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A F444 + te paige de ted Cra lr er en ie “Whe 4 Fee Cage ee 4 et a eh ede iT G-e4 deh ¢ Le, RAH YY 4 » ea See t Uvalde oe 4 MADAM Pa hudt tet bed we ale Aba Mek Rend O Y Tht OG rte diet ae tee 444 ht ty oie ew i bene es | PELs teh ay * m Serie oD koe tye Wdeteds tle a eta hee @ ‘Dae dethea 4 bh latiiden te wacaie te acta DAIL Ie, 1, a, Bh be tet to Oe Pees en BAA te Gee tedu toe toned ih nee 2 OM ed a gig ade “4 t-4- 4 404-6 pie Gs er a woe Peed yd MH ed dal ft gad eis ‘ iy z ~ varted . Ae Oh WAO8 a oe | epetiony Seat f Madetet tet “Pe N-O ae aca ea w Link fe whe 6 SUT OF 1 4ten e o bateh hea acdva VMAS ase ete ag yeah HA AA ARE AT RED YH depen tely ile ari gon a salar Ge a oe ae ae ‘* Ga PEA PE na Might ih terOk aC 4%, Se Eh Ty) oo Cd) Caress aety aed Mas BALA en ant chatty tin kes eek Pa Arts il Nhat Mh tee Mabie Be bs ne SR Ate A ou Py Oe) BER TG HD ek Sek OW pet hy Fay 11 F AT eithe de te Ite ihe + + Rk ete. trues ile aS tet th Sed, eet” fet aay Ag wd +> py t rPP9ths dods ih yt hy TA Teoh od OL Et gett eal ge SALES Oe aw dw ats a4 ¢ 4 Rath-> A VFA page oi Gago kg Gy od 8e4 PTO Nhs Pathe te Heete Why Sri) ts uns i Ct. Cl ee ea) Pee Woe te UN \ + 4 Heh 4aye = mh Seay Op AEE a em Sede 3g $ Oh ae -4rieae gay 600 eh ey Wd Meer ee t Seok, Be a ek DL L409. Fi 2 RH eg O59 O Be Phe Paden Fe " WSs 9 DS , : ‘$4 F a # i | x CF weg SR ae “rite balees ee ateh rh wehtaicanee rs dingi ery ee ern We Y ; + . wd hehe LA Nomar a ate th, 4 rive aaa ae A 4 ' bral bass Wie tortgd phe oh ft Teeth ae let ne gg a . Fs ’ + s 7 - “ ees Tet ey TN ee ta ; . ~ NL 0 Hapedews “On Oe i-¥, Meg EOD A wy. Se Le ip f¢ : Frew LONDON: HARRISON AND SONS, ST. MARTIN’S LANE, Printers in Ordinarp to Her Wajesty. MDCCCLXXXI1Y. LONDON: HARRISON AND SONS, PRINTERS IN ORDINARY TO HER MAJESTY, ST. MARTIN’S LANE, CONTENTS. VOL. XXXVI. No. 228.—November 15, 1883. Mahonia Aquifolia as a Nurse of the Wheat Mildew (Puceinia graminis). mm MRE Hisie erica OTL ieee cece cce-naceseacscnesteJecosacrscerivnsssecnsubeosecsebess sntdesndescasers Description of Teeth of a Large Extinct ae: 2 ca Ser: nodon Ramsay. By Professor Owen, C.B., F.R.S... Me Evidence of a Large Extinct Monotreme nee Ow.) from the Wellington Breccia Cave, New South Wales. By Professor Owen, ee ce ev anos esanednerbacvearnadeieanidiganessepnandenssaveadiaqosetvncitou yiavaqnencece Correction to a paper “On the Determination of Verdet’s Constant ” yee in the ‘ Phil. LYRE” sii Bye J. Ee EH Gordon, Pe eee areca cao crasiacin) od ooh e cat Sagg roves nscductipare coos: dadvansasasspeteesevens vesasasoeseoseay Note on the Ivr i ee in Magnetic Inclination on the West Coast of Scotland. By T. E. Thorpe, F.R.S., and A. W. Riicker, M.A................. On the Circulation of Air observed in Kundt’s Tubes, and on some Allied Acoustical Problems. By Lord Rayleigh, D.C.L., F.R.S.. ....... The Influence of Bodily Labour upon the Discharge of Ni itrogen. By ammnereteas trem rw NOME S20 0c pci ccaecvsscsvenskrnanse. cocvereiven eroceel oaversyaeatd wine Sevan0d0\ Son ogne November 22, 1883. On the Formation of Ripple-mark in Sand. By G H. Darwin, F.R.S Plumian Professor and Fellow of Trinity College, Cambridge................ On the Atomic Weight of Titanium. By T. E. Thorpe, F-RS. «0.0... On the Life History of the Dock Aeidium (ecidium rumicis, Schlecht). oman rms PESO Ea) CWT TG Lats FM foets Soa z ss tletasacet eves ceuceosk cuesccdduecsacse scuelvheesececsesavctese Some Relations of Heat to Voltaic and Thermo-Electrice Action of Metals mmeeecmnonmies: by G. Gore, LT. D., BRS.) cccccccsesecccceccczedensosesecoccecerenee On a “ Rennet ” Ferment contained in the Seeds of Withania coagulais. By Sheridan Lea, M.A., Trinity College, Cambridge .........sccsssssessasesseees Page lV Vovember 30, 1883. ANNIVERSARY MEETING. Page BHEDOFE OL SATIGUCOEN © 5.26 secscons sate secetessceeeeoatnnneeteance saaavare subesesdsdiates'ensiongnsee ea 59 List of Fellows deceased since last ANMIVETSAary ...........ssecssessessrscsrscetesenasees 59 Cece 9 ra... Saxsscn-ccanesnstacstace sessasntorseess-houasnnssss cater aee eeen 60 Address of the: President :.::.......sssssencssseotsscctnenesecs-oooee soveeses eens qndasdi soos maaan 60 Presentation of the Medals ..¢.srassecosegssugesescsesepepsarsegs-a-05s0nenesaaceonnensaaaeteeeeeieenes 73 Election of Comneil and Officers......-...ccs ccs vecseeneosts .0+sesnaseonsieo=s00ss1sn see 75 Bimancial Statement .....cscccescscasscsessnseeesecent-ouconceeedeceseongacesaceese. ceases eee 76—78 PPPOE BUMS | sicesosecsssscenesseceossecnsnsusete sce coseteusteteessoecenncetoien suit c=ss-: eer 79—82 Account of the Appropriation of the sum of £4,000 (the Government Grant) annually voted by Parliament to the Royal Society, to be employed in aiding the Advancement of Science................scocsesseesneeeeseees 83 Account of Grants from the Donation Pumd © s..2,:::5 H SA. lab) JL 1 a TiC], : 4Ag¢Cl= 22 ‘93796 : 69 259383 == jae ¢ 4 Ail e @ SSI NUASALS Wy. IL Ti :O 213) Otay 2 AL AM : H =48 016 ik 1G) eae ae sen TiCl, : T10, =49)-29943): 20 -790e2 = Oil DAtra 1M -O = a) Os) 2 il 4h >: A =47 -969 1 On the assumption that these values have equal weight, the final value becomes— Ue eA 48 ‘014 1D eer eoe anew ar 48 ‘016 LO aa ao eerie: A7 “969 Ti=48 -000 It would appear, therefore, from these observations, that titaniwir must be added to the increasing list of the elements whose atomic weights are sinyple multiples of that of hydrogen. . In these observations, which have occupied me many months, I have sought to eliminate such sources of error as were known to me. It is of course possible, in spite of the agreement between the several values, that the results may be affected by undetected and constant errors. Hxperience warns us that no determination of atomic weight, however well the individual observations may agree among themselves, can be considered wholly satisfactory if it depends upon a single reaction or is referred to a single relation. Itis for this 1883. | On the Life History of the Dock Atcidium. AT reason that I have sought to extend my observations to other compounds of titanium, and to vary the nature of the reactions involved in the chemical process. Unfortunately it is found that comparatively few bodies containing titanium lend themselves to the purpose of atomic weight determination. I am, however, making observations with the tetrabromide, which, in some respects, is to be preferred to the tetrachloride, and the results furnished by its analysis will be given in a second communication, which will also contain details respecting the preparation of the substances used, the methods of weighing, the processes of manipulation, effect of errors, &e. With reference to the tetrabromide, I may here say that I find it can be very easily made by the action of hydrobromic acid gas upon the chloride, and that this proves to be a more convenient method of preparation than that by which it was first obtained by Duppa. III. “On the Life History of the Dock Aicidium C#Heidium rumicis, Schlecth).” By CHARLES B. PLOWRIGHT. Com- municated by W.'THISELTON Dyer, M.A., F.R.S. Received November 10, 1883. This Alcidium, which is common in this country upon Rwinex hydrolapathum, Huds., obtusifolius, Linn., crispus, Linn., and con- glomeratus, Murray, was regarded by Fuckel* and Cooke} as being a condition of Uromyces rumicis (Schum.), is now stated by Wintert in his last work to be a condition of Puccinia magnusiana. During the present year I have conducted a series of cultures, in which the life history of this fungus has been carefully, if not laboriously, worked out, from which it appears that Mcidiwm rumicis bears the same relationship to Puccinia phragmitis (Schum.) (=P. arundinacea, D.C.) as Aicidiwm berberidis, Gmel., bears to Puccinia graminis, Perss. History of the Subject.—Winter, in 1875,§ showed that those botanists who had associated this Aicidium with the Uromyces rwinicis, simply because these two fungi occurred upon the same host plant, were wrong, and that the fungus in question was the ecidiospore of Puceimia phragmitis. Stahl, in 1876, repeated Winter’s experiment, and confirmed it. Now it happens that there are two Puccini common upon Phragmitis communis, the P. phragmitis (Schum.), and P. magnusiana, Korn.|| In March, 1877, Schréter{ placed the spores * Fuckel, “ Symbol. Mycol.,” p. 64. + Cooke, “ British Uromyces,” Grevillea, VII, p. 186. f£ Winter, “ Rabenhorst’s Kryptogamen-Flora,” 1881, p. 222. § Winter, “ Hedwigia,” 1875, vol. xiv, pp. 113-115. | Kornicke, “ Hedwigia,” 1876, vol. xv, p. 179. §] Schréter Cohn, “ Beitrage zur Biologie der Pflanzen,” vol. iii, Heft I, pp. §5-66. 48 Mr. C. B. Plowright. [Nov. 22, of both these Puccinie upon Rumex hydrolapathum (the species Winter originally experimented with), and found that the Aicidium was only produced from P. magnusiana. Winter,* in the ‘‘ Kryptogamen- Flora,’ now in course of publication, accepts Schroter’s statement, and gives as the ecidiospores of Puccinia magnusiana, not only the Ajcidium on Rumea hydrolapathum, but also on LR. crispus, conglomeratus, obtusifolius, and acetosa, and adds a note to the effect that the Mcidium upon Rheum officinale has probably the same life history. Personal Investigations.—In 1882 I performed a number of experi- mental cultures for the purpose of personally observing the life history of the hetercecismal uredines generally. For instance, upon two occasions, a handful of reed leaves and stems were laid upon healthy plants of Rumex conglomeratus; atter a time these plants became affected with Mcidiwm rumicis, and I naturally concluded that this had arisen from the spores of Puccinia maguusiana which I had observed upon the reeds employed. Afterwards, upon three separate occasions, when I had become more expert in performing these experiments, I applied the spores of P. magnusiana to other plants of Rumex conglomeratus and once to Lv. obtusifolvus, but without producing any Aicidium. Subsequent research has rendered clear that on the reeds used in my first two experiments, both Puccinic were present. Being desirous of finding, if possible, the zcidiospores of P. phragmitis, if this plant possessed any, I this year placed its spores upon various Ranuncult (Rh. repens and Iicaria), but without any result. It then occurred to me that Winter might be in error in affiliating all the dock ecidia to P. magnusiana, and that perchance on some of them the ecidiospores of P. phragmitis might occur. ‘This presumption was favoured by the fact that the edicia we have been in the habit in this country of lumping together as AVcidiwm ranwncu- lacearum include two species which, although resembiing each other very closely in appearance, have distinct life histories. I, therefore, on 16th May (1885), placed sporest of Puccinia phragmitis upon Rumex crispus, and in due time obtained an abundant crop of Aicidiwm rumicis. On 16th June, when the Atcidium was perfectly mature, I placed some of its spores upon two plants of Phragmitis communis, where it produced, first the uredo (distinguished from the uredo of P. magnusiuna by the absence of paraphyses), and later the perfect Puccinia phragmitis. Subsequently plants of Rumex hydrolapathum, obtusifolius, conglomeratus, and Itheum officinale, were successfully infected with Puccinia phragmitis spores; whereas the infection of other specimens of these plants with Puccinia magnusiana was in all * Winter, ‘‘ Rabenhorst’s Kryptogamen-Flora,” 1881, p. 222. + The word spore is here employed in the sense that De Bary employs it, namely, to indicate the body produced by the promycelium of the teleutospore. I have elsewhere spoken of these spores as ‘‘ promycelium spores.” 1883.] eases without result. acetosa, but with no result. On the Life Mistory of the Dock Aicidium. Plant infected. 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ODKRODDOOROO pnoyo jo qunowsB UvdTL " *STRIOT, aaquteydoag "* asnsny coe ee Ane me? one co eee eT eo ee Tady 7? * TOIVyL * renig9 7 + Avenue p “$88 19q UL999 IL9Q ULI.AO NT ** 19q00Q “G88 ‘SuUOTY Report of the Kew Committee. 108 “‘punois oy} JO sovzAN [eLOUS oT OAOGV 4oos OY ‘YAdvadourour s UosuIqoy vB Xq poqvorpul sy y Z ‘NV 6 PE 6 PL | "Wap 7 ‘S's ras 8 itt ‘Wd T Tg 6 g WV OL Lz 8 SL ‘Ti WadLTY'WVS] O08 8 SI ‘9 ‘NV 1L 96 62 6 Ze 9) “WA ZHI 8g PT OL ‘Z| ‘wagy L 8s CL 62 ‘WV TT SP SI 62 "N'Y Z Tg OL ¢ | WaO0LR6 6g cI PS "Wd T 8g 6 ou "gOTIUL | ‘SOTTUL “Aq10079 A |'44100f9 A ‘INO, Ajanoy | Ayanoy qSoYVoLy | odBLOAW 9 TT JO JUOWLOAOUL [VIUOZTAOFT 6 6-€€ 06 V-9€ 9T 6-G€ LT 9-0 v G-G6 6 L-61 VG 6-11 AT 6-06 VG 8-06 OT 0-8T 81 0-61 O& 6-96 “sop “OUST *qSOMOT : ‘punors ayy uo 01n4 -v1od ules WINULUTTAL 8-SP P-L €.SV L-VV L.8& 1-68 6-16 g.6& L-6E 8-68 0-VE 8:0V ‘sop WROTA ||'0VVC | qsoySTPT| ‘UBOT ||09Uq T Ler 16 SéL G LET 62 Tht T& SET O& 861 T& STL 86 90T 86 L8 4 64 & POT G SIT ‘sop (‘Onova Us qTnq yorlq) él PEL 861 ScL ron 60T £6 68 99 6S 08 66 ‘sop ‘SABI SUNS UL ong -vroduloy UNUITX'R AAT "AIOYALOSYC) MOST VS 6 9€ GI 9€ GT 8 PI SV VI 8V OL ev OL Ves 96 g Jag 6I 9 9€ 8 Mm "Y || wee “pxLooad Ajrep 4807VOL9 OUTYSUNG JULIE “TIT $148, —'Storjyearosqg [BdLs0[O.100z0 PT VE 00: 661 OV 8T- O8T Sé GL. 89T 8E GI: 98T &V PS. GO’ 8é 9€- SST 66 PS: TVL 96 SV. 1h 8T 8I- 9V OL GV: &G 86 GI. Gh VG GV. 84 Mm “Y ‘auUITSUNS| “poplooat ajqissod | soy yo ose} | JO aoquinu -U9d.10 J [@40T, ** gsoquioydog ee ee ee qsnony reeeee Top ee ee ee oun? ve eeeeee Ke oe eeoe Tidy teeeee doaeyy coos Kreniqoi7 seve Krenue pr “E881 "* Joquredo¢(T ** oq UL.AO \T res 19907900 “6881 “BTJUO TAL Report of the Kew Committee. Table IV. 109 Summary of Sun-spot Observations made at the Kew Observatory. — Months. 1882. BEOIPEOUEI oo 6.5 elec bse «oes INGyeMtber.< cass se sate December... 1883. a2ae SUCHINEEETY, cle ws 5 06,00 00,0 Webruary........ So dneC JUS cn Gee Soe EOC oer August ..... MEP hemiWGRa ae cis co cieuse 0 Motels sa vc Days of observation. 20 10 Number of new groups enumerated. 20 149 Days with- out spots. eo 2O° © US). @ Is --e ..6 110 Report of the Kew Committee. APPENDIX III. List of Instruments, Apparatus, &c., the Property of the Kew Com- mittee, at the present date out of the custody of the Superintendent, on Loan. To whom lent. G. J. Symons, F.R.S. The Science and Art Department, South Kensington. Dr. T. Thorpe, F.R.S. Major Herschel, R.E., F.R.S. Mr. R. W. Munro .. Capt. Dawson, R.A. . Major-General Sir H. Lefroy, R.A., F.R.S. Dr. E. van Rijcke- vorsel Professor W. Grylls Adams, F.R.S. My. E. Mawley..... Professor O. J. Lodge Articles. _—__ Old Kew Thermometer Screen .....2..sc cece Portable Transit Instrument...........-ce0- The articles specified in the list in the Annual Report for 1876, with the exception of the Photo-Heliograph, Pendulum Apparatus, Dip-Circle, Unifilar, and Hodgkinson’s Acti- nometer. Three Open Scale Standard Thermometers, Nos. 561, 562, and 563. Alan nook sien os Gecoo sodden ddu0ne oc do 050500 Invariable Pendulums, Nos. 1821, 4, and 11, Shelton Clock, R.S. No. 34. Stands, and Accessories. Standard Straight-edge.......+ssseereeevees Unifilar Magnetometer by Jones, No. 102, complete, with three Magnets and Deflection ar. Dip-Circle, by Barrow, one Pair of Needles, and Magnetizing Bars. Two Bifilar Magnetometers. One Balance Magnetometer. Two Declinometers. Two Tripod Stands. Two parcels Magnetical and Meteorological MSS. from the Sabine Magnetic Office. Dip-Circle by Barrow, No. 24, complete, with four Needles, and a Pair of Magnetizing Bars. Unifilar Magnetometer, by Jones, No. 101, complete. Small Air Meter, with Robinson’s Cups...... Unifilar Magnetometer, by Jones, No. 106, complete. Barrow Dip-Circle, No. 23, with two Needles, and Magnetizing Bars. Tripod Stand. Date of loan. 1868 1869 1876 1879 1883 1881 1881 1882 1882 1883 -1883 1883 1883 ee ee eee ee eee Presents. Gbiegt Presents, November 15, 1883. Transactions. Brighton :—Health Congress. Transactions, 1881. 8vo. Brighton. Mr. J. E. Mayall. Buckhurst Hill :—Essex Field Club. Transactions. Vol. III. Part 7. 8vo. Buckhurst Hill 1883. The Club. Devonshire :—Devonshire Association. Report and Transactions. Vol XV. (Exmouth Meeting.) 8vo. Plymouth 1883. The Association. Dublin :—Royal Geological Society of Ireland. Journal. New Series. Vol. VI. Part 2. 8vo. Dublin 1882. The Society. Royal Irish Academy. Transactions. Vol. XXVIJI (Science). Nos. 11-13. 4to. Dublin 1882-83. Vol. XXVII (Literature and Antiquities). No. 5. 4to. Dublin 1882. Proceedings. Ser. 2. Vol. Ili (Science). Nos. 9, 10. 8vo. Dublin 1882-83. Ser. 2. Vol. II (Literature and Antiquities). No. 4. 8vo. Dublin 1883. The Academy. Hdinburgh :—Clarendon Historical Society. Publications. Nos. 6-10. Ato. Edinburgh 1883. The Society. Falmouth :—Royal Cornwall Polytechnic Society. Fiftieth (Jubilee) Report, 1882. 8vo. Falmouth. The Society. Glasgow :—Philosophical Society. Proceedings. 1882-83. Vol. XIV. 8vo. Glasgow 1873. The Society. Huddersfield :—Yorkshire Naturalists’ Union. The Naturalist. Nos. 96-100. 8vo. Huddersfield 1883. The Union. Leeds :—Philosophical and Literary Society. Annual Report, 1882-83. 8vo. Leeds 1883. The Society. London :—Anthropological Institute. Journal. Vol. XIII. No. 1. 8vo. London. The Institute. Hast India Association. Journal. Vol. XV. Nos. 2-5. 8vo. London 1885. The Association. Entomological Society. Transactions. 1883. Part 3. 8vo. London. The Society. Geological Society. Quarterly Journal. Vol. XXXIX. Part 3. 8vo. London. The Society. Howard Association. Report. October, 1883. 8vo. London. The Association. Institution of Civil Engineers. Minutes of Proceedings. Vols. LXXII-LXXIV. 8vo. London 1883. Subject-Index. Vols. LIX-LXXIV. 8vo. List of Members. 8vo. The Institution. Institution of Mechanical Engineers. Proceedings. 1883. Nos. 2, 3. 8vo. London. The Institution. 1 Presents. [Nov. 15, Transactions (continued). Institution of Naval Architects. Transactions. Vol. XXIV. Ato. London 1883. The Institution. London Mathematical Society. Proceedings. Nos. 200-206. 8vo. The Society. Meteorological Society. Quarterly Journal. New Series. Vol. IX. Nos. 46, 47. Meteorological Record. No. 9. 8vo. London 1883. 7 The Society. Mineralogical Society. Mineralogical Magazine. Vol. V. No. 24. 8vo. London 1883. List of Members, 1883. 8vo. The Society. _ Musical Association. Proceedings. 1882-83. 8vo. London 1883. The Association. Physical Society. Proceedings. Vol. V. Part 4. 8vo. London 1883. : The Society. Quekett Microscopical Club. Journal. Ser. 2. Vol. I. Nos. 4-6. 8vo. London 1883. The Club. Royal Asiatic Society. Journal. Vol. XV. Parts 3, 4. 8vo. London 1885. The Society. Royal College of Surgeons. Catalogue of Pathological Specimens in the Museum. Second Edition. Vol. II. 8vo. London 1883. Calendar. 1883. 8vo. London. The College. Royal Institute of British Architects. Transactions. Session 1882-83. 4to. London 1883. The Institute. Royal Medical and Chirurgical Society. Proceedings. New Series. Vol. I. No. 8. 8vo. London 1883. The Society. Royal Microscopical Society. Journal. Ser.2. Vol. III. Parts 4, 5. 8vo. London 1883. The Society. Royal Society. 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A chance observation, made in the summer of 1881, drew my attention to the fact that when the ends of an iron wire are connected to the terminals of a galvanometer, a transient current will be observed if the wire be suddenly magnetised while it is held in a state of torsion, or suddenly twisted whilst in a state of longitudinal magnetisation. Further inquiry showed that these currents are satis- factorily explaimable by reference to the results of more direct obser- vations which have been made on the effects of stress on magnetism. They present, however, certain features of interest, and the examina- tion of them, of which a condensed account is given below, may form a useful supplement to any direct investigation of the effects of stress on magnetic susceptibility and residual magnetism. § 2. A straight, moderately soft, well-annealed iron wire, 1 millim. in diameter and 34 centims. long, was placed horizontally in an H. W. position, with one end securely fixed and the other held by a twisting arm, by which any desired amount of torsion might be applied. The twisting arm was provided with a pointer, which travelled over a graduated circular dial. The ends of the wire were connected by long leading wires to a Thomson’s mirror galvanometer of 0°25 ohm resist- ance, with a heavy mirror, which made it fairly suitable for ballistic work. Round the iron wire was a magnetising solenoid of 660 turns, 31 centims. long, in two layers, wound so as to have no longitudinal component parallel to the wire. In circuit with the solenoid was a single large Daniell’s cell and a reversing key. The resistance of this * This condensed version of a paper with the above title, read before the Royal Society, November 17, 1881 (see “ Proceedings,” vol. 33, p. 21), together with a Supplementary Note received later, is printed by order of the Committee of Papers.—G. G. 8. 118 Prof. J. A. Ewing. circuit was 1:36 ohms and, if we assume the electromotive force of the cell to have been 1 volt, the magnetising force was therefore 8 Aa xX o5e x ae =20 c.g.s. units very nearly. 31 ~1:36x109 The ideal diagram (fig. 1) will help in describing the directional relation of the transient currents, the magnetisation, and the torsion. Fie. 1. Reversing Key Ballistic Galvanometer There ab is the iron wire, with the twisting-arm and dial-plate at 0b. The two directions of twist are distinguished by the signs + and —, the latter being used when the twist is that of acommon screw. The two directions of the magnetising current will be called A and B; the connexions for A are shown by the full lines, and for B by the dotted lines. A has the effect of making the dial end (0) of the wire a nominal N. (2.e., a “ north-seeking’’) pole. A transient current will be called positive when it flows along the wire from a to Db. § 3. When the wire was in a state of no torsion the closing of the battery circuit did not of course produce any current in the ballistic galvanometer; nor, when the wire was sensibly free from magnetisa- tion, did twisting it produce any effect. But when the wire was first twisted negatively (like a common screw) and then magnetised by closing the circuit, A, a transient current flowed along it from 0 to a, that is, from N. to 8. Reversal of the magnetising current from A to B, the wire being still held twisted, caused a transient current of twice the quantity of the first to pass in the opposite direction. In like manner, if the magnetising current A was first made and the wire then twisted suddenly lke a common screw, a transient current flowed along it from 0 to a, that is from N. to S., and similar currents were observed when, without maintaining the magnetising force in action, a permanently magnetised wire was suddenly twisted. Un the Production of Transient Electric Currents. 14) 33 § 4. The existence of these transient currents is due to the proluc- tion of a state of circular magnetisation as the result of torsional stress and longitudinal magnetism acting jointly. To prove this, I substi- tuted for the wire a long piece of iron gas-pipe, itself insulated, but carrying in its interior an independent copper wire, which was in circuit with the ballistic galvanometer. The gas-pipe was longi- tudinally magnetised by a surrounding solenoid. The making and reversing of a current in the solenoid whilst the pipe was held twisted, or the sudden twisting of the pipe during or after the operation of the magnetising force, gave transient currents along the insulated wire inside precisely similar to those which had been observed when the two functions of inducing magnet and conductor were both discharged by a solid iron wire. The pipe gave much greater currents, chiefly because of its greater size, but partly also because the metal in it was more advantageously disposed than in a solid rod, both as regards the stress and the subsequent inductive effect on the conductor inside. § 5. That longitudinal magnetisation combined with torsion should give rise to circular magnetism follows from Sir William Thomson’s discovery that zolotropic stress developes an solotropic difference of magnetic susceptibility in iron. When the wire or tube is twisted the stress is equivalent to pull and push along lines perpendicular to the radius and inclined at 45° to the direction of the length. Along one of these the magnetic susceptibility is increased; along the other, at right angles to that, it is diminished. The effect is to change the lines of induction, originally straight and parallel to the axis, into screws, whose circular components produce the transient currents now described. The direction of the currents is that corresponding to increase of magnetism by pull. I shall now give a brief account of the experimental results, and afterwards point out their relation to the discoveries of Villari and Thomson on the effects of stress on magnetism, as well as to certain recent experiments of my own on the same subject. § 6. The wire described in § 2 was twisted oppositely to a common screw by turning the pointer through an angle of 60° to the side marked positive (see fig. 1). As the wire was initially free from any cousiderable magnetisation, this operation gave no transient current. The battery current A was then made, the wire being held twisted. This gave a pusitive transient current along the wire (from a to b), which produced a deflection of 39 scale divisions of the ballistic galvanometer. The throw of the galvanometer will be taken as giving, on an arbitrary scale, a measure of the circular magnetisation of the wire. Then keeping the wire still twisted at +60°, the current A was broken. This gave almost no transient current: in other words, the circular magnetism was scarcely at all affected by the removal of the \ 120 Prof. J. A. Ewing. longitudinal magnetising force. Other experiments with wires of larger diameter and with a tube have shown that to remove the longi-- tudinal magnetising force when the wire is twisted generally produces. a very slight reduction of the circular magnetism, although in some instances it produces an actual increase (see § 22 below). In the present case the breaking of the magnetising current produced no: effect at all comparable with that which was produced by its first establishment. Re-making the current after breaking also gave almost no sensible effect. Reversal from A toB gave a transient current of —/78, showing that the circular magnetism changed to —39, and repeated reversals. of the current gave the same, or very nearly the same, effect. § 7. Again, if instead of twisting the wire first, and magnetising it when twisted, we apply either A or B at the zero of torsion, there is no effect. Let A be kept on, and let the wire be suddenly twisted to +60°: there is then a transient current equal to about +35. The circular magnetisation acquired in this way is therefore somewhat less than that which was reached by twisting first and magnetising afterwards. If now, at +60° of torsion, we reverse from A to B, we have a transient current of —74: in other words, the circular mag- netism is changed from +35 to —39. A subsequent reversal from B to A gives +78, and so on. § 8. If we next keep A made, and change the torsion suddenly from +60° to —60°, we get a current, not of —78, but of only about —72. A twist back from —60° to + 60° gives a still smaller positive: deflection, and successive repetitions of the same operation, under constant magnetising force, cause a gradual diminution of range, until, after many back and forth twistings, the transient currents are —64, when the wire is twisted from +60° to —60°, and +64, when it is twisted from —60° to +60°. This means that the circular mag- netism is then changing between +32 and —82, on the assumption that the effects are symmetrical on the two sides. That they were very nearly so in the experiment cited I have no doubt; there may, however, have been a slight set towards the side on which the first. and greatest circular magnetisation occurred. If, after this steady state has been reached by successive opposite torsions, the battery is — reversed from A to B at +60°, a transient current of —71 shows. that the circular magnetism is at once restored to its normal value of —39. § 9. The foregoing results may be stated more clearly and shortly in tabular form, thus :— On the Production of Transient Electric Currents. 121 Magnetising onion Transient Circular current. current. magnetisation. IN OuA. 273. ..'5)cle-sre leith’ Steady at + 60° +39 + 39 Reverse Ato B...... Es mes —78 —39 sole A Ceae. eee ae aw +78 +39 | AW Waltow Aton! .iecha)s ost + 60° to—60° —72 —33 After several | ac. J a ae A + and —twists, f — 64 — 32 | + 60° to —60° a at el ae —60° to +60° + 64 +32 Then, Reverse A to B. at + 60° —71 —39 BY B to A. _ +78 +39 Also, starting from a neutral state— INWATtIAS OW Y's :0:0 0 «sas | 0° to +60° +35 +35 Reverse AtoB...... at + 60° —74 —39 Pe to AL s ..7%.2 Fie +78 +39 These figures show that if we call +39 the normal circular magneti- sation proper to the given torsion (60°) and the given longitudinal magnetising force, then the first application or reversal of the mag- netising force while the wire is held twisted developes the full normal value of the circular magnetism, whereas the first application or reversal of the torsion under constant magnetising force does not produce the normal value, but something less. Also that this defect of circular magnetism is increased by successive back and forth twist- ings, which finally cause the circular magnetism to oscillate between two considerably reduced values. After this steady state has been reached, a single reversal of the longitudinal magnetising force, the torsion being kept constant, suffices to produce the full normal value of the circular magnetism proper to the state so arrived at. § 10. If after being circularly magnetised by applying longitudinal magnetising force whilst it is held twisted, the wire be relieved of torsion by allowing the twisting arm to return suddenly, but without shock, to zero, a portion of the circular magnetism survives the removal of the stress which gave rise to it. Thus :— Magnetising ater Transient Circular orsion. Se current. current. magnetisation. ene WAN, ieee ere At +60° +39 +39 Wraith cA ton.» 9.5. + 60° to 0° — 24 +15 PANO ay ik ga) cttouents 0 to —60° —48 —33 From the last observation it will be seen that the second step 122 Prof, J, A. Ewing. (0° to —60°) brings us to the value —33, almost identical with that which was reached in § 9 by twisting at once from +60° to —60°. This tendency on the part of the circular magnetisation to follow at a distance instead of accompanying the changes of torsion is still more clearly shown if we divide the whole angle from +60° to —60° into several steps. The following figures give the transient current so obtained after the torsion had been reversed sufficiently often to bring the changes into a steady and sensibly cyclic state. The current A was kept on throughout. Transient Circular Torsion. current. magnetisation. —60° to +60° ...... stiO Ate Seranocciicss +32 ae Sy ara) cooods aT Does + 29 CB) Ae aan 27 eiesere 12 On! BEES Ouse oe MOG a bone —16 2230) come G0 uae aoe had Peo adil ll) with similar values for the return stages. The full lines in fig. 2 give the relation of circular magnetisation to angle of twist during this cyclic operation. They show well how the changes of the former lag behind those of the latter. § 11. The same tendency towards persistence of previous state is exhibited whenever we change the magnetisation of a piece of iron or steel by the alternate application and removal of any kind of stress. It is exhibited also when magnetisation is changed by changing the magnetising force, when it appears as the characteristic ordinarily called retentiveness, to which the existence of residual magnetism is On the Production of Transient Electric Currents. 123 ascribed. It also appears, as was shown first by M. EH. Cohn, and afterwards independently by myself in a paper which I had the honour recently to lay before the Royal Society,* in the changes of thermoelectric quality which occur in iron when it is subjected to eyclic changes of stress. In the instances now referred to this lag- ging seems to be permanent as regards time, so that if it is to be ascribed to molecular friction, the friction to which it is due must resemble the friction of solids rather than the viscosity of liquids. To avoid much circumlocution it is convenient to give this lagging action a name, and accordingly I have called it Hysterésis (from vatepew, to come after, used either of place or time). This name may be properly applied not only in cases where, as here, the persistence of previous state appears to be permanent as respects time, but also in those cases where (as in the relation of strain to stress in a viscous material) the amount of lagging depends on the rate of change of the conditioning quality, and would disappear if that were indefinitely slow. To define the new term more precisely, let there be given two qualities of matter, M and N, of which M isa function of N; then if when N is changed cyclically the corresponding changes of M lag behind the changes of N, we may say that there is ‘“ hysteresis”? in the relation of M to N. The value of M at any particular point of the operation depends not only on the actual value of N but on all the preceding changes of that quantity, and by properly manipu- lating those changes any value of M within more or less wide limits may be found associated with a given value of N. In all the instances of ‘‘ hysteresis”” mentioned above this further characteristic 1s present, that the range through which M varies becomes gradually diminished when a cyclic variation of N is repeated several times, and it would seem that only after an indefinitely large number of repetitions of the cycle of N do the changes of M also become exactly cyclic. § 12. In the paper referred to above I showed that the action here called hysteresis, when it exhibited itself in the relation of thermo- electric quality to stress in a soft-iron wire, could be nearly, if not wholly, destroyed by mechanically agitating the wire during or after * “ Proceedings,” vol. 32, p. 399. t Objection may, perhaps, be taken to the coining of a new word on the ground that the term “ retentiveness,” already in use, expresses sufficiently nearly the same idea. In physics, however, retentiveness is limited by custom to denote the power of retaining magnetism when the magnetising force is removed, whereas one of the instances in which “ hysteresis’? has been noticed has, at least apparently, no con- nexion with magnetism. And unless the word retentiveness be used in a sense much less restricted than is now customary, it will not cover even those cases of “‘ hysteresis’ which occur in magnetic phenomena. 124 Prof. J. A. Ewing. the change of stress. The same thing is true in the present case. After the circular magnetisation has been reduced from 39 to 32 by successive twistings between + 60° and —60° under constant magne- tising force, it can be at once raised again to 39 by tapping the wire vigorously. Again, if in making the steps +60° to 0° and 0° to —60° under constant magnetising force, we permit the wire to spring back freely to the zero of torsion and oscillate there (instead of making the twisting arm come against a stop which arrests vibration), we find that the two steps give nearly equal transient currents—in other words, that at the zero of torsion there is then almost no circular magnetisation. § 18. A still more effective way of restoring the circular magneti- sation to its normal value after it has been affected by hysteresis is to change suddenly the longitudinal magnetisation of the wire. The molecular agitation so produced acts lke mechanical vibration. Almost all trace of the effects of hysteresis vanishes if we simply break and remake the magnetising current in the solenoid. This is especially true of soft iron; with steel the effects of hysteresis are only partially removed by this means. For example, let the circular magnetism be reduced to 382 by successive twistings between +60° and —60° under the A current, then if we break A and remake it, each of these operations gives a small positive transient current, the two together showing that the circular magnetism has risen to very nearly its full value of 39. Or, again, if after applying A at + 60° we untwist to zero, keeping A on,. there is a residual circular magnetism of +15: then let A be broken and remade, and each of these operations will give a negative tran- sient current, the two together amounting as nearly as possible to —15, after which subsequent makes and breaks of the magnetising current will give no effect. If on the other hand we reach the zero of torsion from —60° with A on, the residual circular magnetism is. negative, and in that case positive transient currents are produced when A is broken and remade. Generally, to remove and reapply, or better, to reverse the longitudinal magnetising force while there is no torsion, has the effect of removing any circular magnetisation which mzy have remained from previous operations. § 14. To determine the normal value of the circular magnetisation corresponding to different angles of twist, with the same longitudinal magnetising force, we have simply to bring the twisting arm to any angle, and, nolding it there, reverse the magnetising current more than once. The first reversal wipes out the effect of previous opera- tions and sets up the normal state of circular magnetisation; the second reversal changes that from + to —, and so gives a transient current half of which is to be taken as the measure of the circular magnetisation. The following observations were made at different On the Froduction of Transient Electric Currents. 125 angles of twist from 10° to 60°, the currents being observed after at least one previous reversal of the magnetising force. Transient current given on Circular Angle of reversal of battery. magnetisation. twist ‘paeitea ed (scale reading). amean A to B BtoA 2 + 107 —25 +25 123 —10 +21 —21 10% +20 —41 +43 21 — 20 +42 —38 20 +30 —55 +56 28 — 30 + 54: —52 263 +40 —67 +67 305 — 40 +66 — 64 325 +50 —73 +75 37 —50 +71 —72 36 + 60 —78 + 80 395 — 60 +76 —78 38} The same results are shown graphically in the dotted line of fig. 2 ; comparison of it with the full lines of the same figure will serve to show the part played by hysteresis in the changes of circular magnetisation which are caused by changes of stress. § 15. The torsions which have been hitherto spoken of were well within the limits of elasticity. When the angle of twist was increased beyond 60° the transient currents given on reversal of the battery were not greatly augmented. They reached a maximum at about 90°, at which angle the torsion began to produce distinct permanent set, and for.greater angles they diminished slightly. Moreover, after the wire was twisted beyond its elastic limit, and allowed to come back to its new zero of torsional stress, reversal of the longitudinal magnetism then gave transient currents of opposite sign to those which were given while the stress which caused the set was in operation ; the reason probably being. that the wire, though then free from torsionai stress, had acquired a helical quality with respect to magnetic inductive susceptibility, the susceptibility being less along the lines of permanent extension than in other directions. The lines of induction were therefore screws of opposite sign to the lines of permanent extension. Again, effects of the same sign as those observed would be given by permanent twist if permanent extension produced a state in which the electrical conductivity of the iron was less along than across the lines of strain. After being twisted to +360° the wire was allowed to spring back: its new zero of stress was at +125°. There, after several reversals, B to A gave —7, and 126 Prof. J. A. Ewing. A to B gave +7. By restoring 5° of positive torsion a state was reached in which reversals of the battery gave no transient currents. § 16. The effects which are obtained by twisting and untwisting after the longitudinal magnetising force is removed are somewhat more complex than those already described, on account of the fact that a gradual shaking out of the residual magnetism takes place, which is not, however, complete even after many twistings. For example :— Transient Circular current. magnetisation. At +60°, reverse A to B. FESTA G gee ara Ne +38 Break A. “1, Ba eee sensibly” 2 2p. =: +38 + 60° to Qo eee eeie et lB vas +20 OM, S00. wees ene = Lo Mies Ay ie + l —60 ,, Of aaron nen a eee See Eo Oye) SE GOP eee se foo Cee +17 +60 ,, OVP Eearte cre ate Bea ee eee +138 Oe SOO es amt SS MC Dre ap —60 ,, Ort eve ee a: RS 2 Qe Tot Mea Meares sc a RANKS eS Rito ® +17 O05 OU ence eee eS eiaess ap = OO 5, tO Manse s cee eet ate st ape les +17 Ten more complete wistings; then + 60°40 60 ceciaas 5 ONT a eee +16 SKN oy sr OU cscsuscuss Seo Nanar atid + 8 It is interesting to notice that the circular magnetisation has, so to speak, received a permanent set to the side on which its earliest and greatest value lay. § 17. Another experiment, to show the production of circular out of residual longitudinal magnetism :— Transient Circular current. magnetisation. Make and break A at 0°... er ssiciuct. 0 Mhen,-02 tox 00.42 seer Tithe ae +18 At +60, remake A........ 20M oy ccb, kus +38 § 18. The following table shows the relative amounts of circular magnetism developed in an iron wire (the wire of § 2), with one. constant amount of torsion (60°) by different intensities of longitu- dinal magnetising force. It will be noticed that a maximum of effect is passed at about 15 or 16 c.g.s. units. On the Production of Transient Electric Currents. 127 Transient currents given on reversal of Longitudinal magnetising current. | magnetising 3 force. oe Ue AtoB Bto A Mean. 1°25 — 2 + 2 2 1°64 = + 3 3 2°36 = 7 $7 us 3°20 —15 +15 15 3 64 —21 +21 21 4°2 — 33 +32 32°5 5°0 —46 + 45 45 °5 6°1 —49 +57 58 8-0 —71 +70 70°5 11°3 — 82 +80 81 14:0 —86 + 84 85 15°8 — 86 +85 854 li7feal — 86 + 84 85 1g o7/ — 84. +83 83 ‘5 23 °7 —75 +75 5 A continuation of the same experiment showed that when the magnetising force was increased the transient currents continued to diminish, falling almost to zero, but did not become reversed. Even with a wire of very soft iron a magnetising force of over 100 c.g.s. units still gave effects of the same sign as the above. § 19. Similar series of experiments were made with a piece of pianoforte-steel wire in its ordinary temper. Fig. 3 shows how the linge n° Up Gi 128 Prof. J. A. Ewing. circular magnetisation of the steel wire, starting from the norma value for +90°, was altered by successive twistings between +90° and —90° under the action of a constant longitudinal magnetising force of 20 ¢c.g.s. units. It exhibits very strikingly the lessening of range brought about by successive twistings, which has been already alluded to (§8) as occurring (though to aless extent) iniron. Finally, after several twistings, a sensibly cyclic set of changes was instituted which is shown by the full lines in fig. 4. [The ‘‘normal” curve + ts st = . at Ga r4 ay eas z Saas Ly Weed ee eters ieee peu Sab Sree) Re eeceed be =15)N 7a ee ae © Stee ee op iZ. e fess aac (see § 9) is shown by the dotted line in the same figure.] A remark- able feature here is that when the direction of twisting is reversed the first effect is to continue the same kind of change of circular magnetism as was going on before. The curve rises before it begins to fall, and vice versd. Many other observations have been made, which it is needless to describe, since they are all in obvious agreement with the explanation already offered. It only remains to point out this agreement in the case of those features of the experiments where it is not at once evident. § 20. It was discovered by Villari,* and rediscovered by Sir W. -‘Thomson,t that if an iron rod in a magnetic field be subjected to pull * Wiedemann’s “ Galvanismus,” IT, § 499. + «Phil. Trans.,” Part I, 1879, p. 55. On the Production of Transient Electric Currents. 129 parallel to the lines of force its magnetism is increased, provided that the magnetising force does not exceed a certain value, but decreased if the magnetising force does exceed that limit. Experiments of my own, not yet published, have shown that the Villari reversal of the effect of pull occurs at a particular value of the magnetisation rather than at a particular value of the magnetising force. They have also shown that, apart from its influence on magnetic susceptibility, pull increases residual magnetism when that is not too strong (this Villari had observed), and further, that the changes of either induced or residual magnetism produced by changes of stress always exhibit the action I have called hysteresis, with the characteristic described in § 11, viz., diminution of range in successive operations, with an approach to a cyclic condition when a cyclic change of stress is repeated. The lagging of magnetic change is just such as might, on Weber’s theory of magnetic induction, be ascribed to a frictional resistance opposing the rotation of the magnetic molecules; further, it is capable of being, in great part, destroyed by mechanical vibration. The experiments now under review exhibit the same actions occurring when we deal with the combined pull and push stress set up by torsion. § 21. in view of the discovery of Viilari and Thomson I expected that with a high magnetising force the signs of the transient currents would be reversed, so that they would then indicate decrease of magnetism by pull. This did not occur (§ 18) apparently for the following reason. My own direct experiments show that moderate* pull increases the magnetism of iron only so long as that is less than (very roughly) about three-fourths of its limiting value. Now, when a longitudinally magnetised rod is twisted, the pull and push of which the stress 1s made up act not on the full magnetisation but on com- ponents of it inclined at 45° to the axis. The intensity of magnetism on which the stress acts is therefore rather less than three-fourths of the whole, and hence, even when we increase the magnetising force indefinitely, the action still occurs below, though very near to, the Villari critical poimt. Under these circumstances the transient currents become much diminished in amount, but they preserve the same signs as they have when the maenetising force is small, the signs, namely, which correspond to increase of magnetism by pull.+ * The precise point of reversal depends, amongst other things, on the amount of pull applied. + Sir W. Thomson (éoc. cit., § 229) has applied his discovery of the effects of stress on the magnetic inductive susceptibility of iron to explain G. Wiedemann’s observation that an iron rod traversed longitudinally by an electric current becomes a magnet when twisted, and expresses his surprise at finding no reversal of the poles when a strong current was used; but if the above explanation of the non-reversal VOL. XXXVI. K _ 130 Prof. J. A. Ewing. § 22. It has been mentioned that the removal and re-application of longitudinal magnetising force acting on an iron wire under torsion produced almost no change of the circular magnetism, and that when a small change was visible, it had sometimes the apparently anomalous character of increase of circular magnetism with removal of longitudinal magnetising force. My experiments show that the residual magne- tism of soft annealed iron is generally very great, amounting to as much as 80 or even 90 per cent. of the induced magnetism, provided that care be taken, by the use of a very long rod or a ring magnet, to ~ prevent the existence of any self-demagnetising force when the inducing force is withdrawn (a condition present in these torsion experiments), and also provided that mechanical disturbance be avoided, which, if it occurs, will remove by far the greater part of this large residue. Now any change of circular magnetism which takes place when the longitudinal magnetising force is withdrawn from a twisted wire must be due to the fact that the effect of torsion in producing circular magnetism is either less or greater on the residual than on the total longitudinal magnetisation. The two are so nearly equal that but little change occurs, and in general, when the longitu- dinal magnetising force has not been very intense, the change is of the nature of a diminution. But when the longitudinal magnetisation has been very strong, the 45° components of it, on which the effects of pull and push are felt, may approach so closely to the Villari critical point that the reduction of them which takes place when the magnetising force is removed makes them more susceptible to the action of stress, and so causes an increase of circular magnetism. § 23. To complete the explanation of the results, allusion need be made to only one other point. It was mentioned in § 19 that when by successive twistings from one side to the other, a cyclic condition was established in steel, then at the beginning of each release from torsional stress a slight increase of circular magnetism took place (see fig. 4). My experiments on the effects of stress on magnetised wires show that at the beginning of each loading or unloading the initial change of magnetism is ni relatively to the initial change of stress, if great care be taken to avoid mechanical disturbance. When there is any disturbance at the beginning of the change of load, its effect is to make the magnetisation approach the value which it would assume under vibration. In the torsion experiments the changes of stress were necessarily effected suddenly, and must have been accompanied by some slight vibration. This affords a sufficient explanation of the , of the transient currents be correct, it applies equally to Wiedemann’s result. There, too, the intensity of magnetisation on which the differential effect of pull and 1 push is felt, being Wa of the whole circular magnetism, cannot be increased sufli- ciently to cause the Villari reversal. On the Production of Transient Electric Currents. 131 point now under consideration ; for in the observation shown in fig. 4, the initial effect of beginning to release the wire from stress, instead of being nil, was in fact just that which a small amount of vibration would cause. § 24. The fact that sudden torsion gives a transient current along a magnetised iron or steel rod was observed by Matteucci as early as 1858. An account of his observations is given by Wiedemann (“ Galvanismus,”’ II, § 484:), from which it appears that when an iron rod under the influence of longitudinal magnetising force was twisted like a common screw, the current flowed from south to north. The direction stated is opposite to that taken, under similar conditions, by the currents in my experiments. A possible explanation of this dis- crepancy may be found if we suppose that in Matteucci’s experiments the Villari critical point had been passed, which might have been the case if he applied strong torsional stress in conjunction with strong magnetisation. For it has been shown by Sir W. Thomson,* and confirmed by my own experiments, that the Villari critical point comes earlier with strong than with weak stresses. With the moderate stress used by me, reversal of the effects did not occur even with very high magnetising forces, but it is possible that by using more powerful torsion Matteucci may have brought his rods into the condition which would give decrease of magnetism by oblique pull. This suggestion is borne out by his observations with hard steel, of which it is said that when the magnetising current was broken, the transient currents produced by torsion changed their signs after the residual magnetism had been partly shaken out by the first twistings, showing apparently a passage through the Villari critical point as the magnetisation was reduced. Matteucci has also remarked that the currents become constant only after several back and forth twistings. Curiously enough he says that a twisted rod gives no current when it is magnetised, but it is not unlikely that this (certainly erroneous) observation may have been due to an accidental omission to notice the effect of the first closing of the magnetising circuit after the rod was twisted. Subsequent openings and closings of the circuit do give scarcely any effect. § 25. By using a telephone in place of a ballistic galvanometer, Professor Hughes has observed the production of transient currents in a twisted iron wire by making and breaking a current in a surrounding solenoid, and he has described in a recent .series of paperst this as well as many other closely related results. For example, he placed the iron wire in the battery circuit, and connected the telephone, to the external solenoid. Sounds were then obtained * Toe. cit., §§ 211 and 244. ¢ “Proc. Roy. Soc.,” vol. 31. 132 Prof. J. A. Ewing. by rapidly interrupting the current through the wire. This (whichI have verified with a ballistic galvanometer) is a direct consequence of Wiedemann’s discovery alluded to in a footnote to § 21 above. § 26. Apart altogether from the magnetic origin to which the transient currents described in this paper have been assigned, another cause probably contributes in some small degree to the production of the observed results. From Sir William Thomson’s discovery of the effects of stress on electrical conductivity it follows that an originally isotropic conductor will, when under torsion, possess a helical quality with respect to electrical conductivity, and it has in fact been shown experimentally by Professor W. G. Adams and Mr. J. T. Bottomley that a brass tube, conveying a current longitudinally, becomes when twisted equivalent to a conducting helix. Hence when the longitu- dinal magnetism of a twisted iron rod (forming part of a circuit) is altered, a transient current will be induced in the helical lines of greatest conductivity by the magnetic change of the interior portion of the rod. The direction of greatest resistance in iron is (probably) that of pull, and the lines of greatest conductivity will therefore be helices opposite in sign to the twist of the rod. Magnetisation will therefore give a current from 8. to N. when the twist is that of a common screw. The actual transient current, however, flows from N. to 8. Moreover it is clear that the development of a helical quality with regard to conductivity will not explain the fact that the transient currents pass a maximum when the current in the solenoid is strengthened, nor apply at all to the gas-pipe experiment of § 4. It has been suggested to me that another more recondite partial origin of the transient currents given when a magnetised iron rod is twisted may be looked for in the fact that the diminution of longitu- dinal magnetism brought about by torsion induces a current in the magnetising solenoid, which again reacts on the helical lines of con- ductivity in the rod itself,—an idea which was perhaps present with Professor Hughes when he spoke of the transient currents as “tertiary.” It is safe to say that these and perhaps other influences enter into the production of the effects which have formed the subject of this paper; at the same time it may be affirmed with confidence that the phenomena, as they are observed, find a perfectly satisfactory and ‘sufficient explanation in the setting up of a state of circular magnetisation by the influence of torsional stress on the existing longitudinal magnetism and on the susceptibility to magnetic induction. On the Production of Transient Electric Currents. 133 Supplementary Note to the Original Paper. Received August 30, 1882. In the original paper under this title, communicated to the Royal Society on September 7th, 1881, it was suggested that the phenomena were due to the production of a state of circular magnetisation by the action of twisting stress on longitudinal magnetisation, the effect of twist being to produce a difference of magnetic susceptibility in the two directions of pull and push, inclined at 45° to the axis. Recent experiments of my own on the effect which pull has on the magnetic susceptibility and residual magnetism of iron (an account of which will be given separately) confirmed this conjecture; and, guided by the light which they threw on the subject, I have now made a short supplementary examination of the effects of torsion, which has shown that the conjectural explanation is perfectly satisfactory. To show that the transient currents produced by twisting a magnet are due to the development of circular magnetisation, I substituted for the iron or steel wire used in former experiments an iron gas-pipe, itself insulated but carrying along its interior an insulated copper wire which was in circuit with a ballistic galvanometer. The gas- pipe was longitudinally magnetised by a surrounding solenoid. When the pipe was twisted, a transient current passed along the wire in its interior. Another transient current was given when the longitudinal magnetisation was reversed, the state of twist remaining constant. By this arrangement, in brief, all those phenomena could be repro- duced which were described in the paper as exhibited when the two functions of inducing magnet and conductor were both discharged by a solid iron wire. The transient currents given by the tube were much more powerful, partly because the position of the conductor was more advantageous than when conduction was taking place throughout the twisted metal itself, but chiefly because of the rela- tively large size of the tube. By winding the insulated wire in the centre so that it passed several times through the tube, the effects were proportionately increased. In the paper it was shown that when the longitudinal magnetising force was increased, the transient currents given by reversing that force while the wire was kept in a constant state of twist passed a maximum when (with one specimen) the value of the force was 15 c.g.s. units, after which the effects diminished slowly as the force was raised to 24 c.9.s. units, that being the highest value then used. The effects were such as to correspond to increase of magnetism along the lines of pull. From the discovery of Villari and Thomson that with a certain value of the magnetising force the effect of pull on magnetisation becomes reversed, we might expect the signs of the 134 Prof. J. A. Ewing. transient currents to change if the magnetising force were sufficiently increased. Hecently I have examined the effects with very high values of the longitudinal magnetising force. The transient currents are then exceedingly small, but they obstinately refuse to become reversed, even when the magnetising force is as muchas 100 .g-s. units. The effects still correspond to greater magnetisation along the lines of pull. The explanation of this seeming anomaly les in the fact that the Villari reversal of the effects of stress depends on the intensity of magnetisation rather than on the value of the magnetising force, and that the stress acts here only on a component of the whole magneti- sation. I find that in soft iron, the effect of a moderate amount of pull is to give greater susceptibility so long as the magnetisation does not exceed about three-fourths of its limiting value. With a greater stress the reversal comes earlier, and with a very small stress it comes later. Now, suppose that we apply to a soft-iron wire a powerful magnetising force and thereby approach the limit of mag- netisation. When we twist the wire, the directions of pull and push are inclined at 45° to the direction of magnetisation, and the stress if therefore acts on Ve or about seven-tenths of the ile intensity of magnetisation. Hence pull ought still to increase (though very slightly) the magnetic susceptibility along the lines of pull, and the circular magnetisation ought still to have the same direction as it had when the magnetising force was small; and this is what actually occurs. In the paper, it was noticed that when the magnetising current was interrupted while the wire was held in a constant state of twist, there was scarcely any change of the circular magnetisation. JI now find that although in general the circular magnetisation decreases very slightly in these conditions, nevertheless it occasionally increases when the longitudinal magnetising force isremoved. This happens in soft iron when that force is very high, and its occurrence is in complete agree- ment with direct observations of the effects of pull on magnetism. Jt means that the effect of pull is then greater on the 45° component of the residual magnetism than on the same component of the tem- porary magnetism, and this is the case when the affected component of the temporary magnetism is near that value at which the Villari reversal occurs. The following figures give an observed instance of this action in a very strongly magnetised soft-iron wire which was held in a constant state of twist. Calling the two directions of the magnetising current A and B, and the two directions of circular magnetisation + and —, we have: On the Production of Transient Electric Currents. 