cere fhyes dedeeveures Wi bhit oe aon nen ewan an ee reaper a See an owen on oe enon en ees te a eee the Re ee ee ee eee ste ence ae ee erallom awe Beeee SSFPSESe S3tgagestel PERRET PERE? i it} it SHTeST IIE ES} id SEPSSSDSDDSDPREDI DEE ehDODN ES shag Wh il ish 44 INCI SRN Ww MV, eee Ferret www YY oe WOW dialled Wry vey yeeros Sea : we aie Mecaces POS ag i oS vw IY SS ath ee Taoeer JSS ieee" ee EGS WN ies Jie’ vv ve yoyo acevo gill Nn PP Nd ‘ ‘ Uwys Sows NY Ny OMY As Noe “2 we 5 ee Wi. ¢ ; aw) A GAG oe SUSU SUNY 3. ¥ AC WN vie Ve A A we SP RN IS PR 8 PAV wy Ad yous v WW weretotice Se OOS NO rae ew) eee iS) Be ie) ! NE baal j Naren : 5 . SS ae aA SS CF - j Av Aer, 1" LRG GON er age VUseudeyeye Oe Y ee TON GOO I “y WY) in vw AN Sih dil Mikdd OONoe sitesi owe Riese SUI OUYS te at ASC CAREC ct Spee oie NES ds ue ‘ Mv ; ee AM ch aes 8 YOM OM yd ® we oN ‘ yyhYeyeS OOM eto’ SA om sae wd" , oh : \ di Ns “ f ee) vw 4 : ; 4 Cen } wees EOE pve Wal : we Yin OS seer | | Ay Vw Baw, AN fone et) waGe i enn wae vane ii egy Ne a7 Vv UY UYU I w/ vy ¥ WU wee Rt eth wv. ie Mass Jug Uys Ty Be ey Uae Y hone Muy scoohibaa My ve en VW WW Ye WEY UYU OU. Vids WW sacue poe MOINS es : er revered PSY vy) ht UUs cywoutee vues Uw Jyyeuy Vast YOO GY DS yy sw . yeu YY oy We ey Vdd i f NW f Dw oie Aho faa [paibenl ' WA YUM 4K [tee it Ng ih Te : THE LONDON, EDINBURGH, axp DUBLIN PHILOSOPHICAL MAGAZINE JOURNAL OF SCIENCE. — CONDUCTED BY LORD KELVIN, LL.D. F-.R.S. &e. GEORGE FRANCIS FITZGERALD, M.A. Sc.D. F.R.S. AND WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.C.S. ‘‘ Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster vilior quia ex alienis libamus ut apes.” Just. Lips. Polit. lib. i. cap. 1. Not. VOL. XLI—FIFTH SERIES. JANUARY—JUNE. 1896. .3 1959 LONDOM: LIBRARN TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET. SOLD BY SIMPKIN, MARSHALL, HAMILTON, KENT, AND CO., LD.; WHITTAKER AND CO.; AND BY ADAM AND CHARLES BLACK ;—T. AND T. CLARK, EDINBURGH ; SMITH AND SON, GLASGOW ;--HODGES, FIGGIS, AND CO., DUBLIN ;— PUTNAM, NEW YORE ;-- VEUVE J. BOYVEAU, PARIS ;— AND ASIJER AND CO., BERLIN. “‘Meditationis est perscrutari occulta; contemplationis est admirari perspicua.... Admiratio generat questionem, questio investigationem, investigatio inventionem.”—Hugo de S. Victore. “Cur spirent venti, cur terra dehiscat, Cur mare turgescat, pelago cur tantus amaror, Cur caput obscura Phoebus ferrugine condat, Quid toties diros cogat flagrare cometas, Quid pariat nubes, veniant cur fulmina ccelo, Quo micet igne Iris, superos quis conciat orbes Tam vario motu.” J. B. Pinelli ad Mazonium. CONTENTS OF VOL. XLI. (FIFTH SERIES). NUMBER CCXLVIII.—JANUARY 1896. Mr. E. H. Griffiths and Miss D. Marshall on the Latent Heat eetyaporaiomo: Benzene’. 2... - 6. Haas sbicetae n+ esses Miss Dorothy Marshall and Prof. W. Ramsay on a Method of Comparing directly the Heats of Evaporation of different iiiquidsiat their Boilme-pomts - 22. genccdngee ee eene Mr. F. W. Lanchester on the Radial Cursor: a new addition 2 DE SLAG Ses ATT ogee Ro eae abe a ae Dr. E. H. Barton on a Graphical Method for finding the Focal Lengths of Mirrors and Lenses. .............0-5 Mr. Rollo Appleyard on a “ Direct-reading” Platinum Ther- COTILE SLs pray fe BRP A er Rar oye eee Mr. G. J. Burch on a Method of Drawing Hyperbolas ...... Notices respecting New Books :— Prof. J. J. Thomson’s Elements of the Mathematical Theory of Electricity and Magnetism .............. Mr. R. A. Gregory’s Exercise Book of Elementary Physics for Organised Science Schools etc. .......- Proceedings of the Geological Society :-— Mr. J. E. Marr on the Tarns of Lakeland . .......... Col. H. W. Feilden on the Glacial Geology of Arctic Europe and its Islands—Part I. Kolguey Island .... On Underground Temperatures at Great Depths, by Alexander DUETS HERE eye ee ee? Ree Oe Cer a ee On the Influence of Electrical Waves on the Galvanic Re- sistance of Metallic Conductors, by H. Haga............ Page 1 38 52 59 62 72 75 76 77 77 78 79 1V CONTENTS OF VOL. XLI.—FIFTH SERIES. NUMBER CCXLIX.—FEBRUARY. CONV... 6ns BS eae ee bs Pe Lek be oes eee Poe Prof. A. W. Riicker on the Existence of Vertical Earth-Air Electric Currents in the United Kingdom .............. Mr. J. E. Moore on a Continuous and Alternating Current Magnetic Curye Tracer 20. blk es ee Mr. R. W. Wood on the Dissociation Degree of some Hlec- prolytes ab UP. cle ole kee ee Ce ok eee Mr. R. W. Wood on the Duration of the Flash of Exploding Oxybydrosen itches Ge re oe See es so Mr. F. L. O. Wadsworth on a very Simple and Accurate Cathetometer, 0.20 an ooo ee eee eee ee ee Mr. Charles Davison on the Straining of the Earth resulting trom: Secular Cooline 22. tvs. .5a ue. ee Notices respecting New Books :— M. Vaschy’s Théorie de l’Electricité ................ _ Mr. Risteen’s Molecules and the Molecular Theory of Miaiber chp alec 6a) auslaioe Cese tcc ee Messrs. Loudon and McLennan’s Laboratory Course in ‘ xpemimental Pinysicy +7 .5.°.1. 2... os. bee ee ee Proceedings of the Geological Society :-— Mr. F. Rutley on the Alteration of certain Basic Eruptive “ARocks from Brent Tor. Devons)... ..-:. 2. eee Sir Archibald Geikie on the Tertiary Basalt-plateanx of North-westerw Hurope $379.1, 00. 1..'.1.'. he. Messrs. A. J. Jukes-Browne and W. Hill on a Delimita- tion of the Cenomanian, being a Comparison of the Corresponding Beds in Southern England and Western * ePrainice’ 2 eee ganeeaeckt ctf! 7.!s Le rr G: L. Elles and HE. M. R Wood on the Llandovery and - Associated Rocksrotq@ omumay, 09. ats ee _ Mr. A. I’. Metcalfe on the Gypsum Deposits of Notting- kamshire and Derbystmre 2) wo cee at ee Contributions to the Knowledge of Tropical Rain, by Prof. MW. Wites@mer i. 2 eccrine cee On three different Spectra of Argon, by Dr. J. M. Eder and iH: Waleutayt.%. ot oak at oie okt eet, eee er On the Red Spectrum of Argon, by Dr. J. M. Eder and E. EC en a ae AEN Interference Experiment wach Electrical Wane, by Prof. von Sra ee eo ose tata Salis che tal that atid. Satie ata A On Electrified Atoms, by Prof. J.J. Lhomson 4.2.5. ee On the’ Double Refraction of Electrical Waves, by Prof. Ameuste Ishi "aceite dake Ue Sls wh oe oko s bee Note on Elementary Teaching concerning Focal Lengths, by Prot. (Oliver J. Lodge, yi .trte rt cto eee eat eaeeees eae 1 CONTENTS OF VOL. XLI.—FIFTH SERIES. V _ NUMBER CCL.—MARCH. Dr. E. Taylor Jones on Magnetic Tractive Force .......... 153 Dr. Alfred M. Mayer’s Researches in Acoustics—No. X. .. 168 Profs. W. Nernst and Rk. Abegg on the Freezing-points of MIMS CHS ONMNMOMSAS a oe ole eo ne Ce aioe as econ e ss 196 ror... Everett ow Resultant Tones... ....6..-5-0- 686% 199 Prot. F. Y. Edgeworth on the Compound Law of Error ..,. 207 Mr. R. 8, Cole on Graphical Methods for Lenses.......... 216 J. Elster and H. Geitel’s Electro-optical Investigation of ener MN ee ee awe a aie k Sak a4 Fe uw bees 218 Aug. Righi on “the Production of Electrical Phenomena by MacNIMO MOMMA SS or 5507 ais piece 'c pigle’e bq 4 $asa ck ete eee Ae. COL Notices respecting New Books :— Prof. Thompson’s Dynamo-Electric Machinery........ 234 Prof. Carey Foster and Dr. Atkinson’s Elementary Treatise on Electricity and Magnetism, founded on Joubert’s ‘ Traité Elémentaire d’Electricité’ ........ 234 Prof. Holman’s Computation Rules and Logarithms, with haples eb other usetul TUMcHONS «2.4 fey tg e deers LOO Black Taght, by M, Gustaye Le Bon ,, 225 -¢55ecnceceesy 20 NUMBER CCLI.—APRIT. Prof. Svante Arrhenius on the Influence of Carbonic Acid in the Air upon the Temperature of the Ground . » 2AT Prof. J. G. MacGregor on the Calculation of the Conductivity Mtoe Mixtures of Blectrolytes:.2. 0256 b ae cee ete e en ee 276 Prof. A. W. Witkowski on the Thermodynamic Properties of Josie: GEASS cod 0) See ei ie ee ae 288 Prof. J. A. Fleming and Mr. J. E. Petavel’s Analytical Study Omiueealierignne Current Are il... 62+ - es agentes t: 315 Prof. W. Ramsay and Mr. N. Eumorfopoulos on the De- termination of High Temperatures with the Meldometer .. 360 Mr. W. H. Everett on the Magnetic Field of any Cylin- GeierNch ny re et en a ade St Rey eat y sg ek we ts 367 Prof. Arthur L. Clark on a Method of Determining the Angle GE LAD Bee TR ee Se aie Se ea aie Scar Soper 369 Prof. F. L. O. Wadsw orth on Mr. Burch’s Method of Draw- pebIRPEAOMIS a tee ety de casts est ase nus gs gs BLS Mr. R. W. Wood on a Duplex Mercurial Air-Pump ... .. 378 Notes of Observations on the Rontgen Rays, by H. A. Row- length ik Carmichael and GJ) Brisas... ).. 0.50. 381 Note on “ Focus Tubes” for producing X-rays, by R.W.Wood 382 sal CONTENTS OF VOL. XLI.—FIFTH SERIES, Page Note on Elementary Teaching concerning Focal Lengths, by : BM Barton. 4.0.4 ee se sae ee Re eee 383 Solution and Diffusion of Certain Metals in Mercury, by W. Ji elnmphreys <.. 5. sons Gees oe ae een 384 NUMBER CCLII.—MAY. Dr. Ladislas Natanson on the Laws of Irreversible Pheno- TCM (oo gic en pe Se aeis eh ops ee nee oe en er 385 Dr. John Shields on a Mechanical Device for Performing the Temperature Corrections of Barometers.............++.- 406 Mr. J. H. Reeves on an Addition to the Wheatstone Bridge for the Determination of Low Resistances ............ 414 Mr. R. W. Wood on the Absorption Spectrum of Solutions of Iodine and Bromine above the Critical Temperature .. 423 Dr. G. A. Miller on the Substitution Groups whose Order is OU eee ais wos a ois Wee ees bas 6 eae Oe ee eee J. Elster and H. Geitel on the alleged Scattering of Positive Hlectrenty by Light. (07. oe ees en 437 T. Mizuno on the Tinfoil Grating Detector for Electric WANES Gc bas lane eae eee eet ote ce Ge ene 2. 445 Prof. John Trowbridge on Carbon and Oxygen in the Sun .. 450 Messrs. H. Nagaoka and EH. Taylor Jones on the Effects of Magnetic Stress in Magnetostriction .........2.-s.eeee 454 Notices respecting New Books :— Dr. W. M. Watts’s Index of Spectra, Appendix G..... 462 On an Electrochemical Action of the Rontgen Rays on Silver Bronude, by Prof. Dr. Kranz Streimnitz .... 205). eee 462 Triangulation by means of the Cathode Photography, by John rowbrid@es.-. .vuee. ses oss ox oe 463 NUMBER CCLIIL—JUNE. Prof.S/lasW.Holman on Thermo-electricInterpolationFormule 465 Mr. W. B. Morton on the Electro-Magnetic Theory of Moving Charges (9.09. -- ogee Ger he ee 488 ‘Dr. Charles H. Lees and Mr. J. D. Chorlton on a Simple Apparatus for determining the Thermal Conductivities of Cements and other Substances nsed in the Arts ........ 495 Mr. W. T. A. Emtage on the Relation between the Bright- ness of an Object and that of its Image................ — 504 Mr. Rollo Appleyard on the Adjustment of the Kelvin Bridge. 506 Mr. Julius Frith on the Effect of Wave Form on the Alter- Mae=CUITEMECATC wis seco os tee ee wee Peer 507 Mr. Douglas McIntosh on the Calculation of the Conductivity of Mixtures of Electrolytes having a common Jon ...-.. 510 CONTENTS OF VOL. XLI.—FIFTH SERIES. vil Page Notices respecting New Books :— Wr i du Boiss: The Maenetic Circuit ............-4 517 Hermann Grassmann’s Ausdehnungslehre ............ 518 Mr. a. Hin Barker's Graphical Calculus ....-.......+ 519 Proceedings of the Geological Society :— Mr. G. W. Lamplugh on the Speeton Series in. Yorkshire SEONG INC O MEMS IONIC) te) sy afer hs eps Scien ok a Ko we oe a es 519 Rey. Edwin Hill on Transported Boulder Clay......... 521 Dr. Henry Hicks on the Morte Slates and Associated Beds in North Devon and West Somerset.......... 521 Prof. T. W. Edgeworth David on Evidences of Glacial Action in Australia in Permo-Carboniferous Time.... 522 Mr. Alfred Harker on certain Granophyres, modified by the Incorporation of Gabbro Fragments, in Strath (SMe Reet ro teen ad gee an sao vas cone vars se 523 Prof. E. Hull on the Geology of the Nile Valley, and on the Hvidence of the greater Volume of that River Biced pune i CMO as gay we Weak Pe eset w hig ec de moe 524 On the Diffusion of Metals, by Prof. W. C. Roberts-Austen . 524 Rontgen Rays not present in Sunlight, by M. Carey Lea...- 528 On a new Areometer, by L.-N. Vandervyver.............- 530 Index PLATES, I. & Il. Mlustrative of Prof. A. W. Witkowski’s Paper on the Thermo- dynamic Properties of Air. ERRATA. Page 170, second line of table, Jor Bell-metal at 0° vibrates during 55 secs.; at 100° it vibrates during 15 secs. read ” ” ” 55 ” we 2” 40 ,, - Page 171, line 27 from top, for air of glass tubes of different diameters, renders read air in glass tubes of different diameters, render 5, 178, line 11 from top, dele The frequency of the vibrations of » 195, ,, 12 from bottom, for from the globular read having the globular - 9367, Mr. W. H. Everett’s paper, in first equation, for 7d? read r7d0 THE LONDON, EDINBURGH, ayo DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES.] JANUARY 1896. I. The Latent Heat of Evaporation of Benzene. By BH. H. Grirrirus, M.A., F.RS., Sidney Sussex College, Cambridge, and Miss Dorotay Marsuauu, B.Sce., Un- versity College, London™. il ee method of experiment and the nature of the apparatus employed have been fully described in previously published papers. Although it appears somewhat presumptuous to assume, on the part of the reader, a knowledge of such communications, it would on the other hand seem redundant to devote many pages to the mere repetition of what has already appeared in print. We therefore propose to give an Be atGes statement of the theory and methods employed, but to omit all detailed description of the apparatus. Full references to former communications will be given when necessary, so that all particulars can be ascertained by any who desire them. As reference has frequently to be made to the following papers (by E. H. Griffiths) they are, for convenience, denoted as follows :— Paper J. “‘ The Mechanical Equivalent of Heat,’ Phil. Trans. vol. clxxxiv. 1893, A, pp. 861-504. Paper A. “The Influence of Temperature upon the Spe- cific Heat of Aniline,” Phil. Mag. Jan. 1895. Paper W. “The Latent Heat of Evaporation of Water,” Phil. Trans. vol. clxxxvi. 1895, A, pp. 261--341. * Communicated by the Physical Society: read November 8, 1895. Phil. Mag. 8.5. Vol. 41. No, 248. Jan. 1896. B 2 Mr. E. H. Griffiths and Miss Marshall on the 2. Description of the Method. In order to render our account of these experiments in- telligible, we find it necessary to give the following somewhat lengthy extract from Paper W, pp. 270-273 :— “The method adopted was of such a nature that the results would not be appreciably affected by (1) errors in thermometry ; (2} changes in the specific heat of water ; (3) the capacity for heat of the calorimeter ; (4) loss or gain of heat by radiation, &e. ; and if these points are borne in mind, they may serve to explain some of the contrivances which might otherwise appear uncalled for. “Tf the vessel in which the evaporation is taking place is kept at a constant temperature, we are independent of the capacity for heat of it and its contents; we also dispense with the measurements of changes of temperature. Thus, if matters be soarranged that the loss and gain of heat through- out an experiment are balanced, many fruitful causes of error are avoided. Of course, the actual temperature of the calorimeter during evaporation must be determined, but a small error here is of little consequence. The change in the value of Lis small as compared with the changes in @. In fact, an accuracy of an order of 3), of a degree would be sufficient when determining the actual elevation. _ “The heat was supplied to the calorimeter by means of a wire whose ends were kept at a constant potential difference. The thermal balance could be maintained in one of two ways:— (1) If the heat-supply was too great, the electric current could be temporarily stopped, or, the rate of evapo- ration of the water increased. (The latter was the method generally adopted.) — (2) If the cooling was too rapid, the only mode of main- taining the balance was (in the apparatus about to be described) to reduce the rate of evaporation. “The liquid to be evaporated was contained in a small silver flask, connected with which was a spiral coil of silver tubing 18 feet in length. Both flask and spiral were within the calorimeter, and the water-vapour, after passing through the spiral, emerged from the apparatus at the temperature of the calorimeter. Surrounding the flask, and between it and the spiral, a coil of platinum-silver wire was arranged, and flask, spiral, and coil were entirely immersed in a certain singularly limpid oil consisting of hydrocarbons only, Latent Heat of Evaporation of Benzene. 3 “ The calorimeter (which was filled to the roof with the oil, and the equality of temperature maintained by rapid stirring) was suspended by glass tubes within a steel chamber, whose walls were maintained at a constant temperature. So long, therefore, as the calorimeter and the surrounding walls were at equal temperatures, there was no loss or gain by radiation, &e. If during an experiment the temperature of the sur- rounding walls changed, the method of experiment involved a corresponding change in the temperature of the calorimeter, and, therefore, some loss or gain of heat would be experienced. The apparatus was so designed that any such change in tem- perature was extremely small (in no case amounting to ;}5°), yet, in order to estimate the loss or gain, it was necessary to know approximately the capacity for heat of the calorimeter and contents. : “Small differences between tne temperature of the calori- meter and the surrounding walls would, during an experi- ment, be of no consequence provided that the oscillations were of such a nature that the mean temperature of the calorimeter was that of the surrounding space, and it will be found that this condition was fulfilled. ““In addition to the heat supplied by the electric current, there is also a supply due to the work done by the stirrer, and it was in the estimation of this ‘stirring supply’ that the greatest difficulties were encountered. Fortunately the heat thus generated was only about ;45 of the heat supplied by the current, and thus any small error in that portion of the work becomes of little account. “ Of the accuracy with which the electrical supply could be measured there is no question ; and even if the value of the H.M.F. of the Clark cells, or the absolute resistance of the box-coils given by the standardizations performed during the determinations of J, is in any way inaccurate, such errors would now eliminate, since the value of J was deter- mined by means of the same standards as those by which the quantity of heat developed in these experiments was deter- mined. Hence, by assuming the value of J obtained by the use of these standards, we get the comparison in terms of a thermal unit at 15° C., independently of the numerical value assumed in the reductions. “One further correction remains to be noticed. The tem- perature of the calorimeter has been referred to as oscillating about the exterior temperature, and it might happen that at the close of an experiment this difference was not the same as that at the commencement—if any such difference existed. The magnitude of this correction depended, of course, on the B2 | 4 Mr. E. H. Griffiths and Miss Marshall on the ability of the observer to maintain the thermal balance. In these experiments the correction was usually small, and in any case could be determined with great accuracy. ‘“‘Having indicated the nature of the cbservations, we proceed to state the relation between the various sources of loss or gain of heat. “Let Q, be the thermal units per second due to the electrical supply ; | Q, be the thermal units per second due to the mecha- nical supply ; xq be the total heat-supply during an experiment from any other causes. “Then, if M be the mass of water evaporated, L the latent heat of evaporation at temperature 0, and if the electrical supply is maintained for a time ¢,, and the mechanical for a time ¢,, ML=0.2.4Q7,439. . “Now the D.P. at the ends of the coil was always some integral multiple of the D.P. of a Clark cell. ‘* Let e be the D.P. of a Clark cell, n the number of cells, and R, the resistance of the coil at the temperature 6), then = RJ’ RCI Me Ron he OS (2) “Tf the calorimeter at the commencement and end of an experiment was at exactly the same temperature as the sur- rounding walls, then, if their temperature was unchanged, the term Sg would vanish ; but although this term through- out these experiments was of small dimensions, it could not be entirely ignored. “Tet 6)’ and 6)” be the temperature of the surrounding walls at the beginning and end of an experiment; suppose the calorimeter temperature (@,) to exceed the surrounding tem- perature by d’ at the commencement and d” at the end of an experiment. Then fall in temperature of calorimeter = (6)! +d’) —(0) +d"). Hence the heat given out by the calorimeter in consequence of this fall in temperature is Cy {(O0' + d’)—(0)" + da’ e where C, is the capacity for heat of calorimeter and contents at the temperature 0). “Tf we neglect any small loss by radiation, &c., due to the Latent Heat of Evaporation of Benzene. D differences d/ and d” between the temperature of the calori- meter and the surrounding walls, we may conclude that the whole of the heat thus evolved by the calorimeter was ex- pended in the evaporation of water, hence Sq=C,{(Or'—O0") +(@'—a")}*—_ (8) Hence ; en? xt ML=—. = +Q, x #,+C,,{(6'—0)") + (d’-a")}. (4)” 1 3. The following table shows the comparative mean values of the terms in equation (4) resulting from our experiments on benzene f. TABLE I. No. of Cells. Oe te. Qsis: xq. 5 1 ‘008 +005 4 1 ‘O1ll +:009 3 i 015 +001 We found that the thermal balance was most easily main- tained when the potential-difference was that of 4 cells, there- fore the majority of our experiments were performed with that potential-ditference, the experiments with 5 and 3 cells being used as a check upon the results. To secure an accu- racy of (say) 1 in 1000 in the total heat-supply, the above table shows that it was necessary to measure Qt, to (say) 1 part in 2000, Q.t. ” 1 ” 15, >4 ” Lia % 10 ; but as the sign of the last term was in some experiments positive, in others negative, the above degree of accuracy was * This apparently clumsy method of representing the quantity of heat evolved or taken up by the calorimeter was adopted because, as the method of experiment involved separate determinations of 6,', 6,'', d', and d', the actual temperature of the calorimeter at any time could only be obtained in this manner. + (Experiments Preliminary, XIX. a, XXXV., and XXXVI. were not included when calculating this table, as they are in several respects exceptional.) 6 Mr. E. H. Griffiths and Miss Marshall on the not essential, since, when taking the mean of a number of observations, the effect of any error in Sg would be greatly diminished. We believe that the above order of accuracy was exceeded in the measurement of the respective terms. In the case of the experiments with 3 cells at 20° an order of accuracy of 1 in 50 would be required in the value of Q.¢, to secure the same standard ; hence we do not regard our deter- minations at that temperature as possessing an equal authority with those at higher temperatures. 4. The Method of maintaining the Space surrounding the Calorimeter at a Constant Temperature 9p. A full description of the somewhat elaborate apparatus designed for this purpose will be found on pp. 374-378 of Paper J, and some improvements which were subsequently added are described on pp. 274-276 of Paper W. This portion of the apparatus did not, for some unknown reason, appear to be working with the same perfection this year as it did in the summer of 1894. Oscillations in @) (the external temperature) , amounting to ;4,5° C., were on several occasions observed, the greatest change during the whole series being °0145°. This, however, was exceptional and, as an inspection of our final tables will show, the change in the course of an experiment (2. é.in about half an hour) was usually only _ about a few thousandths of a degree at temperatures varying from 20° to 50° U.; the constancy of @ was therefore sufficient for our purpose. Had it been possible, we should have preferred to determine @ by means of a platinum-thermometer, as we could thus have detected smaller changes ; but a third observer would, in that case, have been required, and circumstances did not permit of this addition*. The mercury-thermometers used for indicating the tem- perature of the steel chamber in which the calorimeter was suspended were graduated in millimetres, and had been care- fully calibrated and compared with two Tonnelot thermo- meters standardized at the Bureau International t.. The stems of these thermometers (where they projected above the tank-lid) were surrounded by glass tubes up which a stream * We believe that such irregularities as present themselves in our final results are partly due to the employment of mercury-thermometers for the determination of the changes in 6). t See “The Measurement of ‘temperature,’ Science Progress, Sept. 1894. Latent Heat of Evaporation of Benzene. 7 of tank-water was forced by means of a pump driven by a water-motor : thus the stem-temperature was always that (or nearly that) of the tank, and the readings were not affected by changes of temperature in the room. The actual value of 0, was of small consequence, an accuracy of 4/,° C. being sufficient ; but it was necessary to read changes of temperature during an experiment to nearly 0°-001 C., and this we believe we were able to do. A full description of the various pre- cautions taken will be found in Paper A, pp. 55 and 56, and Paper W, pp. 275, 276. The observations were taken by means of a reading-tele- scope fitted with a micrometer-eyepiece, which directly divided 1 millim. on the thermometer-stem into 10 parts: thus 0:1 of a millimetre could be directly read, and ‘01 could be estimated. There is no doubt that the actual readings could be taken to 025 millim., that is about 0°°001 C. Thermometer A had a range of 16° to 26°C., and about 27 millim. were equivalent to 1° C. Thermometer II. had a range of 28° to 53° C., and about 20 millim. were equivalent to 1° C. _ All temperatures, both when obtained from these and from the platinum-thermometers, are throughout this Paper ex- pressed in terms of the nitrogen-scale. 5. The Calorimeter and its Connexions. A full description will be found on pp. 276-281 of Paper W, and drawings and sections on plates 5, 6 of the same paper. The brief account given in the description of the method supra is sufficient to indicate the nature of the arrangements to those who are not familiar with that paper. The differences of temperature between the calorimeter and surrounding walls were determined by means of differential platinum-thermometers. A description of the method of standardization and observation of those thermometers is given on pp. 52-56 of Paper A, and some further details on pp. 285-290 of Paper W. Experimental evidence is there adduced in support of the following statement :—“ It follows that differences of temperature could be determined to ‘0004°, and differences of ‘0001° could be detected.” The following Table shows the difference in temperature corresponding to a difference of 1 mean millim. of the bridge- wire whose opposite ends were connected with the thermo- meters :-— 8 Mr. E. H. Griffiths and Miss Marshall on the TaBLeE IL. A®@ for difference of Temp. 1 mean millim. bridge-wire. O° Oo 20 0:009046 30 0:009073 AO 0006101 56 0:009128 . By experiments repeated this summer we found that no change had taken place in the value of the mean bridge-wire millimetre. A slight change (particulars of which are given in a subsequent section) had, however, occurred in the position of the null-point, 7. e. in the reading on the bridge-wire when the temperature of the two thermometers was identical. 6. Brief Description of the Method of obtaining the Value of the Terms in the Expression Total heat = Q,t,+ Q,t,+ 2g. LG: Ont = Sa a The ends of the platinum-silver coil (immersed in the oil surrounding the evaporating-flask and spiral) were kept at a constant potential-difference by means of the arrangements described in Paper J, pp. 382-888. This potential-difference was always some integral multiple (m) of the potential-differ- ence of a Clark cell (e). During the spring of this year the Clark cells used were again compared with the Cavendish standard (R,), which has shown no signs of change since its standardization by Lord Rayleigh in 1883 and by Messrs. Glazebrook and Skinner in 1891. The mean value of the whole set of 30 cells differs from R, by 0:00004 volt only ; and although individual cells show larger discrepancies than in previous years, their mean potential-difference at 15° C. may be taken as 1:4342 volts (see Paper W, p. 297). A number of these cells were always placed in parallel arc: thus when n is given as 4, we were really using 12 cells as four files of 8 each. The arrangement for keeping the temperature of these cells at nearly 15° C. has been described in Paper J, p.385. During the period covered by our experiments, some of the days were extremely hot, and Latent Heat of Evaporation of Benzene. 9 the tap-water became so warm that when turned on by the regulator it was unable to keep down the temperature sufli- ciently. The extreme range in the temperature of the cell-tank during these experiments was from 14°°8 to 16°°3 C. As, how- ever, the movement was always extremely slow, it is probable that the tank-temperature closely corresponded to the effective temperature of the cells, and hence the correction e = 1434251 + (15—6) x 00077} _ applied by us gave the value of e with sufficient accuracy. The time t; was determined by means of a chronograph controlled by an electric clock, whose gaining rate is now less than 1 in 20,000. Any movement of the keys by which the current was switched on to the calorimeter-coil was auto- matically recorded on the tape ; and thus personal errors were eliminated. The times could have been read to j3, of a second, but it was considered unnecessary to read to nearer than 75, t.e. about 1 in 7000 of ¢z. The value of R, is expressed in terms of the “ true ohm ” as given by the B.A. standards, with which (by kind permission of Mr. Glazebrook) the coils used by us have been directly compared (Paper J, pp. 407-410). The increase in R, due to the rise of temperature caused by the current was determined in the manner described in Paper J, pp. 404-407 (see also Paper W, p. 296). | The value of J assumed by us was 4:199 (Paper W, p. 314). We would emphasize the fact to which attention has been previously directed (section 2, p. 38), namely, that even if, in consequence of errors in the standards &c., this value of J is incorrect, it is still the right value to use for the reduction of these observations, for, provided that no change has taken place during the past three years in the standards used (and direct comparisons show no signs of any change which would affect the results), the values of L obtained by us are independent of the numerical values of J and R when expressed in terms of the same units as those assumed during the determination of the mechanical equivalent. The value of Q,¢t, 1s thus expressed in terms of a “ thermal unit abibo 2? (ea See The method adopted for finding Q, (the thermal units per second due to the work done by stirring) has been fully described in Paper W, pp. 290-293. It was there shown that the value of Q, varied approximately as r* (where 7 was the 10 Mr. E. H. Griffiths and Miss Marshall on the rate of revolution of the stirrer), and that this relation was sufficiently close for the reduction of experiments in which the value of + was somewhere between 5 and 6 per second. The value of Q, was found to increase rapidly as @, (the temperature of the calorimeter) diminished. Our recent re- determinations of Q, have explained a discrepancy which caused an uncertainty in the former determination of Q, at 20° and 50°, and we now find that it was due to an arithmetical error in the reduction of the observations. Fortunately, the resulting correction in no way affects the conclusions arrived at in Paper W ; and our present investigation confirms the accuracy of the experimental determinations of Qs obtained in 1894. As the extreme differences between any of our determinations of Qs at temperatures above 20° (after the arithmetical correc- tions at the 20° and 50° points) do not exceed 1 part in 70, even if we include the values found in 1894, and as the mean probable error at any temperature is much below 1 in 100, it is obvious that the values of Q, have been ascertained with more than sufficient precision. 8. Sq = Co, {(Oo! — Oo") + (a’—a)}. We have previously indicated (sect. 4, p. 6) the manner in which 6)! and 6," (the initial and final temperature of the walls of the surrounding chamber) were determined by the direct observation of mercury-thermometers. The value of d (the difference between @, and @p, 2. e. the calorimeter-tempe- rature and that of the surrounding walls) was ascertained by the differential platinum-thermometers previously referred to, and was always small—rarely greater than 01°C. It was usually determined by the reading of the galvanometer-swings without altering the position of the contact-maker on the bridge-wire. When evaporating water, the values of d were so small that an approximate value of the swing (in terms of a length of the bridge-wire) was sufficient. During these benzene experi- ments, however, we found it impossihle to maintain the thermal balance with such perfection. The only values of d which were of consequence were d' and d" (the initial and final values), and, especially in the earlier experiments, the internal temperature (9,) rose so rapidly as soon as the last drop of benzene had evaporated, that it was found impossible to switch off the electric current from the calorimeter-coil at the precise moment necessary to reduce d" to negligible dimen- sicns. As a consequence, the final swings (which were read by means of a micrometer-eyepiece) were often considerable, and therefore it was necessary to determine their value on each oveasion; for, although throughout a series of experiments at Latent Heat of Evaporation of Benzene. at the same temperature the value varied but little, the changes were sufficient to affect the resulting value of Sq in exceptional eases. In the earlier experiments, especially from Preliminary to No. VII., when the difficulty of the final adjustment had not been fully realized, the values of d@’ were unduly large, and their equivalent degree-measurements are therefore some- what doubtful, owing to insufficient determinations of the value of the galvanometer-swings. We feel sure, however, that from No. VII. onwards any errors due to this cause must be very small—certainly not so great as 1 in 50 ; for the value of a swing of 100 (in terms of a millim. of the bridge-wire) would, throughout a group of experiments at the -same temperature, vary (for example) from 1°31 to 1°34 millim.* This change in value would produce no appreciable effect on Xq when the difference between the initial and final swings did not exceed 50 or 60, as was the case in most of our later, and better, experiments. The value of Co, (capacity for heat of calorimeter and contents) remains the same as last year with the exception that 0°1 grm. of the oil was removed at the commencement of July when withdrawing the platinum thermometer for purposes of re-standardization. As the value of Co, varied with @, from 304 to 323, this loss was negligible. The quantity &g represents the heat absorbed by the calori- meter and contents, and it should be remembered that it is by the measurement of a similar quantity that the majority of the determinations of thermal constants have been made by previous observers. We were, however, anxious to diminish the importance of this term as much as possible, for we wished our values of L to be independent of any thermometric errors. As shown by Table II., the average value of =q was only about gdp of the total heat-supply._ In the experiments in which the value of 2q is less than 1 (of which there are many examples), we may say that our final results are independent of such errors, for, as pointed out in Paper W, the value of Qs is independent of temperature measurements, since it depends on the ratio of the rate of rise due to the mechanical supply to the rate of rise due to an electrical together with a mechanical supply (Paper W, p. 331). The values of Co, at 20° and 50° used in this Paper differ somewhat from those given in Paper W. This difference is due to the error, previously referred to, in the value of Qs at those temperatures. Thus the value of Co, at 20° is reduced from 307°5 to 805:2, and 59 5 STENT 3 a2a'l to 322-0. * | millim. of the bridge-wire indicated a temperature-difference of about 0°-009 C. 12 Mr. E. H. Griffiths and Miss Marshall on the This, however, in no way affects the values of L in Paper W, nor, except in the case of two experiments (viz., Preliminary and XIX. a.,znfra), would it, if left uncorrected, have affected the values of L as given in this communication. We believe that the values of Sq are correct to better than - 1 in 100; and Table I. (p. 5) shows that an accuracy of 1 in 10 would have been sufficient. 9, Measurement of Mass. The actual measurement of the mass of benzene evaporated presented several difficulties which were not encountered when working with water. A tube resembling a weight-thermo- meter was filled with benzene, placed in an air-tight case just large enough to contain it, and then weighed against a pre- cisely similar case used as a tare. The weight-thermometer (termed by us a “dropper ”) narrowed at its open extremity to a capillary tube, which was doubled back on itself for rather over 1 cm., and again bent near the open end, so that the last 1 or 2mm. were horizontal. These droppers varied in capacity from about 4 to 63 ¢e.c., and were filled in the following manner :—The dropper (point uppermost) was lowered by a fine wire to the bottom of a tube about 43 ft. long, of which the lower 10 inches or so were filled with benzene, while the upper 3 ft. were surrounded. by a “ condenser-tube ” through which tap-water was continually passing. The lower end, containing the benzene, was transferred at regular intervals from a vessel of water at about 86°C. to a vessel of cold water ; thus the benzene was alternately boiled and cooled without any escape of vapour into the room. Five or six such transferences were generally required to completely fill the dropper. The containing tube was then placed in a bath at about 65° C. until the temperature of the benzene was steady. ‘The dropper was now removed and allowed to stand in the open air for some time, in order to get rid of any benzene adhering to its surface. Although simple and effective, these operations occupied a considerable time, and, as a rule, the whole of the morning had to be devoted to the filling of the droppers required for the experiments, which were usually performed at night. Before an experiment the dropper was lowered, by means of a thread passed through a platinum wire sealed into the closed end, into the calorimeter, where it stood in a vertical position. In Paper W (p. 307) it was shown that, when filled with water, the evaporation through the capillary opening between the time - of weighing and the commencement of an experiment might be neglected. In the case of benzene, however, it was found Latent Heat of Evaporation of Benzene. 13 that, for several reasons, loss of this kind could not be dis- regarded :-— (1) The vapour-pressure of benzene so greatly exceeds that of water at corresponding temperatures that the loss by diffusion through the capillary was appreciable. (2) The surface-tension of benzene is so great that the liquid crept up the sides of the capillary to the opening, and the consequent loss by evaporation was increased. (3) In order to supply the air necessary for starting the boiling when the exterior pressure was removed, a capillary tube, closed at one end, had been sealed within each dropper. It was found that this answered very well during some preliminary trials, when the dropper was placed within a glass tube connected with an exhaust pump so that its manner of discharging could be watched ; but on a second filling with our purest sample (the first filling having thoroughly cleaned the interior surface of the droppers) no action took place even when the surrounding pressure was reduced to a few millimetres. In order, therefore, that the expulsion of the benzene from the dropper should commence as soon as the external pressure was reduced to the right amount, it was found necessary to leave a very considerable air-bubble within the tube. Precautions had to be taken to prevent the expulsion of the liquid by the alternate contraction and expansion of the air-bubble when the temperature was changed from that of the balance- case to that of the tank. . These difficulties were surmounted in the following manner. During the process of filling, as above described, the droppers stood in a vertical position, with the doubled over and open end uppermost, and were never inverted after their removal from the filling-tube, at a temperature of about 65° C., until their insertion into the calorimeter. The co- efficient of expansion of benzene is very large, and, on cooling to the room-temperature, the whole of the upper bend together with a couple of centimetres of the neck between it and the body of the dropper was found to be free from benzene. The dropper was then placed in its case and left in a vertical position in the balance-case for, as a rule, some hours, when the small air-space in the enclosing-case no doubt became saturated with the vapour and thus further evaporation ceased. After being weighed, the dropper and case were lowered into a large tube placed within the tank and left until they acquired the tank temperature @); they were then rapidly 14 Mr. E. H. Griffiths and Miss Marshall on the withdrawn and for the first time inverted—the air-bubble rising to the closed end. The case was opened for a moment and the dropper at once lowered into place by means of the previously attached thread: this operation only occupied a couple of seconds. As the dropper left the case the latter was instantly closed by a second operator to prevent the escape of any benzene vapour left within it. Thus from the time of inversion no change took place in the temperature, and therefore in the volume of the air-bubble; also no appreciable change in the temperature of the calorimeter (@,) was caused by the introduction of the dropper and contents. However, the mere act of opening the tube leading down to the calorimeter caused a slight lowering of 6), and in order to re-establish the equality between 0, and @) before commencing an experiment, it was necessary to switch on, for a second or two, the current from the exterior coil in the tank to the calorimeter coil. When the observer at the differential- thermometer galvanometer announced that @,—6@, was small and steady, the time for commencing the experiment had arrived. 10. In our later experiments, when we had become more expert at the various operations, the time from the insertion of the dropper to the commencement of an experiment was from 3 to 5 minutes. In our earlier observations at 30° the time was, however, much longer—from about 8 to 15 minutes. During this interval there was generally apparent a slight lowering of @,, which made us fear that the evaporation through the capillary was appreciable, and it was not until our tenth experiment that a means of meeting this difficulty suggested itself. It was evidently necessary to wait until 6, became steady before commencing an experiment, and it was difficult to see how to shorten the time required to establish this condition. From Experiment X. onwards the procedure was as follows. A glass rod whose upper end passed through a cork fitting the opening of the entrance-tube was lowered into the calorimeter. Round the lower three inches of this rod was strapped (by fine platinum wire) a thin roll of cotton-wool of which the upper two inches were saturated with benzene while the lower end was left dry, so that there was no danger of drops of benzene falling from it into the silver evaporating- flask. | ‘The rod was withdrawn occasionally and more benzene added if the upper portion of the roll had become dry. Obser- vation of the galvanometer showed when the cooling effect Latent Heat of Evaporation of Benzene. 15 caused by the evaporation had ceased, and we were thus able to determine when the flask and connecting tubes were saturated. The rod was not finally withdrawn until the dropper was introduced : thus the space being saturated, no further evaporation took place; and we believe that from Experiment X. onwards any error arising from evaporation in the time preceding the experiment may be disregarded. After we had completed our experiments, we made some observations with the object of ascertaining the probable magnitude of the error in lixperiments I. to VII. due to evaporation when the flask had not been previously saturated. A dropper was placed within the evaporating flask for 20 minutes and kept at a temperature of 30°C. It was then withdrawn, and the loss determined. As might have been expected, it varied slightly according to the droppers used, _ probably owing to the different sizes of the capillary opening. In 20 minutes, dropper II. lost 10 milligrams, A: :, pec ih ec ” ” ” IV. 5 13_ ” After Experiment VII. we adopted the plan of noting the time from the insertion of the dropper to the commencement of the experiment, but unfortunately we had not previously done so. We consider that the average time in these experiments must have been from 10 to 15 minutes ; the loss during this time would therefore appear to have been about 6 milligrams, or rather more than ;4;. Thus the values of L resulting from Experiments I. to VII. are probably too low by about 0°12. Fortunately we have six independent experi- ments at 30°C. (Nos. XXIX. to XXXIV.) in which this cause of error was absent. We have entered into this matter fully, as it shows the importance of extreme attention to details in work of this kind, and also it was necessary to explain why we practically neglected Experiments I. to VII. when drawing our final conclusions. The same cause of error would slightly affect Experiments VIII. and IX. at 40°C. At this time, however, we were attempting to minimize the evil by allowing as short a time as possible to elapse between the introduction of the dropper and the commencement of an experiment. We have also a note of the time, which in both cases was less than 4 minutes. The loss during this interval would probably not have affected the resulting values of L by more than 05, and we therefore do not consider it necessary to reject these experiments. At the close of an experiment, when observation of the 9? 16 Mr. E. H. Griffiths and Miss Marshall on the galvanometer showed that all evaporation had ceased, the dropper was extracted by means of a bent wire, immediately placed in its case, and weighed again after standing some hours in the balance-case. Let m, and mg be the weights of the case and dropper before and after an experiment; the temperature of the balance-case was usually about 20° C., the specific gravity of benzene at that temperature may be taken as 0°88, hence M (true mass corrected to vacuo) = mM — mM, + (my —m,) x °0012. 11. Before commencing the experiments it was necessary to ascertain if any alteration had taken place in the values of the various constants and variables since their determination in 1894. Thermometers IJ. and A were re-standardized and it was found that a “zero-point rise” had taken place, as is customary with mercury thermometers. Thermometer No. II. had risen 0-4 mm.=0°:02 C. since its standardization in August 1894. Thermometer A had risen 1:°4 mm.=0°-06 (nearly) since its standardization in July 1893, which is about the normal rise of thermometers of this description. The platinum thermometer (AB) was removed from the calorimeter, strapped to its corresponding thermometer (CD), and placed in the tank whose temperature was raised from 18° C. to 40° C. Observations at different temperatures showed a rise of 0°45 mm. in the null-point whose position is now given by the formula 598°8+°:03@ in place of 598°35 + "030. If, however, this change, which probably took place in the arms of the bridge rather than in the thermometers *, had not been detected the resulting error would have been negligible, for a difference of ‘45 mm. in the setting of the null-point is equivalent (at 40°) to a temperature difference of about :0041° C., and the total loss or gain by radiation, &e., corresponding to this difference between @, and @ would not exceed 0°2 thermal gram per half-hour, whereas the actual duration of the majority of these experiments was about 18 minutes. The corrected formula was, however, used throughout these experiments for the adjustment of the contact-maker. * [Note by E. H. G., August 12, 1895.—I have found by re-standard- izing the bridge-arms, that the above supposition was correct. ] Latent Heat of Evaporation of Benzene. 17 12. Value of Ry. The values of R; were redetermined at temperatures 30°, 40°, and 50°. The corrected results showed falls of -0012, "0012, and :0016 respectively from the values of 1894. These quantities have, therefore, to he subtracted from the values given in Paper W, table viii., but the correction is only 1 in 10,000 of R. The following table gives the values of R, used during the reductions of the observations on benzene. (The suffix to R denotes the potential-difference in terms of a Clark cell.) TABLE III. Temp. Rye. Re. Rye. 30 10327 10°329 10:333 30 10351 10353 10°357 40 10374 10377 10381 50 10-399 10-401 10-406 OR per 1° C.=:0024. The re-standardization of the Clark cells has already been referred to (section 6, p. 8). i a No alteration in the values of Q, at 30° and 40° C. appears to have taken place. The values of Qs at 50° and 20° as given in Paper W, pp. 332, 333, appeared to have undergone alteration, and we therefore made a careful redetermination at those temperatures. The method adopted was that described on p. 292, Paper W, viz., the rate of rise in temperature at null-point was deter- mined (1) when the heat-supply was that due to the stirring only =( a ), and eee dt (2) when the heat-supply was that due to the stirring and a Phil. Mag. S. 5. Vol. 41. No. 248. Jan. 1896. C 18 Mr. E. H. Griffiths and Miss Marshall on the potential-difference of 3 Clark cells dO, Hence ees . es gives the ratio of the heat supplied by the stirring to the heat-supply when the potential-difference was that of 3 Clark cells ; and as the latter can be calculated if R, is known, the value of Q, can be obtained without any assumptions as to the thermometric scale, the capacity for heat of the calori- meter, &c. The individual experiments were in close agreement with each other and give the following results :-— At 50°, (2) ='14533 expressed in mm. of bridge-wire sees where rate of stirrmg =5-380, oy). = 001155, at rate 5-380. Hence Q, (at rate 5:380) =-003404 ; but (see Paper W, p. 330) a =a constant = a. hence Qs =°003206 at rate 5-300. A second determination gave Qs =*003202 at rate 5-300. A third gave Q;='003205 at rate 5°300. We therefore assume Qs ='00321 + (7,'—789) x 0000041, as sufficiently accurate. Latent Heat of Evaporation of Benzene. sy At 20°, ( = =-15941 at rate 5-590, 3e8 : — = ‘00427 at same rate. Bence Q, (at rate 5°590)=-01174 ; pitt i =a constant = iD, Ou i OLL72? hence: Q.='00949 at rate 5-300. A second determination gave ‘00951 at rate 5°300, A third . pp OOOO Tesi ide DBO: In this last experiment, however, there is internal evidence of some error in the time over the second interval. If we omit this interval and calculate the value of Q, from the remaining intervals of that experiment, we get ‘00961 as the value. It is evident that ‘00950 is a sufficiently close approxi- mation. We therefore assume Q, =°00950 + (7* —789) x -0000120. Our experiments at 30° and 40° show that the values of Q,; at those temperatures as given in Paper W are correct. The errors at 20° and 50° as given in that paper were due to an arithmetical mistake, a difference having been added, instead of subtracted, in each case. The following Table gives the expressions by which the value of Q, can be obtained at any of the temperatures or rates given in succeeding Tables :— TABLE IV. i Temp. Value of Qs (in thermal grms.). 50 00321 + (7,;4—789) x 0000041 40 00466 + (r,* —789) x 0000059 30 ‘00665 + (r,4 —789) x 0000084 20 0950+ (r,4—789) x 0000120 G2 20 Mr. E. H. Griffiths and Miss Marshall on the These changes in Q, probably indicate the changes in the viscosity of the oil. 14. Alterations in the Apparatus. No alterations have been made except in exterior portions of the apparatus. When working with water in 1894 there were, in the tubes leading to the air-pumps, one or two rubber joints which are now replaced by glass ones. To prevent condensation, the benzene vapour after issuing from the tank passed over a row of small gas-jets and then down into a small Wolff’s bottle, connected with the mano- meter and containing pumice-stone and sulphuric acid. It then passed through another tap* into a large globe (capacity about 35 litres) also containing pumice-stone and sulphuric acid. By means of a water-pump the pressure in this globe was reduced to that of the aqueous vapour at the temperature of the tap-water. Its capacity was so great that the pressure in the Wolff’s bottle could, at any time, be brought below that required, at experiments above 20°, by simply opening the tap communicating with the globe. Thus the water- pump had not to be used during an experiment, and, consequently, the two motors worked with greater regularity. The Wolff’s bottle was also in direct communication with a Geissler’s mercury-pump, by means of which, when working at the lower temperatures, the pressure was greatly reduced near the close of an experiment in order to secure the boiling- off of the last drop of benzene. We found that the mercury- pump had to be kept in constant use during the experiments at 20°. With the exception of the above alterations and additions, the apparatus is the same in every respect as that figured in Plates 4, 5, and 6 of Paper W. 15. On the Purity of the Benzene. The benzene, which was a sample of that used by Professor Ramsay and Miss Marshall for their comparative experiments, was supplied by Messrs. Kahlbaum of Berlin and guaranteed free from thiophene. It was redistilled twice from phosphoric * The grease on the core of taps traversed by benzene was replaced by phosphoric acid. Latent Heat of Evaporation of Benzene. 21 anhydride, until it showed a perfectly constant boiling- point. 16, Description of an Experiment. The dropper was placed in position (as described in section 9) and the contact-maker was then set, by means of a magnifying- glass, to the null-point corresponding to the tank temperature O° When the observer (Observer II.) at the thermometer- galyanometer (G_,) announced that 6, had become steady, three observations of the galvanometer-swing were taken, and the chronograph-key, being pressed at the second of those swings, recorded the time from which t, was estimated. At the same moment Observer I. recorded the reading of thermometer II., which when reduced to the nitrogen scale gave the value of 6)’,—the initial tank temperature. As a rule the initial swings were somewhere between 0 and +50 (a swing of +50 would correspond to about +°006° C.), and, for reasons which will appear later, we preferred to have this initial swing (which gave the value of a’) positive. The Wolff’s bottle (condenser A) had previously been exhausted down to the pressure of the large globe (condenser B) already referred to, but the tap between the two condensers had been closed. A tap (immersed in the tank-water) between the silver flask and condenser A was then opened, and the air expanding into A caused a fallin the manometer attached to it. The tap connecting condensers A and B was then eradually opened, and the pressure in the flask fell until some benzene was expelled from the dropper. The instant this occurred the calorimeter temperature 86, commenced to fall, and Observer I. was acquainted with this fact by Observer II. who, throughout the whole experiment, was engaged in calling aloud the galvanometer-swings which resulted from the inversion of the battery connexions in the differential-thermometer circuit by means of a swinging key. The storage-cell current, which had been running for some time through a platinum-silver coil immersed in oil in the outer tank, was then switched on to the calorimeter-coil, the action recording itself on the chronograph-tape, and the potential balance then adjusted by means of the apparatus described in Paper J, p. 283. This balance had previously been approximately obtained while the current was running through the tank-coil; thus only a small additional adjust- 99 Mrwle EL Griftthis-and. Miss Masdhalluon Whe ment was required and, as the temperature of the calorimeter- wire remained constant, the electrical balance required little attention, for the potential-difference rarely altered by as much as 100,000 throughout an experiment. As the benzene vapour passed into condenser A the pressure in the flask increased, and thus the loss of heat by evaporation diminished. By a rapid movement of the tap between condensers A and B, the pressure could again be diminished and the cooling effect increased. It was found impossible to control the rate of evaporation with the same perfection when using benzene as was the case in the experiments with water. The taps had to be constantly manipulated, and a moment’s inattention on the part of Observer I. was immediately followed by a sudden rise or fall in @,. This was more especially the case during ~ the experiments at low temperatures. From about experi- ment V. or VJ. onwards, however, the swings rarely amounted to as much as 200 or so, except during the first minute when the thermal balance was being obtained, at which time a swing of +400 or 500 was generally experienced. Through- out the whole of an experiment care was taken that any positive swing should be succeeded by a corresponding negative one. Although the announcement of swings of ‘ +200” appeared alarming at the time, the extreme attention devoted to the keeping down of these oscillations was really unnecessary. A swing of +200 indicated that 0) was lower than 6, (at 40°) by about 0°02 C., and the radiation dc. coefficient of the calorimeter being about 00009 (in degrees per second per difference of 1°, Paper W, p. 289), this swing, even if maintained throughout the whole téme that evaporation was proceeding (on an average less than about 7 minutes), would only have resulted in a total loss of about ‘00009 x 318 x ‘0216 x 7x 60='25 thermal gram *. In no case, however, was a swing of such magnitude allowed to remain unaltered for more than a few seconds. The chief difficulty was experienced near the close of an experiment. When working with water, there were always some indications that the end was near, for the pressure had to be diminished in order to maintain the thermal balance if only a drop or so remained, In the case of benzene, however, there were rarely any such indications ; for the galvanometer- * About so50 of the total “ heat-supply.” - Latent Heat of Evaporation of Benzene. 23 swing might be announced as +8 or +10, and before the next announcement could be made it would be found that it had shot up to 800 or 400. After the preliminary experiment, it was of course possible to roughly estimate (knowing the weight of the dropper when filled) the probable duration of an experiment and, by adding it to the observed time of establishing the current, to predict approximately the time whenevaporation would cease. Owing, however, to differences in the size of the air-bubbles necessarily left in the droppers, to the different rates of stirring, &c., and to errors in calcu- lations made while all the attention of the observers was needed elsewhere, the current was very often switched off too late, thus increasing the value of the correction 2g un- necessarily. If any mistake was made, the final value of 6, was in consequence higher than the initial one, for in those cases where the current was switched off too soon, it was always possible to bring 0, up to its initial value by re-estab- lishing the current for a second or two; if, however, @, was too high there was no means of diminishing it, all the benzene having been exhausted. Observer I. endeavoured, if possible, to arrange so that the swing at the close of an experiment should be about —150, for the following reason. Hvaporation having ceased and the current being switched off, the tap between the evaporating-flask and condenser A was closed, and a tap (also immersed in the tank-water) was slowly opened so that air (dried by having passed through sulphuric acid and phosphoric anhydride) was gradually admitted into the evaporating-flask through a 30 ft. copper coil immersed in the tank. Thus the air was at the temperature of the calorimeter. The heat liberated by its compression caused, however, a rise in 0, equivalent to a swing of about 120; thus no heat was, on the whole, gained by the calorimeter, for a corresponding loss had been experienced during the exhaustion. Qn this account we preferred to commence with a small positive swing, as it was not then necessary to reduce 0, so far at the close of an experiment to allow for this final increase. When Observer II. found that 6, had again become steady three final swings were taken, the chronograph- key being pressed at the middle one, thus giving the ter- mination of the time ¢, during which the stirring supply had to be estimated. Thermometer II. was read at the same time, and gave 6”), the final tank temperature. Throughout the experiment, every thousand revolutions of the stirrer had been automatically recorded on the chronograph-tape. 24 Mr. HE. H. Griffiths and Miss Marshall on the The method of removing and weighing the empty dropper has already heen indicated. 17. Remarks on the Experiments. We give particulars of all our experiments with two excep- tions. In No. XXI.a. the chronograph ceased to work during a critical portion of the experiment, and we were thus unable todeterminet;. In XXIYV.a. Observer I. omitted to close the entrance tap to the evaporating-flask before connecting with the exhaust, thus the attempt to diminish the vacuum was a failure and the experiment was relinquished after a minute or so. In these two cases we at once performed other experi- ments to replace the failures, but retained the numbers for convenience of reference. We have, however, rejected, when drawing our final con- clusions, several of the experiments whose details are given. Such experiments are marked by a f in the Tables. We have, in no case, rejected any experiment eacept as a conse- quence of some note made during that experiment; that is, before reducing the observations we had already decided as to those which should be regarded as of little value. Thus we have in no way been guided by the results. For example, XXV. differs from the mean of its group by a greater quantity than either of the rejected experiments at that temperature : however, as we have no note against it, we are compelled to give it equal importance with any of the ‘others. A simpler plan would have been to reject entirely the + experiments, but we think that a fairer idea of the general accuracy of the work is given by including all those that we completed. The reasons for the rejection of the + experiments are given (as they appeared in our original notes) at the end of each group. We have, however, in each case given the mean of all in a footnote, and it will be seen that (except at 30°) our results would not have been appreciably affected by the inclusion of those rejected ones. As a rule, we found that the thermal balance was most easily maintained when the potential-difference was that of 4 cells, but this supply of heat would have been somewhat too great at 20°, when we worked with 3 cells only. At all temperatures above 20° we performed experiments with 3, 4, Latent Heat of Evaporation of Benzene. 29 and 5 cells, and we regard the agreement amongst the results as very satisfactory, and as establishing the validity of the various corrections. In thermal investigations it is as a rule difficult to alter all the conditions in so complete a manner as that caused by the changes above referred to. For example, ifany “ priming ” had taken place (the usual cause of inaccu- racy in determinations of the Latent Heat of Evaporation), its effect must have been greatly increased when the rate of evaporation was nearly trebled, which was the case when the potential-difference was altered from 3 to 5 cells. Again, the importance of the different terms undergoes such changes that any constant error in the determinations of Qf, and 2g would cause the values of L when n=4 to lie between the values when n=3 and n=5. An inspection of the Tables will show that no such effect is visible. We also varied the “ stirring supply” very considerably. The Tables show that (at the same temperature) the values of Q, have been changed from ‘00276 (Expt. XVII.) to -00427 (ixpt. XXIYV.). [ Note by E. H. Grirrirus.—My experience with apparatus of a similar nature to that used in these experiments has con- vinced me of the severity of the test above referred to. During my attempts at a determination of the mechanical equivalent during the years 1887-1891 the results invariably broke down when thus tested. The following quotation, refer- ring to the experiments anterior to 1892, is from p. 364, Paper J :— “The agreement amongst individual experiments taken under the same conditions, was, if anything, at times more marked than in the experiments of 1892 ; nevertheless, when the final reduction took place, fatal discrepancies invariably showed themselves. . . . Hxperiments conducted with a high electromotive force invariably gave too great a value for the time as compared with that obtained when a lower electro- motive force was used.” It appears to me that it is this power of altering all the conditions which renders electrical methods of such great value when applied to thermal determinations. | 26 Mr. E. H. Griffiths and Miss Marshall on the 18. Explanation of the Tables. Tables lettered A give the experimental data; the deductions from those data are given in Tables lettered B. (We have arranged the experiments in order of temperature rather than historical order, as consecutive experiments were not always at the same temperatures.) TaBues A. Col. I. a and b give the number and date of the experi- ment. ns II. a and b give the number of Clark cells in series, and the number of the dropper used. x III. Gives the mass of benzene evaporated, after cor- | rection to vacuo (M). = IV. The time during which the current was main- tained (¢, ). i V. The time from commencement to end of experi- ment (¢,), « ¢., the time during which the “ stirring supply ” has to be estimated. a VI. The number of revolutions per second (7) of the stirrer. » WII. The difference between the initial (0)’) and the final temperature (@)”) of the surrounding walls. , WIII. Let 0,’ (initial calorimeter temperature) exceed 6,’ by d’, and let 6,” (final calorimeter tem- perature) exceed 0)” by d” ; then this column gives the value of d’—d”. Hence { (Oy — 9”) bate (d’—d’") } gives the difference between the initial and final temperature of the calorimeter. £ IX. The capacity for heat of the calorimeter and its contents at the mean temperature of the tank (C,,)- | ie X. The temperature of the Clark cells. - XI. The value of R,,, 7. ¢., the resistance of the calorimeter-coil at temperature @,, when the potential-difference of its end is ne. (From Table IIL. p. 17.) Latent Heat of Evaporation of Benzene. 27 19. Tasies B. (The numbers of the columns are similar to those in the corresponding tables of Paper W, where full particulars of the reductions are given.) (ne)? x t,, Col. XY. The value of Q.t,= R, ea potential-difference of f Clark cell, at the temperature given in Col. X. (supra). The values of R, will be found in Table ILL. p. 17, and, as previously explained, the value of ; J =4°199 (see section 6, p. 8). » VI. The value of Q, deduced from Col. VI. by means of Table IV. p. 19. » XVII. The value of Q¢,, the “stirring supply,” from Cols. V. and XIV. », XVIII. The term 2g=C, {(0/—9)")—(d’—d")}_ from Cols. VII., VILI., and IX. oe EX. Ehesum of Cols. XN, XVII., and XVIIL., that is, the total thermal grams (3) required for the evaporation of M grms. of benzene. , X&X. The mean tank temperature (6)) of the experi- ment, expressed in the nitrogen scale. Po I> The value of Li— ae where e is the Remarks on Experiments at 50°. Hxp. X1X.a. “ Mistake in switching off current, did not do so till 0, had risen so far that d’” could not be obtained by means of galvanometer-swing. Had to readjust contact on bridge at close of experiment. Decided to regard experi- mentas a failure and repeat it.”’ The experiment is included in the table to show that even the large resulting value of the term %¢(—18°64) has but a small effect on the value of L, which differs from the mean at this temperature by less than 1 in 400. This value for L(98°90) should, however, certainly not influence our final conclusions. Exp. XXIII.—“ Mistake in connecting with vacuum, re- duced pressure far below right amount, hence could not obtain proper thermal balance throughout experiment.” Conclusion. When 6,=50:014, 1=99-14. Mr. E. H. Griffiths and Miss Marshall on the 28 666-01 907-01 90F-0T 668-01 09-91 8900:— 09-GT ‘ 1¢00-— LL-GT a 1500-— 89-CT , PI00-— OL-GT 3 0800: — FE-G1 Y 0£00:— v9.41 9700-+ 08-ST é 09¢0-— 08-S1 : 7910-— 08-ST GG&S 0100: ae ‘sITeO jo Oy p= p ‘dw, x ‘XI ‘IITA F900. + L100-+ FG00: + F600: — G000- + P00: + G00: + 0600: — 0 699-¢ | P-GOPL | ¥-TTOT G69-¢ | 0-FL8 9-61F TI¥-G | GPCOL | G-9IP G6L-¢ | 9-L6¢T T-OL0T 616-9 | 6PIEL | 9-6a9 TAL-G | 0-266 1-69¢ TPG | GE6OT | L-S19 9GI-¢ | &-FOGL | 1-019 SITE | L8IIL | P-c29 LOT-G | G6ISL | F8e9 “ity 8, a, IA “A “AT "O o0G 78 sjsu tedx Ty “VA WTayvy, 6686:P 9900-9 9616-4 OSGE-F 6686-7 VS9E-P TPGL-F 9896. TLOL-F 6880-9 m)=121@)) jo ‘ON JUL “SsT[9D jo ST 8I Li LI oT 91 ial al VI vI Aine ayBq vl “AXX IHG DG, “TIXX4 TIX 9 IXX “xX 9 XIX "DXIX+4 TITAX TIAX —— "10qUUN Ny D 29 of Benzene. zon O Latent Heat of Evaporat 1£0-+ 01-66 +E0-+F1-66 48:86 80-66 400-66 60-66 F1-66 L6-66 1€-66 106-86 06-66 06-66 24 ITXX “** gad om oangesodure} siqy ye syuotItedxe [][e epnfout om FT 9000-00000 (4 peyreur esoq} SUT}j1U00) uvoyl cF-0 — F8-G 66-1 — PLS FL:0 — LG-€ GGL — 0G-P 18-0 — 96-€ 84-0 + 06:6 66-6 + CE-§ F9-81— RG-S 16-7 — GL GE-0 = b9-E De SI8% TITAX ‘TIAX 91400: LG¥v00- 6FE00- - 9600: TO0¢00: 06200. L0€00- 08 unity), the interpretation of this being that an increase of pressure is accompanied by an increase in the temperature. The slide therefore does not require to be reversed as in pv and vT calculations ; but with a rule of the Gravet type, owing to the scales C and D being the square roots of A and B, it is necessary to use a fictitious index obtained by dividing —’— by the logarithmic ratio of the Saar g scales, giving Wis" It would also be quite possible to graduate one edge of the index slide with fictitious values to compensate for the ratio of the scale-readings. 4, In the process described in (1) we have the means of plotting a series of adiabatics or isentropics, and each position of the radial cursor on the rule gives in its readings on the index line a corresponding isentropic, and a movement of the cursor to the left corresponds to a gain in entropy and vice versd, and it can be shown that equal increments of linear movement of the cursor correspond to equal increments of entropy. In other words, the scale of inches or centimetres on the edge of the rule may be regarded as a scale of entropy in arbitrary units. 5. The following is a very good example of the use of the radial cursor in practice. The theoretical efficiency of an Otto cycle gas-engine is independent of the working temperatures and is given by the Loy : Ve \? : . . expression 1—() , where v, is the total effective volume 1 of the cylinder and compression-space, and v, = volume of compression-space alone. Taking y=1-408, y—1="408. This is beyond the range of the instrument, so we will employ ~~ = 2°45. 58 The Radial Cursor: a new addition to the Slide-Rule. Fig. 5. > \Y=1 Efficiency of Otto Cycle Gas Engine = 1— ( ae : 1 Focal Lengths of Mirrors and Lenses. 59 Let us suppose that in the case we are dealing with = 1 comes out at °32 (an actual example, see ‘The Hngineer,’ April 6th, 1894). Set the index slide to 2°45 and place cursor accurately opposite middle 1 on scale A (use one of end lines on slide to centre with), and set index line to °32 (=) on scale A (over to the left, fig. 5). | “1 Now using one of the end lines on slide read on scale A opposite to intersection of index line on scale D, but read backwards from the centre 1. This will be found to give ‘37, or the theoretical efficiency of an Otto engine having ratio of expansion °32 is +27. 6. To determine x in such an expression as io. 1 Here z will be a fractional index, and we shall first find -. Set cursor to 1 in centre of scale A. cg Set index line to 7 on scale A, and keeping it there move slide of cursor till index line intersects scale D opposite figure 3 on scale A (use end line of slide). Now read result on index-scale S76: Or t= z7e = “DOS. IV. Graphical Method for finding the Focal Lengths of Mirrors and Lenses. By Epwin H. Barton, D.&c., LRSLE., Senior Lecturer and Demonstrator in Physics at University College, Nottingham*. N his ‘Geometrical Optics’ Aldis gives a graphical method for exhibiting simultaneously the focal length of a cone cave mirror and the distances from it of any two conjugate foci (page 30 in third edition). The present note consists of the extension of this principle to the cases of a convex mirror and thin lenses and its application to the practical problem of finding focal lengths. This experiment is usually a little perplexing to junior students in a physical laboratory. It is therefore hoped that by giving publicity to this method (which, simple and obvious though it is, does not seem to * Communicated by the Author. 60- Dr. E. H. Barton on a Graphical Method for have found its way into any of the ordinary text-books) the labours both-of students and demonstrators may be somewhat lightened. Let the following notation and convention of signs be adopted :— Focal length, — x Distance of object, U. Distance of image, v. All distances to be measured from the mérror or lens, and to be reckoned positive when measured against the direction of the incident light, and negative if with that direction. Then we have :— For mirrors, (2) For the graphical method take two rectangular axes of coordinates OX and OY, and let a straight line pass in any direction through the point M,, whose coordinates are (jf, /); then it follows at once from (1) and elementary geometry that its intercepts on the axes of w and y give a pair of corre- sponding values of u and v respectively for a concave mirror of focal length f (see fig. 1). This is the case already referred to as given in Aldis’s ‘ Geometrical Optics.’ Now if the rota- ting line pass through the point M,, whose coordinates are (—/, —f), we have, as seen from (1) also, the case for a con- vex mirror. Similarly, by consideration of (2), we see that the points L, and Lz, whose coordinates are (—/f,f) and (7, —f), give the completing cases for a concave and a convex lens respectively. The first uses of this graphical method are to afford a picture of the corresponding values of wu and v for any mirror or lens for which f is known, and to enable the student to trace the series of values through which v passes as w changes continuously from infinity to zero. But in this view of the matter no very great advantage is gained, as it is almost as troublesome to the student to remember the — positions of the fixed points through which the revolving line must pass for the various cases as to recall and rightly use the corresponding formule. The second and more important use of this method is its application to the determination of / for a given mirror or lens when the optical bank is available with which to observe L v and for lenses, i v finding the Focal Lengths of Mirrors and Lenses. 61 corresponding values of u and v. This supersedes the use of the formule, or the recollection of the positions of the four Fig. 1. fixed points mentioned above, avoids the cumbrous calculation of reciprocals, and at the same time exhibits a criterion of the accuracy of the experiment. The student has simply to (1) mark off along the axes of « and y with due regard to sign the corresponding values of u and v as observed on the 62 Mr. Rollo Appleyard on a bank ; (2) join the two points thus obtained; and (3) repeat these operations for another pair of values of wu and v. Then the coordinates of the intersection of the two lines give the focal length required. An additional check is obtained by taking a third pair of values of u and v, or by drawing through the origin of coordinates a line inclined at an angle of 45° with the axes. In either case the three lines obtained should intersect in a single point. In any actual experiment this is not likely to be precisely the case; but the value of / can readily be inferred, or, in case of a great discrepancy, the results rejected and the experiment repeated. Below are the data for determining the focal lengths of a concave mirror and a convex lens, which are utilized in the figure. Example I.—Concave Mirror. Observed values of w./Observed values of v. nn iO —n— OOO . em. cm Hirst pain ¢.2.22.5- 60 29°7 Second pair ...... 33 50 Check pair ...... 41 39 Result :—f=20 centim. nearly. Example II.—Convex Lens. Observed values of w.|Observed values of wv. em. cm. Birst palm 2 22s-se: 30°5 —19 Second pair ...... 15 —61 Result :—f=—12 centim. nearly. V. A“ Direct-reading ?? Platinum Thermometer. By Rotito APPLEYARD*. Me SSRS. CaLtnenpar and Grirrirss and their colleagues at Cambridge have proved that the platinum thermo- meter is capable of measuring temperature with an accuracy of one thousandth of a Centigrade degree. For general * Communicated by the Physical Society: read November 22, 1895. Direct-reading”’ Platinum Thermometer. 63 purposes, temperature is never required to be measured with a precision greater than one tenth of a degree. It is my object to consider how the reserve of precision may be utilized in facilitating the processes of testing. The results seem to indicate that it is possible, with a platinum thermometer, to determine ordinary temperatures by a single operation, of such a kind that the readings are “ direct”’—that is to say, no calculation requires to be applied to them. In the course of some experiments upon the variation of the electrical resistance of dielectrics with temperature, an apparatus was needed which, bya quick and simple operation, would measure the temperature within the substance of the dielectric. As dielectrics, generally, are bad conductors of heat, it is desirable to take simultaneous readings of tempe- rature at many points within their mass. A platinum thermometer may be regarded as having an extensible bulb, for the wire may be distributed to various points within the dielectric; the temperature deduced from the platinum thermometer, at any instant, is therefore equivalent to the mean of the simultaneous readings of a large number of dis- tributed mercurial thermometers. Further, the dielectrics, in their protecting covers, are submerged in a tank of water ; the stems of ordinary mercurial thermometers placed, verti- cally, beneath a water-surface would be difficult to observe ; the platinum instrument is far more convenient for this work, for it has the advantage of a portable stem and scale. The resistance of a dielectric* is by no means such a definite quantity as the resistance of a metallic conductor. The difference in quality between samples of the same name, the age of the substance, the nature of the contact between the dielectric and its electrodes, and the so-called “ electrification,” are such variable factors that the term “‘ dielectric resistance ” has only an empirical significance. To arrange for the mea- surement of temperature with extreme precision is therefore unnecessary. Range. For certain practical reasons, the temperatures mentioned in this paper are referred to the Fahrenheit scale. The required range was 32°-120° F.; and, within the present limits of accuracy, it is safe to assume that the resistance, R,, of the platinum coils, at any temperature ¢, within this range, is represented by the expression pene ee ate Tt TS * See “ Dielectrics,” Proc. Physical Soc. xiii. p. 155, 1895; Phil. Mag. 1894, xxxviii. p. 396. 64 Mr. Rollo Appleyard on a The Platinum Coils, There were six platinum coils, forming six thermometers, each having a resistance of about 7 ohms. Lach consisted of about 2 metres of pure platinum wire, of 8 mils diameter, wound in double spirals upon an ebonite rod. Thick copper leads were soldered to the ends of the coils. To determine a and Rz, the six coils were separately tested in melting ice, and then at various temperatures in heated water, side by side with a mercurial thermometer. These measurements were made with the coils submerged in a large tank, the temperatures being controlled by a gas-regulator. The resistances were measured on an ordinary “dial” bridge having german- silver coils. This part of the work occupied much time: a was derived from the mean of the best of 30 determinations ; it was somewhat tedious, but the values Rz, and @ proved, in the result, very accurate. The six coils of the six thermo- meters were afterwards connected in series, and regarded as one thermometer. The mean values were :— Rs, =40:05 ohms (six coils, in series). a= -O02097. The six platinum coils, still connected in series, were then imbedded within their respective dielectrics. Hollow metal tubes, for mercurial thermometers, were inserted at the same time within the dielectrics, for check-readings. The dielec- trics were then immersed together into one tank of water. Measurement of R, by “ Dial” bridge. The apparatus was now complete, and tentative tests were made for R, at different temperatures. The results, when compared with the mean of the readings of the mercurial thermometers in the tubes, were rather discouraging. The temperatures could not be depended upon within about 2° Fahr. These errors were due either to the german-silver coils, or the plugs, of the dial-bridge. Slightly better results were obtained by reducing the battery to a single cell. It was impossible to determine the bridge-temperature, at any time, with accuracy; and, moreover, even if that temperature could have heen found *, the temperature-coefficient for dif- ferent samples of german-silver varies so widely with different samples, that no dependence whatever could have been placed upon values “corrected” by text-book coefficients. The * A platinum coil interwound with one of the resistance-bobbins would probably be the best method under these circumstances. “ Direct-reading” Platinum Thermometer. LL gS oe SIA Z WES LAE | oa! SOS a aPI PP Y DOD DTI IID Phil, ee S. 5. Vol. 41. No. 248. Jan. 1896. iy 66 Mr. Rollo Appleyard on a “ dial” bridge was therefore abandoned, and a slide-bridge of special form was designed for the purpose. Measurement of R, by Slide-bridge. The slide-bridge, fig. 1, consists of a 12-ft. plank, P, with a groove G cut along its whole length. A metre-scale, 8, can slide in the groove, flush with the upper surface of the plank. Datum-marks are made at successive metres along the plank; subdivisions being read upon the sliding metre- scale. The contact-piece, L, is attached to the metre-scale at its zero-point. This saves the cost of an elaborate graduation of the plank ; and keeps the sliding-contact very accurately in position. When necessary, the metre-scale with its con- tact-piece is easily transferred to other such slide-bridges. There is no distortion of the slide-wire, and indentation is almost impossible*. The slide-wire, W, is of platinoid T stretched between two adjustable blocks of copper, B. Its ends are soldered into saw-cuts made in the copper blocks. On the other side of the scale-groove there is a copper wire, J, for the galvanometer-contact. The contact-piece consists of an ebonite block K, with a gap at one end. The platinoid wire slides through a saw-cut M transversely to this gap in the ebonite. A Y-shaped piece of spring-brass, L, is screwed to the ebonite block. One end of the Y, projecting over the gap, is provided at N with a platinum knife-edge. The other two arms of the Y project beyond the other end of the ebonite block, and. carry clips, R, through which the wire for the galvanometer-contact slides. The bridge-coils, fig. 2, consist of five silk-covered platinoid resistance-bobbins, immersed in a double vessel of copper, the inner vessel containing 14 gallons of paraffin-oil. A glow-lamp, submerged in the oil, is used for maintaining the temperature constant at 80° F.; this temperature was chosen as being just above ordinary air-temperature. Copper rods (a, b, c, e,f,g9,%) connect the coils ; their ends pass upward, through the wooden cover of the calori- meter, to the switch. Fig. 2 shows the arrangement of these coils. The two ends of the slide-wire go to f and g respectively ; to which points the 100-ohm coils (7/,e) and (g, a) are connected. By switching p to J, the fixed arm (45 ohms) of the bridge, < is very convenient optical bench could be made by such a grooved ank. é + Platinoid is not good for slide-bridge wires. After about two months’ exposure this wire has become blackened, and I am replacing it by a wire of platinum-silver. Direct-reading” Platinum Thermometer. 67 Fig. 2. SWITCH. Permamemtly lo Switch. : Permanently to Switch. | Mr eibieneeenu Roaslance. P+q free, slo m, valto = Oerew S fo m whem 95 otums are wanted . Jo Slide-Wire Jo SlideWute do Battery. F 2 68 _... Mr. Rollo Appleyard on a connected between a and 3, is balanced against the 45 ohms between 6 and e; the slider has then a position at the middle of the slide-wire. When p is switched to n, the platinum thermometer is substituted for the (0, e) coil. Calibration. To calibrate the bridge, the switch (fig. 2) is set with p, g horizontal, and s screwed firmly tom. This puts 45+10=55 ohms between 6 and e, and the slider has to be moved to a new position along the plank. A simple calculation enables us to find an expression for the temperature, ¢, of the platinum coils in terms of n, the distance in ems. of the sliding-contact from the extreme left of the plank-scale. The actual figures for this particular bridge are here given. Corrected values of the bridge-coils, at 80° F. Between a and 6 = 45:138 ohms. 3 C ty, C= A 10. ee op tt Be sg Ca OOF we Ee. , The coils 100, 100 require no correction ; they were ad- justed at 64°5 F., and we are only concerned with their equality at the slightly higher temperature. Value of vr, the resistance of 1 cm. of the slide-wire.— Balancing (45°15 +10°032) ohms against 45°188 and noting the corresponding value* of n, we have ~45°138[ 100+ 241°95 vr] =55°182[1004 58°05 vr]. Whence r="1301 ohm... |. eee R, 2n terms of ¢.—Putting the values for Rsg and @ in (1), the equation becomes R,=40-05[1+-002097(t—32)], . . . (3) that is, within the required range of temperature. To this may be added, without sensible error, the resistance of the thick copper leads going to the platinum coils ; this was ‘025 ohm, so that R= 37:39 +0°084t. . . R, in terms of n.—The general equation of the bridge will be R,[100 + (800 —n)r] =45°138(100 +- nz). Or 4513°8+5°8745 os 139°04—"13012 ©) * The full length of the slide-wire is n=300 cms. “ Direct-reading”’? Platinum Thermometer. €9 t in terms of n.—From (3) and (5), _ 107406 n—684:9 ? ECE Toe Ne That is, paz L167 4+ 6849 (7) Tm CerTL0b OFOLUNS Ee tees | te. :k From (7) the plank may be calibrated “ directly,” in tem- perature degrees. It will, however, be more convenient to plot a curve co-ordinating n andt. Such a curve does not greatly differ from a straight line ; it is therefore sufficiently accurate to calculate n for every successive five degrees within the range. Accuracy attained. Mr. E. H. Griffiths has been good enough to examine my figures, and he agrees that, if the original standardization of the platinum coils is carefully attended to, this apparatus may be relied upon to measure temperature with an accuracy of one tenth of a Fahrenheit degree. Unfortunately, the platinum coils were sealed hard and fast within their respective dielec- trices before this slide-bridge method was adopted ; so that it has not been possible to check the readings in a liquid, as against a mercurial thermometer. This is very much to be regretted. By taking the mean of the readings of mercurial thermometers in the tank, and the readings of the mercurial thermometers in the tubes within the dielectrics, and com- paring this mean with the value of ¢ derived from (6), it is possible to make a very rough comparison. It should be carefully noticed, however, that “‘ tube ”’ temperatures include all the errors which it is the very object of the present method to avoid. The following table must be regarded with that limitation. Taste I. Tube- | Air- Date. temperature. N. et | temperature. See cele ee pee Bogie ts: fe} ie) ie) Ame. 22) 2.2. 760 F, 135°8 70°9 F. 81 F. Stee hae 125 132°9 72°6 ad Spe OO tana 63:3 1289 68-1 73 See Sane 80°5 139-75 80-4 76 SS | Saee 90°6 147-7 89°6 76 Depbs 20 or): 101-0 156-64 100-1 78 Bt Aye te Sui 110-1 1648 109-9 19 70 Mr. Rollo Appleyard on a It may be remarked here that, with the same apparatus, by taking the mean of the two values of n, corresponding to reversal of the battery, a second approximation could have been made. Also the slide-wire is thinner than is required by the temperature range. A thicker wire would have given greater possibilities of accuracy, and it would have been less liable to mechanical injury and temperature fluctuations. The Action of Sulphur Vapour upon Copper. _ While standardizing platinum thermometers in the vapour of sulphur (444° C.) some mica plates, which formed part of the apparatus within the vapour, were bound together with copper wires which passed through holes in the mica. After five hours’ exposure to the vapour the apparatus was dis- mantled, and, as had been expected, the copper wire was completely demetallized. An examination of the resulting wire, a brittle compound of cuprous or cupric sulphide, showed that it was, in some cases, perforated by a small axial hole ; the wire had, in fact, become a tube of very small bore. I am able to show this to you by projecting upon the screen one of the pieces of mica through which the original wire was threaded; the ends of the sulphide wire were broken off flush with each face of the mica, thus forming a section of the sulphide wire. Prof. Ramsay tells me that, as a rule, it is possible to draw an inner metallic core* from a copper wire which has been treated with sulphur vapour. It therefore seemed probable that my specimen was a piece of sulphide wire out of which a core had fallen. This, however, does not appear to be the explanation, for I have since succeeded in threading an iron wire, of 8 mils diameter, completely through a sulphide wire, which was more than half an inch long and not quite straight. It is impossible that a core of 8 mils could have fallen out of this specimen. : An examination, with the microscope, of the original copper wire does not reveal the slightest perforation ; although the end was carefully removed with nitric acid so as to avoid the closing of the hole, if one existed, by any mechanical cutting of the wire. It was suggested that an occasional hole might occur in the process of drawing the wire. Prof. Boys asked me to try a piece of copper cut from a block. I therefore had a piece, of square section, sawn from a large commutator-bar. After * T have obtained lately several specimens which show this core, “ Direct-reading ” Platinum Thermometer. (il g six hours’ boiling in sulphur vapour, this copper rod became circular in section ; it had a central perforation, as could be proved by passing a wire into it. The colour of the surface was a deep “beetle” blue. In order to show the amount of expansion which the copper experiences during the change to sulphide, a second piece of copper, of square section, was sawn out of the commutator-bar, half the length being turned down to a circular section. This was put into sulphur vapour for six hours, with the result that the diameter of what had been the square part had increased from 215 to 386 mils ; the circular part had increased from 120 to 232 mils ; and a third piece, of ordinary drawn copper wire, increased from 31 to 77 mils. During the transforma- tion from copper to sulphide the diameter in all cases is ap- proximately doubled. The length is only slightly increased; all sharp edges disappear ; and there is a general tendency towards the circular section. The fracture is crystalline, resembling that of an aerolite. A piece of Delta metal submitted to the same test came out of the sulphur vapour without appreciable change. It was discoloured but otherwise unaltered, and I propose to adopt this metal in future for the electrodes of platinum thermo- meters. Summary. The foregoing results indicate that platinum-coil thermo- metry may be reduced to a simple operation, and that the simplified method is sufficiently precise for general work. The exact conditions which determine the numerical limits of accuracy, generally, cannot be very concisely stated. The possible causes of error are well known, and with a little care may be nearly eliminated. The first precaution is to main- tain the bridge-coils at some constant temperature just above the maximum air-temperature. For this purpose the oil-bath and glow-lamp will be found satisfactory. If the temperature of the slide-wire is likely to vary con- siderably, , may be redetermined; or a correction-factor may be applied. This will seldom be necessary ; no such correction was used in the above tests. There must be some easy arrangement for calibrating the slide-wire. ‘The auxiliary-coil test is expeditious. The wire now supplied by good makers is sufficiently uniform ; and, except where great precision is essential, it will not require to be corrected for differences of diameter ; it should be of platinum-silver, TZ _ Mr. G. J. Burch on a Method - The resistance of the leads can generally be added as in equation (4). In other cases one of the “dummy-lead” methods of Siemens or Callendar must be adopted. In conclusion I have to thank Mr. E. H. Griffiths, Mr. W. A. Price, and Prof. W. N. Stocker for their help in preparing this paper; and the Silvertown Telegraph Company, who have kindly allowed me to carry out the experiments and publish the results. VI. Ona Method of Drawing Hyperbolas. By Georce J. Burcu, M.A.. Oxon.* FQ\HE ordinary methods of drawing hyperbolas fail when the portion of the curve required lies some distance from the vertex, small errors of measurement being then so much magnified as to render the results practically useless. Cunynghame’s hyperbolagraph, an admirable instrument for describing the parts near the vertex with a single movement, is also, for the same reason, inapplicable to the cases dealt with in the present communication. In using graphic methods for the investigation of a problem in Opties, the author had occasion, in 1885, to draw a number of hyperbolas all passing through a fixed point far away from the vertices of most of them, the asymptotes and the vertex of each being given. After vainly endeavouring to draw the curves in the usual way, he devised the following method which proved entirely successful, and which is, so far as he has been able to ascertain, a new one. Given the asymptotes Ox and Oy, and the vertex A, to construct an hyperbola. The equation of an hyperbola, when referred to its asym- ptotes as axes of coordinates, is Aay=a? +b’. In the simplest case, that of the rectangular hyperbola, a=), and the equation may be conveniently written “y=c? = a constant. To any point O on Ow draw AC, and from A draw a line parallel to Oy, cutting Ow in B. Make CE upon the axis of x equal to BO, and from HE draw a line parallel to Oy, cutting AC in D. Then yOw being a right angle, and AABC and ADEC * Communicated by F. J. Smith, F.RS, of Drawing Hyperbolas. 73 being similar triangles, bevARs: BC: Di, or BC. DE=AB EHC. Fie. 1. But by the construction, AB and HC are constant ; and also BC=OE=2z; and HOB: Therefore if LD=y, zy=OB. BA = a constant, and D is a point on the hyperbola. It is scarcely necessary to point out that this construction applies also to hyperbolas other than rectangular, since the lines AB and ED are drawn parallel to Oy, the other asymptote. In practice, when it is required to plot several curves, the simplest plan is to draw the asymptotes on a piece of stout paper and then cut it into the shape of a modified T-square, as shown in P, fig. 2, where the edge OBE forms part of the asymptote Oz, the continuation of which is ruled on the paper and represented by the dotted line, and the edge DE is parallel to the asymptote Oy. A distance EC equal to OP is measured along the line Ez, and a fine pin-hole made at C. 74 On a Method of Drawing Hyperbolas. Drawing-pins are fixed in the board at O the origin and A the vertex of the proposed hyperbola, and the asymptotes Fig. 2. drawn. Then the paper square, P, is laid against one asym- ptote and a third pin inserted at C. This can be done with greater accuracy if the line EC is continued to the end of the paper. Itremains to place a straight-edge S against the pins A and C, and to mark the intersection of it with the line HD at D. Then D is a point on the hyperbola, and by shifting the pin C together with the paper square P to a fresh position on the line Ow, another point can be determined in like manner. One great advantage of the method is that the value of y can be found directly for any given value of «. To do so, it 1s only necessary to place the paper P so that OH=a, and proceed as before. Obviously, too, the instrument might be constructed in metal and arranged so as to slide along the asymptote Oa, drawing a continuous curve. It might consist of two brass bars hinged at C, with a cross-bar clamped to one of them in such a way that its distance from C and the angle between it and the bar P could be adjusted. This cross-bar might carry a pencil or writing-point free to slide along it, and pressed by a light spring against the edge of S. A rough model of such an instrument was made at the time by the author, and Notices respecting New Books. 75 was found to work very well. It should be noted that all the long lines being given by the straight edge, great accuracy is easily obtainable, whether with the simple paper square or the more complex instrument. 21 Norham Road, Oxford, September 28, 1895, VII. Notices respecting New Books. Elements of the Mathematical Theory of Electricity and Magnetism. By J.J. Tuomson, M.A., F.R.S. Cambridge University Press, 1895. eae TS of Electricity who desire to read the more mathe- matical portions of the subject, and particularly those who wish to follow the development of the ether theory of electricity and the electromagnetic theory of light, usually find some difficulty in the choice of a text-book. From a first-year experimental course to Maxwell’s treatise is too great a step, in mathematics as well as in physics; some text-book of an intermediate character is there- fore required. Maxwell appears to have realized this, and he attempted to remove the difficulty by his Elementary Treatise, which, unfortunately, he did not live to complete. Inthe present volume Prof. Thomson has a similar aim: he retains nearly the same order of subject-matter as in Maxwell’s treatise, but (with few exceptions) only such problems are corsidered as can be solved by the aid of the differential calculus. By this treatment the mathematical difficulties are greatly diminished, while the physics of the subject is satisfactorily developed and illustrated by a sufficiently large number of examples. The author has made frequent use of Faraday tubes of force in explanations of phenomena occurring in the electricfield: he shows very simply that such tubes will be im equilibrium if the tension along their axes is accompanied by an equal pressure at right angles to them. In discussing the case of an insulated sphere in a uni- form field, the idea of an electric doublet is introduced, and an expression is found for the moment of a doublet representing the | external effect of the charge on the sphere. Among other new modes of treatment we may mention the use of the dissipation function in determining the distribution of currents in any network of conductors. Kirchhoff’s laws are shown to be equivalent to the statement that the currents distribute themselves so as to make the total rate of development of heat-energy a minimum ; by writing down the expression for this heat-energy and making ita minimum, the values of the currents in each branch may be obtained. Prof. Thomson has found a companion for x, the specific inductive capacity, and p, the magnetic permeability, in dimensional formule. The work done by a unit magnetic pole in threading a closed circuit is 47/p times the current flowing in the circuit; as the 76 Notices respecting New Books. definition connects magnetism with electricity clearly p may have dimensions, but the electrostatic and electromagnetic theories each assume it to be a mere number. ‘The result of retaining p is to make p*/ux the square of a velocity. Chemists will probably regret that the subjects of migration of ions, ionic velocity, and electrolytic conductivity find no place in the volume, electrolysis being treated in a very elementary fashion. The chapter devoted to dielectric currents and the electromagnetic theory of light is very readable, even by those who are not familiar with the ordinary equations of wave propagation ; it contains a concise though somewhat brief account of the recent confirmations of Maxwell’s theory by Hertz and others. We notice that the discovery of the action of electric waves in dimin- ishing the resistance of a tube of metal turnings is erroneously attributed to Prof. Lodge: the experiment was originally de- scribed in this form by M. Branly. The volume is nicely printed, with bold headings at the com- mencement of each section, and is of a handy size for students’ use. There is a subject-index at the end of the book, but a list of titles of the various chapters inserted at the commencement of the volume would be of great service to the student. JamMES L. Howamp. An Exercise Book of Hlementary Physics for Organised Science Schools etc.; arranged according to the Headmasters’ Association’s Syllabus of Practical Physics. By Ricuarp A. GREGORY, F.R.AS. London: Macmillan & Co., 1895. Tur Government having at last recognized the suitability of elementary practical physics and mechanics as school subjects, this series of exercises suggests a method of making such subjects effective in training students to acquire habits of observation, accuracy, and carefulness. The exercises include the general operations of weighing and measuring, mechanics and heat ; they are arranged according to subject and in order of difficulty. Spaces are provided in which the results of experiments may be recorded, and in each case the student is left to make his own deductions from his experiments. Some of the directions for experiment are not very explicit ; for example, in order to measure the rise of water in capillary tubes the student is told to take two very narrow vubes, one having twice the internal diameter of the other, and to wash them by drawing distilled water through them. A good student, ard rot a few teachers, will want to know how the diameters of the tubes are to be measured; and the results of the experiment will not be very satisfactory unless the tubes have been previously washed with some cleansing agent, such as potash or alcohol. A few exercises on glass-blowing, soldering, and similar manipulation might be added with advantage. The construction of the model lift or force-pump, used in one of the experiments, would be excellent practice in this direction. Geological Society. OEP ~ The author suggests the use of balances weighing to 0-01 grm., and recommends supplying one balance to every six students. Taking into account the number of experiments requiring the use of a balance this seems hardly sufficient; we incline to the opinion that a larger number of cheaper balances weighing to 0'l grm., say one balance to each pair of students, would be preferable for elementary physical work. Mr. Gregory has rendered good service by suggesting in so practical a fashion a programme of physical work, which indicates the nature of the instruction to be given, without binding a teacher to follow it out entirely or even in consecutive order. James L. Howarp. VIL. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from vol. xl. p. 547. | November 20th, 1895.—Dr. Henry Woodward, F.R.S., President, in the Chair. HE following communications were read :— 1. ‘Additional Notes on the Tarns of Lakeland.’ By J. EH. Marr, cae MEAL. l.R.8.3 See.G.8, This paper is supplementary to one by the author published in tie Q.J.G.8. vol. li. (1895). He gives additional notes on Wateredbath ‘Tarn, describes Hard Tarn on Helvellyn, a pond whose outlet has gradually been diverted from a course over screes to one-over solid rock ; Hayeswater, a lakelet referred to by Dr. H. R. Mill as insome respects intermediate between the mountain-tarns and the valley- lakes; and Angle Tarn, Patterdale, a good example of a plateau- tarn. The results of his fresh observations tend to confirm the views expressed in his former paper. 2. ‘Notes on the Glacial Geology of Arctic Europe and its Islands.—Part I. Kolguev Island.’ By Col. H. W. Feilden, F.G.8. ; with a ‘ Report on the Erratic Boulders from the Kolguev Beds, by ErotlG. Bonney, D.Se., LL.D., F.R.S., F.GS. Kolguev Island, about the size of Norfolk, lies about 50 miles from Arctic Russia and about 130 miles south-west of the nearest part of Novaya Zemlya, with soundings not exceeding 30 fathoms between it and Russia, and probably not more than 75 fathoms between it and Novaya Zemlya. It is entirely composed of a vast accumulation of glacio-marine beds. The northern two-thirds of the island consists of an elevated ridged area with a maximum height of 250 feet. ‘The author has been furnished with notes by Mr. Trevor- Battye concerning the geology of this region. It is inferred from his observations that this elevated region is composed of beds of sand 78 Geological Society. with erratic boulders not less than 80 feet deep, resting on clays— the ‘ Kolguev Clays.’ Mount Bolvana rises as a symmetrical cone above the tundra, detached from the northern plateau, pointing, in the opinion of the author, to the occurrence of marine erosion. The southern portion of the island is tundra, a dead flat of grass, bog and peat-levels reaching to the sea; good sections of the Kolguev Clays are exposed in the gullies traversing it near the sea on the western coast. In the vicinity of the Gobista river the Kolguey Beds consist of clays merging here and there into sands. They are charged with boulders often ice-scratched, indicating continuous deposition in a comparatively deep sea. The beds yielded many shells of Arctic mollusca, such as Saaicava arctica, Mya, ete., apparently dispersed from top to bottom. The ice-pack has forced many fragments of semi-fossil wood on to the shore, no _ doubt worked up from a bed immediately below sea-level. No deposit was. met with in Kolguev Island precisely similar to what is ealled ‘Till’ in Scotland, though there are many Boulder Clays in Britain which are in no measure superior in toughness to those of Kolguev, for instance, those of the Yorkshire coast and the Chalky Boulder Clays of Norfolk. It is suggestive that all the glacial deposits met with by the author in Arctic and Polar lands (except the terminal moraines now forming above sea-level) should be glacio-marine beds. Prof. Bonney in his report describes the rocks brought home by the author. They include granite-gneiss (very like Archean rocks), grit, chert, limestone with Favosites (Silurian or Devonian), lime- stone with Amphipora ramosa (Devonian), limestone with Litho- strotion irregulare (Carboniferous), and a fragment of a Jurassic belemnite. The fossils have been examined by Mr. EH. T. Newton, F.R.S. IX. Intelligence and Miscellaneous Articles. ON UNDERGROUND TEMPERATURES AT GREAT DEPTHS. BY ALEXANDER AGASSIZ. OR several years past I have, with the assistance of our engineer, Mr. Preston C. F. West, been making rock-tempe- rature observations as we increased the depth at which the mining operations of the Calumet and Hecla Mining Co. were carried on. We have now attained at our deepest point a vertical depth of 4712 feet, and have taken temperatures of the rock at 105 feet, at the depth of the level of Lake Superior, 655 feet, at that of the level of the sea, 1257 feet, at that of the deepest part of Lake Superior, 1663 feet, and at four additional stations, each respec- tively 550, 550, 561, and 1256 feet below the preceding one, the deepest point at which temperatures have been taken being 4580 feet. We propose, when we have reached our final depth, 4900 Intelligence and Miscellaneous Articles. 