LbeVR Rain
? ae =, ” meh TY it ra ame .
Rate cpus. ite) we entoe ee aes Deite
* . he Wi be *
i” “Hedin ger 7 se aie
‘ath dite a siticaty oe oe
the aie Pieaes
WOR AEE BE!
ns Melb ey eel i 54m
at iG RG ed
way
fie
toda Wed We Mg
Mey geen
he] ay
oe wie wa CRP La thee aii
i a ‘ah et we we et pictur Hanis
PR wae ys "RAGA
re il
a un / pa
HS at
( a Wht CHANT
Ag Aa Hue gone catwadene 4 ins
“€ sed wea
Pe ue Te ae th RY
mo sah
’
» Piva pi Se Ha eG hy yt ml Wiig
6 A MEH Mh walt onk de Muara sont LAR
re) te fo" pen ee car Hk ese rere ibe ’
” Sef yee beh Ki 1, tall the
re ee | We the ne Ny ee
Ld ites med eo dd
HAE He meh NE Heh ed Lm
toed ed ee mee, 44d
OL Ge ad ae et
He de key hf ‘ay 4 ithe
x ote
Gt tiara
sen ringer
iit mr
4
‘ ination f Wstfoe AL Moe 9
at ee LS AL
yy Pas bs vee. bs bea tte jen yi
hb Rett Us fit wt
| A aa Hey
ott eye fs 4 mite
he M HE tani ae on eS
wide hinah Carey
va
pe i
ei
«9 are 4 as)
a te Ah Ae a ay
oe ee
eral aie «
ohh hea ae RH fog
+: I ARR Wa
ea phe eb tn ty
Bash .
va if fey Al
oy Sie
ea i tae
eet p
D
Navigon We
Sela cucions
eae Hw vi ot ate rh 4
eH wa bi ay sist
. Ht
osx
oe
ped
pera Watts.
aM Wa a et ua
ree
, i
a Ht bani
fa viet mH
\ tne
e Be ne Penny
nf
EE EA ee ih GoW “
’ Westie
Ree dtde WS
He dy tee dae W
eS
h bok OAS,
sha Aid darted 9 Oe 4
Tal b nat JE ANY W wea iwi fag
ait ex a “ Pe i
nay me
84 Wn 4 Waa ya it
A Hei ere WE
« MiYedaN teem
4 t *
pK wha Oa ANS RIN
nin MU Th a
1
Ve
4
1
iene Hh IY ee
‘ety tbe thei (ts gue
usesieih a
Wis «orm VY
baa ngent Wedded
BY + Wath: Wort Mb a
rt
ie fay
Weg \e “iy
A eel
bi
; Oe rN, i Ree vat:
i ay W ett ¥ aH « fale a Pit
HON shale Ii Vp «
Heeb tet qe ft Yetie
Mi A
mane Rede Soba
Leia (he RNY A Ce
Hs 5
| ity dita
4 and Ve way ma 4 %
4 “a ehil
i
{
pa 2 &
\ &
‘ye
i i
VOL. XIII.
LONDON:
PRINTED BY TAYLOR AND FRANCIS,
RED LION COURT, FLEET STREET,
MDCCCLXIY.
CONTENTS.
VOL. XIII.
———=—>—_—
Page
A General Catalogue of Nebule and Clusters of Stars for the Year 1860:0,
with Precessions for 1880-0. By Sir J. F. W. Herschel, Bart., F.R.S. .. 2
Note on Kinone. By A. W. Hofmann, LL.D., F.R.S.........
Researches on the Colouring-matters derived from Coal-tar.—I. On Aniline-
yellow. By A. W. Hofmann, LL.D., F.R.S..........
Researches on the Colouring-matters derived from Coal-tar.—II. On
Aniline-blue. By A. W. Hofmann, UL.D., FLR.S. .......ccceeeeeeee OD
Account of Magnetic Observations made between the years 1858 and 1861
inclusive, in British Columbia, Washington Territory, and Vancouver
Wlaad.s By Captain KR. W. Haig, Rea oii osc ele ese eees pay ts)
On Plane Water-Lines. By W. J. Macquorn Rankine, C.E., LL.D.,
HiRes. & H., Assoc, Inst: NA. 6. fie eae Ce ncoarticocecl capo ncic) os 2 5
On the degree of uncertainty which Local Attraction, if not allowed for,
occasions in the Map of a Country, and in the Mean Figure of the Earth
as determined by Geodesy: a Method of obtaining the Mean Figure free
from ambiguity, from a comparison of the Anglo-Gallic, Russian, and
Indian Arcs: and Speculations on the Constitution of the Earth’s Crust.
By the Venerable J. H. Pratt, Archdeacon of Calcutta.......... Soeaeo [dle
On the Meteorological Results shown by the Self-registering Instruments
at Greenwich during the extraordinary Storm of October 30, 1863. By
James Glaisher, F.R.S., FR.A.S. 2.0... Mi ofeias.cuat Beaks) ev ajiiioteye: etepsl eo; avele »
Anniversary Meeting :—
PEC ROE Oty AWGN OTS erate ran) fol eyelslle) aisle) ale ole che se ahaicieae out OTe PAL 21
List of Fellows deceased, &e. .......enceeveee Md: ivsyhhe cues aie, apayet ike 21
———_————— elected since last Anniversary ..........0.0. iS ea wae
Pea Oibeds) OF THeyETESIGeMb) vigialasiicsiale « vlleisis)s/N af 6 o/elaie « s aysleepateaseusrers haze
Presentation of the Medals .......... eueverels) ate selaiolel'sl «cresh ener anhenaes . 3
Election of Council and Officers ..... SCOR LLN C LAOH GORDIE GeO nitro 39
imamelal Stabemembse. 11h sos aleintarsiele’s lelQal lacs aladeta Oldie blengwie 40 & 41
Changes and present state of the number of Fellows........+++se00. 42
On the Spectra of some of the Chemical Elements, By William Huggins
A AAD pd ovata) 3 oes see. Hehe «6 ey nlvah Stan em :
On the Acids derivable from the Cyanides of the Oxy-radicals of the Di- and
Tri-atomic Alcohols, By Maxwel) Simpson, A.B., M.B., FL.R.S. ...... 44
a2
iv
Page
George Biddell Airy, F.R.S., Astronomer Royal ...........+.sceees 48
On the Sudden Squalls of 80th October and 21st November 1863. By
Balfour Stewart, M.A., F.R.S., Superintendent of the Kew Observatory.
(GEIS Teh Ea in ese RREI ue Sain nin tit henley eain tye nha o's ve 60 date 51
On the Equations of Rotation of a Solid Body about a Fixed Point. By
Walliam Spottiswoodes MAL, PARIS ta. os Pea os sce ane sisicasere come
Experiments, made at Watford, on the Vibrations occasioned by Railway
rains passing through a Tunnel. By Sir James South, LL.D., F.R.S.,
one of the Visitors of the Royal Observatory of Greenwich .........00+ 65
Extract of a Letter to General Sabine from Dr. Otto Torell, dated from
Copenhagen, Dec. 12, 1863 ....... gtcsbweeeescoees cae sae en 83
Results of hourly Observations of the Magnetic Declination made by Sir
Francis Leopold M‘Clintock, R.N., and the Officers of the Yacht ‘ Fox,’
at Port Kennedy, in the Arctic Sea, in the Winter of 1858-59; and a
Comparison of these Results with those obtained by Captain Maguire,
R.N., and the Officers of H.MLS. ‘ Plover,’ in 1852, 1855, and 1854, at
Point Barrow. By Major-General Sabine, R.A., President ......... . 84
Examination of Rubia munjista, the Hast-Indian Madder, or Munjeet of
Commerce. By John Stenhouse, UL.D., FP.R.S. ... ....2 ss eee 86
On the Magnetic Variations observed at Greenwich. By Professor Wolf,
ORAM Maing nee ts cect asec s ees etsvne eas + doer 87
A Description of the Pneumogastric and Great Sympathetic Nerves in an
Acephalous Foetus. By Robert James Lee, B.A. Cantab. ............ 90
On the Conditions, Extent, and Realization of a Perfect Musical Scale on
Instruments with Fixed Tones. By Alexander J. Ellis, B.A., F.C.P.S... 93
On the Osteology of the genus Glyptodon. By Thomas Henry Huxley,
BIST adh hep sive ciel oaibiv sit Unee owitecies b ae bb srs ee 108
On the Great Storm of December 3, 1863, as recorded by the Self-registering
Instruments at the Liverpool Observatory. By John Hartnup, F.R.A.S.,
Director of the Observatory. vo... sce css ce cem ote gs oe p ot oe 109
On the Criterion of Resolubility in Integral Numbers of the Indeterminate
Equation f=ax?+a'z?+a"2'?4+2b2'x"+2b'rx"+2b"2'x =0.
By H. J. Stephen Smith, M.A., F.R.S., Savilian Professor of Geometry
it the Wmiversity Of Oxford “ae os cet oe es toe os 20 110
Results of a Comparison of certain Traces produced simultaneously by the
Self-recording Magnetographs at Kew and at Lisbon; especially of those
which record the Magnetic Disturbance of July 15, 1863. By Senhor
Capello, of the Lisbon Observatory, and Balfour Stewart, M.A., F.R.S.
CEs EE eee se Fig See ee SN aare aoe piece pl sean oe lil
Experiments to. determine the effects of impact, vibratory action, and along-
continued change of Load on Wrought-iron Girders. By William Fair-
bain, L/D, FOR Sond tt) wa tae ae Ie ig Se DS Se - 1
On the Calculus of Symbols.—Fourth Memoir. With Applications to the
Theory of Non-Linear Differential Equations. By W. H. L. Russell, A.B. 126
On Melecular Mechanics, By the Rey. Joseph Bayma, of Stonyhurst
College, Lancashire .,....... BAe te ORR Soe EGR oA Skies Se 126
v
Page
On some further Evidence bearing on the Excavation of the Valley of the
Somme by River-action, as exhibited in a Section at Drucat near Abbe-
Milles “by Joseph Prestwich, WBS. oes csess cece te eesneerees oe» 135
A Contribution to the Minute Anatomy of the Retina of Amphibia and
Reptiles. By J. W. Hulke, F.R.C.S., Assistant-Surgeon to the Middlesex
and the Royal London Ophthalmic Hospitals ............cseeeeeees 188
Notes of Researches on the Acids of the Lactic Series.—No. I. Action
of Zinc upon a mixture of the Iodide and Oxalate of Methyl. By
FE. Frankland, F.R.S., Professor of Chemistry, Royal Institution, and
PUPA, Ccctnc een eis Wieved Soa UAW TRN LA. SRE ine eat ne SUNG s 140
On the Joint Systems of Ireland and Cornwall, and their Mechanical Origin.
By the Rey. Samuel Haughton, M.D., F.R.S., Fellow of Trinity College,
LUTET I 5 Gey Sika Gh OO ee eae) DO ee Bee Oe een re 142
On the supposed Identity of Biliverdin with Chlorophyll, with remarks on
the Constitution of Chlorophyll. By G. G. Stokes, M.A., Sec. R.S..... 144
Continuation of an Examination of Rubia munista, the Kast-Indian Madder,
or Munjeet of Commerce. By John Stenhouse, LL.D., F.R.S. ........ 145
On the Spectra of Ignited Gases and Vapours, with especial regard to the
different Spectra of the same elementary gaseous substance. By Dr.
Julius Plucker, of Bonn, For. Mem. R.S., and Dr. J. W. Hittorf, of
Bene Note alka ae us lcig bina’ She nyora-ateie hel See ctBEs Gam winte’n Abie owas 153
On the Influence of Physical and Chemical Agents upon Blood; with special
reference to the mutual action of the Blood and the Respiratory Gases.
By George Harley, M.D., Professor of Medical Jurisprudence in Univer-
See Me Te ONO ses ea ert oo 4 70's Mad shag» pin ¥Po0 & Sie pp Ahan eh 157
Researches on Radiant Heat.—Fifth Memoir. Contributions to Molecular
Eerie Sane a yh shiny A yt, TER Ss aha) obs3-pieie = yi 6 bi oy s, eiores oho che, dial shalle » ores din vhs 160
Remarks on Sun Spots. By Balfour Stewart, M.A., F.R.S., Superintendent
SCM ENV OUSELVALOLY — savrn ties oh exe Ses 6 Gui wep oe ne te bam oly cies ae 168
Description of an Improved Mercurial Barometer. By James Hicks...... 169
On Mauve or Aniline-purple. By W.H. Perkin, F.C.S. ......eeeeeees 170
On the Functions of the Cerebellum. By William Howship Dickinson,
PMS Ose aft in bs: sinibls. 0» bite hire SicaaiGreh Sirilel whieh olsfasaldsipiateinlers abalews otters 177
An Inquiry into Newton’s Rule for the Discovery of Imaginary Roots. By
Meee VESteDn FEU 5 cai avis heWcvalloke Ay Goslsva alam alate oe Weasels ap biol sls 179
Description of a Train of Eleven Sulphide-of-Carbon Prisms arranged for
Spectrum Analysis. By J.P. Gassiot, FLR.S. oo... eee eee ences 183
The Croonian Lecture.—On the Normal Motions of the Human Eye in rela-
tion to Binocular Vision. By Professor Hermann Helmholtz, For. Mem.
Lhd: Cap cc adil ies IGE Ora eNO DIC Ce On ara Aiea re SIRE ara aaa ara 186
On the Orders and Genera of Quadratic Forms containing more than three
Indeterminates. By H.T. Stephen Smith, M.A., F.R.S. wo... ee ee eee 199
On some Phenomena exhibited by Gun-cotton and Gunpowder under special _
conditions of Exposure to Heat. By F, A. Abel, F.R.S............ 1» 204
On Magnesium. . By Dr. T. L.:Phipson,-FiC.S. ci 0e caves das eae a LE
-.
vi
é Page
On the Magnetic Elements and their Secular Variations at Berlin, as observed
by Acsiirman:. 005. 6 eee Be PO ERS Saath en es ee Sil 2s
On the Action of Chlorine upon Methyl. By C. Schorlemmer, Assistant in
the Laboratory of Owens College, Manchester .......cceeeseececcees 225
On the Calculus of Symbols (Fifth Memoir), with Applications to Linear
Partial Differential Equations, and the Calculus of Functions. By W. H.
Tepassell, “ASB 5 5 e Mee a Shere Ook a ue 0-0 Plate ole © alee een ee 227
Second Part of the Supplement to the two Papers on Mortality published
in the Philosophical Transactions in 1820 and 1825. By Benjamin
Gompertz, FIRS. 0% oe. aoe « oiiee 0 ois, seis viene nla ss = ee 228
Investigations of the Specific Heat of Solid and Liquid Bodies. By Hermann
Kopp, PED... 65. «30 cieweine nos toe 6 0 ain cleh as © 2 © 0\= eles 229
On some Foraminifera from the North Atlantic and Arctic Oceans, includ-
ing Davis Strait and Baffin Bay. By W. Kitchen Parker, F.Z.S., and
Professor T. Rupert Jones, F.G.S. .........00- os oe oe 0 eae eer 239
Note on the Variations of Density produced by Heat in Mineral Substances.
By Ord) die Phipsen, FCS i os eek tee ee eee ay oo ee 240
On the Spectra of some of the Fixed Stars. By W. Huggins, F.R.A.S., and
William A. Miller, M.D., LL.D., Treasurer & V.P.R.S. .....c0ccenee 242
A Second Memoir on Skew Surfaces, otherwise Scrolls. By A. Cayley
Meo aslo nic,e © Gis a Als cre Ore owls, ose vis @ ave #18 62-0, 07ose ome ele 244
On the Differential Equations which determine the form of the Roots of
Algebraic Equations. By George Boole, F.R.S., Professor of Mathe-
mataes'in Queen's College, Cork’: o.oo. i is aes oe 245
A Comparison of the most notable Disturbances of the Magnetic Declination
in 1858 and 1859 at Kew and Nertschinsk, preceded by a brief Retrospec-
tive View of the Progress cf the Investigation into the Laws and Causes
of the Magnetic Disturbances. By Major-General Edward Sabine, R.A..,
President of the Royal Society... ..0. 0... 60 ae ee cee + cists eee 247
On the degree of uncertainty which Local Attraction, if not allowed for,
occasions in the Map of a Country, and in the Mean Figure of the Earth
as determined by Geodesy: a Method of obtaining the Mean Figure free
from ambiguity by a comparison of the Anglo-Gallic, Russian, and Indian
Ares: and Speculations on the Constitution of the Earth’s Crust. By
the Venerable J. H. Pratt, Archdeacon of Calcutta .......ccseeeeees 253
Annual Meeting for the Election of Fellows. ......6.00000++s00 oe enie . 276
Description of the Cavern of Bruniquel, and its Organic Contents —Part I.
Human Remains. By Professor Richard Owen, F.R.S. ...........065 277
On Soules Binary Quadratic Forms. By H.J. Stephen Smith, M.A., ee
Inquiries into the National Dietary. By Dr. E. Smith, F.R.S. .......... 298
On some Varieties in Human Myology. By John Wood, F.R.C.S. ...... 299
Researches on Isomeric Alkaloids. By C. Greville Williams, F.R.S. .... 3803
On the Synchronous Distribution of Temperature over the Earth’s Surface.
iy, Henry, G. Hennessy, 1,320; )0,5) ie oleae ole 0.5 at, sole Miele .teiseaee 312
vu
Page
Experimental Researches on Spontaneous Generation. By Gilbert W. Child,
MORON, Leg RE SELES Ut 55 sks ce hea 680 bow dee Gales Court vo. 31d
On a Colloid Acid, a Normal Constituent of Human Urine. By William
ROR rie aa DI ESE ila. coos «ic ciel vs ood vt sc oce eres ds, « wal bila gee Rae ls Hels 314
Further observations on the Amyloid Substance met with in the Animal
Peony. by Lopert M Donnell, M.D. co.cc es sces kobe beseenteenees ol7
Description of a New Mercurial Gasometer and Air-pump. By T. R.
Semmemsemcreteee Oh Deeg MGT TIE Bi Sa00 Vino abe a bln Saeiald aca gied vs. Seivleis wlaudle Ole 321
On the Distal Communication of the Blood-vessels with the Lymphaties ;
and on a Diaplasmatic System of Vessels. By Thomas Albert Carter,
nas ia. 2g aoe, orale & ob, cha aretsinscokels refs: 3 boseee sob eee penne
Aérial Tides. By Pliny Earle Chase, A.M.,S.P.A.S...... slip ait Ra 329
On the Microscopical Structure of Meteorites. By H.C. Sorby, F.R.S. .. 333
On the Functions of the Cerebellum. By W. H. Dickinson, M.D......... 334
On the Properties of Silicie Acid and other analogous Colloidal Substances.
rpms Graham, PRS. cece ee tence es ee ned ines Hee boee sects 335
Researches on the Colouring-matters derived from Coal-tar.—III. Diphenyl-
eens. W. Homann, LL.D ., FoR: 5 i0 occu aise 00 sess ges ote 341
A Table of the Mean Declination of the Magnet in each Decade from
January 1858 to December 1863, derived from the Observations made at
the Magnetic Observatory at Lisbon ; showing the Annual Variation, or
Semiannual Inequality to which that element is subject. Drawn up by
the Superintendent of the Lisbon Observatory, Senhor da Silveira...... 347
On Organic Substances artificially formed from Albumen. By Alfred H.
Sn LES 2 Se lg ee OR ee ee ere pene eh ee ee mr ie 350
_ On the Reduction and Oxidation of the Colouring-matter of the Blood. By
Pence Are CGy Eee ae as lessen vc ele vasivs cavuscee tens vanes 855
Further Inquiries concerning the Laws and Operation of Electrical Force.
erent SCiVe EIRTTIS, EO EU.O. (7. seis s'v'e 'e ee e'e e's c'e Valve ee ce wee e eee ne 364
On a New Class of Compounds in which Nitrogen is substituted for
ameter cba Peter Gress. coe sst feeiis Cees ob eels Wee tite Gare bale 375
New Observations upon the Minute Anatomy of the Papille of the Frog’s
#onene.. By, Lionel S. Beale, M.B., F.R.S,, FLR.C,P. oe. cere eens 384
Indications of the Paths taken by the Nerve-currents as they traverse the
caudate Nerve-cells of the Spinal Cord and Encephalon. By Lionel S.
Peeeemcte oh be. H.R. (Plate IM.) . occas ots s caine ba Nees 386
On the Physical Constitution and Relations of Musical Chords. By
Puen Se PNiG Bb. BC ES ccc wats ee yt awe wees habe ee eens 6 392
On the Temperament of Musical Instruments with Fixed Tones. By
Ree meee PUNT, Heb ciey EC yes e sieiscre ay sie cys peels vincca eae ae ait 404
On the Calculus of Symbols.—Fourth Memoir. With Applications to the
Theory of Non-Linear Differential Equations. By W.H. L. Russell, a
Lorian IE as SU An Ae I Oe ee OR SRR ce te ntie o b
On the Calculus of Symbols.—Fifth Memoir. With Jey to Linear
Partial Differential Equations, and the Calculus of Functions. By W.
mlb, Housel, (A Bite tances eas ern elena Ra itaae
Vill
Page
Comparison of Mr. De la Rue’s and Padre Secchi’s Eclipse Photographs.
iby Warren De la. Rue, PBB... cc ccec cn ceverse sce ss es see 442
On Drops. By Frederick Guthrie, Professor of Chemistry and Physics at the
Royal College, Maurrtaus 1707.2... a ee alo e's cle ae ee 0 2s sit
On Drops.—Part II. By Frederick Guthrie, Professor of Chemistry and
Physics at the Royal College, Mauritius. (Plates IV. & V.).......... 457
On the Chemical Constitution of Reichenbach’s Creosote-—Preliminary
Notice. By Hugo Muller, Ph.D. a. os. og anne. sale: o = 484
Remarks on the Colouring-matters derived from Coal-tar.—No. IV. Phe-
nyltolylamine: ‘By ‘A. ‘W. Hofmann, LL.D., F.R.S.. . 5... .252eeeeeeee 485
On the Spectra of some of the Nebule. By W. Huggins, F.R.A.S. ;—a
Supplement to the Paper “On the Spectra of some of the Fixed Stars,”
by W. Huggins and W. A. Miller, M.D., Treas. and V.P.R.S........... 492
On the Composition of Sea Water in different Parts of the Ocean. By Dr. —
George Forchhammer, Professor in the University of Copenhagen. .493 & 494
Anniversary Meeting :—
Aeport of Auditors... oc. was ees ow oe fe se sss «ee 494
aiaat, of Fellows decéased, Qe... v.00... os ec ae ‘Se ons 2a 495
——_—_—_— elected since last Anniversary ..cs.cceececcseceeee 495
First Report of the Scientific Relief Committee ............. ee eee A495
Address of the President) 0.5 o.048 vdien ld ows Shek sew eee ae 497
Presentation of the Medals. .2..2.4. 6sas 0d des cd ow aeete ee Cee 505
Election: of Council sand: Officers) 4ic4:50).:05) s00 bs Cole 3 oa 517
Pynancial Statement oi... ec os wees as 5 os oe ee ee oe eee 518 & 519
Changes and present state of the number of Fellows .............. 520
Researches on certain Ethylphosphates. By Arthur Herbert Church, M.A.
Oxon., Professor of Chemistry, Royal Agricultural College, Cirencester. . 520
A Dynamical Theory of the Electromagnetic Field. By Professor J. Clerk
Wilaxwell, ECES. . cc 0 ac ces esc ce eee a ean cle sig Oh slsine 5th ee 531
On the production of Diabetes artificially in Animals by the external use of
@old:), By Henry Bence Jones, M.D., F.RS.. ccies)d 0,34 0 ote eee 537
On the Action of Chloride of Iodine upon Organic Bodies. By Maxwell
Simpson, M.B., FBS. 2... eee os Pons ad See bn elblWls § ool oteie Olea eee aa 540
On Fermat’s Theorem of the Polygonal Numbers, with Supplement. By the
Right Hon. Sir Frederick Pollock, FURS. 0......4. 0.222252 tere oe 542
On the Structure and Affinities of Hozoon Canadense. In a Letter to the
President. By W. 5. Carpenter, M_D., RS... : sae eee 545
On the Functions of the Foetal Liver and Intestines. By Robert James
Lee, B.A. Cantab., Fellow of the Cambridge Philosophical Society ..., 549
Completion of the Preliminary Survey of Spitzbergen, undertaken by the
Swedish Government with the view of ascertaining the practicability of
the Measurement of an Arc of the Meridian. In a Letter addressed to
Major-General Sabine by Captain C. Skogman, of the Royal Swedish
Navy: dated Stockholm, Nov. 21, 1864. (Plate VI.)........... tr
On the Sextactic Points of a Plane Curve. By A. Cayley, F.R.S......... 553
1x
Page
On a Method of Meteorological Registration of the Chemical Action of ‘
Total Daylight. By Henry E. Roscoe, B.A., FLR.S. 20... cece eee eee 555
Obituary Notices of Deceased Fellows :—
A IATLNTESE. CIOTRUIGT AEE A nee tes Oe ag SEM i
iteamiae Ce OSM MAY COOPER. 5). secre onal mica qiaiege els. alate u16 sapere vince + oeeGiarw i
Ji@e Te LEN ae ar ire ne Para No RAE Ge sMels nionate ct memes oa iii
emma rR nN aLeTe VESEY oie: caval e asta elatcle aia! ees bake dhal'a 01's Wisral asta a ak eg iil
Bape MMU ENE UNV cscs 5. a te cine acs) pe ai eats ena ah seis « wal oka “ancieieard « Muaparer omngale Vv
Perpre lim caOe eer is ea hank Has Beas ye eld alee oie kluc, es learn nein V
eee EO eS urate whe nie Oy gles b's wise ae ware eae age vi
Rea xamiral John Washington . 2.6.5.6 08 see gee eee wees ecemes vil
Reese MaMcmete DESPLOEZ ie) cus sds. ais cise Cm eles ea sins oe a em iie a e swe viii
Peebrearcum bit S@Merhely voc. hs ca cee esa nh «ccc ees deletes wy et we sas 1x
Saeed Christian Bumilrer fe. cosa. cent oO Mem sinew ds nfo Xvi
SSCS Bee von oid aioe & wai ayecaes wjaei a's e's ao we gestae ane 561
ERRATA.
Page 153, for 8S. W. Hittorf read J. W. Hittorf.
Pages 201 & 202. The words “If a quadratic form........ Phil. Trans. vol. exliii.
p. 481)” should have been printed as a foot-note in explanation of the term
“index of inertia.”
Page 330, for Flangergues read Flaugergues.
Errata in Opituary (Vou. XIT.).
Page xxxvi, line 8 from bottom, for Poisson read Brisson.
?
In this Volume the following pages are to be cancelled:
xxxvili, line 4 from top, for son read husband.
NOTICE TO THE BINDER.
Pages 83, 227
bo
(eae
, 6406 a ee
100-00
These analyses were performed on specimens prepared at different times.
This acid is soluble in water, alcohol, and ether. It has a pure acid taste.
It melts at about 135° Cent., and at a higher temperature suffers decompo-
sition. The free acid gives an abundant white precipitate with acetate of
lead, soluble in strong acetic acid. It is not precipitated by lime-water.
The neutralized acid yields a bulky white precipitate with corrosive subli-
mate, and a pale brown with perchloride of iron. Copper salts give a
bluish-white precipitate. Chloride of barium is not affected. The forma-
tion of this acid may be explained by the following equation :—
C, H, 0, Cy, +2 a 0,)4+4H0=0,,5° | O,,+2NH,.
I have also analyzed the silver-salt of this acid. As it suffers decompo-
sition at the temperature of boiling water, I was obliged to effect its
desiccation by placing it 2m vacuo over sulphuric acid. Itis slightly soluble in
water. ‘The numbersit yielded on analysis agree very well with the formula
H
Cro ag, fOr aT a
; Theory. Experiment.
ee
fF Il.
CT Ua G67 16°61 See
47,5 Bs 1:39 aes
| OR ay, — =
Ag,” 252255461 AueDs 60-67
100-00
1868. | Oxy-radicals of Di- and Tri-atomic Alcohols. AZ
The ether of this acid is readily prepared by passing hydrochloric acid
gas through its solution in absolute alcohol. On evaporating the alcohol
an oily residue was obtained, which was washed with a solution of car-
bonate of soda and distilled. ‘The greater portion passed over between
295° and 300° Cent. The analysis of this portion gave numbers which
indicate the formula C,, (CH ) 0,,:—
4 5/2
Theory. Experiment.
Le eS
I II.
Crt... 02:94 54°61 54°32
ec Ze 8°09 6°91
Ore Oo 22 —. —
100-00
This ether suffers partial decomposition during distillation; hence the
discrepancy between the theoretical and experimental numbers in the first
analysis. ‘The specimen which served for the second was not distilled at
all, but simply purified by solution in ether. It is a colourless neutral oil
with a very acrid taste. It is somewhat soluble in water. Heated with
solid potash it yields alcohol, and the acid is regenerated. I regret to say
I have not succeeded in obtaining the cyanide (C, H, O, Cy,), which gene-
rates this acid, in a state of purity.
The compositions of the ether and silver-salt of this acid prove it to be
bibasic. It is highly probable that the basicity of an acid produced in
this way depends on the atomicity of the radical in the cyanide which
generates it. If this be so, the cyanides of the mono-, di- and tri-atomic
radicals of the glycols and glycerines should then yield by decomposition
with potash respectively mono-, bi- and tri-basicacids. If it would he pos-
sible to prepare the acid C, H, O, from the cyanide C, H, 0, Cy, it would
be interesting to examine its bearing on this point. Would it prove mono-
basic or bibasic ?
This acid bears the same relation to pyrotartaric that malic bears to
succinic acid. :—
Succinic acid ..,. C, H, O, Pyrotartaric acid .... C,,H,0O,
Malice acid'’.!. 5.2. C, H, O,, New acide a wevsteureny quelle, @
8 10
It has the composition of the homologue of malic acid. Whether it is
actually the homologue of that acid or not I cannot yet say. I propose to
call it oxy-pyrotartaric acid. Formulated according to the carbonic acid
type it is thus written :—
2HO, C, H, 0, 1é oo O,.
We may now, I think, safely answer in the affirmative the questions put
at the commencement of this Paper. The cyanides of the oxy-radicals of
the di- and tri-atomic alcohols can be formed, and the action of the potash
on these cyanides is analogous to its action on the ordinary cyanides.
48 Mr. Airy—Analysis of 177 Magnetic Storms. [Dee.17,
The foregoing research was finished many months ago, but I delayed
publishing it in the hope of being able to announce at the same time the
formation of lactic acid by a similar process. I find, however, from the
‘Annalen der Chemie und Pharmacie’ of last month that I have been
anticipated by Wislicenus, who has succeeded in forming lactic acid in the
manner I have just described,
_ December 17, 1863.
Major-General SABINE, President, in the Chair.
The following communications were read :—
I. “First Analysis of 177 Magnetic Storms, registered by the
Magnetic Instruments in the Royal Observatory, Greenwich,
from 1841 to 1857.” By Gzorer Bippeit Airy, Astronomer
Royal. Received November 28, 1863.
(Abstract.)
The author first refers to his paper in the Philosophical Transactions,
1863, “On the Diurnal Inequalities of Terrestrial Magnetism as deduced
from Observations made at the Royal Observatory, Greenwich, from 1841
to 1857.’ These results were obtained by excluding the observations of
certain days of great magnetic disturbance ; it is the object of the present
paper to investigate the results which can be deduced from these omitted
days.
The author states his reasons for departing from methods of reduction
which have been extensively used, insisting particularly on the necessity of
treating every magnetic storm as a coherent whole. And he thinks that
our attention ought to be given, in the first instance, to the devising of
methods by which the complicated registers of each storm, separately con-
sidered, can be rendered manageable; and in the next place, to the discus-
sion of the laws of disturbance which they may aid to reveal to us, and to
the ascertaining of their effects on the general means in which they ought
to be included.
The author then describes the numerical process (of very simple cha-
racter) by which, when the photographic ordinates have been converted
into numbers, any storm can be separated into two parts, one consisting of
waves of long period, and the other consisting of irregularities of much
“more rapid recurrence. He uses the term “ Fluctuation ”’ in a technical
sense, to denote the area of a wave-curve between the limits at which the
wave-ordinate vanishes. 'The Waves, Fluctuations, and Irregularities, as
inferred from separate treatment of each storm, constitute the materials
from which the further results of the paper are derived.
Table I. exhibits the Algebraic Sum of Fluctuations for each storm, with
the Algebraic Mean of Disturbances, and Tables II. and III. exhtbit the
1863.] = Mr. Airy—Analysis of 177 Magnetic Storms. 49
Aggregate or Mean for each year, and the Aggregate for the seventeen years.
The Aggregate for the Northerly Force is negative in every year. That for
the Westerly Force is on the whole negative ; the combination of the two
indicates that the mean force is directed about 10° to the east of south.
That for the Nadir Force appears negative, but its existence is not certain.
Some peculiarities of the numbers of waves with different signs are then
pointed out. For Westerly Force and also for Nadir Force, the numbers
of + waves and —waves are not very unequal; but for Northerly Force
there are 177-++ waves and 277—waves. In Nadir Force it is almost an
even chance whether a storm begins with a + wave or with a —wave; and
the same with regard to its ending; in Westerly Force the chances at
beginning and ending are somewhat in favour of a +-wave; butin Northerly
Force two storms out of three begin with a —wave, and ten storms out of
eleven end with a —wave. |
The beginnings and ends of the storms are also arranged by numeration
of the combination of waves of different character in the different elements
(as, for instance, Westerly Force + with Northerly Force —, Northerly
force + with Nadir Force +, &c.); but no certain result appears to
follow, except what might be expected from the special preponderances
mentioned above, leaving the relative numbers of the combinations a
matter of chance in other respects.
Tables IV., V., VI. exhibit the Absolute Aggregates of Fluctuations and
Absolute Means of Disturbances without regard to sign. In interpreting
these it is remarked that the large — mean force in the northerly direction
necessarily increases the Aggregate and diminishes the Number of Waves.
With probable fair allowance for this, it appears that the Numbers of Waves
are sensibly equal, that the Sums of Fluctuations are sensibly equal, and
that the Means of Disturbances are sensibly equal for Westerly Force and for
Northerly Force. But the Number of Waves for Nadir Force is less than
half that for the other forces ; while the Sum of Fluctuations is almost three
times as great as that for the others, and the Mean of Disturbances almost
three times as great.
Attempts are made to compare the epochs of the waves in the a
directions, but no certain result is obtained.
: Tables VII., VIII., IX. exhibit for each storm, and for each year, and ©
for the whole period the Number of Irregularities, the Absolute Sum of
Irregularities, and the Mean Irregularity. It appears that the value of Mean
Irregularity is almost exactly the same in the three directions, that the
number of irregularities is almost exactly the same in Westerly Force and in
Northerly Force, but that the number in Nadir Force is almost exactly
half of the others.
It is certain that the times of Irregularities in the Westerly and Northerly
directions do not coincide. There appears some reason to think that Nadir
Irregularities frequently occur between Westerly Irregularities.
In Table X. the Aggregates of Fluctuations and Irregularities are arranged
50. Mr. Airy—Analysis of 177 Magnetic Storms. [Dec. 17,
by months, but no certain conclusions follow. In Table XI. the Wave-
disturbances and the Irregularities are arranged by hours ; for the Wave-
disturbances results are obtained which may be compared with those of
previous investigators; in Table XII. it is shown that these may be repre-
sented by a general tendency of wave-disturbances, different at different
hours, which general tendency is itself subject to considerable variations.
For the Irregularities it is found that the coefficient is largest in the hours
at which storms are most frequent. It does not appear that any sensible
correction is required to the Diurnal Inequalities of the former paper on
account of these disturbed days.
The author then treats of the physical inference from these numerical
conclusions. And in the first place he states his strong opinion that it is
impossible to explain the disturbances by the supposition of definite
galvanic currents or definite magnets suddenly produced in any locality
whatever. The absolute want of simultaneity (especially in the Irregu-
larities), and the great difference of numbers between the Waves and Irregu-
larities for the Nadir Force (in which the Irregularities are just as strongly
marked as in the Westerly and Northerly, and the Wave-disturbances are
much more strongly marked), and those for the other Forces, appear fatal
to this.
It is then suggested that the relations of the forces found from the
investigations above, bear a very close resemblance to what might be ex-
pected if we conceived a fluid (to which for facility of language the name
‘Magnetic Ether” is given) in proximity to the earth, to be subject to”
occasional currents produced by some action or cessation of action of the
sun, which currents are liable to interruptions or perversions of the same
kind as those in air and water. He shows that in air and in water the
general type of irregular disturbance is travelling circular forms, sometimes
with radial currents, but more frequently with tangential currents, some-
times with increase of vertical pressure in the centre, but more frequently
with decrease of vertical pressure; and in considering the phenomena
which such travelling forms would present to a being over whom they
travelled, he thinks that the magnetic phenomena would be in great
measure imitated.
The author then remarks that observations at five or six observa-
tories, spread over a space less than the continent of Europe, would pro-
bably suffice to decide on these points. He would prefer self-registering
apparatus, provided that its zeros be duly checked by eye-observations, and
that the adjustments of light give sufficient strength to the traces to make
them visible in the most violent motions of the magnet. For primary
reduction he suggests the use of the method adopted in this paper, with
such small modifications as experience may suggest.
Broo Roy-Soc Vol. XII PUL |
a
J
ee ee ae
Nov? 21%1863. 1 ™
_
| | emt.
ee
| |
| |
5G
Hl i
a 25:
| |
| 29
| | |
Ee La Of
Positive
(i) Ay ‘tt i]
y'
Nees
INS)
|
|
|
i
!
|
|
Ke YE ' {'
AA
/ v
WW,
4
y)
fa
chy > {--
| Positive
if} 1
i] | i j |
{
St 6h.
ZA
aes TAI
OTFACES
Oy e
OITHHAES
TALS
|
|
Negative
i
1863.] Mr. B. Stewart—Squalls of 30th Oct. and 21st. Nov. 51
II. “On the Sudden Squalls of 30th October and 21st November
1863.” By Barour Stewart, M.A., F.R.S., Superintendent of
the Kew Observatory. Received December 10, 1863.
The 30th of October was windy throughout, and in the afternoon there
was a very violent squall.
The barograph at the Kew Observatory, as will be seen from Plate I.
which accompanies this communication, records a very rapid fall in the
pressure of the atmosphere, which appears to have reached its lowest point
about 3° 9" p.m., G.M.T. At this moment, from some cause, possibly a
very violent gust of wind, the gas-lights in the room which contained the
barograph went out, and were again lit in a quarter of an hour. During
this interval the barometer had risen considerably ; and indeed the baro-
graph curve, although unfortunately incomplete, presents the appearance
of an extremely rapid rise. It may therefore perhaps be supposed that
there was a very sudden increase of pressure accompanied with a violent
gust of wind at the moment when the gas went out, which would be about
3" 9™ p.m., as above stated.
In a paper communicated to the Royal Society on November 23,
Mr. Glaisher has remarked that at Greenwich the time of maximum de-
pression of the barometer was 3° 30™ p.m., while at the Radcliffe Observa-
tory, Oxford, it was 2” 30" p.m. This would indicate a progress of the
storm from west to east, in accordance with which Kew should be some-
what before Greenwich as regards the time of maximum depression. This
anticipation is therefore confirmed by the record of the Kew barograph
which has been given above.
The indications of the Kew self-recording electrometer during this squall
show that about 2" 39™ p.m. the electricity of the air, which before that
time had been very slightly negative, became rapidly positive, then quickly
crossed to negative, became positive again, and once more crossed to nega-
tive about 3" 3™ p.m., recrossing again from strong negative about 3" 51™
p.M., after which it settled down into somewhat strong positive.
It is well, however, to state (what may also be seen from Plate I.)
that the variations of this instrument between 3" 3™ p.m. and 3" 51™ p.m.
were so rapid as not to be well impressed upon the paper.
At Kew there is often occasion to move the dome, so that we cannot
well have an instrument which records continuously the direction of the
wind ; but we have a Robinson’s anemometer, which records the space tra-
versed by the wind, and thus enables us to find its velocity from hour to
hour, though not perhaps from moment to moment. A reference to
Plate I. will show an increase in the average velocity of the wind during
this squall.
A somewhat similar squall took place in the afternoon of Saturday,
November 21st, about 4 o’clock.
In this case the Kew barograph presents a rapid (and, in the curve,
52 . Mr. Spottiswoode—LEquations of Rotation Re [1863,
ragged) fall of the atmospheric pressure, which reached its minimum about
4» 45" p.m. There was then a very abrupt and nearly perpendicular rise
of about five hundredths of an inch of pressure, or rather less, after which
the rise still went on, but only more gradually.
Through the kindness of the Rev. R. Main, of the Radcliffe Observa-
tory, I have been favoured with a copy of the trace afforded by the Oxford
barograph during this squall, in which there appears a very sudden rise of
nearly the same extent as that at Kew, but which took place about four
o’clock, and therefore, as on the previous occasion, somewhat sooner than
at Kew. This change of pressure at Oxford was accompanied by a very
rapid fall of temperature of about 8° Fahr.
The minimum atmospheric pressure at Kew was 29°52 inches, while at
Oxford it was 29°28 inches.
It will be seen from the Plate that at Kew the electricity of the air fell
rapidly from positive to negative about 4" 30™ p.m., and afterwards fluctu-
ated a good deal, remaining, however, generally negative until 5" 22™ p.M.,
when it rose rapidly to positive.
We see also from the Plate that there was an increase in the average
velocity of the wind at Kew during the continuance of this squall. To
conclude, it would appear that in these two squalls there was in both
cases an exceedingly rapid rise of the barometer from its minimum both at
Oxford and at Kew, this taking place somewhat sooner at the former
place than at the latter; and that in both cases the air at Kew remained
negatively electrified during the continuance of the squall, while the
average velocity of the wind was also somewhat increased.
. The Society then adjourned over the Christmas recess to Thursday
January 7, 1864.
“On the Equations of Rotation of a Solid Body about a Fixed |
Point.” By Witi1am Srortiswoops, M.A., F.R.S., &c. Received
March 21, 1863,*
In treating the equations of rotation of a solid body about a fixed point,
it is usual to employ the principal axes of the body as the moving system
of coordinates. Cases, however, occur in which it is advisable to employ
other systems; and the object of the present paper is to develope the funda-
mental formulee of transformation and integration for any system. Adopt-
ing the usual notation in all respects, excepting a change of sign in the
quantities F, G, H, which will facilitate transformations hereafter to be
made, let
A=im(y? +2"), B= Xm(z2?+2’), C= 2m(2*+y’),
—F=myz, —G= Inez, —H=Zmzy ;
_ .* Read April 16, 1863: see abstract, vol. xii, p. 523,
1863. ] of a Solid Body about a Fixed Point. - 53
and if p, g, r represent the components of the angular velocity resolved
about the axes fixed in the body, then, as is well known, the equations of
motion take the form
d , 4
a2 nS 46S 7 =F") + (B—O)gr + Hrp—Gpg, |
|
+H2 ne tp =a —p*)—Hgr+(C—A)rp+Fpq, 7 (1)
— 2 +Eo Se esses me
To obtain the two general integrals of this system : multiplying the equa-
tions (1) by p, g, 7, respectively adding and integrating, we have for the
first integral
Ap? +Bq’?+Cr?42(For+Grp+Hpqg)=h, . . . «° (2)
where 4 is an arbitrary constant. Again, multiplying (1) by
Ap +Hg +Gr,
Hp+ Bq +F7,
Gp+Fq +Cr,
respectively adding and integrating, we have for the second integral
(Ap+Hq+Gr)’?+ (Hp+Bq+Fr)’+ (Gp+Fq+Cr)?=h*, . (8)
where #**is another arbitrary constant. This equation may, however, be
transformed into a more convenient form as follows: writing, as usual,
. 4=BC—F, 8=CA—-G, @=AB—H2, V=|AHG
$=GH—AF, &=HF—BG, %#=FG—CH, HB Fi. (4)
A+B+C=S, GFC
and bearing in mind the inverse system, viz
VA=8C-F, VB=CA-G’, VC=AB—H?
VF=GH-AsS, VG=HI-BG, VH= ark CH. - (
2+8+€=8,
we may transform (3) into the following form :—
(AS—%B—€)p’?+2(FS + H)qr .
+(BS—€C—A)¢°+2(GS + &)rp rete 00)
+(CS—@ —%)r?+ 2(HS+ B)pg=/’,
which in virtue of (2) becomes
— (A-S)p? + (B—-S) P+ (C— SH) +2(For + Grp + Bpg)="—SA. (7)
This form of the integral is very closely allied with the inverse or ae
form of the first integral (2), and is the one used below.