135 Ballistic Circular throw. magnetisation. Reversed, Ato B..... + 8 nee + 4 ei aS a es A POM EMAU i e. o i cise ees —9 ae —13 Miandepisratns vt. ie... aR Le et + 4 |Sreoike: 355 ee + 9 Lees +13 JWiaya WeUs AS ner —17 sisi — 4 Here the circular magnetisation was greater in the ratio of 13 to 4 when the differential effect of torsional stress was exerted on the (comparatively small) amount of residual than on the (comparatively large) amount of temporary longitudinal magnetism. VOL. XXXVI. U 136 Prof. Owen. On Parts of a Human Skeleton. [Dec. 6, December 6, 1883. THE PRESIDENT in the Chair. The President announced that he had appointed as Vice-Presi- dents :— The Treasurer. The Duke of Argyll. Mr. De La Rue. Mr. Francis Galton. Professor Prestwich. The Presents received were laid on the table and thanks ordered for them. The following Papers were read :— I. “ Description of Parts of a Human Skeleton from a Pleistu- cene (Paleolithic) Bed, Tilbury, Essex.” By Professor QweEN, C.B., F.B.S., &e. Received November 26, 1883. (Abstract. ) The subject of the present paper was discovered during the excava- tions of docks now in progress at Tilbury Fort, Essex, at a depth of 32 feet from the present surface. It consists of a considerable pro- portion of a human skeleton, the parts of which are determined and described. The imferences deduced are that they were from a ‘some- what aged male of great muscular strength; and such inferences as to food, as might be drawn from the worn crowns of the teeth in use at his demise, are given. A chemical analysis of the bones is added by Dr. Walter Flight, of the Laboratory Department in the British Museum. A section of the several strata dug through before arriving at the bed is appended. This section determines the man to have lived at the so-called ‘“‘ Paleolithic period.” The author acknowledges his indebtedness to Colonel Du Plat Taylor for the transmission of the skeleton, with a notification of its discovery, in a letter of the lst October, 18835; also to Mr. Donald Baynes, engineer of the dock works, who transmitted a section of the strata. These consist, from the grave-bed upwards, of “sand,” “mud,” “‘ peat,” “mud and peat,” “mud,” “elay.” Figures of the bones and teeth described, and “‘ plan of the seetion,”’ accompany the text. 1883. | Capt. Abney. Solar Spectrum. 137 Il. “ The Wave-lengths of A, a, and of Prominent Lines in the Infra-Red of the Solar Spectrum.” By Captain W. DE W. ABNEY, R.E., F.R.S. Received November 20, 1883. M. Fievez has recently sent me a map of the solar spectrum from C to A* inclusive, and as part of this region is one which I have been measuring, I have examined the new publication with great interest. Photography and eye measurements do not exactly coincide in the detail of the grouping of the little a group as far as A, and A itself is shown by M. Fievez’s map as wanting some details which appear in the photographs. Thus in the photographs there are some seventeen lines, whilst in M. Fievez’s map there are but thirteen. Between A and a there are several lines of marked intensity in the photograph which are not shown in the new map. The wave-lengths of the different lines from above “a” to A are not the same as those given by Fievez, when they are taken from comparison photo- graphs of the Ist order of the red and 2nd of the ultra-violet on the same plate, or when checked by photographs of the 2nd order of the red with the 3rd order of the green taken in a similar ‘manner. In my paper, “Phil. Trans.,” Part IL, 1880, I gave a method of using mirrors by which this could be effected, but since Professor Rowland introduced his concave gratings this is much more readily carried out. He has kindly furnished me with gratings for the purpose, having about 14,400 lines to the inch, with focal distances of 7 feet 6 inches and 12 feet 6 inches respectively. These have been employed in determining the wave-lengths of this part of the spectrum. Cornu’s map was used as a reference for the ultra- violet wave-lengths, and Angstrém’s map for those im the blue and green. The two maps may be taken as equally exact. | \ from \ from Description | comparison | comparison | A according of line. of lst and | of 2ndand | to Fievez. [EBLE 2nd orders. | 3rd orders. ae 7184-4 | 7is45 | 7197-7 {sme ae ee rere ee 7 single line \ 71849. Most refran-| 7593°6 7593 ~7 7600 °0 Angstrém gives 7604 gible edge of A. for the centre of this line, which of the bands be took as A is not clear. Lang- ley gave 7600°9 for this edge. * “ Annales de l’Observatoire Royal de Bruxelles,’ nouvelle série, tome V. Ty 138 Capt. Abney. Solar Spectrum. [ Dec. 6, A from \ from Description | comparison | comparison | A according : of line. of 4st and of 2nd and to Fievez. Remarks. 2nd orders. | 3rd orders. Centre of 7643 °2 7643 °33 7652 °2 6th pair of p lines in the flutings fol- lowing A. The determination of A has been made by Mascart, Smyth, and others, besides Angstrom and Langley, with discordant results. I think the above may be taken as accurate as are Cornu’s and Ang- strom’s maps. It may be useful to forestal the detailed publication of my measure- ments by giving the wave-lengths of a few of the principal lines in the infra-red. The scale numbers refer to my map of the infra-red, which is published in the “ Phil. Trans.,”’ Part II, 1880. | Scale number. Description. Wave-lengths. 1046 This line is a triple line, the two strongest components of which 8226 -4 i have the accompanying wave- 8229 °9 5 lensthsieicg tale etic ee 1441 BESS cac 8496 °8 1509 so dd so0d06 8540 6 VOSS 5 tel Nied | pe aiapeegene bears 8661-0 2175 A double line, the components 8986 -2 of which have the scompany| 8989-5 \ ing wave-lengths.......... : 2638 + * 5 9494 °5 } 9500-1 f 3161 Saou danse" 9633 °8 The measurements of the lines have been made with a micrometer by Hilger. The +5455 of an inch can be easily measured, and in extreme cases the ;5;/955 Of an inch can be recognised. 1883.] Mr. R. H. Scott. On Barometrical Disturbances. 139 | December 138, 1883. THE PRESIDENT in the Chair. The Right Hon. Lord Justice Sir Edward Fry, whose certificate had been suspended as required by the Statutes, was balloted for and elected a Fellow of the Society. The Presents received were laid on the table, and thanks ordered for them. The following Papers were read :— I. “Note on a Series of Barometrical Disturbances which passed over Europe between the 27th and the 31st of August, 1883.” By Rosert H.Scort, F.R.S., Secretary to the Meteorological Council. Communicated by desire of the Council. Received December 4, 1883. Plate 1. The occurrence of sudden temporary derangements of atmospheric pressure has been occasionally noticed at all observatories provided with barographs, either mechanical or photographie. Among the most remarkable of these which have been recorded in these islands have been that of January 16, 1869, which appeared at Aberdeen, and to a less extent at Glasgow, and that of January 30, 1876, which was noticed chiefly at Armagh and Aberdeen, and was described by me in a note published by the Meteorological Society (“ Quarterly Journai,” vol. iv, p. 73). In both of these cases the depression of the barometrical column amounted to about 0'1 inch, and the duration of the entire disturb- ance to about ten minutes. In both cases the anemometers showed sudden disturbances both in the direction and force of the wind, and on the latter occasion certainly a shower fell. In 1869 no self- recording rain-gauges existed. It is evident that both of these disturbances were due to the passage of squalls. The phenomena which I have now to notice are very remarkable, inasmuch as they are not accompanied by any traceable disturbance of any other element than pressure, and they appear as clearly at Coimbra and St. Petersburg as at our own observatories. The broad facts to be recorded are that at the end of August a violent volcanic eruption took place in the Straits of Sunda (in 105° 140 Mr. R. H. Scott. [Deena east longitude). The continuance of the shocks is given at from 4 p.m. on the 26th to daybreak on the 27th, corresponding to the interval from 9 a.m. to 10 p.m. on the 26th, Greenwich time; but they probably continued for a longer period. No precise statement as to the moment of occurrence of any particular explosion or shock has as yet been printed. Two letters have been received at the Meteorological Office from the Board of Trade, one from Her Majesty’s Consul at Batavia, and the other an extract from the log of the Dutch steam ship ‘‘ Governor- General Loudon,” which ship was in Sunda Straits at the time of the eruption, having called at Anjer the day before it took place, and again after the place had been swept by the earthquake sea-wave. Neither of these accounts contains any precise statement as to time of any particular phenomenon. The facts which I have to bring to the notice of the Society are the indications of successive disturbances of the barometer occurring also at the end of August, at regular intervals and at every observatory in urope.. I shall distinguish the four disturbances shown on the engraying by Roman numerals. Greenwich time is used... I. At about 1] lh. a.m. on the 27th, a sudden increase of pressure, followed by a decrease, appeared at St. Petersburg, and a similar phenomenon was noticed at Valencia Island, and at Coimbra in Portugal, as well as at all the intermediate observatories over Hurope from which we have been able to obtain tracings of barograms. The character-of the disturbance was not strictly identical, for at the: western stations the rise of the barometer: was more marked than at the eastern. The general appearance of the barograms at adjacent stations. is strikingly similar. It is, however, difficult to select any peculiarly remarkable phase of the disturbance so .as to recognise it and record the time of its: oecurrence at each observatory. This movement (1) was propagated from east to west at a very high velocity, for the recovery of pressure from the first decrease occurred at St. Petersburg: at noon, and at Valencia at 2h. 25m. P.M. on the same day, thus taking only two hours and twenty-five minutes to traverse the distance of 1,315 miles: between the two observatories. II. A somewhat similar disturbance appeared on the 28th, but was propagated from west to east, reaching Valencia at 3h. 20 m. a.m., and St. Petersburg at 5h. 1O m. A.m., and thus. requiring only one hour and fifty-five minutes for its.passage. The same uncertainty as to identification of the phase exists in this case as in the preceding. Tn all cases, however, the most marked phase of the phenomenon has been noted. III. A disturbance travelling in the same general direction as No. i, 1883. ] On a Series of Barometrical Disturbances. - Lah but from E.S.E. to W.N.W., reaching St. Petersburg at 0h. 20m. a.m. on the 29th, and Valencia at 2h. 28m. a.m. on the same day, and traversing the distance in two hours and eight minutes. IV. A disturbance travelling in the same general direction as No. II, but from W.N.W. to H.S.H., reaching Valencia at 2h. 0m. P.M. on the 29th, and St. Petersburg at 3h. 35m. P.m., and occupying only one hour and twenty-five minutes in passage. Similar disturbances, though of a gradually diminishing intensity, can be traced in most of the barograms, occurring at Valencia at about 3h. P.M. on the 30th and 2h. a.m. on the 3lst. After this time the traces of disturbance become less distinctly recognisable. Some of the oscillations are more marked at some stations than at others; the Scotch observatories, in particular, exhibit the later disturbances very distinctly. The engraving, which has been prepared in the Meteorological Office, and which shows all the records reduced to the same scale and to Greenwich time, exhibits the barograms at the following stations, which are enumerated in order of longitude, going from east to west :— St. Petersburg. Pawlowsk.* Vienna.* Brussels. Paris. Geldeston (near Beccles, Norfolk). Greenwich. Kew. Oxford. Aberdeen. Stonynurst. Liverpool. Glasgow. Falmouth. Armagh. Coimbra. Lisbon.* Sierra da Hstrella.* Valencia. Toronto. The stations marked with * have not been engraved yet. A table _ is appended showing the precise times of occurrence of the different phases of the phenomena at each station as accurately as we can determine them. I may conclude by saying that the actual record on the barograms ‘qyofe odky Lavurpao ur osoyy ‘cojouto1eq oy4 Jo asau v oyeorput oddy onbiyue ul sornsy oy]— ALON, | Deetka} EG €h0: 0 eF0- 0 £F0- 0 MO Oe | oie | Gt wove |S SG © eee) OS py GE) = OFO- OFO- 040. 090. Oy 6 | He ete 6 | ea ello © 08 6 Ge el) Giz 1h) ep ENE oS 960. 620. 90. 6F0- BORG |nOue a ANGis CalnOcnce RCO uta Ree aCel cit ca ccVam Rel Igy a ey See USE UEEy § O00. O00. 080: 00. Gcacleocet |84cp cul Gunes meinen @GRCal) Gute |GSC ei) Remi pees iee ce ee MOMOUNGH 5 820- 00. P90: 9F0- Ig el ey | 3 lone p28 | © 8] G ei Ge LPs © "t+ MoBSU LD “<< 00: 620: P90. 90: eezierrilszei|o z|ShvFls9%]/s6o1|8ST\o T| °° tee? qeanyduoyg > 960- 9V0- 690. 690- 02 BSS a les Boo i es © |) Or S| ES 2) Se Olen 8 BRO TMOG 3 10. KO 00: 080. Ope eS a | Gem) SS 0 |S SO SoS Wl] GB 1 ea © Poh 088 oe Si Be NDAD) ) L977 30 Stonyhurst 5 Sree 13 20 | 26 50 | 50 25 | 62 25 | 87 40 | 97 30 | 124 5 Aberdeen ........| 18 20 |} 27 5 |, 50 30 | 62 30 | 87 20} 98 30 Meonerereresaeei le 15 |, 27 15 | 50, 15 |) 62: 30 = 98 0] 124 5 Greenwich ........| 18 15 k 27 15 MATA ie Aorets ecco 138 15 { 27 30 | 50° 0 | 62:50 Brussels .... 12 35 | 27 45 | 50 O || 62 55 | 86 45 | 98 40 St. Petersburgh ...| 11 15 | 28 40 | 48 30 | 63 50 | 84 40 From these figures are deduced the intervals between the successive passages of the waves from east to west, and from west to east, 146 Lieut.-Gen. R. Strachey. [Dees TS, respectively, or of the times of travelling round the earth, which are shown in Table III, for all the stations except Toronto. Table ITI. Intervals occupied in travelling round the earth Place. From east to west. From west to east. I to ITI.) IIT to V.|V to VII.) Mean. | II tol V.|/IV to VI.) Mean. he me) he am: heme heme haem: hh. am. Shee Valencia ...... Solas | ove 360508 esGnar 35 35 384 5 | 34 50 Coimbra ......| 36 40 ne a 36 40 35 45 oa 35 45 Armagh. cc! of 10 1 3% 95 36 45 avi WOH SiS sO 34 5 | 34 48 Halmouth s.c.0|o7 OST? 32 e878" sie 35 m5 Shes) |) 33) 2 Glasgow .:...-|.97, 5 | 37, © ae yf 3) 85 20 35) 10 35 45 Stonyhurst ....| 37 5 | 37 15 | 36 25 | 36 55 | 35 35] 35. 5 | 35 20 Aberdeen .....| 37 10 | 36 50 oe Sie 0 35) 25 36 0} 35 43 Kew tt. 4 seeelod (ON) S6055* 40386755" lesGnon 3 Is 35 30 | 35 23 Greenwich ....'!| 386 45 ALIS aides ce || (20 40 &2 ne 36 45 35 20 ae 35 20 Brussels ...:..| 37 25°] 36 45 ae BY a5 35 10 30 45 | 35 28 St. Petersburgh | 37 15 | 36 10 ne 36 43 35 10 be 35 10 Mean excluding Toronto ..| 87 4] 36 54 | 36 48 36 57 35 24 35 9. | S35 ae * At these stations the fifth transit cannot be traced. From the results thus obtained it would follow that the wave travelled round the earth from east to westin 36h. 57 m., being at the rate of (1026 hour for one degree of a great circle of the earth, and from west to east in 35 h.17m., being at the rate of ‘098 hour for one degree. From the velocities thus determined the probable time of the origin of the wave has been calculated from the known distance of each place from Krakatoa, the time occupied in the passage of the wave from Krakatoa to the place of observation, and the observed time of the passage of the waves. The mean value thus obtained from the waves moving from east to west for the time of the origin of the disturbance at Krakatoa is 2°52 h. Greenwich mean time, or 9°53 h. local time, that is 9h. 32 m. A.M. of the 27th August. In like manner the waves travelling from west to east will give the following results (Table V) :— The mean value of the time of the origin of the disturbance obtained from the waves moving from west to east is therefore 2°20 h. Greenwich mean time, or 9°21 h. local time, that is 9 h. 13 m. local time. st a EC.Z ee ee 8G.Z ee ae GCc.Z oe ee OV-%G ee ee ee DOD GP 2 O10 KE) AVE cL. 1 19-8 G6: 68 6S. OG. 8V 16 SV €6-G cc- Il 60: 6 G6. 148 | °°" Ysanqs1oz0q “99 < IP-% CL. 98 VE-V8 19. 00.02 | 6&-ZP VL-% 8¢-éI rr OL | GZ- LOL | ~*~ ~ S[essicd S 6OP-'V8 9V- 3G 00. 0S PG. LV 99.4 GZ: ST (KEBLE | feito Eye ee ea TIRES S pe | 8 i 99. 4h | ¥S-% | 92-8T | T4Z-CT | 98 POT |°**°"** Yormuoory .% 0S-% | 80-P2L | 8S- Tel Mig a €9. 8 LG. GG. OG 89. LV GGG GG: S&T SZLAOISMSSAPOl sa oe Gti OI R OL-% 6€. 48 69-18 68-6 OG. OG 89. LP 09-@ §€- ST 64-01 | 8S. FOL | °° °° °° ** Weopreqy 3 Ip-@ | 80-P2T | 49-T6T | S6-2 19. 18 64-8 G9. Gv: OS Lh. Liv 1S-@ S€- ST Z8-OT | Sh SOT °° °° ** ysanqAuoyg S og.z | 9¢-28 | 82-78 | o4-2 | gc-0¢ | e8-2F | zo. | 0G.eT | 88-01 | $0.90T |******** MossETD DY Ss 09-3 | OG. PZT | 06- T2T a ne 6.98 GP-G GP: OG 00- SP LE. oV-SL GO: 11 | $2.40 |" ~~ * WyMourpey S iS 09-3 | OS-PZL | 06- TST | 08-2 cL. 18 c6- 98 L9.@ 19. 0S 00. 8P GV-G 0G. €T Os Ge | la MOe [OPS See Orupsithueaiye RC 66: G8 90.6 OG. 0G PV. SV VE-3G €8- &1 G75 JEJE |] FAO SILL |] ER IGBEN KON) > 9¢-6 | G4-FCL | 6I-2eL | 89 Z 66: 48 PC. C8 US. €8- OG 6G: 8P 8G-G 66: €T Ve-1k | SV-OLL || - =» Bloteleiy 8 ‘st "SIT “SIFT ‘SATT “SAT ‘SI | “St ‘SUTT "SUE ‘SIT ‘SAT "SILT e SS a a oe ae eos rey Ss ii: ee é 2) Oi eoe ob ee 8 Ss tA] ‘oavm | Be | ‘oan |e | cosem eel Peele) Nrel| Meath ie =) 2 | 03.8 |qguesss| GB | 2088 | way Be | ee. B | pam | @S | e032 | sep | es | Be a) 3 = o |pestosqo| g 3 IS 2 |peatesqo] a 9 [poaresqo) 8) 5 o [poatosqo| + d 3 g8 aa : a fc) ae : 5 se = oF 908 I 6B =) B ise K ‘ouIT} UBOUT a ¢ ‘ouy Ureut 2.3 “OUIT] UROUT ZS “ouT] WROUL & eo _ 5 = TPOTMU9@L1) fa. = TOLM W004) "fa TPOTMU9L) ach YOIM W900.) © bp ae ct mS 55 a “AT 919° .D [Dec. 13, Lieut.-Gen. R. Strachey. 148 OT-%@ es 08-2 L9- 86 IV-3 00-86 16-46 0G: 86 66-T 0S: 46 G0-@ 0S- 26 LYV-@ GL. L6 ¢0-T 6€- 96 PI-T LT. 96 "SLT "SUF *poonpop "JATM UISILO YXx1s jO OWLy, peatosqgO ‘OUIT] UROUL YOIMUIALY GG: £6 L8- S6 €Z. S6 T9- G6 6S- G6 6S. 96 TS. G6 SP. S6 86: 96 83. G6 98. V6 £0. 6 “JISUBIY Yyxts yoror 07 OAM IOJ OWL, “Sa AL O€-Z 68-1 €E-G 8E-%G 60. N OO WN €€.- ‘poonpop UID LILO JO ouwty, "OULT] UBVOUL TYOTMUIILL “BAL 68- €9 66- 69 68. 69 OG. 69 0g: 29 GV: 69 &&- 69 GG. 69 GG: G9 19.69 80. 69 “OAM YAN oF peatosqo a8 | ia 61-G V6- 19 10-&@ 6G. 09 TV-G SV. 09 6:6 €&: 09 06:6 TS. 09 G6:% T§- 09 GO: @ &Z- 09 88-T LT- 09 IT-@ 00: 09 82: @ 00-09 60-G 8g. 6G G9: @ GL. 6S 60-4 "SAET "SAF “VISUBLY “poonpop YqANoF UISTLO toro JO OUT], 07 OATM LOfF OUT, dite STEN 19-86 GL. 16 0S 46 Gé- 16 G6: LE 80- £6 68. 92 00. Lé 00. £z G4. 96 G6: 9G OG. 94 "SIL "OATM puooos poarosqg “OULL] UBOUL TOIMUAAL eee | €0- SZ C6, FZ 68. 1% CL. VS CL: VG 08. FZ Gh. 0% “Sa AL “qISUBLY puooos yorod 07 OAVM OF OULLT, "BOYRY VAY UWLOAT d0UR ISI e@eeere08 ** SUBOTI e e e - ° e ° . ° e e e e ‘ Yonqgs1oj0g "49 "*** sjossnag ee ** SIG “YOTMUIOL4) vee ema uws0p10qV qsanyfu04¢ " MOSSRTO YIMowyR iT ' SVU Y * BIQUUIOD * BTOUITB A “OOCT TL 1883. ] On a Series of Barometrical Disturbances. 149 The mean between the two values obtained from the waves travel- ling against the earth’s motion of revolution and those travelling with it is 2h. 24m. Greenwich mean time, or 9h. 24m. local time, 27th August. The velocity of the waves in miles will be for those which travel from east to west 674 miles per hour, and for those passing from west to east 706 miles per hour. The velocity of sound is fora temperature of 50° F. 757 miles an hour, and for 80° F. 781 miles an hour. With a temperature as low as zero F. the velocity will only be reduced to 723 miles an hour, which is still considerably in excess of the greater of the observed velocities. The excess of the velocity of the waves which travelled in the same direction as the earth’s motion of revo- lution, that is, from west to east, over that of those which passed in the opposite direction, is about 32 miles an hour, which might be accounted for by the circumstance that the winds along the paths of the waves would, on the whole, be from the west, which would cause an increase in the velocity of the one set, and a diminution in that of the other, so that the observed difference of 32 miles would correspond to an average westerly wind of 16 miles an hour, which is not im- probable. It should be observed that the path of the wave which passed Toronto approached very near to the North and South Poles, and that the velocity in both directions appears to be somewhat less than in the waves which passed over central Europe. The wave which passed northwards over Asia travelled at the rate of about 660 miles an hour, or about 15 miles an hour slower than the wave which passed over Great Britain from east to west. This reduction of velocity seems to be within the limits of what might be due to the low tem- perature of the regions. The wave travelling from east to west having been perceptible on the barometer traces at several of the stations until about 122 hours after its origin, and its velocity having been 674 miles an hour, it had travelled before its extinction more than 82,200 miles, aud had passed 3+ times round the entire circuit of the earth. It is further worthy of notice that during the 30th and 31st of August and lst September, a very severe cyclonic storm was crossing the North Atlantic, and that the wave coming from the westward early on the 31st, No. VI of the series, must have passed on in front of the cyclone, and that its next transit would have carried it into the very centre of the cyclone near the British Isles on the afternoon of the lst September. This perhaps accounts for no trace of it being found, though the wave coming from the eastward on the morning of that day, just before the cyclone had arrived, No. VII, was discernible. There is no definite statement, so far as I am informed at present, of the true time of any particularly severe shock or explosion at 150 On a Series of Barometrical Disturbances. [Dec. 13, Krakatoa excepting that which is contained in the letter of Mr. Watson (published in ‘ Nature,” 6th December, 1883), whose ship was within a few miles of the volcano on the morning of the 27th August. He refers to an unusually severe explosion as having occurred at 11 h. 15 m. a.m. local time, which is nearly 45 minutes later than the time, 9 h. 32 m., arrived at in the foregoing discus- sion. The point of the disturbance (as indicated by the baro- grams) which has been taken as the front of the wave is the highest point of the first abrupt rise of the trace, and is perhaps on an average not far from one hour after the first signs of disturbance, the increase of pressure having been very rapid during the interval, but broken into two or three steps or oscillations. During the following half-hour there is usually a large decrease of pressure, succeeded by another abrupt rise lasting about halfan hour. Then follow a fall of about an hour, then a rise of an hour and a half, and then a fall of an hour and a quarter. The whole length of the dis- turbance on the time scale is between five and six hours, corresponding to an actual distance of between 3500 miles and 4000 miles. The length of the first main wave of the disturbance is about one hour on the time scale or about 700 miles in length over the earth’s surface. In the present position of our knowledge of the facts, it can only be surmised that the shock of 1] h. 15 m. a.m. of the 27th August observed by Mr. Watson corresponds to the second main feature of the disturbance. That the wave which forms the first feature would have originated at 11 h. 15m. A.M. is apparently inconsistent with the observed velocities, which it has been shown are remarkably consistent, and indicate without much doubt an origin at 9h. 32 m. A.M. The barometric disturbance at Mauritius noted by Dr. Meldrum is said to have begun soon after 11 a.m. local time. The distance from the volcano to Mauritius being about 3450 miles, the wave at the rate of 674 miles per hour would have reached the island in 5h. 7m. Taking the great shock at 2h. 32m. Greenwich mean time, as before reckoned, the wave would reach Mauritius at 7h. 39m. Greenwich mean time, or adding the allowance for difference of longitude, 3h. 50 m., the local time would be 11 h. 25 m., which agrees satisfac- torily with the facts as recorded. In conclusion, it may be noticed that the sea-waves produced by this volcanic disturbance, assuming the time of its occurrence to have been 2h. 32m. Greenwich mean time of the 27th August, were propa- gated with an approximate velocity of 480 miles an hour to Mauritius, of 430 miles an hour to Port Elizabeth near the Cape of Good Hope, and 420 miles to Galle, and a somewhat slower rate to Aden. The details of the occurrence of these waves on the coasts of India will shortly be laid before the Society by Major Baird, who has informed 1883.| Electric Discharge with Chloride of Silver Battery. 151 me that the velocity of the wave between Galle and Aden was 378 miles an hour, and the lengths of the great waves from 287 to 630 miles. Postscript, December 15.—Since the above was read before the Royal Society, a copy of the barometric trace from New York has been received, which shows disturbances very similar to those recorded at Toronto, and at times which are quite in accordance with the conclu- sions stated in the paper. Ill. “ Experimental Researches on the Electric Discharge with the Chloride of Silver Battery.” By Warren DE La Rue, M.A., D.C... Ph.D., F.R.S., and Hugo W. Muuuer, Ph.D., F.R.S. Received December 5, 1883. Seconp Postscript to PartIV. ‘* Par. Trans.,” Part II, vou. 174. Striking Distance. In a postscript to Part IV of our researches,* we stated that, with 14,400 cells, partly of the rod form, partly of the chloride-in-pow der form, the length of the spark between paraboloidal points was 0°7 inc h (17°8 millims.), and between a point and disk 0°62 inch (15°7 millims.), and that it does not appear, therefore, that the law of the spark being as the square of the number of cells holds good beyond a certain number. These results were obtained at the Royal Institution; since the removal of the battery to our laboratory we had not, at the date of the postscript to Part IV of our researches, charged up the whole of it. Recently, however, we have put the battery in thorough order, _ by scraping the zinc rods} of the cells already charged up and added newly made up cells to bring up the total to 15,000 cells, all of the rod form. Having the whole 15,000 cells in perfect order, we thought that it would be desirable to make fresh determinations of the striking dis- tance, increasing the potential a thousand cells at a time, between two very slightly convex disks (planes), a point and disk, and two para- boloidal points. These points are one-eighth of an inch (3°175 millims.) in diameter, and three-eighths of an inch (9°525 millims.) long. In the case of a point and disk, the point was like one of those used for * “Phil. Trans.,” Part II, vol. 174, p. 725, separate copy p. 249. t+ We are at present making experiments in order to prevent the deposit of oxy- chloride of zinc on the zine rods by covering the charging fluid with a layer of paraffin oil. WOE. XXXVI; M 152 Drs. W. De La Rue and H.W: Miller. “Dee: 135 two points, and the disk was 1,3; inch [3°334 centims.] in diameter. The two planes used were 1,5, inch [3°334 centims. | in diameter. As the points, particularly the negative, are deformed at each dis- charge, the precaution was taken to touch up the point after each discharge in the shaping-tool, screwed to the mandril of the lathe, mentioned in Part I of our researches,* and thus to restore it to a true paraboloidal form. The following results were obtained between :— Table I. Two Disks. Striking distance. Cells Inch. Centim. UPA OO Ue Mey side's QeiASs yp aetiee rere 0 3759 P0002 or Se crac OsGOr” tiie were 0 4191 A OOO eee Ore Sl 2) whee, 0 °4597 tS OOO ese OOS tte. Beers 0 *5029 Table IT. A Point and a Disk. Striking distance. Ss >> Cells. Inch. Centim. 1 OOOF oie BRAS HE Os0055. 205, chee 0 -0140 23000) HORS 2 Ox0240:5 Aon eee 0 -0610 3,000 ay BAehiae OcOCO0R sae eae 0 -1524 ASOOOML TAS TOY: OcO950) To tekaes 0 2413 OOOO E tated Of 700mm ee 0 -4318 COOKS eee O 2300 ahaee cee 0 5842 72000: Fir eRe O-27 70) se: CR SE 0 -7039 SiO00h to eel aee OS4500) gene ne 0 -8762 DOOOne a. se wtlar Or S900 leapt aeoee cee 0 -9906 EOLOOORe haste. 0 A540:ha) ehaa 2 1 1028 HN000 fia oa. & 0: A SOR Meese 1 2141 12 OOO iE WSN.) On S200 emirate. sae 1 -3208 LSO00) gGu. s24-& Os SOSOP ata. Beex: 1 4427 VA CQOOMY Fences O ,, 31 15,450 1 -6600 9,307 0°93 31 156 Drs. W. De La Rue and H. W. Miiller. [Dec. 13, Table VI. Two Paraboloidal Points. Bees Differencsoe Intensity of force. E.M.F. in dist g potential per volts. Sec centimetre. centimetres. Volts. Electro- Electro- magnetic. static. 1,000 0:0173 57,866 5:79x 10! 193 2,000 0 :0493 40,568 ALOG. ’;, 135 3,000 0°1282 23,409 2esa 78 4,000 0°3078 12,996 1b 310) oe 43 5,000 0 :5107 9,790 OLSSi Ss 33 6,000 0 6845 8,766 OrSSin ss 29 7,000 0 °8496 8,239 Ons20 oF 8,000 TSO 7,908 On79ReS 26 9,000 1 °1602 Cll 02782 e: 26 10,000 1°2913 7,744: ORT > 26 11,000 1 °3130 7,785 OSes 26 12,000 1 °5243 7,873 O&79 7 -s 26 13,000 1°6271 7,990 OSSORes 27 14,000 1 °7146 | 8,165 Or8Zhes 27 15,000 1°7961 8,351 0°84 ,, 28 15,450 | 1 °8500 | 8,351 0°84 ,, 28 An inspection of the diagram, drawn on a reduced scale from the curves as originally laid down, shows that the curve for approximate planes (slightly convex, to ensure the centres being the most promi- nent) is continuously concave, whereas those for both point and disk and two points are concave only for a certain distance, and then turn off and become convex. Moreover, that the intensity of force per centimetre decreases continuously up to 15,450 volts in the case of planes; but that, in the case of a point and disk, and also in that of two points, the decrease ceases after a certain potential has been reached, and that then it increases so as to become nearly a constant quantity. Between a point and a disk the potential per centimetre at 9,000 volts and beyond is very nearly 9,200; consequently, if the law holds good, to produce a spark 1 décimetre (38°94 inches) long, 92,000 volts, one 1 metre (39°37 inches) long, 920,000 volts,* and a flash of lightning 1 kilometre (0°621 mile) in length, a potential of * To produce a spark between a point and a disk used for example as the dischargers of an induction coil— It would require in E.M.F. In length. volts. IPONON Ss oogaceouag * eyaiey/ VfOOb) csi. wabieete«, 1250;,400 Myards Meisel specie moti coO 1883.] Electric Discharge with Chloride of Silver Battery. 157 920,000,000 volts would be required, but this potential would be lessened by the diminution of the atmospheric pressure at the height of a kilometre, namely 607°4: millims. (799,210 M), or a mean pressure of 713°8 millims. (939,211 M) between 1 kilometre and the earth. Taking the mean pressure 939,211 M, it would require 864,000,000 volts to produce a discharge between a cloud (regarded as a point) 1 kilometre high and the earth. It is extremely difficult to conjecture how a cloud can become charged to such an enormous potential, unless the charged molecules balance each other (as those of a stratum in a vacuum tube may be conceived to do) until a disturbing cause breaks up the arrangement ; and then the whole of them are discharged in one direction with their aggregate potential. We may add that less than 15,000 cells would not have sufficed to make out the fact that the intensity of force to produce a discharge between a point and disk or two points becomes a constant after 9,000 to 11,000 cells has been reached. The following table gives the ratios of the striking distances be- tween a point and a disk and two points respectively, taking those between two disks as unity. And also the relation between the striking distances between a point and a disk and between two points, taking those between a point and a disk as unity. | | | Ratio between point | Ratio between two | Ratio Pe daeee two Cells. __and disk to that points and that | 4144 Les iy : | | between two disks. | between two disks. | 22" P°bween a pon | and disk. With 1,000 0-60 0°84. | 1°40 | 2E00 1°32 1°15 0:87 » 3,000 2-09 1-94 0-93 | » 4,000 2°68 aot 1-26 | » 5,000 3-42 434. 1-27 | » 6,000 3-82 4°65 1°22 pe 72000 3°91 4°72 1-21 | © 8.000 3-94 4°71 1-20 | » 9,000 3-89 465 | 1-20 3, £0,000 3°80 4°51 | 1-19 Peele OOO 3°69 4°35 | 1:18 ,» 12,000 3-58 4°18 1:17 » 13,000 3°46 4-00 1°16 », 14,000 3°39 3°84 1S = ta000. | 3°30 3°68 1°12 | | Mean 1°16 The striking distances from which the above ratios are calculated are those obtained from the smoothed curves. 158 Prof. G. H. Darwin. [Dec. 13, IV. “On the Figure of Equilibrium of a Planet of Heterogeneous Density.” By G. H. Darwiy, F.R.S., Plumian Professor of Astronomy and Fellow of Trinity College, Cambridge. Received December 3, 1883. The problem of the figure of the earth has, as far as I know, only received one solution, namely, that of Laplace.* His solution involves an hypothesis as to the law of compressibility of the matter forming the planet, and a solution involving another law of compressibility seems of some interest, even although the results are not perhaps so conformable to the observed facts with regard to the earth as those of Laplace.+ The solution offered below was arrived at by an inverse method, namely, by the assumption of a form for the law of the internal density of the planet, and the subsequent determination of the law of compressibility. One case of the solution gives us constant compres- sibility, and another gives the case where the modulus of compressibility varies as the density, as with gas. It would be easy to fabricate any number of distributions of density, any one of which would lead to a law of compressibility equally probable with that of Laplace; but the solution of Clairant’s equation for the ellipticity of the internal strata of equal density seems in most cases very difficult. Indeed, it is probable that Laplace formulated his law because it made the equation in question integrable, and because it was not improbable from a physical point of view. The following notation will be adopted :-— For an internal stratum of equal density let— 7 be the radius vector of any point, a the mean radius of the stratum, e the ellipticity, w the density, ¢ colatitude from the axis of rotation, the hydrostatic pressure at the point 7, ¢. For the surface let r, a, &, ty denote the similar things. Let M be the mass of the planet, p its mean density, w the angular velocity of rotation, m the ratio w*/zp. * Since this paper was presented I have seen a reference to a paper by the late- M. Edouard Roche, iv vol. i of the Memoirs of the Academy of Montpellier (1848), in which the problem is solved, when the rate of increase of the density varies as. the square of the radius. See Tisserand, ‘‘ Comptes Rendus,” 23rd April, 1883. + Laplace’s hypothetical law of compressibility arises from a law of internal density for which the problem had previously been worked out, as an example, by Legendre. See Todhunter’s “ History of the Figure of the Earth,” vol. ii, pp. 117 and 337. 1883.] On the Figure of Equilibrium of a Planet, &c. 159 Let & be the ratio of the density of the stratum a to the mean density of all the matter situated inside that stratum, and & the surface value of k.* Let C, A be the greatest and least principal moments of inertia of the planet about axes through its centre of inertia. Let @ be the ellipticity which the surface would have if the planet were homogeneous with density p, so that e=2m. The condition that the surface of the planet is a level surface is satisfied by— CA 2 Miaz(e— Fim)a ee ae Poo Ue The condition that the internal surfaces are also surfaces of equi- librium demands that e should satisfy Clairaut’s equation— 2 a : #—62)| warda +2wa? ie +2)=0 ee al) - a~/ JO a da? da It may be proved from (2), and the consideration that w must diminish as a increases, that e cannot have a maximum or minimum value. Also it may be shown that the constants introduced in the integral of this equation must be such that— (ag / =e ee 2 ~ ~ = +) - > S 3 . ¢ Ae 2eada (ea) ©) when @ is put equal to a after differentiation. The mean density is given by— ap =3) ‘word Peat athe abel ou arse, ofan CE And pe P Neglecting the ellipticity of the strata, we have the moment of inertia about any diameter of the planet given by— C= $x watda shin area elem aA A 15)) 0 The ratio of (1) to (5) gives the precessional constant. The pres- sure and density are connected by the equation— (G2 +400 da+ ¥ [oatda=0 ee eee 1G) ¢ a\w da a Jo * k, k, are the reciprocals of f, f, according to the notation adopted in Thomson: and Tait’s ‘ Nat. Phil.” (edit. of 1883), § 824. 160 Prof. G. H. Darwin. (Dees: Now if w bea function such that wdp=da, the differentiation of (6) leads to— a ue odie da ajo and a second differentiation to—- (8). It is well known that Laplace assumed that the modulus of com- | pressibility of rock varies as the square of the density. Since this modulus is wdp/dw, Laplace’s hypothesis makes w proportional to w, and the equation (8) is at once soluble. After the determination of w as a function of a, the solution of all the other equations follows. In this paper I propose to find a new solution, and to compare the results with those of Laplace. In order to simplify the analysis let the unit of length be equal to the mean radius a of the planet, and the unit of time be such that the surface density fv of the plant is also unity. Now let us assume that the law of internal density is— OR 5g (CSc Then the mean density of all the matter lying inside of the stratum ais a—"/(1—3n). Hence, by definition we have— k=Il—fn-. of 1 oe eC Thus we see that / is a constant for all strata, and therefore also for the surface. In Laplace’s theory é is variable. With our assumed law of density and the special units, p the mean density is equal to the reciprocal of k. It is clear that ~ must be positive, otherwise heavier strata lie above lighter, and it must be less than 3 in order to avoid infinite mass at the centre of the planet. Now let us find the law connecting pressure and density, and the modulus of compressibility. Equation (7) becomes 1883. | On the Figure of Equilibrium of a Planet, Sc. 161 Integrating this, with the condition that the pressure vanishes at the surface, we have, 27 1—a@24—2) PRaeayd=amy ee 20 = 1— PE CLeay Ceo ace oe whence the modulus of ela is Bak, a wen The case of »=1 is Ante, it gives a constant modulus of compressibility equal to 27, and the law of pressure p=2z log w. If nm be less than unity the compressibility, or reciprocal of the modulus, increases with the density, which is of course physically improbable. If » be greater than unity and less than 3, the com- pressibility becomes less the greater the density. The assumed law probably does not give such good results as those of Laplace, because the decrease of compressibility with increasing density is not sufficiently rapid. The range of n=3 to n=1 gives the results which possess most physical interest. In comparing results with those of Laplace there will be occasion to express the modulus as a length; that is to say, we are to find the length of a column of unit section whose weight (referred to the surface gravity of the planet) is equal to the force specified in the modulus. Now if g be gravity n—1 gual Hence the modulus is Zw?» = gal x = a “) =, the units a, fv being n reintroduced to give the expression the proper dimensions. Now gaw is a pressure, and therefore the length of the modulus is zien 2 a ". Thus the surface matter has a length modulus equal to a/n. Now let us find the ellipticity of the internal strata. Substituting for w from (9) in (2), we have, de —2n? —(. a If the solution be assumed of the form e=ca®, 6 must satisfy B(B—1) + 2(8—n)B—2n=0, whence p=—($—n) + /{(Q2—n(B—n)}. 162 Prof. G. H. Darwin. [ Dec. 13, Now n(3—~) is a maximum when it is equal to (2)?, and therefore the square root can never become imaginary. From the sign of the last term in the equation for §, it is clear that one of the values of 8 is negative. Hence to avoid infinite ellipticity at the centre, the ¢ corresponding to the negative root must be zero. Hence the solution of Clairaut’s equation (2) is e=eq—st VIG)? —2B—n)] | The surface value of ; © (ca?) is clearly n—$+ V/{(%)?—n(8—n)}. Thus from (8) we have <=H(u—4) +4 (BP —0(38—0)}. Then substituting for w from (9) in (0), ey AEE 3(5—n) And since M=47p=+4 7 shai we have for the precessional constant: ee (e— tm) Now let us collect these results, and express them in terms of k instead of m. ‘The solution is wa=a-34-). And the mass inside of any radius a is st k aoe she) w3—3k — | an Cesar) 4—6k ae. W3—sk And when k=4, p=2z log w, oemtn (GO) w The length of the modulus at the surface is 1/3(1—k) of the planet’s radius. oe 3—3k+3 v[(e)?- kA] Sai ik+s J {(2)2—k(1—k}. C—A 243k), 4 C 3k z 1883. ] On the Figure of Equilibrium of a Planet, Sc. 163 Any value from unity to an infinitely small value may be assigned to k, that is to say, we may have any arrangement of density from homogeneity to infinitely small surface density, but if & be greater than 2 the compressibility increases with the density, which is physically improbable. The infinite density and infinite pressure, which occur in this solution actually at the centre, may be avoided by imagining the centre occupied by a rigid ‘spherical homogeneous nucleus, of very small radius 6a, and of density 1/kéa7"—”), We have to compare this solution with Laplace’s. For this case / is not constant, and its surface value is k. Let j=, where « is a constant, being the arbitrary constant intro- K duced in this solution; and let @ be the surface value of $.* The solution is— And the mass inside of any radius a is spate la uv p= 2rrx?(w?—1). | ee 3(1—J cot #) The length of the modulus at the surface is 1/(1—@ cot) or 3k0-? of the planet’s radius. ih Nee lek PIL—k @e 62 A Sate eek 76Gb * C=[1—6(1—k)0-?]2Ma?. Oa 1 lat Coen I-60 ho a) The following table gives the numerical values of the solution, together with columns for comparison with the results of Laplace’s theory, for various values of the ratio of surface to mean density. * See Thomson and Tait’s “‘ Nat. Phil.,” 1883, § 824. 164 Prof. G. H. Darwin. [ Dec. 13, The case of K=0 gives the planet infinite mass at the centre, and the values are only inserted in order to complete the series. Length mod. & ae en Come meer C=A | Teha Po ee : where ae @ pee where in terms of (ite eg = C(e—4im). C(e—4m).| cS &as unity. a ney | ei aera a sane | 1:0 00 0:000 |1:000| 7:00 | 1-667 1°67 : =o ‘9 3°333. | 0°132 |1:066| 2-04 | 1-741 neva | — 4.667 8 1:667. | 0-293 |1°147| 2:09 | 1-833 Ly ees oy 1-111 0:488 |1°244) 7°75 | 1°952 1B | —0-067 6 1+1:2 | 0-722 |1°361| 7-27 | 2-111 1°90 |) (0338 5 ez ILO) LOO) gy | Bee 1:98, | 10-66% “4, cs BHO SIL) 129A | Baga 2-07 +} 0°889 3 esi) 1°688 |1°844] 7:47 5222 B17, Np yeleO4S 2 1+2°4 2-093 |2:047| 1-48 A +333 2-28 | 1-167 ‘1 1+2°7 | 2-532 |2:266| 1:56 | 7-667 2-40 | 1:°259 0 1+3:0 | 3-000 |2°500| 12-65 00 2:55) )s anleses | 667, 1-000 | 0-562 |1-281} 1-77 | 2-000 1°85 | pelog w Set TEA) | || aOR GLA RE) | | HOOD) 2°18 | 1-000 Note.—The values in the two columns applicable to Laplace’s theory were found by graphical interpolation from a series of values given in “ Month. Not.,” R.A.S., Dec., 1876, or Thomson and Tait, ‘ Nat. Phil.’ (1883), § 824’. In Laplace’s theory po (w?—1), and the modulus of compressibility « w*. In the present theory the modulus « w’. The value &=°667 corresponds to constant compressibility, and k=°333 to gaseous compressibility. One of the grounds on which Laplace’s solution is held to be satis- factory is that if we take the value of @, as determined by the known anguiar velocity and mean density of the earth, and the value of ¢ as determined by geodesy, and find the value of &, the ratio of surface to mean density, which corresponds with the ratio e/g, this same value of & is found to give a proper value to the coefficient of e—4m, so as to obtain the observed precessional constant. To be more precise, m is found to be 1/289°66, which gives e=1/231°7, and ¢ has been found to be approximately 1/295. These give w/e=1:273, and this corre- sponds with K=1/2:06=-49. This value of &, with the same values of e and m, gives the precessional constant as ‘0033, and Leverrier and Serret give its value as ‘00327. Now it appears remarkable that almost as good a correspondence is obtainable from my solution. The value #/e=1°273 corresponds with k=°675, and when k=°675 the coefficient of e—3m in the pre- cessional constant is 1:99, which gives the same precessional constant 0083. This value of & corresponds very nearly with constant modulus of compressibility, and with pressure determined by p=2z log w. 1883. ] On the Figure of Equilibrium of a Planet, Sc. 165 It is claimed in favour of the Laplacian hypothesis that it corre- sponds to a surface density which is nearly a half of the mean density of the earth, and that we know that average rock has a den- sity of about 2°8. Also it is pointed out in Thomson and Tait’s “Natural Philosophy ” that the length modulus of compressibility of the surface rock is about 1/44 of the earth’s radius, which is very nearly the observed length modulus of iron. These conditions are not well satisfied by the present solution, for the surface density is found to be °675, or 1/1:48 of the mean density of the planet, whence the specific gravity at the surface is 3°7; and the length modulus at the surface is equal to the planet’s radius. It is to be admitted that this density is large, and that the substance is also highly incompressible. Thus in these respects the Laplacian hypothesis has the advantage. It seems to me, however, that too much stress should not be laid on these arguments. We know nothing of the materials of the earth, excepting for a mile or two in thickness from the surface, hence it is not safe to argue confidently as to the degree of compressibility of the interior. There seems reason to believe that there is a deficiency in density under great mountain ranges, and this would agree with the hypothesis that our continents are a mere intumescence of the surface layers. According to this view we might expect to find a rather sudden change in density within a few miles of the surface. Now in any theory of the earth’s density such a sudden change in the thin shell on the surface could not be taken into account, and the numerical value for the surface density should be taken from below the intu- mescent layer if it exists. Hence itis not unreasonable to say that a solution of the problem, which gives a higher surface density than that of rock, hes near the truth. I do not maintain that my solution is as likely as that of Laplace, but it is not to be condemned at once because it does not satisfy these conditions as to the density and com- pressibility of rock. The two cases which are given at the foot of the above table each possess an interest, the first of constant compressibility, because it corresponds with the case of the earth, and the second of modulus of compressibility varying as the density, because this is the gaseous law. With constant compressibility the internal ellipticity varies as the -562 power of a, or nearly as the square root of the radius; with gaseous compressibility it varies as the 1°562 power of a, or nearly as the square root of the cube as the radius. A numerical comparison of the case of constant compressibility with Laplace’s solution for k= gives the following results :— 166 On the Figure of Equilibrium of a Planet, &§c. [Dec. 13, e (Laplace) = = 0) “812 "B44, “902 1-000 (Constant ¢ 4 compress.) p — 0 "459 693 “851 1-000 Thus the Laplacian solution attributes much higher ellipticity to the internal strata. The solution with constant compressibility in fact gives so large a proportion of the mass in the central region, that attraction has a greater influence compared with rotation, than in the solution of Laplace. [ P.S.—If, as is not improbable, the increase of density in the interior of the earth is due rather to the heavier materials falling down to the centre than to great pressure compressing the material until it has a high density, then the determination of a modulus of compressibility would be fallacious, and it would be more logical to leave the expressions for the pressure and the density both as functions of the radius, without proceeding to eliminate the radius and to form an expression for the modulus of compressibility. I owe this suggestion to a conversation with Sir William Thomson.—December 19, 1883. | 1883.] Prof. D. E. Hughes. On’a Magnetic Balance. 167 December 20, 1883. THE PRESIDENT in the Chair. The Right Hon. Lord Justice Sir Edward Fry was admitted into the Society. The Presents received were laid on the table, and thanks ordered for them. The following Papers were read :— I. “On a Magnetic Balance, and Experimental Researches made therewith.” By Professor D, E. Hucuss, F.R.S. Received December 10, 1883. In a paper “On the Molecular Rigidity of Tempered Steel,”’* I advanced the theory that the molecules of soft iron were comparatively free as regards motion amongst themselves, whilst in hard iron or steel they were extremely rigid in their relative positions. I have since widened the field of inquiry by observing the effects of mechanical compression and strains, as well as annealing and tem- pering, upon the magnetic capacity of sixty varieties of iron and steel, ranging from the softest Swedish iron to the hardest tempered cast steel. We know already that soft iron will take a higher degree of tempo- rary magnetism than steel, and that tempered steel retains magnetism more than soft iron; consequently, we might believe that by the aid of an instrument which should give correct measurements, we might be able to include all varieties of iron and steel between the two extremes of softness, as in annealed iron, and hardness, as in high- tempered cast steel. This proved, however, not to be the case, if the iron and steel were not all annealed to one absolute standard, and if magnetised to or near saturation. In a late paper upon the theory of magnetism,+ I said :— “During these researches I have remarked a peculiar property of magnetism, viz., that not only can the molecules be rotated through any degree of arc to its maximum, or saturation, but that, whilst it requires a comparatively strong force to overcome its rigidity or resistance to rotation, it has a small field of its own through which it can move with excessive freedom, trembling, vibrating, or rotating * “ Proceedings Institution of Mechanical Engineers,” January, 1883. + Society of Telegraph Engineers, May 24, 1883. VOL. XXXVI. N 168 Prof. D. E. Hughes. [Dec. 20, through a small degree with infinitely less force than would be required to rotate it permanently on either side. This property is so marked and general that we can observe it without any special iron or apparatus.” In order to observe this in electro-magnets, we must employ an extremely feeble current, such as from one Daniell cell, with an exterior resistance of from 10 to 1,000 ohms, and we then find the following laws hold with every variety of iron and steel :— Ist. That its magnetic capacity is directly as its softness or mole- cular freedom. 2nd. That its resistance to a feeble external magnetising force is directly as its hardness, or its molecular rigidity. This has proved to be the case upon sixty varieties of iron and . steel furnished me direct from the manufacturers, and it was remarked that each variety of iron or steel has a certain point, beyond which annealing cannot soften, nor temper harden; consequently, if all varieties were equally and perfectly annealed, each variety would have its own magnetic capacity; or, its specific degree of value when perfectly annealed or tempered, by means of which, we could at once determine its place and quality. If in place of several varieties we take a single specimen, say hard- drawn Swedish iron wire, and note its magnetic capacity, we find that its value rises rapidly with each partial annealing, until an ultimate softness is obtained; being the limit of its molecular freedom. We are thus enabled to study the best methods of annealing, and to find at once the degree of softness in an unknown specimen. A similar effect occurs in observations upon tempering; from the softest to the hardest temper, until we arrive at its ultimate molecular rigidity. We have thus in each piece of iron or steel a limit of softness and hardness. In soft Swedish iron tempering hardens but 25 per cent., whilst mechanical compression (such as hammering) hardens it 50 per cent. In cast steel tempering hardens it 400 per cent., whilst mechanical compression gives but 50 per cent. Between cast steel and Swedish iron we find a long series of mild steel and hard iron, varying in their proportionate degree between the two extremes mentioned. ; In order to carry out these researches, I constructed an instrument which I have called the magnetic balance. It consists of a delicate silk fibre suspended magnetic needle, 5 centims. in length, its pointer resting near an index having a single fine black line or mark for its zero, the movement of the needle on either side of zero being limited to 5 millims. by means of two ivory stops, or projections. When the north end of the needle and its index zero are north, the needle rests at its index zero, but the slightest external influence, such as a piece of iron 1 millim. in diameter 10 centims. distant, deflects the needle 1883.] On a Magnetic Balance. 169 to the right or left according to the polarity of its magnetism, and with a force proportional to its power. If we place on the opposite side of the needle at the same distance a wire possessing similar polarity and force, the two are equal, and the needle returns to zero, and if we know the magnetic value required to produce a balance we know the value of both. In order to balance any wire or piece of iron placed in a position east and west, a magnetic compensator is used, consisting of a powerful bar magnet free to revolve upon a central pivot, placed at a distance of 30 or more centims., so as to be able to obtain delicate observations. This turns upon an index, the degrees of which are marked for equal degrees of magnetic action upon the needle. A coil of insulated wire, through which a feeble electric current is passing, magnetises the piece of iron under observation, but as the coil itself would act upon the needle, this is balanced by an equal and opposing coil on the opposite side, and we are thus enabled to observe the magnetism due to the iron alone. A reversing key, resistance coils, and a Daniell cell are required. Great care must be taken so that the electromotive force remains a constant, as a small variation in the electromotive force gives large variations in the readings, and many important details of construction are required, in order that it shall give perfect readings for extremely small magnetic force. Still greater care is required that each specimen of iron or steel shall be annealed to its maximum. Several methods of observation have been employed with the magnetic balance, the usual one being the one described, but inte- resting results are attained by observing the influence of earth’s magnetism alone on the iron or steel, or we may magnetise all speci- mens to the same value, and note the amount of current required. We may observe the remaining magnetism after the cessation of the current or the influence of a weak current after the passage of a strong magnetising force. These are more applicable to researches upon the cause of magnetism. By means of this instrument I have tested sixty varieties of iron and steel, mostly in the form of wires, a wire 1 millim, diameter, 10 centims. long, being the standard used. In all comparative expe- riments we require one standard form, to which all the rest must be similar in form and size; at present, we cannot readily compare a square or flat bar with a piece of wire, but if all pieces have the same form, and all are annealed to the same standard, then any difference observed between them must be due to their comparative softness, from which we can deduce its quality and place on the line from soft iron to cast steel. Annealing not only produces softness and consequent molecular freedom, but it entirely frees it from all strains previously introduced N 2 170 Prof, D. E. Hughes. - [Dec. 20; by drawing or hammering. Thus a bar of iron drawn or hammered has a peculiar structure, say a fibrous one, which gives a greater mechanical strength in one direction than another. This bar, if thoroughly annealed at high temperatures, becomes homogeneous, and has no longer even traces of its previous strains, provided that there has been no actual mechanical separation into a distinct series of fibres. Table I. Influence of annealing upon Swedish iron, Sample G. Degrees of softness © indicated upon the magnetic balance. Wire, hard drawn, as furnished by the makers.. 230° Annealed at blackcheat 2.12 cseuin ee eee 255° s dilliredy ences. oer ta gare ee 329° - Ban bughtmed 2). .Andw eat). 438° ¥ yellow to 0.602. Fa eee eee 507° % yellow-whitest.%ik wu. Shecenie eee 525° - From the above table, we notice that a regular increase of softness occurs, as the temperature at which it is annealed increases, the maximum heing at a point under that of fusion. Numerous methods of annealing were tried, the highest results being obtained when the iron or steel was heated as rapidly as possible to a high temperature, and cooled in a neutral surrounding or atmosphere. The facts regarding annealing as pointed out by the measurement of the magnetic capacity of iron, have, no doubt, been in great measure perceived by ordinary mechanical methods; the results of my own researches may be thus formulated :— ; 1. The highest degree of softness in any variety of iron or steel 1 is that obtained by a rapid heating to the highest temperature less than fusion. 2. The time of gradual cooling required varies directly as the amount of carbon in alloy. Thus in chemical pure iron rapid cooling, as in tempering, would not harden it, whilst steel might require several days, even for pieces only 1 millim. diameter. Slow cooling has no injurious effect upon pure iron when cooled in a neutral surrounding, consequently where time is no object, we may employ slow cooling in every case. . A wire or piece of iron, thoroughly annealed, must not be bent, stretched, hammered, or filed, as the hardening effects of a bend are most remarkable, and the mere cleaning of its surface by sand paper hardens its surface several degrees. The following table shows the effect of annealing upon a series of lad | On a Magnetic Balance. «| i71 wires, kindly furnished me expressly for these pei peeiaaus by Messrs: Frederick Smith and Co., of Halifax :— Table IT. Magnetic capacity. Bright hard anaes Annealed. G Best Swedish charcoal iron, Ist variety. . 230 525 F : eee hy, eee 236 510 T ie aedbh hess tae 275 503 -§ Swedish, Siemens-Martin, iron . yew 165 430 H Puddled i ALOT. WEStUDESts a cee Soman a eres 212 340 ve IBessemerySOLLStCels «+c uelnels edie e «eae 150 291 6 Siugemern. Luni sie. ge Pape sns Jee 115 172 Z @ricible-fine cast-steel a. ..cstee 0 os ee 50 84 The above series contains representative irons and steel of all classes, all other varieties yet tried stand between cast steel and Swedish iron, generally classed as hard cast steel, hard steel, mild steel, hard puddled iron, soft iron, Swedish charcoal iron. From the above table it will be seen that every wire rises greatly i in value by annealing, and that we could not estimate the true magnetic capacity of any iron or steel unless special attention was given that all should be annealed to their maximum. The influence of tempering upon the magnetic eye or molecular rigidity has been shown in every piece of iron or steel examined, the molecular rigidity of tempered cast steel being pro- portional to its species. of temper as shown in Table III. Table IIT. Tempering. : 2 Magnetic capacity. Crucible fine cast steel, tempered. Bright yellow heat cooled in cold water ............ 