- pletely surround the exposures of trap and tuff, and occur in such close relation to them as to leave little room for doubt that the igneous series is of Old-Red-Sandstone age. On the other hand, Silurian fossils were met with below the igneous series at a point to the west of Downhead, and render it possible that the igneous rocks may be of Silurian age, and the equivalents of those which are exposed at Tortworth. INDEXED. THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCES. [SIXTH SERIES.] NAMA IO G6: Gp LVI. On the Ionization of Various Gases by the a Particles:of Radium. By W. H. Brace, M.A., Hider Professor of Mathematics and Physics in the University of Adelaide *. N a paper ‘‘ On the Recombination of Ions in Air and other Gases” (Phil. Mag. April 1906, p. 466), Mr. Kleeman and I have described the preliminary steps of an enquiry into the total ionization produced in different gases by the « particle of radium, and the influence of physical conditions thereon. With the assistance of Mr. J. P. V. Madsen, B.Se., I have made many experiments in continuation of thisenquiry. Itis necessarily a lengthy one, and in some respects difficult, so that on many of the points involved no definite conclusions are yet within reach. On others, results have been obtained which are, I think, of some interest and importance. In this paper I propose to describe the work which has been done ; and, in addition, to make some reference to (a) the magnetic deflexion of the « particle, (>) its acquirement of a positive charge. As described in the paper referred to, the total ionization of a gas can be measured in terms of the product of the co- ordinates of a certain point on the ionization curve. The true measure is, of course, the area between the curve and the axes of coordinates. But experiment shows that all ionization curves due to radium in radioactive equilibrium are of the same form, and differ from each other only in the * Communicated by the Author. Phil. Mag. 8. 6. Vol. 11. No. 65. May 1906, 28 618 Prof. W. H. Bragg on the Lonization of application of some factor to all their ordinates or all their abscissee. Thus the product of the coordinates of some standard point is proportional to the area of the whole curve, and may be taken as a relative measure of the total lonization. In all the experiments to which I am about to refer, the a particles cross at right angles a shallow ionization chamber whose upper electrode is a brass plate and the lower a brass gauze ; the distance between the electrodes is about 3 mm. An electromotive force of 300 volts is usually applied to the gauze, giving an electric force of 1000 volts per em. ‘This is generally sufficient to ensure saturation ; that is to say, to avoid all errors due to diffusion, general recombination, and initial recombination. When it is insufficient, the proper correction is found and applied. The ionization chamber is enclosed within a vessel which is satisfactorily air-tight except at higher temperatures, and this again within an electric oven. The gas under observation can thus be subjected to various pressures and temperatures. In the case of such substances as benzene and carbon tetrachloride, a temperature of from 60° to 90° is necessary to ensure a convenient gas-density. There is, however, this drawback to the use of high temperatures, that the insulators begin to lose their efficiency, and the joints cease to be air-tight. I find it necessary to use glass as an insulator instead of sulphur, for the latter cracks under the unequal expansions due to alteration of temperature. In the case of vapours, a certain quantity of air usually finds its way into the apparatus, for, as Just mentioned, the joints leak somewhat at the higher temperatures. The amount so entering is sometimes deter- mined by opening a communication between the vessel and an evacuated bulb, and weighing the quantity of mixture drawn off. The bulb and connexions are placed within the oven, and communication is made by opening a pinch-cock worked by a key projecting outside the oven. In this way, condensation in cold tubes is avoided. This method is not always employed, for as soon as the stopping-power of the gas is sufficiently well known, the proportion of the mixture is much more easily, and I think at Jeast as accu- rately, determined by observation of the range of the a particles therein. The insulation leak is determined by measuring the deflexion of the electrometer first for ten seconds, and then for twenty. With no leak the latter should be double the former; this is never quite the case, and the correction factor can be obtained from a comparison of the two values. Various Gases by the « Particles of Radium. 619 The factor to be applied to a ten-second leak varies from apout 1-03 at 40° C. to about 1-10 at 70° C.: at 90° C. it is much higher. The total ionization is measured in terms of the product R LI. The ordinate R is the range of the « particle, due to that product of radium whose speed is next to that of Ra C. In air at 760 mm. pressure and 20° C., R = 4°83 cm. very nearly. The abscissa I is the ionization produced in the chamber described when the radium layer is at a distance of 4-83 cm. from the middle of the chamber: or, more correctly, it is proportional to the ionization that would be produced in a very shallow chamber at that distance. The effect is wholly due to the particles from RaQ, the chamber being out of range of all the others. These two quantities R and I differ materially from each other in two respects. To take the less important con- sideration first, the former quantity lends itself readily to exact measurement, the latter does not. The range of the a particle in a gas can be measured to an accuracy of one or two per cent. by a few minutes’ observation, and to a much higher degree with greater care: it is perhaps the easiest of the measurements made in these experiments. By far the greatest difficulties which I find in the determination of the stopping-power of a gas lie in the purification and analysis of the gas. On the other hand, the abscissa I is much more difficult to measure. It is affected by variation in the sensitiveness of the electrometer, by leakage through the insulators, by variation of the dimensions of the apparatus, and its true value is not given unless enough electric force is applied. None of these things affects the range. But it is not merely in the details of measurement that these two quantities differ. They appear as physical constants to be in distinct categories: so far, that is to say, as can be observed at present. The stopping-power of an atom is a constant of the atom, un- affected by its association with other atoms in molecular structure, independent of pressure and temperature. In a paper by Mr. Kleeman and myself (Phil. Mag. Sept. 1905), we gave a list of the stopping-powers of various substances, and since then we have made many other experiments in the same direction. In no case have we found a departure from the additive law which was not within the errors of experiment. That is to say, the range of the @ particle in a given gas can always be predicted from the composition of the gas molecule. Not only so, but the stopping-powers of the various atoms are very nearly ae to the square roots of their 9 a! 620 Prof. W. H. Bragg on the Lonization of weights, so that a simple, if approximate, law covers all the phenomena. It even seems justifiable now to go one step further. If the list in the paper quoted be examined, or the more comprehensive list in Table A, it will be found that the TABLE A. Table of Stopping-powers of various Gases. Experimental, Proportional | Proportional | Als aie | | peers value. to Vw. to w. nin | Air=1. | Air=1. Air=1. | 7 eee a god 4 eB a3 | 264 | 0695 ||) eau [FOS 2 oste ee 1055 | ~— 1-054 111 | 1-04 ena) 1-46 152 1:53 1:49 : igs 1-47 151 1°53 | ieee | (OS, eee 2-18 1-95 2°71 | 1:96 ioe 1-11 117 905 1-13 ben ae 1°35 1-44 Oi5 | ee | one. 3°37 3°53 271 | 339 | ees As, 3°59 | 3:6 2-50 3-66 | _ CH, Br 2-09 | 2:03 3:28 2-11 OLR Serene 2-58 Wihees 4-90 | 252 CHCl . 2-36 a oe 2-23 | 230 hoes ee 3-13 | 3:06 5-40 3°20 (CHCl, . ie ae as 381 3-00 | 0,80 3-40 | 367 257 351 t Grol Dapietaaee 4-02 | 359 541 3°68 TABLE B. Table of Stopping-powers of various Metals. Experimental | Proportional Ratio of two | Metal. value. to Vw. preceding Att — Air = 1. columns. AN ese eauee 1-45 137 1-06 | Le ea eee 2:26 1-97 115 i Pekan ta 2-46 2-20 112 ASH tees as. 2-43 2°10 1-16 | AG .eeeeeeeeeee S17 274 1-16 i) eee eee ST 288 117 | EC een 4°16 3°68 115 2. FE Siena Saree 4°45 370 1:20 oe ee 425 378 113 The last column of Table A shows the application of the formula a ¥w+éw > the agreement with the second column is very close, considering that only two constants are used, and one of these is of little importance except in the case of the heavier atoms. But the formula does not appear to apply to the metals where the stopping-power varies very nearly as the square root of the atomic weight. This is certainly a difficulty, Various Gases by the a Particles of Radium. 621 stopping-powers are systematic even in their slight departure from the square-root law. For, whilst dependent mainly on the square roots of the weights, they have a leaning towards the weights themselves. We did not call attention at the time to this fact, for we thought it might be a spurious effect. But it has appeared so regularly in ¢ all further determinations that it seems right to note it, and to attempt an explanation of its physical meaning. If we assume the correctness of the explanation aiready given of the square-root law, viz., that the « particle spends energy for the most part on tearing away electrons from their attachment at the edges of the atom disks, then the natural complement to this is the further assumption that electrons in all parts of the atom disk may be disturbed to vibration by the passage of the particle, which latter there- fore spends a small amount of energy in simple proportion to the weight of the atom. If w be the atomic weight, the stopping-power of an atom should therefore be capable of expression by the formula ax/wtbw; where the former term is usually by far the most important. The close agreement of the figures in the second and fifth columns of Table A shows that this is very nearly the case. As regards pressure and temperature, I have not yet found any effect produced by variation of these conditions. The quantity RP/T appears to be a constant, P being the pressure and T the absolute temperature. This implies that the stopping-power of an atom or molecule is independent of P and T. Examples of the fact that RP is constant whilst T is constant are given in the paper “ On the Recom- bination of Ions in Air and other Gases.” The following experimental result will serve as an illustration of the fact that R is proportional to T when P is constant. The ionization vessel filled with air was raised to a temperature of 90° C., the pressure being 763 mm. R was then found to peo. Now when p=760 mm., and T=20" C3 R=4°83. ue 4-83 x 363 x 760 5-98 x 293 x 763 It has of course been pointed out by several observers that the ionization effects of radium are largely independent of pressure and temperature and of physical and chemical conditions generally. This, however, does not cover the present statement, which refers to the stopping-power of the atom, a quantity 622 Prof, W. H. Bragg on the Ionization of which has not previously been the subject of measurement so far as | am aware. To sum up, the range of the «& particle in a given gas is, in the first place easily measured, and in the second place is simply related to the constitution of the gas and independent of its state. It is a delightful contrast to some other radio- active quantities, and often gives a welcome foothold in difficult places. The quantity I is in quite a different class. It is much more difficult to measure accurately, as I have already described. But there appears to be a more important difference in that the total ionization of a gas is not simply dependent on the weights of the atoms of which it is composed. Molecular structure counts for something. Perhaps, also, the various atoms do not yield ions in simple proportion to the energy spent on them, ‘but this point is not yet sufficiently clear. An example of this want of uniformity has already been given in the paper to which reference has been made. It was shown that RI in ethyl chloride is much greater than RI in air. The difference must be yet a little greater than that shown, as no allowance was made for the small quantity of air mixed with the heavy gas. Again, RI in standard pentane (mostly C;H,,) is nearly half as much again as in air, and the same is almost certainly true of benzene (C,H), but this vapour is harder to treat than pentane, since a high temperature is necessary. Generally speaking, the more complex gases yield the greater number of ions. But the yield does not depend only on the number of atoms in the molecule. Acetylene (CSE 2) ylelds 25 per cent. more than air, yet CO, with only one atom less yields but 5 per cent. more; and ethylene (C,H,) yields the same as acetylene, though it has two atoms more. Of course in the last case the atoms added are very light; and H, itself has, according to my measurements, a slightly lower value (for RI) than air. Rutherford also found this to be the case. On the other hand, the influence of complexity can be illustrated by the cases of acetylene and ethylene as compared with benzene and pentane. In order to bring out the significance of these comparisons, it should be pointed out that the a particle spends exactly the same amount of energy in every gas (Bragg, Phil. Mag. Now 1190). Thus in different gases different numbers of ions are ro) Various Gases by the « Particles of Radium. 623 produced for the same expenditure of energy. It is quite clear, however, that this does not imply that the @ particle finds it easier to produce ions in some gases than others. Fer, if so, there would be some influence on the stopping- power of atoms dependent on the number of ions produced. But the stopping-power is connected with the atomic weight by a simple law: the number of ions produced is not. Plainly the energy spent by an @ particle in an atom and the resulting ionization are not directly connected: there is an intervening link. Hither the ions made by the a particle produce others in some cases, or some of the ions made never emerge from the atoms. ‘There is something which prevents the simplicity of the law governing the expenditure of energy by the « particle from repeating itself in the amount of ionization produced. I think it is increasingly clear from our experi- ments that there is a secondary ionization within the molecule itself. The ions first made, or possibly X-ray pulses accompanying lonization, have, in some cases, enough energy to make fresh ions before leaving the molecule. Thus, for example, one molecule of C,H, is found to rob the « particle of just as much energy as three molecules of C,H,. But more ions are made out of the one C,H, than out of the group of three acetylene molecules. This may be explained on the ground that the twelve atoms are crowded together, so that an ion pe eeiee under ionization from one of the atoms strikes one of the others with an energy undiminished by motion througk the field of the positive from which it was originally separated, and so. capable of detaching a second electron. In further consequence the ions emerging from a O,H, molecule move more slowly than those from a C,H,, and are more liable to initial recombination. This is in agreement with experiment: it is far harder to saturate benzene than acetylene. The secondary ionization would appear to take place within rather than without the molecule, because the amount of it does not depend upon the distance of the molecules from one another. The total ionization is independent of the pressure. It is certainly not due to the electric field, for if it were there would be no saturation value of the current. I’ subjoin the details of two of the many experiments which Mr. Madsen and I have made. We hope to give a fuller description at some future time. 624 Prof. W. H. Bragg on the Ionization of Determination of Stopping-power, and of RI in Pentane. Hlectrodes 3 mm. apart (nearly). Volts applied=300. Temperature of apparatus=35° C. Apparatus charged with vapour from standard pentane. Distance from Ra — to middle of Leak in Pressure inside ionization chamber. — ten seconds. apparatus. 2°8 1982 2°9 1431 41°15 cm. 3°0 1192 ol lata: 32 1193 3°3 1227 41-15 cm. Thin Cu foil over Ra 108 These being plotted, it is found that R=2-95, [=1044, the copper leak having been deducted. Thus R=2-95 in this mixture of pentane and air, ata pressure of 41°15 cm., and a temperature (observed) of 308° (absolute). But at a pressure 760 cm., and 293° absolute, PE eee 4:83 7600 308 | ence the mixture stops - Ge? Baa =3'14 times as much as air. 2°95 4115 293 A special set of readings at 3°2 cm. is now taken, three for 10 seconds and three for 20 seconds. ‘The means are 1196 and 2325 respectively. Comparing these, it is found that the 10-second reading should be multiplied by 1°03 in order to allow for leakage by the insulators. Again, a set is taken with 600 volts between the plates, and it is found that the mean reading when the copper leak is deducted is 1134. At the same time the reading for 300 volts, copper leak being deducted, is 1088. Thus saturation is nearly complete. A quantity of the gas is now drawn over into an exhausted bulb, whose temperature (that of the oven) is 311 (absolute) : the pressure is observed to be 34:5. The weight of this gas is °2536 gr. It is then calculated from a knowledge of the capacity of the bulb that the mixture weighs 2°22 times as much as air. From this it is found that to every molecule of pentane there are °23 molecules of air, assuming the pentane molecule to weigh 2°5 times as much as air. If s=stopping-power of pentane, we have therefore Or Various G'ases by the a Particles of Radium. 62 Again RI=2:95 x 104-4, = 308, uneorrected. Correcting for want of saturation, 1134 Inl=a0e < == 1088? ae On the same day and under the same conditions RI for air=231. The leakage correction is found to be the same for both, and need Sot Te applied. Now, as far as con- sumption of energy is concerned, °23 molecules of air are equivalent to 23/3" 59 molecules of pentane, ="065. Hence if all the energy had been spent as pentane molecules, the value for RI would have been 1:065 x 321—-065 x 231, = 9-1 Finally = 32%. Total ionization in pentane _ 327 Total ionization in air 231 =1°41. It is quite possible that the low density of the mixture (2°22 instead of the 2°5 of pure pentane) is due to an admixture of lighter and more volatile hydrocarbons. If it were so, the result as to the value of RI would not be affected in any essential way. Determination of Stopping-power and Ri of Acetylene (C,H) Same conditions as previous experiment. Apparatus charged to atmospheric pressure with gas ; when tested, gas was found to contain less than 2 per cent. of impurities. Temperature of apparatus=37°°5 C. Barometer=763 mm. Distance from Ra to middle Leak in of ionization chamber. ten seconds. 4-2, 1430 4°3 b2W6 Ard. 1024 AS 818 4-6 698 4-7 688 A°8 701 4-9 698 Cu over Ra. 46 At 5:2 for 300 volts net leak = 688 andyemiOOO.".. 9° 5 4 = 706 626 Prof. W. H. Bragg on the Ionization of Plotting these values it is found that R=4:°57, I (less copper leak)=635. Hence RI, corrected for want of saturation, =298. Hence, Total ionization for C,H, 298 ee ss — 5°29, Total ionization tor air 7 Zol Also stopping-power £4838. 760. 3105 457 163 72930 ie In the paper by Mr. Kleeman and myself, to which I have already referred, it was pointed out that Rutherford had found it more easy to obtain the saturation current from a gas when it was removed from the influence of the ionizing agent. We observed that this could be easily explained by supposing initial recombination to be completed before the gas was subjected to the electric field. It is nevertheless no essential feature of the initial recombination hypothesis that the act of recombination should take place within any set time. The one important point is that the recombination takes place between two ions originally forming parts of one molecule. It is quite conceivable that for a certain time the positive and negative may remain “‘ semi-detached,” their recombination in suspense until precipitated by some change of conditions. Curiously enough Mr. Madsen, working in this laboratory, has not yet been able to repeat ‘Prof. Rutherford’s experiment ; and his results point to a prolonged existence of these pairs. He finds it hard to saturate a mixture of air and ether vapour which has been ionized by radium and then drawn away into a separate ionization chamber. It is not easy to reconcile this result with that of Prof. Rutherford: and it will be necessary to repeat the experiment under varying conditions. ‘The point is one of considerable interest, for the existence of these pairs would help to expiain muck of the mechanism of phosphorescence. ‘hey would appear to be connected with the clusters of J. B. B. Burke, which were produced by ionization, gave rise to phosphorescent glow, contained energy, yet were not electrified. It is of interest in this connexion that the photograph which Various Gases by the a Particles of Radium. 627 Sir William and Lady Huggins made of the phosphorescent glow of radium showed the bands of the gas in which the salt was imbedded. Rutherford also has shown that the « particle can no longer cause phosphorescence when it has lost its power of ionization. The Magnetic Dejlexion of the « Rays. In the Physikalische Zeitschrift for Oct. 15th is a paper by M. Becquerel, ‘‘ Ueber einige Higenschaften der a Strahlen des Radiums.” The author discusses the theory that the a rays gradually lose their velocity as they spend their energy on the ionization of the media through which they pass, a theory which I put forward about two years ago *, and which has the support of much experimental ev idence accumulated by Prof. Rutherford t, and by Mr. Kleeman and myself f. He maintains that the theory is unsuccessful in explaining the experiments which he has himself performed, and in particular he describes one experiment which he has devised as a crucial test and which he considers to show that the theory is incorrect. It is as follows (loc. cit. p. 688) :— The rays from a smali quantity of radium salt are allowed to stream upwards through a narrow slit and fall upon a photographic plate. A powerful magnetic field deflects them slightly to one side. The field is reversed when the experi- ment is halfway through, and as a result two images of the slit appear, slightly separated, upon the plate. Now, M. Becquerel covers half the slit with a thin sheet of aluminium ; and according to the theory which I have advanced, the 2 rays which pass through the sheet are thereby retarded. Jonsequently, M. Becquerei argues, these « rays should be more bent to one side than those which have not passed through the aluminium, and the images on the plate should show a break, the lines being more widely separated in one half of the picture than in the other. But M. Becquerel is under a misapprehension on this point. Paradoxical as it may appear at first sight, no such * Australasian Association for the Advancement of Science Report, Dunedin, January 1904. a Phil. Mae. July 1905. ated dolls Mag. Dec. 1904 and Sept. 1905. 628 Prof. W. H. Bragg on the Ionization of break ought to appear, and the photographic result is quite in accordance with the theory F ig. 1. that the particles lose speed as they pass 7, 4 4’ through matter. In order that this may be-~ clear, it is necessary first to consider the order of the deflexions of the « rays in the magnetic field, on the various theories that have been proposed. Suppose that an « particle is projected from i O in the direction ON with velocity vp, and | that the action of a field H causes it to describe the curved path OA. In the first place, let the velocity be constant throughout, and the path be therefore circular as M. Becquerel supposes. Then, since the curvature is small, AN=a?/2o9, where ON=a, and p is the radius of curvature. O = Ele -a@ AN — Soe Mv 2 In the second place let the velocity diminish as the distance from O increases : and let us take the extreme case, where the velocity vanishes at a distance a from O. Let the path in this case be OA’. It does not make very much difference what law of diminution of velocity we adopt : let us suppose, as my experimental results seem to indicate, that the particle spends its energy at a rate which is inversely proportional to the square of its speed. In this case, dv? ds s being measured from QO, and therefore, ta (a—s), so that Thus BL aN pHi ¢ :)* and we obtain easily that, if p = ds/dy, = 38/4) He patent) Ps MU Various Gases by the a Particles of Radium. 629 Now, provided that \abds is small, this quantity is very nearly equal to A'N, the total deflexion of the ray. But this integral O Dia 3/4 -| {ie (4-2) pas pee 0 2 a Mo He da my’. 7 and this quantity is very small, since it is only slightly greater than AN. Finally then we have that A'N/AN = 8/7. It is easily found that if we had supposed the particle to spend its energy uniformly along its path, we should have obtained the result A’N/AN = 4/3. It will thus be clear that, on any reasonable hypothesis as to the particular law of diminution of velocity, the actual path of the particle differs very little from a circle. In the extreme case which I have considered, the small deviation therefrom at the end of the path is small compared with the widths of the images in M. Becquerel’s photograph. If the particle ceases to ionize whilst its velocity is still great, as has been shown by Prof. Rutherford, the variation is still less. Let us now consider the circumstances of M. Becquerel’s experiment. As a first approximation, suppose the widths of the groove containing the radium salt and of the slit to be negligible. If no magnetic field is acting, all the « particles move in the vertical line ON. The range of the particles from Ra C is very nearly 7-0 cm.; from which it follows that the number which pass any given point P is proportional to the defect of OP from 7:0 em., or, in other words, that the number n which end their flight on any unit of length of ON is a constant. The other three groups of particles have, as their furthest dis- tances of penetration, 4°8, 4:2, and 3°5 cm. respectively. Thus between 4°8 and 4:2, 2n particles end their flight on each unit of length, between 4:2 and 3°5 the number is 3n, and from that point up to the radium 4m. The radium salt is supposed deep enough to supply all these, 7. e. its depth is taken to be at least ‘001 cm. Suppose now a powerful magnetic field to 630 Prof. W. H. Brage on the Jonization of be brought into play, the direction of the lines of force being normal to the plane of the paper. The paths of the particles are curved to one side, and the curvature is greater the nearer the particle is to the end of its course. Let OA and OQ represent two such paths. ‘Their separation from each other is considerably exaggerated in the figure. If all the paths were drawn the locus of Q would be seen to be a curve, whose curvature in contrast to that of the path of any one particle would be greater the further the distance from A. This is in agreement with M. Becquerel’s experiments, as I have previously pointed out*. The width of the trace upon the paper of all the paths of the particles is very small, and is almost too fine to be shown on a diagram. It is perhaps well to point out that there is no break in this trace at the critical points 4-8, 4:2, and 3°5. It is quite smooth from end to end. ‘These points mark the extreme distance to which various bundles of rays penetrate; but the deflexion of an a ray Fig. 2, LV A Q | | oO which ends its course at a given point is independent of the particular radioactive material from which it has come: the only varying characteristic of an particle is its velocity. We must now take into account that the widths of the slit and the groove are not negligible, as is clearly to be seen from the photo- graph under consideration. There is consequently, so to speak, a large penumbra. Thus the trace upon the plane of the paper of all the « rays is suchas is re- presented in fig. 3, the deflexions being all exagge- rated so as to be capable of depiction. Now suppose an alumi- nium plate is placed, as in eee hotographtc Jiale Mi Becquerel’s experiment, 2 over the slit so that the a Rea. * Phil, Mag. Dec. 1904, p. 737 ; Jahrbuch d. Rad. u. Elektr, 1905, p. 14. Various Gases by the a Particles of Radium. 631 particles have to pass through it on the way to the photographic plate. M. Beequerel supposes that there ought therefore to be an inereased displacement of the photographic image. But thisis not so. The path of any one « particle is slightly deflected, but the whole trace is not appreciably disturbed. The aluminium diminishes the range of every @ particle by the same amount, but the only result is to cut off all the rays which would have gone past a certain point, say Q, and to cause them to take the places of those rays which fell short of Q ; these latter being further shortened. This does not in the least affect the position of the outer edge of the trace upon the photographic plate; and though there must be a slight movement of the inner edge, so that the trace is some- what narrower, the change is so small that it could not possibly be detected, as a glance at the photograph will show. Magnetic dispersion of the a rays does exist: it has been directly shown by Rutherford, and, as I think, indirectly by M. Becquerel’s own experiments, in the peculiarities of the curvature of his photographic traces. But it could not be shown in the manner of the experiment which M. Becquerel now describes. ‘That would be analogous to the search for evidence of the motion of the stars in the line of sight in the displacement of the visible spectrum as a whole; whereas the measurement to be made is of the displacement of the Fraunhofer lines in the spectrum, 7.e. of one set of waves which can be isolated for consideration. It is here that Rutherford’s experiment is differentiated from that of M. Becquerel. The former employed as a source of rays a wire coated with a thin layer of Ra C emitting « particles of uniform velocity, which is analogous to confining one’s attention in the star problem to waves of one length. More- over, Rutherford passed his « particles for some considerable distance through a vacuum whilst yet under the influence of the magnetic field. Thus the evidence of the increase of curvature in their paths, originally caused by the loss of velocity in penetrating matter, was accumulated. But if, as in M. Becquerel’s experiment, the path is in the air, then any appreciable increase of curvature closely precedes the cessation of all evidence of motion, and the result must be in any case almost beyond detection. M. Becquerel remarks that there is no evidence in his photographs of the greater precision of the outer line of the trace, which I had anticipated. But the photograph which he now publishes show that there is too much penumbra for such an effect to be visible. 632 Messrs. Hawthorne and Morton on Deflexions caused The Positive Charge of the a Particle. Considerable discussion has recently taken place as to the mode in which the « particle acquires its positive charge. It has been pointed out more that once that it may be explained as the result of ionization by collision (Rutherford, Address to Congress at St. Louis, 1904; Bragg, Phil. Mag. Dec. 1904), and that the same hy pothesis will explain the deposit of the radium emanation on the negative electrode (Bragg and Kleeman, Phil. Mag. Dee. 1904). In the case of the emanation an explanation, which I understand to be similar, has been carefully worked out by Makower (Phil. Mag. Nov. 1995). Rutherford has shown that the « particle is charged at the moment of leaving the radium salt. But I do not think that the resuit is in any way prejudicial to the collision theory. He evaporated a very weak solution of radium on a plate, and supposed that as a result he had an excessively thin layer, so that the particle made very few collisions before emergence. But when such deposits are examined under a microscope, 1t is seen that the salt is gathered in little heaps, and there is no true layer at all. The bulk of the « particles pass through hundreds of atoms before emergence, and there is ample opportunity for ionization by collision. We find that the « particle spends energy in causing the expulsion of electrons trom the atoms of any gas which it traverses. We find also (see Tables A and B, above) that the expenditure of energy by the @ particle follows the same law when the atoms are massed together in a solid. The solid must therefore be ionized, just as the gas is, and we should expect slow-moving electrons to be projected from Ra itself, and from both sides of any solid screen through which the particles pass. Surely this is the effect lately observed by J. J. Thomson, Rutherford, and others. This has been suggested by Soddy (‘ Nature,’ March 1905). LVII. Note on the Deflexions caused by a Break in an Over- head Wire carried on Poles. By W. Hawruornz, 8.A., B.E., and W. B. Morton, 17.A.* [* the modern conditions of electrical power-transmission along overhead wires, it is a matter of practical import- ance to know what will happen in case a wire breaks. The relaxing of tension at one point will throw a one-sided pull on the range of poles on either side of the break; and it is essential for safety that the maximum deflexion thus produced should be below a definite limit. * Communicated by the Authors. by a Break in an Overhead Wire carried on Poles. 633 The theoretical investigation, given below, presents no special difficulty and leads to results of some interest. It is followed by a numerical evaluation of the deflexions for a particular case, in which we have used values for the constants derived from a case occurring in actual engineering practice. We shall suppose the wire to be fastened at its ends to massive “anchor-poles”? whose yielding is negligible, and to be supported by equally-spaced flexible poles. The relation between force and deflexion for a horizontal pull applied to tho top of a pole is supposed known. If this be expressed by the equation T= $(~); then in the region of safe deflexions the function is linear, and @ may be regarded as a numerical constant. The other relation which enters into the problem is that giving the alteration in the horizontal tension of a flat catenary for a small horizontal displacement of its ends. The are of a catenary is connected with the abscissa of its end and the parameter by the equation mane s=c sinh —. C Differentiating this, keeping s constant, ‘ Uv v v Xv dec |{ sinh— — —cosh— }+dw cosh — =0 ON G c ; dx=de (@ — tanh i C G If @ is the inclination of the tangent at the end of the catenary, ve — =log (sec + tan d) ; C so that if @ is small, - is small of the same order, and Phil. Mag. 8. 6. Vol. 11. No. 65. May 1906. 2T * 634 Messrs. Hawthorne and Morton on Deflexions caused If wis the weight of unit length of wire and T the horizontal tension, ‘T= 206s ale evils : vee aT= Futae 2de= ——. x (increase of horizontal span). Bg Zee. ee oT3 We shall write f for Fata Let the flexible poles be numbered from an anchor-pole. Let wz, be the deflexion of the top of the 7th pole, and let the break occur beyond the nth pole. We shall take first the simpler case where there is only one wire suspended, or where, if there are several wires, these all break together. Denote the horizontal tensions in successive intervals by Tor, Lis, .- + Ta@—iya, and the common value before the break occurs by T. Then we have To =T-fu, Hine =T—/(a#.—2)), We —1)n= T —f(&n —_ an =i): ieee — Ox}; Ty, —To3= ee ee u—1 ae n= Ply —1, yet ine = 2. On eliminating the tensions Ty,, Ty., &e., we get the following equations connecting consecutive deflexions, ‘in which for shortness we write A == vale 5) Uy— AX, == i() v3 3 av» + Vy = 0, a, AXny 1 oe Un —92 = 0, (Q-— art ey — by a Break in an Overhead Wire carried on Poles. 635 The first (n—1) equations determine the ratios of the n deflexions, in terms of the single constant a. It will be seen that the relative magnitudes of the yieldings in the suc- cessive poles do not depend on the position of the break. The latter fixes the absolute scale, in accordance with the last equation. The «’s form a recurring series, whose “ generating function ”’ is rm Tea t 7 2. €., @, is the coefficient of y” in the expansion of this fraction in ascending powers. LTxpressed explicitly we have ee Oh ee meee) oe) Pe =e i a a eZ of VGxolr =a )@G—4) ate Le 2eeo se uate Consider now the ratios of consecutive deflexions. We have ——s == 7 Vy v v IL ae =0— el ==, =o Dae Wy IL — =t— =O— 9 V2 U2 il. C= ——= a Up iL =a— ...(7—l)as. vr—1 dl Now, from the nature of the case, a>2; and it can be shown that the continued fraction then approaches a finite limit as r increases*. In fact, if z represents this limiting value, we have | 2=a— > or z satisfies “—az+1=0. The roots of this are }{a+./a?—4}, which are real if a>2. * Cf. Chrystal’s ‘Algebra,’ vol. ii. p. 482. rig ale 636 Messrs. Hawthorne and Morton on Deflexions caused ; ar ; ; Since mI > 1, we take the upper sign and so get wor— Tee ee at /a—s rao Ur—l a 2 Thus at a distance from an anchor-pole the successive deflexions approach a geometric progression. It will appear in the subsequent part of the work that in our actual case this state of affairs is closely approached after seven or eight poles are passed. The existence of this limiting ratio, taken in conjunction with the last equation of the set, leads to the conse- quence that the mavimum deflexion, which of course occurs in the pole next to the break, and which becomes greater as this pole is further removed from the anchor-pole, approaches a limiting value. If this limit is below the allowable safe deflexion, it does not matter how widely the anchor-poles are distributed. To find this limiting deflexion we have Lyn | @-1)- grate | ==, b y= - = 0 G=)=-= Giving the ratio in the denominator its limiting value, we find that the deflexion cannot exceed 2b GI) Ge gu If the orzginal horizontal tension acted on one side of the pole next the break, it would produce a deflexion carers It will be seen that the actual maximum deflexion is less than this, on account of the increased sag of the remaining wires, in the ratio 2:144/ 5. It is easy to extend the analysis to the case where some, only, of a number of similar wires are broken. We shall give the equations arrived at for the deflexions. Let the break occur between the nth pole counting from one anchor-pole, and the mth counting in the opposite direction by a Break in an Overhead Wire carried on Poles. 687 from the next anchor-pole. Call the deflexions on one side of the break #,....: vn, and on the other y; .... Ym, @n ym being on the two sides of the break, and 2’s and y’s being measured away from the break on both sides. Let s represent the number of wires remaining number originally on The equations giving the (n—1) ratios of ws and (m—1) ratios of y’s are the same as those already got. The connecting equations which determine the actual magnitudes are fraction (a—1-+s)a,—#,_4 + SYim— b(1—s) = (a— 1 -- S) Ym Yon 1 + SU. The quantities a and 6 have their former meanings, T and w which occur in them referring to the whole set of wires and not to a single wire. We have . (a =e, = aa, (i har Uap So that the ratios of the deflexions on the opposite sides of the gap are independent of the number of wires broken. If the break is sufficiently distant from both ends of the Uy —1 eel Ym—1 Un Ym row so that we may use the limiting value for 5: we get 2b(1—s) a—2+4s+/a—4 Coming now to the application of our results to the actual case referred to, we have the following data from which to calculate the constants a and 0. ln =Yn= Number of wires 6. Tension of each wire 1000 lbs. Weight of each wire ‘42 lb. per foot. Distance between consecutive poles 100 yards. A test of the stiffness of a pole showed that a deflexion of 3 ins. was caused by a force of 800 lbs. applied to the top in a horizontal direction. From these values we calculate a=221, b =0°40, the units being lbs. and feet. The following table gives the calculated deflexions in feet 638 Messrs Hawthorne and Morton on Deflexions caused when the break occurs after the Ist, 2nd, ... 7th pole, counting from an anchor-pole. | | | Defiexion of..