79 feet, to take an additional rock-temperature and to then publish in full the details of our observations. . In the meantime it may be interesting to give the results as they stand. The highest rock-temperature obtained at the depth of 4580 feet was only 79° F., the rock-temperature at the depth of 105 feet was 59° F. Taking that as the depth unaffected by local temperature variations, we have a column of 4475 feet of rock with a difference of temperature of 20° F., or an average increase of 1° F. for 223°7 feet. This is very different from any recorded observations ; Lord Kelvin, if I am not mistaken, giving as the increase for 1° F., fifty-one (51) feet, while the observations based on the temperature-observations of the St. Gothard Tunnel gave for an increase of 1° F., sixty (60) feet. The ca'culations based upon the latter observations gave an approximate thickness of the crust of the earth, in one case of about 20 miles, the other of 26. Taking our observations, the crust would be over 80 miles and the thickness of the crust at the critical temperature of water would be over 31 miles, instead of about 7 and 8°5 miles as by the other and older ratios. With the ratio observed here, the temperature at a depth of 19 miles would only be about 470°, a very different temperature from that obtained by the older ratios of over 2000° F. The holes in which we placed slow-registering Negretti and Zambra thermometers were drilled, slightly inclined upward, to a depth of ten feet from the face of the rock aud plugged with wood and clay. In these holes the thermometers were left from one to three months. The average annual temperature of the air is 48° F.; the temperature of the air in the bottom of the shaft was 72° F.—American Journal of Science, December 1895. ON THE INFLUENCE OF ELECTRICAL WAVES ON THE GALVANIC RESISTANCE OF METALLIC CONDUCTORS. BY H. HAGA. At the meeting of the Berlin Physical Society on Noy. 30, 1894, M. E. Aschkinass* communicated observations according to which the resistance of a grating of tinfoil was found to be about two per cent. less in consequence of electrical radiation; and this small resistance lasted even after the cessation of radiation, until heating or mechanical agitation restored the former value. Since radiation will produce electrical vibrations in a tinfoil resistance, it appeared worth while to investigate whether in general the resistance of a metallic conductor is also altered by electrical vibrations passing over its surface. Using the apparatus described and recommended by Ebertt, by which long continuous electrical vibrations could be obtained, such vibrations were transmitted through different specimens of copper * Verhandl. der Phys, Gesellschaft zu Berlin, vol. xiii. p. 103. + Wied. Ann. vol. li. p, 144 (1894). 80 Intelligence and Miscellaneous Articles. and iron wire and through tinfoil. No influence could be observed, although in the way the experiments were arranged an alteration in the resistance of 1, per cent. could easily have been observed. After this negative result I returned to radiation, and allowed primary sparks of very various duration to strike across, while the resistances to be investigated were at a distance of less than 50 em. To produce the sparks an induction-coil 25 cm. in length was used worked by three accumulators, but more frequently an induction- coil 60 cm. in length worked by ten accumulators (24 amperes). By means of a spark-resonator it was always ascertained that the primary spark was an oscillating one. The following resist- ances weve used :—Various gratings of tinfoil fastened on ebonite, the thickness of the tinfoil being 0-05 mm. to 0°01 mm., and the resistances 0°478 Q, 3°155Q, 11°31 Q, 36°31.Q; a grating of thin iron wire on an ebonite frame (5°504Q); a german-silver wire (0°578 Q), and a strip of tinfoil (1:068Q): both these last were resonant with the primary spark; secondary sparks could be obtained between the wire or the strip. In none of these resist- ances was any trace of a variation observed (to 54, per cent.). When the gratings were not fastened on the ebonite, but were fixed in an ebonite frame, I observed the phenomena described by Aschkinass, but only when the strips were very close to each other. The variations in the resistances were often very con- siderable. The resistance of a grating of 6°7Q was 3°6Q, after radiation by the primary spark; by an agitation again 5:1, after radiation 3:20. This grating was dipped in solidifying paraffin; it then showed a resistance of 7°39 Q, which became 4-75 Q by radiation, and by shaking increased to 76Q. It was necessary to agitate violently to get back to the original high resistance. No change in resistance could be observed with gratings having great spaces between the strips. In one grating the 22 strips were 0°75 mm. in breadth and likewise 0-75 mm. apart. The resistance 11°85Q was the same after radiation as before. . Hence, from these experiments, the amount of the varia- tion depends on the position of the strips in reference to each other. If these are close the primary spark may give rise to the formation of one or more bridges between adjacent strips, as Branly* assumes with metal filings, and Lodge? in what he calls ‘“‘microphonic detectors.” Although much remains to be explained in the latter investigation, it appears vo me indubitable that, as Aschkinass also thinks possible, the phenomena with metal gratings belong to the same category, and are not to be ascribed to some unknown acticn.— Wiedemann’s Annalen, No. 11, 1895. *® Journal de Physique, p. 459 (1892) ; p. 273 (1895). + The Work of Hertz, pp. 20-26. EE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. > [FIFTH SERIES.] FEBRUARY 1896. X. The Filar Anemometer. By Cart Barus, Hazard Pro- fessor of Physics, Brown University, Providence, U.S.A.* i, A a remarkable paper, published some sixteen years ago, Prof. V. Strouhal+ investigated certain laws subject to which a sound is produced when the wind passes transversely across a slender solid body. Placing his chief reliance on the results obtained with metallic wires, Strouhal found for thicknesses ranging from 0°018 cm. to 0°325 cm., and for speeds from 271 met./sec. to nearly 12 met./sec., that the whole group of phenomena could be expressed by an equation of striking simplicity, n=Cov/d ; where n is the frequency of vibration, v the speed of the wind, d the diameter of the wire, and where ( is constant except as to temperature. When all data are expressed relatively to metres and seconds, this constant has at atmo- spheric temperatures a mean value C=— 67700 - and it is thus at once possible to compute the speed of the air * Communicated by the Author. - It gives me pleasure to acknowledge my indebtedness to the Secretary of the Smithsonian Institution, for materially promoting the present series of researches. ; + Ueber eine besondere Art der Tonerregung, Wurzburg, Stahel, 1878. The subject was suggested by Prof. F. Kohlrausch. Phil. Mag. 8. 5. Vol. 41. No. 249. Feb. 1896. G 82 Prof. Carl Barus on normally to the axis of a given wire, when the note made by the whistling wind is located, at a given temperature, in pitch. Other data*, such as the material, or the tension, or the length of the wire, &c., are without marked effect, except as regards the intensity of the sound produced. Ebai Strouhal further found that whenever the air-tone n, vary- ing continuously with speed v, approaches the fundamental or any of the overtones of the transversely vibrating wire, the sound bursts forth with accentuated intensity. In virtue of this discovery, Strouhal was able to give a degree of pre- cision to his results which for the case of the unassisted air- tone would have been unattainable ; for it was merely neces- sary to work out such speeds as kept the wire in a state of permanent resonance. Indeed. it was now possible to obtain sounds from the wire even after the actuating air-tone alone had ceased to be audible. Commenting on the application of his results, Strouhal notes its immediate bearing on anemometry. The device is peculiarly adapted to the measurement of variable gusts and high winds, and is thus supplementary to the ordinary anemometer. 2. It is from this point of view, 7. e. in relation to what may be called micro-anemometry, that the filamentary ane- mometer interested me during my connexion with meteoro- logical research}. Here is an instrument virtually without mass, which therefore does not state the case summarily, but represents the wind as it actually is. In consideration of the actual complexity of aerodynamic phenomena, the simplicity of Strouhal’s law is an ulterior advantage. Whoever believes that much is to be learned from a more searching investiga- tion of the nature and origin of gusts of wind{ will be in sympathy with the development of what is in many respects an ideal instrument of research. There is another important problem which lies within the scope of the filar anemometer. I refer to the class of researches recently accentuated by the paper of S. P. Langley§ on the work of the wind. * The law applies more accurately in proportion as thickness increases, and may be considered exact for diameters above 0:1 cm. +t Cf. my letter to Prof. M. W. Harrington, in Rep. Am. Assoc. of State Weather Services, Oct. 1892; Bull. U.S. Weather Bureau, No. 7, . 44, 45. a Barus, American Meteor. Journal, March 1895, pp. 488-489; ¢f. Bulletin U.S. Weather Bureau, No. 12, 1895. § “The Internal Work of the Wind,” Smithsonian Contributions, No. 884, Washington, 1893. the Filar Anemometer. 83 If the velocity of air normally to the wire is registered, three wires at right angles to each other would register the respective velocities in three cardinal directions. From this the actual direction of the gust is at once obtainable as the resultant of the three components. It is necessary, however, before a like deduction can be accepted with confidence, to further elucidate Strouhal’s law with data referring to the oblique passage of a wire through the air. For just what will occur under these circumstances cannot certainly be foreseen. It is also desirable to obtain accurate data for the effect of temperature on the phenomenon, an inquiry which Strouhal only carried far enough to appre- hend that the pitch of a note, other things being equal, is depressed with increasing temperature. From a theoretical side, the subject has recently been elucidated by Lord Kelvin*. In constructing my whirling table I aimed at quantitative decision on these questions. I therefore made a whirling machine one end of the axis of which was pivoted to the ceiling of a high room, and the other end rigidly attached to the spindle of an ordinary whirling table about a metre above the floor. The crank-wheel was placed at some distance, so as to allow two horizontal arms, about 1°4 metre long and 1:9 metre apart in the same vertical plane, to rotate freely. Clamp-screws at the end of these arms carried the wire to be tested, vertically stretched and 1:9 metre long. The whole framework was made of gas-pipe and snugly screwed together. It was therefore possible to move the horizontal arms so that the vertical planes through them would subtend a given (small) angle, and the (elongated) wire be rotated through the air obliquely to the line of motion. Due care had to be taken not to carry the obliquity too far. The customary electric brushes were added at the axis of the whirling arm, and thus the rotation could be timed by a chronograph pendulum of the simple kind sketched in a pre- ceding paperf. Contact brushes for other electric apparatus (cf. § 3) were also supplied. On trial, however, the whirling arm at the higher speeds developed a weakness. It was found to yield seriously under ihe strain of rotation, so that I did not feel sure of its con- stants. JI therefore abandoned further attempts at solving the subsidiary questions just specified, for the present. 3. A wire singing on the housetops, however, is as yet no * ‘Nature,’ 1]. pp. 524, 549, 573, 597 (1894); see particularly pp. 524 and 525, where the whistling of a strong wind is discussed. + Barus, American Journal, xlviii. p. 396 (1894). G 2 | 84 Prof. Carl Barus on anemometer, least of all when its own song is drowned for the ear by the noises round about. I therefore proposed to myself in the first place. to devise some means by which this air-tone could be conveyed to any distance without change of quality, and thereafter to endeavour to register this indication automatically. It is only with the first of these problems that the present paper is concerned. All attempts made at — the second, which is seriously difficult, have thus far been failures*. The first condition appeared easy of accomplishment. It seemed merely to be necessary to attach the wire to the plate of a telepbone in order to catch and transmit the sounds from the roof to the office. However, telephonic devices over which I laboured a long time failed to the last to give me any result whatever. I then turned to the microphone, at first equally without success, though finally an arrangement was developed which behaved satisfactorily. I may in passing refer to certain of the earlier forms of microphonic contact, some of which were at times useful. ‘The difficulty encountered arises from the fact that a delicate microphonic contact is to be maintained without breakage, at the end of a rapidly revolving and necessarily vibrating whirling arm. Most devices give sounds interrupted by a terrific racket at the receiver, which is very trying to the ears. Apart from this the effect of centrifugal force in varying the contact is to be counteracted, and the air-resistance or the noises made by moving parts of the microphone eliminated. In figure 1 aa is the revolving wire, attached at its upper end to one arm of the whirling machine (not shown), and at the lower end to the metallic plate or sounding-board 6, at the end of the lower arm of the machine. Near the bottom of the wire a very delicate brass spring cd is soldered on at ¢, carrying a short platinum stylus at d. A similar spring, ef, attached at f to the sounding-board, carries at e a light pellicle of carbon. The latter has been electroplated on one side with copper, so that it can be soldered. The two springs are so adjusted that the microphonic contact is just made at d, e, and kept intact when e is slightly moved up and down, d sliding on the flat face of e in this case. Moreover, as e is relatively heavier than d, centrifugal force will tend to straighten the spring fe more than dc, and the contact is not * Unfortunately the ingenious devices of Prof. C. R. Cross and his pupils (Proc. Am. Acad. XXV. Pp. 233 (1890); May 1892; Jan. 1893) are not available here. the Filar Anemometer. 85 interrupted at high speeds if both springs lie in a plane through the axis and are of proper lengths and curvature. Fig. 1.—Vertical Spring Microphonie Contact on Air- Wire. As f is insulated, the current of four Leclanché cells passes through /, e, d, c, a, g, and the Bell telephone included in the circuit. The sounds are very much increased (and unfortu- nately the thunder due to breaks of contact also) when the primary of a transformer is placed in the circuit with the telephone in the secondary, in the now well-known way*. A great advantage is gained by filing the flat surface of e with a smooth file, probably owing to the carbon powder which lodges in the pores. Polishing the surface on a stone is harmful. High tones seem to require firmer contacts than low tones, and this state of things is brought about by the action of centrifugal force as stated. The position of the spring cd on the wire aa seems to be immaterial. I made tests throughout 30 cm. without marked results. Nor is - much advantage gained from the shape or material of the sounding-board. Curiously enough, the latching of d and e often favoured the intonation of low sounds. No rules can be given for the bending of the springs, and the best contact is usually the result of chance, and is obtained only after many trials. It is with the above arrangement that I once noted a peculiar phenomenon for which I have failed to find an The reader is referred to either Preece’s or Du Moncel’s Treatise on the Telephone. 86 Prof. Carl Barus on explanation. After having made a delicate contact I noticed a low sonorous sound in the telephone, which continued with undiminished intensity for fully five minutes. No spring could have vibrated for this length of time, so that the acoustic apparatus must have contained its own motor. The sound ceased only when contact was broken, but on succeeding days I could not reproduce it. 4, A second microphonic contact with which there 1s usually less racket than in the preceding case is shown in figure 2 in plan. The sounding wire is shown in cross Fig. 2.— Horizontal Spring Microphonic Contact on Air- Wire. section at a; h and k are two very delicate flat springs attached to the wire a at its lower end by two insulating plates of hard rubber 0, 5’, and the insulated clamp screws ¢, c’. The free ends of these springs carry two small carbon pellicles, e and jf, centrally perforated so as to hold the shouldered rod of graphite g loosely between them. The current of four Leclanché cells passes through a, h, e, 9, f, k, 8 (a and B being the terminals) to the enclosed primary of the transformer, and thence back to the battery. The rod g may also fit into cavities in e and /, and be held in place by the very gentle clutch of the springs A and k; or g may be replaced by a short wire of platinum. There is a groove in the middle of g to attach small weights to vary the contact ; h and f& are set radially, so as not to be influenced by centrifugal force. No effect was obtained when either of the microphonic contacts were placed on the sounding-board in which the lower end of the air-wire terminates. It seems essential, therefore, to tap the sound from the wire itself. A weighted sounding-board gives no novel results. A gridiron of wires produced air-tones which the ear appreciated with an in- tensity proportional to the number of wires, but the effect in the telephone did not exceed that of a single wire. Strips of metal in place of the wires were also ineffectual, and it was difficult to keep the sharp edge turned in the direction of motion. In this case, too, the bulging of the central parts of the revolving filament proved to be a serious annoyance, the Filar Anemometer. 87 A regular speed of the wire favours the occurrence of tones, particularly those which are awakened by resonance. _ 5. The beneficial effects obtained in § 8, as the result of filing, induced me to try a form of microphone in which the sensitive contacts are produced by a pulverulent conductor *. After many attempts I finally succeeded in devising an arrangement which is far superior to the forms just described, inasmuch as the thunder is altogether absent, and other extraneous noises are excluded. The sounds heard in the telephone are not loud, but clear and flute-like, and the range of pitch obtained is enormous. I passed almost from utter cessation of motion to the highest speed which I could give the whirling arm, and heard sounds quite inaudible to the unaided ear. _The annexed figure (3) shows the form which seemed to give the best results. Here aa and bb are two tin-plates about Fig. 3.—Granular Microphonic Contact for Air-Wivre. 0:016 cm. thick and 8 em. in diameter, held apart by an interposed flat ring of hard rubber dd about 0-1 cm. thick or less. An elastic band of soft rubber ¢e, is stretched quite around the circumference and secures the plates by pressure against the hard rubber ring. The upper plate is centrally perforated, and a tube, g, about 1 cm. wide and 2 cm. long communicates with the perforation. A stylus c, is soldered to the middle of the lower plate and passing axially through * Originally devised by Hunning, I believe. See Preece or Du Moncel, dine: 88 Prof. Carl Barus on the tube g ends in a hook to which the air-wire A is attached. The whole arrangement is held down horizontally on the sounding-board by two flat clamps (not shown) or by a ring insulated from the plates a and 6. Carbon powder /,is finally introduced into the tube g, not in too large quantity, and not packed tightly. The current therefore passes into the upper plate at «, then through f into the lower plate and out at B, @ and @ being the terminals. My first trials with finely pulverized graphite failed. I obtained the best results with. gas-carbon ground in a mortar and sifted in a way to keep the particles granular. The plates must be clean and bright. The sounds usually start with a creak, as if the powder must first be shaken loose; and tapping frequently improves it. The plates must not be pressed upon the powder, and the part of it around the stylus is chiefly effective. In other forms I have quite filled up the discoid cavity, but it was then frequently necessary to pull up the upper plate with a spring. 6. The following results were obtained with the micro- phone of § 5. A series of wires of different diameters were tested, and those larger than 0°05 em. and smaller than 0°15 cm. were found best adapted for the purpose. Thicker and thinner wires behaved peculiarly, as will presently be seen. It has been stated that Strouhal’s law requires a cor- rection for thin wires( = Gye ee Sy AA 2 cu cn! x ul 2 now used in the Magnetic Observatory of Princeton Uni- versity. It consists, first, of a solid wooden base of circular shape, provided with levelling-screws. From this base arise four vulcanite pillars, which support a vulcanite disk, having 112 Mr. J. E. Moore on a Continuous and a circular opening at its centre. The cover of the instrument rests in a groove in tke wooden base, fitting closely about the circular disk at its top, and is provided with a plane glass window for the admission of a beam of light.. Placed dia-: metrically opposite, on the upper surface of the vulcanite disk,. are two coils of a few turns of stout wire, hereafter to be called the H-deflecting coils. From the centre of this same disk rises a glass cylinder, covered at its upper end by a second vulcanite disk, to which is attached the suspension- tube. The suspension-tube carries at its upper end a torsion head, provided with binding-posts and adjusting devices for regulating the bifilar wires.. From this torsion-head is sus-- pended, by means of the silver bifilar wires, the moveable magnetometer system. The upper or H-magnetometer helix is held by a hard rubber clamp, serving at the same time as a terminal block for the lower ends ofthe bifilar wires. To the lower part of this clamp is fastened a hard rubber shaft, sup- porting centrally, at its lower end, a horizontal hard rubber bar, to the extremities of which are fastened (by means of suitable adjusting devices) the horizontal unifilar torsion-wires carrying the J-magnetometer helix. Hach of the magnetometer helices having the same number of turns of wire will, when so connected as to develop opposite polarities in the ends lying in the same direction, form an astatic combination for horizontal deflexions. If it should be necessary to make the vertical deflexions also independent of the earth’s magnetic field, one can easily arrange a flat coil of wire with its centre in the vertical axis of suspension of the moveable system, and its plane horizontal, and pass through the coil such an electric current as will just equal and neutra- lize, in its magnetic effect, the vertical component of the earth’s magnetic field at the centre of the I-magnetometer helix. § 5. In using the instrument, it should be set up on some firm support (generally, though not necessarily, so that the planes of the H-deflecting coils are parallel to the earth’s magnetic meridian) and properly levelled until the suspended system is perfectly free, and hangs centrally in the instru- ment. The length of the bifilar wires should then be adjusted until the centre of the H-magnetometer helix lies in a hori- zontal line passing through the centre of the H-deflecting coils on either side of the instrument. The stress on the bifilar wires should then be equalized, by means of the adjust- ing devices at either end of the horizontal bar carrying the I-magnetometer helix, the horizontal torsion-wires should be regulated in length, so that the centre of gravity of the Alternating Current Maynetic Curve Tracer. 113 I-magnetometer helix lies in the vertical axis of the suspended system, and the torsion adjusted in the wires until the axis of the helix is horizontal. The torsion-head of the instrument is then turned until the axes of the magnetometer helices are parallel to the planes of the H-deflecting coils. Upon one of the mirrors, carried by the I-magnetometer helix, is projected a beam of light from some fixed source, which after reflection is received upon a screen placed normally to the helices in their undisturbed position. By means of cross- hairs placed in the path of the incident beam of light, one is enabled to mark on the screen the initial or zero position of the magnetometer system, and .to measure any subsequent angular displacement of either or both of the magnetometer helices. The sample to be tested (in the form of a long rod supplied with the proper magnetizing coil) should be placed with its axis in the vertical line of suspension of the magnetometer system. This can be accomplished most conveniently by clamping the sample and its magnetizing coil below the support of the instrument. The sample and its magnetizing coil should then be adjusted vertically, until the magnetic action of the sample, for maximum intensity of magnetization, produces the desired maximum vertical deflexion of the I- magnetometer helix. A compensating coil of a few turns of wire should then be adjusted so as to neutralize, at the I- magnetometer helix, the magnetic action of the magnetizing coil about the sample. The accuracy of the adjustments for horizontal displace- ments can be tested by making the magnetometer helices active, by means of a constant current of one or two tenths of an ampere, and reversing an independent direct current through the H-deflecting coils. This should give the mag- netometer system equal horizontal displacements on either side of the zero position, and, for various current-strengths, the magnitude of these deflexions should be proportional to the respective currents. The accuracy of the adjustments for vertical displacements depends upon the setting of the sample to be tested (with its magnetizing coil) and the balancing coil. This can be tested before beginning an experiment by placing the magnetizing coil (with the sample removed) in the position it will occupy during an experiment, and reversing continuous currents of various strengths through it. There should be no horizontal displacements, and the vertical displacements, on either side of the zero position, should be proportional to the respective magnetic forces due to the magnetizing coil, at the l-mag- Phil. Mag. 8. 5. Vol. 41. No. 249. Feb. 1896. li 114 Mr. J. E. Moore on a Continuous and netometer helix. The compensating coil should be so con= nected in series with the magnetizing coil as to give an opposing magnetic effect at the [-magnetometer helix, and by keeping its plane horizontal, and its centre in the ‘vertical line of suspension of the inagnetometer system, be adjusted in position until the joint magnetic effect of the two coils at the I-magnetometer helix is zero, for all strengths of current. through them. : § 6. The instrument, having thus heen set up and adjusted - and the adjustments tested, is ready to be used for the measurement of energy-losses in iron magnetized by either: direct or alternating currents. If the losses in iron magne- tized by continuous currents are to be measured, a current of | two-tenths of an ampere from some independent battery (a. single cell of storage-battery answers very well) is passed through the helices of the magnetometer system, and kept constant throughout an experiment. The intersection of the cross-hairs in the beam of light reflected upon the recording screen by one of the mirrors carried by the I-magnetometer helix, is taken as the centre of a system of vertical-horizontal. rectangular coordinates. The sample is then placed in the magnetizing coil, which, after being properly connected in: series with the compensating coil, the H-deflecting coils of the instrument, a regulating resistance, and a source of con-. tinuous current, has the magnetizing current through it increased from zero to the maximum value required to produce. the desired maximum degree of magnetization, reduced to. zero, reversed, the same operation performed in the opposite sense, and the cycle completed by returning finally to the first: maximum. The point of intersection of the cross-hairs on the screen will be displaced for every different value of the mag-: netizing current, a distance from each of the coordinate axes’ previously drawn, proportional respectively to the magne-' tizing force acting on the sample and the intensity of: magnetization of the sample. Hence by marking down on the screen the point of intersection of the cross-hairs in the: reflected beam of light, for any desired number of values of the magnetizing current thronghout the cycle of magnetiza-: tion, we have an accurate outline of the magnetization curve for the sample, or, as it is frequently called, the ‘ hysteresis ” curve. By properly varying the magnetizing current, loops. can be traced to any part of the hysteresis curve, or a com- plete set of graded cycles obtained without removing the sample. In measuring the losses in iron magnetized by an alter- nating current, an intermittent current of a mean value of. Alternating Current Magnetic Curve Tracer. 115 two-tenths of an ampere (obtained by means of a revolving contact-maker on the shaft of the alternating-current generator supplying the alternating magnetizing current) is passed through the magnetometer helices, and kept accurately con- stant throughout an entire experiment. For the continuous magnetizing current is substituted an alternating current, adjusted to such a mean value as will give the desired maximum intensity of magnetization. As has been shown, by varying the point in the revolution of the armature-shaft at which contact is made, or current passes in the magneto- meter helices, different deflexions will be obtained, the rectangular components to which are strictly proportional to the magnetizing force, and the intensity of magnetization respectively, at the points in the alter nating-current waves at which the instantaneous direct current passes through the magnetometer helices. Hence by varying the point of con- tact on the revolving contact-maker, through a circular angle corresponding to 360 degrees of phase in the alternating- current waves, we have, as in the case of “static” cycles, the successive positions on the screen of the intersection of the cross-hairs in the reflected beam of light, marking points in the outline of the energy-loss curve. ae an calibrating the instrument for either “ static” or “periodic” cycles, the current through the magnetometer helices is kept the same in kind and magnitude as “during the experiment. The sample is removed from the magnetizing coil, and an accurately measured current sent through either the magnetizing coil or the compensating coil, alone. The deflexion is marked down on the vertical axis of coordinates. Then an accurately measured current is sent through the H- deflecting coils alone, and the resulting deflexion marked down on the horizontal axis of coordinates. By knowing the distance of the resultant magnetic distri- bution, or magnetic poles, from the I-magnetometer helix, we can ¢aléulate, by well-known magnetometer laws, the value of themagnetic force at the centre of the 1-magnetometer helix, due to the long rod, in terms of the distance of the poles from the centre of the helix, the cross section of the sample, and the intensity of magnetization of the sample. It will be plain, by considering the relative position of the long rod and l-magnetometer coil, that this force, 1 | F,, =8I( je poy a 2. (0) where S is the cross section of the sample, I the intensity of magnetization of the sample, R the distance from the 12 6¢ 116 Alternating Current Magnetic Curve Tracer. centre of the I-magnetometer helix to the nearer pole, and R’ the distance from the centre of the I-magnetometer helix to the farther pole. By knowing the distance of the compensating coil during calibration from the I-magnetometer helix, its number of turns, mean radius, and the current through it, we are enabled to calculate its magnetic force at the I-magnetometer helix. If the calibrating coil is a flat coil of only a few turns of wire (as is always most convenient), then, as is well known, its magnetic force at the I-magnetometer helix is expressed by : 2arnCr? 10(d?+72)3 Se ae foe (2) where n is the number of turns in the calibrating coil, C the value in absolute units of the current in it, » its mean radius, and d the distance of the calibrating coil from the I-magnetometer helix. Calling I, any particular vertical deflexion in the course of an experiment, and D, the vertical deflexion during calibration, we have, since the current in the magnetometer system has been kept constant through the whole experiment, the following relation :— Aan Fee) = Substituting in equation (3) from equations (1) and (2) we get ik 1 p, _ S!(q— Re) ; i ale (4) 10 (a? +77): Solving equation (4) for I, we get I= Zier Anes Pe . = To(e+7) SR7—-BD, * 1 7 * @) We are thus enabled to find the value of the intensity of magnetization of the sample in Absolute Units for any point on the entire curve of magnetization. Knowing the number of turns, the length, and the current flowing in the magnetizing coil surrounding the sample, we can at once calculate in Absolute Units the magnetizing force of the coil on the sample. In the calibration of the horizontal deflexions, we know the current flowing in the H- deflecting coils and the displacement it gives along the horizontal axis. We calculate the magnetizing force of the Dissociation Degree of some Electrolytes at 0°. 117 magnetizing coil about the sample for that current, and by direct proportion between horizontal displacement in cali- bration, and the horizontal displacement of any point on the curve, we obtain in Absolute Units the magnetic force corre- sponding to any point on the curve. Having thus calibrated the curves of either continuous or alternating current mag- netic cycles in Absolute Units, the energy losses, \IdH, may be obtained by taking the area of the curves in the usual way. Although this description has only been concerned with the curve-tracer as a means of measuring the magnetic quality of, and the energy losses in iron and other metals, when carried through magnetic cycles, it plainly lends itself to such operations as direct tracing of alternating-current and elec- tromotive-force curves, the investigation of the nature and amount of iron losses in alternating-current transformers, the measurement of the power in any electrical circuit, &e. XIV. On the Dissociation Degree of some Electrolytes at 0°. By R.W. Woop*. ee values obtained by the lowering of the freezing-point _ for the dissociation-degree of dissolved electrolytes are always a little smaller than those calculated from the electrical conductivity. Meyer Wildermannf has recently lessened the difference by the use of a more accurate method for the freezing-point determinations, and has expressed the opinion that the cause of the discrepancies lay in the fact that the electrical con- ductivities have been determined at a higher temperature (18°-25°). At Prof. Jahn’s suggestion, I have determined the conduc- tivity of certain Salts and Acids in solutions of varying concentration at 0°, for the purpose of reckoning the Dis- sociation-degree at this temperature, and the results indicate that, in dilute solutions, the dissociation-degree is practically independent of the temperature. The determinations were made according to the Kohlrausch method, and the conductivity of the distilled water used in the experiments was determined at different temperatures and taken into account. The value expressing the conductivity of infinitely dilute * Translated from the Zeitschrift fiir phys. Chemie, xviii. p. 3 (1895). Communicated by the Author. ? + Phil. Mag. July 1896. 118 Mr. R. W. Wood on the Dissociation solutions was calculated by means of the temperature-coefficient from the values found by Kohlrausch and Ostwald for 18° and 25°. In the case of the acids, it was determined by the aid of the Kohlrausch law. : The results of the determinations made with potassium and sodium chloride are as follows :— Potassium Chloride 0°. Sodium Chloride 0°. yy, d ae We r dv Ae ie 1 61:10 78°53 1 44-59 68:60 2 62°49 80°30 2 48-00 i ie}s) 4 64:46 82°78 4 50-76 78:09 8 66:47 85°44 8 53°31 82°02 16 68°70 88°30 16 55°36 89°17 32 70 66 90:82 32 57-20 88-00 64. 72:60 93°32 64 59°13 90°77 128 73°90 94:99 128 60°10 92°46 256 75°30 96-79 256 61:13 94:06 512 75°90 97°56 512 62°43 96:05 1024 76°35 98-14. | 1024 63°70 98-00 co 77°80 100-00 00 65°00 100-00 V signifies the volume containing a gram-molecular weight of the salt, » the conductivity, and x the dissociation-degree, 55 = V 10 2 30 40 50 60 YO 80 90 100 110 120 130 If we take as ordinates the values obtained by Kohlrausch for the dissociation-degree at 18°, and those which I have * Degree of some Electrolytes at 0°. 119 found for 0°, and as abscissee the values of V, we find that the curves are almost coincident, while the one representing the values obtained by Wildermann from the lowering of the freezing-point runs considerably lower, as the diagram indicates. | The values of X., for 0° in the following table is calculated by means of the temperature-coefficient of the most dilute of the investigated solutions from the values of X. given by Ostwald for 25°. an di- and trichloracetic acids the following values were found :— 1 dx Dichloracetic Acid, = —, =0°0148. rd | Dissoeiation- Xo X for 25°. Av degree by V. ° x, |—_—- me lowering of cee for 0° for 25° freezing- * | Wood. | Ostwald. : point. 32 174 766 252°3 253'1 70°2 64 194:2 85°5 — 2907 80°5 740 128 207°9 91°5 317-4 3175 88:0 84:0 _ 256 21671 95-2 — 337-0 93°4 512 221-9 97-7 3518 302°2 97-6 (ee) 227-:0 | 100-0 — 361:0 | 1000 : ; s, Ulida Trichloracetic Acid, — =, =0°0149. rA aT : 32 206:0 O17 324-0 323'0 90°1 88'1 64 211-9 94:3 333°5 332'8 93-0 94:0 128 2166 |- 96-4 341°5 341-0 95°3 256 219°7 97-7 348°1 3480 97°0 512 221°9 93:7 303 0 3537 98:8 oa) | 224-7 | 1000 = 3580 | 100°0 For control, the conductivity of the two acids at infinite dilution at 0° was calculated from the values obtained for siz normal solutions of their potassium salts, potassium chloride, and hydrochloric acid, according to the Kohlrausch law. The following are the values found, which agree very well with those in the table :— Dichloracetic acid . Awo=—228. Trichloracetic acid . Aw =225°2 The dissociation-degree of the two acids is apparently 120 Mr. R. W. Wood on the Duration of the — independent of the temperature, and Wildermann’s. suppo- sition has not been confirmed. The deviations of the values for the dissociation- see Fer 28s: sail o the two methods still remain. In all net le the cause lies in the ene determina- tion of the freezing-point of dilute solutions. We know from the investigations of Nernst and Abegg* that its exact deter- mination is attended with great difficulty. XV. The Duration of the Flash of pees Oxyhydrogen. By R.-W. Woop Ff. - — ee time ago, in endeavouring to photograph the ex- plosion-wave, if it may be so termed, of electrolytic gas by means of the electric spark, I was struck with the fact that the duration of the flash was exceedingly small. In many cases I found that the glass bulbs, which were thinner than paper, were photographed by the light of the incandescent gas within before the walls had given way. The striations on the glass were sharp and the outlines of the bulb were perfectly distinct, the interior being quite filled with a bright low. . I have recently repeated and enlarged somewhat on these ee with a view to determine the duration of the flash... The bibs. were ee very thin, at a aie like neck at each end. They were filled with a mixture of oxygen and hydrogen by means of an electrolytic apparatus, and two copper wires were then sealed in with wax, with a gap of perhaps half a millimetre between them. A pendulum, made by hanging a heavy lead ball on a fine wire, was hung in front of the bulb, the copper wires of which were connected with the terminals of a small inductorium. From the bottom of the ball projected a pin which came in contact with a slip of platinum foil mounted edgewise before the bulb, and the pendulum and foil were put in circuit with — the primary coil of the inductorium. ‘This arrangement insured the explosion of the bulb at the moment when the pendulum passed its point of equilibrium, and by calculating the velocity of the pin’s head and measuring the amount of blur of the photographic image the duration of the flash could be approximately deterrained. The camera, provided with a Zeiss lens of large aperture, was placed near enough * Zeitschr. fiir phys. Chemie, xv. y. 681 (1894). + Communicated by the Author, Flash of Exploding Oxyhydrogen. ia | to give an image of natural size in order to simplify the measurements. : - With a velocity of 3 metres a second the image of the round pinhead was as sharp as if stationary ; but on. raising the pendulum to a height sufficient to give it a velocity of § metres a second, a blur amounting to a trifle less than ‘) millim. was observed. The pendulum-point moving 6000 millim. in a second would traverse a distance of *5 millim. in the 551.5 ofasecond, consequently the duration of the flash is -~ 1 Cc es ieee » ° somewhat less than 55/55 Sec-, probably about ~.1— sec Of course the total duration of the flash depends on the speed of propagation of the explosion in the mixture, as well as on the actual duration of the flash of each exploding element; Le Chatelier found that this velocity was about 1000 metres a second. aa The bulbs being about 8 centim. in diameter, and the point of ignition in the centre, the explosion would reach the walls in 5-1, of a second. This being about. one half of the total duration, we may suppose it to be about the’ duration of the flash of any small element. 122 Duration of Flash of Exploding Oxyhydrogen. In some cases the luminous gas in the photograph was confined within the walls of the bulb, while in other cases a cloud or outburst was noticed at some particular spot outside the wall. The image of the pendulum wire in one case came in front of this cloud and was found to be much more blurred than the pin, indicating that the light of one of these out- bursts lasts longer than that of the mixture within. This may be due to an admixture of outside. air, which increases the time of combustion. a I find that the light of these exploding bulbs is quite suit- able for photographing small objects in rapid motion such as water-jets ; and in some cases may be preferable to the spark, _the electrostatic strain just before the flash tending to deform the jet. In one of the photographs, where an outburst has taken place directly against the jet, there are curved traces around the drops, apparently where the burning gases are rushing around them. For the purpose of photographing jets, I think that a better device than the thin bulb would be a shallow, rectangular tin tray with a highly polished bottom, such as a box cover. This could be covered with a thin film of mica fastened on with wax, and the vessel filled through two small tubes. The reflecting back would increase the amount of light without increasing the depth of the exploding layer, which of course tends to prolong the flash. i Note.—On receiving the proof of the above paper I was much surprised to find that the photograph, which I had enclosed as a curiosity with the MS., had been reproduced. I had no idea that the picture would be considered of interest enough to warrant reproduction, or I should have taken pains to secure a better one. My best negative came to grief, and the picture reproduced is the first attempt at securing a water-jet by the flash, taken merely to ascertain whether the method was feasible. Much of the detail has been lost in reproduction, but the upper parts of the jet show well, No especial pains were taken to secure uniform jets, though the right-hand one is fairly good. An oblate spheroid, on the end of a liquid thread, then a chain of fine little drops, formed by the breaking up of a thread, then the prolate spheroid. The outbursts of gas show fairly well in this photograph, and at the bottom of the left-hand jet two blurred drops are dimly seen, showing the longer duration of this part of the flash—R. W. W. pease | XVI. A very Simple and Accurate Cathetometer. By F. L. O.. Wapsworts”*. ()* the various standard physical instruments which are usually found in a student’s laboratory, the cathetometer may justly be considered as one of the most instructive and valuable, both because of the many principles involved in its adjustment, and because of the number of measurements which may be made with it. Unfortunately, good catheto- meters (and it is never good policy to use poor instruments for the purposes of instruction) are so expensive, as made at — present, that one or at most two are all that one laboratory can afford. For this reason it may perhaps be of interest to briefly describe a form of cathetometer recently designed by the writer which costs less than one-tenth as much as the best German or English instruments, but which has shown itself in use to be quite as accurate as and in some respects even more convenient of manipulation than the latter. In the new arrangement, the general method of comparison now employed in nearly all of the most accurate linear measurements is followed: 7. e., the images of the observed points and of the lines on a standard bar, placed parallel with the length to be measured, are brought in succession into the field of an observing telescope or microscope, and their relative position determined by means of a micrometer or some equivalent arrangement. In previous forms of catheto- meter, this has been done by rotating the observing-telescope itself on a long heavy-vertical axis; in the new form, all of these heavy rotating parts are dispensed with, the observing-tele- scope is fixed in position and the images of the object and scale brought successively into the field by means of a light silvered mirror mounted on a vertical axis just in front of the objective. A sensitive level attached to the upper end of this axis enables the latter to be set accurately vertical, this adjust- ment being made as in an ordinary cathetometer. The complete arrangement is shown in elevation in fig. 1 and in plan in fig. 2. A, fig. 1, is the mirror frame and B is the level, mounted at the ‘lower and upper end respectively of the short, conical axis C. The boss D, in which this axis turns, is attached by means of a geometrical clamp at E to a split cap which slips over the end of the observing-telescope T and is clamped thereon by means of the screw F. This much * From the American Journal of Science, J anuary 1896, 124 Mr. F. L. O. Wadsworth on a really constitutes all of the essential parts of the new catheto- meter, the teleseope-mounting itself—consisting of the two L- shaped.bars K, G and the adjusting screws H, I—being merely Fig. 1. DM WE = (0) =. nl accessory to the convenient adjustment of the axis C to verti- cality. An ordinary open V-clamp M attached to the lower bar G enables the whole arrangement to be clamped to any convenient support; such, for example, as the upright of a heavy retort-stand, or an iron wall-bracket or even a stiff well- secured water- or gas-pipe on the wall of the laboratory. If a retort-stand or other support with adjusting screws in its base is used, the adjustable support G, K, &., on the telescope Simple and Accurate Cathetometer. 125 itself may be dispensed with, and the clamp M attached directly to the telescope-tube as in fig. 3, which shows the cathetometer in use. . Fig. 3. In the use of the instrument, the mirror is first adjusted until it is parallel to the axis of rotation C and perpendicular 126 Mr. F. L. O. Wadsworth on a to the optical axis of the telescope T. These two adjust- ments are made simultaneously in the same manner as described in a previous article*; 2. e. by bringing the reflected image of the cross-wires into coincidence with the wires themselves, revolving the mirror through 180° and correcting one-half of the resulting vertical displacement by means of the adjusting screws b, b, 6, against the heads of which the mirror rests, and the other half by means of the screw e, which forms part of the geometrical clamp H. The level is then adjusted until it is perpendicular to the axis of rotation by means of the screws /, /, in the usual manner. Lastly, the telescope is set at the height of the object to be measured and clamped in position, and the axis C adjusted to verticality by the screws I and H (or the levelling-screws in the base of this support), the level being placed first parallel to the telescope-tube and then at right angles to itt. The first of these adjustments is made once for all ; the second is tested at the beginning of each day’s work; and the third only is necessary at each setting of the telescope. It is important to notice that a small error in levelling has the same effect in this new form as in the ordinary form ; 7. e. the error is not doubled by reflexion from the mirror, because the telescope and the latter move together, so far as any move- ment in a vertical plane is concerned. Let us consider the effect of a small error in levelling, first, in the vertical plane parallel to the axis of the telescope ; second, in the vertical plane at right angles to that axis. Let @ be the angle which the line of sight to the object makes with the first plane con- sidered, and « the angle which the axis of rotation c makes with the vertical in that plane. Then, if ¢ denote the difference in reading produced by this inclination from the vertical, and rv the distance of the object from the axis of rotation, we have evidently | e=rsin ecos@ ; for the difference produced by an inclination @ in a plane at right angles to this * “ A Simple Method of Determining the Eccentricity of a Graduated Circle with only one vernier,” F, lL. O. Wadsworth, Amer. Journ. of Sci., May 1894, vol. xlvii. p. 373. + The mounting shown in figs. 1 and 2 is especially convenient in per- forming this last operation, as the screws H, I, and the third pivot-point bear respectively in a slot, plane, and conical hole at the three vertices of a right-angled triangle, and the motion of either screw, therefore, affects the position of the axis C only in the vertical plane passing through that screw and the pivot-point. Simple and Accurate Cathetometer. 127 ée=rsin«e’ sin 6; . and for the corresponding errors in comparison of object and scale: A =e —e, =r sina (cos8—cos6,),. . . (1) A’/=¢'—e/=rsin a’(sind—sin@,). . . . (2) In the new form of instrument the best position for the object and the comparison scale is about 90° from the axis of the telescope, or in the direction 0, fig. 2. If we suppose the object and scale 15° from one another, and symmetrically placed on the two sides of the 90° position, we have for 6 and 0, respectively 90°-+ 74° or 974° and 823°. Hence A=026rsineZ'dra. . . . . (3) and A USE rita Pes 9 HD lee a (4) The general equations (1) and (2) show that care in levelling is only necessary in the vertical plane perpendicular to the line of sight ; 7. e. in the new form the plane parallel to the axis of the telescope; in the usual form the plane at right angles to that axis. Hence if the greatest accuracy is to be attained with the ordinary cathetometer, the usual tele- scope level should be placed at right angles to its customary position (or perhaps, better still, a second level added in that position), so as to at once call attention to any error of adjustment in that plane. It is strange that this rather important fact should have been overlooked in previous designs. The actual magnitude of the error in measurement, due to an error in levelling, is, however, always small, unless either the distance of the object from the telescope is considerable, or the difference between the angles @ and @, is larger than 60°. Ifa=5" and @—@,=15° as in (8), the error, A, for objects distant $M. from the axis of rotation, would be about 003 millim., or about the limit of accuracy of setting with the best cathetometers under the best conditions. With a good level sensitive to 5” per division (the best cathetometer levels are from two to three times as sensitive as this), there is no difficulty in setting by reversal to within less than } div. or L’, reducing the error under the above conditions to about 5/55 millim. This shows that we may very considerably increase the angular difference @—@,, without introducing any appreciable error. For when this difference is 60° the value of A is only twice the above values or about ‘001 millim. in the last case, 128 Mr. F. L. O. Wadsworth on a ~ a quantity quite negligible in comparison with the errors of setting. This indicates another method of using this new form of instrument to good advantage; z.e., the method of superposition of object and comparison scale. To accomplish this, the mirror A is half silvered and the scale is viewed directly through the -unsilvered half in the direction o’ (see fig. 4), the object being at the same time seen by reflexion from the silvered half in the direction 0’*. In this case we may make the measurement either by determining the distance between the image of. the point and the image of the nearest millim. division on the scale with an ordinary form of micrometer; or better, by bringing these two images into coincidence by means of a Rochon double micrometer, an opthalmometer or a parallel-plate micrometer. The second method of coincidence has the decided advantages both of greater rapidity, only one setting and reading being necessary: instead of two, and of greater accuracy for the same reason, since any error, due to a change in position of any part of the apparatus in the interval between two settings, is thus avoided. This last advantage fully balances the disadvantage of the greater effect of a given error of levelling on account of the greater angular distance between scale and object. One additional cause of error is introduced, 7. e., that due to a want of parallelism between the mirror A and the axis of rotation ©; but since this should not exceed a fraction of a second, if the first adjustment has been properly made, its effect is negligible. Of the various instrumental means for obtaining coincidence perhaps the simplest and most convenient, as well as one of the most accurate, is the parallel-plate micrometer first invented by Clausen, and quite recently reinvented and much improved by Poynting +, who was the first to adopt it for cathetometric measurements. Figs. 4 and 5 show in plan and elevation a form of this micrometer modified slightly from that described by Poynting, to better adapt it to this particular instrument. It consists simply of a plate of plane-parallel glass, P, rotating on an axis C’ at right angles to the axis C, * The mirror should be half silvered horizontally, 7.e. the line of separation of the silvered from the unsilvered portion should be parallel to the axis of rotation, both because the maximum resolution is required in a vertical direction and because, as will be seen later, this management is the better adapted to'the use of ceitain forms uf micrometer, + Phil. ‘I'rans. vol. clxxxii. 1891 A, p. 588. See also “ On a Parallel Plate Double Image Micrometer,” Monthly Not. of the Royal Astron. Soc., vol, liii. No. 8, 1892, p. 556, Simple and Accurate Cathetometer. 129 and carried in a fork which is a prolongation of the boss D shown in the preceding figures. The rotation of the plate on its axis shifts the ray from 0’, which passes through it, and hence also the image of the scale, Fig. 4. Fig. 5. by an amount A which may easily be shown to be A=tsi ipa COE = sing .[ = Vr —sin?d e @ being the angle of rotation measured from the position in which fhe plate is normal to the Tay is expression may be written-:- i. Ses ___cosh __ \ .ncos ¢ A=. ee oe | {( ie jee = "rang $./(9). The quantity in brackets or /(p) may be shown to be very nearly unity for all values of ¢ between 0° and 30°. In order to determine its exact value, we may develop it into a series as Poynting does, but since this series is only rapidly convergent for low values of gd, it is on the whole better to compute it directly from (1), which is in a form well adapted to logarithmic computation. I have calculated the values of f (¢) for values of ¢ from 5° to 30° and for two values of 2, viz. n= 1°35 and n=1°55, about the mean indices of the glass Phil. Mag. 8. 5. Vol. a No. 249. Feb. 1896. K 130 . Mr. F. L: O. Wadsworth on a most likely to be used for this purpose. These values are given in the following tables ;— ? ; i) eee SUN She ae n—1l : r= 1°); =2=0'3333 eS = win ceee: ; a : | o aa tang ih. 146%, rs=tang a tang ¢. rs—0. 5 02916. 1-00044= 1+ 00044 ||. +0011 4.00066 : 10 | -05878 | 1:00162=| +-00162 = 20021 +-00049 15 | -089382 | 1:00333 +. -00333 - 4.0033 ‘00000 20 | -12132 | 1:00528 |. +:00528 +0045 —-00078 25 | 15544 | 1:00681 +:00681 +0057 — 00111 30 | -19245 | 1:00708 4.00708 +:00708 +:0000 TABLE II. n—l ; n=). = °35484, | "—*tangg. f (0). aes = 03104 1.00024 1+-00024 10 ‘06257 1:00085 +-00085 15 ‘09508 1:00162 +-00162 20 "12915 1-00216 +-00216 25 16547 100188 100188 | 30 -20487 1-00002 +00002 © An inspection of these two tables shows that in the case of * [In a similar table given by Poynting, the sign of 6 is erroneously written negative (probably a typographical error), and there is also-a small error in the value of 6 for 6=10°, which is, however, unimportant since 6 itself is so very small for this angle. ] %y Simple and Accurate Cathetometer. 131 glass of the higher refractive index (n=1°'55), the maximum value of 6 is only 0°2 per cent. of f(f), and since the maxi- mum shifting of the image need never exceed 1 millim. (if comparison is made on a millim. scale), the corresponding correction to the tangent value is only =$>5 millim. and may be disregarded. In this case we may read off the vaiue of A directly on astraight scale ss by means of a pointer, wu, which consists of a thin plate of glass or mica on which is ruled a fine radial line. The distance ro from o, to the point of inter- section of this line with the longitudinal line ss on the scale, equals c’o tang ¢, and hence is directly proportional to A. If we make c’o equal to 172 ¢ in millim., then each millim. on the scale ss corresponds to a shifting of the image through sg millim. For an angle of 30° A= +¢, hence for a shifting of 1 millim. corresponding to this angle, the plate P must be 2 millim. thick, and the distance c’o therefore about 89 millim. as laid off in fig. 6. The scale ss of fig. 5 is graduated in ’ YC’ 2 millim. intervals so that such intervals correspond to 3: millim., but it is easy to set and read the position of the pointer to 5}, div. or =}, millim. | In the case of glass of refractive index 1°5 the proportion- ality between the scale-readings obtained in this manner and the value of A is not so exact, the error amounting in case of an angle of 30° to nearly # of 1 per cent. or to nearly 0:01 millim. This is a quantity too large to be neglected. Poyn- ting suggests a very ingenious system of link-work, whereby the readings on the scale may be made directly proportional 132 A Sunple and Accurate Cathetometer. to A for all values of ¢ ; but this, as he himself recognizes, is hardly practicable on account of mechanical difficulties. We may. however, obtain the desired result very much more simply. An inspection of the values of 6 in Table I. will show that they are roughly proportional to tang d. If we draw a line no (fig. 6), inclined at a small angle a, in each direction from 0, to the longitudinal line on the scale ss, and read in each case to the intersection of this line with the radial line wu on the pointer,—we increase the scale-reading by an amount sr=os tang a tang $, and the new scale-reading is therefore osxc'o tang @.[1+tang «tang ¢]. Hence we have only to make tang a tang @=6, in order to make os the new scale-reading directly proportional to A as before. To find the inclination « of the line n, 0, to the axis of graduation we have only to put tang « tang @=6 for some particular value of ¢. Suppose we do this for g6=30°. Then we find ‘OO71 tanga= 577 or a=42’, Using this value of @ to calculate the values of the scale correction, 7s, at other points, we find the valnes given in the 5th column of Table I. As will be seen, they differ on the average from the corresponding values of 6 by less than 34, per cent. ; or only about 0:0008 millim. at the maximum for o=25°. By this simple method, therefore, the necessity for making any correction to the scale-reading, even in the most accurate work, is entirely avoided. The exact constant of the scale-reading for any particular value of the index, differing from those given above, may be either calculated from the above formula or determined experi- mentally. In order to always make the value of a 1 millim. scale division correspond to some convenient fractional part of a mnillim., the support for the scale is made adjustable in height so that the value of clo may be always made equal to = “, where a is the fractional value desired. One advantage which Straining of the Earth resulting from Secular Cooling. 1383 the rotating plate has over the ordinary eye-piece micrometer, is that its constant remains the same for all distances of the scale from the telescope*. The above form of parallel-plate micrometer may also be advantageously substituted for the eye-piece micrometer in the first instrument described. In this case it should be placed between the objective and the reflecting mirror A, or else mounted on the mirror-frame itself so as to rotate with it. The last position enables the same instrument to be used either in the method of comparison or in the method of coin- cidence, but is objectionable both on account of the increased weight of the moving parts and because of the liability of dis- turbing the adjustment of the axis or mirror while manipulating the micrometer. It is therefore better to place the rotating plate in the first position indicated and adapt it to either method of use if desired, by making it cover only one-half the field of the telescope, that half of course which is opposite the unsilvered half of the mirror when the coinci- dence method is used, and opposite the silvered half when the comparison method is employed. In closing I wish to express my thanks to Messrs. Francis and WKathan, the mechanicians of the laboratory, for the care exercised in the mechanical execution of these designs. ~ University of Chicago, September, 1895. XVII. On the Straining of the Earth resulting from Secular Cooling. By Caarusrs Davison, M.A., F.G.S., Mathema- tical Master at King Edward’s High School, Birmingham fF. STIMATES of the depth of the surface of no strain have hitherto been founded on the assumptions that the con- ductivity and the coefficient of dilatation are constant ft. In the present paper, I propose to calculate the depth on the * The great practical advantage of this form of micrometer over the ordinary form is its much greater simplicity and cheapness. For these reasons it would have been adopted in all of the above instruments, had it not happened that we already had on hand a number of micrometer eye-pieces which were available for this purpose. + Communicated by the Author. A paper with the same title was read before the Royal Society on Feb. 15, 1894. The present paper contains the substance of the former, but has been rewritten. if Rome Trans. 1887 A, pp. 231-249; Phil. Mag. vol. xxv. 1888, pp. 7-20. 134 _ - Mr. G. Davison on the Straining of the - supposition that the coefficient of dilatation increases with the temperature, being ¢+e/v, where v is the temperature. In assuming this law to hold true up to a temperature as high as 7000° F., itis evident that the numerical results here obtained cannot be regarded as reliable. They are given for their qualitative rather than for their quantitative value. Let x» be the internal radius of a thin spherical shell con- ceniric with the earth*, its thickness dr, density p, and coefficient of linear dilatation e. In any given time, let the temperature of this shell be increased by @; then, if the shell were isolated, » would be increased by ve. But, in consequence of the expansion of the mass inside it, let the internal radius be further increased by rk, so that r hecomes r(1+a), where a=k+e@. Also, p becomes p(1—3e@) and dr becomes : [1+ £ (ra)]). Since the mass of the shell remains unchanged, we have there- fore ad 2a + Gah) —8e0=0, which may be written S (72a) = 3e0r, or d d - (kr?) = —7* a (e@). ~ The amount (kr) by which the radius is increased by stretch- ing in the given time is therefore = 3)" S (oer. . . Let ¢ be the radius of the earth and 2 the depth of the surface of radius r, v the excess of temperature at this depth above that at the surface of the earth, and @ the increase of temperature in unit time, so that 0=dv/dt ; also let ¢ be the * The method of proof adopted is similar to that given by Prof. G H. Darwin in his paper in the Phil. Trans, 1887 A, pp. 242-249. Earth resulting from Secular Cooling. 135 coefficient of dilatation at the surface, and e+ e’v that at depth: #, Then, using Lord oo s well-known solution, expression. Q) becomes | =a & opti {ere 2 V(r) Jo where a=2,/ (xt), and infinity is substituted for ¢ in the upper limit, Lord Kelvin’s solution being adapted to the case of a sphere ‘of infinite radius. The shell at depth « will be stretched, unstrained or crushed, according as expression (2) is positive, zero or negative. Depth of the Surface of No Strain—Putting w=ay and €r/ (7) /2 Ve =, we obtain, after division by irrelevant factors, the following equation for determining the depth of the surface of no strain, fc—a) : [yen + (B+ ['eae) (1—2y2)e-#” | dy ee e—2a 2) $4 lowes eae ti re Jae, (2) : = [e—oy)* [yeas at ['e-easya—2y)e* dy. (8) _ Since y is a proper fraction, this equation, omitting un- Eavonant terms, becomes aE fee ae ge Eg BAe +2 8 ~2 ey Be +y?(e — 8B cea) + 93(—2c?a + Bea? — a | + y'(gea?—40° + 28e%a) +y° (L8Pat+3Be)+....- (4) As a first approximation, which is sufficient for most purposes, we have the equation : BS ey(y + B)=8a( V2 448)... . . (3) Putting 6 equal to infinity in the latter, we get y=8a/2e, or w=Oxt/e, . . » » » « « (6) which gives the depth of the surface of no strain on the 136: Mr. C. Davison on the Straining of the | supposition that the coefficient of dilatation is constant, 2. e., an inferior limit to the depth if the coefficient of dilatation increases with the temperature. This agrees of course with the first approximation obtained by Prof. G. H. Darwin and the Rev. O. Fisher*. Putting 8 equal to zero, 1. e., e/e to infinity, we get aie: VJ Qar a A sar 8 °? ot ; v= (=F) 4. Sen ke LO eee : (7) which gives a superior limit to the depth of the surface of no strain so long as the coefficient of dilatation increases with the temperature. In Fizeau’s table of coefficients of dilatation , eighteen determinations for non-crystallized bodies are given as especi- ally trustworthy. Making use of these only, and taking V at 7000° F., the average value of Bis‘1. With this value, the depth of the surface of no strain after 100 million years is 7°79 miles. At the same time, with a constant coefficient of dilatation, it would be 2°17 miles. It is evident from equation (4) or (5) that there is no simple relation between the depth of the surface of no strain and the time. If e’/e be small, the depth varies nearly as ¢: if é/e be large, the depth varies nearly as ¢*. Volume of Folded Rock above the Surface of No Strain.— Since & and e are both small fractions, the volume of that part of the shell of radius rv and thickness 6r which is stretched or folded in unit time is Ardr . 7? —Arrdr(7* + 27. kr) = 8ar(e—x)b2 . kr, where kr is given by the expression (1) or (2). Denoting this by 6U, we have dU _ 16eV./ (xe) dy ~ Ble—ay) v (1 * Phil. Trans, 1887 A, p. 246; Phil. Mag. vol. xxv. 1888, p. 14. + Jamin’s Cours de Physique, vol. ii. 1878, pp. 80-81. Earth resulting from Secular Cooling. 137 where FY={ e—ay*[ye-w 4 G+ [okay aye Jay, _ 16eV / (7k) © f(y) 2S aaa ae ; poe aiganere (8) where s is the value of y at the depth of the surface of no strain. Hence, if SW be volume of rock crushed in time d¢ above the surface of no strain, U=dW/dé, and therefore w= Lf ee jedan This gives the total volume of the rock-folding since consolida- tion, while equation (8) gives the rate at which rock-folding takes place at time ¢. For a first approximation, we may put ieee a c—ay ¢ and Fy) =Aca—yBo' —y?e", where A=3( V 27 +48) /8. We thus get Lo) dy = Acas—4Be?s? — 0 ¢—ay where s=3[—B+ v (6? +4Aac)], and consequently, after reduction. W=16eV v(m)[ = 6%a( 14 a ne Bee! (14 sy 72 A B 1 Oe 1 BCs MAYEN gige 1 ae]. ( + i309 A 180 A 1+ +.) — Aca? — 5, Atta |. (10) If h be the average thickness of this volume of crushed rock spread over the whole globe, then pes -W 4c’. 138 Straining of the Earth resulting from Secular Cooling. If we make e’/e equal to zero, or @ equal to ni in these expressions, we get” = 3 At Otay More Fs. i. : “hE Say amd ce BEV 7/2 Ar )C*. 2p This value of h agrees with that obtained by the Rev. O. Fisher on the supposition that the coefficient of dilatation i is constant”. The mean value of the coefficient of dilatation acai from Adie’s experiments t on six rocks «at temperatures varying from about 50° to 208° F., is °0000057. Taking this as the surface-value e, and as before V equal to 7000° F., and @ to *1, we find that after a lapse of 100 million years the total volume of solid rock is about 6,145,000 cubic miles, and the mean thickness of the layer formed by spreading this ever the whole earth is ‘03120 mile or 164-7 feet. If the coefficient of dilatation were constant and equal to the value above-mentioned, the corresponding figures would be 184,500 cubic miles and 4°95 feet. Alleged Insufficiency of the Contraction Theory.—lf the co- efficient of dilatation increases with the temperature, instead of being constant, it thus appears that the result is a con- siderable increase in the depth of the surface of no strain, and in the total amount of rock-folding due to the cooling of the earth. If the conductivity increases.with the temperature, there will be a further increase of both quantities. It is possible, moreover, that besides their variation with the tem- perature, both the conductivity and the coefficient of dilata- tion may be greater in the material which composes the earth’s interior than they are in the surface rocks. Mr. Rudski has also pointed -out t that the depth of the surface of no strain will be much greater if initially the temperature, in- stead of being uniform, increased with the depth, and there is some reason for supposing that this may have been the case. If, then, we regard the contraction theory as a-theory of the formation of mountain-ranges only, and not necessarily of the continental masses, we may, I think, conclude that calculations as to its alleged insuffictency are at present inadmissible. * Phil. Mag. vol. xxv. 1888, p. 17. . + Edinb. Roy. Soc. Trans. a4 xill. 1836, pp. 354-372. { Phil. Mag, vol. xxxiv. 1892, pp. 299-301, bail ABR XVIII. Notzces respecting New Books. Théorie de V Electricité. By A. Vascuy. Paris: Baudry et Cie., 1896. : & this treatise M. Vaschy presents a purely mechanical theory of electricity founded on the fact, experimentally demon- strated, that an electric field with a measurable intensity exists at every point of space. The connexion between electric intensity and the medium in which it is manifested is not considered; on this point the author remarks :—“ The idea of intensity of the electric field is not more intimately connected with the three fundamental ideas of mechanics than these latter are connected among themselves. We shall therefore consider it as fundamental ; but all others with which we meet in electricity will be derived from it, and from length, time and mass.’ It is shown that the condition of stability of the electric field is the existence of a potential function ; this leads to the discussion of lines of force, equipotential surfaces and conductors. M. Vaschy distinguishes two classes of action at a distance, of which the action between two electric charges and that of an element of a linear current on a magnet pole are the types ; in the former case the force is in the line joining the particles, whereas in the latter case one of the attracting “ masses ” is a vector quantity, and its direction determines that of the force. The two classes may be called Newtonian and Laplacian respectively ; the author shows that any field of force whatever can be completely represented by a suitable distribution of Newtonian and Laplacian masses, with an inverse square law of attraction: a stable field is due only to Newtonian masses, while a solenoidal distribution is produced by Laplacian masses alone. The energy which really exists in every unit of volume of the field is referred in action-at-a-distance theories to these fictitious masses, thus giving rise to the ideas of electric charges and currents. M. Vaschy’s explanation of a current in a conductor is analogous to that of Poynting; in every element of volume of the conductor, the energy of the electric field is constantly being transformed into heat, and new energy must be supplied along definite paths from the battery or other source of electric energy. Assuming that the rate of supply of energy to the element of volume depends only on the instantaneous state of the field at its surface, and not on the mode of transformation of the energy within it, the field of 2 current can be divided into an electrostatic and a magnetic portion. The discussion of variable currents follows, and the detailed treatment of electric waves is a prominent feature in the book. 140 Notices respecting New Books. The aim of the author has been to produce a work bearing the same relation to electrical theory as a treatise on thermodynamics bears to the theory of heat. ‘Temperature in the one case, electric force in the other, are regarded as fundamental quantities; the rest consists entirely of experiment and mathematical deduction. A closer study of the behaviour of heated gases gives us a clue to the physical meaning of temperature; may we not hope to learn from the electrical properties of matter something more definite concerning electric force ? JamMEs L. Howarp. Molecules and the Molecular Theory of Matter. By A.D. Risrusn, S.B. Boston, U.S.A.: Ginn & Co., 1895. THis volume is the outcome of a lecture on the same subject, which the author has greatly amplified, retaining, however, the lecture style, which involves the frequent use of the first person singular. The introduction of this personal element enables Mr. Risteen occasionally to put forward his own views without leading students to suppose them orthodox—if such a term is permissible in connexion with the theory of the constitution of matter. He thus imparts to his subject a greater interest and a more vigorous treatment than it has previously received, except in Maxwell’s discourse on ‘ Molecules,’ and Lord Kelvin’s lecture on the ‘Size of Atoms.’ The first part of the work is devoted te the kinetic theory of a perfect gas; the gaseous laws are explained, and Maxwell’s law of distribution of molecular velocities is enunciated and discussed. This is followed by the statement of Boltzmann’s theorem and the deduction of the relation between the number of degrees of freedom of the molecules of a gas and the ratio of its specific heats, after which diffusion and viscosity are treated according to the principles of the kinetic theory, and molecular free path is illustrated by the radiometer and Crookes’s tubes. The second section of the volume deals with the molecular theory of liquids and solids, and is necessarily more superficial and sketchy than the previous one; it concludes with a good account of the various methods for the determination of molecular magnitudes. The rest of the volume contains short descriptions of the various theories concerning the nature of atoms and molecules. The author has endeavoured to give an outline of the whole subject rather than a detailed mathematical treatment of a portion of it, so that formule are occasionally quoted without proof. In these cases the student might with advantage be referred to a treatise or memoir where the proof is to be found. JAMES L. Howarpb. Notices respecting New Books. 141 A Laboratory Course in Experimental Physics. By W. J. Lovupoy, B.A., and J. C. McLunnan, B.A. New York: Macmillan & Co., 1895. AurTHouGH text-books of practical physics are now fairly numerous, the demonstrators in physics of the University of Toronto appear to have found it impossible to adapt any of the existing ones to the requirements of their students. The same difficulty has been experienced in most. English laboratories, partly on aecount of the diversity which exists between the apparatus of the various institutions, and partly because of the different aims of students working in them. Consequently nearly every laboratory possesses instruction-sheets, either in print or manuscript, which have in some instances been edited and issued in book form ; the present volume is a case in point. The experiments described in the book are arranged in two courses, elementary and advanced, in the former of which weighing and measuring, light and heat, are included, while the advanced course consists of sound, advanced heat, electricity, and magnetism. Some easy experiments in electricity and magnetism might have been included in the elementary course, otherwise the selection is a fairly good and useful one. The section on sound contains figures and descriptions of Helmholtz’s and Konig’s apparatus for various experiments, but many students’ laboratories in this country are, unfortunately, not equipped with large electrically-driven tuning-forks and chronographs. Experimental details are sometimes omitted; for example, in describing the use of the spectrometer as a goniometer, the student is not told how to focus the telescope and adjust the slit so as to obtain a parallel beam of light from the collimator. In the same experiment it is erroneously stated that the edge of the crystal must coincide with the axis of the instrument, whereas the two need only be parallel to each other if the collimator is properly adjusted. Again, in calorimetric measurements, errors arising from radiation between the calorimeter and its surroundings are not very adequately discussed ; the calorimeter is supposed in all experiments to alter - its temperature at a uniform rate, and matters are so arranged that the mean between its initial and final temperatures is that of the atmosphere. In specific heat determinations a preliminary experiment is necessary in order to satisfy the latter condition, and the assumption of uniform rise of temperature is only approx- imately true, even when the body under experiment is a good conductor of heat. The book is printed in a bold, clear type, and its illustrations are good; it will be found a useful addition to the laboratory bookshelf. JAMES L. Howarp. of. Wasg> ee Proceedings of Learned Booteties. - GEOLOGICAL SOCIETY. [Continued from p. 78.] - December 4th, 1895.—Dr. Henry Weodward, F.R.S., President, | in the Chair. : lui following communications were read :— ‘On the Alteration. of certain Basic Eruptive Rocks from Brent: Tor, Devon.’ By Frank Rutley, Esq., F.G.S. Two microscopic sections of rock occurring on the north side ef Brent Tor were examined, and a cursory glance suggested at once the idea that they might originally have consisted to a greater or less extent of extremely vesicular basalt-glass. No unaltered vitreous matter, except perhaps mere traces, can now be detected in these specimens, the interest of which lies in the assemblage of alteration- products which they contain. A third section cut from a small chip collected at the southern side of the base of the Tor consists of a highly vesicular lava of a hyalopilitic character, which may be regarded as an amygdaloidal glassy basalt. - The author gives a detailed account of the microscopic characters of the three sections, and discusses the history of the rocks, com- paring them with Tertiary basic glass, and with the Devonian rocks of Cant Hill, which he described previously. He brings _ forward evidence in favour of the view that the original alteration of both the Brent Tor and Cant Hill rocks was palagonitic, and that while in the Brent Tor rocks the subsequent alteration of the palagonite into felsitic matter, magnetite, secondary felspar, epidote, aud probably kaolin, and some serpentine and chlorite was com- plete, it was only partial in the case of the Cant Hill rocks. We may therefore assume that palagonite is not the ultimate pha g of alteration 1 in basic igneous rocks. 2. ‘The Mollusca of the Chalk Rock.—Part I.’ By Henry Woods, Esq., M.A., F.G.S. ae December 18th.—Dr. Henry Woodward, F.R. 8., President, in the Chair. Me following communications were read :— ‘The Tertiary Basalt-plateaux of North-western Europe.’ By Sir Archibald Geikie, D.Sc., LL.D., F.R.S. ~ The author in this paper gives the results obtained by him in the continued study of Tertiary Volcanic:-Geology during the seven years which have elapsed since the publication of his memoir on ‘The History of Volcanic Action during the Tertiary Period in the _ Geological Society. 143 British Isles.’ His researches have embraced the Western Islands of Scotland, St. Kilda, and the Farée Islands. _ 1. In an account of the rocks of the basalt-plateaux iitecton -§ particularly directed in this paper to a type of banded basic lavas which play an important part in the structure of the volcanic dis- -tricts both of the Inner Hebrides and of the Fardes. The banding sometimes consists in layers of more highly vesicular structure, sometimes in alternations of distinctly different lithological cha- -racter, such as close-grained basalt and more coarsely-crystalline dolerite. These banded rocks are more particularly developed in the lower portions of the volcanic series. At a distance they might be mistaken for tuffs or other stratified deposits. They occupy a ‘conspicuous place in the great precipices of the west and north - the Farde Islands. _ Numerous examples are cited of the ending-off of basalt-sheets in different directions, indicative of many local vents from which the lavas issued. An account is also given of tuffs and other stratified intercalations which occupy a subordinate place in cee ‘structure of the plateaux. - 2, A number of examples are adduced of the volcanic vents wliieh form a characteristic feature of the basalt-plateaux. A remarkable -row of five such vents was met with by the author at the base of the great cliffs on the west side of Stromo, in the Farde Islands. They are occupied with agglomerate, and their saucer-shaped craters -have been filled in by successive streams of lava from neighbouring vents, the whole being buried under the great pile of basalt- sheets forming the island of Stromé. -. An instance of similar structure is described from Portree Hay, the agglomerate in this case being connected with a thick and wide- spread sheet of tuff intercalated among the basalts. Another example is cited from the eastern end of the island of Canna, -where the ejected volcanic blocks are associated -with records of peae epee neers river-action. 3. The paper describes in some detail the evidence for the flow .of a large river across the lava-fields during the time when volcanic activity was still vigorous. Thick sheets of well-rolled gravel are intercalated among the basalts of the islands of Canna and Sanday. ‘These masses of detritus consist mainly of volcanic material, but they include also abundant pieces of Torridon Sandstone: and rocks from the Western Highlands. The current of water which.trans- ported them certainly came from the east. That it flowed while the -voleanic vents continued in eruption is shown by the bands of tuff ‘and the large blocks of slag contained in the conglomerates, as well ‘as by sheets of vesicular basalt interstratified in the same deposits. -From the terrestrial vegetation whereof the macerated remains are ‘enclosed in the tuffs and shales, and from the entire absence. of ‘marine organisms, it may be confidently inferred that the water was ‘that of a river. The large size of many of the rounded blocks that 144 Geological Society :— were swept along proves that this river must have been of con- siderable volume and rapidity. The stream probably drained some part of the Inverness-shire Highlands, and wandered over the volcanic plain, following the inequalities of the lava-fields, sweeping away the loose detritus of volcanic cones, and continually liable to have its course altered by fresh volcanic eruptions. An interesting section is cited from the island of Sanday, where what appears to be a portion of the ravine of one of the tributaries of this river. trenched in the basalts, filled with coarse shingle and buried under later basalts, remains in a picturesque sea-stack. An account is given of the little islet of Fivcnciet about 18 miles to the west of the island of Eigg, which has been identified by Dr. Heddle with the rock of the Scuir of Higg, and which the author has visited in two successive years. ‘The ‘pitchstone’ is precisely like that of the Scuir down to the most minute structure, as is shown by an examination of the rock under the microscope by Mr. A. Harker. There can be little doubt that this rock was a superficial lava like that of Higg, and there seems every prob- ability that it is really a westward continuation of the Scuir. The Hysgeir pitchstone everywhere dips under the sea, so that its bottom cannot be seen. The author considers that the Canna river may have been the same as that which at a later part of the volcanic period had its channel filled up by the pitchstone of the Scuir of Eigg. 4, Many additional details are given to illustrate the structure and behaviour of the basic sills which are so abundantly developed, especially at the base of the plateaux. Some of these sheets are of colossal proportions, as in the Shiant Isles, where a single columnar -bed is 500 feet thick. Others descend to extremely minute pro- portions, such as the slender layers and threads which have been injected into the coal and shale. between the lower basalts in the Portree district. A remarkable instance of a sill traversing the centre of another is cited from the south-east of Skye, the younger sheet having a strongly developed skin of black glass on its upper and under surfaces. One of the most striking instances of a sill rising obliquely across a thick mass of the plateau-basalts is described from Stromo in the Faroe Islands. 5. The author adds some additional particulars, more especially from Skye and St. Kilda, to his published account. of the dykes -which have taken so important a place in the origin and structure of the plateaux. 6. Further observations are narrated regarding the creat bosses of gabbro in the Inner Hebrides. In particular, the peculiar banded structure, already described from a part of the Cuillin Hills, is shown to have a wide distribution in Skye, and to occur also in Rum. The remarkable alteration of the plateau-basalts as they approach the gabbros of Loch Scavaig is referred to, and the microscopic structure of these metamorphosed rocks is described in notes supplied to the author by Mr. Harker. An account is also given of the Tertiary Basalt-plateanx of North-western Europe. 145 ‘gabbros of St. Kilda, which display a considerable variety of texture and composition and include basalts and dolerites. ' 7, The author, having been able to visit St. Kilda, describes the junction of the granophyre of that remote island with the basalts ‘and gabbros. He brought away a series of specimens and photo- graphs which demonstrate that the acid rock has been injected into ‘the basic masses, traversing them in veins and enclosing angular pieces of them. ‘The granophyre is precisely like that of Skye and Mull, and is traversed by veins of finer material, as in these islands. Where it has penetrated the basic rocks it sometimes forms a kind of breccia-matrix in which the pieces of dark material are enclosed. Tt has taken up a certain quantity of the basalt or gabbro, as is shown by the abundant brown mica and hornblende which have been developed in the acid rock, especially round the enclosed basalt- fragments. ‘The results of a microscopic examination of thin slices of the rock at the junction are furnished by Mr. Harker. From Skye examples are given of triple dykes and sills, wherein a central band consists of granophyre or spherulitic felsite, while the two marginal bands are of basalt, diabase, or other basic material. ‘There does not appear to be any ascertainable connexion between the acid and basic parts of such compound intrusions. In some cases the basic, in others the acid portion is the older. - 8. By way of illustrating the probable history of the basaltic plateaux of North-western Europe, the author gives a short summary of the results of recent investigations of the modern volcanic eruptions of Iceland, especially by Th. Thoroddsen and A. Helland. He shows in how many ways the phenomena of that island explain the facts which are met with in the study of our Tertiary plateaux, and how, in some respects, the enormous denudation of these plateaux throws light on parts of the mechanism of the Icelandic volcanoes which are still buried under the erupted material. 9. Reference is made to the evidence of considerable terrestrial movement since the Tertiary volcanic period, as shown by the tilting of large sections of the plateaux in different directions, and also by the existence of actual faults. Besides the normal faults, which are not infrequent among the Western Isles, there occur ‘among the Farde Islands instances of reversed faults, which ee indicate disturbance of @ more serious character. 45 JOP Pie concluding section of the paper deals with the effects af ‘denudation on the plateaux. With possibly some minor intervals of partial depression, the present Tertiary voleanic tracts of the ‘British and Faroe Isles have remained as land ever since the volcanic ‘period. Their valleys were probably begun before the close of the eruptions, and these hollows have been continuously widened and deepened ever since. The result is a stupendous memorial of the potency of the agents of geological waste. While the Inner ‘Hebrides abound in most impressive illustrations of this denudation, Phil. Mag. 8. 5. Vol. 41. No, 249. Feb. 1896. L 146 Geological Society :-— they are inferior in that respect to the Fardes. The long level lines of basalt-sheets furnish, as it were, datum-lines from which the extent ‘of erosion can be estimated and even measured. There is certainly no other area in Europe where the study of the combined influence of atmospheric and marine denudation can be so admirably pro- secuted, and where the imagination, kindled to enthusiasm by the contemplation of such scenery, can be so constantly and imperiously controlled by the accurate observation of ascertainable fact. 2. ‘The British Silurian Species of Acidaspis.’ By Philip Lake, Esq., M.A., F.G.S. January Sth, 1896.—Dr. Henry Woodward, F.R.S., President, in the Chair. The following communications were read :— -1. ‘A Delimitation of the Cenomanian, being a Comparison of the Corresponding Beds in Southern England and Western France.’ By A. J. Jukes-Browne, Esq., B.A., F.G.S., and William Hill, Esgq., F.G.S. The object of the authors is to compare the beds whieh form the lower part of the Upper Cretaceous Series in those parts of Southern England and Western France which are nearest to one another. They briefly trace the history of English and French geological research, and remark that even at the present time French geologists are not agreed as to the beds to be meluded in their ‘ étage Céno- manien.’ The authors feel justified in taking the English succession as a standard, and endeavour to show that the French succession is in accord with it, believing that the confusion of French geologists has arisen from their having taken a set of arenaceous shallow-water beds as the standard of their Cenomanian stage, ina district where these form the local base of the Cretaceous System, and where the typical Albien fauna does not exist. Commencing with the English sections, they describe such as serve to establish the succession in the Isle of Wight, Dorset, and Devon, pointing out that the Gault and Upper Greensand are everywhere so inseparably united that it is difficult even to assign limits to the component zones; further, that the Lower Chalk is clearly marked off from this group, and that no classification can be accepted in England which does not recognize the clear and natural line of division at the base of the Chalk. In Devonshire the representative of the Lower Chalk is found in a set of arenaceous deposits which contain a remarkable fauna, some of the fossils being such as occur in the Upper Green- sand, some in the Chalk Marl, while many have not been found elsewhere in England, but occur in the Cenomanian of France and in the Tourtia of Tournay. This Devonshire ‘ Cenomanian’ includes The Llandovery and Associated Rocks of Conway. 147 the beds numbered 10, 11, 12, and 13 by Mr. Meyer in his Beer Head section, Quart. Journ. Geol. Soc. vol. xxx. (1874) p. 369. Passing over to France, the fine section in the cliffs between Cap la Héve and St. Jouin is described in detail, and the bed which is regarded as the base of the Cenomanian by M. Lennier and Prof. A. de Lapparent is shown to be the representative of the Chloritic Marl of the Isle of Wight; the Greensand and the Gault below forming, as in England, a separate and independent group of beds. An account is then given of a traverse made through the depart- ments of Calvados and Orne as far as Mortagne; succeeded by a brief account of the lateral changes which take place as the Ceno- manien is traced through the Sarthe, this being derived from the publications of MM. Guillier and Bizet. A critical study of the fossils found in Devonshire and Normandy follows, with tabulated lists comparing the Devonshire fauna with that of the French Cenomanian, and the fossils of the Norman Cenomanian with those of the Warminster Greensand and of our Lower Chalk. In this part of the work the authors have received much assistance from Mr. C. J. A. Meyer and Dr. G. J. Hinde. Finally, they claim to have defined the limits of the Cenomanian stage in Western France, and to have shown that this group of beds is simply a southern extension of our Lower Chalk, formed in a shallower part of the Cretaceous Sea and nearer to a coast-line. if Lhe ee and Associated Rocks of Conway.’ By G. t, Elles and E. M. R. Wood, Newnham College. The discovery of beds with Phacops appendiculatus, Salt., near Deganwy, and of shales with a fauna of Upper Birkhill age close to _ the town of Conway, indicates that the break between Ordovician and Silurian is smaller in this area than has hitherto been supposed. In the paper a full description of the representatives of the Birkhill, Gala (Tarannon), and Wenlock beds is given, and the distribution of the fossils (chiefly graptolites) in the various sub- divisions is recorded. Many of the graptolites are forms which have been described from Swedish deposits, but have hitherto been unrecorded in this country. 3. ‘The Gypsum Deposits of Nottinghamshire and Derbyshire.’ By A. T. Metcalfe, Esq., F.G.S. The gypsum deposits of these counties occur in the Upper Marls of the Keuper division of the Triassic system. The author describes their occurrence in thick nodular irregular beds, large spheroidal masses, and lenticular intercalations, and their association with satin- spar, alabaster, selenite, and anhydrite. SOF 148 J XX. Intelligence and Miscellaneous Articles. CONTRIBUTIONS TO THE KNOWLEDGE OF TROPICAL RAIN, BY PROF. T. WIESENER. N incentive to this series of researches carried out in Buiten-_ zorg, Java, in the winter 1893-94, was the question as to the direct mechanical effect of tropical rain on plants, on which subject entirely erroneous views are current. The author first determined the rainfall per second, and. found the highest value to be 0°04 millim. Ifa rain of such intensity had continued, within a day it would almost have hue. a yea fall at Buitenzorg. The masses of rain in tropics even in the heaviest falls are very small in comparison with those from the rose of an ordinary watering-pot. The former are to the latter as 1; 25 up to 100. From the heaviest rainfalls and the smallest number of drops falling on a surface of 100 sq. cm. in a second, the weight of the greatest possible raindrop was calculated at 0-4 gramme. This number is far too great, for the largest drops which can be made (of 0:25-0°26 gramme) break up at a height of fall of over 5 metres into a larger one weighing 0°2 gramme and into several smaller drops. The weight of the largest raindrop in Buitenzorg, mea- sured by the method of absorption, is still smaller, amounting namely to only 0-16 gr. Experiments by the author on free fall have shown that drops of water of 0-0]-0°26 gramme, at heights of more than 5-10 metres fall with approximately uniform velocity of about 7 metres in a second. The acceleration is therefore very soon after the commencement of the fall almost entirely compensated by the resistance of the air. The vis viva of the heaviest drops of rain calculated by the formula pv? =y amounts to 0:004 kgmetre. In heavy falls no doubt several drops fallin rapid succession on a leaf—2-6 large drops per square centi- metre per second,—but the impact of each fallmg drop is diminished by the elastic attachment of the leaf to the stem. It follows from the experiments, that the force which tropical rain falling in a still atmosphere can exert is far too small to ease injury to vegetation. The mechanical action of the strongest tropical rain on plants is seen in a violent agitation of the leaves and twigs. Injuries only occur in isolated cases in the more tender parts of the plants which cannot give way to the impact, for instance on the tender shoots of tobacco when they le on a coarse soil consisting of angular particles of earth and sand. Intelligence and Miscellaneous Articles. 149 The statements that leaves are torn and separated from the stem by the mere impact of the rain, in a still atmosphere, that upright leafy plants are shattered, and the like, depend on errors.— Wrener Berichte, November 21, 1895. 5 y ON THREE DIFFEREN TSPECTRA OF ARGON. BY DR. J. M. EDER AND E. VALENTA, OF VIENNA. In this paper it is demonstrated that besides the “red” and “blue” argon spectrum discovered by Crookes, there is a third separate spectrum of argon which is characterized by different lines as well as by partial displacement of certain groups of lines toward the red. The authors describe also the spectrum of the glow-light at the + and.— poles of the tubes filled with argon.— Wiener Berichte, December 19, 1895. ON THE RED SPECTRUM OF ARGON. BY DR. J. M. EDER AND K. VALENTA. Through the kindness of Lord Rayleigh we became possessed of some argon gas which was very carefully filled into vacuum-tubes by Hr. Goetze in Leipzig. The pressure in those tubes which we used for our investigations amounted to 1-3 millim. For the purpose of analysis by the spectrum, we used a very powerful con- cave grating of ? metre eurvature, and the photographic method. We measured the spectrum of the second order and referred the wave-length to the lines on Rowland’s standards. We examined the red-and-blue argon spectrum which was obtained in accord- ance with the statements of Mr. Crookes, with feeble sparks without leyden-jars or with sparks from the jars themselves. For the red argon spectrum we obtained the following numbers. The lines marked with a star are also present in the blue argon spectrum ; the other lines are characteristic of thered spectrumitself. As specially characteristic lines of the red spectrum may be men- tioned the principal lines \=4628-56, 4596-22, 4522°49, 4510°85, 4300-18, 4272-27, 4259-42, 4251-25, especially the groups 4200°76, 4198-42, 4182:07, 4164°36, 4158°63, and, further, 4044-56, 3949-13, 383433. This, of course, only applies to the region examined by us, and we shall shortly publish further measure- ments in the Memoirs of the Vienna Academy. It may be remarked that the red argon spectrum is resolved if the double line | 419078 appears well separated. If the blue and the red argon spectrum belong to two elements, which is by no means improbable, the above lines would oe erane principal ones. | ' We give the following preliminary list for the region \=5060 to A=3319, in which 2 is the intensity of the lines (the feeblest =1, the strongest = 10). 150 Intelligence and Miscellaneous Articles. Wave-lengths of the Lines in the Red Spectrum of Argon. r. 5060°27 5054-07 4888-27 4876:52 -¥4847-95 - ¥4806°10 4768°80 %4764:99 4753-02 4746°82 %4736°03 #4726°96 4702-38 #465801 4647-75 ~ » 4628°66 +4609°69 4602:63 4596°25 4590-03 4589-40 #4579°49 #4545°28 4523°54 4522-45 4510-83 4501-66 ¥4498°62 ¥4482:03 *4475°15 4460°90 4434-22 ¥4431:13 ¥4430°35 #442615 4424-09 ¥4421-06 ¥4401:17 *4400:20 ¥4379°79 ¥43876°15 #4371:46 %4370°89 4363°93 ¥4348°11 #4345°27 ¥4335°42 ¥4333°64 #4332°15 ¥4331°31 Ss. ° — = : COM POO OM POM RWODe HPD OW eee — mb © 00S OO BO C9 DO BOD OL 09 Oa BED St St St — 4321-77 r. 431227 4300 18 4288-06 4284-24 4278-21 4272:27 #4266°41 4265:40 4259-42 4251°25 4247-68 #4228°30 4212°37 4210°14 4200°76 4198:42 4191-15 4190-76 4182-07 4164°36 4158°63 4150°18 4147:30 4141-65 4134-48 ¥4131°95 _ ¥4104-10 ¥4082°59 #4079°83 *4077°47 *4072°15 405591 405468 404601 4044-56 *4043-02 4033:11 #401397 3979°81 ¥3968'54 3960:24 394913 3947°70 *3932°71 ¥3928'°82 ¥3925 98 *3914-93 3900-04 3894-76 ed foe 2. e pot fol —_ — — So co oS — HOO tt BB et OS tt BD HG BD OO PB PB et et et tt 9 DD FS — Wiener Berichte, October 24, 1895. SCOFrKH RE OONCOCFHKHOnNe r. #389210 3875:°27 +3868'°68 3866°44 #3850°70 383483 #0809°58 3781°46 ¥3781:07 377562 ¥3770°81 ¥*3765°43 3760°43 3743'89 *3738'03 #37 29°44 ¥3718°39 3696-66 8691-07 3675°38 3670°81 3659-70 3649-95 3643°27 363560 3632°83 3606:°77 ¥35988°58 #358251 *3581°83 #357679 #3571°89 *¥3067 84 356448 *3563'°46 ¥3561:13 ¥3559-66 355616 3554-47 ¥3546:07 *3945°87 ¥3514:67 3506°59 *3191-71 *3476°94 3461-21 3393-90 8392-99 3373°64 8319°35 Ss. e ba et BS BOBS C9 DD BOBS BOP BS 69 F* BD BOB 09 09 HDD BO BEB CO HB C9 09 DOH DD Co et DOB OD ODD OO OS Oo Intelligence and Miscellaneous Articles. 151 INTERFERENCE EXPERIMENT WITH ELECTRICAL WAVES. BY PROF. VON LANG. The experiment described corresponds to the well-known acous- tical one of Quincke. ‘The electrical wave from a Righi’s exciter is divided into two parts with unequally long paths ; after joining, the partial waves interfere, which is demonstrated by a Branly’s Coherer. If the one wave is successively lengthened, both waves will be alternately strengthened and weakened, and as many as four maxima and minima can be easily shown. The experiments were made with tubes of nearly 60 millim. diameter. Tubes with half that diameter did not show the phenomenon. If in one of the two tubes a paraffin cylinder is introduced which entirely fills it, the position of the maxima and minima is displaced, from which the refractive index of paraffin can be calculated. The author found for it 1:65-1-70. Similar experiments with sulphur gave for its refractive index 2°33-2°37. These numbers are considerably higher than the values found by Righi, which were, for paraffin 1:43; for sulphur 1°87. The length of the electrical waves in these experiments was 80 millim., the diameter of the knobs of the exciter 106 millim.— Wiener Ber ichte, Oct. 24, 1895. ON ELECTRIFIED ATOMS. To the Editors of the Philosophical Magazine. GENTLEMEN, I find that the view expressed by me in my paper “ On the Relation between the Atom and its Charge” (Phil. Mag. Dec. 1895, p- 541), that a negatively electrified atom moved more rapidly than a positively electrified one in the same electric field, was arrived at from different reasons by Professor Schuster, and given by him more than five years ago in the Bakerian Lecture for 1890. I am glad to find that this view is held by so eminent an authority, and regret that I had previously overlooked such strong evidence in its favour. There is another result given in the same Bakerian Lecture which I ought to have quoted. I allude to Mr. Stanton’s interesting experiments on the escape of electricity from a hot copper rod surrounded in one case by oxygen and in another by hydrogen. I am, Gentlemen, Yours very sincerely, Cavendish Laboratory, Cambridge,. J.J. THOMSON. January 20, 1896. . ; 152 Intelligence and Miscellaneous Articles. QN THE DOUBLE REFRACTION OF ELECTRICAL WAVES. BY PROF. AUGUSTE RIGHI. In No. 2, 1895, of Wiedemann’s Annalen is a memoir by Prof. Mach (Phil. Mag. ‘July 1895), in which are described experiments showing that a plate of pine-wood with faces parallel to the fibres behaves towards electrical radiation just as a double refracting plate towards luminous radiations. This memoir is dated Nov. 1894. Now on May 27, 1894, I communicated to the R. Accademia di Bologna a long paper in which are described experiments equi- valent to those of Prof. Mach, and others of analogous import. In my experiments I not only confirmed the double refraction pro- duced by wood, and the varying absorption of electrical rays according as they are parallel or perpendicular to the fibres, but I also obtained elliptical and circular polarization, using for this latter a wooden plate of such a thickness as to represent a quarter of a wave-length. Thus, like Prof. Mach, I compared the be- haviour of wood to that of tourmaline rather than to that of calc- spar or of quartz. One experiment of Prof. Mach’s I did not make, namely, that in which it is proved that there is no double refrac- tion if the wooden plate is cut perpendicularly to the fibres. I did not think it necessary to make this experiment, the idea of which did indeed occur to me, because from reasons of symmetry the result seemed a priori evident. IT am satisfied that Prof. Mach did not know of my memoir, or at any rate not when I made my communication to the Annalen, and I am glad that his experiments so completely confirm those I had already published. I may add that, like him, I do not believe in the possibility of producing double refraction of electrical radiations by means of a plate of Iceland spar, for the reasons I have explained in my memoir. In any case I intend soon to resume my researches in these directions, which I have been pre- vented from doing by other work.— Nuovo Cimento [4] vol.i., April 1895. Communicated by the Author. NOTE ON ELEMENTARY TEACHING CONCERNING FOCAL LENGTHS. To the Editors of the Philosophical Magazine. GENTLEMEN, In Dr. Debate communication, page 59, I see he follows the usual practice with regard to signs. My experience is that students find it simpler and more natural to take the positive sign for real images always, and the negative sign for virtual ones. Similarly, converging instruments are to have their focal length or their “potency” considered positive, and diverging instr uments negative, whether they be mirrors or lenses. Does Dr. Barton see objection to this course ? Yours faithfully, January 3, 1896. OxiveR J. Lopes. THE LONDON, EDINBURGH, anp DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES.] MARCH 1896. XXI. On Magnetic Tractive Force*. By H. Taytor Jonszs, D.Se., Assistant Lecturer in Physics in the University College of North Wales, formerly Science Scholar of Royal Commis- sion for Exhibition of 1851 f. a former paper { an account was given of experiments in which the value of the magnetic tractive force of a divided ellipsoid was found to agree within 1 per cent. with Maxwell’s expression B?