28 Yellow red Lge eS Bee Ie Ba 32 Bright yellow tempered in ald water let down to BEMEAMECOLONMIS a 05.035 oo deicle,o se be + ve 33 Bright yellow tempered in ad water let down fe bine 43 beet vellowetempered i: oil ........-2-252e8 ee em dl Bright yellow tempered in water let down to white .. 58 Pecoenentntenipered im water ....-...-+04s+.ss0s08% 66 BEeneatbemupered IM. Ol |... <5 -j.. 4.2 0020 le sls cs oe 72 Crucible cast steeliannealed .. .........-..0+22-00- 84 Swedish charcoal iron annealed .............-.505- 625 [Dee. 20, On a Magnetic Balance. Prof. D. E. Hughes. 172 a0e14 P8S-T | 190-0 | F40-0 96¢- T | €OL-O | 92T- 0 24-0 | 440-0 | 260-0 ~EZ-0 | 8IZ-0 €0- O VcE-0 | PEO-0 | SE0-0 P&s-0 | 890-0 | 610-0 €0-0 | SVO-0 , 220-0 90-0 | S1T0-0 | 90814 “gsoUBS URL *snaoydsoyg ‘sosATeue [Bwormoyg 90.0 820- 0 810: 0- 60-0 e0Br4 810: 0 e0vT} 20814 “HOOTIS 69-0 ane) ST-0 OT-0 OT-0 ST-0 OT-0 60:0 “uoqiep gaz 86E 06§ G6E STP S&P | | | | | ‘prey posed ua y, “Ayroedvo orouseyy GLL 162 OVE O&P 60S OTS Gos ‘porvouuy “AT PVD STI OST GILG GOT Gls 9&6 O&G ‘UMBIP PLVY JOS gg 0g Stes O&€ VE Ié O€ 8¢ ‘S110 “your eienbs sod yASuar4s o[Isuay, 80.088 69- CIE Go: 99G G6- 696 GE: 926 29- 661 OF- 86T GG. T6L “suo Jo oysur STISOL [eoLtq09 TH “1oJOULVIP OFO. rod goue Tose etecee ee T9999 4SBO O[QIONIO OUT = pay . [9948 Loulesseg 4JOs snoeuasouIOY ysoq co eeeeeees e+ eqgaq 4seq ‘UOdL po[ppnd ‘ s8e6s TOdT UT}IUYY-suOUIoty Ystpemg eeotbos g 66 Wu eececeoe Z s6 UG seetee T WOUT [BOOTBYO YSTpIMG 4soq “Peytey 1883. ] On the Circumpolar Expedition to Fort Rae. 173 Table IV gives the complete results of the mechanical, chemical, and physical tests upon a series of wires furnished by Messrs. Fre- derick Smith and Co., of Halifax. The tensile strength and electric conductivity are those furnished me by Messrs. Smith and Co. The chemical analyses by Mr. Henry S. Bell, of Sheffield, the magnetic capacity of the bright hard drawn, annealed, and tempered wires, were determined by myself by the aid of the magnetic balance. In the above Table IV there is a complete relation between electric conductivity and magnetic capacity, both progressing in a similar ratio and agreeing in a most remarkable manner. We see here that the electric conductivity and magnetic capacity have a complete relation to each other, but while in every wire measured I have found this true, it is only so when the wire has been completely annealed and free from mechanical strain, and a feeble magnetic force employed, thus the relation exists only in the limited sphere of elastic rotation already mentioned. I believe the relation here shown between electric conductivity and magnetic capacity to be of theoretical importance and of practical utility, as we at once find not only the electric conductivity of iron and steel from a simple reading of their magnetic capacity, but also the iron most suitable for the cores of electro-magnets. II. “ Report on the Circumpolar Expedition to Fort Rae.” By Captain H. P. Dawsun, R.A. Communicated by Professor G. G. STOKES, Sec. R.S. Received December 12, 1883. On the 14th April, 1882, I was informed that I was appointed to the command of the Circumpolar Expedition. I at once proceeded to London, and was occupied until the day of sailing in practice with the magnetic instruments at the Kew Observatory, and the purchase of stores, d&c., for the expedition. On the lst May, Sergeant F. W. Cooksley, Royal Horse Artillery, and Gunner C.S. Wedenby, Royal Artillery, and on the 6th May Sergeant Instructor of Gunnery J. English, R.H.A., reported them- selves to me, and commenced attendance at Kew for instruction. Journey to Fort Rae. We sailed from Liverpool on the 11th May, and arrived at Quebec on the 23rd. Here I spent some days finding that the steamer for the _north did not leave Winnipeg till the 10th June, and my party was 174 ‘Capt. H. P. Dawson. [Dec. 20, - very ‘kindly afforded quarters in the citadel by Lieutenant-Colonel Cotton, commanding the Canadian Artillery at that place. Having obtained a free pass for our baggage on the Grand Trunk Railway, I started at once for Winnipeg, proceeding by the lakes, that being the cheaper route, and the one which on the whole exposed the instruments to the least knocking about. We reached Winnipeg on the 9th June, and left on the following day by the Saskatchewan steamer. On the 26th June we reached Carlton, where it was necessary to engage carts to take our baggage to Green Lake, a distance of 140 miles. On the 29th the carts were taken across the river, and on the 30th we started for Green Lake, which we reached on the 9th July, having been delayed by the extreme badness of the road. The heat of the weather rendered a long halt necessary in the middle of the day, and the flies also prevented our animals from feeding pro- perly, incapacitating them for long marches or fast work, and on one occasion forcing us to halt for a whole day, the oxen being so worried by them as to be unable to march. At Green Lake we entered upon the system of water communica- tion that forms the only roadway in the north, and by way of Portage la Loche and the Clearwater and Athabasca rivers we reached Fort Chipewyan on the 30th July. Here we had to await the Mackenzie River boats, there being no other means of reaching Fort Rae, and it was not until the 17th August that we were able to start on this last stage of our journey. We reached Great Slave Lake on the 22nd, on the evening of which day a gale arose which stove in and sunk our boat, damaging most of our provisions. Fortunately we were able to repair the boat, but it was not until the 25th that the weather allowed us to proceed, and on the 27th we were again detained by a fresh storm, so that it was not until 10 P.M. on the 30th August, that we arrived at Fort Rae. Fort Rae. Fort Rae is situated in lat. 62° 38’ 52” N., and long. 115° 43’ 50” W.., at the south-west extremity of a peninsula that juts out from the north-east shore of a long gulf extending in a north-westerly direc- tion more than 100 miles from the northern shore of the Great Slave Lake. It is almost entirely surrounded by water, as shown in the annexed plan.* The formation islimestone. The land rises toa height of some 200 feet, and is covered in part with moss, in part with pines and scanty brushwood. A few vegetables are grown in the summer in * [It has not been thought necessary to publish the plans accompanying this Report, as they would seem to find a more fitting place in the detailed account of the observations.—G. G. 8., Sec. B.S. ] 1883.] On the Circumpolar Expedition to Fort Rae. 175 the garden attached to the Roman Catholic Mission, but for food the inhabitants chiefly depend upon the produce of the nets, and on deer, which are brought in by the Indian hunters attached to the post. On arrival it was found that the magnetic instruments required a good deal of setting to rights, their boxes being filled with water and the fittings loosened, so that not a single instrument was quite in working order. There was, moreover, no building ready for their reception, so that it was not possible to keep the 3lst August— Ist September as a term day, but we succeeded in getting the meteorological instruments into position so as to commence observa- tions with them at midnight on the 31st. We were fortunate in finding a building that admitted of con- version into a magnetic observatory, it only requiring a floor, fire- place, door and windows to be habitable. This work was at once commenced, and on the 3rd September the declinometer, on the 4th the bifilar, and on the 6th the vertical force magnetometer were mounted in their places. This observatory was finished on the 10th September, and another one commenced for astronomical and absolute magnetic observations, the continual wind rendering out-door obser- vations unsatisfactory. The men of my party were accommodated in the house of one of the sub-officers of the fort, and I had a room in the house of the Hudson’s Bay Company’s officer in charge. _ The instruments, on the whole, suffered but little from the journey. One barometer and one thermometer were broken, and the object glasses of the telescopes of most of the magnetic instruments were nearly opaque, the cement joining the two lenses having from some cause or other melted on the journey. Our provisions were more damaged, 190 lbs. sugar, 30 lbs. of tea, all our rice, and most of our baking powder having been destroyed. The observations were then carried on without interruption until the 3lst August, 1883. Magnetic Observations. The balance magnetometer was the only magnetic instrument whose performance was not satisfactory, as not only did it frequently get out ot adjustment, but in times of magnetic disturbance it often vibrated through so large an arc that exact reading was im- possible. The other instruments were remarkably free from vibration, and there was never any difficulty in reading them, but it was found necessary to extend the scale of the bifilar on the side of decreasing force, owing to the great movements of this instrument. The greatest magnetic disturbance was on the 17th, 18th, and 19th November, 1882, when all the instruments moved at times beyond the yO Capt. H. P. Dawson. [Dee. 20, limits of their scales. On the first of these days the difference between the extreme easterly and westerly positions of the declino- meter magnet exceeded 10°. Aurora. Aurora was observed on almost every clear night, and was usually attended by more or less magnetic disturbance. It did not appear to me, however, that the two phenomena stood in the relation of cause and effect, but rather that they were both due to a common cause. The most marked instance of connexion between the two phenomena consisted in a rapid decrease in both vertical and horizontal magnetic forces which attended a sudden outburst of aurora in the zenith. This was observed on several oceasions. The bifilar almost always showed a reduction of horizontal force during a display of aurora. I also think that the declinometer magnet tended to point towards the brightest part of the aurora, but I have not yet had time to make that careful comparison of the auroral and magnetic observations which will be required to decide this point. It was found impossible to obtain photographs either of the aurora or of its spectrum—the latter invariably presented the characteristic yellowish-green line, and occasionally but rarely several other bright lines were visible for a few moments towards the violet end of the spectrum, and once a bright band was seen in the red. I was also unsuccessful in my attempts to measure the height of the aurora, chiefly from the want of a well-defined poimt to measure to, also from the fact that some hours were required to prepare for this observation, whereas the appearance of a suitable aurora could not be predicted, and was, in fact, not of frequent occurrence, and then often only lasting a few seconds. For this observation two stations some miles apart should be connected by telegraph and occupied for many days, or even weeks in succession. Although I paid attention to the point, I never heard any sound from the aurora, save on the occasion mentioned in a former memo- randum, but I made many inquiries on the subject from residents in the country, both English and French, and their statements agree so well, both with one another and with what I myself heard, that I am forced to conclude that the aurora is at times audible, and that on these occasions it appears to be, and probably is, very near the earth. Meteorological Observations. With regard to the meteorological observations, the station was somewhat unfavourably placed for observations of wind, on account of the hill to the north-east, but as winds from this quarter were rare the effect on the results will not be great, especially as one of the 1883. ] On the Circumpolar Expedition to Fort Rae. ia anemometers was on an island in the lake, in an entirely open situation. The anemometers did not work quite satisfactorily, being at times choked by ice; but I hope by the comparison of the two satisfactory results may be attained. The wind was usually either South-east or North-west; and even when it blew from the former quarter, the motion of the upper clouds often showed the existence of a North-westerly current. The hair hygrometers were found to be useless out of doors in cold weather, on account of the formation of ice on the hair. The earth thermometers were read every alternate day: the obser- vations were interrupted by a carcajou, or other animal, which extracted the thermometers from their tube for the sake of the fur in which it had been found necessary to envelope them, and broke them all; other thermometers were, however, substituted, and the observations continued. It was found impossible to obtain the temperature of the soil at a greater depth than four feet on account of the rocky nature of the ground. A series of observations of terrestrial radiation was made by means of a thermometer placed on the surface of the snow, but the almost continual wind detracts much from the value of these readings. I was told by the residents of the country that the year was an unusually dry one, and certainly the rainfall is remarkably small; they also said that the winter was particularly mild and free from storms, which, from all accounts, and from the journals kept at the fort, seem to be both frequent and severe; as it was, we only expe- rienced one, in February. A plan is annexed, showing the position of the meteorological instruments, and their relative heights. Astronomical Observations. My first determination of the longitude was made by means of lunar distances, and time was found by the method of equal altitudes, but after the observatory was finished both these points were deter- mined by transits, and the first value of the longitude found to be more than a minute in error. The latitude was determined by transit observations in the prime vertical, and is probably within a few seconds of the truth. The longitude may be ten seconds in error. The time was generally correct to within three or four seconds. A more solidly constructed transit instrument would have been desirable, as it was found that in the cold weather it required so much force to move the telescope of the transit theodolite on its axis, that there was great risk of disturbing the adjustments of this instru- ment, composed as it is of so many parts. 178 Capt. H. P. Dawson. — oy" [Dee 20! Food, &c. Our supply of provisions proved quite sufficient. I had brought enough flour to admit of my issuing the usual ration of 2? lb. per diem, and tobacco 1lb. per month to each man. We also had a supply of Chollet’s preserved vegetables, and a reserve stock of bacon, besides tea and sugar. Of the latter we were somewhat short, owing to the loss sustained on the journey up. We usually had fresh meat throughout the winter; in the summer we were occasionally reduced to dried meat. During the journey there and back we chiefly lived on pemmican. The Rev. Pére Roure, of the Roman Catholic Mission, most kindly furnished us with fresh vegetables and potatoes through- out the summer. } The conduct of the men under my command was everything that could be desired. They took great interest in the observations, and did their best to carry them out with accuracy and punctuality, and were always contented and cheerful, in spite of the inevitable dis- comforts of their winter quarters and the occasional hardships of the journey. | | Return Journey. We were running great risk of being overtaken by the winter, and therefure lost no time in our departure. The last hourly observation was made at midnight on the 31st August, 1883, after which the instruments were dismounted and packed, their cases having been previously arranged in readiness out- side the observatory. The remainder of the baggage was already in the boat, so that by 2.30 a.m. on the Ist September we were en route, and reached Fort Chipewyan on the 17th September, and Portage la Loche on the 4th October, having experienced some delay in surmounting the rapids of the Clearwater, the hard frosts having frozen all the small tributary streams, thus considerably lowering the water in the river. The boat awaiting us on the south side of the portage was frozen in, but fortunately the wind changed and the ice broke up before our arrival. Had it been otherwise we must have waited until the rivers were thoroughly frozen, and travelling with dog trains possible. In that case we should have been compelled to abandon our instruments and baggage. On the 21st we reached Carlton on the Saskatchewan, where we were detained a day, the man engaged to transport our bag- gage across the prairie having refused to proceed. Another man was engaged, and on the 3lst October we reached the railway at Qu’Appelle, arriving at Winnipeg the following day. We were fortu- nate in crossing the prairie with so little difficulty, as at the same time last year it was covered with three feet of snow. 1883.] ~~ On the Circumpolar Expedition to Fort Rae. 179 At Winnipeg I remained a couple of days to adjust accounts with the Hudson’s Bay Company, and on the 4th November we started for Quebec, going by rail vid Chicago. We reached Quebec‘on the 8th, and Liverpool on the 20th November. _ In conclusion, I have to acknowledge the assistance received from the officers of the Hudson’s Bay Company, who spared no trouble in carrying out my wishes, especially Chief Commissioner Grahame at Winnipeg, Chief Factors MacFarlane and Camsell, in charge of the Athabasca and Mackenzie River Districts respectively, and Mr. King in charge at Fort Rae. To their hearty co-operation the success of the expedition is in great part due. Results of Hapedition. The following is a list of the observations taken at Fort Rae, the result of our year’s work there, which I have now the honour to lay before the Royal Society :— Magnetic. Hourly— Declination from 3rd September, 1882, to 3lst August, 1883. Hor. Force. ,, 4th 2 A Vert. Force ,, 6th | Term Day— In accordance with programme laid down by St. Petersburg Conference, from 15th September, 1882, to 15th August, 1883. Occasional— Absolute observations of Hor. Force Dip and Declination. 99 39 9) 99 9 9 Meteorological. Hourly— Barometer. From Ist Sept., 1882, to 3lst Oct., 1883. Dry and wet bulb thermometers a - 4 Anemometer : Wind, clouds, and weather - Aurora (when visible) is x Hair Hygrometer (when in working order). Terrestrial Radn. (occasionally in clear weather). Daily— Max. and Min. Solar and Terrest. Radn. Thermos. Rain gauge. Earth Thermometers every two days. 180 Mr. W. Gardiner. [Dec. 20, III. “On the Changes in the Gland-Cells of Dionwa muscipula during Secretion.” By WALTER GARDINER, B.A., Scholar of Clare College, Cambridge. Communicated by W. T. THISELTON-DyeER, C.M.G., F.R.S. Received December 18, 1883. The following observations were made upon leaves of Dioncea mus- cipula which had been fed with the bodies of wood-lice, from which the chitinous coat had been previously removed. The leaves were then placed in absolute alcohol. It is well known that shortly after the application of animal matter the leaves close, and may remain shut for a period varying usually from ten to twelve days, when they open spontaneously. When, however, the leaf is not vigorous or when the amount of animal matter is somewhat large, the leaf may not open at all, but remain closed until its death. There appear to be four periods which attend the phenomenon of digestion in such a leaf, viz., the resting, the secretory, and the absorp- tive periods, and the period of recovery. These periods are fairly well defined in Dionea on account of the slowness with which they proceed. In the resting state the gland cells (fig. 1) exhibit the following structure :—In each cell, the protoplasm closely surrounds the cell- wall, leaving one large central vacuole, which is filled with the usual pink cell-sap. The protoplasm is extremely granular, especially around the nucleus, which is, in consequence, almost entirely obscured from view. The nucleus is situated at the base of the cell, and is shown by reagents to be large and well-defined. , Fre. 1. At the end of the secreting period, which appears to be about twenty-four hours after stimulation, the following changes have occurred (fig. 2). Movements of the protoplasm have taken place, in consequence of which the nucleus now occupies the centre of the cell ; numerous strands of protoplasm radiate from the nucleus to the parietal protoplasm of the cell, in consequence of which several 1883.] Changes in the Gland-Cells of Dionewa muscipula. 181 vacuoles, instead of one large one, are present. The protoplasm now exhibits but little granularity, and may be described as clear and hyaline. The nucleus is clearly brought into view, and appears to have undergone a very considerable diminution in size. Lei GAS Passing to the phenomena of the ordinary leaf tissue, it may be remarked that definite special cell-contents make their appearance after the absorption of the digested food. Sections of leaves which were placed in alcohol thirty-six hours . after feeding, show that the cells contain a very large number of tufts of crystals, which are present in the cell-vacuole and adhere to the inner surface of the cell-protoplasm. The tufts are formed of fine acicular crystals which erystallise out with great regularity and radiate from a central point. The tufts are of a yellow-green colour. They are insoluble in alcohol, in 1 per cent. acetic acid, and in 1| per cent. hydrochloric acid; and soluble with difficulty in 5 per cent. solution of potash. The formation of these crystals may be artificially pro- duced by wetting the surface of a fresh leaf with the fluid from a leaf which has fed for a period of from thirty-six to forty-eight hours. After forty-eight hours the cell-contents are of a different nature. The cells now contain numerous bodies which present the appearance of flat sphero-crystals. They are usually perfectly circular in outline, and are clear and colourless. They are insoluble in alcohol but extremely soluble in water. In Drosera the changes take place much more rapidly, the pheno- menon of digestion usually extending over a period of from three to five days. The gland-cells in the resting state were seen to be much more granular before, than after secretion. In consequence of absorp- tion the cells contain a large quantity of a substance which is precipi- tated in dense granules by alcohol, but is readily soluble in water. The author has not yet worked out Drosera in detail. 182 Protoplasm through Walls of Vegetable Cells. [Dec. 20, IV. “On the Continuity of the Protoplasm through the Walls of Vegetable Cells.” By WALTER GARDINER, B.A., Scholar of Clare -College, Cambridge. Communicated by W. T. THISELTON-DYER, C.M.G., F.R.S. Received December 13, 1883. Since the communications of November 11th, 1882, and April 16th, 1883, the author has been chiefly employed in testing and improving his methods, and adding to the number of plants in which he has been able to demonstrate the existence of a continuity of the proto- plasm between adjacent cells. In certain endosperm cells, e.g., Bentinckia Conda-panna, where the protoplasmic threads traversing the cell walls are particularly well developed, it is possible to see the threads perfectly clearly by merely cutting sections of the endosperm, and mounting them in dilute glycerine. Taking the structure dis- played by such a preparation as normal, the author has compared it with the preparations obtained after the action of Chlor. Zinc. Iod. and sulphuric acid. He finds that his method of swelling with Chlor. Zine. Iod., and staining with Picric-Hoffmann Blue, is in every way perfectly satisfactory, since but little alteration of the structure occurs, and the staining with the Picric-Hoffmann Blue is limited to _ protoplasm. The sulphuric acid method is in the main unsatis. factory, although it is valuable in the case of thin-walled tissue, where violent swelling must be resorted to; and it is also valuable as affording most conclusive evidence of the existence of a protoplasmic continuity in those cases where the protoplasmic processes of pits cling to the pit-closing membrane. He believes, however, that the resalts obtained can only be rightly interpreted in the light of the results obtained with Chlor. Zine. lod. The possibility of seeing the threads depends upon their degree of tenuity and upon the thickness of the pit- closing membrane, and in extreme cases and in what are by far the more general cases, the only evidence of such perforating threads is afforded by the general staining of the pit-closimg membrane. LHvery tran- sition between clearly defined threads in the substance of the closing membrane and the mere staining of that structure as a whole occurs. The author has found that in all pitted tissue a pit-closing mem- brane, which is made evident by staining thin sections with iodine and mounting in Chlor. Zine. Iod., is uniformly present, and that open pits do not occur. The continuity of the protoplasm is always esta- blished by means of fine threads arranged in a sieve-structure, and not by means of comparatively large processes which the occurrence of open pits would necessitate. He cannot therefore agree with ob- servers whose statements necessitate the existence of such open pits. Since the last communication the author has been able to observe 1883. | Note on the Constitution of Chlorophyll. 183 that a continuity of the protoplasm between adjacent cells occurs in Dionea muscipula, being especially pronounced in the most central layers of parenchymatous cells. The parenchyma cells of the petioles of certain plants which, as H. von Mohl showed, are often thick walled and conspicuously pitted, afforded favourable material for investigation. In Awucuba japonica, and Prunus lauro-cerasus, distinct threads could be made out crossing the pit-closing membrane. In Ilex aquifolium there was a doubtful striation, and in the rest examined a mere coloration of the pit-membrane. Examples of continuity have thus been shown to exist in ordinary parenchymatous tissue ; and this materially strengthens the belief that the phenomenon of the connexion of cells with one another is one of universal occurrence. As to the function of the filaments, the author believes that in sieve-tubes and in endosperm-cells they may make possible a trans- ference of solid materials, besides establishing a protoplasmic com- munication; but in ordinary cells the only signiticance of the threads is, that by their means the protoplasm of isolated cells becomes con- nected, and that thus the communication of impulses from one part of the plant to another is insured. Finally, the presence of these minute perforations of the cell-wall need not lead to any modification of our general ideas as to the mechanics of the cell. V. “Note on the Constitution of Chlorophyll.” By Epwarp SCHUNCK, F.R.S. Received December 6, 1883. An examination of some products derived from chlorophyll, which has occupied me for some time, has led to the question of the true nature and constitution of chlorophyll, a question on which widely different opinions prevail. Without entering into matters which concern the physiologist only, it may be said that to the chemist chlorophyll is simply an organic colouring-matter, the substance to which the green colour of leaves and other parts of plants is due. Now colouring-matters are of three kinds. To the first class belong such as occur ready formed and in a free state in vegetable and animal organisms, such as the colouring-matters of turmeric and safflower. The second class comprises those that are formed from colourless chromogens by the combined action of alkalis and oxygen, the colouring-matters of log-wood and archil being well-known examples of this class. These colouring-matters change rapidly when exposed to the further action of oxygen in the presence of alkali, but are quite VOL. XXXVI. 0 184 Mr. E. Schunck. [Dec. 20, stable when in contact with acids. The third class consists of glucosides, bodies which do not undergo any considerable change under the influence of alkalis, but are rapidly decomposed when acted on by acids or ferments, yielding, on the one hand, some kind of glucose, and, on the other, substances in which the tinctorial pro- perties of the parent substance are much more pronounced. To this division belong the colouring-matters of madder, quercitron, cochineal, &c. Now chlorophyll in its general properties so much resembles the members of the last class that one cannot help suspecting that to this class it may belong—that it is in fact a glucoside. It shows con- siderable stability in the presence of alkalis, but acids decompose it rapidly, giving rise to substances which are intensely coloured and show a power of absorbing particular parts of the spectrum much more strongly than chlorophyll itself. Whether, along with the latter bodies, it yields by decomposition with acids some kind of glucose, seemed to me a question worthy of attention. If it was possible to obtain chlorophyll in a state of purity, it would be very easy to settle this question; unfortunately all attempts hitherto made to separate and purify chlorophyll have ended in its decomposition. I consider it as certain that the so-called crystallised chlorophyll which has been described by several authors is in fact a derivative of chlorophyll formed during the process employed for preparing it. It is, however, very easy to obtain a solution of chloro- phyll which shall be quite free from everything soluble in water extracted at the same time from the plant, and therefore free from ready-formed glucose. In order to effect this, I proceed as follows :— Having extracted leaves of any kind with boiling alcohol, I allow the extract to stand for some time, filter off the deposit which usually — forms, and then mix it with its own volume of ether and with about two volumes of water, shaking up well. The liquid now separates into two layers, an upper green one, containing all the chlorophyll of the extract, and a lower bright yellow one, which contains tannin, a yellow colouring-matter, a substance giving the gluccse reaction with Fehling’s solution, and probably other substances besides. The two liquids are separated in the usual way, and the upper one is shaken up with fresh water, which now usually only shows a trace of colour. This process of washing may be repeated, adding each time a little fresh ether, until the lower layer ceases to give the glucose reaction. The upper liquid leaves on spontaneous evaporation a bright green residue, which, though far from being pure chlorophyll, is free from everything soluble in water, and may therefore be employed to determine whether anything soluble in water, such as glucose, is formed by the action of acids on it. If some of the residue be treated with concentrated sulphuric acid in the cold it dissolves, forming a green solution, which, after standing for some time, gives, 1883.) Note on the Constitution of Chlorophyll. 185 on the addition of water, a dark green precipitate. This precipitate consists essentially of two substances, the phyllocyanin and phyllo- xanthin of Frémy, which are undoubtedly products derived from chlorophyll, showing the absorption bands of what is usually called “acid chlorophyll.” The liquid filtered from this precipitate, when mixed with copper sulphate and an excess of caustic alkali, becomes blue, and the mixture, on boiling, deposits cuprous oxide. The experiment may be made in a slightly different manner. The residue left by the green ethereal solution of chlorophyll having been dissolved in alcohol, sulphuric or hydrochloric acid is added to the solution, which is then boiled for some time, evaporated so far as to drive off most of the alcohol, filtered from the products insoluble in water, made alkaline, then mixed with Fehling’s solution and boiled, when the usual glucose reaction takes place. In order to make sure that the reaction was not due to ready-formed glucose, I took in every case the precaution of testing a portion of the green chlorophyliic residue with Fehling’s solution before acting on the rest with acid. This was easily done by treating with weak alcohol, to which a little alcoholic potash and some Fehling’s solution were added, and heating, when the whole dissolved easily, giving a green solution, which, on boiling, in no case deposited the least trace of cuprous oxide, whereas, after adding an excess of hydrochloric acid to the liquid, boiling, filtering off the insoluble products, again making alkaline and boiling, the glucose reaction took place in a marked manner. This experiment has never in any case failed, and it would follow, if uniformly successful, that the green leaves of all plants contain a elucoside insoluble in water, but soluble in alcohol and ether. That this glucoside is, in fact, chlorophyll seems to me highly probable. Nevertheless, absolute certainty cannot be attained, because the matter experimented on is a mixture, and it is possible that one plant out of many might give a decidedly negative result, which would upset the conclusion drawn from the rest. Assuming, however, that the pheno- mena will always occur as above described, and that the reaction with Fehling’s solution indicates the presence of some kind of glucose, it would follow either that chlorophyll is a glucoside, or that it is always accompanied in the vegetable cell by a glucoside of very similar pro- perties. I may add that I attempted to isolate the glucose or glucose-like substance formed under the circumstances described, spinach leaves being the material employed, and obtained a pale yellow gum-like substance which showed no tendency to assume a crystalline form. 186 Transfer of Energy in the Electromagnetic Field. [Jan. 10, VI. “On the Physiology of the Carbohydrates in the Animal System.” "By FE. W. Pavy, MD: ERS. Received sie cember 13, 1883. [Publication deferred. | The Society adjourned over the Christmas Recess to Thursday, January 10th, 1884. January 10, 1884: THE PRESIDENT in the Chair. The Presents received were laid on the table, and thanks ordered for them. The following Papers were read :— I. “On the Transfer of Energy in the Electromagnetic Field.” By J. H. Poyntina, M.A., late Fellow of Trinity College, Cambridge, Professor of Physics, Mason College, Birming- ham. Communicated by Lord Rayueien, M.A., D.C.L., F.R.S. Received December 17, 1883. (Abstract. ) A space containing electric currents may be regarded as a field where energy is transformed at certain points into the electric and magnetic kinds by means of batteries, dynamos, thermoelectric actions, and so on, while in other parts of the field this energy is again transformed into heat, work done by electromagnetic forces, or any form of energy yielded by currents. Formerly a current was regarded as something travelling along a conductor, attention being chiefly directed to the conductor, and the energy which appeared at any part of the circuit, if considered at all, was supposed to be conveyed thither through the conductor by the current. But the existence of induced currents and of electromagnetic actions at a distance from a primary circuit from which they draw their energy, have led us, under the guidance of Faraday and Maxwell, to look upon the medium surrounding the conductor as playing a very important part in the development of the phenomena. If we believe in the continuity of the motion of energy, that is, if we believe that when it disappears at one point and reappears at another, it must have passed through the intervening space, we are forced to conclude that the surrounding medium contains at least a part of the energy, and that it is capable of transferring it from point to point. Upon this basis Maxwell has investigated what energy is contained (1884. |] Some Experiments on Metallic Reflection. 187 in the medium, and he has given expressions which assign to each part of the field a quantity of energy depending on the electromotive and magnetic intensities, and on the nature of the matter at that part in regard to its specific inductive capacity and magnetic permeability. These expressions account, as far as we know, for the whole energy. According to Maxwell’s theory currents consist essentially in a certain distribution of energy in and around a conductor, accompanied by transformation and consequent movement of energy through the field. Starting with Maxwell’s theory we are naturally led to consider the problem, how does the energy about an electric current pass from point to point; that is, by what paths and according to what law does it travel from the part of the circuit where it is first recognisable as electric and magnetic to the parts where it is changed into heat or other forms. The aim of this paper is to prove that there is a general law for the transfer of energy according to which it moves at any point per- pendicularly to the plane containing the lines of eleetric and magnetic force, and that the amount crossing unit of area per second of this plane is equal to the product of the two intensities multiplied by the sine of the angle between them divided by 4, while the direction of flow of energy is that in which a right-handed screw would move if turned round from the positive direction of the electromotive to the positive direction of the magnetic intensity. After the investigation of the general law several applications are given to show how the energy moves in the neighbourhood of various current-bearing circuits. II, “Some Experiments on Metallic Reflection. IV. On the Amount of Light Reflected by Metallic Surfaces. IL.” By Sir JOHN Conroy, Bart., M.A. Communicated by Professor STOKES, Sec. R.S. Received December 15, 1883. In a paper which Professor Stokes did me the honour of communi- cating to the Royal Society, and which appeared in the “ Proceedings,” vol. 35, p. 26, I gave an account of some experiments I had made on the amount of light reflected by polished metallic surfaces when ordinary unpolarised light was incident upon them. The light of a paraffine lamp fell either directly, or after reflection from the metallic surface, on a photometer, and the readings were made by altering the distance at which another similar lamp had to be placed from the photometer in order to produce an equal illumination. I have repeated the experiments with the steel and speculum metal 188 | Sir J. Conroy. [Jans 405 mirrors with polarised light. The polish of the tin and silver mirrors being defective, it was not thought worth while to re-examine them. The general arrangement of the apparatus remained the same; but in order to obtain a more intense light, a magic lantern (the one known as the “Sciopticon” being used) was substituted for the paraffine lamp carried by the goniometer. It was fixed on a wood stage fastened to a stout board about 80 centims. long; a screw, which passed through the board near one end and was fixed in a table, formed an axis about which the board could rotate; the gonio- meter was fixed to the board with its centre vertically over the axis of rotation. A black card, with a slit 54 millims. by 4 millims., was placed in the slide-holder of the lantern, and a Nicol in the collimator tube of the goniometer, and the image of the slit focussed on the paper of the photometer. The metal plates were clamped to the vertical stage, and their adjustment examined by placing a second, or analysing, Nicol in the path of the reflected light and crossing the Nicols, the former being placed with its principal section either in or perpendicular to the plane of incidence, and adjusting the stage screws till the hght re- flected from the plate was completely extinguished. The experiments were made in the manner described in the former paper, the light being polarised in, or perpendicularly to, the plane of incidence by the Nicol. It was found that the illumination of the paper varied with the position of the Nicol, being always greatest when the light which fell on the paper was polarised in the plane of incidence. Table I gives a series of observations made with the steel plate with light polarised in the plane of incidence. The numbers in the first column are the distances, in centimetres, of the sliding lamp from the photometer when the light from the lantern fell directly on the paper; and those in the third when the light was reflected by the mirror. The means of these observations are contained in the second and fourth columns, the angles of incidence in the fifth, and the ratios of the reflected to the incident light—the latter being taken as 100—in the sixth column. : As the intensity of light varies inversely as the square of the dis- tance from the source, the percentage reflected by the plate is obtained by dividing the numbers contained in the second column by those in the fourth, squaring, and multiplying by 100. Table II gives a similar series of measurements with the same plate and ght polarised perpendicularly to the plane of incidence. Three other similar series of observations were made, the actual determinations being about as concordant as those contained in the tables. The four sets of observations, and their means, are given in Tables III and IV. 1884.] ope oper) www w (op) (JS) AAA 0 SROs lop op ono) DADA HD hORG ORRR Bowe lop op op ior) OO Be co Da i on) rv EPWIIS SSDS ANON Ww (op) ne Sr ow DDD HD Ce Ee OV Sond HOt 0560 Ser MONO K SHKS Gorer oO Cy OY J ed Some Experiments on Metallic Reflection. 63 ‘8 63 °6 63 °6 63 °8 64°0 64 <1 64-1 Q 0 © © Orc oOrRN oO SS 00 ros) ME wooct csT~0 J ~J Te —S— eee aT rer mT ward TI oo re ye Se I ~T ra) GO HS no JT (=) ps; (iar aS BE Sa Table I. 84:1 81 ‘2 18°7 76°7 70 °9 69-9 30° 40° 50° 55° 60° 65° 80° 57° 61° 68 ° 81 84 84. 01 °48 ‘09 D8 189 en — own KRORND NHNHONW WHADAS aw3HeHK WOdS NASD BKWD — Ou a] SOPRA WNOD Ws Sir J. Conroy. Table IT. 112° 110° Zs 109 ° Pau HO) 27/ SIS 116 114 118 115 Co Or & ON 3 78 °2 124° 124 124 123 78°8 FOOm BGounw ya eee er i OC NS OU "| ” 128 128 127 129 78°6 136 132 135 131 80 °0 134 °2 149 149° 151° 148 81 °4 149 °7 163 161° onl orf 162 161 °2 170 166° 169° 167° 81°9 168 °2 161 160° 163° 160° 82 °7 161°3 164° 164 162 164 ed OnNnwo BODO ANNO WHHEOD DOEwAT CIM HM wWwwe 123 °9 5000 128 °4: olen 1€3 °7 4006 30° 40° 55° ‘ 60° 70° 80° 80° [Jan. 10, 49°27 45°53 40 °45 37°47 3D *O4 29°57 25 69 23°71 26 °29 26 °46 1884.] Some Experiments on Metallic Reflection. 191 Table III.—Steel, with Light polarised in the plane of Incidence. Angle of Incidence. E 36 Mean. 60-70 64°21 68 °52 74°42 CEST 82°26 86 ‘OL 87 °87 Table IV.—Steel, with Light polarised perpendicularly to the Plane of Incidence. Angle of Incidence. A. AQ -27 45°53 40 °45 37 47 3d “OA 29 °57 25°69 23°71 26°29 50 45 41 37 33 28 26 25 26 "53 39 “24 34 79 88 ‘61 a1) “46 C. 53°67 49°79 43°47 36 *90 31°97 Zt 2 25°38 27 *6U D. 47 -28 44°40 38°78 32 °89 29°70 26°14 24°30 26 °04 Mean. 50°19 46°28 40°98 34°78 30°03 26 54: 24°73 26 ‘60 Similar measurements were made with the speculum metal mirror, and the results are given in Tables V and VI. Table V.—Speculum Metal, with Light polarised in the Plane of Angle of Incidence. 30 40 50 60 65 70 7B 80 Incidence. B. C. 64°09 63 °37 68 °22 65 °14 42°23 69 -04 78°65 UTS 79°68 79 -44, 81°25 84°94 84°20 86°93 86°78 90-96 77°95 Mean. 64°55 67°74 71°45 77°70 80°01 83 -29 85°52 88°74: 192 ! Sir J. Conroy. [Jan. 10, Table VI.—Speculum metal, with Light polarised perpendicularly to the Plane of Incidence. Cas of A. B. C. D. Mean. neidence. 30 59°31 57-86 59 ‘83 59-63 59°16 40 53°30 54 ‘Ol 56°41 54°29 54°50 50 49 -4'7 51-44, 49 ‘61 49-69 50°05 60 41°50 43°36 44-02 43 *83 43°18 65 39 -95 39-12 40 *50 40 ‘85 40-10 70 38-27 35-84 37-42, 38-29 37 “45 "5 36 -20 34°45 36°84. 35 ‘88 35-84. 80 40°51 38 67 41°22 41°15 40°39 The principal incidences and azimuths for both plates were deter- mined in the manner described in “‘ Proc. Roy. Soc.,” vol. 31, p. 486, and vol. 35, p. 32. Four observations were made in each position of the retarding plate, two with the principal section of the polarising Nicol on the right, and two with it on the left of the plane of inci- dence. The means of the several sets of eight observations are given in Table VII; the probable error of the He mean result, calculated by the ordinary formula 0°6745 oes is also given. ED Table VII. Principal Principal incidence. Mean. incidence. Mean. LCC ses seven Be 1 OSS: Me SLY "6 17 Prob. error. 98 3 | Prob. error. 6 vali: I PY aR 98 28 28 2 Oiatcelue 76 42 28 26 Speculum metal.. 74 48) 33 28 7} 7, UB 33 09 | 76 OV Saoe 75 88-575 81+7' 32 40 ei 02 +6’. 75 39 a2 PS) | 75 82 J 33 O01 J A beam of ordinary light being equivalent to two beams of half its intensity polarised at right angles to each other, the percentage of light reflected by the plates, if ordinary unpolarised light were inci- dent upon them, is given by half the sum of the intensities of the light polarised in, and perpendicular to, the planes of incidence. 1884. ] Some Experiments on Metallic Reflection. 193 In Table VIII the numbers obtained in this way are given in the Qnd and 5th columns, the values as determined by the experiments described in the paper already referred to in the 3rd and 6th columns, and in the 4thand 7th columns the results calculated out, as described in a subsequent part of the present paper, from the measurements made with polarised light. Table VIII. Steel, Speculum metal. Observa- tions made Observations made Observations made with Observations made with polarised light. | with ordinary light. | polarised | with ordinary light. J7+ 1? rJ?7+1" light. rJ?+ 7 2 r+1 Ueselic r+ 2 is Observed. | Calculated. Observed.|Calculated. 30 55 *44 54°93 56 62 61°85 66°87 62 39 40 5D 24 55 “62 57°26 Git) 67-26 62°61 50 54°75 56°74 57 *84 60°75 |; 67°26 63-15 60 54°60 57°63 59°04. 60°44 | 66°32 64°31 65 53°70 58°37 59 ‘0 60°05 | 66°53 64°53 70 54°40 58-09 60 *65 60°37 | 67°65 65°51 75 5d 37 58 69 62 °33 60°68 | 67°43 66 °22 80 57°23 63 °56 64°10 64°56 | LOA 69 ‘98 | In addition to the actual numerical differences between the values, the two sets of observations appear to differ fundamentally, for whilst the numbers in the second and fifth columns diminish slightly, and then increase again, as the angle of incidence increases, those in the third and sixth increase with the angle, a result that, as was pointed out in the former paper, is not in accordance with either theory, or ‘previous observations, and which, as was stated in the paper, if erroneous, must have been caused by some defect in the method employed, and therefore common to all the determinations. Further consideration showed that such was really the case, and that the defect in the method was the one pointed out by Professor Stokes in the note appended by him to the paper (‘‘ Proc. Roy. Soc.,”’ vol. 35, p. 39). As has already been stated, the apparent brightness of the paper varied with the polarisation of the incident light, or, in other words, the amount of light irregularly reflected, or diffused, by the paper was different for light polarised in, or perpendicularly to, the plane of incidence. The light being incident upon the paper at an angle of about 30°, whilst the line of sight formed an angle of 194 Sir J. Conroy. [Jan. 10, about 60° with the normal, no regularly reflected light could reach the observer. The terminal faces of the polarising Nicol were perpendicular to its long diameter, and it was of a nearly circular section, so that the amount of light transmitted by the Nicol must have been very nearly, if not absolutely, the same in both positions. Table 1X gives observations made to determine the amount of illumination in both cases, the numbers in the first column being the distances at which the sliding lamp had to be placed when the light was polarised in the plane of incidence, and those in the second, when it was polarised in a plane at right angles to this; each determination being the mean of four observations. Table IX. FOO SA ae ; 85 °3 ZO 3000 gece : 90 °4 68 °8 adic alten 86 9 POLO. Wee ; 88-8 Miao) IO ORO) = hs ae: 87°38 Calling the light diffused by the paper when the incident light was polarised in the plane of incidence 100, it would appear that when the light was polarised perpendicularly to that plane only about 63 per cent. of the light reached the observer. The very considerable difference in the amount of light diffused in the two cases seems the more remarkable, as previous to the publica- tion of the former paper the illuminated surfaces of the photometer were examined with a bi-quartz, and although they showed traces of polarisation it was only, apparently at least, to a very inconsiderable extent. This experiment has been recently repeated, and with the same result ; the lamp light diffused by the paper of the photometer showing hardly any, if any, traces of polarisation, whilst that reflected obliquely from the blackened surface of the board along which the lamp was arranged to slide, when examined in the same way, was seen to be strongly polarised.* * [Of the light falling on the paper, a considerable part would be reflected at various depths before it had lost, through the various irregular reflections and refractions, all traces of its original polarisation, and consequently light derived from that which was originally polarised in the plane of incidence would be more copiously reflected than light derived from that which had been polarised in a per- pendicular plane. But the light so reflected would have to make its way among the fibres of the paper, especially as the angle of emergence was considerable, and in so doing would be pretty well depolarised by the irregular reflections and refractions which it would have to undergo. This accounts for the circumstance 1884.] - Some Experiments on Metallic Reflection. 195 Owing to the unequal reflection of light polarised in and perpen- dicularly to the plane of incidence, the experimental results contained in the paper published in the ‘‘ Proc. Roy. Soc.” vol. 35, p. 26, cannot be the true values of the amount of light reflected by the mirrors. The lamp light which was incident upon the mirrors, being equivalent to two beams of half its intensity polarised in and perpendicularly to the plane of incidence, and light polarised in and perpendicularly to this plane being unequally diffused by the paper, as well as unequally reflected by the mirrors, the observed intensity must, as Professor Stokes pointed out, be r+ l , and not £_— J? +P Assuming the values of J? and I? found from the determinations with polarised light, and the value of r from the measurements contained in Table IX, the value of ele cigs r different incidences were calculated out,* and the numbers thus obtained are given in the fourth and seventh columns of Table VIII. In the case of the steel mirror the observed and calculated numbers agree tolerably, as well, perhaps, as could have been expected, recollecting the nature of the determinations, but with the speculum metal mirror the results are discordant, the calculated results being in all cases too low. The observations with unpolarised light were made immediately after the mirror had been polished, whilst an interval of several months elapsed before those with polarised lhght were finished. Although the mirror was kept in a dry warm room, and in a closed case containing lime, its surface was usually found to be covered with a slight film; this was readily removed by rubbing it gently for a few seconds with a piece of wash-leather, and the surface then appeared perfectly bright. After the conclusion of the experiments with polarised light, the photometer was rearranged in its original form, and three observations were made of the amount of unpolarised light reflected by the mirror at an angle of 30° in order to ascertain whether the reflective power for the two mirrors at that the illumination was so different that was produced by light polarised in the two ways, even though the polarisation of the light coming from the paper was very feeble when the light incident was common light. I overlooked this when I proposed (“ Proc. Roy. Soc.,” vol. 35, p. 39) to measure r by measuring the polarisation of the light coming in this case from the paper, and regarded r as only “a little’ greater than J on the strength of the author’s assurance that the polari- sation was so slight.—G. G. 8. ] * The actual calculations were made with the equivalent formula alas 1 100+7” which r=63'38. 196 Sir J. Conroy. wh | SameRG of the mirror had been diminished by the formation and removal of this film on several occasions. Light reflected, per cent. 62°42 63°04 63°30 Mean: s 2iic). 9 G2202 + The mean of these three observations agrees very fairly with the value deduced from the observations with polarised light, and it therefore seems probable that the differences between the numbers contained in the sixth and seventh columns of Table VIII are due to an alteration in the surface of the mirror, analogous possibly to the surface changes that Seebeck found with freshly polished transparent bodies. The values obtained for the principal incidence, and principal azimuth, with the freshly polished mirror, and with the same mirror at the conclusion of the experiments with polarised light, differ but little from each other, as is shown in Table VII. The first four observations with the speculum metal mirror were made at the end of the experiments, and their means 75° 35” and 33° 12’ agree very closely with the means of the last two observations 75° 29’ and 32° 57’ made with the freshly polished mirror. The amount of light which, according to Cauchy’s theory, ought to have been reflected by the mirrors was calculated out by the formule— le 0” + cos? 1—20 cos € cost ee pee __& cos?i + 1—20 cos e cost ~~ 624+ cos? i+ 20 GOS €cos2 62 cos? i +1+26 cos ecos c and the results set forth in Tables X and XI. Table X.—Amount of Light reflected by Steel Mirror. Observed. po otras. | ened Calculated. ye. rT. iv) Fi mala aa je 30 60°70 50°19 6317 54°95 40 64°21 46 °28 66 °44 51°31 50 68 °52 40 98 70°80 42:09 60 74°42 34°78 76°72 39 *24 65 Mod 80°03 79 -52 35°32 70 82 °26 26 °54: 83 °04 31. °62 75 86 01 24°73 86°85 29 -46 80 87°87 26 ‘60 90:97 32-39 1884. ] Some Experiments on Metallic Reflection. 197 Table XI.—Amount of Light reflected by Speculum Metal Mirror. Observed. Calculated. J, i; J. I, 30 64-55 59-16 69°78 62-82 40 67°74 54°50 72-53 59 74 50 71°45 50°05 76°18 5S BY) 60 77°70 ‘ 43-18 80°77 49°59 65 80°OL 40°10 83 °42 46 °38 70 83°29 37°45 86 °32 43 °53 5 85 °52 35 ‘84. 89 ° 4.4; 4.2 -29 80 88 °74 40 °39 92°77 45°88 As far as the general character of the phenomena the agreement is complete and in accordance with the observations of M. Jamin, but the actual values of the observed intensities always fall short of the calculated intensities, the difference being least with the steel mirror. The probable errors of the values of the principal incidences and azimuths having been ascertained, the theoretical intensities of the light reflected at an angle of 30° were calculated for the two values obtained by adding and subtracting these sums from the means. The probable errors of the photometric measurements for the same angle were also determined, and Table XII gives the values thus obtained. Table XII. Steel Mirror. Observed. Calculated. J. 1 J2, [?, me OL Oe cs OLTOS eels. Gaioo. se Ooney OMS ON as AO OO ne ele ee Oo Aa Speculum Metal Mirror. Sie Oto)... (99 GO) a. iss 70:24 2. 63°35 ARAM. IEOG I Cah, UL sreveue ape CORO ae te OA sory These numbers seem to show that the differences between the calculated and observed results are not merely due to errors of obser- vation, a conclusion that is rendered the more probable by the fact that the difference is always in the same direction. The polish of the mirrors was examined at the end of the experi- ments by the method suggested by Professor Stokes, and described in 198 On the Volcanic Eruption in Sunda Strait. [Jan. 10, the paper already referred to; both the mirrors stood the test satisfactorily, the polish of the steel being very slightly the best. These experiments appear to show that the generally received formule for metallic reflection are approximately correct, but that the actual intensity of the reflected light is always less than the theoretical intensity, and that therefore, unless this be due to defects in the metallic surfaces, the formule do not completely express the laws of metallic reflection. If, as appears to be the case, a change in the reflective power of a plate can occur without any change in the values of the principal incidence and azimuth, it is necessary to regard the formule as only approximately true, and there is additional reason for thinking that, as Professor Stokes has suggested, three constants are required to define a metal optically. I hope hereafter to determine the amount of light reflected by films of silver chemically deposited on glass, and also to make some determinations of the amount of radiant energy reflected by metallic surfaces at various angles, the experiments of MM. de la Prevostaye and Desains on this point having been but few in number. If]. “! tracts from a Report on the Volcanic Eruption in Sunda Strait by Commander the Honourable F. C. P. VEREKER, H.M.S. ‘Magpie,’ dated Singapore, October 22, 1883.” Communicated by Sir FREDERICK Evans, K.C.B., F.R.S. Received December 15, 1883. [PuateEs 2, 3.] * * * On the 18th instant I entered Sunda Strait, passing east of Thwart-way Island. This island had been reported to be split by the eruption into several portions. This is incorrect. The island is intersected by low valleys in several places, these being covered with tall trees did not show so prominently formerly as they do now. The whole of the vegetation having been swept away by the tidal wave the island at a short distance off is apparently divided, the low necks joining the higher portions being only visible on close approach. The surface of the Strait im this neighbourhood is covered with extensive fields of floating pumice stone, often in one to two foot cubes, through which the ship easily forced her way. * * x * * ss I inclose sketches which I trust will convey the general appearance better than a written description. The whole of the neighbourhood is covered with greenish-yellow mud, and all traces of vegetation are everywhere destroyed. ion of August 1883, f Proc. Roy. Soc. 16884: Plode 2. FN SSS SS Sebooko Islana: 2 x of ors ¥ c 5 cs Toland - =a cS Y) Ig(e, ¥) ee) Gina Che as ee CP] (eas ZL : Fia(@ , y) i Iy(@,Y) where z=nt+a and y is arbitrary. But in order that these values may satisfy the equations, a relation among the parameters of the Theta-functions must be satisfied. This is €6C 1005 Cq + C1Cy3Cal4=9.- The solution is not complete, because after satisfying the equations of motion only four constants remain to express the initial conditions, whereas six constants are required. IV. “Evidence of a Large Extinct Lizard (Nottosaurus den- tatus, Ow.) from Pleistocene Deposits, New South Wales, Australia.” By Professor Owrn, C.B., F.R.S. Received January 9, 1884. (Abstract.) In this paper the author describes a fragment of jaw with teeth of a fossil from the pleistocene deposits at the “ Cuddie Springs,” New South Wales, transmitted by H. S. Wilkinson, Esq., of the Depart- ment of Mines, Sydney. ; A series of comparisons are detailed with known recent and fossil Saurians, and the microscopic test is applied to the tissues of the bone and tooth. The conclusion arrived at is that the fossil was part of a lacertian reptile, equal in size to the Megalania, but of carnivorous habits ; distinct from the largest existing toothed and pleurodont lizard (Hydrosaurus giganteus.) For the much larger extinct pleurodont Saurian the author proposes the name Notiosaurus dentatus. 222 Drs. D. Ferrier and G. F. Yeo. [Jan. 24, January 24, 1884. THE PRESIDENT in the Chair. The Presents received were laid on the table and thanks ordered for them. The following Papers were read :— I. “Observations on the Influence of certain Culture Fluids and Medicinal Reagents in the Growth and Development of the Bacillus tuberculosis.” By C. THEODORE WILLIAMS, M.A., M.D., F.R.C.P., Physician to the Hospital for Con- sumption, Brompton. Communicated by Sir JOSEPH FAYRER, K.C.S.L, F.R.S. Received December 28, 1883. [Publication deferred. | II. « The Effects of Lesions of Different Regions of the Cerebral Hemispheres.” By Davin FERRIER, M.D., LL.D., F.R.S., and GERALD F. YEO, M.D., F.R.C.S. Received January 19, 1884. (Abstract. ) This paper contains a detailed account of a series of observations on the effects of localised lesions of the brain of monkeys, made partly by Drs. Ferrier and Yeo, and partly by Dr. Ferrier alone. The operations were performed under anesthetics, and according to the rules and methods of antiseptic surgery. The experiments are illustrated by photographs, showing the posi- tion and extent of the lesions and general condition of the brains, together with sun-prints and microphotographs of sections of the brain and spinal cord, showing the structures primarily involved or secondarily degenerated. As the paper is mainly an anatomical description of the lesions delineated and record of the effects produced, it scarcely admits of condensation in the form of an abstract. The lesions are classified according to their position in the oecipito-angular, temporal, Rolandic. frontal, and hippocampal regions respectively. 