In order to find the third integral, we must find two of the variables in
terms of the third by means of (2) and (7), and substitute in the corre-
54 Mr. Spottiswoode—Equations of Rotation [1868.
sponding equation of motion. The most elegant method of effecting this
is to transform (2) and (7) simultaneously into their canonical forms. If
ep y
a Bn
a, (ee Ya
be the coefficients of transformation, and if [] be the determinant formed
by them, the terms involving the products of the variables will be destroyed
by the conditions
(A wit oe asp 6,8, Cy ¥:7,J=0; >
(A ee Moe hey ae a2, )=0,
(AS Eh eee, eee
(A—S... F.... 068, B.C ny.) =,
(A—- 3... Ly nL um) =0,
(A-S... F... Lae, 0,16 6,6,)=0,
from the last two of which we have
Byy.—Boy : Pay —By.+ By, +B,y >
=Aa+Ha,+Ga,=(A—9)a+ Ba, + fra, i el
Hee
,
: Ha+Ba, +Fo,: Ho+ (GB-—S)a,+ Sa,
:Ga+Fa, +Ca,: Gat ffa,+(@—S)a,;
whence, 0 being a quantity to be determined,
A—-S-—Ao, B dO, (or — G6 =
%H —H6, 6@-S-Bo, £F —F@ i 010)
6 —G), £F —Fo, €—S —Ca
Proceeding to develope this expression, we have the term independent of @
=V'*—(BC+CA+ 9B)S+ &—2*
—(? +62 +B)S
=V’—SSV.
The coefficient of —é
=A{VA—(B+0)5+ 5'}+H(VH+88)+G(VG64+ GS)
= pee
=V(A?+1?+6)+VS
+V (H#?+B?+C’)+VS
+V(@+F?+C?)+VS
=V {A?+ B?+C?+3(BC+CA+ AB)—F’—G’— H?}
=V (84+).
1863. | of a Solid Body about a Fixed Point. 55
The coefficient of — 6°
=V\.-
Hence (dividing throughout by. V7) (10) becomes
6° + 2.86?+ (S?+$)0+SS— V =0;
or, what is the same thing,
(0+S)’—S(6+S8)?+4(0+8)-V=0; . . (11)
or, as it may also be written,
Sees), EF e =
H, B= @-ES), 5
G, F, C—(64+S)
It will be seen by reference to (9) that the values of 6 determined by this
equation are equal to the ratios of the coefficients of the squares of the new
variables respectively in the equivalents of (2) and (7). The coefficients of
transformation are nine in number ; if therefore to the six equations of
condition (8) we add three more, the system will be determinate.
Let three new conditions be
(A..F... 3a aa, )°=1,
(A...F...16 6,6.) =1, e e e e e e (12)
(A.B Dy N1Y%2) =1 3
then the variable terms of (2) will take the form of the sum of three squares,
and the roots of (11) will be the coefficients of the transformed expression
for (7). Or, if 0, 0,, 0, be the roots of (11), (2) and (7) take the forms
poi tar +7r=h,
0p°+6,9¢,°+6,772=h—SA. } Rhee Cy
In order to determine the values of the coefficients of transformation
&, a,, a, we have from (9),
(A—S—Abd)a+ H—HO)a+ (G—Ge)a,=0,
(4 — H0)a+ (8—-S—BO)a+ (f—FO)a,=0, ai et al By
(G&—G0)a+ (F—FO)e+(C€-—S—Coe)a,=0;
from the last two of which
a: BC -(B+G)S+ S°—(BC+C€B—B+CSH)+ BCE?
el — 25F 9 —F°
=a:VA+4S+(B+C44+ BS +CC +2F F)0+ Ae
=a2:VA+GS+(2V —Hh-G&—-AA+84)04+ 90
=a: VA+AS+(V +84) + A?
=a:V(A+60)4+4(S+80+ 6") ;
or, writing for brevity
$+589+¢=T,
56 Mr. Spottiswoode—Hquations of Rotation [1863.
the expression becomes
a:V(A+0)+T@
=a: SF &—(FG+GF)0+ FGO
~ CHF + HS + (CH +HS)9—CHe
=a: VH+9S+S8H0+ He
=a,: VH+TH
=a,: VG+TG,
whence the system
aot, 2a, ah |
=V(A+0)+TA = VH +TH = VG +TG
:VH +7: V(B+0)4TB : VF 4TH er - C5)
: VG +T& : VF +THF : V(C+0)+TE,
with similar expressions for 6, 8,; 8,3 > ¥1> Y2. Obtained by writing 0,, T, ;
6,, T, respectively for 0, T.
Returning to the equations of motion (1), and transforming by the
formule
eer Pi+P “ry "yp
Q=4,),+2,9,+y,") . -& oe (16)
r=0,D, +29, +77
we have
(Aa+Ha,+Ge,)p', =[—F(a,—a,*) + (B—C)a,e,+ Ha,a—Gaa,] p,? | NE
+ (AB-+H6,+G8,)q',+[—F(6?—B,) + (B—C)6,6,+HB,8—G6B,]9,2
+ (Ay+Ay,+Gy,)7, +L Fi’ —y,.") + (B-C)y,7.+ 4 yy—Gyy ln?
+L -2FC.n—Biy.) + (B—©) 6.7.48.)
+H(6,y+By.) -—G(By,+B.ylar,
aii [ at 2F (y,2, ro Y2%,) a6 (B Be C) (77%, ch Ya)
— AA (y,44+ y%,)— G(ya, + ,4) |p,
+[—2F(«,6,—2,8,) + (B—C) (4,8, +2,8,)
+H(4,6+48,) —G(a6,+2,C)1p.q
-=[o,(Ha+Ba,+Fe,) —a,(Ga+Fa,+Ca,)]p,? (17)
+[6,(H6 + BB, +F6,)—6,(G6+ FB, + CB,)]¢,? |
+[y{Hy+By +¥Fy.)—y,(Gy+Fy,+Cy jin? -
+8, Hy+By,+Fy.)—B\(Gy+Fy+Cy,)
+ y,(HB+ BG,+FB,)—y,(GB+F6+C£6,)]q7,
+[y,(Ha+Ba,+Fa,)—y,(Ga+Fa,+Ca,)
+a,(Hy+By,+Fy,)—2,(Gy+Fy,+Cy,)]7,p,
+ (#,(H8+ BB, +FB,)—a,(G6+FS,+C£,)
+6,(Ha+Ba,+Fa,)—B;(Ga+Fa,+Ca,)]p,9,,
1863.] of a Solid Body about a Fixed Point. - 57
with similar expressions for the two other equations. Multiplying the
system so formed by y, y,, y, respectively and adding, the coefficients of ©
p',, 7’, will vanish, and that of 7!, will =1 in virtue of (12); and as regards
the right-hand side of the equation, the coefficient of p,*
Aa+tHa,+Ga,, a, y
Ha+Bea,+Fa,, «4, y,
GatFa,+Ca,, a. Yo»
which, omitting common factors,
(S+O)A+A+(S+0)0, VA+TA+V9, VA+T,A+V0, |
—
—
(S+6)H+®, VH+TB, VH+T.®
(S+0)G+G, VG+T& VG+T,G
eae, VH+T, ® | +V9| VH+T(S+0)H+B
VG+T& VG+T,G VG+T,G(S+0)G+&
(S+0)H+% VH+TH
(S+0)G+G VG+TG
={(S+6)0V(T,—T) + Va(V —T,(S+6))+Vo,(T(S+0)—V )} (H&—FE)
=V(0,—0){T(S+)e—V}(HG:—WG).
T(S-+0)—V =(S+0)(°+80+ 8)—V=(S+0){(S+6—(S+0) + 8}—-V
=(S+6)?—S(S+6)?+S(S+0)—V
=().
Hence, finally, the coefficient of p,? vanishes.
So likewise the coefficient of q,”
AB+HB,+G8, 6 y | =0.
H6+B,+F p, Bay:
GB+F 6,+CB, B, xy
AytHy,+Gy, y¥ y .|=0.
Hyt+By,+Fy n vn
GytFy+Cy, wa. Ys
Similarly the coefficients of g, r,, and 7, p, will be found to vanish; and
lastly, the coefficient of p, ¢,
=a {A (B,y.—P.71) + H(6,y—6y.) + G(Py,—B,y)}
+ a, {H(8,y,—6,7,) +B (B.y—By.) + F (By,—By)}
+ 4,16 (Byy,— Poy.) + F (Boy— By.) +C(By,— By) }
—B {A(1%,—720,) + H(y,4—ya,) + G(ya,—7,.2)}
—B,,{H(y, ot Yo) +B (y.e— ya.) a0 F(ya,— ya) *
ee 6.6 (ym, a ¥20,) apts (y.e— YO) +C (ya,— Me)ts
+V6,
——
—
And that of 7,’,
58 Mr. Spottiswoode—LEquations of Rotation 1863.
which, by reference to (9), may be transformed into
rm) {(Ae+ Ha, +Ga,)?+ (Ha + Ba, + Fa,)?+ (Ga+Fa,+Cza,)’
—(AB+H6,+G6,)+ (e+ BG, + Fe,)’+(G6+ FB, +Cp,)"}
= {(Ae?+Ba2+Ca,? + 2Fa,, + 2Ge,0 + 2Haa,)S
—(AP’?+BB?2+Cp,?+ 2FB,6,+2G68,6+ 2H66, )S
+(A—&)(@— f°) + (B—S)(a—B,7) + (€—8)(a,’—B,”)
+ 2FF(4,% —B,B,) + 2Gi(a,2 — 8,0) + 27)(ae, —BB,)} ;
in which the coefficient of S vanishes in virtue of (12); so that the coeffi-
cient of p,, 4g,
=D {(A—2, B—S, €—3, Ff, G& HY, a, «,)
—(a—8, B—5S, €—S, F, & HVA, By 6.) ;
but, by (12),
(A-S, B-S, C-S, F, & HYa2,2,)’=8,
(A—, B—S, C5, F, G, HYPS,6,)=6,.
Hence the coefficient in question
= [1 (@—8,), 920% ie eee ee
and the equations of motion become
Pr =O 8—-8,) ar,
g¢=f10,.—)r,9,\ .°. . ee
=O 6 —9)r9,.
To find the value of [ in terms of A, B, C, F, G, H, we have from (12)
Aa+He,+Ge,= [1 -\(6,y,—6.7,)s
AB+H6,+G66,= O-My.e,—7.%,)s
Ay+ By, +-Gy,=T]~(¢,6,—2,0,),
Ga+Ba,+Fa,=(-(6,y —6 y,),
HB+BS,+F6,= 0 -y.e —y 4,),
Hy+ By, +Fy,= 74.8 —@ 6),
Ha+ Fa,+Ca,= 1-6 y,—8,y),
GP+FR,+C68,= Oy —- nN),
GytFy,+Cy,= O7(¢2,—4,8).
And forming the determinant of each side of this system, there results
Vee,
or
V = [ape s ~ e ° e e e e ® (20)
— 863.) of a Solid Body about a Fixed Point. | 59
whence the equations of motion (19) become
p'=V 391 — 92) Ms
Se Or, ee ee a. | OT)
r!, =V-2(0—6,) p, g,-
In order to compare these results with the ordinary known form, we must
make
= 0; C—i; H=0,
p,=A"p, g,= Bq, = C27;
which values reduce (13) to the following :
(A*p)?+ (B*g?+ (Cr)? =A, |
—(B+C)Ap?—(C+ A)By?—(A+B)Cr=—ShA;
which last is equivalent to
(A—S)(A*p) + (B—S(B¥y)?-+ (C—S) (C*r)*=h—8h,
or
A(A%p)?*+ B(B¥q)?+C(C*r =?
Also, on the same supposition,
V=ABC, 9=—(B+C), 6,=—(C+A), 0,=—(A+B),
which, when substituted in the above, give
Ap"'=(ABC) 3(B—C)B*C2qr, Bg’=..., Ch'=...,
: Ap'=(B—C)gr, By'=(C—A)rp, Cr'=(A—B)pgq,
as usual. |
It remains only to determine the absolute values of the coefficients of
transformation, the ratios of which are given in (15). For this purpose let
V(A+0,)+T,4=4, VE+T F=F,,
VB+6)+TB=B, VE+TG=G- . . . (22)
V(C+0,)+T€=€, VH+T,H=¥..
Then, from (15),
a 3 Ro &, ;
(A... ... 14,9, ,)? (A... 148,38, F,) (A. LF Coy
we 200 Ee cee
(AH. Uae GY (A an %F,)? A... CG FC,)”
Gi, ,
LAMP TREES Go LOREY
VOL, XIII.
i i
60 Mr. Spottiswoode— Equations of Rotation 1863.
From these relations it follows that ie
8 C,—s,=0, Cr ),—-A,F,=0,
C,A,— G,."=0, oF, B,G,=0, | :
A,33,—1,= 0, dD to C,4= 0,
which relations may be also verified as follows:— _
&A.—-A,S = (VE+T, G)(VE+TH)—-(VA+T,A+ V6,)(VE+T SF)
= VF+VT,(GH +HG —Agf—FA)+T, VF—V0,(VF+T,S)
ViVF_-T,(SHF +SF)4T2 F—Vo.F—Vg+St FG;
. (23)
Since
H&+Bs+FC—0,
and.
(0+S)T—V=0,
or
6T=V —ST.
Hence
&,9,—-A. SF = V FIT —T,.2— Vo}
= VF{T6,(S+0,)—V6,}
==):
From these relations it follows that the first denominator, viz.
(A, B, C, F, G, H, {4,B,G,)?
=AG?+BB2+CG&2+7(FB,G,+6G,a,+H4,B,)
=4 {AG +B, +CC,+2(FF,+ GG, + HB,}
=9,V{A2?+B?+C?4+2(F’+ G?+ H’)+3T,+806,}
=4 V{S’—25+3T,+86,}
=4,V 30,74+480,+5+4+ 8}
=4,V{(S+6,)(S+30,)+ 5}.
Hence, writing (S+6,)(S+30,) +S=©,, we have, finally,
eS Big eee
TE OT RE, AE,
From this we may obtain the following system :
1 ee ee
TE a Oe AR:
36 0
= =gr |) a
A, €,
1863. ] of a Solid Body about a Fixed Point. 61
with similar expressions for 6, 6,, B,; ¥. y» y». obtained by writing the
suffixes 1 and 2 respectively for 0. By means of these we may write the
equations connecting the variables as follow :—
1 1 1 P
i= ©. p+ T + qv }
; 3
es) 46 SF,
= aC, pir 2: Sm Go, ¥ e ° ° ° (25)
Lastly, to complete the transformations, the values of p,, g,, 7, should be
determined in terms of p, g, 7. Now
49, +9.8,4+ G6 F,=(VA+T,.A+ V0,)(VH+T,B)
+(VH+T,)(VB+T,B+T9#,)
Ces +(VG+T,&) (VF+T,B)
=V{(A+B)H+FG}+T.T{(4+%8)i9+ se} + V?H(0,+6,)
+V#(0,T,+6,T,)
=V?(SH+9)+T,T, (2+ VH)+ VHC, + 9,) + V3H(0,T, + 4,7)
=V{V(S+6,+6,) +T,T,}H+(V6,T,+V0,T,+$T,T,+V’)
=T,T,{[—(S+6,)(S+6,)(S+ 6,)+ VJH+ [6,(S+0,)+0,(S+6,)
+8+(S+6,)(S+6,)]H},
plnCce
V=T,(S+0,)=T,(S+0,)=T,(S+6,).
Moreover by (11) we have
(S+0,)(S+0,)(S+6,)=V,
and consequently the coefficient of H vanishes. And it may be noticed, as
a useful formula for verification, that, from the relations last above written,
we may at once deduce the following :
2 T= V?.
Again, the coefficient of # may be thus written:
(S+6,4+0,)(S+0,)+(S+0,+0,)(S+0,)+S+(S+0,)(S+6,) -
— (S8+86,)(8+86,)— (S+6,)(S+9,)
=— (S+0,)(S+0,)—(S+0,)(S+0,)—(S+6,(S+6,) +8
== (),
FE 2
62. Mr. Spottiswoode—EKquations of Rotation [1863.
in virtue of (11). Hence the whole expression vanishes, or
Q6,4+8,8,+GF,=0; . ... . (26)
4,&,+34,F,+ G&€,=0.
Moreover, in virtue of (23), we have
and similarly
Q27+H74+ G=4,2,.
Hence multiplying (25) first by @,, 34,, &&, respectively and adding,
secondly by ,, B, F,
thirdly by & F» C,,
we shall obtain the inverse system
FP Ap+ Bat Gor }
go o=MptBat5r, & 2 2 ee + (7)
n= =G,p+5.q+€.7. ;
Returning to the integrals (13), we derive
(0,—6)9,7 +(0,—0)7>=h’—(S+8 DA,
(6,—6,)7,° +(0 —0,)p’?=2—(S+8,)A,
(8 —8,)p," + (8, —9,)9, =’ —(S+ 8, )h.
Let
rere (ames ETON cosy
then
k?—(S+6,)A .-
a=a/ yoee rae
and
‘ A peu a ee 1
0,—0 iP —(S+OyA
ig (BSE gy. 6,—6 B—-(S+0,)h
ie 0, —0, k’—(S+0 )h be
Substituting in the equations of motion (21) (e.g. the first of them)
and dividing throughout by sin x./#°—(S+0,)h, we have
1863.] of a Solid Body about a Fixed Point. 63
dx 4 1 of or = (S+O)h P
= 0, dt Se 0,—0 0,—0, #—(S+6)h :
or
dy : a si _ 0-6, P—S+0)h . ,
7 Oh ae, 0,0 6,6. F—(S+0)A oo &
or
EE Oe ee ; =:
uk 0,—0 #—(S+0,)h . BO ea B—(S+o)hdt ;
0,6, Fa (S40 hm X
then
x=am(4 /2—* eee y/o BOSTON)
and
p= a / EAST cos am (\/ 29 vE=CT OH),
=a / HSH Oh = sinam (4/2 nh / POST Hh S+Hit-+s)
pan EET a ee Oe pre Po STOne+s)-
These, then, are the integrals of the equations of motion when no exter-
nal forces are acting. The next step is to determine the variations of the
arbitrary constants, due to the action of disturbing forces, when, as in the
case of nature, those forces are small. With a view to this, it will be con
venient to change the arbitrary constants into the following,
/#—(S+0)h=m /h—(S+O)h=n,
(6—0,)h=m?—n’,
(0—0,)k* =(S+0)m’—(S+0,)n? ;
also, for brevity, let
whence
0,—0, 7 ea Ona Gh ee
a bd am(Int +f) =x, ar ee
Then the equations of motion become
cos am(Int +f),
= Fe
— ea sinam(Int+/),
n
— Wire Aam(Int+f).
64 Mr. Spottiswoode—EKgquations of Rotation. [1868. -
Now it is known by the theory of elliptic functions that
d cos ame :
—_—— =— sinamxA ama,
dx
dsinamx
—z—— = cosamxAama,
dx
dA am an
a —k,? smamzcosamz.
Whence P,, iQ; R, being the moments of the disturbing forces about the
present axes, .
: dn d
ce axa pmsinndx(ieae + Z) f
. dm dn df \
“Jaa a Lsxige tone xan (iS +7) r
ie fF "
— ipa ae
R, = a sin y 008 x( eS +7)
From ne we derive
dm ae
GES a 6—6,P, cos x+/0,—6, Q, sin x,
n, of Sets ae eel
mix (iit dt = —/0—6,P, sin x +/ 0,—0, Q, cos x;
dn sin x cos
Ax a =a/0,— TOR, + ha —/0—0,P, siny +,/0,—0,Q, cosy};
or
dn R, 0,—0 msiny cosy ——_ , ——
Tp=v 9.—- ae 06 cn (xy UY 94.2, sing +4/ 6,8, Q,c08y}
R, , 9,—6 1sinx cos
wh ra ae Hy te / 0—6,P siny +4/6,—8, —6,Q, cosx}
fi/o—0, 0,P, cosy +a/0,—0,Q, sinytdt.
And lastly,
d, dn a ted
= lt ; /0—60 6? sin y +4/0,—0 6,.Q, cosy
Re =a ewe —6,Q, sinx}dt
1863.] Sir J. South—Vibrations caused by Railway Trains. 65
“‘Hixperiments, made at Watford, on the Vibrations occasioned by
Railway Trains passing through a Tunnel.” By Sir Jamzs
Soutu, LL.D., F.R.S., &c., one of the Visitors of the Royal Ob-
servatory of Greenwich. Received June 17, 1863*.
In the year 1846 an attempt was made to obtain the consent of the
Lords of the Admiralty to run a railway through Greenwich Park, distant
only 860 feet from the Royal Observatory, which would in the opinion of
many competent judges have been most injurious to that Establishment.
Such consent their Lordships refused ; but as I was assured on high au-
thority that this attempt was to be repeated, and that too with the fullest
confidence of success on the part of its projectors and supporters, I deter-
mined to make experiments which might bear more decisively on the
question of railway tremors, as affecting that Observatory, than those pre-
viously made by myself and others.
For this purpose it seemed indispensable that the station selected for
making them should geologically resemble that of Greenwich, and that
the astronomical means employed to detect the existence and determine
the intensity of the tremors should be, optically, at least equal to the te-
lescope of the Greenwich Mural Circle. |
As much importance was attributed by the advocates of this railway to
the supposed power of a tunnel to render the vibrations imperceptible, it was
also desirable that 7¢ should be one of the conditions of these trials.
Having but little more than a popular knowledge of geology, I relied on
my old and valued friend the late Mr. Warburton, who had recently been
President of the Geological Society, to guide me in the choice of a station ;
and it was on his authority that I fixed on the Watford Tunnel and its im-
mediate vicinity.
There, under a light gravelly soil of 18 or 20 inches deep, lies a bed of
gravel of considerable but variable thickness, sometimes compact, at other
times loose, and immediately under it chalk with occasional flints,
The tunnel, of which the bearing is 41° 19’ to N.W. of the meridian,
and by my measurement is 1812 yards long, passes principally through
chalk ; its arch is about 24 feet in diameter, the crown of it being about
21:5 feet above the rails. The thickness of the brickwork is about 18
inches; the mean thickness of the chalk above the crown of the arch
about 50 feet, whilst that of the gravel, though subject to great irre-
gularity, may perhaps be regarded as 14 feet. If so, we have outside the
tunnel above the horizontal plane of the rails 87 feet of chalk, flint, gravel
and soil, constituting an assemblage of which the power of transmitting
tremors must be comparatively feeble.
There are five shafts in the tunnel, four of which are circular, 8°5 feet
diameter, and one quadrangular, about 26 feet by 34.
* Read June 18, 1863: see Abstract, vol. xii. p. 630.
66 ‘Sir J. South—Vibrations caused by Railway [1863.
The tunnel runs under the park of the Earl of Essex ; and though I had
not the honour of a personal acquaintance with the Noble Earl, nor any
introduction to him, yet on learning my objects he transmitted to me by
return of post, from Carlsbad, a carte-blanche to erect my observatory
wherever I pleased, though it were in the very heart of his choicest game
preserves. To him therefore is mainly due whatever benefit may accrue to
science or to the Royal Observatory from the experiments recorded in this
communication.
The point I selected was 302 yards distant from the centre of the line ;
and the perpendicular from it on the axis of the tunnel meets that at a
pomt 567 yards from the southern or London end of the tunnel, 1245
yards from the Tring or north end, and 594°5 from the fourth shaft. This is
the centre of the Observatory which I erected there: it is of wood, as small
as is consistent with the necessary accommodation, both for portability and
that it might be less agitated by the wind.
It is quadrangular, 12 feet by 10, and its length is in the meridian; the
eaves are 8°5 feet, and the ridge of the roof 10 feet above the floor, this
last being 4 inches above the ground, which is nearly level with that over the
tunnel. The roof is covered with tarpaulins very well secured, so as not
to be torn bya gale of wind. In the south and west sides are four windows,
which can be opened or shut at pleasure, to light the Observatory by day, or
to see powder or other signals at night. In the roof is no opening ; but in its
northern side there is one which can be shut as required: it is little larger
than what is absolutely necessary to allow the reflected rays from the Pole-star
to pass uninterruptedly to the observer’s eye through its whole revolution.
At its centre, parallel with its sides and resting on the undisturbed gravel
4 feet below the surface, is a mass of brickwork laid in excellent Roman
cement, 8 by 3:5 feet at bottom, 7 by 3°5 at top, its length running east and
west. On this stand two piers of similar brickwork, 18 inches by 14, and 46
inches higher than the floor: they are capped by two Portland stones of
similar horizontal section 8 inches thick. In the interior faces of these
stones are firmly fixed the Y-plates, which carry the Ys on which the in-
strument’s pivots rest.
Eighteen inches north of the brick massive, but in the same plane with
its base, is the centre of the base of another pier, brought up alsoin Roman
cement, 24 inches from N. toS., 18 from E. to W.; and it rises 12 inches
above the floor. The upper surface is perfectly horizontal, and serves to
support a vessel which contains mercury. Both this pier and the massives
are insulated from the floor, and touch the ground only at their bases.
The mercury-vessel was 18 inches by 42, with its length in the meridian.
The transit-instrument of the Campden Hill Observatory is far too pre-
cious to be exposed to the risks of such an expedition ; I therefore had one
constructed which might be considered an excellent substitute. The object-
glass (which under favourable circumstances will bear a power of 1000) is
87 inches focus and 4°75 aperture. The transverse axis is 31 inches ; and
1863. | Trains passing through a Tunnel, 67
the Y has sufficient azimuthal motion to enable me to follow the Pole-star
in its whole course, so that at any hour (if clear) I could have the reflected
image of the star in the mercurial vessel ready to testify against the tre-
mors caused by a train.
Supported by timber passing into the ground, but unconnected with the
floor and convenient to a writing-desk which occupies the S8.E. angle of the
building, stands a journeyman clock. It is set by my excellent gold pocket-
chronometer, Molyneux No. 963, and rarely deviates from that more than
one- or two-tenths of a second in three or four hours. The clock of the
Watford Station was compared with the chronometer, going and generally
returning, for the purpose of identifying particular trains.
These details will, I hope, suffice to prove that every precaution was taken
to obtain accurate results, and that those which I did obtain may be fairly
considered as identical with what would have been found in a first-class
observatory under the same circumstances of locality and traffic.
I was at my post to commence observations on December 22nd, 1846 ;
but that and the three following nights were starless. The 26th was fine, but,
owing to the irregularity of the trains, and the want of well-organized signals,
I could only satisfy myself that all was in good working order, and that the
trains caused great disturbance. For thirteen following nights I was at my
post, but in vain; all was dark, with the thermometer from 22° to 31°.
On January 11th, 1847, it cleared, and I observed seven trains with
decisive results, being able to announce their presence before it was known
to my assistants, who were on the watch outside the observatory.
The Pole-star’s image as reflected from the mercurial surface, when
no train was near, appeared
As a very small, perfectly steady disk, thus . . . + » « @ (l.)
which as the train approached broke up into a quin- aan
tuple, thus— . oS Supe a. psa 4 ee 2 if “i Geer (2s)
hes
As the disturbance increased, the form be-) __
came linear at right angles to the length } :*see@@@@e@eeee- (3,)
of the mercury-vessel, thus—
@Se@eo0e-
W i i @
hen the train was considerably advanced \ LeepeoeeGOeocee-: (4)
in the tunnel, a cross formed, thus— .
22006809
©608006800000090
@eeagee0ececeeeo (5.)
observatory, three parallel lines of disks ap-
SCSSCOSGORSOOOD,
And when near the perpendicular from the
[CE ECORI LISS Saimme ihe 5000 ae aaanaae
68. Sir J. South—Vibrations caused by Railway [1863.
still parallel to No.3. As the tremors became more distant, these trans-
formations of the image take place in a reverse order, until the star
resumes its original disk-like form.
These results were strongly conspicuous even in a fully illuminated field,
and equally so whether the magnifying power was 60, 200, or 750. The
phenomena are very striking, from the contrast between the smaller images,
which are blue, while the larger ones are reddish, and from the sudden
way in which they break out.
The nights of the 13th and 14th were fine, and so thoroughly confirmed
my previous observations that I felt it my duty to lose no time in informing
the late Lord Auckland, then First Lord of the Admiralty, of the preceding
details and of my conclusions from them, that a tunnel did not prevent
great tremors from being propagated from it when a train was traversing
it, certainly to the distance of 643 yards, and probably much further.
The impression which these facts made on his Lordship he expressed
in the following letter.
Copy of a Letter from the Earl of Auckland to Sir James South.
“Admiralty, January 26th, 1847.
*‘Srr,—lI have to return you many thanks for the very interesting
report which you sent to me of your experiments upon the distance to
which the vibration caused by steam-carriages within a tunnel extend ;
and I cannot but admire the enterprise and ability with which these expe-
riments were conducted. They would be quite conclusive if the question
of carrying a tunnel through Greenwich Park were again to be agitated.
‘I am, very faithfully yours,
“To Sir James South, &c. &e.” ‘* AUCKLAND.”
The reserve with which I spoke of that further distance arose from the
circumstance that I was not in possession of the exact measurements of the
tunnel and the position of its shafts. I had twice applied for them in vain
to the railway authorities, and was obliged at last to execute the measures
myself*. This consumed some time, and the observations were not com-
pletely resumed till February 24, 1847.
The process was this. About 600 yards before the entrance of the
tunnel a rocket was fired as a signal for attention. At the instant that the
engine passed the south end of the tunnel, one of Lord Essex’s game-keepers
fired one barrel of his gun, and the other about a second after, which was
necessary to distinguish this from the shots of poachers, who were often at
* This delay was not occasioned by any want of courtesy on the part of the Directors
or other officers ; from whom, especially from Mr. Creed, their Secretary, I received the
heartiest cooperation. He not only directed all the officers along the line to aid as far
as possible my investigations, but pressed on me free passes for myself and my assistants.
I was also indebted to Captain Bruyeres for the character of the trains, and to Mr. Stubbs,
the Superintendent of the Watford Station, for the zeal with which he followed out the
Seeretary’s instructions at much —* inconvenience.
1863.] Trains passing through.a Tunnel. 69
work around me. Similar shots were fired when the engine was at the centre
of the 4th shaft (which could be seen from above). Whe times of these sig-
nals were taken by an assistant. During this time I was at the telescope,
and noticed the second when any peculiar phase of disturbance appeared.
The computation of the distance of the engine from the eye at a given time
is very simple. From the known distance of the south end of the tunnel and
the 4th shaft from the eye, we know the times taken by the sound of the gun
to reach the observatory. The temperature was during the whole series so
near 32° that the velocity of sound for that temperature, 363-13 yards, may
be used without sensible error. The effect of wind must also have been
insensible. Hence the signal from the south entrance was 1%*77 too late,
that from the shaft 15-84.
Correcting the times and dividing by their difference the distance of the
shaft from the entrance, 1162 yards, we have the velocity of the train (which,
however, I have given in miles per hour, as affording a more familiar
measure of the disturbing power). Then the difference of the time of
phase and corrected time of entrance gives the place of the engine on the
line, and the perpendicular is given.
In the following record of the observations, the first column contains the
number, the second the times, the third the facts observed, and the fourth
gives the distance, then follow occasional remarks. In the disturbances,
I specially recorded as most definite the cross (4), and the arrangement
of bars of parallel stars (5). The slighter disturbances which precede or
follow the former were seldom entered, though quite sensible.
1847, February 24.—I.
No.| Time. Observations. Yards. Remarks.
hm s
1 | 7 18 43 |Cross very distinct...... 845 |Velocity 11-00, miles an hour; weight
7 19 21 |Shaft gun. of train 77°5 tons ; twelve carriages.
7 22 57 |South gun.
2|7 23 8 jLost sight of cross...... | 74 |
ia
ete 34s Gf CLOSS). oocccieies sues ceseeke | 699 |Velocity 16°6 miles; train 69°5 tons,
34 8 | Shaft gun 231 feet long; ten carriages. Ther-
36 31 | South gun. mometer 24°.
4 36 48 | Lost sight of cross...... 780
III.
5 17 44 40 |Cross; star very faint...) 680 |Velocity 13°8 miles. Star invisible to
44 44 |Shaft gun. the naked eye. Train 58s tons;
47 38 |South gun. engine 14°5 tons; length 185 feet.
6 | 7 47 42 jLost cross ..... SOCCER 678
70 Sir J. South— Vibrations caused by Railway [1863.
1847, February 24.—IV.
No. | Time. Observations. Yards. Remarks.
hm i s
7 59 6 |Shaft gun. Velocity 11°4 miles; train 89°5 tons;
8 2 30 |Star became visible. engine 18 ditto; length 308 feet.
8 2 34 |South gun; star bright. Wind E. Therm. 24°.
7 | 8 3 10 |Cross disappeared ...... 834°5
1847, February 27.—I.
7 28 o |Shaft gun. Velocity 15°4 miles; train 54 tons;
29 7 |Cross first seen, but star engine 14°5 tons; length of train
very faint. 172 feet.
30 34 |South gun.
8 | 7 30 44 |Cross lost; star very
TE Os ree ee ae es 722
iT;
9 | 7 44 43 |Cross seen ...... seeeeeee- 736 {Velocity 25° 6 miles ; train 49°5 tons ;
7 44 51 |Shaft gun. engine 14°5 tons; length of train
be) 45 8 |Cross very strong ...... 470 | 150 feet.
II 45 27 |Line very strong ...... 326
46 24 |South gun.
12 A6n6 |CEOSS 1OSt Ge2.0<228eee ees 915
Lif.
io 7250.25 | Cross SCCN. . serosa ees 706 |Velocity 17°6 miles ; train 270°5 tons ;
56 31 {South gun. two engines 29°5 tons; length of
14 57 45 |Cross very strong ...... 314 | train 663 feet; 37 carriages.
58 46 |Shaft gun.
15 BOSS JICEOSS NOSE. “sca. ctaamsenen 736
IV.
16 | 8 3 36 {Cross very strong ...... 736 |Velocity 31°7 miles; train 112 tons;
3 44 |Shaft gun. engine 21 tons; length of train
17 A. HG \Cross veby HWE 6.0202 377 394 feet; carriages17. Wind N.E.
18 4 14 {Triple line, upper and Thermometer 26°.
lower stars blue ...... 319
4 59 |South gun.
19 5 25. CLOSS 1OSt i sscwtonewase+! 1086
V.
20 | 8 10 56 |Cross SeeN ............».- 727 |Velocity 18°7 miles; train 51°5 tons;
Ir 8 |South gun. engine 12°5 tons; length of train
2k 11 56 (Triple line strong ...... 322 | 187 feet. A train of empty catile-
13 15 |Shaft gun. waggons.
Cross lost from cloud...| lost
Trains passing through a Tunnel. 71
1847, March 11.—I.
No.| Time Observations. Yards.
hm s
22 | 7 18 44 |Cross very distinct ...... 802
19 6 |South gun.
28 2G Shaft gun, cloud.
EE.
| 825 3 |Shaft gun, cloud.
26 15 {South gun, cloud cleared
Remarks.
Velocity 17°73; train 147°5 tons; eu-
gine 12°5 tons; length of train 355
feet.
Velocity 33°0 miles; train 122 tons;
engine 21 tons ; length of train 416
23 26 32 jCross lost by cloud...... g21 | feet. Cross so strong, but for the
cloud it might have been seen 15
or even more seconds longer.
1847, March 12.—I.
f
24. | 6 56 22 ‘Cross very distinct...... 822 |Velocity 28°33 miles; train 68 tons;
56 38 South gun. engine 15 tons; length of train 231
25 56 52 Cross very strong ...... 461 | feet; many carriages but mostly
26 57 16 Star tossed about 3 or 4 empty, many wheels and axles;
of its diameters ...... 302°4 | agitation excessive. Seemed to
58 2 |Shaft gun. keep time with the jolts of the
27 58 8 (Cross PGS acres ae 766 | train.
IE:
See yee ES Cross plain ......... 4 tht yoo +7)
White oe, oak kt 4 5 6 7.
Table II. shows the tones associated with the manuals in each stop ;
capital letters indicate white manuals, small letters black, and small
* Singers and performers on bowed instruments and trombones can produce
any scale whatever. Other instruments are more limited in range and would
require special treatment, similar to the “crooks” of the horns and the various
clarinets.
1864. ] ~ on Instruments with Fixed Tones.’ 101
capitals red*. By this arrangement the fingering of every key would be
the same. The performer would disregard the signature except as naming
the pedal, and play as if the signature were natural. Table V. would
inform him whether the accidentals belonged to the key, its dominant, or
any other key ; and if they indicated another key, he would change the
pedal. It would be convenient to mark where a new pedal had to be used ;
but no change would be required in the established notation §.
Mr. Poole’s organ, which suggested the above arrangement, has 11 stops,
from 5) to 52, and only 12 manuals, which appear to be associated with
the following tones on each stop:
Black .. {2 ({2#) (44) 15¢ ra,
White.. 1 2 3 4 5 6 7
The two manuals whose notes are put in parentheses are inadequately de-
scribed. Mr. Poole’s scale does not include the synonymous minor chords,
which he plays by commatic substitution.
Another method of realizing such a scale is by additional manuals and
additional boards of manuals. Thus three boards of manuals, each with
23 manuals, containing the tones in Table V. cols. III. to VIII., lines 4
* On examining Table II. it will be found that 10 different tones lie on each
pair of manuals, so that there are only 70 different tones. The two missing tones
are, necessarily, ttf # (the acute fourth of the key of + C4), and {{0) (the grave
seventh of the key of {C>); and to this extent the scheme is defective. It would
probably be more convenient to the instrument-maker to use all the70 tones in this
arrangement than to take the inferior number 45 due to schismatic substitution.
A full-sized harmonium at present employs from 48 to 60 vibrators to the
octave, so that the mechanical difficulties to be overcome in introducing 70 are
comparatively slight, By omitting the two very unusual keys of {CD and +Cz,
the 8 tones denoted by ttdD, tF9, ttf, a7) and t Dz, gx, t Bt, ttb in Table IL.
would be saved, and the number of yibrators required would be reduced to 62,
nearly the same as that actually in use. As each new key introduces 4 addi-
tional tones, and the key of C has 14 tones, the number of vibrators required for
any extent of scale is readily calculated. Thus for the 11 keys from 5 flats to 5
sharps, or {D?, A), ED, BD, F, C, G, D, A, E, B, which is Mr. Poole’s range,
and is sufficiently extensive for almost all purposes, only 4x 104+ 14=54 vibrators
to the octave would be required, distributed over 11 stops (exclusive of the tem-
pered notes) ; and such a number of vibrators and stops is in common use.
§ If in Table V. we reject the marks +, {, consider 16 4=27 C, 64 F=81 C,
128 B= 243 C, yoda! paotees leaving the value of the other letters un-
2048’ 2187’
changed, the Table will represent the Pythagorean relations expressed by the
usual notation (which is quite unsuited to the equally tempered scale). The
chords thus formed were too dissonant for the Greek or Arabic ear to endure,
although Drobisch and Naumann (Joc. cit. ad finem) desire this system to be ac-
knowledged as “the sole, really sufficient acoustical foundation for the theory of
music ” (als einzige, wahrhaft gentigende akustische Grundlage der theoretisch-mu-
kalischen Lehre),
12
102 Mr. A. J. Ellis on a@ Perfect Musical Scale [Jan. 21, .
to &, 7 to 11, and 10 to 14 respectively would be nearly complete. The
manuals might be similar to those on General T. Perronet Thompson’s
Enharmonic Organ, which has 3 boards, with 20, 23 and 22 manuals re-
spectively, and contains the chords in Table V. cols. III., lines 6 to 11;
IV. 6 to 12; V., VI., VIL., 5 to 12; VIII. and IX., 6 to 12 (four chords
belonging to col. IX., lines 6 to 9, are not in the Table, but can be readily
supplied, as well as the additional lines 0, —1, named below). ;
Euler’s “genus cujus exponens est 2”. 3’. 5°,” as developed in his
Tentamen, p. 161, must be considered as adapted for an instrument with
two boards of ordinary manuals, such as some harmoniums are now con-
structed. His “soni primarii’’ would occupy the lower, and his “soni
secundarii”’ the upper board. If to these we add their schismatic equiva-
lents, inclosed in brackets, and distinguish white and black manuals by
capital and small letters as in Table II., Euler’s scheme will appear as |
follows, where the notation interprets his arithmetical expressions of pitch y
(‘soni’), and not his notes (“signa sonora”’), which are too vague.
|
|
Euier’s Dousie ScHEME.
Upper Board.
Schism. Equival... [{C, td), tD, &, FD, tF 9), 1G, @, Bb,w, Clg
“Soni Secundari”. BH, ct, Cx, dt, tH, Ei tft, &x, ge tae ee
2
Lower Board. .
“Soni Primarii” . -C, ite D, tat, B& F ftG, tot 4 of Bae
Schism. Equival... [{D9), ttdb, EDD, te), +F9, tG0>, tg), ADD, ta, LBD, to, tab }
Although it is evident from his notation that Euler regarded schismatic
equivalents as identities, he has not especially alluded to them. The above
scheme would contain Table V. col. V., lines 0 to 14, and the major third
+F4 +A# in 15 (with the schismatic error of ¢B) ({DF for By tD TL),
cok, VI. J'to 15; “Vil-9 to 24- VITI. .10 to 24. 1X. 18 to 24
—lto5; IV.0to6. It would be therefore nearly complete in major
scales, but would have only fd, a, e, 6, £3, c#, g# minor, and their compa-
ratively useless schismatic equivalents. It would have no single complete
key, and would therefore require many commatic substitutions in modula-
tion, and the use of the Pythagorean major third in the major chords of
the comparatively common minor scales of tf, te, tg. If only the “ soni
primarii”’ of the lower board are used the substitutions become very harsh,
as for example 44 D F, D F¥ A for B) {D F, D F4 +A. |
Euler’s “soni primarii”’? may be compared with Rameau’s scale *, which
was as follows,
C, ted, 1D, +, L, F, iff, G, tot, A, +0), B,
* Traité de Harmonie, 1721. The values of the tones are determined from his
arithmetical expression of the intervals,
1864. | on Instruments with Fixed Tones. 103
and. therefore only contained the following perfect harmonies, and ¢wo
perfect scales, 4 major and a minor :—
ay jam}
EAC td fa {D{Fit A
+E) G BD), etbg CEG ace A{CHE
ao GC B egd E{GLe.
Prof. Helmholtz has tuned an harmonium with two boards of manuals,
somewhat in Euler’s manner, as follows :—
Hetmuyoutz’s DousLe SCHEME.
Upper Board.
Schism. equiv. [{C, d),{D, &, FD, F, g),tG, &,A, 0, CD]
Tones tuned.. BY, tet, Cx, dt, tH, tER tft, Fx, of, GX, tat, TB.
Lower Board.
Tones tuned.. —C, cH, D, jdt, H, FE, f£G, tot ta, af, B
Schism. equiv. [{D)), tdp, EDD, te), tF), +£F, tg?, Abb, tad, oDd, +6), £00].
This scheme has nearly the same extent and the same defects as Euler’s.
The concertina, invented by Prof. Wheatstone, F.R.S., has 14 manuals
to the octave, which were originally tuned thus, as an extension of Euler’s
12-tone scheme. |
C, ted, D, tag, £, te, £,f% G, tot, A, ta), B, +09.
It possessed the perfect major and minor scales of C and Z. The harsh-
ness of the chords +B) DF, D FA, for Bp tD F, D F4+A has, however,
led to the abandonment of this scheme, and to the introduction of a tem-
pered scale. I have taken advantage of the 14 manuals to contrive 4 dif-
ferent methods of tuning, so that 4 concertinas would play in all the common
major and minor scales. Two of these I have in use, and find them
effective and very useful for experimental purposes. The following gives
the arrangement of the manuals in each, together with the scales possessed
by each instrument, major in capitals, and minor in small letters. Where
commatic substitution makes the dominant chord too flat in major scales,
parentheses () are used ; where it makes the subdominant chord too sharp,
brackets [ |] are used. Minor scales in brackets have only the subdominant
tone too sharp.
The major chord GBD and the tone C being common to all four
instruments, determine their relative pitch. The method of tuning these
and all justly intoned or ¢eleon* instruments is very simple. C being tuned
to any standard pitch, the fifths above and below it are tuned perfect. To
any convenient tone thus formed, as C itself, form the major thirds above,
* A convenient name, formed from réAcov dudornpa, a perfect interval.
104 My. A. J. Ellis on a Perfect Musical Scale [Jan. 21,
as E, tG#, t By, &c., and below as +4), +F?, &c., and then the fifths above
and below these tones. The names of the tones thus tuned are apparent
from Table V. This tuning is much simpler than any system of tem-
perament, and can be successfully conducted by ear only, taking care to
avoid all beats in the middle octave ¢ to ¢’.
ScHEME FoR Four CONCERTINAS.
1. +49 Concertina.
Manuals..C 0), D db, Ete, F tf, Gg, A tad, B tb,
Scales....Dp, +b, tH), (tB)), [FL C; (MLA «
2. tBp Concertina.
Manuals..C te, D ct, tE td, tF ft, G tg, tA to, B tb,
Scales....t 2), +B), tF (tC), [@], D; [el, g, a.
3. C Concertina.
Manuals..C tet, {Dd, E td, F ft. G tot, A ta, BD,
Scales....F, C, G, (D), [A], E; [td], a e.
4. D Concertina.
Manuals..C ct, D td, E te, Et ft, G ot, tA af, B Td,
Seales....G, D, +A, [TE], [B), Fe; [el], 6, fF.
In Table III. the first column shows the number of degrees of any tone,
two tones whose degrees differ by one-sixteenth being schismatic equivalents.