/87 for the electromagnetic stress in the narrow air-space between the two halves, for inductions between 6000 and 20,000 C.G.S. In the present paper further experiments will be described, the chief object of which was to test whether the same agree- ment existed at much higher inductions. Since the magne- tizing force H in the iron was very small in comparison with the induction B in the former experiments, these cannot be considered as deciding between Maxwell’s expression B?/87r and, for instance, the expression 271’, which has also been given as the value of the tractive force §. In order to complete the test it was necessary to continue the experiments to such high inductions that the magnetic force H was a considerable part, numerically, of the induction H+47I. * Partly communicated to the Physikalische Geselischaft of Berlin on June 28, 1895. - t+ Communicated by the Author, in continuation of the paper on “‘ Electromagnetic Stress,” Phil. Mag. March 1895. } E. T. Jones, Phil. Mag., March 1895; Wied. Ann. liv. p. 641 (1895). § Stefan, Wren. Ber. \xxxi. 2 Abth. p. 89 (1880). Phil. Mag. 8. 5. Vol. 41. No. 250. March 1896. M 154 Dr. E. Taylor Jones on _ Apparatus. These inductions were obtained by means of the Ring Hlectromagnet designed by Dr. H. du Bois *. The chief parts of the apparatus are shown in fig. 1, by a vertical axial section ; the left balf is not all shown, but is symmetrical with the right. The pole-pieces were conical, and had a vertical angle of 78° 28’, so that the field near the vertex was as nearly uniform as possibley. Both pole-pieces were axially perforated, the width of the openings being about 5 millim. Into one of the pole-pieces fitted a short cylindrical iron bar, Cy, provided with a flange, so that when pressed home it just reached to the vertex of the cone. Into the opening in the other pole-piece fitted a longer bar, C,, of the same iron as ©, and of equal diameter ; this bar could be moved to and fro in its socket with very little friction. The two bars thus met in the equatorial plane EE! and formed an “ isthmus ” between the pole-pieces. Similar bars were also made of steel. This part of the apparatus was carefully centred, and the inner ends of the bars were turned plane and polished ; in this process the pole-pieces themselves served as “ guard- rings’ before they were completely turned down to their conical form. The surfaces were optically tested as in the former experiments (/.c. p. 262). The bar C, was connected, by a long brass rod M and a cord which passed over a pulley, with a scale-pan, so that the tractive force could be directly measured. For measuring the induction and magnetic force in the isthmus the method of Ewing and Low was employed. A small brass bobbin, on which two coils, each of five turns of thin copper wire, were wound, could be placed on the isthmus near the plane of section, so that when the bar C, was pulled out the bobbin automatically fell out to a distance and was turned so that its plane remained parallel to the field. The diameter of one of the coils was slightly greater than that of the isthmus, that of the other about 2 millim. greater, so that an annular space about 1 millim. wide existed between the coils. Each coil could be connected through a resistance-box with an Ayrton-Mather galvanometer. The movable coil of this instrument was specially weighted to make it suitable for ballistic measurements, * Du Bois, Wied. Ann. li. p. 537 (1894); see fig. 11 there. } Ewing, ‘ Magnetic Induction in Iron and other Metals,’ § 97 (18€3). Magnetic Tractive Force. 155 GK O > 156 Dr. E. Taylor Jones on From the induction-throws obtained with the two coils, the mean induction in the isthmus and the field-intensity just outside the isthmus (which by the principle of continuity of tangential magnetic force is equal to the magnetic force just inside the isthmus) could be calculated. It was assumed that the field in and near the isthmus was so nearly uniform that the induction and magnetic force were constant over the section of the isthmus, and the latter equal to the field in the annular space between the two coils. Theory. The results obtained with this arrangement can be inter- preted in the following way according to Maxwell’s theory. The mechanical force X acting in the direction ov on a body magnetized with an intensity whose components are A, B, C, and placed in a field of magnetic force of components a, B, y, is ™ d dp a K=X,+X,+X,<|||(a% +B +02 Jae dy dan (1) Applying this to the case of the bar C,, taking the origin at the outer end (cf. fig. 1) and ow along the axis of the bar— also considering for the present only the first term X, of the integral, and assuming that A and a are independent of y and z in each section of the bar—we have after integrating by parts, ea i) Se Gbek Ss = Ee ‘ — \ a da where /=length, and S=section of the bar. At the end (w=/) between the pole-pieces we have A=I, while «= H+ 27I, corresponding to the action of the pole- pieces and of the free end of the bar C). The distribution of 2 along the axis was found by throwing out a small exploring coil from different points on the axis. The results showed that a certain region existed in which a was always very small and nearly constant. The ordinates of the curves abe and def, fig. 1, represent the values of « at points on the axis, with magnetizing currents of 7 and 25 amp. respectively. The length of the bar C, was so chosen that it reached to * Maxwell, ‘Electricity and Magnetism,’ vol. ii. § 689. Magnetic Tractive Force. 157 this region where the field was practically zero. We have, therefore, at «=0, also 2=0, and the equation becomes x S or, remembering the relation B=H +47, X, B?—H? I a= BSE {na a ered BN ice (2) This part of the integral in (1) depends only on the longi- tudinal components of the field and magnetization. It may be shown that the part of X depending on the transverse components of field and magnetization vanishes if the value of a@ is constant at the outer end of the bar, da dix in the experiments we may neglect these terms. Equation (2) gives, therefore, the tractive force per unit a calling this P grammes weight per sq. centim., we ave I =I(H +27l) -| Hal, 0 2.e.if —=0 at =0* ; since this was very nearly the case 2__ 772 I pa BM? | inar; ea ocak Sig J Jo or t 2 2 fe eg aP tet; |, Has 87g OTe Gal so that the expression | y/ P+ ting | | aly et ho OL) 9 * An approximate calculation based on Laplace’s equation in cylin- drical coordinates gives X,+X,=(\f (B = +0 "de dy dz 2 See wkr* =) ; 16 dx z=0 where r= radius of section of bar, and &=ratio of mean radial magneti- zation to mean radial “ external” magnetizing force. + In the immediately following section of his treatise (/.¢. § 641), Maxwell explains these forces by his well-known theory of stresses in a medium, and develops the corresponding stress equations, From these the equation (3) might be more shortly deduced. In somewhat different ways similar expressions have been obtained by du Bois, W ied. Ann. xxxy. p. 146 (1888), and by Adler, Wren. Ber. c. 2 Abth. p. 897 (1891). 158 Dr. E. Taylor Jones on in which the first term is generally the greatest, is in the present arrangement, according to Maxwell’s theory, pro- portional to the induction B. In the former experiments B was proportional, neglecting small corrections, simply to V P. The integral \ Hdl is clearly equal to the area enclosed 0 by the magnetization curve, the axis of I,and the line parallel to the H-axis at distance I from it*. This area is very dif- ferent in the cases of hard steel and soft iron. For this reason, and in order to make the test as general as possible, two bars of glass-hard steel were also experimented on. Preliminary Experiments. The ballistic galvanometer was standardized in the usual way by means of a long solenoid and a secondary coil. The core of the solenoid consisted of a glass tube covered with ebonitet+; this was turned accurately cylindrical, and its diameter measured with a Zeiss ‘‘ thickness measurer,” both before and after it was wound with one layer of silk- covered copper wire. From these measurements the field inside the solenoid and the area of the solenoid were calcu- lated in the usual way, The current in the solenoid was measured by a Kelvin “ platform ’’-galvanometer, which was moreover standardized by a copper voltameterf. From the throw of the galvanometer-needle on reversing the primary current, the ballistic sensitiveness of the galva- nometer was calculated. This was not constant but varied, firstly somewhat with the time and temperature, secondly with the resistance of the galvanometer circuit. The first changes were observed and corrected for by withdrawing a small coil from a very constant permanent magnet before and after each set of observations. This was then repeated with various resistances in the galvanometer circuit. At the same time the damping was also observed, 7. e. the ratio m of two successive swings measured from the zero. The results of these observations are contained in Table I.,in which R=total resistance of galvanometer circuit, o=product of R into the throw (¢ being thus proportional to the ballistic sensitiveness of the galvanometer), and * Du Bois, Wied. Ann. xxxv. p, 146 (1888) ; Max Weber, Wied. Ann. liv. p. 35 (1895). t Ebeling, Reichsanst.- Bericht, Zschr. Instr.-Kunde, xv. p. 331 (1895). t The instructions given in A. Gray’s ‘Absolute Measurements in Electricity and Magnetism,’ vol. ii. part ii. p. 421, were observed. Magnetic Tractive Force. 159 o’=0{1+40°5(m—1)—0°277(m—1)? + 0:13 (m—1)}*. o” is proportional to the ballistic sensitiveness of the galvano- meter corrected for the damping of the oscillations. TaBLe I.—Temp. 21°3 C. The value of o’ is therefore within 4 per cent. constant ; in other words, the influence of the resistance of the secondary circuit on the ballistic sensitiveness of the galvanometer is completely, though indirectly, explained by its well-known influence on the damping of the oscillations, and can be eliminated, was as done in all the galvanometer observations. Moreover, the damping was too small to have any effect on the proportionality of throw to quantity of electricity flowing through the galvanometer, as I convinced myself by special observations. The areas of the two isthmus coils were compared electro- magnetically in the uniform field between flat pole-pieces with a standard coil made of a single strip of phosphor bronze wound on a circular glass plate which had been carefully turned, ground, and measured. The connecting strips of the standard coil were exactly laid one above the other so as to enclose no area parallel to the plane of the coil. In using this coil the influence of its resistance on the sensitiveness of the galvanometer was of course, as explained above, taken into account. The total areas of the two isthmus coils were thus found to be 1°235 and 2°553 sq. centim. respectively, that of the standard coil being 1°530 sq. centim. ‘These areas were also calculated from the previously measured diameters of the brass bobbin and of the wire, and the calculated values * Ayrton, Mather, and Sumpner, Phil. Mag. [5] xxx. p. 69 (1890). 160 Dr. Hi. Taylor Jones on agreed within 4 and 3 per cent., respectively, with the values obtained electromagnetically. A series of observations was then made of the tractive force and at the same time of the induction-throws caused by the coils falling from the isthmus, the electromagnet being excited by various currents ranging from 0 to 25 amp. One great difficulty in measuring the tractive force was due to the fact that the iron bar, and, more especially, the steel bar (which in the process of hardening might easily be slightly bent), often got jammed in its socket. If the bar was pulled exactly in the direction of its axis and that of its socket the ‘jamming was avoided, and the friction was very slight. This was determined by removing the other pole-piece and demag- netizing the electromagnet as far as possible in order to remove all magnetic action. By properly guiding the brass rod M, the. position was then found in which the weight necessary to pull the bar out was a minimum, and this was found to be less than 5 grammes weight, which is negligible in comparison with the tractive forces obtained later. But if the bar was pulled only slightly to one side, it became jammed in its socket, and about 700 grms. weight more were necessary to pull it out. In all subsequent measurements therefore the position was found, by properly guiding the brass rod, in which the tractive force was a minimum, and this was taken as the magnetic tractive force. The question as to whether the magnetization had any appre- ciable effect on the friction was tested by pushing the longer bar OC, through both pole-pieces (C, being removed), so that it lay in a symmetrical position of minimum potential energy. No effect on the friction could be detected when the exciting current was made or broken*. ; I - For the graphical evaluation of the integral | HdI it was 2 0 necessary to have the magnetization-curves for the iron and steel. The higher values of H and I were already known from the isthmus experiments. For the determination of the earlier parts of the curves, two bars were used which were cut from the same pieces as the isthmus bars. The curves were then * This arrangement, in which no gap existed in the isthmus, afforded at the same time a means of testing how far the gap in the usual arrangement caused disturbance by spreading the lines of induction. It was found that in the strong fields here used this was a considerably smaller source of error than might be supposed after certain experiments at less intense fields. Magnetic Tractive Force. 161 determined for these by means of a du Bois Magnetic Balance*, which had been tested at the Reichsanstalt. These experi- ments, as well as all the tractive-force measurements, were made with increasing magnetization}. This integral formed only a comparatively small correction, so that it was not necessary to know it very accurately. Final Experiments. From the galvanometer-throws the values of B and H were calculated, and their difference gave, on being divided by 47, the magnetization I. The greatest values of I obtained for the soft iron and the hard steel were 1818 C.G.S. and 1556 C.G.S. respectively, and these occurred at a field of about 10,600 C.G.S. At stronger fields I appears to have rather smaller values{; a similar apparent diminution of I was also observed by Hwing §. It must, however, be remarked that the isthmus method is never very suitable for accurate measurements, and that the arrangement described above is particularly unfavourable to - accurate measurements of I from the difference of B and H; firstly, because of the disturbing influence of the gap in the isthmus; and, secondly, because the bars are not continuous with the pole-pieces, as in the original arrangement of Hwing and Low. No valid conclusions can therefore be drawn from these experiments as to the course of the magnetization-curve ; the induction in the isthmus, however, which is the quantity of chief importance in these experiments, was, in consequence of its direct determination, known with sufficient accuracy. With each value of the current, the measurements were repeated several times. For given values of the galvanometer- _ throws, the minimum tractive force was very constant, so that even at the highest values it could be determined to within about 30 grammes weight. The greatest magnetic tractive force measured was 9430 grms. weight, the cross section of the iron bar being 0°1896 sq. centim. This gives a pull of 49°73 kilogs. weight per sq. centim. (707°4 lb. wt. per sq. inch). * See du Bois, Zettschr. fiir Instr.-Kunde, xii. p. 404 (1892). + The curves obtained with the balance will be published in another connexion. } In later experiments made with a continuous isthmus (see p. 160, footnote) this diminution of I was not observed. Bath § Ewing, J. c. § 93; this was attributed by him to non-uniformity of the field near the isthmus. i 162 Dr. E. Taylor Jones on The greatest value of the integral a) HdI was in the iron 0 990, in the steel 840 grms. weight per sq. centim. This only gives, therefore, a correction of a few per cent. In my former experiments the corresponding correction (there due to the slight non-uniformity of the field inside the coils) was only about 4 pro mil. (Wied. An. |. c. p. 649, footnote). TasLu I1.—Former results (Phil. Mag. l. c. p. 265). B i B. ey, q. vei O.G.8. 0.4.8. N8xg Obaouvell dlc ae Calculated. 493 6198 39°2 39°2 0-0 551 6929 43°9 44-4 +0°5 646 8122 516 51°6 0:0 853 10730 68°1 68°4. +0:3 996 12520 79-4 79-0 —0-4 1163 14630 92:9 92-0 —0°9 1291 16260 103°3 102°9 —0°4 1346 16970 107-7 107:3 —0°4 1400 17690 112°3 111°9 — 0-4 1463 18540 117°7 117-1 —0°6 1550 19730 125°3 123°5 —1°8 1585 20230 128°4 126°7 —17 TasLE IJJ.—Annealed Soft Styrian Iron. Current,| H. B. if a G. Diff Amperes.| C.G.S. | 0.4.8. | O.G.S. 87g"! Obs. mag ne Cale. 0 260* | 17740 1292 113°0 109°5 —3'°5 0:13 613 22050 1707 1405 138:°0 —2°5 0°37 1440 23370 1745 1489 147:0 —1-9 0:93 3470 26140 1805 166°5 162°0 —4:5 1:33 5070 27420 1779 74:7 172:0 —2°7 2°6 8560 | 31220 1803 198-9 1950 —39 38 10520 | 33370 | . 1818 212°5 207°5 —5:0 5°6 12720 | 34660 1746 220°8 219°5 —1:3 79 14230 | 35790 1716 227°9 228°3 +0-4 938 14850 | 36450 1719 232°1 232°8 +0°7 4-9 16030 -| 38270 1770 243°8 239°8 —40 5°0 17690 | 39260 1796 250°1 250-9 +08 * Due to residual magnetisim in the pole-pieces. Magnetic Tractive Force. 163 TaBLE IV.—Glass-hard Wolfram Steel. B Current,| H. B. i pares ig G. vee pores ERG EO ee, | Cras, | VSag | obs |DBterenee- Cale. 0 isi*| 11390 | 892 | 725 | 718 | -07 013 | 558 | 17550 | 1358 | 1118 | 1073 | ~45 0-37 | 1615 | 19750 | 1444 | 1958 | 1913 | —4°5 0-91 | 3470 | 22510 | 1516 | 1434 | 1390 | —4-4 1:31 | 5050 | 24000 | 1508 | 1529 | 1487 | —42 26 | 8670 | 27950 | 1535 | 1780 | 1746 | —3-4 38 | 10750 | 30290 | 1556 | 1930 | 1876 | —5-4 57 | 12830 | 31950 | 1522 | 2035 | 2011 | —24 80 | 14220 | 32860 | 1484 | 2093 | 2073 | —20 99 | 14860 | 33470 | 1481 | 2131 | 2113 | —18 149 | 15970 | 35880 | 1545 | 2254 | 991-9 | —35 250 | 17830 | 36110 | 1456 | 2300 | 2302 | +02 * Due to residual magnetism in the pole-pieces. Tables III. and IV. contain the values of the exciting current, H, B, I, B/ V 87g, of the quantity 2 if G =/P+ a a5 : Hdl, 87g og Jo and, lastly, of the difference B — —_—) V 81909 in iron and steel. Table II. contains the results of my former experiments (J. c. p. 265), which are here reproduced in order to show the ‘complete range experimented over. The results are also exhibited graphically in fig. 2, in which the points +, ©, show the values of G as a function of B in iron and steel respectively, while the straight line represents the function B/ 87g. The points * are taken from the former experiments, and represent the square root of the tractive force per sq. Sig All the observed points lie near the straight line ; =e greatest difference is about 3 per cent. Most of the points lie under the line; this is probably due to the spreading action of the gap in the isthmus, which diminishes the tractive centim., which in that case was theoretically equal to 6 ‘6 tna 7 ‘ 000 mg ; 000°0¢ 000*¢e 000 06 g 000°0T SYINSAL LIWALOT| &- S PLOY-SSDPY “UOLT 7fog + ~ S tp) 0) =| o) a) S p> fas) EH = 4 = Magnetic Tractive Force. 165 force. The agreement is, however, on the whole such that the equation (3) can be regarded as verified. According to Maxwell’s theory (J. c. § 643) the first term 2 sag is the total electromagnetic tension existing in the narrow air-gap between the ends of the two bars ; similarly, H*/87g is the tension in the gap, depending only on the “ external ”’ field H. The correctness of this interpretation of the term H?/8:rg follows from the well-known experiments of Quincke and others. This latter part of the stress is not included in the tractive force in the present arrangement : it merely serves to com- press the brass pillars S,, So, Ss. If the bar C, were firmly fixed in its pole-piece (instead of sliding in it), and if the two halves of the electromagnet were pulled from each other, the pull in grammes weight in this ease, corrected for the tension due to all those tubes of in- duction which do not pass along the isthmus, would be equal to “ aha x area of contact. 87g This case corresponds theoretically to the arrangement of my former experiments, but cannot of course be practically carried out. Measurement of High Inductions. After Maxwell’s law of tractive force, or electromagnetic stress, had been verified as explained above for inductions up to 40,000 C.G.S., its general truth could be assumed. And just as various physicists have conversely used the tractive force for the measurement of lower inductions, it now seemed feasible to apply a similar process to the measurement of the highest attainable inductions, all other known methods failing in this case. I therefore arranged a few more experiments with this object. Two pole-pieces of 120° vertical angle were made of the very best annealed Swedish iron. The point of one was slightly flattened, ground plane, and polished, so that it pre- sented a small circular pole-face whose diameter was only a fraction of a millimetre. Through the opposite pole-piece a. slightly conical hole was bored, through which a long wire of 166 Dr. E. Taylor Jones on annealed soft iron (of diameter 0°586 millim.) could be drawn, which fitted accurately in front and more loosely behind, The friction was thus only a fraction of 1 gramme weight. The end of the wire was also carefully polished and, as well as the opposite small pole-face, examined and measured with a Zeiss microscope. With a magnetizing current of 25 amperes, the weight supported in this case was 249 grms. weight ; this corresponds to a pull of 92°39 kilogs. weight per sq. centim. (1314 lb. wt. per sq. inch). The maximum value of the magnetization was, moreover, determined by means of an isthmus consisting of a bundle of 50 pieces of the same wire pushed through the former pole- pieces of 78° 28’ vertical angle. This value was found to be about 1800 C.G.S. 7 Taking also 500 grms. weight as the approximate value of I the integral = HdI, we have from these data the values of 7/0 B?—H?, and of B—H=47I; from these were deduced the values B=61,900 C.G.S. H=39,300 _,, These experiments were extended still further by drawing out the wire to a thickness of 0°2412 millim., and narrowing down the hole in the pole-piece correspondingly. After the wire had been once more annealed in a spirit-flame and its end ground plane, the weight supported with a current of 40 amperes was 52°5 grms. weight, corresponding to a pull of 114°9 kilogs. weight per sq. centim. (1634 Ib. wt. per sq. inch). Hence follow, as above, the values B = 74,200 C.G.S. H= 51, 600 93 and the permeability is only bL= B/H =a The calculated value of H from the Stefan-Hwing loga- rithmic formula is 50,450 C.G.S., assuming that the conical s0le-pieces are uniformly magnetized with a maximum inten- sity of 1800 C.G.S. To this must be added about 750 C.G.S. due to the direct action of the coils of the electromagnet with Magnetic Tractive Force. 167 a current of 40 amperes. The total calculated field is thus 51,200 C.G.S., which agrees well with the value found above. In this experiment the area of the isthmus was about Sooo Of the area of the base of the conical pole-piece. This induction (B=74,200) exists also by continuity in the narrow air-gap at the contact, and here it is to be regarded as “external” field. This will not be much altered at the moment of separation as long as the gap is narrow in com- parison with its transverse dimension. It was then observed with a magnifying glass that, unless the apparatus was very carefully cleaned, small microscopical iron filings flew into the gap when separation took place and formed new “ isthmuses ” across it, whose thickness was very small in comparison with that of the } millim. iron wire, so that their self-demagnetizing effect could be neglected. The induction B’ in these is thus B/=74200+ 47 . 1800=96,800 C.G.S. We may therefore conclude that inductions of nearly 100,000 C.G.S. can exist in iron without any special occur- rence. If the wire is pulled back so that its end is in the plane of the edge of the opening, the field between the pole-faces is then about 60,000 ©.G.S8.; it only extends, however, over a few tenths of a millimetre *. At the instant of separation a tension of (74200)?/8%q = 224 kilogs. weight per square centim. (3185 lb. wt. per sq. inch) is transmitted across the air-gap; this is about the limit of elasticity of lead. In this connexion it is interesting to remember that the tension between the plates of an air- condenser at atmospheric pressure cannot far exceed 2 grms. weight per square centim. without a spark appearing. An absolute vacuum, however, or a body of high specific induc- tive capacity can transmit much greater tensions. My best thanks are due to Dr. H. du Bois, in whose laboratory the above experiments were carried out, for his help and advice. - Berlin, Christmas, 1895. - * If the field extends over several millimetres an intensity of over. 40,000 C.G.S. can scarcely be reached. See du Bois, Wied. Ann. 1. p. 547 (1894) ; J. B, Henderson, Phil. Mag. Noy. 1894. ee XXII. Researches in Acoustics—No. X. By Aurrep M. Mayer*. [ ConrEnTS.—The Variation of the Modulus of Elasticity with Change. of Temperature, as determined by the Transverse Vibration of Bars at Various Temperatures. The Acoustical Properties of Aluminium. | Summary of the Research. OISSON, in his Traité de Mécanique (Paris, 1833, t. ii. pp- 368-392) f discusses the laws of the transverse vibrations of a bar free at its ends and supported under its two nodes. He shows that the frequency of the vibrations of the bar is given by an equation, which, reduced to its simplest ex- pression, is N= Vx 1-0279 5 5 vibrations per second of the bar, ¢ its thickness, / its length, and V the velocity of sound in the direction of the length of the bar. To ascertain how nearly the frequency of the transverse vibrations of a bar, computed by Poisson’s formula, agrees with the result obtained by experiment, the following method of experimenting was used. Rods of steel, aluminium, brass, glass, and of American white-pine (Pinus Strobus)—substances differing greatly in their moduli of elasticity, densities, and physical structures— were carefully wrought so as to have the length of 15+ metre, the thickness of 0°5 cm., the width of 2 cms., and a uniform section throughout their lengths. The velocity of sound in these rods was determined by vibrating them longitudinally at a temperature of 20°, while held between the thumb and forefinger, and their frequencies of vibration ascertained by the standard forks of Dr. R. Kcenig’s tonometer. Out of each of these long rods were cut three bars of the length of 20 cms., and these bars, also at 20°, were supported on threads at their nodes, vibrated transversely by striking them at their centre with a rubber hammer, and their frequencies of vibration determined by the forks of the tono- meter. The mean departure of the observed from the computed numbers of transverse vibrations (see Table I.) is 33,3; the computed frequency being always in excess of the observed, * From an advance proof from the American Journal of Science for February 1896 communicated by the Author, having been read before the British Association at Oxford, August 1894. + See also ‘The Theory of Sound,’ by Lord Rayleigh, 1894, vol. i. chap. 8. in which N is the number of Dr. A. M. Mayer’s Researches in Acoustics. 169 except in the case of glass, where the computed is s}= below the observed frequency. In Table I. J=length and ¢=thickness of bar in centimetres at 20°; V=velocity of sound in centimetres in bar at 20°; N=number of vibrations per second at 20°. The close agreement of the computed and observed values shows that, by vibrating a bar at various temperatures, the variation of its modulus of elasticity with change in its temperature can be obtained. We observe N at various temperatures of the bar; then V= is computed, 10279 — | we, P and the modulus M=—. As #¢, l, and d (the density of s the bar) vary with the temperature, the coefficient of expansion of each bar and its density at 4° were determined, so that the dimensions and density of the bar could be computed for each of the temperatures at which it was vibrated. Experiments were made on five bars of different steels, on two of aluminium, on one of Si. Gobain glass, one of brass, one of bell-metal, one of zinc, and one of silver. The results of these experiments may be summed up as follows :— The modulus of elasticity of St. Gobain glass is 1:16 per cent. less at 100° than at 0°. Ke a the five steels ,, 2°24-3-09 ,, a - “ ” > brass 9 3°73 9 33 93 99 é i bell-metal » 43 , ” awl 3s 39 ” aluminium 3) 55 9 33 39 7 - ~ silver » 2AT RS pe 60 $3 ” 3) zine ” 6°04 9) %) 62 33 The decrease of the modulus of elasticity of glass, aluminium, and brass is proportional to the increase of temperature ; straight lines referred to coordinates giving the results of experiments on these substances. ‘The five steels, silver, and zine give curves, convex upwards, showing that the modulus decreases more rapidly than the increment of temperature ; while bell-metal alone gives a curve which is concave upwards, its modulus decreasing less than the increment of temperature. (See Curves, fig. 5, p. 185.) The more carbon a steel contains, the less is the fall of its modulus of elasticity on elevating the temperature of the steel. Thus, the modulus of the steel with 1:286 per cent. of carbon is 2°24 per cent. less at 100° than at 0°, while the steel containing 0°15 per cent. of carbon has a modulus at 100° which is 3:09 per cent. lower than its modulus at 0°. So far as experiments on a single steel containing nickel Phil. Mag. 8. 5. Vol. 41. No. 250. March 1896. N 170 Dr. A. M. Mayer’s Researches in Acoustics. permit of any general deductions, it appears that the presence of nickel in a low carbon steel lowers its modulus of elasticity. Thus, steels No. 3 and 4, having respectively -47 and 51 per cent. of carbon, have a modulus of 2130 x 10°; while steel No. 5, containing ‘27 per cent. of carbon and 3 per cent. of nickel, has a modulus of 2080 x 10°, which is 2°35 per cent. lower than that of steels Nos. 3 and 4. The presence of nickel in a steel may, in a diminished degree, have the effect of carbon in lessening the lowering of the modulus when the temperature of the steel is increased. Thus the percentage of the lowering of the modulus, by heating from 0° to 100°, of steel No. 5 containing 0°27 of carbon and 3 per cent. of nickel, is the same as that of steel No. 3 with 0°47 per cent. of carbon. If a bar of any one of the substances experimented on is struck with the same energy of blow, by letting fall on the centre of the bara rather hard rubber-ball from a fixed height, the sound emitted by the bar diminishes in intensity and in duration as the temperature of the bar is raised. Thus: Brass at O° vibrates during 75 secs.; at 100° it vibrates during 45 secs. Bell-metal ‘, Ba by. S 53 i ‘ta S 25 Aluminium es - ADS. 3 KS re 12 ie. J. & C. Cast Steel 4 ts 80 _,, - b Be Bessemer Steel e - 45 _,, ., 3 13.3, St. Gobain Glass - = Ours x‘; ce SOE is Zine at 0° vibrated during 5 secs.; at 20° only during 1°5 sec. At 62° it vibrated for so short a time that it only gave three beats with forks of 1090 and 1082 v.s. At 80° it was not possible to determine the pitch of the bar, and at 100° the bar when struck gave the sound of a thud. The bar of silver acted in a similar manner to the bar of zinc—it was even less sonorous than zinc,—thus flatly denying the “ silvery tones ”’ attributed to it. These phenomena do not depend on the fall of modulus, but on changes in the structure of the metal on heating it, which cause the blow to heat the bar and not to vibrate it. Bell-metal was found to be an alloy peculiarly well suited for bells, as the intensity and duration of its vibrations were the same at 50° as at 0°, all other substances showing a marked diminution of intensity and duration of sound at 50°. A bar of unannealed drawn brass, after it has been heated to 100°, has its modulus at 20° increased ;%6, per cent. (See Table III. and fig. 11, p. 188.) In this research I had the good fortune to have the assistance of Dr. Rudolph Keenig, of Paris. He not only placed at my service the resources of his laboratory and Dr. A. M. Mayer’s Researches in Acoustics. 171 workshop, but generously gave me constant assistance during the experiments—making the determinations of the numbers of vibration of the rods and bars with the standard forks of his tonometer. Without his aid this work could not have been © done. For instance, in the cases of the bars of silver and zinc the beats they give with a fork are so few that they cannot be compared with a chronometer ; but Dr. Keenig, from his long experience in the estimation of beats, was enabled to form an accurate judgment of their number per second from the rhythm of the beats. The determination of pitches extending through such a range of vibrations as occurs in this research can only be made with Dr. Keenig’s “ grand tono- metre ”,—a unique apparatus of precision, giving the fre- quency of vibrations from 32 to 43690 v. s., and really indispensable to the physicist who would engage in precise quantitative work in Acoustics. e now proceed to give accounts of the several operations performed in the progress of this research. Determination of the Velocity of Sound in Rods. In the determinations of the velocity of sound in the rods of 1°5 m. in length, I used the method of Chladmi*. Kundt’s method of obtaining nodal lines of fine powders in a tube, by vibrating a rod whose end carries a cork which fits loosely the end of the tube, is not accurate. The weight and friction of the cork, the necessity of firmly clamping the rod at a node, and, above all, the want of knowledge of the velocity of sound in the air of glass tubes of different diameters, renders this method, so beautiful and ingenious, worthless for accurate measures of the velocity of sound in solids. The curves in fig. 1 show the very diverse determinations of the velocity of sound in the air in tubes of different dia- meters by the physicists Kundtt, Schneebeli t, Seebeck §, and Kayser ||. The velocity of sound in metres is given on the axis of Y; the diameter of the tube in centimetres on the axis of X. Ku stands for Kundt, Sch for Schneebeli, Se for Seebeck, and Ke for Kayser. The most precise measures of velocities are those of Kayser, who closed the end of the tube with a cork attached to the end of a steel bar, while the other end of the bar was securely clamped. The frequency of the transverse vibrations of the bar was registered by a style * Traité d’Acoustique, Paris, 1809, p. 318 et seq. + Bericht. der Akad. der Wiss, zu Berlin, 1867. { Pogg. Ann. 1869, t. 136. § Pogg. Ann. 1870, t. 139. || Pogg. Ann. 1877, t. 2. p. 218. N 2 172 Dr. A. M. Mayer’s Researches in Acoustics. describing the sinusoids of the vibrating bar. Thus the weight and friction of the cork introduced no error. In a . similar manner I obtained the velocity, marked M in He. Ae by vibrating a rod of aluminium. The frequency of the aaa Eeiranmeenannnt sete ae garesaetny aiet 717) 1S GEREN? Of SEBRee 22 ee Sees wie gBBB! ia SESESERERES 18 IBERREORUS us setiestesctiSteratect | Hoag) 5 Ee cancer ate longitudinal vibrations of the rod was measured while the cork at the end of the rod was vibrating in the mouth of the tube. The result agrees closely with Kayser’s. It is needless to discuss the curves of fig. 1. Dr. A. M. Mayer’s Researches in Acoustics. 173 The method of Chladni, used exactly as that eminent man used it, remains the best we have. It is important, however, to note that the rod must be held between the thumb and forefinger when it is vibrated and not clamped when vibrated. When clamped it always gives a higher frequency, as shown by the following experiments : — Steel rod clamped. . ait wee Sy E20 2 Steel rod held between fingers . « 8428-4 Alonumiumerodvclamped . 9. 9. 2 .d3TT0 Aluminium rod held between fingers. 3376°4 The frequency of the vibrations of the rods of steel, brass, aluminium, glass, and pine wood, when held at the middle of their lengths and vibrated so as to give their fundamental tones, gave exactly the octaves of these fundamental tones when held at one-quarter of their lengths and vibrated. Determination of the Lengths of the Long Rods and of the Lengths and Thicknesses of the Bars. The lengths of the rods of 1:5 + metres were ascertained by comparison with the rod of steel whose length was measured at the Bureau International des Poids et Mesures. The lengths and thicknesses of the bars which were vibrated transver ‘sely were measured with micrometer calipers. The readings of these calipers were tested by comparison at 20° with a series of standards of various lengths of inches and fractions of inches, made for me with great care by Mr. George M. Bond, who has charge of the gauge department of the Pr att, Whitney Co. In reducing the comparisons to centimetres, I adopted the value of the inch as equal to 25:4 millimetres. In obtaining the length of a bar, the mean of several measures in the axis of the bar and in directions parallel to the axis and at various distances from it was adopted. The thickness of a bar was taken as the mean of measures taken throughout the length of the bar at points designated by the intersections of lines drawn parallel and at right angles to the axis of the bar. The dimensions of the bars were measured at 20 , except those of steels Nos. 3, 4, 5, which were measured at 18°25, Determinations of the Coefficients of Expansion of the Bars. To determine the coefficients of expansion of the bars, I devised the apparatus shown in fig. 2. In a brass tube, T, 174 Dr. A. M. Mayer’s Researches in Acoustics. the bar, B, rests in slots in the supports, 8, 8’. The tube T is slightly shorter than the bar B. Washers of rubber (shown in black in the figure), of the same diameter as the outside diameter of the tube, are placed in the screw-caps, C, C’. These washers are perforated with holes of diameters smaller than the thickness of the bar. When the caps are screwed up, the rubber washers press against the ends of the bar. This Pie: 2. / C C l M ff Be bee: M pee (FS —= —— Mee str 2 ae =| ms pa pressure is further increased by flat rings which surround the holes in the washers, and are pressed against these washers by means of the springs, D, D'. By this arrangement the sur- faces of the ends of the bars are exposed, while the contact of the washers on the bars makes a water- and steam-tight joint. Thus the bar may be surrounded with ice, or with steam, or with a current of water of different temperatures, and be cooled or heated up to its terminal planes, while the holes in the washers allow the micrometer-screws, M, M’, to be brought to contact with the terminal planes of the bar. Two helical springs are attached to the column A. The other ends of these springs are fastened to rods projecting from the tube T. Thus the same pressure of contact is always made between the bar and the end of the micrometer-screw M. The tube T is supported in Vs, V, V’, and the greater part of Dr. A. M. Mayer’s Researches in Acoustics. 175 the weight of the tube is taken off the Vs by helical springs fastened to a frame above the apparatus. The tension of these springs can be so regulated that the tube rests on the Vs with the same pressure when it has steam passing through it and when it is filled with ice. The column, A, and the Vs, V, V’, are insulated from the base of the apparatus by thin plates of ebonite, e. Between the binding-screws, EH and H’, and con- nected by wires, are the voltaic cell F, the galvanometer G, and a box of resistance-coils, R. The micrometer-screw, M’, with which the variations in length of a bar are measured, is mounted as follows :—The screw passes through its nut in a massive brass plate which rotates around nicely fitted centres at H. These centres are supported by two side plates not shown in the figure. A spring, K, is fastened to the lower part of the swinging nut-plate and brings this plate against the plate, L, firmly fastened to the base of the appa- ratus. When the swinging plate is vertical and the axis of the screw horizontal, the swinging plate fits accurately the surface of the fixed plate, L. By turning the rod, N, the swinging plate and its screw can be rotated away from the bar. This arrangement allows the screw to be swung out of the way while the tube, T, is being placed in the Vs. Also, it prevents any strain between the micrometer-screw, M’, and the column, A; which would take place if M' were fixed and it should be brought in contact with a hot bar in the tube, T. With careful manipulation, successive electric-contacts can be made on a bar in the tube, T, surrounded by ice, so that the variations in a series of measures will not exceed sop Inm., with a resistance of about 200 ohms placed in the circuit. It may be reasonably objected to this apparatus that when the micrometer-screw touches the bar at 0° it is cooled and shortened, and that when it touches the bar at 100°, or at temperatures higher than that of the screw, the latter is heated and elongated. This error, however, is quite small, and may be neglected in our work. If we assume that one centimetre of the screw is heated 10°, which is a large estimate, considering the duration of contact of screw and bar during a measure, the shortening or elongation of 1 cm. of the screw by cooling or heating it 10° amounts to only 0012 mm., or zg¢seq of the length of the bar. This change in the length of the screw will affect the coefficient of expansion of the bars only ‘00000006. 176 Dr. A. M. Mayer’s Researches in Acoustics. Determination of the Densities of the Bars at Ae: The bar whose density was to be determined was immersed in water at 4° for a couple of hours. The bar was then sus- pended by a platinum wire in water at 4° and weighed. The bar was then removed from the wire and a quantity of water equal in volume to the volume of the bar was added to the water in the vessel, and the platinum wire, now immersed exactly as it was when the bar was attached to it, was weighed. This weight, subtracted from the previous weighing, gave the weight of the bar in water. Every precaution was taken to prevent, by means of screens, the action on the balance of the currents of cold air in the balance-case, which are pro- duced by the constant descent of air from the sides of the cool vessel. The Apparatus in which the Bars were Heated and Cooled. On the precautions used so that one is sure of having the real temperature of the bar when it is vibrated. The apparatus used to heat and cool the bar is shown in fio. 3. Ina brass box, C, is inclosed a box, C’, containing the bar, B, supported on its nodes, N, N, by threads held by upright rods. From this central box two tubes, T, P, pass through the outer box C. The inner box is made water-tight and steam-tight by a rubber washer which is pressed between the top of the box and its cover by means of screws. Through the tube, T, the bar is vibrated by letting fall upon its centre a rubber ball fastened to a light wooden rod. On the blow of the ballit rebounds, and the rod is caught by the fingers in its upward motion. The cork is then at once replaced in the tube, T. The sound from the bar is conveyed to the ear, at Hi, by means of a tube (fig. 4). One branch of this bifurcated tube leads through a rubber tube to the pipe, P, of the box, fig. 3. The other branch leads to the fork, F, the number of whose beats per second made with the vibrating bar is measured by a chronometer. ‘The pipe, 8, allows the steam to issue when water is boiled in the box, C’, by a gas lamp. The flow of gas through this lamp was neatly regulated by a stop-cock turned by a long lever. The box, C, is covered, except at the bottom, with thick felt. To determine the frequencies of vibration of a bar through a range of temperature from 0° to 100°, the following method was used. The box, C, was filled witb ice, surrounding the inner box, UC’. It thus remained for an hour so that the boxes were cooled down to 0°, and the mvisture in the inner Dr. A. M. Mayer’s Researches in Acoustics. 177 178 Dr. A. M. Mayer’s Researches in Acoustics. box had been condensed so far as it could be at 0°. The bar, which had been in ice for two hours, was wiped dry and quickly introduced into the inner box. A thermometer, T (made by Baudin and corrected), which entered the boxes through stuffing-boxes, and whose bulb touched the under surface of the bar, was read till it became stationary. The bar was now vibrated, and its frequency of vibration determined for the temperature given by the thermometer. | ‘The lamp was now placed under the box, and the water in it boiled till the thermometer reached its maximum reading and the reading remained stationary during a half-hour. The vibration frequency at this temperature was taken. The flame of the lamp was now lowered and the box allowed to cool very slowly, at the rate of 1° fall of temperature in about eight minutes. When the thermometer read 80°, 60°, 40°, the flame of the lamp was carefully adjusted, so that these successive temperatures were maintained during 15 minutes. We then took the frequency of vibration of the bar. The numbers of vibrations of the forks used in the deter- minations of the pitches of the bars were corrected for tem- perature by the coefficient ‘0001118, determined by Dr. Keenig in 1880 (Quelques Expériences dW’ Acoustique, Paris, 1882, p. 172 et seq.). The subsequent tables show the results of the experiments and give the computations of velocities and moduli founded on them. The curves express graphically the effect of change of temperature on the modulus of elasticity of all the bars experimented on. The circles, on or near the curves, give the data as determined by the experiments. In Table III., T=temperature of bars, =the length, =the thickness, and V=the velocity of sound through the bars, in centimetres. M=the modulus in grammes per square centi- metre section of the bar. g, at Paris, equals 980:96. D=the density, and N=the number of vibrations of bar per second at temperature, T. All of the bars were annealed, except those of Jonas and Colver steel, of the French aluminium, and of brass; these were experimented on just as they came from the draw-bench. For the analyses of the substances of the bars experi- mented on, I am indebted to my colleagues, Professors Stillman and Leeds. ‘eny@A PAAresqo Jo SCS = onyea poAdesqo woay poynduoo Jo oangredop uvopy 179 Dr. A. M. Mayer’s fesearches in Acoustics. 5 ‘SUID GEGEGG= "ggg. = Ajisuog, 0-996 88-96 "BA GL.GL06 X 8L-TLT 608: GL-IP oo ee) ge OU OHO AN Ee LORE GL-6PL ‘ §0-L0L "BA G8CE XG-GET Lvl. 91G-6% ie SSO EUG OR Sas CG.-8GP «é 9L-09F 80 Toe: 20:06 Ds ness oy ORO INT G6-8CFh 66 §G.09F LPLOG: 0: Peer ete s ere m se eeee of Oo é ‘sm 610898 = aie oN 0-697 €4-09P 'B *A F-98E6 X GO0-0GT OTTO: 60:06 ie | ar ae ad were tes ON “sSVIg 0-8F9 ‘c 08-659 Q66F: EEZ0-0Z Te oe eG ‘ON 0-L#9 «sé 16-L*9 16 i 9 20-0: Se eee reece aneesceenes rYo) x ‘sm0 61L909= oy eae oo 9-999 19-869 "8 "A LUSE X G0-0ST S66P- €960-0G gpa RR ee Ri RON “TUNIULUMN Ty 6-099 “10-699 GG0G- _ 660-06 ih aee en Gt ON ras 0-199 6c 16-99 1&0¢. 9F20-06 PO eee sees serene On ‘oO oe ae ‘su BLIP IG= ee 8-099 P ‘4 67-699 ‘8 "A P.LOPE X GO-091 gc0G: GG0:0G Uta Me nccma le ONIGSTS 5 Zl ei. 00% 7 7 0460-1 A=N =,02 38 A 7 if] metal ees ee £q peyndmos 180 Hapansion of Bars. TasxeE II. Tables of Analyses, of Densities at 4°, and of Coefficients of Dr. A. M. Mayer’s Researches in Acoustics. | Dent Coeff't. Tron. | Carbon. | Silicon. | Phos. | Sulph.| Mang. |Nickel. t 1S of Meee Pris Me Expans. J. &C. Steel.|98°259 | 1:286 0015 | 0:059} 0-051 | 0°350} ...... 7827 -0000110 No.3, _-:(98°738| 0:47 0-15 W502 25 ceo. OG2F ane 7°348 -0000118 No.4 ,, |98°628] O51 Qala Sian sO024 ee. 0°68) eres 7845 -0000120 Noman”; 93409) 0:27 OAOU SOLO Se eee a 0-69 | 3°189) S7-e5l 0000s Bessr. ,, (99°03 | O15 0:02 0309) 10:06;4\ 20: Gormiliscere 7841 -0000122 Brass Bell Metal. RC OP PE? 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Mayer’s Researches in Acoustics. 186 i ° ba 4 : =. + . ; fa t is es Hi cs + = rr : sis ptaestat ts ft Rie (e 5 + i n Be z ke ott ERS apes pai: Bree Be id Hi eile FH fritid seages HEH fa f Hf = per ' Z = a } TEE 09 we 2 } H anne H tht ett 3 saps t t Ls H ie ae + 4 H ey r rth a i 53 a 5) +f rt v : Ht igeeeae # i f Q rs H 4 4 Hf i +4 acy geal fi fi He itis Bai EH SEE 3 t ‘ Seta rs see i H sadguseu pedaam neeys ; a 9 x Ett Pet 5 HH H rare H 9 f rm Rcd anaueaeeabaueatct E i i Ht EE tt aa THY essed gored eeay uve taaed pola gocsap igedbdeda esl H it - tH fl fare # aa aaaraiatte = tee PARE EEE BEEEEEE EEE EEE ELH PI EAH HH H B pasa SAGER aneseeaadeteoeeatitees ie HH Bagel cHereaieceel r) oY = i H PHL eee ee HT te REapeeeaRoneaforaa ee H ie Heer H a aesae ‘ fe Eb Eee aetd Seer HE eee Khey A pate 4 ap eal ne °\ HH pase tee Rati Ho) S ° ° a 9. N/ nN Xx agsene hs go 90 100 7oO 50 3a 2.0. uQ 12 9° ee] Dr. A. M. Mayer’s researches in Acoustics. 187 5: y Titi rt E SESE Taide Bese] aT I fea betes esses feees ees EHH HHI Fl Fy bg ied cies CREST Pipa pan rr + tet! a # sd Seal Eoag Lene Bzued apted peers fesse iF Hy D op Sis: sibs Fi i egseeed beaessea a iz] 4 if + ASP 3 Ie 2 — teEe See HT AH Ee bepgs ters | rth Bette 3 3 = 2 FHI 4 sailed t ra; 4) : ii i Bal Hit} ee: Ba 1 Fi if # | Ht i HE =[r Stl ep - | + 2 -- a 1 hatte = t att 4 5] yy : eH 26 : 3° 10 29: 39 40 50 _ 60 7@ go ge 100 i FEE Fea ae + tt: : Bees egbees + is A STAG oH TES ra 2 fy isldfeasifeatvare H FH eS gaea pegag ae) EpGaEBaEE epee Ea +e il 37 ESD H 5 SH) 1 3 =: HET EH bh i HH HITE | it 2 sot : fr 5 ay) Od apes Hy aEgESSS Hl : EEE site Bn "Aaa pH : =. itt + 5 : : A =H E He fa ppasoadesceea! Teatees sea si feet H : i Fess pines @ r : sees + SATE Et oe So + z tH ft @ 2 FH z a Se: sreeetess Atte Ht TH = # f Sos i SS Sees ee 8 = + tH : 4 ea ane ae : 4 =t5 eae gy “10 20° 30 42 90 60. 72 Bo 20 10% Dr. A. M. Mayer’s Researches in Acoustics. 188 : LO. oO i) i F tft au (Zio 20 208) Qo eo 212 20 Joe™-~ “40> Fig. 11. re i BEG HE Bri tH ole 189 Acoustics. CS dt Dr. A. M. 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M. Mayer’s Researches in Acoustics. Fig. 14. : LH 44 i i eee a S S 3 x 79 7° 69° os 7) °° 10 (29 Bone iano) 50 69 rz) Bo .90 “i. * Fig. 15. 1 HA = ‘ : reel © a) $4 # ni bd 3 Bo2 es ip = is 80 a = | t- me ae aH v98 Bee 796 rf 79 : tt t t+ F Hat Sd epee! 9 Hi easy = : 79a Het F fers sddgoagedstess 1 : C) 44 te 4 i. ; 4-4 Y tet peraezedatee He es + = + eo baocs decd 1a bey t espe af fe ze : cobalt F sseriea Secee cote ceeed fused : a cate Ht THE i te afeaey retsedreds 8 aH Fesgragaterstaead is Bert oH tHe Hatt t TH ted gaurd 4 4 4 +. - + F. t PRerICee eet ree teeet eset eats deceate Hirata ETEBEEN i tea eT t r 4 ppp ete teed ee eat ere ee a bs 3 Bheeelonmed cee BE t are eset dated tied (eee cede eeesnoaaa ated aie af : a4 Be 1 +1 i a 782 Hydat ath tf pbesdirs! tH i i ¢ Seated feest Tee nesta feeeapee ed cead ate festd ; HTH : the + # i 99 looy 3.2) tn Acoustics. esearches y) V Dr. A. M. Mayer’s / Hi E fo 9a 80, 7? boa. 3a AQ go 29 ja seeeal Jo oan +t wah th} an missed feeecbeta 5] 10 192 Dr. A. M. Mayer’s Researches in Acoustics. Results obtained by other Experimenters on the change of the Modulus of Llasticity with change of Temperature. I have found five researches on this subject. Wertheim, 1644. Ann. de Chim. et de Phys. TRON. Modulus 5-2 per cent. greater at 100° than at 18°. Modulus 19°1 per cent. less at 200° than at 100°. Tron WIRE. Modulus 4°9 per cent. greater at +10° than at —11°6. Modulus 7-42 per cent. greater at 100° than at 18°. Wire or ENGLISH CAST-STEEL. Modulus 23:23 per cent. greater at 100° than at 18°. Modulus 9°46 per cent. less at 200° than at 100°. Modulus at 200° is 11°57 per cent. higher than modulus at Oe, | STEEL WIRE TEMPERED TO BLUuE. Modulus 1°97 per cent. higher at +10° than at —10°. Modulus 5:1 per cent. higher at 100° than at 18°. CAST-STEEL. Modulus 2°8 per cent. less at 100° than at 18°. Modulus 5°73 per cent. less at 200° than at 100°. SILVER. Modulus 5 _ per cent. less at + 10° than at —13°8. Modulus 1°87 per cent. greater at 100° than at 18°. Modulus 12°87 per cent. less at 200° than at 100°. CoprER. Medulus 6°53 per cent. less at + 10° than at — 15°. Modulus 6°58 per cent. less at 100° than at 18°. Modulus 20 per cent. less at 200° than at 100°. Wire or Berwin Brass (Cu=67°55, Zn =32°35), Modulus 7°95 per cent. less at +11° than at —10°. Kupffer, 1856. fem. de ? Acad. de St. Pétersb. Modulus of iron wire 5:5 per cent. less at 100° than at 0°. Modulus of copper wire 8°2 per cent. less at 100° than at 0°, Modulus of brass wire 3°9 per cent. less at 100° than at 0°. Dr. A. M. Mayer’s Researches in Acoustics. 193 Kohlrausch and Loomis, 1870. Pogg. Ann. Modulus of iron wire 5 per cent. less at 100° than at 0°. Modulus of copper 6 per cent. less at 100° than at 0°. Brass 6°2 per cent. less at 100° than at 0°. H. Tomlinson, 1887. Phil. Mag. xxiii. Says, ‘‘my own experiments show that both the torsional and longitudinal elasticities of iron and steel are decreased by about 24 per cent. when the temperature is raised from 0° to 100°.” M. C. Noyes, 1895. The Physical Review. Modulus of a piano wire of ;4, mm. diam. 5 per cent. less at 100° than at 0°. | The results of Wertheim’s experiments giving an increase to the modulus, as the temperature rises, of iron, Iron wire, wire of English cast-steel, steel wire drawn to blue, and silver, have not been confirmed in any instance by subsequent experiments ; only for cast-steel vod and copper did he obtain a diminution of modulus for a rise of temperature from 15° to 100°. Yet he found that a wire of English cast-steel had a modulus 23 per cent. higher at 100° than at 18°. On the Acoustieal Properties of Aluminium. The low density (2:7) of aluminium combined with a modulus of elasticity of only 712 x 10° render this metal easy to set in vibration ; a transverse blow given to a bar of this metal causes it to vibrate with an amplitude of vibration greater than that which the same energy of blow gives to a similar bar of steel or of brass. This fact has given rise to the popular opinion that aluminium has sonorous properties ereatly exceeding those of any other metal. This opinion is erroneous. If a bar of aluminium and a bar of brass having the same length and breadth and giving the same note, are struck transversely so that the bars have the same amplitude of vibration, the bars give equal initial intensity of sounds; but the bar of aluminium from its low density and because of its internal friction will vibrate less than one-third as long as the bar of brass. Thus, a bar of aluminium and a bar of brass of the same length and width and of such thickness that they gave the same note, SOL, of 768 v. d., were vibrated so that the sounds at the moment of the blows were, as near as could be judged, of the same intensity. The duration of the sound of the brass bar was 100 seconds; the sound of the aluminium bar lasted 30 seconds. The readiness with which a bar of aluminium vibrates when acted on by aérial vibrations of the same frequency as those 194 Dr. A. M. Mayer's Researches in Acoustics. given by the bar, gives one the means of making many charm- ing experiments in which “sympathetic vibrations” come into play. I here describe an experiment which I devised to show the interference of sound in a manner similar to analogous ex- perimeuts in the case of light. The resonant box on which Keenig mounts his UT; (1024 v. d.) fork is open at both ends and has a length of nearly a half wave of the sound of the fork. If this resonant. box is held with its axis vertical, above an aluminium bar in tune with the vibrating fork, the bar does not enter into sympathetic vibration with the fork, because the sonorous pulses, on reaching the aluminium bar from the two openings of the resonant box, differ in phase by one half wave- length. But if the axis of the box is held parallel to the axis of the bar, then the sonorous waves reaching the bar have travelled over equal lengths from the openings at the ends of the box, and these waves conspire in their action and the aluminium bar enters into sympathetic vibration. As this experiment is an interesting one I here give details as to the manner of making it. The bar of aluminium has a large surface, having a jiength of 17 cms. and a width of 5 ems. The two nodal lines, which are at a distance from the ends of the bar equal to 2ths of its length, are drawn on the bar. The bar is supported under these nodal lines on threads stretched on a frame. This frame is of such a height that the under surface of the aluminium bar is 8°4 cms., or one quarter wave-length, above the surface of the table, so that the vibra- tions of the bar and those of the waves reflected from the table will act together. The upper surface of. the bar is covered with a piece of thick cardboard, in which is cut a rectangular aperture, having for length the distance between the nodal lines and a width equal to that of the bar. As this piece of cardboard rests on supports which lift it a slight dis- tance above the surface of the bar, the latter, when it vibrates, does not send to the ear the vibrations of the surfaces of the bar included between its nodal lines and its ends, which vibrations are opposed in phase to those given by the central area of the bar. Thus the sound emitted by the bar is much increased and the experiment rendered more delicate and im- proved in every way. I have found that the experiment succeeds best when the centre of the resonant box is held about 58 cms., or 7 3 above the surface of the aluminium bar, This experiment works best in the open air, away from the action of sound-waves reflected from the walls and ceiling of a room. Dr. A. M. Mayer’s Researches in Acoustics. 195 The fact that aluminium gives, from a comparatively slight blow, a great initial vibration, and that its vibrations last for a short time, render this metal peculiarly well suited for the construction of those musical instruments formed of bars which are sounded by percussion and the duration of whose sounds is not desirable. I had hopes that aluminium would prove to be a good substance out of which to make plates on which to form the acoustic figures of Chladni. Experiments have shown that aluminium is not suited to this purpose. I had plates of aluminium carefully cast, with 2% cms. cf thickness. These plates were turned down on the face-plate of a lathe to thick- nesses of 2mm.and 3°83 mm. Three of these plates were quite homogeneous in elasticity, for the Chiadni figures when obtained on them were symmetrical. Yet the Chladni figures were difficult to produce, because it is difficult to obtain a pure tone from an aluminium plate. The sound is generally more or less composite ; therefore the plate in its vibration tends to form two or more figures at the same time, and the con- sequence is that either no figure is formed or one is given that is not sharply defined. One square plate of 30°8 cms. on the side and °38 cm. thick, gave quite clearly the three following tones :—UT, (1), SOL, (2), and SOL, (3). Cor- responding respectively io the Chladni figures of (1) two lines drawn between opposite points of the centre of sides of plate; (2) figure formed of the two diagonals drawn between the corners of plate; (3) figure similar to (1) but with corners of plate cut off by curved lines. Figure 3 corresponded so nearly to the sound of SOL, that a vibrating SOL, fork when held near the plate set the latter into vigorous vibrat on. Another difficulty met with in using plates of aluminium for Chladni’s figures is that sand,even when entirely free from salt and from the globular grains of wind-blown sand, does not move freely over a vibrating surface of aluminium, whether this surface has been polished or has been slightly tarnished and roughened by the action of alkali. There is one serious objection to the use of aluminium in the construction of musical and acoustical instruments, and that is the great effect that change of temperature has upon its elasticity. If a bar of aluminium and a bar of cast-steel be tuned at a certain temperature to exact unison, a change from that temperature will affect the frequency of vibration of the aluminium bar 23 times as much as the same change of temperature will affect the bar of cast-steel. (oie XXIII. On the Freezing-points of Dilute Solutions. By W. Nernst and R. Apece*. Ae lowering of the freezing-point of dilute solutions has been recently carefully investigated by two observers, Mr. Jonesf and Mr. Loomis f, but they have found very different values for the lowering in the case of non-electr olytes. No reader of the two researches could fail to see that Mr. Loomis had worked with great care, and that Mr. Jones, on the other hand, had neglected some very obvious pre- cautions. Indeed we found that a very dangerous source of error, viz. the influence of the external temperature, which Loomis approximately avoided, made Mr. Jones’s results in the case of non-electrolytes entirely worthless. At the same time we showed how the influence of the external temperature is to be computed, since we developed a mathematical-physical theory for its effect upon the freezing-point. To our surprise Mr. Jones songht to defend his results by attacking our research in a most condemnatory manner. How far he is justified in this can be seen from the following brief observations. Mr. Jones had nothing to say against the above-mentioned theory, except (page 386 of this Journal, 5th series, vol. xl) that ‘‘ the introduction of a correction-term when amounting to more than 20 per cent. would not tend to increase our confidence in the final results.’ Ought such an argument to be taken seriously when a very elementary acquaintance with physical measurements shows that exact determinations can be made in spite of large correction-terms, provided these are correctly computed. So long as Mr. Jones has not proved any error here he must discard his own results. In reference to the same point Mr. Jones remarks, “ Their correction-term ..... appears to me to involve the assump- tion that K for solutions is the same as for water, which assumption is gratuitous and unallowable” [p. 385]. Hvi- dently Mr. Jones has not correctly understood our theory. We have in no way assumed that K, the rate of dissolving (Lésungsgeschwindigkeit) solid substances in solutions and in water is the same; but, on the other hand, we have em- phasized the fact of the great difference in the values for water and solutions, and we have computed them. * Communicated by the Authors. + Zeitschr. f. physikal. Chemie, xi. p. 529; and xii. p. 623. { Wiedemann’s dAnnalen, li, p. 500. On the Freezing-points of Dilute Solutions. 197 We had ourselves called attention to the fact that we had at SEL disposal thermometers reading only to 739° direct, and to ygbo° by estimation, so that our determinations of the lowering of the freezing- “points could for this reason be accu- rate to within only one to two thousandths of a degree. Mr. Io 10,000 ’ shown, untrustworthy to within at bees hundr edths of a degree. Mr, Jones then remarked that it was not “ apparent ” to him why our two series for NaCl in very dilute solutions should vary by 5 per cent. He neglected to remark that in reality such differences are limited to the most dilute solutions, and on that account lie within the limits of experimental errors given by us. Moreover in the second series for NaCl the greater values for the lowerings may be accounted for by the presence of larger quantities of the solid substance, since in this method lar ger quantities of undercooled liquid are intro- duced. In any case it is self-evident to every one who knows the elements of the computation of errors, that no conclusions _can be drawn presupposing a greater degree of accuracy in our results than that given by us. Nevertheless in spite of this Mr. Jones concluded, from our results with ethyl alcohol, that arise of the molecular low ering took place which was far within the experimental errors. That we used substances of sufficient purity for the purpose we had in view, that is, substances whose possible impurities were absolutely unessential, we certainly did not especially mention. Hvery one knows that comparatively pure NaCl, ethyl alcohol, and cane-sugar are easy to obtain. We refrain from criticizing the few new experiments of Mr. Jones, partly because we have not the least interest in carr ying: ona further controversy, partly because the criticism given in our earlier research would simply need to be repeated word for word*, Moreover Mr. Jones admits indeed the influence of the external temperature (page 389), and in that the existence of a great source of error which he formerly entirely neglected. In conclusion a purely personal remark. Mr. Jones spoke (page 385) of “the unusual lack of courtesy.” ‘That Mr. Jones Jones’s numbers, which read to are, as we have * For instance, Mr. Jones maintained that the influence of his “ gentle” stirring was imperceptible, 7. e. determined from his feeling instead of quantitativ ely. That the thermometer-reading remained unchanged is no proof for his assertion according to what our theory as well as experi- ments showed. 198 = = On the F’reezing-points of Dilute Solutions. introduces no proof for this assertion no one could wonder from the above. But that each one may judge for himself we insert the following passage from a paper in which we refer to the results of other authors, and to which alone Mr. Jones’s severe reproach could relate :— “Ttis not without interest to test the earlier values for this source of error through which partly they have been rendered so considerably inaccurate: for instance, for the molecular lowering of the freezing-point (computed from Raoult) for dilute (about 1 per cent.) cane-sugar solutions the following values were found by Arrhenius. Raoult. Jones. Loomis. 2°02 2°07 2°18 Lot but we find, as was mentioned, 1°86 (uncorrected from 1°6 to 21). Arrhenius used the usual Beckmann apparatus with quite an energetic cooling-mixture: this explains why his value is considerably too large. Raoult gives more experi- mental details, and from these one can conclude that he kept the cooling-bath about 3° below the freezing-point of the solution. ‘This investigator seems to have appreciated the essential importance of the cooling-bath, for he says, ‘If the influence of the cooling-bath upon the temperature of the liquid at the moment of freezing is not nought, yet it is indeed the same in the experiments to be compared and vanishes from the differences, so that the lowering of the freezing-point is not influenced by it.’ The assumption which Raoult here makes is identical with the supposition that K has the same value for pure water and for solutions, which is certainly not the case with cane-sugar according to our experience. His values must accordingly be considerably too high. Still more erroneous are the values of Jones, who used a cooling-mixture of ice and salt, therefore an exceedingly strong cooler. If Jones had used a single time in the case of cane-sugar another cooling-mixture, or even only a freezing- vessel of other dimensions, he would have observed with the great accuracy with which he read the apparent freezing- points the influence of these factors, and would have refrained from publishing his essentially accidental numbers. [ Note:— “Since the corrections for Jones’s values amount to hun- dredths of a degree, if the accuracy is to be increased to within 0°0001° with the same external temperature and rate of stirring only by using a greater volume of the liquid, in order to reduce K (¢/. equations (3) and (7) to its hundredth part, it is necessary to increase the linear dimensions of the Prof. J. D. Everett on Resultant Tones. 199 freezing-vessel ie —= , of. page 683) an hundredfold. The accuracy for which Jones strives would have been attained therefore, ceteris paribus, by using a vessel not of a | litre’s capacity but of that of a million. litres!” ] Loomis un- doubtedly worked with precaution ..... Gottingen, November 1895. XXIV. On Resultant Tones. By Professor J. D. Everett, /.R.S.* im : ee received theory of the generation of resultant tones in the ear may be summed up with rough accuracy as follows +:— The drumskin being pulled inwards by the end of the handle of the “hammer,” which is attached to its centre, offers unsymmetrical resistance to displacement in the inward and outward directions, so that the equation for the move- ment of its centre in free vibration would be —i=o'x+ an”, or to a closer approximation —t=0'2+ar7+ Ba’, w, a, 8 being constants. The value of w when the second is the unit of time is less than 60, hence the frequency of free vibration, being @/27, is less than 10. W hen two harmonic forces of frequencies m and n act upon the drumskin, they produce, in addition to their own tones, certain “resultant tones,” the one of largest amplitude being the “first difference-tone,” of frequency n—m. The next sat 2 largest amplitude is about (—*) of this, and belongs to the “first summation-tone,”’ of frequency n+m. Neither of these tones will be audible unless the excursion z is so large that az” is sensible in comparison with wx. There will also be difference-tones of frequencies 2m—n and 2n—m, but neither of these will be audible unless Bx? is sensible com- pared with ww. 2. This theory does not appear sufficient to account for the loud resultant tones which are sometimes heard. When a Helmholtz siren is driven rapidly, with the rows of holes 9, * Communicated by the Physical Society: read January 24, 1896. t See Tonempfindungen, Appendix xii.; Rayleigh on Sound, art. 68 ; i Sa Proce. Phys. Soc. vol. iv. p. 240, arts. 57-69. 200 Prof. J. D. Everett on Resultant Tones. 12, 15, and 18 open, the resultant tone of frequency 3 on the same scale is the most prominent tone in the whole volume of sound. 3, The view which I desire to put forward is closely con- nected with the well-known theorem of Fouricr, that every periodic variation can be resolved in one definite way into harmonic constituents, whose periods must be included in the list 1, 4, 4, +, &c., where 1 denotes the period of the given variation itself. The corresponding frequencies will be as HO? 73, 4, Ws In the majority of cases, when this analysis is carried out, the fundamental constituent, represented by 1 in the above lists, is the largest or among the largest ; but in the case of a variation compounded of two simple tones with frequencies in the ratio of two integers, neither being a multiple of the other, the fundamental will be absent, and the Fourier series. will consist of only two terms, which in the language of acoustics are harmonics of the fundamental. 4, Clearness of thought is facilitated in these matters by supposing a curve to be drawn, in which horizontal distance represents time and vertical distance represents the quantity whose variation isin question. Since the variation is periodic, the curve will consist of repetitions of one and the same form, in other words it will consist of a number of equal and similar waves, and the wave-length stands for the comp!ete period of the variation. : The point on which I wish to insist is, that if such a curve representing the superposition of two harmonics of the funda- mental is in the first instance very accurately drawn, and is then inaccurately copied in such a way that all successive waves are treated alike, the inaccuracy is morally certain to introduce the fundamental. Let y denote any ordinate, and @ the time (or abscissa) expressed in such a unit that 2a is the numerical value of the wave-length or period ; then the amplitude of the funda-. mental is the square root of A’ + B?, where A= +{ > cos Odé, b— L ("y sin @dé. 0 T 0 19 In the original curve both A and B vanish. Let y’ be the altered value of y in the new and inaccurate curve, and let z denote y/—y; then we have, between the above limits, fy cos add=\ y cos 6d¢ +z cos 6d he cos 6d, since Ny cos 6d@ is zero. Prof. J. D. Everett on Resultant Tones. 201 But z may be regarded as a random magnitude, hence it is infinitely improbable that its different values exactly fulfil the condition fz cos @d@=-0. Therefore the new A is finite ; and similar reasoning shows that the new B is finite. If all the ordinates were changed in one uniform ratio, A and B would remain zero, and no new constituent would be introduced ; but any other change, unless specially planned to avoid introducing A and B, is practically certain to give A? + B? a finite value. 5. I maintain that such a change is effected in the form of sonorous waves during their transmission from the external air to the sensory fibres by which we distinguish pitch. The waves are transmitted first from the air to the drumskin, then through two successive levers, the hammer and anvil, to the head of the stirrup, while the foot of the stirrup sits upon the membrane of the oval window, and passes on the vibrations through the membrane to the liquid on the other side in which the sensory fibres are immersed. The levers turn upon ligamentous fulcra, and have rubbing contact with each other. The wave-form cannot run the gauntlet of all these trans- missions without being to some extent knocked out of shape. It is much as if a very accurately drawn curve, representing the original wave-form, were copied and recopied, five times in succession, by five different pantagraphs not very firm in their connexions. The final copy so obtained would be sure to exhibit sensible departures from the original. 6. It appears likely that the chief seat of the disturbing actions in the ear is the junction of the hammer and anvil. “ When the drumskin with the hammer is driven outwards, the anvil is not obliged to follow it. The interlocking teeth of the surfaces of the joint then separate, and the surfaces glide over each other with very little friction’”’*. Such action is likely to introduce derangement, increasing generally with the excursions of the drumskin, but not expressible as a defi- nite function of the ordinates of the wave-curve. For a given pressure on the drumskin, the pressure communicated to the liquid in the cochlea will vary according to the relative position and relative motion of the two portions of this joint. 7. The principal resultant tone due to these actions is likely to be that which corresponds to the complete period of the actions, in other words the highest common fundamental of the two primaries, or what old writers called the “ grave har- monic.” This will not be the same as the ‘first difference- tone” unless the ratio of the two primaries is of the form * Ellis’s ‘Helmholtz, p. 133, 2nd edition. Phil. Mag. 8. 5. Vol. 41. No. 250. March 1896. P 202 Prof. J. D. Everett on Resultant Tones. m:m+1; and I have satisfied myself, both by my own trials and by a study of Koenig’s experimental results, that when the difference-tone and the common fundamental are not identical, the common fundamental is usually the pre- dominant, and often the only audible resultant tone. (See Appendix.) 8. The common fundamental is, however, not the only resultant tone that can be thus accounted for. Similar reasoning to that employed in reference to A and B suftices to explain the introduction of any or all of the harmonics of the fundamental ; but it is to be expected, from the analogy of ordinary experience in harmonic analysis, that the succes- sive constituents will usually be smaller and smaller as we advance in the series. The octave is likely to be the largest of them; and Koenig found, in several experiments with primaries in the ratio of 3:5, that both the fundamental 1 and its octave 2 were distinctly heard as resultant tones. 9. The following investigation bears on the relation be- tween beats and resultant tones. ‘The expression a cosm0+6 cos nO can be reduced to the form A cos (= < “0 —e), where A and e¢ are given by A?=a? +b? + 2ab cos (n—m) 8, a—b, n—m tan e= aah eh 5 0, and the beating together of two tones not differing much in pitch is explained by the fact, definitely expressed in these formule, that the whole effect may be regarded as a succession of waves with gradually varying amplitude. The frequency of the beats is the frequency of the maxima of A’, and is the difference of m and n. We have ascribed resultant tones to alterations made in the wave-form by the action of the ear, such alterations being in general largest at those points at which the excursions of the drumskin are largest. These excursions are measured by +A,and the above investigation shows that their maxima have a frequency corresponding to the difference-tone. This is true whether m and n are commensurable or incommen- surable. If they are commensurable, their greatest common Prof. J. D. Everett on Resultant Tones. 203 measure will be the frequency of the complete cycle of change. This cycle will not be conspicuous in the curve if the ratio of n—m to 4(n+m) is very small, but will assert itself more and more as this ratio increases ; and these remarks will apply to the comparison of the fundamental with the first difference- tone. 10. If the ear is able so to alter the form of waves impinging upon it as to generate resultant tones, it is natural to seek for some instance of a similar action in external bodies. A violin is very susceptible, like the ear, to vibrations of all frequencies between wide limits, and the sound-post serves, like the ossicles of the ear, to transmit vibrations from one portion to another. It is easy to produce resultant tones by bowing two strings of a violin together. For example, in the ordinary process of tuning, when the fourth and third strings with frequencies as 2:3 are combined, the resultant tone 1 is very observable if attention be directed towards it. But more striking effects are obtained when the resultant is at a larger interval from the primaries. The major sixth 3:5, the major second 8: 9, and the minor seventh 5: 9, are suitable intervals for calling out the fundamental 1, the strings em- ployed being either the first and second or the second and third. The deep resultant tone thus obtained can not only be heard by the ear but felt as a tremor by the hand which holds the instrument. This is clear evidence of its objective existence, and I have succeeded in confirming the fact by means of a Helmholtz resonance-globe, the largest of the ordinary set, responding to OC of 128 vibrations. When held with the edge of its mouth resting against the side of the violin, it responds to the combination © of 256 and G of 384 on the 4th and 8rd strings, or to the combination OC of 512 and E of 640 on the 2nd and Ist; or, still better, to the 3rd and 2nd open strings each flattened one note, so as to be C of 256 and G of 384. Here, then, we have distinct evidence that the violin possesses the power which I have ascribed to the ear—-the power of manufacturing the fundamental when the two primaries are supplied. 11. Sir John Herschel, in his treatise on Sound (Enc. Met. arts. 238, 239), mentions the fact that the common fundamental can be called out by sounding two or more of its harmonics on very accurately tuned strings or pipes, and says that the effect cannot be obtained from a pianoforte tuned in the ordinary way, because the intervals are tempered. I find, however, on trying the experiment with an upright _ Broadwood of date about 1860, that C of 64 is easily called out by simultaneously striking eight or ten of its harmonics ; P2 204 Prof. J. D. Everett on Resultant Tones. and the effect is greatly enhanced if the key of C 64 is held down. In the latter case its note continues to be heard for a long time after the keys which were struck are released. From these experiments it appears probable that the sounding- board of a piano possesses the same property which we have proved to exist in the violin. : 12. I now come to the explanation of the experiments of Professor Riicker and Mr. Edser (Proc. Phys. Soc. vol. xiii. p. 412, Phil. Mag. 1895, xxxix. p. 341). They were made with a Helmholtz siren, and in each instance the two primaries were produced in the same box, sometimes the upper and sometimes the lower box. The following explanation is a development of suggestions contained in Appendix xvi. of the Tonempfindungen. The rate of escape of air from the box containing the two rows of holes which are employed may as a first approxima- tion be assumed to be jointly proportional, at each instant, to the aperture for escape and the differential pressure which produces the escape. Again, this differential pressure may be regarded as the algebraic sum of two terms, one of them constant, and representing its average value, while the other represents the difference from the average due to the varying amount of the aperture from instant to instant. As a first approximation, equal increments of aperture must be regarded as producing equal decrements of pressure, so that the variable term will be proportional (with reversed sign) to the excess of the aperture above its mean value. This excess (defect being counted negative) will be a periodic function of the time, and if the ratio of the two primaries in lowest terms be m:n, the frequency for the complete period will be repre- sented on the same scale by 1. In other words it will be the period of their common fundamental. Let the aperture at time ¢ be expressed in a Fourier series, @ being put for 27t/T, where Tis the complete period ; and let the variable part of the expression be denoted by /(@), while a, denotes the mean aperture, so that the aperture at time ¢ is ay+f(@). We shall have J (@)=Asind+... +a, sin (m0 +e,) + ... $6, sin(nO+e,)+... The largest amplitudes will be a, and b, corresponding to the two primaries ; but A, which corresponds to the fundamental, is likely to be sensible. The pressure at time ¢ is proportional to C—-f(@), C being a constant ; and the aperture is ay +f (9). Prof, J. D. Everett on Resultant Tones. 205 Hence the rate of escape is proportional to Cay + (C= 19) f(8) — 17 (8) 9?- @ is comparable with the maximum value of /(@), and C is much greater; hence a) may be neglected in comparison with C. Developing {(/(@)}’, we shall obtain a term 2a4b, sin (m0 + €;) sin (nO -+- Ep) =a,b,[ cos {(n—m)0 +¢,—€,} —cos{(n+m)O+e,+4}], representing a difference-tone and a summation-tone. From (C—ay)f(@) we have the common fundamental (C—a)Asin@, or CA sin 8, and the two primaries Ca, sin (m@+e¢,), Cb, sin (n@ + €). Suppose for simplicity that a,=0,, then, taking the amplitude of each of the primaries as 1, the amplitude of the common fundamental will be A/a, and the amplitudes of the summa- tion-tone and difference-tone will each be a,/C. When n—m=1, the difference-tone coincides with the fundamental, and their joint amplitude may be taken as the square root of the sum of the squares of a,/C and A/a. 13. Professor Riicker and Mr. Edser in experiments i. and ii. obtained the difference-tone 64 from five distinct com- binations of primaries, ) 256 & 320, 192 & 256, 320 &3884, 51:2 & 115:2, 96 & 160, their ratios being 4:5, 3:4, D6, AL 29; Oto The second combination appears to have given a stronger effect than either the first or the third; whence it would appear that low frequencies are favourable to strong effects. Nevertheless the fourth combination is mentioned as giving a rather feebler effect than any one of the first three. This confirms our conclusion that the difference-tone is weaker when it is distinct from the common fundamental than when it coincides with it. Hxperiment iii. was directed to testing for the presence of the resultant 64 when the primaries were 256 and 576. which are as 4:9. Their common fundamental is 64, and it could not be detected. This may have been because the pitch 576 was too high to give a good effect. Or the failure may be an indication that A/a, is decidedly smaller than a,/C. It would be interesting to repeat the experiment, employing 192 and 320 as the primaries. 206 Prof. J. D. Everett on Resultant Tones. 14. Near the end of chapter vii. of the Tonempjindungen Helmholtz makes prominent mention of the slipping of the hammer on the anvil as an important cause of resultant tones, and appears to regard it as exemplifying his mathematical formula for the restoring force as a function of the displace- ment. But it is clear that if the hammer, which holds the drumskin, is liable to shift in its supports, the restoring force cannot be a mere function of the displacement, but must also depend on the relative position and relative velocity of the hammer and anvil at the moment considered. I accept all the consequences which Helmholtz deduces in the passage in question from this slipping, including its application to explain first difference-tones ; but I regard these consequences as lying outside the range of his general mathematical for- mulee as given in Appendix xii. | 15. To sum up my objections to the received mathematical theory of resultant tones :— First. It assumes that the reaction of the drumskin against the air is a definite function of the displacement of the drum- skin from a certain fixed position, whereas this reaction depends also on the position and motion of the further end of the hammer at the time. Secondly. Hven if the vibrations of the drumskin were in accordance with the received formule, there is plenty of scope for the introduction of additional constituents on the road from the drumskin to the liquid in the cochlea. The auditory ossicles, with their ligamentous supports and attachments, probably serve to protect the oval window of the cochlea against shocks and jars, and to smooth down asperities in the wave-form, thus mitigating the harshness of sounds and rendering them more musical. The changes thus introduced are very unlikely to fulfil the special conditions required for the vanishing of the common fundamental. Thirdly. The received theory makes the common funda- mental, when not coincident with the first difference-tone, depend on a term involving the cube or some higher power of the displacement. When the primaries are as 3:95, the fundamental 1 comes in as 2m—n, and depends on the cube of the displacement. When they are as 4:11, the tone l, which Kcenig found to be the loudest resultant, is 3m—n, and depends on the fourth power. When they are in the ratio 4:15, as in Keenig’s experiment with the simple tones ut; and st, the common fundamental utz;, which was the only resultant tone heard, is 4m—n, and depends on the fifth power of the displacement ; the first difference-tone, which depends on the second power and should in theory be the The Compound Law of Error. 207 loudest, being inaudible. This is surely a reductio ad absurdum of the received theory. I do not wish to be understood as denying that the theory has any basis of truth. My contention is that the actions to which it is truly applicable play only a subordinate part in the production of resultant tones. APPENDIX. Hxamples selected from Keenig’s Expériences d’ Acoustique, pp- 102 and 104, illustrating the production of the common fundamental. The “single vibrations” of the original are here reduced to double or complete vibrations :— uf; and si;, which are as 8: 15, gave only uty. ut; and 2816, which are as 4:11, gave ut; corresponding to 1 louder than any other tone. ut; and stg, which are as 4: 15, gave no audible tone but wuts. ut; and 3968, which are as 8:31, gaveno audible tone but Uto- ut, and 3584, which are as 4:7, gave wf, more distinct than the difference-tone sol;. ut, and sig, which are as 8:15, gave wt; distinct, the diffe- rence-tone 7 being inaudible. ut, and 3968, which are 16: 31, gave uf, only. ut, and 4032, which are 32 : 63, gave ut, only. XXV. The Compound Law of Error. By Professor F. Y. Hpgeworts, .A., D.C.L.* * ie compound law of error is an extension to the case of several dimensions of the simple law for the frequency with which a quantity of one dimension (x) tends to assume each particular value. A first approximation to the com- pound law has been obtained by several writers independently, —by Mr. De Forest, in the ‘Analyst’ for 1881; by the present writer, in the Philosophical Magazine for December 1892; and by Mr. 8. H. Burbury, in the same Journal for January 1894. I propose here to employ tbe method of partial differential equations explained in a preceding paper f to verify the first approximation, and to discover a second approximation, to the compound law. To begin with the case of two dimensions: let Q be the * Communicated by the Author. + “On the Asymmetrical Probability-Curve,” Phil. Mag. February 1896. 208 Prof. F. Y. Edgeworth on the sum (or more generally an expansible function *) of a number of elements & &, &c., each of which, being a function of two variables 2 and y, assumes any particular system of values according to any law of frequency ¢,=/,(«, y) ; the functions f being in general different for different elements. If each of these functions is referred to its centre of gravity at origin, and expanded in powers of x and y, it appears, by parity of reasoning with that employed in the case of the simple law, that for a first approximation we need take account only of terms of the second order. Integrate between extreme limits of x/(ay)da dy for each element; and let the sum of all these integrals be &. Also let 1 => \\ey/,(ay)da dy, n= > (\y2f,(ay) de dy ; the integration extending between the extreme limits of each element, and the summation over all the elements. Then z, the sought function which is to express the frequency of Q, will be of the form 2=3D(e, 7; kl, m)T. This expression may be simplified by transforming the axes to new ones making an angle @ with the old ones, such that the new / vanishes. This will be effected if we put tan 20=21+(k—m)t. Thus we may write with sufficient generality :— 2=P(x,y3 km). By superposing a new element after the analogy of the * Cf. Phil. Mag. 1892, xxxiv. p. 481 e¢ seq. + Luse a semicolon to separate the variables (x and y) from the con- stants (k, /, m). t Put x=X cos 6—Y sin 6, y=X sin 6+Y cos 6. The new / =>\\XY, f,dX dY ; where f,is what fi(zy) becomes when for x and y are substituted their values in X and Y; each element is integrated between extreme limits, and all the integrals are summed. Transforming back to the old axes we have for the new Z > \\A(ey) (B(y?—a*) sin 26-bay cos 26)4e dy= 3(m—L) sin 26-+1 cos 20 ; which becomes null when tan 26=21-+(k—m). Compound Law of Error. 209 simple case* we obtain the differential equations 5 da,’ te Mine dain ate ae warns 5 CL.) dz dre TDA tote 2 on ® Other differential equations are obtained by supposing the units of x and y altered; substituting for # and y, #(1+.) and y(1+) respectively. The expression for z thus trans- formed must be multiplied by (1+e)(1+8); since the measure of the solid contents of the parallelopiped inter- cepted between the surface, the plane of x,y, and any two fixed adjacent points in that plane will be increased in that pro- portion. Thus g=(1+a)(1+f) B(z,y; k,m). Regarding # and § as infinitesimal, expanding and neglect- ing higher terms, we have dz dz z -+- v dx + Qh dk — 0, e e ° e e (3) dz dz BE pe 4m 7 =0. e e ° ° e (4) From (3) and (4) we have where ¢ and wf are arbitrary functions. "Whence 1 ( ip y ) c= —_— XxX a ——— a — i [ km Vm? Vm where y is an arbitrary function. The form of y is restricted by the condition that its value is the same for positive and negative values of x and y, the surface being symmetrical about a vertical plane through each axis. For as we take account only of the second powers in the expansion of each element, we might replace the given system of elements by a new system of symmetrical functions having each the same centre of gravity and mean square of error as the old onef. * See the preceding article, Phil. Mag. 1896, xli. p. 90. + This does not mean that the given elements must be symmetrical, as is sometimes carelessly said with reference to the simple law of error. The given elements may have any degree of asymmetry, provided that their number is correspondingly great. 210 Prof. F. Y. Edgeworth on the And a compound of symmetrical elements must itself be symmetrical. We have, therefore, il x = —ax(p eee ee OH (5) To the five equations which have been stated there is to be added the condition that the integral of zdxdy between extreme limits =1. i solve oe system: substitute in (3) and (4) the values of ik = and given in (1) and (2) respectively. We have, then, dz dgg eto th-F,=0, . . 1) ener dz daz etyy, +! a= =0; Gon 2 Integrating (6) with respect to x, and (7) with respect to y, we have a =d¢ty),.... zy+m = pave) Ss - . oY (ae where ¢ and ¥ are arbitrary a Both these functions reduce to zero; as may thus be proved:— From (5) it appears that when #=0, 2 also =0, whatever the value of y. If, then, we put e=0, the left side of equation (8) vanishes for all values of 2 Y. Therefore the right side of the equation vanishes for all values of y. Therefore $(y) is identical with zero. By parity W(y) is null. By equation (8) thus reduced we have 2 Z=Oly) x ert 1 OO) 2 g=V(w)e72n, J, 0 Identifying the right-hand members of (10) and (11) we have 2 y2 $206 Eee so) di where Cis a constant ; which is found to bb —-— from the Qo km Compound Law of Error. 211 i) Bae dy. — 0 J —o condition that Transforming back from the principal axes which we have employed*, we find for the general expression HE —(mx2—2lzy+ky?) Sef iO 2(km—l?) é Qa Vkm—P? By parity of reasoning we obtain as the general form for the law of error relating to any number of variables 2, 22, “3, &e., 1 ar ee ee ar Saag Oi ak 2A (27)? V/A ; where A is the determinant ky hie Li Loy ke log Loy I39 ks (pee i Ceca CONG Cla nee Saale 0 6, @" dx, dt, dx3.... l= > \\. ». ©, #1 By dat, dt, dts <. «=o, the limits of the integrals and extent of the summation being as before ; K, is the first minor of the determinant formed by omitting the row and column containing f/,; Ly, is the first minor formed by omitting the row and column con- taining (;, or ly, ; and go on. * The values of the & and m which we have been employing with reference to principal axes are in terms of our original 4, J, m referred to any axes respectively : k cos’ 6—2/cos 6 sin 6+-m sin? 6, and k sin? 6+ 2/ cos 6 sin 6-+-m cos? 6; where tan 26= (k—m)~21, See note on p, 208. 212 Prof. F. Y. Edgeworth on the If eae) units of the variables be taken so that hy, hay ks, 8c. each = i, then Jyo, l13, &c. will be replaced by 43pj., $043, &e., the coefficients of correlation which have been discussed in a former paper*. To obtain a second approximation to the compound law of error by this method : beginning with the case of two varia- bles, put as before k== ff Cx? dx dy, m=2 \\ &¥? dx dy, principal axes being employed. Also put r= >|) G23 dx dy, P= » &ey » q= » &ay’ » Pk eG as We have then, for z the law of the comune: the following system of equations : — t= 3 de! _.. Raye iia) ee .. aes =F ay .. = yaey - a dr 6 dy?’ * et hit)! 4.5 Sen (6) dz dz dz dz dz dz dz dz dz dz 2AY aa hor ter oe Ta rr ‘ (8) * Phil. Mag. 1892, xxxiv. p. 194 et segg. Compound Law of Error. 213 From (7) and (8) we obtain Se 2 Se .) : a eax Vk? Nm’ ke’ km?” em? m?] 9) Put z, for the first approximation which has already ,been found, viz. : _ ets B / km Put z=2,(1+0). Then for © we may substitute with sufficient generality A= eg eee pee ge ge kz m2 m? k k?m where the 6’s are functions of x and y ; since, the coefficients in (9) being by parity of reasoning with that employed in the case of a single variable* small, second powers do not appear in the expression for z. Since z reduces to 2, in the case of symmetry, @ must be null. For the other unknowns we have from equations (3), (4), (5), and (6), neglecting small quantities, 1p _ ed 2 ion oA ie ate 6 da® * km? ye 2 du*dy i with corresponding equations for 6, and @;. Performing the work we have for the asymmetrical probability-surface, | Ln 2s he 1 p- y ya ( 2h? Wk 3x) Zk /m vm\. k bol i RT Ne ( ate dee oc a ee A AE i mea ae) aay 3) Oo By construction, z satisfies equations (3), (4), (5), and (6). From the form of the expression it is evident that it satisfies equation (9), and therefore equations (7) and (8). By actual trial it is found to satisfy equations (1) and (2) ; as may be seen by breaking up the expression into five terms, and ob- serving that each term separately satisfies those equations. We might also have proceeded by obtaining general solu- tions of equations (1) and (2) in the form of series, after the * See the preceding article, Phil. Mag. 1896, xli. p. 90. 914 Prof. F. Y. Edgeworth on the analogy of the case of a single variable (Philosophical Maga- zine, 1896, xli. p. 95 et seqq.), and then subjecting the general n The form of the solution in series is such that the third dif- d3z sz dg aaay for the circumstance that the functions 6, 6, &c., satisfy equa- tions (1) and (2). Such being the solution for principal axes, the solution for any axes w’', y/ is found by substituting in the above expression for x, x’ cos @—y’ sin @, and, for y, — wx’ sin 0—y’ cos 0; where expression to the conditions that the quantities ferentials belong to the same form, which accounts k! —m! k’, U', m’ corresponding to our original k, 1, m*; and by substituting in (10) for k, m,n, p,q, r the equivalents of those coefficients in terms of k’, I’, m’, n’, p’, q’, 1’ fT. It may be observed that to whatever axes the surface be referred, if we integrate between extreme limits with respect to y, the resulting curve in x is a probability-curve (of the asymmetric kind){. This theorem may be employed to test * See p. 208. + See note to p. 208. { This proposition may be deduced a prior? {rom the reasoning em- ployed on a former occasion to prove the symmetrical compound law of error (Phil. Mag. 1892, vol. xxxiv. p. 522). The proposition may be verified by integrating (10) with respect to y, between extreme limits ; and obsery- ing that, of the five terms within the brackets, the first two remain unaltered because Sa A pee eee ——— 6 2m dy=1 ; —o V Im the third and fifth terms vanish because he URLS ens eve ran e 2m xydy=0; —o 20 and the third term vanishes because “2 De se Cpe e 2m xXy*dy=m. —o TT Thus the integration with respect to y results in an asymmetrical proba- bility-curve identical with that which has been given in the preceding article (z being substituted for y). Compound Law of Error. 215 whether a given set of observations may be represented by a probability-surface. A more summary test is afforded by observing that an strip (or slice) of the surface (or solid) ought to fulfil the condition that the mean-cube-of-error-the mean-square-of- error raised to the power 2 should besmal]. [or it is zero for a strip of the symmetrical probability-surface ; and the asymmetrical pr obability-surface differs from the symmetrical one only by small terms * The condition is often not fulfilled by actual observations. Take, for instance, the statistics of the frequency of marriages between men and women of different ages. I have else- where + constructed a table which may be translated into a surface such that z represents the probability that, out of the Italian marriageable population, a particular man aged wv should marry a particular woman aged y within two years. Consider one strip of the surface, one row of the table, the one indicating the frequency with which women aged 22-23 marry men of different ages. Utilizing the entries in the table, and, for the extreme ages not represented i in the table, the original materials, I find for the centre of gravity of the row 10°7, reckoned from the age of 16°5 as zero, and for the criterion j—# a figure between 2 and 3. It appears, there- fore, that the number of the elements (in relation to their asymmetry) is not sufficiently great to generate a true probability-surface. Analogous expressions for the compound asymmetrical function of many variables may be constructed by parity of reasoning. * The theorem may be verified by putting y=0 in (10); expressing in terms of the coefficients the integrals i vaedx and xdx; and comparing the latter with the former (raised to the power 2). + Journal of the Royal Statistical Society, March 1894. The table there given does not correspond to the well-known stereogram constructed from the same materials by Signor Perozzo, but purports to be an im- provement upon it. Lb oe 4 XXVI. Graphical Methods for Lenses. By R.8. Coun, MA.* HE following graphical methods, which I have not seen published, may be of interest. They depend on the following geometrical construction :— Fig. 1. A, B F D Let AB and C D be parallel straight lines terminated by BD; let A D and BC intersect in H, and draw H F parallel to AB or CD to meet BD in F; then it can be proved that beat 2 1 He Ae CD: This furnishes a graphical method of compounding reciprocals. Adopting the convention of signs which reckons lengths positive when measured from the surfaces (or with thick lenses from the nodal points) in a direction opposite to that of the incident light, the usual lens formula is LB Me i) Lysol pee wie Weiner? ra rime If uw and fare given and v is required, we must draw AB and CD io scale to represent u and / respectively, and then HF represents v; and, on the other hand, if u and v are given, draw A B and EF to represent them, and from these complete the figure; CD will then give the focal length. Negative values of u, v, and fcan be indicated by drawing the lines corresponding below B D. The diagram exhibits the relative sizes of image and object, * Communicated by the Author. Mr. R. 8. Cole on Graphical Methods for Lenses. 217 for they are in the ratio v:u or HF: AB; the image being direct or inverted according as EHF and AB are or are not on the same side of B D. The construction can also be used for finding the focal length of the lens equivalent to any number of lenses in con- tact, for this is done by adding the reciprocals of the focal lengths. An extension can be made to the case of two lenses sepa- rated by a definite interval a, to find the focal length of the equivalent thick lens and the position of its nodal points. Fig. 2. B i oM D Let AB and CD be parallel and let them represent /, and fo; produce them to E and F so that A H=CF=a. Join AD, BF intersecting in H, and BO, ED inter- secting in K. Draw HL and KM parallel to meet BD in L and M, and let HL cut BC inX and KM cut AD in Y. Then it can be proved that aoe eee KY= i XL=YN= Be Westen atfitfe atfitSs athtfe Hence —H X and KY represent the distances of the nodal points from the two component lenses, and X L or Y M represents the focal length of the equivalent thick lens. Devonport. Phil. Mag. 8. 5. Vol. 41. No. 250. March 1896. Q f 218 4 KRVIL Electro-optical Investigation of Polarized Light. By J. Euster and H. Gutrew*. pee photo-electric current produced in an attenuated gas by illumination of the kathode has been shown to be dependent upon the inclination of the vibrations of light to the plane of the kathode, and to attain a maximum when the plane of polarization of the light is at right angles to the plane of incidence, and a minimum for the position at right angles to thist. aS The further examination of this phenomenon proceéds in two directions :—We may ask, “ According to what law does the photo-electric current vary when the plane of polarization of the incident light is made to rotate about the ray as its axis ?” and we may inquire “ how the intensity of this current depends upon the angle of incidence of the light.” We confine ourselves here for the most part to the first of these questions}: towards the solution of the second (which offers greater difficulties) we can here only make some small contributions. As we have previously remarked, we are led by the diffi- culties which present themselves in the production of polarized ultra-violet light, to choose the fluid alloy of sodium and potas- sium as the photo-electric sensitive surface in an atmosphere of a rarefied indifferent gas, which permits the use of light from the region of the visible spectrum. But this involves the necessity of enclosing the metallic surfaces subjected to experiment in glass vessels. It would be of advantage that the polarized beam of light should enter the vessel normally, through a glass plate with parallel plane surfaces. We should thus avoid all change of intensity in the exciting beam, which with oblique incidence against the glass wall is associated with change of azimuth. But the insertion of such plate-glass “windows” in the glass vessels involves the use of some cement, which must be of such a nature that in presence of vapour of the alkali metals in a vacuum it shall neither evaporate nor undergo any chemical change. We have not succeeded in finding a cement that will stand under these conditions. Organic substances such as resins are out of the question, since they contain volatile constituents which con- dense upon the kathode, forming a layer almost insensitive to light. And such inorganic substances as potassium and sodium * Translated from Ann. Phys, Chem. Bd. lv. Communicated by the Authors. + Elster and Geitel, Sttzber. Berl. Akad. Wiss. vi. p. 184 (1894), and Wied. Ann. lii. p. 440 (1894). t These results have been published in part in Sttzber. der Kgl. Acad. Berlin, xi. p. 209 (1895). Electro-optical Investigation of Polarized Light. 219 silicates, and cements composed of phosphoric acid and me- tallic oxides produce a decrease in sensitiveness to light after a time, probably in consequence of the increase of gas-pressure due to the evolution of hydrogen by the action of metallic vapours on the water contained in the cement. A better result was obtained with molten glacial phosphoric acid if the precaution was taken of covering the joints, immediately after the plate had been cemented on, with zinc oxide which had been washed and ignited, and then covering the joint with a layer of a mixture of wax and resin. It is true that with the apparatus so constructed, the sensitiveness also de- creased for the first few days after sealing-off from the air-pump ; but this falling off soon ceased. We were thus able to construct vessels with windows of parallel glass, which might serve at least for control-experiments. These difficulties induced us to use generally simple glass bulbs (cells) blown before the blowpipe, in which the alkali metal and its vapours were in contact only with the glass walls and the platinum electrodes. For most of the experi- ments here described we employed such bulbs of 50 millim. diameter which were half filled with the alloy of sodium and potassium. Hach ray, therefore, that strikes the centre of this metallic mirror must cut the glass wall at right angles, and its intensity will not vary with the azimuth. The cross section of the beam was therefore made as small as the sensi- tiveness of the cell permitted. 