1884.] The Effects of Lesions of the Cerebral Hemispheres. 223 Among the more important results arrived at are the following :— Lesions of the occipito-angular region (occipital lobes and angular gyri) cause affections of vision, without affection of the other sensory faculties or motor powers. The only lesion which causes complete and permanent loss of vision in both eyes is total destruction of the occipital lobes and angular gyri on both sides. Complete extirpation of both angular gyri causes for a time total blindness, succeeded by lasting visual defect in both eyes. Unilateral destruction of the cortex of the angular gyrus causes temporary abolition or impairment of vision in the opposite eye—not of a hemiopic character. Deep incisions may be made in both occipital lobes at the same time, or the greater portion of one or both occipital lobes at the same time may be removed without any appreciable impairment of vision. Destruction of the occipital lobe and angular gyrus on one side causes temporary amblyopia of the opposite eye and homonymous hemianopia of both eyes, towards the side opposite the lesion. As in none of the cases recorded, either of partial unilateral or bilateral destruction of the occipito-angular region, were the amblyopic or hemianopic symptoms permanent, it is concluded that vision is possible with both eyes if only portions of the visual centres remain intact on both sides. Destruction of the superior temporo-sphenoidal convolution on both sides causes complete and permanent loss of hearing, without other sensory or motor defect. Hearing is not impaired by lesions of any other part of the temporal lobe. Destructive lesions of the Rolandic zone (convolutions bounding the fissure of Rolando) cause motor paralysis, without loss of sensation, limited (monoplegia) or general (hemiplegia), according to the posi- tion and extent of the lesion. Lesions of this region are followed by descending degeneration of the pyramidal tracts of the spinal cord. Lesions of the frontal region vary according as they affect the post- frontal (base of the frontal convolutions) or pre-frontal (anterior two- thirds of the frontal convolutions) region. Lesions of the pre-frontal regions alone do not produce any dis- coverable physiological symptoms. Lesions of the post-frontal regions cause temporary paralysis of the lateral movements of the head and eyes. As the symptoms are only temporary so long as any portions of the frontal lobes remain intact, it is concluded that the post-frontal and pre-frontal regions have essentially the same physiological significa- tion, and that portions only of the frontal lobes are sufficient for the exercise of their functions. 224 Eifects of Lesions of the Cerebral Hemispheres. [Jan. 24, Lesions of the frontal lobes are followed by descending degeneration of the mesially situated tracts of the foot of the crus cerebri and cor- responding fibres of the internal capsule, as seen in transverse sections. The ultimate destination of these tracts is uncertain. They cannot be traced in the anterior pyramids. Lesions entirely destroying the hippocampal region (the hippo- campus major and gyrus hippocampi) and neighbouring inferior temporosphenoidal region (without implication of the crus cerebri, basal ganglia, or internal capsule) cause complete anesthesia—cuta- neous, mucous, muscular—of the opposite side of the body, without motor paralysis. The degree of impairment of tactile sensibility in those cases where it is not entirely abolished, is in proportion to the amount of destruction of the hippocampal region. Lesions of the cornu amnionis alone, or gyrus hippocampi alone, do not cause permanent impairment of tactile sensibility. The duration of the effects of total destruction of the hippocampal region has not been determined. No impairment of tactile sensibility has been observed in con- nexion with any of the other cerebral lesions described. 1884.] Determination of Pressures of Granular Substances. 225 January 31, 1884. THE PRESIDENT in the Chair. The Presents received were laid on the table, and thanks ordered for them. Pursuant to notice Anton De Bary, Carl Gegenbaur, Leopold Kronecker, Rudolph Virchow, and Gustav Wiedemann were severally balloted for and elected Foreign Members of the Society. The following Papers were read :— I. “Determination of the Vertical and Lateral Pressures of sranular Substances.” By Issac ROBERTS, F.G.S., F.R.A.S. Communicated by J. F. Bateman, F.R.S. Received November 6, 1883. Part I1.—Wheat and Peas. The investigations which I have the honour to submit in this com- munication have been undertaken to furnish data to engineers and others who are concerned with the erection of structures which have to sustain pressure upon floors and retaining walls, and also to further the objects of science in a field that is believed to be new. Store-houses have been erected, both in this country and in America, which consist of rectangular cells, called bins, and are filled with grain to a height of 50 feet and upwards above the ground. Diligent inquiries have been made for any scientific data or rules by which the necessary strength of the walls and floors of such structures could be computed, or, for instance, what would be the vertical and lateral pressure of a column, say of wheat, 14 feet square at its base and top, and 60 feet in height. It was generally assumed to be something less than the pressure of a similar column of water, but how much less did not appear to be known either in Hngland or America. Last year I made experiments to obtain data, by employing models of square and hexagonal bins, particulars of which were communi- cated in a paper read in Section G, at the meeting of the British Association for the Advancement of Science, held at Southampton. I give briefly, in tabular form, the results. BI" Mr. I. Roberts. [Jan. 31, Table of the Results of Experiments made to ascertain the Vertical Pressure of Wheat stored in Cells or Bins. 3 : ie Sls rica) 2 > 5 = aH | 92 a0 ee a) ses S| ae |e eae |= Description of | #% 1S 2 ee alae owes C o a, = 4 cell. ot 22 H 2 ay ee 2 i oie So eS a oH a i aa) Oa ale un S eee eo a 5 ¢ mq 1A u S fe) 5) an) Ses o Ges o S-s oO a 5 S| 5 S| B | S 5 S Sr pe a a ws > H + i =) ~ ~~ ol ~— fo) oO fe) oO jo) oS) je) ro) fo) 3) (e) 3) QA bat fa et ee lt eh 68 43 165 83 96 38 Sve os ai a a ue 167 78 95 40 150 83 160 82 170 | 80 160 79 238 | 100 75 39 128 81 150 82 | 158 | 87 174 80 206 92 iy ah ae aid Ae at Ne 167 89 195 87 83°5 40 139 | 82 155 82 164 | 83°5 166°6 | 81°8| 213 93 Table VI.—Weighings of the Side or Lateral Pressures of Wheat. Size of the Aperture used=1 ft. Oin. x 1 ft. 0 in.=1 square foot. Wheat 1ft. high | Wheat 2ft. high [Wheat 4 ft. high | Wheat 44ft. 6ins. in bin. in bin. in bin. in bin. 2 = S 2 ee = a a 2 az 2 m 2 a 2 g e oF al ee eae ihn © a | Pie Set gee S| Be |) Ee ee —— 2.79 me 7 Sq a5 e aS S 4 Oo Ses oO Ses o Ses © S 2 | | ee g ales = Az foal P=) ol ~~ onl 25 om — iS) Ss} S rcs 3 S} S) > a < A < A ). dy Let differentials of X, a, t, regarded as independent variables, be 6), 6x, ot respectively. Ov Thus | aE is an integral taken with regard to 2, \ and ¢ being (7;): considered constant. a) Ow ét ale is the differential coefficient of the above integral with dy regard to t, \ and # being considered constant. | A> 2 dn dt \t dt |e aX denotes that Ix is expressed as a function of X, 2, ¢, and dy dy the result integrated with regard to w, \ and ¢ being considered constant. F and H are the symbols of arbitrary functions. Then the equation in \ is shown to be— dn A @ ) éFQ,t) (es dt | eevee) eee aetag)) ae tax] Bis ae olla dy L dy/* J and the current function is dn x dF (A,2) dt | ay MD | dy dy For a vortex of invariable form moving parallel to the axis of y with velocity co (where Y is a function of ¢ only) the equation in i ad becomes — d? , d\dF(,t) _ OED alee) — ==1a/ Fe chy? Ja Sion : a esa, |; ) dy and the current function is SF (At) eorey oe. (2.) Plane motion, referred to polar co-ordinates 7, @. 278 Prof. M. J. M. Hill. Motion of Fluid, part of — [Feb. 7, With notation similar to that in the preceding case, the equation in »X is— dn \* ami ale (Cee alchns Ik a SFO,t) 4 + re dt dr? r dr = aml arm Re 6 dF(A,t) ror >) eal — | ay ; t —— The current function is SHOE) (ede OT ee sf + | ror 7 dé For a vortex of invariable form rotating about the origin with angular velocity = this equation becomes Q Bae ee eee Pde of, pele Ce rdr 72 de? ot 2 al > a can (2) ' l de J and the current function is oF (,t) _ 7? dw ot 2 dt (3.) Motion symmetrical with regard to the axis of z in planes passing through it, referred to cylindric co-ordinates 1, z. The equation in \ is— ns (5 _l za) et 4 |ror| a | r\dr? rdr dz ét dn dz _y h, a ie | ey} The current function is dn \A dF (\,Z) +| rer dt t ot Xu 1884.] which is moving Rotationally and part Irrotationally. 279 For a vortex of invariable form which moves parallel to the axis of z with velocity = this equation becomes— (| AO OL pe een v2 \dr2 + dr dz) st — | | on era t dz and the current function is 6KQ,t) 7? dZ Woas, wehdie Suppose that in any of these cases any particular integral of the equation in ) is taken. It is shown that the components of the velocity can be expressed in terms of X and differential coefficients of \, and that the current function is also known. In the case of a fluid, part of which is moving rotationally and part irrotationally, the boundary surface separating the rotationally moving fluid from that which is moving irrotationally contains the same vortex lines, and may be taken as the surface \=0. Now, if the integral taken of the equation in 2 do actually corre- spond to a case of fluid motion in which part of the fluid is moving rotationally and part irrotationally, the most obvious way to find the irrotational motion will be to find its current function from the con- ditions supplied by the fact that the components of the velocity are continuous at the surface \=0. If after taking any integral of the equation in X it be found theoretically impossible to determine the current function of an irrotational motion outside the surface \=0, which shall be continuous with the rotational motion inside it, then the integral in question does not correspond to such a case of fluid motion. In this method no assumption is made as to the distribution of the vortex lines (as in the method of Helmholtz) before commencing the determination of the irrotational motion. On the other hand, it is not a particular case of a method applicable to motion in space of three dimensions. But it can be shown that Clebsch’s forms for the components of the velocity do also lead to a method which is applicable to the deter- mination of the irrotational motion when the rotational motion in space of three dimensions is known. For the rotational motion being known, the components of the velocity are known for this part of the fluid. Let the components of the velocity be expressed in Clebsch’s forms, so that x, », y are known. Moreover, let the forms be so arranged that the surface separating VOL. XXXVI. U 280 Prof. M. J, M. Hill. Motion of Fluid, part of Melb: the rotationally moving fluid from that which is moving irrotationally is the surface \=0. Then at this surface the components of the velocity are a oe ax. da’ dy dz Now, obtain in any manner a velocity potential ¢ for space outside X=0 continuous with x all over the surface \=0. This is theoretically possible always. If the velocity potential so obtained make the velocity and pres-. sure continuous all over the surface \=0, then a possible case of motion will have been obtained. The conditions to be satisfied in order that the velocity may be continuous at the surface \=0 are that there at dx _do dx _ dp In order that the pressure may be also continuous, it is further necessary that a all over the surface \=0. The most obvious way of obtaining the velocity potential will be to apply Helmholtz’s method of finding the components of the velocity in terms of the supposed distribution of magnetic matter throughout the space occupied by the rotationally moving fluid. It must, however, be remembered, as is remarked by Mr. Hicks in his report to the British Association on ‘‘ Recent Progress in Hydro- dynamics,” Part I,* ‘That the results refer to the cyclic motion of the fluid as determined by the supposed distribution of magnetic matter, and do not give the most general motion possible.” It appears also from Examples [and III of this paper that it is not possible to assume arbitrarily the distribution of vortex lines, even when it can be shown that the equations of motion are satisfied at all points where the fluid is moving rotationally, and then to proceed to cal- culate the irrotational motion by means of the supposed distribution of magnetic matter. For in these examples, values of the components of the velocity of a rotational motion, satisfying the equations of motion throughout a finite portion of the plane of a, y, are found. Thus the distribution of vortex lines, and, therefore, that of the supposed magnetic matter over a finite portion of the plane of z, yis known. The surfaces that always contain the same vortex filaments are found. Inside one of these the supposed magnetic matter is distributed, the current function at external points is calculated by Helmholtz’s method, and it is shown that the velocity so found is not continuous with the velocity at the surface, which separates the rotationally moving liquid from that moving irrotationally. Another way (suggested by Clebsch’s forms) of obtaining the velocity potential will be as follows :— * Report for 1881, Part I, p. 64. 1884.] which is moving Rotationally and part Irrotationally. 281 2 2a Calculate the quantity p= —= (= +7% $e Treating p as the density of a material distribution inside \=0, taking no account of the value of p outside the surface \=0, obtain the potential of this distribution. Let the potential inside \=0 be x’, and outside let it be @, x’ will, in general, differ from x ; first, because y may contain many- valued terms, which may be denoted by P satisfying Laplace’s equa- tion; and, secondly, because x—P may be the potential of a distribu- tion of matter, part of which is outside \=0. Accordingly, it is necessary to examine whether it is possible to find many-valued terms P satisfying Laplace’s equation such that x’ +P=y. Then +P will be the velocity potential of the irrotational motion, provided that it give zero velocity at infinity. The few illustrations which follow are a first attempt to apply the above theory to particular cases. Example 1. x, y being rectangular co-ordinates in a plane, Y any function of the time #, Y its differential co- efficient with regard to the time. f, 4, 6, constants, u, v the components of the velocity parallel to the axes, it is shown that w= (ye ye ¥—(f)=” satisfy the equa- a tions of motion. The surfaces containing the same particles are the elliptic cylinders wy y—Y)? Ce _ ) =constant, For a finite portion of the plane of a, y outside the cylinder a =1, the current function of an irrotational motion a continuous with that inside the cylinder is— as CM Oa ale (F) log (V Het V BF) 2f 2 att i az+b?\ , a@—b? \ eee aoe a Me aM ms _ Cf )a2 +02) oy a BPP Y@TIPFI( ot" cay where e, v are the elliptic co-ordinates ee, the equations Ge Oe re ye a+e b?+e at+y Rea i and —Pb. Example 3. With the same , values for u’, v' as in the last example, except, however, the relation between f aud w, it is shown that an irrotational motion continuous with the rotational motion inside the cylinder ood can exist between this and a confocal elliptic a smooth rigid cylinder surrounding it; provided that confocal elliptic cylinder be made to rotate with the same angular velocity w. The cof the confocal cylinder is— ai ab? Re aN “| &. wo =) = | w y) where —o < -< ——. ab 1884.] which is moving Rotationally and part Irrotationally. 283 The components of the velocity of this rotationally moving liquid are— y(2 —i) and —o( —i). The components of the velocity of the irrotationally moving liquid are— aby' ' C =) Vag es zt nad a) peel al sod Ae ak IN cay er +e lad ab aba’ lige raaal Noaty } Mi +e ff penal SI ap, a f+ }— eget at at Ae pl As TH "{ a? +e ab ab | Example 4. The vortex sheets are coaxial circular cylinders, and the motion is everywhere perpendicular to the radius vector from the axis, and a function of the distance. Thus radial velocity=0, velocity perpendicular radius vector= —F’(7r). This example is given merely to illustrate the expression of the com- ponents of the velocity in Clebsch’s forms, It is shown that A= Fr). W= (ite le'o + “¥'()) x=04 FO) (0 Deere i +f FORE? +H FOF O-[“aroy } If F(a)=0, and the rotational motion be supposed confined to the interior of the cylinder r=a, then a suitable value of the velocity potential at external points is— b=0(—a¥"(a)) +1] 28 (a))2— | R'@))? } Hxample 5. 1, z being cylindric co-ordinates. Z, an arbitrary function of the time ; Z, its differential coefficient with regard to the time. a, b, a positive constants. 7 the velocity from the axis of cylindric co-ordinates in the direction of r. w the velocity parallel the axis of cylindric co-ordinates. It is shown that t=2ar(z—Z); w=Z—2a(z2—Z)?—4b(0?—2?) satisfy the equations of motion. 284 Prof. M. J. M. Hill. On the Motion of Fluid. [Feb. 7, One set of the surfaces which always contain the same vortex lines is given by ar?(z—Z)?+b(7?—a’)’=const. If the constant be 1 /{/a?+0? =) 1 es A.’ Th Pel baee a =a Na #5 EE st?\ NKR FE or since N is equal usually to about two-fifths H, we find that 5 \ = ee Now when £ is very small this is very great. On the other hand, when f is very great this is also very great, but of the opposite sign. As & increases from 0 the expression to which 9, or the amount of turning, is proportional diminishes until when & reaches a value nearly 1:3, ¢ becomes 0, or there is no rotation of the spring pro- duced by an axial force. In fact, for small values of & there is a rotation of the spring in the direction of the coiling, and the amount of rotation becomes the greater the smaller & is, while for values of & greater than 1°3 there is a rotation of the spring opposite to the direction of the coiling, the rotation becoming greater the larger & is. Fig. 3 shows a spring in which £ is greater than 1:3, and it is found that there is an uncoiling on the application of an axial force. Fig. 4 shows a spring made of the same material, but the wire has been passed through rolls so as to flatten it in the opposite way, and now a rotation tending to coil it up is found to be produced by the application of an axiai force. 302 Profs, W. E. Ayrton and J. Perry. [Feb. 14, and the bending torque to Fvsinz. But the twist must be multi- plied by sin «, and the bend by cos « when we project these motions on a horizontal plane. So far then as the total rotation in a horizontal plane of the free end of the spring relatively to the fixed end is con- cerned, it may be regarded as being produced by equal twisting and bending torques, each of them equal to F7sinzcosa; and the total rotation of the free end of the spring relatively to the fixed end, which is the special feature of the springs we are considering, is proportional to the difference between the two angular rotations produced in the wire by these equal bending and twisting torques. The twist alone would cause an increase in the number of coils, that is, a rotation in the direction of coiling which is what we call positive, while the bending, or rather the unbending, alone would cause a negative rotation, or one tending to uncoil the spring. When both occur together in the actual spiral spring subjected to an axial force the total rotation is positive or negative, according as the angular twist or the angular bend is the greater. Hence the flexural and torsional rigidities of the wire alone determine whether the rotation is positive or negative. It is well known, for example, that when a wire of circular section is subjected to equal twisting and bending torques the twist is greater than the bending for almost all substances, that is, substances in which the ratio of the modulus of rigidity to Young’s modulus is 1884.] New Spring for Electric and other Instruments. 303 between one-third and one-half. Hence we may expect that in a spring made of round wire, and with the spires making an angle of 45° with a plane perpendicular to the axis, the total rotation will be positive for an axial force applied so as to lengthen the spring. And experiment shows that this is the case. If the wire be flattened and bent so that the flat side of the strip touches the cylinder on which the wire is coiled, as shown in fig. 3, then the arrangement is such that the bending is greater than the twist. Hence an axial force applied so as to lengthen this spring causes a negative rotation, whereas if the strip be coiled as in fig. 4, so that the edge of the strip lies against the cylinder on which it is coiled, an axial force similarly applied will now cause a positive rota- tion. It is almost certain that for any strip of material the positive value of @ obtained with the latter form of spring is likely to be greater than the corresponding negative value with the former kind, but the difficaity of manufacturing the second form of spring, where k has a very small value, has compelled us to confine our attention to the former type. Permanent Set.—Having constructed some very delicate springs of this kind, one of the first difficulties which we met with arose from their liability to acquire a permanent set, so that it has been necessary to determine the dimensions of the spring which will give the largest amount of rotation with the minimum amount of stress in the material. The shear stress at any point #, y in an elliptic section if the prism has received a twist 7 per unit length, is— N ( wap lt in the direction of y, dy and N ( yt ) in the direction of a, da 2__ 42 h ——— g Hip where / "PL yf where a and 0 are the principal semi-diameters of the ellipse, the axis of y being parallel to the semi-diameter b. Consequently these shear stresses equal— 2b2N ra mee « _ 2N7ya? iE see respectively ; a? + b a ae and the total shear stress is equal to DAN Gres if Sat Aaa J ba + aty?, VOL. XXXVI. nya 304 Profs. W. E. Ayrton and J. Perry. [Feb. 14, From this we see that the greatest shear stress is at the ends of the minor axis, and at the boundary is the least at the ends of the major @x1sS— If C is the twisting couple we know that— Using these values of 7 in the above we obtain for the total shear stress at a point x, y of an elliptic section— = ee and this at the extremity of the minor axis becomes 2C mab? Applying (5) to our case where the twisting couple is Fr cos a, and the bending couple Frsin «, and recollecting that the direction we have chosen for y on the section is perpendicular to the axis of the spiral, we see that ata point w, y on the section bent about the axis of «, that is, # is perpendicular to the plane in which bending occurs the shear stress g equals— QE cos a TA?b® Vv bee tate. . i oe and the tensile or compressive stress p at the point «, y due to bending equals AY Pr sina ee, |. TO And the resultant tensile, or compressive, stress f at the point 2, y is iy (Go Bt a / Ete, Therefore since OP a a a” b? is the equation of the ellipse, the stress at the boundary, ar f= ap(9 sina+ a/ p+eos «(0?—y")) eer (iS) 1884.] New Spring for Electric and other Instruments. 300 We have now to consider for what value of y this expression is @ maximum. The possible values of y are between 0 and 0; and 2 we see that if 1—~ cos? ais positive, f will be greatest when y has its a greatest possible value, namely b. For sections 1, 2, 3, 4, therefore, of the strip shown in fig. 5, where AB is the axis of the spring, MM WD B a the greatest stress will in each case be at B. If, however, b be very large compared with a, which is the case in the section 5, fig. 5, then f will not have its greatest value at B. We find also that when a (b? cos? a—a?)(b?@—a?) ; and when these are equal we have a?’ =b?(1 sin a) . where the positive sign is evidently inadmissible, since our condition above is a less than b. a Hence from b equal 0 through b equal a to b equal Ui the greatest stress occurs at the extremity of the y axis. After that, the point of greatest stress is nearer to a, but still on the circumference of the ellipse. Now if 6 is very great ot with a, then we have as a limit, y=a tan a, Meee 306 Profs. W. E. Ayrton and J. Perry. [Feb. 14, so that the greatest stress can never occur at the end of the semi- diameter a, but may be very near to it. On the Mere then that, relatively to a, b has any value from 0 to ~====—, the greatest stress in an elliptic section occurs at the /1—sina end of the aeeeasne ice b, which is parallel to the axis of y, and this is the case we will first confine ourselves to. Maximum Rotation in Relation to Permanent Set.—If, now, f is the greatest stress at any point of the section, Papp Snecss (Ca) 10 7 35 lisna (Na OE) | The conditions that make this a maximum are those which for a given axial force applied to our spring produce the greatest amount of turning of the free end with the least amount of stress on the material, and therefore with the least chance of permanent set. And as regards the value of a, it is clear that sin z=—i+1V5, or 230" 10’, will give the greatest value. Maximum Rotation compared with Axial Motion.—From equations (3) and (4) we have Ath 4 fay .o. aia : 3 Te! doen! Na? HK and the conditions that make this a maximum are those which for a given axial force applied to the spring give the greatest amount of turning of the free end of it with the least amount of axial length- ening. As regards the value of a, it can easily be shown that — - will fone \/ Be aa Aq? If b is small in comparison with a, which is a condition, as already explained, we are led by facility of construction to adopt, then tan a=t ae As a rough approximation, taking N the modulus of rigidity at two- be a maximum when 1884.]| New Spring for Electric and other Instruments. 307 fifths of Young’s modulus, the ratio given by M. St. Venant, this value of tan « becomes equal to V“625, or a=30 19’, makes = a maximum. We have already seen, from (3), that to merely make @ a maximum for a given axial force, « ought to be 45°, and J and r as great as possible. We are therefore led from three considerations— 1. That an axial force shall produce a maximum relative rotation ; 2. That the rotation shall be great without producing permanent set in the material ; 3. That the rotation shall be great in comparison with the elonga- tion of the spring ; to make the angle of the spiral about 45°. Further, to produce the first two of these conditions, it will be observed that the length of the wire forming the spring ought to be great, while the third condition is independent of the length. Next, with regard to the proper radius r to give to the coils of the spring. @ increases with 7, P is independent of 7, and © varies in- versely as 7. Hence, as the first and third conditions are antago- nistic one to the other, the value of + must be chosen to suii the conditions of the instrument in which the spring is to be used; that is, we must consider in any special case whether the possibility of permanent set or a large axial motion is more to be avoided in the particular instrument in question. Let us now consider how 4, Z and depend onaand b. Refer- ring to equation (3), if 6 is not greater than a, it is clear that the smaller 6 is the larger ¢ will be. Next putting N equal to 2 H, an approximation sufficiently accurate for the substances likely te be employed, we see from equation (10) that : depends on 1 : 5b2 al 3 sa) and as in this first case we are limited to values of b between O and a C= =e or between 0 and about 1°84 aif we put « equal to 45°, a value not far from that which we have already determined to be the best, then it is obvious that the smaller b is the larger will be : : 308 Profs. W. E. Ayrton and J. Perry. [Feb. 14, From equation (11) we see that Q depends on (a?+ b?)H—4Na? . (a?+ 6?) H+4Na?’ or, putting N equal to 2 H, this becomes par alg LADEN ES. 5+13 Hence, remembering as before that b? has only values between 0 and 34a2, we see that the last fraction varies between —0°23 and +0°47. Hence, taking b small, which gives the greatest values for @ and Q +, gives a value for 4 not less than half as great as if we had taken 0 the largest possible value of b. a Finally, therefore, if 6 varies from 0 to ~ === i—sina value of 6 is an extremely small one, or the strip should be wound as in figure 3. , the best practical If 6 is greater than —7= qa conditions other than those given above may make ¢, a and % have their maximum values; but, since the difficulty of manufacturing metal springs of the form shown in fig. 4 must necessarily render their employment but very limited, a mathematical examination of this problem has not much practical value. We therefore merely mention that in this case calculation shows. that 2+ 52 1 b2 cos” a—a? o=Ha tan « (= -3)F ous a “al J alae where f is the maximum stress anywhere in the section, the maximum stress in this case not occurring at the extremity of the 6 diameter. The general conclusions therefore arrived at are, that in order, with a given axial force to obtain a large amount of turning of the free end of the spring, combined with small maximum total stress in the material, and not too much axial motion of the free end of thé spring, the strip of elliptic section should be as long and as thin as possible, should be wound in a spiral such that the osculating plane makes an angle of 40° to 45° with a plane perpendicular to the axis of the spiral, and so that the smaller diameter of the elliptic section is at right angles to the axis of the spiral. 1884.] New Spring for Electric and other Instruments. 309 Under these circumstances, 2a being the major diameter and 2b the minor diameter of the ellipse, 21st a (Pe = —__________j —___ —->___ } . . : ° . 15; > ? mab? Cr =) Cg?) f the maximum stress at a section — (14), Lr? (cos? a , 4sin? « and d= ) SMM ePate P's), Boe 15). 2 N a EK (19) Springs with a Rectangular Section.—For practical purposes it is obviously more convenient to use in the construction of our springs thin strips of a rectangular section rather than of an elliptic section. We have, therefore, now to consider how equations 13, 14, and 15 will be modified if our strip has a rectangular section, the longer side of the section being 2a and the shorter side 2b. In this case ib==“ap i, and since, as was discovered by M. Cauchy in 1829, the torsion rigidity of a rectangle bears to the torsional rigidity of an inscribed ellipse the proportion of their moments of inertia about a line drawn through the common centre perpendicular to their plane, in the case when one principal dimension is several times the other, it follows that A, ab? 863 38 A=Nra x sere —ab? 4, 323 or J\ = ZEN CEO ar Fe Henee o= lF'r sin a cosa/ 3 att Sa, Aab? AN a2 a0 _1IFr ( 3 a®+0? SP ee : hein oon “) 5 or, as 0? is insignificant in comparison with a?, 3lFr sin a COS « ee 16 = 4ab3 52 (ae E atigast _ 31K r? COS? a sin? *) 17 = (St ED ec PP Bat Sys.) CLE 310 Profs. W. E. Ayrton and J. Perry. [ Feb. 14, We will now calculate the value of /, the maximum stress at any point in the rectangular section. The shear stress at any point, zy, in such a section of the prism which has received a twist, 7, per unit of length is, where the axes of « and y are parallel to the edges of the section, and the origin the centre of the section, z being at right angles to the section, N (x2 +2) in the directions of y and z, y and N( y+ in the directions of z and a, where y equals—zwy+an expression which vanishes if the thickness of the strip is very small. Hence since —_=— 72, dy and dy =—TY, dx it follows that the shear stress at a point zy is O in the direction of y, and —2Nvy in the direction of z, so that the whole shear stress at a point is —2Nvy, and the shear stress, g, at the middle of the longer edge of the rectangular section, where we may suppose the shear stress is the greatest, 1s 2N7b. Now if C is the twisting couple, we know that == = AC __3Fr cos 2; _o, 79 hence 1GNacES (a + 6?), and == a (a (a?+0?). Also, since Fr sina is the bending couple, the greatest stress due to bending, | _3lrsina ab? Hence if f is the greatest total stress anywhere in a section, it may be shown that ne Gb . (= Jao fsinet a /14 cos? «(S+2)}- 1884.] New Spring for Electric and other Instrumenis. 311 Or, as a is very large in comparison with 6, Fegan)... . 4. Sy ab? If, as is usual in the case of the springs we employ, the edges of the strip nearly touch one another in two consecutive coils, and the angle of the spiral is 45°, we have the area of the cylinder which the 2rrl metal strip approximately covers, or ca equal to the area of the strip, or 2/a, so that and equations (16), (17), and (18) may be simplified thus— ge 017 EF (ara a) MeO). doc 017 (Get ae ER DUES Ad aN oy ¢ jeUCO SS A GN ate Reece. We have preferred to say that ¢, d, and f are respectively propor- tional rather than equal to the expressions on the right hand side, because when the strip is wide in comparison with the radius of the cylinder about which it is bent, the strip receives in addition to the bending and shear strains which we have considered, a lateral bending also, and the exact effect of this we have not yet fully investigated. Use of Spring to determine 5 Before proceeding to a description of the various measuring instruments in which we have applied this new form of spring, we may mention one interesting application of it to enable us to determine readily the ratio of the modulus of rigidity, N, to Young’s modulus of elasticity, HE, for any material. It is well known that the celebrated conclusion of MM. Navier and Poisson from Boscovich’s molecular theory requires that the ratio of H to N should be 2°5 for all solids. Professor Stokes showed that this con- clusion was impossible if its authors supposed it to apply to jellies and to india-rubber, and that it was probably untrue in the case of metals; and Wertheim, Kirchhoff, Thomson, Everett, and others have experimentally shown its untruth in the case of brass, iron, copper, and glass. In pursuance of the present investigation it has struck us that this ratio may be most conveniently determined by the use of our springs from one experiment. 312 Profs. W. EK. Ayrton and J. Perry. [Feb. 14, When the spring is made of round wire, so that a and 0 are equal to one another, we have from equation (11) Hs “f=tan aan ; we? tan? a let = be called cot B, then it can be shown that os —?2tanatan (a+ B), so thatif is 45° H_ tan 8+1 eee LE P24) N tansp—1l (22) In order to measure tan@ most conveniently, we may employ (fig. 6) a pair of cylindric scales, the distance apart of which, close to the wire of the spring, is a inches. A point, P, on the wire is observed in its position in the upper scale, the reading being 0. Now the spring is elongated by an axial force until the point, P, comes opposite a point on the lower scale, and the reading is now ce. As the two scales are similar and parallel to one another, and as a spirit-level has been employed to make the scales horizontal, it is obvious that as the axis is vertical 1884.] New Spring for Electric and other Instruments. 313: @ d ee SE a ) c—b ro ave so that pee cae) I GG) We have used three springs made from round wire respectively of brass, iron, and steel for the sake of illustration. In all of them we. find that c—d is small in comparison with a, so that roughly we may | 4(c—b) say that the excess of = over 2 is | a that is, is proportional to. . (c—b). The cylindric scale has only been introduced for the sake of | illustration. For an accurate determination of = a telescope would be employed having a motion about the axis of the spring, and also a motion parallel to the axis, and by means of which the motion of a . point on centre line of the wire when an axial force is employed, would be accurately observed. It is sufficient to say that the brass. spring of round wire exhibited. to the Society gives a value of = which is 8 per cent. less than the value given by the similar spring of round iron wire exhibited. Instead of using a round wire, we may use for the experimental determination of a strip of rectangular section, whose breadth is. very great in comparison with its thickness. If the angle of the spiral is 45°, then from equations (16) and (17) it follows that cepa gr_4N iH ee ee ae In iW H_jdt¢r, N d—¢r’ therefore measuring ¢r as c—b, and d as a, by the method just. described, we have 1 gat (c—b) N a—(e—b) Some Practical Uses of the Springs.—By the employment of springs such as we have described, we have succeeded in making ammeters and voltmeters, or instruments for measuring respectively electric currents and differences of potential, in which the pointer moves over in some cases as much as 270° of the scale instead of only 50°, which is all that can be obtained with ordinary galvanometers. One form of the instrument is shown in fig. 7, where AA is a thin hollow tube. 314 Profs. W. E. Ayrton and J. Perry. [Feb. 14, — of charcoal iron attached at its lower end to a brass piece G guided at the bottom in the way shown. To G is attached the lower end of a spring made in the way we have described of silver or hard phosphor-bronze, the upper end of which is attached rigidly by a thin rod to the glass top of the instrument which itself is fastened rigidly _/ a Cn am ll a) Hl i Ml Yy LZ LLL LLL WUMMLULIMUMUU““MM MM“M|M|M IY U R WH alia d | A . qT | [| UU LEE SS _ “aii i : TOT OAT MUM TOTO TEE TTT iil 4 i L } | | j NZ a | 2 — to the framework of the instrument. The rod attached to the glass, and to which the upper end of the spring is attached, also serves as a guide to the top of the iron tube. In the space FF a solenoid wire or Strip is wound, its ends being attached to the terminalsshown. Hence when a current is passed through the wire, the iron tube is sucked into the solenoid, and its lower end G, to which the spring is attached, receives a large rotatory motion, which is communicated directly to the pointer attached to the top of the iron tube. Parallax in taking 1884.] New Spring for Electric and other Instruments. 315 readings of the pointer is avoided by the horizontal scale being on looking glass in the well-known way. By making the iron tube AA very thin, so that it is magnetically saturated for a comparatively weak current, by fixing it so that it projects into the solenoid a fixed distance which has been carefully determined by experiment, and by constructing the spring in conformity with the conditions worked out in this paper, so as to obtain a large rotation with minimum stress, and with not too much axial motion of the free end of the spring, we have succeeded in obtaining deflections up to 270° directly proportional to the current, and without any permanent set being given to the spring. To prevent a spring taking a permanent set for a large deflection, it is of great importance that the spring after being delivered by the maker should receive a large degree of permanent set in the direction in which we wish it to be afterwards strained in ordinary working. In spite of the fact that Professor J. Thomson in the “ Cambridge and Dublin Math. Journ.,” November, 1848, explained the importance of initial strains in materials, the reason is not yet sufficiently well understood why when a round bar has been well twisted beyond the limit of permanent set in a certain direction it has twice as much elastic strength to resist torsion in this direction as in the opposite direction. Now in the very act of manufacturing our springs, that is in the bending of the strip, the material acquires strains which are just opposite in character to the initial strains which we wish it to possess, for, as already explained, if the spring be constructed as in fig. 3, an extension of the spring produces a rotation tending to uncoilit. Hence a spring must not be regarded as ready for use until it receives a good set by means of a weight hung from its end. Theory of the Solenoid Spring Ammeter or Voltmeter.—If C is the current in amperes flowing through the coil, the attractive force on the iron core is KC? 1+SC where S is a constant, which is the greater as the current is smaller for which the iron tube AA, fig. 7, becomes saturated with magnetism. The position of this iron core in the solenoid is so selected that K remains practically constant throughout the small range of downward motion of the core. Since the rotation @ has been produced by an axial force, we know from the theory of the spring already given, that this axial force is po, where p is some constant. Hence _ Ke ASC PP 316 Profs. W. E. Ayrton and J. Perry. [ Feb. 14, and since SC is great in comparison with unity for such currents as we wish to measure, we have a pee | H A SJZIS QQ iS} a XO. re. 2 ce) 99.9989099'1009090 0490 S32) {9} O' Qa Or G Xe) 1exe (o] fo xe} that is, equal divisions of the scale correspond with equal additions to the strength of the current except close to the zero, and we usually do not graduate these instruments within 5° of the zero. Shielded Measuring Instrwments.—W hen it is desired to use the instru- ment close to a dynamo machine or electromotor in action, we have adopted a different and somewhat special form of construction, which is shown in fig. 8, by means of which the instrument is to a great extent shielded from even powerful external magnetic fields. In this instrument the electromagnet consists of a hollow core, part of which, BB, is of charcoal iron, and part, DH, of brass or other non- magnetic metal. The outside tube, CC, and the plates, XX, top and bottom, are also of charcoal iron. The space FF is filled with insu- lated wire in electrical connexion with the terminal, so that when a current is sent through the instrument an intense magnetic field is 1884.] New Spring for Electric and other Instruments. 317 formed between D and E, which are the poles of the electromagnet. To the iron tube AA, also made of charcoal iron, the spiral spring, in this case made of extremely thin hard steel, is attached, the other end being attached to the piece F, which is fixed relatively to the bobbin. The spindle GG, which is fixed to the moving iron core AA, moves freely in bearings HH, so that the only movements of which A is capable are one of rotation and one parallel to the axis of the bobbin. As the iron core A projects into the strong magnetic field between D and E it is strongly attracted towards H when the current flows, and, as before, causes a large rotation of the pointer P over the scale. As ameans of varying the power of the instrument an adjustable iron piece K is provided, which can be screwed nearer to or farther from the core A, and by the use of which the sensibility of the instrument can be adjusted so as to make the instrument “ direct reading,” that is to say, each division of the scale can be made to correspond with 1 ampere of current, or 1 volt difference of potential, and the employ- ment of a constant such as 1:34 amperes, or volts, per degree, which ‘has hitherto been necessary with our measuring instruments, is now avoided. This power of adjustment produced by the use of the movable iron piece K, combined with the ease with which more or less wire can be wound on to the instrument, which also constitutes a second adjustment of sensibility, is of considerable importance, since the employment of a constant has not only led to error and delay in ‘measurements made in electric light factories, but has caused the breakage of the pointer or the destruction of an instrument from a far too powerful current being sent through it by an observer (often a man with little experience in the employment of instruments) having confounded the constant of some other instrument with that of the one he was using. _ The steel strip used in the construction of the spring for these shielded instruments is 0°0017 inch thick, and in a book just pub- lished on “Steel and Iron,” by Mr. Greenwood, he mentions that some specimens of remarkably thin steel, -+, of an inch, were shown in the Paris Exhibition, so that steel we are using is nearly as thin as that referred to by Mr. Greenwood. But within the last few days we have received from Mr. Charles Jowitt, of Sheffield, a specimen of steel rolled for us only just over 0°001 inch in thickness, which is perhaps the thinnest steel yet made. | We have to thank one of our assistants, Mr. Bower, for so earnestly carrying out a long series of experiments on these very delicate springs. Weighing Machines.—Another class of instruments in which we have practically employed this spring are weighing machines, and fic. 9 shows one of the arrangements we adopt. The scale-pan is prevented from turning by the part AB being square and fitting very loosely a square holein C. This arrangement introduces practically 318 New Spring for Electric and other Instruments. y it. 5 | 1884. | Theory of the Magnetic Balance of Hughes. 319 no friction, and prevents the moment of inertia of the scale-pan and load interfering, by means of a rotatory motion, with the rapidity with which the pointer comes to rest when a load is put into the pan. The position of the pointer P, which revolves when a weight is placed in the scale-pan, is read off upon the spiral scale, D, which, in this specimen, we have graduated in pounds. In another of these weigh- ing machines, shown in fig. 10, the arrangement is the same with the exception that a cylindric scale D is fixed to the end of the spring and turns with it, the pointer P fixed on the frame of the instrument points to an indication of the weight on a spiral line drawn on the cylinder D. This second arrangement allows us to employ springs whose ends have a relative motion of five or six revolutions. We have also made certain weighing machines where the weight is placed on a pan resting on the top of a rod passing up through the ~ spring, and attached to the bottom of the spring, but hitherto we have. found that this arrangement introduces too much friction. When a very long spring is required for any purpose, and where the weight of the spring itself would cause greater stresses on the upper part than on the lower part of the spring, it is our custom to let the breadth and thickness of the strip of material remain unaltered, but to let the diameter of the coils diminish towards the upper parts. The formule already given suffice to show how this may be done so as to obtain uniformity of maximum stress at all sections. We also present before the Society a model showing a combination of bifilar and spiral spring suspension, in which great rotation and small axial lengthening or shortening are produced by an axial force. III. “ Note on the Theory of the Magnetic Balance of Hughes.” By Professor Siuvanus P. THompson, B.A., D.Sce., Univ. Coll., Bristol. Communicated by Professor D. E. HUGHES, F.R.S. Received February 7, 1884. [1.] The magnetic balance recently described by Professor D. H. Hughes* promises to be so convenient and useful an instrument in the laboratory, that the theory of its action and graduation deserves attention. In the actual imstrument constructed by Hughes the graduation was empirically determined for a number of values, the remainder being found by interpolation. The instrument consists of a small suspended needle lying in the magnetic meridian provided with a zero-mark placed upon a platform in which a horizontal groove is cut magnetically east and west. In this groove the piece of iron * “ Proc. Roy. Soc.,” vol. 36, p. 167. VOL. XXXVI. Z 320 Prof. 5S. P. Thompson. On the [Feb. 14, or steel whose magnetism is to be tested is laid, in the “first position ” of Gauss (“‘ end on”), within its magnetising coil, a second coil being added on the other side of the suspended needle to compensate the action due to the. coil alone. At a certain distance along the platform, and having its centre upon the line of the plat- form groove, is set a magnet—called by Hughes the ‘‘compensator” —of considerable magnetic moment. The compensator is so pivotted as to be capable of being rotated round a vertical axis through its centre over a scale; and, according to the original design of the instrument, the compensator and scale are provided with an arrange- ment whereby they may be shifted along the platform, so that they can be made to approach nearer to the suspended needle when a more powerful compensation is desired, or removed further away when a more delicate magnetic force is to be compensated. In practice the balance was obtained by fixing the central pivot of scale and com- pensator at a distance of 380 or more centims., and turning the compensator upon its pivot until its magnetic force on the suspended needle, or rather its resolved part in the axial line of the platform, was exactly equal and opposite to that of the piece of iron or steel. reais [2.] Theory of the Magnetic Balance.—In fig. 1, let the hne AX represent the central line of the platform of the balance lying magnetically east and west. The point M is the centre of the 1884. | Theory of the Magnetic Balance of Hughes. 321 compensator NS, which has been turned through an angle OMS=¢ in order to.balance the magnetic force exerted on the suspended needle at B by the specimen of iron or steel placed at A. It is required to determine the relation between the angle of turning ¢, and the magnetic force thereby brought to bear along the axis AX at B tending to thrust back the suspended needle to its zero point. Let the length of the compensator be called 2/,and the distance of B from M=r. It is evident that, in general, the resultant magnetic force at B due to the compensator will not be along the axis AX, but may be resolved into a part acting at right angles to that axis, and a part parallel to it. The former part will be parallel to the magnetic meridian, and, therefore, when the needle is at zero, this part will not tend to move the needle to either side. Its only action is to increase- or diminish (according to circumstances) the directive force of the earth’s magnetism upon the needle, and render it either more or less sensitive. The other part is that which acts along the axis and balances the magnetic force of the iron or steel bar at A. When the compensator lies at right angles to AX this component of the force vanishes by symmetry: consequently the zero of the scale lies in this line. If the compensator be turned through an angle ¢, the com- ponent of its magnetic force in the line AX will increase to a maximum when ¢=90°. The values of the force for different angles may be calculated as follows :— Call (BST. BN=-", angle SBM=a, angle NBM=. Then the forces along BS and BN resolved along AB will give the following resultant F :— in Che el lee pe fll m being the strength of the pole of the compensator. But cos a= See (7? + ?—2rl sin p)? tor r+lsin | cos B= (7 242 +4I8lsin @! and = (72 + ?—2r7l sin od)? 5 r’=(7?+2+ 271 sin p)* Whence F=m ‘ es a OU a ra ee 2». = Page (1) (7? +2—2rl sing)? (?+l+2rlsin no) 72 322 Prof. 8. P. Thompson. On the [Feb. 14, or, writing 7 for the ratio 7/l, —— n—sin d n+sing \ Bi ~ PLG?+1—2nsing)! (®+1+4+2nsin d)? which for brevity we may write F=“’p 12 n—sin d n+sin d where P= ee eee (n?+1—2nsin d)? (n?+1+42nsin g)? It is obvious from the mere form of this expression that it is not accurate to assume that a scale of equal degrees will represent equal increments of the magnetic force; and that no scale ordinarily used in galvanometers or magnetometers, such as a scale of sines or of tangents, will adequately serve the purpose. It is, therefore, necessary to investigate the formula to ascertain how it can be made avyailabie for the graduation of a scale for the instrument. The expression is an awkward one for numerical calculation, owing to the fractional exponents of the denominators; but the process of calculation can be somewhat shortened by taking n as a simple integer, and the successive values of @ such that the sines are simple decimals. In the following tables will be found the values of the function P, calculated for several cases, the angles being in all cases expressed in degrees and decimals of degrees, not in degrees, minutes, and seconds. The object in calculating these values was to ascertain the proportions of r and /, which would enable the scale readings of the compensator to be used without the labour of con- structing arbitrary interpolation tables for the calibration of the readings. Table 1L—(n=1.) Angle. Nat. sine. P calculated. O° 0 0 5 °739 Ont 0 °0355 11 °538 0°2 0°0726— 17 457 0:3 0°1195 23 ‘578 0 °4 0°1576 30 :000 0°5 0°2113 36 *869 0°6 0 °2794 44.°427 0°7 0°3741 53 °130 0°8 0°5271 64 °158 0°9 0°8618 71°805 0°95 1 °3280 90 *000 130) oa 1884.] Theory of the Magnetic Balance of Hughes. Table II.—(n=2.) Nat. sine. 0) 0 °1736 0 -3420 0 -5000 0 64:28 0 -7660 0 °8660 0 -°9397 0 9659 0 °9848 0 -9962 10000 Table ITI.—(n=3.) Nat. sine. ——— AIO OAIOQO S|) OS) On SOHOMTIAAKR ONE Table [IV.—(n=4.) Nat. sine. FOOOCCOCOCOCOCOOOSO COOMMOIMSMAWNE ou OL 0 0 005218 0 -010521 0 -010001 0 -021758 0 -027910 0 -034709 0 041985 0 °050319 0 :054926 0 °059886 0 -065260 0:071111 P calculated. 12 P calculated. calculated. QM IYVAIVOVO OS SI(Joyve) a ae ex D (=) i P observed. QoQ Voaoaooee> (>) OC) ns OO QO 323 324 Prof. 8. P. Thompson. On the _ [Feb. 14, Table V.—(n=5.) Angle. Nat. sine. P calculated. P observed. 0 0 0) 0 5 739 O°1 0 -002848 0 -00267 11 °538 0°2 0 -005809 0 -00545 17 °457 0°3 0°008772 0 -00848 23-578 0-4 0:011715 0°01083 30 -000 0°5 0 -014895 0:01468 36 °869 0°6 0 :018257 0 °01759 44, °4.2'7 0:7 0 :021829 0 :02183 53 °130 0°8 0 :°025741 0 -02564. 58 °211 0°85 0 :027819 0 °02645 64.°158 0°9 0 ‘030000 0-02801 71-805 0°95 0 °032297 0-03081 90 :000 EO 0 °034722 0 ‘03365 The values of P set down as observed in the last column of the preceding tables were obtained by noting the deflexions produced on a tangent magnetometer, with very small needles, by a magnet placed at the requisite distance (measured horizontally at right angles to the magnetic meridian), capable of rotation in a vertical plane passing through its centre and through that of the magnetometer. The read- ings were then multiplied by such a constant as would make the value at 44°°427 coincide with the calculated value at the same angle. The departures at other parts of the scale are partly due to errors of observation, partly due to the fact that the distance between the poles of the magnet is less than the distance between the ends. Table VI.—(n=6.) Angle. Nat. sine. P calculated. om 0 0 5 °739 Ol 0 001708 11-538 0:2 0 -0034:28 17-457 0°3 0 -005163 23 °578 0°4 0 °006966 30-000 0°5 0 -008814: 36 ‘869 0°6 0 -010735 44, °437 SORe 0°012749 53 180 0°8 0 -014796 68 °211 0°85 0°015975 64-158 0:9 0:017150 71°805 0°95 0 °018348 90-000 1) 0 -019592 1884, | Theory of the Magnetic Balance of Hughes. 325 Table VII.—(n=10.) Angle Nat. sine. P calculated. 0 0 0 5 °739 0-1 0 000390 11 °538 0°2 0 000778 17 °457 0°3 0 -001169 23 °578 0-4 0 -001505 30-000 0°5 0 001966 36 °869 0°6 0 °002374 44,°4.27 0°7 0 -002784. 53 °130 0°8 0 °003207 64°158 0-9 0 -003638 71 °805 0°95 0 003858 90 -000 1-0 0 004090 The calculated values of P are plotted out in the two sheets of curves (figs. 2 and 3) accompanying the tables. The curves for n=4 and n=5 are given twice, being drawn again with enlarged ordinates to show on a larger scale their close approximation to straight lines up to about 50°. [3.] From the foregoing tables, and from the curves appended, several conclusions may be immediately drawn with respect to the design of the magnetic balance. A simple inspection of the curves will show that they belong to a family in which, in general, there is a concavity near the origin, and a convexity as the limiting value is approached at the point corresponding to the 90° position of the com- pensator. Those curves for which n=8, or less than 3, show the convexity very markedly. In those for values of m higher than 7 (only one has been drawn, namely, that for n=10) the convexity of . the upper portion asserts itself. The curve for n=10 approximates very nearly to a curve of sines, as indeed might be suspected from the equation. For those values of » which lie between 4 and 6 inclusive, the first half of the curve is very nearly a straight line, so nearly so that for the curves n=4 and n=5 the values of the ordinates do not differ by 1 cent. from those which they would have for actual straight lines lying along the mean slope of the respective curves as far as 45°. In other words, for angles less than 45° the magnetic force exercised along the axis of the balance by the compensator when it is turned 7s proportional, within 1 per cent. of accuracy, to the angle through which it has been turned, provided the distance of the compensator from the needle be not less than four and not greater than five times the half- length of the compensator. This result may be verified from equation (2) by finding what Prof. S. P. Thompson. On the [Feb. 14, Fie. 2. 1884. | Theory of the Magnetic Balance of Hughes. 327 328 Prof. S$. P. Thompson. On the [Feb. 14, value of 7 will give the force when @=45° equal to 2 of the force when ¢=380°. Writing in the sines of these angles and equating 3 times the force at 30° to 2 times the force at 45°, we get the value n=4'6. Or, solving similarly for the case that the force at 60° shall be double the force at 30°, we get n=4'28. Here, however, the errors near the intermediate angle of 45° are not inconsiderable, exceeding 4 per cent. In any case we shall not be far wrong if we adjust the balance so that »=4°5, and confine our readings within 45° of zero. For purposes where great accuracy is not essential the readings might be extended as far as 60°, since the curves for n=4 and n=5, show how very little the straight line is departed from .up to that point. In the original balance of Hughes, the values of rand J/are about 30 centims. and 7°5 centims. respectively, so that n=4. [4.] I now proceed to the consideration of the action of the com- pensator in affecting in different positions the sehsitiveness of the needle. In the original instrament of Hughes, the compensator turned in a horizontal plane; and therefore in every position, save only when at 90° to the zero of its scale or when end-on to the indicating needle, the force exercised by it on the needle would have a component in the magnetic meridian. As remarked above, the effect of this component would be to increase or diminish the directive force of the earth’s magnetism upon the needle, according as the S pole of the com- pensator pointed northwards, or southwards. The sensitiveness of the indicating needle will, of course, be affected by this component; being a maximum when the component is such as nearly to astatise it. But itis evident that if the needle be nearly astatised when the compensator is at zero, it will not be so astatised when the com- pensator is moved right or left. The sensibility of the needle will diminish as the effective force of the compensator increases by its being turned. The calculation for the component of the force at this point is as follows :— Calling T the part of the magnetic force at B (fig. 1) resolved at right angles to AX, we have— sing« sin Lm | 6 ye yl2 Leos (72+ 2—2Qril sin d)” But sin a= | at Lcos@ e ae VAT DS er ee lee sin p (7? + 12+ Qrl sin )3 i i h =ml (23 PO eamh\. (Gade ee le whence T=milcos¢ : (2+ P—2rl sin ara (7?+2+42rl sin p)? j 1384. | Theory of the Magnetic Balance of Hughes. 329 Writing, as before, r=nl, this becomes :— il iL pa aS ee). poe Geel lonen Oy GEL Linen Ot 3) Assuming that the balance is adjusted for the case n=5, we get the following values for this complex function of ¢:— p=0, T=; x 01508. $=30°, T= x 01402. ~=60°, T= x 00938. o=907", T=~x0. 2 The needle, therefore, if nearly astatised when ¢=0, will still be nearly astatised when ¢ does not exceed 30°; but beyond this value the meridional component of the force falls off greatly, and the sensitiveness alters correspondingly. [5.] Suggested Modifications in the Magnetic Balance.