| 1st | 2nd ord Ath 5th | 6th “th | Pole. When 2=1 3) | OA. SOA aS 16 | -36 | -62 <4 2B era» £67 O7-7| 1215 di =26| “43 4) <68 04° )) 6 209, 4) 217 A 27. eA alee 03 | -06 AY | “17. | +28" | 44 eee The limit of the ratio of successive deflexions is 1°58, and the limiting value approached by the maximum deflexion is -696 foot. It will be seen that this is almost reached at seven poles’ distance from the fixed end. JIGS oO PB ww Fig. 1. ES “7 5 ee mm FATATA Fees OIA ZS poonas Ze pe eee ath gre aie zn POLE DEFLEC T/ ON. ' These results are shown graphically in fig. 1. The points corresponding to each position of the break are strung by a Break in an Overhead Wire carried on Poles. 639 together on a curve, although of course the intermediate points on the curves have no physical meaning. ‘The asymptotic approach of the extreme points of the curves to the limiting value is very obvious. If the original horizontal tension acted on one side of a pole, it would cause a deflexion of 1°9 feet, supposing the linear relation to hold up to this range. We have calculated also the maximum deflexions liable to be caused by breakage of 1, 2,....6 wires, the point of break being distant from both fixed ends. No. of Wires broken. Deflexion. ee en ee AQ) at aaah ee ell Spare hor SR A ASR “O07 One Re eee. 1A HNIES SORE POT eC ar h 2195 yak Alte cas sh. Beis 1 dae "367 Oath rete anette a tt: SN, to "696 | ry oe Maximum DEFLECTION. | 2 3 4 5 6 WirES BROKEN These numbers are plotted;in fig. 2. The points lie on an hyperbola, as is shown by the equation obtained above to connect wv, and s. [ et07Ng LVI. The Lsothermal Distillation of Nitrogen and Oxygen and of Argon and Oxygen. By J. K. H. INewis * 1) feo investigations have been made in order to find the relation connecting the composition of the vapour with the composition of the liquid, when a mixture of two liquids is distilled isothermally (see Young’s ‘ Fractional Distillation,’ Macmillan & Co., where a full summary of the literature on this subject may be found); and it has been shown that in some cases the relation takes the simple form Ty=k.7;, where 7, is the ratio of the two substances in the vapour, 7 the corresponding ratio in the liquid, and k a constant. In most cases, however, £ is not an absolute constant but varies slightly with the molecular composition of the liquid; and we thus get mixtures (a) which have a maximum vapour-pressure, (b) which have a minimum pressure, and (¢) which although having neither maximum or minimum vapour-pressure do not satisfy the above relation. These different cases have been very fully investigated by Zawidzki and others at ordinary temperatures ; but the only paper dealing with distillation at low temperatures is one b Mr. HE. C. ©, Baly (Phil. Mag. vol. xlix. p. 517, 1900), who carried out a series of distillations of liquid air under a pressure of one atmosphere. In isobaric distillations, how- ever, the conditions are not so simple as they are when the temperature is constant; so at Mr. Baly’s suggestion I decided to complete his work by making a series of isothermal distillations at low temperatures, and I received considerable help from him in the early experiments when we hoped to make the research a joint one. Many forms of apparatus have been devised for carrying out distillations isothermally, but none of them were suitable for work at low temperatures. Moreover, most of the forms used are open to the objection that care is not taken to ensure that the vapour is in complete equilibrium with the liquid ; and in addition considerable error may be introduced by back condensation, &c. The apparatus used by Zawidzki (Zeit. f. phys. Chemie, vol. xxxy. p. 129) avoids most of these sources of error; but even in this case, since the sample of distillate is obtained by distilling over a small quantity of the liquid, the composition of the liquid may change during this operation, and so introduce error. Such an error would be of considerably greater importance in dealing with * Communicated by the Physical Society: read January 26, 1906. Isothermal Distillation of Nitrogen and Oxygen. 641 liquefied gases; for in this case one cannot work with such large quantities of liquid as Zawidzki used. But this error and many others may be eliminated by circulating the vapour through and through the liquid until no further change in either takes place: and then collecting and analy: sing a eee of the vapour which has in this way been brought into equilibrium with the liquid. With such an arrangement it was necessary to keep the temperature of the distillation-bulb ver y constant for a con- siderable time, and an accurate means of measuring the temperature was also required. The distillation-bulb was therefore immersed in a long cylindrical vacuum-vessel containing about 600 e.c. of liquid air, and the pressure under which this air was boiling was varied by means of a Fleuss pump so as to keep the temperature constant. To measure the temperature, a bulb containing liquid oxygen and connected to a manometer was immersed in the liquid air so that the manometer registered the vapour-pressure of pure oxygen at the temperature of the distillation-bulb. With this arrangement the Fleuss pump was worked at such a rate that the manometer showed a constant pressure. In the different experiments this pressure amounted to either 100, 200, or 300 mm., and the variation of pressure seldom exceeded 0° mm. This variation corresponds to a tem- perature difference of 0°:03 C., 0°:02 C., and 0°01 C. in the three different cases. These pressures, according to Travers (Bhi. Trans. 200. p. 105) .correspond to 74°-7, 79°:07, and 82°09 Absolute measured on the hydrogen scale. The apparatus used for carrying out the distillations is shown diagrammatically in fig. 1, the liquid oxygen bulb and the corresponding manometer being omitted. The rubber cork A, which fits the mouth of the vacuum vessel containing the liquid air, has passing through it the liquid oxygen bulb and several tubes of which three, Tz .o, Jare joined to the distillation-bulb P, and another, not shown in the figure, leads to the Fleuss pump. In an experiment, Bis half filled with the mixture to be distilled, and the vapour, after being thoroughly cooled by the spiral 4, is blown through the liquid i in B, the tube 3 then carrying the vapour on into the circuit. Thetube 1 is joined to the bulb B quite close to the bottom, and for a considerable part of its length consists of an extremely fine capillary drawn out of an or dinar y piece of capillary tubing. This tube is also connected to a gas- holder C, so that ‘when the reservoir of © is lowered liquid is sucked up the fine capillary to a warm part above the liquid air, and there boils as a whole and is collected in the gasholder. 642 Mr. Inglis on the Isothermal Distillation of The circulation of the vapour is carried on by means of the mercury circulator DEFG of the pattern described by Collie (Journ. Chem. Soc. 1889, p. 110). Mercury flows from the reservoir D through a rubber tube furnished with a screw- clip and then falls in drops down the tube EF. As each iaiee, 1 drop falls it drives on the gas contained in the tube HF and pumps gas in the direction KLHE. In this way the circu- lator pumps the vapour up the tube 3 and blows it down 2, Nitrogen'and Oxygen and of Argon and Oxygen. 648 and thus sends it round and round the circuit. The mercury after it falls down the circulator is collected at the exit G, the height of which above or below F is adjusted so as to keep the surface of the mercury just below the side tube leading from F. The sample of vapour is collected in the bulbs L through which the vapour is circulated; by closing the taps HK this sample of vapour is shut off f from communication with the liquid in P, and can be collected by opening the tap M which leads to a Tépler pump. The pressure under which the liquid is boiling can be measured in two different ways. It can either be calculated from the difference in height of the mercury surfaces in F and G and the height of the barometer ; or it may be measured directly by means of the closed manometer NP. The shorter open limb N of this manometer can be shut off from the closed limb P by means of the tap R. By means of the taps QR and the reservoir S the amount of mercury in the manometer can be so regulated that when R is open the mercury surface in N is close below the side tube coming from the tap H. In this way dead space is as far as possible avoided. ‘This manometer could be used for pressures up to 770 mm., and the manometer GF was used only for pressures greater than this. Readings of the manometer NP were made during the circulation, so that one could see when the reading became constant ; but the final readings were taken by means of a telescope after the circulator had been stopped and after the tap T connecting the tubes 2, 3 had been opened. It was found convenient to close the tap RK a moment after T had been opened and before the readings were taken. The gases were stored over water in ordinary glass gas- holders—the argon alone being kept over mercury ; and after passing through soda-lime and phosphorus-pentoxide tubes, were admitted to the apparatus by means of the tap a As regards the gases themselves, the oxygen was in all cases obtained by the decomposition of potassium per- manganate. ‘The nitrogen was prepared by heating a mixture of solutions of ammonium sulphate and potassium nitrite, and was fractionated by means of liquid air before being passed into the gasholders. A small quantity of oxygen was | then added and the gas left standing over water. In this way, any traces of nitric oxide were turned into nitrous or nitric acids which dissolved in the water, and the small quantity of oxygen (0°5 per cent.) remaining did not matter, as mixtures of nitrogen and oxygen were fo be used. The 644 Mr. Inglis on the Isothermal Distillation of argon used, which was kindly supplied to me by Sir Wm. Ramsay, was purified by means of a kot mixture of quick- lime and magnesium, and was fractionated with liquid air to remove traces of helium and neon. Its spectrum showed that it was extremely pure. The analyses in each case were carried out by measuring off 10-13 c.c. of the gas, and then removing the oxygen by means of a pellet of yellow phosphorus. A measurement of the volume of the residual gas then gave the molecular composition. Tests showed that analyses carried out in this way did not have a greater error than 0:1 per cent., which was sufficiently accurate. Two parts of the apparatus needed exhaustive testing before one could be sure of the results. The method of taking the sample of the liquid was based on the assumption that by taking a fine enough capillary, the liquid would evaporate as a whole and would not fractionate itself. The first capillaries employed were found to give very variable, and therefore untrustworthy samples; but by inserting fine drawn-out capillary, as drawn in fig. 1, concordant results were obtained. These tests were carried out as follows :—About 5 litres of dry air were condensed in the bulb B, and samples of the liquid, which half-filled the bulb, were then taken and analysed. The percentages of nitrogen found were 78°77, 78°52, 78°74, 78°66, and 78°84, which results, omitting the second one, give 78°75 per cent. as a mean, the deviation of the second one from this mean being 0-2 per cent. But all the results are lower than the true percentage of nitrogen in the air, which was found to be 79°06, 78°99 per cent. in two consecutive experiments. This difference can be cep ainee as follows :—When the air was condensed, the spiral 4 and the part of the bulb B above the liquid were filled with vapour which was in equilibrium with the liquid, and which therefore did not have the same com- position as the air. The vapour, in fact, contained an excess of nitrogen, so that the liquid contained too high a proportion of oxygen. The vapour also being at a temperature of less than 80° Abs., the dead space contained nearly 4 times as much gas as the same space would at ordinary temperatures. Thus 25 c.c. of dead space represented 100 c.c. of vapour measured at ordinary temperatures. This vapour contained about 5° per cent. of oxygen, so that the dead space con- | tamed 94:5—4x 5:5=72°5 cc. of nitrogen above the proper q amount for the oxygen. This amount of nitrogen is to be : deducted from 5 litres of air ; and this brings down the true ; ‘ i ‘ » ; _ J Nitrogen and Oxygen and of Argon and Oxygen. 645 percentage in the liquid, to 78°69 per cent., which is sufficiently near the mean value 78°75 per cent. found by experiment. It is certainly surprising that the amount of dead space can make so great a difference in the composition of the liquid ; but it is of course due to the temperature of the dead space being so low and to the great difference in the vapour- pressures of nitrogen and oxygen. ‘These tests show there- fore that the sample of the liquid can be taken pretty accurately, the error being certainly not more than 0°3 per cent. and usually not more than 0°1 per cent. The sampling of the vapour offered no possibility of error, but it was necessary to ascertain how long the circulation must be carried on in order to obtain true equilibrium between the vapour and the liquid. About 5 litres of a mixture of nitrogen and oxygen containing about 75 per cent. of nitrogen were condensed in the bulb B, and after ten minutes circu- lation (the circulator pumped the.gas at the rate of about 50 c.c. a minute) samples of the liquid and vapour were taken. Circulation was then carried on for a further fifteen minutes and fresh samples taken, and again for a further twenty minutes and a third pair of samples taken. The tubes K, L, H were then pumped out, and while some more of the mixture was being taken into B through the tap U the tap K was opened, thus filling the bulbs L with the mixture; a second series of experiments was then made exactly as at first. The results are given in Table I. TABLE I, Time of circulation...... 10 min. 15 min. 20 min. 10 min. 15 min. 20 min. Per cent. of Nitrogen fe ; 4 ; ; : rs IVGAUBIG eenee a } [oe me ae are ee? Ue Per cent. of Nitrogen } 93-] 93-0 92-7 93-0 92:8 93:0 MOV APOUT Ye...) 44 These experiments show that the liquid sampling was uot very reliable; but the experiments were made before the method of liquid sampling had been perfected. The vapour samples show slight variations, and equilibrium is apparently reached after ten minutes circulation ; so a minimum of twelve minutes was fixed upon as being sufficient to ensure equilibrium. It should be remembered that the percentage of nitrogen in the liquid sample must steadily fall ; for the vapour is richer in nitrogen than the liquid, and some of the vapour is removed in taking each sample of the vapour. This to a certain extent explains the lower value obtained for the 646 Mr. Inglis on the Lsothermal Distillation of third sample, 7. e. after twenty minutes circulation in each case. The apparatus having thus shown itself accurate and con- venient for working, two series of distillations were undertaken, In the first of these, the results of which are given in Table I1., twenty-three mixtures of nitrogen and oxygen were distilled at that temperature (74°°7 Abs.) at which the vapour-pressure TABLE II. Fen) 0; One C=6:60— 0.0250 Temp. 74°°7 Abs. Pure oxygen has vapour-press.= 100 mm. | Molec. | Molecular percentage | m4.) Pressure: mm | percent. ; Nitrogen in Vapour: ae See rae Part. Part. No.| N,in | Pressure | Pressure | | liquid. | | i Nitrogen.) Oxygen. Obs. obs. | cale. | diff. | obs. smoothed) diff. | | | | lo mim. mm. A254 nf 20:0 00) 0 He A00OIui ghOO:0) | iaeee 00 | 1000 | Di 53 25°5 26:5 |—10 | 1306] 1300 | +5 345 95°5 ae te | 343.1) 336 |= 7°) 1407) 1400" —2 475 935 | Ass tert A! 445 | 447 |— 2); 1629] 162-7 | +1 27 900 | Di see OO) OD-D 550 |+ 5 | 1902] 1900 | +-1| 1045 85'5 | Gea om 20 64), Gib |— 1 | 2112) 2105 || 4-37) ess 81:0 asl 2b 665 | 66:9 |— 41 2322 | 232-7 | 4-1) Toow 770 8...| 30°5 712 | 716 |— 4] 2545] 2550 | —-2] 1825 725 9...| 33°4 736 | 739 |— 3 | 2671 | 2673 | —2 | 1979 69°9 105) — 3805) | F638 | 767 4 4-71.) 2848.1" 285:0 | =) sakes 66°4 [heals 48 800 | 797 |+ 3] 3042] 303-7 | +°2| 2420 61-7 12...)- 445 81:5 | 811 /+ 4] 8156] 3150 | +:°2| 255-4 59°6 13...| 48-4 83:0 | 831 |— ‘lL | 33801 | 3305 | —-1 | 2746 55°9 14... 52:2 8456 «| "S£6 0 | 3464 | 3467 | —1 | 2933 53:4 15.5) 56-4 864 866 2) 3611 | 3630 | —5| 3143 48°7 16.05) OLS 872 | 870 |+ 2} 3660; 3665 | —1); 3188 ATT peel 631 mts 892, 4) - 18922 0| 3887 | 3900 | —3| 3479 42-1 183.) 686. | 910 | SLT |= )-4085. 41b2 | —T Sie 36'6 fee t43 .|. 93:0 93°0 0 | 4325 | 4855 | —-7-| 405-0 30°5 20:..| 792 |. 942 | 943 |— <1 | 4533, 458:0 | +1) 4272 25°8 Divers. | -<95'9 957 |— 2] 4675] 4710 | —8 | 4507 20°3 22. B39 1° 970.) OF Dl Asef") A900 ot aes 14-2 23... 939 | 984 | 984 | 6| 509° | 5090 | +:2; 5008 8-2 o4..| 994 | 999 | 999 | 0] 5800] 5290 | 4+:2| 5285 05 25...| (100°0) |(100-0)| (100) |... | G31-0)| 381-0) |... (531) | of pure oxygen is 100 mm.; and the total pressure, the com- position of the vapour, and the composition of the liquid were determined. In the second series, which was carried out at 79°07 Abs., where the vapour-pressure of pure oxygen is 200 mm., only eleven mixtures were taken; the results are given in Table ILI. Nitrogen and Oxygen and of Argon and Oxygen. 647 TaBue ILI. Py,/Po,=4°605. C=5:48—0:'0207 m. Temp. 79°07 Abs. Pure oxygen has vapour-press.=200 mm. | | Molee. | Molecular percentage | Mota Er recemrete ena percent. | Nitrogen in Vapour; : pe ; Part. Part. Nor} ) N.in Pressure | Pressure liquid. | | Nitrogen.| Oxygen. Obs. obs. eale. | diff. | obs. |smoothed| diff. | hs mm. mm. ee 0 0 Oo ik tase 200 200 es 0 200 eo | ley | 160 | 7 | 2382.) 231-5 | 7) STON 1945 ee lO 39°2 337 | +°5 | 29738 | 2955 | + 8) 1143 181-2 | 4...) 19-7 505 O04 | 1 | 3718) 371d | — 1) 2058 165°7 Dae ees: 65°4 654 | O | 4857 |. 485° | + -0| 2848 150-7 6...) 40°5 70'8 (9 ol 2957) ||) 930'09| —":0 ||) 40272 WBS | Gel OL 82°1 821 | O | (599)x| 604-0 | — 8} 4955 108°5 8...| 60-4 86 4 866 | —2 | 6604 | 6670 | -10| 5776 89-4 Sy 28 91°5 91:3 | +2 | 7460 | 7500 | — °5| 684-7 65°3 10...| 82°8 94°8 94:8 OF Slsoo | SiC: O5 i — Ol F73:0 42-4. Pe 190s 97°6 972 | +4 | 8725 | 8700 | + °3) 845°6 24-4 Lasoo b 99°7 ddido)|) —o) 931-0 | 9285, 42 2) 928-0 0-5 13... (100°0) | (100°0) oe = ae wel) aoe 931°0 0 * In the case of Exp. 7, the total pressure was by a slip read only during circulation and is therefore certainly too low. Discussion of Results. If the ratio of nitrogen to oxygen in the vapour be com- pared with the same ratio for the liquid, it is found that the quotient of these two ratios is a linear function of the mole- cular composition of the liquid. Thus taking the results of Table Il. we find that the experimental values, 7.e. those values given in the second and third columns, approximately satisfy the relation Ratio N,: O, in vapour Ratio N, : O, in liquid where m is the molecular percentage of nitrogen in the liquid. Similarly in Table III. the value of this same quotieht is 548 —0:0207 m. Now by means of these formule we can calculate the composition of the vapour from the composition of the liquid, and these results are given in the fourth column of the tables under the heading “ nitrogen in vapour calcu- lated.”’ It will be seen that the differences from the observed values are slight except when the value of m is small. Now in this case an error of 0:1 per cent. in the liquid corresponds = 6°60 —0:028 m=C, 648 Mr. Inglis on the Isothermal Distillation of to an error of 0°5 per cent. in the calculation of the percentage of the vapour; so that the apparently large differences between the calculated and observed values correspond to only small errors in the analysis of the liquid. The formule given can therefore be fairly used to smooth the experimental results. As regards the total pressure, since this could only be smoothed graphically, the results were plotted on squared paper on which 2 mm. corresponded to 1 per cent. in the liquid, the pressures being plotted full size. A steady curve was then drawn through the experimental points and the “smoothed” values of the total pressure taken a om this curve. Comparison of the “smoothed” and “observed” values shows a fairly good agreement considering how rapidly the vapour-pressure changes with the temperature. From these ‘smoothed ” values of the total pressure and the composition of the vapour, the partial pressures of the nitrogen and the oxygen may be calculated, and these results are given in the last columns of the tables. When now these partial pressures and the ictal pressure are plotted in the usual way against the molecular compo- sition of the liquid (see fig. 2 for the results of Table II.), it is found that the curves obtained, though they have only sight curvature, are certainly not straight lines—a result which was to be expected from the fact that the relation 7,=kr, did not hold good. This relation is the mathematical expression of the property “ the ratio of the concentrations in the vapour is proportional to the ratio of the concentrations in the liquid.””, Hence we might expect to find the concen- tration of either substance in the liquid proportional to its partial pressure as vapour, this being the relation known as Henry’s law. Now the vapour is usually plotted against the molecular percentage, and a straight line for the vapour- pressure would therefore indicate a proportionality between the vapour-pressure and molecular percentage. But since the volume of a gramme-molecule of a liquid is a quantity which is not the same for different liquids, the molecular percentages are not true concentrations. Hence a straight line in the usual method of plotting would indicate a deviation from Henry’s law; andit is therefore evident that the correct method is to plot the partial pressures against the true concentration. To obtain the true concentration one needs to know the density of each mixture used. But a close approximation to the actual value of the density may be obtained by calculating the density of the mixture from the densities of the pure com- ponents, assuming that no contraction takes place. Any Nitrogen and Oxygen and of Argon and Oxygen. 649 contraction would of course make this calculated value wrong ; but the error thus introduced would be of a higher order than the differences in density of different mixtures of the same two liquids. Measurements of the density of liquid eee 3) bt Fee oe PRESSURE IN MILLIMETRES. 75 100 Nz Mots % Vapour-pressures at 74°°70 Abs nitrogen and oxygen have been made by Baly and Donnan (Trans. Chem. Soc. 1902, p. 907); and they found the values 0°8225 and 1:2160 respectively at that temperature at which Baly’s curve for the vapour-pressure of oxygen gives the Phil. Mag. 8. 6. Vol. 11. No. 65. May 1906. 2:U 650 Mr. Inglis on the Isothermal Distillation of vapour as 100 mm.; and the values 0°8022 and 1:1947 respec- tively at the temperature corresponding to an oxygen vapour- pressure of 200 mm. According to Travers (loc. cit.), Baly’s measurements of the temperature are erroneous; but the thermometer used being the same in the two cases the densities given are probably correct. Hence for the results of Table II. the volume of one hundred gramme-molecules of a mixture containing m molecules per cent. of nitrogen will be 28m 32(100—m) 0°8225 1°2160 aa and the molecular concentrations will be obtained from the molecular percentages by dividing each molecular percentage by the corresponding value of thisexpression. Similarly for the results given in Table III. the factor is 28m , 32(100—m) Bu 0°8022 11947 For simplicity, however, the concentrations can be better stated as grams of the corresponding substance per 100 c.c. of the mixture; and the results of Tables IL. and III. are given in this way in Tables IV. and V. If Henry’s law holds, the quotient obtained by dividing the concentration by the partial pressure should be a constant, so the values of this quotient are also given in the Tables. These two tables show that the solubility of nitrogen in the oxygen obeys Henry’ s law quite rigidly up to a molecular percentage of nearly 70 per cent., but that oxygen does not obey this law. The value of the quotient concentaaies for pressure oxygen varies in such a way as to point to association of oxygen molecules when dissolved in nitrogen. Now the surface-tensions of liquid oxygen, nitrogen, argon, and carbon monoxide were determined by Baly and Donnan (loc. cit.), and they concluded that the pure liquids showed no asso- ciation. But looking at their results more closely, we see that the value of the ‘temperature coefficient of the molecular surface-energy of oxygen, viz. 1°917, is not the same as that found for the other three gases, which all have a coeffi- cient nearly equal to 2003. Baly and Donnan concluded that the probable value of this coefficient at low temperatures was too uncertain for any conclusion to be drawn as to association ; but the fact that argon, nitrogen, and carbon monoxide all have the same coefficient points to the value Mitrogen and Oxygen and of Argon and Oxygen. Taste [V.—Temperature 74°°7 Abs. 651 | I | Concen- | Partial | Concen- | Partial | | No. | tration | Pressure! Concen. | tration | Pressure; Concen. | Conc. O, | heeot of Press. of of Press. |(Press.O,)!0 | \Nitrogen.| Nitrogen. Oxygen. | Oxygen. | | | mm. mm. | mote. » 00 0-0 121-6 100-0 1-216 ! (pure) esd | OG 34:5 1624 | 113-4 95°5 1187 aoe 76 475 "1600 | 110-4 93:5 1-180 ee 1-7 (Pat "1602 | 1042 90-0 1:158 ee 16'S 1045 1608 96-7 85°5 131 | Oia peal) 129°5 "1622 90:5 81:0 1117 Megeo5s |< 1557 | 1625 | 841 rae, || 1088: See 29'S 182-5 1633 776 725 1-070 | Disa POLO 197-9 1630 73:7 69-9 1055 10s) 360 | 2186 | 1647 | 684 | 664 | 1-031 | lig |-30:6 | 2490 | -1637 | 630 | 61-7 | 1-029 | 12 : 41°9 255'4 "1641 SEPT, 59°6 1-001 ES sol ocala: Seta | 274.6 "1642 54:9 559 982 [ : 48-2 293°3 1643 50-4 534 "944 | i ae SS 3143 1639 45°5 48-7 954 16 |) 522 | 3188 | -1637 | 444 | 47-7 | -939 tga 566 347-9 "1626 37'8 42°1 “899 | WS «2 60:8 374-6 1628 318 366 "868 630 Le. 65:2 405°0 1610 Zi5e Il 30°5 "824 607 205% 68:3 427-2 "1599 20°5 25°8 “7S 581 21 plete 450°7 “1591 156 20°3 “769 586 22 oO 475°8 1576 10:7 14:2 753 593 23 3 783 500°8 1563 58 8:2 “709 586 24 . 819 528-5 "1550 (0°5) (0°5) (1:0) "25 82:3 (531°0) 1550 ) ) Side | (pure) | Taste V.—Temperature 79:07 Abs. Concen-| Partial | ie Concen-| Partial = Prato leressnre Concen. tration | Pressure| Concen. | Concen. , an Oi On Press. of of Press. | (Press.)'!°- | Nitrogen. Nitrogen. Oxygen. | Oxygen. ee es —_ | | _- mm. mm. ile”. 0 0 ee LINES) 200 597 Di 3°5 37:0 ‘0951 114-2 1945 587 D peel) p Os) 114°3 0948 103-4 181-2 ‘D771 tile LO. 205°8 ‘0944 90-5 165°7 546 5 ...| 26°8 2848 ‘0941 795 TOO "528 (Sy dex Bei 402°2 ‘0938 63°38 127°8 “496 Mees aly AO: 2 495°5 ‘0931 OG 1085 467 8... 534 577-6 6924 40-0 89:4 “447 228 See 62°3 684:7 ‘0910 26°6 65°3 “408 218 O24) 16982 7736 ‘0894 16-4 42-4 "387 221 ae? 74:4 845'6 “0880 86 244 353 219 12) ...| 80:0 928°0 ‘0863 (os (0°5) NS, 80:2 931 ‘0861 0 0 | | 2U 2 6952 Mr. Inglis on the Lsothermal Distillation of of that coefficient being the normal one, so that oxygen must “be slightly associated. The association calculated from these figures would be (For7) =1:068. Now if oxygen is associated so that ~ molecules in the vapour become one molecule in the liquid, we should have, according to Henry’s law, concentration =const. x (pressure)”. But this equation takes no account of any relation between the association and the concentration, and therefore at its best can only approximately represent the facts when the concentration is small. In the equation, n and the constant are both unknown, but may be determined very easily by plotting the logarithm of the concentration against the logarithm of the pressure. If, now, this be done for experi- ments 23-20 of Table IV. (for all of which the concentration of the oxygen is low), it is found that the four points obtained lie close toa straight line the slope of which indi- cates that the pressure and cencentration satisfy the relation, — concentration = const. x (press.)'°?, thus indicating an association factor =1:09. This is of the same order as Baly and Donnan’s factor 1:068, so that the agreement is satis- factory. Similarly the results of Table V. point to an association factor 1°15, but a shght error in the composition of the vapour in experiment 11 in that table would be sufficient to explain the increase from 1:09 to 1:15. Values concentration O, concentration .O, : n - (pressure) 10 (pressure) 1) are given in Tables IV. and V. (for low concentrations of oxygen), and the values obtained show how the relation is satisfied. Since the size of the associated oxygen molecule is not known, one cannot introduce the corresponding modi- fications in-the formula deduced from Henry’s law, so that the formula used cannot be expected to give good results. In addition to this, Richardson (Phil. Mag. [6] vii. p. 266) has shown that one must consider separately the solubilities of the simple and associated molecules. . The results point, therefore, to nitrogen obeying Henry’s law and to oxygen only obeying it when we allow for asso- ciation. Now in the results of the many isothermal distil- lations which have been carried out at ordinary temperatures (see Zawidzki, loc. cit.) agreement with Henry’s law has not been looked for, as investigators have only looked for a linear relation between the partial pressure and the molecular percentage. The same difficulty that we have experienced in the calculation of the densities of the mixtures arises here also in calculating the concentrations ; but it may be over- of the expressions Nitrogen and Oxygen and of Argon and Oxygen. A few of Zawidzki’s come in the same way as before. 653 results have therefore been recalculated as concentrations, and the results showing the relations between concentration and partial pressure are given in thes lables Vik to. Xt: TABLE VI. oOor€: 9) Propylene Bromide and Hthylene Bromide. 8 _ Concen- | tration of aN Propylene Bromide. eet. | 0 fetes. | 4-4 ee. | 5) RA cai ol-3 Dix. 46-7 Feira! 60°7 the aaa 82'°8 eh Srl! 10; 2; 10571 wiv, 122 be 139°5 Welter 5S" Aer, 16371 (15 ...| - 172°0 (16. | fot lifer. W799 Coie 182"7 }19.. | 185°6 Pressure of Propylene Bromide. DWOOWS SND SE ee Coneen. Press. Fe BoE ER BR BR ROOD OO A ooo: CONIA ANDOE ROE AAW DAN | Concen- | tration of | Ethylene | Bromide. 203°4 198°6 186°3 169:0 15276 136°9 1341 D7 | 110-2 | 882 | 69°6 50°5 35'°6 Q4:7 14:9 Wes | 6-2 TABLE VII. Benzene and Ethylene Chloride. | Concen- | tration of Ethylene Chloride. eet 2 S — —_ I Pressure. Concen. Press. Concen- tration of Benzene. 84°5 731 617 61:3 Pressure of = Ethylene Bromide. PRO 167°8 158°6 14571 132°2 121°4 120°8 101-7 100°5 819 64:0 48:0 343 23°5 138 10:1 4:6 Concen. Press. 1-178 1-183 1175 1-165 1-152 1-128 1-110 1-108 1-097 1-077 1-088 1-052 1-038 1-052 1-077 1-123 1-359 49°99 C. Pressure. 268 231-5 189'8 188°5 156°0 127-9 92°5 65°9 21°7 0 Concen. Press. “315 316 LD) ono 332 “O00 339 “B44 “S47 654 Mr. Inglis on the Isothermal Distillation of TABLE VIII. Carbon Tetrachloride and Ethyl Iodide. 49°99 C. | | Concen- | Concen. | Concen- Concen. | No. | tration of | Pressure. Passe tration of | Pressure. “Pres | Iodide. ~* | Chloride. a eee 0 0 as 153°4 306°3 “501 | Ce aide 58 15°3 “381 1486 295°6 5903 | eee 14:3 38°4 O73 141-7 280°8 “005 | aU res a1:8. 5 | 80°6 “394 127°3 249-4 510 > eae 46°3. | 1109 ALT 115°4 225-2 *508 | ; deciee 67:0 153-1 437 97-4 193:0> ie eos La. S41) |1884 "| 459 84:3 167-5 BOR ie Sie. SGui nse D450) SE 0 0 ws TABLE IX. Carbon Tetrachloride and Benzene. 49°:99 C. Concen- | Gon Concen- | C 4 No. | tration of | Pressure. oncen: | tration of | Pressure, | ~2™°®™ Chloride. | Press. | Benzene. Press. ve 0 0 ne AE | BARD 268 ls lees 8:4 185 DO) ee oro 253°4 315 Shee 19°3 40°5 “ae 739 237-1 “312 4... 28°9 BS 7 “484 68°6 221°8 "309 ‘es 41-0 82:9 “494 62-0 202°5 306 GO: 48-0 97-0 “495 58:2 191°3 "304 Fare 63°7 128-7 “495 49°5 165°8 “299 Shee 89:0 176-4 9) 0/9) 39°6 124°6 286 a 106°5 211°8 503 26°0 93°4 wae) LO. 1198 238°5 502 18:7 68°3 273 JN 153°3 306°3 501 O 0 see In two cases, viz. propylene and ethylene bromide and benzene and ethylene chloride, Gawidzki found that the partial pressure of either component of the mixture was pro- portional to its molecular percentage. Now, as will be seen in Tables VI. and VII., the change from molecular per- centage to concentration upsets this relation ; but the deviation from Henry’s law is not very great, and any association would be very slight. In the case of mixtures of carbon tetrachloride with ethyl iodide, Zawidzki obtained slightly curved partial pressure-lines; but it will be seen from Table VIII. that the carbon tetrachloride obeys Henry’s law very closely, while the agreement for ethyl iodide is not so good. Similarly in Table [X., carbon tetrachloride and benzene show a fair agreement with Henry’s law. It must be remembered that in all these cases the concentration has Nitrogen and Oxygen and of Argon and Oxygen. 65d TABLE X. Benzene and Acetic Acid. 49°:99 C. Molec. Concen- ei Concen- tration Concen. | W eight tration |Pressure. Concent No. Pressure.| Pyess, of Acetic Se Press. of heats of Acetic B eid! Acid enzene. Vv ; apour. 1 ...| 845 (268°9) | (314) 0 0 eee. Gor 262°3 318 83:0 1:44 3°63 BOM Lape Mimgod ba) 258°7 316 89-1 351 6°53 aAoe 4 ...| 81:0 257°2 315 90-1 4°50 7°25 593 eee) Ci’ 249°6 310 94-7 8°56 115. T45 G.-| 04:6 2448 305 Ciel EG? 14:2 *839 Wee! 69'S 231°8 “299 99°3 | 18:3 18°4 "994 See, (Ga°9 224-7 "294 100-4 | 22-4 20:5 1-092 See OO 211-2 274 102:0 | 32:1 24:8 1:29 HO) O33 200°9 "265 102°5 | 37-6 27-1 1:39 Ue OL 195°6 263 103°1 39°8 28°7 1:39 pres o3:0 1532 "215 1048 | 62:1 36°3 eZ i) ces 3056 147-2 *208 105:0 | 65:0 36'S Lega 14 ...| 266 apall OW 1054 | 698 40:2 1-74 ese LS 75:3 1157/ 1070 | 87:5 50:7 1°73 WGies. 1:5 13°3 114 O79) 99-9 54°7 1°88 lays: 0:5 3°D "148 107-9 | 101-1 547 | 1°85 too 0 0 uae 101°7 (56°5) (1°80) been calculated from the densities of the two components assuming that no contraction takes place on mixing. Until the densities of these mixtures have been determined, a close relation between the calculated concentrations and the pressures cannot be looked for. It is possible that this explains the fact that in Tables LX. and X. the quotient for benzene rises with the concentration, whereas in Table VII. the quotient falls. But the case of the distillation of acetic acid and benzene, the results of which are given in Table X., is particularly interesting from the point of view of agreement with Henry’s law. Acetic-acid vapour has a molecular weight which shows that the vapour consists of a mixture of simple and double molecules. Now when acetic acid is dissolved in benzene, even in the most dilute solutions, the acetic acid consists entirely of double molecules. Hence, when acetic-acid vapour dissolves in benzene, association takes place, and this ought to be shown if the partial pressure be plotted against the concentration, From Table X. it will be seen that neither the partial pressure of the acetic acid nor that of the benzene is proportional to the concentration, and that the association factor in the case of acetic acid is considerable. 656 Mr. Inglis on the Isothermal Distillation of __ The association varies with the concentration, so that caleu- lations from the partial-pressure curve are not very accurate. If the log of concentration be plotted against the log of the partial pressure as before, the slope of the curve at each point may be taken as a measure of the association for that concentration. The result obtained is an association factor 1°50, when the concentration of acetic acid is 3°51 gr. per 100 c.c. According to the molecular weight the factor should be 1°35. It will be seen, therefore, that again the agreement is not close ; but since the method of calculation dves not take account of the separate solubilities of the single and double molecules, as is really necessary, a better agree- ment can hardly be looked for. Zawidzki’s experiments, therefore, to a certain extent support the view that the relation between the partial pressure and the concentration can be obtained by means of . Henry’s law, so that it may be concluded that oxygen is associated when dissolved in nitrogen and also in the pure state. | Lnstillation of Argon and Oxygen. In the separation of two gases from one another by means of fractionation at low temperatures, it often happens that at the temperature used the one substance is below its melting-point. In this case the relations which hold during distillation are modified by the fact that the total pressure of the saturated solution of the one substance in the other may be greater than the vapour-pressure of either pure substance. This happens in the case of argon and oxygen. The melting-point of argon is only a little below its boiling- point; and at the temperature of fairly fresh liquid air, argon is a solid with a vapour-pressure of over 400 mm. In order to see how a mixture of argon and oxygen behaved when distilled isothermally, a few experiments were made at 82:09 Abs. with the apparatus already described. As, how- ever, the quantity of argon available was only 550 e.c., the greatest percentage of argon that could be used was 13°6 per cent. by volume. The results of these experiments are given in Table XI. The vapour-pressure of pure oxygen at §2°09 Abs. is 300°0 mm., and this value, together with the experiments 2, 3, 4, 5, gives five points on the vapour- pressure diagram. Hxperiment 6 was carried out in quite a different way. A quantity of pure argon was prepared and its vapour-pressure at 82°-09 Abs. was found to be 411-0 mm. On adding a small quantity of oxygen the vapour-pressure rose to 420 mm., and it remained equal to this in spite of Nitrogen and Oxygen and of Argon and Oxygen. 657 continued addition of oxygen so long as any of the argon remained solid. Hence, 420 mm. is the total pressure, above a saturated solution of argon in oxygen at 82°09 Abs. Since the solution is saturated, the partial pressure of the argon must be equal to the vapour-pressure of solid argon at the same temperature. Hence the partial pressure of the oxygen-is (420—411) mm.=9-0 mm. and the percentage of argon in the vapour is = x 100=97°8 per cent. Several samples of the saturated solution were collected in the way used earlier for liquid samples, and it was found that the composition of the hquid remained constant, however the amount of oxygen added might vary, so long as there was solid argon present. The analysis of the samples showed that ithe liquid contained 92°7 per cent. by vol. of argon. Hence we see that the liquid containing 92°7 per cent. of argon gave a vapour containing 97°8 per cent, of ar gon and exerted a vapour-pressure =420 mm, Tasue XI. : Argon and Oxygen. Temp. 82°09 Abs. { | | a Molec. percent. | sass hea aires saa is i Bo, |'Argon |ATE™ 7 VPM | roca, Prosoute| wenn, | easel in SIAN IEEE OOS ee SOLOOL ACT Ox Poet Ne ; Liquid | Pes ie eae ae Obs Cale | | Obs. : : | | a | mm. mm. i ce 0 0 0 | 3000 | 300-0 | 300-0 0-0 ae 330 | 576 | ...- | 38082 | 307-5 | 2905 | 17-0 | ae 56 DAE ae 3108 3120 | 2835 | 285 ee 10-2 16,0) a e320 Ue spite 69-3n i pied ane 13-6 AVM pe (LSB le Ber | CRO) tara Wee 92:7 Me 97-3 | 420:0 | 420-0 90 | 4110 | | Saturated | Since |the densities of mixtures of argon and oxygen at 82°:09 Abs. are not known, and the density of liquid argon at that temperature cannot be measured, one cannot plot the pressures against the concentrations. In default of this, the pressures may be plotted against the molecular per- centages, and this has been done in) ties a. | Lhe- broken lines in this figure are drawn through the points representing the partial pressures for low concentrations of argon ; and it will be noticed that they deviate considerably from the full 658 ‘Lsothermal Distillation of Argon and Oxygen. lines which are drawn to show what the partial pressures would be if they were proportional to the molecular per- centage. It will be noticed also that the partial pressure of oxygen above the saturated solution is much less than would be expected from analogy with the nitrogen-oxygen curve. Fig. 3. 1 4ll 7727728. 