7 In order to obtain a beam of light of small section and great intensity, we obtained a projection lantern (scéopticon) with a _ little disk of zirconia heated in the oxygen-coalgas-flame as source of light. After this had been so adjusted that the image of the piece of zirconia was obtained sharply at a con- siderable distance, a screen with a slit, about 3 millim. long and 1 millim. broad, was placed between the condenser and the projecting lens so that its outline was defined upon the wall of the cell. The sciopticon, which with the screen formed a rigid whole, was capable of rotation in a vertical plane, and in any position could be inclined to the horizontal through about 50° and held fast in that position. If it had such a position that the spot of light which marked the entrance of the ray of light was distinctly seen at A upon the glass wall, then the point of emergence at A’ could also be distinctly recognized. The distances AB and A’B’ of corre- sponding edges of these spots of light from the horizontal surfaces of the fluid metal were measured with a pair of compasses, and the sciopticon and cell were so placed that AB was equal to A’B’. We were thus sure that the ray of light struck the centre of the ae and cut the glass wall at a 9 | 220 MM. Elster and Geitel on the Electro-optical right angle. The point of the anode s was about 10 millim. above M, consisting of a plati- num wire (shown in the figure as a point) whose direction was at right angles to the plane A BA’ B’. The surface of the alkali-metal must be so bright that the place where the light strikes it must appear absolutely black to an eye not in the direction of the reflected ray. Sharper angles of incidence than could be obtained by inclining the sciopticon were obtained by the use of a silver mirror (the metallic side of a piece of plate-glass coated with silver), which rotated about a horizontal axis, and from which the horizontal ray was reflected downwards. In order to determine the angle of incidence of the ray to the horizontal kathode we employed a simple instrument that is also useful in determining the altitude of the sun. From the centre of a quadrant of pasteboard, graduated into half degrees, hangs a plumb-line, the thread of which touches the graduations. In the prolongation of one of the bounding radii of the quadrant across the centre, is placed a pencil at right angles to the plane of the quadrant. The apparatus is so placed that the shadow of the pencil is thrown by the beam of light from the sciopticon in the direction of the radius. The angle of incidence is then equal to the angle between the radius and the thread, and can be read off upon the divided are. | Asin the previously described photo-electric measurements, the cell was placed with the galvanometer previously described in circuit with a battery of 100 to 400 Leclanché cells, of a total H.M.F. of about 450 volts, so that the surface of the alkali-metal was the kathode. The intensity of the photo- electric current was read off with mirror and scale; it is scarcely necessary to observe that the cell was shielded from the light of the lamp used to illuminate the scale, and that no stray light was allowed to escape from the sciopticon. Immediately in front of the cell -was placed a large Nicol’s prism, provided with graduated circle and capable of rotation in horizontal and vertical planes. The cross-section of the beam of light was so cut down by the screen that it traversed the prism freely while it was rotated, as one could easily see by observing the path of the light within the calespar. , If, then, the beam of light, polarized by passing through the Nicol’s prism, fall upon the kathode-surface in the manner described at any incidence other than normal, the galvanometer shows a periodic change of intensity during the rotation of Investigation of Polarized Light. — 221 the Nicol with two maxima and two minima. The maxima occur when the principal section is coincident with the plane of incidence, and the minima in the alternate positions at right angles to the former. If we reckon the angle of rotation @ of the prism from the position of the maxima, for which the plane of polarization of the ray is at right angles to the plane of incidence, and if we denote by J the intensity of the current for the angle a as found from the reading of the galvanometer, then, within the limits of experimental error, the relation between these is expressed by the formula J=Acos?a+Bsin? a, where A denotes the maximum current-intensity (for «=0°), and B the minimum intensity (for 2=90°). In order that this connexion shall be verified without doubt, the positions of maximum and minimum position must be determined with as much sharpness as possible. The changeability of J is, as the nature of the function shows, least in the neighbourhood of a=U° and 4=90°: consequently, it is only possible to _ determine these principal positions by direct experiment with an uncertainty of more than a degree. We therefore pre- ferred to determine the position of the greatest changeability of J, namely, when 2 = 45°. Whilst one of us slowly rotated the Nicol’s prism, the other observed at the gal- vanometer the intensity of the current, and read off the maximum and minimum values A and B. At the same time the corresponding positions of the Nicol were read off on the divided circle. For 2=45°, the formula leads us to expect . the value AeR ae If the Nicol be turned from one of the observed positions _ through 45° we shall always obtain a value of J nearly equal to the calculated value (A+B)/2. By a slow rotation of the _ Nicol we brought it about that this number was actually read off, and regarded the position so obtained as that actually - corresponding accurately to the azimuth 45°. Then, by _ turning on, or back, through 45°, we obtain the corrected principal positions, and obtain for these the old maximum and minimum values A and B again. We must further ‘mention that on rotation of the prism the direction of the emergent beam was not absolutely constant, but there were slight displacements of the positions of entrance and emergence of the beam to be observed on the glass wall (see fig. 1). As there were but very slight changes of direction, and the dis- placements of the spot of light thus produced fel] pretty well within the limits of accuracy of the method of measurement described, we have neglected them. The attempt to eliminate 222 MM. Elster and Geitel on the Electro-optical this source of error by a new adjustment of the ray and cell would have so prolonged the duration of a series of measure- ments, that the change in the zircon-light in the time would, undoubtedly, have proved a source of more serious error. The following Tables contain under I. A—D the values of current-intensity observed with the above-described cell for the angles of incidence 70°, 66°, 40°, 23° for each 15° of azimuth. Table II. gives a series for a cell in which the kathode surface was distant about the half radius from the centre of the glass bulb, III. refers to a receiver with windows of plate-glass. ile Cell I., half-filled with KNa alloy. Azimuth @ vss. | 0. | 15. | 30. | 45. | 60. | 75. | 90. A. Angle of incidence=70°. 27 January, 1895. Current-intensity (observed) .| 149°6| 1388:0| 111°0} 746] -38:9| 12-7) 3-2 Current-intensity (calculated).) 147°3 | 187:°6| 111:°3| 75°2| 389°3| 12:°9| 3-2 ID nigSIRSOVES Sab cdgonecousoscus ooonoC +26] +04) —03) —06| —04| —0-2 B. Angle of incidence = Gn! Current-intensity (observed) .| 144:0| 182°5| 107:0| 72:3) 38:3] 12:5] 4:0 Current-intensity (calculated)} 141°6| 182°4| 107:2| 72:8} 384] 13:2] 4:0 Witterence .isesshewes shtackeeee +2'4) +01) —02} —0-5} —O1] —0°7} ... C. Angle of incidence=40°. Current-intensity (observed) .| 161-3] 149:5| 122:0| 85:9] 47-0] 19:0] 7-1 Current-intensity (calculated)| 161-7] 151°3| 123-1} 845] 45:8] 175) 7-1 Dakorence’s. ek Eee. Oe —04| —1:8) —1-1| 414)-19) Se D. Angle of incidence = 23°. 1 February, 1895. Current-intensity (observed) .| 96:8] 91:8] 79°7| 633] 42:9] 30:0| 281 Ourrent-intensity (calculated)| 97:2} 92:5} 79:9} 62:6] 45:4] 32-7 | 28-1 Difference aruysseescsuiets esr oc aac —04/ —07) —0:2} +07) —2:5| —2:7 _ Investigation of Polarized Light. 223 EL. Cell I1., about + filled with KNa alloy. Angle of incidence = 65°. 31 December, 1894. ATTONE: Os oc0nc snnn0> 0. 15. 30. | 45. | 60. 75. | 90. _— | | | | Current-intensity (observed) .| 1054) 986] 796} 53:8) 280) 87) 21 Current-intensity (caleulated)| 105°5| 986) 79°7) 538] 280| 9:0/ 21 WCE CHEG see oN eNO ape au —01 00} —0O1 0-0 0:0) (=—O3.i.. TLE Cell III., with plate-glass windows. Angle of incidence= 65°. 24 February, 1895. 7AM, erase Soca 0. 15. 30. 45. 60. Dz | 90. a C—O Current-intensity (observed) .| 63°7| 60:1] 485] 33:7) 173] 60] 13 Current-intensity (calculated)| 647) 60:5] 489} 83:0) 17-2| 565) 1:3 ETOCS, az. cone es sexectas —1:0| —04| —0°-4} +0°7| +01] 40:5]... The numbers given as calculated current-intensities are calculated from the formula J=A cos'a+B sin’a in the following manner. The equation may be written =(A—B) cos’ a+B or J—B cos- a A—B= If we subtract the minimum value of B (corresponding to a=90°) from all the other values of J, and divide by the square of the cosine of the corresponding azimuths, we ought to obtain numbers nearly equal. Of these we take the arithmetic mean (M), and write down the numbers obtained from the formula J=M cos’a+B for all azimuths as the calculated current-intensities. As we see from the foregoing tables, the result found wih 224 MM. Elster and Geitel on the Eleetro- optical the cell with parallel glass windows confirms that found with the bulb-shaped ones; and even when the ray directed towards the centre of the kathode-surface cuts the glass wall at an acute angle, as was the case with the cell referred to in Table II., the regularity in the change in value of J is the same. The reason of this is to be found in the fact that the changes in intensity with change of azimuth, which a polarized ray suffers at acute passage through a single surface of glass, are only small even if the angle of incidence differs much from the polarizing angle. _ For angles of incidence less than 40° (Table I. D) as already remarked, the ray was reflected by a silver mirror into the Nicol’s prism. Strictly, we ought to take into account the amount of elliptical polarization due to the reflexion of the light from the silver, which itself would cause a change in the intensity of the light transmitted by the Nicol at different azimuths. But here also the error lies quite within the limits of accuracy of the measurements. Of this we convinced ourselves by measuring the brightness of the emergent beam with a sodium cell with solid kathode at right angles to the ray, during rotation of the Nicol through 90° : it remained almost constant. In order to eliminate the effect of possible change in the zircon-light, the measurement with the first position of the Nicol was repeated after each series of measurements. Only those series were retained in which this control-measurement agreed with the first. The relationship expressed in the above formula between the photo-electric current and the azimuth of the light may be deduced from the assumption, justified by previous experi- ments, that the current-strength is proportional to the intensity of the light, if we make the further assumption that the constant is not the same for light polarized at right angles to the plane of incidence as for light polarized in the plane of incidence. If a denote the amplitude of a polarized ray, whose plane of vibration makes an angle a with the plane of incidence, then the intensities of its components parallel and at right angles to the plane of incidence are respectively a cos aand a*sin°a. The strength of the photo-electric current caused by this ray is therefore J=avcos a+a’y sin’ a, if we represent by w and y the two constants between the intensities of light and current. In this expression, a*x and _a’y are the constants, independent of a, which were denoted above by A and B, A ray of light vibrating in the plane of Investigation of Polarized Light. 225 incidence, therefore, excites a photo-electric current stronger in the ratio «:y or A:B than a ray of equal intensity vibrating in a plane at right angles to the plane of incidence, and therefore parallel to the surface of the kathode. It is easily seen that the ratio A: B must depend upon the angle of incidence. For with normal incidence the position of the plane of incidence is undetermined, and therefore the difference between A and B must disappear. Experiment shows that the common value of the constants for this direction of the rays is comparatively small ; whilst then with increasing angle of incidence A increases rapidly, attaining a maximum at about 60° and then decreasing, B becomes | continually smaller and appears to become zero at a nearly grazing incidence. Thus between 60° and 70° the ratio A: B has the value of about 50:1 (cf. the tables). Experiments, still in progress, make it not improbable that the angle of incidence for which A attains its maximum coincides with the angle of polarization for the potassium-sodium alloy for the most electrically active rays, that is, for the blue rays. It is an obvious suggestion that the different sensitiveness of the metallic kathode-surface to light polarized in and at right angles to the plane of incidence is connected with the greater depth to which, according to Quincke*, the latter penetrates into a metallic surface. We have then the remarkable result that a ray of polarized light exerts a much smaller photo-electric effect at normal incidence than if it strikes the kathode at an acute angle with the plane of polarization at right angles to the plane of inci- dence. But itis to be observed that the like result must follow also with ordinary light, since we may regard this as consisting of two components polarized in planes at right angles, of which one vibrates in the plane of incidence. ‘The one at right angles contributes little to the photo-electric effect at high angles of incidence on account of the smallness of the constant B. In order that this prediction should be verified it is neces- sary that the surface of the kathode should be such a perfect plane as is only attainable by the use of the alkaline metals in the fluid condition. Kathodes of solid sodium or potassium have always a rough crystalline surface, and offer to the light elements of all possible positions. Consequently the increase of the photo-electric current with increasing angle of incidence can only be observed with cells containing fluid kathodes of NaK-alloy, whilst for those with solid kathodes the strength of the current is almost independent of the angle of inci- dence. -_ ® Quincke, Pogg. Ann. cxxix. p. 117 (1866). 226 MM. Elster and Geitel on the Electro-optical This independence is a consequence of the fact that with increasing angle of incidence the surface illuminated increases in the same ratio as the illumination of the unit-surface de- creases. In proof of what has been said, we give the two following series of observations :— Natural Light. 18 Noy. 1894. IT. Solid Metal. I. Liquid Metal. (Surface rough, butas (KNa-alloy.) smooth as possible.) Angle of Incidence 0° ...... 10:2 34:0 “ 33 2D Gees ans 155 33°5 9 ; AD) sense 44:2 33°0 ” 39 OO reere 56°7 30°5 3 9 Oars 8:4 33'1 Since, then, it is possible without the aid of polarization, simply by changing the angle of incidence, to show the in- crease in the photo-electric action of aray of light which takes place when the vibrations of light have a component at right angles to the kathode, it was easy to make the like experi- ment with ultra-violet light ; which, as we remarked at the outset, it is difficult,—possibly impossible with the usual means —to obtain in the condition of linear polarization. We have then the advantage that the kathode may be made of any metallic substance we like, and may be used in the open air. Fig, 2. VLSILIISIILLITI 1A PLL LLL The arrangement of the experiment was as follows (fig. 2) :-— A condenser C was connected with a large inductorium J, the brilliant discharge of which took place between two zinc points S and.8’ in the focus of a Jens Q of quartz. The rays thus made parallel fell upon a plate P of amalgamated zine placed upright, which was capable of rotation over a gYa- duated are K about an axis at right angles to the direction of the rays of light. A wire frame n, n’ connected to earth, and Investigation of Polarized Light. 227 attached to the plate by supports of sealing-wax t, t’, carried a fine copper wire stretched across the space between ¢ and ¢’, When the sparks had passed for a certain time between S and 8’, the ultra-violet light from it withdrew from the plate a greater or smaller quantity—according to the intensity of the light— of the negative charge communicated to it. The fall of potential was observed with an Exner’s electroscope connected to it. From the values V and V’ of the potential before and after illumination, the intensity of the light was calculated by means of the formula J=log V/V’, previously established *. At the beginning of each series of experiments the brightly polished zine plate stood at right angles to the incident rays (a=0°), then the plate was turned through 50° right and then left (2—=-+50°), and finally the initial position was restored. At the beginning the potential was always 258 volts (25 di- visions of the scale of the electroscope); the potentials V’ after 10 seconds’ exposure are given in the following table :— 13 April, 1895. Angle of incidence ............ 0° +50 —50 0 +50 -—50 0 +50 -—50 0 V' in es ie Poot ere coe. To 9 90 7-97-38 91 of the scale. | Series I1....89 79 74 85 80 80 89 735 7:5 9:0 The mean of the observations gives :— For normal incidence V’, =8:9 scale-divisions =117 volts. For oblique incidence V/’,;9=7°7 scale-divisions = 107 volts. Hence for the ratio of the photo-electric action we have J’450 log 258—log 107 J’o log 258—log 117 _ Hence the photo-electric activity of obliquely incident ultra-violet light in the open air is also greater than that of normally incident light, although the differences are much smaller than those found for visible light with alkali- metal surfaces in vacuo. We suspected that this was to be accounted for by the imperfection of the surface of the amal- gamated zinc, and repeated the same experiment with a sur- face of mercury, altering the arrangement of the apparatus so as to suit the condition that the kathode-surface must remain fixed and that the light-ray must now be rotated. But here also the differences were found to lie within the same limits. Consequently either the ratio of photo-electric activity of light polarized parallel and at right angles to the plane of incidence is dependent on the wave-length, so that it ap- proaches to unity for small wave-lengths, or other conditions * Elster and Geitel, Wied. Ann, xlviii. p. 347 (1898). =1'11. 228 MM. Elster and Geitel on the Electro-optical (for example, the difference in pressure) play a part in the phenomenon. Further, induced thereto by the attempts of Herr Wanka* to recognize in the well-known Hertzian experiment of the production of an electric spark by the light of another, the influence of the direction of the vibrations of light to the illuminated kathode, we have looked for a dependence of the same phenomenon on the angle of incidence. The experi- mental arrangement was essentially the same as that already described, only that the action of the light was observed not by the fall of potential of an illuminated surface, but by the discharge of the synchronous, so-called passive spark of a second inductorium in similar phase with the first. The con- denser used with the first is not now required, but it is advisable to connect the second with a Leyden jar in order to give greater intensity to the passive spark, and thus to facili- tate its observation. We have not found any perceptible dif- ference in the action which was clearly recognizable at different angles of incidence (0° and 50°), either with the zinc plate as kathode or with the mercury surface. It is, however, to be remarked that the Hertzian pheno- menon, the resolution of a spark by the ultra-violet illumina- tion of the kathode, is not to be regarded as altogether the same as the scattering of negative electricity in ultra-violet light observed by Herr Hallwachs. This latter is within wide limits proportional to the intensity of the light, and therefore first disappears completely on excluding the light, whilst with the first, for a given distance apart of the elec- trodes, a finite strength of light is necessary and sufficient. On this account the above described experiment would perhaps have given a positive result if the striking distance of the passive spark had each time been adjusted by a micrometer- screw to its maximum value. In regard to the nature of the photo-electric process, the results of the experiments with polarized light on the whole indicate that we have here to do with an immediate action which the light-rays exert by exciting electrical vibrations. In this or a similar sense Herrn Wiedemann and Ebert +, we ourselves {, and Herr Jaumann § have already declared. Yet, * J. Wanka, Mitth. d. deutsch. math. Ges. in Prag. p. 63 (1892). t E. Wiedemann and H. Ebert, Wied. Ann, xxxiii. p. 268, (1888) ; and xxxv. p. 259 (1888). { J. Elster and H. Geitel, Wied. dun. xli. p. 175 (1890), and xliv. p. 736 (1891). § In the above-cited paper of Wanka, p. 58 (1892); also G, Jaumann, Wien, Ber. cxiv., iia. p. 9 (Jan, 1895). Investigation of Polarized Light. 229 if we do not with the first named investigators connect the photo-electrie process with the production of kathode-rays, it remains to be explained why it is limited just to the kathode- surface. To supply this deficiency a further assumption is neces- sary which has recently been made by Prof. J. J. Thomson *, namely, that the kathode-surface in contact with air, or what- ever the gas may be, has a double electric charge, the positive side formed by the molecules of the kathode, the negative by molecules of the gas. If we now imagine that a ray of light so strikes the kathode- surface of metal that the electric displacements in the ray have a component at right angles to the surface, then electric vibrations will be induced in the molecules of the metal in which such a component will also be present. This will cause the place of contact between the molecules of metal and gas, so far as it belongs to the first, to take alternately positive and negative charges in rapid succession. It is perhaps possible that in that phase of the vibrations in which the electric density is negative, the connexion of the metallic molecule with the equally negative gas-molecule may be dissolved in consequence of electrostatic repulsion, and the latter may be driven off into the free gas-space, whilst another that now takes its place communicates positive electricity to the metallic molecule by contact with it, and itself takes a negative charge. This view is supported by the circumstance that alkali- metal cells, which, instead of rarefied hydrogen, contain the much more strongly electro-negative gases oxygen or carbon dioxide, are particularly sensitive to light, and that with similar gaseous atmospheres the sensitiveness to light rises with the electro-positive character of the kathode-metal. We hope to return to these phenomena. It may certainly be urged against the view here expressed, that the photo-electric action does not entirely cease when the electric displacements take place parallel to the kathode- surface, and when consequently the normal component is zero. It appears to us to be of great importance to our knowledge of the photo-electric process to make further investigations into its dependence upon the angle of incidence, using, of course, polarized light. * J. J. Thomson, Phil. Mag. xxxvii. p. 356 (1894). ft 2380.) XXVIII. On the Production of Electrical Phenomena by the - Roéntgen Rays. By Aue. Ricu*. 1. ¥ T is known that the most important properties of the X-rays, that is to say the power of exciting fluor- escence and of acting on photographic preparations (which Rontgen thinks is a secondary effect of the former), belong more especially to the more refrangible of the ordinary rays. Since these, in like manner, are eminently suited to produce photo-electrical properties, I was desirous of examining whether phenomena of this kind would also be produced by the X-rays. As my investigation, though only recently begun, has already given results, I will communicate them to the Academy. For the sake of clearness it is necessary to give a brief account of photo-electric phenomena. 2. A body negatively electrified rapidly loses its charge if exposed to radiations. The rapidity with which the charge is dispersed is greater or less according to the nature of the body and the wave-length of the radiations used. So that, while for most bodies the phenomenon is produced only by the rays of smallest wave-length emitted by the voltaic are (and especially by that produced between carbon and zine or aluminium), or by that of burning magnesium, for some bodies, like amalgamated zinc, the sun’s light is sufficient, and for others, like the alkaline metals, the ordinary artificial lights. I ought more especially to mention here an experimental arrangement, that of the photo-electric couplet. ‘The active radiations fall on a metal disk after passing through wire gauze parallel and close to it, and in connexion with the earth. The radiations dispersing the negative charge which, owing to the difference of potential by contact, the gauze or the disk possesses (they having been placed in contact just before the experiment) produce a deflexion, positive or negative according to circumstances, in an electrometer in connexion with the disk: this deflexion measures sensibly the difference of potential in question f. If, in repeating the experiment, the disk is put further and * Rendiconti dell’ Accademia di Bologna, February 9, 1896. From a separate copy communicated by the Author. t DMem. della R. Acc. di Bologna, series 4, vol. xiv. p. 369; Nuovo Cimento, 1889, vol. xxv. p. 20. t Lbid. page 351. Production of Electrical Phenomena by Réntgen Rays. 251 further away from the gauze, the deflexion increases in ab- solute value if it is positive, and diminishes to zero, or is reversed, if it is negative. The direct cause of this is a phenomenon brought out from my earliest researches on the electrical phenomena of radia- tions: namely, that a discharged body becomes positively charged when it is struck by radiations *. The above phenomenon is expressed by a law which I have established by many experiments, and which can be thus - enunciated: the positive charge of the body on which the radiations fall ceases to increase when the electrical density has attained a certain value, which is constant for a given substance. It follows from this law, that the positive deflexion produced by the radiations becomes smaller if the conductor in con- nexion with the earth is brought gradually nearer the body on which the radiations fall, the capacity of which is thereby increased. Hence to show the positive charge produced by radiations, the body on which they fall should not be too near the uninsulated conductor. In the opposite case, which is that of photo-electric couples, the formation of this final positive charge has almost no influence on the deflexions obtained. 3. In order to examine whether the X-rays disperse the charge of a body electrified negatively, and charge positively an uncharged body, I worked with methods similar to those now described :— (1) I charged a conductor in any given way, and then examined whether its potential, as shown by a quadrant- electrometer in connexion with it, underwent a more rapid diminution than that arising from the usual dispersion of the electric charge when the X-rays fall on it ; or (2) I caused the X-rays to fall on a photo-electric couple and observed whether they produced a deflexion in the electro- meter communicating with the disk, the gauze being put to earth ; lastly, (3) I tried whether those rays falling on an uncharged body produce a positive charge. In combining the most convenient experimental arrange- ments, it was necessary to do so in such a manner that there could be no possibility of any kind of electrical action being produced directly on the electrometer, or on bodies in con- nexion with it, by the apparatus generating the X-rays. I therefore arranged the Crookes’ tubes, together with the coil, the contact-breaker, &c., inside a large metal box in con- * Ibid. page 387; Nuovo Cimento, vol. xxv. p. 128 (1889). 232 Aug. Righi on the Production of Electrical — nexion with the earth. One of the sides of the box is made in chief part of a large lead plate provided with a circular window, in front of which on the inside and ata small distance is that part of a Crookes’ tube which is struck by the kathodic rays. The window may be closed either by a large lead plate or by a thin plate of aluminium. In either case, when the apparatus in the box are at work, no electrical force pro- ceeding from the internal charge of the case is manifested on the outside. } When conductors, electrified or not, are placed in front of the window closed with aluminium, I observed the following phenomena :— 4, If a conductor charged negatively is placed in front of the window, no sooner is the Crookes’ tube at work than the charge rapidly disperses. : If the conductor is uncharged, it becomes positively elec- trified ; and in the same conditions the final charge is dif- ferent according to the nature of the substance : thus, with gas-graphite it is greater than with copper, and with copper greater than with zinc. With the latter metal the deflexion obtained is negative when the distance between it and the aluminium is small enough. This arises from the difference of potential of contact; but at a greater distance the positive charge produced by the X-rays preponderates. In fine, if a photo-electrical couple is placed in front of the’ window, a deflexion of the electrometer is obtained, as if with ultra-violet radiations. I have not yet examined whether this deflexion is exactly equal to that which the latter radia- tions would produce. Hence the X-rays have, in common with the ultra-violet ones, the property of dispersing the negative charge, and of giving rise to positive charges in unelectrified bodies. The electrical action of the X-rays diminishes, as was to be expected, if the bodies on which they act are moved away from the window from which the rays proceed. If a board of pine-wood, or a thick plate of aluminium or of glass, or the hand, is placed so as entirely to cover the aperture, it more or less diminishes the effect produced by the X-rays, but in general does not obscure them completely. A piece of glass-mirror less than a centimetre in thickness absorbs more than pine-wood 6 centim. in thickness. 5. Ultra-violet radiations produce no appreciable action on bodies positively electrified, for if in any case they seem to disperse positive electricity, it may be ascertained that the effect observed was due to the dispersion of negative electricity by the surrounding bodies. Phenomena by the Rontgen Rays. 233 Having given a positive charge to the conductor (gas- graphite, copper, zinc, &.) on which the X-rays fall, I observed the same action as in the case of the negative charge. Accordingly, the X-rays, unlike the ultra-violet ones, produce the dispersion also of bodies electrified positively. Of course, while in the case of an initial positive charge the dispersion ceases when there is on the conductor a charge equal to that which, starting from the neutral state, the rays would impart to it: on the other hand, with an initial negative charge the dispersion continues until the body is discharged, and then the same final result is obtained as it has when the original charge is null or positive. This result may be ex-— pressed by saying that the conductor communicating with the electrometer behaves like an electrode in a conducting medium which acquires the potential of the region in which it is placed, whatever was the initial potential. 6. I desire to call attention to the fact that the new property here mentioned has the advantage of furnishing a means of measuring the X-rays. I believe that to compare the absorp- tion produced by various bodies, it will be better to express this absorption by the velocity of dispersion, rather than by an estimation based on a comparison of the intensity of the shadow projected on a fluorescent screen or on a photographic plate. The new property will evidently have to be taken into account when the time comes for discussing the various hypo- theses proposed to explain the nature of the X-rays. | 7. The following is a lecture-experiment for showing the dispersion of electricity produced by the Réntgen rays. The metal box is dispensed with, retaining only the large lead plate, with the window closed by aluminium. A disk of any metal is placed at a few centimetres from the window on one side of the lead plate, while on the other side is a Crookes’ tube with the apparatus for working it. The disk is connected with a gold-leaf electroscope. The disk being well insulated, a charge of either sign is given to the system —the leaves remain divergent and motionless, but no sooner is the Crookes’ tube at work than they fall and become vertical. If the aperture is closed with a large leaden plate, the phe- nomena are no longer produced. If various other substances are placed against the window, such as the hand, wood, &c., the rate at which the leaves fall is slower. Phil. Mag. 8. 5. Vol. 41. No. 250. March 1896. RB [230 ay XXIX. Notices respecting New Books. Dynamo-Electric Machinery. By S. P. Tuompson, D.Sc., PRS. Fifth Edition. London: H. & F. N. Spon, 1896. a rapid increase in the number of technical applications of Electricity has occasioned the development of many new types of machinery in recent years. Any treatise which aims at giving a complete account of the principles involved in the construction of these machines must therefore grow visibly larger with each new edition. Prof. Thompson’s. work has reached the stage at which a single volume will not contain all the new matter without omitting or condensing part of the text of previous editions; con- sequently he has been obliged to transfer a portion of it to another treatise (‘The Electromagnet’) where it can be more adequately discussed. Hven with this overflow some curtailment of the more theoretical chapters has been found necessary, and it seems evident that the sixth edition, whenever it appears, will be in two volumes. The new matter in the present edition relates mostly to alternate- current machinery ; rotary-field motors have a chapter to themselves ; and the methods of synchronizing alternators to run as two dynamos or as dynamo and motor are described in a separate short section. The volume is enriched by many plates giving details of the construction of typical machines; and the student whose thirst for knowledge on any point cannot be satisfied by the text of the volume may often derive help from the plates, and will find throughout the book copious references to other works. ; J. L. H. Elementary Treatise on Electricity and Magnetism, founded on Joubert’s * Traité Hlémentaire d’Hlectricité’ By G. C. Foster, FL.RS., and HK. Arxinson, Ph.D. London: Longmans, 1896. Tat the French physicists excel in the writing of elementary text-books is evidenced by the great popularity of the treatises by Ganot and Deschanel, the translations of which have passed through very many editions in this country. Although not nearly so well known in England, M. Joubert’s Tratté élémentaire d’ Hlec- tricité has a deservedly high reputation in France: its scope is somewhat wider than that of the other two works, but the subject is treated logically and in a progressive manner throughout. In common with many other text-books, both English and continental, it has, however, the disadvantage of presenting too exclusively the action-at-a-distance character of electric and magnetic attractions, and it does not sufficiently emphasize the importance of the medium which, according to more modern ideas, is the seat of electric force and energy. Undoubtedly, the older view furnishes a beginner with an easy explanation of the simpler phenomena of electrostatics and magnetism, and, once adopted, it can only be discarded with difficulty. Prof. Carey Foster and Dr. Atkinson, taking M. Joubert’s work as a basis, have found much re-writing necessary in their endeavour to present such explanations of all phenomena Intelligence and Miscellaneous Articles. 235 as are consistent with the ideas of Faraday and Maxwell. Familiar terms like charge and current have been retained, but their relation to the ethereal medium is made clear as each arises; by this means the authors have been able to adhere to the order of treatment followed by Joubert. The result is a very satisfactory text-book, with all the advantages that can be imparted to it by teachers of skill and experience. J. L. H. Computation Rules and Logarithms, with tables of other useful functions. By Sitnas W. Horman. New York: Macmillan, 1896; pp. xlv+73. THIs is not a Manual such as the ‘ Manual of Logarithms’ by G. F. Matthews and the ‘ Examples for practice in the use of seven- figure Logarithms’ by Wolstenholme, nor is it conterminous with the ‘Logarithmic Tables’ by Prof. George W. Jones, but-it treats the subject more from the point of view of the engineering and scientific student. This is to be expected from the author’s position of Professor of Physics at the Massachusetts Institute of Technology. The preliminary matter is very clearly put and several practical exercises are worked out. It treats of Rules of Computation (up to date), Logarithms, Antilogs and Cologs, Squares and Square Roots, Reciprocals, the ordinary Trigonometrical Natural and Log Sines, &c., and Slide Wire Ratios (this will be of use to students of physical chemistry). For those who are unacquainted with the terms employed in the previous introduction, definitions and explanations of them are appended. The tables are in the main four-place ones, but space is also devoted to five-place logarithms of numbers and of the Trigono- metrical functions. Prof. Holman has done his work well, and the many contrivances in working and in the printing of the tables evince him to be a thoroughly practical teacher. Wecan accord him no higher praise. XXX. Intelligence and Miscellaneous Articles. BLACK LIGHT. BY M. GUSTAVE LE BON. (Be recent publication of photographic experiments with light of kathodic origin has decided me to make known, though they are still very incomplete, some researches which I have carried on for the last two years in photography through bodies opaque to ordinary light. The two subjects are very different ; only in their results are there some analogies. The following experiments prove that ordinary light, or at any rate some of its radiations, traverses the most opaque bodies without difficulty. Opacity is a phenomenon which only exists for an eye like our own; if it were somewhat differently constructed, we could see through walls. In an ordinary positive photograph-frame place a sensitive plate and above this any ordinary photograph, then above the photograph, 236 Intelligence and Miscellaneous Articles. and in close contact with it, a plate of iron entirely covering the interior of the frame. The plate thus masked by the metal plate is exposed to the light of a petroleum-lamp for about three hours. An energetic and very prolonged development of the sensitive plate carried on to almost complete blackness will give a very pale image of the photograph, but one which is very marked by trans- mitted light. By a slight modification of the preceding experiment, images may be obtained almost as sharp as if no obstacle had been inter- posed between the light and the sensitive plate. Without altering anything in the preceding arrangement, let a plate of lead of any thickness be placed behind the sensitive plate, and its edges bent over until they slightly cover the edges of the iron plate. The sensitive plate is thus enclosed in a sort of metal box, the front part of which consists of an iron plate, the back and the sides being formed of lead. After three hours of exposure to petroleum light, we obtain as before a vigorous image after development. What part does the lead plate play in this second experiment. Provisionally I imagine that the contact of two different metals gives rise to very feeble thermoelectric currents, the action of which adds itself to that of the luminous radiations which have passed through the iron plate. I hope to be able soon to determine the part of the various factors which come into play in producing the preceding results. I hope thus to determine the properties of light after its passage through opaque bodies. The action which might be exerted on the clichés by heat, or that of light stored up, have been entirely eliminated by my experiments. The action of the sun’s light gives the same result as that of petroleum, and does not appear to be much more active. Cardboard and metals, particularly iron and copper, are easily traversed by light. This passage of light through the bodies is only a question of time. If the experiments are repeated in the photographic camera, that is to say, if a metal plate is placed m front of a sensitive plate, and therefore between the latter and the object to be photo- eraphed, on exposure for two hours to the sunlight, an intense blackening is obtained on development, proving the passage of light through the opaque plate, but images are only exceptionally ob- tained and in conditions which I have not yet been able to determine. As they are invisible to the eye, I give the name of black light to those radiations of unknown origin which pass in this way through opaque bodies. Considering the divergences between the numbers of vibrations producing various kinds of energy, such as electricity and light, we may imagine that there are intermediate numbers corresponding to natural forces still unknown. ‘The latter must be connected by imperceptible transitions to the forces we know. The possible forms of energy, although we know very little about them at present, must be infinite in number. Black light perhaps represents one of the forces of which we are ignorant.— Comptes Rendus, Jan. 27, 1896. HE LONDON, EDINBURGH, ayp DUBLIN: PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. ee [FIFTH SERIES.] APRIL 1896. XXXI. On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground. By Prof. Svante ARRHENIUS *. I. Introduction : Observations of Langley on Atmospherical Absorption. A GREAT deal has been written on the influence of the absorption of the atmosphere upon the climate. Tyndail ¢ in particular has pointed out the enormous im- portance of this question. To him it was chiefly the diurnal and annual variations of the temperature that were lessened by this cireumstance. Another side of the question, that has long attracted the attention of physicists, is this: Is the mean temperature of the ground in any way influenced by the presence of heat-absorbing gases inthe atmosphere? TFouriert maintained that the atmosphere acts like the glass of a hot- house, because it lets through the light rays of the sun but retains the dark rays from the ground. This idea was elaborated by Pouillet § ; and Langley was by some of his researches led to the view, that “the temperature of the earth under direct sunshine, even though our atmosphere were present as now, would probably fall to —200° C., if that atmosphere did not possess the quality of selective * Extract from a paper presented to the Royal Swedish Academy of Sciences, 11th December, 1895. Communicated by the Author. t+ ‘Heat a Mode of Motion,’ 2nd ed. p. 405 (Lond., 1865). t Mém. del’ Ac. R. d. Sci. de Inst. de France, t. vii. 1827. § Comptes rendus, t. vii. p. 41 (1838). Phil, Mag. 8. 5. Vol. 41. No. 251. April 1896. S 238 Prof. 8. Arrhenius on the Influence of Carbonic Acid absorption” *. This view, which was founded on_ too wide a use of Newton’s law of cooling, must be abandoned, as Langley himself in a later memoir showed that the full moon, which certainly does not possess any sensible heat- absorbing atmosphere, has a “mean effective temperature ” of about 45° C.f The air retains heat (light or dark) in two different ways. On the one hand, the heat suffers a selective dif- fusion on its passage through the air; on the other hand, some of the atmospheric gases absorb considerable quantities of heat. These two actions are very different. The selective diffusion is extraordinarily great for the ultra-violet rays, and diminishes continuously with increasing wave-length of the light, so that it is insensible for the rays that form the chief part of the radiation from a body of the mean temperature of the earth f. * Langley, ‘ Professional Papers of the Signal Service,’ No. 15. “ Re- searches on Solar Heat,” p. 123 (Washington, 1884). + Langley, “The Temperature of the Moon.” Mem. of the National Academy of Sciences, vol. iv. 9th mem. p. 195 (1890). t Langley, ‘ Prof. Papers,’ No. 15, p. 151. I have tried to calculate a formula for the value of the absorption due to the selective reflexion, as determined by Langley. Among the different formule examined, the following agrees best with the experimental results :— log a=6 (1/A) +e (1/A) *. I have determined the coefficients of this formula by aid of the method of least squares, and have found— b= —0:0463, e= —0:008204. a represents the strength of a ray of the wave-length (expressed in m) after it has entered with the strength 1 and passed through the air-mass 1. The close agreement with experiment will be seen from the following table :— r. a Hee (obs.). a ee (cale.). | Prob. error. 0°358 ps 0904 0-911 0°383 0-920 0°923 0-0047 0-416 0°935 0°934 0-440 0-942 0-941 0-468 0°950 0-947 0:0028 0°550 0:960 0960 0615 0:968 0967 0-781 0-978 0977 0°3870 0982 0-980 0:0017 101 0°985 0-984 1:20 0°987 0987 1:50 0-989 0-990 00011 2°59 0-990 0993 00018 in the Air upon the Temperature of the Ground. 239 The selective absorption of the atmosphere is, according to the researches of Tyndall, Lecher and Pernter, Réntgen, Heine, Langley, Angstrom, Paschen, and others*, of a wholly different kind. It is not exerted by the chief mass of the air, but in a high degree by aqueous vapour and carbonic acid, which are present in the air in small quantities. Further, this absorption is not continuous over the whole spectrum, but nearly insensible in the light part of it, and chiefly limited to the long-waved part, where it manifests itself in very well-defined absorption-bands, which fall off rapidly on both sidest. The influence of this absorption is comparatively small on the heat from the sun, but must . be of great importance in the transmission of rays from the earth. Tyndall held the opinion that the water-vapour has the greatest influence, whilst other authors, for instance Lecher and Pernter, are inclined to think that the carbonic acid plays the more important part. The researches of Paschen show that these gases are both very effective, so that probably sometimes the one, sometimes the other, may have the greater effect according to the circumstances. In order to get an idea of how strongly the radiation of the earth (or any other body of the temperature +15° C.) is absorbed by quantities of water-vapour or carbonic acid in the proportions in which these gases are present in our atmosphere, one should, strictly speaking, arrange experi- ments on the absorption of heat from a body at 15° by means of appropriate quantities of both gases. But such experiments have not been made as yet, and, as they would require very expensive apparatus beyond that at my disposal, I have not been in a position to execute them. J ortunately there are other researches by Langley in his work on ‘ The Temperature For ultra-violet rays the absorption becomes extremely great in accordance with facts, As one may see from the probable errors which I have placed alongside for the least concordant values and also for one value (1°50 »), where the probable error is extremely small, the differences are just of the magnitude that one might expect in an exactly fitting formula. The curves for the formula and for the experimental values cut each other at four points (1/A=2°43, 1:88, 1:28, and 0°82 respectively). From the formula we may estimate the value of the selective reflexion for those parts of the spectrum that prevail in the heat from the moon and the earth (angle of deviation =38 —-36°,\=10-4-24'4 4). We find that the absorption from this cause varies betweeen 0°5 and 1 p. c. for air-mass 1. This insensible action, which is wholly covered by the experimental errors, I have neglected in the following calculations. * Vide Winkelmann, Handbuch der Physik. - + Cf, e.g., Trabert, ee Zeitschrift, Bd. ii, p. 238 (1894), 3 2 240 Prof. 8. Arrhenius on the Influence of Carbonic Acid of the Moon,’ with the aid of which it seems not impossible to determine the absorption of heat by aqueous vapour and by carbonic acid in precisely the conditions which occur in our atmosphere. He has measured the radiation of the full moon (if the moon was not full, the necessary correction relative to this point was applied) at different heights and seasons of the year. ‘This radiation was moreover dispersed in a spectrum, so that in his memoir we find the figures for the radiant heat from the moon for 21 different groups of rays, which are defined by the angle of deviation with a rocksalt prism having a refracting angle of 60 degrees. The groups lie between the angles 40° and 35°, and each group is separated from its neighbours by an interval of 15 minutes. Now the temperature of the moon is nearly the same as that of the earth, and the moon-rays have, as they arrive at the measuring-instruments, passed through layers of carbonic acid and of aqueous vapour of different thickness according to the height of the moon and the humidity of the air. If, then, these observations were wholly comparable with one another, three of them would suffice for calculating the absorption coefficient relatively to aqueous vapour and carbonic acid for any one of the 21 different groups of rays. But, as an inspection of the 24 different series of observations will readily show, this is not the case. The intensity of radiation for any group of rays should always diminish with increasing quantity of aqueous vapour or carbonic acid traversed. Now the quantity of carbonic acid is proportional to the path of the ray through the atmosphere, that is, to the quantity called ‘‘ Air-mass” in Langley’s figures. As unit for the carbonic acid we therefore take air-mass=1, z.e. the quantity of carbonic acid that is traversed in the air by a vertical ray. The quantity of aqueous vapour traversed is proportional partly to the “ air-mass,” partly to the humidity, expressed in grammes of water per cubic metre. As unit for the aqueous vapour I have taken the quantity of aqueous vapour that is traversed by a vertical ray, if the air contains 10 grammes per cubic metre at the earth’s surface *. If we tabulate the 24 series of observations published by Langley in the work cited with respect to the quantities of carbonic acid and aqueous vapour, we immediately detect that his figures run very irregularly, so that very many exceptions are found to the rule that the transmitted heat should continuously decrease when both these quantities increase. * This unit nearly corresponds to the mean humidity of the air (see Table VI. p. 264). in the Avr upon the Temperature of the Ground. 241 And it seems as if periodic alterations with the time of observation occurred in his series. On what circumstance these alterations with the time depend one can only make vague conjectures: probably the clearness of the sky may have altered within a long period of observation, although this could not be detected by the eye. In order to ‘eliminate this irregular variation, | have divided the observations into four groups, for which the mean quantities of carbonic acid (K) and of water-vapour (W) were 1°21 and 0°36, 2°21 and 0°86, — 1:33 and 1:18, and 2°22 and 2°34 respectively. With the help of the mean values of the heat-radiation for every group of rays in these four groups of observations, I have roughly © calculated the absorption coefficients (x and y) for both gases, and by means of these reduced the value for each observation to the value that it would have possessed if K and W had been 1°5 and 0°88 respectively. The 21 values for the different rays were then summed up, so that I obtained the total heat-radiation for every series of observations, reduced to K=1°5 and W=0°88. If the materials of observation were very regular, the figures for this total radiation should not differ very much from one another. In fact, one sees that observations that are made at nearly the same time give also nearly equal values, but if the observations were made at very different times, the values differ also generally very much. For the following periods I have found the egerospende mean values of the total radiation :— Mean Reduction Period. value. factor. L885. Heb. 2l—June 24 .....; 4850 les 1885. July 29-1886. Feb. 16. {344 1:00 1886. Sept. 18-Sept. 18 ...... 2748 2°31 bS8son Oct LI=Nov.:c8 wc... YO) bk eet dane, S=Hebi a 9 .cu.. 3725 1:70 In order to reduce the figures of Langley to comparability with one another, I have applied the reduction factors tabulated above to the observations made in the respective periods. I have convinced myself that by this mode of working no systematic error is introduced into the following calculations. After this had been done,.I rearranged the figures of Langley’s groups according to the values of K and W in the following table. (For further details see my original memoir.) 242 Prof. 8. Arrhenius on the Influence of Carbonic Acid eeeece eevee eercce TABLE I.— Radiation (2) of the Full Moon for | | if | | | | 1-13 0-271 264 25°7 56 1:29 1-04 21:3 21:2 73 1:49 0:87 18:9 20°9 38 151 1-64 18:3 17-9 31 2°26 1:08 16:4 16°6 34 1-93 2°16 15-1 14°5 39-45. | 39-30. | 39°15. 1-12 | 1:16 0-269} 0-32 26°6 | 27-0 34:5 | 29-0 Pinay 1:27 | 1-29 1:07 | 0:86 31-2 | 26-7 97-9 | 25-4 | 135 | 109 | 1:40 | 1:39 0°823) 0-78 28-2. | 23-0 29-4 | 25-4 28 | 25 1:52 | 1-48 2-03 | 1-78 | 27-6 | 24-6 21-4 | 20-2 92 | 5 | 2:26 | 2:96 | 1:08 | 1-08 23-4 | 20:8 25:9 | 21-3 49 | 43 1:92 | 1-92 2:30 | 2:24 128 |148 19-4 |17°3 299 | 35 47 fe) 39. ° fo) 38°45. | 38°30. 1-16 0°32 24'8 24-4 69 1:29 0:86 18:2 21:8 74 1:49 0:89 18:0 186 37 1:48 1°78 27-6 18°5 37 2°26 - ‘1:08 ilikeih 101 23 1-92 2°24 10°3 130 25 1:13 0:271 24°8 23°5 53 1:29 | 1-04 11:0 12°5 38 1:49 0:89 9:2 12:7 17 151 1-95 4:8 5°9 1:16 0°32 12°6 12°5 15) 1:27 0:90 58 86 24 38-15.| 38. 113 | 1-16 0-271) 0-32 20:1 | 43-8 19:4 | 408 Ze lhe | 1-26 | 1-29 0:96 | 0-86 37 1140 12:8 | 264 eae ay 1-49 | 1:50 0:89 | 0-82 144 | 24-6 10:8 | 24-4 23 | 8 151 | 1-48 1-95 | 1:80 36 1176 66 |120 3 | Da 926 | 227 1-08 | 1-06 35 |173 Bl 1147 (Guana ey 245 | 2:37 225 | 2-20 34 | 79 26 | 61 10 | 26 ie) ie) 37°45. | 37°30. 1°13 0-271 65:9 58°0 140 1:27 1:07 32-0 42-1 139 1:49 0:87 348 43-2 70 1°52 2°03 45°5 28°2 37 2:26 1-08 3671 33°9 75 1-92 2°30 20°8 23°4 47 1-16 0:32 744 68:8 206 1-27 1-00 52:3 527 261 1-50 0:84 46:6 55:2 151 1-48 1-67 43-9 40-2 119 2-27 1-06 47°] 48:3 112 2:05 1:93 31:5 in the Arr wpon the Temperature of the Ground. 248 diferent Values of K and W. is) fe) 12) i) | to) fe) ° ° ° ce) 37°15.| 37. | 36°45. | 86°80. | 36:15.| 36. | 35°45. | 35°30. | 35°15.| -35. —— ef i — ga 1:16 | 1:16 | 1:18] 1:18 | 1:27] 1:16] 1-27 12% 1 Ea L-16 ee 0-32 | 032 | 0:34 | 0°34 | 0-48 | 0:32 | 0-48 | 0-48 | 0-48 | 0:32 éobs..../686 | 59 |562 |483 |434 |40:7 |390 |326 |31'5 119-7 éeale....)73°7 [571 1509 |460 |349 |36-4 {31:3 [27-7 |27-3 |19°3 pa) 190 | tes | fis loz" 98. ng a5! oy 20) aa Oe 1:27 | 1-27 | 1°31 | 1:39 | 1:82 | 1:28 | 1:33] 1:33 | 1:33 | 1-25 ‘aoe 1:00 | 1:00 | 1:05 | 1:00 | 1:00 | 0-81 | 051 | 051 | 1:07 | 0-60 4 obs. ...\989 |503 |479 |412 (317 (297. (257 |188 |27°5 |166 Zcale,...,53°0 {51:2 |471 {392 |34:2 /31:1 |30°3 |268 {21:3 |17-2 C Sane 294 | 251 205 | 140 108 98 16 12 39 22 Lae 1-49 | 1:48 | 148 |] 148; 141 | 1:45 | 141] 141 | 1:41) 1:41 ae 0-87 | 085 | 0:85 | 0°85 | 0-97.) 089 | 097 | 0:98 | 0:98 | 0-98 i obs....,43°1 | 364 (35-4 (31:2 |283 |249 |166 |15°4 |10°3 9:2 icale....)55°2 {47:1 |425 |363 |33°0 |29°3 | 27:3 | 22:3 | 22-0 147 Cr veces: Sr | 149 146 127 54 78 32 29 19 lia LS Seren 1-48 | 148 | 1:48} -148 |) 148) 1:48 | 148 | 148 | 148) 1-48 Vi Sire 1:66 | 158 | 1:66 | 166] 183] 166 | 1:83 | 158 | 183 | 1°66 i obs....,47°5 |48°7 |45°8 |3845 (35:0 (275 |28-7 1214 |17-4 | 15-4 deale....,388°2 |434 |42:5 |33:0 [32°00 |236 |234 |178 |154 |116 (ieee cme okie 99.7) S279 | 67 |) Sik 41 | 48 Kee 8 2:26 | 2:12 | 1-91 | 1:90 | 1:91 | 2:09 | 1:91 | 1:90 | 1:90 | 2:12 LO tis Wet ao tie) 110. 118) 1:10) 1-10 1k | 1-15 i obs ...,44°6 |32°0 |27°3 |247 |266 |245 {19:0 |16-:0 |13:9 | 10-1 ieale,...,471 |3835 |382°3 (27:4 |268 |236 |21°3 |17°5 |204 |12°2 (Cees 93 98 66 58 63 72 45 oT 32 31 Aaa PO 2.05 2450) 2:37 \ 24d) 23e | Eon | Lon). Lon), Lon IW anor 2°30 | 1:93 | 2:25 | 2°20 | 2°25 | 2:20 | 2:33 | 2°33 | 2°33 | 2°33 i obs....|247 |33°2 [267 {194 |226 |188 |164 |10-9 |12-1 79 Realtones 2rbaole lag | 184 (214 IGS tee (ito |122 1.84 Gig soak: 56 Maree Maris 63 65 61 32 22 24 16 244 Prof. 8. Arrhenius on the Influence of Carbonic Acid In this table the angle of deviation is taken as head-title. After K and W stand the quantities of carbonic acid and water-vapour traversed by the ray in the above-mentioned units. Under this comes after 7 obs. the intensity of radiation (reduced) observed by Langley on the bolometer, and after this the corresponding value calc., calculated by means of the absorption-coeflicients given in Table II. below. G is the “weight” given to the corresponding 7 obs. in the calculation, using the method of least squares. For the absorption-coefficients, calculated in this manner, I give the following table. (The common logarithms of the absorption-coefiicients are tabulated.) TaBLE [].—Absorption-Coeficients of Carbonic Acid (x) and Aqueous Vapour (y). Angle of Deviation. log x. log y. A. 0 +.0:0286 —0°1506 Be { 0-0000 ~ 01455 | Me 39°45 —0-0296 —0°1105 34:5 39:30 —0:0559 ~0-0952 29:6 39:15 ~0°1070 —0:0862 26-4 39:0 —0'3412 ~0-0068 275 38°45 —0-2035 ~0-3114 24:5 38:30 —0-2438 ~ 0-2362 135 38°15 —0:3760 —0:1933 21-4 38:0 —0°1877 ~ 03198 44-4 87-45 —0:0931 ~0-1576 59:0 37-30 —0-0280 ~0°1661 70-0 3715 —0-0416 — 02036 755 37-0 —0:2067 —0-0484 62-9 —0-2465 +-0:0008 | 2 { — 02466 fin ono nbd 36:30 —0:2571 —0:0507 51-4 ; —0:1708 +.0:0065 SOS ~0°1652 too000 f 30:1 36-0 —0-0940 —0-1184 879 35°45 —0-1992 ~0:0628 36:3 35:30 —0:1742 ~0°1408 32:7 35°15 —0-0188 ~ 01817 29:8 35:0 —0:0891 —0"1444 21°9 The signification of these figures may be illustrated by an If a ray of heat, corresponding to the angle of deviation 39°-45, passes through the unit of carbonic acid, it de- example. in the Air upon the Temperature of the Ground. 245 creases in intensity inthe proportion 1 : 0°934 (log = —0-0296), the corresponding value for the unit of water-vapour is 1:0°775 (log=—0°1105). These figures are of course only valid for the circumstances in which the observations were made, viz., that the ray should have traversed a quantity of carbonic acid K=1°1 and a quantity of water-vapour W=0°3 before the absorption in the next quantities of carbonic acid and water-vapour was observed. And these second quantities should not exceed K=1'1 and W=1°8, for the observations are not extended over a greater interval than between K=1-1 and K=2°2, and W=0'3 and W=2:1 (the numbers for K and W are a little different for rays of different kind). Below A is written the relative value of the intensity of radiation for a given kind of ray in the moonlight after it has traversed K=1 and W=0°'3. In some cases the calculation gives positive values for log w or log y. As this is a physical absurdity (it would signify that the ray should be strength- ened by its passage through the absorbing gas), I have in these cases, which must depend on errors of observation, assumed the absorption equal to zero for the corresponding gas, and by means of this value calculated the absorption- coefficient of the other gas, and thereafter also A. As will be seen from an inspection of Table I., the values of 2 obs. agree in most cases pretty well with the calculated values zcale. But in some cases the agreement is not so good as one could wish. These cases are mostly characterized by a small “weight” G, that is in other words, the material of opserva- tion is in these cases relatively insufficient. These cases occur also chiefly for such rays as are strongly absorbed by water-vapour. This effect is probably owing to the circum- stance that the aqueous vapour in the atmosphere, which is assumed to have varied proportionally to the humidity at the earth’s surface, has not always had the assumed ideal and uniform distribution with the height. From observations made during balloon voyages, we know also that the dis- tribution of the aqueous vapour may be very irregular, and different from the mean ideal distribution. It is also a marked feature that in some groups, for instance the third, nearly all the observed numbers are less than the calculated ones, while in other groups, for instance the fourth, the contrary isthe case. This circumstance shows that the division of the statistic material is carried a little too far; and a combi- nation of these two groups would have shown a close agreement _between the calculated and the observed figures. As, how- ever, such a combination is without influence on the correct- ness of the calculated absorption-coefticients, I have omitted 246 Prof. 8. Arrhenius on the Influence of Carbonic Acid a rearrangement of the figures in greater groups, with con- sequent recalculation. A circumstance that argues very greatly in favour of the opinion that the absorption-coefficient given in Table II. cannot contain great errors, is that so very few logarithms have a positive value. If the observations of Langley had been wholly insufficient, one would have expected to find nearly as many positive as negative logarithms. Now there are only three such cases, viz., for carbonic acid at an angle of 40°, and for water-vapour at the angles 36°45 and 36°15. The observations for 40° are not very accurate, because they were of little interest to Langley, the corre- sponding rays not belonging to the moon’s spectrum but only to the diffused sunlight from the moon. As these rays also do not occur to any sensible degree in the heat from a body of 15° C., this non-agreernent is without importance for our problem. The two positive values for the logarithms belong- ing to aqueous vapour are quite insignificant. They correspond only to errors of 0*2 and 1:5 per cent. for the absorption of the quantity W=1, and fall wholly in the range of experi- mental errors. It is certainly not devoid of interest to compare these absorption-coefficients with the results of the direct observa- tions by Paschen and Angstrom*. In making this com- parison, we must bear in mind that an exact agreement cannot be expected, for the signification of the above co- efficients is rather unlike that of the coefficients that are or may be calculated from the observations of these two authors. The above coefficients give the rate of absorption of a ray that has traversed quantities of carbonic acid (K=1-1) and water-vapour (W =0:3); whilst the coefficients of Paschen and Angstrém represent the absorption experienced by a ray on the passage through the first layers of these gases. In some cases we may expect a great difference between these two quantities, so that only a general agreement can be looked for. According to Paschen’s figures there seems to exist no sensible emission or absorption by the aqueous vapour at wayve-lengths between 0°9y and 1°2 (corresponding to the angle of deviation 40°). On the other hand, the representa- tion of the sun’s spectrum by Langley shows a great many * Paschen, Wied. Ann. 1. p. 409, 1893; li. p. 1, li. p. 209, and liii. p. 334, 1894, especially vol. 1.,tab. ix. fig. 5, curve 1 for carbonic acid, curve 2 for aqueous vapour, Angstrom, Bihang till K. Vet-Ak, Hand- lingar, Bd. xv. Afd. 1, No. 9, p. 15, 1889; Ofversigt af K. Vet.-Ak, Forhandl. 1889, No. 9, p. 558, ; in the Air upon the Temperature of the Ground. 247 strong absorption-bands in this interval, among which those marked p, o, 7, and ¢ are the most prominent*, and these absorption-bands belong most probably to the aqueous vapour, That Paschen has not observed any emission by water-vapour in this interval may very well be accounted for by the fact that his heat-spectrum had a very small intensity for these shori-waved rays. But it may be conceded that the absorption- coefficient for aqueous vapour at this angle in Table II. is not very accurate (probably too great), in consequence of the little importance that Langley attached to the ccrresponding observations. After this occurs in Langley’s spectrum the great absorption-band yf at the angle 39°45 (A=1-4 w), where in- Paschen’s curve the emission first becomes sensible (log y= —0°1105 in Table II.). At wave-lengths of greater value we find according to Paschen strong absorption-bands at A=1°83 w (O in Langley’s spectrum), 7. e. in the neigh- bourhood of 89°30 and atA = 2°64 pw (Langley’s X) a little above the angle 89°15. In accordance with this I have found rather large absorption-coefficients for aqueous vapour at these angles (log y= —0°0952 and —0-0862 resp.). From A=3'0p to X=4'7 w thereafter, according to Paschen the absorption is very small, in agreement with my calculation (log y= —0-0068 at 39°, corresponding to A=4°3 w). From this point the absorption increases again and presents new Maxima ab A=9'D\u, A=6:6 p, and. A=7'7 p, z.e. in the vicinity of the angles 38°°45 (A=0°6 yw) and 38°30 (A=7 1p). In this region the absorption of the water-vapour is con- tinuous over the whole interval, in consequence of which the great absorption-coefficient in this part (log y= —0°3114 and — (2362) becomes intelligible. In consequence of the de- creasing intensity of the emission-spectrum of aqueous vapour in Paschen’s curve we cannot pursue the details of it closely, but it seems as if the emission of the water-vapour would also be considerable at X=8°7 pw (89°:15), which corresponds with the great absorption-coefficient (log y= —0°1933) at this place. The observations of Paschen are not extended further, ending at X= 9:5 w, which corresponds to an angle of 39°-08. For carbonic acid we find at first the value zero at 40°, in agreement with the figures of Paschen and Angstrémf. The absorption of carbonic acid first assumes a sensible value at * Langley, Ann. Ch. et Phys. sér. 6, t, xvii. pp. 823 and 326, 1889, Prof. Papers, No. 15, plate 12. Lamansky attributed his absorption-bands, which probably had this place, to the absorbing power of aqueous vapour (Pogg. Ann. cxlvi. p. 200, 1872). + It must be remembered that at this point the spectrum of Paschen -was very weak, so that the coincidence with his figure may be accidental, 248 ~=Prof. S. Arrhenius on the Injluence of Carbonic Acid | X=1'5 w, after which it increases rapidly to a maximum at XN=2°6 w, and attains a new extraordinarily,strong maximum at N=4'6 (Langley’s Y). According to Angstrém the ab- sorption of carbonic acid is zero at X=0°9 w, and very weak at NX=1°69 yw, after which it increases continuously toA=4°6 w and decreases again toA=6:0y. This behaviour is entirely in agreement with the values of logw in Table II. From the value zero at 40° (W=1:0y) it attains a sensible value (—0°0296) at 39°°45 (X=1'4 u), and thereafter greater and greater values (—0°0559 at 39°30, and —0-1070 at 39°15) till it reaches a considerable maximum (—0°3412 at 39°, A=4'3y). After this point the absorption decreases (at 38°°45=5°'6 w, log «= —0°2035). According to Table II. the absorption of carbonic acid at 88°30 and 38°15 (A=#T yu and 87) has very great values (log v= —0°2438 and —0(°3780), whilst according to Angstrém it should be insensible. This behaviour may be connected with the fact that Angstrém’s spectrum had a very small intensity for the larger wave- lengths. In Paschen’s curve there are traces of a continuous absorption by the carbonic acid in this whole region with weak maxima at A=5'2 w, A=5'9 w, A=6'6 w (possibly due to traces of water-vapour), A=8'4 w, and A=89 w. In consequence of the strong absorption of water-vapour in this region of the spectrum, the intensity of radiation was very small in Langley’s observations, so that the calculated ab- sorption-coefficients are there not very exact (¢/. above, pp. 242-243). Possibly the calculated absorption of the car- bonic acid may have come out too great, and that of the water-vapour too small in this part (between 38°30 and 38°-0). This can happen the more easily, as in Table I. K and W in general increase together because they are both propor- tional to the ‘air-mass.” It may be pointed out that this also occurs in the problems that are treated below, so that the error from this cause is not of so great importance as one might think at the first view. For angles greater than 388° (A>9°5m) we possess no direct observations of the emission or absorption of the two gases. The sun’s spectrum, according to Langley, exhibits very great absorption-bands at about 37°50, 37°:25, 37°, and 36°°40°. According to my calculations the aqueous vapour has its greatest absorbing power in the spectrum from 38° to 35° at angles between 37°15 and 37°45 (the figures for 35°°45, 35°:30, and 35°15 are very uncertain, as they de- pend upon very few measurements), and the carbonic acid between 36°:30 and 37°-0. This seems to indicate that the first two absorption-bands are due to the action of water- G.| in the Air upon the Temperature of the Ground. 249 vapour, the last two to that of carbonic acid. It should be emphasized that Langley has applied the greatest diligence in the measurement of the intensity of the moon’s radiation at angles between 36° and 38°, where this radiation possesses its maximum intensity. It may, therefore, be assumed that the calculated absorption-coefficients for this part of the spectrum are the most exact. This is of great importance for the fol- lowing calculations, for the radiation from the earth* has by far the greatest intensity (about two thirds, of. p. 250) in this portion of the spectrum. II. The Total Absorption by Atmospheres of Varying : Composition. As we have now determined, in the manner described, the values of the absorption-coefficients for all kinds of rays, it will with the help of Langley’s figures be possible to cal- culate the fraction of the heat from a body at 15° C. (the earth) which is absorbed by an atmosphere that contains specified quantities of carbonic acid and water-vapour. To begin with, we will execute this calculation with the values K=1 and W=0'3. We take that kind of ray for which the best deter- minations have been made by Langley, and this lies in the midst of the most important part of the radiation (37°). For this pencil of rays we find the intensity of radiation at K=1 and W =0'3 equal to 62:9; and with the help of the absorption- coefficients we calculate the intensity for K=0 and W=0, and find it equal to 105. Then we use Langley’s experiments on the spectral distribution of the radiation from a body of 15° C., and calculate the intensity for all other angles of devia- tion. These intensities are given under the heading M. After this we have to calculate the values for K=1 and W=U'3. For the angle 37° we know it to be 62:9. For any other angle we could take the values A from Table II. if the moon were a body of 15° C. But a calculation of the figures of Very{ shows that the full moon has a higher temperature, about 100° C. Now the spectral distribution is nearly, but not quite, the same for the heat from a body of 15° C. and for that from one of 100°C. With the help of Langley’s figures it is, however, easy to reduce the intensities for the hot body at 100° (the moon) to be valid for a body at 15° a After having been sifted through an atmosphere of K=1+1 and =0°3. | + ‘Temperature of the Moon,’ plate 5. t “The Distribution of the Moon’s Heat,” Utrecht Society of Arts and Se. The Hague, 1891. 250 Prof. 8S. Arrhenius on the Influence of Curbonic Acid (the earth). The values of A reduced in this manner are tabulated below under the heading N. tl Angle...40°. 3945. 39°30. 39:15. 390. 38°45. 38:30. 38:15. 38:0. 37-46. 37am Mie: 4 ALG 1248 onary St0r 127 SIGE 189 210 210 188 Nero: Sl oO L: (2 ideey “elssie Sw 181 112. 196 444 59 70 Angle...387° 15. 37:0. 36°45. 3630. 3615. 36:0. 35°45. 35°30. 35°15. 35°0. Sum. P.c. NE tceas 147 105 103 99 GUI il 65 62 43 39 2023 100 IN oes 755- 62°9 564. 51-4 - 397 37-9 39°2> 376 36:0 -289 a (45 2eeee 2 For angles less than 37° one finds, in the manner above described, numbers that are a little inferior to the tabulated ones, which are found by means of the absorption-coefficients of Table LI. and the values of N. In this way the sum of the M’s is a little greater (6°8 per cent.) than it would be accord- ing to the calculation given above. This non-agreement results probably from the circumstance that the spectrum in the observations was not quite pure. The value 37:2 may possibly be affected with a relatively great error in consequence of the uncertainty of the M-values. In the following calculations it is not so much the value 37°2 that plays the ‘important part, but rather the diminution of the value caused by increasing the quantities K and W. For comparison, it may be mentioned that Langley has estimated the quantity of heat from the moon that passed through the atmosphere (of mean composition) in his researches to be 38 per cent.* As the mean atmosphere in Langley’s observa- tions corresponded with higher values of K and W than K=1 and W=0°, it will be seen that he attributed to the atmo- sphere a greater transparence for opaque rays than I have done. In accordance with Langley’s estimation, we should expect for K=1 and W=0:3 a value of about 44 instead of 37°2. How great an influence this difference may exert will be investigated in what follows. The absorption-coefficients quoted in Table II. are valid for an interval of K between about 1*1 and 2°25, and for W between 0°3 and 2°22. In this interval one may, with the help of those coetticients and the values of N given above, calculate the value of N for another value of K and W, and so in this way obtain by means of summation the total heat that passes through an atmosphere of given condition. For further calculations I have also computed values of N for atmospheres that contain greater quantities of carbonic acid and aqueous vapour. These values must be considered as extrapolated. In the following table (Table III.) I have given these values of N. The numbers printed in italics are found directly in the manner * Langley, ‘Temperature of the Moon,’ p. 197. in the Air upon the Temperature of the Ground. 2051 described, those in ordinary type are interpolated from them with the help of Pouillet’s'exponential formula. The table has two headings, one which runs horizontally and represents the quantity of aqueous vapour (W), and another that runs verti- cally and represents the quantity of carbonic acid (K) in the atmosphere. “Foren cl ead es pid OANA. | toa 103. | 05. | 10: | 15. | 20. 30. | 40. | 60. | 100. | 2 | | i | } / (kts BEC EE ae ee SD: Eee realness 1 87-2 a5 0 807 | 26-9" | 29-9 | 19-8 | 160+) 107-1 8:9. 12 | 847 132-7 | 286) 25-1 | 222 1178 | 147.) 97>) 80 15 | 315 | 29-6 | 259 | 226 | 199 | 159 | 130 | 84 | 649 | | 2 | 270 | 263 | ar9 | 9:1 | 167 | 131 | 105 | 66 | 53 | ea) as ero | 19'O- | IGG a4 Ptr-0 | 87") 3) 4-2 lp e8 ZOE ABE: | Ve hte Fs) IES 9B. 74. AD | BS. | fe: Set VLT WOO oes, 7e | 6 | 81 | 20 | er. G ote aro es | Pe TS | £9 | 0:98 | |- 10 pe POG ET peso e431 35) 2) 48 |) 101 0-26 20 Pr See Aled 8 le Wy) 0%) \20-75 |2- 039 |, 0-07 40 088| 081} 067) 056| 046 0-82) 024) 0-12| 0-02 Fe a SN NDS eS a ee Quite different from this dark heat is the behaviour of the heat from the sun on passing through new parts of the earth’s atmosphere. The first parts of the atmosphere exert without . doubt a selective absorption of some ultra-red rays, but as soon as these are extinguished the heat seems not to diminish as it traverses new quantities of the gases under discussion. This can easily be shown for aqueous vapour with the help of Langley’s actinometric observations from Mountain Camp and Lone Pine in Colorado*. These observations were executed at Lone Pine from the 18th of August to the 6th of September 1882 at 7° 15™ and 7° 45™ a.m., at 11° 45™ a.m. and 12° 15” p.m., and at 4°15" and 4°45" p.m. At Mountain Camp the observations were carried out from the 22nd to the 25th of August at the same times of the day, except that only one observation was performed in the morning (at 8" 0"), [ have divided these observations into two groups for each station according to the humidity of the air. In the following little table are quoted, first the place of observation, and after this under D the mean date of the observations (August 1882), under W the quantity of water, under I the radiation observed by means of the actinometer, under I, the second observation of the same quantity. * Langley, ‘Researches on Solar Heat,’ pp. 94, 98, and 177. 252 Prof. 8S. Arrhenius on the Influence of Carbonic Acid At a very low humidity (Mountain Camp) it is evident that the absorbing power of the aqueous vapour has an influence, for the figures for greater humidity are (with an insignificant exception) inferior to those for less humidity. But for the observations from Lone Pine the contrary seems to be true. It is not permissible to assume that the radiation can be strengthened by its passage through aqueous vapour, but the observed effect must be caused by some secondary circum- stance. Probably the air is in general more pure if there is more water-vapour in it than if there is less. The selective diffusion diminishes in consequence of this greater purity, and this secondary effect more than counterbalances the insignificant absorption that the radiation suffers from the increase of the water-vapour. It is noteworthy that Hlster and Geitel have proved that invisible actinic rays of very high refrangibility traverse the air much more easily if it is humid than if itisdry. Langley’s figures demonstrate mean- while that the influence of aqueous vapour on the radiation from the sun is insensible as soon as it has exceeded a value of about Ov4. Probably the same reasoning will hold good for car- bonic acid, for the absorption spectrum. of both gases is of the same general character. Moreover, the absorption by car- bonic acid occurs at considerably greater wave-lengths, and consequently for much less important parts of the sun’s spectrum than the absorption by water-vapour*. It is, therefore, justifiable to assume that the radiation from the sun suffers no appreciable diminution if K and W increase from a rather insignificant value (K=1, W=0-4) to higher ones. Before we proceed further we need to examine another question. Let the carbonic acid in the air be, for instance, the same as now (K=1 for vertical rays), and the quantity of water-vapour be 10 grammes per cubic metre (W=1 for *® Cf. above, pages 246-248, and Langley’s curve for the solar spec- trum, Ann. d. Ch. et d. Phys. séx. 6, t. xvil. pp. 823 and 326 (1889) ; ‘ Prof. Papers,’ No. 15, plate 12. Morning. Noon. Evening, = =a ae Pea eee =~ a SSS DD. Wee ey ie Dee ls | LL: D. W. ee Lae 29°3 O61 1:424 oe ee 0-46 1:692 1°715) ) 266 0°51 1-417 1351 | Pine 2I*1 084 1:458 1583 [2679 0-59 1-699 1-721 | 23°2 O'74 1428 1-359 j Mountain f 23:5 0-088 1°790 | “aye 0-182 1-904 1873) { 245 0-205 1-701 1:641 Camp. | 23°5 0153 1-749 f (24:5 0-245 1-890 1917 § | 22°5 0°32 1-601 1597 in the Air upon the Temperature of the Ground. 253 vertical rays). Then the vertical rays from the earth traverse the quantities K=1 and W=1; rays that escape under an angle of 30° with the horizon (air-mass=2) traverse the quantities K=2, W=2; andsoforth. The different rays that emanate from a point of the earth’s surface suffer, therefore, a different absorption—the greater, the more the path of the ray declines from the vertical line. It may then be asked how long a path must the total radiation make, that the absorbed traction of it is the same as the absorbed fraction of the total mass of rays that emanate to space in different directions. For the emitted rays we will suppose that the cosine law of Lambert holds good. With the aid of Table ILI. we may calculate the absorbed fraction of any ray, and then sum up the total absorbed heat and determine how great a fraction it is of the total radiation. In this way we find for our example the path (air-mass) 1°61. In other words, the total absorbed part of the whole radiation is just.as great as if the total radiation traversed the quantities 1°61 of aqueous vapour and of carbonic acid. ‘This number depends upon the composition of the atmosphere, so that it becomes less the greater the quantity of aqueous vapour and carbonic acid in the air. In the following table (1V.) we find this number for different quantities of both gases. TasLe [V.—Mean path of the Earth’s rays. (0, gus be eo, 1, 2. 3, 0-67 169 | 168 1-64 157 1:53 1 1-66 165 161 1:55 1-51 15 1-62 | 1-61 Tar gn a eas): 1-47 oe 1:58 L-57 152 | 146 | 148 At Dalal oeille| Sites Wea Wedge 8 Oya 3 152 151 147 1-44 140 3-5 1-48 1-48 1-45 1-42 | If the absorption of the atmosphere approaches zero, this number approaches the value 2. Phil. Mag. 8. 5. Vol. 41. No, 251. April 1896. E 254 Prof. 8. Arrhenius on the Influence of Carbonic Acid Ill. Thermal Equilibrium on the Surface and in the Atmosphere of the Harth. As we now have a sufficient knowledge of the absorption of heat by the atmosphere, it remains to examine. how the temperature of the ground depends on the absorptive power of the air. Such an investigation has been already performed — by Pouillet*, but it must be made anew, for Pouillet used hypotheses that are not in agreement with our present knowledge. In our deductions we will assume that the heat that is con- ducted from the interior of the earth to its surface may be wholly neglected. If a change occurs in the temperature of the earth’s surface, the upper layers of the earth’s crust will evidently also change their temperature ; but this later pro- cess will pass away in a very short time in comparison with the time that is necessary for the alteration of the surface temperature, so that at any time the heat that is transported from the interior to the surface (positive in the winter, nega- tive in the summer) must remain independent of the small secular variations of the surface temperature, and in the course of a year be very nearly equal to zero. Likewise we will suppose that the heat that is conducted to a given place on the earth’s surface or in the atmosphere in consequence of atmospheric or oceanic currents, horizontal or vertical, remains the same in the course of the time con- sidered, and we will also suppose that the clouded part of the sky remains unchanged. It is only the variation of the temperature with the transparency of the air that we shall examine. All authors agree in the view that there prevails an equi- librium in the temperature of the earth and of its atmosphere. The atmosphere must, therefore, radiate as much heat to space as it gains partly through the absorption of the sun’s rays, partly through the radiation from the hotter surface of the earth and by means of ascending currents of air heated by contact with the ground. On the other hand, the earth loses just as much heat by radiation to space and to the atmosphere as it gains by absorption of the sun’s rays. If we consider a given place in the atmosphere or on the ground, we must also take into consideration the quantities of heat that are carried to this place by means of oceanic or atmo- spheric currents. For the radiation we will suppose that * Pouillet, Comptes rendus, t. vil. p. 41 (1838). in the Air upon the Temperature of the Ground. 255 Stefan’s law of radiation, which is now generally accepted, holds good, or in other words that the quantity of heat (W) that radiates from a body of the albedo (1—v) and tempera- ture T (absolute) to another body of the absorption-coefficient 8 and absolute temperature @ is W=v6y(T!—6'), where y is the so-called radiation constant (1:21.10—” per sec. and cm.”). Empty space may be regarded as having the absolute temperature 0*. Provisionally we regard the air as a uniform envelope of the temperature @ and the absorption-coefficient @ for solar heat; so that if A calories arrive from the sun in a column of 1 cm.* cross-section, eA are absorbed by the atmosphere and (1—a)A reach the earth’s surface. In the A calories there is, therefore, not included that part of the sun’s heat which by means of selective reflexion in the atmosphere is thrown out towards space. Further, let @ designate the absorption- coefficient of the air for the heat that radiates from the earth’s surface ; 8 is also the emission-coefficient of the air for radia- tion of low temperature—strictly 15°; but as the spectral distribution of the heat varies rather slowly with the tempe- rature, 8 may be looked on as the emission-coefficient also at the temperature of the air. let the albedo of the earth’s crust be designated by (l—v), and the quantities of heat that are conveyed to the air and to the earth’s surface at the point considered be M and N respectively. As unit of time we may take any period: the best choice in the following calcu- lation is perhaps to take three months for this purpose. As unit of surface we may take 1 cm.”, and for the heat in the air that contained in a column of 1 cm.’ cross-section and the height of the atmosphere. The heat that is reflected from the ground is not appreciably absorbed by the air (see p. 252), for it has previously traversed great quantities of water-vapour and carbonic acid, but a part of it may be returned to the ground by means of diffuse reflexion. Let this part not be included in the albedo (1—v). yy, A,v, M,N, and a are to be considered as constants, 8 as the independent, and @ and T as the dependent variables. Then we find for the column of air By@t=Byv(T'—-@4)+aA+M. .-.. (1) The first member of this equation represents the heat * Langley, ‘Prof. Papers,’ No. 15, p. 122. “The Temperature of the : wangley 1 Pp 1 Moon,” p. 206. T?2 956 Prof. S. Arrhenius on the Influence of Carbonic Acid radiated from the air (emission-coefficient 8, temperature @) to space (temperature 0). The second one gives the heat radiated from the soil (1 cm.?, temperature T, albedo 1—v) to the air; the third and fourth give the amount of the sun’s radiation absorbed by the air, and the quantity of heat ob- tained by conduction (air-currents) from other parts of the air or from the ground. In the same manner we find for the earth’s surface oa Byv(T*—@) +(1—B)ywT*=(l—ayA+N. . (2) The first and second members represent the radiated quan- tities of heat that go to the air and to space respectively, (1—a)vA is the part of the sun’s radiation absorbed, and N the heat conducted to the point considered from other parts of the soil or from the air by means of water- or air-currents. Combining both these equations for the elimination of 0, which has no considerable interest, we find for T* qu tAtM+ (L~wAd +y)+N(1 + 1/y) 3 Ix YU += By) r+(1=8) For the earth’s solid crust we may, without sensible error, put v equal to 1, if we except the snowfields, for which we assume v=0°5. For the water-covered parts of the earth l have calculated the mean value of v to be 0°925 by aid of the figures of Zenker*. We have, also, in the following to make use of the albedo of the clouds. Ido not know if this has ever been measured, but it probably does not differ very much from that of fresh fallen snow, which Zollner has determined to be 0°78, 2. e. v=0°22. For old snow the albedo is much less or v much greater; therefore we have assumed 0°5 as a mean value. The last formula shows that the temperature of the earth augments with 8, and the more rapidly the greater vis. For an increase of 1° if v=1 we find the following increases for the values of y=0°925, 0°5, and 0°22 respectively :— (3) B. y=0'925, = O-o y=0'22. 0:6 0°944 0-575 0:275 0°75 0:940 0:556 0261. 0°85 0-934 0.535 0-245 0:95 0-428 0512 728 1:00 0:925 0°500 0:220 This reasoning holds good if the part of the earth’s surface * Zenker, Die Vertheilung der Warme auf der Erdoberfliche, p. 54 (Berlin, 1888). 7 M004 in the Air upon the Temperature of the Ground. = 257 considered does not alter its albedo as a consequence of the altered temperature. In that case entirely different circum- stancesenter. If, for instance, an element of the surface which is not now snow-covered, in consequence of falling temperature becomes clothed with snow, we must in the last formula not only alter 8 but also v.. In this case we must remember that ais very small compared to 8. For a we will choose the value 0°40 in accordance with Langley’s* estimate. Cer- tainly a great part of this value depends upon the diffusely reflected part of the sun’s heat, which is absorbed by the earth’s atmosphere, and therefore should not be included in a, _as we have defined it above. On the other hand, the sun may in general stand a little lower than in Langley’s measure- ments, which were executed with a relatively high sun, and in consequence of this a may be a little greater, so that these circumstances may compensate each other. For 8 we will choose the value 0°70, which corresponds when K=1 and W =0°3 (a little below the freezing-point) with the factor 1°66 (see p. 253). In this case we find the relation between T (uncovered) and T, (snow-covered surface) to be Me Pin A(1+1—0:40)+M A(1+0-50—0-:20) +M es, ysl =070)) Hin +. y(1+-0-50=0-35) _ 160+¢ 1:30+¢ Mae beoO) oe MED. | 2 if M@=¢A. We have to bear in mind that the mean M for the whole earth is zero, for the equatorial regions negative and for the polar regions positive. For a mean latitude M=0, and in this case T, becomes 267°3 if T=273, that is the temperature decreases in consequence of the snow-cover- ing by 5°7 C.f The decrease of temperature from this cause ° will be valid until 6=1, z.e¢. till the heat delivered by con- vection to the air exceeds the whole radiation of the sun. This can only occur in the winter and in polar regions. But this is a secondary phenomenon. ‘The chief effect that we examine is the direct influence of an alteration of 8 upon the temperature T of the earth’s surface. If we start from a value T=273 and B=0°70, we find the alteration (¢) in the * Langley, “ Temperature of the Moon,” p. 189. On p.197 he estimates a to be only 0°33. + According to the correction introduced in the sequel for the different heights of the absorbing and radiating layers of the atmosphere, the number 5°°7 is reduced to 4°°0. But as about half the sky is cloud- covered, the effect will be only half as great as for cloudless sky, 7. e, the ‘mean effect will be a lowering of about 2° C, 258 Prof. 8. Arrhenius on the Influence of Carbonie Acid temperature which is caused by the variation of 6 to the following values to be B=060 t=— 5°, 0:80 + 5:6 0:90 4117 1:00 418°6 These values are calculated for v=1, 7. e. for the solid crust of the earth’s surface, except the snowfields. For surfaces with another value of v, as for instance the ocean or the snowfields, we have to multiply this value ¢ by a fraction given above. ; We have now shortly to consider the influence of the clouds. A great part of the earth’s surface receives no heat directly from the sun, because the sun’s rays are stopped by clouds. How great a part of the earth’s surface is covered by clouds we may find from Teisserenc de Bort’s work™ on Nebulosity. From tab. 17 of this publication I have deter- mined the mean nebulosity for different latitudes, and found:— Latitude. . 60. 45. 30. 15. OO. —15. —830,. —45. —60. Nebulosity. 0°603 0:48 0:402 0°511 0°581 0-463 053 0-701 For the part of the earth between 60° 8. and 60° N. we find the mean value 0°525, 7. e. 52°5 per cent. of the sky is clouded. The heat-effect of these clouds may be estimated in the following manner. Suppose a cloud lies over a part of the earth’s surface and that no connexion exists between this shadowed part and the neighbouring parts, then a thermal equilibrium will exist between the temperature of the cloud and of the underlying ground. They will radiate to each other and the cloud also to the upper air and to space, and the radiation between cloud and earth may, on account of the slight difference of temperature, be taken as proportional to this difference. Other exchanges of heat by means of air-currents are also, as a first approximation, proportional to this dif- ference. If we therefore suppose the temperature of the cloud to alter (other circumstances, as its height and compo- sition, remaining unchanged), the temperature of the ground under it must also alter in the same manner if the same supply of heat to both subsists—if there were no supply to the ground from neighbouring parts, the cloud and the ground would finally assume the same mean temperature. If, therefore, the temperature of the clouds varies in a determined manner * Teisserenc de Bort, “ Distribution moyenne de la nébulosité,” Ann. du bureau central metéorologique de France, Année 1884, t. iv. 2° partie, p- 27, . in the Air upon the Temperature of the Ground. 259 (without alteration of their other properties, as height, com- pactness, &c.), the ground will undergo the same variations of temperature. Now it will be shown in the sequel that a variation of the carbonic acid of the atmosphere in the same proportion produces nearly the same thermal effect indepen- dently of its absolute magnitude (see p. 265). Therefore we may calculate the temperature-variation in this case as if the clouds covered the ground with a thin film of the albedo 0°78 (v=0°22, see p. 256). As now on the average K=1 and W =1 nearly, and in this case is about 0°79, the effect on the clouded part will be only 0:25 of the effect on parts that have v=l. If a like correction is introduced for the ocean (v=0°925) on the supposition that the unclouded part of the earth consists of as much water as of solid ground (which is approximately true, for the clouds are by preference stored up over the ocean), we find a mean effect of, in round num- bers, 60 p. c. of that which would exist if the whole earth’s surface hadv=1. The snow-covered parts are not considered, for, on the one hand, these parts are mostly clouded to about 65 p.c.; further, they constitute only a very small part of the earth (for the whole year on the average only about 4 p.c.), so that the correction for this case would not exceed 0°5 p. c. in the last number 60. And further, on the border countries between snowfields and free soil secondary effects come into play (see p. 257) which compensate, and perhaps overcome, the moderating effect of the snow. _ In the foregoing we have supposed that the air is to be re- garded as an envelope of perfectly uniform temperature. This is of course not true, and we now proceed to an examination of the probable corrections that must be introduced for elimi- nating the errors caused by this inexactness. It is evident that the parts of the air which radiate to space are chiefly the external ones, and on the other hand the layers of air which absorb the greatest part of the earth’s radiation do not lie very high. From this cause both the radiation from air to space (@y@ in eq. 1) and also the radiation of the earth to the air (@yv(T'—@) in eq. 2), are greatly reduced, and the air has a much greater effect as protecting against the loss of heat to space than is assumed in these equations, and consequently also in eq. (3). If we knew the difference of temperature between the two layers of the air that radiate to space and absorb the earth’s radiation, it would be easy to introduce the necessary correction in formuise (1), (2), and 3). For this purpose I have adduced the following con- sideration. As at the mean composition of the atmosphere (K=1, 260 7 Prof. 8. Arrhenius on the Influence of Carbonic Acid W =1) about 80 p.c. of the earth’s radiation is absorbed in the air, we may as mean temperature of the absorbing layer choose the temperature at the height where 40 p.c. of the heat is absorbed. Since emission and absorption follow — the same quantitative laws, we may as mean temperature of the emitting layer choose the temperature at the height where radiation entering from space in the opposite direction to the actual emission is absorbed to the extent of 40 p. c. Langley has made four measurements of the absorptive power of water-vapour for radiation from a hot Leslie cube of 106° C.* These give nearly the same absorption-coeffi- cient if Pouillet’s formula is used for the calculation. From these numbers we calculate that for the absorption of 40 p. ce. of the radiation it would be necessary to intercalate so much water-vapour between radiator and bolometer that, when condensed, it would form a layer of water 3:05 millimetres thick. If we now suppose as mean for the whole earth K=1 and W =1 (see Table VI.), we find that vertical rays from the earth, if it were at 100°, must traverse 305 metres of air to lose 40 p.c. Now the earth is only at 15° C., but this cannot make any great difference. Since the radiation emanates in all directions, we have to divide 805 by 1°61 and get in this way 209 metres. In consequence of the lowering of the quantity of water-vapour with the height t we must apply a slight correction, so that the final result is 233 metres. Of course this number is a mean value, and higher values will hold good for colder, lower for warmer parts of the earth. In so small a distance from the earth, then, 40 p. c. of the earth’s radiation should be stopped. Now it is not wholly correct to calculate with Pouillet’s formula (it is rather strange that Langley’s figures agree so well with it), which gives neces- sarily too low values. But, on the other hand, we have not at all considered the absorption by the carbonic acid in this part, and this may compensate for the error mentioned. In the highest layers of the atmosphere there is very little water- vapour, so that we must calculate with carbonic acid as the chief absorbent. From a measurement by Angstrom f, we learn that the absorption-coefficients of water-vapour and of carbonic acid in equal quantities (equal number of molecules) are in the proportion 81:62. ‘This ratio is valid for the least hot radiator that Angstrém used, and there is no doubt * Langley, “Temperature of the Moon,” p. 186. + Hann, Meteorologische Zeitschrift, xi. p. 196 (1894). { Angstrom, Bihang till K. Vet.-Ak. Handl, Bd, xv. Afd. 1, No. 9, pp. 11 and 18 (1889). in the Air upon the Temperature of the Ground. 261 that the radiation of the earth is much less refrangible. Put in the absence of a more appropriate determination we may use this for our purpose ; itis probable that for a less hot radiator the absorptive power of the carbonic acid would come out a little greater compared with that of water-vapour, for the absorption-bands of CQO, are, on the whole, less refrangible than those of H,O (see pp. 246-248). Using the number 0:03 vol. p. c. for the quantity of carbonic acid in the atmosphere, we find that rays which emanate from the upper part of the air are derived to the extent of 40 p. c. from a layer that constitutes 145 part of the atmosphere. This corresponds to a height of about 15,000 metres. Concerning this value we may make the same remark as on the foregoing - value. In this case we have neglected the absorption by the small quantities of water-vapour in the higher atmosphere. The temperature-difference of these two layers—the one ab- sorbing, the other radiating—is, according to Glaisher’s measurements* (with a little extrapolation), about 42° C. For the clouds we get naturally slightly modified numbers. We ought to take the mean height of the clouds that are illuminated by the sun. As such clouds I have chosen the summits of the cumuli that lie at an average height of 1855 metres, with a maximum height of 8611 metres and a minimum of 900 metres+. I have made calculations for mean values of 2000 and 4000 metres (corresponding to dif- ferences of temperature of 30° C. and 20°C. instead of 42° ©. for the earth’s surface). : If we now wish to adjust our formule (1) to (3), we have in (1) and (2) to introduce @ as the mean temperature of the radiating layer and (8+ 42), (0+ 30), or (9+ 20) respectively for the mean temperature of the absorbing layer. In the first case we should use v=1 and v=0:925 respectively, in the second and the third case v=0°22. We then find instead of the formula (3) K —_ Y= TF 918)’ another very similar formula 7 # ~ 1+e(1—py i ee ee Leer) (4) .* Joh. Miiller’s Lehrbuch d. kosmischen Physik, 5*—Aufl. p. 539 (Braunschweig, 1894). . mae ‘ Tt According to the measurements of Ekholm and Hagstrém, Bihang tell K, Sv, Vet-Ak. Handhngar, Ba. xii. Afd. 1, No. 10, p. 11 (1886), 262 Prof. 8. Arrhenius on the Influence of Carbone Acid where ¢ is a constant with the values 1°88, 1°58, and 1°37 respectively for the three cases*. In this way we find the following corrected values which represent the variation of © temperature, if the solid ground changes its temperature 1° C. in consequence of a variation of 8 as calculated by means of formula (3). TaBLE V.— Correction Factors for the Radiation. gs pe Water! |) Snow Clouds (vy = 0°22) at aheight o TA eee 0925) yO ; I Pan | 2000 m. | 4000 m. | | 0-65 | 1:53 1-46 0:95 0:49 042 | 0°87 0-75 1:60 1:52 0:95 0:47 0-40 0°35 0°85 1:69 1:59 0-95 0-46 | 0:38 0:33 0:95 1°81 1:68 0-94 0:43 0:36 0-31 1:00 1°88 1-74 0-94 0-41 0°35 0-30 If we now assume as a mean tor the whole earth K=1 and W=1, we get @=0°785, and taking the clouded part to be 52°5 p. c. and the clouds to have a height of 2000 metres, further assuming the unclouded remainder of the earth’s surface to consist equally of land and water, we find as average variation of temperature 1°63 X 0:23885 + 1°54 x 0°23885 + 0°39 x 0°525=0:979, or very nearly the same effect as we may calculate directly from the formula (3). On this ground I have used the simpler formula. In the foregoing I have remarked that according to my estimation the air is less transparent for dark heat than on Langley’s estimate and nearly in the proportion 387-2: 44. How great an influence this difference may exercise is very easily calculated with the help of formula (8) or (4). Ac- cording to Langley’s valuation, the effect should be nearly 15 p.c. greater than according to mine. Now I think that my estimate agrees better with the great absorption that Langley has found for heat from terrestrial radiating bodies (see p. 2690), and in all circumstances I have preferred to slightly under- estimate than to overrate the effect in question. 288) 4 276\* 2¢6\ 4 * : — _ ‘ = . = e 1:88 (5 = , 1:58 (saa) ,and 1:37 (=) . 246° is the mean absolute temperature of the higher radiating layer of the air, in. the Air upon the Temperature of the Ground. 2638 IV. Calculation of the Variation of Temperature that would ensue in consequence of a given Variation of the Carbonic Acid in the Air. We now possess all the necessary data for an estimation of the effect on the earth’s temperature which would be the result of a given variation of the aérial carbonic acid. We only need to determine the absorption-coefiicient for a certain place with the help of Table III. if we know the quantity of carbonic acid (K=1 now) and water-vapour (W) of this place. By the aid of Table IV. we at first determine the factor p that gives the mean path of the radiation from the earth through the air and multiply the given K- and W-values by this factor. Then we determine the value of 8 which corre- sponds to pK and pW. Suppose now that the carbonic acid had another concentration K, (e.g. K, =1°5). Then weat first suppose W unaltered and seek the new value of p, say p,, that is valid on this supposition. Next we have to seek 8, which corresponds to p,K, (1°5p;) and pyW. From formula (3) we can then easily calculate the alteration (¢) (here increase) in the temperature at the given place which will accompany the variation of 8 from 8 to8,. In consequence of the variation (¢) in the temperature, W must also undergo a variation. As the relative humidity does not vary much, unless the distri- bution of land and water changes (see table 8 of my original memoir), I have supposed that this quantity remains constant, and thereby determined the new value W, of W. A fresh approximation gives in most cases values of W, and @, which may be regarded as definitive. In this way, therefore, we get the variation of temperature as soon as we know the actual temperature and humidity at the given place. In order to obtain values for the temperature for the whole earth, I have calculated from Dr. Buchan’s charts of the mean temperature at different places in every month* the mean temperature in every district that is contained between two parallels differing by 10 and two meridians differing by 20 degrees, (e. g., between 0° and 10° N. and 160° and 180° W.). The humidity has not as yet been sufficiently examined for the whole earth ; and I have therefore collected a great many measurements of the relative humidity at different places (about 780) on the earth and marked them down in maps of the world, and thereafter estimated the mean values for every district. These quantities I have tabulated for the four seasons, Dec.-Feb., March-May, June—Aug., and Sept.-Noy. The detailed table and the observations used are to be found in my original memoir : here I reproduce only the mean values for every tenth parallel (Table VI.). * Buchan: Report on the Scientific Results of the Voyage of H.M.S, ‘ Challenger,’ Physics and Chemistry, vol. ii., 1889, ‘ 264 Prof. 8S. 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Cpe | TG : Bo 4 | ua E o Bo | 3 | | oq | & F o BS | oq | ae SP 2 ee 5 “AVIPIUUN|T eynposqy uvoy(, “APIPIUANFT OAL ULop ‘aInyetod may, Urey ° *, Anpuunyy anjposqp pup aaynjayy ‘ounjnsadua iL UoayI— TA ATV, in the Air wpon the Temperature of the Ground. 265 By means of these values, I have calculated the mean _alteration of temperature that would follow if the qnantity of carbonic acid varied from its present mean value (K=1) to another, viz. to K=0°67, 1°5, 2, 2°5, and 3 respectively. This calculation is made for every tenth parallel, and separately ~for the four seasons of the year. The variation is given in WablosVVE eck | A glance at this Table shows that the influence is nearly the same over the whole earth. The influence has a minimum near the equator, and increases from this to a flat maximum that lies the further from the equator the higher the quantity of carbonic acid in the air. For K=0°67 the maximum effect lies about the 40th parallel, for K=1°5 on the 50th, for K=2 on the 60th, and for higher K-values above the 7Oth parallel. The influence is in general greater in the winter than in the summer, except in the case of the parts that lie between the maximum and the pole. The influence will also be greater the higher the value of vy, that is in general somewhat greater for land than for ocean. On account of the nebulosity of the Southern hemisphere, the effect will be less there than in the Northern hemisphere. An increase in the quantity of carbonic acid will of course diminish the difference in temperature between day and night. A very important secondary elevation of the effect will be produced in those places that alter their albedo by the extension or regression of the snow-covering (see p. 257),and this secondary effect will probably remove the maximum effect from lower ~ parallels to the neighbourhood of the poles *. : _ It must be remembered that the above calculations are found by interpolation from Langley’s numbers for the values K=0-°67 and K=1°5, and that the other numbers must be regarded as extrapolated. The use of. Pouillet’s formula makes the values for K=0:°67 probably a little too small, those for K=1°5 a little too great. This is also without doubt the case for the extrapolated values, which correspond to higher values of K. We may now inquire how great must the variation of the carbonic acid in the atmosphere be to cause a given change of the temperature. The answer may be found by interpola- tion in Table VII. To facilitate such an inquiry, we may make a simple observation. If the quantity of carbonic acid decreases from I to 0°67, the fall of temperature is nearly the same as the increase of temperature if this quantity augments to 15. And to get a new increase of this order of magnitude (3°-4), it will be necessary to alter the quantity of carbonic acid till it reaches a value nearly midway between 2 and 2°5. * See Addendum, p. 275. Ra ONE RR Rt nt ON i a Ee 5 pO Cons 266 Prof. S. Arrhenius on the Influence of Carbonic Acid ap es Oe ae ge | ea COTS) | ade eae 115) C0)15)"| | GeoN cece eceees L Ct ee| fee = — — |ee- 96-6 6-6 |¥-6 |G-6 | T6 [78-4 6-4 16-4 | 6-4 | LL 166-4]/0-9 10.9 0-9 18-4] LE] Le |8¢ |L8 19-6 |ze-e—-| F-e- |ee— |pe— 888-8 [1-6 | 48 19-8 JEL 7-2 | Leh | S-L | 0-L 169-9 9-9 18.6 | 99 | 4-9 IG-¢ |1¢-8 | LE 14-6 | Pe ee-e—-|lP-e- |P-e- lee— G68 |16-8 |9-8 | 18 [6-2 48-9} 0-2 10-4 | 8-9 | 49 196-9 || Fo 16-9 16-4 |6G USE| SE | FS oe |oe] oe-llse- lee— |ze— C9-L)9-L 10-8 | S-4 | 0-4 (99-9 || 2-9 | 2-9 | 9-9 19-9 120-9] Le 139 10-6 10-¢ 1 SE 117-8 oe 1SE 1s ChE EG= |GG = Le- CELL | F-L 16-2 16-2 49-91 9-9 | 9-9 9 V-9 |56.F || 0-4 10-4 16-F | 6-F IS1-8 13S |GS |L-S | Le 120e—-llo.e- |Le— 0-€- GL EL (GL |8-L |¥-L 1oP-9 v9 69 | 0-9 | 9-9 (G6-F || 6-F |6-F | 0-4 |0-G IGT- || L-e | Le 1%-E 1g-¢ 120-e-|1 0.@— 0-E- |0-€- 6G-L || G-2 |3-L | G-L 16-4 [GS-9 || 9.9 : €-9 |9-9 | 4-9 ]60-¢ || 0-4 |6-F |0.G | GE 19G-E 1% | Le 1G-8 1¢.¢ 110-e—1 T C=" |O8 Sa ee L862 (9-4 |6-8 | 48 [48-9] 149 19-9 0-2 |GL1 6-916 0-9 |p 19-6 Ee ll ce |e 12-8 1¢e LLLe— Los | VS 6-6 €8:8/ 8-8 |Z-8 |0-6 | 66 [GP-L)/E-2 |6-9 | 9-4 |6-2] 2-¢||9-¢ | Fe |9.¢ 10-9 Izc.e |1¢¢ lee | 9.8 AS | COG Saal Ce GS Ve L1-6||6-6 |9:8 | 7-6 |9-6 | 4416-2 | 0-4 | 6-4 | 0-8 126-4 ]| 0-9 1¢-¢ | T-9 | 1-9 fco.e|/4-¢ |F-2 19-¢ 12421 @e—| pe- 6:9 a4\(c-6 = 6619-6 |6-8 | 9-6 | 8-6 [48-4 16-2 | 9-2 | 0-8 | 0-8 120-9 || 1-9 13-4 | T-9 | L-9 Iz9-e119-¢ 19-e | L8 | £2 Iez-e—-|l e-e— VES \6-E— £6 F-6 | ¥-6 | &-6 | 1-6 [46-4 || 0-8 | 6-2 |0-8 | 6-2 [¢0.9 || 1-9 | 0-9 | L-9 10-9 Iz¢-¢ |19-€ |9-¢ [FE 1e-e 1 Le-lli Le— |Ppe— Ores Sel 2) s| S| SS)_ 2.218) Sel 21s = See] 2 se aes) 2| sl es O-E=PHyV omoqaey | ‘¢.g=proyoruoqieg | ‘9.=proyomogirg | -¢.T=proy oruoqaeg L9-:0=PPYV o1wogrep ‘poy viuogung fo uoynruny uanb v hq pasnvo ainouaduay fo worm 4 —TTA GTaAV I, in the Air upon the Temperature of the Ground. 267 Thus if the quantity of carbonic acid increases in geometric progression, the augmentation of the temperature will increase nearly in arithmetic progression. This rule—which naturally holds good only in the part investi gated—will be useful for the following summary estimations. 