—The preceding investigation has led to the following suggestions :— lstly. The compensator should be set so as tu revolve against a vertical circle placed at right angles to the magnetic meridian, having its centre on the same level as the indicating needle, and magnetically east or west of it. In this position, which was that chosen for the experiments in which the values of P were observed for the purpose of comparison with the calculated values in the preceding part of these notes, the magnetic force of the compensator has no resolved part in the magnetic meridian at the point where the indicating needle is placed. The sensitiveness of the needle is, therefore, the same in all positions to which the compensator may be turned in its own plane. 2ndly. A small magnet lying magnetically north and south of the indicating needle is used to astatise it to the required degree. srdly. The compensator is placed so that the distance between its centre and that of the indicating needle is about 4°6 times the half- length between the poles of the compensator. If the latter be a not very thick flat straight magnet, it may be approximately assumed that the poles are about one-tenth of the whole length from the ends, so that no very important error can arise if a distance equal to five times the half-length between the ends of the magnet is selected. When this is done it is safe to assume that for all positions of the compensator within 55° on either side of zero, the magnetic force which it exerts on the pole of indicating needle is proportional within 2 per cent. to the degrees of the scale through which the compensator 330 Theory of the Magnetic Balance of Hughes. [Feb. 14, has been turned; and is proportional within 1 per cent. for angles less than 45°. For the practical purposes for which the magnetic balance is designed there will therefore be no need of a special calibration table. 4thly. As it is inadmissible to obtain a great range of compensation for both large and small magnetic forces by diminishing or increasing the distance of the compensator from the indicating needle, it 1s pro- posed to obtain this range by placing over the compensator a second magnet, capable of rotating round the same axis and having the same length between its poles. A third magnet may be added, similarly, to increase the magnetic moment of the compensator. Fig. 4. re “Ta yp 0/7 cn Jo\ / SY | | | lV Gi {i I iu i y | | tH i Lil uty 5thly. In the preceding investigation it has been assumed through- out that the length of the indicating needle was small relatively to rand 1, so that the terms of the second and higher orders due to its length might be neglected. This was not the case in the original instrument of Hughes, in which the needle was 5 centims. in length. The use of a very small needle is open to the objection that it is not so sensitive as an index. It is therefore proposed to substitute as an indicating needle one of the type sometimes termed “unipolar,” that is to say, having one pole set in the axis of rotation, so that only one pole has a moment of couple about the axis of suspension. A steel needle about 5 centims. long has about 1°5 centims. of its length turned up at right angles, the suspending fibre of silk being attached to the turned-up end; a counterpoise is added behind, and a small addi- tional weight is placed below on a brass wire attached immediately 1884. ] Chemical Corrosion and Voltaic Current. 331 below the centre of suspension. This needle is placed, with its one effective pole in the axial line of the balance, level with the centre of the compensator. The balance, with the modifications described, is represented in fig. 4. February 21, 1884. THE PRESIDENT in the Chair. The Presents received were laid on the table, and thanks ordered for them. The following Papers were read :— I. “On some Relations of Chemical Corrosion to Voltaic Cur- rent.” By G. Gorz, F.R.S., LL.D. Received February 11, 1884. The chief object of this research was to ascertain the amounts of voltaic current produced by the chemical corrosion of known weights of various metals in different liquids. The research was also made to throw light upon the conditions which determine the entire conver- sion of potential molecular energy into external (1.e., available) electric current. The method adopted was to take about six or eight ounces by measure of a corrosive electrolyte and divide it into two equal volumes in two similar glass vessels. Two pieces of metal of equal dimensions were then cut from the same sheet, cleaned perfectly, and weighed. One of the pieces was employed as the positive plate of a voltaic cell in one of the portions of liquid, and the other asa comparison corrosion sheet in the other portion. The negative metal of the voltaic cell was in nearly all cases a large cylinder of sheet platinum, and surrounded the positive one. The positive and comparison plates were wholly immersed in the separate portions of liquid, except that the former had a narrow exterior projecting strip for connexion in a circuit. The current from the cell was passed by means of a small sheet silver anode ($ inch by ? inch), and a smaller silver cathode (4 inch by 2 inch) in a third vessel, through a cyanide of silver plating solution containing the least practicable proportion of free potassic cyanide in order to obtain the maximum amount of silver deposit. During each experiment observations were made of any liberation 332 Dr. G. Gore. On some Relations of (Mebe2i of gas or formation of solid coating upon the plates, and of any other circumstance which appeared likely to affect the speed of corrosion, or weight of the plates, or of the deposited silver; and in any case where any solid coating was found, it was entirely removed after the experiment, and previous to ascertaining the losses of weight by corrosion. After the experiment the plates were well washed and carefully dried between hot sheets of filter-paper before weighing. The metals and liquids employed were as pure as could conveniently be obtained, and distilled water was used for all the solutions. The sample of potassic cyanide usually employed was found by analysis to contain 89°14 per cent. of the actual substance. Nearly. all the liquids were at the atmospheric temperature, and in nearly every case the comparison sheet was employed. As the proportion of silver deposited to the amount of external current generated, and therefore also to the amount of positive metal corroded, varied to a very small extent with the density of the current at the cathode in the depositing solution (see “ Hlectrolytic Balance of Chemical Corrosion,” “ Proc. Birm. Phil. Soc.,” vol. ii, 1883, pp. 278-304), the amount of cathode surface was usually varied according to the apparent strength of the current and rate of deposition, being smaller as the strength of current was less. The degrees of electromotive force were measured by the aid of two thermoelectric batteries, each consisting of about 300 pairs of iron and German silver, together with a Clark’s Standard cell (see roe: birm, hail, Soe. viol. iva dou). The following table exhibits the results. In the table the number of square inches given includes in each case the immersed portion of both surfaces of the positive metal and comparison plate. The losses of the plates, and the weight of deposited silver, are in every instance expressed in grains, and the rates of loss of the positive plate are given in column 6 in grains per square inch per hour. If the whole of the corroded portion of the positive metal produced external current, consistent in amount with the atomic weights and valencies of the metals as given in the table, and if that amount be called 100, then the proportions of such current actually obtained in the experiments are those given in column No. 9. The quantities of substance mentioned in column No. 1 were in each case per ounce of water. htemarks. Only those resulis which appeared reliable are inserted in the table; many uncertain ones were omitted. In some cases coatings of solid matter formed either upon the positive or comparison plates, or gas was evolved by the plates. Cases in which the coatings could not be perfectly removed were rejected. 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OTS. 99F- 61 v cen de ge ee (0) - PY | 28 s 03. 84 898. T 668. TPO. 9PL- 63P9- € si tee eae eee ee eS coe OC ets ~ GP -9 OZP- ¢ e9L. 020: OSg.Z 9VGP- 12 rene Ser Siar ZO NH SULTUI GZ 08 S 00- 28 LLG. O6T- 880. 0g¢. SS4T- T T 9 Es ee ee AO SUTURE OO. | 6X ‘yuerIn Jo | *pozisodep -ozed ’ ‘oqeyd : : ke queyTeambea IaATIS |wostaedutoa eel aatytsod Solos *‘sIno FL atte : ais a 4 Jo"queo tog | JO FYSta AA | Aq ssory eens hal Xq ssory aT AN aes tial “OTBIO A. eS - ») 2 n ane w SIn— 2 2 ne +sin( U+24%) et b n sin— 9 a zt) &e. in Ge) 364 Mr. V. N. Nene. Ona Method of Tracing Again, from this new series we see that the mean of the two terms mb 6 from the first term of the mean series is w sin (U+ 5 ae ———, and m sin 5 that the mean of the two terms from the second term of the mean _ nb b sin 1D COS 5 ———, and similarly the mean of the ain. series 18 uw sin (eee b) two terms from the third term of the mean series is _ nb b sin > Cos 7 w sin ( u+"4*) . a 2 hie) nm Sin — 2 and so on. Thus the second mean series will be— lo b ae ; ens sin > COSsS Fe sin( U+ +m +sin(U4+"42 ) 2 2 n sin Sin 6 2 - b sin > COSs +sin( u+2t4 ) 5 Ba &c. se Cone n sin 5 Now in these results we see that the following laws hold— I. When 7 is an odd number the first factors of the terms of the first mean series are the same terms in order as the (2) term of the proposed series. II. When v is an even number the first factors of the terms of the second mean series are the same terms in order as the (a term of the proposed series. III. The second factor in each term of the first or second mean series is a common factor to its own series. IV. Each first factor of the terms of the first or second mean series is the middle term of the proposed series from which the correspond- ing mean term is derived. Thus the investigation established, that the first mean series is Periodictties when the Periods are unknown. 369 proportional with the proposed series from ath term when n is an odd number, and that the second mean series is proportional with the proposed series from ae ih term when 7 is an even number. 2a 8. Suppose in the proposed series that b=—,; then since n ~ no é Sin) —=—Sin m0. 2 b) the mean of the sines of the proposed series will be zero, and conse- quently the first mean series or the second mean series will also be ZeT0. | Gplo eno b SIM =z- sin C08 5 9. The factor = OF is a proper fraction. rie n sin — warn 5 Put = A, thus the first factor becomes sues oe 9 msin A Now sin nA = sin{fA+(n—1)A} =sin (n—1)AcosA + cos (n—1) A sin A,and sin (x—1)A cos A=sin (n—2)A cos? A+cos (n—2)A cos A sin A; and, similarly, sin (n—2)A cos? A=sin (n—3) A cos? A+cos (n—3)A cos? A sin A. sin 3A cos—3) A=sin 2A cos'“-2)A + cos 2A cos'”-3) A sin A. sin 2A cos("—2) A =sin A cos™-Y A + cos A cos”-2 A sin A. Thus sinnA=sin A{cos(n—1)A-+cos(n—2)A cos A+cos(1—3)A cos? A... cos 2A cos”? A+ cos A cos”? A+ cos? At. The number of terms on the right hand side of the equation is n, and the numerical sum (regardless of sign) of the terms in the bracket is obviously less than n, thus the numerical value of sin nA is less than the numerical value of nsin A; and since cos A is numerically less than wiity, the other factor is also a proper fraction. 10. The following conditions will show without proof when the first and the second factors respectively will have the positive or negative sign :— The first factor is positive when nb lies between 27(2N) and 27r(2N+1), and 6 lies between 27(2N’) and 27(2N’+1), or when nb lies between 27(2N+1) and 27(2N+2), and b lies between 27(2N’+1) and 27(2N’+2). 366 Mr. V.N. Nene. Ona Method of Tracing The second factor is positive when nb les between 27(2N) and Q97(2N+1), and b lies between 7(2N’) and 7(2N'+1), or when nb lies between 27(2N +1) and 27(2N+2), and b lies between 7(2N’+1) and 7(2N’+2). The first factor is negative when nb lies between 27(2N+1) and 27r(2N +2), and b lies between 27(2N’) and 27(2N'+1), or when nb lies between 27(2N) and 27(2N+1), and bd lies between 27(2N'+1) and 27(2N'+2), The second factor is negative when nb lies between 27(2N+1) and I7r(2N+2), and b lies between 7(2N’) and z(2N’'+1), or when né lies between 27(2N) and 27(2N+1), and 6 lies between 7(2N’+1) and 7(2N’+2), where N and N’ stand for zero or any integral number. _ nb _ nb b sin Sing COS5 11. To trace the changes in the factor —__— or —_— as the ” sin — sin — 2 2 angle nb varies between 0 and 27, between 27 and 47, between 4 and 67, &c. We shall discuss this subject in a particular case only, viz., when b< 27, as there is no necessity of discussing all the cases for our future purpose. We have already shown that when is or when nb=27 the n factor has the value zero, and it is easy to see that when nb=47 or =67 or =2Nz, where N is some whole number, the factor has also the value zero. We have now to find what value of nb makes the factor a maximum when nb<27. Put aa and therefore eS thus the first factor becomes— sing _ bsinw 2x b b = sin > sin —~ , &e., respectively. WC. 1n place Or eens e by e lave e bs FOR Wemas ios 13. Suppose we have a table ruled with horizontal and vertical lines ; in the first horizontal line let us enter the numerical values of the Periodicities when the Periods are unknown. 369 observations in order. Now let successive means be taken of m obser- vations (m being an odd integer) advancing to the right by one step at each operation, and entering the respective means under the m+ jt a Be 2 3 line of our ene the means in our second line taken in order will be equal to the sum of the terms of the following expressions— , w&c., terms of the observations, thus forming a second Ist mean=u-tn sin(U, +", ) 2 +n, sin( Q on »)— 2 eo s qo + U3 sin (+22, ) Ti &e. = 3 2nd mean=w-+w, sin (U.+24, ) et a sin (Ui+75 a, ) A 2 71 - q2 +Us sin (Wt, ) ents) we. = 3 3rd mean= Sut sin( U, a 1 -+uysin(U, 4 mts bn) — 2 92 + Us sin(U, +" 5° b. J+, &e. 73 {n—(m—1)}"=u+u, sin [+4 aN — od) an + Up sin [U; Se nt] sin [Us + {nh J+, we. 2 Yo 73 If these means which are entered be subtracted from the observa- tions column by column, then the remainders will severally be equal to the sum of the terms of the following expressions— ( : “5b. )e 2 de (oath, as + Us sin (U: +a ts) da! +, we. ~ 73 lst remainder=w, sin (O se =h) 71 2nd remainder=, sin a 1) a= 3rd remainder =, sin (O rae i) fiat YO Oe 370 Mr. V.N. Nene. Ona Method ot Tracing +rgsin (U; a by) BT tay sin (T+ Fb) B= 4, de 2 3 {n—(m—1)}"=w sin {Uit(-"S) bb — 1 + Ug sin{ Uy —- (—") by \n— wk + Uz Sin 1U; _ (»—") iy qs} j 2 72 2 J 73 +, &e. Let these remainders be entered in the third line of our table. Again, if successive means be taken of m of these remainders precisely in the same manner as the means of the observations which were taken before, we shall have a set of second means, and similarly if these means be subtracted from the first set of remainders we shall have a second set of remainders; and, further, if these operations be continued r times we shall have an 7th set of means and an rth set of remainders, and the rth set of means taken in order will be equal to the sum of the terms of the following expressions*— 1 rb;) Gal qi" lst mean=w, sin (t + Ug sin (U; + = rby)) Ghee) ee &e. Qa" 2nd mean=, sin (a+ rb, +b :) 2 + Uy Sin (U; a "Do 2+ bq) en ee &e. ord mean=2, sin (U —— rb, + 2b, ) (a) Cnet ads . Se Vie + Uy Sin (Ut rby+ 2b, je + , we. 2 ga" h (ta ' n—(m—1) ne =U, sin {Tit(—2 3) b, \ Cia 2 qi" eles pea r—-1 + Uy sin ’ Us+ (nS r—1)b,h {qo= ies +, &e. 2 Jo” And similarly each of the 7th remainders will be represented to be equal to the sum of the terms of the following expressions— * See two next paragraphs. Periodicities when the Periods are unknown. 371 lst remainder =, sin (Tt Hr ) ‘a Q +uysin (0; pee “b. - Cie +, &e. a 45 ye Chay 2nd remainder=vw, sin (% soe +u,sin(U,+™ a =n + b. ») ea (qo ae &e. 2 ord remainder =u, sin (U1 otis ~ rb + 2d, )omn os + Uy Sin loom rby+2b, a ie &c. {n—(m—1)r}*=w, sin 1 U; +(2—"Sr-1) by } a l + U Sin {Uat(n—"Sr-1) bs \ (Cos Die &e. qa" Pursuing the mode of entry adopted for the first means and first remainders, the rth means will occupy the 2rth line of our table and the rth remainders the (27+1)th line. In future we shall for shortness write— r—1 a. hae ; U,+- [Mie Ire MACE 14, The following calculations are made for ready reference, and —— 1) WW poets Tr to show how the factors of the form (gl)? and (q—1)" which q’ q” occurred in our vth means and rth remainders are obtained— The factor for— lst means mel Y | lst remainders ea eed Sree q qg 2nd means Stee iD 2nd remainders=—2—— : sete oo a) Ga) Ga!) q q* q” Opa (aly ee 372 Mr. V.N.Nene. Ona Method of Tracing Ne 3rd means =") qd 3rd Seer wa Oss Git lier) irra Oe q° q° q? _~@=1)'G_) Gas q q° —_1)\r-1 7th means fs Clem : q’ rth remainders = Gra) ee Gas CE) ie Gay que q’ q’ _@-)DU Ge) Gee q’ q” 15. We must notice that at each operation of taking means we. lose 5 values at each end of the series, thus the rth mean series : m—1 : p commences in our form after one observations. For this reason suppose strong vertical lines are drawn in our form at the ee) ne observation from each end, and let us confine our attention hereafter to the series embraced between the two strong vertical lines. 16. Then, of the numbers occupying the first vertical column from the first of the strong vertical hnes mentioned above, the following, viz., an observation, an individual of the first set of means, an indi- vidual of the second set of means, an individual of the third set of means, &c.,an individual of the rth set of means, and an individual of the rth set of remainders, will have for their mathematical equiva- lents the following expressions, taken in order, viz., Ist observation from the observation series =u+, sin (V,) +u,. sin (V,)+, &e. lst mean from the first set of means =u+u, sin (V;) i +u,sin (Vo) eee , we. val q2 Ist mean from the second set of means =u, sin (V)) ‘a + uy sin (V9) enw) +, &e. n q 2 lst mean from the third set of means Periodicities when the Periods are unknown. 373 =, sin (V,) Gu +u, sin (V,) Goes +, &e. 71 72 1st mean from the rth set of means _})r-1 _7)r-1 ei ein(y) 6 sin (V,) eb, he. qi qo" Ist remainder from rth set of remainder == Sin (Ny) (dite) Ug Sin (V9) (ome qi qo" and similarly the corresponding numbers from the second vertical column will be represented by the following expressions— 2nd observation from the observation series =u-+u,sin (V,+0,) +4, sin (Vo+b.) +, &e. 2nd mean from the first set of means =u+u, sin (V,+0,) Bs), sin (V,+0,) ee &e. 1 da 2nd mean from the second set of means =u, sin (V,+b,) 2— + usin (Vo+b,) ee &e. JTo~ 1 qn? 72 2nd mean from the third set of means ae Dae na NY ain (V,+2,) ‘ae wy +p 8in (Vp+b,) {2=V" 4, be. 1 q2 « 2nd mean from the rth set of means S| al Wes =u, sin (V, +0) (ii) eh sin (V,+ bd.) Oo +, &e. q Ja" 2nd remainder from the rth set of remainders =u, sin (V;+)) nae + Uy sin (V+ bz) Mises De &e. 1 Og And the corresponding numbers from the (p+1)th vertical colamn will be represented by the following expressions— (»+1)th observation from the observation series =u+u,sin (V,+pb,) tu, sin (V,+pb,)+, &e. (p+1)th mean from the first set of means 1 Sy ae rl Laem Mr. V.N. Nene. On a Method of Tracing (»+1)th mean from the second set of means =u, sin (V,+7p),) ‘ios + sin (Vy+ pb) q2 7 2 (p+1)th mean from the third set of means = 2 ick 2 =u, sin (V,+pb) Giese) +Uyg sin (V+ pbz) (ge—1)" +, &e. val qa” (p+1)th mean from the rth set of means ’ =, sin (VY, + pb,) =" (ies) + ug sin (V,+pb,) 4 Come qi’ qa" (p+1)th remainder from the rth set of remainders =u, sin (V, +pb,) +4 (qa — ay + Ug sin (V_+ pbs) 2 (go—1) fap &e. qi" And therefore if we use a variable integral number P (which may be zero) as a multiple to the angle of the type b, we can make one general expression serve to represent the numbers of any one horizontal line; this will be for the Ist, 3rd, 5th, &c., lines as follows :— lst line, observation series =u+ {usin (V,+Pd,)}+ {usin (V,+ Pd,)}+, &e. 3rd line, lst mean series =u+{u,sin'(V,+Pd,)} ea + {uz sin (V.+ Pb.) ae , we. q q2 5th line, 2nd mean series ={u, sin (V,+Pb Oe 1 + {up sin (Vat Pb) } BS 4, &e. 7th line, 3rd mean series = {u, sin (V+ Phy) LUD" + fu, sin (V)+ Phy) } LL" 4, &e. n° qa" (2r+1)th line, rth mean series =ju,sin(V,+Pd, ie Ee + {uy sin (V,+ Pb, Woes ie &e. ya 2 qn" 2 (2r+2)th line, rth series of remainders fai. sin (Veo B, camer ern (Vat Pb.) LBs, Ge qy" gf x Where when P is put =0, 1, 2, &c., successively the expression in Periodicities when the Periods are unknown. 375 each case gives the value of the first, second, third, &c., numbers respectively to the right of the first strong vertical line. 17. We shall now take the sum of all the mean series and put the result by one series only, thus the sum of all the mean series is equal o— u+{u,sin (Vy +Pb)} 4 + eee rien UF ae | Gh he val qn’ = =P 2 Fs |) \ Bayan (V4-PP,)) — ey Mae \ G2 W2" q2 qa’ wea ee 7) \rea Sai gin (Vy-EP,)} (eee } ye ES eek: q3 q3" at 2 LETINS —7)\r- Suppose peed! GE Ane ine q qY q° q q’ “uaa a (EY (HS) HEY EVP Hence by subtraction gil ‘ 1—-(2—) \ ; q 4 q by division S21 -(=). q 18. From this result we can write the sum of aJl the mean series— i ee Tia lNG =u-+ {u,sin (V,+Pb,)} : 1-(4=) \ val + {raisin (Vp+ Pb) } | 1—-(B=*) +, &e. q2 Thus from one series of observations we get two series, one is the sum of several mean series, and the other the series of last remainders, and of course the sum of these series is equal to the observation series; thus whenever we want the sum of all the mean series we shall get it by subtracting the last remaining series from the corre- sponding observation series. We shall rewrite these series below and call them observation series, mean series, and remaining serves respec- tively. Observation series =u-+{u, sin (V,+ Pd,)}+{u,sin (V,+Pb.)}+, de. . . . . (6). 376 Mr. V.N. Nene. Ona Method of Tracing Mean series =ut {u, sin (V,+ Poy) } 2 =(22=) j + ‘usin (Vo+Pd.)} p-(2) } +, &c.: Se % Remaining series ={u, sin (Vit P6)}(BAY + fegsin (V,+Pb,)} = +, &. (8). iL Throughout these three expressions a particular value of P will correspond to a particular vertical column, the next greater value of P to the next vertical column, and so on. 19. We have up to this point derived these last two results as general with respect to the factors of the type L which depend on the value of q m, and of this we have only said that it is an odd whole number. Our next step is to see what conclusions we shall arrive at when we apply some particular value to m. (1.) Suppose that me is less than K,, therefore itis also less than each of K,, Kg, &c.,and mb,, mby, &e., are each less than 27; thus the factors - mb, ‘ mb, Bim igi 2 2 » e e 1 1 e eo — —, &c., or their equivalents —, —, d&c., are positive. msin—! msin—2 Fal 3 2 2 We have shown before that each of the above factors is a proper fraction, and consequently each of their equivalents is a proper frac- tion; thus each of qj, qo, &c., is greater than one, and therefore the value of each of the factors (ey, (B=), &c., when r is suffi- q 2 ciently great reduces to zero. (2.) Suppose that mc is equal to K,, therefore it is less than each of K,, K,, &e., then, as before, we can show that 5 is zero, and each aor of Go, Jz, &e., 18 positive, and the value of =) or Wer y is one, and the value of each of the factors (ey, (—Y). &c., when r is ve} sufficiently great, reduces to zero. Thus, when me is equal to the period K,, and the number of operations of taking successive means and remainders are sufficiently performed, the remaining series will be reduced to u, sin (V,+P0,), or a subordinate series in the observa- tion whose period is K,. (3.) Suppose that mc is greater than K, and less than 2K,, and Periodicities when the Periods are unknown. OTT less than each of K,, Kz, &., then, as before, we can show that q, is negative, and each of qo, qa, &ec., is positive. Let g,=—Q,, then the factor a =)'= =(1—= i will be equal to 7) (+e)=(45): and the value of each of the factors (B= ‘ Qi Q G2 (2), &c., where r is sufficiently great, reduces to zero. Thus, when mc is greater than the period K,, less than K,, and less than double the period of K,, and the number of operations of taking successive means and remainders are sufficiently performed, the re- maining series reduces to {u, sin (V,+Pb,)} ae =). or a sub- 1 ordinate series in the observation series whose period is K,, and the value of each term of the series is greater than the corresponding Q+1 Q term of the original series: since ( ) is greater than one, and 1 when 7 is large enough, ee can be made as large as we please. 20. Up to this point we have treated the above subject by sup- posing that m is an odd number. By simple inspection it will be seen that when m is an even number the results will be quite similar to the one when m is an odd number, but the labour of operations of taking successive means will be twofold. Because the mean of m values from which the mean is taken will not correspond to any of the values in the lot, but will correspond to the middle of some two consecutive values, and for this reason the mean should be written on the line instead of in the column on our form; and after the opera- tions of these first means are performed, we must take the mean of two consecutive means found out first, at both sides of any particular column, and put it in the column. Then these second means thus found are to be subtracted from the corresponding values from which the two sets of means are derived. Similarly from these remainders new means and new remainders are to be found precisely in the same manner as spoken of above. In order to keep our language the same whether m is an odd or an even number, we shall always, in the case where m is an even number, give the name of first set of means, second set of means, &c., to those means found by two of the opera- tions described above. 21. This suggests that we must always prefer m as an odd number, except when there is real need of preferring m as an even number, since the labour of operations, when m is an even number, is greater than when m is an odd number. It will be seen further on that there is sometimes real need of taking m as an eveu number. 378 Mr. V.N. Nene. Ona Method of Tracing 22. The three results which we have found above are very im- portant, and we shall now show their utility, and discuss some more cases from them which we have not yet discussed, by taking some particular examples by which we can show our method of tracing unknown periods. Suppose we have at our disposal a long series of daily means (say) of barometer observations, and we suspect in it a period of about 20 days. The first thing that we shall do is, that we shall take a small series of daily means and curve it on a curve form, and see generally the period of duration of turning points between successive maxima or between successive minima. Suppose the duration of the period found was from 5 to 10 days, then we shall take the least period of 5 days, that is, we shall adopt 5 as our working value of m, and work the processes as already discussed with the whole series of daily means, ~ until generally each mean of the last mean series is less than 2 (say) in the last place of figures.* We shall take then for further treatment the sum of all the mean series instead of the original series. The sum of all the mean series will be found directly by subtracting the last remaining series from the first daily mean series. We shall take this series for a second set of operations. The number we shall take for operations is 25 (Aa =nearly 36, but we shall take 35 because the operations are simpler for odd number than for even number. Now we shall have 35 as our working value of m, by which we shall con- tinue the operations, say up to 5th, and then curve the 5th remaining series on a curve form. If there be only one period in the series from about 17 to 35 days, we shall begin to get simple harmonic waves in the fifth or in some further remaining series; but if there be more than one period the resuit will be compound, about which we shall discuss presently. But first suppose that there is only one period. If we do not find definitely the duration of simple wave curve in the 5th remaining series, then we shall continue the process on to the 6th remaining series and curve on the same curve form and with the same zero line, until the duration of simple wave curve is definitely found. It may here be mentioned, that if the period is not of an exact number of days, we should have a long series to begin with, so that we shall take some exact number of waves from the last remaining series and find the number of days in them, and divide the days by the number of waves, and the result will be the number of days in the period. We must also remark that if there should be no * We always have some limit of accuracy of observing the instruments and re- ducing the observed values; for example, we observe barometer to a nearest thousandth of an inch, and also reduce daily means to a nearest thousandth of an inch. By less than two in the last place of figures, in this case, we mean less than two thousandths of an inch of barometer, and so on. Periodicities when the Periods are unknown. 379 simple harmonic period of exact duration—25 days—that we have been suspecting and searching for, the process we have been per- forming will still tell us if there be any simple harmonic period of any duration between (say) 20 and 30 days. The only difference we shall have is in these cases that we shall have to increase the number of operations to find the remaining series. In the fol- lowing table we shall give a few numerical results of the factors— em hae 5) Bite ae 35a _ hot 20. sin na | sin 30 ey | 7 tb= and. | be | Aye sl phe) Bbiein | 35 sin 5 ae 20) t Zo) Numerical values of the factors. | f sin 857 307 | . ( sin 30m 4 | 20 ap | 0 1— j 1 | 7 Bi5) Erb 35 sin — 35 sin a0 t 2 [ Zoe | Wyinent 7), es oe 1°1291 1°2168 1, 8157/ a 2-339 3 °886 2 °452 eel sr tc a | 3 :802 8 °4.41 4 ‘094: 55 hea VAS ee | 4293 10 °25 4.°654 aa | dr eee 6:977 22 26 7°770 - pie | 8 °895 32°81 10°04 Ne IAN.0, 1, 18 °43 105-0 21°66 MNO Ord 6.) ocs 5 79-12 1076 :0 100°7 The object of introducing the above table is only to give a rough idea to the reader of the rapidity with which the numerical values of these and such similar factors increase after a certain number of operations of the remaining series. 23. Suppose we have suspected only the period of 25 days, but in reality there is not any period between 5 and 35 days; the result will be, as investigated before, that the range of remaining series will be lessened and lessened, until each term of the last remaining series will be less than two in the last place of the figures. 24. Suppose in the daily mean series we have a real existence of the two periods (say) 25 and 20 days, we shall still find the existence of the period of 25 days. Because the numerical value (regardless of sin —— sign) of the factor is greater than the numerical value 30 sin ae 380 Mr. V. N. Nene. On a Method of Tracing (regardless of sign) of the factor sin —— (refer to the curve of 5 sim —— 3 Toi factors) and consequently Grn =) can be made as large as we please 2 in comparison with Gra) when ¢ is large enough, where (—z) 1 9 ~ stands for the former factor and ( -s) stands for the latter factor. 1 Thus if the compound result in the last remaining series be curved out on a curve form the maxima and minima of 25 days’ period will be apparent. Similarly if any number of compound periods be mixed in the last remaining series, still by sufficiently increasing the number of operations the 25 days’ period will be apparent. In conclusion we can say that among the periods which may have mixed in the last remaining series the one of which the factor of the type (-) has the q greatest numerical value (regardless of sign) will be apparent, whether the period is of 25 days or not. 25. The only case in which the period will not be rendered dis- tinctly apparent is, that when the two periods are such that their factors of the first mean series are equal to one another, and then the two variations will continue combined in the same proportions as in the original observations. 26. We have in the above example stated that when we find syste- matic movements in the daily mean curve, of which the duration is from 5 to 10-days, we must first work the series with five day operations, &c. It is not, however, essential, when the period which we are seeking is of a considerable range compared with that of the shorter period, then the period can be found without it; but when the range is very small the first process of smoothing is quite essential. It is not also essential that we should stop the operations when the limit of the mean series is reduced to less than 2 in the last place of figures in the series, but we may stop at any stage of the process after considering what reduction will take place in the range of the period we are seeking. This is merely a process for making the series of smooth-flowing numbers without sensibly reducing the range of the larger periods. 27. The process of smoothing series generally in practice is to take the mean of two consecutive numbers, and put it down below and on the line between the two numbers, and so on with each pair of numbers in succession. Next from this new series the same thing is repeated up to a certain number of operations. One effect of this process is to reduce the range of each simple harmonic variation of Periodicities when the Periods are unknown. 381 which the original series is composed. The extent of this reduction of range is shown in the following expression for the series that is found after S repetitions of such smoothing operations :— Smoothed observation series* u=-+{u, sin (U,+ Pd,)} cos® ot fu. sin (U,+ Pb) } cos® - +, &. It wili be seen at once that as the period is smaller and smaller, we have greater and greater reduction and vice versd. 28. We shall, however, give a clue when a series contains enormous irregularities, to the distribution of each number amongst the ad- jacent columns, that is effected by our two methods of smoothing. We shall give this by supposing that we have a series whose terms are 13, of which each of the first and last 6 has the value zero, and the 7th has the value 64. The result of six smoothing operations of the second method gives 1, 6, 15, 20, 15, 6, 1. From this we see that the reduction for the middle term which occupies the same column as the number 64 in the original set is rapid, and the distribution amongst the adjacent terms is smooth-flowing and of a convergent character. 29. We shall now apply our first method to a series whose terms are 3/7, of which each of the first and last 18 has the value zero, and the 19th has the value 343. Suppose we have a number 7 for a working value of m to start the operations, we shall after three opera- tions get a series of 19 terms whose values are +1, +3, +6, —1I, —27, —42, +91, +75, +57, +37, +57, +75, +91, —42, —27, —ll, +6, +3, +1. From this we see also that the reduction is rapid for the middle term, and the distribution amongst the adjacent terms is in smooth-flowing waves which grow smaller and smaller and ultimately vanish. Method of finding the Amplitude of a Variation of known Period. 30. The processes which we are going to apply for this purpose are sin Be, * This may be easily understood if we put »=2 in the factor of the series 2 sin — 2 = 9D b : 2 sin— cos — ; sin } 2 b 4 in paragraph 7. When x=2 the factor becomes =~ ——= =cos = for 2 ua 2 sin — ~ the first operation, and in the same way it becomes cos cos . 1.€., cose for the second operation, thus for S operations it becomes cos S This may be taken as a type of the factor for each expression of series of the type {w sin (U + Pb) }. 382 Mr. V.N. Nene. Ona Method of Tracing slightly different from the preceding ones: we shall, therefore, first of all apply them to the general form and then to particular examples. 31. Suppose that mc=K, where K, isa known period and mis some integral number. Then using m as working value let us find as before the first mean series from the observation series, the first series of remainders, and the second mean series; but instead of subtracting the terms of the second mean series from the corresponding terms of the first series of remainders to get the second series of remainders, let us add them in the same order and call this series the first difference and sum series. Again from this series let us find, in the same manner as stated above, the second, the third, &c., and the rth difference and sum series. The rth difference and sum series will, as will presently appear, be of the following form— 2 2 usin (V,+Pb;) (I-s)+% sin (V>+Pb,) (1-3) + am qi q 1 u, sin (Va+Pbn)(1—) + nay cn Giese & UN ee F (9). 32. The following calculations are made for ready reference and to show how the factors of the form (2 =); which occurred in our rth q 9 nr nt] difference and sum series, are obtained. The factor for lst means ae l q The factor for lst remainders =(1 --). The factor for 2nd means =( The factor for lst difference and mean series =(1-")+(1--) “=(1~) (2 +7)=(1-4). q q/ 4 q q q The factor for 3rd means =(1 a) 1 q/ q The factor for 3rd remainders PDE DD The factor for 4th means= (2 --.) (2 —-) 1 q° q/ q Periodicities when the Periods are unknown. 383 The factor for 2nd difference and sum series CDH DED CO DEDED CRO) Thus it can be shown that the factor for rth difference and sumseries witlibe (1-—). q 33. Now the last factors of all the terms in the series (9) contain a term of the type oa so that all these factors are positive, and, as q before, it is easy to see that each of them has a tendency to vanish as r increases, except in the cases where the terms of the type ne Mi have the value zero. The only terms of the type ole whose values @ will be zero, are those which are formed from the sines of the angles Mbn, 2mbn, 3mbp, &c., because these angles alone are some integral multiple of 37. Thus when r¢ is sufficiently great the series (9) will be reduced to— Un S10. (n+ Pbn) + Ung 810 (Ung +2Pb,) + Ung sin (Ung t3Pbn) +, ce. If we curved now the first m values in order out of the last horizontal line of our form which forms our rth difference and sum series, it will be a variation with its full amplitude of the known period m, and if the next m values be curved in the same way we shall have a repetition of the same curve, and so on. 34. Although we have shown that the factors of the form (i) @ when ia is not zero, and r is sufficiently great, reduce to zero, yet the reduction of the factors which are formed for the periods less than mc is so much slower than the factors which are formed for the periods greater than mc, that it is almost impracticable to continue the process to the limit. We shall therefore in what follows, in- vestigate a particular case of a known period, and we shall find it advantageous to use partly our method and partly the usual method of combining the series with the known period. 30. Suppose we have a series of daily means of barometer observa- tions in which we have detected a period (say) of exactly 36 days, by the method already described. We shall, first of all, in the following table, give factors of the kind in series (9) for different values of r and different values of the periods of the type K. VOL. XXXVI. 2D 384 Mr. V. N. Nene. Ona Method of Tracing 4 90° | 108? | 2572-4 | 442°-2 | 6242-6 | g05°-8 | 9862-4 | 1167°-0 | 1347°-6 —— Sind Nel co a fk SN (Period in| 72 60 25-2 | 14°65 | 10-37 | 8-04 | 6-57 | 5-55 | 4-81 days). sea ee ogee So MMM N MIAN al ee | 3 -63622 | 50409 |— 21610 |-+ -12640 |— -o8850 |+ -06721 |— -05348 |+ -o4368 |— -os626 = -40478 | -25411 | 04670 | -01597| -00784| -00452 | -o0286| -o0191 | -00131 1-5 | 59522 | -74789 | -95330 | -98403| -99216 | -99548 | -99714 | -99809 | -99869 Q a =) *| .07471 | -2309 | -78732 | -92260| -96140| -97758 | -98583| -99049| -99346 (= )" -00558 | -05330 | 61987 | -85134| -92428| -95567 | -97186| -98107| 98697 (i-4)" ‘00042 | -01230 | -48804 | -78551 | -88859 | -93423 | -95808 | -97168| -98051 In the above table, the periods less than mc of the type K which we have selected are those that have maxima or minima values of SIN their first factors of the type d so that their factors of the type (=) q q will have the greatest possible reduction, that is, factors for imter- mediate periods will reduce at slower rates. 36. We also see that when ¢ is equal to 5, we have the factor cor-. responding to the period 72 days reduced to 4, and from this we can infer that the factors corresponding to greater periods than 72 days will be reduced to less than 4. So that for all practical purposes we shall make the operations 5, and assume practically that in the fifth difference and swm series we have reduced all series of the periods 72 and greater than 72 days to zero, and retained in their full magni- tude all the series of the periods less than 86 days, whilst the series of periods intermediate between 36 and 72 days will be only partially obliterated. Such a series may be represented by fu, sin (U,+ Pd,) + ug sin (U,+Pb.)+, &e.} ; 2 Y 4, + \ tn sin (U+ P55) tes sin (Un+PE +, to. \ PA Metts 5 i J tes sin (Uwatt Pba)) +: any nin (Us, Pb Re) a 4 de. n+2 In the first pair of brackets of the above expression, we have arranged those terms of the simple harmonic series whose periods are less than the period of 36 days, but not any of the period of the form - where N is any integral number; in the second pair of brackets of the expression, we have arranged those terms of the Poriodicities when the Periods are unknown. 385 simple harmonic series whose periods are of the form _ that is, it contains all the harmonics of 36 days; and in the third pair of brackets of the expression, we have arranged those terms of the simple harmonic series whose periods are greater than the period 36 days. Suppose in the fifth difference and sum series, or in the last horizontal line of our form, we have 36M values where M is some large integral number. Suppose we have another table ruled with more than M horizontal and 36 vertical lines. In the first horizontal line let us enter 36 numerical values from the commencement of the series in order, in the second horizontal line the next 36 numerical values, and so on, in the Mth horizontal line the last 36 numerical values. Let the sum and mean of each vertical column be taken in the (m + 1)th and (m + 2)th horizontal lines respectively; then these means are the subject of our present investigation. 37. The general term of the simple harmonic series in the first horizontal line is— usin (U+ Pb); the general term of the same simple harmonic series in the same vertical column of the second horizontal line is— wsin (U+ Pb+36b) ;sx the general term of the same simple harmonic series in the same vertical column of the third horizontal line is— usin {U+Pb+2 (36d)}; the general term of the same simple harmonic series in the same vertical column of the Mth horizontal line is— usin {U+Pb+(M—1)(36d)}; thus the mean of this vertical column will be— sin Mee pate 1 qn = ye ers then the general series may be written— 36D M 2 usin (U4 gh) Pb fins ee . 366 2, Thus the last horizontal line of means in our new form, which is composed of 36 values, will be of the form— 2D2 386 Mr. V. N. Nene. Ona Method of Tracing ee ee sib i) SS Uy, sin \(+" + Gr 1) +P by \_ M sin 20% * 36b,- sin M—* +u sin { (m+ gee Aes |e ; M sine x Cae sin (at Ps aa) tm sin UntPa)t, &. } ib 36 366, se oo hecel M—1 sin M9 (f2— ain | ta sin} (Unt “5 36bue) + Pho} — x\ Qr44 M sin aia % +, te. And it can be shown that the last factors of the terms in the first and the third pairs of brackets, where M is sufficiently great, reduce to zero (see curve of factors in fig.1). Thus the 36 mean values found in the last horizontal line of our new form will represent the variation of the 36-day period. 38. Next suppose that the period whieh we have detected is not an exact number of days but (say) of 36°4 days, we shall still take the nearest integral number, viz., 36, as our working value of m, and by it find (say) the 5th difference and sum series as already described. Tn this case the amplitude of the variation of the period of 36-4 days will be slightly reduced in the 5th difference and sum series. The reduction of the lst simple harmonic variation that is of the period of 36°4 days will be (1 —°99954), that of 18°2 days will be (1—'99954), that of 12:13 will be (1—‘99954:), and so on. The next thing is to show how the series is to be combined, which we are going to show in the following manner. 39. In the first horizontal line of our new form, we shall enter first 36 values. In the second horizontal line 8 values, from the beginning of the next 37 values, will be entered up to the 8th vertical column, but in the 9th vertical column we shall enter the mean of 9th and 10th values out of the 37 values intended for the second horizontal line; in the rest of the horizontal line the remaining values will be entered. The object of combining the 9th and 10th values and entering the mean result in the 9th vertical column of the second horizontal line is that, since we are dealing with exact days only, we must enter the values in the columns in such a manner, that the error Periodicities when the Periods are unknown. 387 of distribution must not be greater than half a day, and so the mean of the 9th and 10th values, which was found more appropriate to 9th column than any other column, was entered in the 9th column. Similarly up to the mth horizontal line, the values will be entered by properly combining two values for entering in one column as many times as need be in the course of entering the series in the manner stated above. Also the sums and means of each vertical column are taken in the same way as in the preceding example. We will not go into details, as in the preceding example, but can simply say that the last numbers of our new form will be the variation of the period of 36°4 days with its almost full magnitude, and for 36 points, the intervals between which from point to point will be 1,4, days. 40. We should remark that the process of difference and sum series has also an obvious advantage in separatiny the observation series into any number of difference and sum series without affecting the series by the process. By affecting the series by the process, we mean that in the former process for the remaining series and mean series, if we take any arbitrary number as our working value of m, and if there should be periodicities lying between = and mc, we shall get the periodicities mixed up in both the series with a greater amplitude than the original series. These separations are very useful for the first trials when suspecting approximate periods. Application of the Process and Detection of a Period of about 94 Months. 4]. For this purpose we have taken means of barometric pressure at Bombay, from 1847 to 1872 and 1873 to 1878, thus forming our Table I. The first part of monthly means is also given in Table I, page 11, of the volume entitled ‘“‘The Meteorology of the Bombay Presidency,” by Charles Chambers, Hsq., F.R.S., Superintendent of the Colaba Observatory, Bombay; and the last part at the foot of Tables I to VI, pages 58 to 63 of the “ Bombay Magnetical and Meteorological Observations, 1871 to 1878.” The description of the barometer and mode of observation, &c., are fully given in both the volumes. With the numbers in Table I, we have performed one operation to get the first difference and sum series by taking 12 as our working value of m, and the result is entered in Table II. The numbers in Table II are subtracted from the corresponding numbers in Table 1 and entered in Table III. At the foot of Table II we have entered the mean for January in the 24 years, 1848 to 1871, the mean for February in the 24 years, the mean for March, &c., &c., up to December.* These means form the annual variation of barometric * Properly speaking, we should have taken the means of thirty years, 1848 to 1877, instead of 1848 to 1871; but first of all we have taken for our discussion the 388 Mr. V.N. Nene. Ona Method of Tracing pressure for the 24 years. If we add the constant 29°808, the annual mean of 26 years, 1847 to 1872, to the 12 numbers in our Table II, then these numbers will be found almost identical with the numbers at the foot of Table I, given in the Meteorology of the Bombay Presidency. The 12 numbers at the foot of Table IL were then subtracted in order from each of the rows of 12 numbers commencing from January, and ending with December for each of the years 1848 to 1877 of the same table, and the remainders entered in Table IV. Again, with the numbers in Table IV, we have performed three operations, taking 3 as our working value of m to get the third difference and sum series, which we have given in Table V, then the numbers in Table V were subtracted from the corresponding numbers in Table IV, and entered in Table VI. We need not say that the sum of the numbers in Tables III, V, and VI, from July, 1848, to June, 1876, and successive repetitions of the corresponding numbers of annual variation at the foot of Table II, taken in order, will be equal to the corresponding numbers in Table I. The numbers in Tables III and VI are curved in figs. 2 and 3 respec- tively. We presume that the curve of fig. 2 is composed of periods of more than 12 months, and that of fig. 3 is of less than 12 months and greater than three months. By looking at the oscillations of the curve of fig. 2 we suspect that amongst the periods there are periods of 11 or 12 years, 45 years, and 2 years. By looking at the oscillations of the curve of fig. 3, we see that amongst the periods there is a great predominance of a 94-monthly period. This we have ascertained in the following manner:—We have first of all marked by a cross (thus xX) all the minima that have their time-interval from one minimum to next minimum 8 to 11 months, or any integral multiple of 8 to 11 months, and then filled up the rest 8 to 11-monthly minima that were less marked by a mark (thus 0). It is remarkable that the oscillations are more prominent and of greater amplitude from the year 1849 to 1862 than from the year 1863 to 1876. If we count the marks of minima commencing from July, 1848, and ending with November, 1876, they will be found to be 37; thus there are 36 periods in 340 months, 7.e., 95 months, as an average duration for the period. 42. Again, we find that there are intermediate minima which are of less amplitude than already stated, and the duration of which is also from 8 to 11 months. These also we have marked by marks (* and 0), as in the preceding example. In the present case both these series from 1847 to 1872, and have made all the operations we are going to describe. But afterwards it was thought proper to add to the above result the six years 1873 to 1878, which were available. But as the work was far advanced it was not worth while to go into the trouble of doing the work over again for the sake of including those six years. Periodicities when the Periods are unknown. 389 marks are made on the upper side of the curve, while in the preceding case on the lower side of it, to distinguish them from each other. 43. We find from May, 1858, to October, 1866, that the occurrences of these minima have disappeared. From December, 1848, to May, 1858, there are 12 periods, that is 433=95 months for a period, and from October, 1866, to April, 1877, there are 13 periods, 1.¢., 42,6 =92 months for a period. From this we might guess that to form such a curve there must be two prominent periods, which may be as (say) 5- and 95 months. 44. To clear this doubt, we have further taken the numbers in Table VI, and performed five operations to get the fifth difference and sum series by taking 5 as our working value of m. These numbers we have given in Table VII and curved in fig. 4. Then the numbers in Table VII were subtracted from the corresponding numbers in Table VI and entered in Table VIII, and curved in dotted lines with the corresponding curve of fig. 3, and with the same scale and on the same zero line. Now, by looking at the oscillations of the dotted curve, it appears that it is of a simple harmonic character, and it confirms the 94-monthly period as already described. But in both these curves (continuous and dotted) there are a few exceptions to the confirmation of the 93-monthly period. These exceptional periods are—from March, 1857, to December, 1859; June, 1863, to September, 1866; April, 1868, to January, 1871; and November, 1872, to the end. 45. We shall now turn to fig. 4. By looking at the oscillations of this curve we again see that amongst the periods there is a great predominance of a 4;-monthly period. ‘This we have ascertained as in the case of 95-monthly period. If we count all the marks made on the curve, we have 65; thus there are 64 periods in 302 months (from June, 1850, to August, 1875), and 3°2=4°72, 7.e., nearly 4 months,* which is an average duration for the period. We should now here remark that, although in the continuous curve of fig. 3 we found that the occurrences of the subordinate minima have disappeared from May, 1858, to October, 1866, still they appear in the 44-monthly period curve of fig. 4. Application of the Method to find the Duration of an exact Period. 46. The writer had taken a small series of daily means of barometer observations, derived from hourly tabulations of barograph, uncor- rected to standard barometer No. 58, from Ist December, 1875, to 31st December, 1876, for trial, when the method of detecting any * The writer found worth noticing that the period of 42 months is almost an exact multiple of the 36-day period which he has found further on in paragraph 50. 390 Mr. V.N. Nene. Ona Method of Tracing simple harmonic waves of an approximately known period was in its infancy. The aim was to see whether on barometer observations there was any influence of lunar period, the duration of which is about 30 days. The trial which we are going to describe was made in the earlier period of 1878, when the barograph tabulation was under con- sideration. Daily means of barograph tabulations, corrected to standard barometer No. 58, for this same period, may be found in the “ Bombay Magnetical and Meteorological Observations, 1871 to 1878,” pp. 60 and 61. The difference between the daily means, corrected and uncorrected to standard instrument, is very small, and not varying from day to day more than (say) about two or three thousandths of an inch, The treatment which was given to these daily means and the results which followed from it may be considered satisfactory. 47. In order to get the series in smooth-flowing numbers, we have taken 15 as our working value of m, and found first mean series. Then this series has been taken for further operation, and by taking 45 as our working value of m, we have found first, second, &c., up to fifth series of remainders. The first, third, and fifth series of remainders are curved in fig. 5 in plain, dotted, and interrupted lines respectively, with the same scale and on the same zero line. Looking at the plain curve, we see that there are nine turning-points of minima, the dura- tion thereof being moderately uniform. If we take the first minimum in the middle of the small gap that occurs in the curve, we have in 298 days eight periods. Thus an average duration of one period is about 37 days. Again, if we count the days from the second mini- mum, we have 258 days in seven waves, and thus an average duration is still about 37 days. Thus, instead of the lunar period of 30 days, we find a 37-day period. From this it is clear that if there be lunar period in the series at all, the amplitude of it must be much smaller than the 37-day period. 48. The object of drawing the three curves on the same zero line and with the same scale is to show graphically the process of swelling the waves as the operations increase and of their appearance, as in the case of the third wave, which disappears in the first series of remainders. The object is also to impress the necessity of making smooth-flowing numbers before taking them for operation; as in the case of second, third, fifth, and seventh waves, all the irregular move- ments in the first series of remainders are found to appear in the third and fifth series of remainders. With these remarks we conclude witl- out giving the numbers from which the present curves are formed. Second Application. 49. In order to test the reality of the period of about 37 days on a large scale, we have taken a series of weekly means of barometer observations at Bombay, commencing from Ist January, 1848, and Perviodicities when the Periods are unknown. 391 ending with the 2nd January, 1852, as the year 1848 was the first complete year when the system of hourly observations began without interruption at the Colaba Observatory. The weekly means were chosen in place of daily means for two reasons, first that as no observations were made on Sundays and a few holidays, no continuous daily means were available during the period; second, to save comparatively the labour of calculations of the processes. On some occasions when there were atmospheric disturbances, or for similar reasons, observations were made on Sundays and none on Mondays. For this and similar other reasons the weekly means were calculated from all the daily means from Sunday to Saturday. These means are given in Table IX, and curved in fig. 6 in an interrupted line. With these weekly means we have performed 5 operations to get the fifth series of remainders. The numbers in the first and fifth series of remainders are also given in Tables X and XI respectively, and curved with the interrupted line of fig. 6, and with the same scale in dotted and continuous lines respectively. 50. Looking at the continuous curve, it will be seen that from 24th week of 1848 to 8th week of 1849, we have 7 waves of simple harmonic character, and equidistant in duration. Thus there are 36 weeks, or 36x7 days in 7 periods, so that the average duration of a period is exactly 36 days. Again, from 8th week of 1849 to 24th week of 1850 there are 13 waves, also almost equidistant in duration. Thus there are 68 weeks, or 68X7 days in 13 periods, so that the average duration of a period is nearly 36°6 days. Again, from 24th week of 1850 to 34th week of 1851 there are, we presume, 12 periods. It will be observed that out of these there are 7 periods, viz., lst and 7th to 12th, whose waves are quite prominent; with regard to the remaining 5 periods their waves seem to be almost obscured by irregularities. Thus there are 63 weeks, or 63 x 7 days, in 12 periods, so that the average duration of a period is nearly 36°7 days. Jf we now add all the weeks and periods together, to get the mean duration of the period we have 16/7 weeks and 32 periods, therefore the average duration of the period is nearly 36°53 days. 51. We should here remark that as we are dealing with weekly values, there is a possibility of an error, either too much or too little, of one week in the whole period of 167 weeks. If we take 166 weeks for 32 periods, we get an average duration of 36°31 days; and if we take 168 weeks, we get 36°75 days. Thus the period we have found out is approximate to the extent above mentioned. We shall, there- fore, say that the period is approximately 363 days instead of 36°53 days. 52. The object of drawing three curves of weekly means on the same zero line, and with the same scale, is the same as in the preced- ing example of the curves of daily means. The formation into regular 392 Mr. V.N. Nene. Ona Method of Tracing waves of five weekly period of the continuous curve from the numbers corresponding to the interrupted curve for the periods from 31st to 37th week of 1848, and 13th to 25rd week of 1849 is worth noticing. It should also be noticed that the irregular movements that exist in the interrupted curve for the period from 3lst week of 1850 to 15th week of 1851, also exist in the continuous line curve. 53. Let us now combine the result by taking 365 days as an aver- ave duration of the period to get an average range or amplitude of the period, as shown in paragraph 39. Table showing the variations of 364-day period for several groups of periods and for the whole period. Number of points in the | curve (7 °3 days for a point). y 2 e : First group of 7 periods ..... — ‘113 | —-016 | +114] + -081 | — -058 Second group of 13 periods ..| — 041 | — ‘034 | + 018 | + 034 | + -016 Third group of 12 periods ...