300 e5 50 92-7 . Ar. mots % SAT? Soe Argon and Oxygen at 82°'09 Abs. This shows, therefore, that the separation of a solid from a liquid in which it is soluble is a much more complicated dis- tillation-process than the separation of two liquids. A simple separation can be obtained, however, if one can lower the temperature so far that the vapoar-pressure of the pure solid is negligible compared with the vapour-pressure of the other substance. In this case a single distillation effects a complete separation, and therefore in practice one always endeavours to obtain this condition of affairs. In conclusion, I wish to express my thanks to Sir William Ramsay for the kind interest he took in this research. University College, London, W.C. rf 659 LIX. The Construction and Use of Oscillation Vaives for Rectifying High-Frequency Electric Currents. By J. A. Fiemine, M.A., D.Sc., F.R.S., Professor of Electrical Engineering in University College, London*. TTENTION was directed by the author in 1890 to the fact that if two carbon filaments are sealed into a single vacuous glass bulb so as to make an incandescent lamp with two separate carbon loops, the resistance between these filaments, though infinite when the carbon is cold, becomes quite small as soon as the loops are made incandescent +. Moreover, if a metal plate is sealed into an incandescent lamp it was shown that the space between the metal plate and the incandescent carbon filament possesses a unilateral conductivity, negative electricity being able to pass freely from the hot carbon to the plate, but not in the opposite direction $. More recently the author discovered that such an arrangement may be used as a valve to permit the passage of one constituent current only of a high-frequency current or to rectify an electric oscillation§. The reason for this action is now recognized to be the copious emission of negative ions or electrons from the incandescent carbon. ‘This opera- tion has been studied quantitatively by the present writer and many other observers. For the purpose of rectifying electrical oscillations and thus be able to detect them by an ordinary galvanometer, these oscillation valves are now made as follows :—A carbon- filament glow-lamp is constructed, the carbon loop of which is upheld in the centre of a highly exhausted glass bulb (see fig. 1). Around the loop is fixed a small cylinder of nickel, C, which is connected to a platinum wire sealed through the side of the bulb. The valve is used as follows:— The carbon loop is made incandescent by a suitable battery of secondary cells, a sliding rheostat being added to adjust the voltage on the terminals of the lamp. The circuit in which oscillations are to be detected is joined in series with a dead-beat mirror-galvanometer, and the valve connected with the circuit by wires joined respectively to the terminal of the nickel cylinder and the negative terminal of the carbon * Communicated by the Physical Society: read March 23, 1906. t See J. A. Fleming, “On Electric Discharge between Electrodes at Different Temperatures in Air and High Vacua,’ Proc. Roy. Soc. Lond. vol. xlvii. p. 122 (1890); also “ Problems on the Physics of an Electric Lamp,” Proc. Royal Institution, vol. xiii. part 34, p. 45 (1390). t See J. A. Fleming, “On a Further Examination of the Edison Effect in Glow-Lamps,” Phil. Mag. July 1896. § See also Proc. Roy. Soc. Lond. vol. Ixxiv. p. 476, 1905, “On the Conversion of Electrical Oscillations into Continuous Currents by means of a Vacuum Valve.” 660 Prof. Fleming on Oscillation Valves loop. The oscillation valve is most conveniently mounted for this purpose on a special form of stand (see fig. 1). In using the valve the carbon filament must be brought to bright ior: B, Exhausted glass bulb. C, Nickel cylinder. T, T,, Carbon filament terminals. T,, Insulated cylinder terminal. incandescence, about equal to that which in a carbon glow-lamp would correspond to a so-called “efficiency” of 3 watts per candle. So used, the valve enables us to employ a sensitive Bic. 2. P, Primary oscillation circuit. S, Secondary oscillation circuit. G, Galvanometer. V, Valve. 3B, 12-volt battery for imean- descing filament of valve. mirror-galvanometer of the ordinary type to detect the presence of electric oscillations in a circuit and to institute comparative measurements. for Rectifying High-Frequency Electric Currents. 661 Thus, for instance, we form an oscillatory circuit (see fig. 2) by connecting a Leyden jar in series with a square coil of wire of a few turns P, and join the condenser and inductance across a spark-ball discharger connected to the secondary terminals of an inductien-coil. At a certain distance we place another square coil of wire S in series with a galvanometer G and oscillation valve V. We then find that when oscillations are set up in the primary circuit, we obtain a steady deflexion of the galvanometer indicating that o its coils are being traversed by a series of discharges in the oO same direction,-all those in the opposite direction being practically stopped. The author has already described the methods by which the amount of rectification produced by the valve can be ascertained (see Proc. Roy. Soc. vol. Ixxiv. p. 484, 1905). Perfect rectification does not exist, but, as shown, the number expressing the percentage which the actual unilateral electric flow is of that which would flow if the unilateral conductivity were perfect, can be ascertained by sending the current which passes through the vacuous space of the valve through a calibrated galvanometer and electrodynamometer placed in series with each other. In valves as described this rectifica- tion may amount to 90 per cent. We may use the above arrangements to Investigate the effect of different kinds of discharge-balls and different lengths of spark. If we employ a fairly lone spark in the primary condenser-circuit we may find that we obtain a very small effect on the galvanometer in the secondary circuit, but if we shorten the spark-gap until the spark at the balls is hardly visible, the galvanometer deflexion is generally in- ereased. The reason for this is partly because the oscillations are damped out much more by the long spark than by the short one, and partly because with a short spark the con- denser discharges occur more frequently. Hence, although in the latter case the condenser is charged to a less voltace ° e ° fan) owing to the lower discharge potential, the decreased damping and greater charge frequency causes the galvanometer to be traversed by a larger quantity of electricity per second, and therefore to give a greater deflexion. . In the same manner, we can exhibit the difference in the damping due to variations in the material of the spark-balls. Thus, using iron, brass, and zine spark-balls of the same diameter and a spark-length of 0-1 mm., the galvanometer deflexions in one case were respectively 40, 57, and 70 scale- divisions, thus showing the smaller damping of zine spark- balls. The writer has found by this means that carbon in the state used for arc-lamp carbons presents many advant te ages 662 Prof. Fleming on Oscillation Valves asa discharge surface. All who have experimented much with Hertzian oscillators know how the state of the polish of the surface of the metal balls (generally brass) affects the electric wave-producing power. It can be shown by the use of an oscillation valve that for quantitative work a discharger made of carbon rods, as follows, presents many advantages: — A row of are-lamp carbons C, C, C (see fig. 3) are fixed like posts In a piece of ebonite and another row of slightly conical carbon rods B, B are inserted transversely between them, the distances between the rods being fixed so that very small Fig. 3. nt Se ET TO tNOUCTION COIL air-gaps are left between carbon and carbon. We thus con- struct a multiple spark-gap of carbon surfaces which has small damping and great constancy. By enclosing the rods in a non-oxidizing atmosphere we can prevent the rods burning away. Another advantage of the arrangement is the ease with which new surfaces can be brought into use. We can also investigate by the same means whether the use of spark-balls immersed in oil presents any advantages. Also the same arrangements may be used to exhibit the screening action of conductors for high frequency magnetic for Rectifying High-Frequency Electric Currents. 663 fields. For if we interpose between the primary and secondary circuits a sheet of tinfoil or zinc, we see a notable decrease in the galvanometer deflexion, thus making the screening action of the metal very evident. Hmployed in this manner, it enables us to show strikingly the rapid rate at which the field due to a current in a square or circular circuit decreases with distance from the circuit, and therefore to iliustrate one of the disadvantages under which wireless telegraphy by electromagnetic induction labours when com- pared with space telegraphy by electric waves. When using the valve to detect the oscillations in an antenna produced by the impact of Hertzian waves, an oscillation transformer is inserted in the circuit of the receiving antenna, and its secondary circuit is connected through a valve with a dead- beat mirror-galvanometer. We are thus able to receive signals over short distances by the direct effect of the rectified oscillations themselves on the galvanometer. The action of other substances besides incandescent carbon as a cathode in a vacuum-value has also been studied. It has been found by G. Owen* and by A. Wehnelt+ that glowing metallic oxides, including the rare oxides employed in the manufacture of the Nernst lamp-glowers, copiously emit negative ions when incandescent both at atmospheric and at reduced pressures. Wehnelt found that the incan- descent oxides of calcium, barium, and strontium produce an abnormally powerful electronic discharge, and, following the recommendations of the author, he has proposed to employ vacuum-tubes with one electrode covered with such oxides and heated, as rectifying valves for alternating currents. As far back as 1890 the writer showed in a lecture ex- periment at the Royal Institution that the so-called Edison effect, that is the passage of negative electricity across space from an incandescent carbon filament to a metallic plate near it, could take place at atmospheric pressure if the plate was very near the filament. It is easy to show a similar experi- ment with a Nernst electric glow-lamp. If a Nernst lamp is supported with the bare glower horizontal and. placed within a few millimetres of a vertical insulated metal tube kept cold by being filled with water, it is found that negative electricity will pass freely across the glower to the cold metal, but not in the opposite direction. Hence if the glower and metal tube are inserted as a gap in an electric circuit containing a sensitive galvanometer, and if secondary * See G. Owen, Phil. Mag. vol. viii. p. 230 (1904). “On the Dis- charge of Electricity from a Nernst Filament.” T See A. Wehnelt, Phil. Mag. vol. x. p- 80 (1905). “On the Discharge of Negative Ions by Glowing Metallic Oxides and Allied Phenomena.” 664 Prof. Fleming on Oscillation Valves. oscillations are created by induction in this circuit, we find that the galvanometer gives a steady deflexion showing the passage of a continuous current through it, and therefore of the unilateral conductivity of the space between the glower and the metal tube. The distance over which this transference of electricity can take place depends very much upon the temperature cf the glower, and the amount of rectification of the alternating current obtained upon success in keeping down the tempe- rature of the metallic electrode. This is best achieved by circulating water through it. It follows as a consequence from the above facts, that there is a considerable emission of negative ions or electrons from the incandescent portion of the lime cylinder used with the oxy-coal gas-burner to produce the lime-light, and that the space near the incandescent portion of the lime cylinder as well as the space near the Nernst lamp-glower is highly conductive by reason of the presence there of negative ions emitted from the oxide surface. In the practical construction of oscillation valves, the ad- vantage of placing the heated and non-heated electrodes in a vacuum is that the plate which acts as an anode can be placed at a greater distance from the incandescent surface and thereby kept cool, since the electrons ejected from the heated surface are projected toa much greater distance when the atmospheric pressure is reduced. Although platinum coated with calcium or barium oxides undoubtedly emits a much larger electronic current per square millimetre than carbon at the same temperature and under the same surrounding conditions as to gas pressure, I find that for rectifying electric oscillations the carbon-filament oscillation-valve as I have designed it, affords more conveniently all that is required. There are some advantages in employing a thick carbon filament and constructing it to be worked at about 12 volts and take a fairly large current of 2 or 3 amperes. Tor one thing, the filament is much less likely to be destroyed by over- heating in working, and hence the valve lasts longer. In some cases an advantage may ensue from working valves in parallel, that is joining up a number of such carbon-filament valves with their carbon filaments in parallel on the same heating battery, connecting together the insulated metal cylinders contained in each bulb together, and then using the multiple arrangement as if it were a single valve. When used, however, to rectify such oscillations us are employed in the receiving circuits of wireless telegraph apparatus, a single valve will do all that is required because Cymometer for Determination of Resonance- Curves. 669 the quantity of electricity which has to be carried is small and the electronic emission from even a 4-volt l-ampere carbon filament is amply sufficient to carry the negative component of the feeble oscillations used across the vacuous space. It should be noted that such oscillation-valves as are here described have quite a different range of use from other rectifying arrangements suchas the Cooper-Hewitt mercury- vapour tube, and the electrolytic aluminium-carbon valve of Nodon and others. The electrolytic valves produce no rectifying effects with high-frequency alternating currents, because the time element enters into the formation of the aluminic hydroxide film on which their action depends. On the other hand, the mercury- vapour tubes which have been proposed for use with high- tension alternating currents will not operate below a certain minimum potential-difference between the electrodes. The vacuum-valve as here described, however, will pass current unilaterally with a fraction of a volt difference of potential between the incandescent and the cold electrode, and there is no minimum potential difference below which they will not act ; hence their use is conditioned solely by the sensi- tiveness of the galvanometer employed with them. By its simplicity and ease of use the carbon-filament vacuum-valve recommends itself as a useful addition to our resources for experimental work in connexion with electric oscillations and electric-wave telegraphy. LX. On the Use of the Cymometer for the Determination of Resonance- Curves. By G. B. Dyxz, B.Sc.* R. FLEMING has shown in his recent Cantor Lectures before the Society of Arts t, that by the introduction of a hot-wire ammeter into the circuit of his direct-reading cymometer, the effective or root-mean-square value of the oscillation current set up in the cymometer circuit can be measured. This instrument was originally designed for the determination of the wave-lengths used in wireless telegraphy by the direct inspection of a scale, and also for the measure- ment of capacities and inductances; but it has been found that a small addition renders the instrument also available for the determination of resonance-curves, and therefore of * Communicated by the Physical Society : read March 23, 1906. + Cantor Lectures, 1905. Dr. J. A. Fleming on “ The Measurement of High Frequency Suumrenits and Electric Waves.’ Phil. Magos. G.0V ol. 11. No. 65. May. 1906. 2X 666 Mr. G. B. Dyke on the Use of the Cymometer the decrement of oscillation-trains, and of oscillatory spark- resistances. A direct-reading cymometer was used constructed as described by Dr. FI leming in a paper read before this Society on March 24th, 1905 * “The instrument consists essentially of a closed circuit containing a condenser and an inductance, the distinctive feature being the fact that the capacity and inductance are so arranged as to be varied simultaneously and in the same proportion by one movement of a handle. A portion of the closed circuit consists of a straight copper rod, which is placed in the neighbourhood of, and parallel to, the circuit on which the measurements are being made. Then, as Dr. Fleming has shown in the paper referred to above, resonance will take place between the two circuits . when the cymometer is so adjusted that its oscillation constant, that is the square-root of the product of the capacity and inductance, has the same value as that of the cireuit under test. The position of resonance is detected by the illumination of a Neon vacuum-tube connected between the inner and outer coatings of the condenser. The Neon vacuum-tube, although an excellent detector of the position of resonance, gives but little indication of the relative value of the current in any other position of the cymometer, and is of the nature of an indicator rather than a measuring instrument. For the determination of the logarithmic decrement, it is requisite to know the relative values of the current in the cymometer for points in the neighbourhood of resonance, and hence a quantitative current-meter must be employed. The instrument should fulfil the following conditions :— Ga.) Its capacity and inductance should be negligible compared with that of the cymometer, otherwise the disturbance of the scale-readings would lead to erroneous results. (ii.) Its damping factor should be small and should be capable of calculation. Gii.) It should be fairly rapid in its action. The above requirements are fulfilled by an addition to the cymometer, made recently by Dr. Fleming, and shown in his Cantor Lectures referred to above. The ammeter adopted is of the hot-wire type and is inserted into a gap made by cutting the bar of the cymometer ; the current passing through the heated wire being measured by a thermojunction in contact with it. * “On the Application of the Cymometer to the Determination of the Coefficient of Coupling of Oscillation Transformers,’ by Dr. J. A. Fleming. Proc. Phys. Soc. Lond. vol. xix. p. 603 ; and Phil. Mag. June 1905 for the Determination of Resonance- Curves. 667 ioe: Vif, Off, yy G Thermoelectric junction employed with Fleming Cymometer to determine mean-square value of the induced current. 2X2 668 Mr. G. B. Dyke on the Use of the Cymometer The instrument consists of an ebonite block A (fig. 1, p. 667), from the sides of which project lugs BB which are used for connexion to the cymometer. ‘To these lugs are soldered brass rods CC, each about 3 inches long, and between the extremities of these rods 1s stretched a fine platinoid wire a (diameter ‘05 mm.) having a resistance of 3°5 ohms. ‘To the middle of this wire the thermojunction is soldered. This junction consists of two very fine wires, 0, c, one of pure iron (diameter -20 mm.) and the other of bismuth (diameter -17 mm.); these are attached to the platinoid with special solder of fow fusing-point, the contact area being made as small as possible. ‘The other ends of the wires are connected to the galvanometer by a flexible cord. The junction is shielded by the ebonite cap, D, which screws over the plug A. The electromotive force of the couple is observed by means of a low-resistance Paul single-pivot galvanometer, having a resistance of 4°88 ohms and a figure of merit of 19°5 microvolts per division. The method of calibrating the junction is as follows :— For wires so fine as the platinoid used, the high-frequency resistance is the same as that for low-frequency or continuous current. Hence it is only necessary to connect up the hot- wire ammeter in series with an adjustable resistance and a secondary cell, and to pass currents of known strength through it, observing the corresponding deflexions of the oalvanometer. These observations enable a curve to be plotted from which the root-mean-square (or equiheating) value of the current in the cymometer for any deflexion can be readily read off. For the instrument described the calibration curve is such that the deflexion varies as the 1°9th power of the current. An auxiliary resistance is also required and is constructed similarly to the hot-wire ammeter just described, except that the ther mojunction is omitted and the resistance of the fine platinoid wire is 7°2 ohms. This resistance is arranged so that when required ‘it can be put into a second gap cut in the cymometer bar, a short-circuiting strip being used to complete the cireuit when it is notin use. It will be seen that if the cymometer bar is placed in the proximity of a circuit in which oseillations are taking place, the value of the R.M.S. current induced in it can be determined by means of the hot-wire ammeter described above for any position of the cymometer-handle ; that is, for any oscillation constant or any frequency of the oscillations in the cymometer within the range of the instrument. From observations of this R.M.S. current and frequency, it is possible to deduce the logarithmic decrements of both primary and secondary circuits. The logarithmic decrement of _— Jor the Determination of Resonance- Curves. 669 an oscillation per semiperiod is here defined to be the Naperian logarithm of the ratio of two successive maximum oscillations in opposite directions. In this connexion it is to be noted that most German physicists have defined the decrement as the logarithm of the ratio of two successive maximum oscillations in the same direction. The problem of the oscillation transformer has _ been attacked more particularly by Oberbeck, Bjerknes, Drude and Wien; and Bjerknes and Drude have given solutions for obtaining the decrements, and although the proof is very long the final equations are simple and easily interpreted. For the complete proof we must refer to the original papers *; the essential parts, however, have been translated into English nomenclature bye Dic: Fleming g, and are given in his book on “The Principles of Hlectric Wave Telegraphy ” (Longmans, Green & Co.). In this note we can do little more than state the final result of their work. We shall use the following symbols :— 6, = logarithmic decrement per semi-period of the oscillation in the condenser circuit. 6, = logarithmic decrement per semi-period in the secondary circuit inductively coupled with the primary. ny=frequency of oscillation in condenser circuit. n,== frequency in secondary circuit. J=value of R.M.S. current in the secondary circuit corresponding with the frequency Ng. J,=maximum value of R.M.S. curr ent in secondary circuit, 2. €. the ‘‘ resonance current.’ Then Bjerknes shows that the following equation holds;: J Ng S—_ Oh um 1D) / J2—J or, if mg is nearly equal to m, that is the secondary is very nearly resonant to the primary, this becomes 8, +8,=7(1—™) th 7104 -+ N09 = (ny = Writing Pe 1: Ny” (5) y= (| — Te this becomes he r) pO =TeA , =. * V. Bjerknes: Annalen der Physik, vol. lv. (1895) p. 121; and vol. xliv. (1891) p. 74. P. Drude: dAnnalen der Tes vol. xi, (1904) p- 512. 670 Mr. G. B. Dyke on the Use of the Cymometer This equation gives us the sum of the decrements in the two coupled circuits. In order to obtain the values of 6; and 6, separately we require some other relation between them. This relation has been given by Drude. He shows that the resonance current in the secondary circuit can be calculated from a formula equivalent to eg AO gve We Wyle JN as Oy ae where V;=maximum value of primary condenser potential- difference. C, and C,=capacities in primary and secondary circuits respectively. k=coefficient of coupling of the two circuits moe NT e/a where M=mutual inductance between the circuits ; L, and L,=self-inductances of the primary and secondary circuits respectively. Passing now to the delineation of the resonance curve, we proceed as follows :—Insert the hot-wire ammeter into the cymometer circuit and place the cymometer parallel to some straight portion of the primary circuit and at such a distance from it that when the cymometer is adjusted to resonance the current is not too large to be measured on the galvanometer. Then move the cymometer handle slowly from one end of the scale until a readable deflexion appears on the galvanometer. From this point move the handle in small steps, noting at each step the current J in the cymometer as given by the calibration curve of the galvano- meter, and the frequency nz as read on the cymometer-scale. Proceed in this way until the maximum deflexion is passed and the current has again fallen to a small value. Plot the results thus obtained as a curve having ordinates proportional to J, and abscissee proportional to mn). Take off from this curve the maximum value of J. This will be the resonance current J,; and the corresponding frequency will be the resonance frequency, that is, the frequency n, of the primary circuit. Now repeat the observations inserting the auxiliary resistance into the cymometer circuit in addition to the ammeter, taking care not to alter the relative positions of the circuits in so doing. Plot the results as before and obtain the value of the resonance current J,’. The resonance frequency should of course remain unaltered. The two jor the Determination of Resonance-Curves. 671 pve J! eurves should now be redrawn, taking the ratio TOP ae e YL r ° . No ° as ordinate, and the ratio — as abscissa. : 1by We are now in the position to determine the decrements for the two circuits. Take out from the curve corresponding values of a and jee ee , taking the mean for the two sides J, ce of the curve and noting that “ 5 * lies between 0:95 and 1:05, 1 or that ( — "2) is not greater than 0:05. hy I Then, using Bjerknes’ formula obtain a series of values for (6,+6.). Let the mean value of (6,+6,)=X In like manner, if 6,’ is the logarithmic decrement of the auxiliary resistance, obtain a series of values for 8,+6,+5,! by taking out from the second curve corresponding values i I ae (5- : and (1- ~ and applying Bjerknes’ formula. Ui : 1 Let the mean value of (6,+6,+6,')=X'. On writing out Drude’s formula for the two cases we get: when the ammeter only is in circuit (050) Tn, kK? a, 8 6409(6, + 65) and when the auxiliary resistance 1s Inserted Tease 9 CiCy Tw nyk? 7 Se HOWE Oe NOE OOo), =V/ Hence we have the relation J 778o(8; +8.) =I >'2(8y + 65') (6; +45 + 8,'), or oy ne (d5 + 6,/) X', Hence Sse The value of 6,' may either be taken as equal to (X'—X) or may be calculated from its resistance and the frequeney 672 », G. B. Dyke on the Use of the Cymometer and inductance of the circuit, for we have ne x 0? * re An, L, ; where R=resistance of auxiliary wire in ohms, L,=inductance of cymometer in resonance position in ems. n,=resonance frequency. And as 6,/ is known from either of these equations, 6, becomes known, and 6,= X—6, ; therefore 6, is known. Hence the decrements of the two circuits are determined. The resistance of the primary spark can be deduced from the value of 6, in the following manner. Let R'= high frequency resistance of the wire of the primary circuit in ohins. y=resistance of spark in ohms. L=inductance of primary circuit in cms. n,=resonance frequency. Then we know opts (R’ is r)10° Foe 4n,L : F 1 : — 4n, Ld; ee R -- TT == wort ° - ‘ _ 4n, Lo, , 35 Tae —R. The following numerical example of the deduction of the decrements from the resonance curves may be useful as illustrating the method of arranging the work. The primary oscillation circuit consisted of a rectangle of wire (diameter "162 cm.) inductance =5000 cms., a condenser of capacity = 5560 micro-microfarads, and a 2 mm. spark-gap between 1°25 inch iron balls. The oscillations were excited by a high tension transformer. The cymometer was set up parallel to one side of the rectangular inductance and about 6 inches away from it. We will suppose that the resonance curves have been drawn as described above, and the result to be as shown in fig. 2 (@ and §), where ‘the full-line curve shows the result obtained with the ammeter (resistance 3°5 w) only in circuit, and the dotted curve the result with the extra resistance (7:2 a) also connected. for the Determination of Resonance-Curves. 673 ios 2: Frequency. Np 85. 90 “95 100 105x106 We will now form a table showing the relative values of J s and a and the calculated values of (6,+6,) and (6,+6,+6,’). | r: ee S | ate | IH fs ee he 95 0120 “115 “0125 120 90 0165 112 0210 138 85 0205 ‘104 0255 130 80 0255 107 0300 125 75 0298 105 0345 | 124 | 70 0335 1083 | 0385 119 Taking out the means we find Se 10e: xX ="126, OLS Sar0n Mr. G. B. Dyke on the Use of the Cymometer 674 If 6,/ is calculated from the formula ae exe Os ; Aveda 7 R’=7:2@, L,=768000 ems., ,='95 x 10%, we get oO eon oe mean 0,/=:022. From fig. 2 (a) we see J,='164 amps. J,/='104 amps. qi a ea Calculating 6, from the formula LAL ( oe Nar Ls j Uae we get On = 022 Hence mean value of 6,=3/{(X—6,) + (X’--6,—6,’) } | == ONGC q Now the decrement 6 of the ammeter per se is given by the formula aise? oak An, Ly a where R=3°5a, L;=708000 cms., 1, ="95 x 10°. Hence decrement of cymometer per se = 6,—6 =") 22-012 — O10. Passing to the primary circuit, we had the formula An, Ld igi 7 i] —R, for the spark resistance r ; where. =5000'\ems.;» 38, =707 7, | i= 19D ee . for the Determination of Resonance- Curves. 675 According to Lord Rayleigh’s formula where R=low frequency resistance, and d=diameter of wire in cms. In our case R=:0386 ohms., d="162 ems:, oi AiO): oe R’='23 a. Putting in these values we get p= — 1:23 The above example is chosen we as as example of the ease and speed with which reasonably good results can be obtained, than as a criterion of the accuracy of the method, as all the observations necessary for drawing the resonance curves were taken in less than half an hour. If more time is taken over the observations much closer agreement between the calculated and observed values of the decrements can be obtained. The example first worked out is a case of two rather loosely coupled oscillation circuits, and in this case we have seen that the resonance curve has a single peak. If, however, the coupling is at all tight, the resonance curve develops a double hump, the maxima becoming more and more separated as the coupling becomes tighter and tighter, until when the coupling is perfect (7. e. when the mutual inductance is the geometric mean of the two self-inductances), one of the maxima has gone off to infinity, and we are again left with a single- hump resonance curve. Oberbeck has developed the theory of two coupled oscil- lation circuits, and has given formule by means of which the two resonance frequencies may be predetermined. Tor the general solution we must refer to the original paper *, but in one particular case the result deserves special mention on account of its importance in wireless teleg aphy. If the primary and secondary circuits are tuned, “that is, are so adjusted that when far apart they have the same oscillation constant and the same frequency n,, then, when put near together so that the coupling coefficient has a value k, the following very simple relations hold between the two A. Oberbeck, Wied. Ann. der Physik, 1895, vol. lv. p. 623. See ce Dr. J. A. Fleming, “Principles of Electric Wave Telegraphy,” chap. 111. 676 Mr. G. B. Dyke on the Use of the Cymometer frequencies n; and my induced in the secondary cireuit and the natural frequency 79 :— or ny A LEY Now in the case of some oscillation transformers used in wireless telegraphy the coupling may be about 0°5. Hence we should then have iis’ o y= if : Ny 5 ey ‘4 Mera or, The frequency of one wave is about 12 times that of the other. For a coupling of the order of 0°5 the method above de- scribed may be applied to each hump of the double-humped resonance-curve, and will enable a fairly accurate determi- nation of the decrements of the two oscillations to be made; but, as shown by C. Fisher (see Annalen der Physik, vol. xix. p- 182, 1906), when the coupling is very loose we cannot consider the resultant resonance-curve to be identical with the sum of the curves due to each oscillation separately. Fig. 3, “4 85 6 “7 “8 9 1'0 1-1 1:2 1:3 14 15106 The curve shown in fig. 3 was taken from a closely coupled circuit of this type, and may be taken as indicative of the general type of result to be expected. for the Determination of Resonance-Curves. 677 The accurate determination of the logarithmic decrement in open oscillation circuits such as these is a matter of consider- able practical importance, as most of the damping is due to the radiation of energy from the wire, and not to the resistance us is the case with closed or non-radiative circuits; and as the amount of this radiant energy is not easily estimated mathematically, the value of this important quantity must rest on experimental evidence alone. The objection may be raised that the type of ammeter described greatly increases the decrement of the cymometer, as its decrement is almost equal to that of the cymometer per se. It must be remembered, however, that the part of the instrument in the cymometer circuit is a. short piece of very fine wire whose decrement can be easily and accu- rately calculated, and secondly that the decrement of the cymometer itself does not matter, the primary circuit being generally the one whose decrement is required. At first sight it would seem that a very obvious variation of the method could be employed which would not suffer from this defect. Suppose that, instead of cutting the cymometer-bar, a few turns of well-insulated wire are wound round a section of the inductance-coil of the cymometer, and the ends of the: coil connected to the fine wire of the ammeter described above, then currents will be induced in this circuit proportional to the currents in the cymometer. This method, however, has more serious drawbacks than the other, as :— (1) The damping of the cymometer will be just as great if this method is employed, as the same amount of energy has to be supplied to heat the ammeter wire to a definite temperature. (2) The actual current in the cymometer is not measured but only a current bearing some unknown ratio to it. (3) The scale of the cymometer is slightly altered when the ammeter is in place, as the arrangement is of the nature of a transformer with a closed secondary circuit, part of the cymometer inductance spiral forming the primary; this will of course annul a portion of the inductance and so alter the scale. The extent of this alteration of scale may be determined by measurements made at the point of resonance with the Neon tube, first with the secondary open, and second with the secondary closed through the ammeter wire. Several curves have been obtained using the ammeter in this manner, but as the method shows no points of advantage 678 Mr. E. Buckingham on over the one first described and has several inherent disadvantages, it was discarded in favour of what might be called the series arrangement. In conclusion, the author wishes to thank Dr. J. A. Fleming, F.R.S., for his kindness in permiting him to publish the results of these experiments, which were carried out under his direction at the Pender Laboratory, University College, London. LXI. Elementary Notes on Thermodynamics: the Plug Experiment. By HpGar Buckinenam *, <1. ‘HEORETICALLY there are many ways of estab- lishing the thermodynamic sca ale of temperature, but practically, experiments on the properties of gases offer the only mode of attacking the problem that has been followed with any success. For this purpose, what we need to know is the manner in which the internal energy of the gas used in our standard gas-thermometer varies with the volume, when the temperature is constant ; and for the most precise information on this point, we have, at present, to refer to the porous-plug experiment or something equivalent to it. The use of reasoning based on the second law of thermo- dynamics is to be met with very frequently ; and we find, in almost every case, that it inv olves the assumption that the international hy drogen scale, to which the observations are referred, differs only by an additive constant from Lord Kelvin’s thermodynamic scale which appears in the thermo- dynamic formule. It might be expected, therefore, that a clear treatment of the plug experiment would be found in every text-book of thermodynamics, but that Cpe is not justified. Some of our best standard works hardly mention the plug experiment, and the general impression one gcts from most of the lanes I have examined, is that the authors consider the subject either too difficult to be discussed or so simple as to deserve only casual notice. I think, how- ever, that a clear and simple treatment of the theory - some settee or methods by which the relation of the gas scale to the thermodynamic scale might be found, is distinctly worth while, even if there is nothing new about the discussion except, possibly, the form in which it is put. § 2. Beside the original Joule-Thomson form of the plug experiment, in which the flow of gas through the porous * Communicated by the Author. the Plug HLxperiment. 679 plug is adiabatic *, I shall consider a modified scheme, in which energy is supplied to the gas, during its passage through the plug, at such a rate as to make the flow iso- thermal +; and, furthermore, I shall consider a simplified form of Gay-Lussac’s and Joule’s free expansion experiments, in which heat is supposed to be supplied or withdrawn during the free expansion so as to to make it isothermal f. The fundamental equations for these three experiments are very easy to deduce, if one starts by having a clear diagram. Let A (coordinates: p, v, T) represent the initial state of * Objection has been made to calling the flow adiabatic, because heat is generated mechanically in the plug. When we consider that this heat is probably mainly, if not entirely, due to viscosity, and if so, is developed in the gas rtself, and not generated in the solid material of the plug by true friction and then communicated to the gas, the objection does not seem well founded. The term “adiabatic plug experiment 7 iss abealll events, a convenient designation for the Joule-Thomson experiment as distinguished trom the proposed isothermal form. + Phil. Mag. October 1903. { At first sight, it seems doubtful whether we are justified in applying thermodynamic reasoning to an essentially tumultuous process such as the free expansion of a gas; for the use of the two laws in their usual elementary form implies that the system under consideration has a definite temperature, whereas during a tumultuous process, the gas cannot be said to have any definite temperature at all. After the tumultuous motions have subsided and the gas has come to a state of internal equilibrium, both mechanical and thermal, it has again a definite temperature. The reasoning by which, from the assumption of the nonexistence of infinite sources and sinks of energy, we establish the existence of the internai energy, ¢, as a function of the instantaneous coordinates of the system, makes no assumption regarding the nature of the path by which any state of the system may be reached from any other, but assumes only that we may always, by some means or other, make the system pass from any possible state to any other. Hence it is entirely Jegitimate to use the tirst law—the energy law—in comparing any two states, regardless of the nature of the process by which one has actually been reached from the other, provided it be not zr the nature of things impossible to make the system pass again by some path or other from the final to the initial state, 680 Mr. EK. Buckingham on unit mass of the gas. Let D (coordinates: p+dp, v+Av, T+AT) represent the state after the irreversible adiabatic flow through the porous plug. Let B (coordinates: p+dp, vu+dv, T) represent the state the gas would have been in, if the same fall of pressure had occurred without change of temperature. The temperature T is to be understood as measured on the scale of a constant-pressure thermometer filled with the gas under investigation. §3. Consider first the Joule-Thomson, or adiabatic, plug experiment. If the state of flow is steady and no exchange of heat with other bodies than the plug is taking place, the change of internal energy of unit mass of gas in passing through the plug is Eg — €] = PiU] Poe = or, if we let the fall of pressure be infinitesimal, Ae=—A(pv)=—pAv—vdp,. . . . QC) Ap and dp being identical, as is seen from the figure. Let the gas which has thus passed from the state A to the state D be now bréught, at constant pressure, to the state B. If de be the excess of the specific internal energy at B over that at A, we now have de=Ae+Q+W,. . «7. 