5. Geological Consequences. I should certainly not have undertaken these tedious calcu- lations if an extraordinary interest had not been connected with them. In the Physical Society of Stockholm there have been occasionally very lively discussions on the probable causes of the Ice Age; and these discussions have, in my - opinion, led to the conclusion that there exists as yet no satisfac- tory hypothesis that could explain how the climatic conditions for an ice age could be realized in so short a time as that which has elapsed from the days of the glacialepoch. The common view hitherto has been that the earth has cooled in the lapse of time; and if one did not know that the reverse has been the case, one would certainly assert that this cooling must go on continuously. Conversations with my friend and colleague Professor Hégbom, together with the discussions above referred to, led me to make a preliminary estimate of the probable effect of a variation of the atmospheric carbonic acid on the temperature of the earth. As this estimation led to the belief that one might in this way probably find an explanation four temperature variations of 5°-10° C., I worked out the calculation more in detail, and lay it now before the public and the critics. From geological researches the fact is well established that in Tertiary times there existed a vegetation and an animal life in the temperate and arctic zones that must have been conditioned by a much higher temperature than the present in the same regions*. ‘lhe temperature in the arctic zones appears to have exceeded the present temperature by about 8 or 9 degrees. To this genial time the ice age succeeded, and this was one or more times interrupted by interglacial periods with a climate of about the same character as the present, sometimes even milder. When the ice age had its greatest extent, the countries that now enjoy the highest civilization were covered with ice. This was the case with Ireland, Britain (except a small part in the south), Holland, Denmark, Sweden and Norway, Russia (to Kiev, * For details cf. Neumayr, Erdgeschichte, Bd. 2, Leipzig, 1887; and Geikie, ‘The Great Ice-Age,’ 3rd ed. London, 1894; Nathorst, Jordens historia, p. 989, Stockholm, 1894. : 268 Prof. 8. Arrhenius on the Influence of Carbonic Acid Orel, and Nijni Novgorod), Germany and Austria (to the Harz, Erz-Gebirge, Dresden, and Cracow). At the same time an ice-cap from the Alps covered Switzerland, parts of France, Bavaria south of the Danube, the Tyrol, Styria, and other Austrian countries, and descended into the northern part of Italy. Simultaneously, too, North America was covered with ice on the west coast to the 47th parallel, on the east coast to the 40th, and in the central part to the 37th (confluence of the Mississippi and Ohio rivers). In the most different parts of the world, too, we have found traces of a great ice age, as in the Caucasus, Asia Minor, Syria, the Himalayas, India, Thian Shan, Altai, Atlas, on Mount Kenia and Kilimandjaro (both very near to the equator), in South Africa, Australia, New Zealand, Kerguelen, Falkland Islands, Patagonia and other parts of South America. The geologists in general are inclined to think that these glaciations were simultaneous on the whole earth *; and this most natural view would probably have been generally accepted, if the theory of Croll, which demands a genial age on the Southern hemisphere at the same time as an ice age on the Northern and wice versd, had notinfluenced opinion. By measurements of the displacement of the snow-line we arrive at the result,—and this is very concordant for different places—that the temperature at that time must have been 4°-5° C. lower than at present. The last glaciation must have taken place in rather recent times, geologically speaking, so that the human race certainly had appeared at that period. Certain American geologists hold the opinion that since the close of the ice age only some 7000 to 10,000 years have elapsed, but this most probably is greatly underestimated. One may now ask, How much must the carbonic acid vary according to our figures, in order that the temperature should attain the same values as in the Tertiary and Ice ages respect- ively? A simple calculation shows that the temperature in the arctic regions would rise about 8° to 9° C., if the carbonic acid increased to 2°5 or 3 times its present value. In order to get the temperature of the ice age between the 40th and 50th parallels, the carbonic acid in the air should sink to 0°62 —0°55 of its present value (lowering of temperature 4°-5° C.). The demands of the geologists, that at the genial epochs the climate should be more uniform than now, accords very well with our theory. The geographical annual and diurnal ranges of temperature would be partly smoothed away, if the quantity of carbonic acid was.augmented. ‘The * Neumayr, Erdgeschichte, p- 648; Nathorst, 2. ¢. p. 992. | in the Air upon the Temperature of the Ground. 269 reverse would be the case (at least to a latitude of 50° from the equator), if the carbonicacid diminished in amount. But in both these cases I incline to think that the secondary action (see p. 257) due to the regress or the progress of the snow-covering would play the most important réle. The theory demands also that, roughly speaking, the whole earth should have undergone about the same variations of tempera- ture, so that accordin g to it genial or glacial epochs must have occurred simultaneously on the whole earth. Because of the greater nebulosity of the Southern hemisphere, the variations must there have been a little less (about 15 per cent.) than in the Northern hemisphere. The ocean currents, too, must there, as at the present time, have effaced the differences. in temperature at different latitudes to a greater extent than in the Northern hemisphere. ‘This effect also results from the greater nebulosity in the arctic zones than in the neighbour: hood of the equator. There is now an important question which should: be answered, namely :—lIs it probable that such great variations in the quantity of carbonic acid as our theory requires have occurred in relatively short geological times? The answer to this question is given by Prof. Hégbom. As his memoir on this question may not be accessible to most readers of these pages, I have summed up and translated his utterances which are of most importance to our subject *:— “ Although it is not possible to obtain exact quantitative expressions for the reactions in nature by which carbonic acid is developed or consumed, nevertheless there are some factors, of which one may get an approximately true estimate, and from which certain conclusions that throw light on the question may be drawn. In the first place, it seems to be of importance to compare the quantity of carbonic acid now present in the air with the quantities that are being trans- formed. If the former is insignificant in comparison with the latter, then the probability for variations is wholly other than in the opposite case. “On the supposition that the mean quantity of aban acid in the air reaches 0°03 vol. per cent., this number repre- sents 0°045 per cent. by weight, or 0-342 millim. partial pressure, or 0466 gramme of carbonic acid for every cm.’ ef the earth’s surface. Reduced to carbon this quantity would give a layer of about 1 millim. thickness over the earth’s surface. The quantity of carbon that is fixed in the living organic world can certainly not be estimated with the hi Higbom, Svensk kemisk Tidskrift, Bd. vi. p. 169 (1894). Phil. Mag. 8. 5. Vol. 41. No. 251. April 1896. U 270 Prof. S. Arrhenius on the Influence of Carbonic Acid same degree of exactness ; but it is evident that the numbers that might express this quantity ought to be of the same order of magnitude, so that the carbon in the air can neither be conceived of as very great nor as very little, in compa- rison with the quantity of carbon occurring in organisms. With regard to the great rapidity with which the transform- ation in organic nature proceeds, the disposable quantity of carbonic acid is not so excessive that changes caused by climatological or other reasoris in the velocity and value of that transformation might be not able to cause displacements of the equilibrium. “The following calculation is also very instructive for the appreciation of the relation between the quantity of carbonic acid in the air and the quantities that are transformed. The world’s present production of coal reaches in round numbers 500 millions of tons per annum, or 1 ton per km.? of the earth’s surface. Transformed into carbonic acid, this quantity would correspond to about a thousandth part of the carbonic acid in the atmosphere. It represents a layer of limestone of 0:003 millim. thickness over the whole globe, or 1°5 km.’ in cubic measure. This quantity of carbonic acid, which is supplied to the atmosphere chiefly by modern industry, may be regarded as completely compensating the quantity of carbonic acid that is consumed in the formation of limestone (or other mineral carbonates) by the weathering or decomposition of silicates. From the determination of the amounts of dissolved substances, especially carbonates, in a number of rivers in different countries and climates, and of the quantity of water flowing in these rivers and of their drainage-surface compared with the land-surface of the globe, it is estimated that the quantities of dissolved carbonates that are supplied to the ocean in the course of a year reach at most the bulk of 3 km.2 As it is also proved that the rivers the drainage regions of which consist of silicates convey very unimportant quantities of carbonates compared with those that flow through limestone regions, it is per- missible to draw the conclusion, which is also strengthened by other reasons, that only an insignificant part of these 3 km.? of carbonates is formed directly by decomposition of silicates. In other words, only an unimportant part of this quantity of carbonate of lime can be derived from the process of wea- thering ina year. Even though the number given were on account of inexact or uncertain assumptions erroneous to the extent of 50 per cent. or more, the comparison instituted is of very great interest, as it proves that the most important of all the processes by means of which carbonic acid has been in the Air upon the Temperature of the Ground. 271 removed from the atmosphere in all times, namely the chemical weathering of siliceous minerals, is of the same order of magnitude as a process of contrary effect, which is caused by the industrial development of our time, and which must be conceived of as being of a temporary nature. “In comparison with the quantity of carbonic acid which is fixed in limestone (and other carbonates), the carbonic acid of the air vanishes, With regard to the thickness of sedi- mentary formations and the great part of them that is formed by limestone and other carbonates, it seems not improbable that the total quantity of carbonates would cover the whole earth’s surface to a height of hundreds of metres. If we assume 100 metres,—a number that may be inexact in a high degree, but probably is underestimated,—we find that about 25,000 times as much carbonic acid is fixed to lime in the sedimentary formations as exists free in the air. Hvery molecule of carbonic acid in this mass of limestone has, however, existed in and passed through the atmosphere in the course of time. Although we neglect all other factors which may have influenced the quantity of carbonic acid in the air, this number lends but very slight probability to the hypothesis, that this quantity should in former geological epochs have changed within limits which do not differ much from the present amount. As the process of weathering has consumed quantities of carbonic acid many thousand times greater than the amount now disposable in the air, and as this process from different geographical, climato- logical and other causes has in all likelihood proceeded with very different intensity at different epochs, the probability of important variations in the quantity of carbonic acid seems to be very great, even if we take into account the com- pensating processes which, as we shall see in what follows, are called forth as soon as, for one reason or another, the production or consumption of carbonic acid tends to displace the equilibrium to any considerable degree. One often hears the opinion expressed, that the quantity of carbonic acid in the air ought to have been very much greater formerly than now, and that the diminution should arise from the circumstance that carbonic acid has been taken from the air and stored in the earth’s crust in the form of coal and carbonates. In many cases this hypothetical dimi- nution is ascribed only to the formation of coal, whilst the much more important formation of carbonates is wholly over- looked. This whole method of reasoning on a continuous diminution of the carbonic acid in the air loses all foundation in fact, notwithstanding that enormous quantities of carbonic 272 Prof. S. Arrhenius on the Influence of Carbonic Acid - acid in the course of time have been fixed in carbonates, if we consider more closely the processes by means of which carbonic acid has in all times been supplied to the atmosphere. From these we may well conclude that enormous variations have occurred, but not that the variation has always proceeded in the same direction. _ “Carbonic acid is supplied to the atmosphere by the follow- ing processes :—(1) volcanic, exhalations and geological phe- nomena connected therewith ; (2) combustion of carbonaceous meteorites in the higher regions of the atmosphere ; (3) com- bustion and decay of organic bodies ; (4) decomposition of carbonates; (5) liberation of carbonic acid mechanically inclosed in minerals on their fracture or decomposition. The carbonic acid of the air is consumed chiefly by the following processes :—(6) formation of carbonates from silicates on weathering ; and (7) the consumption of carbonic acid by vegetative processes. The ocean, too, plays an important réle as a regulator of the quantity of carbonic acid in the air by means of the absorptive power of its water, which gives off carbonic acid as its temperature rises and absorbs it as it cools. The processes named under (4) and (5) ave of little significance,so that they may be omitted. So too the processes (3) and (7), for the circulation of matter in the organic world goes on so rapidly that their variations cannot have any sensible influence. From this we must except periods in which great quantities of organisms were stored up in sedimentary formations and thus subtracted from the circulation, or in which such stored-up products were, as now, introduced anew into the circulation. The source of carbonic acid named in (2) is wholly incalculable. “Thus the processes (1), (2), and (6) chiefly remain as balancing each other. As the enormous quantities of car- bonic acid (representing a pressure of many atmospheres) that are now fixed in the limestone of the earth’s crust cannot be conceived to have existed in the air but as an insig- nificant fraction of the whole at any one time since organic life appeared on the globe, and since therefore the consump- tion through weathering and formation of carbonates must have been compensated by means of continuous supply, we must regard volcanic exhalations as the chief source of car- bonic acid for the atmosphere. “ But this source has not flowed regularly and uniformly. Just as single volcanoes have their periods of variation with alternating relative rest and intense activity, in the same manner the globe as a whole seems in certain geological epochs to have exhibited a more violent and general volcanic in the Air upon the Temperature of the Ground. 273 activity, whilst other epochs have been marked by a com- parative quiescence of the volcanic forces. It seems there- fore probable that the quantity of carbonic acid in the air has undergone nearly simultaneous variations, or at least that this factor has had an important influence. “If we pass the above-mentioned processes for consuming and producing carbonic acid under review, we find that they evidently do not stand in such a relation to or dependence on one another that any probability exists for the permanence of an equilibrium of the carbonic acid in the - pines An increase or decrease of the supply continued during geological periods must, although it may not be important, conduce to remarkable alterations of the quantity of carbonic acid in the air, and there is no conceivable hindrance to imagining that this might in a certain geological period have been several times greater, or on the other hand considerably less, than now.’ As the question of the probability of quantitative variation of the carbonic acid in the atmosphere is in the most decided manner answered by Prof. Hégbom, there remains only one other point to which I wish to draw attention in a few words, namely: Has no one hitherto proposed any acceptable ex- planation for the occurrence of genial and glacial periods? Fortunately, during the progress of the foregoing calcula- tions, a memoir was published by the distinguished Italian meteorologist L. De Marchi which relieves me from answer- ing the last question*. He examined in detail the different theories hitherto proposed—astronomical, physical, or geo- graphical, and of these I here give a short résumé. These theories assert that the occurrence of genial or glacial epochs should depend on one or other change in the following cir- cumstances :— (1) The temperature of the earth’s place in space. (2) The sun’s radiation to the earth (solar constant). (3) The obliquity of the earth’s axis to the ecliptic. (4) The position of the poles on the earth’s surface. (5) The form of the earth’s orbit, especially its eccentricity (Croll). (6) The shape and extension of continents and oceans. (7) The covering of the earth’s surface (vegetation). (8) The direction of the oceanic and aérial currents. (9) The position of the equinoxes. De Marchi arrives at the conclusion that all these hypotheses must be rejected (p. 207). On the other hand, he is of the ~* Luigi De Marchi: Le cause dell’ era glaciale, oe dal R, Istituto Lombardo, Pavia, 1895, 274 Prof. S. Arrhenius on the Influence of Carbonic Acid opinion that a change in the transparency of the atmosphere would possibly give the desired effect. According to his calculations, ‘‘ a lowering of this transparency would effect a lowering of the temperature on the whole earth, slight in the equatorial regions, and increasing with the latitude into the 70th parallel, nearer the poles again a little less. Further, this lowering would, in non-tropical regions, be less on the continents than on the ocean and would diminish the annual variations of the temperature. This diminution of the air’s transparency ought chiefly to be attributed to a greater quantity of aqueous vapour in the air, which would cause not only a direct cooling but also copious precipitation of water and snow on the continents. The origin of this greater quantity of water-vapour is not easy to explain.” De Marchi has arrived at wholly other results than myself, because he has not sufficiently considered the important quality of selective absorption which is possessed by aqueous vapour. And, further, he has forgotten that if aqueous vapour is sup- plied to the atmosphere, it will be condensed till the former condition is reached, if no other change has taken place. As we have seen, the mean relative humidity between the 40th and 60th parallels on the northern hemisphere is 76 per cent. If, then, the mean temperature sank from its actual value + 5°3 by 4°-5° C., 7. e. to +1°3 or +0°3, and the aqueous vapour remained in the air, the relative humidity would increase to 101 or 105 per cent. This is of course impossible, for the relative humidity cannot exceed 100 per cent. in the free air. A fortiori it is impossible to assume that the absolute humidity could have been greater than now in the glacial epoch. ae the hypothesis of Croll still seems to enjoy a certain favour with English geologists, it may not be without interest to cite the utterance of De Marchi on this theory, which he, in accordance with its importance, has examined more in detail than the others. He says, and I entirely agree with him on this point :—“ Now I think I may conclude that from the point of view of climatology or meteorology, in the present state of these sciences, the hypothesis of Croll seems to be wholly untenable as well in its principles as in its consequences ” *. It seems that the great advantage which Croll’s hypothesis promised to geologists, viz. of giving them a natural chro- nology, predisposed them in favour of its acceptance. But this circumstance, which at first appeared advantageous, seems with the advance of investigation rather to militate * De Marchi, /, c. p. 166. in the Atr upon the Temperature of the Ground. 275 against the theory, because it becomes more and more im- possible to reconcile the chronology demanded by Croll’s hypothesis with the facts of observation. 1 trust that after what has been said the theory pro- posed in the foregoing pages will prove useful in explaining some points in geological climatology which have hitherto proved most difficult to interpret. ADDENDUM™. As the nebulosity is very different in different latitudes, and also different over the sea and over the continents, it is evident that the influence of a variation in the carbonic acid of the air will be somewhat different from that calculated above, where it is assumed that the nebulosity is the same over the whole globe. I have therefore estimated the nebu- losity at ditterent latitudes with the help of the chart published by Teisserenc de Bort, and calculated the following table for | 3 Nebulosity. 2. Reduction factor. K=0°67. ee = —|z8 Pee esd ety ae) ees reed Ge eae Precis rece ribar ee eeetions 58-1 | 66-7 |72-1| 0899] 0-775| 0:864| —2:8) -24| 31 | 2-7 sf 56:3. | 67-6 |55°8) 0-924] 0-763] 0-853) —3:0| —24| 33 | 27 = 45-7 | 63:3 |52-9| 1-057| 0:813| 0-942| -35| -27| 38 | 29 mn 36-5 | 52:5 |42-9| 1:177| 0-939] 1-041| -3:9! —31] 41 | 33 * 98-5 | 47-2 | 38-8) 1:296| 1-:009| 1-120) —4:1| —32} 45 | 35 : 99:5 | 47-0 | 24-2) 1-308] 1:017| 1-087) —4:1| —32| 43 | 3-4 4 50-1 | 56-7 | 23:3] 1-031 | 0-903} 0-933, —3:1]) —27| 33 | 29 2 54:8 | 59-7 |24-2| 0-97 | 0:867| 0-892| —29| —26| 31 | 28 =. 47-8 | 54:0 | 22-5] 1:056| 0-932] 0-96 | —33) —29| 34 | 30 Be 99-6 | 49:6 | 23:3| 1:279| 0:979| 0-972) —4:1| —31| 42 | 32 ar 38:9 | 51-0 |12'5| 1152) 0-958] 0-982] —38) —32| 40 | 3-4 yi 62:0 | 61-1 | 2:5) 086 | 0-837] 0-838) —29| —28| 32 | 31 a 71-0 | 71:5 | 0:9] 0-749] 0-719] 0-719 276. Prof. J. G. MacGregor on the Calculation of the value of the variation. of temperature, if the carbonic acid decreases. to 0°67 or increases to 1°5 times the present quan- tity. In the first column is printed the latitude; in the seeond and. third the nebulosity over the continent and over the ocean; in the fourth the extension of the continent in hun- dredths of the whole area. After this comes, in the fifth and sixth columns, the reduction factor with which the figures in the table are io be multiplied for getting the true variation of temperature over continents and over oceans, and, in the seventh column, the mean of both these correction factors. In the eighth and ninth columns the temperature variations for K=0-°67, and in the tenth and eleventh the corre- sponding values for K=1°5 are tabulated. Me The mean value of the reduction factor N. of equator is for the continent (to 70° N. lat.) 1:098 and for the ocean 0°927, in mean 0'996. For the southern hemisphere (to 60° 8. lat.) it is found to be for the continent 1:095, for the ocean 0°871, in mean 0°907. ‘The influence in the southern hemisphere will, therefore, be about 9 per cent. less than in the northern. In consequence of the minimum of nebulosity between 20° -and 380° latitude in both hemispheres, the maximum effect of the variation of carbonic acid is displaced towards the equator, so that it falls at about 25° latitude in the two cases of K=0°67 and K=1°5. XXXII. On the Calculation of the Conductivity of Mixtures of Electrolytes. By Prof. J. G. MacGregor, Dalhousie College, Halifax, NS.* . RRHENIUS has deduced +, as one of the consequences of the dissociation theory of electrolytic conduction, that the condition which must be fulfilled in order that two aqueous solutions of single electrolytes, which have one ion in common and which undergo no change of volume on being mixed, may be isohydric, 7. e. may on being mixed undergo no change in their state of dissociation or ionisation, is that the concentration of ions, z.e. the number of dissociated gramme-molecules per unit of volume, shall be the same for both solutions. He obtained this result by combining the equations of kinetic equilibrium for the constituent electrolytes before and after mixture. According to the above theory, the specific conductivity of a mixture of two solutions of electrolytes 1 and 2, whose * Abstract of a paper read before the Nova Scotian Institute of Science on the 9th of December, 1895. Communicated by the Author, ~ + Zschr. f. phystkalische Chemie, il. p. 2841888). ~~ the Conductivity of Mixtures of Electrolytes. 277 volumes before the mixture were v,/ and v, respectively, which contained ; and n, gramme-molecules -of the electro- lytes per unit of volume, whose combined volume after mixture is p(v;/+%,), whose coefficients of ionisation after mixture are a, and a, and whose specific molecular con- ductivities at infinite dilution under the circumstances in which they exist in the mixture are ao, and pa,, is given By the expression — plo +e) (ayNyV1 Heo, + AgNgVq ‘pb cd .)* Since in any case in which isohydric solutions are mixed withont change of volume, n,, 4’, m2, %/ are known, a and a readily determinable, and p equal to unity, the specific con- ductivity can be calculated provided we assume that w,., and ft», have the same values -for solutions in a mixture as for simple solutions. In the case in which equal volumes of the constituents are mixed without change of volume, the specific conductivity of the mixture becomes the mean of the specific conductivities of the constituent solutions. Arrhenius has subjected the above result to a aoe of tests. In one he determined by experiment several series of dilute aqueous solutions of different single acids, such that if any two of the members of the same series were mixed in equal volumes the mixture was found to have a conductivity equal to the mean of the conductivities of the constituents. Regarding the solutions of each series as shown thereby to be isohydric among one another, he calculated the concentra- tions of the ions in the various solutions by the aid of data due to Ostwald. The following table gives the result, the numbers specifying the concentration of dissociated hydrogen _ (in mgr. per litre) in the constituent solutions, and those in each row applying to solutions found as above to be UL ce one another :— (COOH),. | ©,H,O, | HCOOH. | CH,COOH. 152-6 a5 21:37 Bola yal 0% 4-09 417 442. | 3-96 A te bees 144 1:33 5. 10807 . 0°381 F 0-402 278 Prof. J. G. MacGregor on the Calculation of It will be observed that while the numbers in the various horizontal rows show a general agreement, they differ very considerably from one another, the extreme differences ranging from 0°7 to 20°5 per cent. He found also that two solutions of Ammonium Acetate and Acetic Acid respectively, which were determined as above to be isohydric, contained, according to Kohlrausch, amounts of the ion CH;COO which were in the ratio 1: 0°79, a ratio which is only very roughly equal to unity. So far as result is concerned these tests are not satisfactory. But the lack of agreement may have been due to various causes: (1) the data for calculation may have been defective ; (2) the change of volume which would doubtless occur on mixing, even with very dilute solutions, may have been too reat for the application of Arrhenius’s deduction; and (3) the difference between the values of w, in simple solution and in a mixture may be too great to admit of the identifica- tion of isohydric solutions by the method employed. On the other hand, Arrhenius has calculated* the conduc- tivities of two dilute solutions containing in each case given quantities of two acids, employing for this purpose a series of approximations based on his own observations of isohydric solutions of the acids; and the calculated values were found to agree with those observed to within 0°5 and 0:2 per cent. respectively. So far as result is concerned this forms a much more satisfactory test than those mentioned above. But the number of calculations is too small to exclude the possibility of accidental agreement. ; The calculation of the conductivity of a mixture of electro- lytes is so severe a test of the ionisation theory of electrolysis that I have thought it well to test its possibility on a more extensive scale, especially as a considerable body of material is available for this purpose in the observations of the con- ductivity of mixtures of solutions of Potassium and Sodium Chlorides made by Bendert. The present paper contains the results of calculations of the conductivities of mixtures determined experimentally by him. Method of Calculation. In order to make such calculations by Arrhenius’s method, it would be necessary to make a preliminary determination of a number of isohydric solutions of the two salts, and to restrict the calculations to very dilute solutions. They may be made, however, without such preliminary experiments and without * Wiedemann’s Annalen, xxx. p. 73 (1887). + Ibid. xxii, p. 197 (1884). the Conductivity of Mixtures of Electrolytes. 279 such restriction by employing a more general form of Arrhe- nius’s deduction. Two electrolytes having a common ion and in a state of equilibrium in the same solution, may be regarded as occupying definite portions of the volume of the solution. If we apply the equilibrium conditions to the parts of the solution occupied by the respective electrolytes as well as to the whole solution, we obtain equations which, mutatis mu- tandis, are identical with those obtained by Arrhenius for isohydric solutions and their mixture, and which give a similar result, viz., that for equilibrium the concentrations of the ions of the respective electrolytes per unit volume of the portion of the complex solution or mixture occupied by them must be the same. With the aid of this result, we can find the ionisation- coefficients of the constituents of a mixture. For if, in addition to the symbols used above, v, and x be taken to represent the volumes of the portions of the mixture occupied by the respective electrolytes, it gives us the equation ee (1) 1 2 We have also Ui ei — PU US Web as kde vid oder. oh erst an (2) and as the coefficients of ionisation are functions of the dilu- tion only, at constant temperature, we have v a=fi( 4), et ee eT vU ao = (a7): ej tried (hist edt SOLS (4) Of the quantities involved in these equations, 7, ng, v1’, vs! are known, and p may be determined by density measure- ments before and after mixture. The form of the functions in (8) and (4) may be determined if measurements of the conductivities of sufficiently extended series of simple solu- tions of the constituent electrolytes are made. We have thus four equations with but four unknown quantities. If we employ the symbol V to represent the dilution (v/nv’), we may write the above equations as follows :—- ay ao Nery . ° e ° e ° ° ° . S) : (1) NoVo! aw). Papin Tavs, 280 Prof. J. G. MacGregor on the Calculation of which, in the case of mixtures of equal volumes, becomes Vi == te ve =p (vy a me ve) Ny ny ay Vv, =H) - Ls) (3) a - V; =¢,( Vo). Cape reels: (bey / 56. oie. cel ee eee (A) I determined e#, and a, from these equations by the fol- lowing graphical process:—Hquation (3) was employed by drawing, from experimental data, for simple solutions of elec- trolyte 1, a curve with values of the concentration of the ions (a/V) as abscissee and corresponding values of the dilution (V) as ordinates. This curve was drawn once for all and was used in all determinations. The curve embodying equation (4) had to be drawn anew for each mixture examined. If this mixture was formed of solutions containing n,; and nm, gramme- molecules per unit volume of electrolytes 1 and 2 respectively, the curve had as abscissee the concentrations of ions of a series of simple solutions of electrolyte 2, and as ordinates, since Bender’s mixtures were: mixtures of equal volumes, n/n, times the corresponding values of the dilutions. Hquations (1) and (2) were applied by finding, by inspection, two points, one in each curve, having a common abscissa (z,/V,;=a,/V.), and having ordinates (V; and 2 V. respectively) of such 1 magnitude as to have a sum equal to p times the sum ef the ordinates of the points-on the curves determined by the dilu- tions (V,/ and V,’ respectively) before mixing. The value of ‘the abscissa common to the two points thus determined gives the concentration of ions of both constituents in the mixture. ‘The corresponding ordinate of the first curve, and that of the second curve multiplied by n/n, give the dilutions (V, and V.) of the constituents in the mixture. The products of the common value of a/V into V, and V» are the required values of a, and a, respectively. | It will be obvious that the values of a, and a, for a solution containing two electrolytes with a common ion may be deter- mined in this way, whether it has been formed by the mixing of two simple solutions or not. It may always be imagined to have been formed in this way ; and if data are not available for the determination of p, special density measurements may be made. icy aka digest scala i Mixtures of Electrolytes. 281 ~ Data for the + Caleuineees * Bender’ s paper contains all the data required for the cal- culation of the conductivities of mixtures of solutions of Potassium and Sodium Chlorides, with the single exception of the specific molecular conductivity of the simple solutions at infinite dilution. Owing to the want of this datum, I have drawn the curves a/V =6(V) by means. of data based - on Kohlrausch and Grotrian’s and Kohlrausch’s observations * of the conductivity of solutions of KCl and NaCl. They are. are as follows : — NaCl Solutions. _| Grm.-molecules F Pectees: Litres per | Concentration olecular _ See per litre. ‘Conductivity: grm.-molecule. of Ions. 05 757 2 0°3682 0: 884 710-42 1°1312 06109 1 695 1 0°6761 1:830 618-59 0-H465 1-1012 2°843 - 39°93 03517 1-4932 3 528 0°3333 15418 a 924 466°35 0:2548 1-7802 ¥: BIS 5 0:2" 1-936 5 085 - - 392°53 01967 1-9416 5:325 37765 0:1878 1:9562 5°42] 37 1°95 0°1845 19611 KCl Solutions. Grm.-molecules ot POLE Litres per Concentration . olecular per litre. Conductivity. grm.-molecule. of Ions. 0°5 958 2 0:3939 0-691 933°43 1-4472 05304 1 919 1 0°7558 1:427 _ 890°70 0:7008 1:0452 2208 855°52 0:4529 15535 3 827 0°3333 20409 3°039 823-95 0°3291 20592 3213 81794 03112 271612 | These data are quite sufficient for drawing the curves repre- senting «/V as @(V) in the parts corresponding to small dilutions, but they are few for the parts corresponding to the _* Wiedemann’s Annalen, vi. p. 37 (1879), and xxvi. p. 195 (1885). 282 Prof. J. G. MacGregor on the Calculation of greater dilutions, where the curvature is most rapid. I there- fore obtained interpolation formule, by means of which I drew in the latter parts of the curves, expressing @/V in the case of each salt in terms of the reciprocals of powers of V. These formule, having no permanent value, need not be given here. The table of results below shows that they were accu- rate enough for the purpose in hand. As Bender measured the specific gravities of both his simple solutions and his mixtures, his paper affords the neces- sary data for determining the change of volume on mixing. Such change will have a double effect on the calculated con- ductivity : (1) it will affect the value of @ as determined from the curves, and (2) it introduces the factor p in the final com- putation. In the case of Bender’s solutions, though in some cases they were nearly or quite saturated, the first effect was so small as to be much less than the error incidental to the graphical process, and I did not therefore take it into account. The second effect was also very small ; but as in some cases it was nearly as great as Bender’s estimated error, I took it into account in all cases. While Kohlrausch’s solutions had at 18° C. both the con- stitution and the conductivity specified in his tables, Bender’s solutions had at 15° the constitution and at 18° the conduc- tivity ascribed to them. I found that it did not appreciably affect the values found for a, and «, to take the concentra- tions at 15° as being the concentrations at 18° ; but that this approximation was inadmissible in calculating the conduc- tivity, as in some cases it made a difference of about the same magnitude as Bender’s estimated error. Hence in the calculation I took the values of n, and ng to be Bender’s values multiplied by the ratio of the volume of the solution at 15° to its volume at 18°. As Bender measured the thermal expansion of his solutions, his paper affords the necessary data for this correction. The conductivities given by Bender as the results of his observations are the actual results of measurements, and are thus affected by accidental errors, which in some cases are considerable. In order that his measurements may be rendered comparable with the results of calculations, these accidental errors must, as far as possible, be removed. I therefore plotted all his series of observations on coordinate paper, drew smooth curves through them, and estimated as well as I could in this way the accidental errors of the single measurements. ‘he correction thus determined is referred to in the table on p. 285 as correction a. Bender himself draws attention to certain differences be- tween his observations of the conductivity of simple solutions the Conductivity of Mixtures of Electrolytes. 283 of KCl and NaCl and those for solutions of the same strength contained in Kohlrausch’s tables of interpolated values, ascri- bing them (1) to his own observations being the results of actual measurement, and (2) to the different temperatures at which their respective solutions had the specified strengths. These differences are shown in the following table :— | H Conductivity. Salt in : Solution. Difference. Bender. Kobirausch. | Nath .3t. a 388 380 | + 8 ofl ee ieee aa 478 | 471 + 7 Weer. gi 702 =O 698 | a4 RECT es ey 916 911 + 5 i 0) GS Seam 977 974 +3 1,5 0) Saale 1217 1209 aS 1°40; OR aS ee 1362 1328 +34 LEC es Ae 1425 1412 +13 MOL 5. a. 3? 1594 1584 +10 | 0) ae ae ea 1741 1728 -eie NACH 2. oe i28.. 03 1745 1728 +17 1S 0) ES is Bs 1845 1846 = 6 0 a eee 2106 PIN — 6 GUO ete mes coins. 2484 2480 + 4 1260) ga i a ae 2820 2822 a SERRE arty eee eN ee es ni ee ee Again, it will be noticed that the differences are all of the same sign up to conductivities of about 1800, and nearly all of the opposite sign for higher conductivities: also that for any given conductivity the difference is of the same sign and order of magnitude for solutions of both salts. If they were due to the first of the above assigned causes, since Kohl- rausch’s interpolated values agree well with his observations, we should expect much more alternation of sign: if to the second, there should be no change of sign: if to both, there should be greater and more irregalar variation in magnitude. The fact that the differences are practically the same for both electrolytes at any given value of the conductivity, would seem to show that the cause of the differences—a defect in the apparatus possibly or in the distilled water—was operative in the measurements of both sets of simple solutions, and there- fore probably in the measurements of the mixtures. Hence, to render the results of calculations based on Kohlrausch’s data for the simple solutions comparable with Bender’s results for mixtures, we must determine what the conductivities of Bender’s mixtures would have been found to be if Kohlrausch had prepared and measured them. To find this out as nearly as possible, I have plotted the data of the above table with Bender’s conductivities as abscissee and the differences between 284 = Prof. J. G. MacGregor on the Calculation of them and Kohlrausch’s corresponding values as ordinates, and drawn a smooth curve through the points. By the aid of this curve I determined the correction b of the table given below. The correction is, of course,.a more or less doubtful one; for it is not certain that the observations -on mixtures suffered from the same unknown source of error as the obser- vations on simple solutions. It seems probable, however, that they did ; and the results of the table pines helew would appear to. render it almost. certain. os It may be well in one case to give an example of the-mode of calculation. We may take for this purpose the mixture of solutions containing 1 grm.-molecule of salt each. It is found by the graphical: process that the value of .«/V for this mixture is-0°718 grm.-molecule per litre, and that’ the dilutions of the mixture are 0-937 and 1: 063 litre per grm.- molecule for the NaCl and the KCl respectively. The den- sities of the constituent solutions were 1-:0444 and 1-0401 respectively, and that of the mixture 1:0422. The expansions per unit volume between 15° and 20° C. were 0:0013569 and 0:0012489 respectively. The values of the conductivity at infinite dilution I took to be 1028 and 1216, according to Kohlrausch’s observations. Hence the conductivity of the mixture, seat . 1 2x 1-0422/1x0°718 x 0937 x 1028 | 1x 0-718 x 1063 x 1216) _ 49.9 2° 20845 ( 1+06x0-00136. * 14+06x0-00125 ) Bender’s observed value (he used the same standard as Kohlrausch) was 814. To this a correction of about —3 must be applied to make the observation agree with the others of the same series (correction a), and a correction of about —3 to make it comparable with a calculated value based on Kohlrausch’s data (correction b). Bender’s reduced result is thus 808, which differs from the calculated value by 1:2 or 0°15 per cent. k= Results of the Calculations. The following Table gives the results of the calculations ; the second and third columns containing the numbers of grm.-molecules per litre in the simple solutions at 15° C.; the fourth column, Bender’s observed values of the conductivities of the mixtures; the fifth and sixth, corrections a and b referred to above ; the seventh, Bender’s redweed values; the eighth, the calculated values; oan the ninth, the excess of the caleu- lated values over those observed, expressed as percentages i the latter. 285 the Conductivity of Mixtures of Electrolytes. a a a ee ee ee eee Constituent Solutions (grm.-molecules per litre). Conductivity of Mixture. No Difference al Bender Corrections. iByaitar (per cent. ). wow uel (observed). b (reduced.) Ctanllantae ad. 5 il. 05 01875 291 Ges G. souk. agit = 289°5 —0:52 2. ‘9 0:375 377 0 Sy 270 373'1 +084 3} fp 0-5 436 0 eG 430 4261 —0:90 4, Fs 0:75 545 1) Sus 540 5376 —()44 5. i, 15 866 1) a9 863 858'3 —0:54 6. 1-0 0:1875 449 95 ice | a eaaG Sho 2 ea 40°52 7. 3 0:375 546 0 255 541 540°6 —0:07 8. 5 0°75 707 0 a4 703 7011 —0:27 9. i; 1:0 814 2233 8 808 809:2 +0°15 10. 15 1014 eeeG ae 1015 1015°2 +.0:02 ole 2-0 1224 EaoG = 9 1209 1200°6 —0:69 12. 20 0:1875 776 0 5 773 773-9 4.012 13. a 10 1085 0 = G 1079 10863 0:68 14. % 2-0 1458 0 —13 1445 1458 +0-90 15. - 3:0 1832 =) 0 1823 18086 —0:79 16. 3-0 1-0 1332 0 TT 1321 | 1394 4+.0:23 17. a" 2:0 1674 0 —10 1664 1660 — 0°24 18. 0 3:0 2003 ) + 4 2007 1988-7 —091 19, 4-0 0-375 1367 he Bion | a tees a as04 4.040 20. a 2°0 1857 0 tT 1858 1849°3 —0°47 21. » 35 2300 0 “<3 2303 2239-2 —2-77 22. a 40 2428 +6 = 2432 93453 —3:56 x Phil. Mag. 8. 5. Vol. 41. No. 251. April 1896. 236 Prof. J. G. MacGregor on the Calculation of It will be seen that in the case of the more dilute solutions Nos. 1-17 and 19, the differences, which are in all cases less ‘than 1 per cent. and for the most part considerably less, are one half positive and one half negative ; and that whether the solutions are arranged in the order of conductivity or in the order of mean concentration, they exhibit quite a sufficient alternation of sign to warrant the conclusion that they are due, chiefly at least, to errors in the observations and the graphical portion of the calculations. In the case of the stronger solutions, Nos. 16-18 and 19-22, the alternation of sign has disappeared. In the weakest solu- tions of these two series the differences are positive and small; but as the concentration increases, the differences become negative and take increasing negative values, the negative difference having its greatest value in No. 22, which is a mixture of a strong solution of NaCl with a saturated solution of KCl. The tendency towards a negative difference as the concentration increases may be recognized also in Nos. 11 and 15; and it is perhaps worth noting that, while the mean value of the positive differences is slightly greater than that of the negative differences up to a concentration of 1 gramme- molecule of salt per litre, the mean negative difference is the greater for higher concentrations. It is manifest from these results that for solutions of these chlorides containing less than, say, 2 gramme-molecules per litre, it is possible to calculate the conductivity very exactly, but that for stronger solutions the calculated value is less than the observed. This excess of the observed over the calculated conduc- tivities shows one or more of the assumptions implied in the mode of calculation to be erroneous. It would seem to be probable that the error is at any rate largely due to the assumption that the molecular conductivity of an electrolyte at infinite dilution is the same whether it exists in a simple solution or in a mixture, and that the discrepancy is thus due to the effect of mixing on the velocities of the ions. The mode of calculation assumes that in the mixture the con- stituents are not really mixed, but lie side by side so that the ions of each electrolyte in their passage from electrode to electrode travel through the solution to which they belong only. They must rather be regarded, however, as passing in rapid alternation, now through a region occupied by one solution and now through a region occupied by the other. The actual mean velocities of the ions in the mixture will therefore probably differ from their values in a solution of the Conductivity of Mixtures of Electrolytes. 287 their own electrolyte only. In the case of dilute solutions the difference will be small, in sufficiently dilute solutions Inappreciable ; but in the case of the stronger solutions it may account in large part for tne discrepancy observed above, We have, however, so far as I am aware, no data for calcu- lating the effect of mixture on the ionic velocities, or the extent to which the discrepancy is due to this effect. To obtain some rough conception of its magnitude, I have calculated the conductivity of the mixture No. 18 on two assumptions, which seemed more or less probable,—viz. (1) that the velocities of the ions of each electrolyte in the mix- ture were the same as they would be in a simple solution of their own electrolyte of a concentration (in gramme-molecules per litre) equal to the mean concentration of the mixture ; and (2) that the velocities of the ions of each electrolyte, when passing through a region occupied by the other electro- lyte, were the same as they would be in a simple solution of the former of a dilution equal to that of the latter. The expression used for the conductivity was i} Uy! ‘We, k= —| ain — + aon. aie 2p 1 Me 22h o. Us where wu, and w, are the sums of the velocities of the ions of electrolytes 1 and 2 respectively in simple solutions of the dilutions which they have in the mixture, while wu,’ and wu,’ are the values these ionic velocities would have according to the particular assumption employed, the velocities in all cases being those corresponding to the same potential gradient. As the graphical process above gave the dilution of each elec- trolyte in the mixture, the values of u and wu’ were readily determined by the aid of Kohlrausch’s table of ionic velo- cities*. I found that according to assumption (1) the con- ductivity would be greater than Bender’s reduced value by 1°6 per cent., and that according to assumption (2) it would be greater by 1°3 per cent. Similar calculations could not be carried out in the case of solutions stronger than No. 18 owing to lack of data. Such calculations are of course of little value ; but they strengthen the suspicion that the excess of the observed values of the conductivity of mixtures over the calculated values is due to the impossibility of taking into account the effect of mixing on the velocities of the ions. * Wiedemann’s Annalen, 1. p. 385 (1893). X2 [ 288 ] XXXII. Thermodynamic Properties of Air. By A. W. WitKowsx1*. [Plates I. & II.] Parr I. A. Thermal Expansion of Compressed Air. gi. Alu of the Work.—It was an important advance in the theory of gaseous matter, when the experimental investigations of Despretz, Pouillet, Rudberg, Regnault, and several others demonstrated the approximate character of the fundamental laws of Boyle and Charles. Instead of a common and single law of compressibility and thermal expansion for different gases, there arose the necessity for determining specific corrections of these laws for every one of them. But as soon as the range of temperatures and pressures had been enlarged, new analogies between the physical pro- perties of these bodies became once more evident. First of all, the theory of the critical state may be mentioned here, supported by the discoveries of Andrews, Cailletet, Wrob- lewski, Olszewski, and many others. On the other hand, these analogies found their expression in the laws of compres- sibility, thanks to the investigations of Natterer, Cailletet, Amagat, and Wroblewski. At the present time the theory of gases seems to be entering a third phase of its development, initiated by Van der Waals, and supported by Wroblewski, L. Natanson, Ramsay, Young, and many other investigators. There are many facts which seem to show that possibly there may be found, not merely an analogy, but even an identity of properties of different gases, provided that for every one of them special specific units of measure (of temperature, pressure, and density) be employed: all matter seems to be built on the same plan ; but the scale is different for various bodies. It is difficult to judge nowadays whether this grand law is an exact truth, or only an approximation: whether it: is really universal, or confined only to certain classes of bodies. To confirm or disprove it, numerous and very exact experi- mental data are greatly needed. Investigations of the compressibility and thermal expansion in very extended limits prove to be the best means of com- paring the thermodynamic properties of gases: in every case * Translated from the xxiii. Vol. (1891) of the ‘ Rozprawy’ of the Cracow Academy of Science (Math. Class), and communicated by the Author. Thermodynamic Properties of Air. 289 they give fuller and more exact information than observations of critical points, or other singular states. Amongst recent work in this direction the very important investigations of Amagat, extending to very high pressures, must be placed in the first rank. They contain exceedingly valuable data, relating to the compressibility and expansion of gases at ordinary temperatures and at higher ones. Amagat’s results give a very clear and extensive idea of the behaviour of several gases, chiefly of those the critical point of which is not far from ordinary temperatures. Until quite recently the so-called permanent gases had not been. investigated at very low temperatures. So far as I know the important paper by Wroblewski, .“‘On the Com- pressibility of Hydrogen,” published after the author’s death in the Sztzungsberichte of the Vienna Academy, is the only one relating to this range of temperatures. This want of information as regards the compressibility and expansion of permanent gases in the vicinity of the critical state has induced me to undertake the experimental investigation of which the present forms an account. ‘The properties of atmospheric air are described here, at temperatures ranging from +100° to —145° Cent., and for pressures from 1 to 130 atmospheres. § 2. Outline of Method.—In order to determine the com- pressibility at different temperatures, and through it also the expansion of gases, two experimental arrangements were chiefly used: in one of them the quantity of gas remains constant, in the other its volume. We might call them the manometric and the volumetric method. In the first of these methods (Andrews, Amagat, &c.) a long calibrated capillary glass tube, enlarged at the open end into a bulb of known volume, is employed. A certain quantity of gas is shut up in the tube by mercury. By means of a compressing arrangement the volume of the gas may be varied at will. The experiment consists in determining the volume and temperature of the gas and the amount of the applied pressure. The method of constant volume was invented, so far as I know, by Natterer. A vessel of known volume was filled with gas under a known pressure. The experiment con- sisted in measuring the quantity of gas contained in the vessel at a certain temperature. This was done in the so- called pneumatic trough, under atmospheric pressure. This method has been used also by Wroblewski in his experiments on the compressibility of hydrogen at low temperatures (the first method being useless here on account of the freezing of the mercury). 290 A. W. Witkowski on the — The determination of the compressibility of a gas at a set of temperatures, together with its thermal expansion under a single pressure (say the atmospheric), gives at once the ex- pansion under any of the pressures employed. And vice versa, if the compressibility at one chosen temperature be known, | it is sufficient to determine the thermal expansion of the gas under different pressures, in order to obtain directly the compressibility at any of the temperatures employed. The first of these two ways was followed by Wroblewski in his above-mentioned work on hydrogen. In the present investigation I have used experimental appliances modelled on those of Wroblewski, and my theoretical aim was a similar one; but I preferred to apply the second way of experimenting, viz., the thermal expansion, instead of the compressibility, has been considered as the principal subject of the experiments. The following considerations have induced me to make this change. first, the difficulty of measuring pressures exactly. Since absolute manometers, suitable for laboratory use and sufficiently trustworthy, are still to be invented, we are compelled to use gas-manometers, founded on the com- pressibility of gases (air or nitrogen). The pressure calculated according to the indications of an instrument of this kind, as well as the law of compressibility of the gas under investi- gation, depend, in this case, directly on the assumed law of compressibility of the gas used in the manometer. Suppose we take this law as known, say through the experiments of Amagat, then our results will be inextricably mingled with these results. The method to be described presently, de- pending on determinations of expansion under constant pressure, on the other hand, furnishes values of expansion entirely independent of any accepted law of compressibility : a dependence of this kind remains only in the values of the pressures applied. Another reason which induced me to depart from Wrob- lewski’s combination of the gas-manometer with the constant- volume method of Natterer, was. the wish to invent a method of constant sensibility as regards pressure- meaurements, and the determinations of expansion and compressibility as well. The gas-manometer is an instrument of variable sensibility ; the higher the pressure measured, the less is the exactness of measurement. On the other hand, the volu- metric method is one of constant sensibility ; ¢. e. like inere- ments of pressure yield approximately equal increments of the quantity of gas. Instead of combining two methods of such opposite cha- Thermodynamic Properties of Air. 291 racter, I preferred to measure both pressures and expansions by the volumetric method. By this device, as 1 hope, the exactness and homogeneity of the results were materially in- creased. § 3. The Coeficient—In order to determine the thermal expansion of air at constant pressure (1 to 130 atmospheres), I have applied the following arrangement :—Two vessels of known capacity are filled simultaneously with gas, under any desired pressure, by connecting them with a reservoir con- taining a sufficient quantity of condensed gas. One of these vessels is cooled or heated to any temperature 0; the other is kept at the constant temperature of melting ice. Let p atmo- spheres be the common’ pressure in both vessels; s, and s, their capacities, at the respective temperatures 6° and 0°, under the common pressure p. The quantities M, and M, of gas contained in the vessels are then brought under atmospheric pressure and temperature : having measured their volumes, we calculate M, and M, in the usual way. As unit quantity of gas I take here, and in the following pages, the mass contained in unit volume (cub. nm.) at 0° Centigr. under the pressure of one atmosphere. The densities of the two masses, when compressed in the vessels s,; and s,, are unequal; the colder one is also the denser. Let their densities be p, and p2, then we have _M _ My Pi 51 3 — 89 7 ame oS Ome out Pa if + An 7 3 therefore he 1 M, Sy pi = Eis 0 : ° . : ° ° (1) This formula may be employed to calculate a); 2. ¢., the mean coefficient of expansion of the gas between 0° and 6°, when under the constant pressure of p atmospheres. It will be remarked that the value of a, is made here to depend on two ? M, In most of the experiments to be described the temperature of the vessel s, was not 0°, but t° (usually +16°). In this case we have Se ie Sh 1+ ayo.’ ven Sf gil Poy. ti ene s ratios,—~ and = and on the temperature @. 2 292 A. W. Witkowski on the . therefore Meets Ano = (1 + yt» t) Mi, = ae 6 0 eee one (2) § 4. Description of Apparatus.—A general representation of the apparatus I have used to obtain the values of the co- efficient 2 will be found in fig. 1. | Fig. 1. M, The vessels denoted above by s, and s, are two thick-walled glass bulbs, melted on to capillary stems o, and o>, the diameter of bore of which is less than mm. On each of the capillary tubes a mark m is drawn at a distance of 3-4 cm. from the bulb, to limit the capacity s. The capacities of bulbs and stems were measured repeatedly, before and during the experiments, by mercury weighings. The capacities s, and s, were nearly 2000 c.mm. (in some experiments at the lowest temperatures, only 1000 c.mm.) ; the capacities of the capillary stems (o, and o,) were not more than 8 to 10 c.mm. The upper end of each stem (o, and o,) is connected with a sort of distributing apparatus, provided with two screw- valves, of which one is used to fill the bulb with gas, the other Thermodynamic Properties of Avr. 293 to transfer the gas to the eudiometer, where its quantity is to be measured. This arrangement is quite similar in plan to that used by Wroblewski in his already-mentioned investi- gations on hydrogen. As regards details, I have adopted, after several unsuccessful trials, the following construction, which proved quite trustworthy and convenient :— A brass cylinder, A (fig. 2), is bored along its axis from Fig. 2. WWW, 6@Q]H_dHnH qu, ppt MX Gua WSS SV RAN \ ARK ANY \ « ANY \\\\ Le Z; LENGYLLL LL SA U both ends ; in its centre the,borings are connected by a very short and narrow channel 7s, communicating with another vertical channel, ¢, of very small capacity. The channel t is connected with the stem oa in the following manner:—On the upper end of o there is cemented, by means of fine sealing- wax, a thick-walled brass tube B, provided near its lower end with a collar. The end of the glass stem, cut perpendicularly to its length, protrudes some +’, of a millimetre from the flat end of B. The glass bulb s, with its stem and brass tube B, form a separate piece, which is to be coanected tightly with the cylinder A. This is done by means of the external screw M, in a way sufficiently indicated by the figure. To ensure 294. A.W. Witkowski on the . perfect tightness a circular perforated plate of lead, dd, care- fully cleaned, is placed between the flat end of B and,the bottom of the corresponding boring in A. Through the pres- sure of the screw the hole in the lead plate gets reduced to a very small size, and at the, same time a perfect pressure-tight connexion is ensured. It is necessary, however, that the metallic surfaces in contact be quite clean and bright. To shut up the compressed gas in the bulb two steel screw- valves, K, are employed (one is shown in the figure). They consist of a cylindrical spindle, carefully turned and polished, provided with a conical end; near the outer end a screw- thread is cut, working in the screw-head G. By means of the same screw-heads Ga number of leather rings, cleaned with ether and impregnated with beeswax and paraffin-oil, are compressed in the stuffing-boxes around the cylindrical polished parts of the spindles. This mode of tightening proved perfectly capable of withstanding the highest pressures em- ployed, although the tightening of the screw-valves.is far. less important than that of the channel r st, which is effected solely by contact with metallic surfaces. On both sides of the channel 7s there are two metallic out- lets, C and D, soldered to A. Through C (fig. 2) the bulb sy, and similarly s,, is charged with compressed gas; to do this simultaneously in both bulbs, stout copper tubes of small bore, soldered in C and C, are connected by means of a metallic T-tube with the reservoir Z (fig. 1) containing compressed air. In the connecting-piece another screw-valve P is in- serted, through which the interior of the bulbs may be made to communicate with the atmosphere. The valves N, and No, facing C and C, will be called here for brevity the “ charging valves.” Through the second pair of outlets D and D (fig. 2) the charges of air, compressed in the bulbs s, are delivered for the purpose of measurement; this is done by unscrewing the “discharging valves” R, and R, (fig. 1). The measurement of gas-quantity has been effected in special glass flasks E, and H, (fig. 1), which may be called eudiometers. For the sake of distinctness of drawing, H, and Kj, are represented in the figure on opposite sides of the appa- ratus ; in reality they were placed near one another. The discharging-tubes D and D were connected with the eudiometers by means of capillary copper tubes a, a, (fig. 1), ending on the eudiometer side in perforated steel stoppers ; these were cemented in the upper ends of the eudiometers by means of sealing-wax. ? Kach eudiometer consists of a vertical glass tube, some Thermodynamic Properties of Air. 295 80 cm. in length, on which five bulbs of nearly equal capacity have been blown; the connecting-pieces are provided with divisions in millimetres. The eudiometers are surrounded by wide cylindrical jackets of clear glass filled with water. Two thermometers, 6, and @,, immersed in the water give the temperature of the gas; air-streams blown in through p’ and p”’ serve to equalize the temperature of the water. The eudiometers are connected by means of thick-walled indiarubber tubing with open mercury-manometers M, and M,, fixed to two sliding pieces on a vertical wooden support (cot shown in the figure). The calibration of the eudiometers was effected after they were put in their place and surrounded with water. To do this by mercury-weighing, the glass stop-cocks near the lower ends of the eudiometers were provided. Positions of the mercury meniscus were read by means of a cathetometer, placed in a position where it was to remain during the rest of the experiments. In this manner both eudiometers were cali- brated twice. From the results of calibration I prepared a table giving capacities in cubic millimetres (at the standard temperature of +17° C.) corresponding to every scale- division. Hach of the five glass bulbs had a capacity of nearly 40 c.cm., the whole eudiometer about 210 c.em. One milli- metre on the glass necks corresponded to 60 c.mm. capacity. Therefore the smailest volume which could be appreciated was about 3 c.mm. After calibration of the eudiometers, I made another set of measurements in order to determine the capillary depres- sions &c. These corrections (of small importance) have been determined for every scale-division in an obvious manner. § 5. Preparation of Gas.—To complete the description of the apparatus, a few words remain to be said about the reser- voir of compressed air and the mode of compressing and purifying the gas. One of the well-known carbonic-acid bottles of 11 litres capacity, resisting 250 atmospheres, is used as air-store. The usual screw-valve is replaced by a simple stopper of brass with a copper tube soldered in it, connecting the reservoir Z with two drying-tubes 8’, 8”. These are made of steel, and are filled with finely grained chloride of calcium and potassium hydroxide, stoppered by thick layers of cotton-wool. A considerable quantity of these substances is also contained in the reservoir Z% in a vertical tube of wire-gauze. The air submitted to experi- ment is compelled to pass the drying-tubes twice—during the charging of the reservoir, and again on its way to the apparatus. Besides that, it remains a long time in contact with the drying-substance in the reservoir itself. To condense the gas, a Natterer condensing-pump has been 296. A. W. Witkowski on the . employed. The usual oiled leather piston is replaced by one packed with fibrous asbestos, and lubricated by a very small quantity of water (a device used also by Wroblewski). Although this arrangement renders the working of the pump exceedingly tedious, nevertheless I found it absolutely neces- sary, as the oiled piston yielded a very impure gas. The air was taken from the outside of the laboratory ; it passed through several washing-bottles filled with solutions of potassium hydroxide and sulphuric acid. After condensation, it was dried in the manner described above, The air treated in this way was submitted repeatedly to chemical tests, and proved to be sufficiently pure and dry. § 6. Determination of s, and s.—Before commencing the experiments, it was necessary to determine very exactly the capacities of the bulbs s, and s,. This was done by mercury- weighings at the temperatures 0° and +100°. The true capacity during experiment depends on the temperature of the bulb and on the pressure employed. To calculate the capacity at low temperatures, I used the coefficient of expansion of glass, determined in the interval . 0° to + 100°, and corrected it in accordance with the expe- riments of I. Zakrzewski on the expansion of solids at low temperatures *. The influence of pressure on the capacity of the bulbs has been determined directly by submitting them to known pres- sures while filled with well-boiled mercury. From the observed variations of position of the meniscus in the calibrated stem, it is easy to calculate the variations of capacity with the aid of Tait’s and of Amagat’s determinations of the compressibility of mercury. In the limits of pressure used this dependence was a linear one. Denoting the corresponding coefficient by #&, we may write s,=s(1+ 2p). For a pair of bulbs of very unequal capacity (1: 2), I have found #=0:0000062 and «=0:0000064 (per atmosphere). These values refer to ordinary temperatures. As there is nothing known about the variations of elasticity of glass at very low temperatures, I have always used the above value of «; I consider the error resulting from this proceeding as altogether insignificant, the more so as the correction itself, depending on pressure, is very small. § 7. Mode of Ewperimenting—I will now describe the mode of experimenting and calculation of the results. * Transac. Cracow Acad, vol. xx. (math. class.). Thermodynamic Properties of Air. 297 The apparatus having been filled repeatedly with pure and dry air, I bring the movable manometric tubes M, and M, to such levels as to fill both eudiometers E, and H, with mercury; the meniscs are then brought as near as possible to the zero marks of the eudiometer-divisions. (The stopcocks P, N,, N,, R,, R, are opened for this purpose.) The small volumes in the eudiometer-tubes left between the meniscs of mercury and the zero marks will be denoted here by w, and w). As soon as equality of pressure in the interior of the appa- ratus and in the atmosphere (=0) has been established, I close the discharging-valves R, and Re, as well as P, and charge the apparatus with compressed air at that particular pressure for which the expansion is to be measured. During the charging both bulbs s; and s, remain in connexion with the large store of air contained in the reservoirs Z, 8’, 8”. This connexion ensures great constancy of pressure in case there should be a small leakage of air somewhere. During the charging of the bulbs I determine their tempera- tures (¢ and @), as well as the temperature (=7) of the sur- rounding air. Next, I shut the charging-valves N, and N, both at the same instant, and immediately after that I open the discharging-valves R,, R,. The interval of time during which the charge remains imprisoned in the bulbs is less than one second. The air flows now from the bulbs into the eudiometers. During this I lower the manometric tubes M, and M,, so as to reduce the gas (which fills now several bulbs in each eudio- meter) as nearly as possible to atmospheric pressure. The temperatures of the water-baths surrounding the eudiometers having been equalized by air-currents blown in through p’ and p’”, I proceed to determine, with the aid of the telescope of the cathetometer ,— (1) The temperatures 3, and 3, of the gas in both eudio- meters ; (2) The volumes uw, and wa of air in both eudiometers, reckoned from the zero marks ; (3) The differences of level of mercury in the eudiometers E and in the corresponding manometric tubes M, and Mg. Taking into account the corrections mentioned in § 4, as well as the barometric pressure, it is easy to find the pressures of air in the eudiometers H, and in the bulbs s, which are now in communication with H. I shall denote these pressures by B, and By. | _ During these determinations the temperatures of the bulbs are again measured (=¢/ and 6’), | In this manner every single determination of the coefficient 298 A. W. Witkowski on the - a has been conducted. It takes some time, from 10 to 20 minutes, to perform the necessary measurements. At the lowest temperatures this time was considerably longer, because in this case it is necessary to provide a sufficient quantity of the freezing substance (solid carbonic acid, liquid ethylene) ; to regulate the speed of the pneumatic pumps and of the gas- motor by which they were driven, in order to obtain the required temperature ; to compare the electric thermometer for low temperatures with the hydrogen thermometer, &c. Under such conditions it happened that during a day I was not able to make more than one or two determinations—to say nothing of the frequent occurrences, when, after several days of laborious preparations, the intended experiment has been entirely lost, through some mischance or other. I think it necessary to mention these difficulties of experimenting in order to explain the comparatively small number of results obtained at the very lowest temperatures. § 8. Calculation of Results —By means of the experimental data gathered in the manner described above, the results have been calculated as follows :— The bulbs being charged, and the charging-valves closed, we have the following quantities of gas in the apparatus :— 1. In the bulb of capacity s (index 1 or 2 omitted, since the same formula applies to both) there is the quantity M (§ 3) under the pressure of p atmospheres, at @ and ¢ (re- spectively) degrees. In the stem o, and the narrow channels 7 s¢ connected with it, there is confined a quantity m; under the same pressure p, but at the temperature 7 of the circumambient air. I shall use the letter x to denote the small capacity of this space. Adding together we find in the apparatus the quantity orb M+m=A under the pressure p. 2. In the copper tubes a, and a, (fig. 1)—TI shall use the same letters to denote their capacities—and also in the eudio- meters themselves (in the spaces denoted above [§ 7] by W1, W2), we have air under the barometric pressure 0. I shall use for brevity the symbol w(, 6) to stand for the expression jis DE yh On I+y5° 760? y being the coefficient of expansion of air of ordinary density at ordinary temperatures (=0-00367, very nearly a constant). Thermodynamic Properties of Air. 299 Then the above quantities are a(t, b) +w(S, b) expressed in normal volume-units. This same quantity of air which occupied after charging the spaces s, o, a, and w, fills after discharge a space increased by that capacity in the eudiometer (uw is now the volume occupied in it) in which the mercury has been replaced by air, plus a small capacity (K=42 c.mm.) laid open by un- screwing the valve R (the valves were always opened by the same number of turns of the spindle). The whole quantity of air supports now the common pressure B. Consequently we have a new expression for the whole quantity of air, nanely: s(@, B)+o(7, B)+K(7, B)+a(7, B) +u(S, B). Equating we find the formula : A=M+m=u(S, B)—w(S, 6)+a(7, B—D) +(e Deep Kee |(r B) ower eon 6 73) § 9. Corrections—We have now to calculate the small amount m which is to be subtracted from A. Consider the bulb No. 2, charged at temperature t= +16° C. Suppose the temperature of the corresponding space o were also exactly + 16°, then obviously we could write 02 m,=A,—_ . S94 Oe Taking into consideration the small difference of temperature between bulb (+16°) and stem (72) we write instead 1+yt Oo =A aaa ee e e e e e 4 *1+97 Sg +o ( ) Mg Simultaneously in the space oj, corresponding to bulb No. 1, we have the following quantity of air: L+yt s3+¢’ my, = As because in every case Mm 9; Mop co) 300 A. W. Witkowski on the In this manner we find, finally, M,=A,;—m,; M,=A,.—m, ; these values substituted in (1) or (2) lead directly to the coefficient e,p,9. . § 10. Corrections continued.—The first of the small capa- cities denoted above by a and o I determined by a simple volumetric method, with the aid of the calibrated eudiometer E and manometer M. It is superfluous to enter into par- ticulars. I will mention only that the value of a has no influence on the final result, provided we have exactly B=6 ; in general any small error in a influences the result quite insignificantly. The second of these capacities, viz. 7, is composed of two parts: the capacity of the glass stem, and of the narrow channels 7s ¢, together with the very small hole in the tighten- ing lead plate. The capacity of the glass stem, reckoned from the mark m, is obtained directly by weighing of mercury. In order to find the rest (3 or 4 c. mm.) of the space a, I stopped the connexion between the glass stem and the rest of the space o by interposing another (not perforated) lead plate and charged the channels several times with com- pressed air, at 50 or 60 atmospheres. The quantity of the collected gas having been measured with the aid of the eudiometer, it is easy to calculate the capacity of the channels, by applying Boyle’s law, or better Amagat’s results, for the compressibility of air at ordinary temperatures. § 11. Determination of Pressures.—The just mentioned results of Amagat* render also possible the determination of pressures. The pressures p, as already mentioned, I measured by applying the “constant volume” method, with variable quantity of gas. This I will now explain. If a given quantity of air be compressed more and more, by application of increasing pressure, then, as is well known, the product of. volume and corresponding. pressure—far from being constant, as it would be according to Boyle’s law— diminishes at first, until a certain pressure is reached, and increases afterwards indefinitely (so far as known at present). Let us denote by v, the volume occupied under the pres- sure of one atmosphere (=p), then we may express the law of compressibility of air by the formula OUI Se ENA e denoting a coefficient variable with the pressure p. The * Comptes Rend. 1884, p. 1154. Thermodynamic Properties of Air. 301 values of ¢ at ordinary temperature (+16°) have been de- termined with great care by Amagat with the aid of a huge mercury-manometer. Consider now a closed vessel, capacity s, charged with compressed air, under a pressure p, at ¢ degrees. Since a unit volume of air, exerting the pressure of one atmosphere (at +16°), gets reduced to v= when submitted to p atmo- spheres (by the last formula), then we infer that the air-mass compressed in the closed vessel when liberated and submitted to unit-pressure would occupy the volume = or, in the normal condition, when cooled to 0°, the volume : ps e(L+yt)’ It will be seen now that the apparatus described in the fore- going paragraphs may be used also as a manometer, recording pressures to be calculated by the formula : M poe = provided that t equals that temperature for which the values of e were determined, or at any rate that the difference be not too great. For this reason one of the bulbs of my appa- ratus was always immersed in a water-bath at +16°, together with a stirrer and a mercury-thermometer divided in 35 of a degree. Since the temperature 7 of the space o differed but slightly from +16°, we may write with sufficient accuracy : Se eee) on s+o The method chiefly employed till now for measurements of high pressures consists in the use of manometers charged with a constant quantity of gas. I thought it interesting to compare this method with the constant-volume method used by myself. For this purpose I connected my apparatus with a gas-manometer, charged at first with dry air, afterwards with pure dry nitrogen. From a large number of comparisons at various pressures, there resulted a slight but systematic difference of results: the values of pressures, as determined by my method, were constantly less, by several tenths per Phil. Mag. 8. 5, Vol. 41. No. 251. April 1896. Y 302 A. W. Witkowski on the cent., than the values recorded by the gas-manometer ; this applies as well to the air- as to the nitrogen-manometer. The sign of the difference led me to suspect a leakage of gas in some part of my apparatus. Therefore it was indispensable to submit the apparatus to a severe test, the more so as any leakage in it would vitiate the results, as regards expansion, to an incalculable extent. To test the apparatus I charged it (both bulbs at +16°) with compressed air, under a sufficiently high pressure, the value of which was determined simultaneously with the aid of the gas-manometer. The bulbs were then immediately dis- charged into the eudiometers. Next I repeated this same experiment, using the same pressure (as indicated by the gas- manometer), but instead of discharging the bulbs immediately I left them charged for a relatively long time (an hour or two). I was satisfied to find that the quantity of air collected after long imprisonment was not less than in the first case. As an instance of this sort of testing, the following numbers may be given :— first experiment.—Nitrogen-manometer = 89-06 atm. The bulbs discharged immediately after charging. Temp. of fe Bulb. bulb. sG@mm ocmm Ac.mm. (cale. by 5). Nose aeab —IhG 901°90 8°7 17723 88°60 No.2... ¢=16 1919-47 — 15°0" © 164903 88°49 Second experiment.—Nitrogen-manometer = 89:10. Bulbs kept charged 1 hour 15 min. Temp. of Bulb. bulb. S. o. A. Dp. Nona. <1 he 901°90 Si 17783 88°67 No. 2.5. $16 191047" ~ 15:0 WG5096 88°60 It will be remarked that the pressure indicated by the gas- manometer exceeds in both cases that calculated by (5) by 4 . per cent. nearly. At the same time it is apparent that there was no sensible leakage, since in the long-charge experiment the difference of pressure is even less than in the first. Iam not able to give a sufficient explanation of the observed difference, but considering that the constant-volume method employed in the present work deals with larger quantities of gas, and enables us to measure them with greater accuracy, Il am inclined to think that the results obtained with my apparatus are at least not less trustworthy than those recorded by an ordinary gas-manometer. Thermodynamic Properties of Air. 3038 § 12. Determination of Temperatures.—All temperatures referred to in this paper are reduced to the scale of the con- stant-volume hydrogen-thermometer. In all experiments at temperatures below zero there was placed in contact with the cooled bulb s, in the same freezing-mixture, the bulb of a hydrogen-thermometer. Yet the temperatures of the bulb during the experiments on expansion were not read directly on the hydrogen-thermometer—because of the waste of time unavoidable in such readings, and because of the slowness of indications, which renders the hydrogen-thermometer un- suitable to follow rapid variations of temperature. For this purpose I constructed a small working thermometer based on the variations of electric resistance of a fine platinum wire. A description of this instrument will be found in the appendix to the present paper. Here it will be sufficient to say that its sensibility was about 5, degr. Centigr. and its quickness very considerable. This electric thermometer has been compared very often with the hydrogen-thermometer, and a table has been drawn interpreting its indications in terms of the hydrogen-scale. Nevertheless I never used the electric thermometer otherwise than under control of the hydrogen-thermometer, because slight secular changes of its resistance manifested themselves. Comparisons of the working and the hydrogen-thermometer were made in the intervals between two consecutive experi- ments on expansion. During the experiments themselves an assistant read the electric thermometer a first time simultaneously with the charging of the bulbs, a second time immediately after dis- charging them (it will be understood that the freezing-mixtures used to obtain very low temperatures do not keep their tem- perature quite steady) ; the mean of these two readings has been accepted as the temperature (@) of the bulb. Finally, the temperature of the bulb was determined a third time (0’) during the measurement of the gas-quantity in the eudio- meters ; this temperature has been used to calculate the exact value of the gas-quantity remaining in the bulb. § 13. The Low Temperatures —In the manner explained above I executed some hundred and twenty determinations of the coefficient of expansion a, 9, using different pressures up to 130 atmospheres. One of the bulbs of the apparatus being kept at + 16°, the other was heated or cooled to the following temperatures :— +100° (steam), 0° (ice), —35° (a freezing- mixture of pounded ice and crystallized chloride of calcium), —78°5 (solid carbonic acid and ether), —103°5 (liquid ethylene, boiling under atmospheric pressure), — 130°, —135°, YZ | 504 _ A.W. Witkowski on the —140°, —145° (liquid ethylene boiling under reduced pressure). ae, | The arrangement of the thermostat in which liquid ethy- lene has been boiled under reduced pressure is represented in fig. 3. A tall cylindrical glass vessel A, standing ona horizontal Fig. 3. £® Hydrogen Therm. Lthylene | Electric Therm. P RQSSMM LLL Z Zz tA vA vA A iA A Z CA vA vA cA cA iA vA vA Z A A Z Z Zz Zi Z Zz 4 A A cA % A 4 (7 2 4 A A Z 4 A Z a Z A 4 A iA A 2 CA A A 2) cA cA A A A A A vA 2 A Z A A (A vA vA Zz; ‘4 tA vA A A iA Zz) A vA cA Zi Zz Zz A 2 a tA tA 7 | Zz Zz) 2 Zz Z 'Z) Zz Zz Z A kA lA iA tA Zz Z) A KA KA IA iA A Zz tA Zz A A A i] Z| Zz 4) tA iA A A 2) 2) A Z y Zz A tg Z : MA PEZDZETIEEZ Wi LL: 2, 77? MET brass plate, is covered with another brass plate PP, the dia- meter of which is somewhat larger than the diameter of the: upper flat edge of the glass vessel. By means of three brass pillars, fastened to the lower plate, and screw-heads pressing» Thermodynamic Properties of Air. 305 on the upper one, the cover can be made air-tight. Near the centre of the upper brass cover there are four circular open- ings. A fifth opening, with a short brass tube soldered in it, is placed near the circumference; it is connected by means of a lead tube with the pneumatic pumps. The just mentioned four openings are intended to introduce into the apparatus (1) the bulb s, which is to be cooled ; (2) the bulb T of the hydr ogen-thermometer ; (3) the electric thermometer T’. The stems of these three pieces are held by indiarubber stoppers cut into two halves and tightened by a beeswax cement. Through the fourth opening enters in like manner the delivering tube of the well-known apparatus of Wroblewski and Olszewski for liquefying ethylene. The cold liquid ethylene flows down into the thin-walled tall glass beaker C, surrounded by a wide glass tube B. This tube rests on three elastic pieces of indiarubber which press its upper edge firmly against the brass plate P. This double walling is intended to cool the surroundings of the beaker C by cold ethylene vapour, which is forced to circu- late as indicated by the arrows, until finally it is drawn out by the pumps. Liquid ethylene is very liable to get superheated and to evaporate in an explosive manner, especially when boiling under diminished pressure. This property is a great incon- venience when it is to be used to obtain constant tempera- tures. After trying different contrivances to avoid it (air- eurrents, Gernez’s air-bubbles, &.), I contented myself with the use of a large flask D inserted just before the pumps, in order to diminish the fluctuations of pressure accompanying the strokes of pistons. With the aid of this arrangement, it is possible to vary the boiling temperature of ethylene through a range of some forty degrees. Any desired temperature may be obtained by varying the number of air-pumps (I had three large Bianchi at my disposal), by inserting Babinet’s stopcocks, or by vary- ing the speed of the gas-motor driving the pumps.. With some practice it is possible to limit the range of fluctuations of temperature in one series of experiments to no more than 2 or 3 degrees. § 14. Construction of Isothermal Curves.—The temperature 6 of the bulb s in different experiments belonging to one series was not exactly the same. To obtain strictly isothermal values of the coefficient a, the following graphical method of interpolation was used. All series of experiments having been completed I constructed, on a large scale, a diagram similar to that represented on Pl. I., using uncorrected values 306 A. W. Witkowski on the of a. By means of graphical interpolation isothermals were then drawn, differing but little from the final ones given on Pl. I. With the aid of these isothermals I constructed another large diagram on which the values of « were col- lected on lines of equal pressure; z. e. temperatures were drawn on the axis of abscisse, the values of a belonging to like pressures formed the ordinates. The inclination of these lines to the axis of abscisse could now be used to find the correction which was to be added to the coefficient a,-33 say, in order to obtain the value of ay,-35, belonging to another isothermal, but to the same pressure p (—35° in this example being the mean value of temperatures in the chloride-of-calcium series). This I did by drawing through the point a,» (experimental value) a short piece of the corresponding isopiestic line, to its inter- section with the ordinate — 35°, or any other desired tempe- rature. In most cases these lines were nearly straight ; instead of drawing them I found it convenient to use a glass plate on which a straight line had been drawn with a diamond point. In some cases, however, the corrections were con- siderably larger, so that it was no longer possible to disregard the curvature of these lines; they were then drawn with reference to the inclination and curvature of the neighbouring isopiestic lines. § 15. Results—The whole of the results obtained are repre- sented in a graphical form on PI. I. The isothermal lines for the nine temperatures experimented on have been drawn by hand along the dots, representing experimental results*. Although some of these dots fall off rather considerably from their respective mean curves, yet, considering the whole of the diagram, I suppose the final results may be considered accurate, at least to four decimals. It is scarcely possible at present to aim at a greater accuracy: this will be admitted on considering the discrepant values of the coefficient of ex- pansion of air given by different experimenters in the relatively simple case of atmospheric pressure and temperature of boiling water. From the diagram Pl. I., drawn on a large scale, I took the mean values of the coefficient «, 4, reproduced in the following table :— * Tn the original memoir extensive tables are reproduced giving full information on the particular data belonging to every experiment. | 125...) ... | 466] 503 | 551 Thermodynamic Properties of Air. 307 TABLE of the mean Coefficients of Expansion of Atmospheric Air. (Values of 100000 . a, 9.) Temperatures 0. Pressures atm. +100°0 |+16°0 | —35°0 |—78:5 | ~103°5 | — 130-0 | — 135-0 | —140:0 | — 145-0 10, =.) . 375 376 15...| 379 382 | ... a see eae 420 427 20...} 383 BOLT ese 401 | 410 427 440 450 25...| 388 Ss Mee 411 | 422 443 ; 463 479 30...| 392 B98 |) se | 420 | 434 462 477 492 519 * ao.<.| SOT 403 | ... 429 | 448 | 483 506 538 40...| 402 408) |) «2. 438 | 461 508 544 632 45...) 406 ANAND MZ... 448 | 474 536 594 50...| 410 419 | 480 | 457 | 487 569 | 619 55...| 414 424 | 4386 | 467 | 500 598 623 60...| 418 429 | 442 | 476; 512 610 622 65...} 421 434 | 448 | 485} 525 612 621 70...) 425 438 | 454 | 494) 536 612 15...| 428 442 | 461 | 503 | 547 610 80...| 431 446 | 467 | 512] 557 607 85...} 434 449 | 473 | 520 | 566 90...| 437 452 | 479 | 527 | 572 95...| 439 455 | 485 | 532 | 577 100...| 441 458 | 489 | 5387 | 579 105...| 443 460 | 493 | 542 | 580 110...) 445 | 462) 497 | 545) 580 115...) 447 463 | 499 | 548) 579 120...; 449 465 | 501} 550 | 577 574 551 | 571 * Corresponds to 29 atmos. This table, or, better still, the diagram on PI. I., shows very clearly the kind of variation of the coefficient of expansion in its dependence on pressure and temperature. For increasing pressures the coefficient increases, at every temperature, to a maximum, and decreases subsequently. The higher the temperature, the less pronounced is this maximum. The pressure corresponding to the maximum of expansion diminishes with the temperature. From this it follows, that the rate of increase of expansion is the higher, the less the temperature. In the vicinity of the critical state (temp. = —141°, pressure 39 atm. nearly) the rate of increase of ex- pansion is extremely great, the corresponding isothermal runs here nearly vertically. The same holds good for temperatures below the critical, at points where liquefaction occurs, for instance at —145° and 30 atm. The isothermal lines of the coefficient of expansion form a fan-shaped bundle converging nearly to one point, namely, to the value 0°00367 at 1 atm. of pressure. If this were 308 A.W. Witkowski on the- - strictly true, the expansion of air, subject to a constant pres- sure of 1 atm., would be independent of temperature. Now this is known to be approximately the case ; but on the other hand it is certain that the isothermals cannot converge strictly to this point, since the pressure at one atmosphere has nothing in common with the internal constitution of air. From some experiments it would appear that the isothermals do not intersect at all low pressures; they come very near one another, descending toa minimum at certain low pressures, and probably return afterwards in a steep course towards higher values. : B. Compressibility at Low Temperatures. | § 16. Definitions—It is now a simple matter to calculate the compressibility of atmospheric air at any one of the nine temperatures investigated above ; the compressibility at + 16° being assumed as known through the work of Amagat (§ 11). Let vg denote the normal volume (at 0° and 1 atm.) of a certain quantity of air. When heated or cooled to any temperature @, and submitted to a pressure of p atmospheres, the air assumesa volume v. Admitting Boyle’s and Charles’s law, we should write v= (1+ 98); or pu=v%)(14+ 78). Now, in reality, the product pv is not independent of the pressure p, and its dependence on @ is not a linear one. Instead of the above, we must write : Pv=]n .%, o>... re n( p@) denoting a certain function of p and 6, the values of which are to be calculated. This we may do as follows :—Consider a volume 1% of air in the normal state. Heat it, at constant pressure (=1 atm.) to +16°; the volume increases to v(1+y. 16). At this temperature submit it to a pressure of p atmospheres, then according to the notation of § 11 we obtain the volume 2 v(l+y . 16) 3 iY finally heat it at the constant pressure p to @ degrees. Denoting by «, ,, and @, , the coefficients of expansion corre- sponding to the pressure p and to the ranges 0-16 and 0-0, we get u(l+y.16) 14+06.a56 ey p 1F 16. 16 Thermodynamic Properties of Air. 309 Now this is identical with . Vo ae theref g erefore es 1+16.¥ | Dae NGiieslig tc 9) - . CT) be evident when we remark, that the quantity of air =M (expressed in normal volume-units) contained, at a tempe- rature 0 under p atmospheres, in a vessel of capacity s is M=—?S, n I preferred to calculate the values of 9 according to (7) because it is easier to obtain values of the coefficient free from accidental errors than those of 9. The following table contains values of the function »(p,@) calculated in the manner indicated. TABLE of Compressibility of Arr. 2 Temperatures. H ae ee | Rae | Fs +100) +16} O | —35 |—78-5|—103-5| —130| —135 —140 | —145 SS = —— | | 1.../1:867 |1-0587 1-0000 0:8716 0-7119 | 0-6202 (0:5229 0:5046 0-4862(0-4679 eG 11-3678 11-0550 09051 |: ae = ae me ees | 15...|1:8685 |1-0529| 9923 On iy 2 04095 0-3786 | 20.../1°3691 |1:0509 | 9897 0:6778 | 0°5697 |0-4410 3808 | 3447 25...|1°3698 |1-:0488 | 9869 6689| 5559] 4183] ... ‘| 3476! 3015 | 30.../1'3704 |1-0468 | 9842 6599 | 5417) 39360-3502} 3063 2444* _ 85.../1:3713 |1-0449 | 9816 | 6510| 5270} 38650} 3115] 2419] | 40.../1:3725 |1-0433 | 9793 | 6423} 5125} 3329) 2598] 1128 | | 45 ..|1:3738/1:0419| 9772) ... | 6335] 4980) 2963] 1942 | 50...11°3754/1-0408 | 97540-8288] 6252} 4839) 2544! 1605) 55...|1°3770 |1:0399 | 97388} 8253} 6170} 4701| 2171| 1553 60...[1-3784|1-0390| 9723) 8219} 6089} 4567) 2013| 1556. 65.../1°3802 |1:0384 |. 9710} 8187] 6011} 4439) 1985| 1576 | 70...|1:°3821 |1:0381| 9701| 8158! 5937| 4318] 1989 | 75...|1°8842 |1:0375| 9694} 8132] 5863} 4206] 2013 80...|1°3866 |1:0379 | 9688} 8105) 5796| 4103} 2043 85.../1°3887 |1°0380} 9684] 8081| 5734] 4014 90...|1:3908 |1:0382} 9681} 8058| 5680} 3948 95...|1:3929 |1:0386 | 9680} 8038} 5634) 3903 100...|13951 |1-0390 | 9681} 8023} 5600) 3881, 105.../1°3977 |1-0897 | 9685; 8013| 5568| 3874 | 110...|1-4004 |1-0406 | 9690, 8006] 5544) 3877 | 115...|1:4034 |1:0418 | 9699| 8004! 5530} 3892 120...|1:4065 |1:0432 | 9710| 8006| 5520) 3914 | 125...) ... {1:0448| 9722] 8012| 5520] 3944 | £20: . 1:0467 a :.. -| 5528] 3981 | } * Corresponds to 29 atmos, 310 A. W. Witkowski on the These numbers are represented in a graphical form on Pl. IJ. by means of so-called curves of compressibility (abscissee = pressures, ordinates=isothermal values of y=pv ; the axis of abscissee through the point (1). It may be well to remark that, on assuming Boyle’s law to hold for all pressures and temperatures, these curves would be straight lines parallel to the axis of abscissze. Every one of these curves shows a minimum of the pro- duct pv for a certain value of p (depending on the tempera- ture of the corresponding isothermal). This expresses the fact, verified for many gases at higher temperatures, that with increasing pressure the compressibility exceeds at first that given by Boyle’s law until a maximum is reached, afterwards it diminishes indefinitely. In the vicinity of the critical point the curves of compressibility run downwards very steeply ; at points where liquefaction occurs their course is vertical. § 18. Comparison with other Gases——The general proper- ties of atmospheric air as regards expansion and compressi- bility are quite analogous—apart from the large difference of critical temperatures—with those of other gases which have been investigated hitherto in this respect. It is interesting to inquire whether this resemblance of properties is merely a qualitative one, or whether it is more deeply rooted ; in other words, is it possible to calculate beforehand the properties of a gas, assuming the properties of another to be known ?—this is the thesis of van der Waals. Wroblewski, in his memoir on the Compressibility of Hydrogen, asserts the possibility of such predictions. Take for any one gas the critical pressure for the unit of pressure ; for the unit of temperature its critical temperature (absolute) : then Wroblewski’s theorem asserts that the dependence between the temperature and that value of the pressure for which the product pv is a minimum, is the same for all gases. A more general theorem is due to L. Natanson, namely, that all gases have a common character- istic equation, 2. e., a common relation (not necessarily that of van der Waals) between pressure, temperature, and volume, provided that these elements be measured by means of units specially adapted to the nature of every gas; the critical elements form one of the infinitely numerous groups of such units. The critical elements of air are given by Olszewski as follows :—crit. pressure = 39 atm. ; crit. temperature = — 140° Cent. ‘These data are also confirmed by my own experiments ; I should only consider —141° as a nearer approximation to the true value of the critical temperature. A comparison of atmospheric air with other gases may be best effected on the Thermodynamic Properties of Atr. dll basis of Wroblewski’s theorem. With the aid of the table of compressibility given in the preceding paragraph, we calculate the following values of the pressures for which the product pv is a minimum :— Temperature. Pressure. Min. pv (approx.). +100 Lessthan10 atm. 1°367 + 16 19 10379 0 95 0°9680 — 395 115 08004 — 78°5 123 0°5519 —103°5 106 0°3873 —J1a0° . , 00 0°1985 —135 o7 0°1551 The points corresponding to these values of p and pv are connected on Pl. Il. by a dotted curve. _ Now, changing units, take the values 132° (abs. crit. temperature) and 39 atm. as new units of temperature and pressure (which will be denoted on this convention by + and a), then the foregoing table turns into the following :— T= 2°82 mT <0°25 aula = 2°03 ee Od . yy 2°44 et thad ar ero su AAs i ole » 1:29 saree ” 1:08 ” oo » 10d ae L4G Draw a curve taking the 7’s and m’s for abscisse and ordinates, then according to Wroblewski this should be one curve for all gases. Now it will be found that the curve plotted in accordance with the above numbers runs really very near that drawn by Wrobiewski*, and based chiefly on experi- ments on carbon dioxide and methane. It is difficult to tell if the remaining differences are real or else depend merely on experimental errors. At all events it may be taken for granted that these coincidences, as they stand now, are most remarkable. I have limited my experiments to the gaseous states of air, but at the same time I tried to approach to tlie limits of lique- faction as near as possible. It is a very difficult. matter to experiment near those limits ; very constant temperatures are of great importance. It happened frequently that, in con- sequence of a slight variation of temperature, the glass bulb of my apparatus was found full of liquid air, instead of com- pressed gas. for the present time I abstained from an ex- * Pl. iv. of the paper on Hydrogen, 312 .. A.W. Witkowski on the - ploration of the region of liquefaction ; | intend to go through it on ancther occasion, when investigating the properties of simple gases. In concluding I wish to express my dhonke to Dr. J. Ved krzewski, to whom I owe many valuable suggestions, and who undertook a great part of the very considerable labour which was necessary to obtain the results given in the present paper. Cracow, Physical Laboratory of the Yagellonian University. = May 1891. [To be continued. | APPENDIX. Electrie Thermometer for Low Temperatures*. Variation. of the electric resistance of wires depending on variation of temperature has been often employed to construct thermometric appa- ratus. Fig. 4 shows (nearly true size) a disposition of electric thermometer which the author has found-very useful in low- temperature work, on account of its sensi- bility and quickness. A short cylinder r of thin sheet-copper is soldered at one end of a narrow brass tube ¢ through wkich passes a rather thick silk-covered copper wire d cemented with a mixture of resin and india-rubber. ‘The outer end of the brass tube ought to be carefully covered with this mastic in order to prevent con- densation of moisture on the thermometric wire. The copper wire and the brass tube are furnished with binding-screws a, b to | introduce the current. On the outer side of the cylinder v there are wound 2 or 3 metres of a very fine silk-covered platinum wire (diameter about 7¢g millim.) ; one of its ends is soldered to the cylinder r, the other to the end of the copper wire d. To protect the coiled wire, another sheet- copper cylinder 7’ of somewhat greater diameter is pushed over it. Both cylinders y and 7” are joined by a small quantity of solder applied round the circumference of their bases. -* Bulletin internat. de U Acad. de Se, de Cr ee, ae 189], Thermodynamic Properties of Arr. 318 In this-manner a platinum resistance is obtained of some 220 ohms at.0°. It forms one branch T (fig. 5) of a Wheat- stone bridge. A second branch is formed by a resistance of german-silver wire contained in a case K of exactly the same construction as shown on fig. 4, but on a larger scale ; it is kept at the constant temperature 0° by melting ice. The third and fourth branches of the Wheatstone bridge are resist- ance-coils in one and the same box R, namely, a coil of 1000 ohms and a variable resistance R. B is a battery of two elements of oo M a commutator, Ga sensitive galvanoscope. To every temperature of T there corresponds a iioomniate resistance R in the box. By comparison with a normal hydrogen-thermometer, it is possible to construct a diagram, or a table, with the aid of which one may find by inspection | the temperature T corresponding to any observed resistance R. Such a table does not cease to be true when the apparatus, after having been dismounted, -is to be used again several days or months later; the relation of T and R is of course independent of the electromotive force of the pee or the sensitiveness of the galvanoscope. A table of. this kind is -given: below; at the same time it shows the relation of resistance and temperature (hydrogen- = —- a. certain platinum 1 wire. Be Gi 314 Thermodynamic Properties of Air. ie ie Ae R. 4-50 1105-9 =a) 801:8 0 10000 —100 778-9 =10 978-5 = 110 755°8 —320 956-9 —120 732-4 = 3 9352 — 130 708-9 —40 913-4 Say 685°3 —50 891°4 = 150 661°5 60 869°3 = 160 637-3 —70 847:0 ~—170 612°7 — 80 824-5 —180 — 588-0 The variation of resistance is about 2 ohms per degree ; therefore it is easy to obtain a sensibility of 31,° Cent. Experience has shown that the relation between resistance and temperature undergoes slight changes when the thermo- meter is employed at widely different temperatures. For this reason it is better to avoid heating a thermometer destined for low temperatures ; this might cause a variation of resist- ance which would not disappear until after several months. Note added by the Author. It has been found since that fine iron wire answers the purposes of low-temperature thermometry still better than platinum. Both constancy and sensitiveness are greater. The following data apply to an iron thermometer which has been now four years in use. Diameter of wire =0°035 millim., resistance at 0° about 576 ohms. Displacement of Zero-point. January 1892 . ... . BR, =1001°380 ohms Marnchy pf .1e92hee ak ah se - 1001;50- +5 June 1892 aceis Tati 1001°23 =, Hebruaty1S98- qoieule: = 1000°97 - .,, December 1893 . . . . LOOL1O... & March O04 Sa eches 10017 ie Hebruary 1896; )h 14. 1001-12. -4 - The sensitiveness is also nearly doubie that of platinum- thermometers, as will be seen by the following table : — Anilytical Study of the Alternating Current Arc, 315 dR (ohms per Temp. = at Bee) 0 1001°2 4°65 — 55 761°9 4*20 — 65 720°4 4°12 — 79 663°6 4-02 —100 5381°0 3°87 —130 467°3 3°66 —182 291:0 The author prefers now a slightly different type of electric thermomeier, differing from that shown on fig. 4 in this par- ticular, that the brass tube ¢ joins the outer cylinder 7’. Although rather more difficult to construct, it allows the resistance-coil to embrace the bulb of a hydrogen-thermo- meter or any other piece of apparatus the temperature of which is to be determined. XXXIV. An Analytical Study ofthe Alternating Current Arc. By J. A. Furmine, WA., D.Sc., F.R.S., Professor of Electrical Engineering in University College, London, and J. H. PETAVEL*. aes the physical phenomena of the Electric Are have received of late years very considerable attention, there are many points in connexion with the study of the alternating current arc which seem to us to have been insufficiently explored. The investigation which is here described is a contribution to the further examination of the mode in which the variation of the luminous and electric effects takes place in the alternating current arc. The first portion of the research is concerned with an analytical study of the variation of the light thrown out from different radiating regions in the arc, and the delineation of the periodic value of this illuminating power by graphical methods. The object of the first set of experiments was to record and represent by an appropriate graphical method the periodic value of the light thrown out from the carbons and from the true electric arc region when the arc is supplied with electric power of known constant amount and varying magnitude, and at the same time to record the periodic variation of current through the arc, and potential-difference of the carbons. The instrumental appliances involved in the first place the employment of means for keeping constant and _ * Communicated by the Physical Society: read February 28th, 1896. 3816. Prof. J. A: Fleming and Mr. J. E.