The second column contains the notes of the tones. The third column
contains the logarithm of the ratio of their pitch to that of c, whence the
ratio itself, the absolute pitch, and the length of the monochord are readily
found. In the fourth column # marks Euler’s primary, and £” his secon-
dary tones; H, H* the tones on Helmholtz’s lower and upper board; 7,
the 40 tones of General T. Perronet Thompson’s Enharmonic Organ ; P,
the 50 tones of Mr. Poole’s Euharmonic Organ; ¢, the 72 tones of
Table V., cols. III. to VIII. ; s, the 24 tones out of these 72 which may be
played as their adjoining schismatic substitutes without injuring the har-
mony; se, the 3 tones which, if played as their schismatic equivalents,
would produce a slight but sensible error; ¢, not followed by either s or se,
the 45 tones which form the minimum number of a justly intoned or teleon
scale; et, the 12 tones of the equally tempered scale. The seven tones of
the major scale of C are printed in capitals in the second column.
1864. } _on Instruments with Fixed Tones. 105
Taste |.—Principal Musical Intervals.
Name. Example. Ratio. or Log. |Deg.
LS 001. Gan eer Gis ec 131 eet ‘00000 | 0
AP eM. 3 i. o's 8 fee tee © 32805 : 32768/38.5 :2% |-00049| 0’
Ti» Diaschisma .....4.... ¢ : Bt 2048 : 2025 21; 3? . 5700491 | 1%
jj (Gita Bae, Cee TG SG 81 :80 BP 22°. 8 00540) Is
TF Pythagorean Comma § TtBE: ec 531441 : 52488 312;219 ~—|-00589| 1
Pe Piccigee ts. .cces--| . Ds tet 128 : 125 97:53 —_|01080| 2
tt Minor Semitone ...... tof: c 25 :24 62°: 23. SOL (soe
(Ged Bias re TB 256 : 243 oP Foe 02263 | 4
f Sharp, or Greater Limma| c#: 135 :128 (383.5 :2? 02312 | 4'
T (pt Equal Semitone*,,.. oe c 4/2 21 #24 + 34 , 5702509 | 4,7,
Greater Semitone . P Guests 16 :15 24:3 .5 |'02803 | 5
Greatest Semitone ...... Teo, ¢ 2187 : 2048 37:24 = |-02852| 5
Greatest Imma” <.,.:.6.|. Td % eg 2h 3 28 i. 33 ; 6? ‘03343 | 6%
MMmOE TONG oc ec ness hss a 0 10 :9 2eO oe 04576 | 8'
Create LONG y iy si0is 8405 ss d -i5,¢ 9:8 3? ; 23 ‘(05115 | 9
Extended Tone .......... oe tet Sif BAS BT) ‘05799 |102
Contracted 3rd .......... gues dl 716 7 :2 ,8 |:06695 112
Pythagorean Minor 8rd .. i530 2 +27 DP 5 38 07379 [13°
MEMOE AUG pews ri vee vse: es 6 6:5 2 ae 55 ‘07918 14
ESFOG MG says ies oe as qe 5:4 5 323 ‘09691 |17'
Pythagorean Major 3rd ..| te : c¢ 81 :64 34 ; 26 ‘10231 |18
Fourth, or Perfect 4th.... Pee 4:3 aoe "12494 |29
False 4th Merete Ce ke eittete’s eas 6 27 +20 3? +2? . & |:18033 |23°
Contracted 5th ...5..55.. A 7:5 7 3:5 14613 |258
Diminished 5th ........ ae! 64 : 45 98 +32 5 ("15297 |a7"
Balse Of asasiisisices. Rae AO 26, (2920. + 38 ‘17070 |30'
Bowal St. recs ris cenee ie 3)-e A/a: 1 #214 + 87 -. 5 |'17560 [31
Fifth, or Perfect 5th i & gs £6 os ?2 eg ‘17609 |31
Pythagorean Minor 6th ,. e :{fE 128 : 81 27 +34 19872 |35
Miao, Gthy «9 ree een ak oe c: EK 8:5 oF. 2.0 ‘20461 |36*
LETC ih hae eee dq be 5:3 SES ‘22185 |39'
Pythagorean Major 6th ..| fa :¢ 54 +32 2.33 : 25 29794 |40
Diminished 7th.......... 1,2 5G2 128 : 76 27:3 = , 5723215 |41"
Hxtended 6th: 0.05.6 .6 e's d :gF eg Dagar t ‘23408 |413
Pemect TW i. vaso... af: G 7:4 7:2 |-94804 |494"
DMR ACHE gs ice 6 osc ss 1 eal 16:9 24 : 32 ‘24988 |4.4”
Acute Minor 7th ........ +b? : ¢ 9:5 37:5 — |-25527 |45°
TAROT TOW Nah est wet ore ea ee or) bie 15 :8 BS a5, 228 ‘27300 |48'
JEN Sarin r aes (: Geta G: ait an L 30103 |53
§ Hence the symbol {J for Pythagoras, with the + (comma) prefixed.
* Approximately.
=)
QR
=|
rac
>
eet
Mr. A. J. Ellis on a Perfect Musical Scale
106
el
eee | peer | een: | ee | | | NS | | |
afd) tat
fa qt
q | hx
fx | at
a | at
An a
qi}
dat |
at | dq
x] dats
at a
gat | ca
qqx | dat
Coa oe
qt | cat
tv | @
(AL? ode fa
4 |xs D4
V+ | #3 o4
ve | ot | BD
vt | 2h | Bo
Vix} 3+ | #9
V+ | fer | 9
ot ee
fee co ee
Weel eth)
Vv «| ¢ Bi
Vv | Ge ra)
i uf a
iW 0
Vv ott Cote
vi stt | got
v | ae r9)
1) 0t 6
XJ at
XJ Ata
xj T+
ty at
me nt
gL | Ga
I+. | Fal
ee a
ABE NE
Ht A
a ui
J at
J At
J at
gor | at | gat
J | ni
8 | L
mL} Hopd
wkd | for
aap juut
a be
a H+
me Ihesaaet
Cee
Gxt | a
a |
Cc a
at | Gx
at | ou
at |
cox | ca
cqe | a
ae |
9 q
[dojs qove Jo e30u
-Loy oy} syteur (x) Ystloyse poxyord v : spentreut yor stoz}0] [[euIs “pas speqrdeo qpeuus ‘opeya quesordor speqideg |
ap ‘a+
pt |ta
pt a
pt |ta
tpt | a
apt dx
tpt | a
je)
ay at
rae at
cP at
pit | dat
ptt | cdt«
ptt | cat
Gptt | cat
90) ‘at
t g
xo ik (kee IB TS:
Oo Oi eee seed ners ©
to ees? Means G
a Ore |) se ediens |
all 9 hy ae CURTIS (C
all Oe aly oe aaseciiens. 7
tort fe) OORT G Bie er |
Tot Ox |e remae Ny
fot 9 OR LEE oe SN) 0
of ‘@) eeeee eevee SIV SG
q@ ot eee SSR RNG
q ot Be os ENB SD
© ot eocrveve S}eT G
SIG ASO RMS oe Ue ae kes
oft | Godel tt" SsyBH Z
fo 9 "tes ngrodute 7,
S T ‘doyg Jo oureyy
“MUNIUOULIBTT 10 UvSIQ woajaz 10 Spouoquy Asng v uo sdojg—']] TIAVY,
1864. | on Instruments with Fixed Tones. 107
| Taste III.
General List of Musical Tones.
Deg. | Note. | Log. Remarks. Deg. | Note. | Log. Remarks,
0 C |-00000|E, H, T, P, t, et.) 19 |tte |-10770 {t.
0' | +b# |-00049 It, s. 20" | ttf |-11365 |t.
Tr | te |-00540/T, t. 20'" | tet |-11464 |T.
2" | ttt |-01233 |T. 204 | cf |-11810/P.
27 |ctdd |-01579 |P. Fe Tee | Ost IM. Pt.
3' |tta) |-01724 It, s. 21" | ett |-12003 |E2, H, P, t, se.
a ie tet |.01773 |B, T, P, t. 22 F |-12494 |K, T, P, t.
4 td) |-02263 |P, t, s. 22' | +tett |-12543 |H2, t, s.
4! 02312 |E, H, T, P, t. es See
t pn toe | ie 19543 let = tet.
45. 02509 |et. REALE EES
me lee (O28 o3 «| te |-130383 (7, t.
5 dp |-02803 T, t. 232 |zted |-14073|P.
5 tet |-02852 |H2, P, t, s. 95" | tft |-142967 |T, P, t.
7" |+td |-04036 {t. 26 te) |-14757 IP, t, s.
7Z | 2d |-04431)P. 26! f+ |-14806 |E, H, T, P, t.
8' | td |-04576/T, P, t. eT
8” | ex 04625 |B, He, t,s, | 202 | IIB [15051 let. ‘H
gs: | ja (05017 let, oT ep) |:15297 |T, t.
ae 28 Se SH +ft |-15346 |E?, H2, P, t, s.
9° eDD |-05066 |t, s. 28° | +tft |-15886 |t.
9 D |-05115|E, H,T,P,t. | 29" |tte |-16530|t.
10° | td |-05655 It. 29" | tf |-16579 |T.
11" | ttdt |-06349 |T. 294 | go |-16925 |P.
11z | ze? |-06695|P. S00 ie det betZ070 1, Pete
12’ | te? |-06839|t, s. SOMO ese 7 | 7109 RPS He PSG, 9.
12” | tdt |-06888/E, H, T, P,t. | 3 aD |-17560 It, s.
13 e) |-07379|T, P, t. ee
13' | dy (07498 (Er, H2, P,t,s, | °0t | le [17560 et=adp.
iat | jaz [07526 let. 31 G |-17609 |E, H, T, P, t.
BA 32 tg 18149 It.
14 | ted |-07918)T, t. 33'” | tte# |-18843 |T.
14 | td# |:07967 |t, s. 332 | gad |-19189|P.
16" | te {|-09151)T, P, t. 34' | tad |-19833 |t, s.
164 |cte |-09547 |P. 34" | tot |-19382|E, H, T, P, t/
1% ff) |-09642|t, s. 35 a) |-19873 |T, P, t.
int BE | 096g Ee T, Pets 7 35° ot |-19922|E2, H2, P, t, se.
172 | |je |-10034 let. let 120068 let.
r f? |-10181|t, s. 36° | tad |-20412/T, t.
18 | te |-10231|K2, H2, T, P, t. | 36 tot |:20461 It, s.
108 Prof. Huxley—Osteology of the genus Glyptodon. [Jan. 28,
Tas eE III. (continued).
Deg. | Note. | Log. Remarks. Deg. Note. | Log. Remarks.
45° | thd |-25527/T, t
452 | cto) |-26567 |P.
47! 1. th. | 267611, Pe
48 te) |-272511t, s.
48! B - |-27300|E, H, T, P, t.
38" | ta |-21645 /T, P, t.
882 |cta |-22040 PP,
39' | A |-29185\E, T, P, t.
89" | gx |-29984 A, t, s.
393 lla |'22577 let.
40° bob |-22675 It, s.
40 ta |-29794 |E
4Y | tta |-28264 It.
42" |\ttbd |-23908 It.
42" | tat [23958 |T:
P
P
48.7. | |Ib . |:27594 |et.
AQ’ cp |:27791 It.
49 th |-27840|E
50’ |+tb {28380 It.
bl) | tha -2G024ar
T
P
494 | chp |-24304 51" | tht |-29078
43' | thd |-24448 P, t, s. 514 | ge |-29419 |P.
43" | aft \O44O7 IE IPs 4° 152! | te |) 20568 eae
44. bD |-24988 /T, P, t. 52” bi |-29612 |E2, H2, P, t, s.
44' | +tatt |-25037 |E?, H2, P, t, s.
STEE
1 | llatt |-25086 jet.
January 28, 1864.
Major-General SABINE, President, in the Chair.
The following communications were read :—
b)
I. “On the Osteology of the genus Glyptodon.” By THomas Henry
Huxtey, F.R.S. Received December 30, 1863.
In 1862 the author communicated to the Royal Society an account of
the more remarkable features of the skeleton of a specimen of the extinct
genus Glyptodon which had been recently added to the Museum of the
Royal College of Surgeons ; and he then promised to give a full description
of the skeleton, illustrated by appropriate figures, in a memoir to be pre-
sented in due time to the Royal Society. The present communication con-
sists of Part I., and Sections 1 and 2 of Part II., of the promised memoir.
Part I. contains the history of the discovery and determination of the
remains of the Hoplophoridz, or animals allied to, or identical with Glypto-
don clavipes. Part IT. is destined to comprehend the description of the
skeleton of Glyptodon clavipes (Qwen)—Hyplophorus Selloi? (Lund); and
the Sections 1 and 2 now given contain descriptions of the skull and the
vertebral column.
The preliminary notice already published in the Proceedings (Dec. 18,
1862, vol. xii. p. 316) will serve as an abstract.
| To face p. 108.
Masi Minor. Masor. Minor.
y,| VIII. EX, X,
ee es eA Miata hie lila alee My
L| cpp Ep ita te 4
5 | bb Bo 1 ie :
3 e o 3
4 tA yl tb) tid i
ee
G G
( 7
: 8
nig
et |tCz ime {G 1d {ex ia 10
ie tbg | 11
D Ttdt ff x| 12
tes< ls
bt | Et tGx B 14
f x| Bg {Dx He ae ‘ ae 15
eX iH XG ADS a Cx iid ke okX) axl
em we | Cs) es. GK) axe | OX » eraiealZ
IX Xx
Magsor.
E>) Gp
E
+E) Gb
ae
oo
tA
Cc
TE
tp +E) +
+p | ch tebb gD
t
+c
Il.
Ii.
By HA
tH
1B
ThE
HB 4DE tt
Tasie IV.—Schismatic Equivalents.
[To face p. 108,
qe =tBt Whence and
4|d = te x q ie =b btct = db
fe = dx tt Bie bh cx = td
qf = tet 4 tab = pe = ep
fle = tf x q b= d btae = ted
‘ja = gx 4] te? = td bey =tf
qb = tax | i =e se =i
q 2 =te bifz = 9D
be = tab | 4 tgp = fe b fx = tg
ibd = ey q abb= ¢ bet =
be =t# 4] fa) = tgp ten = tad
tee | a eae | pee ey
s= a = 7a ph =
heen bib = @
b= te) lb b: = ite
btbz = c
Taste V.—Related Systems.
Minor. JOR Minor. Magsor. Minor. Mason. Minor.
IV. VI. VII. VIII. IX, X.
fp abb td |tkp aoe Ob |tta> $8 tab ltt) 44 tab [tte ttab ite | | > tl
: ebb t +d i fob tab oh tS BN} {tO ny) HE TD tie
foo bbb t ee {D? | te? ig) {bd| tH 1G 1B) tte 19 te
tap £ {D AD| tb) tab te | 4B) $ID tPF [tte tb tt
Sie et tF tA tc [tta te +
@ 5 ig BD e & e tO tH ig ua te te
bp f iD F ig bb id | iG ¢B {D |te te tb
e i? e@ ji A © f a | iD tre th td tft
a Se ee
, tb d |G B D b | E ¢G# B | tet “ec tet |tCHt {GH |tatt tet te
eee |S fen ‘ B ibe F i > ae togtpe De tek deh ine
ta te te tA OftE he e a At Of | t ft af |TDETFX At |tht tdi tt
te tg tbh {tH Gr +B Cr ET G aft ct et | AT{Cx Epiffx af tex
> ia iff HB DETEH| gh tb at BE Dg! et bt | ERIGx Be ltex ef 4
Deaton |p me rca) ia) SE rk gad] i fx|BEEDx Fx{tex be tax
tot tte t +On +H +G: dag +At Cx tER fx tat cx Fx Ax Ox|tdx fx ax
ton ttb ti +Gt +BE tD#| t +bt | TEx Gx tBr) cx tet Bx Cx EX Gx|]ax ex ex
Iv. Vv. Vil. VIM. DX. x
1864.) Mr. Hartnup—Record of ihe Storm of Dec. 3, 1868. 109
Il. “On the Great Storm of December 3, 1863, as recorded by the
Self-registering Instruments at the Liverpool Observatory.” By
Joun Hartnup, F.R.A.S., Director of the Observatory. Com-
municated by General Saprnz, P.R.S. Received January 21,
1864.
[This Paper is accompanied by a diagram, which is deposited, for reference,
in the Archives of the Royal Society, and of which the author gives the
following explanation. |
The accompanying diagram exhibits the strength and direction of the
wind, the height of the barometer, and the rain-fall for three days pre-
ceding, two days following, and during the great storm of December 3,
1863, as recorded by the self-registering instruments at the Liverpool Ob-
servatory. The barometer-tracing is a facsimile of the original record pro-
duced by King’s self-registering barometer ; the force and direction of the
wind and the rain-fall have been taken from the sheets of Osler’s anemo-
meter and rain-gauge ; the time-scale for the anemometer has been slightly
increased to adapt it to that of the barometer, and the scale of wind-pres-
sure for each five pounds has been made uniform, instead of leaving the
spaces greater or less according to the strength of the springs as in the
original record. The tracings of the recording-pencils for the direction of
the wind and the rain-fall are faithfully represented, but it is scarcely
possible to copy the delicate shadings and every gust recorded on the
original sheets by the pencil which registers the force of the wind ; all the
heavy pressures are, however, correctly represented, and may be taken from
the diagram as accurately as from the original sheets. The figures at the
bottom of the diagram show the readings of the dry- and wet-bulb
thermometers and the maximum and minimum thermometers as recorded
at the Observatory during the six days; the wet- and dry-bulb thermo-
meters were read each day at 8 and 9a.m. and at 1, 3 and 9 p.m.; the
registering dry thermometers were read and readjusted each day at | P.M.
The time marked on the diagram for all the instruments is Greenwich
mean time.
For four days previous to the 30th of November the barometer had been
high and steady, the readings ranging from 30°13 in. to 30°33 in., the
latter at noon on the 29th being the highest ; from this time to midnight
the fall was slow and pretty uniform; from midnight November 29 to
midnight December 5 the changes of barometric pressure, the strength and
direction of the wind, and the rain-fall are shown on the diagram. The fall _
of the barometer on the day of the great storm was rapid from midnight to
6 A.M.; heavy rain and hail fell from 3" 30™ to 7" 20™; and from 5" 50™ to
6° 45™ it was nearly calm, during which time the wind shifted from E.
through S. to W. Between 6°45™ and 8" 15™ the pressure of the wind
increased from 0 to 16 lbs. on the square foot, and at about twenty-five
110 Prof. H. J. 8. Smith—Criterion of Resolubilty, &c. [Jan. 28,
minutes past eight it increased from 16 to 43 lbs. in the short space of two
or three minutes ; the barometer, being at its minimum, suddenly rose about
three-hundredths of an inch, and during the heaviest part of the storm it con-
tinued to rise at the rate of about one-tenth of an inch an hour. The oscil-
lations in the mercurial column, as will be seen by the diagram, were large
and frequent during the storm, one of the most remarkable being imme-
diately after 10" a.m. and nearly coincident with two of the heaviest gusts
of wind ; the depression in this case amounted to between four and five
hundredths of an inch, the rise following the fall so quickly that the clock
moved the recording-cylinder only through just sufficient space to cause a
double line to be traced by the pencil.
III. “On the Criterion of Resolubility in Integral Numbers of the
Indeterminate Equation
f= aan? + ala! + allal2 1 Vhg! gl! +2blag" + Db" e!ev—0.”
By H. J. StepHen Smiru, M.A., F.R.S., Savilian Professor of
Geometry in the University of Oxford. Received January 20,1864.
It is sufficient to consider the case in which / is an indefinite form of a
determinant different from zero. We may also suppose that f is primitive,
i. e. that the six numbers a, a’, a”, 6, 6’, 6” do not admit of any common
divisor. We represent by © the greatest common divisor of the minors of
the matrix of f, by AQ? the determinant of f, and by QF the contravariant
of f, 7. e. the form
(62°—ala")a2+ 2.605
QA? will then be the determinant of F, and Af its contravariant. By
Q, A, and QA we denote the quotients obtained by dividing Q, A, and OA
by the greatest squares contained in them respectively; w is any uneven
prime dividing Q, but not A; 5 isany uneven prime dividing A, but not O;
and @ is any uneven prime dividing both © and A, and consequently not
dividing QA. We may then enunciate the theorem—
«The equation f=0 will or will not be resoluble in integral numbers dif-
ferent from zero according as the equations included in the formulee
“ @-6. 0-0 CB-60)
The symbols (5); (=) and (=) are the quadratic symbols of
Legendre; the symbols (5) 5 4)” (Z) , ¢ ) are generic characters of f
(see the Memoir of Eisenstein, “‘ Neue Theoreme der hoheren Arithinetik,”
in his ‘Mathematische Abhandlungen,’ p. 185, or in Crelle’s Journal,
vol. xxxv. p. 125).
The theorem includes those of Legendre and Gites on the resolubility
1864.] Magnetograph-traces at Kew and Lisbon. 111
of equations of the form az®*+a'z’*+a"z'2=0 (Legendre, Théorie des
Nombres, vol. i. p. 47; Gauss, Disq. Arith. arts. 294, 295, & 298). Itis
equally applicable whether the coefficients and indeterminates of f are real
integers, or complex integers of the type p+ qi.
It will be observed that if f, f', f" ...are forms contained in the same
genus, the equations /=0, f/=0, f’=0, &e. are either all resoluble or all
irresoluble.
IV. “Results of a Comparison of certain traces produced simulta-
neously by the Self-recording Magnetographs at Kew and at
Lisbon ; especially of those which record the Magnetic Disturb-
ance of July 15, 1863.” By Senhor Carztto, of the Lisbon
Observatory, and Batrour Stewart, M.A., F.R.S. Received
January 14, 1864.
The National Portuguese Observatory established at Lisbon in connexion
with the Polytechnic School, and under the direction of Senhor da Silveira,
has not been slow to recognize the advantage to magnetical science to be
derived from the acquisition of self-recording magnetographs. Accordingly
that institution being well supported by the Portuguese Government, de-
spatched Senhor Capello, their principal observer(one of the writers of this
communication), with instructions to procure in Great Britain a set of self-
recording magnetographs after the pattern of those in use at the Kew Ob-
servatory of the British Association.
These instruments were made by Adie of London, and when completed
were sent to Kew for inspection and verification, and Senhor Capello resided
there for some time in order to become acquainted with the photographic
processes. The instruments were then taken to Lisbon, where they arrived
about the beginning of last year, and they were forthwith mounted at the
Observatory, and were in regular operation by the beginning of July last.
It had been agreed by the writers of this paper that the simultaneous
magnetic records of the two observatories at Kew and Lisbon should occa-
sionally be compared together, and the opportunity for such a comparison
soon presented itself in an interesting disturbance which commenced on the
15th of July last. The curves were accordingly compared together, and
the results are embodied in the present communication.
We shall in the first place compare the Kew curves by themselves, se-
condly the Lisbon curves in the same manner, and lastly the curves of the
two Observatories together.
Comparison of Kew Curves.
The disturbance, as shown by the Kew curves, commenced on July 15th,
at 9" 13™5 G.M.T., at which moment the horizontal-force curve recorded
an abrupt augmentation of force. The vertical component of the earth’s
magnetic force was simultaneously augmented, but to a smaller extent ;
while only a very small movement was visible in the declination curve.
112 Senhor Capello and Mr. B. Stewart—Comparison of (Jan. 28,
The disturbance, which began inthis manner, continued until July 25th,
if not longer; but during the period of its action there was not for any of the
elements a very great departure from the normal value; probably in this
respect the declination was more affected than either of the other com-
ponents.
While frequently there is an amount of similarity between the different
elements as regards disturbances of long period, yet there is often also a
want of likeness. If, however, we take the small but rapid changes of
force, or peaks and hollows, as has been done by one of the writers of this
paper in a previous communication to the Royal Society (Phil. Trans. 1862,
page 621), we shall find that a disturbance of this nature which in-
creases or diminishes the westerly declination at the same time increases or
diminishes both elements of force. This will be seen more distinctly from
the following Table, in which + ‘denotes an increase and — a diminution of
westerly declination, horizontal, and vertical force respectively, and the pro-
portions are those of the apparent movements of the elements on the pho-
tographic paper.
Taste I.
: . | Vertical-force
Date a a hs Declination. a ae change =unity
bs each instance.
a
1363.
July 17 2 46°5 —1I'o —I'9 —I'o
17 2. 495 —I'l —2°0 —I'o
17 3 21°5 —tI1‘o —2”°0 —t1‘'o
17 7 Sa"G not similar. —2°O —I'o
17 16 13°0 +3°5 +2°2 +1°0
18 24,.22°5 +3°0 +2°0 + 1'0*
19 © 35°5 not similar. +13 +10
19 2 %3°5 +11 +1'9 +1'o
Ig 2 38°70 Ard a7 +10
19 S225 + 1°0 +1°9 +t1'o
I9 {| 17 51°0 +2°8 +2°0 +1of
19 | 18 o'o +3°6 +2°0 +1'of
Ig | 20 29°5 ar ai aan +1'o
20 3 21°0 +10 +1°6 +10
20 | 18 52°5 +40 Ez +1°0
21 © 22°0 —16 —2°3 —I‘0
2 |
21 to —14 —2'1 —1r°o
2. 5
21 5 38°0 +1°4 +2°'0 +10
22 | I9 20°5 —4'0 —2°0 —10
22 | 39.3275 —3°4 —2°'0 —I'o
22] 2% 40°O +3°5 +2°0 | +10
23 | 18 34°5 +3°5 +2°2 +1'0
23.| 19 26°5 +3°4 +2°0 +1ot
24 3 355 +1'2 +2°0 +10
24.| 16 44°5 +32 +2'0 +rot
* Doubtful. + Vertical force too small to be accurately measured, but horizontal-
force change reckoned =2"0,
1864. | Magnetograph-traces at Kew and Lisbon. = = ‘118
From this Table it will be seen that the signs are always alike for the
‘different elements, and also that the small and rapid movements of the
horizontal force are double of those of the vertical force—a result in con-
formity with that already obtained by one of the writers in a previous com-
munication. On the other hand, the declination peaks and hollows do not
bear an invariable proportion to those of the horizontal and vertical force,
but present the appearance of a daily range, being great in the early morn-
ing hours, and small in those of the afternoon. Indeed this is evident by
a mere glance at the curves, which, it so happens, present unusual facilities
for a comparison of this nature.
Comparison of Lisbon Curves.
1. Declination- and vertical-force curves.—The peaks of the waves, or
the elevations in the curve of declination, are always shown in hollows or
depressions in the vertical-force curve, and vice versd. We have never seen
an instance to the contrary either in the curves under comparison or during
the whole time of the operation of these instruments. This curious
relation is exhibited in a Plate appended to this communication, from
which it will be seen that we have not only a reversal, but also a very
nearly constant ratio between the ordinates of the two curves. At Lisbon
therefore an increase of westerly declination corresponds to a diminution of
vertical force, and vice versd; also an almost constant proportion obtains
between the corresponding changes of these two elements.
2. Bifilar and Declination Curves.—July 15. A great disturbance,
which at 8" 37™ Lisbon mean time, or 9" 13"°5 Greenwich mean time,
abruptly and suddenly augmented the horizontal force.
The curve of the declination continues nevertheless nearly undisturbed
for about 30 minutes after this, and only at 9" 41™5 G.M.T. it com-
mences to descend very slowly.
July 16.—At about 13° 6" G.M.T., avery regularly shaped prominence
of some duration occurs in the declination, but is quite invisible in the hori-
zontal force.
July 17.—We see in the bifilar curve half-a-dozen small peaks repro-
duced in the declination in the same direction, but to a smaller extent.
July 18.—One or two accordant peaks. A large prominence of some
duration in the declination at about 17° 56" G.M.T. is reproduced as a
slight depression in the horizontal force.
July 19.—A reproduction in the declination of several small peaks of the
horizontal force ; nevertheless there are others also small which one does -
not see there, or only reproduced to a small extent. Not much accordance
between the great and long-continued elevations and depressions.
July 20.—An accordance between the small peaks.
July 21.—The same.
July 22.—The curve is well marked with small peaks. Coincidence of
several small peaks, but a want of agreement between the more remarkable
114 Senhor Capello and Mr. B. Stewart—Comparison of [Jan. 28,
peaks. The peaks of the horizontal force more developed than those of the
declination.
July 23.—The same appearance of the horizontal-force curves. One
remarks on 22nd and 23rd that the small peaks of the declination and
horizontal-force are more numerous and more developed in the morning
hours.
July 24.—Agreement between the small peaks. A strong disturbance
about 103" G.M.T., no agreement between the waves. A well-marked pro-
minence of declination (154) does not alter at all the horizontal-force curve.
We derive the following conclusions from the comparison which we
have made between the Lisbon curves :—
1. The waves and the peaks and hollows of declination are always repro-
duced at the same instant in the vertical force, but in an opposite direction ;
that is to say, that when the north pole of the declination-needle goes to
the east, the same pole of the vertical-force magnet is invariably plunged
below the horizon, and vice versd. During five months of operation of
these instruments there has not been an example of the contrary.
2. The more prominent disturbances of the horizontal force do not in
general agree with those of the declination or vertical force either in dura-
tion or time.
It is certain that when one of the two elements (bifilar or declination) is
disturbed, the other is also; and sometimes one appears to see even for
several periods of one of the curves, an imitation of the general march of
the other; but when this is examined a little more minutely, and rigorous
measures are attempted, one easily perceives that the phases do not arrive
at the same time, but sometimes later and sometimes earlier, without any
fixed rule. |
In the same curve one generally sees contradictions of this kind.
Nevertheless it is certain that the agreement in direction and time is more
complete when the elevations or depressions are of shorter duration.
3. The small peaks and hollows are generally simultaneous for the
three curves. The direction of these is the same for the horizontal force
and declination, while that for the vertical force is opposite.
The ratio in size of the peaks and hollows is generally variable between
the horizontal force and the declination, while it is always constant be-
tween the latter and the vertical force.
Our next deduction requires a preliminary remark. It has been shown
by General Sabine, that if the disturbances of declination at various places
be each divided into two categories, easterly and westerly, these obey dif-
ferent laws of daily variation, this difference not being the same for all
stations.
This would seem to indicate that for every station there are at least two
simultaneous disturbing forces acting independently, and superposed upon
one another.
This interesting conclusion, derived by General Sabine, appears to be
ENDER Game
pati
ir ad
HGP RINS FH eS
.
SAE) ea PRIOR HEP
[To face page 115. |
TaBLE [I.—Comparison of the time of the
|
hm |hm |hm |h m|h
KEW. jisi3.- 9g 10 9 15 9.34 — |e Aga aa
July 15 ...|4 Lisbon...... Baa7 8 42 Ota 9 43/11 |
Differences | 0 33 ora3 Ge 2) 6 340 'or
OW cccenee 5: O 23 G32 I 24 I 40) 2
Sa oa (5) as)
# Ve usbon ac aga 23 15H. oO 46 7 2m
Differences | 0 39 °o 38 ° 38 © 38] o
RC Weer I 30 x 32 T 37 1 5012
17 ...|4 Lisbon...... O57 I oO £83 1 22
Differences | 0 33 O 32 © 34 © 34| 04
KW osesaes. I 23 1 48 es 5 52| 64
7S t2.| 4 uisbon..-... ° 47 I iI I 29 5 151464
Differences | o 36 O 37 o 36 G37 1-0 3
(18) |
Mow 2i2.2. Xo O 14 2ate) 3 21 44
FO ox (18) (18) !
Lisbon...... 22, On| 23 ak I 338 2, Aan
\ Differences | o 34 O 33 O 34 Oo 341509
Kewitie- ss O 12 2 42 3°19°5 | 4 Ts aS
es (19) |
ins Wdisboma: 25 23 40 219 2 45°5 | Boaz eee
Differences | 0 32 on ge 8) 5 O 33) 84
WEWecc cass I 32°5 | “2-00°S | 5 36°5.) F oolmo rs
21 ...|4 Lisbon...... O 57 Te24cs ss CO 6 22/10 14
Differences | 0 35°5 | © 36 Oo 36°5 | © 381) ola
TOW iis oe as I 24 4 02 5 6 8 26.9295
22 eels SOO. fas. © 51 3 29 AS 7 53112 2
Differences | 0 33 O193 6.133 OQ 33) soa
Kiewieissc:. 232, 3 11 3°35 7 Agee
23 +..| Lisbon...... TS 7, 2237, epee 6 29) beg =
| Differences | 0 35 O 34 © 34 © 35sno 3¢
WCW -2 es 3 29°5 | 4 21 4 50 5 2sls s¢
ANS Lisbon...... 2 56 3 49 4 19 453) B32
Differences | 0 33°5 | © 32 O38 © 32) © 34
1864. ] Magnetograph-traces at Kew and Lisbon. 115
verified by the behaviour of the Lisbon curves. From the relation, always
invariable, between the waves of declination and vertical force, as well as
from the almost total absence of agreement between these two curves and
the horizontal force, one has a right to conclude —
1. That there is approximately only one independent force which acts
at Lisbon, if we consider the vertical plane bearing (magnetic) east and
west. Now the ratio of the disturbing forces for the vertical foree and
declination is, in units of force, between 26 : 48 and 26: 36. This would
give the inclination of the resultant between 29° and 36°.
2. The absence of agreement in time, and the variability in direction,
between the waves of the horizontal force and those of the declination and
vertical force, appear to lead to the conclusion that there is another dis-
turbing force besides that already mentioned, which acts in the direction of
the magnetic meridian and almost horizontally.
Comparison of the Kew and Lisbon Curves (14-24 July).
1. Horizontal force (north and south disturbing force).—The curves
of the horizontal force at Kew and at Lisbon exhibit a very great simili-
tude *, as will be seen at once from the Plate appended to this communi-
cation. Almost all the waves and peaks and hollows are reproduced at both
places. At the same time one does not see the same resemblance during
the great disturbance of 15th July. In the commencement, and for the
first four hours, there is a resemblance for all the waves, but from that
time until 193° G.M.T. one remarks little agreement between the different
elevations and depressions. But from 193" until the end of the dis-
turbance the likeness reappears. There are, however, one or two cases of
small resemblance in the other curves, but these are of short duration.
In order to demonstrate the similarity between the two curves, reference
is made to Table II., in which the principal points are compared together
with respect to time; that employed being the mean time for both
stations.
From this Table it will be found that the average difference between the
local times of corresponding points is 343, while that due to difference of
longitude is 35"°3. We attribute this apparent want of simultaneity to
various causes :—
(1) Loss of time in the commencement of movements of the registering
cylinder.
(2) Difficulty in estimating precisely the commencement of certain curves.
(3) It was only in the morth of August that the exact Lishon time of
the astronomical observatory was obtained by a telegraphic connexion.
(4) To these must be added the uncertainty in estimating the exact
turning-point of an elevation or depression of a blunt or rounded form.
* We speak of the Kew curves reversed so as to have their base-lines above, the dis-
position of the registering arrangement at Kew being the opposite of that at Lisbon.
This reversal has been made in the Plate which accompanies this paper.
VOL. XIII. KR
[To face page 115.
Tasxe I1.—Comparison of the time of the principal corresponding points of the Horizontal-Force Curves at Kew and at Lisbon.
July 15...
7) taas
Sites
19
20...
21...
22 «..
PI eel
TM
Differences
OS8F ORY OWF OPN OD
h
9
9
°
I
(eo)
te}
wo OHR OHM
OFF OBWW OFM OUN On
m
34
I
33
24
46
38
37
K)
34
h
fe)
9
°
w
- ON
OFM OF 013K ODN OW
m
a7)
43
34
40
h
II
II
°
rs
OND OFPN OW
m
43
9
34
m
43
10
WW
of OXvP Ow
w
aS
h
19
0)
°
4
ONnR OW
m
42
fo)
32
09
31
38
51
16
35
h m
20 40
20 9
© 31
4 42
h m
OwF 0”
oc
20 28
h m
18 43
18 6
@ sh7/
5 43
5 99
© 33
21 58
21 24
© 34
21 52
21 19
@ 3h33
18 41
13 8
2) 233}
h m
h m
6 59
6 25
© 34
hm
h m
7 22
6 48
@ Mt
hm
h m|
II oo
IO 25
O35)
II 12
10 38
© 34
hm
Ir 51
Ir 18
©) 543
116 Senhor Capello and Mr. B. Stewart—Comparison of [Jan. 28,
The following Table exhibits approximately the proportion between the
disturbance-waves of the horizontal force at Lisbon and at Kew.
TABLE ITI.
Proportion between the disturbance-waves of
the horizontal force reduced at both places
Date. to English units (Lisbon wave = unity).
July 15. Variable between 1 : 1°3 and 1: 1°9
16. . 1 21°83 and 1-43
Wee ae 1o-el 26
18. 1: 1°9 and 1: 2°5
19. 156
18. as 175
19, ae T2125
20. a 1 4°7
21. a | As te
PAs aS Lo14
Ze. “ Le bs
DA. . 12 146
—
Dn
Mean
[To face page 116.
Curves at Kew and Lisbon.
TasiE [V.—Comparison of the times of the principal corresponding points of the Declination Curves at Kew and Lisbon.
[To face page 116.
Ke Wersasenvern
July 15 ...|4 Lisbon.........
Differences ..
1);/60c09n000700
20 Lisbon.........
Differences
( Kew Ae a0bO0RETou
17 «14
Lisbon.........
Differences
Kew .......e cee
18 .../4
Lisbon...
Differences
Kew............
19 .../4
2 Lisbon.........
KE) ce}
2m 9211) TE} TA mooe cor
Differences ...
Kew....secccens
PP on
Lisbon.........
Differences ...
Kew........005
23 ...|4 Lisbon.........
Differences
Wewasecs
<}
Orw ornw 00
wo
=
RP OWNW OF
cy
OWP OWW CH
h
17
17
fe}
3
3
°
on
OnD ODN OF
m
47
038
39
51
16
35
45
h
18
17
°
12
C)
oman OMmnm ON
h
18
18
°
14
m
53
16
37
II
37
34
20
h m
19 49
19 12
O83 7)
16 22
15 45
©) EW/
3 59
h
25
21
°
18
m
51
17
34
26
52
34
40
h
20
~
ow
m
h m
21 16
20 42
hm
h m
21 4
20 31
h m
18 37
18 6
© 31
h m
19 51
19 20
© 31
1864. | Magnetograph-traces at Kew and Lisbon. 117
‘It would thus appear that the declination at Kew, judging from the waves,
_ is subject to greater disturbing forces than at Lisbon in the proportion of
16:1. This ratio is not, however, quite so great as that for the hori-
zontal force.
3. Vertical disturbing force.—The curves of vertical force are nearly
quite dissimilar. Sometimes the general march of the curves appears to
coincide durmg some time; but in these cases we do not find an appre-
ciable general agreement for the majority of the various points of the wave,
On the other hand, the small peaks and hollows of the Kew curves are
generally reproduced in those of Lisbon, but in the opposite direction, that
is to say, a sudden augmentation of the vertical force at Kew corresponds
to a sudden diminution of the same at Lisbon, and vice versd.
In Table VI. we have a comparison of the principal points of the vertical-
force curves with respect to time.
Tasie VI.—Comparison of the time of the principal corresponding points
of the Curves of Vertical Force at Kew and Lisbon.
Kews .:...: hm hm hm |hm hm hm
July 15 .../4 Lisbon No similarity.
Differences
Weiyeeie ak. 2 21 ON 07 |
Bea 50 VASHON... I 47 20 45
Differences | 0 34 On 32
1G pees 2 AGTO iiss 3220 Ti Suh 16) 115
Pes Lasbon:..... Padi: id ahs 2 19°5 2 49 gi OE 15 39
Differences} 0) 33°5 | © 32°5 Oo 31 O 34 O 32°5
GOW. «shi: 7%O0 9*33 Dye ples
15 ...|4 Easbon...... 6 29 g 00 20 50
Differences | o 31 Ona O32
RCW i ace: Ox IO Zale, 2 Or hy a aor 17, AGUS Ey uso: S
1G Sis | hon eee 23 38 tr 36°5 2) OB, 2 46 17 18 yin HLs
Differences} 0 32 © 35°5 0.3475, 0, 335 © 3m°5.| @ 33°5
TEOW. csies os 3 19°5 18 51 22 03
20M Lisbon. -.:,. 2 46°5 18 18°5 eat
Differences | 0 33 Or 325 O 32
HEE WE cci08 i 3 2 10 5 36°5 6 43 |
2 te nen AS bOM: ss. I 36 5 O15 6 09
Differences | o 34 O 35 O 34
ONES. ae s2n 5 06 8 24 1256.) TOc1H}, org iam, |e 48s
Be | 5 ISOM can: Ang Wo 5y 2 922 18 46 Tied, BS) 2; Bee)
Differences | 0 33 @' 33 O 34 oO 33 O 34 © 34°5
Hews 3.2: 18 33 18 37 ps icy. all
DH i. Lisbon...... 18 oI 18 05 222,
Differences | 0 32 O 32 O 32
Kew......... 2° 29°5 4 10 5 59 16 43
24 ...|4 Lisbon...... 2G 8) 37 Ge ZOrs | TOSS
Differences | 6) 4975 fo) 33 « (ionig’s O 34°5 |
ee ne
* Only the points marked with this sign are in the same direction, all the athena are in
the opposite direction ; that is to say, an augmentation of force at Kew corresponds to a
diminution of the same at Lisbon, and vice versa.
118 Senhor Capello and Mr. B. Stewart—Comparison of [Jan. 28,
From this Table it will be seen that the average difference between the
local times of corresponding points is 33™°1, while for the horizontal force
this was 34"°3, and for the declination 34™°0, the mean of the three being
33™°8. The measurements from which these numbers were obtained were
made at Lisbon independently for each element: another set of measure-
ments, made at Kew, but of a less comprehensive description, gave a mean
difference in local time of 33"°7, which is as nearly as possible identical
with the Lisbon determination. We have already observed that we attri-
bute the difference between 33"°8 and 35-3, the true longitude-difference
of local times, to instrumental errors, and not to want of simultaneity in the
corresponding points.
In Table VII. we have a comparison in magnitude and sign of the peaks
_and hollows at the two stations.
From this Table it will be seen that the magnitude of these is generally
greater at Kew than at Lisbon. The curious fact of the reversal in direc-
tion of the vertical-force peaks between Kew and Lisbon has been already
noticed.
We shall now in a few words recapitulate the results which we have
obtained.
1. In comparing the Kew curves together for this disturbance, the
peaks and hollows of the horizontal force always bear a definite proportion
to those of the vertical force, the proportion being the same as that ob-
served in previous disturbances. On the other hand, the declination peaks
and hollows do not bear an invariable proportion to those of the other two
elements, but present the appearance of a daily range, being great in the
early morning hours, and small in those of the afternoon. The peaks and
hollows are in the same direction for all the elements.
2. In comparing the Lisbon curves together, the elevations of the decli-
nation-curve always appear as hollows in the vertical-force curve, and vice
versd, and there is always a very nearly constant ratio between the ordi-
nates of the two curves. The horizontal-force curve, on the other hand,
presents no striking likeness to the other two. We conclude from this
that there are at least two independent disturbing forces which jomtly in-
fluence the needle at Lisbon, but that the declination and vertical-force
elements are chiefly influenced by one force.
The peaks and hollows are generally simultaneous for the three curves.
The direction of these is the same for the horizontal force and declina-
tion, while that for the vertical force is opposite. The ratio in magnitude
of the peaks and hollows is generally variable between the horizontal force
and the declination, while it is always constant between the latter and the
vertical force. :
3. When the Kew and Lisbon curves are compared together, there is a
very striking likeness between the horizontal-force curves, one perhaps
somewhat less striking between the declination-curves, and very little like-
ness between the vertical-force curves. It is perhaps worthy of note that
119
Magnetograph-traces at Kew and Lisbon.
1864.]
0°066
o7041
K
(17 and 18)
For the other days
ursebeacrnde ceeteeedie—=O1OHO
Foo cadausaacheaucneeeeeini=sOro2l0
aT
O°O41
K
izontal force ...
Declination ......... K=0'024 ...
Vertical force ...... K=0'024 ...
Hor
Net:
3
a a
eee
Ps =|
© eat
|
ten!