| — 018 | + 016 | + °028 | + 004 | — -Q19 Combined above three ea 048 | —-O11 | 4-042. |) 2803S ene Of S2PELIOdS ele veaieetlel a: Combined whole series.......| — ‘048 | —°012 | + 036 | + These results are curved in figures 7 to 11 respectively. It must be mentioned here that the ranges which we see in these ( : (7 \? | sin 361 results are not exact, but enlarged by our process and | |———__2 sin 7 es 365 =nearly 2°7, is the extent to which our results are enlarged. But we must also notice that the facts that the period is not an integral number of weeks, that our method of combination is in consequence rather rough, and that the number of points in the curve is too small, tend to reduce the range of the period. If the process had been applied to the continuous daily means instead of to weekly means the results would have been of a larger and equal amplitude of several groups of the period. 54. The writer feels himself under great obligation to his superior, C. Chambers, Esq., F.R.S., Superintendent of the Bombay Observa- tory, for the warm interest he tock in carefully reading this tract, and in giving here and there some very valuable suggestions. 1847... 1848... 1849... 1850... 1851... 1852... 1858... 1854... 18565... 1856... 1857... 1858... 1859... 1860... 1861... 1862... 1863... 1864... 1865... 1866... 1867... 1868... 1869... 1870... 1871... 1872... 1878... 1874... 1875... 1876... 1877... 1878... Periodicities when the Periods are unknown. February. March. 29°903 | 29°872 “916 906 earl 901 *830 April. i) 29°791 ‘770 820 Table I. SI 5 Ss fe | iia 15} > August. 29°722 | 29-621 | 29°651 | 29°707 741 “714 649 624 639 631 630 *644 654 672 643 699 660 673 °618 658 610 *649 670 *706 °700 736 "697 September. 29°748 °812 October. 29°825 *826 841 5 5 a Ss 29°693) 29°897 *909 "922 "889 O11 “891 “949 °838 "946 °905 923 *863 "955 *923 *933 °939 "944 °897 "932 °918 *981 "927 *944 °851 °931 “Oi “919 °867 *932 °8538 “887 °895 *947 *920 °931 “890 *918 $27 °969 7983 *981 "920 963 *908 *904 “900 *936 °870 °932 °866 °892 935 °943 *920 °953 °923 938 *896 °957 “921 °917 °836 *$82 394. Mr. V.N. Nene. Ona Method of Tracing Table If. 3 P . rey a be 8 8 ven | 2) 8 [ogi] to atl el 2) ee SG mee S a El = 2 2 a = é 2 a es = < = 5 5 < D 5 Z a 1848.../+ °130}+ 118 + °031 |— -031 }|— -061 |— °154 |— -150 |— -099 |+ -006| + -020 | + °103 | +-116 1849.../+ °141]+°102 + -068 |— -022 | — -086 |—°175 |—-125 |— -099 |— °¢72';+ 042 + -088 | +~-110 1850...|+ 076 |+ 7124 + 080 |+4 -010 |— :044 | — °167 |—~164 |— -071 |—-020 |— -020 |+ -086 |+ °144 185].../+ °155 |+°100 + 058 |— -020 |— -\58 |— 165 |—-196 ;— 098 |— °013 |+ °033 |+ °042 |+ °150 1852.../+ °133 |+-106 + °030 |— -006 |— °055 |— 173 |— 144 |— 074 |— -050 |+ -049 | 4-097 |+ °114 1853...|+ 131 |+ 063 + °048 |— -016 | — -038 |—°170 |— -142 |— -074 |— °023 |+ -039 | +. +049 |+ °141 1854.../-+ °122 |+-110 + +075 |— -017 | — 048 |—-133 |— +187 |— 092 |—~090 |— -021 |4+~115 |+ °124 1855...|-+ °125 |+ °120 | + °038 |+ -002 | — -031 |—-156 |— -162 |— °077 |— °033 | + -007 | + 120 |+ °128 1856... |+ °170 |+°110 + °025 |— -022 |— -089 |— +153 |— -194 |— -095 |— -002 |+ 034 | + -097 |+-133 1857...|+ °131 |+ °069 + -030 |— -013 | — -070 |—-166 |— -158 |— °128 | + °001 | + -046 |+ -106 |+ °168 1858 |+ 107 |+7125 + °038 |— -016 |— -140 |— °116 — -144 |— -095 |— °036]+ °009 + °112 |+ -129 1859 |+°118 }+ -104 + -064 |— -027 |— -025 |—°151 |— -184 |—-080 }|— °031 |+ °046 | + 043 |+ 125 1860...|-+ °147 |+ -070 | + -040 | + -024 |— -039 | — 152 |— 170 |— -075 | — "064. |+ -010 |+ °119 |+ °122 1861...|+ “111 |+ °101 |+-061 |— -032 | — -084 | ~ °130 |— -158 |—-109 |— °025 |+ 059 | + °069 |+ °135 1862...|-+ °124 |+ -076 | + -068 |+ -009 | — -004 | — °154 |— -161 |— -095 |— 089 |+ -001 | + 073 |+ °107 1863...|-+ °159 |+ -102 |+ -057 |— -037 |— -052 | —-183 |— -155 |— -098 |— -033 |+ -006 | + -086 |+ -135 1864...|-+ °129 |+ °104 |+ -065 |— -003 |— -012 |— °154 |— -169 |—-087 | — °034 |+ -039 |+ -094 |+ 108 1865...|+ °150 |+ -090 |+ -057 |— -016 | — 073 |—-144 |— 156 | — 7146 |— 024) + -037 | + -079 |+ °105 1866...;+ °145 |+ °091 |+ -051 |— -001 | — -043 | —-145 |— -159 |— -114 |— -025 |— -012 |+ °106 |+ °148 1867... + °144 |+ -096 + -058 |— -002 | — -086 |— °150 |— -155 |— °130 |— °074 |+ 000 |+ °156 |+ °152 1868.../+ °107 |+ -089 |+ -047 |— -004 |— -040 |— -164 |— -138 |— -096 |— -021 |+ -021 |+ -086 |+ °131 1869...]+ °136 |+ -109 |+ 055} -000 | — -044 |— -155 |— -142 |— -102 |— -074 |+ -022 |+ -108 |+ °107 1870...|+ °083 |+ 081 |+ 040} -000 |—-031 |— +145 |— -160 |— -074 |— -044 |+ -008 |+ -099 | + °133 1871...|+ 092 |+ -087 |+ °059 |— -012 | — -037 | — -164 |—-134 |— °073 |— °027 |+ -016 |+ -065 | + °127 1872...|+ °128 |+ °104 |+ -049 |— -024 | — -032 |— -158 |—-139 |— -119 |— 085 | + °024 !+ -071 |+ 096 1873...|+ 127 |+ 096 |+ 058} -000 | — 072 |— -161 |— -168 |— -069 |— “026 |+ -009 |+ 120 |+ -129 1874...!+°161 |+ °111 |+ 044 |+ -015 | — -089 |— -180 |—~152 |— -086 |— 065 |— -004 | + -115 |+ -148 1875...|+ °113 |+ °100 |+ -043 |— -026 | — -034 |— °155 |— -152 |— -088 |— 7054 |+ -024 ‘+ °115 |+ -129 1876...|+ *112 |+ °093 }+ -056 |— -055 | — -052 |— -135 |— -189 |— -094 |— -028 |+ -047 4: +065 + 123 1877...|+ °139 |+ -097 |-+ -046 |— -016 | — -055 |— -123 |—-100 |— -083 |—-035 |+ -024 |4 -083 |+ -083 Mean.../+ °128 |+ °098 |+ -052 |— -010 | - :054 |— °155 —~159 |— -095 |— -037 |+ -020 | + 092 |+ -129 Vee a ee ee Year 1848 1849... 1850... 1851... 1852... 1853... 1854... 1855... 1856... 1857...| 1858... 1859... 1860... 1861.. : 1862... 1863...) 1864... 1865... 1-66... 1867... 1868... 1869 . 1870... STA 2 1872... 1873... 1874... 1875... 1876... TSTiicn - January. Periodicities when the Periods are unknown. February. ...|29°797 | 29°798 | 29-799 -304| -804| -802 -802| -803| +805 -303| -801| -799 -796| -797| +799 -g09| -810| 811 -g13| -811| -810 -810| °812| °815 -815| -812| -810 -799| 800] -801 °814 "814 °814 -g15| 814] -814 -306| -805| 805 1796] +796] “796 796 | °795| -794 ‘730 | -781| -781 -816| -819| -822 -g22| -820| -817 -314| -814| -816 -821| -820| -821 -330| 832] -834 -830| 827] -824 -796| -796| -796 -g02| -804| -804 -804| -803| -801 -797| °799| -801 -g14| -814| -813 -305| -805| 806 -g10| 811) 812 -937| -839| ‘842 April i 29°801 °801 806 799 °800 °813 *809 °816 Table III. May. — —— - | —————— - 29°802 | 29°803 | 800 807 797 801 °813 808 °818 °807 °805 °814 814 803 June, *799 °806 °796 803 814 807 819 °804 806 July. 29°804 Sho, 807 | 804 | °807 August. September. ————s = 29°805 | 29-806 TE) || Sf) 807 *806 795 795 805 °806 °816| °816 804 805 820 820 802 801 809 810 °815| °814 81] °810 800} 799 798] -799 784 782 795 800 °831 828 812 812 | *820) 820 822 824 833 838 807 | 804 27S | eas 806 806 796) °795 811 814 806 *805 8038 808 822} °825 °845 | °843 828 “E41 395 B |g | 29°806 | 29°806 ‘801! +801 *805 | 805 -796| 796 -808 | -809 *814| -814 -308| -809 *819| +816 -300| +799 g12| -813 *815| 815 808] +806 798| 797 798| +797 780] +780 809 312 826] +923 811] 813 821| “821 827| +829 834] +832 800] -797 801} +803 805 | +805 -195| +796 *815| -814 805] +805 808} 809 -831| +834 | 834 Mr. V.N. Nene. Ona Method of Tracing 396 Table IV. | eae 3 | 2c) aie Coe ee eo mip ee Pel 3 | & g a a 5 iS aI ES a © ° o 5 es = < S 5 5 = D os) i a j 1848...|+ -002 | + -020 |— -021 |— -021 |— -007 |+ -001 | + -009 |—-004|+ 043} -000 | + -o11 |—-013 1849.../+ 013 |-+ 004 |-+ -016 ;— -012 |— -032 }— -020 | + -034 )— -004 |— -035 |— 022 |— -004|— 019 1850...|— 052 |-+ -026 |+ "028 |+ 020 | + -o10 |—-012 | — -005 | + -024 | + -017 |— -040 |— -o06 |+ -015 1851...|-+ 027 |+ -002 |-+ -006 |— -010 |— -004 }— -010 |— -037 |— -003 | + -024 |+ -013 |— -050 |-+ -021 1852...{-+ -005.|-+ -008 |— -022 | + -004 |— -001 |— -018 | + -015 | + -021 | —-013 |+ -029 |-+ -005 |— -015 1853...|-+ 003 |— 035 |— -004 |— -006 |+ 016 |— -015/ + -017 | + -021 | + -014 |+ -019 |— -043 |+ -012 1854...|— +006 | + -012 |-+ -023 |— -007 |+ -006 | + 022 |— -028 |+ -003 |— -057 |— -041 |-+ -023 |— -005 1855...|— 003 |-+ -022 |— -014 | + -012 | + -023 |— -001 |— -003 |+ -018 | + -004 |— -013 |-+ -028 |— -001 1856...| + 042 | + -012 |— -027 |— -012 |— -035 |+ 002 |— 035] -000 | + -035 | + -014 |-+ -005 |+ -004 1857...|+ 003 |— -029 |— -022 |— -003 |— -o16 |— -011 | + -001 | — -033 | + -038 |+ -026 |-+ -014 |+ -039 1858...|— 021 |+ -027 |— -014 |— -006 |— -o86 |+ -039/+ 015] -000/+-001 |—-011 |+-020] -000 1859...|—-010 |-+ -906 |-+ -012 |— -017 | + -o29 | + -004 |— -025 |+ -015 |+ -006 | + -026 |— -049 |— -004 1860...|-+ 019 |— 028 |— 012 | + -034|+ -015 |+ -003 |— -011 |— -o20 |— -027 |— -010 |-+ -027 |— -007 1861.../— °017 |-+ :003 |+ -009 |— -022 |— -030 | + 020 |+ -001 |— -014}+ -012 |-+ -039 |— -023 |+ -006 1862...|— 004 |— -022 |+ -016 |+ -019 |+ -050 |+ 001 |—-002| -000 |— -052 |—-o19 |— -o19 |— -022 1863... + -031 |-+ -004 |-+ -005 |— -027 | + -o02 |— -028 | + 004 |~ -003 |+ -004 |— -014 |— -006 |+ -006 1864...|-+-001 |-+ -006 |+ 013 |+ -007 | + -042 |+ -001 |— -010 | + -o08 | + -003 |+ -o19 |+ -002 |—-021 1865...|+ 022 |— 008 |-+ -005 |— -006 |— -019 |+ -011 | + -003 |— -051 | + -013 |+ -017 {— -013 |— -024 1866...) 017 |— 007 |~ -001 |+ 009 |+ -011 |+ 010] -000 |—-019 | + -o12 |— -032 |+ -014 |-+ -019 1867...|-+ 016 |— -002 |+ -006 | + -008 |— -032 |+ -005 | + -004 |— -035 |— -037 |— -o19 |-+ -064 |-+ -023 1868...|— 021 |— -009 |— -005 | + -006 |+ -014 |— -009 | + -021 |— -001 |+ -016 | + -001 |— -006 |+ -002 1869...|-+ 008 |-+ 011 |-+ -003/+-010|+-010} -000}+ -017 |— -007 |— -037 | + -002 |+ -016 |— -022 1870...— *045 |— -017 | — 012 |+ -010 | + -023 |+ -010 |— -001 | + -021 |— -007 |— -012 |-+ -007 |+ -004 1871...|— 036 |— 011 |-+ -007 |— -002 | + -017 |— -009 | + -025 | + -022 | + -010 |— -004 |— -027 |— -o02 1872...| 000 |+ 006 |— -003 | — -014 | + -022 |— -033 |+ -020 |— -024 |— -002 |+ -004 |— -021 |— -033 1873...|— 001 |— -002 | + -006 | + -010 |— -018 |— -006 |— -009 |+ -026 |+ -011 |—-011 |+ -028] -000 1874...|+ 033 |+ 013 |— -008 | + -025 |— -o35 |— -025 |+ -007 |-+ -009 |— -o28 |— -024 |+ -023 |+ -o19 1875.../—°015 |-+ -002 |— -009|—-016|+-020] -000|+ -007 |+ -007 |— -017 |+ -004 |+ -023] -000 1876...|— 016 |— 005 | + -004 |— -045 | + -002 |+ -020 |— -030 | + -001 |-+ -014 |-+ -027 |— -027 |— -006 1877...|+ 011 |— 001 |— -006 |— -006 |— -001 |+ -032 | + -059 |-+ -012 |+ -002 | + -004 |— -009 |— -046 Periodicities when the Periods are unknown. 397 Table V. Year. 5 5 5 = & 3 S a 2 8 2 g eee ies mal leaies ea ie (2S |oaz 8 Ee | Oe ee .. _|-+001 |— -014 |+ -021 | -010 |-+ -004 |— -008 1849...}+ °006 |— :005 |+ °010 }+ °003 |— °013 ;— -011 "030 ;— °005 |— 028 ;+ -021 |+ °007 000 1850...|— -027 |-+ 018 |+ -013 |— -004 |+ -004 |— -o08 |— 011 |+ -014 | + -015 |— -025 | + -001 |+ -008 1851...{+ -006 |— -009 | + -004 |— -006 | + -005 | + -o09 |— -017 |— -004 | + -019 | + -009 |— -036 | + -022 1852...|-+ -003 |-+ -001 |— -015 |+ -010 | + -006 |— -017 | + -011 |+ -013 |— -014|— -006 | + -007 |— -005 1853...|+ °016 |— °015 |+ °003 |— °003 }4+ °012 | —°014 |+ -001 |+ °003 °000 | + °014 |— 025 |+ °019 1854...|— °007 |— °001 |+ °016 |— °015 °000 |+ °017 |— 021 |+ 025 |— °019 |— 015 |+ °029 |— °012 1855.../— °009 |+ °018 |— °018 |+ °001 |+4 °013 |— -008 |— °009 }+ °014 |— :002 |— °012 |+ °014 |— :020 1856...)+ °015 |+ °003 |— °015 |+ °008 |— :009 | + -021 |— °017 |— °006 |+ °018 |— °007 |— °006 | + -002 1857...| + °009 |— °011 |— °002 |+ °011 |— -007 | + °003 |+ °011 |— °028 |+ °022 |— -001 |— °010 |4 °019 1858...|— °026 |+ °015 |+ °001 |+ °014 |— -044 |+ °036 |+ 002 |— °011 |+ °003 |— -009 |} + °014 |— 001 1859...;— °01] |+ °006 |+ °008 |— °023 }+ °020 |+ -005 = 017 |+ °002 |+ °002 | + 023 |— °035 | + °005 1860...|-+ °028 | — °022 |— °010 |+ °019 |— -004 |— -005 }+ °002 |+ °004 |— :009 |— °005 |+ °021 |— -006 1861...|— °014 | + °006 |+ °015 |— 009 |— -016 |+ -024 |— °001 |— °019 |+ °005 °024 |— °027 |+ :009 1862...|+ °007 |— °014 |+ -006 |— :004|+ -018 — ‘016 |— :001 |+ 7018 |— -019 | + -009 | + °005 |— -014 1863...|-+ -019 |— :004 |-+ -001 |— -010 | + -015 |— -014 |-+ -006 |+ -001|+ -005 |—-007| -000 | + -007 1864...;— °003 |+ °001 *000 | — °011 |+ °019 |— -006 |— -009 |+ °008 | — 006 |+ -010 °000 |— :016 1865...|-+ °019 |— °009 }+ °004 |+ :001 |— -016 |+ °017 | 4+ °012 |— °034 °015 |+ °017 |— °010 |— °013 1866...|-+ °019 |— 006 |— -005 | + -003 |— -001 | + -004 |— -o02 |— -009 | + -025 |— -017 |— -007 |+ -010 1867.../-+ °005 |— °012 |+ °004 |+ °013 |— -024 |+ -007 |+ 014 |— -004 |— -008 |— -020 |+ 7034 “C01 1868...}— °021 | + °006 |}+ 002 |+ 002 |+ -006 |— :012 |+ -011 |— -008 | + -006 "000 |— °005 000 1869...|-+ °003 | + °003 |+ °005 |+ :003 000 |— -009 |+ °014 |+ °004 |— °022 |+ :006 |+ °019 |— °007 1870...|— °013 |+ °011 |— °003 |— °002 |}+ -009 °005 |— :009 |+ -016 |— °005 |— °012 }+ °010/+ -011 1871...}— °019 | + °002 }+ -009 |— °005 |+ °009 |— -015 |+ °006 |+ °003 *002 |+ :003 | — °012 | + -006 1872...) -000 |+ -005 |— -001 |— -010 |+ -012 |— -010 | + 014 |— -017 | + -002 |+ -014 |— -005 |— -o12 1873...|+ °O11 |— °003 |— °001 |+ °009 |— °008 |}+ °001 |— °008 |+ -015 *000 |— °018 |+ °014 |— :007 1874. °012 |— °005 |— °016 |+ °028 |— -016 |— :012 |+ °013 |4+ °014 |— °014 |— -014 |+ °018 |+ °006 1875...|— °017 |+ °009 °000 |— °018 |+ :015 |— °008 °000 |+ °009 |— 014 |— °002 |+ °014 "000 1876...|—-014|+ -007 |+ -018 |— -030 | + -009 | + -023 |— -022 |— -003 | + -006 | + -017 |— -021 |— -001 1877.../+ °013 }— °002 °000 |+ 001 |— :010 -000 398 Year. + + + Mr. V. N. Nene. February. March. Table VI. Se et es HS hs + 008 — -019 |— -009 |+ -004 + 006 |— :004 |+ 006 — *009 |— -019 |'-— -020 — 007 |— :001 |-+ :004 + 004 |— :001 |+ -016 + 006 |+ :005 |— -007 + 010 |+ -007 |+ :006 — +026 |— 019 |— -018 — :009 |— :014 |—-010 — 042 |+ -003 |+ -013 -009 |— -001 |— -008 “019 |+ -008 |_— 013 — 014 |— -004 |+ -002 + 032 |+ °017 |— -001 — 013 |— -014 |— -002 + °023 |+ -007 |— -001 — 003 |— -006'|— -009 + ‘O12 |+ -006 |+ -002 — +008 |— -002 |— -010 + 008 |+# 003 |+ -010 + 010 |+ :009 |+ -003 + °014 |+ -015 |+ -008 + 008 |+ °006 |+ °019 + :010 |+ -007 |+ -006 —-010 |— -007 |— -01 — 019 |— -013 |— :006 + '005 |+ :008 |+ -007 — 007 |— :003 |— -008 + °018 |+ :030 + + + + + + September, On a Method of Tracing November. December. Periodicities when the Periods are unknown. ie eS Year. a 5 1850... 1851...;-+°009 | +°001 1852...) +°003 | +°009 18538...| —"003 | —°004 1854...] +°002 | +°009 1855...! +°001 | —°004 1856...| +°013 | +°002 1857...| —"001 | —°005 1858...} —"005 | +°012 1859... °000 | —°002 1860...| °000 | —"004 1861...| —°003 | +°001 1862...} —°008 | —-009 1863...} +°011 | +°003 1864...) °000 | —-003 1865...| +°003 | +°001 1866...| °000 | —-002 1867. “000 | +001 1868...) —°006 | —-015 1869...| +°002 | +°001 1870... —"010 | —°010 1871...| —°005 | —*002 1872...| +°006 | +°004 1873...} —°003 | +°005 1874,..| +°005 | +°006 1875.,.| +°003 | —-009 VOL. XXXVI. March. +009 —°002 —°003 +°007 —°004 —°005 —°006 “000 —°002 +°001 —*006 +°001 —°001 +°0038 000 +°003 000 —*006 —"004 —'001 000 +°004 —‘003 +°008 +°002 —*007 April. +°010 -000 —-002 +002 —-004 +7001 —*002 +*004 —:001 +°002 +7005 —-001 +°003 —'010 +:003 —+004 —-002 —"004 +:007 —-002 +°010 +-002 —-007 +003 —-002 —-001 Table VII. b 3 =) —'008 +°002 =—°001 +002 —°002 +°001 —*002 +°007 —*022 +°004 +°011 —*003 +'011 —‘003 —*008 +003 +°003 ‘000 +°007 +°002 +°005 000 +004 —*009 —°010 +°005 September. | | | +006 +°007 —°008 +006 —'0138 “000 +:002 +°003 —'007 +°001 —°002 —°003 —°006 +°001 +005 +°004 —*005 —°018 +°004 —°008 —°002 +°003 +°002 +003 —°007 —°066 October. bo November. 399 December. 400 Year. January. ---| +7012 .} —"001 .| —°010 Soo | LO .| +7005 .| +°014 .| —°005 -| +°010 .| +°001 -| —°009 “000 .| —°008 ---| +°001 -| +7004 “000 .| —°002 -| +°011 -| +°006 -| +7003 -| =°022 .-.| —°012 ...| —°006 ---| —°009 -| +°016 -| —*001 Mr. V. N. Nene. February. Table VIII. a June, +°014 | +°009 —*011 | —:013 —"006 | —"001 +°002 | +°009 +°008 | —°002 +°009 | +7006 —°024 |} —-022 —'016 | —-013 —°020 | —-008 +°005 | +001 +008 | +°002 — 011 | —-005 +°021 | +°016 —°010 | —-012 +°015 | +°010 —006 | —007 +°009 | +°002 —*008 | —014 +°001 | +°005 +°008 | +°005 "009 | +°014 a +°008 | +7013 +006 | +7005 —-001 | —°002 —:009 | —-013) July. +004 —012 +°005 +7014 —012 +:004 —'012 —°005 +'001 +°004 —-008 +°001 “000 —°008 +°007 —"008 —'001 —019 +7010 +7002 +°013 +°016 +7003 “000 =-013 "000 | +-002 | + °004 August. —*001 —*007 +°010 +°013 —-022 +°003 +003 +003 +7006 +°004 —"013 +:007 —°017 —°008 +°003 —°009 —°007 —"018 +°009 —'004 +°007 +°012 —*003 +°003 —*009 +004 September. —*004 —°002 +°009 +008 —°025 +006 +°015 +°013 +7005 +°003 — ‘016 +°019 —°027 —°002 +°004 —°006 —*008 —011 +006 —°007 +°001 +005 —°006 +°008 —°007 +003 On a Method of Tracing October. —*004 000 +011 +°004 —°022 +°009 +°017 +022 +°005 —°003 — 007 +°009 —°028 —°005 +°0038 —"004 —*005 +°001 +°003 —010 —°003 —*002 —°012 +011 —°002 +°004 | November. ' “000 000 +°004 —-003 ="012 +°014 +011 +028 +°003 —°009 —-003 +°002 —°020 —°002 +°003 —- 005 +006 +°009 +°001 —°016 —-008 —-006 — ‘016 +°015 +°001 December. Periodicities when the Periods are unknown. AOL Table IX. Week.| 1848. | 1849. | 1850. | 1851. }Week.| 1848. | 1849. | 1850. | 1851. 1.. | 29°931 | 29°955 | 29°924 | 26°965 | 27..|29°736 | 29°678 | 29°720 | 29°613 923 "930 849 °9384 | 28..] -600 “740 649 936 ‘918 "926 843 *982) 9295.1) .-620 688 583 "697 | 923 °962 878 OO ese co50 “609 057 er "965 "948 *920 "942 | 31..| ‘692 583 °735 ‘713 975 969 "877 | 32..| “693 704 697 ‘737 -O7 904 "929 "915 | + 33..] 693 748 °748 ‘695 885 *830 906 868 | 34..| °722 "740 752 663 Oo MO TP A PF w Ww Ne} [op) ive) ‘818 | -911| -901| -885] 35..| -756| -665| -747| -724 10 800 | -879| -883| -847]| 36..| -778| -695| -778| -714 11 865 | -937| 879 | -811] 37..| -834] -715 | -742 | -846 12..| -8388| -853| :884| -ss2/ 38..| -855| -642) -811 | -836 13 826 | -781 | -902] -864] 39 781 | °832| -801| -753 15 846 765 795 810 | 41 851 781 806 834. 16 721 758 829 731 | 42 882 859 755 817 17 704: 795 801 683 | 43 853 889 752 937 18 777 780 792 730 | 44 825 846 817 802 19 759 722 789 795 | 45 871 817 846 829 20 704 704. 758 761] 46.. 881 915 818 804 rl Pe 706 703 764: 7044 47.. 962 911 942 902 22 693 | 668 728 645 | 48. 981 925 961 “926 23 651 662 667 0383 7 49. 901 848 928 ‘975 24 571 625 592 “703 | 50. 899 885 933 | "929 402 Mr. V. N. Nene. Ona Method of Tracing Table X. | Week. | 1848. | 1849. | 1850. | 1851. |Week.| 1848. | 1849. | 1850. | 1851. Iba ac +°019 | +'023 | +°004 } 27..] +°087 | +°029 | +:092 | —-010 Zine 50 —‘013 | —:057 | +:029 | 28..| —°067 | +°097 ‘000 | —-088 Ome oe —'024 | —"065 | +°039 | 29..| —°057 | +°025 | —:073 | +°061 4,.| —'012 | +°019 | —:024 | —-023 | 30..} —‘019 | —°070 | —‘113 | —-081 5..| +°036 | +°023 | +°021 | +016 | 31../ +°025 | —°104 | +°061 | +°054 6..| +°055 | +°053 | +°062 | —-0385 | 32..]+°004 | +°027 | +:009 | +051 7..| +:020 | —012 | +°017 | +:022 | 33..| —‘O19 | +-070 | +-082 | +:007 8..| —"003 | —:082 | —-006 | —"010 | 34..| —°016 | +047 | +-009 | —-064 9..| —°052 | +013 | —-006 | +°016 | 35..} —"006 | —°036 | —:007 | —-021 10..| —-030 | +-008 | —-015 | —-020 | 36..| +-004 | —-025 | +-010 | —-038 11..| +:031 | +-083 | —-008 | —-040 | 37..| +:057 | —-017 | —-036 | +-089 12..| +-010 | +-008 | +:013 | +°039 | 38..| +-060 | —-096 | +-025 | +-055 13..| +012 | —-042 | +-041 | +043 | 39..] —-032 | +-066 | +-014 | —-042 14,.| +-003 | —-023 | +-003 | +-003 | 40..| —112 | +-044 | +-033 | —-064 15..| +:058 | —-023 | —-041 | +-024 | 41..] +:028 | —-031 | +-012 | +-014 16..| —-056 | —-014 | +-006 | —-042 | 42..| +-057 | +-022 | —-044 | —-o02 17..| —-062 | +-037 | —-001 | —-076 | 43..| +014 | +-040 | —-049 | +-111 18..| +:025 | +-034 | +-002 | —-015 | 44..] —-050 | —-014 | —-002 | —-044. 19..| +028 | —-010 | +009 | +074] 45..] —-023 | —-063 | +-004 | —-081 20..| +033 | —-015 | +001 | +068] 46.., —-015 | +-036 | —-048 | —-078 21..| +-004 | +:008 | +-037 | +008 | 47..| +-059 | +-033 | +-050 | +-021 22..| +014 | +-004 | +-022 | —-040 |] 48..| +-064 | +-032 | +-045 | +-022 23..| —:027 | +010 | —-019 | —122 | 49..] —-028 | —-068 | —-004 | +-056 24..| —104 | —-024 | —-089 | +-069 | 50..| —-041 |—-032 | —-016 25..| —-042 | —089 | —-019 | +:042 | 51..| —-009 | +042 | +-029 26..| +°101 | —:018 | +006 | —‘0380 | 52..| +°026 | +°080 | +-006 53... a0 oe —°027 1848 Patera oye 0c! VOU. 36. FU, 4. 1859 1860 1861 1862 +:040 + jae ya, eee +-020 - ptt ——_t—f-—|++020 +} s i an 1 ‘ ‘000 = =) + 3) 7 : ~ = al — ma 000 [ - | Xv (orale iN | —:020 | ia va i i= 020 ic 4 == Wo | gore ) | i _.940 =I | | x | 3 | ee 1874 1875 1876 1877 | +040 { +020 “000K -- 42 = —-020 I 7 | x —-O40 t | 1848. BE 1850 We we) 33 36 39 42 45 48 51 | 2 | axeal ! ie Sasa +-100|— a i K_129-300 | 7 Za Lay | Al ee E +000 z | . 29-800 1 = H aE am | <7 | if iE sea a 2 a a a ‘429-7000 5, i x. f ~ — | i - { is | | } a i jest qniee : iE : Ss a ES py yor aI a ; ! SE io 4 ; \ ! a Sa ay -000 T + + - | - ; a 29-800 + ' ‘ \ Zz | ee a4 tt ad 29-700 : Boeke fast py} {3 | | T : fi aE t | ie H [ NW i } H wl i | | Sense es=ssse= on 2 18 24 27 30 33.°~—S«aG aN So Shae i) iS 4 KR RB | | 3 i i = Lf a — West Newman. &% C° se, i) x o 2 ns : 2 g = oS ea a 2 ¢ : s a s = FS = S6h day pertod i na {| iit f » 4 2 re 2 & = we o me = 5 2 S s s 5 a 4+ 4 g i i } je ° 8 s aU BRBUEBP Ltt Pt | LP ° 3 Q boys} SHU OGNOHNNNHOUa 8 S S 2 3 5 eet HTT eM 9 8 8 E 2 3 | Ht bury : HAAAMAOANALEGI == SUQ00 ER LSLEGH : ft Arar ete SRBARHHRRE HH ny TH as Sere HH it i I = Pio. ae TA Seer ‘ eee ane pee eeU Ab tL OS ed LL Fore e J saan }dede fad d SAHA 4 b4-+-] }—}+- 4-4 alll ji g {| { nual INnOOH ‘ tS | nit e un + 4 Ht LY tL une Le e 2 - Ane eee Sea t 4-4 a =e = 1 t THA et HAHA CLECTHLEREELELH y ae SREP) SUGEEST) SEE MS oS. PERTH ETCETERA MONON SUOHOTOEOGE mi — 3 CCEA et { ae SLES BE AYA Aeyq 01 1380" 1 4870 t i 1861 i t : i { =f i n + + i i uly gz HH 1260° - 1863 7 i 1860 t +— Tt tt aa 1874 + t { = T { t a i aa au [ ith CEST udyar + rH Bie 3 LH || | ~ =] HH es eS 7 tH Le 3 HTL NAOT ARENHODGSS e300 UAE : vend HHTTHEEaET EEE 5 = 2 wAYTE? 44. 4 CO: on ni a | 3 \ Uf ae | S 2 ie rn | BUY ty wOWT | Mr = Ht qa | aa =| 2 Tile 4 Tr 1 eq] vr] i aa = a a ala ae ahtrritH 5 s pti STH [ 2 WIRE TH Ns 3 | TSP Ht Ht : . = aan a wan 2 2 Hit SS : 7 , >| i I 91 ana 3 ey fi i ! iS St enue DADURRURRRRERR AE le DUERnE = 2 “RIP b q i GOnR aa SPY AB CY 1k HB Bs ee ce og oo af - ~ TRE fg j wep 6%, oy 3 “ins y a ay ° a : : tf & = = 9L8) PC i : 8 * 3 - iN Bg S a iS “| [ i Ca ac" = aT Trane RT el Ape er kp ie. aaa * 5 U ) ° i) ‘S) Ss S So is > f 8 alll + + + i i 1 a) g a = jj 3 s alt 2 ~ ¥ 2 4 2 4 S| 4 A 3 = ot 2 S ut a o 2 ES | 2 -) & / 2 3 | 2 3 i a . 2 rt ce = 2 3 . fs as / cE) a nfl A i t i 1 | 2 3 E i S - 3 4 a & Gye Ager & = oe on + : A adie. ae a en eer ‘ Leda aut lsc aerate iced tliat Date dee ey BE ; i ' Bs i ; ma : j ko accaies pale 7 . : ia ee ; 7 i! ‘ ; + A o Me ; bats, . r) 4 Pe by j Sper i ‘ee > > > “ : “ se | te pce ekg t cee eyn bam dhe mw canines miscret ij 5 a a Y 3 : o S i . 7 ge’ a nes aha E> aad Et tne na maa Etre Peres} ‘ ey). ae." — ite erent ey RE | pain Tay) i kt Sen, Pee oe <. » i , A (ee | j Spee Cae eer Se tl : ee . z oe wie” “yi ) a Ty eS ’ i‘ + 7 ny “4 ’ ~ _ . = ‘ ! eeeaP t > = 1 Pang ( f rats < ¥ wr " » me . oe bg 4 ; } om ‘ . a . 3 > ad > gel a a A - :~ ; 1 ; ‘ee é Ra ea me . a a A f gee ded ees 2 é 1 5 - m ; | md a , 2 el id . ‘ t ; . cing . ‘ Seo q 7 , ’ \ : ‘ z y as i c a, es. e Sp. » + | Be Gen 9 A ot ame ete A+; ‘ tw a thing ' Fe wears oe to eae , ee , ol A ma | x Week. SOO et RT OUST tee roe See ne ee PO JS hens RS) RO) TRG APNG PS PE pe ps eS SS a a 24. VOn. 1848. — 055 —°073 + O11 +°031 +°019 +°018 + °062 —°033 — "194 —°043 +°165 XXXVI. Periodicities when the Periods are unknown. 1849. + 052 —°035 — 087 — 009 + °067 +085 —°015 —‘134 — ‘020 + °033 +118 — "004 — 051 — ‘047 —°'012 +°O11 + 055 +°033 —°037 — ‘064 — 011 +°061 +073 —°001 — 1386 — ‘065 1850. + 049 — “084 — ‘106 — 012 +061 +071 —-003 — ‘032 —°024 —°020 — ‘009 +°030 + ‘047 — 006 — 057 + 004 + °029 +005 — 034 —'034 + 064 +063 +006 — 143 —°049 + °040 Table XI. 1851. [Week. —014] 27.. +°023 | 28.. +060] 29.. —040 | 30.. — 004] 31 — 055 | 32 +045 | 33.. +021 | 34.. +°037 | 35.. —'047 | 36.. — 058 | 37. | +-004 | 38. +°046 So +°039 | 40.. +046 | 41. — 050} 42.. — 112] 43.. — 042} 44, +101} 45. +'142 | 46. —015 j 47. —120] 48. —143 | 49, +°106 | 50. +127] 51. — 021] 52. 53.. 403 1848. +143 — 108 —°120 — ‘016 +°106 +°053 —'013 — ‘060 —°056 — ‘006 +°113 +°080 — 074 — 175 + 044, +°137 + 067 — 103 — ‘094 —016 +112 + 084: —°060 — "099 — ‘014 +086 1849. +051 + °185 + °036 — 129 — 171 +052 +°180 +°064 —°047 — “056 — "020 — "046 + °088 +027 — 049 +006 + °043 —°018 = 112 404 Candidates for Election. March 6, 1884. THE PRESIDENT in the Chair. The Presents received were laid on the table, and thanks ordered for them. In pursuance of the Statutes, the names of Candidates for election into the Society were read from the Chair, as follows :— Allman, Professor George John- ston, LL.D. Atkinson, Professor PhD: Bagot, Alan, C.H. Baird, A. W., Major R.E. Balfour, Professor Isaac Bayley, D.Sc. Baxendell, Joseph, F.R.A.S. Bell, James, F.I.C. Bidwell, Shelford, M.A. Blake, Rev. Professor J. F., M.A. Browne, Walter Raleigh, M.A. Burdett, Henry Charles, F.L.S. Buzzard, Thomas, M.D. Claudet, Frederic, F.C.S. Carpenter, Philip Herbert, D.Sc. Colenso, William, F.L.S. Conroy, Sir John, Bart., M.A., Ta CaSy. Kdmund, Creak, Httrick William, Staff Commander R.N. Cunningham, Allan Joseph Champneys, Major R.H. Curtis, Arthur Hill, D.Se. Forbes, Professor George, M.A. Goodeve, Professor Thomas Min- chin, M.A. Green, Professor A. H., M.A. Hartley, Professor Walter Noel, F.R.S.E. Herschel, Professor Alexander Stewart, M.A. Hicks, Henry, M.D. Hicks, Professor William M.,M.A. Hudleston, Wilfrid H., M.A. Japp, F. R., Ph.D. Kent, William Saville. Laughton, John Knox, M.A. Lamb, Professor Horace, M.A. Lewis, J. R., M.B. Lyster, George Fosbery, M.I.C.E. MacGillivray, Paul Howard, M.A. McKendrick, Professor John G., M.D. Manson, Patrick, M.D. Marshall, Professor A. Milnes, M.D. Meldola, Raphael, F.R.A.S. Miller, Francis Bowyer, F.C.S. Milne, Professor John, F.G.S. Nobel, Alfred. Ord, William Miller, M.D. O’Sullivan, Cornelius. Pattison, Samuel Rowles, F.G.S. Perry, Professor John. Pritchard, Urban, M.D. Pye-Smith, Philip H., M.D. Ransome, Arthur, M.D. Rawlinson, Sir Robert, M.1.C.E. Rendel, George Wightwick. Cae 1884. | On Magnetic Polarity and Neutrality. 405 Rodwell, George F., F.R.A.S. Thomson, Joseph John, M.A. Roy, Prof. Charles Smart, M.D. Tidy, Charles Meymott, M.B. Riicker, Professor Arthur Wil- | Tonge, Morris, M.D. liam, M.A. Topley, William, F.G.S. Smith, Willoughby. Tribe, Alfred, F.C.S. Spiller, John, F.C.S. Vivian, Sir H. Hussey, Bart. Stotherd, Richard Hugh, Colonel | Warren, Sir Charles, C.M.G., R.E. Lieutenant-Colonel R.E. Tate, Professor Ralph, F.G.S. Warrington, Robert, F.C.S. Tenison-Woods, Rev. Julian H., | Watson, Professor Morrison, M.A. M.D. The following Papers were read :— [. “Magnetic Polarity and Neutrality.” By Professor D, E. HuGues, F.R.S. Received February 23, 1884. In recent papers upon the Theory of Magnetism,* I gave the opinion drawn from a long series of personal researches, that mag- netism in iron and steel is entirely due to the inherent polarity of its molecules, the force of which could neither be destroyed nor aug- mented ; that, when we have evident magnetism, the molecules rotate so as to have all their similar polarities in one direction; and that neutrality is a symmetrical arrangement or a balancing of polar forces, as in a elosed circuit of mutual attractions. The series of researches which I now present bear unmistakable testimony to the truth of these views, showing the opposite polarities which exist in an apparently neutral bar of iron; and that it is by this means alone that external neutrality occurs in the iron cores of an electro-magnet upon the cessation of the inducing current. The instrument used for measurementst consists of a delicate silk fibre-suspended magnetic needle, always brought to its zero-mark by the influence of a large magnet at a distance, the angle of which gives the degree of force required to balance any magnetised body placed on the opposite side of the needle. It can also employ electro- magnetic effects by the use of two opposing coils on each side of the needle, balanced so that an electric current passing through the coils has no influence on the needle, except when a piece of iron or steel is placed inside one of the coils; this again being balanced and measured by the large revolving magnet. * “Proc. Roy. Soc.” (vol. 35, p. 178), and “ Journal of the Society of Tele- graph Engineers,” vol. xii, 1883. , + “On a Magnetic Balance, and Researches made therewith,” by Professor D. E. Hughes, “ Proc. Roy. Soc.” (vol. 36, p. 167). D9 Ve Oe 406 Prof. D. E. Hughes. [ Mar. 6, Before commencing my researches upon neutrality, I felt that it was necessary to observe the curves of magnetic penetration, whilst under the influence of its inducing cause. It is well known, however, from the researches of Gaugair, Du Moncel, and Jamin, that the magnetism does not penetrate to a very great depth with its full force, decreasing rapidly from the exterior to the interior. Most observations have been made by means of tubes of various thickness, introduced into each other. These, however, introduce an element of error, as, In separating them, they are necessarily drawn over each other. Jamin’s method of dissolving the exterior of a steel magnet in diluted sulphuric acid gave results free from experimental error, but this could only be employed after the cessation of the inducing cause, the observations being really upon the permanent remaining magnetism. The methods employed by myself consisted, first, in superposing” twenty flat iron strips, $ millim. thick, 20 centims. long, and 3 centims. in width. These could be built up intoa solid rod 1 centim. total thickness. Hach piece was carefully selected and measured for its magnetic capacity, so that they should all be equal in value whilst under the influence of an inducing force, as well as their remaining magnetism when the influence ceased; the remaining magnetism being about } of its capacity in the size and kind of iron employed. These strips forming a compound bar were placed in contact with the poles of a strong permanent magnet, or they could be laid on one pole, the object being to polarise the lower bar only by contact, and observe the degree of penetration. The upper strip was carefully separated whilst the remainder was left under the polarising influence. We could thus separate each bar while under the influence without fear of reactions taking place between the separated bar and its companions. We had thus a bar or strip, separated while under the inducing influence, and, knowing its coefficient of remaining mag- netism, we could estimate its full power when under the polarising influence. By this means the values were plotted graphically, giving curves of varying degrees, as the inducing force was changed, or the material of the strip from soft iron to hard steel. These curves were verified by a somewhat similar method, using a separate: strip whose coefficient of remaining magnetism was known, and drawing this over the poles of a magnet, but separated from it by different degrees of thickness of iron. These again were verified by an electro-magnetic method, in which a series of concentric tubes divided lengthwise was employed, so as to allow separation without friction, confirming the numerous curves obtained by the previous methods, showing that with a limited magne- tising power acting upon homogeneous iron or steel, the penetration is inversely as the square of the distance from the inducing power, but 1884. ] On Magnetic Polarity and Neutrality. 407 with high powers the exterior soon arrives at its saturation, the distant layers rise in value, and also if the bar is not homogeneous there is a consequent deformation, owing to the comparative rigidity of its molecules. Tn all cases, whatever the force employed, or nature of the iron or steel, there are no reversals of polarity in the interior, but a constant diminishing curve of penetration from the outside to the centre. This changes, however, the instant the exterior polarising force ceases, the different degrees of force between the external and internal react upon each other, producing the following results :— Internal Waves of Opposite Polarity. All varieties of iron and steel have a high magnetic capacity whilst under the influence of its inducing force, such as the electro- magnetic coils, or strong permanent magnets, but this power in a great measure disappears on the cessation of the inducing influence, a return more or less perfect towards neutrality being the result; remaining magnetism is therefore a partial neutrality, more perfect in soft iron, where the molecules are in a greater state of freedom, than in comparatively rigid cast steel. Our so-called permanent magnets are simply the remains of a far higher magnetic state, and it is already in most cases half-way down on its road to neutrality. Jt is absolutely necessary in a theory of magnetism that we should know the cause of neutrality, for it is really the starting point to appreciate how polarity becomes evident. In my previous researches upon neutrality | used the induction balance, but in these I have employed more simple methods, which allow of repetition by the most simple means. The first consists in forming compound bars of ordinary hoop- iron, 4 millim. thick, and 30 or more centims. long, twenty or more of which could be superposed, bound together by a fine copper wire and forming a rod of any desired thickness; they were magnetised by drawing over magnets of various powers, and the degree of approach to neutrality observed by the amount of its remaining magnetism. Now, on carefully separating them, there were invariably found violent curves of opposing magnetism, previously held bound by the closed circuit of mutual attractions. The second method consists in superposing the divided concentric tubes, already mentioned, bound together by a fine copper wire, and macnetising them in the electro-magnetic coils of the measuring balance; by this means we could observe the charge or full magnetic capacity under the influence of an electric current, the remaining magnetism upon its cessation, and after taking out the tubular core, separate it, and observe the polarity of its successive internal layers. This method is objectionable, as the slightest rubbing of one tubular 408 Prof. D. E. Hughes. [ Mar. 6, surface against another may alter the true value. The electro- magnetic method is however infinitely superior when observations are made on solid bars, or tubes of different degrees of thickness, to observe the influence of depth or thickness, in producing a perfect return to neutrality after cessation of the inducing effect of the coils. The third method was a chemical one, somewhat similar to that employed by Jamin, except that as the object was to study the curves of neutrality, the bars were of annealed steel, highly magnetised in the coils, and afterwards reduced almost to a zero, by vibrating them, or beating them gently with a wooden mallet. We had by this means aided the molecules to follow their inclination, as they do in soft iron, for when a soft steel rod is in a state of vibration, its molecules are comparatively free; but they rigidly retain the true curve of neu- trality when not vibrated. We are thus enabled by dissolving the exterior in various dilute acids, and by taking repeated observations, to draw graphically the waves of opposing UNS which have produced external neutrality. The curves obtained by the different methods are identical in form. The simplest and most accurate method is the first, as we can choose a hard variety of iron, such as ordinary hoop-iron, and by slight vibrations, or blows with a mallet, allow the molecules sufficient freedom to form their curve before separating, and as the material is. sufficiently rigid not to be influenced by mere contact, or even frictional drawings, we have on each strip a perfect record of its state, and can thus analyse the internal state of a neutral compound bar. If we take a compound bar of the hoop-iron, and draw the lower side over the south pole of a magnet, it will be found nearly neutral, or if not sufficiently so, we can reduce it by slight blows with a mallet: suppose the united bar gives still a remaining magnetism of 18° on the magnetic balance, on separating the components and observing the same ends we find the lowest (or the bar which had touched the magnet) 150° north polarity, the next may be slightly north or zero; the rest will have varying degrees of south polarity, from 60° to 10°, the total of which exactly balances the north polarity of 150, less 18°, which we already observed as the remaining magnetism. If we do not wish to approach a perfect neutrality, we should not vibrate the rods. In this case we may have 75° of remaining magnetism, and find on separating the strips, that we have on lower strip 150° north, and the total opposing south polarity of the interior but 75° south, leaving the remaining 75° of north polarity first observed on the compound bar unbalanced. The mutual reactions between the magnetic molecules in a solid bar are precisely similar to those between two or more separate bars, 1884. ] On Magnetic Polarity and Neutrality. 409 the reactions in the solid bar being more pronounced and complete than those obtained throngh a separation of air; the greater the separa- tion the less the reaction, but in no case will the law of neutrality be changed. In homogeneous iron or steel, we have a well-defined curve, the distance of which can be calculated from observation upon the remaining magnetism, but if the interior is harder than the exterior, the inner portion will from its rigidity preserve its previous magne- tism, reversing entirely the outer portions. This occurs also in small electro-magnets where from the small number of molecules in the interior compared with the vastly greater exterior, and also all the surrounding inducing lines of magnetic force acting on the centre from all sides, the outside is completely reversed to a remarkable depth. I have been enabled to prove this by the chemical method, em- ploying either dilute sulphuric acid, acidulated bichromate of potass, or dilute nitric acid (1 pint acid to 5 water), the latter being far more © rapid and equal in its action. The following experiment will show rapidly the influence of the outside reversal polarity. Let us take a soft steel wire 1 millim. diameter, 10 centims. long. Magnetise it in a coil, or by drawing over a strong permanent magnet, so that it has perhaps a remaining magnetism of 200°. If we vibrate this rod or give several blows from a mallet, we can reduce this to 25°; we have now almost perfect neutrality, having only a remaining magnetism of 25°, which remains a constant for years if not remagnetised. Place this rod in dilute nitric acid, and in fifteen minutes it will rise to 50°, or double its previous value, in one hour to 75°, and two or three hours to 100°, or four times its previous force; the increased force of 75° has been rendered evident by dissolving an equal opposing polarity of 75°, so that we have already found 754+75+25 =175°, or 87 per cent. of its highest force. This is so easily repeated with soft steels of all sizes and dimensions, that there can no longer be any doubt as to the existence of the outside reversed polarity. The experiment is more difficult to repeat with soft iron, as from the freedom of its molecules a fresh outside reversed curve is formed anew as the exterior is dissolved, the balancing curves reproducing themselves until we have almost entirely dissolved the iron; still with care, and iron not too soft, we can render evident all the neutral curves seen in steel.* The curves obtained by the various methods are so numerous, each requiring more space than the limits of this paper will allow, that I * Thin flat steel, such as clock-springs, saw-blades, or ribbon steel, well annealed, are most suitable for this experiment. They may be of any width or length; the thickness may vary between 4 and $ millim. i have found that strips of } millim. thick give the highest result. 410 Prof. D. E. Hughes. [ Mar. 6, am forced to give roughly the general outlines, as in fig. 1. Suppose we take a compound bar of iron, of eleven strips, and draw it over a permanent magnet, polarising its lower side only, its neutrality may be found nearly perfect, or 15° of remaining north polarity at the north end; now on carefully separating these rods and observing the same ends, we have for the lower or the side which had been + NORTH: 2140" ¢ POLARITY ~ 120°" A W100 | NEUTRAL FE ieee rf | SOUTH | POLARITY. © MILIMETRES OF IRON IN THICKNESS. magnetised, 350° north; the following successively observed would give 10° south, 35° S., 55° S., 60°.S., 50° S., 40° S., 22° S., 10° S., 6° S:, 5°S.; here all the superposed bars are opposite in polarity to the exterior 350° north, the total south observed being 292, plus 30° south obtained from the exterior, by the coating of its lower face with the zo milim. of iron strip already mentioned. We are thus enabled to account for 323° degrees south, and 350° north, leaving a remaining magnetism unaccounted for of 12°, which was doubtless disseminated on the surface of each bar on separation. The above curves were obtained from the same polar (north) end of a compound bar of iron, the south or opposite end of the bar would give reversed curves to these. The curves are reductions to a similar force, but do not exhibit the perfection of the curves obtained on a larger scale. No. 1 represents the typical curve of penetration of a bar of iron, whilst under the influence of an exterior polarising force, applied at A, or only at one side of a bar. When the force is applied to the whole of the exterior surface (as in a coil), A would represent the polar force on its surface, whilst B the interior. In all cases there would be a depression at the centre; great if the bar is thick, and com- paratively small if the bar is thin. The curve rises with the exterior polarisation force, but in no case can a reversal ensue whilst under its influence. The instant, however, that it ceases, the higher magnetic power of the exterior layers reacts gradually and successively upon the weaker interior layers, rotating them through neutrality to a strong opposite polarity. 1884. ] On Magnetic Polarity and Neutrality. — All This is seen in No. 2, which represents exactly what takes place in No. 1 upon the cessation of the inducing influence. We notice that the first portion of the exterior has rotated to south polarity, followed by an intense north, but not of great density ; its reaction, being more violent, rapidly rotates all the interior to a south polarity, gradually weakening in intensity as the distance increases from the inducing north polarity. The exterior, in fact, reacts upon its interior precisely as before the inducing exterior magnet reacted upon the whole. In No. 1 the south pole of the permanent magnet produced a continuous curve of north the instant this ceased, the north of the exterior produced an interior south, and if these are perfectly balanced, then and then only will the bar become neutral. When both sides of a bar are polarised at the same time, then we have two similar curves to No. 2, as shown at No. 3, the diminishing curves of internal opposing polarity overlapping each other; the curve represents those obtained on bars 2 centims. in thickness. If the inducing force is great the penetration is greater and more intense, reacting more violently, and the central depression of the opposing waves is less pronounced. If we keep the previous force and diminish the thickness of the bar, the two central waves cross each other, and at last, as in No. 4, we have only one wave; this occurs with bars of but 3 millims. thickness. We notice here that from a want of sufficient material in the centre of the iron, it is constrained to force its central wave to a far higher degree, and that the exterior now also commences to be reacted upon more violently. Hvidently the conditions are strained, and we shall see the result later. This want of sufficient material to form the internal opposing wave of polarity is shown when we reduce the thickness of the bar to 1 millim., the width being 3 centims., and the length 30 or more, as in all pre- vious cases. Here there are no traces of an internal curve, the opposing polarity, as shown in No. 5, being entirely on the sur- face. I have shown that we may clearly perceive this curve by dissolving its exterior in dilute nitric acid, but as I employed vibrations to reduce it to neutrality, this might give rise to objections on the score of mechanical reactions. To meet this objection several strips of magnetised steel of various forms, but all 5 millim. in thickness, were reduced almost to neutrality by simply heating them to a dull red heat, allowing them to cool slowly. These gave remarkable results, proving that the vibrations caused by heat are similar in results to mechanical vibrations, and I found that in most cases their external evident magnetism was increased 100 per cent. by an immersion of fifteen minutes, and 600 per cent. in one hour. Interesting results can be obtained by this method, but if rapidity of chemical action is desired we must first remove the scale or oxide 412 Prof. D. E. Hughes. [ Mar. 6, on the exterior by polishing with emery paper, or dissolve this first in acidulated bichromate of potass. A perfect curve of these opposing polarities can be obtained by placing a glass vessel containing the steel and solvent in the balance itself, taking continual observations during its solution, and we may thus observe the gradual rise in force to a maximum, then its fall to zero, to an opposing polarity, completely verifying all previous obser- vations. Supposing the magnetised steel previous to heating gave 200° we should reduce it to 50° if heated to dull red, a bright red heat would probably reduce it to 20°; we should then start from an almost perfect neutrality to find, on dissolving its exterior (and allowing for the reversed polarity of the reversed portion), all its previous polarity. Faraday remarked that the magnetic qualities of iron disappeared at yellow-red heat (1050° C.), reappearing gradually when cooled to red heat (700° C.). I have found that if we heat the steel to yellow- red heat the whole previous structure disappears, and does not re- appear on cooling. No satisfactory explanation, as far as | am aware, has been offered relative to the disappearance of the magnetic qualities of iron and steel at certain temperatures, but noticing that its internal structure is also changed, the following hypothesis may explain the phenomenon. Assuming that increased heat increases molecular vibration, and that molecules would oscillate to a degree dangerous for the stability of any previous structure, a moment would arrive when the oscilla- tions were so great that all structural formations disappear; and precisely at this instant there would be no externai evidence of polarity, or magnetic quality, as the molecules would be oscillating through a range on both sides of external neutrality. On cooling (the previous structure having disappeared) they would satisfy their mutual attractions by the shortest path, forming probably, if perfectly free, a closed circuit of two, grouping themselves as a double mole- cule; but if a directing influence, such as a continuous current of electricity, was passed through the bar, then they would obey this influence, and in the latter case the closed magnetic circuit would be in concentric circles, as I have demonstrated in previous papers. A similar effect is caused by mechanical vibrations. I have already shown that we increase the internal curves by gentle blows of a mallet, thus allowing the molecules sufficient freedom to follow their path, as in the case of red heat; but if we strike violently upon the end of the rod, the whole structure is broken down by the violent oscillations of its molecules, and the neutrality now resembles exactly that produced at yellow-red heat. The theory of symmetrical neutrality which I have demonstrated, 1884. ] On Magnetic Polarity and Neutrality. 413: requires that there should be a sufficient thickness in a bar of iron or steel in order to produce asymmetrical opposing polarity. Coulomb’s. theory of the neutrality taking place in the molecule itself requires. no thickness except that of a molecule. Ampére’s theory could allow of heterogeneity on the surface as easily as in the interior, con- sequently thickness of a bar would, according to these theories, have no favourable result; but if the theory that I have advanced is true,, thickness should have the greatest possible influence. An extremely thin strip or bar of iron should have an infinitely higher proportionate: remaining magnetism from the want of interior reaction, whilst an extremely large solid bar should have infinitely less proportionate remaining magnetism. This at once allows us to test the truth of the theory by an independent method free from all experimental errors, as we may place in the coil of the magnetic balance bars of iron or steel of different degrees of thickness, observe their magnetic capacity whilst under the influence of an electric current, and the degree of remaining magnetism on its cessation, and note the extraordinary influence which thickness has in allowing space for the opposing waves: of polarity to produce instantly a higher degree of neutrality than is possible without its aid. The conditions of the experiments are really those of ordinary electro-magnets, the iron or steel under observation is simply at the time of observation a core of an electro-magnet. Numerous experiments were made on this subject, all confirming the views advanced. A few examples will be sufficient to include them all, for if we place in the coil of the balance different thicknesses of the same diameter and length of iron or steel, we notice a marked rise in its exterior force or magnetic capacity while under the influ- ence of the electric current, and upon its cessation an equally marked return to a more perfect neutrality with each increase of thickness. The table on the following page contains sufficient examples to show this clearly. This table gives the results of round cores; experiments, how- ever, were also made with flat bars with like results, the form or length haying no direct influence, as the reactions are transversal and localised from a point in the exterior to one in the interior. Comparing No. 1 of the table (consisting of an extremely thin sheet-iron tube) with No. 2 (a solid bar of iron of exactly similar size), we have for the thin tube a remaining magnetism of 50 per cent. of its previous polar force, and in the solid bar we have only 3 per cent.; whilst in the solid bar, where the opposing waves of polarity could easily form and produce a near approach to neutrality, we find that its polar force under the influence of the coil is 400 per cent. greater than that of the thin tube. Although, as well known, hard steel has a higher retaining power, 414 Prof. D, E. Hughes. [ Mar. 6 Es g.2 “a ial ga | &S ~ Ol a2 & S| 8% &0 cob) fe gas | aes dao ale 1 Daniell] 898 element.| ¢¢ 1. Tube of thin soft iron, 2 centims. diameter, 20 centims. 5 E lomesy- 2. anil limi iniclan ess erreelererpeeeicienslei-lenerate terreno 106 2. Similar size solid rod of soft iron. 960 29 3. i », cast steel, tempered ...... 458 18 4. 5 », bundle of 1 millim. diameter soft i iron wires | 1268 142 5. x », glass tube filled with iron filings... 160 15 6. Soft Swedish iron wire, 1 millim. diameter ...........| 455 105 7. Hard tempered cast-steel wire, 1 millim. diameter..... Mai 16 8. Brass Hlectro-plated with f {3 centims. dia meter 0:95 0-94 tube iron extremely thin PAO long.. 9 Electro-plated with iron 109 ; os to =, millim. thickness a ” 10. 5 Ditto, 1 millim. thickness » 401 72 Tak 1 centim. ‘ 4 contin! diameter | 1075 35 99 3) still, this can be reduced far below that of the soft thin iron if sufficient thickness is allowed in order to produce the internal reactions. ‘This is shown in No. 3, where a solid 2 centims. diameter of hard-cast steel has double the force of the thin soft iron under polarising influence, and its remaining magnetism only 4 per cent. of its previous force. This shows clearly that Jamin’s views of the superiority of thin steel bars over thick where permanent magnetism is desired, are fully confirmed, as in order to have raised the cast- steel 2 centims. thick bar to a high remaining magnetism, we should have had to employ at least fifty times stronger inducing force than that necessary for the thin bars. The proportion of remaining magnetism in iron or steel to the inducing force is almost similar throughout the entire range up to saturation, where the remaining magnetism is no longer proportional to the inducing power, but remains a constant, no matter how high and powerful the influence excited. The molecules have simply then rotated to parallelism and cannot rotate further without diminishing its force, and the sudden spring back to a partial neutrality is then the same for all forces above that of saturation. The proportion of remaining magnetism to that of its magnetic capacity under the influence of an inducing field, is shown in Nos. 6 and 7, where iron and steel wires of similar diameter have not a wide difference, the remaining magnetism here 1884. | On Magnetic Polarity and Neutrality. 415 being 25 per cent. for iron, and 33 per cent. for steel of its propor- tionate previous force. The most conclusive experiments, however, will be seen in Nos. 8, 9,10,and11. No. 8 being a brass tube coated with an exceedingly thin transparent coat of iron (I was unable to measure its thickness), this thin coating of iron was easily raised to its saturation by a feeble battery, from which point no increase of battery power had the slightest effect, giving always 0°°95. The extraordinary effect of thinness was seen on taking off the inducing influence, no perceptible movement of the needle on the balance occurred, indicating that its retaining power was the same as its capacity or 100 per cent. of retention; vibrations and hammering which reduce a solid bar at once to perfect neutrality had no effect. I have, however, marked it down as 0°94 asa limit of experimental error; if we assume only 80 per cent. of its previous force it is still sufficiently remarkable. At No. 9 where the brass was coated to a measurable thickness of ~5 millim., we already see a better return to neutrality, having now only 50 per cent. of proportionate remaining magnetism; at No. 10, where we have 1 millim. thickness, we have improved our neutrality by having only 20 per cent., and at No. 11 we have, by means of an increased thickness of 1 centim., almost completely allowed the balancing waves of opposite polarity perfect formation, the remaining magnetism now being only 3 per cent. of its proportional power; and if we even neglect the proportional power, we see that the 1 centim. bar has far less remaining magnetism than that of 1 or 5 millim., whilst its magnetic capacity is far higher. No. 4 shows that while bundles of wires have a higher remaining magnetism than solid (due to the want of homogeneity allowing perfect formation of the opposing waves), still from their increased surface exposed to the inducing effect they give a higher magnetic effect, the differential effect (as that employed in temporary electro- magnetic and induction coils) is greater, being here for a solid bar 960—29=931, and for the bundles of iron wire 1,268—142=1,126 useful effect.* The effect of thickness even upon finely divided iron such as filings is Shown in No. 5, where the remaining magnetism is only 9 per cent. against 50 per cent. as shown in No. 1, and we have precisely similar * If we require a continuous magnetic effect, as in the field magnets of dynamo machines or small constant electro-magnets for extremely feeble electromotive force, solid cores or bundles of wire of large diameter should be employed, but as the time of charge and discharge increases with the diameter, it would be unsuitable for electro-magnets requiring rapid charges, such as those employed for telegraph relays, large electro-magnets requiring several seconds to charge them to saturation, while extremely small electro-magnets may be saturated in the +545 part of a second. A16 On Magnetic Polarity and Neutrality. [ Mar. 6. results with thin slices of iron filings as we do with the solid iron in ‘Sheets or tubes. . It would be difficult to explain these effects upon any hypothesis except that of molecular rotation. For, if we regard it as simply a case of magnetic induction, the stronger reacting upon the weaker, we fail to explain the perfect spiral form of the opposing waves, and ‘above all, the reversal of the exterior, which was evidently the most ‘strongly polarised, but if we suppose that the similar polarities of all the molecules have rotated, symmetrically pointing their north polarities to the evident north end of the bar, we have only to imagine a series of magnetic needles superposed with all their north polarities pointing in one direction brought and held there by the influence of a strong external magnet. If this influence was nearer the first needle than the last, we should have a slight spiral due to its diminishing effect, precisely as we notice in the curve in iron whilst under external influence. Now withdraw the exterior force, the needies would react against each other, and as they are free to move in all directions, there would be an increased spiral, the outside being reversed to its previous position, while the spiral would continue in the interior, reversing the larger portion of the needles until they all found a position of equilibrium, which would then represent neutrality. If we had no frictional resistance to molecular rotation, we should obtain perfectly balanced curves in comparatively thin iron, but as this resistance is great and demonstrated by the loosening influence of mechanical vibrations, we require a certain depth of iron so that a complete curve shall be easily obtained with comparatively infinitely small motion of each molecule. That inherent magnetic polarity is a quality of all matter, solid, liquid, gaseous, and the ether itself, varying only in degree and not in nature, seems demonstrated by a series of researches I have been making upon the mechanism employed in magnetic conduction through the atmosphere and Crookes’s vacuum. These researches are being made by means of the induction and magnetic balance. They prove that the atmosphere, and presumably the ether as well as all liquids and gases, have their saturation point similar to iron, that the curve is the same as in perfect soft iron, and that the highest magnetic capacity of iron does not exceed that of the atmosphere by more than forty times, consequently we may fairly assume that the ether may be regarded as an extremely magnetic body, obeying the same laws as those of iron; and as I regard the symmetrical rotation of magnetic molecules as the cause of evident magnetism in iron, and as the difference in force between iron, copper, and ether is simply a differential one, I believe that the neutrality which appears in all paramagnetic and diamagnetic bodies, wherever 1884. ] On the Origin of Fibrin Ferment. A17 the exciting influence is withdrawn, is formed by mutual molecular reactions producing closed circuits of mutual attractions as demon- strated in iron. A line of force between a magnet and its armature is to me simply a line of molecular rotation, lines would neither be added nor subtracted, they could simply be rotated from a symmetrical neutrality to an equal symmetrical point of saturation. In my paper upon the theory of magnetism, I showed that there were several molecular arrangements which produced external neutrality, the circular chain of molecules, when an electric current passes through an iron wire, a neutrality produced by an artificial superposition of a weaker contrary magnetism upon one more internal, and made the supposition that were it possible to have a piece of iron free from the influence of the earth, then (if there had been no previous magnetisation directing the structure) the molecules would short circuit their mutual attractions in the shortest path. The experiments cited in this paper are of an extremely simple nature, and after being verified by independent observers can no longer leave doubt as to the cause of neutrality. W hatever theory we adopt as an explanation of evident magnetism, it will be found that neutrality occurring after the cessation of an external inducing force upon a bar of iron or steel, is the result ot symmetrically opposed polar forces, producing apparent waves of opposite polarity, or reactions between the exterior and interior of a bar of iron. II. “On the Origin of the Fibrin Ferment.” By L. C. Woot- DRIDGE, M.B., D.Sc., George Henry Lewes Student. Com- municated by Professor M. Foster, Sec. R.S. Received February 26, 1884. The “fibrin ferment’ which makes its appearance in shed blood is generally, I believe, supposed to arise from the cellular elements of blood, either from ordinary white corpuscles or from some special kind of corpuscles, the cells so concerned discharging the ferment into the blood or setting it free by their actual disintegration. Without wish- ing to deny that this may be one source of fibrin ferment, I am able, I think, to bring forward evidence that ferment may make its appear- ance in blood-plasma perfectly free from cellular, and indeed from all formed elements, in which case it must arise from some constituents of the plasma itself, and not from cells of any kind. It will be most convenient, perhaps, if I state the facts which I have to bring forward in connexion with two series of experiments. 