2 es in which Q and W are, respectively, the heat added to and the work done on the unit mass of gas during the isopiestic change DB, which brings it back from (T+AT) to its original temperature T. We suppose, for simplicity, that all quantities of heat are expressed in ergs. If we let w be the ratio of the fall of temperature to the yall of pressure, 7. e. AT/dp, we have AT=ydp, and the value of Q is evidently * Q=—pC,dp, ee (3) C, being the specific heat at constant pressure. ‘The value of W is given by the equation W=—p(de—Ap)... . ae We also have =. nae Ov eae ov u dv—Av=(—AT) (SF = wdp( Sr) 3 ees so that Av tlaee (Sp), me. Se * The figure as drawn corresponds to the ordinary case in which there is a fall of temperature during the flow through the plug. The sign of x, as here defined, is then positive, while dp is negative, so that the value of Q as given in (3) is in fact positive, as it is evident from the figure that it must be. the Plug Hxeperiment. 631 By substituting in equation (2) the values given by equations (1), (3), (4), (5), and (6), we get de— — pdu—vdp—pGndp 3)... 4 = ."(7) and since the differentials which appear in this equation all refer to the isothermal change AB, we may write it in the form * (S;),= ics ee Bok ay, This equation is, of course, not new, but few writers of text-books on thermodynamics seem to think it worth deducing. The equations for the other two experiments come out much more directly.. In the case of the isothermal plug experi- ment, in which the gas passes at once from the state A to the state B, let p be the ratio of the energy abstracted from the gas to the fall of pressure dp. ‘Then we have, obviously, HE (UUW sPOUD, oe hea or by the same considerations as before, Oe yanked Op In the irreversible isothermal free expansion from A to B, the external work is zero. If we let X be the ratio of the energy (heat) which must be added, per unit mass of gas, to the increase of specific volume dv, in order to make the final temperature of the gas, after its tumultuous motions have subsided, the same as its initial temperature, we have LET NAVD Wie ae ane we ee enc) or Pe) < =) = Xn. ° ° e ° e ° e * (C) _§4. In deducing equations (A), (B), and (C), no use is made of the second law; hence they do not involve the thermodynamic temperature @ at all, and cannot, by them- selves, tell us anything about it. But suppose, finally, that the gas passes from the state A to the state B by a reversible isothermal expansion. Jor any reversible change of state of a system having only two degrees of freedom and acted * Constancy of temperature is indicated by the subscript @: if @ is the thermodynamic temperature, T is evidently constant whenever @ is constant. Phil. Mag. S. 6. Vol. 11. No. 65. May 1906. Bux 682 Mr. E. Buckingham on on by no external forces except a uniform normal pressure, we have de=Odn—pdv, . . . . 2 a which is merely a statement of the two laws of thermo- dynamics for such a system, 7 representing the entropy. If the process is isothermal, we may write equation (10) in the form (S<) = 0 (22) -p. ee To give this a physical meaning we have to eliminate the entropy 7, by means of the familiar ‘ thermodynamic relation ”’ @ ") 2) thus obtaining the equation ($2) =-p+0($h) § 5. By comparing equation (D) with (A), (B), and (C) successively, we get three equations es when slightly transformed by means of the relation ($2) ($5) (5,),<—5 may be written 0(S5) = 8+ HCr » =a Ov 9( 59), =o ..: a baa: i+ >) and which give relations between @ and the data to be obtained from the three experiments. Hxpressing these in integral form we have Y Cae log 5 =|" RE (p=7=constant), . . (H) nO, i ies ae + Yn log a | a (p=7 =constant)) Se log gs = ae (v=¢=constant) (J) = 0 pol == x 5 ; i the Plug Hxperiment. 683 Hquations (H) and (I) show how we may, if the experi- mental data are at hand, tind the ratio of the numerical values of any two temperatures denoted by @ and @ on the thermodynamie scale, at which the specific volume of the gas has the values v and vw at the constant pressure 7. Hqua- tion (J) gives us similar information in terms of pressure at the constant specific volume ¢. By using the equation pv=RT which defines the absolute temperature T of the gas- thermometer, when either p or v is constant, it is, of course, easy to replace v or p by the absolute temperature measured by a constant-pressure or constant-volume thermometer filled with the gas in question. These deductions, which make no pretence of novelty, are all quite simple enough to be put into the most elementary text-book of thermodynamics. In view of the difficulty students have in getting any clear ideas about the thermo- dynamic scale of temperature from Joule and Lord Kelvin’s papers on the plug experiment, I think it would be well if some such simple discussion were more commonly given. For although this treatment is only formal, any one can see from the equations what experimental data are needed and how we must use them if we wish to go on to find actual numerical relations. The main thing is to have the conviction that there is a definite way in which the experimental data might be used if we had them, and anyone who has not attained that conviction by the “ seeing-is-believing ” process must sometimes feel rather at sea in using thermodynamics. § 6. In order actually to perform the integrations indicated in equations (H), (1), and (J), we have, in the case oz the adiabatic plug experiment, to know the values of « and C, as functions of v for the given constant pressure used in our constant-pressure gas-thermometer ; and it may be noted that the value of Joule’s equivalent is also involved, unless we have the values of Cy measured directly in ergs. Tor the isothermal plug experiment, we need merely the value of p as a function of v. at the same constant pressure. By supplying this energy p electrically, it may be measured in ergs as exactly as the absolute accuracy of our electrical standards permits. This method would not serve us in the case of hydrogen above —80° C., nor for other gases above their, as yet unknown, inversion temperatures, though it is conceivable that in such cases the Peltier effect might be utilized for electric cooling. or the free expansion experi- ment the data needed are the values of » in terms of p at the given specific volume used in the constant-volume gas- thermometer. It may be remarked, in this connexion, that 2Y 2 684 On the Plug Experiment. some degree of uncertainty must always attach to the substitution of experimental values of wu, p, and 2 for differ- ential coefficients : we can only hope that the extrapolation from finite to infinitesimal differences of pressure is allowable. The quantity >, or (Oe/Ov),, is useful for expressing the deviations of the behaviour of any real gas from the simple Boyle-Gay Lussac law, and it would be convenient to have values of X tabulated for tae various gases. Such a tabulation has been given by Amagat* for carbonic acid and ethylene up to 1000 atmospheres, for several temperatures between 0° and 200° C.; also for oxygen, nitrogen, air, and hydrogen for the mean temperature of 50° up to 1000 atmospheres, and for the mean temperature of 25° from 1000 to 4000 atmo- spheres. The computations were made by means of equation (G) from Amagat’s measurements of p and (0p/0@),, on the assumption that @ and T are identical. These tables are interesting and valuable, but for the particular purpose ot finding the relation of @ and T, we need similar but more detailed and exact values for such pressures as are used in gas-thermometers. Kquations (A), (B), and (C) show the relation of X to pw and p; i.e, how A might be computed from the results of either form of the plug experiment. I have not made any such computations, but it seems not beyond the bounds of possibility that with our present experimental refinements the quantity 7 might be measured directly. § 7. The two most interesting problems of thermodynamics at the present day are both concerned with the scale of temperature. The first is the performance of the plug experiment at very low temperatures. For it is a highly interesting question whether such temperatures as 1°7 absolute, as given in a recent paper by Olszewski +, would really be anything like that if we could measure them on the thermodynamic scale. At present we cannot say whether they would or not. The other problem is the purely theoretical one of inventing a radiation scale which shall be based on the two laws of thermodynamics in their accepted form, and on nothing else except experimentai facts that we are sure of and familiar with. The Stefan-Boltzmann law comes nearest to this. Boltzmann’s deduction depended ultimately on the assumption that Maxwell’s distribution of stress in the electromagnetic field was the real one. As Maxwell’s reasoning on this point does not pretend to be conclusive, Boltzmann’s deduction of * Jour. de Phys. (8) iii. p. 807 (1894). t+ Annalen der Physik, 1905, no. 10. Some Measurements of Wave-Lengths. 685 Stefan’s law for the black body could also not be considered conclusive. This state of affairs has been changed since we know, from the brilliant experiments of Lebedew and of Nichols and Hull, that the light-pressure does exist and does 7 very appr oximately at all events, the value deduced a priort from Maxwell’s theory. It still remains, however, highly desirable that another absolute radiation scale should be devised, so that we may have another and independent check on our high temperature measurements. Planck’s formula resis on too many assumptions to be satisfactory theoretically ; and Wien’s. displacement law, while its theoretical foundation is nearly as good as that of the Stefan- Boltzmann law, does not, by itself, offer a good method from the point of view of experimental accuracy. U.S. Department of Agriculture, Washington, Jan. 17, 1906. LXIL. Some Measurements of Wave-Lengths with a Modified Apparatus. By Lord Rayunicn, 0.4, Pres. R.S.* S the result of discussions held during the last three or four years, it seems to be pretty generally agreed that the use of the diffraction-grating in fundamental work must be limited to interpolation between standard wave- lengths determined by other means. Even under the advantageous conditions rendered possible by Rowland’s invention of the concave grating, allowing collimators and object-glasses to be dispensed with, the accuracy attained in comparisons of considerably differing wave-lengths is found to fall short of what had been hoped. I think that this disappointment is partly the result of exaggerated ex- pectations, against which in 18887 I gave what was intended to be a warning. (Quite recently, Michelson t has shown in detail how particular errors of ruling may interfere with results obtained by the method of coincidences ; but we must admit that the discrepancies found by Kayser § in experiments specially designed to test this question, are greater than would have been anticipated. Under these circumstances, attention has naturally been directed to interference methods, and especially to that so * Communicated by the Author. + Wave Theory, Enc. Brit.; Scientific Papers, 11. p. 111, footnote. { Astro-physical Journal, xviii. p. 278 (1903). § Zeitschrift fiir wiss. Photographie, Bd. ii. p. 49 (1904). 686 Lord Rayleigh : Some Measurements of skillfully worked out by Fabry and Perot. In using an accepted phrase it may be well to say definitely that these methods have no more claim to the title than has the method which employs the grating. The difference between the erating and the parallel plates of Fabry and Perot is not that the latter depends more upon interference than the former, but that in virtue of simplicity the parallel plates allow of a more accurate construction. In Fabry and Perot’s work the wave-lengths are directly compared with the green and red of cadmium; and they have obtained numbers, apparently of great accuracy, for artificial lights from vacuum-tubes containing various substances, e. g. mercury, for numerous lines from an iron are, and also for various rays of the solar spectrum. While, so far as I can judge, there has been every disposition to receive with favour work which not only bears the marks of care but is explained with great discrimination, it must still be felt that, in accordance with an almost universal rule, confirmation by other hands is necessary to complete satisfaction. It was with this feeling that about a year ago I commenced some observations of which I now present a preliminary account. I was not without hope that I might be able to introduce some variations which would turn out to be improvements, and which would, at any rate, promote the independence of my results. In this method the interference rings utilized are of the kind first observed by Haidinger, dependent upon obliquity. Their theory is contained in the usual formule for the reflexion and transmission of parallel light by a “thin plate.” Thus, if X% be the wave-length of monochromatic light, k=2m7/d, 6 the retardation, e the reflecting power of the surface, we have, in the usual notation for the intensity of reflected ight *, _ 4eé sin? (5 6) ie 1 —2e cos d+ ¢4' ) and d=2ut cosa. .. . | 2 ee where ¢ denotes the thickness of the plate, w the refractive index, and «’ the obliquity of the rays within the plate. Another form of {1) is it (1—e?)? >z=l R ie de? sin? (Ix6)’ (3) * See, for example, Wave Theory, Enc. Brit.; Scientific Papers, iii. pp. 64,65. —- Wavre-Lengths with a Modified Apparatus. 687 and from this we see that if e=1 absolutely, Ae aid ae for all values of 6. If e=1 very nearly, R=1 nearly for all values of & for which sin (4«6) is not very small. In the light reflected from an extended source, the ground will be of the full brightness corresponding to the source, but it will be traversed by narrow dark lines. By transmitted light the ground, corresponding to general values of the obliquity, will be dark, but will be interrupted by narrow bright rings whose position is determined by sin ($«6)=0. In permitting for certain directions a complete transmission in spite of a high reflecting power (e) of the surfaces, the plate acts the part of a resonator. There is no transparent material for which, unless at high obliquity, e approaches unity. In Fabry and Perot’s appar- atus the reflexions at nearly perpendicular incidence are enhanced by lightly silvering the surfaces. In this way the advantage of narrowing the bright rings is attained In great measure without too great a sacrifice of light. The plate in the optical sense is one of air, and is bounded by plates of glass whose inner silvered surfaces are accurately flat and parallel *. The outer surfaces need only ordinary flatness, and it is best that they be not quite parallel to the inner ones. It will be seen that the optical parts are themselves of extreme simplicity; but they require accuracy of construction and adjustment, and the demand in these respects is the more severe the further the ideal is pursued of narrowing the rings by increase of reflecting power. Two forms of mounting are employed. In one instrument, called the interferometer, the distance between the surfaces-—the thickness of the plate— is adjustable over a wide range. In its complete developinent this instrument is elaborate and costly. The actual measure- ments of wave-lengths by Fabry and Perot were for the most part effected by another form of instrument called an étalon or interference-gauge. The thickness of the optical plate is here fixed ; the glasses are held up to metal knobs, acting as distance-pieces, by adjustable springs, and the final adjustment to parallelism is effected by regulating the pressure exerted by these springs. The theory of the comparison of wave-lengths by means of this apparatus is very simple, and it may be well to give it, following closely the statement of Fabry and Perot f. * The most important requirement is the equidistance of the surfaces, and would not be inconsistent with equal and opposite finite curvatures, {t Ann. de Chimie, xxv. p. 110 (1902). A good account is given in Baly’s ‘ Spectroscopy.’ 688 Lord Rayleigh: Some Measurements of Consider first the cadmium radiation X. It gives a system of rings. Let P be the ordinal number of one of these rings, for example the first counting from the centre. This integer is supposed known. The order of interference at the centre will he p=P+e. We have to determine this number e, lying ordinarily between 0 and 1. The diameter of the ring under consideration increases with e€; so that a measure of the diameter allows us to determine the latter. Let e* be the thickness of the plate of air. The order of interference at the centre is p=2e/X. This corresponds to normal passage. At an obliquity 2 the order of interference is p cos?. Thus if « be the angular diameter of the ring P, p cos$ «=P; or since x is small, pak (1+ =). In like manner, from observations upon another radiation X’ to be compared with A, we have pH’ (14 = 5 sis whence if e be treated as an absolute constant, PFW es TREN fi = le aa ( “pp aes ) : eee The ratio X/A’ is thus determined as a function of the angular diameters x, x’ and of the integers P, P’. One of the principal variations in my procedure relates to the manner in which P is determined. MM. Fabry and Perot + say :—“ L’étalon, une fois réglé, est mesuré en fonction des longueurs d’onde du cadmium, par les méthodes que nous avons précédement décrites ; ’emploi de interféro- métre est nécessaire pour cela.” I wished to dispense with the sliding interferometer, and there is no real difficulty in determining P without it. For this purpose we use a modified form of (4), viz. :— ey oN Oe ia pp =o(1+95-2),- ° . e e (5) expressing P’/P as a function of d/X’, regarded as known, and of the diameters. ‘To test a proposed (integral) value of P, we calculate P’ from (5). If the result deviates from an integer by more than a small amount (depending upon the accuracy ot the observations), the proposed value of P is to be rejected. * Now with an altered meaning. t Loc. ext: p. TAQ: Ware-Lengths with a Modified Apparatus. 689 In this way, by a process of exclusion the true value is ultimately arrived at. The details of the best course will depend somewhat upon circumstances. It will usually be convenient to take first a ratio of wave-lengths not differing much from unity. Thus in my actual operations the mechanical measure of the distance between the plates was 4°766 mm., and the first optical observations calculated related to the two yellow lines ot mercury. The ratio of wave-lengths, according to the measurements of Heron and Perot, is 1:003650; giving after correction for the measured diamiciew 1:003641 as .the ratio P’/P. From the mechanical measure we find as a rough value of P, P=16460. Calculating from this, we get P’=16519-92, not sufficiently close to an integer. Adding 22 to P we find as corresponding values P=16482, P’=16542-00, giving P as closely as it can be found from these obser- vations. This makes the value of P for the cadmium-red ring observed at the same time about 14824, and this should not be in error by more than +30. Having obtained an approximate value of P for the cadmium red, we may now conveniently form a table, of which the first column contains all the so far admissible (say 60) integral values of P. The other columns contain the results by calculation from (5) of comparisons between other radiations and the cadmium red. The second and third columns, for example, may relate to cadmium green and cadmium blue. These almost suffice to fix the value of Na but any lingering doubt will be removed by additional columns relating to. mercury green and mercury yellow (more re- frangible). An extract from the table (p. 690) may make the matter clearer. Inasmuch as the ratio of cadmium red to cadmium green is 1°2659650, very nearly 5:4, only every fourth number for red is admissible on this ground alone. If we consider a number such as 14803 not excluded by the comparison with cadmium green, we see that while it would pass the mercury green test, it is condemned by the cadmium blue and still more by the mercury yellow test. The only possible value ot P is found to be 14814. The criticism may probably suggest itself that, although other values of P may be excluded, “the agreement of the row containing 14814 with integers is none too good. It is to be remembered that these observations were of a preliminary character, and were taken without the full precautions with 690 Lord Rayleigh: Some Measurements of regard to temperature afterwards found to be necessary. The formula at the basis of the calculation assumes that e, the thickness of the plate, is constant, but in fact it changes Ca Gienddhard Ca He He red. green. | blue. oreen. yellow. ——_ Aya ican wooed Se 14788 =|: 18721:03 | =19836-04 17439°24 | 9 14790 | | | 1 al ara peat . | 19840-07 Ze ST2609" 3 aM le re aerate | 19844-09 5 18729°89 | | | 6 18731°15 | | a Malls gee opess 19848-12 | / 1873495 19350-80 TASOOSA. Wi reese. keee ae 19852°14 18740:01 19856:16 17459-04 1651868 Se oe | 19860-19 eet ae a 19862°87 18748°88 | | 18750°14 19866-90 17462°36 | 1481 18753°94 1987092 17465:90 16530°96 OF WWE OOMNHAOF WMH OOO with temperature. On this account alone erreneous results will be obtained unless the observations are well alternated, so as to eliminate such effects. The numbers finally arrived at, in substitution for the row in the table, are 14814, 18753°95, 19870°95, 17465°97, 1653100. The deviations from integers still outstanding have their origin in a complication which must be admitted to be a- drawback to the method and might at first sight be estimated even more seriously. The optical thickness e of the plate, on which everything depends, is not really constant, as has been assumed, when we pass from one part of the spectrum to another somewhat distant from the first. The question is discussed by Fabry and Perot. If, to take account of this Wave-Lengths with a Modified Apparatus. 691 factor, we denote the thicknesses for the two wave-lengths by &, ey, we have p i Gy nr po aN and accordingly in place of (5) /2 ie aren UGLY HD - See Cod as ska Ghnt ne alan (ss But although I was prepared to find the calculated values of LP! differing somewhat from integers, I was disturbed by the amount and at first by the direction of the difference. For in their paper of 1899 * Fabry and Perot remark :—“ Le surface optique du métal pour la radiation rouge est, par suite, située un peu plus profondément dans le métal que celle de la lumiére verte, et @ une distance de 4 wu.” At this rate e, (red) would exceed e,, (green), and the introduction of the new factor in (6) would increase, and not remove, the discrepancy. It would seem, however, that the passage above quoted is in error and inconsistent with the discussion given in the later paper +, itself indeed embarrassed by several misprints f. The amouut of the correction required to bring the number for cadmium green up to an integer—about 24 parts in a million—is 24 times as great as one would expect from [abry and Peroi’s indications §. As to this, it may be observed that the wave-lengths employed in the calculation of the cadmium radiations are those of Michelson, and were obtained by a method free of the complication now under discussion. If these are correct, as there is no reason to doubt, and if there is no mistake in the identification of the ring—and there can be none here—it follows that the change of optical thickness in passing from red to green is determined by the numbers given and may be used to correct ratios of wave- lengths not previously known with precision. If we wish to make the results of the present method entirely independent, we must obtain material from obser- vation sufficient to allow the variation of thickness with wave- length to be eliminated, that is, we must use the same silvered * Ann. de Chinue, xvi. p. 311. + Z. c. pp. 120-124. { Of these it may be worth while to note that the sign of 6°6 yu on p. 128, line 5 should apparently be — instead of +. § It is known that the effect depends upon the thickness of the silver films ; perhaps also upon the process used in silvering and upon the con- dition of the surfaces in other respects. Surfaces that have stood some time in air are almost certain to be contaminated with layers of volatile greasy matter. 692 Lord Rayleigh: Some Measurements of plates at two different distances. In Fabry and Perot’s work the sliding interferometer was employed ; the silvered surfaces. were brought to very small distances, and the coincidences of two band systems, e. g. cadmium red and cadmium green, were observed, the telescope being focussed upon the plate, and not as before for infinity. It appears that excellent results were obtained in this way, affording material for eliminating the complication due to change of optical thickness. It is rather simpler, in principle, and has the incidental advantage of allowing the sliding interferometer to be dis- pensed with, if we follow the same method for the small as for the greater distance. If the calculation be conducted on the same lines as before by means of (5), we ought to obtain the same fractional part again in the value of P’, e. g. °95 for cadmium green referred to cadmium red. Tor, as we see from (6), the proportional error in P’/P as calculated from (5) is (€)'—€,)/e,. Inthe second set of operations, writing 7 for e, we find as the proportional error (y,—7,)/m,, 11 which — Nx! —M =e, —€, 3 £0 that the proportional errors are as 7 : @, or inversely as Por P’. Thus the absolute error in P’, as calculated from (5), is unaffected by the change of e to 7. If the fractional part is not recovered,within the limits of error, it is a proof that the assumed ratio of wave-lengths calls for correction, and the discrepancy gives the means for effecting such correction. The above procedureis the natural one, when it is a question of identifying a ring or of confirming ratios of wave-lengths already presumably determined with full accuracy ; but when the object is to find more accurately wave-lengths only roughly known, it has an air of indirectness. Otherwise, we have as before, 2¢.=pn, 20. =p and again for a smaller interval between the surfaces, 2n, =TA, 2n, =D’. Hence Xe a= (pan BQ = lan ee and €.—M=ey—M, $0 that XN _ pn’ a eget Vo. 3 Hence p, 7, p’, 7’ are the ordinal numbers at the centre. They are to be deduced, as before, from the integral numbers proper to the rings actually observed and from the measured angular diameters of these rings. Wave-Lengths with a Modified Apparatus. 693 It is obvious that p and 7 must not be nearly equal. If p be the larger number corresponding to the greater interval, am should not exceed +p. On the other hand, too great a reduction of 7 cal. lead to difficulties on account of the increased angular diameter of the rings. Perhaps it was for this reason that Fabry and Perot adopted an altered course. In my experiments the longer interval was, as already mentioned, about 5 mm., and the shorter aver val was about 1 mm., so that the angular diameter of the rings was rather more than doubled in the latter case. The facility with which angular diameters larger than usual could be observed is due, in part at any rate, to the special construction of my apparatus. MM. Fabry and Perot employed a fixed inter ference-gauge and a fixed telescope, measuring the diameters of the rings by an eyepiece micro- meter. ‘There are, I think, some advantages in a modified arrangement, w hereby it becomes possible to refer the rings to a wire fixed in the optic axis of the telescope. To this end the wire is made vertical, and the rings are brought to coincidence with it by a rotation of the gauge, which is mounted upon a turntable giving movement round a vertical axis. The middle plane of the gauge is vertical and adjusted so as to include the axis of rotation. In this way of working the reference wire is backed always by the same light, whether opposite sides of one ring or of different rings are under observation. It is perhaps a more important advantage that the same part of the object-glass is always in use, and toa better approximation the same parts of the plates of the gauge. The diapnragm which limits the latter should be as close to the plates as possible (or to their image near the eye), but when the multiple reflexions are taken into account it is impossible to secure that exactly the same part should always be in action. The revolving turntable carried with it a vers strip of plate-glass upon which was scratched a radial line. The point observed described a circle of 10 inches radius, and the rotation was measured by means of a travelling microscope reading to ‘001 inch. The angles involved are sufficiently small to allow the diameter of a ring to be taken as pro- portional to the difference of readings at the microscope. As regards the gauge itself, the plates are by Brashear. For the mounting of the 5 mm. gauge, which is of brass, I am indebted to my son Mr. R. J. Strutt. The 1 mm. gauge is of iron and was made by my assistant Mr. Hnock. They are much after the design of Fabry and Perot. For the final adjustment to parallelism the eye is moved in various directions 694 Lord Rayleigh : Some Measurements of across the line of vision so as to bring different parts of the plates into action, and for this purpose it may be desirable to increase the aperture. A dilatation of the rings means that the corresponding parts of the plates need approximation by additional pressure. The aperture employed in the actual measurements was of about 9 mm. diameter. The (achromatic) object-glass of the telescope is of 15 inches focus. In rigid connexion with it is the vertical reference wire accurately adjusted to focus, and close to the wire a small frame suitable for carrying the horizontal slits (eut out of thin sheet zinc) necessary for the isolation of the various colours *. The eyepiece is a single lens of 5 inches focus, mounted independently, so that it can be re-adjusted without fear of disturbing the object-glass and reference wire. The change of position required for the best seeing in passing from red to blue or even from red to green is so great as to occasion surprise that good results can be attained in the absence of such a provision f. The separation of the colours was usually effected by direct- vision prisms held between the eyepiece and the eye. Of these two were available. The larger containing (in all) three prisms was usually the more convenient, but sometimes a smaller and more dispersive combination containing five prisms was preferred. It is better to use more dispersion than unduly to narrow the slit. The refracting edges of the prisms are, of course, horizontal. In order to secure that the proper parts of the ring systems should be visible, the axis of the telescope was adjusted in the vertical plane with substitution for the slit of a horizontal wire coincident with the middle line of the former. The advantage of this arrangement is that the ring systems (or at least so much of them as is necessary) of the various radiations emitted by one source of light are all in view at the same time. In some cases, direct-vision prisms held between the 5-inch eye-lens and the eye do not suffice. The soda lines, for example, require a high dispersion. ven the yellow lines of mercury, which are about three times as far apart as the soda lines, could not be fully separated by the prisms already spoken of. Here a good deal depends upon chance. If the rings of one mercury system happen to bisect approximately those of the other system, both can be measured in the inter- ferometer-gauge, and the only question which remains open * Fabry and Perot, C. R. March 27, 1904. + Especially in using the method of coincidences. I ought perhaps to mention that my eyes have now very little power of accommodation. Wave-Lengths with a Modified Apparatus. 695 is the distinction of the two systems. For this purpose a prism of moderate power, by which one system is lifted a little relatively to the other, suffices. If, however, the two ring systems chance to be nearly in coincidence, a much more powerful dispersion is required in order to measure them separately. In such cases recourse was had to a special direct-vision prism of glass and bisulphide of carbon through which a selected ray of the spectrum passes without refraction at all at any of the surfaces *. In this instrument the upper edge of the beam traverses 20 inches of glass and the lower edge 20 inches of bisulphide of carbon. This prism cannot be inserted between the eyepiece already described and the eye, which latter must be placed at the image of the object-glass. Additional lenses are therefore required. These are merely ordinary spectacle-lenses and constitute a telescope of unit magnifying power. A more precise description is postponed, as | am not sure that I have as yet hit upon the best arrange- ment. It may suffice to say that with this instrument rings formed of spectral rays even closer than the soda lines could be readily separated, and that without too great a contraction of the slit limiting the visible porticn of the rings. The source of light, sometimes very small, was focussed upon the diaphragm at the gauge, and it is necessary that the aperture be completely filled with light. This gives the ratio. between the distances of the lens from the source (uw) and from the gauge (v). Again, the angular diameter of the field of light, which must not be too small, fixes the ratio of the aperture of the lens to v; so that only the absolute scale of the three quantities is left open. It is desirable that the lens be achromatic. I have used a one-inch lens from a small opera-glass, and this worked well with wu = 2} inches and v = 4 feet. | As sources of light in experiments involving high inter- ference, vacuum-tubes aré by far the most convenient, and their introduction is one of the many services which Optics owes to Prof. Michelson. At the head of the list stands the helium tube, both on account of its not requiring to be heated and also of the brilliancy of the yellow radiation. Hitherto, however, the wave-lengths have not been measured with the highest accuracy. The tube that I have employed was made some years ago by my son and had already seen a good deal of service in experiments designed to answer the question : “Is Rotatory Polarization influenced by the Harth’s * Nature, Ix. p. 64 (1899) ; Scientific Papers, iy. p. 394. 696 Lord Rayleigh : Some Measurements of Motion? *” From the overpowering brilliancy of the yellow line, it may be inferred that the pressure is not very low. Mercury too, for which the principal wave-lengths have been determined with great accuracy by Fabry and “Perot, is con- venient as requiring only a very moderate heating ; and cadmium, in spite of the higher temperature demanded, is indispensable. Not only is the cadmium red by general consent the ultimate standard, but a comparison of the red and green ring systems, even without a prism, gives rapid information as to the condition of the gauge, slightly variable from time to time on account of temperature and of necessary readjustments. Thus, in most of my observations, the red ring under measurement was in very approximate coincidence with a green ring. If, owing to rise of temperature, this ring had so far expanded as to make it advisable to substitute the next interior one, there could still be no uncertainty as to the order (one higher) of the ring actually under observation. As cadmium tubes appear to have been found troublesome, it may be well to describe a simple construction specially adapted to private workers whose skill in glass-blowing is Hmited. It was thought that alloying and consequent expansion of platinum sealings was a likely source of difficulty, and these were accordingly dispensed with. The diagram exhibits half the complete ‘tube. The working capillary A, the enlargement B D, and the lateral tube © for sitoehante to the pump are much as usual. But the enlargement is. continued by a second capillary DH, perhaps 14 mm. in diameter and 15 cm. long, through which passes with approximate fit a straight aluminium wir e, serving as electrode. The air-tight joint at E between the wire and the glass is made with sealing-wax. The length D E must be sufficient * Phil. Mag. vol. iv. p. 215 (1902). Wave-Lengths with a Modified Apparatus. 697 to allow E to remain cool, although D, enclosed in a copper ease, is hot enough to keep the cadmium vapour uncondensed. The lateral tube C projects from the case, and the cadmium condensed in it may need to be driven back from time to time by temporary application of the flame of a spirit-lamp or bunsen-burner. This construction, used with cadmium, mercury, and thallium, has so far answered my expectations Cadmium tubes, apart from failures by cracking, are said often to deteriorate rapidly. My experience did not contradict this; for after four or five evenings’ work the red radiation, which at first had. been very brilliant, was no longer serviceable, although the green did not seem to have suffered much. At this stage the tube was re-exhausted and then appeared to behave differently, the red radiation being much better maintained. One must suppose that something deleterious had been emitted and been pumped away. There is much in the behaviour of vacuum-tubes which at present defies explanation. To excite the electric discharge a large Ruhmkorff, actuated by five small storage-cells, was usually employed. Sometimes, especially in the comparison of the cadmium radiations, an alternate current was substituted; but there was no per- ceptible difference in the measurements. In this case a transformer of home construction was fed from a De Meritens magneto machine. The radiations from zine (and occasionally from cadmium) were obtained by an arrangement similar to Fabry and Perot’s “trembler”*. The behaviour was very capricious. Sometimes, even when actuated by five secondary cells only, the zine rings were magnificent ; but the deterioration was usually rapid as the zinc points lost their metallic surfaces. This change appears to be independent of oxidation. When the current was from a dynamo giving about 80 volts, the apparatus was less troublesome, but even then required careful management. ‘The fineness of the points needs to be accommodated to the current employed. As an example of the observations and calculations there- from, I will take a series of Dec. 20, 1905, relative to the three radiations from the cadmium vacuum-tube. In this series the temperature conditions were more favourable than usual. # C, R. 130. p. 406 (1900). Phil, Mag. 8. 6. Vol. 11. No. 65. May 1906. 22 698 Lord Rayleigh: Some Measurements of Cadmium (5 mm. gauge). Rep. GREEN. BuveE. | Right. Left. || Right. Left. Right. Left. 398 291 || =-401 217° | 406° eee 399 29) -402 ‘217 404:. |) 2 “399 220 =| ~=—--402 216 ‘406 | 210 3987 2907 ‘4017. | +2167 4053 | 2118 = | Diff. — :1780 Dik "1850 «| Diff. = -1940 The numbers entered are the actual readings of the microscope in inches for settings on the right and left sides of the rings. Hach horizontal row constitutes really a complete set. In order to eliminate temperature effects as far as possible, the readings are taken in a certain sequence. Thus in the first row the sequence was Red (R), Green (R), Blue (R), Blue (LL), Green (LL), Red (L). The differences, representing the diameters of the rings, are thus appropriate to the middle of the time occupied. If, as happened here and usually, the temperature was rising, so that the rings dilated, the first reading (*398) on the red is too small, but the error is compensated in the last reading (*221), which is equally too small. As a matter of convenience the next row would be taken in the reverse order, beginning with a repetition of Red (Li), and so on. Since the radius of the circle described by the point of observation is 10 inches, the angular diameters (x) of the rings are as follows :-— Rep. GREEN. | Buve. eee 01780 | 01850 01940 | oP ahh 10-*x3:168 1074x3422 | 1074x3-764 es ne 10-*x-3960 | 10-*x-4977 | 1074-4705 | | DYE, eS ee See eer 1074-0317 | 107*x:0745 The calculation now proceeds by means of (5). If P refer to cadmium red and P’ to green, we have with Michelson’s Wave-Lengths with a Modified Apparatus. 