3 5
> Z
& e)
a FQ
om N
= =
ro) |
or
Sars)
o 2
So
~
ao
wy
=e)
Qed °
Mp 3
oe |
en) eae
a a
be 3
2 oreo es
on) ica)
3)
is|
a E
a ee
S|
@
Are|
o
ia)
es]
&
72)
—_
aa]
a
gZ000.0 | o£0.0—
gL000.0 | 0£0.0—
0100.0 | o¥o.0—
gz000.0 | O10.0—
L1100.0 | S¥o.o-+
+or100.0 | oVo.o +
gZ000.0 | O10.0—
gloo00.0 | 0£0,0-++
gZ000.0 | O10.0-+
gZ000.0 | 0£0.0—
gzo00.0 | O10,0—
gLl000.0 | 0£0.0—
$g000.0 | $%o.0—
6£000.0 | S10.0—
$g000.0 | $70.0 —
6£000,0 | SI0o.0—
6£000.0 | $10.0—
$g000.0 | $%0.0—
0100.0 | 0OV0.0—
6£000.0 | S10.0—
97Z000.0 | O10.0-+-
6£000.0 | $10.0+
6£000.0 | $10.04
“q1un :
ysysug |
"UOgsl'y
Trews Ar90A
Boro00.0 | $¥o,0-++
eee yreurs Ar0A
gvoo0.o | oz0.o+
37000.0 | 070.0
9000.0 | $zo.0—
©9000.0 | $zo.0—
09000.0 | $ze,o4+
3000.0 | $£0.0—
g£000.0 | $10.0—
3000.0 | 070.0-+
09000.0 | $zo,0o+
g7000.0 | 070,0-+
v8 []euts
ae AJOA {
%g000.0 | S£0.04+
zL000.0 | of0.0-+
goroo.o | $0.04
z£100.0 | $So.0o+
é é
gV000.0 | 0z0,0-+-
g0100.0 | S¥o.0—
OZ100.0 | o$0.0—
3000.0 | S£0.0—
$%g000.0 | $£0.0—
“yun :
ysysug | PMT
"MOY
“QOL0F [COTIAI A
ZO100.0 | $zo.0+ | £z100.0 | of0.0+
gz£o0.0 | 0g0.0+ | 69£00.0 | 060.0-++
€z100.0 | o£0.0-+ | Ev100.0 | $£0.0-+
Z0100.0 | $zo.o+ | 7gro0.0 | S¥o.0o-++
7000.0 | 070.0+ | VgI00.0 | OVO.0-+-
ZO100.0 | $z0o.0— | $0z00.0 | o$0,0—
£Z100.0 | O£0.0— | $0Z00.0 | o$0.0—
Ev100.0 | S£0,.0+ | Soz00.0 | o$0.0-++
+9100.0 | o¥o.o— | Lo£o0.0 | $Lo.0—
ae Trews A194 | 4100.0 | $£0,0—
19000.0 | $10.04 | ¥g100.0 | $¥0.0+
é é 9100.0 | 00,04
1¥000.0 | 010.0-++ | ¥9100.0 | OO,0-+-
ZO100.0 | $zo.0-+ | EV100.0 | $£0.0+4
19000,0 | $10.0+ | £o100.0 | $z0.0-++
3100.0 | S¥o.0+ | Lgzo00.0 | $90.04
¥gt00.0 | ov0.0+ | $0z00.0 | 0$0,0-+-
$zz00.0 | $$0.0+ | Lofoo.o | $Lo,0+
$o0z00.0 | 0$0.0-+ | o1Vo0.0 | 001.0+
sf Trews A190 | €Z7100.0 | o£0,0+
g6100.0 | of0.0-+4 | ¥groo.0 | $¥o,0+
£9£00.0 | $S0.0— | 69£00,0 | 060,0—
¥9790.0 | o¥o.o— | O1700.0 | OO1.o—
g6100.0 | o£0.0— | Lotoo.o | $40.0—
86100.0 | o£0.0— | Lgzo00.0 | $90.0—
Un ‘ “910 5
ysysug | “OP "L | ysyfaq | Ml
"uOqsT'T "MOV
"2010F [CJWUOZIIO PT
obvo00.0 | o10.0-++ | 0z100.0 |oS0.0+ fs
00100.0 | $70.04 | z£100.0 | $$0.0-+ \ if
00200.0 | $z0.0+ | VvI100.0 | ogo.0-+ } ei
OZ1I00.0 | o£0.0+ | gg100.0 |oL0.0+
09000.0 | $10,0-+4 | g9100.0 | oL0,0-+
ov100.0 | $£0.0— | oz00.0 | Sg0.0o— bzz
ovro0.0 | $£0.0— | oFz00.0 | Cor.o—
09000.0 |} St0,0+ | 7g000.0 | $£0.0-F |
obvro0.o | $£0,0— | 0Z100.0 | 0S0.0—
ovo00.0 | O10,0— | 09000.0 | $z0.0—
0Z100.0 | O£0.0-+ | g1Z00.0 | 0o69.0-+
ob000.0 | 010.0-+ | gv000.0 | 070.0-+ 2
obvr100.0 | $£0.0-+ | g$100.0 | S$go.o-+
00100.0 | $zo.0-+ | g$100.0 | $90.0+ |
09000.0 | $10,0-+ | ¥go0o.o | $£0,0+ |
0g000.0 | 0z0.0-+ | g090.0 | $£0,0+
09000.0 | $10.04 | go00.0 | $£0,0-+4+
on 3 OZ100.0 O80. Oo
o00I00.0 | $zo.0-+ eels :
0Z100.0 | o£0.0-+ | goroo.0 |$¥o.0+ gr
09000.0 | $10.0-++ | gg100.0 |oL0.0+
obo00.0 | @10.0— | 0z100.0 joSo.0o— 7 Zr Ane
oF000.0 | 010.0— | 96000.0 | ov0.0 — f
oF000.0 | O10.0— | 96000.0 | ov0,0— }
“qrum : “yun A
ysysug | PML | qsysug | PM
“U0gsl'y “MOM
"TOT}CUIpII
‘TOGSTT PUL MOY JV SMOT[OF] pur syvog oy} Jo udig pus opnylucep— ]TA FIAV],
120 Magnetograph-traces at Kew and Lisbon. [Jan. 28,
the Lisbon horizontal-force curve, in which we may suppose two indepen-
dent forces to be represeated, is probably on the whole the most like the
corresponding Kew curve. Corresponding points occur at the samie abso-
lute time for both stations.
The disturbance-waves for the horizontal force and declination are
greater at Kew than at Lisbon.
The Kew peaks and hollows are simultaneously produced at Lisbon in all
the elements, but to a smaller extent than at Kew; also the direction is
reversed in the case of the vertical force, so that a sudden small increase of
vertical force at Kew corresponds to a diminution of the same at Lisbon.
The writers of this paper are well aware that before the various points
alluded to in their communication can be considered as established, a more
extensive comparison of curves must be made. But as the subject is new
and of great interest, they have ventured thus early to make a preliminary
communication to the Royal Society. They will afterwards do all in their
power to confirm their statements, which in the meantime they submit to
this Society as still requiring that proof which only a more prolonged in-
vestigation can afford.
Note regarding the Plates.
Increasing ordinates denote increasing westerly declination, and also in-
creasing horizontal and vertical force.
The following are the scale coefficients applicable to the different
diagrams :—
Horizontal force, Kew. One inch represents 0:041 English unit.
Ditto Lisbon. > 4; is 0:035 3 for July 15
Ditto do. a fe 0:066 ae for July 17.
Ditto do. a * 0:041 ,. for the other
curves.
Declination do. os * 0:040 ¥,
Vertical force do. es a 0°026 *
ARORA IY callie rn cc arta ik, coh WN ot iy ect cumin LAL Sia
Proc feoy-500. Vol XHL PULT.
Dectanatim, Lusbon ie CMT.
s October 8. |
= |
= |
~ \
S
=~ !
2 Vertical Force, Lisbon |
:
Ss
ee
s
S SHON Socrates |
SS eclnatiy, Lisbon, SGI, 22% 87" GMT
t
I
1
1
'
¥
'
!
1
1
!
1
i)
|
ee eee
Vertucal, force, Lishor:
| Dechination, Lisbon:
Hor. Force, Hew.
Vertical Force, Lisbon:
/. Baswre, lth;
. "it a ey Ah.
ae
Oetcbein G0:
PR
Li Ee
@
aati 22
-
Lisbon.
bs is
= 3 ra A x
Vertical Force, Lisbon:
}
|
D
SCAT, SMG ML.
Sil Zh. P50 CML.
LEGMT.
LW Duby UY 5 LHD bby Uh PY? hee
Lt oL FL
Oct?8. Th
UOQSLT "09.L0,J LOH
' THD nulB UM : yp LHe Dubted U4ay
es way “ODIO toy Fis 0a eres
MOQXNT, BILD LO LWIutlyo 14 if
u“ : ie
ae MO OIL] LOL
Zoe se
Tioulgg were §— MOET P07 WO 1709 aly? 06 2 oe
oa | UD gS a0 MOT
re L 9 £ as Mal L
: F,
m9 t99 eA LHI uu 4 <
2 S LHD Fiubly AL
‘
MOY 2240 sop]
THO uhh AY
MOY “0M “LOFT
1864.] 121
February 4, 1864.
Major-General SABINE, President, in the Chair.
The following communication was read :—
“Tixperiments to determine the effects of impact, vibratory action,
and a long-continued change of Load on Wrought-iron Girders.”
By WixiiaM Farreairn, LU.D., F.R.S. Received January 2C,
1864,
(Abstract.)
The author observes that the experiments which were undertaken, nearly
twenty years ago, to determine the strength and form of the Tubular Bridges
which now span the Conway and Menai Straits, led to the adoption of cer-
tain forms of girder, such as the tubular, the plate, and the lattice girder,
and other forms founded on the principle developed in the construction of
these bridges. It was at first designed that the ultimate strength of these
structures should be six times the heaviest load that could ever be laid upon
them, after deducting half the weight of the tubes. This was considered
a fair margin of strength ; but subsequent considerations, such as generally
attend a new principle of construction with an untried material, showed the
expediency of increasing it; and instead of the ultimate strength being
six times, it was in some instances increased to eight times the weight of
the greatest load.
The proved stability of these bridges gave increased confidence to the
engineer and the public, and for several years the resistance of six times
the heaviest load was considered an amply sufficient provision of strength.
But a general demand soon arose for wrought-iron bridges, and many were
made without due regard to first principles, or to the law of proportion ne-
cessary to be observed in the sectional areas of the top and bottom flanges,
so clearly and satisfactorily shown in the early experiments. The result of
this was the construction of weak bridges, many of them so ill-proportioned
in the distribution of the material as to be almost at the point of rupture
with little more than double the permanent load. The evil was enhanced
by the erroneous system of contractors tendering by weight, which led to
the introduction of bad iron, and in many cases equally bad workmanship.
The deficiencies and break-downs which in this way followed the first
successful application of wrought iron to the building of bridges led to
doubts and fears as to their security. Ultimately it was decided by the
Board of Trade that in wrought-iron bridges the strain with the heaviest
load should not exceed 5 tons per square inch; but on what principle
this standard was established does not appear.
The requirement of 5 tons per square inch did not appear sufficiently
definite to secure in all cases the best form of construction. It is well
VOL. XIII. L
122 Mr. Fairbairn—Ezperiments on the Effects [Feb. 4,
known that the powers of resistance to strain in wrought iron are widely
different, according as we apply a force of tension or compression ; it is even
possible so to disproportion the top and bottom areas of a wrought-iron
girder calculated to support six times the rolling load, as to cause it to yield
with little more than half the ultimate strain or 10 tons on the square inch.
For example, in wrought-iron girders with solid tops it requires the sectional
area in the top to be nearly double that of the bottom to equalize the two
forces of tension and compression ; and unless these proportions are strictly
adhered to in the construction, the 5-ton strain per square inch is a fallacy
which may lead to dangerous errors. Again, it was ascertained from direct
experiment that double the quantity of material in the top of a wrought-
iron girder was not the most effective form for resisting compression. On the
contrary, it was found that little more than half the sectional area of the top,
when converted into rectangular cells, was equivalent in its powers of resist-
ance to double the area when formed of a solid top plate. This discovery
was of great value in the construction of tubes and girders of wide span, as
the weight of the structure itself (which increases as the cubes, and the
strength only as the squares) forms an important part of the load to which
it is subjected. On this question it is evident that the requirements of a
strain not exceeding 5 tons per square inch cannot be applied in both cases,
and the rule is therefore ambiguous as regards its application to different
forms of structure. In that rule, moreover, there is nothing said about the
dead weight of the bridge ; and we are not informed whether the breaking-
weight is to be so many times the applied weight plus the multiple of the
load, or, in other words, whether it includes or is exclusive of the weight
of the bridge itself.
These data are wanting in the railway instructions ; and until some fixed
rinciple of construction is determined upon, accompanied by a standard
measure of strength, it is in vain to look for any satisfactory results in the
erection of road and railway bridges composed entirely of wrought iron.
The author was led to inquire into this subject with more than ordinary
care, not only on account of the imperfect state of our knowledge, but from
the want of definite instructions. In the following experimental researches
he has endeavoured to ascertain the extent to which a bridge or girder of
wrought iron may be strained without injury to its ultimate powers of resist-
ance, or the exact amount of load to which a bridge may be subjected with-
out endangering its safety—in other words, to determine the fractional strain
of its estimated powers of resistance.
To arrive at correct results and to imitate as nearly as possible the stram
to which bridges are subjected by the passage of heavy trains, the apparatus
specially prepared for the experiments was designed to lower the load quickly
upon the beam in the first instance, and next to produce a considerable
amount of vibration, as the large lever with its load and shackle was left
suspended upon it, and the apparatus was sufficiently elastic for that
purpose.
1864.] | of Impact, &c. on Wrought-Iron Girders. — 123°
The girder subjected to vibration in these experiments was a wrought-iron
_ plate beam of 20 feet clear span, and of the following dimensions :—
Area of top... 6.5.6 ssceeecs eee ee 4°30 Square inches.
Fives Gl DOCCON 6 BUEN as 0 Ses seey 240 i
Area of vertical web .......... ve os 290 ye
Total sectional area ........ cece ce 8°60 Z,
Depth ssw... ss Pe Nee bbe Ea les 16 inches.
DION, a a's ww u's we c- f CWhe DOTS
Breaking-weight (cileulated).. : wwcece’ 12 tons:
The beam having been loaded oil 6 6643 Ibs. equivalent to one-fourth of
the ultimate breaking-weight, the experiments commenced as follows :—
Experiment I.
Experiment on a wrought-iron beam with a changing load equivalent to
one-fourth of the breaking-weight.
Number of | Deflection
Date. changes of | produced by Remarks.
Load. Load.
1860.
March 21 ...... ° O17 Strap loose on the 24th March.
eepEIe f 2.24.20. 202,890 O17 Strap broken on the 2oth April.
May Tees... ceeees 449,280 o°16
| May 14 ......008 596,790 0°16
The beam haying undergone about half a million changes of load by
working continuously for two months night and day, at the rate of about
eight changes per minute, without producing any visible alteration, the load
was increased from one-fourth to two-sevenths of the statical breaking-
weight, and the experiments were proceeded with till the number of changes
of load reached a million.
Experiment IT.
Experiment on the same beam with a load equivalent to pelos ett of the
breaking weight, or nearly 33 tons. 3
Number of | Deflection, |
Date changes of | in inches. Remarks.
Load.
1860.
May 34) ..023..0 fe) 0'22 In- this experiment the number of
JHE GQ)’. 25 uk. 236,460 o'21 although the beam had already un-
dergone 596,790 changes, as shown
in the preceding Table.
JUNE 26 ..cccc0e- 403,210 0°23 ‘The beam had now suffered one mil-
; | lion changes of load.
Ls es eae 85,820 0°22 changes of load is counted from o,
EZ
124 My. Fairbairn—Ezperiments on the Effects [Feb. 4,
After the beam had thus sustained one million changes of load without
apparent alteration, the load was increased to 10,486 lbs., or 2ths of the
breaking-weight, and the machinery again put in motion.. With this addi-
tional weight the deflections were increased, with a permanent set of *05
inch, from *23 to *35 inch, and after sustaining 5175 changes the beam broke
by tension at a short distance from the middle. It is satisfactory here to
observe that during the whole of the 1,005,175 changes none of the rivets
were loosened or broken.
The beam broken in the preceding experiment was repaired by replacing
the broken angle-irons on each side, and putting a patch over the broken
plate equal in area to the plate itself. A weight of 3 tons was placed on
the beam thus repaired, equivalent to one-fourth of the breaking-weight,
and the experiments were continued as before.
Experiment IIT.
Number of 6 Permanent
Date. changes ee set, in Remarks.
filioad.9| °° ~~ al inmehes.
1860, ;
August 9 ss... TSO) Visaeaesene He ovremeaay .. |Dhe load during these changes
was equivalent to 10,500 lbs.,
or 4'6875 tons at the centre.
With this weight the beam
took a large but unmea-
sured set.
August 12 ...... 12,950 During these changes the load
August 13 ...... 25,900 0°22 % in the beam was 8025 lbs.,
or 3°58 tons.
August 13 sss 25,900 o'18 fo) Load reduced to 2°96 tons, or
December 1 ...| 768,100 o'18 O’OI _ th the breaking-weight.
1861.
Mareh2. cscs cee 1,602,000 0°18 O'OI
IVI GA. a cians ont 2,110,000 O°17 O'OI
September 4 ...| 2,727,754 O°17 oor
October 16...... 3,150,000 O°17 O‘oI
At this point, the beam having sustained upwards of 3,000,000 changes
of load without any increase of the permanent set, it was assumed that it
might have continued to bear alternate changes to any extent with the
same tenacity of resistance as exhibited in the foregoing Table. It was
then determined to increase the load from one-fourth to one-third of the
breaking-weight ; and accordingly 4 tons were laid on, which’ increased the
deflection to *20.
1864. ] of Impact, &c. on Wrought-Iron Girders. 125
Experiment IV.
Number of : Permanent
Date. changes ne set, Remarks.
of Load. in inches.
: 1861.
October 18...... fo) 0°20
November 18...| 126,000 0°20 °
December 18...) 237,000 0°20
1862.
MEMEO OF yese-| 313,000 | Psiiececsl | cei weeeee | Broke by tension across the
bottom web.
Collecting the foregoing series of experiments, we obtain the following
summary of results.
Summary of Results.
|
= Weight Strain
cS on mid- Sapien per sq. pa Dede
a Date. dle of the) 4) if inch |P& *4: tion, in Remarks,
iE beam, in | “22°85 lon bot-| 2 | inches.
fe} p24.) 0b, Load: on top.
7, tons. tom.
1| From March
21 to May 596,790) 4°62 | 2°58 | *17
14, 1860...
2| From May
14 to June 403,210] 5°46 | 3°05 | ‘23
26, 1860...
3| From July Broke by tension a short
25 to July GI 7a of Fee 4:08 35 distance from the cen-
23, 1860... tre of the beam.
Beam repaired.
4| Aug. 9, 1860) 4°68 158| 7°31 | 4°08 .... | The apparatus was acci-
RP Aue: 11 & 12) > 3°58 25.JAZ) 5G | giz | 522 dentally set in motion.
6
13, 1860 to 3,124,100) 4°62 | 2°58 18
Oct. 16, 1861
From Oct. 18,
1861 toJan.| + 4°00 413,006) O25") | 374G |)! "20
9, 1862
From Aug.
2°96
Broke by tension as be-
fore, close to the plate
riveted over the pre-
vious fracture.
From these experiments it is evident that wrought-iron girders of ordi-
nary construction are not safe when submitted to violent disturbances
equivalent to one-third the weight that would break them. They, however,
exhibit wonderful tenacity when subjected to the same treatment with one-
fourth the load ; and assuming therefore that an iron girder bridge will bear
with this load 12,000,000 changes without injury, it is clear that it would
require 328 years at the rate of 100 changes per day before its security
was affected. It would, however, be dangerous to risk a load of one-third
126 The Rev. J. Bayma on Molecular Mechanics. [Feb. 11,
the breaking-weight upon bridges of this description, as, according to the
last experiment, the beam broke with 313,000 changes ; or a period of eight
years, at the same rate as before, would be sufficient to break it. It is more
than prohable that the beam had been injured by the previous 3,000,000
changes to which it had been subjected ; and assuming this to be true, it
would follow that the beam was undergoing a gradual deterioration which
must some time, however remote, have terminated in fracture,
February 11, 1864.
Major-General SABINE, President, in the Chair.
The following communications were read :—
I. “On the Calculus of Symbols.—Fourth Memoir. With Applica-
tions to the Theory of Non-linear Differential Equations.” By
W.H.L. Russexrz, A.B. Communicated by Professor Cayipy.
Received July 31, 1863.
(Abstract. )
In the preceding memoirs on the Calculus of Symbols, systems have been
constructed for the multiplication and division of non-commutative symbols
subject to certain laws of combination ; and these systems suffice for linear
differential equations. But when we enter upon the consideration of non-
linear equations, we see at once that these methods do not apply. It
becomes necessary to invent some fresh mode of calculation, and a new no-
tation, in order to bring non-linear functions into a condition which admits
of treatment ky symbolical algebra. This is the object of the following
memoir. Professor Boole has given, in his ‘Treatise on Differential Equa-
tions,’ a method due to M. Sarrus, by which we ascertain whether a given
non-linear function is a complete differential. This method, as will be seen
by anyone who will refer to Professor Boole’s treatise, is equivalent to find-
ing the conditions that a non-linear function may be externally divisible by
the symbol of differentiation. In the following paper I have given a nota-
tion by which I obtain the actual expressions for those conditions, and for
the symbolical remainders arising in the course of the division, and have
extended my investigations to ascertaining the results of the symbolical
division of non-linear functions by linear functions of the symbol of differ-
entiation.
Il. “On Molecular Mechanics.” By the Rev. JosepH Bayma, of
Stonyhurst College, Lancashire. Communicated by Dr. Suarpey,
Sec. R.S. Received January 5, 1864.
The following pages contain a short account of some speculations on
molecular mechanics. They will show. how far my plan of molecular
1864.] The Rev. J. Bayma on Molecular Mechanies. 127
mechanics has been as yet developed, and how much more is to be done
before it reaches its proper perfection. Of course I can do no more than
point out the principles on which, according to my views, this new science
ought to be grounded. The proofs would require a volume,—and the more
SO, aS existing wide-spread philosophical prejudices will make it my duty to
join together both demonstration and refutation. But there will be time
hereafter, if necessary, for a complete exposition and vindication of the
principles on which I rely; at present it will be enough for me to state
them.
The aim of ‘molecular mechanics” is the solution of a problem which
includes all branches of physics, and which may be enunciated, in general
terms, as follows :—
‘From the knowledge we gain of certain properties of natural substances
by observation and experiment, to determine the intrinsic constitution of
these substances, and the laws according to which they ought to act and
be acted upon in any hypothesis whatever.”
In order to clear the way for the solution of this problem, three things
are to be done.
First. From the known properties of bodies must be deduced the essen-
tial principlés and intrinsic constitution of matter.
Secondly. General formulas must be established for the motions of any
kind of molecular system, which we conceive may exist 7m rerum natura.
_ Thirdly. We must determine as far as possible the kinds of molecular
systems which are suited to the different primitive bodies; and be pre-
pared to make other applications suitable for the explanation of pheno-
mena.
Of these three things, the first, which is the very foundation of mole-
cular mechanics, can, I think, be done at once. The second also, though
it requires a larger treatment, will not present any great difficulty. The
third, however, in this first attempt, can be but very imperfectly accom-
plished ; for sciences also have their infancy, nor am I so bold as to ex-
pect to be able to do what requires the labour of many: I shall only say
so much as may suffice to establish for this science a definite existence and
a proper form.
In order to give an idea of my plan, I will now say a few words on each
of these three points.
I. PrincreLes oF MotecutaAR MECHANICS.
First, then, (to say nothing of the name of “‘ molecular mechanics,” which
will be justified later,) in all bodies we find these three things, extension,
inertia, and active powers, to one or other of which every property of bodies
may be referred. In order therefore to arrive ata clear idea of the con-
stitution of natural substances, these three must be diligently investigated,
Extension.—I have come to the following conclusions on this head, which,
128 The Rev. J. Bayma on Molecular Mechanics. ([Feb.11,
I think, can be established by evident arguments drawn from various con-
siderations.
1. All bodies consist of simple and unextended elements, the sum of
which constitute the absolute mass of the given body. The extension
itself, or volume, of the body is nothing but the extension of the space in-
cluded within the bounding surfaces of the body ; and the extension of space
is nothing but its capability of being passed through (percurrzbilitas) in any
direction by means of motion extending from any one point to any other.
2. There is no such thing possible as matter materially and mathema-
tically continuous—that is to say, such that its parts touch each other with
true and perfect contact. There must be admitted indeed a continuity of
forces ready to act; but this continuity is only virtual, not actual nor
formal.
3. Simple elements cannot be at once attractive at greater, and repulsive
at less distances. To this extent at least Boscovich’s theory must be
corrected. Ifan element is attractive at any distance, it will be so at all
distances; and if it be repulsive at any distance, it will be repulsive at all
distances. This is proved from the very nature of matter, and perfectly
corresponds with the action of molecules and with universal attraction.
4. Simple elements must not be confounded with the atoms of the chemist,
nor with the molecules of which bodies are composed. Molecules are,
according to their name, small extended masses, 2. e. they imply volume ;
elements are indivisible points without extension. Again, molecules of what-
ever kind, even those of primitive bodies, are so many systems resulting
from elements acting on each other; consequently elements differ from
molecules as parts differ from the whole; so that much may be said about
separate elements, which cannot be said of separate molecules or chemical
atoms, and vice versa. Element, molecule, body have the same relation
to each other in the physical order, that cndividual, family, state bear to
each other in the social order; for a body results from molecules, and
molecules from elements holding together mechanically, in a similar way to
that in which a state results from families, and families from individuals
bound together by social ties.
So much regarding extension; for I do not now intend to proceed to
the demonstration of these statements, but simply to he down what it is
I am prepared to prove.
Inertia.—There would scarcely be any need of saying anything on this
head, were there not some, even learned men, who entertain false ideas
about it, and from not rightly understanding what is said of inertia by
physical philosophers, throw out ill-founded doubts, which do more harm
than good to science. I say, then,
1. Inertia implies two things: (a) that each element of matter is per-
fectly indifferent to receiving motion in any direction and of any intensity
from some external agent ; (4) that no element of matter can move itself
by any action of its own. |
1864.] The Rev. J. Bayma on Molecular Mechanics. 129
2. It follows as a sort of corollary from this, that to be inert does not
_ signify to be without active power; and that the very same element, which
on account of its inertia cannot act upon itself, may, notwithstanding this
inertia, have an active power, by which it may act upon any other element
whatever.
3. Inertia is an essential property of matter, and is not greater in one
element than in another, but is always the same in all elements, whether
they are attractive or repulsive, whether their active power is great or
small.
4, That which is called by natural philosophers the vis inertia is not a
special mechanical force added on to the active forces of elements, but is the
readiness of a body to react by means of its elementary forces, against any
action tending to change the actual condition of that body.
These four propositions will remove many false notions, which give rise to
confusion of ideas and impede the solution of many important questions.
Active power.—The questions relating to the active power of matter are
of the greatest importance, since on them depends nearly the whole science
of nature. On this point I am convinced, and think I can prove, that
1. No other forces exist in the elements of matter except locomotive
or mechanical forces; for these alone are required, and these alone are
sufficient, to account for all natural phenomena. So that we need have
no anxiety about the vires vcculte of the ancients, nor need we make
search after any other kind of primitive forces, besides such as are mecha-
nical or locomotive. Hence chemical, electric, magnetic, calorific and other
such actions will be all reduced to mechanical actions, complex indeed, but
all following certain definite laws, and capable of being expressed by mathe-
matical formule as in general mechanics. Hence in treating of molecular
mechanics we do not make any gratuitous assumption or probable hypo-
thesis, but are engaged ona branch of science founded on demonstrable
truths, free from all hypothesis or arbitrary assumption.
2. There are not only attractive, but also repulsive elements; and this
is the reason why molecules of bodies (as bemg made up of both sorts)
may at certain distances attract, and at others repel each other.
3. Simple elements, in the whole sphere of their active power, and con-
sequently also at molecular distances, act (whether by attracting or repel-
ling) according to the inverse ratio of the squares of the distances. This
proposition may seem to contradict certain known laws, as far as regards
molecular distances ; but the contradiction is only apparent, and this appear-
ance will vanish when we consider that the action of elements (of which
we are now speaking) is not the same as the action of molecules. From
the fact that cohesion, e. g., does not follow the inverse ratio of the square
of the distance, it will certainly result that molecules do not act according
to this law, and this is what physical science teaches: but it does not fol-
low that elements do not act according to the law. This truth is, as all
must see, of the utmost importance, since it is the foundation of molecular
130 The Rev. J. Bayma on Molecular Mechanics. [Feb. 11,
mechanics, of which it would be impossible to treat at all, unless the law
of elementary action at infinitesimal distances were known. ‘This truth
universalizes Newton’s law of celestial attraction by extending it to all
elementary action, whether attractive or repulsive, and makes it applicable
not only to telescopic, but also to microscopic distances. It is clear there-
fore that I am bound to prove this law most irrefragably, lest I construct
my molecular mechanics on an insecure foundation.
4, The sphere of the activity of matter is indefinite, in this sense, that
no finite distance can be assigned at which the action of matter will be null.
It by no means, however, follows from this that the foeee of matter has an
infinite intensity.
5. The natural activity of each element of matter is exerted tmmediately
on every other existing element at any distance, either by attracting or
repelling, according to the agent’s nature. Thus, e. g., the action which
the earth exerts on each falling drop of rain is exerted immediately by each
element of the earth on each element of the water (notwithstanding the dis-
tance between them); itis not exerted through the material medium of the
air, or of ether, or any other substance. The same must be said of the action
of the sun on the planets. This proposition, however, it is evident, holds
only for the simple action of the elements, 2. e., attractive or repulsive.
For it is clear that complex actions causing vibratory motions, such as
light or sound, are only transmitted through some vibrating medium. This
conclusion is also of immense importance, because it solves a question much
discussed by the ancients about the nature of action exerted on a distant
body, and removes all scruples of philosophers on this head.
6. Bodies do not and cannot act by mathematical contact, however
much our prejudices incline us to think the contrary; but every material
action is always exerted on something at a distance from the agent.
7. There is another prejudice which I wish to remove, 2. e. that one
motion is the efficient cause of another motion. It is easily shown that
this mode of speaking, though sometimes employed by scientific men, is
incorrect, and ought to be abandoned, because it tends to the destruction
of all natural science. Motion never causes motion, but is only a condition
affecting the agent in its manner of acting. For all motion is caused by
some agent giving velocity and direction; but the agent gives velocity and
direction by means of its own active power, which it exerts differently
according as it is found in different local conditions. Now these local
conditions of the agent may be differently modified by the movement of
the agent itself. The impact of bodies, the change of motion to heat, the
communication of velocity from one body to another (always a difficult
question), and other points of a like nature can only be satistactonily
explained by this principle.
These are the principal points that have to be discussed, defined, and
demonstrated in order that molecular mechanics may be established on
solid principles.
1864. ] 7 The Rev. J. Bayma on Molecular Mechanics. 131
II. MaruematicaL EvoLuTION OF THESE PRINCIPLEs.
After establishing principles, we must proceed to investigate the formulas
of motion and of equilibrium, first between the elements themselves, then
between the several systems of elements. The difficulties to be overcome
in establishing the principles were chiefly philosophical: the difficulties
which occur in the present part are mathematical, and can only be over-
come by labour and patience.
As long as we confine ourselves to two elements, the mathematical for-
mula expressing their motion is easily found. Thus, if there are two attrac-
tive elements of equal intensity, and if v be the action of one for a unit of
distance in a unit of time, 2a the distance between them at the beginning
of motion, x the space passed through by one in the time ¢, the equation
of motion will be
=a / 78 ( vaca) +0. tang = hee)
And since it is clear, from other considerations, that these two elements
must vibrate together indefinitely in vibrations of equal times and constant
extent, the time of one oscillation will easily be found from the above
formula.
_ If the two attractive elements have unequal forces, or if one be attractive
and the other repulsive, or both repulsive, the equation of motion may easily
be obtained.
But when we have to do with a more complex system of elements, after
obtaining the differential equations corresponding to the nature of the
system, it is scarcely possible to obtain their integration, as will appear
from the examples which I shall give below. Consequently, if we wish to
deduce anything from such equations, we must proceed indirectly, and a
long labour must be undertaken, sometimes with but slender results. This
material difficulty will be diminished, or perhaps disappear, either by some
new method of integration (which I can scarcely dare to hope for, though
it is a great desideratum) or by certain tables exhibiting series of numerical
values belonging to different systems.
But there occurs another difficulty in these systems. For since the
agglomerations of simple elements can be arranged in an infinite variety,
and it would be neither reasonable nor possible to treat of all such agglo-
merations, we must limit the number of them according to the scope we
have in view, i. e. according to the use they may be of in explaining natural
phenomena. Even this isavery difficult matter. How I have endeavoured
to overcome this difficulty I will briefly explain.
First. I considered that the molecules of primitive bodies, such as oxygen,
hydrogen, nitrogen, &c., cannot reasonably be supposed to be trregular—
a conclusion which, though I cannot rigorously demonstrate, yet I can
render probable by good reasons. Consequently, while treating of primi-
tive systems I may confine myself to the examen of forms that are regular.
182 The Rev. J. Bayma on Molecular Mechanics. [Feb. 11,
Secondly. I divided these regular systems into different classes according
to their geometrical figure. Of these I have investigated the tetrahedric,
octahedric, hexahedric, octohexahedric, pentagonal-dodecahedric, and icosa-
hedric.
I then divided these classes into different species, viz. pure centrata,
centro-nucleate, centro-binucleate, centro-trinucleate, &c., also into acen-
trate (without centre), truncate, &c. To enumerate the whole would take
too long; indeed I only mention these to show how in such a multiplicity
of systems I endeavoured to introduce the order necessary for me to be able
to speak distinctly about them. |
Lastly, besides classes and species, it was requisite also to consider cer-
tain distinct varieties under the same species. And in this way I seemed
to myself to have embraced all the regular systems of elements possibly
conceivable.
Thirdly. The several parts of which any system of elements can consist
are reduced by me to a centre, nuclei toany number, and an external enve-
lope. And thus I obtained not only a method of nomenclature for the dif-
ferent systems (a most important point), but also a method of exhibiting
each system under brief and intelligible symbols. Thus, e. g., the tetra-
hedric system pure centratum (2. e. without any nucleus), in which the
centre isan attractive element, and the four elements of the envelope repul-
sive, will be represented thus,
m=A+4R,
in which expression m signifies the absolute mass of the system (in this case
m= 5), A represents the attractive centre, and 4R the four repulsive ele-
ments of the envelope. The letters A and R are not quantities, but only
indices denoting the nature of the action.
In a similar way, the following expression
m=R+6A+8R!
denotes a system whose centre R is repulsive, whose single nucleus 6A
ig octahedric and attractive, and whose envelope 8R’ is hexahedric
and repulsive: m, which, as before, indicates the absolute mass of the
system, here =15.
This will suffice to show how the different species and varieties of the
afore-mentioned systems may be named and expressed.
Then I had to find mechanical formulas for the motion or equilibrium of
the several systems; for it is only from such formulas that we can deter-
mine what systems are generally possible in the molecules of bodies. Speak-
ing generally, no system pure centratum, of whatever figure it be, can be
admitted in the molecules of natural bodies, whether gaseous, liquid, or
solid.
Let v represent the action of the centre, and w that of one of the elements
of the envelope for a unit of distance ; and let 7 be the radius of the system,
i. e. the distance o ‘any one of the elements of the envelope from the centre ;
1864. ] The Rey. J. Bayma on Molecular Mechanics. 133
_ the general formula of motion for any system pure centratum (expressed as
above by m=A-+ 7R) will be
ar
de
where M signifies a constant, ay the actions which tend to increase 7 are
taken as positive.
If the system is tetrahedric, M=0:91856
= (v— Mw),
pi octahedric, M=1:66430
a hexahedric, M=2°46759
re octohexahedric, M=4:11170
3 icosahedric, M=4:19000
pentagonal dodecahedric, M=7°82419.
Now none of these varieties satisfies the conditions either of solid, liquid,
or gaseous bodies; because they either will not resist compression, or they
form masses which are repulsive at all great distances; or if they could
constitute gaseous bodies, they do not allow the law of compression to be
verified, which we know to hold for all gases.
Passing on to the systems centro-nucleata, the formulas will differ according
to the several figures of the nuclei andenvelope. Taking, e. g., the system
m=R+6A+8R’,
which is hexahedric with an octahedrie nucleus, and taking v, v', w to
represent respectively the actions of the centre, one element of the nucleus,
and one element of the envelope; taking also 7 and 0 for the radii of the
nucleus and envelope, the equations of motion for such a system will be
ay v—M'’ PU en Be OND
7 i ae +4w
dt Ee aJ (oer BEY 4 2er “)
ti
(0° ‘ee Zen Oy creme G ee =a)
dp __vt+Mw _ 3, prvi p—rVi
dt? 2
p a/ (ee ay We (FER a. He
where M=2:46759, and M'/=1°66430. The conditions of equilibrium
will be obtained by making the two first members equal to zero.
What systems of this class (centro-nucleata) can satisfy the conditions
of solid, liquid, or gaseous bodies, is exceedingly difficult to determine, for
reasons which I have above touched on, viz. that the formulz of these
systems are not integrable, and we have consequently to proceed indirectly
with great expenditure of time and trouble. It seems to me, however, as
far as I can judge, that some of these systems may be found im rerum
natura.
Passing to another class of systems (centro-binucleata), we shall have
three equations to express its laws of motion. Taking, e. g., the system
m=A+4R+4A'+ 42,
-
134 The Rey. J. Bayma on Molecular Mechanics. (Feb. 11,
which is tetrahedric with two tetrahedric nuclei; taking 2, v', ’, w for the
respective actions of the elements acting from the centre, first and second
nuclei, and envelope ; taking 7, 7", p for the radii of the two nuclei and
the envelope, the equations of motion will be as follows:
dy! Ras Mo'—v — lt i 37! —r"!
dé 72 (t+r"') ("+9 Dplyll )
V 3
'
Rene ee on ea —_—_—
oO Teen BY
pall ine re
d*r = Me Me 2 4g 1 37!!—r!
a
aE (er? /( eae 2rrity
he ae
iid
355 oe 4 3r'—p
(e+r a (eee ee,
3
dp _Mw—v, y ee
dt’ p oa a) e+e ey 24 Fi “)
3p—7"!
=o SE
wary | (e+ ey
(etary
in which equations M=0°91856.
The discussion of these equations and similar ones will afford a useful
occupation to mathematicians and natural philosophers. Whatever conclu-
sions may be drawn from them cannot fail to throw great light on the
question of the nature of bodies.
It is evident that we might go further and pass on to ¢rinucleate, qua-
drinucleate, &c. systems; but the number of equations will increase in
proportion, together with the difficulty of dealing with them.
It is not enough to consider the laws of motion and equilibrium in each
system separately, but it is also necessary to know what action one system
exercises on another, whether like or unlike, placed at a given distance.
For since many of the properties of bodies depend on the relation which
the different molecules bear to one another, e. g., liquidity, elasticity, hard-
ness, &c., it isnot enough to know what is the state of a system of elements
(i. e. a molecule) in itself, but we must investigate also how several such
systems (or molecules) affect each other. Now in this ulterior investigation
it is clear that the difficulty increases exceedingly, since the equations
become exceedingly complex. Here also then may natural philosophers
pf!
1864.] On the Excavation of the Valley of the Somme. 135
find matter for industry and patience. I have done a little in this subject,
‘but not enough to deserve any special mention. In order, however, to
diminish the difficulties, the investigation may be provisionally restricted te
the mutual actions of the envelopes, neglecting for the time that of the
nuclei, which may be considered as a disturbing cause, for which some
correction may afterwards have to be made.
So much then for the mathematical and theoretic development of mole-
cular mechanics. There remains the third part, which, though the most
laborious of all, will yet give the greatest pleasure to scientific men; since
it is less dry, and opens a way for attaining the end aimed at in the natural
sciences. Of this third part I will add a few words.
Ill. AppLicaTION OF THE PRINCIPLES OF MOLECULAR MECHANICS.
[Under this head the author points out the various properties of bodies
which would have to be explained, and of which he conceives an explana-
tion might be afforded could the mathematical calculations be effected
which are required for the elaboration of his theory, and enunciates the
following conclusions as deduced from his explanation of the impact of
bodies. |
1. If a body does not contain any repulsive elements, it cannot cause any
retardation in the movement of any impinging body.
2. Again, if the medium through which a body moves contain no repul-
sive elements, no retardation of its motion can take place.
3. Ifa medium does contain repulsive elements, retardation must neces-
sarily take place.
4. Consequently, as the planets in their movements through the ether
do not suffer any loss of velocity, it must be concluded that the eether does
not contain any repulsive elements at all, and that its elasticity must be
explained without any recourse to repulsive forces.
This last inference is somewhat wonderful, and decidedly curious: but-
after much consideration it appeared to me so natural, and so well harmo-
nizing with other truths and scientific theories, that I ceased to hesitate
about its adoption and gave it a most decided assent; whether wisely or
not, I leave others to judge.
Ill. “On some further Evidence bearing on the Excavation of the
Valley of the Somme by River-action, as exhibited in a Section
at Drucat near Abbeville.’ By JosrrpnH Prestwicn, F.R.S.
Received January 29, 1864.
On the occasion of a late visit to Abbeville, I noticed a fact which appears
of sufficient interest, as bearing upon and confirming one of the points
treated of in my last paper, to induce me to submit a short notice of it to the
Royal Society. It occurs in a tributary valley to that of the Somme, but
necessarily forms part of the general phenomena affecting the whole basin.
136
The small stream (the Escardon) which joins
the Somme at Abbeville flows through a nar-
row chalk valley extending afew miles north ot
Abbeville. Three miles up this valley is the
village of Drucat; and on the hill above the
village, and about 100 feet above the stream, is
a small outlier of high-level gravel which I
have before described, and which is remark-
able for the number and size of its sand- and
gravel-pipes penetrating the underlying chalk.
One of these which I measured was. 22 feet
across at the top and 18 feet at a depth of
30 feet, and I estimated its depth at not less
than 100 feet from the surface. It was filled
in the usual way with sand and gravel in ver-
tical cylindrical layers. M. Boucher de Perthes
has two flint implements which are reported to
have come from the pit; but I never myself
found any there, or any mammalian remains.
The sand and gravel is clean and light-coloured,
and very similar in character to some of the
beds at Menchecourt, and in so far has the
appearance of a fluviatile gravel, and, like it, is
overlain by a variable bed of loess. This bed
was supposed to form an isolated outlier; but
on my last visit I found another bed, though of
coarser materials, on a hill of the same height
on the opposite side of the valley, above I’ Heure.
The valley at the foot of the hill on which the
-Drucat gravel is worked is about a quarter of a
mile wide. A lane leads direct down the slope
of the hill from a point near the gravel to the
valley ; anda roadside cutting exposes a section
of calcareous tufa or travertin several feet thick,
and containing in places numerous land shells,
of recent species, and traces of plants. Half a
mile beyond, the bed is of sufficient importance
to be worked for building-purposes. This bed
is overlain by the valley loess, and is in places
intercalated with it; it commences a few feet
below the level of the gravel at about 70 feet
above the valley, and continues to near the foot
of the hill.
Mr. Prestwich on the Excavation
/HIGHLEVEL GRAVEL
CA
[Feb. 11,
“FIRST OUTB URST™ OF THE TUFA” SPRING
E
OW ARID
‘A
ce ate en ET Mabe
LEVEL OF THE VALLEY AT’ THE
Bs Ox
OleRE.
SSS SS
—- .
4—4, Line of present water-level. Y. Gravel-pipe.
Now it is well proved that in all purely chalk districts the line of water-
level proceeds from the level of the streams and rivers traversing the dis-
1864.] | of the Valley of the Somme. 137
trict, in a slightly inclined and continuous plane rising on either side under
the adjacent hills with a slope varying from 10 to 40 feet in the mile, the
latter being an extreme case. If we take a mean of 20 feet, as the gravel-
pit is not above one-third of a mile from the valley, the rise in the water
underneath would not probably exceed 10 feet above the level of the stream.
The chalk formation is so generally fissured and permeable that I know of
no instance of a line of water-level or of springs occurring above the ge-
neral line dependent upon the level of the adjacent rivers. It is also well
known that strong springs are common at the foot of the hills along many
of our chalk valleys, as, for instance, that at Amwell, those at Carshalton,
and many along the valley of the Thames. These springs are more or less
calcareous, often highly so.
It is evident that the travertin at Drucat has been formed by a deposit
from a spring of considerable volume ; and it further appears that it flowed
while the loess was in the course of formation. For the tufa could only
have been formed at or near the level of the spring; so that its continued
deposit down the slope of the hill shows the spring to have been gradually
lowered as the valley became deeper, and while subject to the continued
-inundations which deposited the loess. The line of present water-level in
the chalk here is about 90 feet below the summit of the hill, as proved by
a well in an adjacent farmhouse, and at the gravel-pit they have gone down
60 feet without reaching water. But the level of the upper part of the
tufa shows the line of water-level or of springs to have been at one time
70 feet above the valley, which could only have happened when the bottom
of the valley was on a level 60 to 70 feet higher than itnowis. The gradual
deepening of the valley is indicated by the gradual lowering of the spring
until it reached to within from 20 to 30 feet of the present valley-level, when
it became extinct. Further, we have in the adjacent bed of high-level gravel
evidence of the origin of this important spring; for the sands and gravel-
beds are not only very thick, but they are also perfectly free from calca-
reous matter and very permeable, and they show in their numerous gravel-
pipes how great must have been the volume and solvent power of the rain-
water which at one time percolated through them. The water, after pass-
ing through the gravel and acting upon the underlying chalk to form these
large vertical cavities, would, upon reaching the original line of water-level,
have flowed off horizontally and escaped in a strong spring at the base of
the adjacent slope. It there parted with its excess of the carbonate of lime,
and so formed the calcareous tufa. This case furnishes therefore new and
good evidence on two points:—first, on the connexion of the sand- and
gravel-pipes with the percolation of fresh water through calcareous rocks ;
and secondly, on the condition of the former land surface and of the springs,
only possible on the hypothesis of former higher levels of the bottom of the
valley and of its gradual excavation.