418 Dr. L. C. Wooldridge. [Mar. 6, I. A measured quantity of blood was received directly from the carotid of a dog into a vessel containing an equal bulk of a 10 per cent. solution of common salt, great care being taken that the com- plete admixture of the blood and salt solution was effected as rapidly as possible. By the help of the centrifugal machine plasma was sepa- rated from this ‘salted blood,” and this plasma was again subjected to the action of the machine until all traces of formed elements were removed. As is well known, a portion of such a plasma diluted with five times its bulk of water coagulates rapidly, whereas the undiluted plasma remains liquid for an almost indefinite time. According to commonly received opinions, such a “ salted plasma ” contains all the fibrin factors, including the ferment, the latter having already passed out of the cells into the plasma; and the reason given of the absence of coagulation in such a salted plasma and its occurrence upon dilution is, that the presence of the salts presents a hindrance to the action of the fibrin ferment, and that this obstructive influence of the salt is removed by the dilution of the mass. No one, however, as far as I know, has taken the trouble to ascer- tain whether fibrin ferment is present in such salted plasma. And, as a matter of fact, itis not; whereas it does make its appearance as soon as dilution with water has taken place, as the following experi- ment shows :— . A portion of the undiluted salted plasma was treated with absolute alcohol in large excess, and the precipitate after being allowed to remain under the alcohol for three or four weeks was dried at a low temperature and extracted with water—that is to say, the plasma was treated in the way usually adopted for obtaining a solution of ferment fairly free from proteids, &c. A portion of the diluted plasma, or rather of the serum resulting from the coagulation of the diluted plasma, was treated in an exactly similar manner. The aqueous extract of the diluted plasma brought about coagula- tion in specimens of magnesium sulphate plasma (such as is usually employed for testing the presence of fibrin ferment) in from ten to fifteen minutes. The aqueous extract of the undiluted plasma brought about no coagulation in specimers of the same magnesium sulphate plasma, even after the lapse of eighteen hours. The conditions of each experiment were made as exactly alike as possible; and the conclusion seemed inevitable that ferment is present in the diluted and coagulated plasma, but absent from the undiluted plasma. This conclusion is, moreover, supported by the following experi- ments:—To a portion of the undiluted plasma above mentioned a small quantity of fibrin ferment was added, in the form of the dried precipitate thrown down by alcohol, 1.e., a mixture of coagulated proteids and ferment. Coagulation took place. I have no record of 1884. | On the Origin of Fibrin Ferment. 419 the exact time elapsing between the addition of ferment and the appearance of the clot, but it was certainly not longer than three or four hours. II. Of the so-called peptone-plasma (1.e., plasma of the blood of a dog after the injection of peptone into the veins, such blood, as is well known, coagulating with great difficulty), freed from all cellular elements by the centrifugal machine, two portions were taken. To the one (A) a quantity of lecithin was added, the lecithin being rubbed up with the plasma so as to be diffused through it; the other (B) was left untouched. Through both a stream of carbonic acid was passed, with the result that while A clotted in about ten minutes, B after the lapse of half an hour showed no disposition whatever to coagulate. Both portions were then treated with excess of alcohol for the extraction of fibrin ferment in the usual way. The aqueous extract of A proved to be exceedingly rich in ferment, producing coagulation in magnesium sulphate plasma in about ten minutes. The similarly prepared aqueous solution of B produced no coagulation at all. Now I have elsewhere,* in discussing the action of lecithin in pro- moting coagulation, shown that the coagulation which is brought about by the addition of lecithin is not due to the lecithin or to any of its products of decomposition acting after the manner of a ferment, or to its carrying a fibrin ferment with it. In this case, therefore, as in the previous case of “ salted”’ plasma, the ferment appears to be absent before coagulation, but to be present after coagulation. I may here call attention to an observation made by Rauschenbach.* This observer found that the addition of yeast to plasma, prevented from coagulating by exposure to cold, brought about coagulation, and at the same time gave rise to the appearance of a large quantity of fibrin ferment. Nevertheless, he completely failed to extract any fibrin ferment from the yeast itself. Now yeast is very rich in lecithin, and it seems highly probable that the coagulation caused by yeast was due to the lecithin contained in it, and hence the appear- ance of the fibrin ferment after the addition of yeast, and consequent coagulation, is quite parallel to the result of the experiment with lecithin and peptone-plasma recorded above. In both cases the ferment appears to have arisen out of the plasma itself. It is possible to obtain a coagulation in peptone-plasma without the addition of lecithin. For this purpose large dilution is necessary, followed by the passage of a stream of carbonic acid gas. But in such a case, however, coagulation is not only long in making its appearance, but the fibrin is formed, so to speak, in successive crops. Thusa feeble coagulation first appears, and if the clot so formed be removed, a * “Journ. of Physiol.,”’ vol. iv. p. 226. + “ Blutplasma u. Protoplasma,” Inaug. Diss., Dorpat. VOL. XXXVI. 2G 420 On the Origin of Fibrin Ferment. [ Mar. 6, succeeding coagulation is observed some time later, to be followed in turn by a third, and so on. When lecithin, on the other hand, is added, without previous dilution, the clotting is speedy and complete. If the serum thus resulting from the coagulation of peptone-plasma brought about by large dilution and treatment with carbonic acid, be examined for fibrin ferment in the usual way, it will be found to con- tain ferment, though much less than could be obtained from a corre- sponding quantity of the same plasma coagulated rapidly by the addition of lecithin. The relative amount of ferment appearing under different circumstances is illustrated by the following experiment :— Of three equal portions of the same peptone-plasma, one portion was simply treated with a stream of carbonic acid gas, without any dilution, and did not coagulate; a second was treated with a stream of the same gas after large dilution, and coagulated slowly ; to a third lecithin was added, and a stream of carbonic acid passed through it, with the result of producing a rapid and complete coagulation. All three portions were treated in the same way for the extraction of the fibrin ferment, and the activity of the three aqueous extracts then prepared was tested under exactly the same conditions, with the help of magnesium sulphate plasma. The first produced no coagulation after the lapse of twenty hours. The second produced coagulation in four hours. The third produced coagulation in five minutes. The amount of ferment seems to be in proportion to the energy of cougulation and the presence of ferment after simple dilution, and the action of carbonic acid gas shows that the ferment appearing after coagulation by the help of lecithin does not come from the lecithin itself. Thus there is a remarkable coincidence between the occurrence of coagulation itself and the appearance of the fibrin ferment, and that in plasma freed most carefully from all cellular elements. I believe, therefore, that I am justified in concluding that though fibrin ferment does not pre-exist in normal plasma, it may make its appearance in that plasma in the absence of all cellular elements, and must therefore come from some constituent or constituents of the plasma itself. I am still engaged in investigations directed to find out what that. constituent is, or what those constituents are. 1884.] — Researches in Spectrum Photography. A21 March 13, 1884. THE PRESIDENT in the Chair. The Presents received were laid on the table, and thanks ordered for them. The following Papers were read :— I. “ Researches in Spectrum Photography in Relation to new Methods of Quantitative Chemical Analysis. Part II.”* By W. N. Hartuey, F.R.S.E., &., Professor of Chemistry, Royal College of Science, Dublin. Communicated by Pro- fessor G. G. STOKES, Sec. R.S. Received February 28, 1884. (Abstract. ) This paper includes an introduction recording the methods which have been proposed by different authors for the quantitative estima- tion of various metallic elements. An account is then given of the length and strength of metallic lines in solutions of definite strength. Under given conditions each solution emits a characteristic spectrum. In the case of magnesium, a minute description is given of the spectra presented by various solutions containing from 1 per cent. to 0:00000001 per cent. of the metal, but in the case of other elements. tabular descriptions of the spectra of solutions containing 1, 071, and 0:01, in some instances 0:001, of metal are given together with care- fully drawn maps. The substances thus treated of are magnesium, zinc, cadmium, aluminium, indium, thallium, copper, silver, mercury, tin, lead, tellurium, arsenic, antimony, and bismuth. The sensitiveness of the spectrum reaction is practically unlimited when applied to magnesium compounds dissolved in water, since it. was shown that with a given length of spark, -55o5555 Of a milligram could easily be detected; when, however, the strength of spark was. greatly increased, but the striking distance between the electrodes left unaltered, the sensitiveness was increased ten thousand-fold. In point. * For Part I see “ Phil. Trans.,” Part I, 1884. 2@2 422 Capt. H. P. Dawson. [ Mar. 13, of fact, one part of magnesium was detected in 10,000,000,000 parts of water, the lines seen under these circumstances being those with wave-lengths 2801°6 and 27941. The spectrum reaction of arsenic is the weakest, those of antimony and tellurium are also weak, while that of bismuth is not strong. In fact it is noticeable that the more strongly basic elements are those with the most persistent lines. HKvidence is afforded in the case of the aluminium spectrum that it is not invariably the longest or strongest line which is the most persistent. The line with wave-length 35844 is both longer and stronger than a pair of lines adjacent thereto with wave-lengths 3612°4 and 3601:1, but whereas the first is not seen in solutions containing 0°1 per cent. of aluminium, the pair are still visible in solutions containing 0°01 per cent. Under certain conditions this single line appears the longest in the whole spectrum, whereas other- wise, and under most circumstances, the lines with wave-lengths 3960°9 and 3943°4 are longest. As a rule, even the longest lines are inottered by great dilution of the solutions, but there is a pair of lines in the spectrum of copper with wave-lengths 3273°2 and 3246°9 which become greatly attenuated, yet nevertheless remain long lines till they finally disappear. It is shown by one or two examples how the tables of spectra and accompanying maps may be employed in rendering quantitative results. The snecial applications of this method it is proposed to describe in a further communication. Il. “On the Mean Diurnal Variation of Magnetic Declination, from Hourly Observations at Fort Rae.” Communicated by Professor G. G. STOKES, Sec. R.S. By Captain H. P. Dawson, R.A. Received February 28, 1884. The accompanying diagrams represent the mean diurnal variation of declination for each month from September, 1882, to August, 1883, at the Circumpolar station at Fort Rae, British North America. These curves are plotted from the hourly means for each month, and include the effect of disturbances which have greatly influenced them during the winter months, especially in November. One effect of an unusual amount of disturbance is an increase of the mean declination; the easterly disturbance, or that tending to increase the declination, being always in excess. 1884.] Mean Diurnal Variation of Magnetic Declination. 423 Mean Diurnal Variation of Magnetic Declination from Hourly Observations at Fort Rae. 2 10 NOON 2 | ie mess saebecattstezi| "Mean -40-ee7 11 ee geass ; heey | | et PEN Eh SCE ECE PPE eee NL, ener j | 1 | a i | : } fe A | a | — AEE | T | EEN Ee | zh } } i ! i. | 4 te tots IN EE 424 - Capt. H. P. Dawson. [ Mar. 13, Mean Diurnal Variation of Magnetic Declination from Hourly Observations at afte Sas elas tsi S ck t : 3 BERS Ale . Phe fracas: PEER 1884.] Mean Diurnal Variation of Magnetic Declination. 495 Mean Diurnal Variation - Magnetic Declination from Hourly Observations at Fort 10 NO Rae. ON 2 eevee eer Bane \ | = | 426 Prof. T. G. Bonney. On the [Mar. 13, III. “ Notes on the Microscopic Structure of some Rocks from the Andes of Ecuador, collected by Edward Whymper, No. II. Antisana.” By Professor T. G. BonnEy, D.Sce., F.R.S. Received February 29, 1884. Antisana is a much loftier and grander mountain than Pichincha, for its summit rises to an elevation of about 19,000 feet above the sea,* and the upper part of the mountain (some 4,000 feet) is covered with snow and glaciers. The crevasses on the latter are described by Mr. Whymper as being of an enormous size, probably the largest he had ever seen, and on his first attempt to ascend the peak he was pre- vented from reaching the summit by chasms and cliffs of ice, among which his party, in consequence of the mists, had become entangled. A second attempt proved successful, but the snowy summit of Antisana is evidently not one likely to be reached by unpractised mountaineers. The mountain is situated slightly to the south of the equator, to the east-south-east of the city of Quito, and nearly due east of the town of Machachi. ‘The extent of ground covered by Antisana,” accord- ing to Mr. Whymper, “‘is, perhaps, as great as that covered by any of the Ecuadorian Andes, and more than is occupied by most of them. From north to south it extends over more than 20 miles of country, and not much, if at all, less from east to west. From most points of view at a distance, the mountain in form appears more like a ridge than a single summit. A close approach on the western side shows that this appearance is somewhat misleading, and that Antisana has two principal summits, the larger and higher being an immense snowy flat-topped boss, and the second (not less than 1,500 feet lower than the other) a sharp peak, which is probably at all times completely inaccessible.” The lowest point to which the glaciers extend on the western side is 15,294 feet; on the northern and southern they descend to about: the same level; but Mr. Whymper is not able to say how far they come down on the eastern side. ‘In that direction the most notable feature of the mountain is a very extensive shoulder running out from near the summit, at a height of about 17,000 feet above the sea, in an east-north-east direction. It is singularly level and unbroken in outline, and is entirely obscured by a snow-covered glacier, suggest- ing by its form that there is an old flow of lava concealed beneath. “There is no trace of a crater anywhere near the summit upon any side, but the snow covering the flat-topped boss, forming the higher * Whymper, mere. bar., 19,335 feet; Reiss and Stiibel, A, 18,885 feet. It is thus about third or fourth in order of elevation among the summits of Ecuador, being about as high as Cayambe, but lower than either Cotopaxi or Chimborazo. 1884.] Microscopic Structure of Some Rocks from Ecuador, 427 point, may possibly fill and hide a crater. The diameter of the nearly level area which forms the summit is about equal to that of the lip of the crater of Cotopaxi. It is also certain that there is no open crater on any part of the western slopes of the mountain.” Of the remainder Mr. Whymper says: “I speak with less confidence of the northern and southern sides, as I have not seen completely round them, and of the eastern side I can only speak of the parts not more than 1,000 feet below the summit. Upon my first and unsuccessful attempt to ascend the mountain we were stopped for a considerable time (by the difficulties encountered) at a height of somewhat more than 17,000 feet above the sea, and, whilst waiting, we noticed several pufis of strongly sulphurous vapour. We did not, however, observe either upon the summit, or when viewing it from a distance, anything of the nature of an eruption, or learn from the persons living in the vicinity of the mountain that any eruption had occurred to their knowledge.” Mr. Whymper’s collection from Antisana consists, as in the case of Pichincha, of a series of ten specimens obtained in Quito, and fourteen collected by himself. Four of the latter shall be described first, as they come from the lower part of the mountain, from a spot ealled Antisanilla, which however is 12,340 feet above the sea. Here a hacienda abuts against a great lava stream which has descended from the mountain, and is the one most familiar to the natives of the dis- trict. Mr. Whymper remarks that it was the only large stream of lava which he observed on the western side of the mountain running on towards the west: “ Its full extent Ido not know, owing to mist. We coasted its southern side for 5 or 6 miles on the way to the Hacienda of Antisana (13,300 feet), and the small Hacienda of Antisanilla, an appendage of the large establishment, is built by the side of the lava stream, which was by various persons several times termed in my hearing the lava of Antisanilla. The surface of the stream was extremely rugged and well-nigh inaccessible.” From this lava Mr. Whymper collected specimens: the one selected for microscopic examination is a black sub-vitreous rock, containing small crystals of white felspar, whose diameter is commonly not more than 0°125 inch. The general aspect of the specimen shows it to be one of the darker varieties of andesite, a member of the group of rocks that have been variously named melaphyre, pitchstone-porphyrite, &c. The crystals belonging to the earlier stages of consolidation which are included in the slide are rather small, no one of the felspars ex- ceeding 0°1 inch, and only one or two approaching this size. They are plagioclastic, but as the majority have broken away in grinding the slide, one cannot venture to give a more definite name. The crystals of pyroxenic minerals are yet smaller; most of the latter occurring either in small scattered crystals about 0°006 inch long, of rather 428 Prof. T. G. Bonney. On the [Mar. 13, elongated form or in small granules. Owing to the smallness and rather indefinite character of the pyroxenic constituents it is difficult | to speak very positively about them; augite, however, is certainly present, and possibly hypersthene. Minute crystals and grains of an iron oxide, probably magnetite, as we might expect from the colour of the rock, are rather abundant. The ground-mass appears to consist of a clear glass, faintly tinged with brown, and densely crowded with microliths. These are lath-like crystallites of felspar, generally not exceeding 0°005 inch long, not seldom composed of two or three individuals, and belonites, of a very faint green tinge, not exceeding about 0°001 inch by 0:0002 inch, probably hornblende. The evidence as to the felspar is conflicting ; probably both oligoclase and labradorite are present, but my observations tend to the conclusion that the latter is the more abundant species. The rock on the whole agrees best with augite-andesite. Its specific gravity, determined for me by Mr. J. J. H. Teall, is 2°656. A second specimen from the same locality resembles the former in structure, but is of a dull india-red colour. It is so evidently the same rock, differently coloured by conversion of the black oxide of iron into the red oxide, that I have deemed it needless to examine its microscopic structure. The two other specimens are simply scori- aceous varieties of the latter rock. It is difficult to fix the precise localities of most of the specimens obtained by Mr. Whymper from the collector at Quito, as the places mentioned on the labels are not known to the former, and in most cases, he thinks, are of no more general acceptation than the names attached by Alpine herdsmen to the crags and pinnacles in the vicinity of their chalets. All, he believes, are from the south-western or western side of the mountain and from localities whose height above the sea is not likely to exceed about 13,000 feet. Three are pro- bably derived from some one subsidiary crater on the south-western flank of Antisana, named Guagra-ialina, though there is a slight variation in the spelling. The first of these is labelled Corriente de lava de Guagrahialina volcan, Lado 8.0.0. Antisana. It is a dark grey rock, of scoriaceous aspect, with many small vesicles, usually less than 0°1 inch in diameter, and several specks of whitish felspar. It resembles some of the dark grey lavas of Auvergne, and, like them, is no doubt an augite-andesite. As the specimen presents no features of special interest, I have not examined it with the microscope. The next is simply labelled Antisana, Guagrayalina volcan. It is a com- pact dull grey rock, with a slight purplish tinge, containing occa- sional crystals of glassy felspar, sometimes rather more than 0°] inch in length. These, on examination with the microscope, prove to be a plagioclastic felspar, but there is so much variation in the extinc- tion angles that it is impossible to decide upon the species. They con- 1884.] Microscopic Structure of Some Rocks from Ecuador. 429 tain, in variable amount, cavities with bubbles, brown glass enclosures, and other microliths, some being elongated prisms which may be apa- tite; but probably more than one mineral is present. There are also some small fairly well-defined crystals of augite, but I have not suc- ceeded in identifying any hypersthene. A remnant of a glassy base appears to be present in the ground-mass, but itis so crowded with fel- spar microliths, and with granules of iron peroxide and of augite, as to be with difficulty distinguished. The felspar microliths are lath- shaped ; they area plagioclase ; but, as in the case of the larger crystals, it is probable that more than one species is represented. The rock is an augite-andesite, and its general aspect reminds me of some of the porphyrites of the Cheviots (e.g., a hypersthene-andesite from Coquet, near Windy Haugh). ‘The third specimen, labelled Guagra-ialina volcan, lado S8.O. del Antisana, is a rather duller coloured, less markedly porphyritic rock than the last, having some minute vesicles. The microscopic structure does not differ materially from that of the last described. Possibly a little hypersthene is present, but this is not conspicuous; thus the rock is an augite-andesite, and all these Specimens may have come from different parts of the same flow or from a closely related series of flows. _ From Quebrada de Urcucuy come two specimens of pitchstone. One, labelled entre Tablarumi y Urcucuiloma, is a dark greenish-grey rock, traversed by numerous cracks; its fracture is very irregular, and it ex- hibits the resinous lustre characteristic of pitchstone. A few minute scattered crystals or grains of a glassy felspar are visible, and there is a very faint indication of a fluidal structure. When examined microscopically, the rock exhibits as a base a clear and colourless glass. In this are scattered a large number of microlithic enclosures together with some scattered crystals of larger size. The general parallelism of the longer diameters of both of these, and the occa- sional filamentous streaks of an aggregated grey dust render the fluidal structure more conspicuous microscopically than macroscopi- cally. The great majority of these microliths are little prisms or columns, usually about 0:001 inch long, and commonly about one- sixth of this in breadth. They are almost colourless, but appear to have a slightly green tinge. I think it probable that, like the belonites in the Arran pitchstones, to which they present some resemblance, they are hornblende. SBesides these, we find opacite, with occasionally a fleck of brown mica or felspar crystals of small size. The “dusty”? bands are found to resolve themselves, when viewed with a quarter-inch objective, into streams of microliths, like to, but perhaps slightly smaller in size than, those described above. Among the larger crystals are felspar: of this mineral orthoclase and a plagioclase are present. Some of the crystals are rather broken or rounded in outline, but others have well-defined external angles ; the 430 Prof. T. G. Bonney. On the [Mar. 13, latter are generally smaller and clearer, containing a few belonites, and but little else. The former are often “dirty,” containing glass enclosures, cavities, and various microliths, as if belonging to an earlier stage of consolidation. Besides these are several crystals of brown mica and a few of hornblende, well defined, together with scattered grains of magnetite. The cracks are marked by a pale green staining, and there are no indications of a perlitic structure. The other specimen of pitchstone labelled entre Tablarumi y Chacana is of nearly the same colour as the last described, but contains many rounded whitish spots, roughly about ;5 to 4 inch diameter, which are seen on examination to be spherulites ; « portion of the specimen is vesicular. The description given of the base of the last specimen will serve for this, except that there is little indication of a fluidal structure. There are a few scattered crystals of felspar, brown mica, and hornblende. The spherulites are rather peculiar, they have a rather irregular bluntly lobed outline, are nearly opaque, but exhibit a faintly fibrous structure, something like that of groups of blunt-pointed camel’s hair brushes. So far as can be ascertained, they consist of a brown glass traversed by belonites of a paler mineral, and trichites of a darker one, but it is very difficult to determine their exact structure. They generally enclose a small crystal of hornblende or felspar, in one case both are present, but not centrically disposed. Without chemical analysis one cannot decide whether these two rocks are glassy forms of the rhyolites or of the dacites, but I should be disposed to class them with the latter.* A third specimen from Quebrada de Urcucuy, labelled in addition Entre Tablarumi y Ureucuy, is a crumbling pale cream-coloured rock, which, on closer examination, gives indications of having been glassy and of a somewhat perlitic structure. This is confirmed by micro- scopic examination, though the nature of the rock has prevented the preparation of a good slide. It is evidently a decomposed perlitic pitchstone, and very probably when in a fresh condition was nearly related to the two others from this neighbourhood.* From the south western side is a specimen labelled Quebrada azufre grande, 8.0. Reiss and Stiibel, as Mr. Whymper informs me, mention a ‘“‘ Quebrada azufre grande,” giving a measurement Parte inferior de la Loma al lado derecto de la Quebrada, &c., 4,040 métres: (13,255 feet). The name signifies ‘“‘Great Sulphur” ravine. This * Since the reading of this paper Mr. J. J. H. Teall, F.G.S., has kindly deter- mined for me the specific gravity and silica percentage of the former of the two pitchstones. S.g.=2°337; Si0,=72°99, the loss on ignition being 115. These determinations fully confirm the microscopic analysis. + A spherulitic pitchstone from Antisana is described by Vom Rath, “ Verh. Nat. Ver. Preuss. Rheinl.,”’ Folg. 4, Bd. 1; “ Sitzungsb.,” pp. 173, 174 (1874). 1884.] Microscopic Structure of some Rocks from Ecuador. 481 altitude is a little lower than the Hacienda of Antisana* (13,300 feet), and so, if the indication of direction be correctly given, cannot be so near as it to the summit. The specimen is a rather compact cream-coloured rock, at first sight not unlike one of the South Tyrol dolomites, but slightly vesicular in places, and spotted here and there with pale yellow sulphur. It is evidently a volcanic rock from the vicinity of fumaroles which deposit sulphur, and presents the usual aspect of a trachyte which has been thus treated. From the appearance of the rock, and a certain resemblance to one of those described, from Quebrada de Urcucuy, I should think it probable it had once been a pitchstone. A specimen is labelled Del Nevado Pic O, principio del Arenal; the ““snowy peak” and the “sandy plain” of Antisana are localities un- known to Mr. Whymper. The rock is subvitreous, dark in colour with slightly redder streaks, and numerous scattered crystals of white felspar, commonly not more than about 0°1 inch long, but now and then twice or thrice as large. In the earliest stage of consolidation are (1) plagioclase felspar (probably in part at least labradorite), some- times irregular in external form, often crowded with glass cavities, having fixed brownish bubbles, with microliths of augite (?), and with opacite ; (2) augite; (3) very characteristic crystals of hypersthene ; (4) granules of iron oxide and a few scales of iron glance. The rock has a glassy base, but this is crowded with lath-shaped felspar microliths (plagioclase), and in most parts is rendered almost opaque by dusty opacite and ferrite, the redder streaks being the more transparent parts, in which a glass, now clear, now brown, may be distinguished. The rock is a hyperstheniferous augite-andesite. The locality of the next specimen, labelled Cuspide del Achupallas Lado O. del Antisana, is also unknown to Mr. Whymper. The rock has a deader lustre, and more scoriaceous aspect than the last described, and contains greater crystals of whitish felspar, their diameter being sometimes fully 0°3 inch. Under the microscope the larger of these are seen to contain glass enclosures and other microliths, and are probably labradorite; the smaller, which are more lath-shaped, agree better in their extinctions with oligoclase. There is a fair amount of well characterised brown mica and of hornblende, both brown and pale green varieties, with some granules of the latter or possibly of augite, and some grains of iron oxide. There is a clear glassy base, * Reputed to be the highest farm in Ecuador. ‘‘It is situated on the western slopes of Antisana, in a cheerless situation, without a tree in sight, and is enveloped in fog the greater part of the year. The lower slopes of Antisana are of immense length and very devoid of character on this side. The upper 4,000 feet of the western side of Antisana is almost entirely covered by glacier. The nearest to the hacienda ends at an elevation of 15,295 feet.”” (EH. W.) 432 Prof. T. G. Bonney. On the [Mar. 13, but it is crowded with microliths of felspar, of a pyroxenic mineral, of brown mica, ferrite, &e. The rock is thus a mica-hornblende- andesite. The last specimen is labelled Cuspide del chusa longo. It is a dark grey vesicular rock, the proportion of solid to cavity being about two to one. The cavities commonly are not more than 0-2 inch in longest diameter, irregular in form, slightly drawn out in one direction, and coated with brown iron oxide. The rock is compact in structure, with a general resemblance to the matrix of the last described, but contains only very minute crystals of whitish felspar, rather irregular in form, and hardly more than 0°05 inch in diameter. It is no doubt: an andesite, and is not unlike some of the scoriaceous varieties of that rock which are obtained from the Auvergne volcanoes. I have not thought it necessary to examine it with the microscope. The remaining ten specimens brought back by Mr. Whymper are all representative of the highest part of Antisana. They were col- lected from the upper part of a moraine, by the side of which he encamped for the night, at an elevation of about 16,000 feet above the sea, or 3,300 below the actual summit. The materials of this moraine are derived from several rather small crags of rock which here and there crop out from the snowy slopes above. None of them were touched by Mr. Whymper during his ascent on the following day, for they are not numerous and are generally in inaccessible positions. He was careful to bring a specimen of every marked variety which caught his eye, so that the series is probably a fair representation of the rocks which constitute the Peak of Antisana. Of these specimens (1) and (2) are vesicular rocks of a dull reddish colour, no doubt scoriaceous forms of a rock closely allied in composi- tion to (4) and other dark varieties described below. (8) is a tuff, consisting of a fine yellowish paste, in which are numerous fragments up to the size of a small nut of a slightly vesicular, subvitreous,, blackish rock, evidently closely allied to the next mentioned. (4) isa biackish subvitreous rock, containing glassy-looking felspar crystals. up to about 0°2 inch diameter. A few minute vesicles are present. The microscopic description is given below. (5.) A very similar rock, a little lighter in colour, also described more fully below. (6.) Closely allied to the last, but paler, probably a little more decomposed. (7.) A dark compact rock, with some small crystals of felspar; very like the: specimen from Antisanilla. (8.) A compact blackish rock, mottled with small spots of dull gray, in the inner part of which a small vesicle may be seen; a very few crystals of felspar, not exceeding 0-1 inch diameter, are visible; its microscopic structure is described below. (9.) A rather vitreous, slightly vesicular, rock, a fluidal structure being indicated by reddish and blackish layers, containing crystals of a whitish felspar, rarely exceeding 0'1 inch in diameter. The microscopic structure is described below. (10.) A large fragment 1884.] Microscopic Structure of some Rocks from Ecuador. 433 of dull reddish-gray not very vesicular scoria, probably lthologically in close alliance with (1) and (2). The following is a description of the microscopic structure of No. (4). In the earlier stage of consolidation are (a) felspar crystals, probably in great part labradorite. The enclosures are frequently variable in nature, quantity, and arrangement. Sometimes their dis- position is zonal and external, sometimes it is central. Among these enclosures are pale green belonites (? hornblende), colourless belonites, pieces of brown glass, often abundant, containing gas cavities and crystallites of magnetite, cavities containing bubbles, which occupy one-sixth or one-seventh of the whole space. The exteriors of the crystals are frequently broken-looking or corroded. (6) A pyroxenic constituent, of which some is certainly augite, but a part (the smaller) probably hypersthene. The former rather frequently contains enclo- sures; among them are magnetite and grains of a slightly irregular oval outline, sometimes nearly 0°003 inch diameter, occasionally asso- ciated with gas cavities (? felspar). (c) Grains of iron oxide, pro- bably magnetite. The part of later consolidation is a pale brownish glass, speckled with opacite and crowded with acicular microliths, six or seven times as long as broad, which generally do not exceed 0°001 inch long. ‘These are colourless and probably to a large extent felspar. No. (5) differs from the last rock but little in its microscopic structure; it has a rather clearer ground-mass and perhaps not quite so many granules of black iron oxide. The crystals of felspar are similar, but there is also a large number of well-formed lath-shaped crystals, measuring in longer diameter above 0°01 inch. Two varieties of augite, a greenish and a brownish, are present, together with a little of the greenish mineral which, as it has an orthorhombic extinction, I refer to hypersthene. Microscopic examination of (8) shows it to be not materially different from (4), except for the presence of the more decomposed spots, mentioned above. The glassy base is perhaps a shade more colourless. Both augite and hypersthene are present. No. (9.) In the first stage of consolidation we have rather numerous felspar crystals, with the usual variable enclosures—glass cavities with fixed bubbles, microliths, nearly all of which exhibit the charac- teristic twinning of plagioclase, though one or two show Carlsbad twinning and may be orthoclase. The former usually extinguish at moderately large angles, ranging from rather less than 10° to more than 20° with the twin-plane. In one, where the twinning is sharply defined, the extinctions are 21° and 30° respectively on either side of the twin-plane. It is therefore probable that these crystals are neither albite nor oligoclase. The pyroxenic constituent appears, as above, to be of more than one kind. The most abundant is a brownish, rather dichroic mineral, black bordered, and sometimes rather “ dirty,” owing to inclusions. In colour and general aspect it more resembles 434 Prof. F. Elgar. On the Variation of [ Mar. 13, hornblende, but the angles of cleavage (which, however, is in no case very well defined) and of extinction make it more probable that the mineral is augite. There are two or three crystals of a slightly greenish colour, which show the characteristic form and cleavage of augite, and one which in all respects better agrees with hypersthene. The ground-mass consists of fairly numerous, lath-shaped crystallites of a plagioclastic felspar, prisms of augite (?), often darkened with ferrite, granules of opacite and ferrite, and possibly in some cases flakes of mica. These are scattered in what may be a glassy base, but it is so densely crowded with extremely minute acicular crystallites (colourless, probably felspar), and with a minute dust (ferrite in the browner streaks, opacite in the darker) that, as the slide is rather thicker than usual, I cannot be quite sure. Although, to the unaided eye, and even when examined with low powers, this rock appears to differ considerably from (5) and (8), yet with high powers the resem- blance becomes much closer, so that we may, I think, confidently refer it to the same group, and regard it as merely a more slagey variety. It follows, then, from the above examination that the rocks which form the actual peak of Antisana are augite-andesites, containing at any rate occasionally hypersthene, and to the same group belongs, though perhaps it is slightly more basic, the rock of the great lava stream which has descended to Antisanilla, while the pitchstones of Quebrada de Urcucuy must be representatives of a group with a higher percentage of silica, z.e., rhyolites or dacites, probably the former. IV. “The Variation of Stability with Draught of Water in Ships.” By F. Enear, Professor of Naval Architecture in the University of Glasgow. Communicated by Professor Sir WILLIAM THOMSON, F.R.S. Received March 6, 1884. (Abstract. ) Of all the properties possessed by a ship none is more vital to her safety and efficiency than that of stability. At the same time none is dependent for its existence and amount upon so many or such diverse and variable circumstances as it. The stability of a ship, both as regards moment and range, is affected not only by the position of her centre of gravity, which largely depends upon stowage, but also by draught of water. If the centre of gravity be kept fixed in position at various draughts of water, the stability will still vary very consider- ably with the draught, and often in a manner that contains elements of danger. The usual practice in investigating a ship’s stability is to calculate a curve of metacentres, and one or more curves of stability at certain 1884. ] Stability with Draught of Water in Ships. 435 fixed draughts of water and with given positions of centre of gravity. The curve of metacentres gives the height at all draughts of water above which the centre of gravity cannot be raised without making the ship unstable when upright, and eausing her to lie over more or less to one side. The ordinates of the curve of stability represent the lengths of the righting arms, which, multiplied by the: weight of the ship, give the righting moments at all angles of inclination from the upright. The stability of numerous vessels, both of the Royal Navy and Mercantile Marine, have been investigated in this manner for certain draughts of water, and a great amount of information obtained respecting the variation of stability with inclination at such draughts, and the angle at which the stability vanishes in many classes of ships. The peculiar dangers attaching to lew freeboard, especially when associated with a high centre of gravity, have been fully discussed and made known. Curves of stability having been chiefly constructed for deep and moderate draughts, the character of the stability which is often to be found associated with very light draught, appears to have hitherto escaped attention. As a matter of fact, light draught is often as unfavourable to stability as low freeboard, and in some cases more so. The general opinions that have till recently prevailed upon the subject appear to have been based upon a vague impression that so long as a vessel has a high side out of water, and any metacentric height, she will have great righting moments at large angles of inclination and a large range of stability. It was shown at the ‘* Daphne ” inquiry, held by Sir E. J. Reed, in July last, that these opinions largely prevailed and were erroneous. It fell to my lot to make some investigations respecting the stability possessed by the “Daphne” at the time of the disaster which happened to her, and to give evidence respecting the same. I after- wards pointed out, by way of explanation of my evidence, in a letter to the “Times” of the lst September last, some of the considerations which obviously apply to ight draught stability. The first, which so far as I am aware had never before been stated, is that any homogeneous floating body which is symmetrical about the three principal axes as the centre of gravity—such as a rectangular prism or an ellipsoid— will have the same moment of stability at equal angles of inclination, whether floating at a light draught with a small volume below water, or at a deep draught with a similar volume above water. For instance, if a homogeneous prism of symmetrical cross-section 5 feet high float at a draught of water of 1 foot, it will then have precisely the same moment of stability at equal angles of inclination, and consequently the same curve of stability throughout, as if it were loaded—without altering the position of the centre of gravity—till it had 4 feet draught of water, and 1 foot of freeboard. From this it VOL. XXXVI. x 2H 436 Variation in Stability in Ships. [Mar. 13, follows ‘that, in such elementary forms of floating bodies, lightness of draught has‘the same effect upon stability as lowness of freeboard ; and if a low freeboard is unfavourable to stability, so also, and precisely to the same extent, is a correspondingly light draught of water. This proposition can be made still more general, as it applies to homogeneous bodies of any form of cross-section which revolve about an horizontal axis fixed only in direction. From this may be deduced the results given by Atwood in his papers read before the Royal Society in 1796 and 1798 respecting the positions of equilibrium and other peculiarities connected with the stability of floating bodies. In considering the stability of a ship at various draughts of water, and comparing it with that of the class of figures above described, modifications require to be made for the departure from symmetry of form, and for ‘the extent to which the vertical position of the centre of gravity differs from what it would be if the external surface enclosed a homogeneous volume. This has been attempted in the present paper, and curves of stability, which I call cross curves, have been given for various geometrical forms of floating bodies, and also for a large passenger steamer of ordinary type, showing how the stability varies with draught of water at constant angles of inclina- tion. In dealing with these cross curves of stability the curves of righting moments require to be constructed, and not merely curves of lengths of righting arm. ‘The ordinary curve of stability is usually made for lengths of righting arm, because the displacement is con- stant, and the same curve therefore gives upon different scales, either lengths of righting arm or righting moments. In the cross curves of stability, however, such as are now being dealt with, draught, and therefore displacement, is one of the variable quantities, and curves of righting moments are of a very different character from curves of righting arm. The curves given in the figures are therefore, in all cases, curves of righting moments. Complete cross curves for a ship, from which ordinary curves of stability can immediately be obtained for any draught of water and position of centre of gravity, can be constructed in a few days with the aid of Amsler’s mechanical integrator. The main object of this paper is to show the necessity of regarding the stability of a ship from the point of view of variation of righting moment with draught of water, the angle of inclination being constant, instead of from that of variation of righting moment with angle of inclination, the draught being constant, as is usually done; or rather of considering the subject from both points of. view instead of almost exclusively from the latter. It also shows that it is necessary to investigate more fully than has formerly been done, the moments and range of stability of ships and other structures that may be intended to float at very light draughts of water. + 1884.] Hexperimental Researches in Cerebral Physiology. 437 March 20, 1884. THE PRESIDENT in the Chair. The Presents received were laid on the table on thanks ordered for them. The following Papers were read :— I. “Experimental Researches in Cerebral Physiology.” By Victor Horsuey, M.B., B.S., F.R.C.S., and Epwarp ALBERT SCHAFER, F.R.S. Received March 6, 1884. I. On the Functions of the Marginal Convolution. (Preliminary communication.) The present communication is intended to be the first of a series giving the results of an experimental investigation which we are at present engaged upon, into the physiology of the cerebral cortex and its connexion with other portions of the nervous system. We propose in this way briefly to publish any general results which appear to us to be well enough substantiated, as they are obtained ; reserving most of the details of the experiments for a more complete memoir in which the various facts which may have been accumulated can be collated, and compared with the results obtained by other experi- menters. In the present research we have closely followed the methods employed by Ferrier. The animals used have been monkeys, most, if not all, some species of Macacque. In some the portion of the brain under investigation has been stimulated by the interrupted (induced) current, and the resulting movements recorded; in others (two in number) the cortex has been removed over the region in question, the removal being effected by the aid of the galvanic cautery and under antiseptic precautions, and the resulting pareses of voluntary move- ment observed. It was found disadvantageous to attempt both these observations upon the same individual, partly on account of the relative prolongation of the operation and the consequent danger of losing the animal from the resulting shock, partly because the carbolic spray which is used when it is intended to preserve the animal, appears temporarily to depress the functions of the portions of the cortex which are exposed to its influence, and either no reaction is obtained on stimulating them or a stimulus must be employed so , 2u 2 438 Messrs. V. Horsley and E. A. Schifer. [ Mar. 20, strong as to involve the risk of its spreading to neighbouring parts, The anesthetic used has generally been ether, sometimes mixed with chloroform ; in one case in which morphia had been employed the results of Sibnalinnson were much interfered with by the drug. The induction coil used is of the du Bois-Reymond pattern, with the Neef interrupter; and the Helmholtz side-wire is always introduced for the purpose of equalising the effects of the make and break shocks. The electrode wires are carefully guarded except at their points, which project slightly on one side, and the electrodes are so constructed as to pass between the falx and the mesial surface of the brain with as little disturbance as possible. We have for the most part throughout all our experiments taken care only to employ an excitation just sufficient to call forth the activity of the part of the brain immediately under the electrodes. The best physiological test of the strength of the interrupted current consists in placing the electrodes on the tongue, and many of our results have been got with a stimulus which is only just perceptible when tested in that manner. Results so obtained are of the greatest value for the purpose of localising the function of a part, because under these circumstances there can be no question that the current does not spread beyond a very small area; and with such a minimal stimulus applied for but a short time it is not unfrequently found that but a single muscle, or at most two or three, generally in succession, are called into action. But for thus exactly localising centres for indivi- dual muscles a much larger number of experiments will be necessary than we have up to the present been able to make; we will, therefore, reserve for a future communication, in which we hope to deal more fully with this question, the few positive results of this kind that we have obtained, and here only consider the more general movements called forth by excitation of particular parts of the convolution. We have in this way explored the mesial surface of the hemisphere, or rather the marginal convolution of that surface, for it soon appeared evident that on other parts of the mesial surface positive results were not to be expected from electrical excitation. We have ascertained that the excitation of definite localised portions of this convolution gives rise to the contraction of perfectly definite groups of muscles, or in some cases of single muscles, producing more or less co-ordinated movements of the trunk and limbs, in the same manner as has been shown by Ferrier and others to be the case with excitation of localised portions of the external surface of the hemisphere. We can best explain the extent of the excitable portion of the mar- ginal gyrus by reference to certain easily recognisable furrows on the external surface of the hemisphere. One of the most conspicuous of these is the furrow of Rolando, which, as in man, terminates superiorly near the margin of the hemisphere, a little in front of the posterior 1884.] Experimental Researches in Cerebral Physiology. 439 up-turned end of the calloso-marginal sulcus on the mesial surface. Behind the furrow of Rolando and opposite this end of the calloso- marginal furrow there is a small, but constant, obliquely-placed depression (fig. 1,2), which serves to mark the separation between the ascending parietal gyrus and the parietal lobule. In front of the furrow of Rolando, and separated from it by the upper end of the ascending frontal gyrus, is another small depression (), also extremely constant in occurrence, although varying considerably in develop- ment, having a direction parallel to the margin of the hemisphere, from which it is a few millimetres removed. Still further forward, and at a much greater distance from the margin, is the well-marked transverse frontal furrow, the antero-posterior limb of which (tr. fr) is shown in the figure. And in front of this again is another small and apparently unimportant depression (fig. 1, y), but very constant in the Macacques, which has a transverse direction, 1.e., perpendicular to the hemisphere-margin, and which, in some instances, comes nearly up to the margin, conducting a considerable vein towards the longitudinal sinus. The excitable portion of the marginal convolution extends from about oppesite this small transverse sulcus (F) backwards along the whole length of the convolution. In front of the level of the sulcus y no movements are, as a rule, obtained as the result of electri- cal excitation. A remarkable relation was found on the whole to hold good between different parts of this convolution and the parts of the body thrown into movement by their excitation, to the effect, namely, that when the stimulus was applied anteriorly the resulting move- ments affected the upper limbs (and in one or two instances muscles of the head and neck) ; when applied near the middle of the excitable part of the convolution, the muscles chiefly or primarily affected were those of the trunk (erector spine, abdominal muscles, &c.), whilst, when applied posteriorly, muscles of the lower limb alone were called into action. Indeed, it appears probable that, if we regard only the results of minimal excitations, and especially if we take into account only those muscles which are primarily called into action, this rule will prove to obtain in astill more special manner, and that we may arrange the movements which are produced by stimulation of points which succeed one another from before back in the following order, viz.: 1. Movements of the forearm. 2. Movements of the humerus and scapula. 3. Movements, chiefly rotation and flexion, of the upper part of the trunk. 4. Movements of the lower part of the trunk and abdomen. 5. Movements of the pelvis. 6. Movements at the hip. 7. Move- ments at the knee. 8. Movements at the ankle-joint. 9. Movements of the toes. The general results of our experiments will best be understood by a reference to the accompanying figure (fig. 1). Thus, in the part of 440 Messrs. V. Horsley and E. A. Schafer. [Mar. 20, the marginal convolution marked I, I’, extending from just in front of the small vertical sulcus y to a point on a level with the anterior third of the small antero-posterior sulcus z, excitation is followed by either movements of the forearm (flexion or extension) or by adduction of the arm and retraction of the shoulder combined with outward rota- tion, or by any of these movements of shoulder and arm either com- bined or succeeding one another in definite order, according to the point in the area which is stimulated. Retraction of the shoulder (combined with flexion of the forearm) is alone produced by excita- Fre: 1. WY CT. Sm OTILCRLi gS WEF ad ye tion of the posterior portion of this area, and when manifested ,as the result of excitation applied here, is apt to be associated with move- ments of the trunk, pelvis, or hip, which, as the overlapping of the contours of the areas shows, may also be called forth by excitation of this part. In the next area, II, Il’, we get movements of the trunk muscles as the result of excitation, the chief effect produced being a rotation of the body to the opposite side to that stimulated, combined with an arching of the spine, with the concavity directed towards the opposite side. In the anterior part of the area the chief effect is upon the dorsal region, but in the posterior part it is upon the lumbar region and pelvis. 1884.] Experimental Researches in Cerebral Physiology. 44] This area is largely overlapped by the next one, III, III’, excitation within which is followed by movements of the hip, at some points the flexors only, at others the extensors only, at others both sets of muscles being called into contraction simultaneously. As will appear from the overlapping of the areas in the figure, these movements of the hip are apt to be associated with the rotatory and bending movements of the trunk above mentioned; but in the anterior part of the area it is generally the rotation of the trunk and pelvis which is first seen, and this is followed by hip movements, whereas in the centre of the area movements of the hip may be the first to appear, or with a very weak excitation may be the only ones visible. The next area, IV, IV’, is very extensive. It considerably overlaps the areas II, Il’, and ITI, IJI', and extends to the posterior limit of the con- volution. Its excitation calls up contractions of the thigh muscles, and especially of the hamstrings, which in some parts are the only muscles affected by weak stimulation—indeed, in some instances the contractions of the individual hamstring muscles were perfectly localised. But in most parts of the area, as the overlapping of the contours shows, these movements are associated with those of other muscles, viz., anteriorly with the trunk and hip muscles, and posteriorly with muscles which move the ankle and toes. These associated move- ments may be simultaneous, but are most commonly successive, as when by stimulation of one point there was produced, first a contrac- tion of one of the abdominal muscles, then of one of the thigh muscles, and then of one of the muscles which move the ankle. In like manner the area marked V, V’, may be looked upon as the specialised part from which the movements of the ankle are con- trolled, these being usually the first to appear on exciting the area, although very generally associated with or followed by movements of the hip and knee. And VI, VI’, may for a similar reason be looked upon as specially controlling certain movements of the toes, generally associated, however, with other movements of the lower limb. As before, mentioned with regard to the other areas, the particular movements called forth differ according to the point in the area which is excited, but our experiments do not as yet enable us to make sufficiently positive assertions as to the localisation of these specialised points. In the two animals from which the excitable portion of the marginal convolution has been removed, the resulting pareses of voluntary movement, so far as these can be determined, are precisely such as might be expected to occur from removal of those portions of the cortex by which the voluntary movements of the muscles which are _ealled into action by stimulation of this convolution may be assumed to be governed. Since, however, as Ferrier has shown, certain of the muscles are also caused to contract by excitation of portions of the external surface, the paralysis of these would not be so complete as of 442 The Apex of the Leaf in Osmunda and Todea. [Mar. 20, those which are solely connected with this convolution. Accordingly it is found that there is a considerable difference in the amount of paralysis for voluntary movement produced in the different muscles, and especially that some of them are found to undergo a considerable amount of recovery in the course of a relatively short time, while others remain permanently and completely paralysed. The paralysis (for volitional impulses) is most pronounced in the muscles of the toes and hind feet, and in the hamstrings and glutei. The paresis is sufficiently obvious, but less marked in the arm-muscles than in those of the lower limb, while in the trunk-muscles it is extremely difficult to determine what movements are purely voluntary, what are asso- ciated movements, and what are purely reflex movements. We are unable, therefore, to say positively how far the influence of the will over these muscles has been abolished by the establishment of the lesion.