-Petavel: - measuring the mean value of the power supplied to the are. This was accomplished by the use of a suitable non-inductive resistance and a bifilar reflecting wattmeter, the series coil of which was in the circuit of the arc, and the shunt coil of which was connected across the carbons of the arc. The following is a description of this wattmeter :— The series coil was wound with 10 turns of thick copper wire (No. 10 8.W.G.) and had a resistance of ‘(01 ohm. The shunt coil was wound with 23 turns of thin wire, and had a resistance of 3°76 ohms, and was placed in series with a non-inductive platinoid resistance of 1200 ohms. The shunt- coil was suspended by two fine silver wires, which also served to conduct the current in and out of the coil. The con- trolling and deflecting forces so balanced each other at small displacements as to make the angular displacement of the movable coil very nearly proportional to the power passing through the wattmeter. The movable coil was provided with a mirror by means of which the image of a wire illuminated by an auxiliary arc lamp was reflected on to a fixed scale. This scale was carefully graduated, so as to read directly in watts. It was found that the earth’s magnetic field caused a small deflexion of the movable coil when using continuous currents and when the shunt current was passing through it, when at the same time no current was flowing in the series _ coil, This terrestrial field was neutralized by magnets, or else the scale was shifted so that the part of the deflexion of the shunt coil due to the terrestrial field was eliminated. The best way would have been to have turned the wattmeter round through a certain angle, but as it had to be screwed up against the wall in a fixed position for steadiness, it was found that the above method was the simplest plan for obviating this source of error. The vibrations of the movable coil were damped by means of a mica vane dipping into a dash-pot filled with oil. When all the adjustments were made, it was found that this wattmeter produced a deflexion of the spot of light on the scale almost exactly proportional to the power passing through the instrument. This wattmeter was then connected up to the arc lamp, so that the whole current actuating the arc lamp passed through the series coil, the terminals of the shunt coil being connected to the carbons ‘of the arc. 3 _ A series of preliminary experiments were then made for the purpose of enabling us io eliminate from the wattmeter- ‘readings, firstly, the power taken up in the wattmeter itself ; secondly, the power taken up in the shunt coil of the arc- lamp and other shunt:resistances ; and, thirdly, the power Analytical Study of the Alternating Current Arc. 317 taken up in the carbons themselves, right up to the point where the are is being formed. The observations, when reduced by applying these corrections, gave us at once the true mean power being taken up in the arc. The wattmeter was constructed with all the precautions necessary in making a wattmeter for measuring alternating-current power, so that it served to measure the power taken t up either in alternating or continuous current arcs. The current supplied to the are passed through a series of non-inductive resistances, con- sisting of carbon plates, in such a manner that the power given: to the are could be regulated with the greatest exact- ness. In addition to the wattmeter, an ammeter was placed in series with the arc lamp so as to measure the current passing through the arc, and a voltmeter connected to the carbons so as to measure the potential-difference of the carbons, these instruments being suitable both for continuous and alternating currents. In all the experiments the mean power was kept constant in the arc, and this was done by adjusting the current so that the wattmeter took a certain deflexion corresponding to the power desired, and the watt- meter was kept at a constant deflexion by regulating the carbon resistances in series with the arc. In addition to the instruments described above, a lens was fixed so as to enable the length of the arc to be measured in the usual manner. In the course of the experiments three arc lamps were employed—a hand-regulated are lamp in which the distance of the carbons was adj justable by a screw with great accuracy ; a continuous-current are lamp (the Waterhouse Are Lamp); and an alternating-current arc lamp (the Helios Arc Lamp) ; these last two being selected as excellent arc lamps of their respective types, our object being to select an arc lamp, the mechanism of which enabled it to be worked with electric powers varying over wide limits, and yet to yield a perfectly steady arc. In addition to these instruments there was set up the apparatus for delineating the curves of current of electromotive force, which have been described by one of us in the ‘ Hlectrician,’ vol. xxxiv. p. 460, and which consists of a synchronizing alternating-current motor, having its fields separately excited and its armature circuit traversed by a shunt current from the circuit operating the are lamp. This alternating-current motor was set up on the photometer bench, and it was used to drive an aluminium disk pierced by four openings, in such a manner that the disk revolved synchro- nously with the alternating current operating the arc. In addition to this duty the alternating-current motor carried a Phil. Mag. 8. 5. Vol. 41. No. 251. April 1896. Z 318 Prof. J. A. Fleming and Mr. J. Bi. Petavel : contact-maker on its shaft for the purpose of enabling the curves of current of electromotive force to be delineated. A brief description of the motor is as follows :— It consists of two sets of field magnets M, M (see fig. 1), having eight poles on each side which are secured to two cast-iron disks. Between these field magnets revolves a small armature A, the iron core of which is formed of a very thin strip of transformer iron wound up into a ring, the armature coils being wound on this ring. The armature coils are joined up in series with one another, so as to give a series of alternating magnetic poles round the ring when a current flows through the armature circuit. The diameter of this armature is about six inches. The field magnets have eight poles, and the armature eight coils. The field magnetic coils are bobbins about 2 inches long and 14 inch in diameter, and when joined up in series in the proper manner the field magnets take a current of about eight amperes to give them a proper amount of saturation. ‘The armature is carried upon a hard wooden boss fixed to a steel shaft ; and the steel shaft is carried through small ball bearings made like bicycle bearings. In order to prevent any side shake of the armature, there are at opposite ends of the base cast-iron pillars with a gun-metal screw through each, against which the rounded end of the shaft bears; the position of the shaft can thus be adjusted with great nicety, and runs with great freedom from friction. The ends of the armature circuit are brought to two small insulated collars fixed on the shaft, against which press two light brass brushes marked B, B kept against the shaft by means of an expanding steel wire W. The armature shaft carries on one side an ebonite disk with a steel slip let into it. Two insulated springs 8, 8 are carried on a rocking arm H; this rocking arm can be traversed through half a circumference, and is centred upon the gun-metal screw which ‘prevents side shake in’ the shaft, and a pointer and graduated scale enables the exact position of the contact- springs 10 be determined. One of the stop-screws keeping the shaft from side shake is pierced with a longitudinal hole, and through this hole passes a stiff steel wire ; this serves to drive an aluminium disk 27 centims. in diameter and 4 milli- metres thick. This disk is carried on a shaft which runs in a cast-iron bearing, and the disk is therefore driven syn- chronously by the motor. This aluminium disk has four slits in it separated by angular intervals of 90°; the slits are 0°5 centimetre wide and 4:5 centimetres long. If the field- magnets of the motor are excited by a continuous current of Analytical Study of the Alternating Current Are. 319 about eight amperes, and if an alternating current of about two amperes is passed through the armature of the motor, then, on turning the motor rapidly round by hand, which can [‘e6sT ‘oop *d ‘arxxx ‘joa “ueprqooTy , om} wo.4y | ‘IOOVL], OAIND JUOLING SuyeuITY SY] —'T “Wy best be done by passing a strap round the shaft and pulling at the strap so as to spin the motor like a top, the motor will, Z 2 | 320 | Prof. J. A. Fleming and Mr. J. H: Petavel : if sufficient speed be gathered, drop into step with the alter- nating current driving it. Since the motor has eight mag- netic poles, it makes one complete revolution in four complete periodic times, so that if the motor is being driven from an alternating-current circuit having a frequency of 100, then the motor has to run at 1500 revolutions per minute before it will drop into step, but at that speed it will fall into step with the current passing through its armature, and will be driven as a synchronous motor. Under these circumstances, if a ray of light is passed transversely to the disk in such a manner as to pass through the slits of the aluminium disk during the progress of rotation of the disk, the beam of light will be interrupted, but will obtain passage four times during each revolution through the slits in the disk as it goes round. If the motor is being driven by the same alternating current circuit which supplies the alternating current to an are lamp, it is evident that, on looking through the slits in the revolving disk at the alternating current arc, it will be seen in one constant condition during its periodic variation, such instant being determined by the position of the slits with reference to the phase of the current. Without entering into a longer description, it will be evident that this synchro- nizing motor driving a disk and a contact-breaker enabled two things to be done—first, to delineate all the current and electromotive-force curves of the arc taken in the usual way; and, secondly, a ray to be taken from the arc selected at one particular instant during the complete period through which the variation of illumination passes. These arrangements were completed by the construction of a photometer of a particular kind. Owing to the slow variation of position of the electric discharge in the alternating current are, it would have been useless to photometer the instantaneous value of the light coming from the alternating current arc against any fixed standard of light; but it was found possible to make a very exact comparison between the intensity of the light coming from any part of the are, and selected at any one constant instant during the complete phase, with the mean value of the light coming from that same part of the are during the complete period ; in other words, it was found possible to photometer the are against itself, and so eliminate to a large extent the difficulties arising from slow periodic variations of the light sent out from the are in any one direction. It is well known that the light of an alternating current arc, taken in any one direction, undergoes a slow periodic variation quite independently of the variation of Analytical Study of the Alternating Current Arc. 321 current during the phase, neither is it dependent upon any variation of the mean square value of the current, because it takes place even when that current is perfectly constant. It appears to be due to slow changes of position of the points on the carbons between which the discharge takes place. The discharge is as it were seeking out new points between which to take place, and it continually changes these positions as the are burns. The photometric arrangements finally adopted were as follows, and are shown in outline in fig. 2 :— Arrangement of the Photometer and Revolving Disk. A represents an alternating current arc. This are was enclosed in a metal lantern in which were three openings. The light from this are passed through a lens L, in a hori- zontal direction and fell upon a mirror M, placed at an angle of 45°, capable of being rotated at this constant inclination round a horizontal line co-linear with the axis of the revolving disk, and the motor placed in front of the lens L,. The ray was then reflected upwards into another mirror Mg, and by this mirror reflected at an angle very nearly equal to 45° in such a manner as to pass through the slits in the revolving disk D, when any one of the slits was in a position to allow the ray to pass. The two mirrors M, and M, were rigidly connected to a rocking-arm so centered that the line M, M, could be rotated round into any required position, always moving parallel to a radial line of the disk D. The disk D was the disk carried on the shaft of the synchronizing motor above described ; the motor, together with its associated disk, was placed on the photometer bench in the required position opposite to the arc-light lantern. In fig. 2 the motor itself is not shown, but its position is indicated by the letter C. The angular position which the rocking-arm carrying the two mirrors M, and M, occupied with respect to the vertical line passing through the centre of the revolving disk could be a2 Prof. J. A. Fleming and Mr. J. H.: Petavel : observed on a graduated scale. Ii will be clear, then, that if the disk driven by the motor was in synchronism with the alternating current producing the alternating are at A, an observer, looking through holes in the rapidly revolving disk, would see by reflexion in the mirrors M, and M, the alterna- ting current arc at A; but he would see it, not as it is seen when looked at directly, but in some constant condition taken at one definite instant during the phase, which instant would depend upon the position of the line M, M, with regard to the vertical line through the centre of the disk. Thus by rocking over the arm M, M, in various positions the observer coald see, through the window W as the disk revolved, the are at A, either in the condition when the electric discharge is taking place, or when the true are is extinguished, according to the position in which the arm M, M, was set. If, instead of observing with the eye, a disk of paper with a photometric grease spot upon it was placed at P, the lens L could be so ad- justed as to throw an enlarged and well-defined image of the are upon the disk at P; and by rocking over the arm carrying the mirror into successive positions, the observer would see the image of the are pass slowly through all those successive phases which in the are itself actually take place during one periodic time. As the image of the are is much larger than the photometer disk, it was possible, by shghtly shifting one of the mirrors, to bring any desired part of the image of the true are or of the craters of either of the carbons to cover the grease spot. In addition to this interrupted ray, another ray was gathered fron: the same part of the arc by a lens Ly, placed on the same level with the lens L, but slightly to one side of it. This lens gathered a beam which was reflected by a mirror M; placed at an angle of 45°, and which reflected the ray upwards to another mirror M,. In fig. 2, for the sake of clearness the lens L, is shown beneath the lens Ly, but it must be understood that in the real apparatus the lenses L, and L, were on the same level and placed side by side. The ray reflected from the mirrors M; and M, was set horizontally, so as to be received ona lens Ls, and by this lens LL, was gathered to a focus ata point I. The lens Ly was so adjusted as to form a large image of the are on the screen which carried the lens Ls, and by slightly moving the mirror M, any part of this image could be made to cover the lens L;. It will be seen, therefore, that the light gathered together at a focus at the point I could be made to be light coming from any assigned area in the are or from the craters. A movable stand carried two other mirrors M; and M, fixed at Analytical Study of the Alternating Current Arc. 323 angles of 45° in such a way as to reflect the ray coming from focus at 1, and reverse its direction so as to bring it round and make it fall on the left-hand side of the photometer-disk P. It will thus be seen that, by moving the mirrors M; and Mg, the light falling on the left-hand side of the photometer-disk P could be made to have any desired intensity within certain limits, and could be gathered from any desired part of the are or craters ; and, moreover, this illumination was the mean illumination, or proportional to the mean illuminative power of any part of the are selected for examination. It will thus be clear that the arrangement enabled us to project on to the right-hand side of the photometer disk P the rapidly inter- ~mittent ray taken from any part of the arc, and always gathered at one constant phase condition during the complete period ; whilst on the left-hand side of the photometer disk we could project a ray gathered from the same part of the arc, but not interrupted. We could therefore compare the mean value of the light proceeding from any part of the are with the instantaneous value of the light taken from the same part of the are and selected at any assigned instant during the period. Thus the are itself became its own standard, and difficulties due to slow fluctuation of the mean light of the are disappeared. At the same time the contact-maker on the motor enabled us to delineate in the usual manner the curves of current and potential-difference of the arc, and thus to record the variation in the are of the are current, the carbon potential-difference, the power expended in the arc, the resistance of the arc, and the luminous intensity of any part of the arc. A long series of experiments was then made with alternating current arcs of different lengths and powers, the periodic electric quantities being delineated and the light being taken, either from the centre of the true arc halfway between the carbons or from one of the craters of the carbon terminals,—generally the bottom carbon. The process of taking measurements was as follows :— After setting the lenses and the mirrors so that the lens Ly and the mirrors M, and M, gave a sharp image of the arc on the right-hand side of the photometer disk with the selected area of the image covering the grease spot, the mirrors M; and M, were moved backwards and forwards until the balance was obtained between the illumination falling on the right- and on the left-hand side of the photometer disk. The right- hand side of the photometer disk being illuminated by an intermittent stream of light always selected in the same phase, when considered as belonging to a periodically varying illu- 324 Prof. J. A. Fleming and Mr. J. E. Petavel : minating beam, whilst the light falling on the left-hand side of the photometer disk is a uniformly illuminating beam of the same quality and colour coming from the same part of the arc but not interrupted, and representing therefore the mean value of the light emitted from that selected area of the are. Observers were deputed to measure all the various quan- tities by the different instruments, and a power of constant definite amount was supplied to the electric are from an alternating-current machine driven by a continuous-current motor. By means of the carbon resistance and the reflecting wattmeter this power was kept constant at a selected value for a sufficient time to enable all the various periodic quan- tities to be observed at sufficiently frequent intervals during © the phase. In all cases the arc was allowed to burn quietly for half an hour to get the carbons into a constant position before any observations were taken. It is hardly necessary to go into the details of delineating the current and electro- motive-force curves, as the process of doing this is now well understood. The Kelvin vertical multicellular voltmeter, having a half microfarad condenser placed across its ter- minals, was employed for the measurement of the potential difference of the carbons in the following manner :— The voltmeter, with its associated condenser, was connected, through the contact-maker driven by the shaft of the alter- nating motor, to the carbons of the arc; the contact-maker thus closed the circuit at a certain instant during the phase, and the voltmeter gave the instantaneous value of the potential- difference of the carbons. In series with the are was placed a non-inductive resistance of suitable magnitude. A switch was arranged so that the voltmeter with the condenser in parallel with it, both being in series with the revolving contact-maker, could be put across either the terminals of this non-inductive resistance, or else between the carbons of the arc. By rocking over the arm carrying the spring- brushes of the contact-breaker, the voltmeter circuit was closed at a particular instant during the phase, and the volt- meter reading gave therefore, when corrected, the instanta- neous value either of the potential-difference of the carbons or the instantaneous value of the current through the are. As the Kelvin multicellular voltmeter used by us only begins to read at 60 volts, in order to get readings for lower values than 60 volts, it is necessary to add a known electromotive force to the voltmeter circuit in order to block up the needle of the voltmeter to a false zero. This was done by connecting a known number of small Lithanode secondary batteries, the Analytical Study of the Alternating Current Arc, 325 potential of which was determined by the same voltmeter, in series with the voltmeter. In this way the series of obser- vations were successively taken of the following quantities :— First, the instantaneous value of the potential difference of the carbons taken at equidistant intervals throughout a com- plete period ; secondly, the instantaneous values of the current through the are taken throughout the complete period ; and, thirdly, the instantaneous values of the luminous intensity of a certain selected portion of the are taken at intervals throughout the complete period and expressed in terms of the true mean luminous intensity of the same portion of the are at that time. These quantities having been obtained, it was then possible to plot them down in a series of curves, and to deduce therefrom curves representing the periodic variation of power through the arc, and the periodic variation of the resistance of the arc. Five sets of experiments were made, taken for different frequencies and different lengths ‘of arc, each set comprising an observation taken with the light proceeding from the centre of the true are, and also an observation taken with the light proceeding from the centre of the crater of the lower carbon. The frequencies employed were 83, 50, and 26. In all cases the current was kept at 14 amperes (mean square value); the results of these observations are embodied in the following 10 tables arranged in 5 pairs. Table IA, for instance, gives the results of the observations taken with an arc having a fre- quency of 83:3, the light being taken from the centre of the true arc. Table I. B gives similar results of observations for the same arc, the light being taken from the centre of the lower crater. By holding a magnet at the back of the arc, noticing which way the instantaneous image of the true arc was projected by the magnet, and noting the pole of the magnet presented to the arc, it was possible to determine when the lower carbon was positive and when it was negative; and the diagrams corresponding to the above 10 tables are marked so as to show the half of the wave when the lower carbon is positive and when it is negative, in all those diagrams which refer to the light coming from the crater. The results of the observations given in the 10 tables are delineated graphically in diagram in figs. 3 to 12; and on referring to these diagrarns a periodic line will be seen in each, delineating the variation of the potential difference of the carbons, and another periodic line indicating the varia- tion of the current through the are, whilst a third line indicates the periodic variation of the luminous intensity of the selected 326 Prof. J. A. Fleming and Mr. J. E. Petavel: portion of the are. In the diagrams figs. 13 to 17 are given curves representing the periodic variation of the light from the crater in the various cases, and extending over several periods. It will be noticed that those diagrams represent- ing the periodic variation of the light from the are show that this light undergoes a regular fluctuation between: a maximum and a minimum, the maxima having equal values, The light in the centre of the true arc never falls quite to zero. This seems to be due to a little luminosity which hangs in the interspace between the carbons, but at the present moment it is difficult to say whether this persistence is due to a very small admixture of stray light (although every effort was made to keep this out), or to a persistence of the illuminating-power of the incandescent vapour in which the arc has been formed. On examining the true are during its complete periodic variation, it is found that the blue or purple strip of light forming the true are undergoes a periodic variation in intensity. As far as the eye can judge, the blue or purple light completely vanishes at a certain instant during the phase; but there is, outside the true arc, a ~ dim halo of golden light which is persistent; and it is therefore probably on account of this persistent aureole of faint light round the true are that the ordinates of the curve representing the periodic variation of the luminous intensity of the are never become zero, but always indicate the outstanding constant amount of light. On the other hand, in the diagrams ~ which represent the periodic variation of light coming from the centre of the crater of the lower carbon, we find the luminous intensity of the crater varies between a minimum value and two maximum values of different magnitude. During the time when the crater is positive it reaches a higher inaximum intensity of illuminating power than during the time when it is negative, and, moreover, the curve representing the periodic variation of light rises more steeply than it comes down, which indicates a slow cooling of the carbons after they have been heated ; in other words, they heat more quickly than they cool. This is particularly noticeable in that part of curve corresponding to the crater being negative; and it is only what would be expected, because after the carbon has reached its negative maximum and is beginning to cool, the opposite carbon is cooling from a condition in which it has been positive, and as it has been heated to a higher tempera- ture than the negative carbon, it must assist by its radiation in keeping up the temperature and retard the cooling of the negative carbon, These diagrams will also show many other Analytical Study of the Alternating Current Arc. 327 interesting facts: they show, for instance, that in the case of the long are the self-induction of the arc is more marked than when the short are is employed, and in that case there is_a very distinct lag of current behind the potential- difference. It may also be noted in comparing the diagrams V. B and IV. B in figs. 12 and 10, which represent the carves for ares of the same frequency but of lengths 1:2 centim. and °32 centim. respectively, that in the case of the long arc there is no lag of light behind power as far as regards the points of maximum when the carbon is positive, but in the case of the short are there is a sensible lag. This inight be expected to be the case, because for a long are the influence of the opposite carbon in keeping up. the temperature of its neighbour as ‘his last is cooling is less felt than in the case of a short are. Broadly speaking, the facts may be summed up as follows :— The purple light of the true are undergoes a periodic varia- tion, and, as far as the eye can judge, is completely extin- guished during a certain interval during the phase ; it has equal maxima values during the period, at instants’ slightly lagging behind the instants of maximum power-expenditure in the are. On the other hand, the illuminating-power of the carbon erater varies between a minimum value and two maxima of unequal values ; the greatest maximum occurring when the carbon is positive and at an instant slightly lagging | behind the instant of maximum power-expenditure in the are. . 6) 5.) Oe Length of are. *. °. Jote tol. “Se AO iemons Potential-difference (P. D.) no: carbons Y_ 29 Gale (mean square value) . at mae \ i. ee Current (mean square value) . . . . = 14 amperes. ‘Power expended in arc’. % . . . . =046 watts: Pressure at alternator terminals. . . = 99 volis. Angle re ee of Gictone Angl e | Intensity of of (instanta- _ (instanta- of EE he) Phase. | cous value iimeousnalae)! Phase. | centre of Arc. 0 +19: eg 0 44 20 +141 +385 | 32 13 Arc out. 40 2 Be 4.27 55 ll : fee Ce | 4 2 ae) elo 77 18 80 — 22 —16 100 ily 100 — 63 56 eral 122 45 120 —15°5 —37'5 | 144 74 140 ies —47 =|. 165 68 160 —198 —54 187 52:5 180 —19°5 —54 _ 208 32 200 —148 —50 _ 230 85 220 - 79 — 34 252 9 240 — 19 —11:2 273 11 Are out. 260 4+ 19 A153 coral, 294 26 ties 280 + 7:2 +31 315 (71)? 300 +126 4.36 336 68 320 +1955 +40 356 49'5 340 +21°7 +473 348 68 360 +19°8 +46°3 4 B2k 45 N.B.—Owing to an accidental shift of the brushes, in this table the angle corresponding to the instantaneous light is not the same as that corresponding to the current. The position of the curve of instantaneous light with regard to the E.M.F., current, and power curves cannot therefore in this case be determined. Analytical Study of the Alternating Current Arc. 331 TABLE II. B. Observations on the Periodic Variation of the Inten sity of the Light of an Alternating Current Arc. Light from Crater. Medium Are. Ritequeteme piers. tt. Pe 8. SOO ES Meneiheorare =.) Bee ai, eg = Oe Oem Potential-difference of hone (mean isquarcenmmalue) oi... fay (a) spe hs) = 108, Volts: Current (mean square value) . . . . = 14 amperes. Power expended inare . . SEI =O eau: Pressure at alternator ter ane pine ee ee OO olts: Current itl De Intensity of Angle of through Are of Carbons Angle of Light from Phase. (instantaneous | (instantaneous Phase. Crater of value). value). lower Carbon. 0 56 20 43 30 + 63 +17 40 — 45 50 —.05 — 295 60 32 70 — 39 —22 80 39 100 52 120 137 140 277 160 277 180 227 190 —11:3 200 165 210 — 55 —22 220 63 230 + 01 a 240 64 250 + 42 REGIE a8 260 61 270 +11 +28°4 280 78 300 85 320 72 340 87 360 (37)? 340 269 320 75 302 Prof. J. A. Fleming and Mr. J. Ei. Petavel : TABLE III. A. Observations on the Periodic Variation of the Intensity of the Light of an Alternating Current Are. Light from centre of Arc. Medium Arc. FrequemtYen. a set els a Length of are. 6 20 a se Potential-difference (P.D.) of carbons t= 387 volts. (mean square value) ... . Current (mean square value) . . 14 amperes. Power expended in-arc. . i) .) w)). .) == 5/8 )iyentier Pressure at alternator terminals . . . = 62 volts. el iaeenlce of ae nee Tice iad pee (instanta- (instanta- pre Centre of neous value). | neous value). Are. 0 +19 +45 7 45 20 +12°5 +39°5 28 26 40 + 58 +21°5 49 6 Arce out. - 60 + 05 + 2:5 71 12 > as 80 = 22 —22'5 92 7 oy 100 — 97 —24 114 14 Arc just starting. 120 —16°8 —345 136 67 140 —195 —45°5 158 71 160 —21°8 —47°5 180 66 180 —193 —50 202 24 200 —11'5 —42 224 19°5 Are out. 220 — 48 —22 246 4 per 240 — 05 — 2 268 8 33 ans 260 + 20 +17 290 22 280 +10°8 +26 312 40 300 +158 +36 333 57 320 +207 +475 304 75 340 +213 +50 15 53 360 +19 +48 340 +21 +51 345 62 320 +20 +48 323 70 Analytical Study of the Alternating Current Arc. 333 TABLE III. B. Observations on the Periodie Variation of the Intensity of the Light of an Alternating Current Are. Light from Crater. Frequency . Length of arc. -. .. : e e ° Potential-difference (P.D.) of carbons (mean square value) . Current (mean square value) Power expended in are cae es Pressure at alternator terminals Af 2 Current Angle of through Arc Phase. (instantaneous value). 0 +18 20 +143 40 + 67 60 + 1 80 — 12 100 — 5 120 —17°5 140 —182 160 —20°6 180 —20 200 —l11 220 — 5 240 -— 1 260 + 2 280 + 895 | 300 +14 320 +19 340 +22 360 +21 PD: of Carbons (instantaneous value.) +52 +55 424-5 + 45 ~21 Medium Arc. 26 ~. 0°63 cm. 39 volts. 14 amperes. 546 watts. 62 volts. Intensity of Light from Crater of lower Carbon. Phil. Mag. 8. 5. Vol. 41. No. 251. April 1896, 2A 334 Light from centre of Are. Frequency Length of are Potential-difference (P. D. of eee 7 TasLe IV. A - Observations onthe Periodic Variation of the Intensity of the 7 Light of an Alternating Current Are. (mean square value) _ Current (mean square value) Power expended in are Pressure at alternator terminals See Current Angle of through Are Phase. (instantaneous value). 0 +18-4 20 +13°8 40 + 57 60 + 06 80 — 6 100 —131 120 —19 140 —19 160 —183 180 —14-4 200 —102 220 — 5:0 240 + 11 260 + 86 280 +145 300 +18°9 320 +2271 340 +20°3 360 +18:1 340 +21°5 320 4+21°1 PD, of Carbons (instantaneous value). +41-4 +38°4 +21 — 86 =o —25 43 —46°5 a —46 —44-6 —20 + 68 +226 +29 +376 +40°6 +44 +426 +454 +40°4 Angle of Phase. Short Are. D0 14 504 Intensity of Light from Centre of Are. 28 15 24 13 14 18 28 20 0: 36 volts. Prof. J. A. Fleming and Mr. J. EH. Petavel : ~~ 32 cm. amperes. watts. 85 volts. Are going out. Arc out. Arc out. Are going out. Are out. Are out. Analytical Study of the Alternating Current Arc. 335 TABLE LV. B. Observations on the Periodic Variation of the Intensity of the Light of an Alternating Current Arc. Light from Crater. Short Arc. Hrequetieyime = 2 ns + ae | SOS Henethemaned taeircs We 12h) $1) - ore) ) OB 2.ema! Potential-difference of carbons (mean) _ 38 vol SUMATENVAITIC) 6 0 eof se te } ae el Current (mean square value) . . . = 14 amperes. Power expended inarc . . . . . =582 watts. Pressure at alternator terminals . . = 98 volts. Current | Intensity of | Angle of through Are | Angle of Light from Phase. (instantaneous Phase. Crater of a4 value). | lower Carbon. | 0 | nen | | 20 li. BE 20 61 | 40 | + 72 | 41 56 60 ae eee 1 63. 45 | 80 | — 50 | 84 58 | 160 ee 105 Bl | | 120 ieee ete | 126 101 | TARAS we aie ie St | 148 220 160 Pees | 170 227 in Oe gene | 191 216 Zt lS ae ee | 212 111 220 — 63 | 232 64 240 = Odo 268 eye 260 PAG oe Ihe 298 66 280 +12: 294 63 300 SITGe ey -| 315 77 320 POOLS 4 335 60 lie Tes eats etc 2 | 359 63 360 2a ereee foe seein ye | easy 88 | | 36 | 79 | | | 2A 2 336 Prof. J. A. Fleming and Mr. J. E. Petavel : TABLE V. A. Observations on the Periodic Variation of the Intensity of the Light of an Alternating Current Arc. Light from centre of Arc. Long Are. Frequency 3. @ 2. ee = liengthofareé 1 * «© 6 6 s » » = (aie Potential-difference (P.D.) of carbons . _ 53 valk (mean square value)? (7 je) 2: } ii? oe Current (mean square value) . . . = 14 amperes. Power expended inarc . . . . . =742 watts. Pressure at alternator terminals. . . = 88 volts. oen Pee Intensity of through Arc | of Carbons || Angle Light fon (instan- (instan- of Ostine taneous taneous Phase. | value. ) value.) eae. 420-4 4586 10 40 +15°9 +48°6 ol 44 4. 8-4 4+26°4 52 9 + 07 — 76 76 12 Arc out. = 88 246 98 19 tee — 81 —53°6 120 24 —15:1 —63°6 142 72 —18°6 — 676 164 50 —196 —68 187 63 —176 —67 209 44 —12°6 —53°6 232 12 Are out. — 56 Soi 253 7 mee. = Ne 424 275 7 ae + 44 +47 ifs aie + 84 +53 320 62 +17°4 +55 343 87 +214 | +596 348 63 * +23°4 +596 326 78 420-4 4556 +224 +59°6 | +21°4 +586 Analytical Study of the Alternating Current Are. 337 TABLE V.B. Observations on the Periodic Variation of the Intensity of the Light of an Alternating Current Are. Light from Crater. Long Arc. requeneye | ees fof 6 os eet DOP Length of arc. esa iene aed ewe ame) fey 2k Potential-difference (P.E.) of carbons) _ 53 wl (mean square value) . . . . } Fe bee ie Current (mean square value) . . . = 14 amperes. owerexpemded Im ab¢ay. +. = 742 watts. Pressure at alternator terminals . . = 98 volts. Current Intensity of Angle of through Are Angle of Light from Phase. (instantaneous Phase. Crater of value). lower Carbon. 0 359 92 20 +15°9 18 92 40 4117 36 98 60 + 16 53 84 80 — 44 70 70 100 87 76 120 105 14 140 123 207 160 142 175 180 160 280 200 179 265 220 — 65 199 193 240 0:0 218 76 260 + 4:4 238 84 280 + 10°4 257 71 300 277 66 320 296 101 340 315 98 360 334 107 Fig. 3. The ordinates of the firm line marked “ Light Curve” represent the peri- odic variation of illuminating-power of the centre of the true are of an alternating-current arc. The other curves marked E.M.F., Current, and Power represent the variation of potential difference of the carbons, current, and power in the are. Carbons, 15 mm. cored; ~ = 83'3 ; amperes=14; volts =39; length of arc, 0°55 cm.; volts at alternator terminals=104, (See Table IL. A.) Fig, 4.—Intensity of Light from Crater. Volts Frequency =83'3 ~, Length of are=0"42 em. (See Table L B.) Analytical Study of the Alternating Current Arc. 339 Fig. 5.—Intensity of Light from Are. Frequency =50~ ? See fable TA 20 40 100 120 140 160 60 \80 180 200 220 240/ 260 280 300 320 340 360 / 340 Prof, J. A. Fleming and Mr. J. E. Petavel : Fig. 6.—-Intensity of Light from Crater. \ / /Carbon Negative 90 180 Angle of Phase »-—_ Time Frequency =50~. Length of are=0-63 cm. (See Table II. B.) Analytical. Study of the Alternating Current Arc. 341 Fig. 7.—Intensity of Light from Centre of Arc. e0 Frequency = 26—~ Length of arc. = 0.63cm See table IA w c 3) o a eo 2 oS © > %10 z @ S 2 4 S Ww Angle of Phase 0 60 «180 200 220 B40 260 280 300 320 340 d42 Prof. J, A. Fleming and Mr. J. Hi. Petavel: Fig. 8.—Intensity of Light from Lower Carbon. Frequency = 26~y Length of Arc = 0-63cm 70 oot See fable I B Amperes Scale of = Angle of Phase “\.80 100 120-140 - 160. 180. 200. ee0 \ * = Scale of Volts - Scale of Amperes Analytical. Study of the Alternating Current Arc. °343 Fig. 9.—Intensity of Light from Centre of Are. Frequency=26 ~~ 70 Length of Arc = 0-32cm A aa See Cable IV a 50 $ w So Scale of Volts. 20 40 a} 80 100 120 140 160 180 200 220 f240 260 280 300 320 40 360 Time 344 Prof. J. A. Fleming and Mr. J. E. Petavel : Fig. 10.—Intensity of Light from Centre of Arc. Frequency=50 ~. Length of arc=0°32 cm. (See Table IV. B.) Fig. 11.—Intensity of Light from Centre of Arc. Amperes Frequency=50 ~. Length of arc=1:2 cm, (See Table V. A.) Analytical Study of the Alternating Current Arc. 345 Fig. 12.—Intensity of Light from Crater. ' VBS Ps \ y om / . / ‘ z 5 J x6 / \ “ ; / / | i ‘ U / \ 2: ( / \ at \ / s/ \ / . Ons 2 a : \ 1 .y \ / \ bi Lass i # : 2/ ey b | 7) : a, Rg id q ye \ i = \ / 6 \ , Carbon Positive Dogs 1 “= re s = 6 . eee - ae \ \ J 5 ?” Carbon negative n 1 egative, \ , Angle of Phase Kame ¥ 4d fe) 90 : ; \ igo 7 270 ‘\ Time. 7 0S cee oad 360 Frequency=50 ~. Length of are=1:2 cm. (See Table V. B.) 346 Prof. J. A. Fleming and Mr. J. E. Petavel 080) O80! CH IT 1481) ‘“wiyued g9.9 ory Jo WASUerTT ‘Eg = Aouonbaz ow 022 _ 09¢ ie Y og @AlyeBau vogue) | BAI}ISOY UOqueD ee ew es we we ee ee ‘OIY JUIN SUIPVUAEILY JO 1o}VIQ WOT FY SVT Jo uae A — FL, Sh Ca T1981) “wryuce Zp.9= oy jousuey ‘g.gg= Aouonbery awit * aseug jo a|Buy O22 ose 08! 1 aaiedan uoquey + oN BAIYISOY uogred ‘OLY JUOLING SUTPVUIO}TV JO loyeI_D WOT, JYSIT] Jo UOTWIIBA—'ET “OLY 347 Are. rrent tl eon Analytical Study, of the Alternating C 080! _ 0801 CAAT 1981) “wues e.9 = o1W Jo YoUeTT ‘OG = AouONbary owl eseyuy jo ajBuy 022 . o9f 08! aAIVeDanNy UOQIeD) 4} SAI}ISOY Uogiry | ‘OLY JUOLIN() SUILUAEZ] YW JO TopyeIG WOIZ WYSITT Jo UOYVUVA—'OT “oL,T (AHI 1") “69-0 = atV Jo yI8ueT ‘9g = Aouonbery awl) ————— ase 0 ajdu 022 oof peace MY BAIWDIN U0g.ed 08! {aanis0d uoquey ‘TY JUOLING SUTBUAEZTY JO LoyVIQ WOIF WYSTT Jo uoTWwIIEA—'GT ‘SIT sae ewe wwe ewe = — e e Prof. J. A. Fleming and Mr. J. H. Petavel 348 CIA MGR) ‘wyues g.[ oy JO qZoueyT ‘og = Aouonbosyz awit (>) asPuy jo a]Ouly BAIYeBaN uoqury BAIJISOY Uogsey ‘OLY JuaLIND Suyeusojzpy Jo 1oyeag) Woy FYSTY Jo MOIWUEA—*ZT “SI Analytical Study of the Alternating Current Are. 349 The second portion of the experimental work here recorded consisted in an investigation of the efficiency of the alternating- current arc as a light-giving agent, when compared with the continuous-current are taking up the same mean power. The question in all its generality, whether alternating-current arcs are less efficient as light-giving agents for a given amount of power expended in them than continuous-current arcs absorb- ing the same power, is not one which we have attempted to settle, for the simple reason that a far more extended series of experiments would be necessary before it would be possible to say whether an alternating-current arc can or cannot be made to give the same mean spherical candle-power as a continuous- current arc absorbing the same mean power. Limitations of time compelled us to reduce our investigation to one definite problem. Taking alternating-current arcs, formed with the length, voltage, and the current and the carbons as described below, and taking continuous-current arcs also with the length, current, and voltage and carbons most usually employed in practice, we have investigated the relative magnitude of the mean spherical candle-power produced by these arcs for equal expenditure of powers in the arcs varying from 200 to 600 watts. This, it will be observed, is an investigation which has nothing whatever to do with the relative mechanical or elec- trical efficiency or excellence of the arc-lamp mechanisms, but it is purely a physical measurement made of the two arcs them- selves under the conditions which are found to obtain in practice. In order to settle this question, an alternating- current arc lamp was taken with good regulating qualities ; it was furnished with cored carbons 15 mm. in diameter, and being placed under the conditions above described, in which the power supplied to the arc could be regulated and mea- sured, a series of observations was made of the mean spherical candle-power of the are for different powers expended in the are and for two frequencies of 83°3 and 50~. A similar set of experiments was made with the continuous-current arc, using in one case the same carbons—15 mm. carbons, both cored—and in the other case the positive carbon 15 mm. cored and a negative carbon 9 mm. solid, These sizes were chosen because the 15mm. cored and 9 mm. solid sizes are those that are frequently employed in continuous-current arc lighting. The arrangements for obtaining the mean spherical candle- power consisted of a mirror—the coefficient of reflexion of which had been determined—which was employed to reflect the light from the are proceeding in different directions to the horizon into the photometer, the ray always falling upon the mirror at an incidence of 45. ‘The standard of comparison Phil. Mag. 8. 5. Vol. 41. No. 251. April 1896. 2B 350 Prof. J. A. Fleming and Mr. J. H. Petavel : was an incandescent lamp, which was worked at rather a high temperature in order to diminish the difficulty of making the photometric comparison by diminishing as much as possible the colour-difference in the lights compared. ‘This incan- descent lamp was kept constantly standardized against another standard incandescent lamp worked at a rather lower tempe- rature. The means of comparison was a Sugg’s Star Disk Photometer. It was found that by focussing the eye to a point rather nearer the eye than the images of the Star Disk as seen in the two mirrors, the difficulty of discriminating between a small difference in the brightness of the two images in spite of a small colour-difference was toa great extent dimi- nished. We abandoned as perfectly useless any comparison of the two lights in terms of red and green candle-power. By the employment of the reflecting wattmeter and carbon resist- ance as above described, it was perfectly possible to keep the power expended in the arc constant to a certain number of watts throughout long periods. In the case of the alternating- current arc lamp experiments, the alternating-current are lamp was turned round its vertical axis so as to take a series of observations quickly in different directions, but at the same angle to the horizon, and the mean of these observations was taken as the effective illuminating-power in any angular direction ; at the same time, the current through the are and the potential-difference of the carbons were observed. These observations having been taken, involving many hundreds of photometric measurements, the results were set out in a series of photometric diagrams, as shown in figs. 21 to 24, which delineate the respective form of the photometric curves for the two ares and for different wattages expended in the are. These photometric diagrams were then integrated, and the mean spherical candle-power calculated in the usual way by means of a Rousseau’s diagram, and finally the results embodied in one complete table and diagram, as given below (pp. 356, 357). The results in the Table are graphically embodied in the diagram in fig. 25, from which it will be seen that, taking the alternating-current arc as employed, the total mean spherical candle-power is always considerably less than that of a con- tinuous-current arc, taking the same mean power. Lowering the frequency seems to increase the efficiency of the alter- nating-current arc, as one might naturally assume it would do, and it is obvious that increasing the diameter of the lower carbon of the continuous-current are would diminish its total mean spherical candle-power at any given wattage. This table and diagram therefore, we think, settle the question that for a given expenditure of power in the arc a greater _ Scale of Amps. Scale of Amps.: Analytical Study of the Alternating Current Arc. 351 Fig. 18.—Curves of Current, Potential Difference, Power, and Resistance of 360 Watt Alternating Current Arc. Scale of Watts Scale of Resistance in ohms, 2B2 Scale of Volts 19 2 3 Scale of Volts eS oS Gn oO Scale of Amps. Scale of Amps. x 20 352 Prof. J. A. Fleming and Mr. J. E. Petavel : Fig. 19.—Curves of Current, Potential Difference, and Power of 500 Watt Alternating Current Arc. 70 rent * xr = eeeeta. ~783.3 7 --~. 6 : 25 Ox0: oe eae j000 ee 502 oO > S 40 ae Tc Vv wn 30 $ 20 10 Angle of Phase 30 45 60 75 90 105 120 135 50 —— Time 10 20 30u Pa) Oo > _— 40° ov _ Vv w 50 60 Scale of Amps. ~~ b& HM ow Ss ®& 20 Analytical Study of the Alternating Current Arc. 353 Fig. 20.—Curves of Current, Potential Difference, Power, and Resistance of 600 Watt Alternating Current Arc. DOg OY. PL yxren cl % c ets cn 800 Mean Watts a = ’ Angle of Phase 45 “a E = S = a =) = s Se nn oO we . poererecsene” N.B.- Watt meter Reading = 640 eopecse® ™~ uN Scale of Volts SA 105 120 24\ 150 165. 180 195 20 225 240 255 270 285 3 J 330 345 360: “Oo 24 356 Prof. J. A. Fleming and Mr. J. H. Petavel : g, 23,—Photometric Curves of Alternating Are Lamp ~ 83°3. re" 7 g0 -FO0 -60 gen - 50 ~N/ ae nie os . XN U Sees ; "4 Ber SA / S ao" 7 . Tie PV Jian Fi a 400 Bc 350 ee | cau IRSA oar ARO 400 450 S * 80 Prof. J. A. Fleming and Mr. J. HE. Petavel 308 "ore OY} UI dn uUoye} s44VA\ UL pornsvom JoMOd uvom oNnIy oY} YIIM 9e18e oJInb you seop sonyeA wee 9Sey} Jo qonpoid oy} ynq ‘eTqe oY UL WOATS son[eA UeoT oy} pey pue “yueqysuCO AToJeuTxoidde oOM s}[OA pue JUoTIND OIL], "F[NSOL STY} OINDS 04 SB OS POT[OIJWOO OTE SUOgIvD OY JO TeMaMejod jo sdUeIEyIP pue yuoIIND oT], ‘queqysuoo 4ydoy seat ora ore oy} ut dn uoyez ‘s}98M UL pornsvom ‘ToAOd oY} SBM 4I AVY} pojoU oq 4sNUT 4I 9[GQey BAOGe 94} SUIpeer UT "QUIT O44 JO O[OYM OY} SULINP SUISSIY SEM OAL OY SUOT]VATESqO ose} UT » 46-0] 66-0|46-0 alee | iy O-V1) i-St) OT GG | 16 | 66 VGG | G6E | 96S 80E | 6S7 | 96¢ 96-0 | 96-0 910-0 | SaT-0 AGL | LAS TL 1G 86 OSG | 9S¢ G0& | vOr ‘~()G Aouenboa yy “~ @.69 Aouonbely7 0-1 0-1 190-0 | £08-0 8 GOL OF 09 TVS | G8 Glé | 209 0-1 0) Dell L0:0 L-8 6-0) 07k 0-1 | STZ-0 L-3| 9-01 ar | OS SGV | SLO O86] 68S “+++ Joq0Ry IOMOT deen * goaqour -1}U00 UL O1@ JO YYSuOT Meier sorodure UI 018 Ysno1yy JusrIND "+" Sq7OA UI SUOgIvO jo 90UeleyIp yerjuejog cose oe ee ee ee zaMmocl -9[puvo jeotzeyds uvoyy Fetters + gaaem ur ome oy} UL popuedxo s0MOog 7 ee © © ‘pes0d “Wu GT suogrvo YQ0q "O18 JUIIINI-SUTJVULOF] W *pet0o “UIUL GT ; suoqive qyOq ‘pljos “uml G wOqIeD — ‘po10d “Wu GT UOgaeVg+ ‘OAIB YUOLINI-SNONUTJUOD Analytical Study of the Aliernating Current Arc. 399 Fig. 25. 800 5 3 S S Mean Spherical Candle-Power of Are (White Light) Li) True Power in Watts Expended in the Are. amount of mean spherical illumination can be obtained, if that power is supplied in a continuous-current form than if it is supplied in an alternating form. It has been suggested that, with proper carbons and under proper conditions, the alter- nating and continuous-current arc should give the same mean spherical candle-power for the same expenditure of power, as has been shown to hold true in the case of the incandescent lamp by the investigations of Profs. Ayrton and Perry. We think, however, that no @ priort reasoning can apply in the case of the are. It is perfectly clear that, owing to the interval of cooling that elapses, the mean temperature of the two carbons in the case of the alternating-current are must be less than the temperature of the positive crater of the continuous-current are, and that therefore the result we have obtained is only what might be expected. If the question is asked, how do we account for the difference in efficiency ? the answer must be that the energy absorbed in the case of the alternating-current are is radiated at a lower temperature, and the two ares were therefore exactly in the same condition as regards comparison that two incandescent lamps would be, both taking the same total power but worked at different temperatures, and therefore different watts per candle, and therefore giving different mean spherical candle-powers with the same total power expended in them. It may be observed in all cases the alternating-current arcs we employed in our experiments took 16 to 17 amperes, and 360 Prof. W. Ramsay and N. Eumorfopoulos on the the power was varied by varying the potentialkdifference of the carbons, and the alternating-current arc lamp used was one which effected this variation automatically, even although the power expended in the are was varied from 200 to 600 watts. In order to complete the comparison of the continuous and alternating-current arcs, it will be necessary to compare the behaviour as regards illuminating-power of alternating- current arcs, taking the same mean power but formed with larger currents and less carbon potential-differences ; that is to say, comparing alternating arcs of equal power-absorption, but taking very different currents and therefore having dif- ferent lengths. We hope to extend this investigation to cover these additional questions at some future time. The above observations have necessitated an enormous . number of photometric and electrical measurements, and we have in the above work been very efficiently aided by Messrs. L. Birks, W. H. Grimsdale, A. M. Hanbury, E. N. Griffiths, and others, to whom our thanks are due. XXXV. On the Determination of High Temperatures with the Meldometer. By Wituiam Ramsay, PA.D., FB.S., Professor of Chemistry, University College, London, and N. Eumorroroutos, B.Sc., Demonstrator of Physics, Uni- versity College, London*. A hes meldometer, an instrument devised by Dr. Joly, has been sufficiently described by him (Proc. Roy. Irish Acad. 3rd series, 11. p. 88, or Chem. News, vol. lxv.), and we need therefore only give a very brief account of it here. The essential part of the instrument is a length (about 10 centim.) of thin uniform platinum ribbon, about 1 millim. wide. This is heated by a current of adjustable strength, and the increase in length of the ribbon is measured by a delicate micrometer- screw, the ribbon being kept gently stretched by a small spring. The temperature of the ribbon is, of course, lower where the two forceps hold it; but if it is suitably cut at each end nearly to a point, a length of, say, 6 centim. in the middle may be made of a very uniform temperature, as can be proved experimentally by taking the reading of the melting- point of the same substance at different points along the ribbon. An infinitesimal quantity (scarcely visible with the naked eye) of the substance to be melted is placed on the ribbon and viewed with a low-power microscope. The small quantity of * Communicated by the Physical Society: read February 14, 1896. Determination of Temperatures with the Meldometer. 361 the substance-required enables it to be purified very com- pletely. The current is then put on and increased rapidly until the substance melts, and thus an approximate reading is obtained. This is repeated more cautiously, to obtain an exact reading. Several readings can be taken by remelting the same, and also by using fresh substance, the latter method being usually adopted. To translate the readings into temperatures, it is necessary to standardize the instrument by taking the readings with substances of known melting-points. Of these, unfortunately, there are none known with certainty beyond about 350° C. | One reading is obtained by taking the temperature of the air, another is the melting-point of potassium nitrate (339°), and for a third one the melting-point of potassium sulphate (1052°) was adopted, for reasons that willappear. The melting-point of silver is irregular, apparently because of absorption of oxygen, and consequent spitting. Gold can be used, and also palladium. As, however, the expansion of the ribbon is almost a linear function of its temperature, and as the obser- vations hitherto taken did not extend beyond about 1050°, it was considered unnecessary to take readings with palladium, the general character of the expansion of the ribbon being already known from Dr. Joly’s observations. The question next arises, what is the melting-point of gold? There have been two or three determinations of value, which unfortu- nately differ from one another. M. Violle (C. &. 1879) determined it by a calorimetric method, and obtains as a result 1045° (on the air-thermo- meter). | _ Messrs. Holborn and Wien (Wied. Ann. xlvii. and lvi., 1892 and 1895), who give 1072°, compared a thermo-element with an air-thermometer, and then used the former for deter- mining the melting-points of silver, gold, and copper. This was done by inserting in a porcelain crucible the thermo- element, and also two platinum wires connected by a wire of the substance whose melting-point was to be taken. The platinum wires formed part of a circuit containing a battery and a galvanometer. When the wire melted, the circuit was broken, and the temperature read at the same moment with the thermo-element. The melting of the substance must in general lag a little behind the thermo-element ; and as no mention is made of the rate at which the temperature was raised, it is difficult to know how far the results can be trusted. They obtain, however, very concordant readings. Besides these, there are two determinations with the plati- num pyrometer : one by Professor Callendar (Phil. Mag. Feb. 362 Prof. W. Ramsay and N. Eumorfopoulos on the 1892), and the other by Messrs. Heycock and Neville(J. C. 8. Trans. 1895, p. 160). By a somewhat violent extrapolation * from a formula which, as far as we know, has been compared with the air-thermometer only to about 625°, they obtain :-— Heycock and Callendar. Neville. Freezing- or melting-point of silver ... 982° Soule Fa ” cold... 1091° 1062°7 Callendar then, taking the melting-point of silver as 945°, makes the melting-point of gold 1037°. Now Violle’s deter- mination for silver is 954°, which, using Callendar’s formula, would give for gold 1049°. Holborn and Wien’s value for silver is 968°. In view of the variance between the numbers, it was determined to take Violle’s value, though the correct value may be a few degrees higher (compare Le Chatelier, C. R, exxi. p. 323, 1895). In any case, allowance can easily be made, when further researches have determined the true melting-point. The gold used by us was a very pure specimen obtained from Messrs. Johnson and Matthey. The salts used, with the exception of some of the iodides, were pure specimens, pre- pared specially by ourselves. In a few cases the salts so prepared were recrystallized, and melting-points were taken both of the recrystallized salt and also that obtained from the mother liquor. No difference could be detected, and hence no further mention is made of these determinations. Gold on melting alloys with the platinum, and hence must destroy to a certain extent the uniformity of the ribbon. A * In Holborn and Wien’s last paper (doc. cit.) the resistance of pure platinum is determined at different temperatures with their thermo- element, and their results cannot be expressed quite satisfactorily (“zr ungentigend”) by means of Callendar’s formula. The resistance of two of their pure platinum wires began to differ beyond about 900°, while agreeing below this temperature. They therefore consider this property unsuited to extrapolation. + In a recent paper (J. C. S. Trans. 1895, p. 1025) Heycock and Neville state that “ Callendar did not rigidly follow the method of cali- bration, which was afterwards developed by Griffiths and himself, and which we have always adhered to. That method requires that the resistance of the pyrometer should be determined at three standard tem- peratures,” yiz., at 0°, 100°, and the boiling-point of sulphur, 444°-5. And lower down they say, “ If Callendar had standardized his thermo- meter on the boiling-point of sulphur....;” hence they infer that Callen- dar did not use the boiling-point of sulphur for this determination. But the determination of this boiling-point 1s given in Phil. Trans. 1891, 2. e., it was published before the paper referred to, and the latter is also later than another paper (Phil. Mag. July 1891, p. 109), in which the boiling- point of sulphur is directly referred to. We do not quite see how to reconcile the various statements, Determination of Temperatures with the Meldometer. 363 remedy for this is to dust the ribbon lightly with finely powdered tale. This, however, is not very satisfactory, and interferes somewhat with the observations; but with care, fairly good results can be obtained, as the following numbers show:— With tale. Without talc. Ee Irpen, 36,-Noc7g9g° 792° KeCO? (492 ©." 883 880 Hoes ee 752 762 Ba(NO%)?. . (583 575 It was then found that the melting-point of potassium sulphate is very little different from that. of gold, viz., 7 degrees higher or 1052°; and this salt was afterwards used instead of the gold ; thus there is no need to use tale. Some melting-points are sharply marked, others are not. In these cases the lowest point was taken at which spreading over the ribbon could be detected. For purposes of comparison determinations by other ob- servers are given; some determined the melting-points (e.¢., Carnelley,and Meyer, Riddle and Lamb), others the freezing- points (Carnelley, Le Chatelier, Heycock and Neville, and McCrae). The data are taken from the following references:— Carnelley (calorimetric method): J. C. §. Trans. 1876, pat oo: IS, p. ob); 1818, p. 213. | Le Chatelier (thermo-electric method, assuming melting- point of gold as 1045°): Bull. Soc. Chim. t. xlvii. p. 301 ; C. hy. t. cxvi. pp. 390, 711, and 802: V. Meyer, Riddle and Lamb: Ber. xxvii. (1894) p. 3129. —In this method the salt has been previously fused in a platinum tube with a wire down its centre, and to this wire is attached a weight passing over a pulley. When the salt melts, it is pulled out by the weight, and the temperature is determined at the same moment by an air-thermometer. J. McCrae (Wied. Ann. lv. p. 95), relying on Holborn and Wien’s results, standardized his thermo-element with boiling diphenylamine (304°) and_ boiling sulphur (444°°5). For his thermo-element he used platinum against an alloy of platinum rhodium, and also against an alloy of platinum and iridium. The numbers in brackets given below refer to the latter, and the others to the former. It will be noticed that they do not agree perfectly. This may, of course, be due to his metals not being of the same purity as those of Holborn and Wien. The latter alsofrom their observations find that the iridium alloy is not as well suited as the rhodium alloy. 364 Prof. W. Ramsay and N. Eumorfopoulos on the Salts of Lithium. The lithium carbonate bought as pure gave a conspicuous sodium coloration to the Bunsen flame. It was purified by successive precipitation and washing, until it gave a brilliant carmine coloration to a Bunsen flame, free from yellow fringe, showing an absence of sodium. The melting- points are not very well marked as a rule. Ramsay & Eumorfopoulos. Carnelley. Le Chatelier. TiS OF se hesaeanee 853 $18 830 ai* COS + hi datimee 618 695 710 Dt CT he she cticl 491 598 IDES eae eames a eee, 442 547 d D7 Cpe Seo a ae below 330 446 It will be noticed that there is here no agreement between the results of different observers. Our results are as a rule about 100 degrees lower than Carnelley’s, except that of the sulphate. Our resistances did not allow us to take the melting-point of lithium iodide, as we had not arranged for temperatures below 330°, but its melting-point is below that of potassium nitrate (339°). Lithium iodide is very hygro- scopic, so that on placing it on the ribbon it quickly liquefies; then on putting on the current, it becomes solid and then liquid again at the temperature given above, 2. e., it has melted, and remains so indefinitely. Salts of Sodium. The salts of sodium and potassium were prepared from the bicarbonate, precipitated by carbonic acid from a solution of the pure carbonate. The melting-points are well marked, though all are not equally so, e. g., the iodides. Meyer, Ramsay & Le Cha- Riddle MHeycock & Eumorfopoulos. Carnelley. telier. & Lamb. Neville. McCrae. Na?SO4... 884 861 860 863 883 883 Na?CO?... 851 814 820 849 852 861 (854) NaCl... ces: 792 172 778 815 vies 813 NaBr...... 733 708 aie 758 ee 761 INGE Ge ecens 603 628 a 661 si 695 (668) The agreement between Messrs. Heycock and Neville’s results and our own is only apparent, as they find 1062° as the melting-point of gold, while we assume 1045°. The fact that they are determining freezing- and not melting-points may introduce some difference. Determination of Temperatures with the Meldometer. 365 Salts of Potassium. Meyer, Rawsay & -Le Cha- Riddle Heycock & Eumorfopoulos. Carnelley. telier. & Lamb. Neville. McCrae. K750*.... 1@a2 he 1045 1078 10665 1059 (1166) K?C0*... 880 834 860 79 aa 893 (885) WECT. 5.2 762 734 740 800 -s 800 ?Be 733 699 = 722 = 746 (709) ee 614 634 640 685 ial 723 (677) M. Le Chatelier gives an earlier value 1015° for potassium sulphate, and also 885° for potassium carbonate. Our value for potassium sulphate is 7 degrees above that of gold. Messrs. Heycock and Neville’s is 4°5 above their value for gold, but they mention that there may be an error of 2 degrees, due to the alkalinity of their potassium sulphate. Salts of Calcium, Strontium, and Barium. The salts of calcium, strontium, and barium were prepared from their carbonates precipitated from the purified nitrates. Their melting-points are not well marked, especially those of calcium ; and here again the iodides are less well marked than the chlorides. Meyer, Ramsay & LeOha- Riddle McCrae. Eumorfopoulos. Carnelley. telier. & Lamb. =€2(NO*)*...... 499 561 0 Sere 710 719 755 806 802 Car .2.c.-52 485 676 4 Ia eee 575 (?) 631 Sr NO... <2 570 645 STE Sager te 796 825 840 832 Bd4 foial 1 ge ep eeeper 498 630 Srl’. 22 ne 402 507 Ba(NO*)? ... 578 593 592 Bae oes. -- 844 860 847 922 916 (941) Babes... 728 812 iS) Geer eereee 539 Calcium chloride is very difficult to observe, as it slowly softens. We found it practically impossible to take the melting-point of calcium iodide, as it is exceedingly hygro- scopic, and, on heating, it is almost immediately oxidized. We do not think it can be above the value given, though it may be below it. Salts of Silver and Lead. These were prepared by precipitation. Their melting- points are well marked. Phil. Mag §. 5. Vol. 41. No. 251. April 1896. 2 366 Determination of Temperatures with the Meldometer. Ramsay & Hamecetap silos Carnelley. 654 451 427 527 498 499 | 383 A curve is appended with the melting-points of the salts of potassium marked on it. In drawing this curve there must Temperature. Tare, ' Standardisation points Melling points of sal ts obtained by Graphic interpolulion _____O 1 Number of revolutions of the micrometer-screw. The Magnetic Field of any Cylindrical Coil. 367 of necessity be a small uncertainty, as there is no datum-point between 339° and 1052°; but this cannot amount to more than a very few degrees. In conclusion, we may point out that plotting our meldo- meter-readings against other observers’ melting-points does not give a smooth curve. University College, London. XXXVI. The Magnetic Freld of any Cylindrical Coil. By W. H. Everett, B.A.* _ eek Ampére’s formula for the magnetic force at any point due to an element of current, the force perpendicular to any plane circuit, carrying a current 2, is found to be, at any point P, oh Ce ae Z, =i {ores 3 h being the distance of P from the plane of the circuit, and r, 6 the polar co-ordinates of any point of the circuit referred to the projection of P as origin. The longitudinal force at any point due to a current in a cylindrical coil, or solenoid, is given by a second integration. It is the sum or difference of two terms, each of the form ae / 72 + |i? é where fA denotes the distance of the point from an end plane of the solenoid, and n the number of turns per unit length of h. The depth of the coil, normal to the cylindrical surface, is assumed to be inconsiderable. The limits of integration are 0 and 27 for any point whose projection, taken parallel to the axis, falls within the solenoid. Similarly, the transverse force at any point, due to a sole- noid, is found to be 1 1 : in ( Vrthe Vv pe) ae the summation being vectorial. The latter two formule can be readily applied, for approxi- mate calculation, to a cylindrical coil of any cross-section, Tidak * Communicated by the Physical Society, being abstract of paper read November 8, 1895. 2C 2 368 The Magnetic Field of any Cylindrical Coil. including coils of circular and rectangular sections. But in the case of rectangular coils the formule become integrable. Let p be the perpendicular distance of any point P from one of the faces of the rectangular coil, and a one of the two parts into which the corresponding side of a cross-section is divided by the perpendicular from P. Then the longitudinal force at P is given by the algebraic sum of sixteen terms, each of the form dx (#2 + 2) / 22 +p? + hh?’ ah MV (a® +p?) (RP + p*) Z=inhp\ 0 e ei =n sin And the transverse force at P is the resultant of eight terms, each of the form R=a| C— ae Weep Vea nt) pth? at Vat+p? +h? FOR Th? * 24724 f2) Poth a+ Vatp thy The first formula in the paper can be used to find an ex- pression for the force due to a circular current, at any point P in the plane bounded by the circle. Draw any chord through P, and call its segments 7, 7’. Write ¢ for the distance of P from the centre, b for half the minimum chord through P, and a for the radius. Then for the force at P the tormula reduces to Oe ak ee ee = |, /a?—c? sin2@ . dé. This can be written .8 Fata ; s being the perimeter of the ellipse with a and 6 as semi- axes, and having some value between 2zra and 4a, according to the position of the point considered. [ 369 ] XXXVII. A Method of Determining the Angle of Lag. By Artuour L. CiarKk, S.B., Prof. of Mathematics and Physics, Bridgton Academy, North Bridgton, Maine, U.S.A.* Nel power or rate of expenditure of energy at any given instant of time, on an electrical circuit, may always be found from the equation W=EI; where W is the power in watts, H the E.M.F. in volts, and I the current in amperes. But if the average power is desired this formula is not general. It suffices only where EH and I are constant or nearly so. It is a problem at the present time to measure the power expended on circuits through which flow alternating currents whose E and I vary harmonically with the time. In this case the formula becomes W= = cos $; where ¢ is the difference in phase or is the angular magni- tude of the delay of the rise of I behind H. E and [ are the maximum values of the H.M.F’. and current respectively. It is obvious that cos ¢ is a very much desired value, and different methods for determining it have been conceived. There have been several phase-indicators brought before the scientific world during the past year or two, but of these there are very few, if any, wnich furnish a convenient means of accurately measuring a difference of phase. The instrument herein described is the outcome of ex- tended investigation carried on by the author during the past year at the Worcester Polytechnic Institute. Many of the different forms of apparatus which depend upon the inter- ference of sound waves, vibrating wires, &c., were constructed and experimented upon, with unsatisfactory results. It was found that indicators which are influenced to a marked degree by small variations of the vibration-period are of little value. As this variation interferes seriously with results, and as no dynamo furnishes a current absolutely periodic, such an indicator is worthless commercially. The well-known Lissajous’s figures bave been used at different times as a means of determining the angle of lag, and are the basis of the herein described apparatus. The eurrent from the dynamo passes through a single loop of wire * Communicated by the Author. 370 Prof. A. L. Clark on a Method of clamped at one end, and carrying a small mirror on the other end, which is free to vibrate. This loop is suspended between the poles of a magnet (electro or permanent), so that with every change of direction of the current through this loop, it will tend to rotate one way or the other according to Max- well’s rule, z. e., “ Every portion of the circuit is acted upon by a force urging it in such a direction as to make it enclose within its embrace the greatest possible number of lines of force.” Now if a beam of light falls on the mirror, the reflexion will be drawn out into a line by the vibration of the mirror. This beam of light coming from this mirror falls on a second mirror, arranged as the first but actuated by another current and with its plane of vibration perpendicular to that of the first. In the resultant reflexion we find our means of mea- suring the amount by which one mirror leads the other, or, in other words, by how much the phase of the current in the first leads that in the second. We will call the direction of vibration of the beam of light as given by each mirror alone the axes of X and Y respectively. That is, the axis of X is the figure from the first mirror while the second is stationary, and the axis of Y that from the second while the first is stationary. The equation of a simple harmonic motion of amplitude a along the axis of X may be expressed “=a sin 8, where @ is a linear function of the time. Also the equation of another harmonic motion of amplitude 6, along the axis of Y, whose time differs from @ by an amount @, is y=bsin (0—¢;. Combining by eliminating @ since sin =, cos O= - Va? — 2”, the resulting equation is y= (x cos 6— /a*—2? sin d), an equation in # and y, independent of the periodic time. This equation is the equation of an ellipse. The resultant reflexion, then, is an ellipse whose shape depends upon a, 3, and ¢. Determining the Angle of Lag. 371 The equation of the long diameter of the ellipse is b Then since the short diameter is perpendicular to this, its equation is Pe tiie Treating either of these equations as simultaneous with the equation of the ellipse, the coordinates of the intersection of these diameters with the curve may be found, from which may be deduced the lengths of the diameters in terms of @. This result is general but too cumbersome to be of service. Suppose a=), a condition which may be easily attained by increasing or decreasing the current in the vibrating loops, or by varying the strength of the actuating magnets. The equation of the ellipse would then be y=xcosd— Y1—2’ sin ¢, the equation of a family of ellipses whose parameter is ©. The equation of the diameters is y= te. Combining this with the equation of the curve, there re- sults as the squares of the coordinates of intersection Sine Ap mm as sin? @ Q — 2— —— _ e vi 2(1+ cos ¢) ’ ‘ 2(1+ cos ¢) The upper sign in the denominator belonging with the positively sloped and the lower with the negatively sloped diameter. The squared length of the semidiameters is the sum of these squares, or ane 1l+cos@ The whole diameter is double this semidiameter, so calling D, the positively and D, the negatively sloped diameter, 4 sin? d ie el a Di 1—cos ¢’ yee A sin? *~ 1+cos ¢' 372 Prof: EF. 123: Wateworth on Dividing the first by the second we have DD, __1+cos¢ D2 1l—cos@’ from which D,?—D,? The reflexion is examined in a telescope with micrometer eyepiece, having two separate scales so that the lines on these scales may be made perpendicular to the long and short dia- meters of the ellipse. It makes no difference what the scale- divisions are, if they are alike on both scales. When the ellipse becomes a straight line, D.2=0 and cos $6=1, from which ¢=0, or the currents are in phase. If the ellipse becomes a circle, D,?=D,? and the numerator be- comes 0, consequently cos d=0, and ¢=90°, or the currents are in quadrature. The amount of self-induction in the apparatus itself is in- appreciable, and the loops keep well in time with the current. Even a considerable variation in period does not hinder the vibrations, which in this case are forced. This is possible since the mirrors, while moving very slightly, still vibrate sufficiently for telescopic observation. Thus we have overcome the two great difficulties of many forms of this apparatus, namely, self-induction and the in- ability of the vibrating wires to follow a change of period. And with these objectionable features eliminated and a method of finding the exact value of cos ¢, we have a practical means of determining the difference of phase. Worcester Polytechnic Institute, Worcester, Mass. XXXVIII. A Note on Mr. Burch’s Method of Drawing Hyperbolas. By ¥. L. O. Wansworrn, #.M., M.E., Assistant Professor of Physics, University of Chicago*. 18 the January number of the Philosophical Magazine Mr. Burch describes a very simple and convenient method of drawing an hyperbola by the use of two similar triangles. This method is very similar to one which I have been using for some time and which I have described in my lectures for the past two years, although I have never pub- lished it. Mr. Burch’s invention of the method antedates * Communicated by the Author. Mr. Burch’s Method of Drawing Hyperbolas. 373 mine, however, by several years, as he states that he first used it in 1885, while it first occurred to me in 1893. In the present note I only wish to call attention to the fact that the particular construction described is only one example of a general class of solutions of this character, and to describe two or three others which are, I think, equally simple and convenient. In general, if in any two similar triangles two dissimilar sides are kept constant and the other sides varied, itis evident that these two varying sides, which are proportional to the two fixed sides, will be asymptotic coordinates of an hyperbola - of which the modulus is the product of the two constant sides. The simplicity of the corresponding graphical or mechanical tracing of the curve depends simply upon our choice of tri- angles and choice of sides. In the method of construction which I most frequently employ, the two similar triangles have a common vertex at the origin 0, fig. 1, and the two LL F716. 2. sides ob, be and od, de parallel to the asymptotes of the re- quired hyperbola. Then if we put 00= 2, de=y, be= 1, we have at once vy 0d: Hence if we draw a series of triangles in each of which be 374 Prof. F. L. O. Wadsworth on . a’ +b 4 de, of any pair represent coincident values of x and y in the corresponding hyperbola. These coincident values laid off along their respective axes give a series of points on the curve from which it is easy to trace the curve itself. In practice, the whole operation may be rapidly and easily per- formed by means of a T-square and a single triangle of which one angle is equal to the angle yox between the axes *. First draw the line mn (fig. 2) parallel to and at unit distance from the axis of w, and the line dq parallel to the axis of y a? + b? 24 is unity and od is constant and equal to , the sides ob, and at a distance from it equal to Then to the points c ¢ c' on the first line draw the lines oc oc! oc’ &e. by the aid of the edge of the T-square or an auxiliary ruler, and the lines cd, cb’, cb" by means of the triangle or bevel-gauge. Project the points of intersection e, e’, e” of the first set of lines with the line dg upon the second set of lines, giving us the points s, s’, s’’ on the required hyperbola. This method is particularly rapid and convenient in plotting rectangular hyperbolas on cross-section paper, the only instrument then necessary being a rule to draw the radial lines oc, oc’, &e. If desired, an instrument can easily be constructed on these lines to trace the curve mechanically, but generally the graphical process is more rapid. A whole series of contours to the thermodynamic surface (pv=const.) can be drawn by this process in a very few minutes, the same set of lines oc, oc’, oc’, and cb, c’b’, c’’b’’, answering for all the curves. 2nd method.—Make the vertices of the two similar triangles coincide at c instead of o as before, and make ab=oc=a2, and cd=y (fig. 3). Take a point a on the axis of y at unit dis- tance from the origin and draw from it the lines ae, ac’, ac’’ to points on the axis of x, and the lines bc, b/c’, bc’ parallel to the y axis as before. Mark off a distance equal to a® + b? ete eS 4 On the edge of a triangle (or bevel-gauge), Q, of which the angle at d is equal to the angle yoa, and slide this triangle along each of the lines dc, 6’c’, b’’c!’, &e., until the point f intersects the corresponding line ae, ac’, or ac’. The points d, da’, d’’ will then evidently be points on the hyperbola. In practice it is not necessary to draw the lines de, 6’c’, &e. at all, it suffices to place a T-square whose blade is parallel to the axis of y, so that its edge passes through any of the * It is convenient to use for this purpose an ordinary steel bevel- gauge the two blades of which may be adjusted to the required angle. Mr. Burch’s Method of Drawing Hyperbolas. 375 points on the axis of «x; slide the triangle along this edge until the point f falls on the corresponding line from a, and ¥ FICS: mark the position of the vertex d of the triangle (see fig. 4), This method is perhaps even more rapid and convenient than the first, as it involves the drawing of only one set of lines | ac, ac’, &c. Like the first, it involves the use of only a triangle and a T-square. 3rd method.—Let the vertices of the two similar triangles coincide at b (fig. 5). Then if bc=unity we have as before vy =o. To determine the points on the curve graphically in this case, we need a triangle or bevel-gauge of an angle equal to you and a parallel ruler. The side bc of the triangle or bevel- a? +b? 4 laid off on the side bg. The triangle is placed with its side bq coinciding with the axis of z, and one edge of the parallel ruler is brought against the point ¢ of the triangle and a pin placed at the origin. The other blade of the parallel ruler is then moved out until it passes through the point f on the gauge should be of unit length and a distance fb= 376 | Prof. F. L. O. Wadsworth on - horizontal edge of the triangle, as in fig. 6. The point e at which the blade of the ruler intersects the side be of the mo eC Fic. 5 E | b a I ee EES Fre. 6. triangle will be one of the points on the required curve, the others of which may be found by sliding the triangle along the axis of w, always keeping the two edges of the parallel ruler in contact with the three points 0, c,and f. This method is somewhat simpler mechanically, but not quite so rapid and convenient as either of the preceding. It is evident that there are six other possible solutions to be obtained by combining the sides ac, ae (fig. 1) with each pair of adjacent sides. But these solutions are unsatisfactory graphically, because simultaneous values of # and y will be represented by lines inclined to each other at an angle dif- ferent from the angle between the axes. If the angle at a is made equal to the angle between the axes, we have one of the three solutions already considered. The use of two similar triangles in the graphical, and more particularly the mechanical tracing of curves, is of wide ap- plication. By their aid we may always express the product or quotient of two variable quantities geometrically as the length (tensor) of one of the sides. Other applications of this principle will be found in a recent paper of the author’s on the mountings of concave grating spectroscopes*. * “Fixed Arm Concave Grating Spectroscopes,” F. L. O. Wadsworth. Astro-Physical Journal, vol. ii. p. 370 (Dec. 1895). _ Mr. Burch’s Method of Drawing Hyperbolas. 377 The Use of the Quadruplane as a Hyperbolagraph.—The two asymptotic coordinates of any hyperbola evidently form two sides of a parallelogram of constant area. Hence any hyperbola can be readily traced by the use of the Sylvester- Kempe quadruplane linkage, the four vertices of which lie at the four angular points of a parallelogram of constant area and constant obliquity*. The product of the adjacent sides of this parallelogram, or as Sylvester calls it the “‘ modulus” of the cell, is equal to 2 9 Sin a, SIN ay =i ee sin? aha where B and A are the distances between the pivotal points of the long and short links of the cell, #, and a the angles adjacent to the line joining the pivotal points, and @ the angle subtended by this line at the intervening vertex. If we make each link of the cell symmetrical we have a =a,=90—8/2, and B?— A? oe M= 4 sin?6/2 ° The obliquity of the parallelogram is equal to 0. | Hence to describe an hyperbola whose axes are a and b we must make the modulus of the cell equal to the modulus of the hyperbola, or _@4+P ay 4 and the angle @ equal to the angle between the asymptotes, or M y 2ab _.Then if one vertex of the cell is fixed and an adjoining vertex is moved along a straight line (the edge of a T-square or straight edge for example), passing through the fixed vertex, the vertex diagonally opposite the latter will describe the required hyperbola, having the fixed point as origin and the straight line as one of the asymptotes. To describe different hyperbolas it is necessary to be able to vary both 0 and M. ‘he first may be easily done by making each link in two halves, pivoted together at the vertex of the link with a divided sector and clamp, by means of which the desired @=sin— * See “The History of the Plagiograph,” Sylvester, ‘ Nature,’ vol. xii. p. 214; also Kempe, ‘ Lecture on Linkages,’ p. 25 et seg. 378 Mr. R. W. Wood on a angle @ may be laid off. The modulus of the cell is best changed by varying either A or B. This may be conveniently done by making each of either the long pair or the short pair of links like the legs of a pair of proportional dividers. A small model of an instrument on the above lines has been constructed and found to work very easily and accurately. Like all hyperbolagraphs, however, the range of motion is limited (although larger in this than in most forms), and a considerable amount of time is necessary for the preliminary adjustment. For these reasons I have generally found one of the preceding graphical solutions more rapid and con- venient, especially when a number of curves are to be drawn on the same sheet. | This application of the quadruplane, which occurred to me recently while making an application of the Peaucellier linkage to a concave grating mounting *, seems so simple and obvious that I feel sure it must have occurred to others as well as myself; but as I have not been able to find any sug- gestion to this effect in any of the papers on the subject that I have examined, I have ventured to present the foregoing description as another illustration of the practical application of the beautiful geometrical discovery of Prof. Sylvester and Mr. Kempe. Ryerson Physical Laboratory, University of Chicago, U.S.A., January 1896. XXXIX. A Duplex Mercurial Air-Pump. By R. W. Woop ft. : fe working with highly exhausted tubes, such as are used for the production of the Roéntgen rays, one of the difficuities met with is the speedy deterioration of the vacuum due to the liberation of gas from the electrodes and the glass. If the tube be thoroughly heated, while on the air-pump, this trouble is partially remedied, but even with this precaution the tubes are not very durable and have to be pumped out frequently. In order to overcome this difficulty I have con- structed a new form of mercurial air-pump, which can be made on a very small scale and attached permanently to the Rontgen tube. By this arrangement, any traces of gas that * “On the Use and Mounting of the Concave Grating as an Analyzing or Direct Comparison Spectroscope,” The Astro-Physical Journal,’ vol. iii. p. 47 (Jan. 1896). + Communicated by the Author. Duplex Mercurial Air-Pump. 379 make their appearance can be easily pumped out. The apparatus is so compact that it can be held in the hands while in operation, not requiring mounting on a board. The pump is very simple, and a glance at the accompanying diagrams will make its construction clear. It will be seen to consist of two bulb-pumps joined at the base by a U-tube of glass (fig. 1). The pumping is done by rocking the apparatus, the mercury filling the exhaust-bulbs A A alternately. This duplex action makes the pumping very rapid, for one bulb exhausts while the other fills, there being no lost time. The traces of gas liberated in the discharge-tube are pumped over into the ex- hausted bulbs BB, where they are stored, being prevented from returning by the mercury which remains in the W traps between A and B. The upper bulbs are joined by a tube H, which has a small lateral tube P blown into it ; this arrange- ment being necessary for the preliminary exhaustion. Mercury is first introduced through P until the bulbs A A are half full. A gentle rocking of the apparatus is necessary, as the fluid is held up in the bulbs B by the compression of the air in A. When enough mercury has been introduced, the apparatus is placed in the position shown in fig. 3, when the fluid should stand at the level indicated in the diagram. The side tube P is now drawn out into a thick-walled capillary in a blast-lamp, in order to facilitate the subsequent closing of the apparatus. This tube being connected with a good mercury- pump by means of a well-greased, thick-walled rubber hose, 380 Mr. R. W. Wood on a Duplex Mercurial Air-Pump. the apparatus is exhausted as completely as possible. During the exhaustion it must be supported in the position shown in fig. 3; otherwise the air escaping from the discharge-tube will throw the mercury violently against the top of the bulbs. It is a good plan to carefully heat the bulbs and the discharge- tube by means of a Bunsen burner while the pump is in action, in order to drive off moisture. ‘The current of a fair- sized induction-coil should also be passed through the dis- charge-tube for a few minutes to rid the electrodes of air as completely as possible. It will be found that the vacuum cannot be made perfect enough to give a Crookes dark space of more than an inch, owing to the leakage through the rubber hose. The capillary part of P is now heated to fusion in a small flame which hermetically seals the entire apparatus. The comparatively poor vacuum in the discharge-tube can now be made as perfect as is possible with any mercury-pump by slowly rocking the apparatus, holding it by the bulbs AA. If the pump is properly made, the traps hold and require no attention : if not, a little dexterity is required, to prevent the mercury from running out into the bulb, and they have to be constantly watched. Care must of course be taken that the air-bubble, compressed into the trap by each stroke, is driven entirely around the bend and into the reservoir B. If for any reason the pump requires to be subsequently opened, it must be placed in the inclined position and a file scratch made on the tube P. A bit of red-hot glass pressed against the scratch will cause a crack through which the air will slowly enter. If the tube be broken open suddenly, the mercury will be forced over into the discharge-tube. I con- Intelligence and Miscellaneous Articles. 381 structed my apparatus with the Roéntgen tube projecting to one side, as shown in the side view, fig. 2. This makes a support for the pump so that it will stand alone. A pump of this description in connexion with an ordinary “‘ Dark-space”’ tube makes a very convenient piece of lecture-room apparatus for showing the character of the discharge at different pres- sures. By tipping the pump far enough the upper trap can be emptied, and the air stored in B returned to the discharge- tube again, showing the phenomena at higher pressure. — Owing to the absence of rubber connexions and stopcocks, the mercury remains always clean and there is no leakage. I am now constructing a pump on this principle on a large scale for general laboratory use in which the rocking motion is to be effected by water-pressure, which, if found serviceable, will be described in a subsequent paper. The chief objection, of course, is that the entire pump is in motion, which makes its connexion with a stationary receiver somewhat difficult. This can perhaps be done by bringing the exbaust-tube into coincidence with the axis of rotation, and using a rubber tube surrounded with mercury as a joint. The small pump can be ordered witb or without the Roéntgen tube from Herr Glasbliser R. Burger, Chaussee- str. 2E, Berlin, Germany. Berlin: Physikalische Institut. XL. Intelligence and Miscellaneous Articles, NOTES OF OBSERVATIONS ON THE RONTGEN RAYS. BY HENRY A. ROWLAND, N. R. CARMICHAEL, AND L. J. BRIGGS. HE discovery of Hertz some years since that the cathode rays penetrated some opaque bodies like aluminium, has opened up a wonderful field of research, which has now culminated in the discovery by Rontgen of still other rays having even more remarkable properties. We have confirmed, in many respects, the researches of the latter on these rays and have repeated his experiments in photographing through wood, aluminium, card- board, hard rubber, and even the larger part of a millimetre of sheet copper. Some of these photographs have been indistinct, indicating a source of these rays of considerable extent, while others have been so sharp and clear cut that the shadow of a coin at the distance of 2™ from the photographic plate has no penumbra whatever, but appears perfectly sharp even with a low-power microscope. So far as yet observed the rays proceed in straight lines, and all efforts to deflect them by a strong magnet either within or without the tube haye failed. Likewise prisms of wood and vulcanite have Phil. Mag. 8. 5. Vol. 41. No. 251. April 896. 2D) 382 Intelligence and Miscellaneous Articles. no action whatever so far as seen and, contrary to Rontgen, no trace of reflection from a steel mirror at a large angle of incidence could be observed. In this latter experiment the mirror was on the side of the photographic plate next to the source of the rays, and not behind it as in Rontgen’s method, We have, in the short time we have been at work, principally devoted ourselves to finding the source of the rays. For this purpose one of our tubes, made for showing that electricity will not pass through a vacuum, was found to give remarkable results. This tube had the aluminium poles within 1™™ of each other, and had such a perfect vacuum that sparks generally preferred 10° in air to passage through the tube. By using potential enough, however, the discharge from an ordinary Ruhmkorff coil could be forced through. The resistance being so high, the discharge was not oscillatory as in ordinary tubes but only went in one direction. In this tube we demonstrated conclusively that the main source of the rays was a minute point on the anode nearest to the cathode. At times a minute point of light appeared at this point but not always. Added to this source the whole of the anode gave out a few rays. From the cathode no rays whatever came, neither were there any from the glass of the tube where the cathode rays struck it as Rontgen thought. This tube as a source of rays far exceeded all our other collection of Crookes’ tubes, and gave the plate a full exposure at 5 or 10™ in about 5 or 10 minutes with a slow-acting coil giving only about 4 sparks per second. The next most satisfactory tube had aluminium poles with ends about 3°" apart. It was not straight but had three bulbs, the poles being in the end bulbs and the passage between them being rather wide. In this case, the discharge was slightly oscillatory but more electricity went one way than the other. Here the source of rays was two points in the tube, a little on the cathode side of the narrow parts. In the other tubes there seemed to be diffuse sources, probably due in part to the oscillatory discharge, but in no case did the cathode rays seem to have anything to do with the Rontgen rays. Judging from the first two most definite tubes, the source of the rays seems to be more connected with the anode than the cathode, and in both of the tubes the rays came from where the discharge from the anode expanded itself towards the cathode, if we may roughly use such language. As to what these rays are it is too early to even guess. That they and the cathode rays are destined to give us a far deeper insight into nature nobody can doubt.—American Journal of Science, March, 1896. NOTE ON “FOCUS TUBES” FOR PRODUCING w-RAYS. BY R. W. WOOD. The tubes for producing the #-rays which are furnished with a concaye kathode for focussing the kathode rays on the glass, in order Intelligence and Miscellaneous Articles. 383 to diminish the size of the source and increase its intensity, have the fault that, owing to the great heat developed, the glass is very apt to crack. I have had some success with a tube which Il made in which the kathode hangs as a pendulum from the centre of a spherical bulb, by the slow rotation of which one brings a fresh and cold surface into the focus continually, thereby avoiding over- ss ee ee ee ae eer wr wr OO | ao — — — A ee a re s 7 le heating. The concave kathode hangs by an aluminium wire from a short cylinder of aluminium fastened into a glass tube, through which a platinum wire passes which lies in the axis of rotation. The anode is also in the axis of rotation, so that the connexions with the coil can be easily made. My tube has the fault that many kathode rays emanate from the upper surface of the concave plate and are lost. This might be overcome by covering the kathode with a cap of glass. As a suggestion for further experimenting, this note may be of interest to persons working with the new rays. Berlin, March 8, 1896. NOTE ON ELEMENTARY TEACHING CONCERNING FOCAL LENGTHS. To the Editors of the Philosophical Magazine. GENTLEMEN, With respect to Prof. Lodge’s question on page 152 as to the simplest convention of signs in dealing with focal lengths for junior students, it appears to me to be a matter which can be best settled by one who has had experience in teaching two or more methods. Hence, as this is a qualification to which I can lay no claim, I forbear to dogmatize. It would seem to me, however, undesirable, apart from weighty reason, to teach an elementary student to let the algebraical sign of a given line depend, not upon its direction, but upon the physical 384 Intelligence and Miscellaneous Articles. nature of the optical image at which the line terminates. Still there is a manifest advantage in the convention proposed, since it allows the relation of focal length and conjugate focal distances to be represented by asingle equation for both mirrors and lenses. I give below the adaptation of the graphical method to the convention of signs proposed by Prof. Lodge (and used in Ganot’s ‘Physics’), viz. :—Distances to real images to be considered positive and distances to virtual images negative. The fixed points through which the rotating lines pass are now in the right-hand upper quadrant both for convex lenses and concave mirrors, and in the left-hand lower quadrant for concave lenses and convex mirrors. That is, referring to Fig. 1, page 61, L, is now shifted so as to coincide with M, which remains unmoved, and L, similarly is made to coincide with M,. Yours faithfully, Uniy. Coll., Nottingham, Epwin H. Barton. Feb. 21, 1896. SOLUTION AND DIFFUSION OF CERTAIN METALS IN MERCURY. BY W. J. HUMPHREYS, The investigation, of which this is a suimmary, was begun with the object of determining the extent to which these phenomena differ, if at all, in this case from the solution and diffusion of non- metallic solids and liquids. The method of investigation was to filla vessel of constant cross section with pure mercury, put on its surface a freshly amalgamated piece of the metal to be examined, and after allowing it to stand a definite length of time in a place free from external disturbances and of fairly constant temperature, to remove from known depths below the surface samples of the amaloam and analyse them. The metals examined were lead, tin, zinc, bismuth, copper, and silver, and the results indicated that there is no essential difference between the solution and diffusion of these metals in mereury and the same phenomena in any other case. Probably the most interesting results were those given by copper and silver, both of which dissolved to a much less extent than any of the other metals examined, but diffused more rapidly. At 28° C. the silver dissolved to the extent of only about one part in two thousand, and the copper to a still less extent—about three parts in a hundred thousand; while the rate of diffusion of the silver was about twenty millimetres per minute, approximately sixty times that of copper and fully six hundred that of zinc. This investigation, of which the details will soon be published, was suggested to me by Dr. J. W. Mallet, F.B.S., of the University of Virginia, and carried out there under his supervision during the months of August and September, 1895.—John Hopkins University Circulars, February 1896, THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FIFTH SERIES.] MAY 1896. XLI. On the Laws of Irreversible Phenomena. By Dr. Lapistas Natanson, Professor of Natural Philosophy in the University of Cracow *. T can scarcely be doubted that the theory of dissipation of energy is still in its infancy. Reversible phenomena are well understood, but they do not involve dissipation at all; and what is known about irreversible phenomena is merely the qualitative aspect of their general laws. In fact, of the general quantitative laws of irreversible phenomena we are as yet utterly ignorant. Now I venture to think there is a general principle underlying irreversible phenomena which is easily seen to be consistent with fact in various cases well investigated : it is an extension of Hamilton’s Principle, ~and (with much diversity, of course, as to form and gene- rality) has been stated by Lord Rayleight, by Kirchhoff f, by v. Helmholtz §, and by M. Duhem ||. It seems that propo- * From the Bulletin International de l Académie des Sczvences de Cra- covie, Mars 1896. Communicated by the Author. + Proceedings of the London Mathematical Society, June 1873. The Theory of Sound, i. p. 78 (1877). }t Vorlesungen tiber Math.-Physik. Mechanik, 1876, Vorlesung xi. § Borchardt-Crelle’s Journal f. Mathematik, Bas € (1886) ; Wissen- schaftliche Abhandlungen, Bd. iii. p. 203; ibid. Ba. ii. p- 998; Bd. ii. 119. 5 || Journal de Mathématiques de Inouville-Jordan (4) vol. viii. p. 269 (1892): vol. ix. p. 293 (1893); vol. x. p. 207 (1894). See further, Prof. J. J. Thomson's ‘ Applications of Dynamics to Physics and Che- mistry, London, 1888, where the fundamental standpoint is a very similar one, the chief object of investigation being, however, the theory of reversible phenomena. Phil. Mag. 8. 5. Vol. 41. No. 252. May 1896. 25 386 Prof. L. Natanson on the © sitions equivalent to those indicated by these investigators could be enunciated in the form of a simple and very general formula ; we venture to think that the fundamental principle which it embodies is worth attention. Besides, it seems to afford the proper foundation for an attempt to arrive at some deeper insight into the laws of dissipation of energy. Parr I. § 1. Introductory.—Conceive a system: it may be either finite or infinitely small ; it may be an independent system, or it may be only a part of some other system. Let the state of the system, at time t, be determined by the values of certain variable quantities, g,, and of their first differential coefficients with respect to the time, s, or dq,/dt. We shall suppose that the energy of the system consists of two parts, the first of which, T, is a function of the g, and the s, homo- geneous of the second degree with respect to the s,, and the second, say U, is a function of the g, only. Let 5 denote the absolute temperature of the system : 5 may be an independent variable, or otherwise it must be a definite function of the variables. Suppose that the quantities g,, s, received certain arbitrarily chosen infinitesimal increments 6g,, 6s, ; the energy T will then become T+6T, and U will become U+6U. Let then &P,69, be the work done on the system reversibly, during the transformation, by extraneous forces, and let 6Q or {R,dg, be the quantity of heat simultaneously absorbed by the system from the exterior; P, will then be the generalized or Lagrangian extraneous “ force” in the “direction” of the variable g,, and R, will be the ‘caloric coefficient,” as it is called by M. Duhem, or the generalized “thermal capacity” of the system with respect to the variable q,. With respect to the quantity 6Q we now make the following assumption, which we shall find is in accordance with fact. Let us suppose that every variation 69, takes the special value dq, or st; then the values of the variables g, will become g,+q,; the energies T and U will become T+aT, U+dU ; the work done by external forces will be =P,dg,; and the quantity of heat absorbed will be dQ or =R,dq,. If now the variables be allowed to return to their primitive values g,, T and U will resume their former values T, U, the external work —=Pidg; will be done, but the quantity of heat absorbed will generally not be dQ but a different quantity, say d,Q. Laws of Irreversible Phenomena. 387 Write ot Q=-FaQ ae eae 63 21) and a — 1d Ot 0 (eee (2) therefore —@Q=—d,Q—d’Q.. . . . . (8) We have | +dQ = +0Q+d’'Q, LL 10 Fenty Soe rote (C2) and = OQ Qs d' Qi sais h oe OD) thus d°Q is the reversible, and d/Q the irreversible part of the heat absorbed. Now, if we assume that these quantities © are of the form ed. sd ORG. 5 aes a we may consider the new quantities 6&°Q+6’Q gives again 6Q. Let us generally define 6Q, 5°Q, 6’Q to represent the expressions which result if in the ex- pressions of the quantities dQ, @°Q, and d’Q (which we sup- pose to be empirically known *), variations 6g, are substituted in place of the corresponding differentials dq,. § 2. Statement of the Principle—Let us consider a given period of time, from i=t, to t=t,. Let d9,, ds, oT, 6U, >P,5g, as usual, represent variations which, between the limits t=¢) and ¢=¢,, are functions of the time susceptible of being differentiated, and which vanish at these limits them- selves; finally, let dQ, 6°Q, JQ be the corresponding in- finitesimal expressions calculated as above stated. The following principle seems then to hold in physical phenomena: between t=¢) and ¢=¢, events which occur in the system must be such that the equation { ‘acqor—s0 +5Pq,48Q}=0 | hig ah is satisfied. For brevity, this, when necessary, will be re- ferred to as the Thermokinetic Principle. * To write down the expressions of dQ and d'Q, a much greater number of variables would evidently be required in most cases than to write d°Q ; thus in most cases many of the coefficients R} will be equal to zero. A similar remark applies to the coefficients P,, dT/aq; dT. and 9U/9y,. 2H 2 388 Prof. L. Natanson on the — § 3. Lagrangian [quations.—From (1.), remembering the definitions laid down, we obtain by a well-known calculation a(9T\_ dT , aU le tag These equations, a thermokinetic extension of Lagrange’s well-known dynamical equations, have been given implicitly by Helmholtz and explicitly by M. Duhem; the form they take in an important particular case had been previously ex- plained by Lord Rayleigh. § 4. Conservation of Hnergy.—Considering a real trans- formation dq,, ds, multiply each of these eqnaiee by s,dt respectively, and bade we find dl 4+dU—SPdq,—dQ=0. . . =e The principle of conservation of energy in its general form is thus seen to follow from the thermokinetic principle. That inversely the thermokinetic principle cannot be deduced from conservation of energy is an obvious proposition which scarcely requires special mention. § 5. Free Energy—We shall suppose in the following (except when the contrary is expressly stated) that one inde- pendent variable is the temperature; and accordingly we shall use g, to indicate all the other variables. That work is not required for merely changing the temperature of a system is an experimental fact ; hence, when the variables $3, g,, and s, receive increments 63, 5g,, 6s,, the work done on the system will be still }P,8g, (in our present modified notation) and no term including 68 willappear. Variables with such properties attributed to them have been employed by Lord Kelvin as long ago as 1855 ; they have been often adopted in general thermodynamical investigations. M. Duhem calls them “normal” variables. Let us suppose that 5, g, represent a system of “ normal ” variables. Write 5 0U * 39, The function V, if it exists, will be called the free energy of the system, because, as we shall find hereafter, V defined by equation (1) will agree in the case of Reversible Thermo- OV 6 RS — Ga oa se . . . \ U Pam > a q; 255 89; (1) Laws of Irreversible Phenomena. 389 dynamics with what, from Helmholtz, received that designa- tion. Hquation (1.) accordingly becomes { a{ at—3 9° 7,4 3P.89,— (25 —R5 a9 +99 \ =0. (2) 0%; os Now let us further assume that the following equations are ples CHE Aa ae ao ee s5 0 aa Gm: mrt oF i 3.) dt they are found to hold good in all cases of which we have precise knowledge ; lastly, let us suppose that there is no term containing 63 in the expression for 6’Q. (With respect to this point compare § 12.) iquation (2) may now be divided into oU 55 Rs =0, - Beige coer We) and fra 1 iL o7 54,4 3P3y,+8Q | (WIL) 0 This equation expresses the principle in a form similar to that of equation (I.). It is a useful equation, owing to the readiness with which it admits of application in various cases, but its abstract generality is of course much more restricted than that of the fundamental equation. § 6. Reversible Dynamics.—In Dynamics properly so-called, 2.€. in Reversible Dynamics, ideal phenomena of motion are dealt with, and the notion of temperature is not taken into account. ‘Therefore, in Reversible Dynamics a function V can be considered, depending on the remaining variables gq, only, which does not differ, except by a constant, from the “ poten- tial energy ’’ U ; this isa remark already made by M. Duhem. Of course it must be restricted to the Dynamics of points and of rigid bodies, since, for instance, in Hydrodynamics and Aerodynamics the difference between the quantities V and U is variable and depends on the compressibility of the fluid. From (III.) we obtain, leaving out the irreversible term 6'Q, the fundamental principle of Reversible Dynamics. § 7. Electromagnetic irreversible phenomena.—Hnergy stored in the ether can be transferred to matter and converted into heat; this phenomenon, when it occurs, is a thoroughly ir- reversible one. 390 Prof. L. Natanson on the’ Here, therefore, we may put R;=0 and 9U/09q,=0V/0q, ; and the equation will be ty i) dis? 80 4 EP, 89,4 7Q}=0. 2 a to We shall return to this case in § 13 below. § 8. Reversible Thermodynamics —At present the imme- diate object of the science called Thermodynainics is the study of states of equilibrium. The modifications assumed in Ther- modynamics to occur in a system are, for that reason, virtual reversible transformations which lead from one state of equi- librium to another one. Let us admit the following assump- tions :—first, that that part of the energy which we call T is a constant quantity; secondly, that the variables are “ normal” variables ; thirdly, if a function of the variables 3 and q,, called the entropy, be denoted by §, that the term 6°Q is of the form os os S55 Sean ye S . = 3 and, lastly, that the supposed transformation being reversible, the term 6’Q is equal to zero. Hence the laws of ordinary Thermodynamics must be contained in oU ols 55 25579 . or and ty i a3" 34,4 3P 89.) =0, poets (3) where : on aio Eye, fol Seon Se - . *. Sie Since the adopted variables 3, g, are “ normal” ones, we are at liberty to define the quantity U—SS as representing what in § 5 has been called the free energy of the system; hence OV a ON, “Ve +O; 55 and thus we are led to that well-known form of thermo- dynamical equations which we have learned from MM. Massieu, Gibbs, Duhem, Helmholtz, and others. § 9. Irreversible Dynamics.—Let us now proceed to con- sider cases of motion bearing perfect analogy with ordinary +S8=0, <« eee Laws of Irreversible Phenomena. 391 dynamical phenomena, except that, being irreversible, they do not satisfy the condition d/Q=0. Lord Rayleigh has shown how in many cases we can put EO ON ve ee ee (1) employing F to indicate a function of the variables g, (sup- posed to be “normal ’’ones) and s,, homogeneous of the second degree with respect to the s,, which he calls the Dissipation Function. The assumption we make is therefore that ad o= pea. = Fak ee 3 ewer va (2) and that or Re ee a a Logg tk Si eG t Os; ) following the rule laid down in § 1 we put or = a See: . ° . e 3 Q=—ES 8). (4) and from (III.) we obtain i “ae{B-BS" 84,4 8PBy,—¥S 843 =0: ey : re) hence fol Olu oN oF pa | a lenee VA ATS ee ———() pre 206 dt sa) Oa. 9 a) Oe. (6) These are Lord Rayleigh’s equations, with V written in the place of U. § 10. Irreversible Hydrodynamics.