VOL. XIII. M
138 Mr. Hulke on the Minute Anatomy of the Retina. [¥eb. 18,
February 18, 1864:
Major-General SABINE, President, in the Chair.
The following communications were read :—
I. “A Contribution to the Minute Anatomy of the Retina of Amphibia
and Reptiles.” By J. W. Hurxs, Esq., F.R.C.S., Assistant-
Surgeon to the Middlesex and the Royal London Ophthalmic
Hospitals. Communicated by W. Bowman, Esq. Received
February 4, 1864.
(Abstract.)
The animals of which the retina was examined were the frog, the black
and yellow salamander, the edible turtle, the water- and the land-tortoise,
the Spanish Gecko, the blindworm, and the common snake. The method
adopted was to examine the retina (where possible) immediately after
decapitation of the animal, alone and with chemical agents; and to make
sections of the retina hardened in alcohol or in an aqueous solution of
chromic acid, staining them with iodine or carmine, and adding glycerime,
pure and diluted, to make them transparent. The following is a summary
of the results of the examination.
1. The rods and cones consist of two segments, the union of which is
marked by a bright transverse line.
2. Kach segment consists of a membranous sheath and contents.
£'3. The outer segment, or shaft, is a long narrow rectangle (by inference,
a prism or cylinder). It refracts more highly than the inner segment. Its
contents are structureless, and of an albuminous nature. It is that part
which is commonly known as “ the rod.’ It is smaller in the cones than
in the rods, and in the cones narrows slightly outwards.
4, The outer ends of the shafts rest upon the inner surface of the
choroid, and their sides are separated by pigmented processes, prolonged
from the inner surface of the choroid between them to the line that marks
the union of the shaft with the inner segment. The effect of this is that
the shafts are completely insulated, and rays entering one shaft are pre-
vented passing out of it into neighbouring shafts.
5. The inner segment of the rods and cones, or body (the appendage of
some microscopists), has a generally flask-shaped form, longer and more
tapering in the rods, shorter and stouter in the cones. It is much paler
and less conspicuous than the shaft. It fits in an aperture in the membrana
limitans externa.
Its inner end always encloses, or is connected by an intermediate band
with an outer granule which lies in or below the level of the membrana
limitans externa. Its outer end, in cones only, contains a spherical bead
nearly colourless in the frog and blindworm, brilliantly coloured in the
turtle and water- and land-tortoises, and absent from the common snake and
Spanish Gecko. In addition to this bead, where present, and the outer gra-
1864.] Mr. Hulke on the Minute Anatomy of the Retina. 139
nule, the body contains an albuminous substance which in chromic acid pre-
parations retires as an opaque granular mass towards the outer end of the
body. The inner end of the body is prolonged inwards, in the form of a
pale, delicate fibre, which was sometimes followed through the layer of
inner granules into the granular layer. It does not appear to be struc-
turally connected with the inner granules. It is essentially distinct from
Miller’s radial fibres, and bears a considerable resemblance to the axis-
eylinder of nerve. That it ever proceeds from the outer granule associated
with the rod- or cone-body is doubtful, from the consideration (a) that where
the body is large, and the granule lies within at some distance from its
contour, the fibre is seen to leave the inner end of the body distinct. from
the granule, and ((@) that the fibre appears to proceed from the outer
granule only where the body is small, as in the frog, and where the
granule does not lie within the body but is joined to this by a band.
Ritter’s axial fibres are artificial products.
6. The ‘outer granules” are large, circular, nucleated cells. Each
cell is so intimately associated with a rod- or cone-body that it forms-an
integral part of it.
7. The intergranular layer is a web of connective fibre. It contains
nuclei.
8. The inner granules are roundish, in chromic acid preparations poly-
gonal cells. They differ from the outer granules by their higher refraction,
by the absence of a nucleus, and by receiving a deeper stain from carmine.
They lie in areole of connective tissue derived from Miiller’s radial fibres,
and from the intergranular and granular layer. They are more numerous
than the outer granules, and consequently than the rods and-cones.
9. The granular layer is a very close fibrous web derived in part from
Miiller’s radial fibres, and from other fibres proceeding from the connective
frame of the layer of inner granules. It transmits (a) the radial fibres,
(() fibres proceeding radially outwards from the ganglion-cells and bundles
of optic nerve-fibres, and (y) fibres passing inwards from the rod- and cone-
bodies.
10. The ganglion-cells communicate by axis-eylinder-like fibres with the
bundles of optic nerve-fibres, and send similar fibres outwards, which have
been traced some distance in the granular layer.
11. In the frog and Spanish Gecko the author has a few times traced
fibres proceeding from the bundles of optic nerve-fibres for some distance
in a radial direction in the granular layer.
12. Miller’s radial fibres arise by expanded roots at the outer surface
of the membrana limitans interna, pass radially through the layers,
contributing in their course to the granular layer, to the areolar frame of
the layer of inner granules, and end in the intergranular layer and at the
inner surface of the membrana limitans externa. They are a connective
and not a nervous tissue, and do not communicate between the basilary
element and ganglion-cells.
M 2
140 Messrs. Frankland and Duppa on the [Feb. 18,
13. The orderly arrangement of the several layers and their elementary
parts is maintained by a frame of connective tissue which consists of—
1, an unbroken homogeneous membrane bounding the inner surface of the
retina, the membrana limitans interna; 2, a fenestrated membrane which
holds the rods and cone-bodies, the membrana limitans externa, first
correctly described by Schultze; 3, an intermediate system of tie-fibres—
Miiller’s radial fibres—connected with which in the layer of inner granules
are certain oblong and fusiform bodies of uncertain, nature; 4, the inter-
granular layer; 5, an areolated tissue, open in the layers of outer and
inner granules, and very closely woven in the granular layer.
14. No blood-vessels occur in the reptilian retina.
II. “ Notes of Researches on the Acids of the Lactic Series.—No. I. Ac-
tion of Zinc upon a mixture of the Iodide and Oxalate of Methy].”
By E. Franxxanp, F.R.S., Professor of Chemistry, Royal Insti- _
tution, and B. F. Dupra, Esq. Received February 10, 1864. .
In a former communication by one of us*, a process was described by
which leucic acid was obtained synthetically by the substitution of one
atom of oxygen in oxalic acid by two atoms of ethyl.
The relations of these acids to each other will be seen from the following
formulee +t :—
C, H
. C,H,
Cee : Cee 0
OH 2
OH OH
OH
Oxalic acid. Tienes acid.
This substitution of ethyl for oxygen was effected by acting upon oxalic
ether with zincethyl. On distillmg the product with water, leucie ether
came over, which on treatment with an alkali yielded a salt of leucic acid.
We have since found that this process may be much simplified by gene-
rating the zincethyl durmg the reaction, which is effected by heating a
mixture of amalgamated zinc, iodide of ethyl, and oxalic ether in equivalent
proportions to the necessary temperature.
The operation may be considered complete when the mixture has soli-
dified to a resinous-looking mass. This, treated with water as in the for-
mer reaction and distilled, produces quantities of leucic ether considerably
greater than can be obtained from the same materials by the first mode of
operating. Thus the necessity for the production of zincethy] is entirely
obviated, the whole operation proceeds at the ordinary atmospheric pressure,
and a larger product is obtained.
We find that this process is also applicable to the homologous reactions
with the oxalates and iodides of methyl and amyl. By it we have obtained
* Proceedings of the Royal Society, vol. xii. p. 396.
t The atomic weights used in this paper are the following :—C=12, O=16 and Zn=65.
1864. ] Acids of the Lactic Series. 141
numerous other acids belonging to the lactic series, which we have already
more or less perfectly studied, and the history of which we propose to lay
before the Royal Society as our researches proceed, reserving for a later ©
communication our views regarding the constitution of this series of
acids, and the theoretical conclusions arrived at in the course of the inquiry.
In the present communication we will describe the application of this re-
action to a mixture of iodide of methyl and oxalate of methyl.
= Two equivalents of iodide of methyl were mixed with one of oxalate of
methyl, and placed in contact with an excess of amalgamated and granu-
lated zinc in a flask, to which an inverted Liebig’s condenser, provided
with a mercurial safety tube, wasattached. The flask was immersed during
about twenty-four hours in water maintained at a temperature gradually
rising from 70° C. to 100° C. as the reaction progressed towards com-
pletion. At the end of that time the mixture had solidified to a yellowish
gummy mass, which, on distillation with water, yielded methylic alechol
possessing an etherial odour, but from which we could extract uo ether.
The residual magma in the flask, consisting of iodide of zinc, oxalate of
zine, and the zinc-salt of a new acid, was separated from the metallic zine
by washing with water. It was then treated with an excess of hydrate of
baryta and boiled for a considerable time; carbonic acid was afterwards
passed through the liquid until, on again boiling, the excess of baryta was
completely removed. To the filtered solution recently precipitated oxide
of silver was added until all iodine was removed. The solution separated
from the iodide of silver was again submitted to a current of carbonie acid,
boiled, and filtered. The resulting liquid, on being evaporated in the water-
bath, yielded a salt crystallizing in brilliant needles possessing the peculiar
odour of fresh butter. This salt is very soluble in water and in alcohol,
but nearly insoluble in ether, and perfectly neutral to test-papers. On
being submitted to analysis, it gave numbers closely corresponding with
the formula
3
CH,
Ce 4. @
|OH
| OBa
The acid of this salt, for which we provisionally propose the name di-
methoxalic acid, is obtained by adding dilute sulphuric acid to the concen-
trated solution of the baryta-salt and agitating with ether. On allowing
the ether to evaporate spontaneously, prismatic crystals of considerable size
make their appearance. These yielded, on combustion with oxide of copper,
results nearly identical with those required by the formula
142 The Rev. 8S. Haughton on the Joint Systems [Feb. 25,
Dimethoxalic acid is a white solid, readily crystallizing in beautiful prisms
resembling oxalic acid. It fuses at 75°°7 C., volatilizes slowly even at com-
mon temperatures, and readily sublimes at 50° C., being deposited upon a
cool surface in magnificent prisms. It boils at about 212° C., and distils
unchanged. Dimethoxalic acid reacts strongly acid, and unites with
bases, forming a numerous class of salts, several of which are crystalline.
In addition to the baryta-salt above mentioned, we have examined the silver-
salt, which is best formed by adding oxide of silver to the free acid, heating
to boiling, and filtering, when the salt is deposited in star-like masses of
nacreous scales as the solution cools. On analysis, this salt gave numbers
closely corresponding with those calculated from the formula
LO Ag
Attempts to produce an ether by digesting the free acid with absolute
alcohol at a temperature gradually raised to 160° C. proved abortive, traces
only of the ether being apparently formed.
Thus the final result of the action of zinc upon a mixture of iodide and
oxalate of methyl is perfectly homologous with that obtained by the action
of zincethyl upon oxalic ether. In the methylic reaction, however, no
compound corresponding to leucic ether was obtained. ‘This cannot create
surprise when it is remembered that dimethoxalic ether approaches closely
in composition to lactic ether, which is well known to be instantly decom-
posed by water. We have sought in vain to obviate this decomposition of
dimethoxalic ether by adding absolute alcohol in place of water to the pro-
duct of the reaction.
February 25, 1864.
Major-General SABINE, President, in the Chair.
I. “Qn the Joint Systems of Ireland and Cornwall, and their Me-
chanical Origin.” By the Rev.Samurt Haventon, M.D.,F.R.S.,
Fellow of Trinity College, Dublin. Received February 8, 1864.
(Abstract.)
This paper is a continuation of a former paper ‘On the Joints of the
Old Red Sandstone of the Co. Waterford,” published in the ‘ Philosophical
Transactions’ for 1858, and contains the results of the author’s observations
for some years, in Donegal, the Mourne and Newry Mountains, Cornwall,
and Fermanagh, with deductions from theory.
The author establishes the existence in Waterford of a Primary Conjugate
System of Joints, and of two Secondary Conjugate Systems, lying at each
side of the Primary at angles of 27°5' and 37°11’. -
1864. | of Ireland and Cornwall. 143
_ In Donegal there exists a Primary Conjugate System, and a Secondary
System, making with the Primary an angle of 32°24’. Inthe Moume and
Newry Mountains there is a Primary Conjugate System, and two Secondary
Systems at each side of the Primary, making angles of 31°46’ and 30°56’.
In Cornwall there is a Primary and also a Secondary Conjugate System,
making an angle of 27° 28’. And in Fermanagh there are Primary and
Secondary Systems, forming an angle of 31°1’.
Having given, in detail, the observations on which the preceding results
are founded, the author says :—“‘ Collecting together into one Table the
results of the preceding observations, we find the following Table of Primary
and Secondary Joints (True Bearings) :—
Name. Waterford.| Donegal. | Mourne. | Cornwall. | Fermanagh.
: N. of E. | N. of E. | N. of E. | N. of E. | N. of E.
Primary System (A) eeccessececaece 32° 26’ | 26° 16’ | 39° 40’ | 32° 34! 21° 30’
: : W. of N.| W. of N.| W. of N.| W. of N. Ww. PN.
Primary Conjugate (C) Caditameatels ta 31° 37’ | 29° 35/ een 32° 55! ate
: , N. of E.| N. of E. | N. of E. N. of E
First Secondary (A’) Puuveuseudtine oc { 58° 11’ | 58° 49’ Soe 40’ Aaa 54° Q!
ni A080) (alt beens boo le ee foe 2. EL eee
Conjugate to First Secondary (C’) | ee — bey pee os were :
Second Secondary (A”) ae | —« = ae rt —=—
Conjugate to Second Secondary E. of N. | W. of N.| W. of N.
Pe eettrcticececscdnccesassccccens 4° 30' 7° 38! 6° 30!
The only remarkable agreement as to direction of jomts disclosed by the
preceding Table is that between Waterford and Cornwall. If we compare
together the Primary and Secondary Joints in each locality, we find the
following Table of Angles between Primary and Secondary Joints :—
| Waterford. Donegal. Mourne. Cornwall. | Fermanagh.
Between Primary (A, C)
and First Secondary
GAN fal hits cannanicrendan +27° 5’ | +32° 24’ | +31° 46’ —— +31° 1'
Between Primary (A, C)
‘and Second Secon-
Gary CA)’ ©") .4,...0% —37° ll’ — —30° 56’ | —27° 28’ —-
ee es SS ee
This Table discloses a very interesting and unexpected result; viz. that
in Waterford, Donegal, Mourne, and Fermanagh, the angle between the
Primary and first Secondary Joint-Systems ranges between the narrow
limits of 27°5’ and 32° 24’, and that in Waterford, Mourne, and Cornwall,
the angle between the Primary and second Secondary Joint-Systems ranges
from 27° 28’ to 37° 11’.
144 Supposed Identity of Biliverdin with Chlorophyll, &c. [Feb. 25,
The paper concludes with a brief deduction of the observed laws of
Conjugate and Secondary Joints from known mechanical principles.
II. “On the supposed Identity of Biliverdin with Chlorophyll, with
remarks on the Constitution of Chlorophyll.” By G. G. Sroxzs,
M.A., Sec.R.S. Received February 25, 1864.
I have lately been enabled to examine a specimen, prepared by Professor
Harley, of the green substance obtained from the bile, which has been
named biliverdin, and which was supposed by Berzelius to be identical
with chlorophyll. The latter substance yields with alcohol, ether, chloro-
form, &c., solutions which are characterized by a peculiar and highly di-.
stinctive system of bands of absorption, and by a strong fluorescence of a
blood-red colour. In solutions of biliverdin these characters are wholly
wanting. 'There is, indeed, a vague minimum of transparency in the red ;
but it is totally unlike the intensely sharp absorption-band of chlorophyll,
nor are the other bands of chlorophyll seen in biliverdin. In fact, no one
who is in the habit of using a prism could suppose for a moment that the
two were identical ; for an observation which can be made in a few seconds,
which requires no apparatus beyond a small prism, to be used with the naked
eye, and which as a matter of course would be made by any chemist work-
ing at the subject, had the use of the prism made its way into the chemical
world, is sufficient to show that chlorophyll and biliverdin are quite distinct.
I may take this opportunity of mentioning that I have been for a good
while engaged at intervals with an optico-chemical examination of chloro-
phyll. I find the chlorophyll of land-plants to be a mixture of four sub-
stances, two green and two yellow, all possessing highly distinctive optical
properties. The green substances yield solutions exhibiting a strong red
fluorescence; the yellow substances donot. ‘The four substances are soluble
in the same solvents, and three of them are extremely easily decomposed by
acids or even acid salts, such as binoxalate of potash ; but by proper treat-
ment each may be obtained in a state of very approximate isolation, so far
at least as coloured substances are concerned. The phyllocyanine of Fremy*
is mainly the product of decomposition by acids of one of the green bodies,
and is naturally a substance of a nearly neutral tint, showing however ex-
tremely sharp bands of absorption in its neutral solutions, but dissolves in
certain acids and acid solutions with a green or blue colour. Fremy’s
phylloxanthine differs according to the mode of preparation. When pre-
pared by removing the green bodies by hydrate of alumina and a little
water, it is mainly one of the yellow bodies ; but when prepared by hydro-
chloric acid and ether, it is mainly a mixture of the same yellow body
(partly, it may be, decomposed) with the product of decomposition by acids
of the second green body. As the mode of preparation of phylloxantheine
* Comptes Rendus, tom. ]. p. 405.
1864. | Dr. Stenhouse on Rubia munjista. 145
is rather hinted at than described, I can only conjecture what the sub-
stance is; but I suppose it to be a mixture of the second yellow substance
with the products of decomposition of the other three bodies. Green sea-
weeds (Chlorospermee) agree with land-plants, except as to the relative
proportion of the substances present ; but in olive-coloured sea-weeds (Me-
lanospermee) the second green substance is replaced by a third green sub-
stance, and the first yellow substance by a third yellow substance, to the
presence of which the dull colour of those plants is due. The red colouring-
matter of the red sea-weeds (Rhodospermee), which the plants contain in
addition to chlorophyll, is altogether ‘different in its nature from chloro-
phyll, as is already known, and would appear to be an albuminous substance.
I hope, before long, to present to the Royal Society the details of these
researches.
“Continuation of an Examination of Rubia munjista, the East-
Indian Madder, or Munjeet of Commerce.” By Joun Sren-
House, LL.D., F.R.S. Received December 21, 1863 *.
In the former, preliminary notice of the examination of the Rudia mun-
jista t, the mode of extracting munjistine from munjeet, and a number of
its properties, have been already described. I now proceed to detail some
results which have been subsequently obtained.
When munjistine is extracted from munjeet by boiling solutions of sul-
phate of alumina, as the whole of the colouring matter is not extracted by
a single treatment with the sulphate of alumina, the operation must be
repeated five or six times instead of two or three as was formerly stated.
During the boiling of the munjeet with sulphate of alumina, a large quantity
of furfurol is given off. I may mention, in passing, that the most abundant
and economical source of furfurol is found in the preparation of garancine
by boiling madder with sulphuric acid. If the wooden boilers in which
garancine is usually manufactured were fitted with condensers, furfurol
might be obtained in any quantity without expense.
In addition to the properties of munjistine already described, I may
mention that acetate of copper produces in solutions of munjistine a brown
precipitate but very slightly soluble in acetic acid.
When bromine-water is added to a strong aqueous solution of munjistine,
a pale-coloured flocculent precipitate is immediately produced ; this when
collected on a filter, washed and dissolved in hot alcohol, furnishes minute
tufts of crystals, evidently a substitution-product.. Unfortunately these
crystals are contaminated by a resinous matter, from which I have been
unable to free them, and therefore to determine their composition.
When munjistine is strongly heated on platinum-foil, it readily inflames
and leaves no residue; when it is carefully heated in a tube, it fuses, and
crystallizes again on cooling. If heated very slowly in a Mohr’s apparatus,
* Read January 14. See Abstract, page 86. tT Proceedings, vol. xii. p. 633.
146 Dr. Stenhouse on Rubia munjista. [1864
munjistine sublimes in golden scales and broad flat needles of great beauty ;
these have all the physical characters and the same composition as the
original substance. If the sublimation be continued for a long time at the
lowest possible temperature consistent with its volatilization, the wees of
it is obtained with scarcely any loss.
The following are the results of the ultimate analysis of different samples
of munjistine :—
I. -314 grm. of munjistine yielded *732 grm. carbonic acid and +106 grm.
of water.
II. :228 grm. of munjistine yielded ‘535 grm. carbonic acid and -0765
grm. water.
. III. +332 grm. of munjistine yielded +7795 grm. of carbonic acid and
"1125 grm. of water.
IV. -313 grm. of munjistine yielded °734 grm. of carbonic acid and
"1095 grm. of water.
Theory. f. II. III. TY.
C,,—96 64: 00 63°60 64:00 64°04 63°97
H,= 6 4-00 3°77 375 3°76 3°89
O, =48 32°00 32°63 32°27 32°20 32°14
The carbon in No. I. is rather lower than that of the other three; this is
owing to the specimen not being quite free from alumina; moreover it was
burnt with oxide of copper, the others with chromate of lead. No. III. is
the sublimed munjistine. All the analyses were made on specimens pre-
pared at different times.
; Lead Compound.
When aqueous or alcoholic solutions of munjistine and acetate of lead
are mixed, a flocculent precipitate of a deep orange-colour falls, which
changes to scarlet on the addition of a slight excess on acetate. The best
method of preparing it is to dissolve munjistine in hot spirit and add to
the filtered solution a quantity of acetate of lead insufficient to precipitate
the whole of the munjistine, then to wash thoroughly with spirit, in which
the lead compound is but slightly soluble, and dry first in vacuo, and then
in the water-bath.
I. *836 grm. lead compound gave 407 grm. oxide of lead.
II. -625 grm. lead compound gave ‘302 grm. oxide of lead.
III. -428 grm. lead compound gave *2075 grm. oxide of lead.
IV. -523 grm. lead compound gave *253 grm. oxide of lead.
V. °2705 grm. lead compound gave °3445 grm. of carbonic acid and
‘0445 grm. water.
VI. °5350 grm. lead compound gave 6830 grm. carbonic acid and -0920
grm. water.
Theory. 1 Il. Ill. Iv. V. VI.
C,, =486 Sa De Sark eta. «(0 vee. Bete ey 4 OG fee eee
Hy = 25 T° O20 eae Sees ai EWE 3H 1°83" tase
O,, =200 14°55 6. a) ae
.6PbO 669°6 48°70 48: 70 48°32. 48: 50 48° 38
1864.) Dr. Stenhouse on Rubia munjista. 147
_ All the specimens were prepared at different times, except IV. and V.,
which are analyses of the same specimen. The lead compound therefore
seems to approach nearly to the somewhat anomalous formula 5(C,, H, O,)
+6PbO, being a basic lead-salt ; it is, however, perfectly analogous to the
lead compound of purpurine, 5(C,, H,;O;) +6PbO, described by Wolff
and Strecker*.
_ From these analyses of the lead compound and also from the ultimate
analyses of munjistine itself, it is pretty evident that its true formula is
C,, H, O,:
Neither sublimed munjistine nor that obtained by crystallization from
aleohol, when dried at the ordinary temperature in vacuo, loses weight at
110°C. It is not improbable, however, that the gelatinous uncrystallizable
precipitate, which separates on the cooling of boiling saturated aqueous
solutions of munjistine, is a hydrate.
From some experiments made on a considerable scale, I find that ordinary
madder does not contain any munjistine. In order to ascertain this fact, a
considerable quantity of garancine from Naples Roots, and likewise some
which had been subjected to the action of high-pressure steam according to
Pincoff and Schunck’s process, were treated with boiling bisulphide of car-
bon, and the product obtained on evaporating the bisulphide repeatedly
extracted with large quantities of boiling water ; the solution, when acidu-
lated with sulphuric acid, gave an orange-red precipitate from which I was
unable to obtain any munjistine. Professor Stokes succeeded, however, in
detecting the presence of alizarine, purpurine, and rubiacine in it f.
The production of phthalic acid from alizarine, purpurine, and munjistine,
together with a comparison of their subjoined formule, indicates the very
close relationship between these three substances, the only true colouring
principles of the different species of madder with which we are acquainted.
Mligarine ol Ble eet C,, H, O,,
Purpurme 2 avs Shee ee. C,, H, O,,
Munjistineé ......:..... C,,H;O,.
Two other very convenient sources of phthalic acid are—first, the dark
red resinous matter, combined with alumina, which is left undissolved by
the bisulphide of carbon in the preparation of munjistine; secondly, the
large quantity of green-coloured resinous matter which remains behind
after extracting the alizarine from Professor Kopp’s so-called ‘‘ green aliza-
rine” by means of bisulphide of carbon. I have repeated Marignac’s and
Schunck’s experiments of distilling a mixture of phthalic acid and lime;
and, like both of these chemists, I observed a quantity of very aromatic
benzol to be produced, which, by the action of strong nitric acid, readily
yielded nitrobenzol, and from this, by the action of reducing agents, aniline.
The only impurity in the benzol from phthalic acid appears to be a minute
* Annalen der Chemie, Ixxv. p. 24.
+ He has since informed me that he has succeeded in demonstrating the absence of
munjistine.
148 Dr. Stenhouse on Rubia munjista. [1864.
quantity of an oil, having an aromatic odour, resembling that produced from
cinnamic acid by the action of hypochlorite of lime.
Tinctorial power of Munjistine and Munjeet.
Prof. Runge stated, in 1835, that munjeet contains twice as much avail-
able colouring matter as the best Avignon madder. This result was so unex-
pected, that the Prussian Society for the Encouragement of Manufactures,
to whom Professor Runge’s memoir was originally addressed, referred the
matter to three eminent German dyers, Messrs. Dannenberger, Bohm, and
Nobiling. These gentlemen reported, as the result of numerous and carefully
conducted experiments, that so far from munjeet being richer in colouring-
matter than ordinary madder, it contained considerably less. This conclu-
sion has been confirmed by the experience of my friend Mr. John Thom,
of Birkacre, near Chorley, one of the most skilful of the Lancashire printers.
From a numerous series of experiments I have just completed, I find
that the garancine from munject has about half the tinctorial power of the
garancine made from the best madder, viz. Naples Roots. These, however,
yield only about 30 to 33 per cent. of garancine, while munjeet, according
to my friend Mr. Higgin, of Manchester, yields from 52 to 55 per cent.
Taking the present prices therefore of madder at 36 shillings per ewt., and
munjeet at 30 shillings, it will be found that there will be scarcely any
pecuniary advantage in using munjeet for ordmary madder-dyeing. The
colours from munjeet are certainly brighter, but not so durable as those
from madder, owing to the substitution of purpurine for alizarine. There
is, however, great reason to believe that some of the Turkey-red dyers are
employing garancine from munjeet to a considerable extent. When this is
the case they evidently sacrifice fastness to brilliancy of colour. By treating
such a garancine with boiling water, and precipitating by an acid in the
way already described, its sophistication with munjeet may very readily be
detected. The actual amount of colouring matter in munjeet and the best
madder is very nearly the same; but the inferiority of munjeet as a dye-
stuff results from its containing only the comparatively feeble colouring
matters, purpurine and munjistine, only a small portion of the latter being
useful, whilst the presence of munjistine in large quantity appears to be
positively injurious. So much is this the case, that when the greater part
of the munjistine is removed from munjeet-garancine by boiling water, it
yields much richer shades with alumina mordants than before.
PURPUREINE.
Action of Ammonia on Purpurine.
When purpurine is dissolved in dilute ammonia and exposed to the air in
a vessel with a wide mouth in a warm place for about a month, ammonia
and water being added from time to time as they evaporate, the purpurine
almost entirely disappears, whilst a new colouring-matter is formed which
dyes unmordanted silk and wool of a fine rose-colour, but is incapable of
1864. ] Dr. Stenhouse on Rubia munjista. 149
dyeing vegetable fabrics mordanted with alumina. If, however, strong
ammonia be employed to dissolve the purpurine, considerable heat is pro-
duced—a rise of temperature of as much as 20°C. taking place if the
bulb of a thermometer be immersed in finely divided purpurine and strong
ammonia poured on it.
The purpurine employed in these experiments was prepared by Kopp’s
process, and I am indebted for it to my friend Professor Crace Calvert.
The solution of the new substance, purpureine, is filtered to separate dust,
&e., as well as a black substance insoluble in dilute ammonia; it is then
added to a considerable quantity of dilute sulphuric acid, boiled fora short
time, and allowed to cool. When cold, the impure purpureine is collected
on a filter, well washed, and dissolved in a small quantity of hot alcohol.
The spirituous solution is again filtered into a quantity of very dilute boil-
ing sulphuric acid, about 1 part acid to from 50 to 100 of water; when cold,
the precipitate is collected and again well washed.: A crystallization out of
boiling very dilute acid now renders it quite pure. This somewhat long
and tedious process is necessary to free it from an uncrystallizable black
substance, a part of which is separated when the crude purpureine is dis-
solved in alcohol, and a part is left behind at the last crystallization.
This compound being in its mode of formation and physical properties
very analogous to orceine, I have called it purpureine. When crystallized
by the spontaneous evaporation of its alcoholic solution, or from boiling
dilute sulphuric acid under peculiar conditions of aggregation, it presents a
fine iridescent green colour by reflected light ; whilst under the microscope
it appears as fine long needles of a very deep crimson colour. As obtained
by the process above described, it has, however, but little of the iridescent
appearance, being of a brownish-red colour with a faint tinge of green, It
is almost insoluble in cold dilute acids, and is in great part precipitated from
its aqueous solution by common salt, thus greatly resembling orceine. It
is almost insoluble in bisulphide of carbon, very slightly so both in ether and
in cold water, much more so in hot, and very soluble in spirit both hot and
cold and in water rendered slightly alkaline. Itis'readily soluble in cold con-
centrated sulphuric acid, and is precipitated unaltered by water; on heat-
ing, however, it is destroyed.
Its aqueous solution gives a deep-red precipitate with chloride of zinc;
with chloride of mercury a purple gelatinous precipitate ; and with nitrate
of silver a precipitate of a very dark brown colour slightly soluble in am-
monia, I have been favoured with the following optical examination by
Professor Stokes :—
* Its solutions show bands of absorption just like purpurine in character,
but in some cases considerably different in position. The etherial and
acidulated (acetic acid) alcoholic solutions show this strongly. The tint is so
different in purpurine and its derivative, that the intimate connexion revealed
by the prism would be lost by the eye. A drawing of the spectrum for pur-
purine would serve for its derivative (purpureine), if the bands were simply
pushed a good deal nearer the red end.”
150 Dr. Stenhouse on Rubia munjista. [1864.
I. -3435 grm. pupureine gave ‘8230 grm. carbonic acid and +1240 erm.
of water.
II. -340 grm. purpureine gave 813 grm. carbonic acid and *123 erm. of
water.
III. +336 grm. purpureine gave ‘01552 grm. nitrogen.
IV. ‘535 grm. purpureine gave ‘02453 grm. nitrogen.
Theory. I, If. Ill. IV.
Cy, = 396 65°13 65°36 64422 ,
H,, = 24 3°95 4:01 4:02 ohne
Nour 28 4:60 pia tex 4°62 4°58
O,, = 160 26°32
608 100-00
The formula therefore appears to be C,, H,, N, O,,?
Nitropurpureine.
When purpureine is dissolved in a small quantity of moderately strong
nitric acid, spec, grav. about 1°35, and heated to 100° C., it gives off red
fumes, and on being allowed to cool, a substance sevarates in magnificent
scarlet prisms somewhat like chromate of silver, only of a brighter colour ;
it is quite insoluble in water, ether, and bisulphide of carbon, and very
slightly soluble in spirit, but soluble in hot moderately strong nitric acid,
from which it separates on standing fora considerable time. If boiled with
strong nitric acid, it is slowly decomposed. When heated, it deflagrates :
from this circumstance, and considering its mode of formation, it is evidently
a nitro-substitution compound ; I have therefore called it nitropurpureine.
Owing to the small quantity which I have hitherto been able to procure,
I have not yet determined the composition of this beautiful body, which is
finer in appearance than any of the derivatives from madder I have as yet
met with.
Action of Ammonia on Alizarine.
The alizarine which was employed for the subjoined experiments was
obtained by extracting Professor KE. Kopp’s so-called green alizarine* with
bisulphide of carbon. It yields only about 15 per cent. of orange-red ali-
zarine. This was crystallized three times out of spirit, from which it usually
separates as a deep-orange-coloured crystalline powder. Unfortunately this
alizarine still contains a quantity of purpurine, from which it is impossible
to purify it either by crystallization or sublimation. Accordingly, when
treated with ammonia by the method already described for purpurine,
while it yields a substance analogous to purpureine, the product is impure,
being contaminated with purpureine, This mixture has been examined by |
my friend Professor Stokes, who finds that it contains purpureine, derived
from the purpurine present as an impurity in the alizarine employed, and
another substance very like alizarine.in its optical properties, probably
a new substance (alieareine), bearing the same relation to alizarine that
* I amalso indebted to Professor Calvert for the “ green alizarine.”
hain cae
1864.) Dr. Stenhouse on Rubia munjista. 151
purpureine does to purpurine*. The following is an extract from a letter
I received from Professor Stokes :—
‘It would be very unlikely @ priorz that such a simple process as that
of Kopp should effect a perfect separation of two such similar bodies as
alizarine and purpurine ; and as I find his purpurine is free from alizarine,
it would be almost certain @ priori that his ‘ green alizarine’ would contain
purpurine, and the two would be dissolved by bisulphide of carbon, and
might very well afterwards be associated by being deposited in intermingled
crystals, if not actually crystallizing together.” :
Action of Ammonia on Munjistine.
This reaction with munjistine was only tried on a very small scale, but
the results were by no means satisfactory. The munjistine was completely
destroyed, the greater part being changed into a brown’ humus-like sub-
stance, insoluble in ammonia,—the remainder forming a colouring-sub-
stance, analogous to purpureine, but not crystalline. It dyed unmordanted
silk a brownish-orange colour. :
The combined action of ammonia and oxygen, therefore, on the three
colouring-substances alizarine, purpurine, and munjistine, is to change
them from adjective to substantive dye-stuffs. I think it not improbable
that if this archilizing process were applied to various other colouring mat-
ters, they would be found capable of undergoing similar transformations.
Action of Bromine on Alizarine.
A boiling saturated solution of alizarine in alcohol is mixed with about
six or eight parts of distilled water, and to this when cold about one or one
and a half parts of bromine water are added, when a bright yellow amor-
phous precipitate is produced. After standing twelve or sixteen hours, the
solution is filtered ; and if the clear filtrate be now carefully heated so as to
expel the spirit, a substance of a deep orange-colour is deposited, consisting
of very fine needles, which are contaminated with a small quantity of resin
ifa great excess of bromine has been employed. These needles are soluble
in spirit and ether, insoluble in water, and soluble in bisulphide of carbon,
from which they crystallize by spontaneous evaporation, in dark-brown
nodules. With soda they give the same purple colour as alizarine. They ;
dye cloth mordanted with alumina a dmgy brownish red, very different
from the colour produced by ordinary crystallized alizarme. The follow-
ing optical examination is from a letter of Professor Stokes :—
“* Bromine Derivative of Alizarine.”
**T can hardly distinguish this substance from alizarine. The solutions
* Since this paper was communicated to the Royal Society, I find by a notice in Kopp
and Wills’s ‘ Jahresbericht’ for 1862, p. 496, that a similar experiment upon alizarine
had been made by Schiitzenberger and A. Paraf. The vroduct of one preparation which
they obtained, and to which they have given the name of alizarinamid, yielded a formula
C4) Hy; NOj., and another preparation gave the formula Cg) H33 Nz O.4, both being, when
dry, nearly black amorphous substances. It appears, therefore, from the results of MM.
Schiitzenberger and Paraf’s experiments, that these gentlemen were not more successful
in obtaining a pure product from the action of ammonia on alizarine than I have been.
152 Dr. Stenhouse on Rubia munjista. [1864,
in alcohol containing potassa show three bands of absorption just alike in
appearance. By measurement it seemed probable that the bromine sub-
stance gave the bands a d¢t/e nearer to the red end; but the difference, if
real, was very minute. The fluorescent light of the ethereal solution was,
I think, a trifle yellower in the bromine substance, that of alizarine being
more orange.”
The following are the results of the ultimate analysis of the brominated
alzarine dried at 100° C.:—
I, +375 grm. of substance gave ‘207 grm. bromide of silver.
II. -703 grm. of substance gave *389 grm. bromide of silver.
III. -401 grm. of substance gave *221 grm. bromide of silver.
IV. *543 grm. of substance gave *300 grm. bromide of silver.
V. *3575 grm. of substance gave ‘695 grm. of carbonic acid and ‘0760
grm. of water.
VI. 454 grm. of substance gave ‘8790 grm. of carbonic acid and *0965
grm. of water.
Theory. I. at. III. IV. V. VI.
©, 860° 5294-00000, 20 oe eee
H,= 16 2°35 .... oh eee
Br, = 160° 23°53. 23°49 23°54 23°45 23°51 eee
OPE Ae WES ee ee.) Rae see
680 100-00
From this somewhat anomalous formula,
C,, Hy, Br, 0,,=C,, H, O,, 2(C,, H, BrO,),
I was for some time inclined to think that it might be a mixture of bromi-
nated. alizarine with free alizarine ; but as all the six samples analyzed were
prepared at different times, itis highly improbable that such uniform analy-
tical results could be obtained if they were from a mere admixture of sub-
stances. The existence of a brominated compound is also confirmed
by its dyeing properties, which differ so remarkably from those of
alizarine.
Action of Bromine on Purpurine.
When pure purpurine is dissolved in spirit mixed with a considerable
quantity of water, and an aqueous solution of bromine added, as in the
case of alizarine, a yellow amorphous precipitate is produced. The solution
separated from this by filtration, when heated to expel the spirit, gives no
precipitate whilst hot; but on cooling, a very small quantity of a brown
resinous powder is deposited. From this it is evident that the presence of
a small quantity of purpurine in alizarine will not interfere with the pro-
duction of pure brominated alizarine, if the precaution be taken to collect it
from the solution whilst it is still hot.
I think it right to state that the experiments and analyses detailed in the
preceding paper have been performed by my assistant, Mr. Charles
Edward Groves. I cannot conclude this paper without again acknowledg-
ing the essential services I have received from Professor Stokes, who kindly
submitted the different products obtained by me to optical examination.
1864.) 153
March 3, 1864.
Major-General SABINE, President, in the Chair.
In accordance with the Statutes, the names of the Candidates for election
into the Society were read, as follows :—
Alexander Armstrong, M.D. leeming Jenkin, Esq.
William Baird, M.D. William Jenner, M.D.
Sir Henry Barkly, K.C.B. Kdmund C. Johnson, M.D.
Henry Foster Baxter, Esq. Prof. Leone Levi.
Sir Charles Tilston Bright. Waller Augustus Lewis, M.B.
William Brinton, M.D. Sir Charles Locock, Bart., M.D.
John Charles Bucknill, M.D. Kdward Joseph Lowe, Esq.
Lieut.-Col. John Cameron, R.E. The Hon. Thomas M‘Combie.
T. Spencer Cobbold, M.D. Sir Joseph F. Olliffe, M.D.
The Hon. James Cockle, M.A. — George Wareing Ormerod, M.A.
Henry Dircks, Esq. Thomas Lambe Phipson, Esq.
Alexander John Ellis, B.A. John Russell Reynolds, M.D.
John Evans, Esq. William Henry Leighton Russell,
William Henry Flower, Esq. B.A. |
Sir Charles Fox. William Sanders, Esq. |
George Gore, Esq. Col. William James Smythe, R.A.
George Robert Gray, Esq. Lieut.-Col. Alexander Strange.
Thomas Grubb, Esq. Thomas Tate, Esq.
Henri Gueneau de Mussy, M.D. Charles Tomlinson, Esq.
Wilham Augustus Guy, M.B. George Charles Wallich, M.D.
George Harley, M.D. Robert Warington, Esq.
Sir John Charles Dalrymple Hay, | Charles Wye Williams, Esq.
Bart. Nicholas Wood, Esq.
Benjamin Hobson, M.B. Henry Worms, Esq.
William Charles Hood, M.D.
The following communication was read :—
“On the Spectra of Ignited Gases and Vapours, with especial regard
to the different Spectra of the same elementary gaseous sub-
stance.” By Dr. Junius Pricxer, of Bonn, For. Memb. RB.8.,
and Dr. S. W. Hirrorr, of Munster. Received February 23,
1864.
(Abstract.)
In order to obtain the spectra of the elementary bodies, we may employ
either flame or the electric current. The former is the more easily managed,
but its temperature is for the most part too low to volatilize the body to be
VOL. XIII. N
154 Drs. Pliicker and Hittorf on the Spectra of _[Mar. 3,
examined, or, if it be volatilized or already in the state of gas, to exhibit its
characteristic lines. In most cases it is only the electric current that is
fitted to produce these limes ; and the current furnished by a powerful in-
duction coil was what the authors generally employed.
In the application of the current, different cases may arise. The body to
be examined may be either in the state of gas, or capable of being vola-
tilized at a moderate temperature, such as glass will bear without softening,
or its volatilization may require a temperature still higher.
In the first two cases the body is enclosed in a blown-glass vessel con-
sisting of two bulbs, with platinum wires for electrodes, connected by a
capillary tube. In the case of a gas, the vessel is exhausted by means of
Geissler’s exhauster, and filled with the gas at a suitable tension. In the
case of a solid easily volatilized, a portion is introduced into the vessel,
which is then exhausted as highly as possible, and the substance is heated
by a lamp at the time of the observation. In the third case the electric
current is employed at the same time for volatilizing the body and render-
ing its vapour luminous. If the body be a conductor, the electrodes are
formed of it ; but the spectrum observed exhibits not only the lines due to
the body to be examined, but also those which depend on the interposed gas.
This inconvenience is partly remedied by using hydrogen for the interposed
gas, as its spectrum under these circumstances approaches to a continuous
one. If the body to be examined be a non-conductor, the metallic elec-
trodes are covered with it. In this case the spectrum observed contains the
lines due to the metal of which the electrodes are formed, and to the inter-
posed gas, as well as those due to the substance to be examined.
Among the substances examined, the authors commence with nitrogen,
which first revealed to them the existence of two spectra belonging to the
same substance. The phenomena presented by nitrogen are described in
detail, which permits a shorter description to suffice for the other bodies
examined,
On sending through a capillary tube containing nitrogen, at a pressure of
from 40 to 80 millimetres, the direct discharge of a powerful Ruhmkorff’s
coil, a spectrum is obtained consisting, both in its more and in its less re-
frangible part, of a series of bright shaded bands: the middle part of the
spectrum is usually less marked. In each of the two parts referred to, the
bands are formed on the same type; but the type in the less refrangible
part of the spectrum is quite different from that in the more refrangible. In
the latter case the bands have a channeled appearance, an effect which is
produced by a shading, the intensity of which decreases from the more to
the less refracted part of each band. In a sufficiently pure and magnified
spectrum, a small bright line is observed between the neighbouring channels,
and the shading is resolved into dark lines, which are nearly equidistant,
while their darkness decreases towards the least refracted limit of each
band. With a similar power the bands in the less refrangible part of
the spectrum are also seen to be traversed by fine dark lines, the arrange-
1864.] Ignited Gases and Vapours. 155
ment of which, however, while similar for the different bands, is quite
different from that observed in the channeled spaces belonging to the more
refrangible region.
If, instead of sending the direcé discharge of the induction coil through
the capillary tube containing nitrogen, a Leyden jar be interposed in the
secondary circuit in the usual way, the spectrum obtained is totally differ-
ent. Instead of shaded bands, we have now a spectrum consisting of bril-
hant lines having no apparent relation whatsoever to the bands before
observed. If the nitrogen employed contains a slight admixture of oxygen,
the bright lines due to oxygen are seen as well as those due to nitrogen,
whereas in the former spectrum a slight admixture of oxygen produced no
apparent effect.
The different appearance of the bands in the more and in the less refracted
portion of the spectrum first mentioned suggested to the authors that it
was really composed of twospectra, which possibly might admit of being sepa-
rated. This the authors succeeded in effecting by using a somewhat wider
tube. Sent through this tube, the direct discharge gave a golden-coloured
light, which was resolved by the prism into the shaded bands belonging to
the less refrangible part of the spectrum, whereas with a small jar inter-
posed the light was blue, and was resolved by the prism into the channeled
spaces belonging to the more refrangible part.
By increasing the density of the gas and at the same time the power of
the current, or else, in case the gas be less dense, by interposing in the
secondary circuit at the same time a Leyden jar and a stratum of air, the
authors obtained lines of dazzling brilliancy which were no longer well
defined, but had become of appreciable breadth, while at the same time
other lines, previously too faint to be seen, made their appearance. The
number of these lines, however, is not unlimited. By the expansion of
some of the lines, especially the brighter ones, the spectrum tended to
become continuous.
Those spectra which are composed of rather broad bands, which show
different appearances according as they are differently shaded by fine dark
lines, the authors generally call spectra of the first order, while those
spectra which show brilliant coloured lines on a more or less dark ground
they call spectra of the second order.
Incandescent nitrogen accordingly exhibits two spectra of the first, and
one of the second order. 'The temperature produced by the passage of an
electric current increases with the quantity of electricity which passes, and
for a given quantity with the suddenness of the passage. When the tem-
perature produced by the discharge is comparatively low, incandescent
nitrogen emits a golden-coloured light, which is resolved by the prism into
shaded bands occupying chiefly the less refrangible part of the spectrum.