* It will, therefore, be more advantageous to defer the complete account of the condition of these animals until the opportunity is afforded by post mortem examination of verifying the extent of the lesion and of tracing the resulting secondary degenerations. If. “ Preliminary Note on the Apex of the Leaf in Osmunda and Todea.” (From the Jodrell Laboratory, Royal Gardens, Kew.) By F. O. Bower, F.L.S. Communicated by W. T. THISELTON-DykER, C.M.G., F.R.S. Received March 7, 1884. It has long been accepted, in accordance with the investigations of Sadebeck, that there is at the apex of the young leaf of the fern a two- sided, wedge-shaped, apical cell, and that, after this cell has lost its identity by periclinal, and subsequently by anticlinal divisions, the erowth of the leaf is continued at the margin by the persistent activity of a linear series of marginal cells. It is true that this is the mode of development of many fern-leaves, but, as my observations show, it does not apply for all cases, while those exceptional cases are particularly interesting as occupying an intermediate position in this, as also in other, respects between the true ferns, on the one hand, and the Marathacee and Cycadee on the other. It is among the Osmun- * Since the above was written we have removed in two other animals the excitable portions of the external surface, in addition to the excitable portion of the marginal convolution. Complete hemiplegia has been the result; the paralysis affecting not only the muscles of the limbs but also those of the head and neck and of the trunk, whereas in animals in which only the excitable portions of the external surface (the motor regions of Ferrier) have been removed the paralysis is but partial, and confined chiefly to muscles of the limbs.—(Note added March 20, 1884.) 1884.] On the Most Widened Lines in Sun-spot Spectra. 443 dacece that these exceptional cases occur. In the young leaves of Todea superba and of Osmunda cinnamomea it was found that the apex is occupied by a well-marked, three-sided, conical, apical cell, from the three sides of which segments are cut off in regular succession, as at the apex of the stem of Hqguisetum. The apical cell is so placed that one side faces the ventral side of the leaf, while the remaining two sides are obliquely disposed with regard to the dorsal side of the leaf. No clearly marked marginal series of persistently active cells have been found giving rise to the pinne, as is stated to be the case for the typical ferns. Further, there appears to be no strict relation between the points of origin of the pinne and the segments cut off from the apical cell. The pinne arise in acropetal order. In itself no great importance is to be attached to the difference between a three-sided and a two-sided apical cell. For example, it has been clearly shown in a paper by Treub, on the vegetative organs of Selaginella Martensii, that the two forms of apical cell are to be found on different shoots of the same species. But in the case of the leaf of the fern, the whole development, as described by Sadebeck and by Ruy, is so closely connected with the existence of a two-sided cell that a departure from that arrangement is to be regarded as of more importance than would otherwise be due to it, and it appears to me to supply an intermediate step towards the more complex leaf of the Marathacee and Cycadec. | Finally, it is believed that this is the first described case of a clearly marked, three-sided, apical cell occurring in the leaf of any plant. Holle asserts that there is a wedge-shaped apical cell at the apex of the leaf of Angioptris, and describes it as being “of irregular cross- section.” My own observations on this point, which will shortly be described in detail, show that there is no single, functionally active, apical cell in the leaf of Angiopteris evecta. , III. “ On the most Widened Lines in Sun-Spot Spectra. First and Second Series, from November 12, 1879, to October 15, 1881.” By J. N. Lockyrr, F.R.S. Communicated to the Royai Society at the request of the Solar Physics Com- mittee. Received February 22, 1884. (Abstract.) A preliminary report by Mr. Lockyer, written before the reduction of the observations given in the present paper was complete, was read to the Royal Society on December 15, 1881, and printed in the Proceedings (vol. 33, p. 154). In the present paper the authcr describes the plan of the observations and of their discussion, and presents some general conclusions. 444 Mr. J. N. Lockyer. On the [ Mar. 20, When observations of spot spectra were commenced in 1869, the original idea was to observe the behaviour of every line widened or “brightened in the spectra of each spot. It was soon found, however, that in this climate it was exceptional to do this completely on any one day. Still, when it can be done, it is most important to secure such observations, and accordingly a com- plete method of reduction of such observations was suggested, laid before the Solar Physics Committee, and published by them in their Report. Laboratory observations soon indicated the importance of having a series of strictly comparable observations. It became obvious there- fore that the observations would require to be considerably restricted. One reason why it was important to obtain such a series was that they might be compared with the complete records of bright lines seen in prominences given by Tacchini and others. This consideration led to the suggestion that it would be advisable to take only the most widened lines, by which is meant the lines relatively the most thickened in the spots: accordingly the six most widened lines in each of the two regions, F to b, b to D, have been taken on every available opportunity. In this way a number of strictly com- parable observations have been obtained. Besides these observations, attempts have been made to photograph the spectra of sun-spots, and several photographs have been obtained. In all H and K were seen reversed over the spots, just as Young saw them at Sherman, while the blue calcium line was not reversed. The dispersion employed, however, up to the present has not been sufficient. Previous researches had shown— 1. That with increased density in the spot-vapours we might expect an increase in the number of lines radiated, and therefore absorbed, either in the case of one vapour or of a mixture of vapours. 2. That an increased quantity of any one vapour in a mixture would increase the number of lines visible in the spectra of that substance. 3. That since absorption will vary with temperature, and as absorp- tion is effected at different heights in the solar atmosphere, where the temperatures are different, depending upon the height on the average, the lines observed will vary according to the position of the absorbing stratum. information on all these points could be obtained by the method proposed, if the lines belonging to each substance were separately discussed afterwards. An individual discussion of each substance then formed part of the plan of the work. Some General Conclusions. 1. In the photographs of spectra of sun-spets the H and K lines were always reversed, while the blue calcium line was not. - 1884. ] Most Widened Lines in Sun-spot Spectra. 445 2. On February 26th, 1880, faint lines not marked in Angstrém’s atlas appeared among the most widened lines. 3. A change took place in the spectra of the sun-spots in May and June, 1881, the old lines faded away and new lines appeared. 3A. The lines of iron fade away from the spots as the maximum sun-spot period is approached. 4. In October, 1881, a similar change took place, only much more abrupt. 5. During the second hundred observations a much greater number of Fraunhoferic lines have been seen wider than in the first, but with less frequency. 6. The most widened lines have shifted towards the less refrangible part of the spectrum. 7. In some spots certain lines have indicated change of refrangi- bility, while other lines in the same region have not done so. 74. On several occasions certain lines of iron have been seen in motion, while other lines in the same field of view have been at rest. 8, There are immense inversions in the lines seen widened in the spots from spot to spot, and from day to day. 9. There is a great inversion between the iron lines seen among the most widened lines. 10. There are yet greater variations between the lines brightened in prominences and widened in spots. 11. On comparing Young’s chromospheric lines with the most widened lines, it is found that the number of common lines increases till the end of the third period, and then it falls. lla. There is a great difference between the lines seen in promi- nences by Young at the maximum and those seen by Tacchini at the minimum sun-spot periods. lls. In the region between F and 6 there are no iron lines common to the most widened lines and Tacchini’s observations of promi- nences. 12. Hven with a six-fold complexity 1 was unable to classify the most widened iron lines. 13. The spectrum of iron in the sun is more like that given by the spark than that given by the arc. 14, Of three iron lines at 4918°0, 4919°8, and 4923°1 the two former have been seen in spots among the most widened lines, while Tacchini and others have seen the latter without the former in prominences. 15. The prominence line 4923°1 is sometimes seen under certain conditions brighter than the longest iron line, in the region at 49567. 16. The lines of iron, manganese, zinc, titanium, nickel, and copper most frequently seen in spots are different from those most frequently 446 On the Most Widened Lines in Sun-spot Spectra. [Mar. 20, seen in prominences, whilst in cobalt, chromium, and calcium they are the same. 17. The lines of iron, cobalt, chromium, manganese, titanium, and nickel seen in the spectra of spots and prominences are usually coincident with lines in the spectra of other metals with the dispersion employed, whilst the lines of tungsten, copper, and zinc are not. 18. All the lines of titanium seen among the most widened lines have either been greatly developed in passing from the are to the spark, or else have been seen only in the spark. 19. The lines of titanium, zinc, and nickel, seen widened in the fourth period, are not the same as those seen in the first. 20. Several of the new lines seen among the most widened lines occupy positions near those occupied by titanium lines. 21. No lines of cobalt, manganese, chromium, copper, or tungsten, were seen in the fourth period. 22. A strong barium line has been seen once among the most widened lines; it is a line greatly intensified in passing from the are to the spark. 23. A hundred and one lines have been seen among the most widened lines which have no corresponding lines (so far as is known) in the spectra of the elements. One of these lines has been seen frequently in prominences by Young. 24. So far as the observations have gone, there has been no differ- ence caused by the nearness of the spot to the limb. 1884.] On the Human Lachrymal Bone and its Ossicles. 447 March 27, 1884. THE PRESIDENT in the Chaiv. | The Presents received were laid on the table, and thanks ordered for them. The following Papers were read :— I. “Notes on the Varieties and Morphology of the Human Lachrymal Bone and its accessory Ossicles.” By A. MAc- ALISTER, F'.R.S., Professor of Anatomy in the University of Cambridge. Received March 14, 1884. (Abstract. ) The author has examined 1000 lachrymal bones and the soft parts of over 300 orbits, and has deduced therefrom notes on the following points :-— I. Cases of absence of the lachrymal bone. II. Rudimentary conditions :— a. Development of an orbital plate only. B. Division into two detached ossicles. y. Development of a crest only. 6. Fenestration. e. Presence of marginal fontanelles. II. Varieties in outline, suturation, and frequency of ankylosis. IV. Varieties of crista :— A. Simple lamellar forms with no crest. B. Simple carinate forms, C. Carino-acuminate forms. I). Carino-hamate. VY. Measurements of the bone in adult male and female, and the deduction of lachrymal index esl — VI. The vascular relations of the bone, which are shown to be almost exclusively with the infra-orbital artery, not with the angular. VII. The disposition of the periosteum and soft parts, and the relation thereto of the tendo oculi and muscles, as well as the relations of the bone to the neighbouring cavities in the ethmoid. 448 Lord Rayleigh. On the [ Mar. 27; VIII. The accessory ossicles developed in its vicinity, which are six. One, a detached portion of the lachrymal itself, with a second ossific centre (ossiculum hamuli); one, a detached portion of the os planum behind it (ossiculum ethmo-lachrymale superius); two, which are detached nodules connected with the maxilla (ossiculum ethmo-lachrymale inferius and ossiculum canalis naso-lachrymale) ; one, which belongs to the system of the Jugal bone (ossiculum infra- orbitale) ; and one, a detachment of the nasal process of the maxilla (ossiculum maxillo-frontale). To this last-named the sutura notha is always related. IX. The history of the development of the human lachrymal from its first appearance in the eighth week, and the changes in position and slope shown by it. X. The racial varieties shown by this bone, and the system of inter- lachrymal indexes whereby the degree of downward divergence and orbital splay of the bone can be measured. XI. Comparative anatomy and morphology of the bone. Those points have been briefly referred to which help to interpret the human conditions. II. “On the Electro-Chemical Equivalent of Silver, and on the Absolute Electromotive Force of Clark Cells.” By Lord RAYLEIGH, D.C.L., F.R.S. Received March 17, 1884. (Preliminary Notice.) The investigations upon this subject which have been carried on by Mrs. Sidgwick and myself during the last year and a half, though not yet quite finished, are so far advanced that no doubt remains as to the general character of the results; and as these results have application in the daily work of practical electricians, 1t is thought desirable to communicate them without further delay. The currents are measured by balancing the attraction and repul- sion of coaxal coils against known weights, as described before the British Association in 1882, a method which has fully answered the favourable expectations then expressed. To what was said on that oceasion it will be sufficient for the present to add that the readings are taken by reversal of the current in the fixed coils, and the difference of weights thus found (about 1 gram) represents the double force of attraction, free from errors depending upon the con- nections of the suspended coil, and other sources of disturbance. The difficulties which have been experienced, and which have been the cause of so much delay, have related entirely to the behaviour of the silver voltameters, of which never less than two, and sometimes 1884. ] Electro-chemical Equivalent of Silver, §c. 449 as many as five, have been included in the circuit of the measured current. In order to render the deposit more compact, and thus to diminish the danger of loss in the subsequent manipulations, acetate of silver was added in the earlier experiments to the standard solution of nitrate. Hxperience, however, has shown that the principal risk is not in the loss of metal, but in the obstinate retention of salt within the fine pores of the deposit, leading to an over-estimate of the amount. When the texture is very compact this danger increases, and deposits from a solution containing acetate are often decidedly too heavy, even after the most careful and protracted washings. On heating to low redness a portion, at any rate, of the retained salt is decomposed, NO, is driven off, and a loss of weight ensues. With pure nitrate, to which we finally recurred, the risk is much less. The actual weights of deposited silver were usually from 2 to 3 grms.,and, so far as the mere weighings are concerned, should have been correct to ;5355- Discrepancies three or four times as great as this are, however, actually met with, whether due to retention of salt or to loss of metal it is difficult to say. The final number, expressing in C.G.S. measure the electro-chemical equivalent of silver, is a little lower than that (1:119 x10?) given on a previous occasion (“ Cam- bridge Proceedings” for November 26, 1883). It approximates closely to 1:11810-?, and is thus in precise agreement with the number announced within the last few weeks by Kohlrausch, viz., 1:1183x10-?. Its substantial correctness can therefore hardly be doubted, more especially as it does not differ very much from the number (1:124) obtained by Mascart. In terms of practical units, we may say that the ampere current deposits per hour 4025 grms. of silver. When we are provided with means for the absolute measurement of currents, the determination of electromotive force is a very simple matter if we assume a knowledge of absolute resistance. A galvanic cell is balanced against the known difference of potentials generated by a known current in traversing a known resistance. The difficulty relates entirely to the preparation and definition of the standard cells. A considerable number of Clark cells have been set up and tested at intervals during the last six months, and their behaviour has been satisfactory, the extreme range (after the first ten days) not much exceeding 5z55- A modified form of cell in which the solid zinc is replaced by an amalgam, is at present under trial. In Mr. Latimer Clark’s own determination the B.A. unit is assumed to be correct, and the H.M.F. of the cell at 15° C. was found to be 1457 volt. On the same assumption, we obtain the not greatly differing value 1:453 volt. If we take the true value of the B.A. unit as ‘9867 ohm, 1°453 will be replaced by 1°454. Experiments are also in progress to determine in absolute measure 450 Prof. J. C. Ewart. On the Natural and [Mar. 27, the rotation of the plane of polarisation of light in bisulphide of carbon under the action of magnetic force. Of the results obtained by Gordon and Becquerel, differing by about 9 per cent., our preliminary measurements tend rather to confirm the former. IIf. “ On the Natural and Artificial Fertilisation of Herring Ova.” By J. Cossark Ewart, M.D., Regius Professor of Natural History in the University of Edinburgh. Communicated: by THE PRESIDENT. Received March 19, 1884. It is well known that for centuries herring have been in the habit of congregating on inshore banks around the coast of Britain in order to deposit their spawn. In 1862 the Royal Commission (of which Professor Huxley was a member) appointed to report on the trawling for herrings on the coast of Scotland, arrived at the conclusion that herring visit our shores for this purpose twice a year, some shoals arriving during the autumn, while others make their appearance during the winter. The herring which spawn during the autumn (and which at another time I shall endeavour to show differ from the winter herring) chiefly frequent banks on the east coast, while the herring which spawn during winter are most abundant on the west coast. Of the west coast spawning-grounds, the Ballantrae Bank, which lies off the coast of Ayrshire, is one of the most important and is certainly the most famous. To this bank herring are known to have resorted for at least 200 years, always bringing in their train numerous codfish, whiting, and sometimes shoals of dogfish, por- poises, and dolphins, and while on the bank they have afforded an abundant harvest to the fishermen of the surrounding districts, and to the flocks of gannets and gulls which people Ailsa Craig. The herring fishery being one of the most important industries in Scotland (the autumn fishery engaging nearly half-a-million people, and being worth in good years about 2.500,000/. sterling), there has been since 1809 a Board specially charged with guarding its interests. This Board (formerly known as the Board of Fisheries, but since 1882 as the Fishery Board for Scotland) in 1862-63 endeavoured, under the direction of Professor Allman (then a member of the Board), to gain some information as to the habits of the herring, and more especially as to the nature of the spawn and the spawning grounds. Since 1863 little has been done in this country by way of continuing these experiments until last autumn, when the new Fishery Board, recognising the importance of the investigations so ably initiated by Professor Allman, appointed a Committee of its, 1884. | Artificial Fertilisation of Herring Ova. 451 members to continue the observations, and extend them so as to embrace as far as possible the consideration of all the food fishes. But while little has been done in this country to increase by means of continuous observations our information as to the habits and life history of the herring, important results have been obtained by the German Fish Commissioners, and from observations made for the Norwegian and Swedish Governments and the United States Com- missioner of Fish and Fisheries. Nearly all the work hitherto done is Summarised in the valuable ‘‘ Reports of the United States Com- missioner of Fish and Fisheries,” more especially in Parts III and VI, where Widegren, Lyungman, and Sar’s researches are referred to, and a full account of D. H. A. Meyer and Dr. C. Kupffer’s work will be found in the “ Jahresbericht d. Commission z. wissenschaftlchen Untersuchung d. deutschen Meere in Kiel f. d. Jahre 1874, 1875, 1876,” and the “‘ Vierter Bericht d. Commission f. d. Jahre 1877 bis Les.” During the autumn two members of the Fishery Board Committee (Sir James R. Gibson Maitland and myself) having had H.M.S. “Jackal”? (Lieutenant Prickett, R.N., commander) placed at their disposal by the Admiralty, were enabled to examine the more impor- tant spawning-beds in the Moray Firth, and to make experiments with the view of determining the best mode of artificially fertilising and hatching herring ova. ° oo is] wa Ss 2 a] oc o re agi ee as a = aXe ¢ (ga |) 2 = S 45) 3 — 3 ™T “an 3a QO ry aq |E ot i o 1S ea Soe = oi a Hy e a 8 S g me | © oA eS o X B |S = 2 =| ao Seed oa |odo Fei alte; Bult eae Sey) eae 8 84 H S33 a) & A) aes 5 ook ad o | q 52 AES 3S Passi SS =n) jog) 24 |B/2| 8 | 88 | & 8s) Sage A: 16 <5 2) a fe Fe H ja O°" Saas 25 |°0004908 | 207| 2 | 1,000 | 5,121 | 6,121 | 1267 | 7-047 | 7-047 5 = | 20 |°0003141 | 150) 3} 1,000 | 5,121 | 6,121 918 | 5°106 | 5°043 4 2 | 16 | 0002010 | 115] ‘0 | 10,000 | 51,210 | 61,210 704 | 3°916 | 3-608 ez ‘= | 14 | 0001539 | 110] O | 10,000 | 51,210 | 61,210 673 | 3°743 | 2-953 8 |-0000502 | 37] 0 | 10,000 | 51,210 | 61,210 | 226 | 1-257 | 1-276 Constant deflection from standard Daniell cell =12,252’. E g = & 5 Sees 3.8 Fle | 2 s |g.| ¢ @2 |e |zels 6 |e s q ae, Se q os Fa SH. = 5 = oO eS ap Bo | Soeoms SaaS om : += » 5s SO) pasion fea oO o g 2 a 3 x Oe : a S) ons nL aly © wo |og 2, |e 8 3 = Fa| © faq .| ©2 lease oa lo , eo. S28 5 5S i seat 24 a's Bq x o | Oe as o Sg ae sae = ‘a 4 q o 3 ear S| Se elle $ |88| & [B26] 2a |e 8] SVS Stead 2 Ale co Fa AB | OoF i@nman 38 | :001134 | 121 | 3,|1000+488 | 512 | 2000 | 2420 |13-461 |13 -461 qd | 20 | -0008141 | 123 | ,, 488 | 512 | 1000 | 1230 | 6-841 | 5-140 = | 18 | -0002544 | 104 | ,, 488 | 512 | 1000 | 1040 | 5-785 | 4-389 -= | 141 -0001539 | 142 | ,, 88 | 512 | 600 | 852 | 4:739 | 3-010 = | 11 | -0000950 | 100 | ,, ss | 512 | 600! 600 | 3:337 | 2-097 - 8 | :0000502 | 76 | ,, 88 | 512 | 600] 456 | 2-536 | 1-300 ———$$——— The results are plotted out in fig. 8. It will be seen that the observed and calculated results agree to a considerable degree of accuracy except in the case of platinum, which behaves as in the previous experiments, and is generally found to be irregular in its quality. These experiments were made upon wires exposed to the air, where radiation is free. I am anxious to repeat them upon wires covered in insulating material and buried in the ground, but I have not been able to do so up to the present moment. The law with reference to such wires has a very important bearing on the size of electric light 1884. | Spectroscopic Studies on Gaseous Explosions. AT1 leads, for it shows the necessity of making them large enough to prevent the possibility of their being heated above normal tempera- tures, otherwise points of danger are very easily reached by increments of current. III. “Spectroscopic Studies on Gaseous Explosions. No.I.” By G. D. Liverne, M.A., F.R.S., and JAMES Dewar, M.A., F.RS., Professors in the University of Cambridge. Received March 28, 1884. Having occasion to observe the spectrum of the flash of a mixture of hydrogen and oxygen fired in a Cavendish eudiometer, we were struck by the brightness, not only of the ubiquitous yellow sodium line, but of the blue calcium line and the orange and green bands of lime, as well as of other lines which were not identified. The eudio- meter being at first clean and dry, the calcium must be derived either from the glass or from some spray of the water over which the gases with which the eudiometer was filled had been confined. It seemed incredible that the momentary flash should detach and light up lime from the glass, but subsequent observations have pointed to that con- 472 Profs. G. D. Liveing and J. Dewar. [ Apr. 3 clusion. Our next experiments were made on the flash of the com- bining gases inclosed in an iron tube, half an inch in diameter and about 3 feet long, closed at one end with a plate of quartz, held in its place by a screw-cap and made tight by leaden washers. Two narrow brass tubes were brazed into the iron tube at right angles to the axis, one near each end, and one of these was connected with an air- -pump, the other with the reservoir of gas. Into one of these brass tubes was cemented a piece of glass tube with a platinum wire fused into it, whereby the electric spark was passed to fire the gas. _ The tube was placed so that its axis might be in line with the axis of the collimator of a spectroscope, and the flash observed as it travelled along the tube. _It was seen at once that more lines made their appearance in the iron tube than in the glass vessel, and one conspicuous line in the green was identified in position with the E line of the solar spectrum, Several other lines were identified with lines of iron by comparison with an electric spark between iron electrodes. There could be no doubt that the flash in an iron tube gave several of the spectral lines of iron. We supposed that this must be due to particles of oxide shaken off the iron by the explosion, and proceeded to try the effect of introducing various substances in fine powder, and compounds, such as oxalates, which would give fine powders by their decompo- sition in the heat of the flame. Several interesting observations were made in this way. When some lithium carbonate was introduced, not only were the red, orange, and blue lines of lithium very brilliant, but the green line hardly less so. After the lithium had once been intro- duced into the tube, the lithium lines continued to make their appear- ance even after the tube had been repeatedly washed. When the lithium had been freshly put in, the red line was observed to be much expanded, very much broader than the line given by lithium in a Bunsen burner reflected into the slit for comparison. The light was dazzling unless the slit was very narrow; and it was noticed that if the spark by which the gas was fired was at the distant end of the tube, so that the flame travelled along the tube towards the slit, there was a reversal of the red line; a fine dark line was plainly visible in the middle of the band. When the spark was at the end of the tube next the slit, no reversal was, in general, seen. Later observations showed that some other metallic lines might be reversed in this way, and photographs taken of the reversals. These observations with the eye on the reversal of the red lithinm line were made with a diffraction grating, and were repeated many times. They show that there are gradations of temperature in the flame, and that the front of the advancing wave of explosion is somewhat cooler than the following part. The combination of the gases is not so instantaneous that the maximum temperature is reached at once. When some magnesia was 1884.] Spectroscopic Studies on Gaseous Hxplosions. AT3 put into the tube the continuous spectrum was very bright, but the iron lines were still brighter. No line which could be identified as due to magnesium was observed with certainty; there was only a doubtful appearance of 6. With sodium, potassium, and barium car- bonates, only the lines usually seen when salts of those metals are introduced into a flame were noticed; but eye observations of this kind are extremely trying, on account of the suddenness of the flash and the shortness of its duration. Thallium gave the usual green line. Subsequently we had the interior of the tube bored out so as to present a smooth bright surface of iron, and noted the iron lines which were conspicuous in the flash. For the purpose of identification the pointer in the eye-piece was first placed on one of the strong iron lines given by the electric discharge between iron electrodes, and then, the discharge being stopped but the field sufficiently illuminated, the eye was fixed steadily on the pointer while the gas in the tube was exploded. In this way it was not difficult to see whether any given line was very bright in the flash. The lines thus identified were those having the wave-lengths about 5455, 5446, 5403, 5396, 5371, 5327, 5269 (4B), 5167 (0,). These lines were all many times observed in the way described, and as a rule were always present in the flash. Lines with wave-lengths about 5139 and 4352 were seen, and may possibly have been due to iron, and several more lines were seen occasionally, but were not so regularly seen that they could be well identified. The lines \. 4923 and » 4919 were specially looked for, but neither of them could be seen. A group of blue lines were noticed, and were after- wards identified by photography, a method much less trying than observations by eye. To give intensity to the photographs ten or twelve flashes were usually taken in succession without any shift of the instrument, so as to accumulate their effects in one photograph. For identification the spark between iron electrodes was also photo- graphed, but with a shutter over the lower part of the slit, so that the image of the spark should occupy only the upper part of the field. The following is the list of wave-lengths of the iron lines thus photographed :— AA CNISTIUSSY Fen aner teens 3920 FA QAR a0) i ok 3 eae AOE Is A sath Boog ante hs 3902 °5 BONO LNs) “is sks as AQG2 Oily ost earae 4 t 3898 *4: AOA if 1) isiinre 6 0 AAS ety yal degen 3885 OMY Ty} assesvays's AQOL SG ue” je heads 3877 °4: MEAs Bi be He sles acs SIO Maebiae, Litorcnsbot 3859 °2 AOE OS «0s oie tyeis SOOT Sesh iP asichseneks 3849 °7 MEO hot4) 1, sieed ort DO Mpa ik uieusttotaals 3840 °3 “02S re Oo ike ih osteitis 3833 °6 AT4 Profs. G. D. Liveing and J. Dewar. [Apr. 3, DOLL MOUNT EL Lae IAD BASE. N 3580 °5 BOZOLZS Miia aiets B1OOTO Geli a 3568 “9 SSL Saha cae B(B4°D ELE 3064 BELOTD Wl wan ael MEST AC TRING Ie dee 3520 °7 BLVD TR nee BALONC WNL 3496 °8 SQN T TRI ys SY AUS TELa ha ai un er 3489 °8 BESTS Ra BYU De as leo E 3476 SOO SOUT Te. can 3647 Ste 3465 °5 BUOSEA Whats etee DOS LG ONT eel. ie O 3440 SLOT We eshte SOLS 2 AE eae BIAS 2 Vi eke Glee SOO SMA Me sate T 3019 8 3747 °2 As a rule no iron lines above O make their appearance; in a few plates T is visible, and it is possible that other lines may be obscured by the water spectrum, which always comes out and extends from near s to below R. Above T no line at all is visible in any of the photographs, though the spark lines come out strongly enough, and several of the strongest groups of iron lines, both of spark and arc lines, are in the region beyond T. The spark by which the gas was fired passed in ochre between a platinum wire and the side of the small brass tube, and was out of view ; but in order to make quite sure that the lines were not due at all to the spark, the brass tube was lined with a tube of platinum foil which projected beyond the brass tube a short distance into the larger tube, and the spark passed between the platinum wire and the platinum tube. It was found that the same iron lines made their appearance in the flash whichever way the spark was passed. Other experiments were made with explosions of carbonic oxide and oxygen, and with coal-gas and oxygen. The explosions of these gases were attended with much more continuous spectrum, and the metallic lines were not always as well developed as they were with hydrogen and oxygen, but on the whole there were as many metallic lines photographed from the flashes of carbonic oxide as from those of hydrogen. There is an uncertainty about the explosion of the carbonic oxide mixture which we cannot account for, even when we take into account the remarkable effects of relative dryness of the gas on the explosions discovered by Mr. Dixon. Sometimes the explosions were so violent as to break the plate closing the end of the tube, though this had resisted the explosions of the hydrogen mixture, while at other times the wave of explosion passed slowly along the tube. The gas was in all cases confined over water and passed directly from the gasholder into the tube. When the iron tube was lined with copper foil, only one copper line in the visible spectrum, ) =5104'9, was seen, and in the ultra- 1884. Spectroscopic Studies on Gaseous Explosions. AT95 violet two lines, \ 3272 and 2 3245°5. All three lines were very strong, and the two ultra-violet lines were in some cases reversed. These lines were also frequently developed when no copper linjng was in the tube, probably from the brass of the small side tubes. Copper also gave a line in the indigo, \ 4281 about, decidedly less refrangible than the copper line, \ 4275, coincident apparently with the strong edge of one of the bands developed when a copper salt is held in a Bunsen burner. A lining of copper which had been electro-plated with nickel developed only one nickel line, \ 5476, in the visible part of the spec- trum, but gave by photography the following lines in the ultra- violet :— Reso pofyeiesei ties s DOAN, je pail lat sichltis 3445 °d SMMC Ah) eC bicaeicecs Dea ee cle odes 0432 S75) HAO hay Res aeereon 3422 RMR AC apes) S sea aja oS Pea aed 3413 °2 2101100) SB) a eR OA Oh Oil Givens ap. 39391 °5 210] E75 ee ae DAD Me liie tea ciated 3378 *4 2057) i SMO D ee ih probeiterss 6s 3369 6 PDN yo ua. « Bid os DAO a atric Sus, ks 3367 *4 3565 When nickel oxalate was put into the tube, lines with wave-lengths 3670°5, 3470°3 and 3389°6 in addition to the preceding were developed. It is doubtful whether the line 13451 be a nickel line. That at X=3453 1s ascribed to cobalt by Cornu, but it seems to be a nickel line as well. When copper wire electro-plated with cobalt was put into the tube cobalt lines appeared with the approximate wave-lengths :— 41) LS) i Aa LOU AIMEE Se shetite, eh 3492 ? AUSOE bleep sss BOOS M AM sree ee ee 3474 Or ia aes DOOM Meee thee 5462 30 We) able Re Ea as 355 | biradiitty oy 3453 260/21 rain GOL cise: 3431 30,07) tae ea Osman ees So che tart 3411 DiCAND) «Mae AE ae AO ERY Mare cle erat 3404 3601 The lines 13528 to 3522 form a continuous band in the photo- eraph, so that these three lines may not represent the whole group at that spot. It is doubtful whether \ 3492 be a cobalt line as well as a Ni line. No other metal gave anything like the number of lines that were given by iron, nickel, and cobalt. 476 Profs. G. D. Liveing and J. Dewar. [Apr. 3, A lining of lead gave the lines \ 4058, 3683°3 and 3639°3 strongly, and these lines were frequently developed, though less strongly, when there was no lead lining; the metal being without doubt derived from the leaden washers used to make the ends of the tube air-tight. A strip of silver gave the lines \ 3381°5 and 3278, and these lines were sometimes reversed. No trace of the channelled spectrum of silver was developed even when silver oxalate was put into the tube, and furnished plenty of silver dust after the first explosion. A magnesium wire about 2 millims. thick and two-thirds the length of the tube gave the b lines very well; that is to say b, and by were well developed, and 6, was also seen, but as the iron and magnesium components of b, are very close together, and the iron line had been observed before the introduction of the magnesium, it was not possible to say with certainty whether or not the magnesium line were present too. No other magnesium line could be detected. The blue flame line was carefully looked for, but could not be seen. The photographs showed none of the magnesium triplets in the ultra-violet, nor any trace of the strong line \ 2852, which appears in the flame of burning magnesium, and is yet more conspicuous in the are when that metal is present. Metallic manganese, introduced into the tube in coarse powder, gave the group at wave-length about 4029 with much intensity, but no other manganese line with certainty. In the visible part of the spectrum the channellings in the green due to the oxide were visible. A lining of zinc produced no zine line, and zinc-dust gave only a very doubtful photographic impression of the line 13342. 4 : 1 II. Description of Teeth of a Large Extinct (Marsupial?) Genus, Scepar- nodon Ramsay. By Professor OWEN, C.B., F.RS. . : : : 3 IIT, Hvidence of a Large Extinct Monotreme (Hchidna Ramsayi, Ow.) from the Wellington Breccia Cave, New South Wales. By Professor . Owen, C.B., F.R.S. . y : : : : i h : 4 4: IV. Correction to a paper “On the Determination of Verdet’s Constant ” ‘ ce m, the ‘* Phil, Trans.,” 1877. se J. HE. H. Gorpoy, M.S.T.E. : : ’ : : i : : PITA: V. Note on the Irregularities in Magnetic Inclination on the West Coast of Scotland. By T. H. Tuorrs, F.R.S., and A. W. Ricker, M.A. . 5 VI. On the Circulation of Air observed in Kundt’s Tubes, and on some Allied Acoustical Problems. By Lorp Rayxeicu, D.C.L.,F.RS. . 10 VII. The Influence of Bodily Labour upon the Discharge of Nitrogen. By W. Norra, B.A., F.C.S. . k E : : : aie ee Hey Ae 12 November 22, 1883. I, On the Formation of Ripple-mark in Sand. By G. H. Darwin, F.R.S., Plumian Professor and Fellow of met Ce Cam- Paes. , ; : . . . : : : PRT ee is TI. On the Atomic Weight of Titanium. By T. E. Tuorps, F.BS.. . 43 _ For continuation of Contents see 4th page of Wrapper. Price Four Shillings. PHILOSOPHICAL TRANSACTIONS. A ees Part IT, 1883. CONTENTS. IX. On the Skeleton of the Marsipobranch Fishes. Part I. The Myxinoids (Myzxine and Bdellostoma). By Wittiam KircHEN PaRrxKer, F.R.S. X. On the Skeleton of the Marsipobranch Fishes. Part II]. Petromyzon. By WittramM KitcHEN PARKER, F.R.S. XI. On the Organisation of the Fossil Plants of the Coal-Measures. Part XII. By W. C. Wiuttamson, LL.D., F.R.S. XIJ. Experimental Researches on the Electric Discharge with the Chloride of Silver Battery. Part IV. By Warren Dz La Ruz, M.A., D.C.L., Ph.D., F.R.S., and Hugo W. Mutter, Ph.D., F.R.S. XIII. On Electrical Motions in a Spherical Conductor. By Horace Lamp, ~ M.A. XTV. Researches on the Foraminifera—Supplemental Memoir. On an Abyssal type of the Genus Orbitolites ;—a Study in the Theory of Descent. By Wirtiam B. CARPENTER, C.B., M.D., LL.D., F.R.S. XV. On the Affinities of Thylacoleo. By Professor OWEN, C.B., F.RB.S., &e. XVI. On the Morphology and the Development of the Perithecium of Weliola, a Genus of Tropical Epiphyllous Fungi. By H. 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On the Production of Transient Electric Currents. 135 Ballistic Circular throw. magnetisation. Reversed, Ato B..... + 8 + 4 Ore ST ee eral a ay coke Al. f eta ek ta — 9 —13 es Ess. Ue Sheer cate +17 ie + 4 PEOKE Bn iota ve es =e 8 sews +13 Bee: AL s.cc estat sisi —17 Eysiees — 4 Here the circular magnetisation was greater in the ratio of 13 to 4 when the differential effect of torsional stress was exerted on the (comparatively small) amount of residual than on the (comparatively large) amount of temporary longitudinal magnetism. PUBLISHED BY Her Magsesty’s STATIONERY OFFICE, . CATALOGUE OF SCIENTIFIC PAPERS, Compiled by the Royal Society. Vols. 1 to 8. Price, each volume, half morocco, 28s., cloth, 20s. A reduction of one-third on a single copy to Fellows of the Royal Society. Sold by J. Murray, and Triibner and Co. CONTENTS (continued). | PAGE III. On the Life History of the Dock Aécidium Bae rumicts, eee By Cuagtes B. PlowRIGHT . . , 47 IV. Some Relations of Heat to Voltaic and Thermo-Electric eee of Metals in Electrolytes. By G. Gonz, LL.D.,F.R.S. . 3 242550 Y. Ona “ Rennet”’ Ferment contained in the Seeds of Withania coagulans. By Sueripan Lea, M.A., Trinity College, Cambridge . : Bente 51 _ November 30, 1882. ANNIVERSARY MHETING. Report of Auditors . j : ‘ é : : : hay Tia List of Fellows deceased since ie fat 7 : : ; ; : Tera elected . : ; ; ; : : F Z eee Addvess of the President . y : ‘ : : : : ‘ . Miata, Presentation of the Medals. : i , : i } : : Aeon i Election of Council and Officers. : : i : : ; See 5: Financial Statement . : s f : ; : ‘ : . %é—78 Trust Funds . : 5 79—82 Account of the EAS oe of the sum of £4, 000 (the Gcsoumeee Grant) annually voted by Parliament to the Royal ee to be employed in aiding the Advancement of Science . : ‘ : \ 5 wy SSS Account of Grants from the Donation Fund . A a : : E At SoG, Report of the Kew Committee i 2 , d 2 f - 2 F187 List of Presents : : : is t : : : , ie OU apie ye [iP On the Production of Transient Hlectric Currents in Iron and Steel Con- ductors by Twisting them when Magnetized or by Magnetising them when Twisted. By J. A. Ewine, B.S8c., F.R.S.H., Professor of Mechanical Engineering and Physics in the Univarsits oe Tokio, Japan, now Pro- fessor of Engineering in University College, Dundee : : : mg By Now published. Price 20s. CATALOGUE OF THE SCIENTIFIO BOOKS IN THE LIBRARY OF THE ROYAL SOCIETY. First Srecrion :—Containing Transactions, Journals, Observations and Reports, Surveys, Museums. SECOND SECTION :—General Science. A Reduction of Price to Fellows of the Society. HARRISON AND SONS, 45 & 46, ST. MARTIN’S LANE, W.C., AND ALL BOOKSELLERS. PROCEEDINGS OF Tot Por AG SOCLETY, ‘VOL. XXXVI. No. 229. oY oq 2210" coNTENTS. ee O™ December 6, 1883. ae asth PAGE I. Description of Parts of a Human Skeleton from a Pleistocene (Paleolithic) Bed, Tilbury, Essex. By Professor Owen, C.B., F.R.S., &e. ‘ . 136 II. The Wave-lengths of A, a, and of Permanent Lines in the Infra-Red of “the Solar Spectrum. By Captain W. pE W. Asney, R.E., F.R.S. . 187 December 13, 1883. I. Note on a Series of Barometrical Disturbances which passed over Europe between the 27th and the 31st of August, 1883. By Ropert H.Scort, _E.RB.S., Secretary to the Meteorological Council. (Plate 1) ‘ - 139 tT: 'N ote on the Foregoing ae By Lieutenant-General R. STRACHEY, E.R.S. : , : : : : . 1438 III. Experimental Researches on the Electric Dicclake with the Chloride of : Silver Battery. By Warren De La Ruz, M.A.,D.C.L., Ph.D.,F.RS., and Hugo W. Muuer, Ph.D., F.R.S. z : : poe) 051 es IV. On the Figure of Equilibrium of a Planet of pees Density. By G. H. Darwin, F.R.S., Plumian Professor of Astronomy and Fellow of Trinity @allece Gibeidec : : : . ; ; . 158 December 20, 1883. I. On a Magnetic Balance, and Experimental Researches made therewith. By Professor D. E. Hucuss, F.R.S. . : . = ed OE Il, Report on the Circumpolar nga to Fort Rae. by Cup is bined 2 Dawson, R.A. . : : : oe ee IIT. On the Changes in the Gland Cells of Dionea ean during Secretion. By WALTER GARDINER, B.A., Scholar of Clare College, Cambridge . 180 For continuation of Contents se 8rd and 4th pages of Wrapper. Price Five Shillings. Part II, 1883. see Le CONTENTS. SE IX. On the Skeleton of the Marsipobranch Fishes. Part I. The Myxinoids. — (Myzine and Bdellostoma). By Witttam KitcHen Parker, F.R.S. a X. On the Skeleton of the Marsipobranch Fishes. Part II. Petromyzon. _ By Witt1amM KircHEN Parker, F.RS. = XI. On the Organisation of the Fossil Plants of the Coal- HESS Oe Part XII. By W. C. Witt1amson, LL.D., F.B.S. 4 XII. Experimental Researches on the Electric Discharge with the Chloride of — Silver Battery. Part IV. By Warren Dz La Rogz, M.A., D.C... Ph.D., F.R.S., and Hveo W. Muier, Ph.D., F.RS. - XTIT. On Wie ical Motions in a Spherical Coaductan By Horace Lams, M.A. 4 XIV. Researches on the Foraminifera—Supplemental Memais Gad an Abyssal — type of the Genus Orbitolites ;—a Study in the Theory of Descent. By WitiiaM B. CaRpENTER, CB., M.D., LL.D., F.R.S. ~~ XV. On the Affinities of Thylacoleo. By Professor OWEN, C.B., F.R.S., &c. — XVI. On the Morphology and the Development of the Perithecium of Meliola, — a Genus of Tropical Epiphyllous Fungi. By H. MArsHatn Warp, ~ = aa BiA; XVII. On the Atomic Weight of Glucinum (Beryllium), By T. 8. Homprper, Ph.D., B.Sc. XVIII. On the Chances which take place in the Tievetions oaene Standard Com- q - pass in the Iron Armour-plated, Iron, and Composite-built Ships of the — Royal Navy, on a considerable change of Magnetic Latitude. By Staff- ae Commander E. W. Creax, R.N. XIX. Pelvic Characters of Thylacoleo carnifex. By Professor Own, C.B., : - XX. The Limiting Thickness of Liquid Films. By A. W. Retnonp, M.A., and : A. W. Rucrer, M.A. XXTI. The Direct Influence of Gradual Variations of Temperature upon the | 4 Rate of Beat of the ae s Heart. By H. Newett Martin, M.A., M. So ~ D.Se. Index to Part II. 233 : ede —— Price. £2 10s. = Se — E xtra yolume (vol. 168) containing the Reports of the Naturalists attached to the a _ Transit of Venus Expeditions. Price £3. a Sold by Harrison and Sons. : Separate copies of Papers in the Philosophical rvasenentone commencing with 187 5. may be had of Triibrer and Co.,.57, Ludgate Hill. CONTENTS (continued). te aie ig: Z fee 7 ol oy IV. On the Continuity of the Protoplasm through the Walls of Vegetable Cells. By WALTER GARDINER, B.A., Scholar of Clare College, Cam- bridee. 2s. aOR 2 : : . 182 . VY. Note on the Constitution of F Chloropl = EDWARD SCHUNCK, ~ eee WR:S: es . 183 VI. On the Physiology of the i Gael pasate in the ee cee = F, ee aga MADR Bas ae es SS a Seige January 10, 1884. I, On the Transfer of Energy in the Electromagnetic Field. By J. H. Poyntine, M.A., late Fellow of Trinity College, es Professor of Physics, Mason College, Birmingham _. d 186 II, Some Experiments on Metallic Reflection. IV. On the Anca of Light Reflected by Metallic Surfaces. I]. By Sir Jonn Conroy, Bart., M.A. : : : 5 : : : : . 187 IIZ. Extracts from a Teehons on the Volcanic Eruption in- Sunda Strait by Commander the Honourable F. C. P. VeREKER, H.M.S. mes dated Singapore, October 22, 1883. (Plates 2, 3) : : . 198 IV. Report from H.B.M. Consul at Batavia, inclosing Extract relating to the : - Volcanic Outbursts in the Sunda Strait, from the Logbook of the Steam-ship ‘‘ Governor-General Loudon” . ‘ . : - 199 Y. Experimenta! Researches on the Electric Discharge with the Chloride of Silver Battery. By Warren De La Ruz, M.A. D.C.L., Ph.D., F.R.S., and Hugo Murer, Ph.D., F.R.S.. eee : : . 206 January 17, 1884. E On a New Method of eae pee: 7 J. A. Kenpatt, F.LC., E.C.S. : : 2 ‘ : 5 é . 208 - IE. On the Electrolysis of Dilute Salphurio Acid and other Hiypdcbled Salts. By J. H. Guapstonez, Ph.D., F.R.S., and ALFRED TRIBE, Lecturer on Chemistry in Dulwich Wallere : . : : : . 215 III. Qn the Dynamics of a Rigid Body in Elliptic space By R. 8. Hearn, B.A., D.Sc., Fellow of Trinity College, Cambridge : ‘ . 219 IV. Evidence of a Large Extinct Lizard (Notiosaurus dentatus, oo from Pleistocene Deposits, New South Wales, seRUe TEs By Professor Owen, C.B.,F.RS. . - é soa a : : : : p xeak January 24, 1884. I. Observations on the Influence of certain Culture Fluids and Medicinal Reagents in the Growth and Development of the Bacillus tuberculosis. By C. Turopore Wittiams, M.A., M.D., F. R. ©:P5 ees to the Hospital for Consumption, ion = . 222 II. The Effects of Lesions of Different Regions of the Cerebral iat By Davip Ferrier, M.D., LL.D., F.R. S., and GERALD F. ee WeDS FLR.C.S: . eo ne Ee eee : : : . 222 CONTENTS (continued). January 31, 1884. I, Determination of the Vertical and Lateral Pressures of Granular Sub- stances. By Isaac Rozerts, F.G.S., F.R.A.S. . ) 3 . 225 . II, Notes on the Microscopic Structure of some Rocks from the Andes of Ecuador, collected by E. Whymper, F.R.G.S. No. I. Pichincha. _ By Professor T. G. Bonney, D.Sc., F.R.S. seciah ds ; ; 248 ITI, Report on the Tidal Disturbances caused by the Volcanic Eruptions at Java, August 27 and 28, 1883, and the Propagations of the ** Super- tidal” Waves. By Major A. Barrp, R.E.. : : ; : . 248 PAGE List of Presents . 2 ; 3 : Z : ; F z . 253 35 On a New Standard of Illumination and the Measurement of Light. By Witu1am Henry Preece, F.R.S. . : ; : : j . 270 | February 7, 1884. I. On the Motion of Fluid, part of which is moving Rotationally and part Trrotationally, By M. J. M. Hill, M.A., Professor of Mathematics at the Mason Science College, Ti Gainehara: : . ; : . 276 II. Supplementary Note on the Constitution of Chore “By EDWARD Scuunck, F.R.S. eh Set rs Mme 5 28 PUBLISHED BY HER Magszsty’s STATIONERY OFFICE, CATALOGUE OF SCIENTIFIC PAPERS, Compiled by the Royal epee Vols. 1 to 8. Price, each volume, half morocco, 28s., cloth, 20s. A reduction of one-third on a single copy to F ellows of the Royal Society. fold by J. Murray, and Triibner and Co. Now published. Price 20s. _ CATALOGUE OF THE SCIENTIFIC BOOKS IN THE LIBRARY oe THE ROYAL SOCIETY. First Section :—Containing Transactions, Journals, Observations and Reports, Surveys, Museums. SEcOND SECTION :—General Science. A Reduction of Price to Fellows of the Society. HARRISON AND SONS, 45 & 46, ST. MARTIN’S LANE, W.C., AND ALL BOOKSELLERS. PROCEEDINGS OF EYE ROYAL SOCTE TY. VOL. XXXVI. ; No. 230. a») 4 . é > rey 90.4904 CONTENTS. February 14, 1884. i wa a: a PAGE I. On a New Reflecting Galvanometer of Great Sensibility, and on New Forms of Astatic Galvanometers. By THomas GRay, B.Sc., #_B.S.E., and ANDREW Gray, M.A.,F.RSE.. . . . . 287 II. A New Form of Spring for Electric and other Measuring Instruments. __ By Professors W. E. Ayrton, F.R.S., and Joun Perry, M.E. . Og III. Note on the Theory of the Magnetic Balance of Hughes. By Professor Sirvanus P. THompson, B.A., D.Sc., Univ. Coll., Bristol . , . 3819 February 21, 1884. I. On some Relations of Chemical Corrosion to Voltaic Current. By G. Gore, F.R.S., LL.D. 331 II. On an Explanation of Hall’s Phenomenon. By SHELFORD BIDWELL, NMGAS Es. : : 5 ‘ : : : . 3841 February 28, 1884. I. On the Structure and Functional Significance of the Human Corpus callosum. By Professor D. J. Haminton : : - ; . 849 II. On the Surface Forces in Fluids. By A. M. WorrHineton : . 3851 ! List of Presents . E ! 3 : : 3 : za x : PEE: | On a Method of Tracing Periodicities in a Series of Observations when the Periods are unknown. By VinaYEK Narayev Nenzr, First Assistant, Government Observatory, Colaba, Bombay (Plate 4) . - : . 3861 | | | Price Four Shillings. PHILOSOPHICAL TRANSACTIONS. Part III, 1883. CONTENTS. XXII. On the Ciliated Groove (Siphonoglyphe) in the Stomodeum of the | Alcyonarians. By Sypnry J. Hickson, B.A. ¥ XXIII. On the Determination of the Number of Electrostatic Units in the | q Electromagnetic Unit of Electricity. By J. J. Thomson, M.A. ' XXIV. The. Development af Renilla. By Epmunp B. Witson, Ph.D. XXV. On the Continuity of the Protoplasm through the Walls of Vegotablal ig Cells. By WALTER GARDINER, B.A. i XXVI. Supplement to former Paper, entitled—“ Experimental Inquiry into the | a Composition of some of the Animals Fed and Slaughtered as Human — ) Food.”’—Composition of the Ash of the entire Animals, and of certain ‘separated parts. By Sir J. B. Lawes, Bart., and Dr. J. H. Gitprrr. 4 XXVII. The Baxertan Lecrure.—On Radiant Matter Spectroscopy : The Detection and wide Distribution of Yttrium. By W.Crooxzs, F.R.S. © XXVIII. On a new Crinoid from the Southern Sea. By P. Herperr CaR- | PENTER, M.A. : 7 X XIX. An Experimental Investigation of the Circumstances which determina whether the Motion of Water shall be Direct or Sinuous, and of the Law of Resistance in Parallel Channels. By Professor OSBORNE” REYNOLDS, F.R.S. { Index to Volume. Price £1 12s. Extra volume (vol. 168) containing the Reports of the Naturalists attached to the | Transit of Venus Expeditions. Price £3. ; 4 Sold by Harrison and Sons. Separate copies of Papers in the Philosophical Transactions, commencing with 1875. may be had of Tritbner and Co., 57, Ludgate Hill. Periodicities when the Periods are unknown. 403 Table XI. Week.| 1848. | 1849. | 1850. | 1851. |Week.| 1848. | 1849. | 1850. 1851. +-052 | +-049 | —-014 | 27..| +143 | +-051 | +-191 | —-o24 —-035 | —-084 | +-023 | 28..|—-108 | +185 | —-003 | —-092 —-os7 | —-106 | +-060 | 29..| —-120 | +-036 | —-105 | +-072 —-009 | —-012 | —-040 } 30..| —-016 | —-1z9 | —-151 | —-097 t 2 3 4. De. ee +°067 | +°061 | —004 } 31..| +°106 | —171 | +-161 | +°080 6 +°085 | +°071 | —‘055 | 32..| +°053 | +°052 | +°058 | +°051 7 8 9 te —°015 | —-003 | +045 do..| —'013 | +°130 | +°034 | +°062 eee | 134 | —-032 | +-021 | 34..| —-060 | +:064 | —-035 | —-120 -=| 2. | —*020 | —-024 | +037 | 35..| —-056 | —-047 | — 017 —'073 ee eee 033 | —-020 | —-047 |- 36 [006 | —osr +008 | —-031 u..| .. | +118 | —-009 | —-o58 | 37..| +-113 | —-020 | —-o44 | +-162 12.) .. | —004 | +030 | +:004] 38..| +-080 | —-046 | +-008 Peat ee | — O51 es 39..| —074 | +-088 | +-012 14..; .. | —-047 | —-006 | +°089 | 40.., —175 | +-027 | +-054 15..{| .. | —012 | —-057 | +-046 f 41..) +044 | —-049 | +-004. 16..| —-055 | +-011 | +-004 | —-050 }] 42..| +-187 | +-006 | —-049 17..) —073 | +°055 | +:029 | —-112 | 43..| +-067 | +-043 | —-020 18..| +°O11 | +°083 | +005 | —-042 } 44 | 103 —'018 | +°025 19..| +-031 | —-037 | —-034 | +101 | 45..| —-094 | —-112 | +-017 21..| +°018 | —‘O11 | +:°064 | —-015 22..| +°062 | +°061 | +°063 | ith ho (>) 48..| +°084 | +065 | +:027 23..| —°033 | +°073 | +:006 | —°143 —‘140 | —:020 50..| —°099 | —100 | —-039 24,.| —"154 | —:001 | —*148 | +°106 25..| —°043 | —°186 | —:049 | +°127 | 51..} —-014 | +:-042 | +-036 26..| +165 | —-065 | +:040 | —-021 | 52..| +-086 | +-148 | +-019 53.. we ate tees 20..| +°019 | —‘064 cece 46..| —‘016 | +°048 | —-052 SS Con © | (=) op) (=) WOle, XXXVI. 2 _ PUBLISHED BY Her MAJSESTY’S SraTlONERY Oreicr, CATALOGUE OF SCIENTIFIC PAPERS, Compiled by the Royal Society. 3 1 to 8. Price, each volume, half morocco, 28s., cloth, 20s. a, e-third on a single copy to Fellows of the Royal Society. : sia J. Murray, and Triibner and Co. egen Now published. Price 20s. CATALOGUE OF THE SCIENTIFIO BOOKS IN ‘THE LIBRARY OF > THE ROYAL SOCIETY. Kirst SECTION :—Containing Transactions, J: ournals, Observations and Eepoae Surveys, Museums. Szeconp Secrion :—General Science. A Reduction of Price to Fellows of the Society. HARRISON AND SONS, 45 & 46, ST. MARTIN’S LANE, W.C., AND ALL BOOKSELLERS. PROCEEDINGS OF THE ROYAL SOCIETY. VOL. XXXVI. wy No. 231. Oho: 2. aa ER Oe aN Ait BD 1824 [22 ea ED CONTENTS. ee { a a! mS Prone a \ Maree 6, 1884. a) PAGE List of Candidates . : . 404 I, Magnetic Polarity oa Mecuanie By eee eeae D. E. Huanns, E.R.S. : 405 II. On the Origin of she Bibrin Roum nt: “Be a C. Tlnnees MB. D.Sc., George Henry Lewes Student . : pAsans ; . ALT March 13, 1884. I. Researches in Spectrum Photography in Relation to new Methods of Quantitative Chemical Analysis. Part I]. By W. N. Harriey, _#F.RS.E., &c., Professor of Chemistry, Royal College of Science, Dublin : 3 421 — II. On the Mean Diurnal Waennion of iuie sneue vera ean FiGuely Observations at Fort Rae. By Groin H. BP. Dawson, BOALe 24 422 III. Notes on the Microscopic Structure of some Rocks from the Andes of Ecuador, collected by Edward Whymper. No. ff. Antisana. By Professor T. G. Bonney, D.Sc., F.R.S. : : : : : . 426 IV. The Variation of Stability with Draught of Water in Ships. By F. Ene@ar, Professor of Naval Architecture in the University of Glasgow. . 3 : ; Spee : : : : : - 434 March 20, 1884. I. Experimental Researches in Cerebral Physiology. By Vicror Horstxy, M.B., B.S., F.R.C.S., and Epwarp ALBERT ScHAFER, F.R.S. . . 4387 TE. Beeininiacy Note on the Apex of the Leaf in Osmunda and Todea. : (From the Jodrell vial cr Royal Gardens, Kew.) By F. O. Bower, F.L.S. . : , ¢ i - 442 ITI, On the most Widened tee in ce Spot ee First and Second Series, from November 12, 1879, to October 15, 1881. By J. N. Lockyer, F.R:S. ‘ : A i ; 3 3 é . 4435 For continuation of Contents see 4th page of Wrapper. Price Siz Shillings. PHILOSOPHICAL TRANSACTIONS. Part III, 18838. CONTENTS. XXIT. On the Ciliated Groove (Siphonoglyphe) in the Stomodeum of Aleyonarians. By Sypney J. Hickson, B.A. XXIII. On the Determination of the Number of Electrostatic Units in the : Electromagnetic Unit of Electricity. By J. J. THomson, M.A. XXIV. The Development of Renilla. By Epmunp B. Witson, Ph.D. XXV. On the Continuity of the Protoplasm through the Walls of Vegetable | | Cells. By WaureR GARDINER, B.A. XXVI. Supplement to former Paper, entitled—‘‘ Experimental Inquiry into the” Composition of some of the Animals Fed and Slaughtered as Human © Food.’’—Composition of the Ash of the entire Animals, and of certain — separated parts. By Sir J. B. Lawes, Bart., and Dr. J. H. Greer. XXVII. The Bakerran LectuRE.—On Radiant Matter Spectroscopy: The ' Detection and wide Distribution of Yttrium. By W. Crooxzs, F.R.S. XXVIII. On a new Crinoid from the Southern Sea. By P. Herpert Car- PENTER, M.A. / X XIX. An Experimental Investigation of the Circumstances which determine whether the Motion of Water shall be Direct or Sinuous, and of the Law of Resistance in Parallel Channels. By Professor OsBoRNE REYNOLDS, F.R.S. j “Index to Volume. Price £1 12s. Extra volume (vol. 168) containing the Reports of the Naturalists attached to the Transit of Venus Expeditions. Price £3. . Sold by Harrison and Sons. Sane copies of Papers in the Philosophical Transactions, commencing with 1875 q may be had of Triibuer and Co., 57, Ludgate Hill. PUBLISHED BY HER MAJESTY’sS STATIONERY OFFICE, CATALOGUE OF SCIENTIFIC PAPERS, Compiled by the Royal Society. Vols. 1 to 8. Price, each volume, half morocco, 28s., cloth, 20s. A reduction of one-third on a single copy to Fellows of the Royal Society. Sold by J. Murray, and Triibner and Co. Now published. Price 20s. CATALOGUE OF THE SCIENTIFIC BOOKS IN THE LIBRARY OF THE ROYAL SOCIETY. First Section :—Containing Transactions, Journals, Observations and Reports, Surveys, Museums. SECOND SECTION :—General Science. A Reduction of Price to Fellows of the Society. HARRISON AND SONS, 45 & 46, ST. MARTIN’S LANE, W.C., AND ALL BOOKSELLERS. CONTENTS (continued). March 27, 1884. I. Notes on the Varieties and Morphology of the Human Lachrymal Bone and its accessory Ossicles. By A. Macauister, F.R.S., Professor of ' Anatomy in the University of Cambridge . TI. On the Electro-Chemical Equivalent of Silver, and on the Absolene Hlectromotive Force of Cl cae Cells. By Lord Rayzrrieu, D.C.L., F.R.S. : ‘ 2 : Til. On the Natural ud neiiaecall Warkiieanie® of Heriee i Ova. By J. Cossak Ewart, M.D., Regius Professor of Natural History in the University of einen : ; April 3, 1884. I. Remarks on the Atomic Weight of Beryllium. By W.N. Hargtrey, F.R.S.E., &c., Professor of Chemistry, Royal College of Science, Dublin : : ; , : ; II. On the Heating Effects of Bere Gin Re Wiittram HENRY Preece, F.R.S. mAs REN St A. IIT. Spectroscopic Studies on Gokecus Henlicowe ‘No. i. “By Gea Liverne, M.A., F.R.S., and James Dewar, M.A., F.R.S., Professors in the University of Cambridge : TV. On the Action of a Secretion obtaimed from ihe Medicinal tr ae on the Coagulation of the Blood. By Joun B. Haycrart, M.B., F.RS. (Edin.), Professor of Physiology in the Mason and i: ueen’s Colleges, Birmingham ; : : : . April 24, 1884. I. On the Relation between the Electrical Qualities and the Chemical Composition of Glass and Allied Substances. Part I. By THosas Gray, B.Sc., F.R.S.E., and ANDREW Gray, M.A., F.R.S.E., Assis- tant to the Professor of Natural Philosophy in the Universe of Glasgow, and J. J. Dossrz, M.A., D.Sc. (Hdut.), Assistant to the Professor of Chemistry in the University of Glasgow . - II. Influence of Change of Condition from the Liquid to the Solid State on Vapour-Pressure. By Witiram Ramsay, Ph.D., Professor, and SypNEY Youne, D.Sc., Lecturer and Demonsteder of Chemistry in University College, Bristol . List of Presents Observations on the Influence of certain Culture Fluids and Medicinal Reagents in the Growth and Development of the Bacillus tuberculosis. — By C. THEropore Witiiams, M.A., M.D., F.R.C.P. a to the Hospital for Consumption, Eeaapion : ; : Index. : Title and Contents. Obituary Notice:-- CHaBLes WATKINS MERRIFIBRID ar *~ QO 2 Gk O44.) > 450 462 464 471 478 499 500 | 510 ian rent ce