—Let us now proceed to consider a viscous fluid; we shall call w its coefficient of viscosity. Owing to the viscosity of the fluid its motion is accompanied by irreversible production of heat ; owing to its compressibility, there is reversible production or destruction of heat. We shall suppose that every such loss or gain in every element of the fluid is being immediately and exactly compensated, so that the temperature of the element remains constant. At the interior of a large quantity of fluid we take a portion, of mass \\\ dudydzp, p being the density at the point (2, y, 2). Let p be the ordinary mean pressure ; wu, v, w the components of the velocity, X, Y, Z the components of the extraneous acceleration, at the point (wz, y, z) and time ¢. The equations of motion, as given by Navier, Poisson, Stokes, and Maxwell, are as follows :— 392 Prof. L. Natanson on the’ du _ Op 2. i pee —pa, +p® rack alee: Rey (i CWP ee feo Sete rar foc Veet Yee Jue} eee e e #8 © © # @ with the usual signification of VY? and 6. Write PA pA, pAaS - 2. (rer for the pressures, parallel to the co-ordinate axes, on the element dS of the boundary of the portion we are considering. If the direction of the inwardly directed normal be denoted by n, we shall have :— La [p—2n(S2 -46)] cos (nx) - (22 s") cos (ny) da OY —1(S 4 o) cos (nz); 24 mney 25 = (5° = I cos (na) + pa —30)] cos ae oy 20 p= —u( se or) cos (na) —n( + or) cos (ny) Geen (Se —36)]eos(nz). . (6) If now a system 6x, dy, 6z of infinitesimal virtual displace- ments be imposed upon the fluid, the temperature being kept constant, then the work =P,6g, done by extraneous forces will be \\dS@,8e + p,oy + p,62) + \\\de dy dz p( Xda + Yoy + Zoz);(6) the variation of the energy T will be ST =\\\ da dy dz p(uSu + rdv+ wow) ; oa the variation of the energy V, which in Hydrodynamics it is usual * to call “ intrinsic ” energy, will be * See, for example, that otherwise excellent treatise ‘ Hydrodynamics ’ by Prof. Lamb, ed. 1895, pp. 11-12, 469, 507. It is not with the true intrinsic energy U, but with the free energy V that we are here con- cerned; the customary use of the word “intrinsic” seems, therefore, to involve a serious error. Laws of Irreversible Phenomena. 393 plaid Ode , Ody , O&% 6V= {lV de dy dep (S te a7 as =) sep ented) and, lastly, the quantity of heat which must be ‘absorbed ”’ in order to compensate the effects of viscosity will be | BY -Q-G)- oO —{\\da dy dz2dt sae ye 8 oY ER) fe) od. Oe y4\0 0 a 20) Se +(5,-29) Sy, +(5r 9) SF Ow , dv\(/dde , Ody +3(— + + = —{\\ de dy dz 2m a ats eS. a > (9) * 9a | fo) : a od e ee 2 Sa + a) J In order, therefore, to comply with the rule respecting 5'Q we have to write a 5 =n Jon * (ar ee ) foley Ox Oy Oy +(@ 30) +4 + 92) Ooy s1Q= — (\V de dy de oe a 02 / \ (40) +S + =) Ne ao | Se ae U A Ge Se * Sy) Let us now verify whether in the present case our general principle applies. From (1) we find du __ op 1 09 [* aejfaeaya: [—e = +pX a + pV7ut aH, \on =0; (11) to +| Saga. aisle: <3 | dy +[ aoe iota ] dz 13929 9(24_yo) 4 22" 4B) 4 B®, Buy 394 Prof. L. Natanson on the so that from (8), (10), (12), and again from (8), (4), (5) we obtain {if dedy az { [92 + uvrut gu So Je 4[... Jey +... Jd} = —6V + 8/Q—(\\ de dy az{ 2 (pdx) + S (vey) a “. (p82) } ; | + eet (S181) 318 -46)9] + SE ly [Sle Oe) 22+ 2] 14 7|+) ‘ + [ded dens S[(Se + S2)ae] +2 (M+ 82 )0 + 8: aloe 2] +2 ((S+ 2), | = —6V+9Q+\\d8(p, da+p, dy +p, 82). - ee 4 Further, we see that an dt \\{ da dy dz (5 ba + 5 =. "by +S te.) hi dt8T, (14) because da dy dzp does not vary ; and collecting our results we see that (11) reduces to t (“aetor—sv-+5P,8),+8Q}=0, ae to with equations (7), (8), (6), (10) to define the terms within brackets. § 11. Diffusion.— We next take two gases which are diffusing into one another. Let the masses of the portions considered be \\\ day dy, dz, p, and \\V datz dyzdz,p,3 and Sy, and §, their respective boundaries. When the motion of the _ gases is going on, three irreversible phenomena will occur, viz., internal friction in the first gas, internal friction in the second, and mutual interdiffusion of both ; in the following both the first and the second are neglected. Let again w, 1, w, Uo, Vg, W2 denote the velocity components, X,, Y,, Z;, Xz, Yo, Ze those of extraneous acceleration, 7, p2 the mean pressure, at the time ¢ and a given point of space, where at that time both the elements dx, dy, dz, and day dy, dz, of the gases happen to be momentarily situated. The quantities u, and w,, v, and v9, Laws of Irreversible Phenomena. 395 w, and w, being, however, quite different, the elements will, of course, separate after a time infinitely short ; likewise 62, and 622, dy, and dy, dz, and dz. must be understood to be quite independent variations. Let us write q, [aqar—av + 3P.a4,49Q}=6, . Sg ae fo and let us adopt, as a definition of the terms, the following equations :— Shoo fee. te ce ee) OVESONG HONG oe ae 14 = ee) Tj=3 i\f da, dy, dz piu +ove+w*), . . (4) T= iy dk, dys dzy po(us? +e +"), + + (5) ) ) dz = —J\Jae, dy, dz, p — ale vn i ov), «ee Bio) 8. ) ) a —f{\f dite Ay, dz. rf 5 + — + oa), Sees Falidh) SPog, = \\\ da, dy, dz py (X, 8a, + Y, 6y, + Z, 82;) +\\) datz yy dzq Pz (Xe Sito + Yo dy_ + Ze S22) +§\\d Si pi {cos (m2) ba, + cos (ny) dy, + cos (nz) 82;} +I{j AS, p{ Cos (Ngx) Sarg + C08 (ngy) Syq + COs (rz) 622}. (8) The quantity of heat generated in time dt by diffusion may be written fj da dy dz Ap, po{ (U2—%) (dary — dy) os (v2—V}) (dy2 — dy) + (we—w,) (dzg—d)}, (9) the expression dx dy dz being understood to mean indifferently dx, dy, dz, or dx, dy2dz, and A being a constant coefficient intimately connected with the ‘ coefficient of diffusion” of the gases. If the temperature is to remain constant, the quantity (9) must be taken away ; hence oQ= —\\j dx dy dz Api pof (tg — uy) (62—82,) + (v% —v,)(8y2—6y;) ot (wg — w;) (dzg— 62) }. (10) 396 Prof. L. Natanson on the Substituting (2), (3),.... (8), and (10) in (1), we find fe | -p ay 2 pce + A pipo( Uy — Uy) Jee} Pla ty lal dt dx dy dz \: IN ne dua _ Ops | +{- Ber Tah, + poX2 + Apop, (u1— uy) le +[ ... . ]Oyg4 fs oe dees +[.... 10y,+[... 2 qos which shows at once that ee = =f oP =p, X,+Apipo(ug—%4), He. . (12) du re) 5 | Dee oe a =p,X_o+ Apopi(uy—ue), &e. . (13) These equations have been established long ago by Maxwell and Stefan. § 12. Conduction of Heat.—Fourier’s equation of conduc- tion of heat appears to belong to the class of conservation of energy equations. At first let us avoid employing “ normal ” variables. Since the motion of the medium and the inter- vention of extraneous forces are immaterial for conduction of heat, we may put 6T=0, &P6g,=0, and d°Q=0 ; therefore 5U=6V, and t; | di{—oU+0'Qt=0,. .- 2 {ae fy : _ouU OF =O0 0 —o @) Hence, in any real transformation, we have od 2 aE - =0, iyi. A+ that is to say, in “normal’”’ variables :-— OU ds OU dg dQ - { 03 di ogiaE tao ae This is the general form of Fourier’s equation ; usually 0U/d4 is assumed to be of the form dx dy dzpc, in an element dx dy dz, p being the density and c the well-known thermal capacity; and the remaining QU/dq, are usually neglected. We shall reconsider the present case from a different stand- point in § 19. Laws of Irreversible Phenomena. 397 § 13. Electromagnetic Dissipation. — In Helmholtz’s memoir “ Das Princip der kleinsten Wirkung in der Elektro- dynamik ” *, it is shown in great generality that the thermo- kinetic principle holds for electromagnetic phenomena ; nevertheless we beg leave to consider here the simplest (but for our purpose most important) case, to which in the second part of the paper we shall have again to refer. Consider isotropic conducting substances, at rest. Let us suppose that energy- dissipation of the simplest or Joulean type is the only possible irreversible phenomenon. Let the components of electro- motive intensity at the point (x,y,z) be H,, H,, H,; those of extraneous electric forces, F,, F, F,; and the components of magnetic force H,, H,, H,. Let C be the electric con- ductivity, K the dielectric inductive capacity, and mw the magnetic permeability. If dA dA dA =— a =—— y ——— z E, dt ? Jo dt y) KE, dt ate = (1) then the vector A, whose components A,, A,, A, are, may be taken to represent the “electromagnetic momentum” at (@,y,z). We assume that 4or(B,—F,) + Kou: OH. _ OH, 9 at OY 02” Wes oie ot 4 KH —F Sa ee Liab ira ie : oa poe) | © Oe oe oso. | 4 (G48) ae oe pe: PP. TT \ Zz F)+K ae = a OY 2) enone Oo e | Oy 702 | Ol on eos (3) is ee ar Mitcear ay Oe Oy’ Mr. Heaviside and H. Hertz, it is well known, have con- structed the whole of Maxwell’s Theory upon two systems of equations, one of which is the system (2) above, whilst the second follows at once from (1) and (3). We shall take A,, A,, A, to be the independent variables ; that is the choice * Sitz. Berl. Akad. 12 Mai 1892; Wiss. Abh. Bd. iii. p. 476. See also Boltzmann, Vorlesungen iiber Maxwell's Theorie, vol. ii. p. 7. 398 Prof. L. Natanson on the which Lord Kelvin, Prof. Boltzmann, and other writers adopted when endeavouring to find dynamical analogies for electro- magnetic phenomena. The part of the energy, called T, which depends on the quantities dA,/dt, dA,/dt, dA,/dt, will be then the electric energy = (dee dy dz K(B? + B24 2) >a ees the other U, connected with the collocation of the variables Ayia, As themselves, will be = £ [ffde dy dz p(H2 + H+ HP). aes Supposing 6A,, 6A,, dA, to be variations as usual and K, ©, » and dz dy dz not to be subject to variation, we shall have dk oH. aH . SE a ae) ee SA T Yt, tal at ee llOeiar [kere se. lone (6) This equation is readily transformed. Tirst : es ae ey pS = t6T aI, di \\de dy dz K\ 778A, + 7 #88, + — 8A.) , at, (0) and ey qy -{ dt \\\de dy dz O(F 6A, + Pod, +F,6A,)= i d=P 6g. as) fy ty Then, from the well-known Maxwell-Helmholtz principle, on the continuity of properties oa surfaces of separation between different media, and from the equations (8), we obtain = Lf aeflfaedy ae (5 — Sr) pa.4 (2S Fas, om oF “5p Jee } oe Gee OoA, | aA, a or Oy! ody 2... Or? meer aula Gebines 1 foyelt pore. 06A, oA, AGEs 06A, =i}, dt \\\da dy de ae — 2) st- (S95 =) r 1 (Paz _ 24) B54, _ (24, a DSA, | Oz ox/ Ox Oy re oy S| aa... | ce re Laws of Irreversible Phenomena. 399 If, therefore, the general principle is applicable here, the terms in (6) containing 47CH,, &c., should reduce to ey +{ LEO Qs om Me* Hate B47 C10) to Now the quantity of energy which becomes absorbed from the sether and converted into heat is, for the time dt and the volume \\\ de dy dz, —|\fde dydzeC(H,dA,+E,dA,+EHdA,); . (11) hence | §Q=)) | de dy dz C(H,8A,+ E,sA,+H,5A,);. (12) and thus the principle contained in (I.), or in (III.), is again seen to hold good. Part II. § 14. Introductory.—The foregoing naturally raises the question, Does a general law exist concerning the infinitesimal expressions d@’Q and 6’Q, which have been found to charac- terize dissipation of energy in the various particular cases discussed ? | venture to answer this in the affirmative ; but the hypothesis I advance does not profess to be more than a conjecture and an approximation. Let us consider in every particular case the quantity ad! oY = oF ay. | Pre tr ele Va) In the case of irreversible Dynamics, § 9, the function F is _ well known, and has been called by Lord Rayleigh the ‘Dissipation Function ;” I should suggest that this term be extended to all cases covered by equation CIV. 2): Let us imagine a material (or at any rate partly material) system. Suppose that it is not in equilibrium, and observe in a quantitative manner, the disturbances which its state involves. Let it be isolated so as not to be disturbed by ex- traneous action. We know from experience that under such circumstances the disturbances in the system must finally subside and tend to disappear. This general behaviour may be called the coerczon of disturbances, because of the contrast it offers with inertia. (See Phil. Mag. for June 1895, p. 509.) For definiteness let us consider a continuous body. Let dxdydzp be the mass of an element dadydz, and let dudydzpf represent its dissipation function, so that F, the dissipation function for the portion \\ da dy dz of the body, 400 Prof. L. Natanson on the be =| | {de dydzpf. Then, generally speaking, F is suscep- tible of three kinds of variation, and dF‘/dt is the sum of three terms :—1. A surface-integral relating to the action between the body and the exterior world through the boundary of the body; 2. A volume-integral expressing ‘ action at a distance ”’ between the body and the exterior world ; and 3. A volume- integral representing “ coercion,” 2. ¢., that intimate action whose constant tendency it is to attenuate and finally to efface inequalities and disturbances, if there is no extraneous action to maintain or to excite them ; and whose ultimate nature is, of course, unknown to us. It would not be difficult to translate our statement into symbols. Let us adopt, for instance, that general Molecular Theory due to Maxwell, which we have called (on a former occasion) “Kinematical Molecular Theory.” Let u+£, v+%7, w+ denote the components of the velocities of individual molecules, / a function of the (u+£), (v+m), and (w+), f the mean value of f within an element, and D/Dé the rate of “ coercion.” Then p= — {2 ob) + 2 (oni) + 3:(et7} + xB v2 122) Pie ae (1) hence 2 ns qi) dedyde pf = ANN) dSp{Ef cos (nx) + nf cos (ny) + $f cos (nz)} - + [Jaedy dzp( X84 vee, 7.2L) 4 §ffdady dep sy. (2) The three terms on the right-hand side refer to the three kinds of variation as above stated. The assumption we propose to examine is that the third, or coercive term DF/D¢t is always proportional to the value of F. Thus, writing 7 for a constant period of time, DF 2F DeSoto = This equation, we shall find, is general; in the neighbour- hood of states of equilibrium at least it is exactly fulfilled. The period of time 7 was first considered by Clerk-Maxwell ; Laws of Irreversible Phenomena. 401 in an important case it received the name of the modulus of the time of relaxation* and may, without inconvenience, be called so in other similar cases. Equation (V.) may be verified in various cases, which we shall take in order. § 15. Irreversible Hydrodynamics.— From 10 we have | 19 ie 48) 7 F= {de dy dz " & a (37 Sl dee )+( L poe oytse) t a +3(So+ Sy) | Viber shoe) Caer pry for the usual components, we have pomp i): rem), and four other equations of the same form. These equations, it is well known, must be fulfilled if the dynamical equations of Navier, Poisson, Stokes, and Maxwell are to be true; they may be described, therefore, as being in agreement with ex- perience, and so also may be equation (1). Hence Seis Oe p)? + ( ee )? + ( aed ae, 43 =. gy es ay (p Pew P Pu—p . 3) dy + Qpye + Wert Wry: Again, if the disturbance is not a very violent one, we have the equations t¢ D(poa—p) _ 2,(24— a = Dp Ow ae Aft 10); = . (4 = s =AS +S) - and four other equations, to be written down from symmetry ; it may be well to point out that they are “ kinematical” equations, therefore independent of any particular molecular hypothesis. Now, if we put Pa ahaa (ees aca good Ol we obtain from (2) and (4) D(pus—P)___ Pas P, Dpye_ _ Pz (6) Dt RM hla ire oo ce ae * Philosophical Transactions, 1867, p. 82. See also ‘Treatise on Electricity and Magnetism,’ third edition, vol. i. p. 451. + Philosophical Transactions, 1867, p. 81. Phil. Mag. 8. 5. Vol. 41. No. 252. May 1896. 2¥F 402 Prof. L. Natanson on the and four similar equations ; and from (3) and (6) D Cae D ee ( (pa— 2) 5 + (PP) BY D(p.2—Pp) B= {lf de dy deg 4 4 (Px —?) age a \ (a | Dpyz Doze Da L + 2pye yy + 2Pee ye + Pay whence, by (3), we infer that DF/Dé=—2F/r, as stated above. The value of 7 in air, at the temperature 0° C. and normal pressure, is approximately 9.10~° of asecond (Maxwell, Phil. Trans. 1867, p. 83). We may also compare the relative values of tin two fluids. Jn doing so we may assume, in accordance with Prof. Van der Waals’ leading idea, that the values of + would bear a constant proportion if they were calculated for “ corresponding” states of the fluids *. Hence the coefficients of viscosity will likewise, in corresponding states of two fluids, bear a constant numerical ratio +. §16. Diffusion.—The signification of the symbols being the same as in § 11, we find the dissipation function of diffu- sion to be F =3\\( da dy dz Apypo{ (ug — v1)? + (t2— 1)? + (Wg)? }- (I) The theory of diffusion can be deduced, in the case of two gases, from “ kinematical” equations and from the following equations “of coercion,” in which D/Dé refers to the total coercive action of both gases : De =APa(ue—%) 3 Dp Aertel; - (2) and four other equations of similar form. If the dynamical equations of Maxwell and Stefan are true, equations (2) must likewise be fulfilled ; they may be said therefore to agree with experience. Let us now pass to the usual case of slow and quiet diffusion (Maxwell, Phil. Trans. 1867, pp. 73-74). If we write 3 for the temperature, R for the gaseous con- stant, we shall find the value of the coefficient of diffusion, or h say, to be RS/A(p, +p) 3 and, if p=p,+Pe, the charac- * See Kamerlingh Onnes, Algemeene Theorie der Vioetstoffen, Tweede Stuk, p. 8, 1881. + See Kamerlingh Onnes, ‘Communications from the Laboratory of Physics at the University of Leiden,’ no, 12, p. 11, 1894. Laws of Irreversible Phenomena. 403 teristic period 7 for the coercion of the disturbance will be 1 wi (Prt Po) h 3 ~ Aleit ps) P ie In a system composed of Ruipone and oxygen, at 0° C. and normal pressure, the value of + “(from v. Obermayer’s experi- mental results) is about 4°5 x 107" of a second. Returning to (2) we obtain D(u,— 1) Ug — Uy er C) T and two other equations which may be written down from symmetry ; hence (1) reduces to F=-4 i sy da dy dz Apipst J ap ees Wer sal i yee + (w=) (= = 5 ©) and this gives DF 2F Drie 6) Let us verify that, as stated above, 2F is the rate at which, owing to diffusion, heat is being irreversibly generated. First, from conservation of energy, we have uit vi + wi +82 + 9? + 2) pill ae dy de pr (ui 1 1 : 1 ‘ 5a Panes. =i (7) t + po (us + 02+ wat & +73 +83) Then, from (2) we obtain D | Did 42 dy de dpi(uf + v7 + w?) =f) de dy dz Apyps X {u, (Ug— tM) +0, (Vg v1) + 1 (wg—wW1)}, . (8) = \\V da dy dz 4po(u2+ v2 + w3) ={\\ de dy dz Apopr X {U(u— Us) +.¥2(0) — V2) + We(wi — W2)}, » (9) whence by (7) it follows :-— D 1 e212 te (2 ie @ = \\V\ da dy dz Apyp,{ (ug —%)? + (%2.—%)? + (w2—w1)"} i tM iat. i, ola ea a Se’ oo, LO) and this proves the proposition. | 242 404 _ Prof. L. Natanson on the §17. Electromagnetic Dissipation —The electromagnetic dis- sipation function is - F=3 (\\ de dy dz C(H2+F2+E), . . . (1) the symbols being defined as in § 13. The disturbance settles down obeying the well-known equations DE DE DE *—_4qCH : K—_¥=—4rCH; K z 2 Dt ee Dt aaa iby; they are therefore the electromagnetic “ coercion ”’ equations. If we take t=K/47C, as has been done by Maxwell and many others, we see that =— 4nCH ; (2) (3) r= —4(\f de dy dz 1C(B, =~ +E, see ea : and ip hee oe T fe) eh ate eae (4) Prof. J. J. Thomson has shown* that for water with 8°3 per cent. of H,SO,, 7 cannot differ much from 2.10—" of a second ; and for glass at 200° C. from about 10-° of a second. § 18. Irreversible Dynamics.—In the case of § 17 the energy we have called T is proportional to the dissipation function F; the same holds in § 16 if we have p,w,+p2u2=0 (see Maxwell, Phil. Trans. 1867, pp. 73-74). Hence, in such cases equa- tion (V.) becomes DT/Di=—2T/7. Again, in the Irreversible Dynamics of § 9, if the additional dissipative forces —R,’ be proportional to the corresponding components of momentum, the same proportionality holds. For example, let SR! 28s Oy) ol a rn represent the additional dissipative force acting in the q,-direc- tion; then T=7F; and since from (5), § 9, it is easily shown that Dia ae cee e e ° : ° © (2) * ‘Notes on Recent Researches in Electricity and Magnetism,’ 1898, § 32 Laws of Irreversible Phenomena. 405 D/Dt being the rate of variation of the kinetic energy arising from the dissipative forces, we see that, in this case, DF/Di=—2F/7 and DT Di ees. (3) Cf. Lord Rayleigh, ‘The Theory of Sound,’ vol. i. p. 78. § 19. Dissipation Function of Conduction.—In the Philo- sophical Magazine for June 1895, p. 506, it was shown that in conduction of heat the dissipation function is of the form | | Y 6 Y 2F =—3 (\{ da dy az} pre ee = + prot (1) the symbol 6 being employed to denote (P47+2). From (12) and (39) in the paper referred to, we have Der, _ 00 Dpr, ‘ou. Wpr > 08 | ea) Di = Peed Di Pa dy? Dt =P 25, 2? (2) Dpr, _ 5p Dpr DP yy Dor _ op ae ae 3 —— ee ane 3 ag 3 3 De: Bi bas Bett eDe: rag ©) equations (2) are the “ kinematical,” and equations (3) the “ coercive ” equations of the problem. They must be fulfilled in order to make the equations hold : 0 0 6d pr=— ko”, pry=—k op AS, dy wot4) and, therefore, to secure applicability for Fourier’s equation. The time of relaxation we define as TSO ete eee er i on (O) neglecting differences p—p,,, &c. From (1) and (4) we obtain : 1 . aE =§ (ll de dy dz {(pr,)?+(or,)*+ (pr,)?}, - (6) and from (1) and (2) we have: D ay es 2B = — 5, [l) deay de Z ((pr.)?+ (on) +(0r,)4}, (7) whence, by (5), we find again DF 2F To = a ee ee. OS) § 20. Connexion between the periods +.—Let T, be the 406 Dr. J. Shields on a Mechanical Device for characteristic period t for conduction of heat in a given gas, and let +,, denote the period relating, for the same gas, to internal friction. The coefficient of conductivity in Fourier’s equation, as usually written, is 3c¢,k, k denoting the same quantity asin § 19. Now in the Kinetic Theory of Gases it is shown that this coefficient is equal to 15 4g Yee, + + if y be written for the ratio ¢,/c, of specific heats, and w for the coefficient of viscosity [for example, see Prof. Boltzmann’s Vorlesungen uber Gastheorte, equations (2885 (54), and (57) |. Hence =Hy—l)ty or = 3T) s) @ ee since, strictly speaking, our calculation requires the gas to be monatomic. Ina similar manner may all the periods of relaxation, corresponding to the various powers of coercion of a given body, be mutually connected ; and every such simple equation, if it holds, is equivalent to a definite physical law. XLIT. A Mechanical Device for Performing the Tempera- ture Corrections of Barometers. By JoHN SHIELDS, DSc, Eh = pas height of the barometer is generally reduced to 0° C. by means of the formula where By is the reduced height, B, the observed height at the temperature t, and 8 and vy the coefficients of expansion of the mercury and scale respectively ; or, since @ and y are in general both very small, we may write By=B,[1—(8—y)¢]. In order to facilitate the reduction, tables containing the corrections corresponding to definite temperatures and observed heights have been compiled, and in the laboratory it is only necessary to consult such a table, and if necessary perform a simple interpolation in order to find the correction which * Communicated by the Author. the Temperature Corrections of Barometers. 407 must be subtracted * from the observed height to reduce it to OFC Graphic methods are sometimes used to obtain the tem- perature correction, and one of the best of these, which was first brought to my notice by Prof. Ramsay, is described in the Appendix as it seems to be little known. During the course of an investigation it was necessary for me to read and correct the barometer several times daily, and as this operation became rather tedious I was induced to make a barometer which indicated the height and the cor- rection simultaneously. The construction of the barometer presents no great difficulties, and as it is extremely useful in its new form I now beg to lay a description of it before the scientific world. It can be read with certainty to 0°1 millim., which is sufficiently accurate for most purposes. Whether an improved method of reading and better workmanship than I have been able to bestow upon it would make it suitable for meteorological observations must be left for meteorologists to decide. For ordinary laboratory work, however, it meets all the requirements. It is not necessary to know the temperature at all ; and by mentally subtracting the correction as indicated by the correcting instrument from the observed height (also obtained directly by setting the barometer), the observer is enabled in one entry to write the corrected height of the barometer in his note-book. The most suitable form of barometer to employ with the correcting instrument is that described by Dr. J. Norman ’ Collie f, but an ordinary syphon barometer may also be adapted for the same purpose. ‘The lower end of the baro- meter is cemented or otherwise securely fitted into a brass cap A, fig. 1, to which is attached a rod B, which moves vertically in a guide in order to prevent the barometer from rotating when it is raised or lowered by means of the screw C. The barometer itself is kept in a vertical position by the guides D D which are attached to the framework. The back of the framework consists of a long, narrow board, the lower end of which is shown at H, and to which the nut carrying the screw is fixed. A plate-glass mirror F, carrying the graduations, is firmly screwed down on the main trame b means of the picture-frame moulding G G, which is planed down at the back to such an extent that the mirror is held tightly clamped in position. The plate-glass mirror is care- fully graduated between 700 and 800 millims., and has also * For temperatures below 0° C. the correction must be added. + Trans. Chem. Soc. (1895), p. 128. 408 Dr. J. Shields on a Mechanical Device for : Fig. 1. a zero line etched on it, but the space between zero and 700 millims. may be left ungraduated. This particular form of mounting the barometer, independent of the correcting instrument which has yet to be described, is in itself very useful; as by setting the lower meniscus of the barometer at the zero line by means of the screw at the bottom of the frame, the uncorrected height can be read off directly, and this obviates the ~ necessity of taking down the upper and lower readings and adding or subtracting as the case may be. | Before proceeding to show how the device for indicating the amount of the temperature correction can be attached to a barometer mounted in this way, it is well to note that the areas of the upper and lower reservoirs of the barometer are supposed to be equal, and are in fact approximately so, if these reservoirs are cut from adjacent parts of the same piece of tubing. Assuming now that the baro- meter is accurately set, and that the pressure of the atmosphere then changes, if the pressure rises or falls n millim., then, on again adjusting or setting the barometer, any point on the stem will ob- viously be raised or lowered n/2 millim. Should, however, the cross section of the capillary tube, which connects the main stem of the barometer with the lower cistern, be large when compared with the cross section of the lower cistern, then the above relation will not hold good. This source of error may be eliminated either by making the cross section of the capillary small, or by selecting a lower cistern with a proportionally larger area. It may also be eliminated, if necessary, in graduating the scale of the correcting instrument, but any slight error intro- duced in this way has scarcely any ap- preciable effect on the accuracy of the readings. the Temperature Corrections of Barometers. — 409 The precision of the complete barometer is limited not so much by the accuracy of the temperature correction, as this can easily be made to read correctly to 0:01 millim., but by the precision with which the barometer can be set and by the accuracy of the graduations. As has already been mentioned, the combined error in setting the barometer and reading the scale at the top should not exceed 0-1 millim. Of course all danger from the above source is removed if the common syphon form of barometer is employed; but as Collie’s modification presents other advantages which are clearly set forth in his paper * , his form of barometer is to be preferred, especially as it is only necessary for the purposes of the ~ correcting instrument that the above relation between n and n/2 should hold good within a millimetre or two. In designing the correcting instrument use has been made of the fact that the variation in position of a point on or attached to the stem of the barometer is proportional to the variation of the height of the barometer. The point is repre- sented by a horizontal thread of mercury H (figs. 1 and 2), contained in an ungraduated thermometer which is firmly attached to the stem of the barometer in a horizontal position. Behind the horizontal thread of mercury is fixed a scale or small plate of curves K, in such a position and drawn in such a manner that the position of the horizontal thread of mercury (the ordinates) indicates approximately the height of the barometer. The correcting instrument is shown on a larger scale in fig. 2, The distance from the top to the bottom of the plate of curves, z.e. from L to M, is actually 50 millims., but this, from what we have already said, represents altogether 100 millims., the position of L corresponding to a barometric height of 800 millims., whilst M corresponds to 700 millims. The position of the horizontal thread of mercury at the time of setting the barometer thus corresponds approximately to the actual height of the barometer. A series of lines 1, 2, 3, 4, &c. millim. are drawn or engraved on the plate K, so that the position of the meniscus of the horizontal thread of mercury gives the temperature correction directly in millimetres. The method of drawing these lines requires some explanation. It is desired to reduce the height of the barometer to 0°C. Obviously, then, the line of zero correction 00 must lie immediately behind the point corresponding to 0°C. on the horizontal thermometer, and it must furthermore be vertical, as no matter what the height of the barometer may be the correction at 0° C. must always remain zero. * Collie, loc. cit. 410 Dr. J. Shields on a Mechanical Device for Before the position of the other lines can be fixed, it is necessary to ascertain the length in millimetres corresponding to 1°C. of the horizontal thermometer. Let this be n millim. Fig. 2. We have already seen that the formula for reducing the height of the barometer to 0° C. is Bo=B{1—(8—)¢], hence the correction which must be subtracted from the observed height is (B—y) Be. che Temperature Corrections of Barometers. 411 In order to fix the position of the top of the lines giving the corrections 1, 2, 3, 4 &c. millim., all that we have to do is to make B,;=800, and calculate the temperature ¢, which would make the above expression equal to 1, 2, 3, 4 &c. millim. Thus, for the top of the line representing a correction of 4 millim., we have (8—y) . 800.t=4. For all ordinary purposes we may make 8—y for mercury and a glass scale=0°0001381 —0-000009=0-000172, hence 4 “= 9000172 x 800° But since the thermometer is not graduated, we must multiply the value of t so found by n to get the distance in millimetres of the point 4 from the point 0. Similarly the tops of the other lines may be found, but in general it will be found sufficient to calculate the greatest correction only, and then to divide the distance between it and 0 into the required number of equal parts. In the same way the corrections correspond- ing to a barometric height of 700 millims. (the lower ends of the lines) may be obtained by making B;=700. ‘Then, since the correction is proportional to the height of the barometer, straight lines joining 1 and 1, 2 and 2, and so on will repre- sent the corrections between 700 and 800 millims. The spaces between 0 and 1, &c. may also be subdivided into halves or tenths if necessary. The scale is either drawn or engraved on paper, a plate- glass mirror, or other convenient material, and then mounted on a bridge in front of the stem of the barometer and behind the correcting instrument. The final adjustment is made by moving the correcting thermometer into the proper position before clamping it tightly to the stem of the barometer. A piece of wood or other soft material interposed between the stems of the barometer and thermometer prevents any risk of breakage on screwing up. In adjusting the correcting instrument or thermometer, care must be taken that, firstly, the zero point of the thermometer is precisely in front of the line of zero correction, and, secondly, that the thread of the mercury is truly horizontal, and that its position between the 700 and 800 millim. lines of the correcting scale corresponds as nearly as possible with the actual height of the barometer at the time. For convenience, the completed barometer should be sus- pended on a vertical wall with a good light falling on it.. In 412 Dr. J. Shields on a Mechanical Device for order to take a reading it is first gently tapped, the lower meniscus is then set exactly at the zero line by means of the screw at the bottom, and the temperature correction as indicated by the correcting instrument at once read off lest the heat of the body should cause any alteration ; the height of the barometer is then observed at the top of the instru- ment, which, after subtraction of the temperature correction, gives the barometric height reduced to 0° C. ‘By considering the correcting instrument it is obvious that, the temperature remaining constant, the rise or fall of the barometer is accompanied, after setting the lower mercury meniscus to zero again, by an upward or downward displace- ment of the horizontal thread of mercury, and, consequently, to an increase or decrease in the correction. Similarly, a rise or fall of temperature is accompanied by an increase or decrease in the correction. | ~The instrument I have just described is one out of four possible modifications. Both scales may be fixed whilst the barometer and thermometer are displaced simultaneously or vice versd. Again, the barometer and correcting scale may be fixed whilst the other parts are adjustable or vice versd. The first two will probably be found most useful. Distinct advantages might be gained by fixing the barometer with the thermometer above it, and at the same time etching the barometer and correction scales on the same piece of plate- glass mirror, which could be placed behind them and be moved vertically by a set screw at the bottom of the instrument. University College, London. APPENDIX. Fig. 3 illustrates a convenient graphic method for obtaining the temperature correction of a barometer or other column of mercury. The ordinates represent the height of the mercury column* and the abscissze the correction in millimetres. The correction for any temperature not represented by a diagonal line passing through the origin is easily obtained by a graphic interpolation. As fig. 3 is too much reduced in size to be of any value, a diagram of convenient size may be obtained by plotting the ordinates on a piece of curve paper ruled into * In this particular case the height is supposed to be measured with a glass scale. If a brass scale is used the correction is always about GO per cent. less. the T. emperature Corrections of Barometers. 413 inches and tenths of inches, each inch representing 100 millim., whilst each millimetre of correction is represented on the lower horizontal axis by two inches. A series of lines, each Fig. 3. 8° 10° 12° {4° 16° 18° 20° 22° 24° 26° 28° 30° aN WN | i/o WY MZ ——— 1.0 2 representing a difference of 2°C. of temperature, are then ruled through the origin to the points on the upper horizontal axis marked 8°, 10°, 12°, &. The position of these points is easily obtained from the formula (@—y)B,=correction in millim., by substituting for ¢ the values 8°, 10°, 12°, &., for B, the value 800, and for 8 and y the coefficients of expansion of mercury and the material of which the scale is made respectively. [ 4d] XLII. An Addition to the Wheatstone Bridge for the Deter- mination of Low Resistances. By J. H. Renvus, I.A., City and Guilds of London Central Technical College *. HILE it can be assumed with fair certainty that even in moderately equipped laboratories there will be found one sensitive galvanometer and a good set of resist- ance-coils arranged in the form of a Wheatstone bridge, it is by no means so common to find a convenient method for determining low resistances, such as, for example, a Kelvin bridge. The piece of apparatus which forms the subject of this paper is a comparatively cheap addition to the ordinary bridge, and enables the resistances of exact metre-lengths of even thick wires to be directly measured with almost as much ease as larger resistances can be determined with the ordinary Wheatstone bridge. The method also possesses the advantage that all the measurements are made in terms of a standard wire with fixed contacts, and, therefore, not subject to the wear which accompanies the frequent use of a slider ; further, in the case of copper wires no temperature-correction is needed. The apparatus is represented in fig. 1. On a mahogany Figs 1. baseboard are stretched close to one another two wires—one, ABCD, being the standard of comparison, while the other, EFGH, is the wire to be tested. A and E are two massive pieces of brass which can be joined together by a plug P. D and H are smaller pieces of brass with binding-screws attached. The standard BC is permanently fixed to A and D, whilst two clamps F and G fixed respectively to EK and H form the means of fixing in its place the wire to be tested. KL and NM are two brass springs which pass over but do not touch BC. They are provided with binding-screws at K and M, and with two knife-edges L, N exactly one metre apart, which press on the wire FG when in position, while * Communicated by the Physical Society: read March 18, 1896. Determination of Low Resistances. 415 two screws 8, 8’ will raise the springs when required for inserting or removing this wire. At points B, C in the standard are soldered two short lengths of wire terminating in binding-screws Q and T. The gauge of the standard wire, which is of copper, and the distance apart of B and C are so chosen that the resistance between B and C is 0°01 ohm at the temperature of the wire at the time of its final adjustment, which should be noted. The method of determining these points is given later on. The arrangement is a variation of the Kelvin bridge, with this difference : that in the latter the measurements are made by varying the length between the knife-edges of sliders © which press on the standards, of which several are required : whilst in the former only one standard resistance is employed, and the measurements are effected by the alteration of the other resistances in thearrangement. If the whole apparatus had to be bought, the Kelvin bridge would be the cheaper, but the new Addition utilizes the box of coils, which as before- mentioned is sure to be available, and only requires in addition one standard to be made and adjusted. The theory of the Kelvin bridge is to be found in the text- books. In Gray’s ‘ Absolute Measurements,’ for example, vol. 1. p. 359, it is proved that if fig. 2 represents the usual arrangement, and, if R, 7, x, y, a, 6, s are as marked, the following relationship must hold in order to obtain balance:— dE eee Further, it is shown that when s is small compared with a and b the accuracy of the equation Bile | pan” is not affected by a small want of equality between the ratios Sand =: Z b In addition to the galvanometer and set of coils there is 416 Mr. J. H. Reeves on an Addition required a slide-wire bridge, which may be of a rough descrip- ticn but should have a resistance of an ohm or so. At the end of the paper it is shown how this latter and the Addition can be united in one. The whole arrangement is joined together as shown in fig. 8, the dotted lines indicating the temporary connexions. By comparing this with figs. 1 and 2, no detailed description is necessary, as R, 7, 2, y, a, 6, s are lettered to correspond. The battery may with advantage he a storage-cell with two resistances in series with it. One, p, may be an adjustable carbon resistance, while p! may be constructed of wire and should have a considerable resistance. This latter terminates in mercury cups m and n, so that by joining these cups together with a short connector the resistance can be easily short- circuited. The resistances « and yare resistances unplugged from the box of coils forming the ordinary Wheatstone bridge; y is the 1000-ohm coil of one of the ratio arms, and 2 is in the adjustable arm. If sucha set of coils be not available, y may be any 1000-ohm coil, and # any box of coils containing resistances up to 5000 ohms. The two leads joining 2 and y to B and B" respectively should be as stout and short as possible. The resistances from d, d' to I form the a6 of fig. 2. To make a measurement, insert the wire whose resistance is required in its proper clamps, taking care that it lies quite straight between them. Its diameter and material being known, the resistance of one metre of it can be approximately to the Wheatstone Bridge. 417 calculated. Calling the resistance R,, choose 2; in the box so that na R, 1000 ~ 0-01" Remove the plug P, and, including p’ in the battery cir- cuit, obtain balance by shifting the slider I, the galvanometer being also shunted if necessary. The arrangement is now an ordinary Wheatstone bridge, at+h, «4, FR b+r y p? ini spas Ry _k approximatel ead he PP y: Next insert the plug P, short-circuit p’ so that now a strong current passes when the battery circuit is closed, and obtain balance by altering «7. Let the new value be 2. Then, since approximately °= a we have, by the formula quoted above, . he = 4 eg eal Pe Ly : R= Fea approximately. In any case this new value of R is very much nearer the true value than the approximate value R,. Ifthe value of « has to be but little altered, it may be taken as the true value of R, but if, on the other hand, the first estimate was con- siderably in error, and, in consequence, a large alteration has to be made in 2 in order to obtain balance, the much closer value thus obtained must be taken as the first approxi- mation, and both experiments repeated. Now, since the wires are so close to one another, their tem- perature can be called the same, and, if the tested wire be of copper, their temperature-corrections are the same. There- fore, if R be a certain fraction of r at one temperature, it will be the same fraction at any other. But in the actual bridge on which the experiments described later on were first made, this temperature was 17°7 C. Therefore, substituting numerical values in the last equation, x x R= 7000 * ©! = 700,000 - Of course, if R be not made of copper, the temperature must be noted and allowed for. The accuracy and sensibility of this method depend on three conditions :— | . Phil. Mag. 8. 5. Vol. 41. No. 252. May 1896. 2G ohms at 17°7 C. 418 Mr. J. H. Reeves on an Addition (1) The accuracy of the ratio 7 (2) The accuracy of the value of r ; (3) The sensibility of the galvanometer. As far as condition (1) is concerned, 2 and y being taken from a good box have an error of certainly less than 0-1 per cent. Condition (2) is discussed later, and the effect of condition (3) can be best seen by reference ‘to tests made in the labora- tory of the Central Technical College with the apparatus : arranged as in fig. 8, except that, at the start, the battery 4 consisted of a single Daniell cell, the galvanometer being a 4 four-coil reflecting one having a ‘resistance of 687 ohms and a sensibility of about 400 scale-divisions per microampere. TABLE I. Tests made on high conductivity copper, R= ————-~ oliniz: S YORE OO 100,000 Diameter. a Obsersahiny a R Specific | Specific coninti y: mils. ; / ; Pe Resistance. Stands 4324 | 4 div. deflexion left. 22 | 2807 | 4326 |Small ,, right. |bo-04825 | 8341 | 1616 4398 |lddiv. right. 9618 |1. ,, SN SEE, 355 2620 |Small |, left. | bo-02e21 | 8918 | 1572 2622 |4div. |, right. 3 » mig 488 {|ia|7” ” Mere, |}oordais| seiz | 1-602 S028 3s meh” lett: | a 64:2 803 |, * left. | $0-008032| 8907 | 1-572 804 | 2 ,, hs might. |] (| 515 | 24, iy 80:1 516 |Small |, left. | $0:005163] 8888 | 1-566. AopBiie) din ee eke: 1032 { er aa , Dee } o-oos145 8904 | 1-585 106-9 { be aby, D se \ o-oo2916 8940 | 1580 71 39 ” 1038 {| 359/77” ” sent | }0'008086] S870 | 1588 : 309 |2 ,, oy alee f : 1or2 {| 310/37 = wept, | $ 0°008008] S801 | 1-580 Matthiessen’s standard has been taken to be a specific resistance (resistance per cubic centimetre at 0° C.) of 1:620 International Microhms. Towards the end of this table it will be seen that even a sensitive galvanometer barely allowed an accuracy of 0-1 per cent. The Daniell cell was therefore removed, and a small accumulator with a resistance of 2 ohms in series with to the Wheatstone Bridges 419 it substituted. The last three wires were then again tested, and a marked improvement was at once seen, for now an alteration of 1 ohm in « produced a difference of deflexion of 10-15 scale-divisions, thus giving the interpolated figure correct to the first place given, z. ¢., R correct to 1 partin 3000. To further test the capabilities of this method,a strand cable composed of 7 copper wires, each of No. 16 8.W.G., was taken, the strands being flattened to pass under the Springs, which had not been constructed for a wire of such a large diameter. The results, using the same cell and resist- ance, are shown in the next table. TABLE IT. re Observation. R. 117 6 divs. deflexion left. 118 1k ,, ii et: 0:001183 119 53 el i right, _ Here only 4% divisions correspond with a change in « of 1 ohm : thus an error in reading of 3a division means an error in R of 0-1 per cent. The effect of using a still larger current was next tried, the 2-ohm coil being removed, and the two resistances p, p! of fig. 8 substituted. An ammeter was also included in the battery-circuit, so that the actual current could also be measured. Now, on passing a strong current both wires heat, and if the wire r has the smaller diameter it will heat the faster. Therefore its resistance will also increase the faster, and hence the resistance of the wire R will apparently diminish, and vice versa. In order to see how much this diminution might amount to, the resistance p! was short-circuited, and p was adjusted until the battery-current was 6 amperes, and the results are shown in Tables III. and IV. TABLE III. With the current only continued long enough to measure the deflexion: current 6 amperes. oe ‘Observation. R. 118 3 divs. deflexion right. 00011812 119 3: Erion, 2G2. 420 Mr. J. H. Reeves on an Addition TABLE LY. - After the current had flowed continuously ee 3 minutes: - Say 6 amperes as before. 2. Observation. R. 119 28 divs. deflexion left. 118 4 ,, “ left. 0:0011784 117 20 a right. The difference between these two results is about 4 per cent., while the deflexions are more than sufficient for an accuracy in R of 0:1 per cent. A few days later these experiments were repeated with a current of 2 amperes. The slight discrepancy in the value of R was due to the fact that in the interval the cable, which was not quite straight, had been removed. On replacing it a slightly less length must have been included between the knife-edges. As, however, these experiments were being made solely to find the sens¢bzlzty of the measuring arrange- ment, no attempt was made to straighten it. The results are shown in Table V., experiment (a) being for the short dura- tion of current, and (6) the result after the current had flowed continuously for 3 minutes. TABLE V. Current 2 amperes. Experiment. 2. Observation. R. | 119 16 divs. deflexion left. Cd tama eda as Bie , left 0-001178 | 117 tO: Sip cae ats (b) { 118 Ae pyc ene | 0:001177 117 ee ye, eles From the above results it will be seen, firstly, that 13 divisions correspond with 1 ohm difference in x, thus making the fourth significant correct, in other words, an error in R is less than 0°1 per cent.; and secondly, the passage of a current of 2 amperes only produced in 3 minutes a difference of like amount. : No larger cable was tried, nor was any wire smaller than to the Wheatstone Bridge. 421 No. 22. S.W.G., but between these limits an accuracy of 0°1 per cent. was easily obtained so far as the senszbility of the method was concerned. The accuracy of the standard now remains to be considered. This can be best seen from a description of the method by which the correct length between the points B,C was de- termined. | In order that this length might be of a convenient amount to suit the dimensions of the base-board, it should have been made of copper wire No. 17 8.W.G.; buta piece of this gauge which was bought for the purpose proving unsatisfactory, a piece of No. 16 was taken and stretched till of the required — diameter. One, Q B, of the two short arms of fig. 1, was soldered on, the other, T C, being left loose. The whole was then screwed to a rough board, and the wire annealed by passing through it a current of about 50 amperes till it was too hot to touch and then allowing it to cool, the operation being repeated ten times. The arrangement represented in fig. 4 was next made. Fig. 4. eS —_ Con oe oe oS ' : ; , 1x =10uW, ¥ =1000w rtRRALZA PN fry \ i _ By following out this figure, it will be seen to be the same arrangement as fig. 3, except that now the place of the plug is taken by the gap P. The standard was a l-ohm coil of. manganin wire, constructed by Messrs. Nalder, Bros. Its terminals rested in mercury-cups from which the various leads were taken, the ends of all wires dipping in the mercury bein freshly amalgamated. The leads joining the 10- and 1000- ohm coils together and to the binding-screws T and M respec- tively were short and stout. | The arm TC was then put approximately in position, and good contact at C was maintained by pressure. To avoid thermoelectric effects this pressure was made with a piece of wood, and in order to see if any such effects were present a commutator, not shown in the figure, was put in the battery- circuit. It was then found that if balance had been obtained 422. Determination of Low Resistances. for one direction of the current, a reversal produced no appre- ciable deflexion, thus showing that this piece of wood had en- tirely prevented such effects. As a precaution, however, the current was reversed each time balance was obtained, and in no instance was any deflexion caused by the reversal. The experiments were then conducted in the same order as before. With the gap open, balance was obtained by moving the slider I. The gap was then closed and balance obtained by altering the position of the arm TC. The gap was next opened, and the slider moved till again no deflexion was noted. This motion was very slight, and the alteration, after closing the gap, was not found to have produced any observable want of balance. The correct position of C was thus determined. In order to see with what degree of accuracy this position had been arrived at, the arm was shifted 1 millim. in both directions, and the want of balance was indicated by a de- flexion on either side of zero of one division; hence, as the length between B and C was over one metre, the error in the position of C was well under 0:1 per cent. The arm TC was then soldered to the wire, and the tests repeated. No deflexion was observable with the ratio — but on adding a 1-ohm coil to the 1000, making the ratio == the want of balance produced nearly 2 divisions de- flexion, The wire was then screwed in its proper place and there tested in a similar fashion with the same result, viz., with the ratio oe no deflexion was noted, while with the ie | : ror ratio 7ho3 a deflexion of over 1 division showed the want of balance. A thermometer lying beside the wire indicated 17°-7 C. Thus the resistance between B and C was 0:01 ohm at 17°-7 C., with an error of less than 0°1 per cent. Thus on all three conditions an accuracy of 0:1 per cent. was obtained. This simple apparatus is, therefore, capable of measuring the resistances of metre-lengths of wires between the limits of No. 22 8.W.G. and a stranded cable of 7 No. 16’s (and probably over a still greater range) with an accuracy throughout of 0:1 per cent., an accuracy quite suffi- cient for all commercial purposes. Although in the above simple form of The Addition a slide- wire bridge is necessary, it may happen that this latter is not Absorption Spectrum of Iodine and Bromine. 423 available. At a slight additional cost this slide-wire can be made an integral part of the apparatus. In fig. 5 is repre- sented a rather more elaborate design. The slide-wire is Fig. 5. ee ese easily recognized. The contact-piece of the slider S must be made adjustable so as to be able to press on either part of this wire. The circle K represents an ordinary Wheatstone- bridge key. It will be seen that this design is very self-contained. All the connexions to be made consist of : a battery, with its supplementary resistance, to the binding-screws B, B’, a galvanometer to g and 8, and two resistances between X, Y and Y, Z. The former, marked R,, is an adjustable box of coils, and the latter, Rj, is a single coil of 1000 ohms re- sistance. — XLIV. On the Absorption Spectrum of Solutions of Iodine and Bromine above the Critical Temperature. By R. W. Woop *. ie examining solutions of iodine above the critical tempera- ture with a spectroscope, I have found that the fine lines which characterize the absorption spectrum of gaseous iodine may be either present or absent, depending on the amount of the solvent present. These lines are not present in the spectrum of iodine solutions, and their disappearance under the above-mentioned conditions seemed to be due either to the pressure exerted by the vapour, or to something akin to solution. _ The tube containing the liquid was heated in an iron tube provided with two vertical slits, cut opposite each other, for the passage of a light ray, which was subsequently analysed with a large spectroscope of high dispersion. - * From the Zeitschrift fiir Phys. Chemie. Communicated by the Author, . | . 424 Mr. R. W. Wood onthe Absorption.Spectrum of For the preliminary investigation four tubes of similar size were prepared (1, 2, 3, & 4, fig. 1) containing equal amounts of iodine, but successively increasing amounts of bisulphide of carbon. Fig. 1. Fig. 2. Fig. 8. {j— — — — — — — — — — = — — — g A 3 y \ S y & SN) S Q SN 2 S Q S S These tubes were successively heated until their contents were homogeneous, and their absorption spectra observed. No. 1 showed the lines almost as distinctly as iodine alone: in No. 2 they were fainter but still visible: it was with difficulty that they could be seen in No. 3, while in No. 4 they . were entirely absent. No. 4 was then opened, and a little more iodine added. On reheating, the lines appeared. Variations in the temperature had no apparent effect. A mixture which at 300° showed the lines faintly, showed no change when heated to 350°. : A large number of experiments were tried with varying amounts of iodine, and with various solvents such as chloro- form, liquefied sulphur dioxide, and water, and all were found to act in the same way. It was difficult to get reliable results with water owing to its action on the glass with formation of iodides. To determine the effect of a greater pressure with less density, an apparatus (fig. 3) was constructed of glass, in which pressure could be developed by the electrolysis of water. The long arm, which contained the iodine, was heated in the Todine and Bromine above Critical Temperature. 425 iron tube, and a current of electricity sent through the water in the short arm. The absorption spectrum was watched for an hour and a half, at the end of which time the apparatus exploded, but up to the very end the fine lines lost nothing in distinctness. The pressure was calculated from the time, the current strength, and the capacity above the liquid, and was found to have been about 250 atmospheres, or more than double the critical pressure of bisulphide of carbon. This indicates that the disappearance of the lines is due to the density of the vapour rather than to its pressure. The quantitative investigation of these phenomena was next undertaken. A powerful are light was substituted for the incandescent lamp, and a lens so arranged as to throw an image of the “crater’’ on the heated tube. By this arrangement, the spectra of much denser solutions could be observed. A tube provided with a long capillary neck, of the form shown in fig. 2, was constructed and carefully graduated. The contents of this tube could be varied without altering its volume by cutting off the tip of the capillary, and by warming or cooling the tube cause the liquid to run out or in; the tip could then be sealed once more. This operation could be repeated about 60 times before using up the capillary, only about 2 mm. being removed at each filling. A certain amount of iodine and bisulphide of carbon being introduced, the tube was sealed, heated, and examined. If the lines were present in the spectrum, a little more of the bisulphide was added, and this was continued until the lines just disappeared, indicating complete solution. The density was determined by noting the amount of fluid as measured by the graduations, since, when the contents are homogeneous, these values are proportional. Just before complete solution the lines are so faint as to be invisible in the stationary spectrum, but by moving the telescope to the right and to _ the left, they could be detected, the eye being more sensitive to a moving faint object than a stationary one. By using this device, the density necessary to just cause the disappear- ance of the lines could be determined with considerable accuracy. The iodine was measured in the following manner. A saturated solution in CS, was made at 12° and a capillary pipette (p, fig. 2) was dipped into it. The fluid rose to a certain height, which was marked. The iodine solution was then washed out of the capillary into the small tube ¢ by means of a drop or two of CS, put into the wide top of the capillary. This was immediately transferred to the graduated tube in the manner described. The amount held by the capillary 426 Mr. R. W. Wood on the Absorption Spectrum of pipette made only a small drop of the saturated solution, and held 000031 gr. of iodine. This was determined by filling and emptying the pipette ten times, and determining the iodine volumetrically, with sodium thiosulphite. The graduated tube was divided into 20 parts, and the amounts of iodine that could be present with amounts of CS, varying from 1 to 10 divisions, without showing the iodine- gas spectrum, were determired. With the tube half-full ot CS,, it was possible to add iodine until the tube was quite opaque ; consequently densities greater than °5 that of liquid CS, could not be investigated. The values found directly are not in shape for discussion, since as we increase the density of the vapour we also increase its amount ; in other words, we are working with varying amounts of solvent as well as varying densties. To reduce these varying amounts of solvent to unity is very simple, and the results are given in the following table. For the various densities 6 are given the amounts of iodine y which can be mixed with 1 gram of the CS, vapour without the lines appearing in the spectrum ; or, in other words, the amounts of iodine which 1 gram of CS, will dissolve at different densities. If the tube contain m grams CS, with m! grams of iodine, and if v be the volume of the tube in c.cm., then ; / m m o— Be Saae: 1 Gram C&,. 6 (2,0= 1): x, iodine in grs. 05 "00300 "10 700325 "15 00350 20 00375 "25 "00440 30 "00514 *35 "00600 "40 "00686 "45 00741 "50 "00851 The values plotted on co-ordinate paper (fig. 4), the 8 values as abscissee, the y as ordinates, show that the solvent power increases rapidly with the density. Any point on the .plane to the left of the curve represents a mixture which shows the iodine lines in the spectrum, any point to the right a mixture in which they are invisible. If the tube holds a Iodine and Bromine above Critical Temperature. 427° mixture represented by some point on the curve, and a portion be removed, 8 is thereby diminished, while yx remains. unchanged. The point corresponding to this mixture lies to Fig. 4. 0085 | “0080 | 0065 | "0060 | | | 0055 | *0035 Le eae Todine in CS, vapour. the left of the curve, and the lines should appear. This was found to be the case. Similar investigations were made with bromine, the absorp- tion spectrum of which is very similar to that of iodine. A. different method of measuring the halogen was adopted, however. Seven drops of fluid bromine were brought into. 428 Mr. R. W. Wood on the Absorption Spectrum of the tube, and bisulphide of carbon added up to the 11th mark. The absorption spectrum showed no trace of the lines. Half of the contents was then removed, and the amount of bromine in this determined. On sealing and reheating the tube the lines were distinctly visible, as was to be expected, and CS, ‘was added little by little until the lines just disappeared. Half of this new quantity was then removed, and the same process repeated. In this way data were obtained from ~ which the following table has been made. The curve is shown in fig. 5. 1 Gram C§,. 8(H,O=1). x, bromine in grs. area 05 "0182 : 6°1 °10 °0200 6°1 “15 "0241 6°9 20 "0263 7:0 25 "0299 6°8 °30 "0350 6°8 “20 "0415 6°9 “40 "0499 Ge "45 "0623 8°4 50 "0802 9°4. In the third column of the table is given the ratio of the x values for bromine and iodine for the corresponding 6 values. A given amount of CS, vapour at any density from °05 to ‘40 will dissolve from 6 to 7 times as much bromine as iodine. liquid bromine and CS, appear to be miscible in all proportions. These investigations show that to a certain amount of CS, vapour a certain definite amount of iodine vapour (depending on the density of the CS,) can be added without causing the lines characterizing the spectrum of iodine vapour to appear. If more iodine vapour be added, the lines are at once seen. The conclusion that one naturally draws is that the iodine molecules bind themselves in some way to the CS, molecules, and are incapable of exercising the selective absorption peculiar to the molecules of pure iodine gas. On this supposition, we may look on the curves in figs. 4 and 5 as solubility curves, and may consider, in a certain mixture of CS, and iodine or bromine vapour, the halogen as existing in two states, one part dissolved in the OS, vapour, and the other free. ; Hannay and Hogarth have shown (Proc. Roy. Soc. xxx. pp. 178 & 484, 1880) that non-volatile solids in solution are- Todine and Bromine above Critical Temperature. 429 not precipitated when the solutions are heated above the critical temperature, but remain dissolved in the vapour. - - I have made a rather hasty quantitative investigation of this phenomenon, and have obtained curves similar to those obtained for iodine and bromine by the optical method. An Fig. 5. *070 | “055 | = “050 és 040 “035 “030 | 025 & 020 Dore 10 15 20. "25 30 35 “40 45°50 | Bromine in CS, vapour. ethereal solution of HgI,, and an alcoholic one of KI, were used. In the first case the tube held a solution so strong, that when the contents became homogeneous above the critical temperature, a portion of the salt was thrown down 430 . Absorption Spectrum of Iodine and Bromine: on the wall-of the tube, which was then inverted quickly, and cooled at the bottom by an air-blast: the vapour con- densed here, and the salt remained above on the wall. The Fig. 6. “0070 “0065 | “0060 | "0055 | 0050 | "0045 | “0040 0035 “0030 tube was then opened, and the amount of dissolved solid determined. In the second case a more accurate method was used; °02 gr. of the salt (KI) was brought into the tube, and alcohol added little by little until no pr ecipitation 0 occurred above the critical temperature. Substitution Groups whose Order is Four. 431 The tube was heated in an air-bath and illuminated by a beam from an arc light, so that the faintest crystal film could be easily observed, and the amount of alcohol necessary to completely dissolve the salt in the gaseous state very accurately determined. ' Half of the contents was then removed, the tube resealed and heated. A thick film appeared on the wall, which corresponds exactly to the reappearance of the lines in the spectrum, in the experiments with iodine and bromine. More alcohol was added until the vapour had the density requisite for the solution of this amount of salt. _ The following values were reckoned for 1 gram of solvent at different densities :— 1 Gram Ether. : 1 Gram Alcohol. 8 (HO,=1). x (Hel, in grs.). 8(H,O=1). x (KI in grs.). "020 "0010 08 "00083 053 0016 eat LAY, 00106 "080 "0024 "195 00195 114 ‘0050 21 "00270 133 ‘0068 273 "00450 The curves plotted from these values (fig. 6) are quite similar to the curves for iodine and bromine as determined by the spectroscope, which is not unfavorable to the supposition that the halogen vapour is in part dissolved in the vapour of the bisulphide of carbon. If the dissolved substance is volatile at the temperature used, as is the case with iodine and bromine, the undissolved portion is in the state of a free gas ; if non-volatile, as in the case of HglI, and KI, it is precipitated as a crystalline film on the wall. In conclusion I wish to thank Prof. Warburg for the means of carrying on the investigations which he has placed at my disposal and for the interest that he has taken in the work. Berlin, Physikalische Institut. XLV. The Substitution Groups whose Order is Four. By G. A. Mituer, PA.D.* le seems proper to say that Professor Cayley began the enumeration of all the regular substitution groups of a given order since he determined these groups for the first order that presents any difficulties, viz., for the order 8f. * Communicated by the Author. + Phil. Mag. vii. (1854) pp. 40-47 and 408-409; xviii. (1859) pp. 34-37. . : 432 - Dr. G. A. Miller on the Substitution Later he gave a list of all the regular groups whose order does not exceed 12 together with a geometrical representation of them*. Kempe had previously given such a listf, but his results were not quite correct. Since all groups are isomorphic to regular groups { and two distinct regular groups cannot be simply isomorphic §, it is clear that the enumeration of all such groups within certain regions is very important. Complete enumerations for the first part of the two following series of orders have been published: (1) when the order of the groups is the product of a given number of prime factors ||, and (2) when it does not exceed a given number. Two more comprehensive enumerations with respect to order may be mentioned, (1) the enumeration of all the tran- sitive groups of given orders, and (2) the enumeration of all the groups of given orders. The latter of these includes the former, and each of them includes the regular groups. It may happen that the transitive groups of a given order are also regular. This is, for instance, the case when the order is a prime number, or the square of a prime number. When the order is a prime number (p) there is one group for every degree which is a multiple of p: z.e. there are » groups of order p whose degree does not exceed np, n—1 of these are transitive, n being any positive integer. It should be observed that the number of the transitive groups of a finite order is always finite, while that of the intransitive groups of any order is infinite. When the order of the groups is a composite number, the problem of determining all the possible groups becomes more complex. We shall confine our attention to the groups whose order is four. Since none of the transitive constituents of these groups can be of an odd degree, we see that the degree of such a group must be even and not less than four. We may therefore represent the degree by 2n. To find all the cyclical groups of degree 2n we have only to construct a 1,1 correspondence between a cyclical transitive groups (2 25 ) and a 2,1 correspondence between * American Journal of Mathematics, xi. (1889) pp. 139-157. + Phil. Trans. clxxvii. (1886) pp. 37-43. { Jordon, Traité des Substitutions, p. 60. , § Netto, é Theory of Substitution Groups’ (Cole’s edition), p. 110. i Hilder, Mathematische Annalen, xliii. (1893) pp. 301-413; Cole and Glover, American Journal of Mathematics, xv. (1893) pp. 191-221 ; Young, ibid. pp. 124-179. | Miller, Comal Rendus, cxxii. (1896) pp. 370-372, Groups whose Order is Four. 433 each one of these groups and a group of the second order whose degree is 2n—4a. The number of such groups for a given value of n is therefore equal to the largest value of a, and the individual groups may be given by assigning to @ the successive integers beginning with unity. To find all the non-cyclical groups of degree 2n we may construct a 1,1 correspondence between @ four-groups*, and (1) a 2,1 correspondence between each one of these groups and a group of the second order whose degree is 2n—4a, (2) a 1,1 correspondence between each one of these groups and a group of the fourth order which is of degree 2n—4a and contains n—2a systems of intransitivity. The number of the groups of the first one of these two types is the same as that of the cyclical groups, and the individual groups may be given in the same way. The number of groups of this and the cyclical type is therefore twice the largest value of a. The groups of the second type of non-cyclical groups present somewhat greater difficulties. Here a may assume the value zero in addition to its values in the two preceding cases. We shall first determine the groups when « is zero ;. z.€., we shall first seek all the Groups which contain 2n Elements and n Systems of Intransitivity. The average number of elements in the substitutions of such a group is nf, and the number of elements in all of its substitutions is 4n. The number of systems of two elements is therefore 2n. These 2n systems must occur in three sub- stitutions. If the smallest number of systems in any one of these three substitutions is represented by 8, we have g=2n mae For each value of S which satisfies this relation there must be at least one group, since we have only to use the remaining systems for the second generating substitution in order to construct such a group. In general we have the following :— * Bolza, American Journal of Mathematics, xi. (1889), p. 297. + Frobenius, Crelle’s Journal, ci, (1887) p. 287. Phil. Mag. 8. 5. Vol. 41. No. 252. May 1896. 2H 434 Dr. G. A. Miller on the Substztution Value _ Number of Number of systems of two elements of S. Groups. in the substitutions. 1 1 1 n—1 n 2 n—I1 n—1 G 3 n—3d nN : Z {3 n—2 n—1 4 n—A4 n 4 3 4 n—3 n—1 4 n—2 n—2 H) n—9d n 4) 3 5 n—4 n—1 5 n—3 (0 ( m n—m n | m n—m+1l n—1 (m even) 7 +1<: : | é on) ae } m Dae a— > m | (m n—™m n | m n—m+1 n—1 (m odd) Le A: 50 \CH\Gasia 2 2 The groups for the same value of 8S are all distinct ; but it may happen that two groups which correspond to different values of § are identical. This can, however, not occur so long as the value of S satisfies the relation ie S=<5 Identical groups can therefore only occur when the value of S is such that eee, 5 < * and deduct from this sum the sum of | = Ee) terms of the corresponding series (A). These operations are indicated in the following formula :— (sle=) [3 ](3 ] +) moves) (5-5 (Le ]-3+?) (F]@) G]#)G1")=) («GE By means of this formula we can readily determine the number of groups which contain 2n elements and n systems of intransitivity for any particular small value of n. The individual groups may be found by assigning to S the successive integers from 1 to [FI and rejecting the identical groups according to series (A) when the value of S satisfies the relation The groups of the second type of non-cyclical groups, which correspond to the other values of a, are found in exactly the same way. Their number may therefore be found by means of the given formula provided we use instead of n the following series in order, : n—2, n—4, n—6, ..., 2 ord. By adding the double of the largest value of a to the sum of the numbers of these groups corresponding to the different possible values of «, we obtain the number of groups whose order is four and whose degree is 2n. Two of the groups are transitive when is 2, For the other values of n all the groups are intransitive. Example. It is required to find all the groups whose degree and order are 14 and 4 respectively. * The brackets indicate that the largest integer which does not exceed the inclosed fraction is to be used. 2 Eb Z 436 The Substitution Groups whose Order is Four. To find the number of these groups we observe that the largest value of ais 3. Hence there are 6 groups of the first two types. To find the number of groups of the third type, 2.e. of the second type of non-cyclical groups, we assign the following three values to n:— (ie Ore cy Hence we have for 7, 24—(4—3)?=7, n=9, 2.3—1—(3—2)?=4, 38, 138—(2—1)?=2. The total number of groups is 6+7+4+2=19. The individual groups are given in the following list * :— Number. Groups. ibs { (abed.efgh.ijkl)cyc.(mn) dim. 2. { (abed.efgh) cyc. (y.kl.mn) }dim. 3. { (abed) cyc. (ef.gh.27.kl.mn) tdim. A, { (abed.efgh.zjkl)4(mn) dim. dD. {(abcd.efgh) ,(tj.kl.mn) tdim. 6. {(abed) ,(ef.gh.t7.kl.mn) }dim. 7. (ab) (cd.ef.gh.ty.kl.mn). 8. (ab.cd) (ef.gh.27.kl.mn). 9. (ab.cd) (cd.ef.gh.tj.kl.mn). 10. (ab.cd.ef)(gh.tj.kl.mn). Ils (ab.cd.ef) (ef.gh.27.kl.mn). 12. (ab.cd.ef.gh) (gh.tj.kl.mn). 13. (ab.cd.ef.gh) (ef.gh.y.kl.mn). 14, { (abed) ,[ (ef) (gh.zj.kl.mn) ] 1. 15. { (abed) 4| (ef.gh) (y.kl.mn) ] 444. 16. { (abed) 4[ (ef.gh) (gh.yj.kl.mn) ]t14. 17. {(abed),| ef.gh.i7) (y.kl.mn) | 443. 18. { (abed.efgh).[ (7) (kl.mn) ]*11. 19. { (abcd.efgh),| (4.h1)(kl.mn)]} 1. * The notation is that which Professor Cayley used and explained in his articles in the Quarterly Journal of Mathematics, vol. xxy. Alleged Scattering of Positive Electricity by Light. 437 When only the number of the possible groups for a given degree is required, and when n is a large number, it is very desirable to avoid assigning so many different values to nas _ are necessary if we employ the given formula. By observing that all the fractions in this formula are increased by integers when n is increased by 6, we may readily find the following formula. By means of it we can find the number of groups (N) directly for any value of n. m represents any _ positive integer, and «, represents the largest value of a, 1. e. the largest integral value of « which satisfies the relation i ee 3° When n=6m, N=m(3m?+ 6m +1) | 2 i eae ue Ie sata Ore ch orice) 2 » n=b6m+2, N=3m(m+1)(m4+2)4+1 Na (2m+1) (8m? +9m+4) p + 2a, slates A aa » n=b6m+3, » n=bm+4, N=(m+1)(8m?+9m+4) _ 38(m+1)(2m?+7m+4) ue 2 » n=6m+5, N Hence there are 4(96 tee) oe 249.84.85 +1+500=1,778,361 ,, Ziirich, Switzerland, March 1896. 4 = 346 groups of degree 50, » L000, &e. XLVI. On the alleged Scattering of Positive Electricity by Light. By J. Ester and H. Garren *. é Uae question whether light which facilitates the passage of negative electricity from a conductor into the sur- rounding gas can, in like manner, accelerate the discharge of positive electricity is not without significance for the proper apprehension of the photoelectric process. * Translated from the Ann. der Physik und Chemie, Bd. lvii. (1896) ; from a separate impression communicated by the Authors, 438 Profs. J. Elster and H. Geitel on the Alleged If, in fact, this action of light can be shown to take place, then it is no longer possible to believe that we have here to do with a specific phenomenon of the kathode, and, moreover, the view that the photoelectric process depends upon the discharge of the one (the gaseous) coating of an electric double layer which is continually renewed at the surface of contact between the conductor and the gas must be put to experimental proof, since the nature of the electricity escaping in light must always be the same as that which the gas in contact with the conductor itself takes. From this point of view, therefore, it would not be intelligible that one and the same conductor in the same-atmosphere should give off both electricities more easily in light than in darkness. Now experiment shows that the illumination of a negatively charged surface, with proper choice of light and of substance illuminated, causes an active discharge of electricity into the surrounding gas, whilst the corresponding phenomenon for positive electricity—if it takes place at all—must be much more insignificant. Thus Hrn. Stoletow and Righi have not been able certainly to recognize the action of ultra-violet light upon positively charged surfaces, and we ourselves have so far not been able to observe any loss of positive electricity in light which was not sufficiently well accounted for by the usual loss of electricity or by the sources of error to be more definitely spoken of in what follows. A paper by Herr H. Branly has recently appeared*, in which the acceleration of the electric discharge by ultra-violet light is maintained to hold good also for positive electricity. On account of the importance of the subject we have repeated the experiments described in this paper, and with the arrange- ments which seemed to us best suited to exclude sources of error, and following the method of Herr Branly as closely as possible in essential points. After we had failed in obtaining the same result as Herr Branly, we tried whether the alkali metals, which are so sensitive to ordinary light with negative electrification, would show a photoelectric discharge also with positive electricity. In what follows we venture to report upon the results obtained in these experiments. The most obvious method of observing the scattering of electricity in light, which method was also employed by Herr Branly, is to connect the electrified surface to be examined with an electroscope, and to judge of the loss of electricity produced by the light in a given time from the decrease in the divergence of the leaves. This method has the disadvantage that, on account of the high tension employed, the whole of the * Compt. Rend. cxx. p. 829 (1895). Scattering of Positive Electricity by Light. 439 electrified system of conductors must be extremely well insulated so that a feeble action of the light may not be hidden by the loss of electricity not connected with the action of the light. But apart from this, there is a disturbing cause arising from the fact that each time the observer changes the sign of the electric charge, there is a return current from the insulating supports of that electricity which had passed to them during the previous electric condition. Much less exposed to these sources of error is the arrange- ment which Herr A. Righi and we ourselves have often em- ployed in photoelectric experiments, especially if it is necessary to recognize feeble action. In this method the electrical measuring apparatus, together with the conductor to be illuminated, are at the commencement of the experiment at zero potential, and the strength of the action of the light is measured by the velocity with which the potential becomes equal to that of a conductor kept at constant potential, which stands opposite to the illuminated surface at a small distance from it. The arrangement of the experiment was as follows :—The ultra-violet light was furnished by the spark of a condenser, which was connected with the poles of an induction-coil actuated by 4 to 8 large Bunsen elements, the spark having a maximum length of 18 centim. The current was broken by means of a Wagner’s hammer with platinum contacts, and the spark of the condenser was taken between two alu- minium wires at a distance of 2 millim. The galvanic battery, the induction-coil, spark-space, and all the necessary con- nexions were placed in the open air in front of the closed window of the observing room. One of the panes of the window was replaced by a plate of thin iron connected to earth, which was provided with a circular opening, in which was inserted a quartz lens of 50 millim. diameter. Since the focus of this lens coincided with the spark, a parallel beam of ultra-violet light was formed by the lens within the room, whilst at the same time the electrostatic action of the induction- coil and of the electrified air from the spark was shut off from theroom. Within the room, at a distance of about 25 centim. from the window and at right angles to the beam of light, was placed a piece of iron-wire gauze with a mesh of about 1 millim., and parallel to this, at a distance of 2 to 4 millim., the insulated plate of the substance to be examined. From this a wire went to the quadrant electrometer (sensitiveness, 1 volt=23 divisions), whilst the wire gauze was charged to a potential of about 525 volts by a battery of several hundred: Leclanché cells. According as the wire gauze was 440 Profs. J. Elster and H. Geitel on the Alleged charged with positive or negative electricity, the plate parallel to it must become charged with negative or positive electricity. If now the earth connexion of the electrometer was removed, then as soon as a passage of electricity took place between the gauze and the plate, the change of potential in the latter could be read off on the electrometer. It is to be observed that with a positive charge of the gauze, the plate to be tested has negative electricity on its surface, and that therefore from this clean metallic surface in ultra-violet light a free discharge towards the gauze was to be expected and a consequent positive charge of the plate. We used for the experiment a disk of amalgamated zinc, also similar pieces of zinc covered with a thin layer of paraffin or tallow, and also a plate of wood covered with tallow. According to Herr Branly, such surfaces covered with paraffin or tallow suffer a greater loss of positive than of negative electricity when exposed to light. ‘We observed the deflexion of the electrometer-needle which took place in one minute, both with positive and with negative charge of the gauze, and both in the dark and when illuminated with light from the spark. The Wagner’s hammer was so arranged that it came into action of itself upon closing the current, it was therefore only necessary to keep the current closed for one minute. The results of a series of measurements are brought together in the following table. The numbers give the change of potential of the plate, measured in volts, which took place in one minute: each number is the mean of two readings :— Amalgamated Paraffined Zine Plate covered Weg ae Zine Plate. Zinc Plate. with Tallow. covered with Tallow. Tllumi- Tlumi- Tllumi- Tllumi- Dark. nated. Dark. nated. Dark. nated. Dark. nated. Gauze nae +0-40 (£153 +054 | +069 | +079 | +038 | +058 | +0:52 Gauze eae —016 | —0-40 | -022 | —o16 | —0-09 | —0-06 | —o52 | —o-52 As was to be expected from what has been said, we have in this series of observations evidence of the great photoelectric dispersion from a plate of amalgamated zinc charged with negative electricity. We were not able to expose the plate for a full minute to Scattering of Positive Electricity by Light. 441 the light, as the deflexion of the electrometer on the scale could not then be read off. Therefore the plate was exposed only five seconds, and the deflexion—reduced to volts—was multiplied by 12*. But beside this action of the light— undoubted and already known—the numbers show no other. There are, it is true, deflexions of the electrometer-needle in the dark as well as in the light, which, however, in no case reach the amount of one volt, and which on account of their inconstancy are to be referred to an irregular passage of electricity from the gauze to the plate, probably caused by the dust of the air. Only in two cases is this feeble transference of electricity slightly greater in light than in the dark, viz. with a nega- tively charged gauze opposed to a plate of amalgamated zinc, and with the gauze positive and the plate of paraftined zinc. If one wishes to find in this a proof of an action of light, then only the first case can be taken to show a photoelectric dispersion of positive electricity. But here also a sufficient explanation is to be found in the fact that the ultra-violet light reflected from the polished surface of the amalgamated zinc strikes the side of the gauze turned towards it and pro- duces a passage of negative electricity from it to the plate, so that in this case the photoelectric discharge is not from the positively charged plate but from the negatively charged auze. A We have now to describe an experimental arrangement in which this action of the reflected light appears perfectly clearly. All the observations show that the paraffined or greased surfaces are not photoelectrically sensitive; in no case is the scattering of electricity from these found to be greater with a positive charge than with a negative charge or in the dark. The small deflexions of the electrometer observed in the * A more accurate calculation of the change of potential during an ex- posure of one minute would be obtained by use of the formula V-2, =V - e—kdt,, in whick V denotes the potential of the charging battery, V, that of the illuminated plate, & a constant, J the intensity of the light, and ¢, the time of exposure. From this we should have for two times of exposure t, and ¢2 and the corresponding potentials v, and 2, : oe (OH) =m (C5 from which v, can be easily calculated. In the foregoing case we obtain for v, the value shown in brackets, +123 volts. ‘ 449 Profs. J. Elster and H. Geitel on the Alleged dark, which always indicated a loss in the charge of the gauze, show that the instrument is too delicate for experi- ments such as these, in which a thin plate of air is exposed to a fall of potential of more than 100 volts per millimetre. We have therefore repeated these experiments with the much less sensitive aluminium-leaf electroscope, and were able to make the charge of the gauze and the time of exposure twice as great as before. But then also the photoelectric discharge took place only when the gauze had a negative charge. Thus the charge of an amalgamated zinc plate rose in five seconds to 400 volts, of an oxidized zinc plate in two minutes to 190 volts, and with greased or paraffined zine or wood plates the potential remained at zero, irrespective of the sign of the charge of the gauze. | From the result of this experiment we concluded that in the experiments of Herr Branly some unsuspected source of error must have existed. In order to discover what this may have been, we have repeated the experiment of Herr Branly, essentially according to his arrangement as far as was possible from the data which he gives. The sparks of the induction- coil were taken within a box of sheet-iron connected to earth, in the side of which there was a quartz window. Opposite to this was the insulated and electrified plate con- nected with an aluminium-leaf electroscope. Since there was no gauze placed in the way of the light rays, any elec- tricity escaping from the plate must be lost in the air or partly pass to the side of the iron box, and from there pass to the earth. So long as the plate was some distance (about 50 centim.) from the quartz window, we also observed with this arrange- ment an increase of electric dispersion in light with a negative charge. But if the plate is brought to within a few centi- metres of the window, and, consequently, near to the box, it may happen, if the surface of the plate is covered with tallow or with paraffin, that a positive charge decreases in light more rapidly than a negative charge. But here, as in the above discussed analogous case, it is to be remembered that the positive charge of the plate collects negative electricity upon the side of the box turned towards it by induction ; if there- fore this surface is struck by the ultra-violet light reflected from the surface of the layer of fat, a passage of negative electricity from it to the plate must result, and give the same effect as if a photoelectric dispersion of positive elec- tricity from it had taken place. _ This suspicion was converted into certainty by the obser- vation that the phenomenon is dependent upon the nature of Scattering of Positive Electricity by Light. 443 the surface of the bow. If this is covered with bright metal—as tin-foil—the transference of electricity largely increases, and becomes strikingly great if a piece of amalgamated zinc is placed upon it. Since Herr Branly gives no information as to the distance of the illuminated plate from the quartz window of the metal box, we may consider it not improbable that this was chosen too small, and that the dispersion of positive electricity observed by him in ultra-violet light was caused by the deceptive action of the light reflected from the surface of the electrified disk. We believe that we are justified, by the results of the experiments described, in asserting that an increase in the dispersion of positive electricity by illumination of the elec- trified surface by ultra-violet light has not been proved. The striking inability of surfaces of alkali-metal to retain a charge of negative electricity in ordinary light might suggest that a possible action of light with a positive charge might be expected to take place most readily with such surfaces. As we have mentioned in a previous paper*, exhausted glass globes of which the one electrode is formed by an alkali- metal, the other by platinum, also allow a photoelectric current to be observed in more or less distinct manner when they are reversed, 27. e. when the alkali-metal forms the positive pole. But we had also arrived at the conclusion that in this case the photoelectric action had its seat not at the surface of the alkali-metal, but at the platinum electrode. There is, in fact, formed upon the platinum a superficial layer by condensation of the vapours of the alkaline metal from which in light negative electricity passes to the anode. By heating the platinum wire with a galvanic current this layer is volatilized, and the photoelectric cell becomes—in its reversed arrangement—for a short time insensitive to light. When we recently repeated this experiment with better arrangements and greater care, we found that after the wire had been heated there remained a small amount of sensitive- ness to light, which, perhaps, had its origin in a scattering of positive electricity from the surface of the alkali-metal. It seemed important to determine the seat of this action without doubt, whether anode or kathode. We started from the observation that the current as usually produced by illumination of the kathode is dependent upon the position of the plane of polarization of the incident light with respect to the surface of the kathodet. It was to be * Elster and Geitel, Wied. Ann. xliii. p. 286 (1891). tT ? Cf Elster and Geitel, Wied. Ann. lii..p. 440 (1894), 444 Alleged Scattering of Positive Electricity by Light. expected that any discharge possibly produced by light at the anode would also be in some way dependent upon the direction of the light-vibrations toward the surface of the anode. The experiments made in this direction gave, how- ever, a negative result: if we allowed a ray of light to fall through a Nicol’s prism upon the fluid surface of the sodium-potassium alloy which formed the anode, and _ altered the position of the plane of polarization by turning the Nicol, we found the photoelectric dispersion to be independent of the azimuth of the light. It must be remarked that in the “ reversed ” arrangement of the cell here employed the current strength, even in strong light, is far too small to give a measurable deflexion, even on the very sensitive galvanometer which we employed to measure the photoelectric currents. We therefore employed the same method which we had used in the experiments upon ultra- violet light, z.e. we connected the alkali-metal surface with the positive pole of the above-described battery, and the opposed platinum electrode with the quadrant electrometer. The passage of electricity through the cell betrayed itself then by the constant increase in the deflexion of the electro- meter-needle. A constant condition of the instrument may be attained by making an earth connexion through a very large resistance (a pencil mark on an insulating surface) to the wire leading to the electrometer. Not only does the fact that the transference of electricity is not affected by change in the direction of the light-vibrations ‘with respect to the plane of the anode prove that the seat of photoelectric action is not at the anode, but we have the further evidence that this action is perceptibly increased if the platinum wire which serves as kathode is exposed to the direct action of the light. It even continues of the same intensity when by inclining the bulb the alkali-metal is made to flow over into the side bulb and is thus removed from the cell*. Since a clean platinum-wire in a vacuum shows no photo- electric action in ordinary light, its sensitiveness can only have been communicated to it by contact with the alkali- metal or its vapour. As we see, the result of this experiment also leads us to the conclusion that the light has acted not on the anode of alkali-metal but on the platinum kathode made sensitive by its superficial coating, and we might expect that the “reversed” cell would lose its sensitiveness upon ignition of the platinum wire. But, as we have said, this expectation was, curiously enough, not verified by experiment. There * The form of the cell is shown in fig., Wied. Amn, xlii. p. 564 (1891) ; see also Phil, Mag, 1896, xli. p. 220, Tinfoil Grating Detector for Electric Waves. 445 remained then only the supposition that the inner glass wall of the bulb had become covered with a layer, by contact with the alkali-metal, from which negative electricity escaped when the light fell upon it. In order to remove this source of error also the whole wall of the cell must be maintained at the © same potential as the anode of alkali-metal, so that there could be no fall of potential from it to the wall. We attained this result by covering the outside of the bulb with silver by pre- cipitation; with the exception of a small space where the kathode-wire was melted into the bulb and a “ window ” for the entrance of the light. If now the alkali-metal surface and, with it, the glass wall of the bulb was charged with positive electricity, and the kathode-wire was connected to earth, then immediately after ignition of the wire no loss of electricity occurred in light, not even when a beam of sunlight entered through the window in the silver coating. Not until after some time, when the wire on cooling had again covered itself with a coating of alkali-metal, could the photoelectric discharge be again ob- served with increasing distinctness. Thus the experiments with ordinary light on surfaces of alkali-metal in a vacuum lead to the same result as those with ultra-violet light, namely, that the photoelectric action is limited to the kathode. _. We have pleasure in gratefully acknowledging the assistance we have received in this work from the Elizabeth Thompson Science Fund in Boston. XLVII. The Tinfoil Grating Detector for Electric Waves. By T. Mizuno, Rigakushi, Professor of Physics, First Higher Schools, Tokio*. § 1. i a paper +, which not long since I communicated to this Journal, I suggested that the change of the resistance of the grating might be due to a mechanical effect exerted upon it by impinging trains of electric waves. In other words, electric waves might give impulses to some of the strips of the grating in such a way as to let leaflets on their margins come in contact with one another, thereby causing a diminution of resistance. In order to confirm this view, further inquiries were carried out soon after the com- munication of the above-mentioned paper. * From a separate impression from the Journal of the College of Science, Imperial University, Tokio, Japan, vol. ix. part 2. Communicated by the Author. Tt “Note on Tinfoil Grating as a Detector for Electric Waves,” Phil. Mag. vol. xl. p. 497 (1895). 446 T. Mizuno on the Tinfoil Grating § 2. Having constructed about forty gratings and tested their action, | found to my surprise that while some were extremely sensitive, others were not, being even utterly indifferent to the impulses of electric waves, although they had all been prepared with the same care and apparently with the same success. This led me to undertake a closer examination of such gratings, which gave results that. throw much light upon their nature. But before these results can be stated, it is necessary to describe in detail my way of preparing the gratings, because upon that their sensibility wholly depends. § 3. The face of a flat wooden block of convenient size, say 10 centim. on a side, was pasted over with very fine tinfoil, as described in my former paper. ) Then came cutting lines into the tinfoil, to which particular attention was given. Along the edge of a bamboo ruler a sharp knife, held always inclined away from the ruler, was drawn lightly across the surface of the tinfoil. In this way many fine parallel slits were cut in the tinfoil, Ae so as to make one continuous, regular, zigzag Pig line, as shown in fig. 1. A few of the gratings, thus carefully pre- pared, were found to be sensitive. But experience has taught me that success in preparing good detectors depends, to a large extent, upon the nature of the wood block on which the tinfoil is pasted in the first place, and next upon the degree of adhesion of the foil to the wood. A soft wood is preferable to a hard one, and the paste used should not be thick enough to make the foil adhere too firmly. § 4. The majority of the slits of the sensitive gratings, when examined under a microscope, presented such an appearance as that shown in fig. 2. AB and C D represent two strips of foil with the very narrow slit or gap ab between them that has been formed by the knife. The shaded portion indicates the slope of the tinfoil found at one edge of each strip. For the sake of clearness, there is shown in fig. 3an end view, that is, a section of the two strips perpendicular to their lengths. The shaded portions indicate the tinfoil strips, A B and C D in fig. 2, of which the edge of one strip, C D, extends some distrance into the gap, ab, and forms the slope mentioned above. Along this slope the tin- foil presents many folds or wrinkles, which seems Detector for Electric Waves. 447 to show that the tinfoil strip was somewhat stretched along its edge by the act of cuttingit. Non-sensitive gratings eompganene of ue eters de Fig. 3. appearances, but had the gap between the strips ! ee. deciol clone sale ast) ean, appreciable folds along the edges of the strips. Hence for a grating to be sensitive, it appears to be necessary that the gaps should be narrow and their margins sloped and in folds. § 5. Although I have been unable to see clearly the interior of a gap, yet it is quite reasonable to assume that in sensitive gratings there will be numbers of leaflets along the margins of adjacent tinfoil strips; and the existence of such leaflets once admitted, the explanation of the action of the gratings becomes clear. For in a properly constructed grating some of the leaflets may easily come in contact with one another under the action of the electric waves, because of the extremely small distance between any two opposite leaflets in the narrow gap. Then, too, it seems to me that these leaflets must be of various dimensions and, accordingly, some of them will be extremely sensitive, others less so but still highly sensitive, others again only moderately so. This being the case, the amount of change in the resistance of the grating must depend upon the intensity of energy of the impinging electric oscillations, for, when it is not great enough, only the most sensitive leaflets will come into play, but when it is sufficiently great all the effective leaflets will be brought into action. All the experiments I have yet made are in agreement with this representation of the matter. § 6. A grating, well prepared so as to fulfil the conditions mentioned above, proves to be an extremely sensitive detector for electric waves, as will be seen from the experiments which I now describe. Experiment 1. A Hertzian parabolic vibrator, ABC, was placed horizontally with aperture turned upwards, as shown in fig. 4. The aperture was covered with a sufficiently large Fig. 4. wooden plate, ADC, entirely re coated with tinfoil. A grating, whose initial resistance was about 71 ohms, was placed at about 5 centim. from the plate and in 6) a vertical line with the primary conductor, O, radiating electric B waves of 60 centim. wave-length. Then, exciting the primary oscillations, I always found that - 448 T. Mizuno on the Tinfoil Grating the resistance of the grating was diminished by from 1 to nearly 2 ohms. The experiment was repeated after raising the plate, ADO, parallel to itself and keeping it at some height from the aperture, AC. Similar changes of resistance were also ob- served in this case. This phenomenon may of course be understood by considering the fact that some electric waves, which pass out of the uncovered portions of the parabolic vibrator, will, after going through the room and being reflected from the surrounding walls, ceilings, &., come back ultimately to the grating in a much enfeebled state. Experiment 2. The above experiment was modified by placing on the plate, ADC, a zinc box, abcd, 17 centim. by 27 centim., without top or bottom and putting the grating inside it. In this case also, a change of resistance was observed, though smaller. It is then certain that although the side effects were got rid of, the top effect still ) remained, through which traces of waves might affect the re- B sistance of the grating. The fact that we can annul the change of resistance by completely closing the top of the box with a metallic plate, seems especially to favour the above explanation. Experiment 3. The grating was connected with the Wheat- stone bridge by means of two leading wires, and at the same time placed inside the zinc box, justas in Hxp. 2. After balance had been well established and the top of the box closed, the primary oscillations were excited. This time, the balance was at once destroyed and the resistance of the grating showed an appreciable diminution, in spite of the fact of the grating being wholly enclosed in a metallic box. Taking away one of the leading wires the phenomenon yet remained the same, though the change of resistance seemed somewhat smaller than in the former case. The leading wires thus appeared to catch up electric oscillations and guide them to the grating. Hence in experiments with electric waves it is necessary to keep the grating free from any exposed wires, which might easily take up electric disturbances. Such effects due to leading wires were observed also by Herr Aschkinass during his researches with these gratings. § 7. To what extent the sensibility of the grating reaches Detector for Electric Waves. 449 will now be quite clear from the results of the above experi- ments. It is next of great importance to describe some experiments as to the variation of the sensibility. In its primitive state, the grating properly constructed is so sensi- tive that it can detect even the smallest electric oscillations. But after having been used a few times, its sensibility under- goes a sudden and decided diminution, and then remains nearly constant. At first, when the grating is exposed to electric waves and its resistance consequently diminished, a single tap given to it is almost enough to restore the resistance to its initial or primitive value. But when we have used the grating repeatedly, we find it necessary to give it a greater number of taps to effect this restoration. Later on, when the sensibility has diminished to a certain value, it seems to retain that value without any decided further change for a long time. This variation in the sensibility may be accounted for in the following way :—As mentioned in § 5, the effective leaflets along the margins of the several tinfoil strips may be of different sizes, and some of them possibly very small. The smaller the leaflets the more sensitive to electric disturbances, and consequently the more liable to fatigue will they be. Hence in the primitive state such leaflets are easily affected by even very weak electric impulses, but soon lose this sensibility as a result both of the repeated electric distur- bances and of the mechanical taps given to them each time, § 8. Though the sensibility of the grating thus always diminishes to a certain extent by a little use, still it is even in such a state far superior to that of an ordinary Hertzian resonator. Hyen where the latter fails, the grating always shows the presence of electric waves if there be any. Experi- ments on the nature of electric waves, namely, on rectilinear propagation, reflexion, refraction, diffraction, polarization, &c., can all be easily carried on by means of a properly constructed grating. Moreover, such a grating gives not only qualitative, but also quantitative results, to a certain extent, because the amount of diminution of the resistance depends upon the quantity of energy of the impinging waves. Hence, I believe, it may prove to be of great advantage to make use of such ‘gratings in all lecture experiments as well as in laboratory researches on electric waves. In conclusion I wish to express my thanks to Mr. U. Takashima for the kind and earnest assistance he has given me in the preparation of many of these gratings and in carry- ing out researches upon them. Phil. Mag. 8. 5. Vol. 41. No. 252. May 1896. 21 [. 45024) XLVIII. Carbon and Oxygen in the Sun. By Joun TROWBRIDGE*. ‘N 1887 Professor Hutchins, of Bowdoin College, and myself brought forward evidence to show that the peculiar bands of the voltaic-arc spectrum of carbon can be detected in the sun’s spectrum. They are, however, almost obliterated by the overlying absorption-lines of other metals, especially by the lines due to iron. In order to form an idea of the amount of iron in the atmosphere of the sun which would be necessary to obliterate the banded spectra of carbon, I have compared the spectrum of carbon with that of carbon dust, and a defi- nite proportion of iron distributed uniformly through it. The carbon dust and iron reduced by hydrogen was formed into pencils suitable for forming the arct. Chemical analysis showed that the iron was uniformly mixed with the carbon dust ; specimens taken from different sections of the terminals showed in the carbons which [ burned in the electric are 28 per cent. of iron and 72 per cent. of carbon. The method of experimenting was as follows :—That por- tion of the spectrum of the sun which contains traces of the - peculiar carbon band lying at wave-length 3883°7, and which had been almost obliterated by the lines of absorption of other metals, among them those of iron, was photographed. The pure carbon banded spectrum was photographed on the same plate immediately below the solar spectrum, and the spectrum of the mixture of iron and carbon immediately below this. The sun’s spectrum can be regarded as a composite photo- graph, and the iron and carbon can also be regarded as a composite photograph. It was speedily seen that from 28 to 30 per cent. of iron in combination with 72 to 70 per cent. of carbon almost completely obliterated the peculiar banded spectrum of carbon. This proportion, therefore, of iron in the atmosphere of the sun, were there no vapours of other metals present, would be sufficient to prevent our seeing the full spectrum of carbon. The iron in the carbon terminals which I employed greatly increased the conductivity, as will be seen from Table I., which was obtained in the following manner. The carbons were separated by means of a micrometer- screw, and the current and difference of potential were mea- * Communicated by the Author. + I am indebted to Mr. John Lee, of the American Bell Telephone Co., for his skill in making the carbons and for analysis of the composite carbons. Carbon and Oxygen in the Sun. 451 sured with different lengths of arc. Table I. gives the results for pure carbon; Table II. for 28 per cent. of iron and 72 per cent. of carbon. TABLE I. pene et Amperes. Volts. | igi Linkter een as 25 yi eat hr 23 24 Fy eh WO Oe 225 20 Ate Bed eked 20 18 glia |) eh 16°5 15 TaBieE IT. Peet or te Amperes. Volts. in millims. LO Bet ee 30°5 30 Zep ta Nt kas oh a 29 30 2 nS e Mae Zt 5 28 2 Ag ee 2A 25 i ee, Race as 22, » 20 Op iseitdo. 2162; ani 20 20 Pa rete A ee 18 1, 3 a te A 16 18 The length of the are could be nearly doubled with the same current and the same voltage by the admixture of 28 per cent. of iron. The light was apparently greatly increased, but the difference in colour between the pure carbon light and the iron-carbon light made measurements unreliable. Moissan* has shown that the carbon in an electric oven through which powerful electric currents have flowed is free from foreign admixtures. Deslandres has confirmed this, and finds only a trace of calcium present. The self purification comes from a species of distillation of the volatile impurities. The purest carbon is found at the negative pole. The light of the electric furnace is due to the combustion of carbon. Can we conclude that the sun is a vast electric furnace ? | If the voltaic arc is formed in rarefied air or under water, its * Comptes Rendus, cxx. pp. 1259-1269 (1895). 