At a higher temperature the light is blue, and is resolved by the prism into
channeled bands filling the more refrangible part of the spectrum. Ata
still higher temperature the spectrum consists mainly of bright lines,
N 2
156 On the Spectra of Ignited Gases and Vapours. [Mar. 8,
which at the highest attainable temperature begin to expand, so that the
spectrum tends to become continuous.
The authors think it probable that the three different spectra of the
emitted light depend upon three allotropic states which nitrogen assumes
at different temperatures.
By similar methods the authors obtained two different spectra of sul-
phur, one of the first and one of the second order. The spectrum of the
first order exhibited channeled spaces, like one of the two spectra of that
order of nitrogen; but the direction in which the depth of shading in-
creased was the reverse of what was observed with nitrogen, the darker
side of each channeled space being in the case of sulphur directed towards
the red end of the spectrum.
Selenium, like sulphur, shows two spectra, one of the first and one of the
second order.
Incandescent carbon, even in a state of the finest division, gives a
continuous spectrum. Among the gases which by their decomposition,
whether in flame or in the electric current, give the spectrum of carbon,
the authors describe particularly the spectra of cyanogen and olefiant gas
when burnt with oxygen or with air, and of carbonic oxide, carbonic acid,
marsh-gas, olefiant gas, and methyl rendered incandescent by the electric
discharge; they likewise describe the spectrum of the electric discharge
between electrodes of carbon in an atmosphere of hydrogen. The spectrum
of carbon examined under these various conditions showed great varieties,
but all the different types observed were represented, more or less com-
pletely, in the spectrum of cyanogen fed with oxygen. The authors think
it possible that certain bands, not due to nitrogen, seen in the flame of
cyanogen, and not in any other compound of carbon, may have been due
to the undecomposed gas.
The spectrum of hydrogen, as obtained by a small Ruhmkorff’s coil,
exhibited chiefly three bright lines. With the large coil employed by the
authors, the lines slightly and unequally expanded. On interposing the
Leyden jar, and using gas of a somewhat higher pressure, the spectrum
was transformed into a continuous one, with a red line at one extremity,
while at a still higher pressure this red line expanded into a band.
The authors also observed a new hydrogen spectrum, corresponding to
a lower temperature, but having no resemblance at all to the spectra of the
first order of nitrogen, sulphur, &c.
Oxygen gave only a spectrum of the second ointer: the different lines of
which, however, expanded under certain circumstances into narrow bands,
but very differently in different parts of the spectrum.
Phosphorus, when treated like sulphur, gave only a spectrum of the
second order.
Chlorine, bromine, and iodine, when examined by the electric discharge,
gave only spectra of the second order, in which no two of the numerous
spectral lines belonging to the three substances were coincident. The
1864.] Influence of Physical and Chemical Agents upon Blood. 157
authors were desirous of examining whether iodine would give a spectrum
of the first order the reverse of the absorption-spectrum at ordinary tem-
peratures. The vapour of iodine in an oxyhydrogen jet gave, indeed, a
spectrum of the first order, but it did not agree with what theory might
have led us to expect.
In the electric discharge, arsenic and mercury gave only spectra of the
second order. The metals of the alkalies sodium, potassium, lithium,
thallium show, even at the lower temperature of Bunsen’s lamp, spectra of
the second order.
Barium, strontium, calcium in the flame of Bunsen’s lamp show bands
like spectra of the first order, and in each case a well-defined line-like
spectra of the second order. On introducing chloride of barium into an
oxyhydrogen jet, the shading of the bands was resolved into fine dark
lines, proving that the band-spectrum of barium is in every respect a
spectrum of the first order.
Spectra of the first order were observed in the case of only a few of the
heavy metals, among which may be particularly mentioned lead, which,
when its chloride, bromide, iodide, or oxide was introduced into an oxy-
hydrogen jet, gave a spectrum with bands which had a channeled appear-
ance in consequence of a shading by fine dark lines.
Chloride, bromide, and iodide of copper gave in a Bunsen’s Jamp, or the
oxyhydrogen jet, spectra with bands, and besides a few bright lines. The
bands in the three cases were not quite the same, but differed from one
another by additional bands. Manganese showed a curious spectrum of
the first order. When an induction discharge passed between electrodes
of copper or of manganese, pure spectra of these metals, of the second
order, were obtained.
March 10, 1864.
Major-General SABINE, President, in the Chair.
The following communication was read :—
“On the Influence of Physical and Chemical Agents upon Blood ;
with special reference to the mutual action of the Blood and the
Respiratory Gases.’ By Grorcr Hartzy, M.D., Professor of
Medical Jurisprudence in University College, London. Com-
municated by Dr. SHarpey, Sec. R.S. Received March 8,
1864.
(Abstract.)
This communication is divided into two parts. The first is devoted to
the investigation of the influence of certain physical agencies, viz. simple
diffusion, motion, and temperature, and of the conditions of time and the
age of the blood itself. The second part includes the consideration of
158 Dr. Harley on the Influence of Physical and [Mar. 10,
the influence of chemical agents, especially such as are usually regarded as
powerful poisons.
The paper commences with a description of the apparatus employed,
and the method followed in conducting the inquiry; and the details of the
several experiments are then given. The following is a brief statement of
the results.
Part I,
1. The experiments on diffusion showed that venous blood not only
yields a much greater amount of carbonic acid than arterial blood, but
also absorbs and combines with a larger proportion of oxygen.
2. Motion of the blood was found to increase the chemical changes
arising from the mutual action of the blood and the respiratory gases.
3. The results of the experiment on the influence of time led to the con-
clusion that the blood and air reciprocally act on each other in the same
way out of the body as they do within it, and that their action is not in-
stantaneous, but gradual.
4. It was ascertained that a certain degree of heat was absolutely essential
to the chemical transformations and decompositions upon which the inter-
change of the respiratory gases depends. The higher the temperature up
to that of 38° C. (the animal heat), the more rapid and more effectual were
the respiratory changes; whereas a temperature of 0° C. was found totally
to arrest them.
5. The influence of age on the blood was found to be very marked, espe-
cially on its relation to oxygen. The older and the more putrid the blood
becomes, the greater is the amount of oxygen that disappears from the air ;
and although at the same time the exhalation of carbonic acid progressively
increases with the age of the blood, yet its proportion is exceedingly small
when compared with the large amount of oxygen absorbed.
6. The average amount of urea in fresh sheep’s blood was ascertained to
be 0°559 per cent., and its disappearance from the blood during the putre-
factive process was very gradual, there being as much as 0°387 per cent. in
blood after it was 304 hours old.
Part II.
The chemical agents employed were animal and vegetable products and
mineral substances.
1. The effect of snake-poison was found to be an acceleration of the
transformations and decompositions occurring in blood, upon which the
absorption of oxygen and the exhalation of carbonic acid depend.
2. The presence of an abnormal amount of uric acid in blood was also
found to hasten the chemical changes upon which the absorption of oxygen
and exhalation of carbonic acid depend.
3. Animal sugar, contrary to what had been anticipated, retarded the
respiratory changes produced in atmospheric air by blood.
1864. ] Chemical Agents upon Blood. } 159
4, The influence of hydrocyanic acid was studied both upon ox-blood
and human blood, and found to be the same in each case, namely, to
arrest respiratory changes.
5. Nicotine was also found to diminish the power of the blood either to
take up oxygen or give off carbonic acid gas and thereby become fitted for
the purposes of nutrition.
6. The effect of woorara poison, both on the blood in the body and out
of it, was ascertained to be in some respects similar to that of snake-poison,
namely, to increase the chemical decompositions and transformations upon
which the exhalation of carbonic acid depends; but differed in retarding,
instead of hastening, the oxidation of the constituents of the blood.
7. Antiar poison and aconite were found to act alike, inasmuch as both
of them hastened oxidation and retarded the changes upon which the
exhalation of carbonic acid depends ; in both respects offering a striking
contrast to woorara poison, which, as has just been said, diminishes oxida-
tion and increases the exhalation of carbonic acid.
8. The effect of strychnine on the blood, both in and out of the body,
was studied, and found to be in both cases identical, namely, like some of
the other substances previously mentioned, to arrest respiratory changes.
Moreover, in one experiment in which the air expired from the lungs of an
animal dying from the effects of the poison was examined, it was ascer-
tained that the arrest in the interchange of the gases took place before the
animal was dead.
9. Brucine acts in a similar manner as strychnine, but in a much less
marked degree.
10. Quinine also possesses the power of retarding oxidation of the blood,
as well as the elimination of carbonic acid gas.
11. Morphine has a more powerful effect in diminishing the exhalation
of carbonic acid gas, as well as the chemical changes upon which the
absorption of oxygen by blood depends.
Under this head the effects of aneesthetics upon blood are next detailed ;
and in the first place, the visible effects of chloroform upon blood are thus
described :—If 5 or more ‘per cent. of chloroform be added to blood, and
the mixture be agitated with air, it rapidly assumes a brilliant scarlet hue,
which is much brighter than the normal arterial tint, and is, besides, much
more permanent. When the mixture is left in repose, it gradually solidi-
fies into a red-paint-like mass, which when examined under the micro-
scope is frequently found to contain numerous prismatic crystals of an
organic nature. If the blood of an animal poisoned from the inhalation of
chloroform be employed in this experiment, the paint-like mass will be
found to be composed in greater part of the crystals just spoken of; the
crystals in this case being both larger and finer than when healthy blood is
employed. Chloroform only partially destroys the blood-corpuscles. Its
chemical action is to diminish the power of the constituents of the blood to
unite with oxygen and give off carbonic acid.
160 ‘Prof. Tyndall—Contributions to Molecular Physics. [Mar.17,
The action of sulphuric ether upon blood differs in many respects from
that of chloroform. In the first place, ether has a powerful effect in de-
stroying the blood-corpuscles, dissolving the cell-walls’ and setting the
contents free. In the second place, ether prevents the blood from assum-
ing an arterial tint when agitated with air. The higher the percentage of
the agent, the more marked the effect. In the third place, ether neither
diminishes the absorption of oxygen nor the exhalation of carbonic acid by
blood; and lastly, it has a much more powerful effect in causing the con-
stituents of the blood to crystallize. For example, if an equal part of ether
be added to the blood of a dog poisoned by the inhalation of chloroform,
as the ether evaporates groups of large needle-shaped crystals are formed.
Under the microscope the crystals are found to be of a red colour and
prismatic shape.
Alcohol acts upon blood somewhat like chloroform ; it arrests the che-
mical changes, but in a less marked degree.
Amylene was found to act like ether upon blood, in so far as it did not
diminish the absorption of oxygen or retard the elimination of carbonic
acid. It differed, however, from ether in not destroying the blood-cor-
puseles.
In the last place, the action of mineral substances is stated, viz. :
1. Corrosive sublimate was found to increase the chemical ees
which develope carbonic. acid, and to have scarcely any effect on those ae
pending upon oxidation ; its influence, if any, is rather to diminish them
than otherwise.
2. Arsenic seems to retard both the oxidation of the constituents of the
blood and the exhalation of carbonic acid.
3. Tartrate of antimony increases the exhalation of carbonic acid gas,
while it at the same time diminishes the absorption of oxygen.
A. Sulphate of zinc and sulphate. of copper both act like tartrate of
antimony, but not nearly so powerfully.
Lastly, phosphoric acid was found to have the effect of increasing the
chemical transformations and decompositions upon which the exhalation
of eaybonic acid depends.
March 17, 1864.
Major-General SABINE, President, in the Chair.
The following communications were aa —
I. “ Researches on Radiant Heat.—Fifth Memoir. Contributions to
Molecular Physics.” By J. Tynpatz, F.R.S., &c. Received
March 17, 1864.
(Abstract.)
Considered broadly, two substances, or two forms of substance, occupy
universe—the ordinary and tangible matter of that universe, and the
1864.] Prof. Tyndall—Contributions to Molecular Physics. 161
intangible and mysterious ether in which that matter is immersed. The
natural philosophy of the future must mainly consist in the examination of
the relations of these two substances. The hope of being able to come
closer to the origin of the ethereal waves, to get some experimental hold of
the molecules whence issue the undulations of light and heat, has stimulated
the author in the labours which have occupied him for the last five years,
and it is this hope, rather than the desire to multiply the facts already
known regarding the action of radiant heat, which prompted his present
investigation.
He had already shown the enormous differences which exist between
gaseous bodies, as regards both their power of absorbing and emitting
radiant heat. When a gas is condensed to a liquid, or a liquid congealed
to a solid, the molecules coalesce, and grapple with each other, by forces
which were insensible as long as the gaseous state was maintained. _ But
though the molecules are thus drawn together, the ether still surrounds
them: hence, if the acts of radiation and absorption depend on the indi-
vidual molecules, they will assert their power even after their state of
aggregation has been changed. If, on the contrary, their mutual entangle-
ment by the force of cohesion be of paramount influence in the interception
and emission of radiant heat, then we may expect that liquids will exhibit a
deportment towards radiant heat altogether different from that of the vapour
from which they are derived.
‘The first part of the present inquiry is devoted to an exhaustive examina-
tion of this question. The author employed twelve different liquids, and
operated upon five different layers of each, which varied in thickness
from 0°02 of an inch to 0°27 of aninch. The liquids were enclosed, not
in glass vessels, which would have materially modified the heat, but between
plates of transparent rock-salt, which but slightly affected the radiation.
His source of heat throughout these comparative experiments consisted of
a spiral of platinum wire, raised to incandescence by an electric current of
unvarying strength. The quantities of radiant heat absorbed and trans-
mitted by each of the liquids at the respective thicknesses were first deter-
mined; the vapours of these liquids were subsequently examined, the
quantities of vapour employed being proportional to the quantities of liquid
traversed by the radiant heat. The result of the comparison was that, for
heat of the same quality, the order of absorption of liquids and that of
their vapours are identical. There was no exception to this law ; so that, to
determine the position of a vapour as an absorber or radiator, it is only
necessary to determine the position of its liquid.
This result proves that the state of aggregation, as far, at all events, as
the liquid stage is concerned, is of altogether subordinate moment—a con-
clusion which will probably prove to be of cardinal moment in molecular
physics. On one important and contested point it has a special bearing. If
the position of a liquid as an absorber and radiator determine that of its
162 = Prof. Tyndall—Contributions to Molecular Physics. [Mar. 17,
vapour, the position of water fixes that of aqueous vapour. Water had
been compared with other liquids in a multitude of experiments, and it was
found that as a radiant and as an absorbent it transcends them all. Thus,
for example, a layer of bisulphide of carbon, 0-02 of an inch in thickness,
absorbs 6 per cent., and allows 94 per cent. of the radiation from the red-
hot platinum spiral to pass through it ; benzol absorbs 43, and transmits
57 per cent. of the same radiation ; alcohol absorbs 67, and transmits 33
per cent., and it stands at the head of all liquids except one in point of
power as an absorber. The exceptionis water. A layer of this substance,
of the thickness above given, absorbs 81 per cent., and permits only 19 per
cent. of the radiation to pass through it. Had no single experiment ever
been made upon the vapour of water, we might infer with certainty from the
deportment of the liquid, that weight for weight this vapour transcends all
others in its power of absorbing and emitting radiant heat.
The relation of absorption and radiation to the chemical constitution of
the radiant and absorbent substances was next briefly considered.
For the first six substances in the list of those examined, the radiant
and absorbent powers augment as the number of atoms in the compound
molecule augments. Thus, bisulphide of carbon has 3 atoms, chloroform
5, iodide of ethyl 8, benzol 12, and amylene 15 atoms in their respective
molecules; and the order of their powers as radiants and absorbents is
that here indicated—bisulphide of carbon being the feeblest, and amylene
the strongest of the six. Alcohol, however, excels benzol as an absorber,
though it has but 9 atoms in its molecule; but, on the other hand, its
molecule is rendered more complex than that of benzol by the introduc-
tion of a new element. Benzol contains carbon and hydrogen, while alco-
hol contains carbon, hydrogen, and oxygen. Thus, not only does the
idea of multitude come into play in absorption and radiation, that of com-
plexity must also be taken into account. The author directed the parti-
cular attention of chemists to the molecule of water; the deportment of
this substance towards radiant heat being perfectly anomalous, if the che-
mical formula at present ascribed to it be correct.
Sir William Herschel made the important discovery that beyond the
limits of the red end of the solar spectrum, rays of high heating power
exist which are incompetent to excite vision. The author has examined
the deportment of those rays towards certain bodies which are perfectly
opaque to light. Dissolving iodine in the bisulphide of carbon, he ob-
tained a solution which entirely intercepted the light of the most brilliant
flames, while to the extra-red rays of the spectrum the same iodine was
found to be perfectly diathermic. The transparent bisulphide, which is
highly pervious to the heat here employed, exercised the same absorption
as the opaque solution. A hollow prism filled with the opaque liquid was
placed in the path of the beam from an electric lamp; the light-spectrum
was completely intercepted, but the heat-spectrum was received upon a
1864.] Prof. Tyndall—Contributions to Molecular Physics. 168
sereen, and could be there examined. Falling upon a thermo-electric
pile, its presence was shown by the prompt deflection of even a coarse
galvanometer.
What, then, is the physical meaning of opacity and transparency, as
regards light and radiant heat? The luminous rays of the spectrum differ
from the non-luminous ones simply in period. The sensation of light is
excited by waves of ether shorter and more quickly recurrent than those
which fall beyond the extreme red. But why should iodine stop the
former, and allow the latter to pass? The answer to this question, no
doubt, is, that the intercepted waves are those whose periods of recurrence
coincide with the periods of oscillation possible to the atoms of the dis-
solved iodine. The elastic forces which separate these atoms are such as
to compel them to vibrate in definite periods, and when these periods syn-
chronize with those of the ethereal waves the latter are absorbed. Briefly
defined, their transparency in liquids, as well as in gases, is synonymous
with discord, while opacity is synonymous with accord between the periods
of the waves of ether and those of the molecules of the body on which
they impinge. All ordinary transparent and colourless substances owe
their transparency to the discord which exists between the oscillating
periods of their molecules and those of the waves of the whole visible spec-
trum. The general discord of the vibrating periods of the molecules of com-
pound bodies with the light-giving waves of the spectrum may be inferred
from the prevalence of the property of transparency in compounds, solid,
liquid, and gaseous, while their greater harmony with the extra-red periods
is to be inferred from their opacity to the extra-red rays.
Waiter illustrates this transparency and opacity in the most striking
manner. It is highly transparent to the luminous rays, which demon-
strates the incompetency of its molecules to oscillate in the periods which
excite vision. It is as highly opaque to the extra-red undulations, which
_proves the synchronism of its periods with those of the longer waves.
If, then, to the radiation from any source water shows itself to be emi-
nently or perfectly opaque, it is a proof that the molecules whence the
radiation emanates must oscillate in what may be called extra-red periods.
Let us apply this test to the radiation from a flame of hydrogen. This
flame consists mainly of incandescent aqueous vapour, the temperature of
which, as calculated by Bunsen, is 3259° C., so that if transmission aug-
ments with temperature, we may expect the radiation from this flame to
be copiously transmitted by the water. While, however, a layer of the
bisulphide of carbon 0°07 of an inch in thickness transmits 72 per cent.
of the incident radiation, and every other liquid examined transmits
more or less of the heat, a layer of water of the above thickness is entirely
opaque to the radiation from the flame. Thus we establish accord be-
tween the periods of the molecules of cold water and those of aqueous
vapour at a temperature of 3259° C. But the periods’of water have
already been proved to be extra-red; hence those of the hydrogen flame
164 Prof. Tyndall—Contributions to Molecular Physics. [Mar. 17,
must be extra-red also. The absorption by dry air of the heat emitted by
a platinum spiral raised to incandescence by electricity was found to be
insensible, while that by the ordinary wndried air was 6 per cent. Sub-
stituting for the platinum spiral a hydrogen flame, the absorption by dry
air still remained insensible, while that of the undried air rose fo 20 per
cent. of the entire radiation. The temperature of the hydrogen flame
was as stated, 3259°C., that of the aqueous vapour of the air was 20° C.
Suppose, then, the temperature of our aqueous vapour to rise from 20°C.
to 3259° C., we must conclude that the augmentation of temperature is
applied fo an increase of amplitude, and not to the introduction of periods
of quicker recurrence into the radiation. 3
The part played by aqueous vapour in the economy of Nature is far
more wonderful than hitherto supposed. ‘To nourish the vegetation of
the earth, the actinic and luminous rays of the sun must penetrate our
atmosphere, and to such rays aqueous vapour is eminently transparent.
The violet and the extra-violet rays pass through it with freedom. ‘To
protect vegetation from destructive chills, the terrestrial rays must be
checked in their transit towards stellar space, and this is accomplished
by the aqueous vapour diffused through the air. This substance is the
great moderator of the earth’s temperature, bringing its extremes into
proximity, and obviating contrasts between day and night which would
render life insupportable. But we can advance beyond this general
statement now that we know the radiation from aqueous vapour is inter-
cepted, in a special degree, by water, and reciprocally, the radiation from
water by aqueous vapour ; for it follows from this that the very act of noc-
turnal refrigeration which produces the condensation of aqueous vapour
upon the surface of the earth—giving, as it were, a varnish of liquid water
to that surface—imparts to terrestrial radiation that particular character
which disqualifies it from passing through the earth’s atmosphere and
losing itself in space.
And here we come to a question in molecular physics which at the
present moment occupies the attention of able and distinguished men. By
allowing the violet and extra-violet rays of the spectrum to fall upon sul-
phate of quinine and other substances, Professor Stokes has changed the
periods of those rays. Attempts have been made to produce a similar
result at the other end of the spectrum—to convert the extra-red periods
into periods competent to excite vision—but hitherto without success.
Such a change of period the author believed occurs when a platinum wire
is heated to whiteness by a hydrogen flame. In this common experiment
there is an actual breaking-up of long periods into short ones—a true
rendering of invisual periods visual. The change of refrangibility here
effected differs from that of Professor Stokes, first, by its being in the
opposite direction, that is from lower to higher; and secondly, in the
circumstance that the platinum is heated by the collision of the molecules
of aqueous vapour, and before their heat has assumed the radiant form.
1864.] Prof. Tyndall—Contributions to Molecular Physics. 165
But it cannot be doubted that the same effect would be produced by
radiant heat of the same periods, provided the motion of the ether could
be rendered sufficiently intense. The effect, in principle, is the same
whether we consider the platinum wire to be struck by a particle of aqueous
vapour oscillating at a certain rate, or by a particle of ether oscillating at
the same rate.
By plunging a platinum wire into a hydrogen flame we cause it to glow,
and thus introduce shorter periods into the radiation. These, as already
stated, are in discord with water; hence we should infer that the trans-
mission through water will be more copious when the wire is in the flame
than when itis absent. Experiment proves this conclusion to be true.
Water, from being opaque, opens a passage to 6 per cent. of the radiations
from the flame and spiral. A thin plate of colourless glass, moreover,
transmitted 58 per cent. of the radiation from the hydrogen flame; but
when the flame and spiral were employed 78 per cent. of the heat was
transmitted. For an alcohol flame Knoblauch and Melloni found glass to
be less transparent than for the same flame with platinum spiral immersed
in it; but Melloni afterwards showed that this result was not general,
that black glass and black mica were decidedly more diathermic to the
radiation from the pure flame. The reason of this is now obvious. Black
mica and black glass owe their blackness to the carbon diffused through
them. The carbon, as proved by Melloni, is in some measure transparent
to the extra-red rays, and the author had in fact succeeded in transmitting
between 40 and 50 per cent. of the radiation from a hydrogen flame
through a layer of carbon sufficient to intercept the light of the most bril-
liant flames. The products of combustion of the alcohol flame are carbonic
acid and aqueous vapour, the heat of which is almost wholly extra-red.
For this radiation the carbon is in a considerable degree transparent, while
for the radiation from the platinum spiral it is in a great measure opaque.
By the introduction of the platinum wire, therefore, the transparency of
the pure glass and the opacity of its carbon were simultaneously aug-
mented ; but the augmentation of opacity exceeded that of transparency,
~ and a difference in favour of opacity remained.
No more striking or instructive illustration of the influence of coinci-
dence could be adduced than that furnished by the radiation from a car-
bonic oxide flame. Here the product of combustion is carbonic acid; and
on the radiation from this flame even the ordinary carbonic acid of the
atmosphere exerts a powerful effect. A quantity of the gas, only one-
thirtieth of an atmosphere in density, contained in a polished brass tube
four feet long, intercepted 50 per cent. of the radiation from the carbonic
oxide flame. For the heat emitted by solid sources, olefiant gas is an in-
comparably more powerful absorber than carbonic acid; in fact, for such
heat the latter substance, with one exception, is the most feeble absorber to
be found among the compound gases. For the radiation from the hydro-
gen flame, moreover, olefiant gas possesses twice the absorbent power of
166 Prof. Tyndall—Contributions to Molecular Physics, [Mar.17,
carbonic acid; but for the radiation from the carbonic oxide flame at a
common tension of one inch of mercury, while carbonic acid absorbs 50 per
cent., olefiant gas absorbs only 24. Thus we establish the coincidence of
period between carbonic acid at a temperature over 3000°C., the periods
of oscillation of both the incandescent and the cold gas belonging to the
extra-red portion of the spectrum.
It will be seen from the foregoing remarks and experiments how impossible
it is to examine the effect of temperature on the transmission of heat, if
different sources of heat be employed. Throughout such an examination
the same oscillating atoms ought to be retained. The heating of a pla-
tinum spiral by an electric current enables us to do this while varying the
temperature between the widest possible limits. Their comparative opacity
to the extra-red rays shows the general accord of the oscillating periods of
our series of vapours with those of the extra-red undulations ; hence, by
gradually heating a platinum wire from darkness up to whiteness, we
gradually augment the discord between it and our vapours, and must there-
fore augment the transparency of the latter. Experiment entirely confirms
this conclusion. Formic ether, for example, absorbs 45 per cent. of the
radiation from a platinum spiral heated to barely visible redness; 32 per
cent. of the radiation from the same spiral at a red heat ; 26 per cent. of
the radiation from a white-hot spiral, and only 21 per cent. when the spiral
is brought near its point of fusion. Remarkable cases of inversion as to
transparency occurred in these experiments. For barely visible redness
formic ether is more opaque than sulphuric ; fora bright red heat both are
equally transparent, while for a white heat, and still more for a nearly
fusing temperature, sulphuric ether is more opaque than formic. This
result gives us a clear view of the relationship of the two substances to the
luminiferous ether. As we introduce waves of shorter period, the sulphuric
augments most rapidly in opacity ; that is to say, its accord with the shorter
waves is greater than that of the formic. Hence we may infer that the
molecules of formic ether oscillate as a whole more slowly than those of
sulphuric ether.
When the source of heat was a Leslie’s cube filled with boiling water and
coated with lampblack, the opacity of formic ether in comparison with
sulphuric was very decided; with this source also the position of chloro-
form, as regards iodide of methyl, was inverted. For a white-hot spiral, the
absorption of chloroform vapour being 10 per cent., that of iodide of
methyl] is 16 ; with the blackened cube as source, the absorption by chloro-
form is 22 per cent., while that by the iodide of methyl is only 19. This
inversion is not the result of temperature merely ; for whena platinum wire
heated to the temperature of boiling water was employed as a source, the
iodide was the most powerful absorbent. Numberless experiments, indeed,
prove that from heated lampblack an emission takes place which synechro-
nizes in an especial manner with chloroform. This may be thus illustrated.
For the Leslie’s cube coated with lampblack, the absorption by chloroform
1864.] Prof. Tyndall—Contributions to Molecular Physics. 167
is more than three times that by bisulphide of carbon ; for the radiation from
the most luminous portion of a gas flame the absorption by chloroform is
also considerably in excess of that by bisulphide of carbon; while for the
flame of a Bunsen’s burner, from which the incandescent carbon particles
are removed by the free admixture of air, the absorption by bisulphide of
carbon is nearly twice that by chloroform ; the removal of the incandescent
carbon particles more than doubled in this instance the relative transparency
of the chloroform. Testing, moreover, the radiation from various parts of
the same flame, it was found that for the blue base of the flame the bisulphide
was the most opaque, while for all other portions of the flame the chloroform
was most opaque. For the radiation from a very small gas flame, consisting
of a blue base and a small white top, the bisulphide was also most opaque,
and its opacity very decidedly exceeded that of the chloroform when the
flame of bisulphide of carbon was employed as a source. Comparing the
radiation from a Leslie’s cube coated with isinglass with that from a similar
cube coated with lampblack, at a common temperature of 100° C., it was
found that out of eleven vapours all but one absorbed the radiation from the
isinglass most powerfully ; the single exception was chloroform. It may
be remarked that whenever, through a change of source, the position of a
vapour as an absorber of radiant heat was altered, the position of the liquid
from which the vapour was derived was changed in the same manner.
It is still a point of difference between eminent investigators as to whether
radiant heat up to a temperature of 100° C. is monochromatic or not.
Some affirm this, others deny it. A long series of experiments enables the
author to state that probably no two substances at a temperature of 100°C.
emit heat of the same quality. The heat emitted by isinglass, for example,
is different from that emitted by lampblack, and the heat emitted by cloth
or paper differs from both. It is also a subject of discussion whether rock-
salt is equally diathermic to all kinds of calorific rays,—the differences
affirmed to exist by one investigator being ascribed by others to differences
of incidence from the various sources employed. MM. De la Provostaye
and Desains maintain the former view, Melloni and M. Knoblauch main-
tain the latter. The question was examined by the author without changing
anything but the temperature of the source. Its size, distance, and sur-
roundings remained the same, and the experiments proved that rock-salt
shared in some degree the defect of all other substances ; it is not perfectly
diathermic, and it is more opaque to the radiation from a barely visible
spiral than to that from a white-hot one.
The author devotes a section of his memoir to the relation of radiation to
conduction. Defining radiation, internal as well as external, as the com-
munication of motion from the vibrating molecules to the ether, he arrives
by theoretic reasoning at the conclusion that the best radiators ought to
prove the worst conductors. A broad consideration of the subject shows
at once the general harmony of the conclusion with observed facts.
Organic substances are all excellent radiators ; they are also extremely bad
168 Mr. Balfour Stewart on Sun Spots. [Mar. 17,
conductors. The moment we pass from the metals to their compounds, we
pass from a series of good conductors to bad ones, and from bad radiators
to good ones. Water, among liquids, is probably the worst conductor ; it
is the best radiator. Silver, among solids, is the best conductor; it is the
worst radiator. In the excellent researches of MM. De la Provostaye and
Desains the author finds a striking illustration of what he regards as a
natural law—that those molecules which transfer the greatest amount of
motion to the ether, or, in other words, radiate most powerfully, are the
least competent to communicate motion to each other, or, in other words,
to conduct with facility.
II. “ Remarks on Sun Spots.” By Batrour Stewart, M.A., F.R.S.,
Superintendent of the Kew Observatory. Received March 8,
1864:
In the volume on Sun Spots which Carrington has recently published,
we are furnished with a curve denoting the relative frequency of these phe-
nomena from 1760 to the present time. This curve exhibits a maximum
corresponding to 1788°6. Again, in Dalton’s ‘ Meteorology’ we have a list
of auroree observed at Kendal and Keswick from May 1786 to May 1793.
The observations at Kendal were made by Dalton himself, and those at
Keswick by Crosthwaite. This list gives—
For the year 1787 ....27 aurore, For the year 1790 .... 36 aurore;
ISS 2 Oo Ff 17912 aie
WSO AG = 179224 2a 3
showing a maximum about the middle, or near the end of 1788. This
corresponds very nearly with 1788°6, which we have seen is one of Car-
rington’s dates of maximum sun spots.
The following observation is unconnected with the aurora borealis. In
examining the sun pictures taken with the Kew Heliograph under the
superintendence of Mr. De la Rue, it appears to be a nearly universal law that
the faculee belonging to a spot appear to the left of that spot, the motion
due to the sun’s rotation being across the picture from left to right.
These pictures comprise a few taken in 1858, more in 1859, afew in 1861,
and many more in 1862 and 1863, and they have been carefully examined
by Mr. Beckley, of Kew Observatory, and myself. The following Table
expresses the result obtained :—
No. of cases of No. of cases of No. of cases of No. of cases of fa-
Year. _—facula to left facula to right facula equally on culz mostly be-
of spot. of spot. both sides of spot. tween two spots.
‘bere chee ARNE SPU SR te OR sees Re A O rach se eee ee Oj.
fe) ae es AC My ge aoe ss Sim etre th set Os ate eee 3
Oat tes e Oe ee eee Ihe auh hea Oe ee ee 0
1862.2. Of es eee EP a a T RE 3
1863 Sits AG. Fs be OW Ose ee A gepress ae cnn ts 2
RS Gd eran oe Ba. UG f iO) ee 2 Siete Ryedale tele 1
1864..] “Mr. Hicks on an Improved Barometer. 169
III. “Description of an Improved Mercurial Barometer.” By James
Hicks, Esq. Communicated by J. P. Gasstor, F.R.S. Received
March 16, 1864.
Having shown this instrument to Mr. Gassiot, he wished me to write a
short description of it, which he thought would be of interest to the Royal
Society.
Some time since I constructed an open-scale barometer, with a column
of mercury placed in a glass tube hermetically sealed at the top, and per-
fectly open at the bottom. The lower half of the tube is of larger bore
than that of the upper.
If a column of mercury, of exactly the length which the atmosphere is
able at the time to support, were placed in a tube of glass hermetically
sealed at the top, of equal bore from end to end, the mercury would be held
in suspension ; but immediately the pressure of the atmosphere increased,
the mercury would rise towards the top of the tube, and remain there
till, on the pressure decreasing, it would fall towards the bottom, and
that portion which the atmosphere was unable to support would drop out.
But if the lower half of the tube be made a little Jarger in the bore
than the upper, when the column falls, the upper portion passes out of the
smaller part of the tube into the larger, and owing to the greater capacity
of the latter, the lower end of the column of mercury does not sink to the
same extent as the upper end, and the column thus becomes shorter. The
fall will continue until the column is reduced to that length which the
atmosphere is capable of supporting, and the scale attached thus registers
what is ordinarily termed the height of the barometer.
From the above description it will be evident that, by merely varying
the proportion in the size of the two parts of the tube, a scale of any
length can be obtained. For example, if the tubes are very nearly the
same size in bore, the column has to pass through. a great distance before
the necessary compensation takes place, and we obtain a very long scale,
say 10 inches, for every 1-inch rise and fall in the ordinary barometer.
But if the lower tube is made much larger than the upper, the mercury
passing into it quickly compensates, and we obtain a small scale, say from
2 to 3 inches, for every inch. To ascertain how many inches this would rise
and fall for an ordinary inch of the barometer, I attach it, in connexion with
a standard barometer, to an air-pump receiver, and by reducing the pressure
in the air-pump I cause the standard barometer to fall, say 1 inch, when the
other will fall, say 5 inches; and so I ascertain the scale for every inch,
from 31 to 27 inches.
It was on this principle that I constructed the open-scale barometer,
which has since been extensively used. But having been asked to apply a
vernier to one of these barometers graduated in this way, I found this im-
practicable, as each varied in length in proportion as the bore of the tube
varied, so that every inch was of a different length.
VOL. XIII. oO
170 Mr. Perkin on Mauve or Aniline-Purple. [1864.
I have now remedied this defect, and made what I believe is an absolute
standard barometer, by graduating the scale from the centre, and reading
it off with two verniers to the ;5,th of an inch. The scale is divided
from the centre, up and down, into inches, and subdivided into 20ths.
To ascertain the height of the barometer graduated in this way, take a
reading of the upper surface of the column of mercury with the vernier,
then of the lower surface in the same way, and the two readings added to-
gether will give the exact length of the column of mercury supported in the
air, which is the height of the barometer at the time.
There is another advantage in this manner of graduating over the
former, that if a little of the mercury drops out it will give no error, as the
column will immediately rise out of the larger tube into the smaller, and
become the same length as before; but by the former scale the barometer
would stand too high, until readjusted, which could only be effected by
putting the same quantity of mercury in again. :
I have introduced Gay-Lussac’s pipette into the centre of the tube, to
prevent the possibility of any air passing up into the top.
The Society then adjourned over the Easter Recess to Thursday, April 7th.
“On Mauve or Aniline-Purple.’” By W. H. Perxin, F.C.S. Com-
municated by Dr. Srennousz. Received August 19, 1863*.
The discovery of this colouring matter in 1856, and its introduction as a
commercial article, has originated that remarkable series of compounds
known as coal-tar colours, which have now become so numerous, and in
consequence of their adaptibility to the arts aud manufactures are of such
great and increasing importance. ‘The chemistry of mauve may appear to
have been rather neglected, its composition not having been established,
although it has formed the subject of several papers by continental chemists.
Its chemical nature also has not been generally known; and to this fact
many of the discrepancies in the results of the different experimentalists
who have worked on this subject are to be attributed.
The first analysis I made of this colouring matter was in 1856, soon
after I had become its fortunate discoverer. The product I examined was
purified as thoroughly as my knowledge of its properties then enabled me,
and the resultst obtained agree very closely with those required for the
formula I now propose. Since that time I have often commenced the study
of this body in a scientific point of view, but other duties have prevented me
* For abstract see vol. xii. p. 713.
+ The substance I examined was doubtless the sulphate, of which I made two com-
bustions :—
No. I. gave 71°55 per cent. of carbon and 6:09 per cent. of hydrogen.
No. II. gave 71°60 5 % Beh) o
Theory requires 71:5 4 y 5°5 ”
1864.] Mr. Perkin on Mauve or Aniline-Purple. 171
from completing these investigations; but, although unacquainted with its
correct formula, its chemical characters have necessarily been well known
to me for a considerable time. When first introduced, commercial mauve
appeared as an almost perfectly amorphous body ; but now, owing to the
great improvements which have been made in its purification, it is sent into
the market perfectly pure and crystallized.
On adding a solution of hydrate of potassium to a boiling solution of
commercial crystallized mauve, it immediately changes in colour from
purple to a blue violet, and after a few moments begins to deposit a
crystalline body. After standing a few hours, this crystalline product is
collected on a filter, washed with alcohol once or twice, and then thoroughly
with water. When dry, it appears as a nearly black glistening substance,
not unlike pulverized specular iron ore.
This substance, for which I propose the name Mauveine, is a powerful
base. It dissolves in alcohol, forming a blue violet solution, which imme-
diately assumes a purple colour on the addition of acids. It is insoluble, or
nearly so, in ether and benzole. It is a very stable body, and decomposes
ammoniacal compounds readily. When heated strongly it decomposes,
yielding a basic oil, which does not appear to be aniline.
The following analyses were made of specimens dried at 150° C. :—
I. -301 grm. of substance gave ‘8818 of carbonic acid and ‘162 of water.
II. *2815 grm. of substance gave °8260 of carbonic acid and °145 of water.
Direct Nitrogen determination.
III. °3435 grm. of substance gave41°0c.c. N at23°C. and 766 mms. Bar.
__41°0 cub. centims. (766-0 millims. —20°9)
ot 824°1 millims.
37°7 X 0012562 grm.='04735 grm. of N.
These numbers correspond to the following percentages :—
y! =37°7 cub. centims.
I. II. III.
CMON sesso cee -19'9 80:0 —
Elydrogene. ona... (5°98 5°72
INTET OREM) sca s ee a 13°75
The formula, C,,* H,, N,, requires the following values :—
Theory. Mean of experiment.
BSI TS
Ce sien ire 24 80°19 79°95
Bg i's Shnwtoe tere 24 5°94 5°85
UN GH ede Persia es 56 13°87 13°75
404 100°
Hydrochlorate of Mauveine.-—This salt is prepared by the direct combi-
nation of mauveine and hydrochloric acid. From its boiling alcoholic solu-
tion it is deposited in small prisms, sometimes arranged in tufts, possessing
* C=12,
o 2
172 Mr. Perkin on Mauve or Aniline-Purple. [1864..
a brilliant green metallic lustre. It is moderately soluble in aleohol, but
nearly insoluble in ether. It is also, comparatively speaking, moderately
soluble in water.
Different preparations dried at 100° C. gave the following numbers :-—
I. °306 grm. of substance gave *8255 of carbonic acid and *162 of water.
II. -308 grm. of substance gave *8275 of carbonic acid and *163 of water.
III. °310 grm. of substance gave ‘8345 of carbonic acid.
IV. °3165 grm. of substance gave 851 of carb. acid and °16525 of water.
V. :2447 grm. of substance gave °6603 of carb. acid and *1356 of water.
VI. -627 grm. of substance gave *205 of chloride of silver.
VII. -560 grm. of substance gave °195 of chloride of silver.
VIII. -69 grm. of substance gave ‘2266 of chloride of silver.
Direct Nitrogen determination.
IX. °3497grm. of substance gave 40 c.c. N at 20°C. and 777°2 mms. Bar.
40 c.c. 72—17°4 aos
Ve are e.c. at 0° C. and 760 millims, Bar.
37°2 cub. centims. x 0012562 grm.=-04673 grm. N.
These numbers correspond to the following percentages :-—
i Le III. IY:
(Carbon -% osc... 73°5 73°27 73°4 73°3
Hydrogen.....-...- 5°88 5:88 ae 58
Nitrogen, 225.2 °-% 4 ~ ass SAE,
(Chiorme. ©. 26 yee = eee sa Bee
V. VI. Vi. . VOL ae
arbor. oie es sae 73-50 eee
Hydrogen .........- 16 ———
Nitroven o.).4 425... ;- Se ee es
Ghilomue: 2s ts 3s —— 8:08 8:06 8:1 Bes.
These numbers agree with the formula C,, H,,N,H Cl, as may be seen
by the following Table :-—
Theory. Mean of experiment.
eras 7 Fatt 324-7355 73°41
EL so Sia cee 25° 5°67 0°93
Nc Baie tees ons 56° 12°73 13°30
AO Ro. eee i, 2 35°95 8°05 8°07
440°5 100-00
I have endeavoured to obtain a second hydrochlorate containing more
acid, but up to the present time have not succeeded.
Platinum-salt.—Mauveime forms a perfectly definite and beautifully
crystallme compound with bichloride of platinum. It is obtained by
mixing an alcoholic solution of the above hydrochlorate with an excess of an
1864. | Mr. Perkin on Mauve or Aniline- Purple. 173
alcoholic solution of bichloride of platinum ; from this mixture the new salt
separates as a highly crystalline powder. I have generally preferred to use
cold solutions in its preparation; but if moderately hot solutions be em-
ployed, the salt will separate as crystals of considerable dimensions.
This platinum-salt possesses the green lustre of the hydrochlorate, but,
on being dried, assumes a more golden colour. It is very sparingly soluble
in alcohol. The following numbers were obtained from various preparations
dried at 100°.C. :—
I. -44125 grm. of substance gave ‘072 of platinum.
IT. -4845 grm. of substance gave °079 fe
III. -511 grm. of substance gave -083
IV. -510 grm. of substance gave °083
V. °6345 grm. of substance gave *1035
VI. -618 grm. of substance gave °101 ”
VII. °31275 grm. of substance gave 60525 of carbonic acid and ‘118
of water.
VIII. -30675 grm. of substance gave °595 of carb. acid and*110 of water.
IX. °3795 grm. of substance gave 27 of chloride of silver.
These results correspond to the percentages in the following Table :—
33
I II II. IV V. VI.
Carbon .... —— aa —-- wae oe ——
Hydrogen .. —— oe a —_ ss ——— ——
Chlorine .... —— we a ——— — ———
Platinum .. °16°31 16°3 16°24 16°27 16°3 16°3
VII. VIII. IX.
Carhons sa 664 52°77 52°86 a
Piydrogen. .. 4 4°19 3°98
Chlorine ...... — —— 17°6
Platinumys3 . 2... sess
The formula, C,, H,, N, H Pt Cl,, requires the following values :—
Theory. Mean of experiment.
C. 324 53°09 52°81
[2 ene 4-09 4°19
N, 56° 9-2 =
Pt 98°7 16°16 16°28
Cl, 106°5 17°46 17°6
610°2 100:°00
Gold-salt.—This compound is prepared in a similar manner to the
_ platinum-salt, only substituting chloride of gold for chloride of platinum.
It separates as a crystalline precipitate, which, when moist, presents a
much less brilliant aspect than the platinum derivative; it is also more
soluble than that salt, and when crystallized appears to lose a small quan-
tity of gold. The following results were obtained from a specimen dried
at 100° C, :—
174 Mr. Perkin on Mauve or Aniline-Purple. [1864.
I. ‘47175 grm. of substance gave °1245 of gold.
II. *35525 grm. of substance gave °094 of gold.
III. :309 grm. of substance gave °495 of carbonic acid and *101 of water.
Percentage composition :—
iF II. IIl.
Carbon —— ——— 43°68
Hydrogen — — 3°6
Gold 2673 26°46
The formula, C,, H,, N,, H AuCl,, requires the following percentages :—
Theory. Mean of experiment.