699 values of the wave-lengths: | p= 12659650 (1 —-00000317) = 1:2659610, which with P=14814 gives P’=14814 + 3939:945 = 18753°945. In like manner for the blue referred to the red, s = 1-3413733 (1—-00000745) = 13413633, whence P’=14814+4 5056-955 = 19870-9955. The wave-lengths of the various radiations from a single source can thus be compared with great ease, and but little fear of temperature error. A set of observations from which this error is practically eliminated can be made in a short time and a few repetitions give all the security necessary. But the situation is not so favourable when we compare radiations from different sources. More time is occupied and there is corresponding opportunity for temperature change. It is necessary to alternate the observations, taking the first source twice and the second once, or preferably the first three dimes and the second twice. Even with this precaution I believe that temperature change was the principal source of error in the results of a single evening’s work. In the observations with an interval of one millimetre between the silvered surfaces, the influence of temperature is of course much less perceptible. For a similar reason the identification of the rings isa much easier matter. I will give as a specimen a series of operations (Feb. 9) in which helium was compared with cadmium. The first and third sets, each containing a repetition, related to cadmium ; the second set (twice repeated) related to helium. Only the mean diameter for each set is here recorded :— Cadmium. Red. Green. | Blue. ie Oe vas. cya h hc Le, nan Miata hea ie seeee” 749 ‘COOm Mm nET 6 El je Ree 752 6438 | 643 Mean ... 750 639 642 700 Lord Rayleigh: Some Measurements of Helium. : | Red Red Yellow | Green | Green | Blue Violet | 7065 6678 5876 | 5016 4922 4713 4472 Tecan ee 704 ‘673 ‘721 | -630 684 “665 ‘637 The first question is as to the ratio P’/P derived by (95) from these numbers for cadmium. The integral value of P for the cadmium red ring was 3328. From this we find P’ cad. green = 4213-946, 2 Yeade blue) == 4164593 5 on the basis of Michelson’s wave-lengths. For the green the fractional part is practically identical with that deduced above from one set of observations with the 5 mm. gauge. In the case of the blue the fractional part is now distinctly lower. The above are the results of work on single evenings. On the mean of all the comparisons with the two intervals there resulted :— Cadmium. 5 mm. 1 mm. edits Rececsacseal 14814 3328 Greet. oa ceeses: 18753°95 4213-95 ite. ce eee es 19870°95 4464-94 As already explained the agreement of the fractional parts constitutes a complete verification of Michelson’s ratios of wave-lengths, accurate to one part in 2 millions in the case of red and blue and to a still closer accuracy in the case of red and green. And it appears further that the phase- changes, upon which depend the deviations from integers, are decidedly greater than in the examples recorded by Fabry and Perot. The above results for cadmium suffice to indicate what deviations from integral values are to be expected when any radiation is compared with cadmium red assumed integral. In so far as the expected fractional parts appear in the results, so far are the ratios of wave-lengths assumed in the calcula- tion verified. The following are the wave-lengths, reckoned in air at 15° C. and 760 mm. pressure, whose ratios to. Wave-Lengths with a Modified Apparatus. 701 cadmium red have been verified by my observations to about one part in a million :— 6438:°4722 Cadmium< 5085:8240 Pisin AT99°911 5790°659 9769°598 5460°742 4358°343 6362°345 4810°535 4799-164 Fabry & Perot. 4680°138 — | 9895:932 5889-965 Mercury Fabry & Perot. Zine Soda —SsSs_ _« = SO 5 re } Fabry & Perot. I have spoken of an agreement to about 1 part in a million. In several cases the confirmation was decidedly closer. In one only, that of zine red, did there appear an indication of a disagreement rather outside the limits of error. My ob- servations would point to a wave-length avout 1 millionth part greater than that of Fabry and Perot; but in view of the difficulty of observations with the trembler, | am not dis- posed to insist upon it. The soda observations were on light from a cadmium vacuum-tube in which soda accidentally presented itself. The numbers quoted from Fabry and Perot relate to a soda-flame. As an example in which the ratios of wave-lengths were less accurately known beforehand, I will give some details relative to helium, beginning with observations of Feb. 9 by the 1 mm. gauge, already referred to. The Table I. annexed gives, in the second column the wave-lengths of the various helium lines recorded by Runge™*, in the fifth the same reduced to Michelson’s scale as employed by Fabry and Perot. The third column gives the corrections for obliquity as calculated from the observations with the 1 mm. apparatus already recorded, the fourth the differences from the corresponding quantity for cadmium red. Taking, for example, the helium ray of longest wave-length in com- parison with cadmium red, we get by (5) 1 9999 04388472 i FR These numbers should be integers, were the wave-lengths * Astrophysical Journal, January 1896, | | | | | | | | | Some Measurements of Wave-Lengths. 702 O8P-ILbP SLL-SILP C66: LC6V LL9-ET 0S €¢9-GL39 GL-8L99 F6-G90L ‘(poqoort00) Y (O8F- 1 LFF) (GLT-SLLP) 126. 1G6F Z89-G10G S19.618G LF1-8199 GGL: *(popoatatod) Y ‘SUPUOT[[ICU UL UOLOIALOD G6: C6: 86. 10: GO: C6: se eevee 00-8466 OF-OLOGT 68-66C91 LO-G8GF 1. 16-86FEL G6-6G281 ‘d oH Udd19d po "SU JUOLppIU UT MOTIOLIOZ) 66-66LF CO-LEP 96-6°EP 90-EL6P 86-9F96 10:COGE 60-6606 8SEE (uu Gee eva, OSPF. 1 LEP 86-1 610-61 LP 1G-T G16: 1é6Ph OG-1 LFG-C1OG 80-6 699 GLEG FG: G1-8L99 LET G6-C904 F8 ‘(peonper) Y ‘pd (‘wut [) ‘] @1a4Vy, OF9- LEP GIG-E1LP 960-GE6P GSL-G10G OL8-G184¢ LE 8L99 8F-G90L ‘(adunsy) Y seeeteeesens gry = Doe pO Vibrations of Conducting Surfaces of Revolution. 703 accurate, and were there no phase change. On account of the phase change as determined from the cadmium obser- vations, the fractional parts should be those entered in the 7th column. The differences are trifling, except in the cases of 5016 and 4713. The proportional corrections by which the 2’s of column 5 are to be increased are set out in column 8 expressed in millionths ; but of course an accuracy of 4 or 5 millionths is hardly to be expected in results from a single set of observations with the 1 mm. gauge. In the observations (Table II.) with the 5 mm. gauge the comparisons were with the cadmium green, for which P is assumed to be 18753°95, corresponding to 14814:00 for cadmium red. The numbers given embody the results of three days’ observations, but they do not include the wave- lengths 4713, 4472. The procedure is the same as for Table I. If the observations with the 5 mm. gauge stood alone, we should be in doubt whether P for 5016 should be 19016°95, or 19015°95. The results with the 1 mm. gauge show that the latter alternative must be chosen. Except in this respect, the 5 mm. results are independent; and they are of course to be preferred as presumably more accurate. The final numbers for helium are therefore those given in column 6 of Table IT. The only further remark that I will make is that the observations on the helium yellow (5876) are not improbably somewhat embarrassed by a companion of feeble luminosity which could not be separated. In the 5 mm. apparatus the two components would be nearly but not quite in coincidence. | | LXUI. The Symmetrical Vibrations of Conducting Surfaces of Revolution. By J. W. Nicnouson, B.A., M.Se., Scholar of Trinity College, and Isaac Newton Student in the Una- versity of Cambridge *. aT a previous paper +, the author investigated the possible electrical periods of the space between two perfectly conducting elliptic cylinders belonging to a confocal system. The vibrations of symmetrical type were alone considered. The object of the present paper is to obtain a list of the simpler surfaces of revolution, including cylinders as a particular case, whose vibrations admit readily of analytical treatment, and to examine certain important cases in detail. * Communicated by the Author. + Phil. Mage. Aug. 1905. 704 Mr. J. W. Nicholson on the Symmetrical The entire investigation is confined to symmetrical vibrations, which are the most interesting from a physical point of view. The electric and magnetic vectors are first expressed in a convenient manner in terms of two potential functions satisfying a certain differential equation. Let any point of space be defined by (1) cylindrical co- ordinates (pwz), where isin? 2 gat (#4) { AT ya(kr) + BJ_,_ (kr) . (14) n=0 i * Messenger of Math. vol. xix. + Loc. crt. 708 Mr. J. W. Nicholson on the Symmetrical In the mode in which y=0, the only non-zero electrical components are (z, y, c). Since a=0, the magnetic force at the surfaces is tangential, and the surface condition is merely y=O, or et =(. This leads to Macdonald’s equation for the periods. The mode defined by wy leads to the other set of periods. The case n=0 makes all the components zero, and leads to no vibration. The most interesting case is that of a single sphere. The most general components in a symmetrical oscillation inside the conductor are, if ¢ is the radius, od Senegal) fs LET) a = na (Ao r) : P, (4) Cos (kVi+e), IN dP, (u 2» Y=—P1P3 oe Wa ai AG Jal (ky ris cost i t+e), Bee eA Paty il ee Git) PS aaa c=— V pg ona3 (hr) Sint soe au, sin (kVt+e), taken for all roots k of ad s a | ena athe) } = (), sn pact ak eee (15) together with Bn(n+1 . = PE ie P,.(u) cos (kVt +e), nabbed ne dP, (ps) : b=— © (x 2, (de )) du «cs (EVES), = o5 Jnaa(kr) -s in? SE sin VE 8) taken for all roots k& of Jag key=O.>. 2.» 2 ei The gravest modes of the first and second systems (corresponding to n=1 in each case) are given by the least roots of (4o~ j=) tan he + 1=0, Sie and tan ke= ke, - 5 ° ° . : (18) respectively. | e ] . Vibrations of Conducting Surfaces of Revolution. T09 Vibrations of Confocal Spheroids. The proper transformation in the case of spheroids of ovary form is 2 tp —c Cos (@AaUS) hit a 2 CLO) which gives 1 p=csinhasin@= —, P 3 oe) =? (cosh? «— cos? 8). Thus the characteristic equation (10) becomes _ o¢ o¢ OG p22 = ts — + kc? (cosh? « —cos? 8) d=0. + Ae coth 38 cot Bag + (cosh? « —cos? B) 6=0 To obtain a solution of the proper form, we may write, if A is some constant, o¢ —coth a Be Sa! (Fe? cosh? a—rA)d=0, . (20) Oe ee Ge (Novae (COS: ONG ala (2) room 38 In the sphere, X=n.(n+1). Its proper values for the spheroid are to be determined so as to make @ recur when & increases by 27, and are of the form A=n(n+ 1) +6,(ke)? + 6,(ke)* + where e,, d,, ... are functions of n only. Write @=sinha.sin@.A.B, where A is a function of a only, and B of 8 only. We thus obtain 2 3 cot B43 + BARE? cos? B—cosec?B)=0 (23) These equations are included in a form considered by Niven * when discussing the conduction of heat in ellipsoids of revolution. His solution is unsuited to the present problem, but we may quote his value of A. In the present case, it is found that +3) 2n? ++ 2n—3 ve n(n-+1)(r+2)(r + a Pe ia Si LS A N= n(n+1)+ (Ke) Gea on 3) (ke) 1 (a—2)(n—1)(n) (a+ 1) fe ~ (2Qn—3)(Qn—1)8 ean ae * Phil. Trans. 1880, p. 1388. (24) (2n+1)(2n +3) (2n + 5) fk) ; Mr. J. W. Nicholson on the Symmetrical Thus when n=0, %= (kc)? up to and including the seventh order. This is found to correspond to no vibration. Yor the first three types of vibration, given by n=1, 2, 3, the values of X are il B 4 8 ype ae 5 Che)” — a3 Re) + Ip (he): 5 (25) 3 ; 4. 8 < NO + = 7 (he)? — 378 (ko)t+ a3 93 (ke) —. aisier ies (26) As= 12+ 55 (ke) <5 merely eres | After the first term, these series converge very rapidly for values of ke which are not very great, and more rapidly as n increases. Now for the fundamental, and for the vibrations near to it in a sphere of radius a, ka is not much greater than 1 or 2, and unless the spheroids differ greatly from the spherical shape, these series may be conveniently used in calculating the gravest vibrations of the doubly infinite system. ‘For ¢= ae, where a is the semi-axis major and e the eccentricity. Let ke be denoted by e. We may pass from the spheroidal coordinates to spherical polars (7, 0, #) by making « great and e small, so that r = ae B=. It is known that the equation corresponding to (20) when a is infinite and ¢ zero, is satisfied by the form = uals where 7, denotes a terminating polynomial in descending : powers of ekr, which is useful foe calculation for only moderate values of kr. Write cosh e = ¢ in (20), and it becomes (eae +(e? —N)b=0. 2) eae (28) dt? If in this transformed equation we write, following the method suggested by the case of the sphere, aes el Cr Cr+ Pass iC aes vs; (vet )?t! a: = we find that + = 0. Thus cases ( 1+ 2 + poet eh | ao Vibrations of Conducting Surfaces of Revolution. 711 where the series will not, in general, terminate. Denoting the series in brackets by 8, and substituting in the equation, we obtain, if z = te, (+6 y(t 2) 4 (¢ 2) CU een From this equation, the relations among successive coeflicients become 2(m+1)enz1 = (PF —A+M.m+1)en—2m— le Pem-1 +(m—1)(m—2)een—2 . « (80) Ho ey LS) | ts ++ a) bo | es we ae 6¢3 = (6 + €°— DN )Co— 2e7¢}. In the case of n=0, & =X to the seventh order. ‘Thus ¢,=0, and therefore c. and successive coefficients are all zero. In fact, the solution in this case is, to this order, @ = A cos(kecosha)-+- Bsn (kecosha) .. .,.(1) so far as @ is concerned. The conjugate equation in # is ph db STAD de cot Bs mae sin f= 0; whose solution is accurately p=C cos(ke cos 8) + Dsin(kecos8). . . (82) Now this is a function, which, even for great values of kc, is perfectly periodic in 8. and is therefore a possible solution for n=0 for any value of kc. But there is only one such solution. Thus we infer without further calculation that for n=O, all the terms of Niven’s series will vanish except tke), which is the accurate value of Ay Although this result is interesting from the point of view of several pro- blems, it is not to be expected, from the analogy of the sphere, that it corresponds to any vibration in this case, and in fact, on writing down the values of the electric and magnetic forces by previous equations, it is found impossible to “make them finite on the axis (@=0) unless they are everywhere zero. We therefore pass to the case n=1, which leads to the 712 Mr. J. W. Nicholson on the Symmetrical 2 true fundamental series of periods. Whenn=1,X=2+ = to the second order, by (25), 2 € = 5 to the same order, and ¢, and all higher coefficients commence with eé*. Thus a solution for n=1, with small eccentr icity, 1s 9 5—2eé €~ € U ai 5uecosha 5(ze cosh a)? cS 5(ve cosh a)* \ (33) dy = tke cosh a Another solution ¢,' is obtained by changing the sign of «. When —2, A=6+ oe by (26)5 aa Gan The Z : ea = Te —3, = oS, i = and the higher coefficients commence with e+. Thus i= Ve 91—5e aa cticeosh a ne 21—2e ee DE by 3 Tuecosha T(ste cosh a)? 9 e 9 e 2 as (vecosh x)? 7° (ve cosh ai BAC, and a solution @,' is obtained by changing the sign of «. Similarly, al eld 995 —2I¢2 Ones | emer Ti 90 —4e 25 —22e 75 —24e l5vecosha | 15(vecosha)? 5 ue cosh a)? 10? 10é ~~ (ve cosh a)* a (te cosh a)? j

mm., have given the mean results shown below. Values of the distance apart 2x of the divergent curves on the plates were ebtained for distances from the lower edge corresponding to integral numbers 7 of turns of the screw used in measuring the vertical coordinates, the pitch of the screw being 0:94684 mm. The corresponding heights y were calculated from the inclination of the plate in each experiment. If the results of the observations are plotted on a large scale, a sinuous curve is obtained whose mean position gives the true trajectory. Theoretically, in a uniform magnetic field and zn vacuo, this trajectory should be circular. I had previously realized that, for increasing values of y, the circles normal to the field which pass through the source, the upper portion of the slit and a point of the trajectory, have progressively increasing radii, and the actual experiments confirm this result. But, as will be seen, this conclusion does not apply to the radius of curvature of the trajectory, and is due to an inexact interpretation founded on imperfect knowledge of the actual distance of the slit from different points of the photographic plate. If the origin of coordinates is taken at the intersection of the edge of the plate with the bisector of the two pencils, it is observed that the curves do not pass through this origin, but cut the y-axis below the edge of the plate. Different trials have shown that it is possible to draw through the mean position of the points representing the observations a the a Rays emitted by Radium. 725 parabolic are whose radius of curvature varies sufficiently slowly within the given limits to render it indistinguishable from a circle. Let y= kn be the height of a point above the plane against which rests the photographic plate, ke the distance of the slit below this plane, kng=a the distance of the source below the same plane. ‘Then the equation of a parabola whose axis is parallel to the x-axis, and which passes through the source, the slit, and the point (x, 7), may be written 2Re=(y+a)(y+ke) * or 2Ruv=k?(n4-1)(r+e). Ae é Pate -, which are nearly coincident N+ Np with the straight line z=(n+e)6, were calculated in gpoths of a mm., so that The values of z= iS 6 a value which is practically identical with the radius of curvature of the parabola aaa eae p=Ri14+ (y+ >) |. The following tables show the extent of the agreement between the observations and the mode of interpretation explained above. Experiment C. 19/10/1905.—a= 25:15 mm. ; k=0°920 ; H=10,809. Trajectory through air only. R =< x 600, Hal, Oe Se lk Ce lo elite? | TARR ogalatoy | §=1-5546 ; 2x (obs.)=| 57°5) 105-2) 157-4, 210-2) 272-5] $33:0| 391-4) 458-5| 529°8| 602-7 cd=0°43 { observed=|2-01) 3:55| 514) 6-65) 835] 9-91] 11-31] 12-87) 14-47| 16-02 (+6)0 calculated =| 1°98) 3:°54/| 5°09) 6°65) 8:20) 9°76 | 11°31] 12°87) 14-42) 15-97) pe | Te IC Fes ate | i eae 2x (obs.) =| '755:0 | 8296 | 925-0 | 1018-7) 1096-2) 1193-0) 1297-0) 1397 | 1493-7 [ observed =| 19:06 | 20-42 | 22:23] 23-90 | 25-11| 26-74! 28-43) 29:97 3 (n+e)0 4 | _ caleulated=| 19:08 | 20°64 | 22°19} 23°75 | 25°30 | 26:86 ~ S He — In this form will be recognized the principal term of the expression which gives the radius of a circle passing through the three points, so [| (yta)(ythe) , we? (a—key? | 29°97] 31:52 726 Prof. H. Becquerel on some Properties of Experiment A. 17/11/1905.—a=11:65 mm. ; k=0°937; | FSS 12 ast In AIR ONLY. ; Turougu ALUMINIUM. eo=1i 60=1°39 o6=1-7248 (n+) C= 1-934 (m+e)6 20 2 2Qx —— 2. (observed). observed. calculated. | (observed). observed. calculated. 3 pee 92-4 6:26 6:28 143°9 9°13 9:13 Aoi! 134°] 8:50 801 1881 beso 11:06 Dies 1663 9°92 973 2332 As 12-99 Ges: 205°9 11°59 11°46 Srl! 15:19 14:93 erated: 2Zo71 13°44 13:18 333'°2 16°86 16°86 Sree 294-6 14:91 14:91 392°5 18:90 18°79 Oct as 343°8 16°55 16°63 451-4 20°74. 20°78 OMe 395-2 18:16 18°35 aan 22-65 22°66 Ties 456-7 20-06 20-08 584-1 24-56 24°59 Ziti Soko? 21°85 21°81 660-4 26°66 IEDS easy: 576-4 DA 2a Do 724-1 28°10 28°46 Ae Y 644:3 25-01 25°25 790°0 29-52 30°39 iG eotees (222, 26:98 26°98 888°7 32°01 32'o2 NGesete 791:°3 28-50 28°70 985:2 34:26 34-26 1 (sees 872°6 30°34 30°43 i cwep tee 950°8 31°94 32°15 Ae oe 1034°5 33°62 33°88 20). 5.8. hsirs 39°61 35°60 ZA a a eae 37°63 37°33 DO 1318°7 39°05 39°05 a a 1437°0 41-24 40°7 BHxperiment A. 16/11/1905.—a = 25°15 mm.; k = 0:920; H = 12,148. In Arr ONLY. Turovugu ALUMINIUM, 66 =0°70 60=0°84 é€=1-7318 ima +e)d 6=1:9037 (n+e)d 2Q4¢ — Dat i =i aa n (observed.) observed. calculated.| observed. observed. calculated. lets 729 2°55 2-43 81:0 2°83 215 ee ae 1183 3°99 417 1878 4°65 4°65 = eee 182-0 5°94 590 2043 6:67 6°55 At a 233°9 7-40 7°63 268°9 8:50 8°46 Bye erat 305°4 9°36 9°36 336'1 10-30 10°36 Goes 371°8 11:06 11°09 412-4 12:26 12:26 iad is 440-3 12°75 12°83 436°5 14.05 14:17 Seen. 5166 14:50 14:56 5b1°7 15°49 16:07 Oey ied 598°4 16°34 16°29 Ore 678-0 18:02 18-02 11) eee 769° 19-93 19°76 Loan, 842-7 21-27 21:49 Experiment A. 18/6/19038.—a = 20-4 mm.; & = 0-983; H2=)9955) jour sonly. | | i m= [2 | 8 ae ae ce) 7)! (8 sonia ie | 01-6808; 2x (obs.)= 101-0 141-2 193+1 245°7 291-9 357-0 417°6, 483-2] 550-2) 6245 | | 6=107 ( observed= 4:44 5-94 7-80) 9°54 10-91) 12°86 14°52) 16-24) 17°88) 19-67 | \n+e)d | éalbulated=| 4-44! 6-12) 7-20 P48 1116 1284 1452) 1620 1788 19°57 | the a Rays emitted by Radium. C2h It will be noticed that within the limits of each table, 7. e. within a length of about 2 cm., the radius of curvature varies but little, or at least that the ‘variation, if it exists, is within the limits of experimental error. The results may be summarized thus :— Value of product k? Hx 600 RA= ——— No. of experiment. _‘ Field intensity a (ems.). Lees i. in air. Perse ten VL / P9052... 12,148 1165 Sle lO? Pe ae lS) 6/1903......... D999 2-040 3°43 x 10? eee UO/TO/T90S.......-< 10,809 2°515 3°53 xX 10? yee oy LL 1905... cso. 12,143 2°515 3°56 x 10° The two experiments carried out with the same apparatus but with different field intensities have given concordant results. Such, however, is not the case if we compare two experiments corresponding to different arrangements of apparatus. It would appear that the principal cause of the divergence is the imperfect knowledge of the coefficient k which enters in the second power, and which in these experiments could not be determined as accurately as the other data. With this restriction, a comparison of experi- ments 1 and 4 of the preceding table would indicate a decrease of curvature along the trajectory. I would more particularly call attention to the table relating to the old plate (A. 18/6/1903), in connexion with which radium rays were used and the results obtained with which have already been published. It is seen that, taking into account the distance e, the numbers correspond very closely to a circular trajectory. It becomes therefore necessary to reject definitely the explanation which I had previously advanced and the hypothesis of an increase in the radius of curvature along the trajectory. A comparison of the trajectories of rays which have traversed a sheet of aluminium 0 015 mm. thick and of ravs which have only traversed air leads to conclusions similar to those which have been explained at the beginning of this paper, as is shown by the following summary :— Values of 0. No. of experiment. EEE Ratio. In Air. Through Aluminium. A GU LSO Tessas 17318 1°9037 1-099 7 WARS 015) ave ghee 17248 19334 1-121 I may finally add that measurements made with respect to the interior and with respect to the exterior edges of the deflected images, with a view to detecting dispersion, have not yielded differences excee eding errors of ‘observation. 728 Intelligence and Miscellaneous Articles. To sum up, the measurements described confirm the existence of a retardation of the « rays wheu they traverse a sheet of aluminium such as has been observed by Rutherford. The « rays of radium have behaved in these experiments like the « rays of bodies rendered active by the emanation. I have been obligingly assisted in the above experiments by M.. Matout, preparation-room assistant at the Museum. LXV. Notices respecting New Books. Ueber den Gegenwdrtigen Stand der Frage nach einer Mechanischen Erklarung der Hlektrischen Erscheinungen. Von Hans WIT Ts, Dr. phil. Mit 14 Figuren und einer Tafel. Berlin: E. Ebering. 1906. Pp. xii+282. ipeY aspects of physical science have claimed the attention of so many distinguished investigators as the dynamical inter- pretation of electromagnetic phenomena. The number of different dynamical theories of the electromagnetic field is some- what perplexing, and the student who first approaches the subject cannot help feeling bewildered by the enormous mass of material. to be dealt with. The author of the monograph under review, which is the first of a series to be issued under the general title of Naturwissenschaftliche Studien, has performed a signal service by his remarkably lucid and thoroughly systematic examination of the various possible dynamical theories of electromagnetic pheno- mena. In it he has included all past and present theories, and has clearly exhibited their relationships. The work is divided into 4 sections. Section I. deals with general notions, fundamental laws and classification of theories. The very brief Sections If. and ILI. are devoted to action-at-a-distance and emission theories respec- tively—now only of historical interest. Section IV., which forms the bulk of the book, contains an examination of wave theories. A useful bibliography is given at the end of the book. We can heartily recommend this unique monograph to all advanced students ot electromagnetic theory. LXVI. Intelligence and Miscellaneous Articles. To the Editors of the Philosophical Magazine. GENTLEMEN,— 24th April, 1906. ‘QINCE the publication of my note on a mercury-sealed tap in your March number I have received from Dr. Thiele, of Dresden, a copy of a paper published in the Annulen der Physik in 1901, Bd. 6, in which he describes a tap of design identical with mine, as well as certain improvements upon it. I much regret that I was not previously acquainted. with _Dr. Thiele’s work, and I shall esteem it a favour if you will insert this letter in your Magazine. I am, Gentlemen, Yours obediently, A. P. Caatrock, INDEXED THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE... [SIXTH SERIBS.] \\», etre ear - JUNE 1906. LXVII. The Field of Force in a Discharge between Re a Plates. By J.S. Townsenn, M.A., £.R.S.* 1. Fo, the theory which has been given by the author t to explain the large difference between the sparking- potential and the potential required to maintain a discharge, it is to be expected that large variations in the electric field accompany changes in the current between two parailel plates ina gas. A number of experiments have been made with a view to obtaining evidence as to the nature of these changes. The results are in good accordance with the general indications given by the theory, but, owing to im- perfections in the experimental methods which are employed, it is impossible to obtain accurate determinations of the electric field. The only practical method that has been employed to determine the potentials at various points of the discharge is by means of a wire placed in the path of the discharge. It has generally been assumed that the wire does not disturb the potential in the discharge, and when the gas is conducting the wire is supposed to acquire the potential at any point which would exist there if the wire were removed. It is difficult to see why this should be universally the case; and on consideration it would appear that when the wire is near one of the electrodes, the potential-fall between the electrode and the wire is probably much greater than the potential-fall * Communicated by the Author. + Philosophical Magazine, March 1905. Phil. Mag. 8. 6. Vol. 11, No. 66. June 1906, 3.5 730 ~~~ Prof. J. 8. Townsend on the Field of Force between the electrode and the same point in the gas when the wire is removed. In the following investigation it will be assumed that the conductien in the gas is produced in the manner which has been explained in the previous paper. According to the theory, practically all the ionization is produced by the colli- sions of positive and negative ions with the molecules of the gas. On ihis supposition the following result has been obtained : eX ny Xu=ix Z(2) x | (Z@yxexae, 0 “(a—B)dax where Hae i; , 7? being the current per unit area of the electrodes, 2 the distance of any point in the gas from the negative electrode, e the charge on an ion, u and v the velocities of the negative and positive ions respectively, nm, the number of negative ions per c.c. at any time at the point #, m, the number of positive ions, a@ the number of molecules of the gas ionized by a negative ion in moving through a distance of one centimetre under the force X, 6 the number ionized by a positive ion under similar conditions. It will suffice for present purposes to consider very small currents, so that the potential will not be appreciably affected by the charges on the ions, and the electric force will be practically uniform between the plates. As the quantities a, B, u,and v depend only on the electric force and the pressure of the gas, these quantities will not vary with the distance 2, so that the above equation reduces to the form iB exnyXu= gage Yt) The equation ta (p—a)(a—2 may be similarly found. The ratio 14,U eae B aha a ace 1 nv a 1—¢&-4)(e—2) represents the proportion of the current carried by the nega- tive ions to that carried by the positive ions. The values of a and 8 have been found over considerable ranges of forces and pressures, so that with the aid of the above formula it is possible to find the ratio of the currents carried by the ions of opposite sign at various points in the gas. ana Discharge between Parallel Plates. 731 It is interesting to ‘consider the cases for two different pressures above the critical pressure. Thus let the plates be 8 millimetres apart, and let the gas be hydrogen at 2 millimetres pressure. In this case the sparking-potential is 282 volts, which is also the potential required to maintain a small current. The value of x will therefore be 176, and the corresponding values of = and B are 2°41 and ‘055 respectively *; so that «=4°83 and an, The following are the values of the ratio ae corresponding to different distances from the negative electrode:— ts." ©, Ie 2. 3. 4 5. 6. 7. 8. eo | | Ch | — —_ |_| | - Nu Nv Oly) 0143") 088" 078) | sbO" 28% |" -o9" 1-58 O It may thus be seen that for the greater part of the distance between the plates the current consists principally of a stream e e e e e nN U e e of positive ions, since the ratio ae is less than unity for more v 2 than 6 millimetres of the distance. Ata point between 6 and 7 millimetres from the negative electrode, the numbers of positive and negative ions passing unit section are equal, and from that point up to the positive electrode the current carried by the negative ions exceeds the current carried by the positive ions. It is interesting to see how the numbers change as the pressure and sparking-potential rise. As before, let the plates be 8 millimetres apart and the pressure 9°27 millimetres instead of 2 millimetres. In this case the sparking-potential is 487 volts, and the values of « and 6 are 6°03 and :05 respectively. The corresponding ratios for various values of the distance x are :— NV | If the negative electrode be taken as at zero potential and the positive electrode at potential V, the potential at a point * J. 5. Townsend, Phil. Mag. Noy. 1903. 3 B2 732 Prof. J. 8S. Townsend on the Field of Force in the gas 2 millimetres, for instance, from the negative electrode would be - when the current is small. The question then arises, whether a fine wire placed at a distance of 2 millimetres from the negative electrode would assume a potential of s It is easy to see that if the wire is brought to a potential 7 and then insulated, it would rapidly acquire a higher potential. Considering the case in which the hydrogen is at a pressure of two millimetres, the calculations which have been made show that when the field is undisturbed, the wire being at potential ie the number of negative ions passing the wire per second is less than 4 per cent. of the number of positive ions. The number of positive ions discharged on the wire would be largely in excess of the number of negative ions; it would therefore acquire a positive charge, and its potential would rise above r The positive charge on the wire would tend to repel positive ions and attract negative ions until the numbers of each kind acquired per second become equal. It would be almost impossible, owing to the mathematical difficulties, to calculate the amount to which the potential would rise ; but it would be undoubtedly very considerable. A com- parison between the tables given for the two pressures shows that the discrepancy between the potential of the wire and the undisturbed potential of the gas increases as the pressure rises. It will be noticed that between 6 and 7 millimetres from the negative electrode the positive and negative currents are equal, so that in that neighbourhood the wire would most probably take up the potential of the gas. | It may also be seen that the wire would assume a potential lower than that of the gas when placed near the positive electrode. 2. It is interesting to examine on these principles what might be expected with pressures above the critical pressure when a large current is flowing, and the number of ions in the gas produce an appreciable alteration in the distribution of electric force between the electrodes. According to the theory, the charge in the gas would alter the field of force so as to give rise to a fall of potential, across a layer of gas near the negative electrode, of the same order as the minimum sparking-potential. Nearly all the ions which constitute the in a Discharge between Parallel Plates. 733 current are generated in this layer where the force is large, and the negative ions proceed from it under a comparatively small force along the positive column to the positive electrode. The layer near the cathode where the ions are generated con- tains approximately the same amount of gas as is required between parallel plate electrodes to obtain the minimum sparking-potential. The currents of positive and negative ions will be equal ata point near the end of this layer, so that a wire placed in that position would assume the true potential of the gas. For points very near the negative electrode, the current of positive ions exceeds the current of negative ions, and the wire would assume a potential higher than the potential of the gas. Along the positive column the electric force is compara- tively small, so that in this portion of the discharge compa- ratively few molecules are ionized. The stream of negative ions must therefore be in excess of the positive stream, so that in the positive column the wire would assume a potential lower than the gas. As the positive electrode is approached the number of positive ions in the current diminishes and the number of negative ions increases, and at the electrode the current consists altogether of negative ions. When the wire is near the electrode, it would therefore assume a potential much lower than that of the gas. This is a well-known expe- rimental result; but the above investigation shows that it does not follow that there is any discontinuity in the electric force near the electrode when the wire is removed. There is therefore no reliable evidence to show that the so-called anode fall of potential really exists. 3. In order to investigate experimentally the field of force and a current between parallel plates the apparatus which is shown in fig. 1 (p. 734) was used. The current passed between the two zinc plates Aand B. The upper plate B was fixed to a micrometer-screw 8 which passed through the brass plate C, and in order that the screw should not shake in its bearing the upper portion was reduced so as to fit exactly into a hole in the cock-piece Ff. The plate C was fixed firmly to the lower plate A by means of four ebonite pillars EH. The axleS earried a divided circle D, so that the distance between the plates A and B could be determined accurately. By means of the arrangement shown in the figure, it was possible to move the fine wire W to any position between the electrodes. The wire was stretched between the ends of two ebonite rods R which passed through holes in the brass plate C. The split brass tubes T were fixed to the brass plate, and fitted over the ebonite rods, so that the latter moved up and down 734 Prof. J. S. Townsend on the Field of Force easily. The upper ends of the rods were screwed to a piece of brass X having a hole in the centre through which the upper portion of the axle 8 passed freely without touching. Fig. 1. V WP Nw \’ , \\ kA ZZ, = es F. 4 D = _—_N BI e/a The wire W, the brass piece X, and the two rods R thus formed a rigid rectangular frame which could be moved up or down, and the brass tubes T exerted sufficient pressure on the ebonite rods to keep the frame in any position in which it might be placed. In order to raise the frame the screw S was rotated until the disk D moved the brass piece X to the required position. The frame was lowered by screwing down the axle so as to make the short piece of ebonite G on the top of the axle to press on the upper side of X. It was arranged that the wire W should be one millimetre below the plate B when the ebonite G was pressing on X. When the distance between the plates A and B did not exceed 8 millimetres it was possible to place the wire accurately at any distance from the lower plate, except that it could not be brought nearer than one millimetre to the upper plate. Electric connexion was made with the upper plate and the wire through ebonite plugs in the side tubes of the glass cover, and the connexion with the lower plate was made by the base. A sensitive electrostatic voltmeter which gave readings to in a Discharge between Parallel Plutes. 739 2 avolt from 80 to 265 volts, and an aluminium-leaf electro- scope graduated to read potentials above 150 volts were used to determine the potential-differences between the wire and the electrodes. When either the voltmeter or the electro- scope were connected to the wire and charged with a small replenisher, they maintained their charges without any appre- ciable diminution for several minutes, showing that the in- sulation was satisfactory. ‘The cases of the voltmeter and electroscope were also insulated. 4. An unexpected difficulty arose when preliminary expe- riments were being made, which was subsequently traced to an effect arising from the capacity of the insulated system of the voltmeter or the electroscope in connexion with the wire in the gas. The following experiment illustrates the general nature of the effects which are produced. The plates were set at 8 millimetres apart and the wire was placed midway between the plates, the gas being hydrogen at 6-7 mms. pressure. The terminals of a battery of 452 volts were connected through a galvanometer and resistances amounting to 371,000 ohms to the electrodes, which gave a constant current of 2:1 x 10-* ampere through the gas. The potential- fall along the external resistances being 18 volts, the differ- ence of potential between the electrodes in the gas was 374 volts. This was verified by another electrostatic volt- meter which gave a constant deflexion of 374 volts when it was connected to the electrodes. When the sensitive electrostatic voltmeter was used to find the potential-differences between the wire and the electrodes, the following results were obtained :— volts Potential-fall between wire and negative electrode . . 178 ” 9 yy) positive AS less than 80 The sum of the potentials should be 374 volts instead of being less than 258 volts, which shows that the potential of the wire must be disturbed by connecting it to the voltmeter. It was found that the discrepancy could not be due to faults in the insulation or to errorsin the voltmeter, as the readings of the latter were found to be very accurate over the whole range of the scale when tested with voltages that had been measured with a standard milliampere balance. In the above experiments the connexions to the voltmeter were made with ordinary copper wires having small resistance. A number of experiments were made to find the cause of the disturbance of the potential of the exploring wire and to eliminate the effect if possible. 736 Prof. J. 8. Townsend on the Field of Force It was found that perfectly consistent results were obtained when the connexions from the electrode and the exploring- wire in the gas to the terminals of the voltmeter were made through high resistances of about 5 megohms. A dilute salt solution in a capillary tube 3 or 4 centimetres in length is a convenient form of resistance for this purpose as it has a small capacity. It is necessary to have a high resistance in each line leading to the voltmeter, and it is of advantage to have the resistance tubes as near as possible to the electrodes and the exploring-wire. With the high resistances thus placed in the lines conducting to the electrostatic voltmeter, the following readings were observed :— Potential-difterence between exploring-wire and negative electrode 270 volts ” ” 69 positive » 102 volts The sum of the potentials only differs by 2 volts from the ascertained difference of potential between the electrodes, so that the disturbing effects produced by the capacity of the. voltmeter are eliminated when high resistances are used in the connexions. The following experiments are of interest in this connexion as they show the effect of capacity in a simple manner. A high resistance was joined to the base, another to the rod P,, and a third to the rod P,, and the connexions to the voltmeter were made through these resistances, so that the potential-differences between the wire and each of the electrodes were not disturbed by using the electrostatic voltmeter to make the necessary observations. The effects produced by connecting one set of plates of a condenser to the wire W and the other set of plates to either A or B may then be easily examined. Tor this purpose, a small air-condenser was used which consisted of an inner plate P 12 centimetres square and two outer plates Q in metallic connexion and slightly larger than the plate P. The air-space between the inner plate P and the plates Q was approximately 1 centimetre, so that the capacity of P was about 23 electrostatic units. The plate P was fixed in a vertical position to the rod P; making contact with the wire W through the ebonite plug in the side tube of the cover-glass, and the plates Q were set up on a paraffin block so as to be equidistant from it on either side. There was thus complete air insulation between the plates P and Q ; nevertheless the potential of the wire when the current was flowing depended upon whether the outer plates Q were joined to the positive or negative electrode in the gas. Using the same current as in the previous experiments the following results were obtained :— in a Discharge between Parallel Plates. 