212 | 452 Prof. J. Trowbridge on Carbon brilliancy diminishes greatly. On the other hand, an atmo- sphere of oxygen greatly augments its vividness. The question therefore whether oxygen exists in the sun is closely related to questions in regard to the presence of carbon, when we consider the temperature and light of the sun. If suppositions also are made in regard to the magnetic condition of the atmosphere of the sun, it is of great interest to determine whether oxygen exists there, for oxygen has been shown by Faraday, and later by Professor Dewar, to be strongly magnetic. Professor Henry Draper brought forward evidence to prove the existence of bright oxygen lines in the solar spectrum. Professor Hutchins, of Bowdoin College, and myself examined this evidence, and after a long study of the oxygen spectrum in comparison with the solar spectrum, came to the conclusion that the bright lines of oxygen could not be distinguished in the solar spectrum. We published our paper in 1885. Ihave lately studied the subject from another standpoint ; having carefully examined the regions in the solar spectrum where the bright lines of oxygen should occur, if they manifest themselves, in order to see if any of the fine absorption-lines of iron in the spectrum of iron were absent, for it is reasonable to suppose that the bright nebulous lines of oxygen would obliterate the faintest lines of iron. The method adopted by Draper. for obtaining the spectrum of oxygen consisted in the employment of a powerful spark in ordinary air. To obtain this spark, the current from a dynamo running through the primary of a Ruhmkorf coil was suitably interrupted. By the use of an alternating machine and a step-up transformer, powerful sparks can be more readily obtained. Since the time of exposure with a grating of large dispersion is long, considerable heat is developed in the transformer from the strong currents which are necessary to produce a spark of sufficient brilliancy. I have therefore modified the method in the following manner. The spark- gap is enclosed in a suitable chamber, which can be exhausted. When the exhaustion is pushed to a certain point, the length of the spark can be increased ten or twenty times over its length in air, and a suitable spark for photographic purposes can therefore be obtained by the employment of far less energy in the transformer. )8 HEGI+K-K)G te ty), 1 K” Peer laeet ge). le + K—K’ Mer Poa ay K” Py = Py =— (7 +K+ 5 By IT Bes age =-(- +K-+ K jie, = Py = Pe —(z +K+— ap. These expressions reduce to those of vy. Helmholtz if it. be assumed that K’”=0, and to those of Maxwell for electric stress (Art. 106) if we put KK = 6; and a specific inductive capacity of the medium. It will be seen from these expressions ae Kirchhoff S * Wied. Ann. xxiv. p. 52 (1885); Ges. Abh., Nachtr ag, p. 91 (1891). e 456 H. Nagaoka and H. T. Jones on the Effects theory makes the stress depend principally on the coefficients K/ and K”. The experiments of Villari, Lord Kelvin, and Ewing on the effects of longitudinal stress on magnetization show that ae / pen , Young’s Modulus. /K’ a ON ee Space re (3 +K in iron is a quantity which may amount to 10° for moderate magnetizations, so that in this case K is quite negligible in comparison with one or both of the two other coefficients. The preponderating influence exercised by these latter factors will, perhaps, explain the existence of a maximum elongation in iron and the continual contraction in nickel. Maxwell’s expressions for magnetic stress (Art. 644), in the case when B and H have the same direction, are, however, apparently by a coincidence deduced from the above expressions of Kirchhoff by putting K”=0, K’= K=susceptibility. About the same time Lorberg* and J. J. Thomsonf discussed the present problem in a manner similar to that of Kirchhoff. More recently Hertz} arrived at expressions of precisely the same form as those given by v. Helmholtz. In comparing his expressions with those given by Maxwell for the general case of a magnet in which the induction and magnetic force -have different directions, Hertz says (p. 281) :— _ “A difference of far greater importance (7. e. than the effect of a change of density by electromagnetic strain) is that in Maxwell’s theory the tangential stresses P,, and P,z have different values, while in our theory they are identical. Under our system of stresses every material element, when left to itself, will only change its shape; under that of Maxwell it will also experience a rotation as a whole. The Maxwellian stresses cannot therefore arise from processes in the interior of the element, and can have no place in the present theory. They are, however, admissible on the assump- tion that in the interior of the body in motion, the ether remains at rest and furnishes the necessary fulcrum for the rotation which takes place.” In attempting to calculate the change of dimensions of a body due to magnetization we are at once placed face to face with the question as to whether these stresses actually * Wied. Ann. xxi. p. 300 (1884). + Application of Dynamics, §§ 35-37 (1886). } Ausbreitung der electrischen Kraft, p. 275 (Leipzig, 1892). Hertz, speaking of equation (6c), p. 284, which is obtained as a simplified form of stress agreeing in the general case with that found by v. Helmholtz, says that the stress is the same as that given by Maxwell in Art. 642 of the treatise, His expression, however, is not that given in Art, 642 but in Art. 105, of Magnetic Stress in Magnetostriction. 457 exist in the body, or whether they, existing ina medium in which the particles of the body are imbedded, produce modi- fied stresses in the body. Kirchhoff supposed the surface tractions acting on a piece of magnetized soft iron to be the same as if the stresses P,, actually existed in the iron and in the surrounding air, where K, K’, K” are put =0, and proceeded to calculate the changes in the dimensions of a soft iron sphere placed in a uniform magnetic field, due to a system of stresses which satisfy the ordinary equations of an elastic solid and at the surface of the sphere have the above given values. Having obtained the general solution for the strain ae a sphere, Kirchhoff gives a numerical example, neglecting the terms affected with (K—K’) and K”, supposing ‘these quan- tities to be very small in comparison with K®, Kirchhoff’s final value for the elongation of a soft iron sphere is therefore pre- cisely the same as that which would be given by Maxwell’s system of stresses (Art. 644). __ Proceeding exactly on tbe lines of Kirchhoff, Cantone* has calculated the variations 81 and 8v of length and volume ‘of a soft iron ellipsoid of revolution, and finds that for an ellipsoid of great eccentricity and length l, SATE elie RS aaa Led i Ga Blan si 2KAi+, 2K) & P¢ ee ok rAtonenl ao th {7 1K: 1K2 ee eae where H=Young’s Modulus for the iron (on the supposition that the Poisson ratio =). Healso measured experimentally the changes of length and volume of a soft iron ellipsoid due to uniform magnetization, and, assuming that these were due entirely to Kirchhoff’s system “of stresses, deduced the values of K’ and K”. He found the change of volume to be negligibly small, and for K’ and K” the values 44 000 and —92,000 for the mean field-intensity (H=33 C.G. Ee H (in iron) = 3°95, L=250) which he ST * Mem. R. Ace. Line. ser. 4, vol. vi. p. 487 (1890); Wied. Electr. iii. p- 740. + More exactly, aie . Z _ 4nP = IH KH? KY? = on (59 + ORL 428) — 20 420)n ~ QE’ where 6 is a constant defined by the equation E (1+28) _p..-4. os ( ) = Rigidity. 1+30 458 H. Nagaoka and E. T. Jones on the Effects The change of length of a soft-iron ellipsoid has, however, been investigated over a much greater range of field-intensities by one of us*, and the results represented by curves as functions of magnetizing force, of the square of mag- netization, and of the former, respectively. If the change of length due to Kirchhoft’s system of stresses be calculated from Cantone’s formula, and the result subtracted from the observed change of length, these curves (K’ and K” being pro- visionally disregarded) assume the forms shown in figs. 1, 2, 3. Since the coefficients K’ and K” are not known with any accuracy, for the iron used, the correction due to them cannot at present be calculated. The ordinates of the full-line curves represent therefore the changes of length produced by uniform magnetization, corrected on Kirchhoft’s theory for the partial stresses represented by terms containing H and K, which were measured at the same time. The residual change of length, represented by the ordinates in figs. 1, 2, 3, must be due to the other unknown terms in the expressions for the stresses, or to some change of molecular arrangement accom- panying the magnetization. A similar process was followed by More+, who measured the change of length of part of an iron wire magnetized by a coil, lt was assumed, however, that there existed in the wire 2 a contracting stress = , the reason given for this assumption being that if the wire were cut in two, the two ends would 2 be held together by a force a ing both to Maxwell’s theory and to that of Kirchhoff, the e nasty e e B? tension in a narrow air-gap in the wire is Sa? and this 7 per unit area. Now, accord- has been experimentally verified by one of us over a large range of magnetizing field}; but both theories give different values for the stress inside the iron. Even if the wire were cut in two, the force holding the parts together would not be B? Sq Per unit area unless the coil were also cut into two parts, into which the pieces of wire were rigidly fixed, so that part of the total tractive force is due to the mutual attraction of the two coils. | * H. Nagaoka, Wied. Ann, lili. p. 487 (1894). + Phil. Mag. Oct. 1895. } See du Bois, Magnetische Kreise, § 104; E. T. Jones, Wied. Ann. lvii. p. 271 (1896); Phil. Mag. March 1896; Wiedemann’s Electr. iii. p. 640. of Magnetic Stress in Magnetostriction. 459 Further, as has been already pointed out by Chree*, the longitudinal stress in iron is, according to both theories, a DPIAZIALLO D ------ PAVIIAA OIVA2 tension, not a pressure ; its effect is therefore to lengthen, not to shorten a piece of soft iron along the lines of force. * ‘Nature,’ Jan, 23, 1896, lett fey] 2s ap et rH 7) ac) S =) BS La ~ = S dp) 5) q ° ar E ea Ss = Si S c i) ie} ei Zi es 460 of Magnetic Stress in Magnetostriction. AGL 2 This use of the expression es , incorrect according to existing theories, appears to have been first made by 8. Bidwell *. | As to the stresses inside the iron, Maxwell’s theory He — combined with BH O71 a longitudinal tension ae along the lines of force ;” while Kirchhoff’s theory gives a hydrostatic pressure (Art. 642) gives “a hydrostatic pressure ee Pe | _xl bela Sa dby 2 dT combined with a tension Fa | es Sen: 8 ae Gs FE {+K+>}H mien os along the lines of force. Other systems of stresses in an isotropic elastic medium, which are equivalent to gravitational and electrostatic forces in certain cases, are discussed by Chreet+, and shown to be essentially different from that given by Maxwell (Art. 105). So far there does not appear to be sufficient experimental evidence to enable one to decide between these theories. Calculating the strain of an anchor-ring according to Kirch- hoff’s theory, we easily find that | Bho) H i by. 4a P38) eee _1b Tes sie n denoting the rigidity. As the principal factor K’ can be found from the measure- ment of effect of pressure on magnetization, the easiest method for making the crucial test would be to try experiments on an anchor-ring. Moreover, it is worth while to notice that the volume-change would in this case amount to the order 10~°. in iron and to—10-*. v in nickel, calculating the value of K! from the experiments of Bidwell on rings of these two metals. In conclusion, we would express our thanks to Dr. H. du Bois, at whose suggestion the preparation of this com- munication was undertaken. B 2 ene March 25, 1896. * Phil. Trans. clxxix. p. 217 (1888). é + Proc. Edin. Math. Soc. xi. p. 107 (1892-93). [) 62: L. Notices respecting New Books. Index of Spectra. Appendia G. By W.Marsuatn Warts, D.Sc., FI.C. Manchester: Abel Heywood and Son, 1896. 7 present Appendix to Dr. Watts’s ‘Index of Spectra’ brings the record of spectroscopic work down to the present time, and contains results of observations published within the past three years. It opens with Rowland’s table of standard wave-lengths, which is followed by an account of the researches of Eder and Valenta. These include the spark-spectra of sodium, potassium, and cadmium, and the line and band spectra of mercury. The oxyhydrogen-flame spectra of several metals and oxides, observed by Hartley, are next tabulated, and the record is brought to a close with an account of the recent work of Runge and Paschen on helium and par-helium, the two constituents of cleveite gas.—J. L. H. LI. Intelligence and Miscellaneous Articles. ON AN ELECTROCHEMICAL ACTION OF THE RONTGEN RAYS ON SILVER BROMIDE. BY PROF. DR. FRANZ STREINITZ. “Me Rontgen we are indebted for his great discovery of the property of the x-rays of exciting fluorescence and producing chemical reductions on a photographic plate. According to his previous experiments, these properties are the only ones which the rays have in common with those of light. Now light alters not only the electromotive deportment, but also the conductivity of the silver haloids. The proofs of this were furnished by Becquerel and Svante Arrhenius. It can therefore scarcely be doubted that electrochemical changes will be produced by the Rontgen rays; of course it is a different question whether they will be accessible to observation. Experiments were made in both directions. In order to establish the fact of a change in the conductivity, a method used by Arrhenius (Wiener Berichte, vol. xcvi. p. 831, 1887) was adopted. On a glass tube a silver wire was wound bifilar, and then coated with ammoniacal solution of silver chloride. After the ammonia and water had been evaporated, the glass tube was then placed in a light-tight box, out of which the ends of the wire projected. These ends were connected with a source of electricity and a very sensitive galvanometer (Thomson- Carpentier). The deflexion in the galvanometer showed variations when discharges were passed through a Hittorf’s tube near to the box. These, however, were manifestly due to inductive actions on the galvanometer circuit. For when the induced circuit was open, an increase in the deflexion could not with certainty be established—as ought to be the case, since there was an increase of the conducting power—in comparison with the deflexion which was obtained before the discharge was set up. Experiments on the influence on electromotive behaviour were attended with better success. A square platinum-foil, 2 cm. in the side, was coated electrolytically with an exceedingly thin layer of Intelligence and Miscellaneous Articles. 463 silver bromide. Combined in dilute potassium-bromide solutions with a standard electrode, the electrode in question showed sensitiveness to light. This is easily proved with the help of a quadrant electrometer (Luggin, Ostwald’s Zeitschrift fur phys. Chemie, xiv. p. 387, 1894). A candle placed at a distance of 25 em. from the electrode produced in half an hour a diminution of 0-022 Y. in the electromotive force of the combination Zn/Zn SO, aq+K, SO, aq+BrK aq+ Br Ag/Pt. A‘ the same time it is to be remembered that the light only struck one side of the platinum-foil, while the other, which was also sensitized, remained dark. If now a carefully enclosed discharge- tube through which induction-sparks passed was substituted for the candle, a diminution in the electromotive force could also be observed. With a small induction-coil the change amounted to 0-017 volt in the course of 45 minutes, and in another experi- ment with a larger induction-coil to 0:019 in 40 minutes. By a corresponding increase in the delicacy of the method, the electrochemical deportment of Rontgen rays may possibly furnish a more convenient method of investigating them than that with the help of photography.— Wtener Berichte, Feb. 6, 1896. TRIANGULATION BY MEANS OF THE CATHODE PHOTOGRAPHY. BY JOHN TROWBRIDGE, Photography by means of the Rontgen rays seems already to be of great importance in examining certain portions of the human body to determine the presence of metallic bodies, calcareous formations, and fragments of glass. The shadow pictures as they are taken at present, however, do not give the approximate position of the shots, for instance, embedded in the flesh. They indicate only the line in which they are situated. It occurred to me that the principles of triangulation could be applied with success to determine more exactly the position of the metallic particles. I was led to this conclusion by considering Rumford’s photometer. This instrument, it is well known, consists merely of a vertical rod placed opposite a suitable screen of white paper. The two lights, the intensities of which are to be compared, are placed in a fixed position, and throw two shadows of the rod on the screen. From a measurement of the positions of the lights when shadows of equal intensity are thrown on the screen, an extinction of the brightness of the lights can be obtained. More- over, by measuring the distance between the shadows, and by drawing lines from them to the lights, the position of the rod throwing the shadows can be determined. This position is evidently at the intersection of these lines. I have used two Crookes’ tubes with two terminals making an angle with each other, and have employed a to-and-fro excitation by means of a Tesla coil. A suitable screen of glass shielded the sensitive plate first from one cathode and then from the other. From the distance between the shadow pictures of a shot, for instance, on the back of the hand and from the position of the 464 Intelligence and Miscellaneous Articles. | terminals, the height of the shot above the sensitive plate could be estimated. It seems to me that this method promises to be of importance in the surgery of the extremities of the body; for the question whether to make an incision from the palm of a child’s hand or from the back of the hand is an important one. Stereo- scopic pictures can also be obtained. The use of a Tesla coil in obtaining shadow pictures is advan- tageous in certain respects, for by changing the size of the spark- gap in the primary circuit of the Tesla coil one has a great range of electrical energy at command. This range can be still further increased by putting the spark-gap in a magnetic field. I have taken such pictures in less than a minute, showing the bones in the fingers. The tubes were, at first, destroyed by disruptive sparks over the surface of the tube which apparently penetrated the glass between the platinum terminals and the glass. I have lately discovered, however, that if the terminals of the tube are placed in a vessel filled with paraffin oil, and if the oil is kept cool by an outside vessel filled with snow or ice, the entire energy developed by the Tesla coil can be employed, and the tubes are not destroyed. I have tried wooden lenses, both double convex and double concave, in order to see whether the rays travel slower or faster in wood than in air, but my results are negative. A copper ring placed on a double convex lens of wood of approximately six inches focus, and one also on a concave lens of the same radius as the surfaces of the double convex lens, gave shadow pictures of the ring which were of the same size and character as those of an equal copper ring placed in air at the same distance from the sensitive plate. sh We naturally turn to Maxwell’s great treatise on Electricity and Magnetism, to see if a hint of this new phenomenon cannot be found there: for I believe there is no manifestation of electro- magnetism since the death of Maxwell which has not been predicted or treated by him in one form or another in his remarkable book. In section 792, vol. ii. of the treatise on Electricity and Magnetism, he says :—‘‘ Hence the combined effect of the electrostatic and the electrokinetic stresses 13 a pressure equal to 2p in the direction of the propagation of the wave. Now 2 also expresses the whole energy in unit of volume. Hence in a medium in which waves are propagated there is a pressure in the direction normal to the waves, and numerically equal to the energy in unit of volume. Thus, if in strong sunlight the energy of the light which falls on one square foot is 83°4 foot-pounds per - second, the mean energy in one cubic foot of sunlight is about 6-0000000882 of a foot-pound, and the mean pressure on a square foot is 0°0000000882 of a pound weight. S*e. Note.—With regard to the Avenarius, Thomson, and Tait expressions, it may be remarked that they are not only mutually equivalent, but that if t, or rt, becomes 0° C. they reduce at once to the ordinary parabolic form of two terms : Sie =at+bt. They are all, therefore, forms which must apply if the latter Thermo-electric Interpolation Formule. 467 purely empirical expression for the same temperature ranges applies, and with the same closeness, so that it is unnecessary to test more than one of the first four expressions against any one set of data. Also the fact that the Avenarius and Tait equations approximately conform to the observed data does not necessarily in any material degree strengthen the hypo- theses which are adduced to show that these equations are a natural expression of the law. Without attempting here a further analysis of the com- ponents making up the resultant E.M.F. =?e, which is the measured H.M.F’. of the thermo-couple, the proposed interpo- lation formule will be merely developed and applied. It may, however, be suggested in passing, that there seems to the writer to be little hope of arriving at a close approxima- tion to the natural law except through an expression which shall contain separate terms representing the temperature function of the component arising at the contact of the dissimilar metals, and that arising from the inequality of temperature of the ends of each (homogeneous) element (Thomson E.M.F.). The parabolic and Avenarius formule would comply in part with this requirement on the supposi- tion that the E.M.F. at contact varied as the first power, and the Thomson E.M.F. in both wires as the square of the temperature. And looked at from that point of view, the neutral point would seem to have an explanation materially different from that usually accorded to it. The Proposed Formule. Exponential Equation.—The significance of this proposed expression may be thus stated. Suppose the cold junction of the couple be maintained at the absolute zero of temperature, 7=0°, and its E.M.F. to be consequently zero. Let the other (hot) junction be at any temperature 7,° absolute. The pro- prosed equation is based on the assumption that the total H.M.F of the couple would then be representable by /=mt", where m and n are numerical constants. If then the cold junction were raised to any temperature 7,°, there would be introduced an opposing E.M.F’. e”, which would be expressible by e'=mr”. The resultant E.M.F Se would then be e'—e", and there- fore expressible by Somat =i OP a (6) 2K 2 468 Prof. Silas W. Holman on If in any instance, as is frequently the case in measurements, the temperature of the cold junction is maintained constant while that of the hot junction varies, then m7” becomes a constant, and it will be convenient to denote this constant by B when t=273° abs. =0° C. So that for this special case where the cold junction is at 0°C, and the hot junction at t°C., we have | Sje=mr"—B. sl feneneag ; “ . (7) - This expression is not advanced as a possible natural form ‘of the function f(A, c). It is essentially empirical, and is not designed to account separately for the several distinct com- ponents entering into =e. The fact that it closely fits the experimental data arises chiefly from the well known adapta- bility of the exponential equation to represent limited portions of curved lines. The equation also leads to certain inferences which appear inconsistent with the known thermo-electric laws, and fails to explain some known phenomena. _ The evaluation of the constants m,n, and fis unfortunately attended by considerable labour. No application of the method of least squares readily presents itself, but by a method of successive approximations the values can be obtained with any desired degree of exactitude. Only two measured pairs of values of Soe and ¢ are necessary for this approximation method, the third required pair being furnished by %)e=0 and t=0; although, of course, by the employment of three pairs of values well distributed in the data, a more closely fitting equation might frequently be obtained. The calibra- tion of a thermo-couple for pyrometric work can thus be effected by the employment of but two known temperatures, and this, on account of the uncertainty of our knowledge of high melting-points, is of great importance in high tempera- ture work. - Let t;=0° C., /, and ¢” be the selected observed tempera- tures from which to compute the constant, so that r,=273°, 7! =t! +273°, c!=t4273° abs. And let Sf e=0, She, Bo e be the corresponding observed H.M.F’s. of the couple. Then, by substituting these in equation (7), and combining the three expressions, or their logarithms, we easily deduce t! 0€ Ss (Su ee Thermo-electric Interpolation Formule. 469 log (85'e+8)—log (Set 8). log 7" —log t! : >) e+8 oe+B = 10 st. 3! Gh os By means of these the numerical values of the constants may be calculated from those of 7’, 7’, S$ e, &z., as follows :— 1. Assume asa first approximation some value of n, sayn=1, unless some better approximation is in some way suggested, Substituting this value in (8), compute the corresponding value of 8. 2. Using this as a first approximation, substitute it in (9) and compute the corresponding value of n. 3. Using this value as a second approximation to n, insert it in (8), and compute a second approximation to 8. 4, With this compute a third approximation to n, and so continue until consistent values of 8 and n are found to the desired number of figures. Then compute m by (10). The rate of convergence is not rapid, but after one or two approximations have been made an inspection of the rate will enable the computer to estimate values of 2 which will be nearer than the preceding approximation, and thus hasten the computation. Where an equation is to be computed to best represent a progressive series of observed values of ¢ and % e, this method is of course open to some objections, since it incorporates in the constants the accidental errors of the selected observa- tions from which the constants are deduced. This difficulty can be sufficiently overcome by computing residuals between the equation and the data, and amending the equations: if necessary to give them a better distribution. Logarithmic Formula.—A very simple expression for inter- polation i is of the general form Yoe= mt’, when m and n are constants. This serves fairly well fe a short range, ¢/’—t’, when t’—0° is not less than one third of —_ t’. The convenience of the expression arises from two facts : first, that its two constants are very easily evaluated either by computation or graphically from the logarithmic expression pernence the name) _ log Ste=nlogt+logm. -second, that its logarithmic plot is a sumaight line, since “this 470 Prof. Silas W. Holman on expression is the equation to a straight line if we regard log Se and log ¢ as the variables. If, therefore, a series of values of e and ¢ are known for a given couple, points obtained by plotting log ¢ as abscissas and log > eas ordinates should lie along a straight line. Thus a couple may be com- pletely “calibrated ” for all temperatures by measuring > e and ¢ for any two values of ¢ (suitably disposed). The con- stants m and n may be computed, or a plot of log > eand log¢ may be made, and a straight line be drawn through them. Graphical interpolation on this line will then of course yield the values of log ¢ and hence of t corresponding to observed values of } e, and vice versa, and, if desired, the constants mand n. The expression for ¢ as a function of Ze is of course : t NON ' é\- t=m' (Sie)", or t= Zoe) (Xo ) y) ™m This formula is well adapted to pyrometric work not of the very highest grade of accuracy, and has been advantageously employed in connexion with the Le Chatelier thermo-electric pyrometer in a method to be described in a later article. Test of Formule. This will be made by applying the several formule to the experimental data of Barus, Holborn and Wien, Chassagny and Abraham, and Noll. These investigators employed modern methods of thermometry and of electrical measure- ment. ‘Temperatures are either made in or reduced to the scale of the hydrogen (C. & A.), or of the air thermometer (B., H. & W., N.). Constants for the formule will be deduced, and the residuals or deviations of the data from the equations (7.e. 6=data—equation) will be computed for the observed points. Jor discussion these deviations will be e e 6 e e expressed in percentages, viz. 100-, rather than in micro- € volts or degrees. This is preferable because the process of measurement of the E.M.F., and to some extent at least of the temperature, is such as to yield results of a nearly constant fractional or percentage precision at all temperatures rather than of a constant number of microvolts or degrees. Thus by comparing percentages we eliminate a complication arising otherwise from the increasing value of 6 as ¢ increases. Incidentally there are also other well recognized advantages frequently attending the comparison of percentages rather than of.absolute quantities. The Barus Data,—Taking the data in the order of priority, Thermo-electric Interpolation Formule. A471 those of Barus-will be first employed. The measurements to be used consist of very elaborate and painstaking direct com- parisons of several 20 per cent. irido-platinum thermo-couples with several porcelain bulb air-thermometers used under the constant-pressure method. Quotations of, or rather interpolations in, his original data* are given by Barus t later, as a basis from w hich to deduce constants for his proposed equation eae a1 Se ph te. Barus’s numerical values for the constants are: €) =45680 microvolts. 7 he A610 a O=1106. 10-4 P'= 2-849 a CO ht AO These constitute his “equation 3,” for which e) corresponds to 20°C. The data and the deviations which I have computed for it, viz. 6=data—equation, are given in Table I. The last column gives the deviations expressed in percentages, MZ. 1008, where H=e+e+1880. This value of EH is adopted to make the percentages comparable with those in subsequent discussions. The number 1880 is 1730+ 150, which are the values of e and =*° e of the next two pages. TABLE I, Barus’s American Journal of Science Data. | | p e+e,mv. e+e, computed | 16 1005 : ae observed. from “ Equ. 3.” mv. eee oe — 150 100 +680 653 | $27 +111 200 1650 1657 —7 —0°20 300 | 2760 2788 — 28 —0-60 400 3950 3994 —d —0-80 600 6560 6551 +9 +0-11 800 9310 9273 +37 +0°34 1000 12200 12140 +60 +0°43 * Barus, C., U.S. Geol. Sury. Bull. no. 54 (1889); Phil. Mag. xxxiv. p. £ (1892). = + Amer, Jour. Sci. xlviii. p. 882 (1894). See also xlvii. p. 366 (1894), 472 Prof. Silas W: Holman on The lines AB and CD on the diagram (page 483), constructed with percentage deviations as ordinates and temperature as abscissas, show clearly that the deviations are systematic. Upon inspection of this plot it appears that the data may be separated into two groups, one including 0°-300°, the other 400°-1000°, which appear to have entirely distinct forms of systematic error. This division corresponds to two distinct groups of data, one extending from 0° to 300°, the other including the second group and extending from 350° to 1075°. The latter were given in the Bulletin as the final results of the high temperature comparisons of the irido- platinum couple with porcelain bulb air thermometers. The detailed statement of the 0°-300° comparison I have not seen. Although the discrepancy between the two sets of systematic deviations is not extremely large, yet it has seemed to me that it is beyond the limits of concordance in the higher temperature work, and that it would be better for the present purpose to deal solely with the 350°-1075° data. Two points regarding Barus’s work should be noticed: one the strikingly high degree of concordance between individual observations even with different thermometer bulbs and different thermo- couples ; the other the remark in which Barus notes a possi- bility of being able still further to reduce the “ stem error entering into the result, which so far as I am aware has not yet been done. The high temperature air-thermometer comparisons (Bul- letin, Series I, IIL., III., IV., and V.) of Barus are so numerous (108) ‘and so distributed that the labour of utilizing them simply for deducing constants and testing an equation would be excessive. Also they are too concordant to permit interpolation on.a-direct. plot without a sacrifice_of some of their precision. For the purposes of discussion, therefore, I averaged them in nine groups. The first group contained all where the E.M.F. lay between 3000 and 4000 microvolts : the second group between 4000 and 5000 mv.; and so on by steps of 1000 microvolts, except that the seventh group covered 2000 mv. from 9000 to 11000. These groups were not exactly equal in number of observations, and therefore in weight, nor is the arithmetical average a strictly legitimate value where the function is not linear ; but, as easily seen by inspection of the originals, the errors thus introduced are negligible. In Table II. columns 1 and 2 give the direct values of the averages. Column 8 reduces 2% e to > See by adding 150 mierovolts, the value of Xoo e 2 being elsewhere given by Barus. as —150 microvolts, Thermo-electric Interpolation Formule. 473 TaBueE II. Barus’s Air-Thermometer Comparisons, Series I.-V. | | Avenarius, | Exponential. Logarithmic. t i's. Sree Soe as RE, AER SRR ICES 1 0°. | 200 | 206. | 3 | Per cent. | 3 Per cent. ‘Per cent. | | | } ’ 6 ’ rs j > H eae: =100- ‘Da. — Eq. =100- Da.—Eq. =1008 | | ee ee | ee | | IC). mv. my. my. mv. my. 0-0 | (—150) 0 0 0-0 +23 +1:3 3785 | 3679 3829 —84 —4-0 —66 —1:2 —33 — 0°60 440°3 | 4508 4658 +18 +0:28 +18 +0:28 +30 +0°47 522:0 | 5486 5636 — —0:07 —25 — 0-34 — 36 —0 50 588°4 | 6404 6554 +70 +11 +33 +0:40 +9 +012 672°1 | 7550 7700 | +110 +1°5 +60 +064 | +26 +0:28 745°6 | 8530 8680 +82 +092 | +26 +0°25 —9 —0:10 840-1 | 9898 | 10048 | +101 +1-0 +49 +041} +26 +0:22 946°6 | 11396 | 11546 +9 | +007 | —19 —014| -13 —0:10 1019-7 | 12475 | 12625 —45 —032 | —45 —0°32 | —10 —0:07 Average percentage deviations ...... 093 | 0:53 | The Avenarius equation applied to these data yields Xo e=9'104t + 3-249.10-8 ¢? microvolts. Range 350° to 1075° C. Computing from this equation values of X$e for the successive values of ¢ in column 1 and subtracting them from the data in column 3 gives the deviations between data and equation. These are expressed in microvolts in column 4, and in percentages in column 5, the percentage being reckoned in terms of e, as deduced by the exponential formula. Objections may be felt to this use of e) (here as throughout the subsequent tables) as a basis, since e, involves e which is an extrapolated value, certainly not exact, and possibly wide of the truth. Such a criticism is valid, but inasmuch as the values of ¢ employed are nearly equal, and as the percentage deviations are used merely for purposes of expressing relative accuracy, the possible error involved is nearly annulled. Hence, although it would be better to compute 8 ¢, and express this as a percentage of the absolute temperature 7, the added ‘labour did not seem justified by the small gain, 474 Prof. Silas W. Holman on The exponential equation applied to the Barus data yields S56 e=0°7691 7° — 1730, or e,=0°7691 7°", and B=1730 my. Range of data 350° to 1075° C. [N.B. This equation was deduced with the value 0°C.= 273°°7 absolute, whereas in all subsequent tables 0°C.=273°0 absolute is employed as a more probable value. The numerical values of the constants are therefore subject to a slight modi- fication, but as for the present purpose we are concerned only with 6, which would not be sensibly changed, the recomputation i is not worth while. | Columns 6 and 7, Table II., give 6 and its percentage value for the exponential equation. The Barus Equation.—The excessive labour involved in the evaluation of the constants P, Q, P’, and Q’ of Barus’s proposed equation detracts so seriously from its usefulness that I have also allowed it to deter me from computing them ~ for the above tabulated values. The comparison of the values of 6 for his “ equation 3,” and for an approximate exponential of my own based on the same data, is, however, decidedly in favour of the latter. The logarithmic equation applied to the Barus data yields Soe=2°665 1, or its equivalent, log Soe=1'220 log t+ 0°42570. The deviations are given in the last two columns of Table II. Holborn and Wien Data.—This important comparison * of the rhodo-platinum thermo-couple with the porcelain bulb air thermometer up to high temperatures was performed under the auspices of the Reichsanstalt at Berlin, and appears to be on the whole the most important and reliable contribu- tion to this subject in recent years. The experimental work was evidently conducted with great care, and although not showing the concordance of results, nor the multiplication of observations of Barus’s work, yet in respect to stem- exposure correction, to exposure of the thermal junction, and to direct measurement of the coefficient of expansion of the bulb, it is probably more free from systematic error. It is to be regretted that the results were not more thoroughly discussed, and that neither a chemical analysis nor even a * Holborn and Wien., Zeit. f. Instk. xii. pp. 257, 296 (1892); also in full in Wied. Ann, xlvii. p. 107 (1892). Thermo-electric Interpolation Formule. 475 statement was given to indicate the reliability of the stated percentage composition of the various alloys used. For when closely examined, the data seem to indicate a definite relation between tbe composition and the H.M.F’., as was shown by a relation discovered between the constants in my exponential equations for the various alloys. The deviations were only such as might be attributed to uncertainty of composition, but as no measure of the latter was given, a statement of the relations and interesting inferences from, them is not warranted. It is also unfortunate that an analysis, or at least a definite statement of the percentage purity, was not given for the gold, copper, and silver whose melting-points were observed. The assertion that the gold showed on qualitative analysis only a trace (“Spur”) of copper, and the silver a “trace”’ of iron, is hardly definite. The value of the whole work would have been enhanced by these additions far more than in proportion to the comparatively small labour demanded by them, and such completeness is naturally to be expected in work emanating from this source. It is to be hoped that a continuation of this research is in progress, and that additional high melting-points may be measured. Table III., columns 1 and 2, quotes the interpolated mean values of several comparisons expressed in international microyolts and degrees centigrade. With regard to these data it should be stated that below about 400° they were not supposed to be of as high accuracy as above that point. Also, that owing to unavoidable circumstances the data below 300° were obtained with only a single air-thermometer bulb, and similarly those above about 1300° with one bulb only, but a different one, while the data intermediate between 400° and 1300° are the mean of observations with the two bulbs. This fact may partially account for the erratic character of the residuals above 1300°, where the deviations are so great and so distributed (see diagram, page 483) as to render these observations of very little service. Direct comparison with the air-thermometer was made with one 10 per cent rhodo- platinum couple “ A” only. The parabolic formula applied to these by Holborn and Wien, when corrected as to decimal points *, is t= 1:376.10-"(S$e) —4°841.107°(She)? + 1°378.10-1( 34 e)8, Range— 80° ©. to +1445° C, The residuals are given in Table III., columns 3 and 4. * The equation at both references, and stated to be in microyolts and degrees, is erroneously printed as “t= (e) =13'76e—0:004841e?-+.0-000001878e°,” 476 Prof. Silas W. Holman on - TABLE III, = Sa tcase 1 Holborn and Wien.—Air-Thermometer Comparisons, Alloy A. | H. and W. Eq. | Avenarius. Exponential. Logarithmic, | | 10 Se PY 7) 6 ) “| my, | =Data |Per Cent.) —Data |Per Cent.. —Data |Per Cent.) —pata |Per Cent. —Eq. | =100° | —Ea- | =100°| —Eq- | =100°| —Ea. | 100% my. e mv. e mv. e my. e — 80) —361 —_ = _ i at = 0 0 0 0 0 0 0 0 0 +82) +500; —84 | —46 —107 | —51 —69 | —36 +40 | +2:20 154; 1000} —147 | —61 —166 | —72 —122 | —48 +11 | +0°50 220) 1500} —135 | —5-0 —199 | -—71 —140 | —47 —27 | —1:00 273) 2000| —150 | —45 —142 | —43 —85 | —26 +16 | +0°50 329} 2500| —1380 | —36 —124 | -—33 —73 | —19 +11 | +0°30 379] 3000| —60 | —1-4 —66 | —1°5 —24 | —0°57 +45 | +1:00 431) 3500| —380 | —060 —41 | —0°90 —6 | —012 +45 -| +0:90 482} 4000 0 0-00 —14 | —0:22 +8 | +015 +41 | +0°80 533} 4500] +10 | +0:17 —1 0 +9 | 40:15 +27 | +0°50 584) 5000 0 0:00 0 0 —2 | —0:03 +1 | +001 633) 5500 ) 0:00 +9 | +013 —4 | —006 —13 | —0°20 680} 6000} +10 | +011 +28 | +0°38 +5 | +0:07 --15 | —0°20 725) 6500} +30 | +0°40 +58 | +0°74 +26 | +0:33 —1 | —001 774; 7000} —10 | —012 +35 | +0°42 —5 | —0°06 —39 | —047 816] 7500} +20 | +0:22 | +78 | +090 | +383 | +0°37 = 6 e010 862} 8000 0 0:00 +69 | +0°74 +19 | +0:20 —24 | —0:26 906) 8500} —20 | —0:20 +72 | +0°74 +19 | +0:20 —25 | —025 952) 9000} —55 | —0:55 +44 | +0°43 —10 | —0:10 —53 | —052 996) 9500} —88 | —0-80 +29 | +026 —24 | —0-22 —67 -| —0°60 1038) 10000} —88 | —0:40 +29 | +0°25 —20 | —0:18 —57 | —0°50 1080} 10500} —100 | —0°85 422 | +020 —23 | —0:20 —54 | —043 1120) 11000] —100 | —0-80 +31 | +0:25 —7 | —006 —22 | —019 1163) 11500} —140 | —1:10 —6 | —0:05 —33 | —0:26 —51. | —0-40 1200) 12000} —96 | —0:74 +26 | +0-20 +9 | +0:07 ee) SE 1241} 12500} —96 | —0:70 0 0 —3 | —0:03 —8 | —0:06 1273] 13000 0 0-00 +84 | +0°60 +94 | +067 | +111 | +0°80 13:1) 13500} +86 | +0:24 | +84 | +057 | +110 | +080 | +140 | +0:90 1354| 14000] +24 | —017 | +10 | +007 | +58 | +038 | +107 | +070 140z/ 14500} —60 | —(-40 | —141 | —0-90 —65 |} —0-41 +2 | +001 144515000] —72 | —045 | —2381 | —140 | —128 | —0'80 —38 | —0:23 a.d.for Oto 1445. 1:12 1:15 O77 eed a. d. for 481 to 1445. 0°39 0:43 0:25 - 0:38 a. d. for 431 to 1241. 0°43 0°36 015 0°34 The Avenarius Formula applied to the Holborn and Wien data with constants deduced from ¢=584° and 1273° becomes yoe=(t—to) {72188 + 0:0022994( Wem: or = 7°2188¢+ 2°2994.10-* 2’. Range 0° to 1445° C, Thermo-electric Interpolation Formule. 477. The deviations in microvolts and percentages from this equation are given in columns 5 and 6, ‘Table III. _ The exponential equation fitting these data most closely, and coinciding with them at nearly the same points as the others, viz. at about 584° and 1250°, is 3he=0°57674 71°" —1310, or e=0°57674 7377, 8= 13810. Range 0° to 1445°C. The deviations in microvolts and percentages are in columns 7 and 8, Table III. The logarithmic equation applied to the Holborn and Wien data on A yields So e= 21682 1, or log >) e=1:2156 log ¢+0°36610. The deviations are given in the last two columns of Table III. | Holborn and Wien not only compared the ten per cent. rhodo-platinum couple A directly with the air thermometer, -but compared with A seven other couples in which one element was platinum, and the other a rhodo-platinum alloy, the percentage of rhodium being stated respectively as, for C, and C,, 10 per cent. (these two I have combined under C), D, 9 per cent., H, 11 per cent., F, 20 per cent., G, 30 per - cent., H, 40 per cent. For the present purpose I have com- bined these data, which were differences of E.M.F. between C and A, D and A, &c., with the corresponding E.M.F. of A, and thence have deduced the exponential equations for each Tass IV. | SL etnpane --, Nominal k Expon. Eq. Coustants. | Se | aa al Rhodium. mM. Nn. B : mv. she D Baris 9 13671 1-250 1517 Se a 10 0°95596 1-310 1485 Bees 11 0°81734 1°336 1469 As eon. 10 0:57689 1377 1305 Mane sce 20 0:22865 1522 FGh oe Gt 30 0065990 1-708 956 aes eh 40 0:063034 1-720 977 478 of the alloys. these alloys from the exponential equation (data—equation), and Table IV. shows the values of m, n, and £8 for those equations. Prof. Silas W. Holman on TABLE V. Holborn and Wien.—Comparison of Alloys. Table V. gives the percentage deviations of t. ee 154 273 379 482 584 680 Wes 862 952 1038 1120 1200 1273 1354 1445 a. d. 400-1200 a. d. 400-1445 0°52 —4:8 26 ~0:57 40°15 — 0:03 +0:07 —0:06 +.0:20 —0-10 —0:18 —0-06 40:07 +067 40:38 —0°80 O15 0:25 Direct from | Air Th. C E. —40 —27 | —22 —0°80 | —0-60 —0-:03 0 +0:19 | +0:08 +013 | +0°18 —0:08 | —0:02 +0:20 | +0°20 0 —O1l —010 | —021 —0:09 | —0-02 0 +0:10 +070 | +0:80 +060 | +0 67 —0°38 | —0°50 0:09 0-10 0:21 0:24 Ns | ~2°3 pore — 0°60 +013 +0712 —0'12 +0:09 —0-15 —0:27 +0-10 0 +0°80 +051 012° (0-24) | l G. | —5:0 —3°5 —0-60 +0°22 +0:30 —0-16 —()-42 40°15 40:09 +0:04 40-01 +004 40:43 +0:30 —9:90 0:16 0:23 H. —4:4 —2°3 —0°25 +0:46 —0:03 — 0:26 — 0-46 = (at — 0:24 —014 +0-22 0 +1:00 +1:00 —0-40 0-21 0:36 Average. Chassagny and Abraham Data*.—The apparently very careful measurements of these observers cover a range of 0° to 100° CO. with observations at 25°, 50°, and 75° only. The range is too short and the intervals are too great to render the work of much service in testing a general formula, but if (1892), eccececces eoecesccos 100 = 9 é. TABLE VI. 15 OC 1093°3 8951 1123:0 1685:1 ee | * Chassagny et Abraham, Ann. de Chim. et de Phys. xxvii. p. 355 Thermo-electric Interpolation Formule. 479 its accuracy is as high as about 0°-01, as it appears to be, this - in part offsets the disadvantage. Wessaeements of Soe and ¢ were made with four thermo-couples, with the results shown in Table VI. (international microvolts and degrees centi- grade on hydrogen scale). Lhe Avenarius equation was applied to these data by Chas- sagny and Abraham in the form >} e=at +bt?. They evaluated the constants from the 50° and 100° data. With these they computed the temperatures which the equa- tion would yield by insertion of the observed values =>” ¢ and 3% e, These values are given in Table VII., columns 2 and 3. The exponential equanien applied to these data for Fe—Pt becomes So ¢=105:096 2°" — 65253 [Range 0° to 100° C.]. The values of ¢ corresponding to the observed values &6° é and >/°e are given in Table VII. It has not seemed for the present purpose worth while to make similar computations for the other couples, as they would not materially affect the inferences to be drawn. The logarithmic equation yields 6 = 19°2946 go . log 36 e=0:970595 log ¢+1:285436. The deviations are given in the Table. TaBLE VII. Avenarius. Exponential. Logarithmic. Couple. ) 100 d/e . 6 t. ot. t. ot. mv. | per cent. ~ my. Be-Cu 22.2... 24-88 40:12 : c Fe-Pt Rh...) 24-885} 0-115 He Agi cys. 24:87 0-13 Fe-Pt .... .| 24:87 0:13 | 2480 | +0:20) —2°6 |—0-037 | +0:52| —6°7 Fe-Cu ...... 7513 | —013 Fe-Pt Rh... 75:185} 0:185 TC Eoncince 75°1385| 0135 ; Be-Pt ...... 75135! 0°185| 75:15 | —0-15 | +2°5 | +0032 | —0-26) +4:3 | | 480 Prof. Silas W. Holman on ° The Noll Data.—A contribution of much permanent value to the data on thermo-electrics has recently been made by Noll*, who has measured 3} e and ¢t for thirty-two couples over a range in most cases of 0° to 218°C. The metals em- ployed (including carbon) were usually of a high and stated degree of purity, and consisted of eighteen different sub- stances, two of which were alloys (german silver and brass), and the remainder samples of different degrees of purity or hardness of the pure substances. The couples contained, as one element, for the most part, either copper or mercury. Temperatures were reduced to the air-thermometer scale. The Avenarius formula was applied to fourteen of the more important of them by Noll. The deviations are given in Table VIII. ) : TasueE VIII. Noll’s Data on Pure Metals. B Ay. Pct. Deviation. - Couple m n aL Avenarius. | Expon. Au-He ...... 4-6954.107? | 2:136 | 750-4 | +027 +017 Ag-He ...... 28637 .10-* || 22068 | 677-84 038 “O15. INGE ONe, fae. 8:-2333.107-! | 1-511 | 3950-2 0:30 0-17 (d= = 37617. 10-"! | 4-94 40°7 0:48 3:40) BrCl 2-4969.10~! | 1-366 | 581-1 | 0:14 0-13 Zn-Hg ...... 8-2890.107> | 2420 | 651-6 O15\,/) 20a PooCu 22. 1-7674.16~< | 1800 | 429-0 0-05 0:07 Gu, He... 4:6726 . 105 2/130 | 768-4 0:12 O11 [Fe-Hg ...... 1-:0913.107? | 0-7220 | 6264-2] Go-He 7 8:3205.1075 | 2166 | 1575-2 0:26 0:22 Pi=Ca. 2:1475.1075 | 2:266 | 711-1 0-08 012 Pt-Cne 1:1095.1075 | 2353 | 599-0 0-19 0:25 SnCu ee 4-2021.107* | 1667 | 482°8 0-21 009 - Mg-C(u ...... 2:0449.10—2 | 1-782 | 448-7 0-15 0-17 ieOn oo 7-5643.107? | 1:590 | 5653 0-11 0-12 G.s.-Cu...... 2:0454.107! | 1-684 | 2589-9 0:08 0:05 Average omitting Cd—Cu and Fe-Hg ............ +0:17 +014 The exponential equation I have applied to the same data, It has not seemed essential to reproduce here the entire series of data, and the deviations of both equations. They are therefore, presented in a somewhat more digested form. * Noll, Wied. Ann. iii. p. 874 (1804). Thermo-electric Interpolation Formule. A81 Table VIII. gives the constants for the exponential equation (those for the Avenarius may be found in Noll’s article), the mean deviations (=data— equation) for each series, and the mean percentage deviations (=100 6/e)._ (See remark as to use of e under “ Barus Data.”) Table IX. groups the per- centage deviations under their nearest values of ¢ for exhi- biting their systematic character. The fact that the experi- mental method brought the observations all very nearly to the respective temperatures ¢ given in the table renders this grouping possible. I have taken the liberty of correcting a few obvious numerical errors, and of dropping a very few values evidently containing a mistake. It may, perhaps, not be out of place here to caution those who would make use of Noll’s data to their full accuracy that his original, and not his interpolated, numbers should be resorted to. The approximate linear interpolation which he has employed is not as accurate as his experimental data demand. | ~The logarithmic equation applied to the Cu-Hg couple as typical of the Noll data yields | 3) ¢= 257434 417, one «: 7 ——--- Jog Bo e= 12250 log ¢+0°410665. — e The residuals to this expression are given in Table IX. Tasue IX. Avenarius Hquation.—Data minus Equation in Per Cent. 15°. | 57°, | 100°. | 138°. | 1819, | 198°. | 217°. ‘Au-He | —0:10 | —040 | 0 | +005 | +060 +0-90 0 | Ag-He | —0:13 | +0-20 Os 021 050% = 1:30 | 0 ‘Ni-Cu | —026 | —0-15 0 0 —0-22 | —0°31 | —117 Pee 2) |) 010 | 0 | 4-020 | +0-17)|.+035 | 0 Zn-He | ... | —008 O | +009 | +041 | +040 | 0 Pea | .. | —0-03 Oe eir | 019) — 0:04 |. 0 | Ou,-Hg| +002 | -0-16 0 | +001 | +0-15 | +0:38 |Co-Hg |... * Oo | +4042 | 0 | 56 Petal = 4-012) |), 0)»: | 0-06. |. +009. 4.021 peu ei SO | O18. |) @ +067 | —0-21 ee Ou) Vit 20208 + 0 0 +034 | +0:40 | +0:30 Me-Cu |} ..: | +011 0 9) +420:22.| 037 40-11}; 0 Weee cl go> 04G. |.) 0. | +018 10184). -1015.). 0 GeO 1, | = 001 Oo tC te Oi te... 0 | em | Average| —0°712 | —0:07 0 +009 | +005 | +0716 | —012 Phil. Mag. 8. 5. Vol. 41. No. 253. June 1896. 21 482 Prof. Silas W. Holman on Table 1X.—Continued. Exponential Equation—D ata minus Equation in Per Cent. L5°. N(O. 100°. 138°. 181°. 198°. AMIS? Au-Hg | +001 | —0°12 | —006 | —0:06 | +009 | +012 | —0:80 Ag-Hg | —018 | +0-22 0 +0:05 | —0:03 0 —0'50 Ni-Cu — 0:26 —0:16 0) +0:07 0:00 0 | —0°72 Br-Cu ae —0:06 | —0-01 | +012 | +0-20 | —0:26 —0:13 Zu-Hg & —0-30 | +002 | +014 | +010 | +0°65 | —0°04 Pb-Cu 5 Me —0:10 0 —0:25 | +0:04 0 0:00 Cu,-Hg| —0°19 | —0-27 | +001 ola —0-03 0 —0:25 Co-Hg oe --0°05 | +001 | +0-48 —001 safe — 1-00 Pt,—-Cu as —015 | +003 | —0:06 | +0:17 0 —0°31 Pt,-Cu By. —0°56 0 —010 | —0-16 | +0:70 0 Sn,-Cu ee —0°04 | +0°04 | —0:29 | +012 | +0-06 0 Mg-Cu an +0:18 0 +015 | —0°52 | +017 0 Al-Cu Ents +016 0 +0712 | —0:24 | 40:18 0 Gs-Oul 4 0 O71 001) 00s. ae 2. ORO Average} —0'16 | 40:08 | +001 | +0°03 | —0-02 | +014 | —0-27 Logarithmic Equation.— Data minus Equation in Per Cent. Ou. +2:3 [+10 | 0 [040 | 0 +050 | -+0:80 Discussion of the Deviations. Plots are given in the following diagram with temperatures as abscissas and percentage deviations between the data and the sundry equations as ordinates, 2. e. 100 6/e where 6=data— equation. Inspection will show that with one exception (viz. the logarithmic equation applied to the Barus data) these plots, whether the equation is the ordinary parabolic, the Avenarius, the Barus, the exponential, or the logarithmic, have the same general form, which may be imperfectly described as follows. If the equation be made to conform to the data at 0°C. and at two higher points, a and 0, then the deviation will be of the negative sign from 0 to a, positive from a to }, and negative above 6. The slight departures from this general form are clearly due either to accidental errors, or to failure to make the equation conform to the data at all three points, or at suitable ones. The evidence is therefore conclusive Thermo-electric Interpolation Formule. 483 that for all of the expressions the deviations are systematic and not purely “ accidental’ in character. One of two inferences is therefore warranted :— 1. That neither the parabolic, Avenarius, Barus, exponential, nor logarithmic equation is the natural expression of the function. BskUS, AM. J oe BARUS. AVEN.-—-— &£x?0N--—— LOGAR=- ~~~" I r t ! ORDINATES OF ALL PLOTS = nes ARE PERCENTAGE DEVIATIONS, 4 Ev ! ! HO QWIEN. 2 x Z BORN € Oa CHASSAGNY & ABRAHAM. AvVEN —-— EXPON. 2. Or that the scale of temperature to which the values of t are referred in the foregoing investigations departs from the 2b 2e 484. Prof. Silas W. Holman on normal scale by an amount and system roughly indicated by the above residual plots. ; ? The latter inference, suggested by Chassagny and Abraham in the interpretation of their results, does not seem to possess much weight, notwithstanding the urgent need of renewed elaborate experimental investigation of the relation between the hydrogen, air, and thermodynamic scales of temperature. As to the relative usefulness of the various expressions for — purposes of interpolation and extrapolation some further inspection is necessary. The Barus equation 3, line CD, . shows slightly smaller deviations on the plot than do the Avenarius and exponential, lines HE and FF. This, how- ~ ever, is due to the fact that the data against which 3 is tested are mean interpolated values, and hence have a sensibly less variable error than those against which the other equations are tested. An approximate exponential equation showed less deviations than 3 against the same data. There seems, therefore, to be no advantage in this equation sufficient to offset the difficulty of evaluation of its constants. Applied to the Barus data from 350° to 1250°, the ex- ponential equation shows deviations considerably less than one half as great as those of the Avenarius, while those of the logarithmic equation are so small as to lie far within the range of the variable errors, and they moreover show no clear evidence of systematic error between these limits of tempera- ture. For interpolation in the Barus data, therefore, the logarithmic equation ts far preferable, and must be conceded to be representative of the data. or extrapolation it is un- doubtedly better than the Avenarius, which (as would the exponential in less degree) would certainly give above 1000° extrapolated values of Xe too large, or of ¢ too small. The - advantage due to its simplicity is also to be noted. Applied to the Holborn and Wien data from 400° to 1450° the exponential equation shows (line K K) the same sort of superiority to both logarithmic (line LL) and Avenarius (line II) that the logarithmic shows to the others with the Barus data, but in a still more marked degree. Within the limits 450° to 1450°, in fact, the distribution of the residuals to the exponential is such as not to warrant of itself alone any inference of systematic departure, especially when the mean line M M from all the couples is considered. It will be noted as an important confirmation of both the exactness of the electrical measurements in the investigation and the applicability of the exponential formula through a considerable range of alloys (and therefore of values of m and n)- that this Thermo-electric Interpolation Formule. 485 mean line M M is almost identical in form with the line K K for alloy A. Relatively to the Holborn and Wien formula (line HH), the exponential possesses a similar advantage, with also the merit of greater simplicity of form. It may therefore be affirmed that for interpolation between 450° and 1450° in the H.and W. data the exponential equation as abundantly exact. For extrapolation above 1450° it would not be entirely safe, although presumably better than the others, since the departure between O° and 450°, and the similarity of the form to others, make a systematic Sapna sufficiently certain. Applied to the Chassagny and Abraham data, 0°-100°, and to the Noll data, 0°-218° (see diagram), the Ayenarius and exponential formule show about equal deviations, but with the advantage slightly on the side of the former. In the case of the Noll data, the line indicates that the systematic error is slightly greater for the exponential than for the Avenarius expression. The average deviations in Table [X., on the contrary, show that for each individual equation the concor- dance is greater for the exponential than the Avenarius. This discrepancy is due to the fact that, in order to eliminate local accidental errors, the equations (both Avenarius and expc- nential) are not all made to coincide with the data at the same temperatures, so that the process of averaging by which the data for the Noll plots is obtained is not numerically rigid. This does not, however, sensibly affect the general form of the curve. The greater ease of computation of the numerical constants of the Avenarius expression, and its applicability where both ¢ and ¢) change, ought not to be overlooked. For extrapolation the exponential would be safer, for the reason that it has been shown above that for long ranges its syste- ‘matic error is less. . The logarithmic equation fits the Noll data very badly, as shown by the deviation in Table IX. (not plotted), and also is much less close to the Chassagny and Abraham data than are the others. The general conclusion as to applicability, then, seems to be that, while the Avenarius expression may be equally good or better than the exponential for interpolation over short ranges, yet for interpolation over long ranges and for extra- polation above the observation linuts the eaponential is decidedly preferable. ‘The exponential form is also preterable to the remaining expressions with the exception noted. The logarithmic form, although closely applicable to the Barus data, is of more doubtful general value, yet on account 486 Prot. Silas W. Holman on of its great convenience it may find application in industrial pyrometry, as will be elsewhere indicated. Although failing below 300° or 400°, it may probably be applied to the irido- or rhodo-platinum couple between 400° and 1200° C. with a maximum error not exceeding about 5°. If extended to cover 400° to 2000° the error might rise to 15° or 20°. More in detail it may be briefly noted by way of summary :— That the logarithmic equation fits the Barus data between 400° and 1250° with scarcely sensible systematic error, and within the limits of variable errors of the data. That the exponential equation similarly fits the Holborn and Wien data within the limits 400° to 1445°. That when made to coincide with the data at about 450° and 1200° the systematic deviations of the exponential equa- tion from the Barus data, and of the logarithmic equation from the Holborn and Wien data, are in general of opposite sign and of roughly equal magnitude. Barus Melting and Boiling-Point Data. From the foregoing demonstration of its applicability, it seems proper to apply the logarithmic formula to the Barus thermo-electric data on melting-points*. Whether the extrapolation above 1000° by the logarithmic formula is entitled to any great weight may be questioned, . but there is no obvious reason why it is not more reliable than by any of the others. I have employed the equation given on page 474, which represents very closely Barus’s high temperature air-thermometer comparisons, calculating thence the temperatures ¢ corresponding to the values of }4e given by Barus for the various points, assuming Barus’s value 2%e=150 mv. The results are given in column 3 of Table X. Column 4 quotes the most reliable previous determinations of the same points by other observers. As to which of the two columns of results best represents Barus’s work, there can be little doubt from the above evidence that below 1000° it is the second, that is, the one computed from the logarithmic equation. These combine both his own air- thermometer and melting-point work. Above 1000° the logarithmic values are probably slightly too high. * Amer, Journ. Sci. xlviii. p. 832 (1894). Thermo-electric Interpolation Formule. 487 TABLE X. Barus Melting and Boiling Points. C ted | Co ted Syae 3. by iio Eq, Data by other Observers, O° ie) Mercury (B. Pt.) 307 359 356°76 | Callendar and Griffiths. LC SREP a 420 423 AI7‘57 ; - Sulphur (B. Pt.) 446 449 444-53 be Aluminium ...... 638 641 635 Le Chatelier. Selenium (B. Pt.) 694 697 Cadmium (B. Pt.) 782 782 Zine (B. Pt.)...... 929 926 930 Deville and Troost. SUEVED tensecorseuee Jc 986 985 968 Holborn and Wien. 954 Violle. 6) eee ae 1091 1090 1072 Holborn and Wien. 1035 Violle. @opper s-csasesa0-- 1096 1095 1082 Holborn and Wien. 1054 Violle. Bismuth, c5..ccanes 1435 1441 INvekel se tt. ces 1476 1485 1450 Carnelly and Williams. Palladium ......... 1585 1597 1500 Violle. PIG GMUMY fees sony 1757 1783 1775 Violle. Remark. Review of the laborious researches which have been devoted to the direct comparison of thermo-electric elements with the air thermometer, mainly for the purpose of advancing the art of pyrometry, has enforced the conviction that, at least for the immediate future, this end would be better served by accurate gas-thermometer measurements of melting-points of metals. Hach such determination made upon a reducible metal of known high purity under proper reproducible con- ditions fixes an enduring and reproducible reference-point, a pyrometric “bench mark.” And there are enough inex- pensive metals, together with a possible system of simple alloys, to give points of sufficient frequency. These would then afford a convenient means of obtaining accurately known high temperatures for purposes of study of all high temperature phenomena, and particularly for calibrating thermo-electric, electrical resistance, optical, or other secondary pyrometric interpolation apparatus,—for it must be remembered that all such apparatus is necessarily secondary, the gas thermometer being inevitably the primary. On the other hand, comparison with the air thermometer of ‘a thermo-couple, or of a resistance pyrometer, or the study of 488 Mr. W. B. Morton on the © any progressive thermal phenomenon, while it possibly may result in the eduction of a natural law, is very unlikely to lead to anything more than the establishment of an approxi- mate equation with constants characteristic only of the individual materials actually employed, and not transferable to other, although similar materials. Such results are obviously of a much more ephemeral character than the melting-point measurements. Hven when any pyrometer thus tested is applied to the establishment of melting-points, it must at best yield results inferior to direct application of the gas ther- mometer, except in cases where the latter is hampered by want of sufficient quantity of the metal to be experimented upon,—a condition which need only affect such costly sub- stances as gold and platinum. | | Stated broadly, the great need of the art of pyrometry is convenient methods of producing, or of recognizing when produced, a series of accurately known high temperatures. The analogous problem has been partially solved for ther- mometry at temperatures up to 300° C. by the investigation of boiling-points of certain chemically pure substances under controlled pressures. 5 _ Rogers Laboratory of Physics, Massachusetts Institute of Technology, Boston, September, 1895. LIL. Notes on the Electro-Magnetic Theory of Moving Charges. By W. B. Morton, B.A.* ie fe subject has been brought into prominence re- BE cently by the use which Mr. Larmor has made of moving electrons in his dynamical theory of the ether. The matter was investigated in 1881 by Prof. J. J. Thomsonf, who showed that a point. charge moving so slowly that the electric displacement it carries is not sensibly disturbed generates magnetic force like a current element according to Ampére’s rule ; and by Mr. Heaviside t, who investigated the matter more generally in 1889, and showed that in steady rectilinear motion at any speed less than that of light, the lines of displacement continue to be radial but are concen- trated towards the plane perpendicular to the direction of motion. The displacement at distance 7, in a direction * Communicated by the Physical Society: read March 27, 1896. + Phil. Mag. April 1881, July 1889; Recent Researches, pp. 16-23. t Electrical Papers, ii. pp. 504-518; Electromagnetic Theaee a, pp. 269-274," oe ets Electromagnetic Theory of Moving Charges. 489 making an angle @ with the line of motion is proportional to | 1 2 3 u $ ae Eas 2 ] (1 yesin 6) where w is the velocity of the moving charge and V the velocity of light. The lines of magnetic force are circles round the line of motion. 2. This solution of course represents the state of affairs at a great distance from a small charged conductor of any shape. It would also give us the distribution of charge on a moving - sphere if it were correct to assume that the lines of displace- ment meet the charged surface at right angles. This assumption was made by Prof. Thomson and, at first, by Mr. Heaviside, but the latter, quoting a suggestion of Mr. G. F. C. Searle, subsequently pointed out that when there is motion the electric force is no longer derived from a_ potential function, and as a consequence does not meet the equilibrium surface at right angles. Substituting the correct surface condition, he showed that the charged conductor, whose motion would give at all points the radial distribution found for a point charge, was not a sphere but a spheroid of certain ellipticity. : : 3. lt seemed of some interest to inquire what the distri- bution of charge on a moving sphere would be. The surface- density at a point of the surface is now the normal component of the displacement at that point. By carrying the investiga- tion a step further I have found that, if the conductor be a sphere or any ellipsoid, the ordinary static arrangement of charge is unaltered by the motion ; 7.¢. the number of tubes of displacement leaving each element of the surface is unchanged, but the tubes no longer leave the surface at right angles. We may imagine that the motion has the effect of detorming the tubes, keeping their ends on the conductor fixed. The proof of this, involving a consideration of the general case, is here given and is followed by a note on the energy of a moving charge in a magnetic field. sf 4, Suppose we have any distribution of charge movin with uniform velocity u parallel to the axis of z, and that the field has assumed its steady configuration. We shall denote Uz 1— y2 Py k?, V being the velocity of light. Then since we have a steady state, | >) 490 Mr. W. B. Morton on the Also, since each element of charge produces a magnetic field with no z-component, we have y=0 in the general case also. Using these two data, the equations connecting the displacement (7,9, ) and the magnetic force (a, B,y) become OB ua df Ee = —Aru He ao dg ae = ae dB da dh de Cue eae dg dh _ u da dz dy AmV?dz dh) San SS ae da dz AV? dz’ dees, diy Taare t These equations together with dj dg. an. Tic ee ee are satisfied by colet JOD Shes oh SOD a ty ee = — ae VS = dy’ = k 5) pepe oes Oe anaes = an where ¢ is any function satisfying ban a 30 OL, AR ot diy? +k ie —((} | These results have been obtained by Prof. Thomson and Mr. Heaviside. The particular case of a point charge, e, is got by putting iiss e An V k?(a? + y") +27 Evidently in the general case ¢@ must vanish at infinity. 5. Mr. Heaviside points out that ¢=constant is the con- dition holding at a surface of equilibrium. The matter may be stated thus :—If we suppose the field to terminate at the surface of a conductor, inside which the vectors vanish, we must see that the “ curl”’ relations of the field are not violated Electromagnetic Theory of Moving Charges. 491 for circuits which lie partly inside the empty space enclosed by the conductor. In particular, if there is a vector whose line integral round every circuit in the field vanishes, the lines of this vector must meet the surface at right angles. Otherwise we should have a finite value for the integral round a circuit drawn close to the surface outside and completed inside. In other words, if a vector is derived from a potential function, this function must be constant over the surface. In the ordinary static case it is the electric force (X, Y, Z) which is so derived; but in the case of a steadily moving field it is the vector (X, Y, al which meets the surface at. right angles. 6. Let F(«yz)=C be the equation of the charged surface. Then («x yz) has to be constant over this surface and satisfy Ph OO, 0h _ det a dy? +k Ie =). Put z=ké, then ¢ is a function of x, y, &, which is constant when F(a, y, k€)=C, and which satisfies 2 2 2 oe Oe , 28 0, da?" dy? * dt? Therefore if we regard (« y €) as Cartesian coordinates of a point, ¢ is the potential at external points of an electrostatic free distribution on the surface F(a, y, kf)=C. The com- ponents of electric force due to this distribution, at a point (z y €) on the surface, are ee LO) ee Oe dx’ dy’ dg° This force acts in the normal to the surface, and is pro- portional to the surface-density at (wv y ¢), which we shall eall oc’. Therefore : dp dpb dd\_ aw dk al (EY dK \2 dF \2 oe ade) at ONG ap ie)/ Ga) = iy) the) But tie pies | ge h erefore, denoting differentiation with respect to wy z by ubscripts 1 2 3, (pi, ba $3)= —Ao’(Fy, Fy, F)/ VFP+ F408? Now let o be the surface-density at (# y z) on the moving conductor F(z y z)=C, then equating o to the normal com- 4992 Mr. W. B. Morton on the ponent of (fg h) oath + oF, -- APs | ; VEP+ E+E or putting in the values we have found for (fg h) in terms of ¢, . Sones Pik + oF. + h’psFs VF?+F4+ 23 _ aa, (REFERER? RY’? +F?+ F,? ° Now the perpendicular from the origin on the tangent plane to F(x y z)=C at the point (2 y z) 1s et ek, + yk, + zi’, amr sey Peo 3 and the perpendicular from the origin on the tangent plane to F(a, y, k8)=C at (a y €) is dF, dk | ak ie See dF? mea) Ge — &F+yF,+kCR; Et VF? +F2+2FZ _ aE +yFo+2F3 VF +FR2+ Fe _ Ap oe ~If now F(«yz)=C is an ellipsoid, then we know that o’ x p’, therefore also o a p, that is the arrangement of © charge on the moving ellipsoid is the same as if it were at rest. 7. Applying the above to the ellipsoid (a b c), we find that d as a function of (wy ¢) is the potential of a free distri- bution on the ellipsoid | a PPE? 7 es ee e o’ esis ae es, . cl Charges. 493. Hi of te +9)(U+%) \(a+) an dx — ven | s\ po Li V (a? +A) (0? +A)(e? TE, where be is given by e y? ¢ a+ pb a b? + pb a3 @ oy 1 poe or x ae 2 a? +p a b? + is C+ hu i Determining the oe of the constant © so that the density at a point shall be Fo he a , we get e dr ef ECS NCES CET) Putting b=a, c=ka, we get é en aay CE Soe Showing that, as Mr. Heaviside pointed out, the field of a point charge is given when the conductor is an oblate spheroid whose axes have the ratio 1: &. For a sphere the integral becomes 0+ ka er are ean” °86—Kha where Pe fie = = and @ is given-by Marty") | 2 Gea + mo To test the value of ¢ let us make k’ approach zero, 7.e. the motion becomes infinitely slow. @ is then =r. ee eH) Then See er gilts k'a) ae k’a) e 2a e 494 Electromagnetic Theory of Moving Charges. 8. The mutual energy of a moving charge and external magnetic field has been given by Mr. Heaviside for the case — of motion which is very slow compared with the ,velocity of radiation. It is ewA.cos (wA),*where A is the circuital vector potential of the external field. Mr. Larmor, in the second part of his “‘ Dynamical Theory ” ( Phil. Trans. 1895, p. 717), concludes that the same expression holds good for motion at any speed. He seems, however, to overlook the fact that in the general case the displacement-currents in the medium—being no longer derivable from a potential function —will make their appearance in the result as well as the convection-current eu. If (F GH) is the vector potential, the part of the energy corresponding to the displacement currents will be \(E/+ Go + Ha)dr, which in the case we have been considering becomes df. dg. dh e Cd ad 4 yoy UO But by a well-known transformation, when we take the integral through all space, we have \rzs { Uette a HSS ar dx dz dy dz = °(5-+ dG a5), Walaa as vad), Fe, i = 0 since (F GH) is circuital. .. The expression for this part of the energy reduces to 2 3 2 —u(1 -18) {H = dt =— eH dt. Therefore if the velocity u ceases to be negligible in com- parison with V, we have a correction of the second order in the ratio - in addition to the expression involving the convection-current simply. It also appears from the above that the force on the moving charge cannot, unless this term be neglected, be expressed in terms of the magnetic intensity at the charge, but will depend on the entire field. [ 495 J LIV. On a Simple Apparatus for determining the Thermal Conductivities of Cements and other Substances used in the Arts. ByCuHaruss H. Luzs, D.Sc., and J. D. CHORLTON, B.Sc., Joule Scholar of the Royal Society”. «Mee following method of determining the thermal con- ductivities of bad conductors has been designed with the object of simplifying as much as possible the apparatus and observations required in making determinations which are not required to be of the highest order of accuracy, but — in which errors of more than 2 per cent. are to be avoided. When the constants of the apparatus have once been deter- mined, the only observations necessary to determine a conductivity are the thickness of a sheet of the substance used and the temperatures of three thermometers. It is hoped that this simplification will lead those who require bad conductors of heat for structural purposes to carry out their own tests of the materials they have available. Method.—The apparatus consists of a flat cylindrical metal box, of 11°4 cms. diameter and 3 cms. depth, through which steam: can be passed. The bottom of the box consists of a circular brass plate 1:3 cm. thick in which a radial hole reaching to the centre is bored. In this hole a thermometer is placed with its bulb at the centre of the plate. The top and sides of the box are covered with green baize to prevent loss of heat as far as possible. This vessel is supported on a circular plate of the material to be tested, which in its turn is supported on a brass disk similar to the one forming the base of the heating vessel, and like it provided with a radial hole and thermometer. The lower disk is suspended horizontally from a support by three strings attached to three short pegs projecting from the edge of the disk, and hangs about 30 centims. above the table. About 10 centims. above the table a thermometer is placed horizontally, with its bulb under the centre of the lower plate to give the temperature of the air ascending to the disks. The bulb of the thermometer is protected against radiation from the lower disk by a bright metal screen. The two surfaces of the disks which come into contact with the material to be experimented on are amalgamated, so that if the material is a solid, contact over its entire surface may be obtained by using a thin mercury film between the solid and disks. In order to determine the thickness of the * Communicated by the Authors. 496 Dr. Lees and Mr. Chorlton on the Thermal material used, two short pegs of brass, one vertically above the other, project from the disks, and their distance apart is measured by means of a wire gauge or calipers, when the disks are in contact and when the plate to be tested is between, the difference is the thickness of the plate of the material tested. The under surface of the lower disk may be kept polished, or it may be painted, in order that the heat radiated from it may remain constant during a series of experiments. When steam is passed through the upper cylinder the tem- perature of the upper disk is raised to nearly 100° C.; heat flows through the plate of material experimented on to the lower disk, the temperature of which is therefore raised above that of the surrounding air. It begins in consequence to lose heat by radiation and conduction to the air, and eventually a stage is reached when this loss of heat is equal to the heat received from the material experimented on. | Hence if the amount of this loss is found by a separate experiment, a determination of the temperature gradient in the material experimented on at its surface of contact with the lower plate, will enable the thermal conductivity of the material to be found. | Theory. If 6 is the temperature at a point w above the under surface of the lower plate, 0) the temperature of the air, 4, the internal conductivity, 4, the external conductivity or “ emissivity,” Newton’s law being supposed to hold for the limits of tem- perature used, p the perimeter, g the area, of cross section of the plate, the differential equation for the motion of heat in the plate, the isothermals being assumed plane, is satisfied if phy ,; phy 0—-0=A, cosh A/ PR 4+ By sinh aE 2, gry where A, and B, are constants. The condition for continuity of flow at the under surface is be =o tore —O. ky a / bls 5 B= Ay; ghy oe @— =A, { cosh /PM wt —“L— sinh Phe) qe fe No Conductivities of Cements and other Substances. 497 Now for the lower brass disk po=2rr/ar 2/9 (—Ssol, while k, for brass =*25, and it will be shown presently that h,='0008 about. Hence / 8 pin ae and since the thick- ness of the plate is 1°3 cm. the maximum value of the expression in brackets is B08) 2S ss a aK WB xp nh °026=1:0018; or ae temperature of the lower plate varies less than } per cent., and for the purpose of the present experiment may be taken to be uniform throughout and equal to the indication 6, of the thermometer in the centre of the disk. The ee ture of the lower disk is therefore given completely by the equation = I 6 O=16; =A} { cosh, Tea pe sin aa The rate of flow of heat into the lower disk, the thickness of which is 1:3 centim., is given by &, a fom == los. - litvis therefore 3 | =k, a [els {0,—0)} { sinh 026+ aul — .cosh 026} : hee pen qhy = (0, — aCe 00026 hy +026 ky rye qky =(6,—%)(hy+hy’), say, where hy’ =-00013. Ifk is the internal, / the external conductivity of the medium under test, the temperature 0 at a point « above its under surface is given by :— ph ph @— 6 =(0,— 6) cosh Lat sinh /EE 2}, where B is a constant, the value of which is fixed by the Plul, Mag. 8. 5. Vol. 41. No. 253. June 1896. 2M 498 Dr. Lees and Mr. Chorlton on the Thermal condition for continuity of flow at the surface of contact of the material and the lower plate, 2. e. k Ni = B=(6,—6)(hy +h’). Hence in the material under test 06—O,={0,—%} { cosh, / 2h. a+ as oh y/ Pt as q k ee gk Tf 6 is the thickness of the material, at c=6b we must have 6=86,, the temperature indicated by the thermometer in the upper brass plate, 2z. e. —4,=(0,— ~4)(coshy /Ph. b+ 07h nh / Pt i) a u The maximum value of VA BD for materials experi- mented on is ‘2; hence the hyperbolic functions can be expanded in ascending powers of \) - .6, and terms invol- ving cubes can be neglected. Thus :— eet eo 0,—6)= (0) (14 Po vr4 BE 4 [eh ), ka / Ph ae gk o1 ag 0; =e (dath’ + Be »). The last term in the bracket never exceeds 4 per cent. of the first two terms, and the final result will be affected only to a very small extent if for h, h; is substituted. Hence we have k= Ga phy ) 1+ Dg sib which enables & to be Aa from the result of the expe- riment if A, has been previously determined. Determination of hy.—To determine the value of this quan- tity the two plates were separated by a layer of air 3 mm. thick, enclosed by a ring of badly conducting material upon Conductivities of Cements and other Substances. 499 which the upper plate rested; steam was passed through the box at the top, and the temperature of the upper plate raised to nearly 100°C. The lower plate was next heated a few degrees above 100° C. by means of a gas-flame and then allowed to cool, and as soon as its temperature fell to 100° C. the supply of steam to the upper can was cut off and the hot water in the can allowed to run out. Both plates were then found to cool at almost the same rate; the difference in the temperatures of the two plates never exceeded 1° C., the upper plate being always the warmer. Since the conductivity of air is only about -00005 C.G.S. units, the amount of heat conducted from the upper plate to the lower is negligible, so that each plate cools independently of the other. The thermometer in the lower plate was watched as the temperature fell, and the times at which the mercury passed every alternate degree were observed ; the results are given in the table below. The temperature of the air was steady at 18° C. Temperature of Fall of Loss of hae a lower plate. Tj heat, gram-] 7°" PS a ime. | temp. per |q em., gram-| A. degrees per | 4... second. second, | Cesrees per Oi oo second, HG: Ee We TEL. 8 96 78 3.17.42 94 76 18.37 | 0370 3°92 0255 ~—- | 000886 92 74 19.32 304 75 43 28 90 ti 20.30 340 60 34 25 88 70 21.30 325 44 23 19 86 68 22.33 308 26 12 12 84 66 23.40 301 14 04 09 82 64 24.46 290 O07 0199 if 80 62 25.58 274 2°90 86 03 78 60 27.12 263 79 81 02 76 58 28.30 256 71 76 03 74 56 29.48 250 65 72 O7 72 54 31.10 244 56 68 11 70 52 32.32 235 49 62 12 68 50 34.0 220 33 51 02 66 48 35.34 208 20 43 000298 64 46 27.12 197 08 35 93 62 44 38.57 187 1-98 29 93 60 42 40.46 180 i 24 95 58 40 42.40 169 79 16 90 56 38 44.42 156 65 07 82 54 36 46.57 146 59 0101 81 52 34 49.15 140 48 0096 82 50 32 51.43 500 Dr. Lees and Mr. Chorlton on the Thermal | The numbers in the 4th column are found by subtracting alternate times in the 8rd column from each other and dividing 4° C. by the differences. The numbers in the 5th column are cbtained from those in the 4th by multiplying by 1140 grams, the mass of the lower disk, and by ‘093, the specific heat of brass, z.e. by 106. The numbers in the 6th column are obtained by dividing by the total radiating surface of the lower disk, plus half the radiating surface of the nonconducting ring = 148°5 + 5:5 =154 sq. centims. : The values of h are obtained from these numbers by dividing by the excess of the temperature of the lower disk over that of the air. Haperiments. The following account of an experiment on a plate of glass will show the method of treatment in each case :— A disk of plate-giass of diameter equal to that of the brass plates—11°4 centims.—was placed between them, and contact made by means of thin mercury films. Good contact was easily secured between the glass and the lower plate; but with much more difficulty in the case of the upper plate. Contact was eventually obtained by covering the surface of the upper plate with mercury, so that it adhered in pendent drops, at the same time placing a few drops of mercury on ihe surface of the glass, and then carefully lowering the upper plate on to the ylass and allowing the excess of mercury to run out at the edges. Steam was then passed through the box attached to the upper brass plate, and thermometers inserted in the upper and lower plates, the temperature of the air being indicated by a third thermometer placed as described above. After a time, the duration of which depended on the con- ductivity and thickness of the substance experimented upon, the thermometers became steady and the temperatures were observed. 6, = temperature of upper plate = 961°C. 0 = 92 aaa y= be Fa abe == 20-058: Thickness = *292 centim. Oi = i 5, lower Conductivities of Cements and other Substances. 501 The thickness was obtained by measuring with a micro- meter-gauge the distance between the two pegs, first, when the plates were in contact with each other, and, secondly, when the glass was between them. The following table gives the observations taken during each experiment, and shows the method of determining the conductivities from the observations :— Remarks on Specimens Experimented on. (a) The plates of Portland cement and plaster of Paris, &c., were made by pouring the liquid cement on toa glass plate, on which three equal beads strung together were laid, a second glass plate was pressed down upon these beads, after a few hours the glass plates could be removed and a plate of cement of uniform thickness was obtained. The plate of plaster of Paris and sand consisted of two parts by weight of plaster of Paris to one part by weight of sand. (6) When the substance experimented upon was a powder, the brass plates were kept apart by three stops of wood, and the powder was prevented from falling out at the edges by a very narrow circular ring of fibre. (c) The three values given for the conductivity of garden-soil refer to three specimens of soil of the same kind but containing different amounts of moisture; the first value refers to dry soil, the second to slightly moist, and the third to damp soil. The results show how greatly a small amount of moisture affects the conductivity. (d) The calico in the first experiment was dry, and weighed 8°91 grams, In the second experiment it was exposed for some time to a damp atmosphere, and its weight increased to 9:06 grams, so that the con- ductivity of calico increases 20 per cent. for 1°6 per cent. increase in weight due to moisture absorbed. (e) In the three experiments on old flannel, the flannel contained different amounts of moisture. In the first experiment the flannel was quite dry and weighed 8:21 grams, in the second it was exposed to a damp atmosphere, and its weight was 8:29 grams, and in the third experiment was damped with water and its weight increased to 9°05 grams. Thus the conductivity of flannel increased about 11 per cent. fur 1 per cent. increase in weight due to absorbed moisture, and afterwards increased 25 per cent. more for a further increase of 10 per cent. in weight. The flannel in the third experiment is almost as good a conductor as dry calico. The new flannel, flanelette, silk, and linen were dry. Dr. Lees and Mr. Chorlton on the Thermal 502 LIT 91-6 18-4 | 89-6 61: 18-9 GFT Co-P PG.1 68-P G96: PE EGE: IL-6 916-1 | 61-4 Pe: 18:3 916. SL-G ZSL9- 86-7 1G-G 9-61 PA 8-F1 09-2 9-61 ™o—"9| (9-9 Wo—'g | °@—"o . 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[rete a“ $1000: | 662: LPG: PSE | 90F| FF S 0-81 | #-9¢ 0-46 | OIG. forests | jouuRE pio (9) Zc000: | &GF- E36 g.ce | 9.cz aa I GOL 8-1. 8.96 GG |cereestseeesensetensceny ae | 81000: | TIF. 98-1 | BZ | 1-83 ia I GLI | 69 GG ale TGGe |b Aeterna TOOT) (B) 09100: | 1F-8 TrG | $59 | 6-11 lt ¢ G61 | 1-88 OGG: cal OGOM ai se heen ae ae OLL00: | 4e.z 86h | F-89 | 9-FT Lt ¢ G81 | 618 JaCoTa ae OTE Pg aa PAE TA I €8000: | 9TL- Col | Lr | 9-e¢ OF g O6L | L469 | G16 | OGG. [ott T [los BepaRy (9) 62000: | 62-T 66-3 | 8.4¢ | F-8% oF g G61 | 0-4 Us| Pe came SBP e91000- | 928. 169: LIS | @¢F ia g 8:06 | &3¢ 0:86 | OPG. [ot asnpaeg 97000: | 10-1 G81 | L6F | 26 OF g 0-06 | 1-69 LL6 | OGG. [ott por 4snpyzortg 88000: | Ze. 7O1 | GLb | 208) 9F000. £0000: 8-61] O29 | LL6 | Opa [ott moped gsnpyong [50a] LV. On the Relation between the Brightness of an Object and that of its Image. By W.T. A. Emracs, M.A.* ‘he an object situated in a medium of refractive index p forms an image by means of rays refracted through any number of surfaces and finally into a medium of index p’, the luminosities, I, I’, of object and image satisfy the relation 1 epee oa supposing no light to be lost by reflexion at the surfaces or by absorption in the media. This is generally proved, in the case where the pencils are not all very narrow and along an axis of revolution of the refracting surfaces, by showing that if this relation did not— obtain we could get an image brighter than the object by viewing this through a suitable combination of lenses; a _ result which would be contrary to experience. The following direct proof may, however, be given for pencils of any sort:— We notice first that if a small luminous surface sends a certain quantity of light to a second small surface, for the second to send the same quantity of light to the first it must be equally bright with it. For if s,, sg are the areas of the two surfaces, I,, I, their luminosities, d the distance between them, and 0,, @, the inclinations of their normals to d, the lights winch they send to each other are T, 5; s) cos 0, cos 4, J I, s, s& cos 0, cos 05 ae eS P E And for these to be equal I,=Ty. Now let s be a small area of an object in a medium of refractive index py, and let it send out a sheaf of rays which is refracted across the surface RT into a second medium of index py. The cone of rays from s converging to the point Kt is refracted into a cone of different solid angle. If7 and r are the angles of incidence and refraction at R, the angular breadths of these solid angles in the plane of refraction are di, dr; and their angular breadths at right angles to this plane are proportional to sinz, sin’. Now ", pf, cosidi=pycos r dr. * Communicated by the Author. On the Brightness of an Object and that of its Image. 509 And if the solid angles are @,, @2 @, disin? _— mw, cosr w, drsinr py’ cost Now let I, be the luminosity of s, and I, that of the surface RT as seen in the medium p, by the light coming originally from s. 1, is the luminosity RT must have to send back to s the same amount of light as s sends to it, that is, as RT sends on into wy. If s, is the area of the surface RT, the quantities of light received and sent on by it are I, s;@, cos 7, and I, s; w, cos r. And these are equal. Thus from above T, : Lp=p,? : pp”. In the same manner the luminosity of the second surface across which the rays pass, as seen in the third medium of index pz, is proportional to uw”; and so on. If the rays on passing across the last surface form a true image of s, so that the combination of surfaces is aplanatic for s, the brightness of this image is the same as that of the last surface ; for it subtends the same solid angle at the point of view as the portion of the surface which sends the same quantity of light to the point of view. Thus, if w, yw’ are the refractive indices of the medium in which the object is and that in which the eye is which sees the image, and I, I’ the luminosities of the object and image ; | Be ed) ke eae [ 506 ] LVI. Adjustment of the Kelvin Bridge. By Rotto APPLEYARD*, ib a recent paper by Mr. J. H. Reevesf an alternative method of adjusting the ratios of the resistances in the Kelvin bridge was described; the following remarks may be regarded as a note upon that paper. The measurement of a resistance by the arrangement adopted by Mr. Reeves involves two operations. It may be shown, however, that for certain purposes the two adjust- ments can be combined mechanically, and halance effected by a single test. : Fig. 1. Consider the conductors R, 7, a, b, z, and y in fig. 1. It is required to compare R with r. In the accepted form of the Kelvin bridge a, b, x, and y have fixed values, such that ay=b«, and balance is obtained by the one operation of varying Ror 7. Mr. Reeves prefers to keep R and r fixed ; and, consequently, he has first to find provisional values of a, b, x, and y such that ay £ bx; and then to balance again, using these values, to find R:7; with the plug, this time, inserted at P. Fig. 2. But fig. 1 suggests that a+6, and #+y, or convenient parts of them, may each be formed into a slide-wire, and that these two slide-wires may be placed parallel to one * Communicated by the Physical Society: read April 24, 1896. } Supra, p. 414. Effect of Wave Form on the Alternate Current Arc. 507 another, with a double sliding-contact between them, as shown in fig. 2. Then, in whatever position the slider may be, the fundamental ratio ay=6z is always maintained, and the first condition of the Kelvin bridge is mechanically ful- filled. The one adjustment consists in moving the double slider along the bridge until there is no deflexion of the galvanometer at g ; in which case Gre Ape ke Dae ee Since writing the above, I have referred to the original paper of Lord Kelvin (Proc. Roy. Soc. vol. xi. p. 318, 1861), and find that he proposes the use of parallel slide-wires for his auxiliary conductors; I have no doubt he had in view some such apparatus as that which I have here suggested. A Kelvin bridge with a single slide-wire was used by Mat- thiessen and Hockin in their differential method; it is described by Clerk-Maxwell in ‘ Elec. and Mag.’ vol. i. p. 406 (1873). LVIL. The Hffect of Wave Form on the Alternate Current Are. By Jvuutus Frirn, 1851 Lexhebition Scholar*. N the paper by Dr. Fleming and Mr. Petavel, recently read before the Physical Society, on the Alternate Cur- rent Aref, I think too little attention was paid to the wave form of the alternate current used. It is known that if the arc is allowed to exert a prepon- derating influence at all on the alternate current circuit, it alters the wave form of both the current and the P. D. in a very marked degree. As an illustration of the change produced in the wave form by the character of the external circuit, I give some curves for alternate current arcs taken from a paper which I read before the Manchester Literary and Philosophical Society in March 1894. Here is shown, first the E.M.F. curve of the machine on open circuit, which is rather more peaked than a sine curve and involves the third harmonic largely. Next is shown the curve obtained under the same conditions, but with an are lamp taking 10 amperes at 40 volts joined direct to the machine. The lag recorded is due to the self-induction of the machine, * Communicated by the Physical Society : read April 24, 1896, + Supra, p. 315. JadLATID ry i WES ta cae eh 7109L19 UL a = S & ~ —_ b> — — SN (je ~— S Dd SS i i) — ~~ rr) ~ S = + OE Py i) a OF: dun gy quajsua ab0710/ Luu TIA YIN SAAATD on the Alternate Current Arc. 509 which was a “ Wilde” alternator, the armature of which contained iron. It will also be noticed that the first ordinates of the curves are not quite equal to the last ordinates ; this is due to the curve being slightly asymmetrical. The whole period is only one third of the revolution of the alternator (shown as 120 degrees in the figure). In one complete revolution this lack of symmetry would of course disappear. It is seen that the are alters the wave form from a peaked curve to a very flat topped curve, changing sign almost instantaneously, and with two small maxima, which occur respectively just before and just after each reversal. The next curve shows the effect of adding a resistance of 1 ohm in series with the arc. This smooths out the two maxima, but otherwise does not affect the shape materially. 7 The current and P.D. curves with 5 ohms in series with the arc are next shown. Both waves now assume much more the form of the E.M.F. curve on open circuit, except at the zero line. Here the P.D. curve crosses the line twice in each direction, and the current curve runs parallel to the zero line for some way before crossing it. These curves show, I think, the great effect that the arc has _ on the wave form, and also how this effect can be destroyed by placing resistance in series with the arc. In a paper by Rossler and Wedding, which appeared in the ‘ Hlectrician’ for August 31st, 1894, it was proved that an alternate current arc is more efficient, that is, gives a higher candle-power for the same electric power consumed, when the alternating current feeding it has a flat-topped than when it has a peaked wave form. Réssler was, however, mistaken, I think, in assuming that the machine was making that curve. Indeed, this mistake runs through the whole of this otherwise most valuable paper. Réssler took three machines giving, as he thought, wave forms from the extremely peaked to the extremely flat wave, and determined the efficiencies of the same are lamp for each of. them. Whereas exactly the same results might have been obtained from one machine alone on causing it to give a higher voltage by increasing the field excitation and then absorbing the excess of voltage in resistance, exactly as in the case of the Wilde alternator above referred to. I understand that in the experiments described by Dr. Fleming and Mr. Petavel there was always a resistance amounting to 7 ohms outside the arc, and hence a wave form was forced upon the are which, as Roéssler has proved, is not the most efficient one, and which the arc would conyert into a 510. Mr. D. McIntosh on the Conductivity of form better suited to itself if it had been allowed to do so, as it isin commerce. This consideration must affect, not only the efficiency, but also the curves which Fleming and Petavel obtained for the variations in the luminous intensity. Further, this action of the arc in modifying the wave form may throw some light on the discrepancy between the efficiency of alternate current arcs as determined in the labora- tory and that stated to be obtained in practice. When an arc is run in the laboratory a large resistance is almost certain to be put in series with it to ensure that degree of steadiness which 1s essential to exact measurement, and hence the are cannot alter the wave form. In the commercial use of ares, on the contrary, the circumstances are widely different. In this case, for economic reasons, the are must form a large percentage of the total “ reactance ” of the circuit, and there- fore can easily alter the wave to the form required for the greatest efficiency. | It is interesting to note that the wave form giving the best result for the arc is almost exactly the opposite to that giving the best efficiency for transformers. In the former case a flat-topped wave is best, while for the maximum efficiency of transformers an exceedingly peaked wave is best, as lately found by Dr. Rossler. This points to the building of alternators for use with transformers in such a way as to give peaked wave-forms. In the case of the arc the building of machines to give the most efficient wave form is not so necessary, since, generally, the arc itself has the power of automatically converting any wave form into the one best suited to its requirements. Nevertheless, when the arc has to run in series with a large resistance it is of the utmost importance for obtaining the best efficiency that the machine should give a flat-topped wave. City and Guilds of London Central Technical College, April 2, 1896. LVIII. On the Calculation of the Conductivity of Mixtures of Electrolytes having a common lon. By Doucias M°Intosu, Physical Laboratory, Dalhousie College, Halifax, N.S.* iO a paper published in the April number of this Maga- zine (supra, p. 276) Prof. MacGregor showed how to obtain, by a graphical process, from observations of the elec- trical conductivity of a sufficient number of simple solutions * Abstract of a paper read before the Nova Scotia Institute of Science on the 13th of April, 1896. Communicated by the Secretary of the Institute. Mixtures of Electrolytes having a common Ion. 511 of two electrolytes having a common ion, the data necessary for the calculation of the conductivity of a solution containing both electrolytes, according to the dissociation theory of electrolytic conduction ; and in order to test this theory he calculated the conductivities of a series of mixtures of solu- tions of sodium chloride and potassium chloride, which had been measured by Bender. He found that for dilute solutions his calculations agreed with Bender’s observations within the limits of experimental error; but that as the strength of the solutions increased the differences became larger, until with a mixture of solutions containing each four gramme-molecules per litre of salt (the strongest solutions with which Bender worked) a difference of 3°6 per cent. was found. The method of calculation assumed that the ionic velocities of the con- stituent electrolytes were not changed by the mixing; and Prof. MacGregor attributed the differences between the calcu- lated and observed values to the change which, as he pointed out, would probably be produced in these velocities by mixture. 7 At his suggestion I have made the observations and calcu- lations described in this paper with the object of determining (1) what the differences between the observed and calculated values are, in the case of mixtures of sodium and potassium chloride solutions of greater strength than those examined by Bender ; and (2) how the calculated and observed values are related in the case of solutions containing sodium chlo- ride and hydrochloric acid—electrolytes whose ionic velocities differ from one another much more than those of sodium and potassium chlorides. Preparation of Solutions and Determination of Conductivities. The paper of which this is an abstract contains a full statement of the experimental methods employed and the precautions taken to secure accuracy. It will be sufficient here to make a general statement merely. | The salts and acid used were purchased as chemically pure, and the former re-purified by crystallization. They were found by the usual tests to be free from prebable impurities. The water was doubly distilled and was also tested. Simple solutions of salt or acid having been prepared their concentration was determined by volumetric analysis, the pipettes and burettes used having been tested by weighing the water they delivered. The volumetric analyses were found to be accurate to 0:1 per cent. when applied to solu- tions specially prepared by the mixture of exactly determined quantities of salt and water. 7 Mr. D. M°Intosh on the Conductivity of - The mixtures in all cases consisted of equal volumes of the constituent solutions. In preparing them the same pipette was used for both solutions in exactly the same way, having been washed out before use in each case with a portion of the solution with which it was to be filled. In all cases solutions were prepared and analysed at 18°C. The method employed in the observations of conductivity was that of Kohlrausch with alternating current and telephone, the apparatus consisting of a bridge-wire of german-silver about 8 metres long, wound on a marble drum, a set of resist- ance-coils (of which I needed to use but one), a small induction- coil with a very rapid vibrator, and an ordinary Bell telephone. I calibrated the bridge-wire by the method of Strouhal and Barus, and was able to determine resistances to within from 0:2 to 0°3 per cent. The electrolytic cell was of a U-shape, and was placed in a water-bath kept at or near 18° C. by a thermostat and stirred by a current of air. Its temperature was read by a ther- mometer graduated to 0-1 degree Centigrade, and capable of being read easily to 0°05 degree. Its errors had recently been determined at the Physikalisch-technische Reichsanstalt, Berlin. When the bath could not be kept at 18°C., the temperature coefficient was determined. In the platinizing of the electrodes, and in the whole procedure of the deter- mination of the conductivity, I followed carefully the recom- mendations of Kohlrausch’s recent papers. As I was to employ Kohlrausch’s observations as data in the calculations, I reduced all my observations of conductivity to his standard (the conductivity of mercury at 0°C.). The factor requisite for this purpose was determined by comparing my own observations for certain solutions with the values iven by him for the same solutions. This factor I found (as Bender had also) to vary somewhat with the conductivity of the solution used in finding it, but not with the nature of the solution. I therefore found its values as given by using a series of solutions of different conductivities ; and in reducing the observed conductivity of a mixture to Kohlrausch’s standard I used the value of the factor corresponding to the conductivity of the mixture. All observations given below are expressed in terms of Kohlrausch’s standard. Results of Observations on Mixtures. The following tables give the concentrations of the con- stituent solutions of the mixtures examined and the observed conductivities of the mixtures : — Mixtures of Electrolytes having a common Jon. 513 (A).—Sodium and Potassium Chlorides. Constituent Solutions (gramme-molecules per litre). Conductivity x 10°. KOl NaCl 3.98 512 2494 3-90 “ 2326 ia ‘ 2029 3:88 512 2494 : 4-98 2404. . 3:37 2316 i 2:56 2196 (B).—Sodium Chloride and Hydrochloric Acid. Constituent Solutions (gramme-molecules per litre). Conductivity X 10°. NaCl. HCl. 2-02 4°55 4932 . 3:89 4492 it 3°29 4089 ‘ 3:19 4073 e 3:06 3958 a 2-66 3623 be 2-56 3489 % 9:34 3323 1-04 4-55 5069 Mi 3:97 4682 ss 3:80 4315 . 3:10 3989 - 2°86 3696 i 2-18 3112 a 911 3025 - 1:93 - 2824 = 1:58 2427 - 1:15 1928 0°607 1-120 1813 n 0-970 1620 i 0815 1412 ce 0:730 1296°5 “ 0-603 1114 0-485 952 Phil, Mag. 8. 5. Vol. 41. No. 253. June 1896. 2 N 514 Mr. D. M'Intosh on the Conductivity of The Data for the Calculations. The method of calculating the conductivity of the mixtures was that described by Prof. MacGregor in the paper referred to above. It requires as data the change of volume on mixing (if not negligible), the conductivities of sufficiently extended series of the simple solutions of about the same dilution as the solutions mixed, and the molecular conductivities of the simple solutions at infinite dilution. Specific gravity determinations showed that the change of volume on mixing was in all cases so small as to produce no ractical effect on the calculated value of the conductivity. Kohlrausch’s tables* of the conductivity of solutions of sodium and potassium chlorides furnished sufficient data for calculating the conductivity of mixtures of these salts ; but I found it necessary to make additional observations on solu- tions of hydrochloric acid. They are as follows :— Concentration Molecular Concentration Molecular (gramme-molecules | Conductivity| (gramme-molecules | Conductivity per litre). Or per litre). x 10%: 1-58 2550 2°80 2065 1°93 2403 2°88 2052 2°11 2347 3°15 1960 2°18 2305 3°29 1914 2°24 2290 3°39 1890 2°46 2245 3°60 1789 2°51 2192 3°83 ZG 2°56 2164 4:13 1636 2°66 2141 4-55 1534 2°78 2090 4:87 1456 The values of the specific molecular conductivity at infinite dilution for potassium chloride, sodium chloride, and hydro- chloric acid respectively, were taken to be 1220x107, 1030 x 10-8, and 38500x10-° according to Kohlrausch’s determination f. RESULTS OF THE CALCULATIONS. (A) Sodium and Potassium Chlorides. The following table contains in columns 1 and 2 the con- centrations of the constituent solutions in the mixtures. Column 38 gives the calculated values of the conductivity ; * ‘ British Association Reports’ (1893), p. 148. y+ Wiedemann’s Annalen, xxvi. p. 204. Mixtures of Electrolytes having a common Jon. 515, column 4 the observed values obtained by graphical interpo- lation from the observations given above ; and column 5 the excesses of the calculated over the observed values expressed as percentages :— Constituent Solutions (gramme-molecules per Conductivity . 5- vol. CPI 2Sees aes ay, AEA ene. | aE cage ae nea 5s Beer Eieeee , Phil.Mag .S.5 Vol. 41 .P) | t ele z paeeesees2c5 ena i | I it Cl it — ea | i BSS ee i ch a 5 ic + Sia | oe ECE LCL CCCeUe Geel Se a Be GB +. BEVEScsamene son oC | J + 4h se ch ea A eS at + ale — j= te lis io + al els | H | oe ee JE] dL 4 F | a Mi =e | : eiratesstaceat Sreserresettitt | I | { | ae [ ~ + ie ——! ieee Dge Caso o LI | GREG [ 1 | iat { | | Ja Sui uu? | + EE —- ae . a E140, } ia a = atl ails fa aa : (Le = id Se peal IES : odioeadoceaastfasoatii | sib baal Sy) > | maa Be eet | meee Pall -B5 ain i ++ i T $ == +— == z f C a +{100 zi a - ale ii +f T zi T iS r = i jer [a= iat |e + =F + _ aie Zi IL i} Al i 40 50 | [ 60 70 80 90 100 uo 120 140 =~ ae ee LI : coetticient: of clilatetion of air. = : Le ee ns Me SSS SS SSS ee Phil. Mag. S.5.Vol.41.PLI1. a AEH EC HaCEEEP CEE EEE ere a ee AT POPP PONCE CRORE RRRRUERDRE ts JGRGEE pe STEIN ERED ERR ENGR EERE ies eed { ——_" 190 ia a ee ee ie BNAWAWEMEAT SERBRASERL ODDS PECL NO PEELE NP PCCP POCA EEE POECCCCR CECE SL PrP ELE et oR AMARGS /SURROOUEVZO0NDZE PACE ee LEP PICT Bet Ce Bannan) SHER? @962c40H EDF ALL Vevapoannene i COIL VV Leg LUV MAA ieee VA ie eA ATA meee cece el Ls ee Sy al Phil Mag.S.5.Vol.41.P1.11. ; 2 anaes aie es) eae sca | | Pe I t 7 at [I ae I an | : See 22eeeee ss -- 4 = ee eee Ll =i sk if — j—— 4 SS ir E Saeesa si SS Ie | aaa alae es ee KS o's L N a See ee ea es : \ = eer eee cee aE L c "lig ¥ ae = eee t HE SS EES t V2 ncn me me a Seer erent Sareea tah te one Sa [Now Ready, Free on application.] (No. 257.) A CGafaloque of Books on fhe 2Watbematics, pure and applied, Asfro- rronty, Wefeorology, Chemistry, &e., from fhe {iBraries of fhe Cafe Ssenrvy 3. Stephen Smith, ot. R.S., Savilian Mrofessor of Geometry in fhe Biriversify of @xford, A. 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