FE
Ce ee 43°53 43°68
ji Bees 25 3°34 3°6
Ngan. S056 7°44 ——
AM eta OT 26°61 26°38
1 ae 19-08 es
744 100:00
- Hydrobromate of Mauveine.—This salt is prepared in a similar manner
to the hydrochlorate, which it very much resembles, except that it is less
soluble in alcohol. Analysis of preparations dried at 100° C. gave the
following numbers :—
I. *3935 grm. of substance gave 1515 of bromide of silver.
II. :450 grm. of substance gave *173 of bromide of silver.
III. -3265 grm. of substance gave -79675 of carb. acid and ‘158 of water.
IV. °35125 grm. of substance gave °86075 of carbonic acid and °1675
of water.
Percentage composition :—
I. II. III. IV.
Carbon ——. —— 66°55 66°8
Hydrogen —— 5°37 5°29
Bromine’ 16°38 16°37 cae
These numbers agree with the formula C,, H,, N, H Br, as shown by
the comparisons in the following Table :— |
Theory. Experiment.
My Tae aS
cs . 324 66°8 66°67
|b RR ern) 745) 5°15: 5°33
Neciiwin ob 11°56 ee
Broidg-«7 0 16°49 16°37
485 100-00
Hydriodate of Mauveine.—In preparing this salt from the base, it is
necessary to use hydriodic acid which is colourless, otherwise the free
iodine will slowly act upon this salt. It crystallizes in prisms haying a
1864.] Mr. Perkin on Mauve or Aniline-Purple. 175
green metallic reflexion. It is more insoluble than the hydrobromate.
The products used in the subjoined analysis were recrystallized three times,
and dried at 100° C.
I. :5115 grm. of substance gave *22575 of iodide of silver.
II. -248 grm. of substance gave ‘549 of carb. acid and °10975 of water.
III. -2985 grm. of substance gave 663 of carb. acid and °1265 of water.
IIV. °2765 grm. of substance gave °615 of carb. acid and °1145 of water.
Percentage composition :—
I. II. III. IV.
Carbon —— 60°46 60°57 60°65
Hydrogen 4°9 4°7 4°7
Todine 23°8
The formula, C,, H,, N, HI, requires the following values :—
Theory. Experiment.
eG REN
Be » O24> 60°89 60% 56
LE eT 25° 4°69 4°7
IN ee Mae 508 10°54 —.
I Sn aaa 23°88 23°8
532°] 100-00
Acetate of Mauveine.—This salt is best obtained by dissolving the base
in boiling alcohol and acetic acid. On cooling, it will crystallize out; it
should then be recrystallized once or twice. This acetate is a beautiful
salt, possessing the green metallic lustre common to most of the salts of
mauveine. ‘Two combustions of specimens dried at 100°C. gave the fol-
lowing numbers :— |
I. °28325 grm. of substance gave °778 of carb. acid and °153 of water.
If. *29275 grm. of substance gave *806 of carb. acid and ‘1645 of water.
Percentage composition :—
I. Il.
Carbon 74-9 75°0
Hydrogen 6-0 6:2
These numbers lead to the formula
C. 15 bs N, 0,=C,, H,, N, C, H, O,,
as shown by the following Table :—
Theory. Experiment.
ee aa US
Celene Ns, 79° 74°95
ee 2G 6° 6:1
ING warmer oO 12°06 ——
O, . 32 6°94 —
464 100-00
Carbonate of Mauveine.—The tendency of solutions of mauveine to
combine with carbonic acid is rather remarkable. If a quantity of its solu-
176 Mr. Perkin on Mauve or Aniline-Purple. [1864.
tion be thrown up into a tube containing carbonic acid over mercury, the
carbonic acid will quickly be absorbed, the solution in the mean time pass-
ing from its normal violet colour to purple. To prepare this carbonate, it
is necessary to pass carbonic acid gas through boiling alcohol containing a
quantity of mauveine in suspension. It is then filtered quickly, and car-
bonic acid passed through the filtrate until nearly cold. On standing,
this liquid will deposit the carbonate as prisms, having a green metallic
reflexion. A solution of this salt, on being boiled, loses part of its carbonic
acid and assumes the violet colour of the base. When dry this carbonate
rapidly changes, and if heated to 100° C. loses nearly all its carbonic acid
and changes in colour to a dull olive; therefore, as it cannot be dried’ with-
out undergoing a certain amount of change, its composition is difficult to
determine. However, I endeavoured to estimate the carbonic acid in this
salt by taking a quantity of it freshly prepared and in the moist state, and
heating it in an oil-bath until carbonic acid ceased to be evolved. The
residual base was then weighed, and also the carbonic acid, which had
been collected in a potash bulb, having been previously freed from water
by means of sulphuric acid. The foilowing results were obtained :—
I. 1°88 residual base obtained ; *190 carbonic acid evolved.
II. 1:375 residual base; °1385 carbonic acid evolved. +190 of CO, is
equal to -268 of H,CO,; this, added to the residual base, will give the
amount of substance experimented with, viz. 2°148. The amount of CO,
obtained from this quantity, therefore, is 8°8 per cent.
Calculating the second experiment in a similar manner, the amount of
carbonate operated upon would be 1°5702 grm.; the percentage of CO,
obtained is therefore equal to 8°8. A carbonate having the formula
(C,, H,, N,), H, CO, would contain 5:1 per cent. of CO,, and an acid
carbonate having the formula O,,H,,N,, H,CO, would contain 9:4 per
cent. of CO,.
Considering that this salt when prepared begins to crystallize before it
is cold, probably the first portions that deposit are a monocarbonate, while
the larger quantity which separates afterwards is an acid carbonate. Hence
the deficiency in the amount of CO, obtained in the above experiments.
I hope to give my attention to this remarkable salt at a future period.
In the analysis of the salts of mauveine great care has to be taken in
drying them thoroughly, as most of them are highly hygroscopic.
I am now engaged in the study of the replaceable hydrogen in mauveine,
which I hope will throw some light upon its constitution. From its for-
mula I believe it to be a tetramine, although up to the present time I
have not obtained any definite salts with more than 1 equiv. of acid.
When mauveine is heated with aniline it produces a blue colouring
matter, which will doubtless prove to be a phenyle derivative of that base.
A salt of mauveine when heated alone also produces a violet or blue
compound. These substances 1am now examining, and hope in a short
time to have the honour of communicating them to the Society.
Oe 3QiA ci
fir i a! :
4, i BU, LOU g,
sik
4
1864. | ‘ Pe OR
April 7, 1864.
Major-General SABINE, President, in the Chair.
The Rev. Dr. Salmon was admitted into the Society.
The following communications were read :—
I. “On the Functions of the Cerebellum.” By Wit1t1am How-
sHie Dickinson, M.D. Cantab., Curator of the Pathological
Museum, St. George’s Hospital, Assistant Physician to the Hos-
pital for Sick Children. Communicated by Dr. Bencz Jones.
Received March 8, 1864.
(Abstract.)
The paper is divided into two Parts; the first gives the results of expe-
riments on animals; the second, of observations upon the human being.
Part I.
Assuming that the great divisions of the brain preserve each the same
function through the vertebrate kingdom, it is maintained that experiments
which can be performed only on such of the lower animals as are very
tenacious of life, will afford deductions of universal application.
The method of proceeding with regard to each species was to remove,
first, the whole encephalon, with the exception of the medulla oblongata ;
then in a similar animal only the cerebrum was taken away. The only
difference between the two cases was in the fact that one animal had a
cerebellum, and the other had not. A comparison was believed to show, in
the powers which one had more than the other, the function of the organ
the possession of which constituted the only difference.
Finally it was ascertained in each species what is the effect of taking
away the cerebellum alone.
The use of the organ was thus estimated in two ways—by the effect of
its addition to the medulla, and of its subtraction from the rest of the
nervous system.
The species so treated are arranged in an ascending scale, according to
the comparative weight of the cerebellum. The field-snake, frog, sala-
mander, toad, land-tortoise, eel, water-tortoise, pike, perch, tench, dace,
carp, gold-fish, rudd, loach, and gudgeon were subjected to these opera-
tions ; besides which, many experiments of a less systematic character were
made upon birds and mammalia.
The results are these :—
In Reptiles, with the exception of the snake, the cord, together with the
medulla oblongata, is sufficient to give the power of voluntary or sponta-
neous motion-—limited, but usually enough to allow of feeble locomotion.
With the addition of the cerebellum, all actions dependent on the will
appear to be naturally performed.
VOL. XIII. P
178 Dr. Dickinson on the Functions of the Cerebellum. [April 7,
The removal of the cerebellum shows that the cerebrum by itself is
unable to give more than a limited amount of voluntary motion, and that
of a kind deficient in balance and adjustment.
It is therefore inferred that the cord, together with the medulla oblon-
gata, is a great source of spontaneous motor power, in which function both
the cerebrum and the cerebellum take part, the cerebellum to the greater
extent ; it also appears that a certain harmony in the use of the muscles
depends on the possession of the latter organ.
Regarding Fishes, the cord and medulla oblongata seem unequal to the
performance of voluntary motion.
When the cerebellum is added, the powers become so far extended that
movements are made in obedience to external stimuli. Generally speak-
ing, a determined position is maintained and locomotion accomplished,
without the use, however, of the pectoral fins.
If the cerebellum only be taken away, there is a loss of the proper
adjustment between the right and left sides; so that oscillation or rotation
takes place. All the limbs are used, but apparently with a deficiency of
sustained activity.
It is therefore concluded that with Fishes, as with Reptiles, the power
of intentional movement is shared by both cerebrum and cerebellum; the
former in this case has the larger influence.
Such movements as depend on the cerebrum are destitute of lateral ba-
lance, are sudden in being affected by any external cause, and are emotional
in their character. Such as depend on the cerebellum are mutually ad-
justed, of a continuous kind, and less directly under the influence of con-
sciousness.
The same facts were supported by experiments on the higher orders of
animals: in these it seemed that the cord and medulla are insufficient to
excite voluntary movements. The muscles, as with fishes and reptiles,
acknowledge a double rule, from the cerebrum and from the cerebellum.
The anterior limbs are most subservient to the cerebrum ; the posterior to
the cerebellum. The limbs on one side are in connexion chiefly with the
lobe of the opposite side. The absence of the cerebellum destroys the
power of lateral balance.
From the negative results of the experiments, it is inferred that the cere-
bellum has nothing to do with common sensation, with the sexual pro-
pensity, with the action of the involuntary muscles, with the maintenance
of animal heat, or with secretion.
The only function which the experiments assigned to the cereuellenl is
such as concerns the voluntary muscles, which receive therefrom a regu-
lated supply of motor influence. Each lateral half of the cerebellum affects
both sides, but the one opposite to itself most.
The cerebellum has a property distinct from its true voluntary power,
which harmonizes the action of the voluntary muscles, and has been de-
scribed as ‘‘ coordination.”
1864.) Prof. Sylvester on Newton’s Rule, &c. 179
The voluntary muscles are under a double influence—from the cerebrum
and from the cerebellum. The anterior limbs are chiefly under the influ-
ence of the cerebrum; the posterior, of the cerebellum. Cerebellar move-
ments are apt to be habitual, while cerebral are impulsive. The cerebellum
acts when the cerebrum is removed, though when both organs exist it is
under its control.
Part IT.
From an analysis.of one case of congenital absence of the cerebellum, one
of disease of the whole organ, and 46 of disease of a portion of it, the fol-
lowing deductions are stated :—
The only faculty which constantly suffers in consequence of changes in
the cerebellum, is the power of voluntary movement.
When the organ is absent or defective congenitally, we have want of
action in the muscles of the lower extremities.
When the entire structure is changed by disease, we have loss of volun-
tary power, either general throughout the trunk, or limited to the lower
limbs—which results are about equally frequent.
From the manner in which the paralysis was distributed in cases of disease
of a part of the organ, it is inferred that each lobe is in connexion as a source
of voluntary movement with all the four limbs, but in the greatest degree
with the limbs of the opposite side, and with the lower more than with the
upper extremities.
The occasional occurrence of logs of visual power, and alterations of the
sexual propensity, is referred to the conveyance of irritation to the corpora
quadrigemina in one case, and the spinal cord in the other.
From both sources of knowledge it is concluded that the cerebellum has
distinct offices.
It is a source of voluntary motor power to the muscles supplied by the
spinal nerves. It influences the lower more than the upper limbs, and pro-
duces habitual rather than impulsive movements. Each lobe affects both
sides of the body, but most that opposite to itself.
Secondly, the cerebellum has a power which has been described as
that of “coordination,” which is similarly distributed.
Finally, it is suggested that the outer portion of the organ may be the
source of its voluntary motor power, while its inner layer is the means of
regulating its distribution.
II. “An Inquiry into Newton’s Rule for the Discovery of Ima-
gimary Roots.” By J. J. Sytvuster, F.R.S., Correspondent of
the Institute of France. Received April 6, 1864.
(Abstract.)
In the ‘ Arithmetica Universalis,’ in the chapter ‘“ De Resolutione Equa-
tionum,”” Newton has laid down a rule, admirable for its simplicity and
generality, for the discovery of imaginary roots in algebraical equations, and
P2
180 Prof. Sylvester on Newton’s Rule for [April 7,
for assigning an inferior limit to their number. He has given no clue
towards the ascertainment of the grounds upon which this rule is based, and
has stated it in such terms as to leave it quite an open question whether or
not he had obtained a demonstration of it. Maclaurin, Campbell, and
others have made attempts at supplying a demonstration, but their efforts,
so far as regards the more important part of the rule, that namely by
which the limit to the number of imaginary roots is fixed, have completely
failed in their object. Thus hitherto any opinion as to the truth of the rule
rests on the purely empirical ground of its being found to lead to correct
results in particular arithmetical instances. Persuaded of the insufficiency
of such a mode of verification, the author has applied himself to obtain-
ing a rigorous demonstration of the rule for equations of specified degrees.
For the second degree no demonstration is necessary. For cubic equa-
tions a proof is found without difficulty. For biquadratic equations the
author proceeds as follows. He supposes the equation to be expressed
homogeneously in 2, y, and then, instituting a series of infinitesimal linear
transformations obtained by writing x+y for 2, or y+Az for y, where h is
an infinitesimal quantity, shows that the truth of Newton’s rule for this
case depends on its being capable of being shown that the discriminant of
the function (1, +e, e, te, 1 (a, y)* is necessarily positive for all values of
e greater than unity, which is easily proved. He then proceeds to consider
the case of equations of the 5th degree, and, following a similar process,
arrives at the conclusion that the truth of the rule depends on its being
gapoble of being shown that the discriminant, say (D) of the fanenen
(a: ee, 7°, 0, 1K, y)’s which for facility of reference may be termed
“the (e, 7) function,” is necessarily positive when e*— en’ and n*—ye* are
both positive. This discriminant is of the 12th degree in e,y. But on
writing a=en, y=e’ +7’, it becomes a rational integral function of the 6th
degree in x, and of the second degree in y, and such that, on making
D=0, the equation represents a sextic curve, of which z, y are the
abscissa and ordinate, which will consist of a single close. It is then
easily demonstrated that all values of e, 7 which cause the variable point
x, y to lie inside this curve, will cause D to be negative (in which case the
function e, n has only two imaginary factors), and that such values as cause
the variable point to lie outside the curve, will make D positive, in which
case the e, 7 function has four imaginary factors. When the conditions
concerning ¢, » above stated are verified, it is proved that the variable
point must be exterior to the curve, and thus the theorem is demonstrated
for equations of the 5th degree.
The question here naturally arises as to the significance of the sign of D
when such a position is assigned to the variable point as gives rise to ¢magi-
nary values of e, 7, which in such case will eS conjugate quantities of the
form \+ipn, \—tp respectively.
The curve D will be divided by another sextic curve into two portions,
for one of which the couple e, 7 corresponding to any point in its interior is
1864. | the Discovery of Imaginary Roots. 181
real, and for the other conjugate. This brings to view the necessity of
there being in general a theory for equations with conjugate coefficients,
which for greater brevity may be termed conjugate equations, analogous to
that for real equations in respect of the distinction between real and imagi-
nary roots in the latter. A conjugate equation is one in which the coeffi-
cients, reckoning from the two ends of the equation, go in pairs of the form
pxiq, with the obvious condition that when there is a middle coefficient
this must be real. Such an equation may be supposed to be so prepared
that, when thrown into the form P+7Q, P and Q shall have no common
algebraical factor; and when this is effected, it may easily be shown that
the conjugate equation can neither have real roots nor roots paired together
of the form \+-7p, A—7z respectively. How, then, it may be asked, is the
analogy previously referred to possible? On investigation it will be found
that the roots divide themselves into two categories, each of exactly the
same order of generality,—viz. solitary roots of the form e, and assoct-
ated roots which go in pairs, the two roots of each pair being of the form
pe, 1 ga respectively ; so that, following the ordinary mode of geometrical
representation of imaginary quantities, the roots of a conjugate equation
may be denoted by points lying on the circumference of a circle to radius
unity (corresponding to solitary roots), and points (corresponding to the
associated roots) lying in couples on different radii of the circle at reci-
procal distances from the centre, each couple in fact constituting, accord-
ing to Prof. W. Thomson’s definition, electrical images of each other in
respect to the circle. If the circle be taken with radius infinity stead of
unity (so as to become a straight line), then we have the geometrical
eidolon of the roots of an ordinary equation, the’ solitary roots lying on a
straight line, and the associated or paired (imaginary) roots on each side of,
and at equal distances from the line.
In the inquiry before us, whether the variable point belong to the real
or conjugate part of the plane of the D curve, it is shown to remain true that
the number of associated roots will be two, if it lie inside the curve, and four
if it lie outside. The author then suggests a probable extension of Newton’s
rule to conjugate equations of any degree. In conclusion, he deals with a
question in close connexion with, and arising out of the investigation of
this rule, relating to equations of the form 2+(ax+6)"=0, to which,
for convenience, he gives the provisional name of ‘ superlinear equations ”’
(denoting the function equated to zero as a superlinear form), and esta-
blishes a rule for limiting the number of real roots which they can con-
tain, which is, that if such equation be thrown under the form
A, (@te)™+A, (@te,)"+ ..-. HA, (@+e,)"=0,
and ¢,,¢,,. . - ¢, be an ascending or descending order of magnitudes, the
equation cannot have more real roots than there were variations of sign in
the sequence A,,A,5-*+ + + Aw (—)"A,-
182 Prof. Sylvester—Discovery of Imaginary Roots. [April 7,
This theorem was published by the author, but without proof, in the
‘Comptes Rendus’ for the month of March in this year.
But the method of demonstration now supplied is deserving of particular
attention in itself; for it brings to light a new order of purely tactical con-
siderations, and establishes a previously unsuspected kind of, so to say,
algebraical polarity. The proof essentially depends upon the character of
every superlinear form being associated with, and capable of definition by
means of a pencil of rays, which may be called the type pencil, subject to
a species of circulation of a different nature according as the degree of the
forn: is even or odd, which he describes by the terms “‘per-rotatory”’ in the
one case, and “ trans-rotatory ”’ in the other ; so that the types themselves
may be conveniently distinguished by the names “‘per-rotatory”’ and “‘trans-
rotatory.’ By per-rotatory circulation is to be understood that species in
which, commencing with any element of the type, passage is made from it
to the next, from that to the one following, from the last but one to the last,
from the last to the first, and so on, until the final passage is to the element
commenced with from the one immediately preceding. By trans-rotatory
circulation, on the other hand, is understood that species in which, com-
mencing with any element and proceeding in the same manner as before
to the end element, passage is made from that, not to the end element
itself, but to its polar opposite, from that to the polar opposite of the next,
and so on, until the final passage is made to the polar opposite of the ele-
ment commenced with, from the polar opposite of its immediate ante-
cedent. The number of changes of sign in effecting such passages, whether
in a per-rotatory or a trans-rotatory type, is independent of the place of
the element with which the circulation is made to commence, and may be
termed the variation-index of the type, which is always an even number for
per-rotatory, and an odd number for trans-rotatory types. A theorem is
given whereby a relation is established between the variation-index of a
per-rotatory or trans-rotatory and that of a certain trans-rotatory or per-rota-
tory type capable of bemg derived from them respectively; and this purely
tactical theorem, combined with the algebraical one, that the form f(a, y)
cannot have fewer imaginary factors than any linear combination of
= o leads by successive steps of induction to the theorem in question,
but under a more general form, which serves to show intuitively that the
limit to the number of real roots of a superlinear equation which the
theorem furnishes must be independent of any homographic transfor-
mation operated upon the form. ‘The author believes that, whilst it is
highly desirable that a simple and general method should be discovered for
the proof of Nzwiton’s rule as applicable to equations of any degree, and
that the strenuous efforts of the cultivators of the New Algebra should be
directed to the attainment of this object, his labours in establishing a
proof applicable as far as equations of the 5th degree inclusive will not
1864. ] Mr. Gassiot—Prisms for Spectrum Analysis. 183
have been unproductive of good, as well on account of the confirmation
they afford of the truth of the rule, towards the establishment of which on
scientific grounds they constitute the first serious step yet made, as also,
and still more, by reason of the accessions to the existing field of algebraical
speculation to which they have incidentally led.
Ill. “ Description of a train of Eleven Sulphide-of-Carbon Prisms
arranged for Spectrum Analysis.” By J. P. Gasstor, F.R.S.
Received March 17, 1864.
The principles which should regulate the construction of a battery of
prisms have been alluded to in the description of the large spectroscope
now at Kew Observatory, which has a train of nine dense glass prisms with
refracting angles of 45°*.
While for purposes of exactitude, such as mapping out the solar spec-
trum, flint glass stands unrivalled; yet when the greatest amount of dis-
persion is the desideratum, prisms filled with bisulphide of carbon present
obvious advantages, on account of the enormous dispersive power of that
liquid—the difference of its indices of refraction for extreme rays being,
according to Sir David Brewster, as 0°077 against 0-026 for flint glass.
In the fluid prisms of the ordmary construction, the sides are cemented
on with a mixture of glue and honey. This cement, on hardening, warps
the sides, and confusion of the spectral lines is the consequent result. To
obviate this source of error, it has been proposed to attach an additional
pair of parallel sides to such prisms, a thin film of castor-oil beg interposed
between the surfaces. The outer plates are then secured by means of
Sealing-wax, or some cement, at the corners. In the battery of prisms now
about to be described, Mr. Browning has dispensed with this attachment at
the corners, which is likely to prove prejudicial, and has secured the second
sides in their proper position by extremely ight metal frames which clasp
the plates only on their edges.
Thus arranged, the frames exert no pressure on the surfaces of the
plates, and are quite out of the field of view, and they can be handled with-
out any fear of derangement.
On account of the lower refractive power of bisulphide of carbon, as com-
pared with flint glass, a refractive angle of 50° was given to the fluid prisms.
Eight such prisms would cause a ray of light to travel more than a circle,
and would be the greatest number that could be employed had the ordi-
nary arrangement been adopted.
In place, however, of giving to the fluid prisms two pairs of parallel
sides, Mr. Browning, taking advantage of the difference between the re-
fractive and dispersive properties of crown glass and bisulphide of carbon,
has substituted a prism of crown glass having a refracting angle of 6° for
one of the outer plates of each prism—the base of this crown-glass prism
being brought to correspond with the apex of the fluid prism, thus :—
* Proceedings, vol. xil. p. 536.
184 Mr. Gassiot on a Train of Eleven [April 7,
Crown-glass prism.
By this means the angle of minimum deviation of the prisms is so much
decreased, that eleven of them thus constructed can be used in a circle
instead of eight. An increase of dispersive power, due to refracting angles
of 150° of the bisulphide of carbon, is thus gained, minus only the small
amount of dispersion counteracted owing to the dispersive power of the
crown-glass prisms being employed in the contrary direction.
From the well-known low dispersive power of this medium, however,
this loss is inconsiderable, amounting to scarcely more than a fifteenth of
the power gamed. Owing to the minimum angle of deviation being
lowered, the further advantage is also secured of a larger field of view being
presented to the telescope by the first and last prism of the train.
Each prism, in addition to the light metal frame referred to,
has a separate stand, furnished with
screws for adjusting the prisms, and
securing them at the angle of mini-
mum deviation for any particular ray.
The prism stands within a stirrup fur-
nished with a welled head. By this
arrangement the prisms can be removed
and replaced without touching their sides
—a matter of some importance, as all
fluid prisms show different results with
every change of temperature.
For the sake of simplicity, the metal
framing of the prisms, and the various
adjusting-screws, have been omitted in
the last sketch.
The very unfavourable state of the weather prevented any observations
* Direction of ray as it would pass through two pair of parallel sides.
+ Direction of ray as altered by interposing the crown-glass prism.
1864.] Sulphide-of-Carbon Prisms for Spectrum Analysis. 185
being made on the solar spectrum with these prisms until Saturday the
12th inst. The results then obtained may probably not be considered
devoid of interest. They are as follows :—
The prisms were arranged so as to enable that portion of the spectrum
to be observed in which the well-defined D line of Fraunhofer is situated.
This line, long since resolved as double, presented an angular separation of
3! 6’, measured from the centre of one to that of the other principal line,
this measurement being made by Mr. Balfour Stewart by means of the
micrometer attached to the telescope; the value of the divisions of the
micrometer he had previously determined relatively to the divided circle of
the spectroscope. A centre line (clearly defined and figured in Kirchhoff
and Bunsen’s map) was distinctly visible, and nearly equidistant from the
centre towards the violet ; five clearly defined lines were perceptible, as also
two faint lines on each side of the principal lines, between the centre line
of Kirchhoff towards the red. Several faint lines were also perceptible.
The lines as represented in the diagram were drawn by Mr. Whipple,
one of the assistants in the Observatory, as they were observed by him
about 3.45 p.m Some of these may possibly be due to the earth’s atmo-
sphere, but the five most refrangible lines were observed at an earlier
period of the day by Mr. Stewart, Mr. Browning, and myself.
The great angular separation of the double D line to 3! 6" is a proof of
the power of this arrangement of the sulphide-of-carbon prisms, and offers
the means of mapping out the entire solar spectrum on a scale not hitherto
attained.
Received April 6, 1864.
Note.—Since the preceding observations were recorded, an inspection
has been made of the region of the spectrum towards the refrangible side
of double D; and, from the comparisons made with a map of lines ob-
tained by means of the battery of glass prisms with that given by those of
the sulphide-of-carbon prisms, many new lines are produced in addition
to those observable by the former, while the battery of glass prisms itself
gives a number of additional lines to those that are depicted in Kirchhoff’s
map.
186 [April 14,
April 14, 1864.
Major-General SABINE, President, in the Chair.
The Croonran Lecture was delivered by Prof. Hermann Hetm-
uoitz, For. Memb. R.8., ‘‘On the Normal Motions of the Human
Hye in relation to Binocular Vision.”
The Motions of the Human Hye are of considerable interest, as well for
the physiology of voluntary muscular motion in general, as for the
physiology of vision. ‘Therefore I may be allowed to bring before this
Society the results of some investigations relating to them, which I have
made myself; and I may venture perhaps to hope that they are such as to
interest not only physiologists and medical men, but every scientific man
who desires to understand the mechanism of the perceptions of our senses.
The eyeball may be considered as a sphere, which can be turned round
its centre as a fixed pomt. Although this description is not absolutely
accurate, it is sufficiently so for our present purpose. The eyeball, indeed,
is not fixed during its motion by the solid walls of an articular excavation,
like the bone of the thigh; but, although it is surrounded at its posterior
surface only by soft cellular tissue and fat, it cannot be moved in a per-
ceptible degree forward and backward, because the volume of the cellular
tissue, included between the eyeball and the osseous walls of the orbit,
cannot be diminished or augmented by forces so feeble as the muscles of
the eye are able to exert.
In the interior of the orbit, around the eyeball six muscles are situated,
which can be employed to turn the eye round its centre. Four of them,
the so-called rect: muscles, are fastened at the hindmost point of the orbit,
and go forward to fix themselves to the front part of the eyeball, passing
over its widest circumference—or its equator, as we may call it, if we con-
sider the foremost and the hindmost points of the eyeball as its poles. These
four recti muscles are from their position severally named superior, inferior,
internal, and external. Besides these, there are two oblique muscles, the
ends of which come from the anterior margin of the orbit on the side next
the nose, and, passing outwards, are attached at that side of the eyeball
which is towards the temple—one of them, the superior oblique muscle,
being stretched over the upper side of the eyeball, the other, or inferior,
going along its under side.
These six muscles can be combined as three pairs of antagonists. The
internal and external rec¢i turn the eye round a perpendicular axis, so that
its visual line is directed either to the right side or to the left. The supe-
rior and inferior vecfi turn it round a horizontal axis, directed from the
upper end of the nose to the temple; so that the superior rectus elevates
the visual line, the inferior depresses it. Lastly, the oblique muscles turn
the eye round an axis which is directed from its centre to the occiput, so
1864. | On the Normal Motions of the Human Eye. 187
that the superior oblique muscle lowers the visual line, and the inferior raises
it; but these last two muscles not only raise and lower the visual line ;
they produce also a rotation of the eye round the visual line itself, of which
we shall have to speak more afterwards. )
A. solid body, the centre of which is fixed, and which can be turned
round three different axes of rotation, can be brought into every possible
position consistent with the immobility of its centre. Look, for instance, at
the motions of our arm, which are provided for at the shoulder-joint by the
gliding of the very accurately spherical upper extremity of the humerus in
the corresponding excavation of the scapula. When we stretch out the arm
horizontally, we can turn it, first, round a perpendicular axis, moving it
forwards and backwards; we can turn it, secondly, round a horizontal axis,
raising it and lowering it; and lastly, after having brought it by such
motions into any direction we like, we can turn it round its own longitu-
dinal axis, which goes from the shoulder to the hand; so that even when
the place of the hand in space is fixed, there are still certain different posi-
tions in which the arm can be turned.
Now let us see how far the motions of the eye can be compared to those
of our arm. We can raise and lower the visual line, we can turn it to the
left and to the right, we can bring it into every possible direction, through-
out a certain range —as far, at least, as the connexions of the eyeball permit.
So far the motions of the eye are as free as those of the arm. But when
we have chosen any determinate direction of the eye, can we turn the eye
round the visual line as an axis, as we can turn the arm round its longi-
tudinal axis?
This is a question the answer to which is connected with a curious
peculiarity of our voluntary motions. In a purely mechanical sense, we
must answer this question in the affirmative. Yes, there exist muscles
by the action of which those rotations round the visual line can be per-
formed. But when we ask, ‘“‘Can we do it by an act of our will?”’ we must
answer, “‘ No.” We can voluntarily turn the visual line into every possible
direction, but we cannot voluntarily use the muscles of our eye in such a
way as to turn it round the visual line. Whenever the direction of the
visual line is fixed, the position of our eye, as far as it depends upon our
will, is completely fixed and cannot be altered.
This law was first satisfactorily proved by Professor Donders, of Utrecht,
who, in a very ingenious way, controlled the position of the eye by those
ocular spectra which remain in the field of vision after the eye had been
fixed steadily during some time upon any brightly coloured object. I have
used for this purpose a diagram like fig. 1: the ground is grey paper, and
in the middle, along the line a 4, is placed a narrow strip of red paper on
a broader strip of green paper*. The centre of the red strip is marked
by two black points. When you look for about a minute steadily and
without moving your eye at the centre of the diagram, the image of the
* (Green is represented in the figure by white ; red by the central dark stripe.
188 Prof. Helmholtz—Normal Motions of the [April 14,
coloured strips is projected on the nervous membrane of your eye; those
parts of this membrane on which the light falls are irritated, and in con-
sequence of this irritation, their irritability is exhausted, they are fatigued
A
mm
i.
i
ma
and they become less sensitive to that kind of light by which they
were excited before. When you cease, therefore, to look at the coloured
strips, and turn your eye either to the grey ground of the diagram, or to
any other part of the field of vision which is of a uniform feeble degree of
illumination, you will see a spectrum of the coloured strips, exhibiting the
same apparent magnitude but with colours reversed, a narrow green strip
being in the middle of a broader redone. The cause of this appearance is,
that those parts of your retina which were excited formerly by green light
are less affected by the green rays contained in white or whitish light than
by rays of the complementary colour, and white light, therefore, appears
to them reddish; to those parts of the nervous membrane, on the other
hand, which had been fatigued by red light, white light afterwards appears
to be greenish. The nervous membrane of the eye in these cases behaves
nearly like the sensitive stratum in a photographic apparatus, which is
altered by light during the exposure in such a way that it is impressed
differently afterwards by various agents ; and the impression of light on
the retina may be, perhaps, of the same essential nature as the impression
made upon a photographic plate. But the impression made on the living
eye does not last so long as that on sensitive compounds of silver ; it vanishes
very soon if the light be not too strong. Light of great intensity, like
that of the sun when directly looked at, can develope very dark ocular
spectra, which last a quarter of an hour, or even longer, and disturb the
1864. ] Human Eye in relation to Binocular Vision. 189
perception of external objects very much, as is well known. One must be
very careful to avoid the use of too strong a light in these experiments,
because the nervous apparatus of the eye is easily injured by it; and the
“brightness of these coloured strips when illuminated by common day-
light is quite sufficient for our present purpose.
Now you will perceive easily that these ocular spectra are extremely well
adapted to ascertain the position of the eye-ball, because they have a fixed
connexion with certain parts of the retinaitself. Ifthe eyeball could turn
about its visual line as an axis, the ocular spectrum would apparently un-
dergo the same degree of rotation ; and hence, when we move about the eye,
and at last return to the same direction of the visual line, we can recognize
easily and accurately whether the eye has returned into the same position
as before, or whether the degree of its rotation round the visual line has
been altered. Professor Donders has proved, by using this very delicate
test, that the human eye, in tts normal state, returns always into the same
position when the visual line is brought into the same direction. The
position and direction of the eye are to be determined in this case in refer-
ence to the head of the observer; and I beg you to understand always,
when I say that the eye or its visual line is moved upwards or downwards,
that it is moved either in the direction of the forehead or in that of the
cheek ; and when I say it is moved to the left or to the right, you are to
understand the left or right side of the head. Therefore, when the head
itself is not in its common vertical position, the vertical line here under-
stood is not accordant with the line of the plummet.
Before the researches of Donders, some observers believed they had
found a difference in the relative positions of the eye, when the head was
brought into different situations. They had used either small brown spots
of the iris, or red vessels in the white of the eye, to ascertain the real
position of the eyeball; but their apparent results have been shown to be
erroneous by the much more trustworthy method of Donders.
In the first place, therefore, we may state that the position of the eye-
ball depends exclusively upon the direction of the visual line in reference
to the position of the head of the observer. But now we must ask, what
is the law regulating the position of the eye for every direction of its visual
line? In order to define this law, we must first notice that there exists a
certain direction of the visual line, which, in relation to the motions of the
eye, is distinguished from all other directions of the eye; and we may call
it the central or primary direction of the visual line. This direction is
parallel to the median vertical plane of the head ; and it is horizontal when
the head of the observer, who is standing, is kept in a convenient erect
position to look at distant points of the horizon. How this primary direc-
tion of the visual line may be determined practically with greater accuracy
we shall see afterwards. All other directions of the visual line we may
call secondary directions.
A plane which passes through the visual line of the eye, I call a meri-
190 Prof. Helmholtz—Normal Motions of the [April 14,
dian plane of the eye. Sucha plane cuts through the retina in a certain
line; and when the eye has been moved, we consider as the same meridian
plane that plane which passes through the new direction of the visual
line and the same points of the retina as before. . .
After having given these definitions, we may express the law of the
motions of the eye in the following way :—
Whenever the eye ts brought into a secondary position, that meridian
plane of the eye which goes through the primary direction of the visual
line has the same position as it has in the primary direction of the eye.
It follows from this law that the secondary position of the eye may be
found also by turning the eye from its primary position round a fixed axis
which is normal as well to the primary as to the secondary of the visual
line.
[The geometrical relations of these different positions were explained by
the lecturer by means of a moveable globe placed on an axis like the common
terrestrial globes. |
It would take too long to explain the different ways in which dif-
ferent’ observers have tried to determine the law of the motions of the
eyeball. They have employed complicated apparatus for determining the
angles by which the direction and the rotation of the eye were to be
measured. But usually two difficulties arise from the use of such instru-
ments containing graduated circles, in the centre of which the eye must be
kept steady. In the first place, it is very difficult to fix the head of the
observer so firmly that he cannot alter its position during a contmuous
series of observations, and that he reassumes exactly the same position of
the head when he returns to his measurements after a pause,—conditions
which must necessarily be fulfilled if the observations are to agree with
each other. Secondly, I have found that the eye must not be kept too
long a time in a direction which is near to the limits of the field of vision ;
else its muscles are fatigued, and the positions of the eyeball corresponding
to different directions of the visual line are somewhat altered. But if we
have to measure angles on graduated circles, it is difficult to avoid keeping
the eye too long in directions deviating far from the primary direction.
I think that it depended upon these causes, that the observations carried
out by Meissner, Fick, and Wundt agreed very ill with each other and
with the law which I have explained above, and which was first stated by
Professor Listing of Gottmgen, but without any experimental proof.
Happily it is possible, as I found out, to prove the validity of this law by
a very simple method, which is not subject to thosesources of error I have
named, and which I may be allowed to explain briefly.
In order to steady the attitude of the head in reference to the direction
of the visual line, I have taken a little wooden board, one end of which is
hollowed into a curve fitting the arch of the human teeth; the margin of
this hollow is covered with sealing-wax, into which, after it had been
‘softened by heat and had been cooled again sufficiently, I inserted both
1864..| Human Eye in relation to Binocular Vision. We).
series of my teeth, so that I kept it firmly between my jaws. The impres-
sions of the teeth remain indented in the sealing-wax ; and when I put
my teeth afterwards into these impressions, I am sure that the little board
is brought exactly into the same position, relatively to my head and my
eyes, as it was before. On the other end of that little board, which is
kept horizontally between the teeth, a vertical piece of wood is fastened,
on which I fix horizontally a little strip of card pointed at each end, so
that these two points are situated about five inches before my eyes, one
before the right eye, the other before the left. The length of the strip of
card must be equal to the distance between the centres of the eyes, which
is 68 millimetres for my own eyes. Looking now with the right eye in
the direction of the right point of that strip, and with the left eye in the
direction of the left point, I am sure to bring the eyes always into the same
position relatively to my head, so long as the position of the strip of card
on the wooden piece remains unaltered.
As a field of vision I use either a wall covered with a grey paper, in the
pattern of which horizontal and vertical lines can be easily perceived, or a
drawing-board covered with grey drawing-paper, on which a system of
horizontal and vertical lines is drawn, as in fig. 1, and coloured stripes are
fastened along the line ad.
Now the observer at first must endeavour to find out that position of
his eyes which we call the primary position. In order to do this, the ob-
server takes the wooden piece between his teeth, and brings his head into
such a position that his right eye looks to the centre of the coloured stripes,
in a direction perpendicular to the plane of the drawing. Then he brings
his head into such an attitude that the right end of the card-strip appears
in the same direction as the centre of the coloured stripe. After having
steadily looked for some time to the middle of the coloured stripe, he turns
away his gaze to the end of either the vertical or horizontal lines, ad, ed,
which are drawn through the centre of the coloured stripe. There he will
see an ocular spectrum of the coloured stripe, and will observe if it coin-
cides with the horizontal lines of the drawing. If not, he must alter the
position of the strip of card on the wooden bar to which it is fastened, till
he finds that the ocular spectrum of the coloured stripe remains horizontal
when any point either of the line ad or cd is looked at. When he has
thus found the primary direction of his visual line for the right eye, he
does the same for the left.
The ocular spectra soon vanish, but they are easily renewed by looking
again to the centre of the stripes. Care must be taken that the observer
looks always in a direction perpendicular to the plane of the drawing
whenever he looks to the centre of the coloured stripe, and that he does
not move his head. If he should have moved it, he would find it out im-
mediately when he looks back to the strip, because the point of the card-
strip would no longer cover the centre of the coloured stripe.
So you see that the primary direction of the visual line is completely
192 Prof. Helmholtz—Normal Motions of the | April 14,
fixed, and that the eye, which wants only to glance for an instant ata
peripheral point of the drawing, and then goes back again to the centre,
is not fatigued.
This method of finding the primary position of the eye proves ms the
same time that vertical and horizontal lines keep their vertical or hori-
zontal position in the field of vision when the eye is moved from its pri-
mary direction vertically or horizontally ; and you see, therefore, that
these movements agree with the law which I have enunciated. That is
to say, during vertical movements of the eye the vertical meridian plane
keeps its vertical position, and during horizontal movements the horizontal
meridian.
Now you need only bring either your own head into an inclined position,
or the diagram with the lines, and repeat the experiment, putting your
‘head at first into such a position that the centre of the diagram corre-
sponds with the primary direction of the visual line, and moving after-
wards the eye along the lines a 6 or cd, in either a parallel or perpendicular
direction to the coloured line of the diagram, and you will find the ocular
spectrum of the coloured line coinciding with those black lines which
are parallel with ad. In this way, therefore, you can easily prove the
law of Listing for every possible direction of the visual line.
I found the results of these experiments in complete agreement with
the law of Listing for my own eyes, and for those of several other persons
with normal power of vision. ‘The eyes of very short-sighted persons, on
the contrary, often show irregularities, which may be caused by the elon-
gation of the posterior part of those eyes.
These motions of our eyes are a peculiar instance of motions which,
being quite voluntary, and produced by the action of our will, are never-
theless limited as regards their extent and their combinations. We find
similar limitations of motion of the eyes in other cases also. We cannot
turn one eye up, the other down; we cannot move both eyes at the same
time to the outer angle; we are obliged to combine always a certain de-
gree of accommodation of the eyes to distance, with a certain angle of
convergence of their axes. In these latter cases it can be proved that
the faculty of producing these motions is given to our will, although our
will is commonly not capable of using this faculty. We have come by
experience to move our eyes with great dexterity and readiness, so that
we see any visible object at the same time single and as accurately as
possible; this is the only end which we have learnt to reach by muscular
exertion; but we have not learnt to bring our eyes into any given position.
In order to move them to the right, we must look to an object situated
on our right side, or imagine such an object and search for it with our
eyes. We can move them both inwards, but only when we strive to look
at the back of our nose, or at an imaginary object situated near that
place. But commonly there is no object which could be seen single by
turning one eye upwards, the other downwards, or both of them out-
1864..] Human Eye in relation to Binocular Vision. 193
wards, and we are therefore unable to bring our eyes into such positions.
But it is a well known fact, that when we look at stereoscopic pictures, and
increase the distance of the pictures by degrees, our eyes follow the motion
of the pictures, and that we are able to combine them into an apparently
single object, although our eyes are obliged to turn into diverging direc-
tions. Professor Donders, as well as myself, has found that when we
look to a distant object, and put before one of our eyes a prism of glass
the refracting angle of which is between 3 and 6 degrees, and turn the
prism at first into such a position before the eye that its angle looks to the
nose and the visual lines converge, we are able to turn the prism slowly,
so that its angle looks upwards or downwards, keeping all this time the
object apparently single at which we look. But when we take away the
prism, so that the eyes must return to their normal position before they
can see the object single, we see the object double for a short time—one
image higher than the other. The images approach after some seconds of
time and unite at last into one.
By these experiments it is proved that we can move both eyes outward,
or one up and the other down, when we use them under such conditions
that such a position is required in order that we may see the objects single
at which we are looking.
I have sometimes remarked that I saw double images of single objects,
when I was sleepy and tried to keep myself awake. Of these images one
was sometimes higher than the other, and sometimes they were crossed,
one of them being rotated round the visual line. In this state of the
brain, therefore, where our will begins to lose its power, and our muscles
are left to more involuntary and mechanical impulses, an abnormal rota-
tion of the eye round the visual line is possible. I infer also from this
observation, that the rotation of the eye round the visual axis cannot be
effected by our will, because we have not learnt by which exertion of our
will we are to effect it, and that the inability does not depend on any
anatomical structure either of our nerves or of our muscles which limits
the combination of motion. We should expect, on the contrary, that, if
such an anatomical mechanism existed, it should come out more distinctly
when the will has lost its power.
We may ask, therefore, if this peculiar manner of moving the eyes,
which is determined by the law of Listing, is produced by practical exer-
cise on account of its affording any advantages to visual perceptions. And
I believe that certain advantages are indeed connected with it.
We cannot rotate our eyes in the head, but we can rotate the head with
the eyes. When we perform such a motion, looking steadily to the same
poimt, we remark that the visible objects turn apparently a little round
the fixed point, and we lose by such a motion of our eye the perception of
the steadiness of the objects at which we look. Every position of the visual
line is connected with a determined and constant degree of rotation, accord-
VOL. XIII. Q
194 Prof. Helmholtz—Normal Motions of the [April 14,
ing to the law of Donders; and in altering this rotation we should judge
the position of external objects wrongly.
The same will take place when we change the direction of the visual line.
Suppose the amplitude of such motions to be infinitely small; then we may
consider this part of the field of vision, and the corresponding part of the
retina on which it is projected, as plane surfaces. If during any motion of
the eye the optic image is displaced so that in its new position it remains
parallel to its former position on the retina, we shall have no apparent mo-
tions of the objects. When, on the contrary, the optic image of the visible
objects is dislocated so that it is not parallel to its former position on the
retina, we must expect to perceive an apparent rotation of the objects.