7 73 Potential-difference between No capacity attached toW. Inner plate P joined to W, and outer plates Q to negative electrode. Inner plate P joined to W, and outer plates Q to positive electrode. : oe : 82 wire and positive electrode. rp Ne Potential-difference between 270 194 285? wire and negative electrode. SUIT, Bee BA eee 372 372 367? In the last experiment the pointer of the voltmeter was considerably over the scale, so the potential was determined approximately with a graduated aluminium-leaf electroscope. The potential must of course in this case be 290 (372—82), since the difference of potential between the wire and the electrode is not affected by the voltmeter as the connexions to it are made through high resistances. These and other experiments show that when one set of plates of a small condenser is joined to the wire W and the other set to one of the electrodes, the potential-difference between the wire and that electrode is diminished. The condenser has no effect when the connexions to it are made through high resistances. The effect may also be observed by having the leaves of an electroscope connected to the wire and the case to the negative electrode. No change in the divergence of the leaves is produced when the electrostatic voltmeter is con- nected up through high resistances, but when the connectors are of small resistance an increase in the divergence of the leaves is observed when one terminal of the voltmeter is joined to the wire in the gas and the other to the positive electrode. The opposite effect is produced when the voltmeter terminal is joined to the negative electrode. Similar results were obtained when air was used instead of hydrogen for these experiments. It is difficult to see how these effects arise, but it is most probable that they are due to the unsteadiness of the current. A telephone placed in the circuit leading from the battery to the electrodes gave a rumbling noise, which showed that there must have been slight variations in the current. The noise was generally diminished (without altering the intensity of the current as given by a galvanometer) by increasing the potential of the battery and the external resistance, but no reliable method was found of producing silence in the telephone. 738 Prof. J. S. Townsend on the Field of Force lt has been suggested that the unsteadiness is due to faults in the connexions of the battery, but although the connexions were carefully examined and renewed in places where there might possibly have been a fault, still there was no diminution in noise in the telephone. It was also found that the telephone gave no sound when the wires leading to the electrodes in the gas were connected together, and the resistance of the circuit increased so as to bring the current to its original value. It appears therefore that the slight variations in the current must be attributed to the nature of the conductivity of the gas. ixperiments were also made with a current (maintained by a battery of lead cells) through a gas at low pressure in a glass tube of diameter 2°4 centimetres. The electrodes were flat aluminium disks 14 centimetres apart, and a wire projected into the tube in the usual manner near one of the electrodes so as to obtain the cathode fall of potential. The telephone showed that in this case also the current was not perfectly uniform, but the effect of the capacity of the voltmeter could scarcely be detected, and the ordinary value of the cathode fall of potential was obtained. The potential of the wire is therefore more stable in a long discharge which fills a glass tube, but of course this apparatus would have been useless for these investigations, as one of the principal objects was to obtain small currents in a uniform field. 5. A number of experiments were made to determine the potential of the wire at different distances from the large parallel plate-electrodes, using large resistances in the connexions to the voltmeter. The following curves represent the results for hydrogen at different pressures. The three curves shown in fig. 2 give the potentials of the wire at different distances from the electrodes for three different currents. The currents expressed in amperes per square centimetre of the electrodes corresponding to the curves 1, z and 3 were 1:2 x 10-®, 6 x 10-§, and 3 x 10° respectively. The pressure of the hydrogen was 1:37 millimetres, which corresponds to the minimum sparking-potential for the distance of 8 millimetres between the plates. The small difference between the curves 1 and 2 shows that when the current is small, the potential of the wire is not affected by changing the intensity of the current. It is most likely in these cases that the charge on the ions is too small to affect the field of force appreciably, and thatif the wire were removed the field would be uniform. The ratios of the currents carried by ions of different sign are independent of the absolute value of in a Discharge between Parallel Plates. 739 the current when the force is uniform ; so that the potential assumed by the wire ought to be the same for all small currents, although it may differ from the potential of the gas. Fig. 2.—Hydrogen-pressure 1°37 mm. Seay) - “N Ss > 200 200 “XN ww = S 150 150 & 9 “N = 100 100 BS KR re K o 50 50 a j 2 3 4 5 6 7 8 DISTANCE OF WIRE FROM NEGATIVE ELECTRODE IN MMS. 1. Current=1-'210—6 amperes per sq. cm. of electrodes. . ” 6x 107% ” ” ” 3. ” 3 1059 ” ” ” It would be easy to make a calculation of the charge in the gas in this case, and to estimate the extent to which the charge on the ions disturbs the uniformity of the field, if the velocity of the positive ion were known. A rough estimate may be made from the numbers found for the velocity at higher pressures and smaller forces by supposing that the velocity is proportional to the electric force and inversely proportional to the pressure. The value thus found for the larger forces and smaller pressures would be a lower limit to the velocity. It may be conjectured from the determinations at higher pressures both of the rate of diffusion and the velocity under an electric force, that the ions are accompanied in their motion by a group of molecules. If the group remained the same for the lower pressures and higher forces, then the velocity would be inversely as the pressure and pro- portional to the electric force. It is most probable that for large forces and small pressures the group would diminish ; and so the velocity under an electric force would increase more rapidly than the quotient = It may be shown from ) 740 Prof. J. 8. Townsend on the Field of Force the experiments that have been made that, on the average, the velocity does not increase much more rapidly than = for the forces and pressures used in the experiments. For this purpose, it is necessary to examine to what extent a current of 1:2 x 10-® ampere disturbs the uniformity of the field. The effect of the charge is greatest near the negative electrode, and the calculations of the ratio of the positive and negative currents which have been given above show that the stream of positive ions exceeds that of the negative ions for the greater part of the distance between the plates. The quantity n»xexXv measured in electrostatic units is of the order 1:2 x 10-* x3 x 10° for the space near the negative electrode, as nearly all the current is carried by positive ions; € 3 so that the charge n,.xe becomes oes v being the velocity ot the positive ion. i The velocity of positive ions in hydrogen at 760 mms. pressure under a force of J. volt per centimetre is 6°7 cms.. per second*; so that for the force 260~+°8 volts per centi- metre and a pressure of 1°37 millimetres the velocity would be 1:2 x 10° cms. per second. Near the negative electrode the positive charge would be 3 x 10-? electrostatic units per cubic centimetre, if all the current were carried by the positive ions. A simple calculation shows that if a charge of 3x 107° electrostatic units per cubic centimetre be placed in a layer of the gas 6 millimetres wide near the cathode, the potentials in volts at different distances from the cathode are :— | Distance from Cathode. co ay Nias lett 9 V’ being the potential-difference between the plates, which in this case was 256 volts. As these changes are so small the current might have been considerably larger without having much influence on the potentials. The actual potential of the wire at 2 millimetres from the negative electrode was 102 volts; so that this large increase over the potential 64°62 is most probably due to the fact that the stream of positive ions is so much greater than that of negative ions. There isa marked difference in the * Zeleney, Phil. Trans. 1900, p. 193. in a Discharge between Parallel Plates. 741 curves obtained experimentally when the current rises to 3x 10-° amperes. It may be deduced from the calculations which are given above that in this case the charge on the positive ions must preduce a large effect on the distribution of force in the field, and the experiments show that the potential of the wire at 2 millimetres from the negative electrode changes from 102 to 147 volts. It will be noticed that the curve corresponding to a current of 6 x 10-§ ampere lies a little above the curve for 1:2 x 10~® ampere, and the calculations show that the charge in the gas would begin to produce increases of 2 or 3 volts in that case. The numbers which have been given for the increases of potential are not very accurate. They must be considered as indicating the order of effects which would be produced under the assumptions that have been made in calculating the velocity. The velocity 1:2 x 10° which has been found is the final velocity that a positive ion attains under these conditions, and the estimate of the effect of the charge has been made on the supposition that a positive ion travels along its whole path in the gas with this mean velocity. As a matter of fact, it would be more correct to consider the ion as starting from rest from the place where it is generated, so that the ions take a longer time to traverse their paths, and consequently the charge i in the gas has been underestimated. It is interesting to find how long it takes an ion to traverse 6 millimetres if it starts from rest when x has the value Dao» as in these experiments. I The equation of motion of a body of mass m and charge e in an electric field of intensity X is dex dx mM 5 =eX —k— ap k being a constant depending on the retardation of the ion. The final velocity = has been estimated at 1:2 x 10° ems. per second, X being 1'1 approximately in electrostatic units. Hixperiments on diffusion at the higher pressures show that m is roughly 30 times the mass of a molecule of oxygen ; m =. . so that the value of — in the above equation becomes e 3°6x10-. When these values of the constant are sub- stituted, the solution of the equation becomes w==12 x 105 x t—4-8[ 1 —e 29x 105x4], 742 Prof. J. S. Townsend on the Field of Force The time required for the ion to travel 6 millimetres may be obtained by substituting for x the value ‘6, and it is thus found to be approximately 2°2 x 10—* seconds. This is more than four times the length of time 5 x 10-7 seconds required to travel the distance 6 millimetres at the uniform velocity 1:2 x 10° cms. per second. It must, however, be borne in mind that it requires some time for a large group of molecules to collect round a positive ion, and during the first part of its path the ion is travelling with a mass practically equal to the mass of a molecule of hydrogen. It is quite conceivable that during the short time of the order 10—’ second the positive ion moves as if it had a comparatively small mass, and possibly the value 5x10-“ seconds is a more correct estimate of the time required to travel a distance of 6 millimetres. These considerations show that it is very difficult to make an accurate calculation of the charge in the gas even for a field of force that is practically uniform; nevertheless it is — of interest to see that the experimental results are in fair agreement with the rough indications given by the theory. The theory shows that the potentials at 2, 4, 6, and 8 millimetres from the negative electrode ought to be the same as the potentials at 1, 2, 3, and 4 millimetres respectively from the negative electrode when the pressure of the gas is doubled and the distance between the plates reduced from 8 to 4 millimetres. It was found that the potentials were 107, 155, 205, and 260 at the distances mentioned when the pressure of the hydrogen was 1°37 millimetres and the distance between the plates 8 millimetres; and for the pressure 2°74 millimetres with the plates 4 millimetres apart, the potentials were 108, 154, 202, and 257 at the corresponding reduced distances. a 6. Further experiments were made at a pressure of 2°74 millimetres with the plates 8 millimetres apart. The results are shown by the curves, fig. 3. The velocity of the positive ions is much slower in this case as the potential required to maintain a small current rises only to 316 volts as compared with 256 volts at the lower pressure. In order that the field of force should not be apprecially influenced by the charge, it is necessary to use smaller currents since the charge in the gas is inversely proportional to the velocity. it was found that the field, as indicated by the potential of the wire, did not vary for currents between 2x 10-®° and 2x 10-7 ampere, so that for these small currents the charge is too small to make an appreciable effect on the field of force. It will be seen that for a current of 4x 10—* ampere a large ina Discharge between Parallel Plates. 743 change occurs in the field of force, and a cathode-fall of potential of about 240 volts is developed in the layer 4 millimetres thick near the cathode. The curve shows that the potential between the electrodes required to maintain the current diminishes when the cathode-fall of potential is developed. Fig. 3.—Hydrogen-pressure 2°74 millimetres. POTENTIAL OF WIRE 1N Vo“tTs. DISTANCE OF WIPE FROM NEGATIVE ELECTRODE IN MMS. 1, Currents less than 2x 10-6 ampere per sq. cm. 2. Current=4 x 10-6 ampere per sq. cm. The calculations which have been given for the distribution of the current between positive and negative ions show that at a point between 6 and 7 millimetres from the negative electrode, the two streams are equal over a range of pressures between 2 and 9:27 millimetres, and the wire should take up a potential nearly equal to the potential of the gas at those points. The latter potential would be represented by a straight line joining the two ends of the curve for the smaller currents, and the figures show that these lines would intersect the potential curves determined by the wire at points about 6 millimetres from the negative electrode. It is not easy to find other potential curves intermediate between those given in the figure as the current is unsteady for values between 2 x 10-§ and 4x10-S ampere, where the charge in the gas exercises an appreciable effect on the field. 744 Prof. J. 8. Townsend on the Field of Force It would be possible, no doubt, to use a very high electro- motive force and a large external resistance, and most probably a steady current of any value could then be obtained, but for a preliminary investigation it was not considered necessary to make experiments in that direction. Experiments were also made at higher pressures, but owing to continued use of the apparatus the electrodes underwent some change and the glow did not spread uniformly over the surface of the electrodes. It frequently happened that the current passed through a narrow column of gas, so that it was impossible to make observations of potential or to determine the density of the current per square centimetre of the electrodes. From a theoretical point of view it is better to make experiments at the lower pressures (2 or 3 times the critical pressure) in order to obtain experimental evidence of the transformation of the electric field, as the potential of the wire does not differ so much from that of the gas at these pressures for the smaller currents. It may be seen from the numbers that have been given for the ratio of the currents of positive and negative ions that the number of negative ions in the gas near the negative electrode diminishes as the pressure rises. 7. Another set of experiments of a different kind have been made to test the results which are indicated by theoretical considerations. It has been shown that the sparking potential is the same as the potential required to maintain a small current, but as the field of force near the negative electrode is increased by the positive charge in the gas, the potential required to maintain a large current diminishes. If this theory is correct, it should be possible to produce sparking or to maintain a small current between parallel plate-electrodes, if the force near the negative electrode is increased by having a positively charged body near it. This can easily be arranged by having a grating of fine wires near the negative electrode and charging it by means of a battery or a small replenisher. A simple form of apparatus to illustrate this effect is shown in fig. 4. A pair of plane parallel electrodes N and P were fitted in a glass tube of about 24 centimetres in diameter. A grating of fine wires was mounted on a brass ring R which was fixed to the end of an ebonite tube T. The ebonite tube was shaped so that the ring fitted over the end and the wires of the gauze rested on the front of the ebonite that projected into the ring. The negative electrode fitted inside the ebonite tube and could be placed at any convenient distance from the grating. The wires of the grating were wn a Discharge between Parallel Plates. T45 about ‘1 millimetre in thickness and 1 millimetre apart, and were parallel to the surfaces of the electrodes. Fig. 4. R UMMM ah Yam N e WILL 7 YL e ner ee VELL ig A battery of known electromotive force was connected through a galvanometer to the electrodes in the tube, and the potential of the wire was gradually raised until sparking took place. The following table represents the results of the experiments, V denotes the potential-difference between the electrodes, and V’ the potential-difference between the negative electrode and the gauze when sparking occurred. Ven etcas. 550 600 640 680 700 Wiles icna§- 240 210 170 150 100 It thus appears that the sparking potential between the two electrodes may be lowered by 150 volts by increasing the strength of the field near the negative electrode, The same results were obtained by a different arrangement for charging the grating. A known electromotive force was applied to the electrodes, and the grating was insulated and connected to one terminal of an electrostatic voltmeter, the other terminal being connected to the negative electrode. A small quantity of radium was held outside the tube opposite the space between the grating and the positive electrode. The grating thus acquired a positive charge slowly, and when the potential as shown by the voltmeter attained a certain value, sparking took place between the electrodes. The greater the potential-difference between the electrodes, the less is the charge acquired by the grating before the spark passes. The results obtained in this way were practically the same as those given in the above table. Phil. Mag. 8. 6. Vol. 11. No. 66. June 1906. oO E746 J LXVIII. The Black Spot in Thin Liquid Films. By H. 8. Jononnort, Jun., Ph.D.* N some previous work + on this subject it was found that, in general, the black film consisted of two portions. That first formed varied in thickness between 40 wy and 12 wy. The first black was found to break naturally into the second when the atmosphere was incompletely saturated. With a thoroughly enclosed film it was necessary to heat the system in order to form the second black film ; which had, apparently, a constant thickness of 6 py in all cases. Effect of Change in Pressure.—Recently it was discovered that great changes in the character of these films could be produced by changing the pressure on the atmosphere surrounding the films. A sudden increase in the pressure was accompanied by a rapid thinning of the film; while, on the other hand, a sudden diminution of the pressure was accompanied by a correspondingly rapid increase in the thick- ness. On subjecting the first black film to sudden increase in pressure it was possible to convert it quickly into a second black; if then the pressure was suddenly diminished, the second black became a first black. In many cases it was possible to continue this thickening until the film showed the yellow of the first order. The evident explanation of these effects is that the heating due to adiabatic compression is accompanied by an increased vapour-pressure and, consequently, evaporation from the surface of the film. While, on the other hand, adiabatic expansion causes cooling and condensation on the film. Fig. 1 represents a simple arrangement for producing these effects. The film is formed ona rectangular frame of glass-fibre, ', mounted on a rubber stopper. This stopper fits firmly into the mouth of an inverted beaker containing the solution {. Blowing or sucking in a rubber tube, attached at P, the pressure in the upper vessel is varied without contaminating the solution. If the upper vessel is carefully chosen the films may be observed quite advantageously with a low-power microscope. A simple gas-jet makes an * Communicated by the Author. + Phil. Mag. vol. xlvii. p. 501 (June 1899). ¢{ The solution was made in the following manner:—7 grams of oleic acid (refined) and 2 grams of caustic soda are thoroughly boiled in about 100 c.c. of distilled water. This gives about 7-5 grams of oleate of soda which is diluted to about 50 of water to 1 of soda and again boiled. An excess of acid is not harmful, while an excess of soda is decidedly so. The Black Spot in Thin Ligud Films. TAT excellent illuminant, and at the same time may be used to heat the film. Fig. 1. PAAAMSAAANS ANAAAANNY | | Let the temperature be adjusted with the flame and the pressure with the mouth until the first black film is about to break into the second. Then pinching the tube with the fingers will cause the second black to appear as small perfectly round spots in the first black film; releasing the pressure, after the film has become the second black, will cause the first black to appear, in a similar manner, as spots in the second black. Thickness of the Black Film.—In view of these circum- stances, it was thought advisable to repeat the measurements on the thickness of the black film. The work was begun in the Ryerson Physical Laboratory of the University of Chicago, and through the courtesy of the officers of instruction, in kindly lending the necessary apparatus, was carried to com- pletion elsewhere. | In order to vary the thickness, by changing the pressure, and at the same time to measure the thickness, a different form of the interferometer was required. In fig. 2 is shown a familiar form of the Michelson interferometer that was used. ‘The object that was to he gained was simply that both a Or2 748 “Dr. He S: Tohenncat on the optical paths should lie alike in the atmosphere of the films. The long brass box in which the films were formed is shown at B. The films were 221 in number and formed on frames of glass-fibre asin the former work. The box was sealed, Hier 2: ee. Pat Tees TUT and connected to a manometer and suitable apparatus for varying the pressure. The fringes were viewed with a tele- scope. All other details were much the same as in the earlier work, and may be found described therein. At the first trial it was apparent that the reading of the number of fringes displacement could not be made as promptly as the thickness could be altered by varying the pressure. This was due to the distortion produced in the fringes by quickly changing the pressure. It was very difficult to obtain trustworthy data when working with rapid changes in the pressure, and, on the whole, this part of the work was somewhat disappointing. Nevertheless, with less rapid alter- ations in the pressure, it was possible to pass the black film through all its phases with little if any distortion in the fringes. A large portion of the time was spent in working with no variation in the pressure. The method usually employed was to form the films in the morning and take readings of the thickness throughout the day, with a more or less rapidly rising temperature. The box was surrounded with a large water-jacket to maintain a uniform temperature. It was found that this outer box filled with air served the purpose uite as well. The following table was taken with no variation in pressure. The box containing the films was firmly sealed. The tem- perature recorded was the mean of the readings of two thermometers, placed within the box, B. Black Spot in Thin Liquid Films. 749 TABLE I. Age of | Fringes No. Mean Mean. : Film. Deflect. Films. | Thickness. | Temp. Leeman. hr. min joy. °¢, i .18 4-0 221 16:0 25°5 All first black. 4 33 4:1 221 16°4 25°0 fp 55 ios 60 221 24-0 23°5 Fy i" 21 33 38 221 15:2 25°3 ” ” 26 23 3:0 217 12-2 26:5 Two second black. ip, il 2°5 217 10°15 28:0 2h. 3 15 215 616 28°7 All second black. In the light of the results recorded in the former paper, this table requires littke comment. The increase in the thickness with falling temperature; the limiting thickness of the first black film at about 12 4m; and the mean thick- ness of the second black at about 6 up, were therein illustrated a number of times. In the above table, however, since the number of films was over four times as great, the number of fringes displace- ment was correspondingly greater. In the former paper it was remarked that, “a number of observations indicated that the thickness of the second black film was not constant.” With the number of films there employed the deflexion was only about °35 fringes, when all of the frames held second black films. In the present case the corresponding deflexion was 1°5 fringes. With this greater sensibility it was at once apparent “that the second black film was of variable thickness. While the limiting thickness of the second black was approximately 6 wy, the upper limit, in many cases, was at least 50 per cent. greater. In fact, in behaviour, the black films were found to be guite similar; 72.e¢., with a sealed atmosphere and a rising temperature, a rapid thinning immediately after birth was characteristic of both types. This rate of thinning became smaller and smaller as the limiting thickness was approached. The rate of thinning of the second black was so great, at first, that usually ie limiting thickness was weaned before observations: could be made. The persistence of the black films at the limiting thickness, together with the tendency to reach this condition quickly, seems to indicate that the films were of quite uniform thickness, at the limit. The data in Table IJ. were taken from a number of tables similar to Table I. The thickness is given in micro- millimetres (um). 750 Dr. E. 8S. Johonnott on the TaBueE LI. A. Limiting Thickness of First. Black Film. 11:05, 12:20, 12:20, 13°15, 11°10, 12°30, 11:75, 12°60, 13°30. B. Mean Thickness of the Second Black Film. 6:03, 6-24, * 9:25, 5°52, 617, 5:05, 6:28, *7-30, * 9:50, 5°40, 6-40, * 80. Mean It would be difficult, in section B, to distinguish between the values corresponding to the unstable condition and the condition of limiting thickness. The larger values, marked with the asterisk, were, however, in all cases followed by smaller values included in the table. If we take the mean of the values, not including these larger values, to determine the limiting thickness of the second black, we obtain 5°88 my. This would indicate that the limiting thickness of the second black is, approximately, half that of the first. No very great thickness was measured in the first black, since it was impossible to count the coloured fringes for such large deflexions. Variable Atmospheric Pressure.—The following readings were obtained when changing the pressure on the atmosphere surrounding the films. TasxE III. | | : Fringes | No. | Mean | Temp.|Pressure Time. | “geflect. | films. | thick. | ° ©. | change. oe A.M. py ems, Hg 9.08 films | formed. 178 9.32 30 101 26°38 | 20°70 | none. | All first black. 9.50 2°3 100 20°3 20:0 ” 23 ” 10.20 2:0 98 18:0 21:0 ” 99 ” —46 34 98 30°6 a0 3 98 +9°2 | All second black. 10.23 ‘9 98 81 | 216 oie 9 ie System) allowed 'to comje to normal pres/sure. 10.40 20 97 18-2 none, | All first black. —6°4 | 42 96 38°5 see ” ” | +128 95 84 | 21:2 Sse All second black. 10.44 ‘9 | a Black Spot in Thin Liquid Films. 751 A large bottle, containing some of the solution, was con- nected to the film-box by a long rubber tube. The pressure was altered by changing the elevation of this bottle. As shown in the table, the films were allowed to thin to the first black, then the pressure was diminished by 4°6 cms. of mercury. This caused the films to thicken from 18 pp to 30°6 wy. The pressure was then increased by 9:2 cms., and the films were quickly thinned to the second black at a mean thickness of 8°1 pp. Surface-tension in the Black Film.—In this connexion it may be of some interest to describe some work that was undertaken to determine the surface-tension in the black film. The method of Sondhaus * was employed. A ring, 15 centimetres in diameter, was made of glass- fibre. This was attached to one arm of a sensitive Oertling balance and lifted trom the surface of the solution. The film formed, although a catenoid, was quite approximately a cylinder. ie following table is a typical record of the observations made. TasueE LV. Age of | Supporting} Surface- | Temp. Pec film. fc 5 tension. 2 O: Bomarks: min. mgs. mgs.percm. 2495 26°5 24:0 No colour. 2 2475 26°35 238 Coloured quickly. 8 2465 26°20 aie 5 per cent. first black. 18 2455 26°07 at All % 9 | 29 2450 26:00 aes 10 per cent. second black. 37 2445 25°95 25 All 5 b, 44 2440 25°90 ao ss 6 “ | 56 2435 25°83 26 :s » » With these results plotted in a curve, it is quite evident that to the discontinuity in the thickness, there, apparently, corresponds no discontinuity in the tension. Otherwise, however, the varying rate with which the tension falls is quite similar to the manner in which the film thins. And it should be observed that these phenomena point to a variable condition in the second black film, both with respect to tension and thickness. The Five Black Films.—Viewing the films with a micro- * Sondhaus, Poge. Ann. Ergbd. vill. p. 266. (52 Dr. E. S. Johonnott on the scope, in the arrangement shown in fig. 1, it is oftentimes possible to distinguish as many as five black films. These break, one into another, in the same manner in which the black film is ordinarily formed, each succeeding film being, apparently, the thinner. The first three formed are, how- ever, quite evanescent and seldom extend over an elevation greater than two or three millimetres. The fourth and fifth are identical with those which have been termed the first and second black films, respectively. Oftentimes all five films are in the field of view at once. Speculations—The apparent continuity of the surface- tension in passing from one black film to the other has been observed by Professors Reinold and Riicker. Based on what may be termed Lord Kelvin’s* minimum surface- tension principle, they suppose the tension to remain constant as the films thin to the limiting thickness of the coloured film. Then the tension is supposed to fall as the film continues to thin until a minimum tension is reached, after. which the tension rises. Now it is evident that, for these thinner films, equilibrium could not be reached unless the thinning continues so far that the tension again rises to that of the coloured film. On this theory it should be possible to have the black film in equilibrium with the coloured film of various thicknesses. Their experimental observations substantiate this theory in a very interesting manner. If a discontinuity occurs in the thickness between the successive black films, it is reasonable to suppose, as Poynting and Thomsen } have remarked, that a variation in the tension, similar to that which has been described, takes place. Laplace’s theory of capillarity shows that the inference to be drawn is that we have alternate molecular forces of attraction and repulsion as we pass from one black film to the next. Or according to the mioimum surface-tension principle, there should be as many undulations in the curve representing thickness and tension as there are black filins. Another theory of these discontinuities might be proposed, which may be little more than an analogy. Long ago, Professor James Thomson f, in discussing the unstable condition supposed to exist between the super- * Phil. Trans. 1886, Part 11. p. 679. T ‘ Properties of Matter,’ p. 166. t Maxwell, ‘ Theory of Heat,’ p. 127. Black Spot in Thin Liquid Films. 733 saturated vapour and superattenuated liquid states, says :— “ We cannot expect experimental evidence on this part of the curve unless this state of things may exist in some part of the thin superficial stratum of transition from the liquid to its own gas, in which the phenomena of capillarity take lace.” : Suppose that we imagine a liquid film in equilibrium with its surrounding saturated atmosphere. Let heat be applied to the system. nen may it not be that the film will become coated with a thin stratum of superattenuated liquid which will continue to thicken until, possibly, its outer portion passes over into the unstable condition, causing the attenuated layer quickly to evaporate ? If, on the other hand, heat taken from the system should produce a corresponding layer of supersaturated vapour next to the film, it should be expected that a thickening of the film would result from condensation. Observations made with the apparatus shown in fig. 1 accord with this theory. For example, suppose that we obtain a first black filin near its limiting thickness, so that a slight increase in the pressure will cause the second black film to appear. This second black at first appears as small, perfectly round, black spots in the first black film, which expand to replace the first black as the pressure is increased. If then the pressure be slightly lessened, perfectly round spots of the first black will appear in the field of the second black film. This latter effect is more difficult to obtain than the former, indicating that the supersaturated vapour con- dition is more difficult to realize than the superattenuated liquid. In fact, the thickening process ordinarily is so rapid that a second black film will appear to pass, as has already been remarked, continuously, to even the yellow of the first order. Of course this is merely speculation. Possibly the best excuse for making such is contained in the following words of Maxwell :—“'The surface which forms the boundary be- tween a liquid and its vapour is the seat of phenomena, on the careful study of which depends much of our future pro- gress in the knowledge of the constitution of matter.” Rose Polytechnic Institute, Terre Haute, Indiana, Feb. 14, 1906. ie vat dl LXIX. The « Particles of Uranium and Thorium. By W. H. Braae, I.A., Elder Professor of Mathematics and Physies an the University of Adelaide *. HIS paper is divided into two parts. The first contains a discussion of the magnitude of the ionization current due to a layer of radioactive material scattered on the floor of an ionization-chamber, and covered by a uniform sheet of metal foil. The result is expressed in a formula which is somewhat complicated in its general form, but is capable of simplification under suitable conditions. Account is taken of the variation of ionization with velocity. The second contains an account of experiments which show:— (a) That the values of the current in various cases, calcu- lated from the formula, agree very well with the results of observation. (6) That the ranges of the a particles of uranium and thorium are very nearly, perhaps exactly, equal to the range of the @ particle of radium. (c) That the rate at which thorium atoms break down is nearly ‘19 of the similar rate for uranium. Part 1. The method which was used by Mr. Kleeman and myself in the determination of the ranges of the a particles emitted by radium and its products does not lend itself to the corre- sponding determinations in the cases of uranium and thorium. It is a necessary feature of the method that all « particles except those moving normally to the horizontal layer of radioactive material should be prevented from reaching the lonization-chamber, below which the radium is placed. This is done by the use of a bundle of vertical tubes which stop all 2 particles other than those moving in the desired direction. But this limitation diminishes very greatly the number of effective « particles, and in the cases of uranium and thorium the effect is reduced below the limits of con- venient measurement. ‘This is the case even when a large surface of radioactive material is employed. In order to determine the ranges of uranium and thorium another method must be devised. I have therefore calculated the ionization due to a radio- active layer over which a screen has been placed. The result is a function of the relation of the stopping power of the * Communicated by the Author. The « Particles of Uranium and Thorium. 755 screen to the range of the particle: so that if experiment is made the one can be found in terms of the other. The stopping power of the screen may be made the subject of a direct measurement, and so the range of the a particle can be determined. I find it better, however, to compare the range of the uranium or thorium e particle with that of radium, working the experiment by a substitution method: for the range in the case of radium is known with some accuracy, and the method itself is accurate enough when employed in comparing ranges, but a little uncertain in its application to direct determinations, as will be explained later. Experiments of this kind have already been made by several observers, notably by Professor Rutherford and Miss Brooks (Phil. Mag. July 1900). But at the time when they were made it was believed that the ‘a rays” were absorbed according to an exponential law: it was not known that each « particle possessed a definite range or penetrating power. Consequently the results were not in all cases expressed in such a way as to render them available for the calculation of the range. I have therefore found it con- venient to repeat them. In the following theoretical treatment of the question three cases are considered :— (a) When the layer of radioactive material is so thick that the a rays from the bottom of it are unable to reach the air above: such a thickness is of the order "002 cm. (6) When the layer is extremely thin. (c) When the layer is thicker than in (6) but not so thick ashi (@)s The first and second are really special cases of the third. Uranium and thorium are conveniently treated under case (a); radium under (c) ; and the induced activities under (0). Cask (a): Thack layer of radioactive material over which a sheet of absorbing material is laidi—Let the surface of the radioactive material be of unit area: the full range of the a particle in air be R, and the range lost by passing normally through the absorbing sheet be D. Let the stopping power of the radioactive material per radioactive atom bes. This means that if an a particle passes, parallel to the axis, along a cylinder containing only as much matter as goes with one radioactive atom of the radioactive material, the loss of range is, on the average of a great number of such passages, s times the loss when an average air molecule is substituted for the other matter. The length of the cylinder is, of course, immaterial. 756 Prof. W. H. Bragg on the The @ particles, when they emerge into the air, will pene- trate to distances depending on the quantity of matter traversed before emerging. Consider in the first place all those whose ranges in air after emergence lie between r and r+dr. These move at various inclinations to the surface: the number emerging at any inclination depends on that inclination, and may be reckoned as follows. Consider only those whose inclinations to the normal lie between @ and 0+d6@. All these come from a layer of a certain thickness at a certain depth below the surface. The depth does not concern us, but the thickness does, for we need to know the number of radioactive atoms in the layer. Let n be the number of radioactive atoms in a cub. cent. of the material, n) the number of molecules ina cub. cent. of air. Ana particle loses the same range in traversing a distance ér in air, as in traversing a distance mdr/ns in the radioactive Absorbing layer. htadioaclive material | 9 material. Hence if PP’ is the layer in question, O the radioactive atom, OS the course of the @ particle, we have OQ = nor/ns and ON = norcos @/ns. This last expression is also the volume of the layer from which the a particles come, since we are considering unit area of the material ; and therefore the number of radioactive atoms in it is ndr cos 6/s. Let each atom emit N e@ particles per second. N is a very small fraction. Then the number emitted by each particle between the inclinations 6 and 6+ d@ is N . 2a sin 0. 60/4 = N sin 6. 80/2. Hence finally the number of @ particles whose ranges in air after emergence lie between r and 7+ 6,7, and which have inclinations to the normal varying from @ to 0+ 68, is N sin @. ny cos 067r66/2s. The limits of @ are zero and such a value of @ that the a particles which come from the very surface of the radioactive a Particles of Uranium and Thorium. 757 material and move at this inclination to the normal have a range 7 in the air after penetrating the absorbing sheet. This value of @ is given by Dsec@+r = R. Integrating between these limits we find that the total number of e particles whose ranges lie between r and r+6r _ Nn { D? as 1 (Ree i Each of these moves a distance r through the air of the ionization chamber before it ceases to ionize. Now I have shown (Phil. Mag. Nov. 1905) that the @ particle spends energy on ionization at a rate which is inversely proportional to the energy which it possesses; so that we may say that de = kér/e, where e is the energy of the particle and de the energy spent in traversing a distance ér._ Hence we find that ex “(r+c), where ¢ is a constant. The value of the latter I have shown (loc. cit.) to be 1°33.. Hence the ioni- zation produced by the @ particle in the last r cm. before it ceases to ionize may be written l/r + 1:33 —4/1°38). Even if this expression should prove to be based on im- perfect theory, it nevertheless expresses the actual fact very nearly. Finally, therefore, the whole ionization (=?) — Nin eas f DD? Seer 75 Ta {, ‘ beer | (/rt+d—/ad)dr, the proper limits being given to r in the integral. After some reduction the value of this integral can be found to be Nin ted _ R/Sd d ph? BR ARES Rea +—— log = ; VR ed J/D(/R+d+V/a) If we put D=0, we obtain the value of the current (I) when the radioactive material is uncovered, viz.: Ning 7-5 a 2q8 7h T= —"(3(R+d)i-34_RyV/d}. Simpler formulz may be found by neglecting the variation of ionization with velocity. Ifwe put the ionization due to 758 Prof. W. H. Bragg on the traversing 7 cm. equal to l’r, we find that a NUL ots ee and I= Niing R?. 8s Curves may be plotted from these formule giving the relation between 7/I and D/R. In the case of the latter FULL CURRENT=/ 3 | “2 FULL RANGE = formula the form of the curve is independent of the value of R; but in the more accurate formula it is not. Actual trial shows, however, that the curve in this case shifts very little when the value of R is altered, and always lies close to that given by the simpler formula. In the interpretation of the experiments with uranium and thorium, I have used the curve A (see fig. 1) in which R=5: it gives results of a Particles of Uranium and Thorium. 759 sufficient accuracy, though the actual value of the range of the a particle from these substances is nearly 3:5. The curve is plotted from the following figures: — D/R... | 067 | -110 | °167 | :250 | °333 -442°| -568 | ‘667 | °833 A Nae scon -773 | -657 | 532 | °378 | 262 | 148 | ‘069 | -030 | ‘010 Case (b). Very thin layer of radioactive material.—Let D be the air equivalent of the layer of radioactive material, i. e.the loss of range which an @ particle would experience in crossing the layer normally. The limits of @ are now 6,+ 4), where D sec 0, +7=R and (D+D") sec @,+r=R. Hence the total number of particles whose ranges lie between r and 7+ 67 is ji Nm ((D+D¥__D_ fe (Re (iar Nn, DD’ or 2s (Rar)? Hence the ionization (2) = tl eee 0 neglecting 1D”. (an) NimD! (py) /g_—P JS R(i/R+d+/ R4+d—D) 2s uy of ag J/D(/R+d4vV a) i and when D=0, the ionization (I) _ NinD’ 5, (VR +d—V a}. If we had here neglected the variation of ionization with velocity and supposed the ionization caused in traversing a distance r to be proportional to 7, we should have found that ND) D D 1h “Yo (R—D+ nee): More difference is made in this case by neglecting the variation of ionization with velocity. Curve B is plotted from the more accurate formula for the values R=7, d=1°33. The curve is plotted from the following figures :— D/R... | O61 -|. 124 "833 ile ‘807 | 672 023 | i) Re ‘467 | -335 500 | -690 aga cOCr 760 _ Prof. W. H. Bragg on the Case (c). Layer of moderate thickness.—Let the air equi- valent of the radioactive layer be D’. This case must be considered in two parts :— (a) When ris such that D+D’+r and those of », 0 and cos” ps Hence Nae eo D2 j opades | aici | /r+d—/d)dr Ning R-D-D’ (D+D’)?—D?? a % 4s i { (R—r)? $ (/r+d—V/d)dr. and = 3(R+d—D)'—3(R+d—D—D!)'— 2’ vd-D/ RD mt td elo Db? / D+ D'(4/R+d+./R+d—Dy 4+ (D+D)/(R+d-D—D'+ Jk+d °./D(/R+d+./R+d—D—D) _ DP+2DD"). VRC VW R+d+ VWR+d—D—D) Curve C shows the result of plotting this formula for the Gase when R=3 5, Dd ,and d= 133. The curve is plotted from the following figures :— 200 | =257.| “380-500 || sla DR es Obi =) e143 ‘39 | “449 | 288 | “174 | 044 Ai, 833 | -642 Parr Il. The apparatus employed was of the usual form, and very similar to that described by Rutherford (‘ Radioactivity,’ 1905, p. 98). As shown in fig. 2, the material was laid on the high-potential plate B, at such a distance from the upper plate A that no @ particle could reach it. Thus every a@ par- ticle ran to its extreme range; and, to make more certain of catching all the ions, the upper plate was extended down- wards at the sides. /R+d ~ /D+D'( Rae ~ + ee ee jo a Particles of Uranium and Thorium. 761 Uranium. The uranium was used in the form of the green oxide, U3Qx, and was freed for the time from UrX. This was not ne- cessary, but convenient, as it diminished the @ ray correction. Fig. 2. To BATTERY The uranium was ground toa fine powder and placed in a shallow depression turned in a metal plate, the diameter of the recess being 3°17 and the depth =, inch, which was far more than enough to make sure that the a rays from the lowest stratum could not get out. The surface of the material was carefully smoothed by the aid of a polished metal plate. A potential of 300 volts was used, which was nearly sufficient to saturate: more was not necessary, as only relative ioni- zations were in question. Aluminium-foil was used as the absorbing layer: the weight and area of each piece being measured so as to obtain the product of the density (0) and the thickness (d). In the following table (p. 762) the first column gives the value of pd of the foil used, and the second the corresponding current, being the mean of five readings of the leak for ten seconds. The last line shows that when two layers of tinfoil were added to the aluminium-foil already covering the uranium, the leak was reduced to 34. ach layer of foil was equi- valent to about 17 mm. of air, and the aluminium to about 21; so that the whole cut off the a rays completely, for their range was known to be not more than 3°5 cm. This leak of 34 was therefore due to 8 rays and the normal leak of the apparatus. The third column shows the result of subtracting 34 from all the figures of the second column and reducing to a decimal of I. The numbers so obtained have then been Phil, Mag. 8. 6. Vol. 11. No. 66, June 1906. 3 D 762 Prof. W. H. Bragg on the 1% TT. if OE iy: V. : , From d of full 6 p pa x10" e: = Curve A. | range X 10°. 0 1044 1-000 TH 317 811 "768 ‘0705 448 633 635 "595 139 462 949 494 "456 "205 463 1265 376 °339 "275 460 1620 275 239 “B00 458 1930 201 "165 "495 455 2610 97 "062 580 449 3290 55 021 ‘718 458 +2 layers of tinfoil. 34 0 considered as so many ordinates of the thick-layer curve A; and the corresponding abscissee found and placed in the fourth column. It was then possible to obtain from each reading a determination of the pd of that aluminium sheet which the a@ particle of Ur could just penetrate. For example, the table shows that the sheet for which pd=‘000949 is 20°5 per cent. of the necessary thickness, and so the pd of the fully intercepting sheet is °000949/:205=:00463. All these separate determinations are shown in the fifth column. Their close agreement with each other is good evidence of the truth of the formula used in obtaining them. Taking ‘00456 as the mean of the figures in the last column, the final result may be thus stated:— The a@ particle of uranium can just penetrate a sheet of aluminium for which pd=:00456. Although this may at once be interpreted so as to give the range of the a particle in air, yet it is better to measure the ranges of radium and thorium also in terms of aluminium-foil. Radium. The application of this method to thorium and radium is somewhat more difficult than in the case of uranium, since it is necessary for success that the radioactive material should issue a particles of one range only. It might no doubt be possible to allow for the existence of other a particles if their range and relative number were known. Some method of — this kind must doubtless be used for Th X, and Th emanation. But it is obviously more direct, in the case of radium and thorium, to deal with the pure materials, if possible. Re iam a Particles of Uranium and Thorium. 763 A very small quantity of radium bromide was evaporated on a platinum plate, which was then raised to a bright red heat for some minutes. This freed the radium from ema- nation, Ra A, and some RaC. The ionization current due to this plate fell off quickly; and in three hours was down to half its first value. The remaining RaC had then disappeared. It was reheated, to get rid of any fresh emanation; and it was then assumed that the great majority of the a particles emitted from the plate were due to radium itself (Bragg & Kleeman, Phil. Mag. Sept. 1905, p. 324). The following table shows the result of experiment with the plate so prepared. The aluminium-foils were the same as those used in the uranium experiments. The curve em- ployed was of course not the same, since the layer was thin. According to the experiments of Kleeman and myself such a layer may be considered as equivalent to 5 mm. of air. The results were therefore calculated from curve C. E. iit tole IV. V. pax 10". G yi. cence ae soc 108 0 1454 1:000 317 1126 772 O75 423 633 927 634 143 443 949 765 522 204 473 1265 645 426 265 ATT 1617 488 331 343 472 1933 388 261 ‘407 476 2613 216 150 582 473 3289 104 ‘072 675 488 Tinfoil 11 0 These figures show an agreement between calculation and observation which is nearly as good as in the case of uranium. There is indeed a gradual increase in the figures of the last column; but such an effect should be expected, as there were present some a particles of longer range than those of radium, but none of shorter range. Neglecting this effect, the mean of the results of the last column is 466; and we may take this to express the product of the thickness and density of that aluminium sheet which the @ particle of radium can just penetrate, with the reservation that itis probably too high by a small but uncertain amount, the error being caused by a slight want of purity in the material used. This statement 3) De 764 Prof. W. H. Bragg on the applies only in considering the relative ranges of uranium and thorium; other considerations enter when the method is used to determine ranges absolutely. The falling of the first two results in column V. below the average of the column may in part be due to the fact that the first layer or two must cut off the easily absorbed radiation whose existence has been proved by J.J. Thomson and by Rutherford. I am not aware of any measurement of the amount of ionization due to this radiation. If in this expe- riment only 4 per cent. of the whole ionization current when the material is uncovered is supposed due to this cause, and if the foil whose pd=:000317 cuts off three quarters of it and the next addition of foil the remainder, then the figures in the last column become, in order, 488, 487, 487, 496, 486, 490, 502, 514. Thus the existence of a small quantity of radiation of this sort would explain the present discrepancies in the experiment. It will be seen later that a similar effect occurs with thorium. It is not so noticeable in the uranium experiment, as will be seen on turning back to the table of results. Still the first of these is rather smaller than the others; and a special measurement made with a very thin layer for which pd=-000133 gave a value for the full range equal to ‘00426, which is smaller still. nip OF As a further test of the method, I have used it to determine the range of the a particle of RaC. The special difficulty in this case was due to the rapid decline of the activity. It was avoided by taking readings of the current due to the uncovered active plate before and after each measurement with the covered plate. The geometric mean of these was taken and compared with the smaller measurement. ‘The readings were properly spaced in time, so as to make this correct. The leak due to 8 rays and external causes was found by placing six sheets of tinfoil, each equivalent to about 15 mm. of air, over the active plate. Tinfoil was used as the absorbing sheet. The results were as follows :— I. Preis: ce III. IV. OR ae if. From Curve B, | 07 of fat range 479 518 34-2 224 98 | 935 73:0 210 | 1437 072 1125 204 | a Particles of Uranium and Thorium. 765 The results are in rather better agreement with theory than the last column seems at first sight to show ; for the first and third observations fell on such points of the curve that errors of measurement were magnified in calculating the result. The second measurement has the greatest chance of being accurate, and is very nearly the mean of the three. An independent experiment showed that tinfoil for which pd= "000536 was equivalent to 1°88 cm. of air. Hence the range of the a particle found by this method = 210 x 1°88/535 = 7-4. The value found by Kleeman and myself, using the direct and more accurate method, was 7°1 nearly. Thorium. The material was used in the form of thorium oxide which had been freed as far as possible from other radioactive substances by means of the processes described by Rutherford and Soddy. The treatment employed, which included heating to a bright red heat as the final stage, was judged to have been successful for the following reasons. In the first place, the recovery of activity was not marked by an initial drop, so far as could be observed : in the second, it rose at a rate which showed that it would be haifway to the final value in four days, the final value being about four times the initial. In the third place, no emanation came off the material when first prepared; even when no draught was employed the readings did not alter in 15 minutes: and in the fourth place, the observed results fitted closely to the caleulated curves, showing only a slight variation as in the case of the radium. The results of one experiment are shown in the following table :— I. IT. III. TV. He od of full range pd i ase a/I. From Curve A. 4 ake. 244 &13 055 444 474 670 108 439 780 544 162 480 1061 412, "227 468 1573 "271 328 480 2073 1735 "417 499 2607 ‘106 ‘d04 517 The mean of the figures in the last column is ‘00477. 766 Prof. W. H. Bragg on the In another experiment the thorium was_ precipitated twice at intervals of two days and then five times at intervals of 12 hours. The results were as follows :— if 1D Lhe Ve oe os A a/I. From Curve A. | 4% 0 ge 534 "655 114 470 1046 "425 “221 473 1633 "248 "347 471 2133 154 "438 486 In this case the mean of the figures in the last column is "00475. As in the case of radium, this result is probably a little too high as it is impossible to get rid of all the radioactive products of thorium, and all these have ranges higher than thorium itself. For Rutherford has shown that the a particle of the induced activity of thorium has the same penetrating power as the a particle of the induced activity of radium; and some rough experiments which I have made with ThX go to show that, as in the case of Ra, the second and third active products have ranges intermediate between the first and fourth *. It may also be calculated from an experiment of Ruther- ford’s (‘ Radioactivity ’ 2nd ed. p. 263) that the range of the emanation a@ particle is about 6 cm.; but there is some uncertainty as to the stopping power of the mica sheet which he used. The general conclusion is therefore that uranium, thorium, and radium eject 2 particles of nearly, if not exactly, the same speed. Considering the many parallelisms already known to exist between the processes of disintegration of these substances and their products, this new fact is certainly suggestive. It would be very interesting to know the ranges of Th X and Th emanation. An expression is found in Part J. of this paper for the total ionization over an uncovered deep layer of active * An experiment by Schmidt (Phys. Zeit. No. 25, p. 897) has shown that Ra A has two-thirds of the penetrating power of RaC. Hence its range must be the longer of the two intermediate ranges, determined by Kleeman and myself, viz. 4:83; and the range of the emanation must be 4:23. Thus in the radioactive sequence each explosion is more violent than the last. a Particles of Uranum and Thorium. 767 material. By its aid we may find the relative numbers of a particles emitted by uranium and thorinm, when the ionization currents due to known areas of the layers have been measured. Since the ranges are so nearly alike, it is sufficient to use the simpler formula Nin 2 it 85 . R?, If now the suffixes U and T refer to uranium and thorium, we have Iy Lis N uRise : and therefore Nr Hed TrRysr Each time that a thorium experiment was completed, a comparison was madé of the currents Iy and Iy. In the first case Iy/Iy was found to be °234, in the second *234. (Ry/Ry)?, as may be seen from the results given above, can be taken as equal to (456/476 )?=-916. Also sp _ V 232 +24/16 _ 23-2 su 4/2394+8V16 2672” assuming the square-root law (Bragg and Kleeman, Phil. Mag. Sept. 1905) to hold for uranium and thorium. Hence finally New 23-2 N, = 234K 916x 555 SKU) This result may bea little too small, since the range of the a particle of thorium may be slightly overestimated. The square of the range enters into the formula of comparison ; but on the other hand, any @ rays of long range which have not been removed from the thorium would make Ir too large. On the whole, therefore, the actual value cannot be far from "20; 7. e. the uranium atoms break down very nearly five times as fast as the thorium. I have preferred to make the method one of comparison of ranges rather than of absolute determination. For there are two or three difficulties in using it for the latter purpose, In 768 The a Particles of Uranium and Thorium. the first place, it is not easy to make the thin aluminium-leaf lie very close to the radiating surface ; and the layers of air close to the surface contribute a relatively large number of ions. ‘To make this error uniform I have used a net of very fine wires, with a mesh of 2 of an inch to keep the foils down. Again, there is a disturbing effect due to the secondary ionization of the absorbing sheet. Mme. Curie has called attention to effects of this kind (Rutherford, ‘ Radioactivity,’ 1905, p. 189). JI find that there is slightly more ionization when, of two layers of foil, Al and Sn, the latter is on top. Using tinfoil, the range always comes out rather larger than when aluminium-foil is employed. This may possibly be - because the tinfoil lies closer to the surface. All these effects are small, and disappear in a comparison method. By direct measurement I found that aluminium-foil for which pd=:00329 was equivalent to 2°30 em. of air. Hence the range of the a particle of radium as measured by this method = 2°30 x 466/329=3°26. The actual value, as found directly, is 3°54. One other difficulty lies in the way of a direct determination. As has already been mentioned bv Kleeman and myself (Phil. Mag. Sept. 1905), the loss of range of the @ particle of Ra C in going through a given sheet of material appears from the ionization curves to be slightly greater than the loss of an a particle of Ra A; and it is not quite clear whether this difference is real or apparent. I owe my grateful thanks to Dr. W. T. Cooke who carried out for me all the necessary chemical operations. Since the above was written I have received the February number of the Philosophical Magazine containing an article by Mr. N. R. Campbell on “The Radiation from Ordinary Materials.” In finding the formule necessary to his investi- gation, Mr. Campbell has anticipated part of the work in Part I. of this paper; but as the fuller treatment which I have given is required for my own experiment, I have thought it better to allow it to stand without alteration. In a footnote Mr. Campbell expresses his inability to understand why I inserted an obliquity factor cos @ into the preliminary calculations in my first paper on the @ rays (Phil. Mag. Dec. 1904). The mistake is mine. I did not discover it until I had occasion to reconsider the matter in connexion with the present investigation. ewogn | LXX. On the Number of Corpuscles in an Atom. By Prof. J. J. Toouson, M.A., F.RS* [ CONSIDER in this paper three methods of determining the number of corpuscles in an atom of an elementary substance, all of which lead to the conclusion that this number is of the same order as the atomic weight of the substance. Two of these methods show in addition that the ratio of the number of corpuscles in the atom to the atomic weight of the element is the same for all elements. The data at present available indicate that the number of corpuscles in the atom is equal to the atomic weight. As, however, the evidence is rather indirect and the data) are not very numerous, further investigation is necessary before we can be sure of this equality ; the evidence at present available seems, however, sufficient to establish the conclusion that the number of corpuscles is not greatly different from the atomic weight. It will be seen that the methods are very different and deal with widely separated physical phenomena; and although no one of the methods can, I think, be regarded as quite con- elusive by itself, the evidence becomes very strong when we find that such different methods lead to practically identical results. To enable the argument to be more easily followed, I shall begin with a general description of the. methods and the results to which they lead, and postpone the details of the theory of each of the methods to the latter part of the paper. ‘The first method is founded on the dispersion of light by gases. If we regard an atom as consisting of a number of corpuscles dispersed through a sphere of uniform positive electrification, it is evident that the dispersive power of a medium consisting of these atoms will depend upon the mass of the positive electrification as well as upon the mass of the corpuscles, and will vanish if either of these masses is zero. For consider what takes place when the electric force in the light-wave strikes the atom. Since the wave-length is large compared with an atom, the latter may be regarded as being in a uniform electric field ; under this field the corpuscles will be displaced in one direction, the positive sphere in the opposite; and if the force persists long enough, this displace- ment will go on until the force exerted on the corpuscles in their displaced position by the positive electricity is equal and * Communicated by the Author. 770 Prof. J. J. Thomson on the opposite to the force exerted on them by the electric force in the light-wave. The displacement of the corpuscles relatively to the sphere of positive electricity will polarize the atom, and the collection of polarized atoms will increase the specific inductive capacity, and therefore the refractive index of the medium. If the mass of either the positive electricity or of the corpuscles were zero, then, however short the time for which the electric force in the light-wave acted, the corpuscles and the positive electricity would adjust themselves in exactly the same way as if the electric force were continuous ; so that the specific inductive capacity and the refractive index would be the same for short waves as for long, and there would be no dispersion. If, however, the masses of both the positive electricity and the corpuscles are finite, the relative displace- ment of the corpuscles and the positive electricity will depend upon the period of the electric force; and since the specific inductive capacity and refractive index depend upon this displacement, the refractive index of the medium will depend upon the period of the electric force, and there will be dispersion. In the latter part of the paper the expression for the refractive index of a monatomic gas is investigated; and it is shown that if w is the refractive index of such a gas for light of frequency p, then wW—-1l_ = 4m7NE(Me+mE) (1) we+2 4ap(Me+mE)—Mmp” ° ~ * where N is the number of atoms in unit volume of the gas, m the mass of a corpuscle, M the mass of the sphere of positive electrification, e the charge on a corpuscle, E the whole charge on the sphere of positive electrification, p the density of the electrification in this sphere; e, H, and p are expressed in electrostatic measure. If the term in p? is small, equation (1) may be written | Mn se) ge a) E ¢ M+nm 4zp since E=ne, where 2 is the number of corpuscles in the atom. If a is the radius of the sphere of positive electri- fication, H=4-pa’, 2. e. Ae =N47a’?=volume of the atoms per cubic centimetre of gas; this is the value of w?—1/y?+2 when p=0, 7. e. for infinitely long waves. Writing Po for Number of Corpuscles in an Atom. iy i this quantity, we see, if X is the wave-length of the light, eal gm ar 24g tot tO RT NOM tam) 0? ) where EH’ and e’ are the values of E and ¢ in electromagnetic measure. This is the expression for the refractive index of a monatomic gas. I have not been able to find any deter- minations of the dispersion of such gases. Lord Rayleigh, however, found that the dispersion of helium was of the same order as that of diatomic gases. If the atoms in the molecules of a diatomic gas are not charged, the preceding expression will hold for the refractive index of such a gas ; if, however, the atoms carry electrical charges, the theory subsequently given shows that this expression has to be modified. We know that as a matter of fact the atomic refraction of some elements, oxygen for example, depends upon the kind of compound in which the oxygen is found. This variation may be ascribed to the charges carried by the atoms in the molecules. The atomic refraction of hydrogen seems, however, to be constant; and I shall, in the absence of data for monatomic gases, apply the preceding formula to this gas. From Ketteler’s measurements of the refractive index of hydrogen for light of ditferent wave-lengths, we find that for hydrogen at atmospheric pressure eet at _,. 2x 10-4 Hg = By 2014 x 10 4 oh. Comparing this with the equation | i 4p oM m i om pete 2 ON) i PIN IER an ee we find M m it pend ls ae ~8. Tamm oe but moe, = Teq x Ow amd Neen or hence 1 an Me He 1, approximately ; or, since K'=ne’, = Be rOximatel M+amn » approximately. This result shows (1) that » cannot differ much from unity, and (2) that M, the mass of the carriers of positive electricity, 772 Prof. J. J. Thomson on the cannot be small compared with nm, the mass of the carriers of negative electricity. Hence we infer that m, the number of corpuscles in a hydrogen atom, is not much greater than unity. This result has been deduced from the consideration of the properties of a diatomic molecule ; and if the atoms in the molecule were charged, the expression for (u?—1)/(u?+2) would have to be modified ; but since the dispersion of helium is by Lord Rayleigh’s result comparable with that of hydrogen, aes Mi we see, since the dispersion 1s proportional to Maca that there cannot be a very large number of corpuscles in the helium atom ; for if m were large, the dispersion of helium would be far too small. 2nd Method. Scattering of Réntgen Radiation by Gases.— It is shown in my ‘ Conduction of Electricity through Gases’ that when Rénigen rays pass through a medium in which there are N corpuscles per cubic centimetre, the energy in the radiation scattered per cubic centimetre of the medium is N 4 a where E is the energy of the primary radiation passing through the cubic centimetre, e the charge, and m the mass of the corpuscle. Barkia has shown that in the ease of gases the energy in the scattered radiation always bears, for the same gas, a constant ratio to the energy in the primary whatever be the nature of the rays, 7. e. whether they are hard or soft; and secondly, that the scattered energy is pro- portional to the mass of the gas. The first of these results is a confirmation of the theory, as the ratio of the energy scattered Q Soha - - O77 ~, se to that in the primary rays is = N(e*/m?), aud is independent of the nature of the rays; the second result shows that the number of corpuscles per cub. centim. is proportional to the mass of the gas: from this it follows that the number of corpuscles in an atom is proportional to the mass of the atom, z. é. to the atomic weight. Barkla measured the ratio of the energy in the scattered radiation to that in the primary in the case of air, and found that it was equal to 2-4 x 10—. Thus, for air 87 Ne eEeDS —4 3 ne =2°4x 10™. Now e/m=1'7 x 10‘ and e=1:1 x 10-”°; hence Ne=10. Number of Corpuscles in an Atom. 173 But if 2 is the number of molecules per c. c., ne="4; hence N=25n. From this we deduce that there are 25 corpuscles in each molecule of air, and this indicates that the number of cor- puscles in the atom is equal to the atomic weight ; for the scattering by air is very nearly the same as that by nitrogen, and 25, the number of corpuscles in the molecule deduced from Barkla’s experiment, is near to 28, the number in each molecule if the number in the atom were equal to the atomic weight. 3rd Method. Absorption of B Rays.—We regard the absorption of the 8 rays as due to the effect of the collisions between these rays and the corpuscles which they meet with in their path through the absorbing substance. If X is the coefficient of absorption, it is shown in the latter part of the paper that r _ 4aNe* V,* LaV? m t ar V4 3 log< =w55- Hoe Ne SAE RIN, 202 where N is the number of corpuscles per cubic centimetre, V the velocity of the 8 particles, Vo the velocity of light, e the charge ona corpuscle in electromagnetic measure, m the mass of a corpuscle, and @ a length comparable with the distance between the corpuscles in an atom. If 6 is the density of the absorbing substance, M the mass of an atom, n the number of corpusclesin the atom, we have L M=6; so that nr 2 4 2 Ne eee ee Te oe (5 ae ) m? M’° V8 DV ee Now 2/6 is approximately constant whatever be the nature of the absorbing substance ; hence since the logarithmic term only varies slowly, we conclude that x must be proportional to M, z. e. that the number of corpuscles in an atom is pro- portional to the atomic weight. To find the number of corpuscles in an atom, let us apply the formula to the case of the 8 particles from uranium, for which, as Becquerel has shown, V=1'6 x 10”; and Rutherford finds that for copper and silver A/6=7. Putting e/m=1°7 x 10”, e=10-29, V)=3 x 10%, we get Gems 1:4 x 104 54 HS =) 0 T74 Prof. J. J. Thomson on the The value of the logarithmic term is somewhat uncertain,. involving as it does the indeterminate quantity a; it cannot, however, be large enough to alter the order of the term on the right-hand side. If M’is the mass of the hydrogen atom, e ia M’ =10 9 hence we have . my M aA: M’ mV2 a 3 log ( Voie 1) 2. € nis of the same order as M/M’ the atomic weight of the element. Thus these three very different methods all lead to the result that the number of corpuscles in the atom of an element is of the same order as the atomic weight of the element ; and from the first method we conclude that the mass of the carrier of unit positive charge is large compared with that of the carrier of unit negative charge. If we suppose the whole mass of an atom to be that of its charged parts, e/m for positive unit charge would be of the order 10*. An obvious argument against the number of corpuscles in the atom being as small as these results indicate, is that the number of lines showing the Zeeman effect, which must therefore be due to the vibrations of corpuscles, in the spectrum, say, of iron is very much greater than the atomic weight of iron. This objection would be conclusive if it could be shown that all these lines are due to the vibrations of corpuscles inside the normal atom of iron; but I submit that there is no evidence that this is the case. Whenan atom of an element is giving out its spectrum either in a flame or in an electric. discharge, it is surrounded by a swarm of corpuscles; and combinations, not permanent indeed, but lasting sufficiently long for the emission of a large number of vibrations, might be expected to be formed. These systems would give out characteristic spectrum-lines; but these lines would be due, not to the vibrations of corpuscles inside the atom, but of corpuscles vibrating in the field of force outside the atom. Such lines would not be reversed by cold vapour, though they might be by very hot vapours, by the vapours in flames or in the neighbourhood of an electric discharge : the number of lines showing the Zeeman effect reversed by cold vapours is, however, very limited. We shall now proceed to consider the theory of the method on which the preceding results are based. Number of Corpuscles in an Atom. (ie Index of Refraction of a Collection of Atoms. If an atom consisting of corpuscles dispersed through a sphere of uniform positive electrification is in the path of a wave of light, the electric force in the wave will displace the corpuscles in the atom; the motion of these charged corpuscles will produce a magnetic field in addition to that in the wave before it struck the corpuscle; the existence of this field will alter the velocity of propagation of the wave by an amount which we shall attempt to calculate. Index of refraction of a monatomic gas whose atoms contain as much positive as negative electricity.—Consider an element of volume so small that throughout it the electric force in the wave may be regarded as constant. Throughout this volume the atoms will all be affected by the electric force in the same way. If &,,,, §- are the displacements parallel to the axes of x, y, 2 of the rth corpuscle of an atom, 2 the displacement of the centre of the sphere of positive electrification, e the negative charge on a corpuscle, E the charge of positive elec- trification in the sphere, N the number of atoms per unit volume; then X’, Y', Z’, the components of the electric force due to the displacement of the corpuscles, are given by the equations X'=47N(He— eé,) MeN (Ky Sen he ei ee ow CL) L' =4aN(Ez —Xe€,) the summation is for all the corpuscles in one atom. The equations of motion for the corpuscles and sphere of positive electrification are a?x M f= (X+X’)E —4mped(x—E.), 2 A oy NON geese where m is the mass of a corpuscle and M that ef the sphere of positive electrification. If all the quantities vary as ¢’?’, we get from these equations ese o ~ 42p(Me+ mE) —mMp” o. (X +X‘) HM 4aro(Me+mi) —mp* 2E.= 776 Prof. J. J. Thomson on the Therefore from equation (1) we have 4a7N(X+ X’) (mH? + MEHe) x A 4qrp(Me+ mE) —mMp? or WO ek aa pa where Bu 4arN (mi? + ME) vi 47rp (Me + mE) —mMp? In consequence of the motion of the charged corpuscles, Ky dX 4a dt’ where Ky is the specific inductive capacity of the ether; but this current plus the convection current N @ ae ae =); the current is no longer the polarization-current thus wu the total current parallel is given by the ae _K,dX, 3 dX’ "Agr dt Aa dt If a, 8, y are the components of the magnetic force, ap ad ATru= a3 ar and dB, 0X ah dy . dV Lak gue a d= Hence, since we have du OX x be ax "dt da dy?) The or CX 3d ed ea 4 VX ° dt? CE de a) es OX » BE CK ex ak, ae od? PR ae Saat) di? ee Hence, if » is the refractive index, a = il Sep i1—p’ or pr—1 ine 4a N (mE? + mEe) (2) wr+2 Farp(Me +mE)—mMp? ~* ° Number of Corpuscles in an Atom. 777 For very long waves, when the term mMp? may be neglected, we have _4eNE. $mp ° or, since H=4rpa*, where a is the radius of the sphere of positive electrification, 2 peta pi +2 This is the value given by Mossotti’s theory when the atoms are assumed to be perfectly conducting spheres of radius a. Case of a diatomic molecule, the atoms carrying electrical charges equal in magnitude and opposite in sign.—In this case the refractivity P will contain a term due to the motion of the charged atoms relatively to each other under the electric field due to the light-wave. We can calculate this term as follows :—Let M,, M, be the masses of the two atoms, EH’ the charge on the first atom, —E’ that on the other. Let 2, be the displacement of the centre of the first atom, x, that of the other. The equations of motion will be of the form = 4qNa’. dx, ! ms Poa XE'—¢(D)(«2,— 22), ad? 25 ; Moe — — XH — $(D)(«2—2), where #(D) is a function of D, the distance between the atoms, the value of this function depending on the law of force. If the variables as before vary as e‘?’, we find M,H'X (pS aE (Ma + M2) 6(D) — Ma Mop" nets M,E'X ee ih + Ma) 6D) — Mp The contribution to P of the motion due to the coordinates 21, L218 proportional to N'(u/G! -By'S?) N’E,?(M, + M,) 3) (Mi + Mz)¢(D) —M, Mg p?” where N’ is the number of these diatomic molecules per unit volume. The consideration of this expression shows that Phil. Mag. 8. 6. Vol. 11. No. 66. June 1906. 3 EK or to 778 Prof. J. J. Thomson on the the part of the refractivity arising from the coupling of two atoms together may easily be comparable with the part due to the corpuscles within the atom. Thus, to take the case when the waves are so long that we may neglect the term in p”, the contribution to the refractivity due to the coupling is N'E/? | ie If the force between the atoms changed as slowly as the force between the two charges H’ and —E’ at a distance D, $(D) would equal 2H?/D*, and (1) would become N’D? gre If we compare this with 2N'a?, the value due to the corpuscles inside the atom, a being the radius of the atom, we see that unless the force between the two atoms varies very rapidly with the distance, a considerable part of the refractivity may be due to the coupling between the atoms. If AP, is the part of (u?—1)/(uw?+2) when 2X is infinite due to the charges on the atoms in the diatomic molecule, we see from equation (3) that the part of (uw?—1)/(w?+2) due to these charges is approximately equal to ~ MM, 1. 4x? 6) ii, Bi,’ (i ) Nae where EH,’ is the value of the charge in electromagnetic units. In the case of a molecule consisting of two charged atoms, the charge on the negative atom will be due to the presence on the atom of extra corpuscles which can move freely about. Thus, if M, refers to the negative charge, M,/Hy,' will equal m/e, where m is the mass and e the charge on a corpuscle ; for the positive atom M, will equal the mass of the atom, while HE, will equal e, if the atoms are monovalent, 2e, if they are divalent, and so on. Comparing the part of the coefficient of 1/X? which is due to the charge on the atoms, with that (given by equation (2)) due to the corpuscles inside the atom, we see that the factor M,/H,’ in (5) is the same as mje’ in (2) ; while if there are many corpuscles in the atom, the factor i ae will be much larger than E AP, +(AP,)? (M + nm)’ for EH,’ will only be a small multiple of e,, while E is equa to ne,, where n is the number of corpuscles in the atom. Thus, unless AP, is very small compared with Po, the dis- Number of Corpuscles in an Atom. 779 persion of the gas will depend more on the charges of the atoms in a diatomic gas than on the corpuscles inside the individual atoms. The theory of the second method is given in my ‘ Con- duction of Hlectricity through Gases.’ We proceed to the consideration of the third method, which depends on the absorption by matter of rapidly moving corpuscles. If we suppose that an atom consists of a number of corpuscles distributed through positive electrification, we can find an expression for the absorption experienced by the corpuscles when they pass through a collection of a large number of such atoms. The rapidly moving corpuscle will penetrate the atom, and will be deflected when it comes near an inter-atomic corpuscle by the repulsion between the cor- puscles. This deflexion will produce an absorption of the cathode particles. If the corpuscle in the atom is held fixed by the forces acting upon it, the colliding corpusele will, after the collision, have the same velocity as before, though the direction of its motion will be deflected. If the inter- atomic corpuscle A is not fixed, the colliding corpuscle B will communicate some energy to it and will itself go off with diminished energy. Without solving the very com- plicated problem which presents itself when we take into account the forces exerted on A by the other corpuscles, we can form some idea of the effects produced by the constraint introduced by such forces by following the effects produced by increasing the mass of A. The general effect of great constraint would be represented by supposing the mass of A to be very large, while absence of constraint would be represented by supposing the mass of A to be equal to that of B. Let M,, M, be the masses of the corpuscles A and B respectively. We shall suppose that the velocity of the colliding corpuscle is so great that in comparison the cor- puscles in the atom may be regarded as at rest. Let V be the velocity of A before the collision, b the perpendicular let fall irom A ongV. It 26 is the angle through which the direction of relative motion is deflected by the collision, we can easily show that 1 b?V+/ M,M, 7a laa tae the force between two corpuscles separated by a distance r being assumed equal to e?/r?. Hence, if wu, u' are the 3 Hi 2 sin? @= é 780 Prof. J. J. Thomson on the velocities of B parallel to a before and after the collision, Miu M, W+M,- S008 (io the upper limit being determined by the condition that B comes into collision with the A corpuscles one at a time, so that the shortest distance between B and the corpuscle with which it comes into collision must be small compared with a, the distance between two corpuscles. If 7 is the shortest distance between the A and B corpuscles, we can easily show that 6? 2e? M, +M, Putting r=a, we see that b' is of order fa 2e7 M,+ M,\2 ( Wa MM, ) Integrating the expression on the right-hand side of equation (6), we get dU kad Lae) N 5 M, e*(M, + M,)? 1 (1 Fe al ), dx M, + M,. V4+(M,M,)? ee ra > M, Since the logarithmic term only varies slowly, we may put for b; any quantity of the same order without greatly affecting the result, putting yale eM ~ @&a MM, d a0 AdNe* (M, 4. M,) 5 aV? MM, ) ieee. Vs poe gS =. Number of Corpuscles in an Atom. 781 Thus U, the number of corpuscles crossing unit area in unit time, varies as e~**, where , — 4a Net (M, + My) vt Wi 1), Vi MM? 2 @ M+M, +)? X is the coefficient of absorption. If M,=M,, 2. e. if the corpuscles are quite free to move in the atom, eae fe ees 1) eM GN? | conus Hy If M, is infinite, ¢. ¢. if the corpuscles are held fixed by the forces between them, we have AmNe* 1 M,aV? ene a the value used in Method 3. We can get an approximate value of X very simply by the following method. Consider a stream of corpuscles moving horizontally ; the forward motion of any particle will be stopped by a collision in which its direction of motion is turned through an angle equal to or greater than a right i angle ; 7. e. if @ is equal to or greater than = or sin? @> : , sin’ 6 will be greater than 1/2 if e* (A42) SVE Mg he b? The number of collisions made by a corpuscle for which 6 is not greater than this value, as the corpuscle moves over a distance Az, is awNe* (M, ae A v west) 4* Hence, if U is the number of corpuscles crossing unit area in unit time, we have, if we neglect the effect of collisions which do not result in a total stoppage of the particle, au). Nae* /M,+M,\7 au. EA or, if » is the coefficient of absorption, y= Neat Mae ik cer) Se leit FOS LXXI. Fluorescence and Lambert’s Law. By R. W. Woon, Professor of Experimental Physics, Johns Hopkins University *. a is well known, the intensity of the radiation emitted from a surface element of a white-hot solid or liquid varies as the cosine of the angle of emission. The result of this circumstance is that the intrinsic intensity, or apparent luminosity of the surface, is independent of the direction in which it is viewed, not being increased by foreshortening of the surface. The same law does not hold in the case of a transparent gas, the intensity of a flat gas-flame increasing as it is turned edgewise. In this case the radiation of a surface element is constant in all directions, not varying with the cosine of the angle. It is worthy of note that the emission of X rays is governed by the same law that holds in the case of a gas, as can be shown by making photographs of the anti-cathode of an X-ray tube from directions normal to, and at nearly grazing incidence with the surface, with a pin-hole camera. This is rather what we should expect, for the radiations originate at the points where the electrons collide with the target, in other words in free space. The radiations from fluorescent surfaces sometimes appear to be goyerned by the same law. Ifa rectangular glass tank, or even a beaker glass, is partly filled with a solution of uranin (fluorescein) and a condenser discharge passed between cadmium electrodes close to the surface, the phenomenon can be very clearly seen. The surface is powerfully fluorescent, ~ and if it be viewed from below, the intrinsic intensity will be found to increase rapidly as the surface is foreshortened, becoming of dazzling brilliancy at grazing emission. If a glass plate is interposed between the spark and the fluid, the effect of foreshortening becomes less marked or disappears entirely, for in this case the fluorescence is chiefly caused by the radiations which penetrate the body of the fluid, and the powerful surface fluorescence, excited by the ultra-violet rays, disappears. A still better method is to illuminate one face of a right-angle prism of crown glass with the light of the spark, which causes a blue fluorescence of the surface-layer. The luminous surface is to be viewed through the other face of the prism. The intensity viewed in the normal direction is very slight, as can be seen by looking at the reflexion of the luminous surface in the hypothenuse face of the prism. Seen * Communicated by the Author. Fluorescence and Lambert’s Law. 753 edgewise the intensity is fully thirty times as great, as was found by measurement at an angle of 5 degrees with the surface. This increase in the intrinsic intensity of a fluorescent surface when seen foreshortened, from a point of view within the medium (so to speak), must have been noticed by many observers, but I have been unable to find any mention of it in the literature upon the subject. A very careful photometric study of the variation of the intensity with the angle has been made by my assistant, Mr. H. E. Ives, with apparatus arranged as shown in fig. 1. 7 A portion of the light from the spark fell upon the prism, while another portion, after traversing a sheet of ground glass, and a blue screen, was passed through a pair of Nicol prisms and reflected to the eye by means of the narrow strip of silvered glass A, mounted on a pivot in front of the prism. By turning one of the nicols the intensity of the light seen reflected in the strip could be balanced against the fluorescent background, against which it was seen. The colour was very accurately matched by means of a thin sheet of cobalt glass combined with a gelatine film stained with one of the blue aniline dyes. The intensity in the normal direction was measured by matching the reflected light against the image of the fluorescent surface seen by total reflexion in the prism. The fluorescent prism was mounted on the table of a small spectrometer and viewed through the telescope, the lenses of which were previously removed, and a small slit put in place of the eyepiece. In this way the angular direction from which the luminous surface was viewed could be easily determined. 784 Prof. R. W. Wood on A number of corrections were of course necessary, for the angles in air are greater than the angles within the glass, on account of refraction. Then, too, there is a smallloss due to reflexion within the prism which becomes greater as the angle is increased. The values obtained are shown graphically in fig. 2, Fig. 2. J ae iit | | | | at Ni} | | | ae SS Baie Oo a on intensities being plotted as ordinates, and angles as abscissa. The observed values, which have been corrected for the small loss due to internal reflexion, are represented by circles, while the curve drawn through them is the theoretical eurve, calculated on the assumption that the intensity of the radiation from each fluorescent molecule is independent of the direction within the glass. Under such conditions the intensity of the illumination of the surface would double each time its apparent area was halved by foreshortening. As will be seen, this condition appears to be pretty nearly — fulfilled, though accurate measurements between zero and five degrees were difficult. The fluorescent radiations obey therefore within the medium the same law which holds in the ease of a transparent radiating gas. Outside of the medium, that is in air, the case is very different. The intrinsic j Fluorescence and Lambert's Law. 785 intensity of the surface is greatest when it is viewed in the normal direction, while at grazing emergence scarcely any fluorescent light at all is visible. This is without doubt due to refraction, for the rays which emerge at grazing incidence were incident upon the boundary at very nearly the critical angle, and a large amount of energy is thus lost by reflexion. It is moreover clear that a cone of rays coming from a fluorescent molecule below the surface, which embraces a solid angle equal to twice the critical angle for the glass, is, upon refraction out into the air, spread out into a cone of 180 degrees, that is over a hemisphere. The intensity within the medium is in a corresponding degree increased by total reflexion, practically doubled in fact within a given angular range. To prove the existence of this reflexion of the fluo- rescent layer at the boundary between the two media, it is only necessary to place a cube of quartz in front of and against the fluorescing surface, witha small drop of glycerine pressed out between the two. The quartz and glycerine are both quite transparent to the radiations from the spark which excites the fluorescence ; consequently all changes which are observed are due solely to the alteration of the refractivity of the medium in front of the glass surface. The intensity of the fluorescence of the surface in contact with the glycerine will be found to be much less than the surrounding surface, when viewed from the glass side, while it is much greater when viewed from the quartz side. A more complete study could be made if the refractive index of the medium could be made the same on both sides of the fluorescent surface, or varied at will ; but it is difficult or impossible to find suitable media which are transparent to the ultra-violet waves which excite the fluorescence. If we try to get round this difficulty by using media which fluoresce under the influence of less easily absorbed radiations, we no longer have the fluorescence confined to the necessary shallow layer. The subject of fluorescence in its connexion with Lambert’s law has been discussed by Lommel in a paper which appeared in Wiedemann’s Annalen in 1880*. In this paper Lommel deduces Lambert’s law for a medium which has a high absorbing power, and which is emitting light in virtue of its high temperature. Applying the same method to a partially transparent medium, and to fluorescent media, he comes to the conclusion that in these cases the emission is not proportional to the cosine of the angle, but to a certain function of the cosine, which has the value 1 for normal emission and 0 for an emission at 90 degrees. * Wied. Ann, x. p. 449 (1880), 786 Prof. R. W. Wood on For these cases there would be a marked increase in the intrinsic intensity as the surface of the source was fore- shortened, but it would not be as great as in the case of a gas-flame, or the fluorescent prism which we have considered. Lommel observed this increase in the apparent intensity by immersing a vessel containing the fluorescent medium in a tank of water, and observing the luminous surface at dif- ferent angles. Lommel considered his fluorescent medium as partially absorbing for the fluorescent radiations, in which respect it differs from the crown glass used in the present experiments, which is almost perfectly transparent to the blue fluorescent light which it emits. Irom what has been already stated it is clear that the intensity of the fluorescent surface, when viewed from the air side at varying angles, is profoundly influenced by re- fraction. We should naturally expect radiations originating at a small depth within the medium to be refracted on emergence into the air, but it is not quite clear what would happen to radiations leaving the surface-layer of molecules. Millikan came to the conclusion, from a study of the polarization of the fluorescent light, that these radiations are refracted in the same way as radiations coming from a finite depth within the medium. In the case of fluorescence pro- voked by light, it is probable that the radiating layer is of con- siderable thickness as compared with the molecular diameter, for the light undoubtedly penetrates to the depth of a wave- length or two. It seemed possible that an effect more super- ficial in its nature might be obtained by exciting the fluorescence with cathode rays. A glass sphere was mounted in a vacuum-tube in front of the cathode, but it was found that the appearance was the same as with ultra-violet illumi- nation. ‘The tube was so constructed that the sphere could be bombarded either with cathode rays or canal rays; and it was found that if the latter were caused to play upon the surface, a phosphorescence was obtained which did not obey Lambert’s law, for the light appeared much more intense around the edge of the sphere, where the surface was con- siderably foreshortened. This light, as is well known, shows the D lines strozgly, and comes without doubt from a shallow layer of gas, which clings close to the surface. It is possible, however, that in this case we have an emission of light from the ete molecules alone ; in other words, the effect which was sought for in the cathode-ray phosphorescence. The canal rays have without doubt much less penetrating power, and may excite a purely superficial phosphorescence. My feeling about the matter, however, is that the luminous Fluorescence and Lambert's Law. 787 sodium molecules have been wholly freed from the medium, for the radiating layer seems to ohey the same law which holds in the case of a gas-flame. The effect can be seen in the usual form of canal-ray tubes furnished by the instrument- makers, the yellow phosphorescence appearing much brighter in the regions where it is considerably foreshortened. The best plan of all, however, is to mount a flat plate of rock-salt in a canal-ray tube, for in this case we obtain a brilliant line of yellow light when we view the surface at an angle of about 85 degrees with the normal. An examination of the yellow light with a large three- prism spectrograph showed that the D lines were quite as narrow as in the case of the sodium flame, and it is highly improbable that a radiation of this nature could be given off from the surface molecules of a solid. Professor Rutherford has recently shown that the intensity of the radiation from flat surfaces made radioactive is in- dependent of the direction, that is the same law holds as in the case of X-rays. This condition was demonstrated by the very ingenious device of coating the sides of short prisms with thin layers of radioactive material, and standing them on photographic plates, curious star-shaped patterns resulting, which were shown to be exactly in accord with the theory that the radiation intensity was independent of direction. I have succeeded in producing surfaces which radiate light in air according to the same law, and have obtained photographs exactly similar to those obtained by Professor Rutherford. It is only necessary to shake up some finely powdered Balmain luminous paint in a box, introduce the body which is to be rendered luminous, and allow the dust, which is suspended in the air, to settle upon its surface. The distance between the luminous particles must be several times their average diameter. If such a surface is exposed to the light of an arc-lamp and examined in a dark room, its intrinsic intensity will be found to increase as it is fore- shortened. If we coat the outer surface of a cylinder with the powder, expose it to light and examine it in the dark, the edges of the cylinder will appear as luminous lines much brighter than the rest of the surface. This will be recognized as the analogue of Rutherford’s first experiment, in which a pin- hole photograph of ‘a radioactive wire showed two lines of light parallel and close together. A square nut, with its sides coated, was placed in the dark upon a photographic plate, and after an exposure of two hours a picture precisely similar to the one obtained by Rutherford was obtained (fig. 3). 788 Fluorescence and Lambert’s Law. If the luminous particles are so close together as to be nearly or quite in contact, the radiation from the surface obeys Lambert’s law, which in this case follows as a result of the screening action of the particles upon the radiation coming from their neighbours. Suppose now that the luminous particles fuse together into a continuous surface. The irregular refractions and reflexions, which resulted in a screening action, are now replaced by regular refraction at the surface, all rays incident upon the surface at an angle greater than the critical being totally reflected back into the medium. It is probable that no other action than that of refraction is required to explain Lambert’s law in the case of transparent media, a conclusion which has also been reached by Uljanin (Wied. Ann. lxil. p. 528). In the case of an incandescent metal surface it is also probable that refraction plays some part, since the emitted light is partially polarized at certain angles. The law of emission can be ascribed to the absorption of radiations coming from points beneath the surface, the relation having been worked out by Lommel. So little is known, however, about the nature of the vibra- tions of incandescent solid and liquid surfaces, that it is difficult to formulate any very definite conception of the processes which are directly responsible for Lambert’s law. It is perhaps worthy of remark that complete irregularity of the phases of the vibrations is necessary. If the vibrating particles on the surface of a white-hot metal plate could be brought into the same phase, the plate would emit a plane wave, and would cease to be visible. No light would be perceived at all unless the eye were located on some normal to the surface, in which case a very brilliant point source would be seen in the direction of the normal. f 7890) LXXII. Note onthe Focometry of Concave Lenses and Convex Mirrors. By Prof. A. AnpERsoN, I.A., LL.D* Te those who are interested in neat ways of making physical measurements, the following methods of finding the focal length of a concave lens and of a convex mirror may be of some interest. They have not, I think, been noticed before. They are pin-point methods, and as easy in practice as the well-known pin-point method of finding the focal length of a concave mirror. For the measurement of the focal length of a concave lens a concave mirror is required, and for that of the focal length of a convex mirror a convex lens is required. Fig. 1. The figures explain the methods. The pin-point is placed at P, and the adjustment consists in making it coincide with its image, in which case the rays of light, after passing through the lens, diverge from (fig. 1), or converge to (fig. 2) the centre, O, of the mirror. Jn both cases the mirror, when properly placed, causes the rays to retrace their paths in the opposite direction. Note.—I have since found that a method, which is practically identical with that shown in fig. 2, is given in Edser’s ‘ Optics,’ pa 17. * Communicated by the Author. aU 9 LXXUI. The Velocities of the Ions of Alkali Salt Vapours at High Temperatures. By Harotp A. Witson, IA., DUS, M.Sc, 2. Rss: , Fellow of Trinity College, Cambridge and Pr ofessor of Phi ysies, King’s College, London* | oe a paper on “The Hlectrical Conductivity of Flames containing Salt Vapours,” Phil. Trans. A. vol. 192, 1899, the writer gave an account of a series of experiments atch included measurements of the velocities of the ions of salt vapours in flames and in hot air. The method employed was to find the electric intensity necessary to make the ions move against a stream of gas moving with a known velocity. The following table gives the results obtained :— (1) Positive ions of various salts of Cesium, Rubidium, Potassium, Sodium, and Lithium in a Bunsen flame. Velocity 62 cms. per sec. for one volt per cm. (2) Negative ions of same salts in a Bunsen flame. Velocity 1000 cms. er sec. (3) Positive ions of salts of Czesium, Rubidium, Potassium, Sodium, and Lithium in air at 1000° C. 7:2 cms. per sec. (4) Positive ions of salts of Barium, Strontium, and Calcium in air at 1000° C. 3:8 cms. per sec. (5) Negative ions of salts of Barium, Strontium, Calcium, Cesium, Rubidium, Potassium, Sodium, and Lithium in air at 1000° C. 26 cms. per sec. In 1900 Dr. KE. Marx published an account (“ Ueber den Potentialfall und die Dissociation in Flammengasen,” Annalen der Physik, 1900, no. 8) of a valuable series of experiments on the conductivity of flames, including determinations of the ionic velocities for different salt vapours in the flame. His method depended on observations of the potential gradient in the flame, and was quite different from that employed by the writer. He obtained for the velocity of the negative ions of any alkali salt in the fame 1000 cms. persec. ior the positive ions of any alkali salt in the flame he found the velocity to be about 200 cms. per sec. The experiments of Dr. Marx and the writer thus agree in showing that all alkali salt vapours in flames give ions having under the same conditions nearly equal velocities, and that the velocity of the negative ions is much greater than that of the positive ions. In 1901 the writer published a paper on the “ Hlectrical Conductivity of Air and of Salt Vapours” (Phil. Trans. A. vol. 197, 1901), in which it was shown that, above 1850° C., and with an H.M.F. of over 1000 volts, all alkali salt vapours * Communicated by the Physical Society: read March 9, 1906. elocities of the Ions of Alkali Salt Vapours. 791 conduct equally well if the amount of each one taken is pro- portional to its molecular weight. The temperature above which this result holds good was nearly the same for every salt. Above this temperature the current was independent of the temperature and of the P.D. used, provided the latter was sufficiently great. Since the lowest temperature at which this maximum current could be obtained was the same for all alkali salts, it follows that at such high temperatures the salts tried all gave ions having the same velocity ; for if some salts had given ions having a smaller velocity than others, then a higher temperature and larger P.D. would have been required to obtain the maximum current with these salts. The writer has recently, in collaboration with Mr. E. Gold, B.A., carried out a series of experiments on the conductivity of flames containing salt vapours for rapidly alternating currents. We have found that the conductivity for rapidly alternating currents varies as the square root of the corres- ponding conductivity for steady currents. It is shown in the paper *, that this result can be explained by supposing that all the salts tried give ions having equal velocities in the flame. In 1903 Prof. Moreau published an account (Annales de Chimie et de Physique, Sept. 1903) of some measurements of the velocites of the ions of salt vapours in flames by a method which was described by the writer in the paper referred to above in 1899. Prof. Moreau found, in good agreement with the earlier work, that all the alkali salts tried gave positive tons having a velocity of about 80 cms. per sec. For the negative ions of salts of potassium and sodium, how- ever, Prof. Moreau obtained results which do not agree with those obtained by Dr. Marx and the writer. Prof. Moreau’s results for sodium and potassium salts are as follows :— With equal molecular concentrations the velocity of the negative lons is independent of the nature of the acid radical of the salt. It varies with the metal in the inverse ratio of the square root of the atomic weight. For a particular salt vapour the velocity of the negative ion increases as the concentration of the vapour diminishes. Prof. Moreau gives the following numbers :— Molecular Concentration of Solu- } 1 1 1 1 1 tion sprayed into the Flame ... 4 4 16 64. 256 Velocity of Negative Ions in} K...... 660s Visagmo85 118 1320 Pras Per SCCn ceara acre vans as Na $00 1040 1280 Thus with large concentrations the sodium ions seem to have larger velocities than the potassium ions. * Phil. Mag. April 1906. 792 Velocities of the Ions of Alkali Salt Vapours. The method used by Prof. Moreau was to find the P.D., between two vertical electrodes, required to make the salt ions move across from the bottom of one electrode to the top of the other. Then, assuming the electric field uniform and knowing the upward velocity of the gases between the electrodes, the velocity of the ions was calculated. Now the electric field in a flame is very far from being uniform, but it is no doubt nearly the same in different cases when the conductivity of the flame is the same. Consequently, if we compare Prof. Moreau’s results for potassium salts with his results for sodium salts, taking such concentrations that the flame has the same conductivity for the potassium salts as for the sodium salts, then we ought to get the relative velocities of the potassium and sodium salt ions free from error due to variations of the potential gradient with the conductivity of the flame. Potassium salts conduct about four times as well as sodium salts when the concentration is small, so that Prof. Moreau’s numbers may be tabulated thus :— Concentration of Potassium 1 1 1 Sails b.295 tee oe. ete ccd ead int 1p 4 16 64 Concentration of Sodium | 1 ] 1 AGS pete scctereaasoeanelsotece tg cag 4 16 Velocity of Negative Ions rp for Potassium Salts ...... \ pate) g i> 995 1180 Velocity of Negative Ions for Sodium Salts ......... } pes” “w LO — Thus, comparing velocities with concentrations giving nearly equal conductivities, the velocities found by Prof. Moreau are very nearly the same for potassium salts as for sodium salts. The apparent variation of the velocity with the concentration of the salt vapour is no doubt due to the variation of the fall of potential between the electrodes with the conductivity, and not to any real variation of the velocity with the concentration. The mean of Prof. Moreau’s results for the velocity of the negative ions is about 1000 cms. per sec., and so agrees very well with the earlier results obtained by Dr. Marx and the writer. If Prof. Moreau were correct in supposing that the velocity of the negative ions varies inversely as the square root of the atomic weight of the metal, it would follow that salt vapours are ionized into a metal ion carrying a negative charge and a positive ion the same for all salts. Such a conclusion is altogether inconsistent with our knowledge of the ionization of salts. | Some Properties of the a Rays from Radiothorium. 793 Tf all salts give positive and negative ions having the same velocities in a flame, this can be explained by supposing that a salt molecule emits a corpuscle which is the negative ion, and that the positively charged salt molecule forms an agoregate of molecules whose size depends only on the charge, and so is the same for all salts. This view is consistent with the fact that the velocity of the positive ions is only about 60 cms. per sec. while that of the negative ions is 1000 ems. per sec. According to Prof. Moreau’s results, the positive and negative ions ought to have nearly equal velocities, for the atomic weight of the metals is comparable with the molecular weight of the acid radicals. The experiments done by the writer in 1899 showed that lithium (Li = 7) salts give ions having the same velocities as the ions from cesium (Us = 133) salts; which proves clearly that the velocity of the negative ions does not vary inversely as the square root of the atomic weight of the metal—a conclusion which Prof. Moreau has drawn from experiments on potassium (K = 39) and sodium (Na = 23) salts. It has been shown by Prof. Lenard that the salt vapour emitting light in flames moves in a strong electric field as though it were positively charged. I have verified this result, which clearly proves that the metal goes to form the positive ions, for the light is undoubtedly emitted by the metal atoms and not by the acid radical of the salts. I think therefore that the view that all alkali salts in flames give ions having nearly the same velocities is really supported by Prof. Moreau’s observations as well as by those of Dr. Marx and the writer. LXXIV. On some Properties of the a Rays from Radiothorium. 1.) By O. Haun, Ph.D.* ‘ioe a previous papery, I have given an account of the methods of separation and the radioactive properties of a very active substance, called radiothorium, which was prepared from the Ceylon mineral thorianite. It was shown that radiothorium was probably a slowly changing product of thorium—the latter is then supposed to be inactive—which lies between thorium and thorium-X. Radiothorium possesses in an intense degree all the radio- active properties of thorium, for it gives rise to thorium-X, * Communicated by Prof. EH. Rutherford, F.R.S. + Proc. Roy. Soc. March 1905; Jahrbuch. d. Radiaktivitdt, I. 3. 19085. Phil. Mag. 8. 6. Vol. 11. No. 66. June 1906. 3 7 794 Dr. O. Hahn on some Properties of the thorium emanation, and the characteristic active deposit. On account of its great activity, radiothorium is a far more suitable. source than the feebly active thorium for the investigation of the properties of its radiations. In this paper an account will be given of investigations on the following points :— 1. Range of the @ particles in air from the active deposit of radiothorium by the methods of scintillations and by the electrical method of Bragg and Kleeman. 2. Proof that the product called thorium B is complex, and consists of two distinct a ray products which have different ranges of ionization in air. 3. The magnetic and electrostatic deflexion of the a particles from the active deposit (preliminary). Activity of Radiothorium. Before discussing the properties of the @ rays, a brief account will be given of some measurements that have been made to determine the activity of the preparation of radio- thorium which had been used in these experiments. The first method was the same as that used in the previous paper. The emanating power of a known weight of radio- thorium was compared with that of a known weight of thorium nitrate under, as far as possible, similar conditions. 10 grs. of pure thorium nitrate were dissolved in 35 c.c. of water, and the emanating power measured by passing a constant air-current through the solution into a testing vessel, the rate of movement of the needle of an electrometer being a measure of the amount of emanation present. Then 1 ; é io mg: of radiothorium was measured under exactly the same conditions, 10 grs. of inactive sodium chloride being added to have about the same concentration of the solution. The = mg. had been prepared by successive dilution from a pre- paration of about 2°7 mg. of radiothorium, the activity of which had been calculated in London to be somewhat over 200,000. ‘This time the strength of the a mg. to the 10 grs. was found to be as 1°5:1, showing that the radiothorium gave about 150,000 times more emanation than an equal weight of thorium. The order of magnitude of the active thorium product was, therefore, almost the same as was expected, though the result seems to show that the propor- tionality of the emanating power to the weight does not remain constant for a very large difference in concentration. the a Rays from Radiothorium. 71995 A second method of determining the activity was to compare the y rays of the radiothorium with those of a large amount of commercial thorium. A quantitative comparison was kindly made by Mr. Eve, working at the same laboratory, by means of a sensitive electroscope which was covered with a sufficient thickness of lead to absorb all the Grays. Mr. Hive compared 1 kg. of pure thorium nitrate with L0°9 mg. of a radiothorium preparation, which was formerly measured by the writer by an indirect method and supposed to be about 23 times stronger than the above-mentioned 2°7 mg. It was now found that both preparations were of the same order, the 10°9 mg. being about 130,000 times as strong as thorium, when comparing weight by weight. These results led me to make a more careful investigation to see whether radiothorium was slowly losing its activity. Two thin films of radiothorium, each about a mg., were obtained on two watch-glasses and their activity measured from time to time. A slight decrease was noticed after some months, but no definite statement can yet be made, asa very thin film of radium, measured under similar conditions, showed even a greater decrease. I have recently prepared another sample of radiothorium, placed it in a watch-glass, and covered it witha thin sheet of mica, so that it is perfectly airtight. Under similar conditions, Eve has shown that radium does not appreciably decrease in activity. It is hoped, in this way, that it may be possible to settle definitely whether radiothorium loses its activity at a measurable rate. Even if we shall find a slow decrease of the activity of radio- thorium with the time, it is certain that we are dealing with a very slowly changing product entirely different from thorium-X, which is known to decay to half value in probably less than four days. Previous experiments indicated that the « ray activity of thorium in equilibrium is due to four different products : radiothorium, thorium-X, emanation, and thorium B, while apparently thorium itself, and certainly thorium A, are “rayless.” In order to begin the investigation with a single active product, it was found very convenient to obtain an active deposit of thorium B on a thin copper wire by exposing the negatively charged wire to the thorium emanation, after the method used by Rutherford for radium. In the case of thorium, it is not necessary to use the active source in solu- tion, because unheated thorium oxide or carbonate emanates strongly in the solid state. The 10 mg. of radiothorium were placed on the bottom of a small brass cylinder. A thin 3 F 2 796 Dr. O. Hahn on some Properties of copper wire was attached through an insulating rubber cork so as to remain just over the radiothorium. The active deposit was collected on the wire, which was charged negatively to about 110 volts by means of the lighting circuit. After about two and a half days’ exposure equilibrium is reached and the wire has become strongly radioactive, for it discharges an electroscope immediately, and gives distinct luminosity to sensitive screens. Scintillation Method. In order to find the maximum range of the a particles of the thorium B, the scintillation method was first employed. A small piece of glass was coated with zine sulphide and placed vertically over the active wire, the latter being fixed on a small disk, which could be moved up and down to any desired distance of the screen. As iong as the screen was in the range of ionization of the @ particles, the scintillations were seen without difficulty by means of a lens. It is, ot course, necessary for the eye to be first accommodated to the dark. Beyond the range of ionization the scintillations dis- appear fairly abruptly. The maximum range at which scintillations were still visible was found to be 8°3 cm., while at 8 cm. the luminosity could be seen quite easily. This result showed at once that the @ particles of the active thorium deposit are even more penetrating than the most penetrating « rays of radium, which were found by Bragg and Kleeman to be those of radium C. For comparison, some radium © was collected at a thin copper wire and its range of ionization determined with the same method. It was found to be 6°8 cm., Rutherford having found the same when using the same method *, while Bragg and Kleeman f found 7:0 cm. when using the electrical method. It may be mentioned here, that the electrical method of determining the range of the a particles is somewhat more delicate than the optical one. McClung t, using Bragg’s method of determining the ionization curve of radium GC, covered his active wire with thin sheets of aluminium-foil in order to see whether the range of ionization decreased in proportion to the number of foils used. He found that one aluminium-foil about 0:00031 em. thick corresponds to about 0°51 cm. of air, Rutherford § having found about 0°53 cm. for the same foil. The same result was obtained by the writer by the scintilla- tion method. Different layers of aluminium-foil were placed * Phil. Mag. July 1905. + Phil. Mag. Dec. 1904. t Phil. Mag. Jan. 1906. § Phil. Mag. Jan. 1906. the a Itays from Radiothorium. Cos)el over the active wire, and the maximum range again deter- mined. Column I. of the table gives the number of sheets of aluminium-foil used, column II. gives the distance at which scintillations were cull distinct, column III. gives the thickness of air which corresponds always to one layer of foil. i RI. Te 0 8-0 1 C5 0:50 3 6°75 0515 7 4:1 0 9 3°05 0°55 Il 2°15 0°53 13 1-10 0:53 14 0O°'7 0:53 Average 0°53 The values given in column III. are approximately constant, and the mean 0°53 is exactly that which Rutherford found for the rays of radium C. Another series of measurements was made with very thin foils of Dutch metal, the result of which was in even better agreement. For some purposes, it is very convenient to have a means of cutting down the range of the a particles by any required amount, and it was for this reason that the above-mentioned measurements were under- taken. We shall state later in this paper the amount of air equal to a very thin mica plate—a screen which has the great advantage of cutting off radioactive emanations completely, while the sheets of metal are always porous and almost useless for that purpose. The scintillation method above described for investigating the maximum range of the a@ particles in air can be used with advantage when dealing with a single product like radium C, or when deter mining only the range of the most penetrating of a number of different rays. The method does not throw any light on the range of the « rays which have less than the maximum range, nor does it indicate whether we are dealing with a homogeneous or complex pencil of « rays. It was of special importance in the present case to know whether there was present only Th. B or some other active product besides 798 Dr. O. Hahn on some Properties of it, for instance Act. B. The latter would then, of course, come from actiniam in the radiothorium preparation, and would show that it was not pure in the radioactive sense of the word. There was, however, but little probability of such an occurrence, since no evidence of the presence of actinium had been obtained from an examination of the decay curves, which had been obtained for the emanation and the active deposit. In order then to test the point more completely, I made use of the method developed by Bragg and Kleeman ”*, wio made with so much success a complete analysis of the « rays emitted by the various radium products. The apparatus employed by the writer was similar to that of Bragg and Kleeman and of McClung.