As long as the motions of the eye describe infinitely small angles, the eye
can be moved in such a way that the optic image remains always parallel
to its first position. For this end the eye must be turned round axes of
rotation which are perpendicular to the visual line; and we see indeed that
this is done, according to the law of Listing, when the eye is moving near
its primary position. But it is not possible to fulfil this condition com-
pletely when the eye is moved through a wider area which comprises a
larger part of the spherical field of view. For if we were to turn the eye
always round an axis perpendicular to the visual line, it would come into
very different positions after having been turned through different ways to
the same final direction. |
The fault, therefore, which we should strive to avoid in the motions of
our eye, cannot be completely avoided, but it can be made as small as pos-
sible for the whole field of vision.
The problem, to find such a law for the motions of the eye that the
sum of all the rotations round the visual line for all possible infinitely
small motions of the eye throughout the whole field of vision becomes a
minimum, is a problem to be solved by the calculus of variations. I have
found that the solution for a circular field of vision, which corresponds
nearly to the forms of the actual field of vision, gives indeed the law of
Listing.
I conclude from these researches, that the actual mode of moving the
eye is that mode by which the perception of the steadiness of the objects
through the whole field of vision can be kept up the best; and I suppose,
therefore, that this mode of motion is produced by experience and exercise,
because it is the best suited for accurate perception of the position of ex-
ternal objects.
But in this mode of moving, rotations round the visual line are not com-
pletely avoided when the eye is moved in a circular direction round the
primary position of the visual line ; and it is easy to recognize that in such
a case we are subject to optical illusions.
Turn your eyes to a horizontal line situated in the highest part of the
field of vision, and let them follow this line from one end to the other.
1864. | Human Eye in relation to Binocular Vision. 195
The line will appear like a curved line, the convexity of which looks down-
ward. When you look to its right extremity, it seems to rise from the left
to the right ; when you look to the left extremity of the line, the left end
seems to rise. In the same way, all straight lines which go through the
peripheral parts of the field of vision appear to be curved, and to change
their position a little, if you look to their upper or their lower ends.
This explanation relates only to Monocular vision; we have to inquire
also how it influences Binocular vision. |
Each eye has its field of vision, on which the visible objects appear dis-
tributed like the objects of a picture, and the two fields with their images
seem to be superimposed. Those points of both fields of view which ap-
pear to be superimposed are called corresponding (or identical) points.
If we look at real objects, the accurate perception of the superimposition
of two different optical images is hindered by the perception of stereoscopic
form and depth; and we unite indeed, as Mr. Wheatstone has shown, two
retinal images completely into the perception of one single body, without
being able to perceive the duplicity of the images, even if there are very sen-
sible differences of their form and dimensions. To avoid this, and to find
those points of both fields of view which correspond with each other, it is
necessary to use figures which cannot easily be united into one stereoscopic
projection.
In fig. 2 you see such figures, the right of which is drawn with white
lines on a black ground, the left with black lines on a white ground. The
horizontal lines of both figures are parts of the same straight lines ; the
vertical lines are not perfectly vertical. The upper end of those of the
right figure is inclined to the right, that of the left figure to the left, by
about 11 degree.
Now I beg you to look alternately with the right and with the left eye
at these figures. You will find that the angles of the right figure appear
to the right eye equal to right angles, and those of the left figure so appear
to the left eye; but the angles of the left figure appear to the right eye to
deviate much from a right angle, as also do those of the right figure to the
left eye.
When you draw on paper a horizontal line, and another line crossing it
exactly at right angles, the right superior angle will appear to your right eye
too great, to your left eye too small; the other angles show corresponding
deviations. To have an apparently right angle, you must make the vertical
line incline by an angle of about 11 degree for it to appear really vertical ;
and we must distinguish, therefore, the really vertical lines and the appa-
rently vertical lines in our field of view.
There are several other illusions of the same kind, which I omit because
they alter the images of both eyes in the same manner and have no ‘influs
ence upon binocular vision ; for example, vertical lines appear always of
greater length than horizontal lines having really the same length.
Q 2
196 Prof. Helmholtz—Normal Motions of the [April 14,
Now combine the two sides of fig. 2 into a stereoscopic combination,
either by squinting, or with the help of a stereoscope, and you will see that
the white lines of the one coincide exactly with the black lines of the other,
as soon as the centres of both the figures coincide, although the vertical
lines of the two figures are not parallel to each other.
man
Therefore not the really vertical meridians of both fields of view corre-
spond, as has been supposed hitherto, but the apparently vertical meridians.
On the contrary, the horizontal meridians really correspond, at least for
normal eyes which are not fatigued. After having kept the eyes a long
1864.] Human Eye in relation to Binocular Vision. 197
time looking down at a near object, as in reading or writing, I found some-
times that the horizontal lines of fig. 2 crossed each other; but they be-
came parallel again when I had looked for some time at distant objects.
In order to define the position of the corresponding points in both fields
of vision, let us suppose the observer looking to the centres of the two sides
of fig. 2, and uniting both pictures stereoscopically. Then planes may be
laid through the horizontal and vertical lines of each picture and the
centre of the corresponding eye. The planes laid through the dif-
ferent horizontal lines will include angles between them, which we may call
angles of altitude ; and we may consider as their zero the plane going
through the fixed point and the horizontal meridian. The planes going
through the vertical lines include other angles, which may bé called angles
of longitude, their zero coinciding also with the fixed point and with the
apparently vertical meridian. Then the stereoscopic combination of those
diagrams shows that those points correspond which have the same angles
of altitude and the same angles of longitude; and we can use this result
of the experiment as a definition of corresponding points.
We are accustomed to call Horopter the aggregate of all those points of
the space which are projected on corresponding points of the retine.
After having settled how to define the position of corresponding points, the
question, what is the form and situation of the Horopter, is only a geome-
trical question. With reference to the results I had obtained in regard
to the positions of the eye belonging to different directions of the visual
lines, I have calculated the form of the Horopter, and found that gene-
rally the Horopter is a line of double curvature produced by the inter-
section of two hyperboloids, and that in some exceptional cases this line of
double curvature can be changed into a combination of two plane curves.
That is to say, when the point of convergence is situated in the middle
plane of the head, the Horopter is composed of a straight line drawn
through the point of convergence, and of a conic section going through
the centre of both eyes and intersecting the straight line.
When the point of convergence is situated in the plane which contains
the primary directions of both the visual lines, the Horopter is a circle
going through that point and through the centres of both eyes and a
straight line intersecting the circle.
When the point of convergence is situated as well in the middle plane of
the head as in the plane of the primary directions of the visual lines, the
Horopter is composed of the circle I have just described, and a straight
line going through that point.
There is only one case in which the Horopter is really a plane, as it was
supposed to be in every instance by Aguilonius, the inventor of that name,—
namely, when the point of convergence is situated in the middle plane of
the head and at an infinite distance. Then the Horopter is a plane
parallel to the visual lines, and situated beneath them, at a certain distance
which depends upon the angle between the really and apparently vertical
198 On the Normal Motions of the Human Eye, [April 14,
‘meridians, and which is nearly as great as the distance of the feet of
the observer from his eyes when he is standing. Therefore, when we look
straight forward to a point of the horizon, the Horopter is a horizontal plane
going through our feet—it is the ground upon which we are standing.
_ Formerly physiologists believed that the Horopter was an infinitely
distant plane when we looked to an infinitely distant point. The differ-
ence of our present conclusion is consequent upon the difference between
the position of the really and apparently vertical meridians, which they did
not know.
When we look, not to an infinitely distant horizon, but to any point of
the ground upon which we stand which is equally distant from both our
eyes, the Horepter is not a plane; but the straight line which is one of its
parts coincides completely with the horizontal plane upon which we are
standing.
The form and situation of the Horopter is of great practical importance
for the accuracy of our visual perceptions, as I have found.
Take a straight wire—a knitting-needle for instance—and bend it a little
in its middle, so that its two halves form an angle of about four degrees.
Hold this wire with outstretched arm in a nearly perpendicular position
before you, so that both its halves are situated in the middle plane of your
head, and the wire appears to both your eyes nearly as a straight line.
In this position of the wire you can distinguish whether the angle of the
wire is turned towards your face or away from it, by binocular vision only,
as in stereoscopic diagrams; and you will find that there is one direction
of the wire in which it coincides with the straight line of the Horopter,
where the inflexion of the wire is more evident than in other positions.
You can test if the wire really coincides with the Horopter, when you look
ata point a little more or a little less distant than the wire. Then the wire
appears in double images, which are parallel when it is situated in the
Horopter line, and are not when the point is not so situated.
Stick three long straight pins into two little wooden boards which can slide
one along the other; two pins may be fastened in one of the boards, the third
pin in the second. . Bring the boards into such a position that the pins are
all perpendicular and parallel to each other, and situated nearly in the
same plane. Hold therm before your eyes and look at them, and strive to
recognize if they are really in the same plane, or if their series is bent
towards you or from you. You will find that you distinguish this by
binocular vision with the greatest degree of certainty and accuracy (and
indeed with an astonishing degree of accuracy) when the line of the three
pins coincides with the direction of the circle which is a part of the
Horopter.
From these observations it follows that the forms and the distances of
those objects which are situated in, or very nearly in, the Horopter, are
perceived with a greater degree of accuracy than the same forms and
distances would be when not situated in the Horopter. If we apply this
1864] Prof. H. T. 8S. Smith on Quadratic Forms. 199
result to those cases in which the ground whereon we stand is the plane of
the Horopter, it follows that, looking straight forward to the horizon we
can distinguish the inequalities and the distances of different parts of the
ground better than other objects of the same kind and distance.
This is actually true. We can observe it very conspicuously when we
look to a plain and open country with very distant hills, at first in the
natural position, and afterwards with the head inclined or inverted, looking
under the arm or between our legs, as painters sometimes do in order
to distinguish the colours of the landscape better. Comparing the aspect
of the distant parts of the ground, you will find that we perceive very
well that they are level and stretched out into a great distance in the
natural position of your head, but that they seem to ascend to the horizon
and to be much shorter and narrower when we look at them with the head
inverted: we get the same appearance also when our head remains in its
natural position, and we look to the distant objects through two rectangular
prisms, the hypothenuses of which are fastened on a horizontal piece of
wood, and which show inverted images of the objects. But when we invert
our head, and invert at the same time also the landscape by the prisms, we
have again the natural view and the accurate perception of distances as in
the natural position of our head, because then the apparent situation of
the ground is again the plane of the Horopter of our eyes.
The alteration of colour in the distant parts of a landscape when viewed
with inverted head, or in an inverted optical image, can be explained, I
think, by the defective perception of distance. The alterations of the
colour of really distant objects produced by the opacity of the air, are well
known to us, and appear as a natural sign of distance; but if the same
alterations are found on objects apparently less distant, the alteration of
colour appears unusual, and is more easily perceived.
It is evident that this very accurate perception of the form and the
distances of the ground, even when viewed indirectly, is a great advantage,
because by means of this arrangement of our eyes we are able to look at
distant objects, without turning our eyes to the ground, when we walk.
April 21, 1864.
Major-General’ SABINE, President, in the Chair.
The following communications were read :—
I. “On the Orders and Genera of Quadratic Forms containing
more than three Indeterminates.” By H.T.SrepHen Smiru,
M.A., F.R.S., Savilian Professor of Geometry in the University
of Oxford. Received March 22, 1864.
Let us represent by 7, a homogeneous form or quantic of any order
containing indeterminates ; by (a), a square matrix of order x; by
200 Prof, H. T. S. Smith on Quadratic Forms [April 21,
n
(a¢ ), its ith derived matrix, 7. e. the matrix of order _ ee the con-
le |jz—2
stituents of which are the minor determinants of order z of the matrix
(a); and lastly, by /;, a form of any order containing I indeterminates,
the coefficients of which depend on the coefficients of f. When f, is
transformed by (a), let /; be transformed by (2) ; if, after division or
multiplication by a power of the modulus of transformation, the meta-
morphic of f; depends on the metamorphic of 7, in the same way in
which f; depends on f,, f; is said to be a concomitant of the 7th species
of f,. Thus: a concomitant of the Ist species is a covariant; a con-
comitant of the (n—1)th species is a contravariant ; if m=2 there are
only covariants ; if x=3 there are only covariants and contravariants ;
but if 2>3, there will exist in general concomitants of the intermediate
species.
There is an obvious difference between covariants and contravariants on
the one hand, and the intermediate concomitants on the other. The
number of indeterminates in a covariant or contravariant is the same as in
its primitive ; in an intermediate concomitant, the number of indeterminates
is always greater than in its primitive. Again, to every metamorphic of a
covariant or contravariant, there corresponds a metamorphic of its primi-
tive ; whereas, in the case of a concomitant of the intermediate order 7, a
metamorphic of the primitive will correspond, not to every metamorphic
of the concomitant, but only to such metamorphics as result from trans-
formations the matrices of which are the zth derived matrices of matrices
of order x.
It is also obvious that, besides the 2»—1 species of concomitance here
defined, there are, when is >3, an infinite number of other species of
concomitance of the same general nature. For from any derived matrix
we may form another derived matrix, and so on continually; and to
every such process of derivation a distinct species of concomitance will
correspond.
The notion of intermediate concomitance appears likely to be of use in
many researches; in what follows, it is employed to obtain a definition of
the ordinal and generic characters of quadratic forms contaiming more than
3 indeterminates. (The case of quadratic forms containing 3 indeterminates
has been considered by Eisenstein in his memoir, ‘‘ Neue Theoreme des
hoheren Arithmetik,” Crelle, vol. xxxv. pp. 12} and 125.) Let
pH=ng=n
f= B= SLA &
‘e
pelg=l Pg? 4
represent a quadratic form of m indeterminates; let (A) be the sym-
metrical matrix of this form, and (A) the zth derived matrix of (A) ;
(A®) will also be a symmetrical matrix, and the quadratic form
ge — ¢
fi Se BAO .% Kin tao cele
will be a concomitant of the ith species of 7. It is immaterial what
1864.] containing more than Three Indeterminates. 201
principle of arrangement is adopted in writing the quadratic matrix (A),
and the transforming matrix (2); provided only that the arrangement
be the same in the two matrices, and that in each matrix it be the same in
height and in depth.
For example, if f.=a, 27+ a, 23+ a, 02 + a,x, + 26, v,2,+ 26, 2, 234+
26, 2,27,+26,7,27,+26,x, 2,+26, x, x, be a quadratic form containing four
indeterminates, the form f, =
(;—4, a,) xt + (65-4, a;) xX 5 (65 —4, a,) XS
+ (62—a, a,) X32 + (b3—a, a,) X3 + (62—a, a,) XB
+2(4, b,—4a, b,) Xx, X, a 2(6, Go ay ey) X, X,
—2(6, 6,—4, 6.) X, X, ae 2(0, 6; ite 6) X, X;
ad 6,—6, b,) X, X, a 2(4, 6,—4, 7) X, X,
+2(6, Oa, b,) X, X, me 2(d, O52 O% b,) X, X,
— 2(6,6,—a, 6,) X, X, — 2(6, 6,—6, 6;) X, X,
as 2(0, 6;—4%, 6,) X, X, a 2(6, b,—4a, 2) X, X,
+2(6,6,—a, 6,) X,X, — 2(6,6,—a, 6,) X, X,
+2(6; 6,—4,5,) X, X,
is the concomitant of the second species of /.
The n—1 forms defined by the formula (A), of which the first is the
form /, itself, and the last the contravariant of f,, we shall term the funda-
mental concomitants of f,; in contradistinction to those other quadratic
concomitants (infinite in number) of which the matrices are the symme-
trical matrices that may be derived, by a multiplicate derivation, from
(AM)... . Passing to the arithmetical theory of quadratic forms—z. e.
supposing that the constituents of (A“) are integral numbers, we shall
designate by V,, V»--+ Vn the greatest common divisors (taken posi-
tively) of the minors of different orders of the matrix (A“)), so that, in
particular, v, is the greatest common divisor of its constituents, and VY» is
the absolute value of its determinant, here supposed to be different from
zero. By the primary divisor of a quadratic form we shall understand the
greatest common divisor of the coefficients of the squares and double rect-
angles in the quadratic form ; by the secondary divisor we shall understand
the greatest common divisor of the coefficients of the squares and of the
rectangles ; so that the primary divisor is equal to, or is half of, the
secondary divisor, according as the quadratic form (to use the phraseology
of Gauss) is derived from a form properly or improperly primitive. It
will be seen that V,, VY.» -- +» Va—1 are the primary divisors of the forms
uiese= Als pai Tespectively.
We now consider the totality of arithmetical quadratic forms, contain-
ing 7 indeterminates, and having a given index of inertia, and a given de-
terminant.
If a quadratic form be reduced to a sum of squares by any linear trans-
formation, the number of positive and of negative squares is the same,
202 Prof. H.T.S. Smith on Quadratic Forms _— [April 21,
whatever be the real transformation by which the reduction is effected.
For the index of inertia we may take the number of the positive squares ;
it is equal to the number of continuations of sign in a series of ascending
principal minors of the matrix of the quadratic form, the series com-
mencing with unity, 7. e. with a minor of order 0, and each minor being
so taken as to contain that which precedes it in the series (see Professor
Sylvester “On Formule connected with Sturm’s Theorem,” Phil. Trans.
vol. exliii. p. 481). The distribution of these forms into Orders depends
on the following principle :—
«Two forms belong to the same order when the primary and secondary
divisors of their corresponding concomitants are identical.” -
Since, as has been just pointed out, there are, beside the fundamental
concomitants, an infinite number of other concomitants, it is important to
know whether, in order to obtain the distribution into orders, it is, or is
not, necessary to consider those other concomitants. With regard to the
primary divisors, it can be shown that it is unnecessary to consider any
concomitants other than the fundamental ones; 7. e. it can be shown that
the equality of the primary divisors of the corresponding fundamental
concomitants of two quadratic forms, implies the equality of the primary
divisors of all their corresponding concomitants. And it is probable (but
it seems difficult to prove) that the same thing is true for the secondary
divisors also.
Confining our attention (in the next place) to the forms corte in
any given order, we proceed to indicate the principle from which the sub-
division of that order into genera is deducible.
If F, be any quadratic form containing 7 indeterminates, and F, be its
piconet of the second species, we have the identical equation
E— 7
d¥,
Fi (@ys Uap 6 0 Br )X EY y Yo» - -y)-4|2 y" a |
Hh ile ieee 4 k=1 | oe a
Y» Yor 22 e Y, J
in which the symbol F, On oe .) indicates that the deter-
Yi» Ya vita Yr
Uy Voy 0 0 0y Up
minants ( ) are to be taken for the indeterminates of
19 99 © 8 99 ra
F,, the order in which they are taken being the same as the order
in which the determinants of any two horizontal rows of the matrix
of F, are taken in forming the matrix of F,. Let i= — J, for every
value of z from 1 to n—1; it will be found that, if we form the concomi-
tant of the second species of 6, its primary divisor is the quotient
Viti. Vi
Vivre wed
vol. cli, p. 317) is always an integral number. Let 6; be any uneven
, which, as has been shown elsewhere (see Phil. Trans.
1864. | containing more than Three Indeterminates, 203
prime dividing = = we infer from the identity (B) that the
i s—1
numbers prime to 6;, which can be represented by 0,, are either all qua-
dratic residues of 3s’, or all non-quadratic residues of 6;. In the former
case we attribute to f, the particular character (= +1; in the latter
the particular character (5)=-1. If v,=1, i.e. if the form f, itself
do not admit of any primary divisor beside unity (which igs the only
important case), the product (Pe + Bent) x (Want Yams) Nee
Vn-1 Vn-2 Vn-2 Va-3
“.; whence, inasmuch as every prime that divides V, also
n—1
is equal to
divides —“” , it appears that a primitive quadratic form will always have
n=
one particular character, at least with respect to every uneven prime
dividing its determinant, and will have more than one if the uneven
Vit+1 3 Was
Wie Sei
The subdivision of an order into genera can now be effected by assign-
ing to the same genus all those forms whose particular characters co-
incide. But it remains to consider whether the above enumeration of par-
ticular characters is complete. It is evident that we might apply the
theorem (B) to other concomitants besides those included in the funda-
mental system ; and it might appear as if in this manner we could obtain
other particular characters besides those which we have given. But it can
be shown that such other particular characters are implicitly contained in
ours; 7.e. it can be shown that two quadratic forms, which coincide in
respect of the particular characters deducible from their fundamental con-
comitants, will also coincide in respect of the particular characters dedu-
cible from any other concomitant. Again, it will be found that if the
determinant be uneven, there are no particular characters with respect to
4 or 8. For this case, therefore, our enumeraticn is complete. But
when the determinant is even, besides the particular characters arising from
its uneven prime divisors, there may also be particular characters with
regard to 4 or 8. There ig no difficulty in enumerating these particular
characters; nevertheless we suppress the enumeration here, not only
because it would require a detailed distinction of cases, but also because
there appears to be some difficulty in showing that the characters with
regard to 4 or 8, which may arise from the excluded concomitants, are
virtually included in those which arise from the concomitants of the fun-
damental set.
prime divide more than one of the quotients ~~
204 Mr. Abel on the Combustion of [April 21,
IL. “On some Phenomena exhibited by Gun-cotton and Gunpowder
under special conditions of Exposure to Heat.” By F. A. Asst,
F.R.S. Received March 29, 1864.
The experiments upon which I have been engaged for some time past, in
connexion with the manufacture and properties of gun-cotton, have brought
under my notice some interesting points in the behaviour of both gun-
cotton and gunpowder, when exposed to high temperatures, under parti-
cular conditions. I believe that these phenomena have not been previously
observed, at any rate to their full extent, and I therefore venture to lay
before the Royal Society a brief account of them.
Being anxious to possess some rapid method of testing the uniformity
of products obtained by carrying out General von Lenk’s system of manu-
facture of gun-cotton, I instituted experiments for the purpose of ascer-
taining whether, by igniting equal weights of gun-cotton of the same com-
position, by voltaic agency, within a partially exhausted vessel connected
with a barometric tube, I could rely upon obtaining a uniform depression
of the mercurial column, in different experiments made in atmospheres of
uniform rarefaction, and whether slight differences in the composition of
the gun-cotton would be indicated, with sufficient accuracy, by a corre-
sponding difference in the volume of gas disengaged, or in the depression
of the mercury. I found that, provided the mechanical condition of the
gun-cotton, and its position with reference to the source of -heat, were in
all instances the same, the indications furnished by these experiments were
sufficiently accurate for practical purposes. Each experiment was made
with fifteen grains of gun-cotton, which were wrapped compactly round the
platinum wire; the apparatus was exhausted until the column of mercury
was raised to a height varying from 29 inches to 29°5 inches. The flash
which accompanied the deflagration of the gun-cotton was apparently
similar to that observed upon its ignition in open air; but it was noticed
that an interval of time always occurred between the first application of
heat (or incandescence of the wire) and the flashing of the gun-cotton, and
that during this interval there was a very perceptible fall of the column of
mercury. On several occasions, when the gun-cotton, in the form of
“roving,” or loosely twisted strand, was only laid over the wire, so that it
hung down on either side, the red-hot wire simply cut it into two pieces,
which fell to the bottom of the exhausted vessel, without continuing to
burn. As these results appeared to indicate that the effects of heat upon
gun-cotton, in a highly rarefied atmosphere, differed importantly from
those observed under ordinary circumstances, or in a very imperfect va-
cuum, a series of experiments, under variously modified conditions, was
instituted, of which the following are the most important.
It was found in numerous experiments, made with proportions of gun-
cotton varying from one to two grains, in the form of a loose twist laid
double, that in highly rarefied atmospheres (the pressure being varied
1864. ] Gun-cotton and Gunpowder. 205
from | to 8 in inches of mercury) the gun-cotton, when ignited by means
of the platinum wire, burned very slowly, presenting by daylight an appear-
ance as if it smouldered, with little or no flame attending the combustion.
I was at first led by these results to conjecture that this peculiar kind of
combustion of the gun-cotton was determined solely by its ignition in
atmospheres rarefied beyond a certain limit; and I was induced, in con-
sequence, to institute a number of experiments with the view of ascertain-
ing what was the most highly rarefied atmosphere in which gun-cotton
would burn as in the open air—with a flash, accompanied by a body of
bright flame. In order to ensure uniformity in the degree of heat applied
to the cotton in these experiments, the platinum wire employed was suffi-
ciently thin to be instantaneously melted on the passage of the voltaic
current. About fifty different experiments were made with equal quanti-
ties of gun-cotton (0°2 grain), placed always in the same position, so that
the platinum wire rested upon the material. A tolerabiy definite limit of
the degree of rarefaction was arrived at, within which the gun-cotton was
exploded instantaneously, as in the open air. When the pressure of air
in the apparatus was reduced to 8-2 in inches of mercury, the gun-cotton
still exploded with a flash, but not quite instantaneously ; on reducing the
pressure to 8 inches, the cotton underwent the slow kind of combustion in
the majority of cases; on a few occasions it exploded with a flash of flame.
The same occurred in a succession of experiments, until the pressure was
reduced gradually to 7*7 inches, when instances of the rapid explosion of
gun-cotton were no longer obtained.
Although these results were moderately definite when the conditions of
the experiments were as nearly as possible uniform, it was found that they
could be altered by slight modifications of any one particular condition
(such as the quantity of gun-cotton, its mechanical condition, its position
with reference to the source of heat, the quantity of heat applied, and the
duration of its application). In illustration of this, the following results
may be quoted.
If the gun-cotton was wrapped round, instead of being simply placed
across the wire, its instantaneous combustion was effected in atmospheres
considerably more rarefied than with the above experiments.
In employing a small piece of gun-cotton (0°3 of an inch long and
weighing 0°3 to 0°4 of a grain) loosely twisted, laid across the wire, or
upon a support immediately beneath the latter so that the wire rested
upon it, the slow combustion established in it by the heated wire, under
greatly diminished atmospheric pressure (amounting to 0°6 inch in this and
the following experiments), proceeded uniformly towards each end of the
piece of twist, until the whole was transformed into gas. But if a piece
of the same twist, of considerably greater length (say 4 inches long and
weighing about 2 grains), was exposed to heat in an atmosphere of the
same rarefaction, the gun-cotton being laid over the wire and hanging,
down on either side, it was cut through by the passage of the current, and
206 Mr. Abel on the Combustion of [April 22,
the two pieces, falling to the bottom of the vessel, ceased to burn almost
immediately. Of a piece of gun-cotton weighing 2°17 grains, there re-
mained unchanged 1°80 gr.; the quantity burned amounted therefore to
0-37 gr., and corresponded closely to the quantity which was completely
burned in the preceding experiments. (The depression of the mercurial
column in this experiment, by the gases generated from the gun-cotton,
amounted to 0-2 inch.)
A piece of the twist, 13-inch long, was placed across the wire, and
supported by a plate of plaster of Paris, fixed immediately beneath it. The
current was established to an extent just sufficient to heat the wire to the
point of ignition of the gun-cotton, and then interrupted. The twist
burned slowly in both directions until about a quarter of an inch was con-
sumed on either side of the wire, when the combustion ceased. The
same result was obtained in repetitions of the experiment, the wire being at
once raised to a red heat, and thus maintained until the gun-cotton ceased
to burn. But upon increasing the battery-power, doubling the thickness
of the wire, and maintaining the heat, while a similar piece of twist was
burning in both directions, the slow combustion continued until the entire
quantity was transformed into gas. The same result was obtained by re-
peating this experiment with similar and larger quantities of gun-cotton,
placed in the same position as before with reference to the wire.
In the next experiment, the mass of cotton exposed at one time to heat
was increased by doubling a piece of the twist (4 inches long) and laying
it thus doubled across the wire, as before. The current was allowed to
pass until the wire was heated just sufficiently to ignite the gun-cotton,
and then interrupted. In this case the slow combustion proceeded through-
out the entire mass of the cotton. The permanent depression of mercury in
this experiment was 0°6 inch. It was particularly noticed on this occasion,
that, as the decomposition of the gun-cotton crept slowly along the mass,
the burning portions or extremities of twist were surrounded by a beautiful
green light, more like a phosphorescence than a flame, and in form some-
thing similar to the brush of an electric discharge.
Eight inches of the twist were laid fourfold over the wire, which was
heated just sufficiently to ignite the cotton. The decomposition proceeded,
as before, gradually throughout the mass of the gun-cotton, but became
somewhat more rapid towards the end, when the green glow, observed at
first, was superseded by a pale yellowish lambent flame, very different in
appearance from the flame which accompanies the combustion of gun-cot-
ton under ordinary conditions. The permanent depression of the column
of mercury in this experiment was 1°2 inch.
The various modifications in the nature and extent of combustion which
gun-cotton may be made to undergo, as demonstrated by the above experi-
ments, when exposed to heat in highly rarefied atmospheres under variously
modified conditions, are evidently due to the same causes which affect the
rate of combustion of fuses under different atmospheric pressures, and which
1864. ] Gun-cotion and Gunpowder. ; 207
have already been pointed out by Frankland in his interesting paper on the
- influence of atmospheric pressure upon some of the phenomena of combus-
tion. The heat furnished by an incandescent or melting platinum wire is
greatly in excess of that required to induce perfect combustion in gun-
cotton which is actually in contact with, or in close ‘proximity to it; and the
heat resulting from this combustion, which is contained in the products of
the change, will suffice to cause the transformation of the explosion to pro-
ceed from particle to particle. But if the pressure of the atmosphere in
which the gun-cotton is submitted to the action of heat be reduced, the
gases resulting from the combustion of the particles nearest to the source of
heat will have a tendency, proportionate to the degree of rarefaction of the
air, to pass away into space, and thus to convey away from proximity to the
cotton, more or less rapidly and completely, the heat necessary to carry on
the combustion established in the first particles. Thus, when the heated
wire is enveloped in a considerable body of gun-cotton, the ignition of the
entire mass is apparently not instantaneous, if attempted in a highly rarefied
atmosphere, because the products of the combustion first established in the
centre of the mass of gun-cotton escape rapidly into space, conveying away
from the point of combustion the heat essential for its full maintenance ;
the gun-cotton therefore undergoes at first an imperfect form of combus-
tion, or a kind of metamorphosis different from the normal result of the
action ef heat upon this material. But the effects of the gradual generation
of heated gases from the interior of the mass of cotton are, to impart some
of their heat to the material through which they have to escape, as well as
gradually to increase the pressure of the atmosphere in the vessel, and thus
to diminish the rapidity of their escape; hence a condition of things is in
time arrived at when the remainder of the gun-cotton undergoes the ordi-
nary metamorphosis, a result which is accelerated by maintaining the
original source of heat. If, however, the gun-cotton ke employed in a
compact form (in the form of twist or thread), and placed only in contact
with the source of heat at one point, the heat will be so effectually conveyed
away by the escaping gases, that the material will undergo even what may
be termed the secondary combustion or metamorphosis for a limited pe-
riod only ; so that, if a sufficient length of gun-cotton be employed, it will
after a short time cease to burn, even imperfectly, because the heat essen-
tial for the maintenance of any chemical activity is soon completely abs-
tracted by the escaping gases. These results may obviously be modified in
various ways, as shown in the experiments described : thus, by increasing
and maintaining the source of heat independent of the burning cotton, the
slow combustion may be maintained through a much greater length of the
material until the pressure of the atmosphere is increased, by the products
disengaged, to an extent sufficient to admit of a more rapid and perfect
metamorphosis being established in the remainder of the material ; or the
same result may be attained, independently of the continued application of
external heat, by employing a thicker mass of cotton, or by using the
208 Mr. Abel on the Combustion of [April 21,
material in a less compact form. In these cases the maintenance of the
chemical change is favoured either by radiation of heat to the cotton, and
provision of additional heat, from an external source, to the gases as they
escape and expand, or by establishing the change in a greater mass of the
material, and thus reducing the rapidity with which the heat will be con-
veyed away by the escaping gases, or, finally, by allowing the gases, as they
escape, to pass to some extent between the fibres of the cotton, and thus
favouring the transmission of heat to individual particles of the material.
In the description of the two experiments last referred to above, I have
stated that some peculiar phenomena were observed to attend the imperfect
kind of combustion induced in the gun-cotton in rarefied atmospheres.
In order to examine these phenomena more closely, I instituted a series of
experiments, in a darkened room, with equal quantities of gun-cotton (4
inch of twist=0°3 gr.) placed always in the same position, across the
platinum wire, the only varying element in the experiment being the
pressure of the atmosphere in the vessel, which was gradually increased.
The following were the results observed :—
Experiment 1.—Pressure=0°62 inch. The wire was heated just suffi-
ciently to ignite the material; the current was then interrupted. The
gun-cotton burned very slowly in both directions, emitting only the small
green phosphorescent flame, or brush, already described.
Exp. I1.—Pressure=1 inch. In addition to the green glow whieh sur-
rounded the burning ends, a very faint yellowish flame was observed hover-
ing over the gun-cotton.
Exp. WiI.—Pressure=1*5inch. The cotton burned a little faster, and
the faint yellowish flame was of a more decided character ; indeed two sepa-
rate flames were observed, each following up the green light as the cotton
burned in the two directions.
Exp. 1V.—Pressure=2 inches. The results were the same as in the
preceding experiment, excepting that the yellowish flames became more
marked.
Exp. V.—Pressure=2°5 inches. The same phenomena, the cotton
burning considerably faster.
Exp. V\1.—Pressure=3 inches. ‘The same phenomena, the yellow flames
increasing in size.
Exp. Vil.—Pressure=4 inches. The rapidity of combustion of the
cotton increased again considerably ; the other phenomena observed were as
before.
Exp. VIII.—Pressure=6 inches. The pale yellow fiame had increased
in size considerably, no longer forming a tongue, as in the preceding experi-
ments, but completely enveloping the burning ends of the gun-cotton.
The green glow, though much reduced, was still observed immediately
round the burning surfaces. |
Exp. 1X.—Pressure=8 inches. The green glow was only just percep-
tible in this instance, and the cotton burned very rapidly, almost with the
1864.] Gun-cotton and Gunpowder. 209
ordinary flash ; but the flame was still of a pale yellow. In the preceding
experiments clouds of white vapour were observed after the decomposition
of the gun-cotton; in this and the following experiments this white vapour
was produced in much smaller proportion. |
Expts. X. to XV. inclusive.— Pressure=10, 12, 14, 18, 20, 24 inches.
The phenomena observed in these experiments did not differ in any im-
portant degree from those of Experiment IX.
Exp. XVI.—The same pressure (24 inches) was employed as in the last
experiment, but the piece of gun-cotton-twist was laid double across the
wire. In this instance the gun-cotton burned with a bright yellow flash,
as In open air.
Hap. XVI1.—Pressure=26 inches. The gun-cotton was laid singly
over the wire, as in all experiments but the last. It burned with a flash o
bright light, as in open air.
It appears from these experiments that gun-cotton, when ignited in small
quantities in rarefied atmospheres, may exhibit, during its combustion, three
distinct luminous phenomena. In the most highly rarefied atmospheres, the
only indication of combustion is a beautiful green glow or phosphorescence
which surrounds the extremity of the gun-cotton as it is slowly transformed
into gases or vapours. When the pressure of the atmosphere is increased to
one inch (with the proportion of gun-cotton indicated), a faint yellow flame
appears at a short distance from the point of decomposition ; and as the
pressure is increased this pale yellow flame increases in size, and eventually
appears quite to obliterate the green light. Lastly, when the pressure of
the atmosphere and consequently proportion of the oxygen in the con-
fined space is considerable, the cotton burns with the ordinary bright yellow
flame. There can be no doubt that this final result is due to the almost in-
stantaneous secondary combustion, in the air supplied, of the inflammable
gases evolved by the explosion of the gun-cotton. It was thought that the
pale yellow flame described might also be due to a combustion (in the air
still contained in the vessel) of portions of the gases resulting from the de-
composition of the gun-cotton ; but a series of experiments, in which
nitrogen, instead of air, constituted the rarefied atmosphere, showed that
this could not be the case. The results obtained in these experiments cor-
responded closely to those above described, as far as relates to the produc-
tion of the green glow and of the pale yellow flame. With rarefied atmo-
_ spheres of nitrogen ranging down to one inch of pressure, the green flame
was alone obtained; and the pale yellow flame, accompanying the green,
became very marked at a pressure of 3 inches, as in the experiments with
air.
It would seem probable from these results, that the mixture of gaseous
products obtained by the peculiar charge which heat effects in gun-cotton
in highly rarefied atmospheres, contains not only combustible bodies, such
as carbonic oxide, but also a small proportion of oxidizing gas (possibly
protoxide of nitrogen, or even oxygen), and that when the pressure of the
VOL, XIII. e R
210 Mr. Abel on the Combustion of [April 21,
atmosphere is sufficiently great this mixture, which has. self-combustible
properties, retains sufficient heat as it escapes, to burn, more or less com-
pletely, according to the degree of rarefaction of the atmosphere.
A series of experiments instituted with gun-cotton in highly rarefied
atmospheres of oxygen, showed that the additional proportion of this gas
thus introduced into the apparatus, beyond that which would have been
contained in it with the employment of air of the same rarefaction, affected
in a very important manner the behaviour of the explosion under the in-
fluence of heat. If eight or ten grains of gun-cotton are placed round the
platinum wire, and the pressure of the atmosphere of oxygen in the vessel
be reduced to four or three (in inches of mercury), the cotton explodes in-
stantaneously, with an intensely bright flash, when the wire is heated. In
a series of experiments made under gradually diminished pressures, oxygen
being used instead of air, it was found that the gun-cotton exploded instan-
taneously, with a bright flash, until the pressure was reduced to 1:2 inch ;
from this pressure to that of 0°8 inch it still burned with a flash, but not
instantaneously ; and at pressures below 0°8 inch it no longer burned with
a bright flash, but exhibited the comparatively slow combustion, accom-
panied by the pale yellow flame, which has been spoken of as observed
when gun-cotton was ignited in air rarefied to pressures ranging from ] inch
to 24 inches.
The interesting phenomena exhibited by gun-cotton in highly rarefied
atmospheres, induced me to make some experiments of a corresponding
nature with gunpowder. The same apparatus was used as in the preceding
experiments, but a small glass cup was fixed immediately beneath the
platinum wire, so that, by bending the latter in the centre, it was made to
dip into the cup, and could be covered by grains of gunpowder.
Two grains’ weight of small grain gunpowder were heaped over the wire,
and the pressure of air in the apparatus was reduced to 0°65 inch. The
wire being heated to redness, three or four grains, in immediate proximity
to it, fused in a short time and appeared to boil, evolving yellowish vapours,
no doubt of sulphur. After the heat had been continued for eight or ten
seconds, those particular graims deflagrated, and the remainder of the
powder was scattered by the slight explosion, without being ignited. No
appreciable depression of the mercurial column occurred during the evolu-
tion of the yellowish vapours ; the permanent depression, after the defla-
gration, was only 0°15 inch.
The experiment was repeated with small-grain gunpowder, amounting to
four grains, and the same phenomena were observed, with this difference,
that a second slight deflagration followed shortly after the first, probably in
consequence of a grain or two of the powder falling back into the cup.
A single piece of gunpowder, weighing 14 grains, so shaped as to remain
in good contact with the wire, was placed over the latter, being supported
by the cup. The pressure of air in the apparatus was, as before, equal to
0°65 inch of mercury. There was no perceptible effect for a short time
1864. | Gun-cotton and Gunpowder. 211
after the wire was first heated to redness; vapours of sulphur were then
given off, and slight scintillations were occasionally observed ; after a time
the wire became deeply buried in the superincumbent mass of gunpowder,
which fused, and appeared to boil, where it was in actual contact with the
source of heat. After the lapse of three minutes from the commencement
of the experiment, the powder deflagrated. ‘The permanent depression of
the mercury column amounted to 1°35 inch.
The experiment was repeated with a similar piece of powder, weighing
16 grains ; the same phenomena were observed; and five minutes elapsed
between the first heating of the wire and the deflagration of the powder.
The experiments were continued with fine-grained gunpowder, and under
pressures gradually increased, in successive experiments, from ‘07 to 3 in
inches of mercury. The same weight of gunpowder (4 grains) was used in
all the experiments. In those made under a pressure of 1 inch, the results
observed were similar to those obtained in the first experiments ; single
grains of gunpowder were successively deflagrated, burning very slowly,
and scattering but never igniting contiguous grains of powder. Eventually,
after the lapse of from ten to twenty seconds, 3 or 4 grains were defla-
grated at once, the remainder of the powder being thereby projected from
the cup. At a pressure of 1°5 inch, the same phenomena were observed,
but the successive deflagrations of fused grains of powder followed more
quickly upon each other, and the final ignition of several together occurred
in about ten seconds after the wire was first heated. At a pressure of 2
inches, at first only one or two of the fused grains were ignited, singly ;
and several were deflagrated together after the lapse of five seconds. A
larger quantity of the powder was burned, but a portion was projected
from the cup as in preceding experiments. At a pressure of 3 inches, no
grains were ignited singly; the combustion of the powder was effected
after an interval of about four seconds, and the greater portion was burned ;
the combustion, though it had gradually become more similar to that of
gunpowder in open air, was still very slow.
Experiments made with gunpowder in highly rarefied atmospheres of
nitrogen furnished results quite similar to those described; nor was any
important difference in the character of the phenomena observed when
oxygen was substituted for air, except that the scintillations and deflagra-
tions of the powder-grains were in some instances somewhat more bril-
liant.
The above experiments show that, when gunpowder is in contact with an
incandescent wire in a highly rarefied atmosphere, the heat is, in the first
instance, abstracted to so great an extent by the volatilization of the sul-
phur, that the particles of powder cannot be raised to the temperature
necessary for their ignition, until at any rate the greater part of that ele-
ment has been expelled from the mixture, in consequence of which the por-
tions first acted upon by heat will have become less explosive in their cha-
racter, and require, therefore, a higher temperature for their ignition than
R 2
212 Mr. Abel on the Combustion of [April 21,
in their original condition. The effect of the continued application of heat
to the powder thus changed is, to fuse the saltpetre and to establish che-
mical action between it and the charcoal, which, however, only gradually
and occasionally becomes so energetic as to be accompanied by deflagration,
because the gas disengaged by the oxidation of the charcoal continues to
convey away much of the heat applied, in escaping into the rarefied space.
For the same reason, the grains of unaltered powder which are in actual
contact with the deflagrating particles are not ignited by the heat resulting
from the combustion, but are simply scattered by the rush of escaping
gases, at any rate until the pressure in the vessel has been so far increased
by their generation as to diminish the rapidity and extent of their expan-
sion at the moment of their escape. The disengagement, first of sulphur-
vapour and then of gaseous products of chemical change, unattended by
phenomena of combustion, when gunpowder is maintained in contact with
ared-hot wire in very highly rarefied atmospheres, are results quite in har-
mony with the observations made by Mitchell, Frankland, and Dufour, with
regard to the retarding influence of diminished atmospheric pressure upon
the combustion of fuses. The phenomena described are most strikingly
exhibited by operating upon single masses of gunpowder, of some size, in the
manner directed above, when the application of the red-hot wire may be con-
tinued from three to five minutes (the gases disengaged during that period
depressing the column of mercury from 0°5 to 0°7 inch) before the mass is
ignited. There is no doubt that the products of decomposition of the gun-
powder, obtained under these circumstances, differ greatly from those which
result from its explosion in confined spaces or in the open air under ordi-
nary atmospheric conditions.. In all the experiments conducted in the
most highly rarefied atmospheres (at pressures of 0°5 to 1°5 in inches of
mercury), the contents of the vessel, after the final deflagration of the
powder, always possessed a very peculiar odour, similar to that of horse-
radish, due to the production of some sulphur-compound ; nitrous acid
was also very generally observed among the products. It is readily con-
celvable that the chemical action established between the constituents of
gunpowder, under the circumstances described, must be of a very imperfect
or partial character, the conditions under which it is established being un-
favourable to its energetic development.
In describing the phenomena which accompany. the ignition of gun-
cotton in atmospheres of different rarefaction, I have pointed out that, at
pressures varying from one to twenty-four in inches of mercury, a pale
yellow flame was observed, which increased in size with the pressure of the
atmosphere; and that a flame of precisely the same character was pro-
duced in rarefied atmospheres of nitrogen. The experiments instituted in
nitrogen show that the explosion of loose tufts of gun-cotton in atmo-
‘eho of that gas, even at normal pressures, was arava attended with a
pale yellow flash of flame, quite different from the bright fiash produced by
igniting gun-cotton in air, Thesame result was observed in atmospheres
1864. | Gun-cotton and Gunpowder. 213
of carbonic acid, carbonic oxide, hydrogen, and coal-gas. In operating with
pieces of gun-cotton-twist or thread of some length instead of employing
the material in loose tufts, the results obtained in the two last-named gases
were very different from those observed in atmospheres of nitrogen, carbonic
acid, and carbonic oxide. When ignited by means of a platinum wire
(across which it is placed) in vessels filled with either of those two gases,
and completely closed or open at one end, the piece of twist burned slowly
and regularly, the combustion proceeding much more deliberately than if
the same piece of gun-cotton had been ignited in the usual manner in air,
and being accompanied by only a very small jet or tongue of pale yellow
flame, which was thrown out in a line with the burning surface when the
gun-cotton was ignited. The same result was obtained in currents of those
gases when passed through a long, wide glass tube, along which the gun-
cotton twist was laid, one end being allowed to project some distance into
the air. The projecting extremity being ignited, as soon as the piece of
twist had burnt up to the opening of the tube through which the gas
was passing, the character of the combustion of the gun-cotton was changed
from the ordinary to the slow form above described. On repeating this
form of experiment in currents of hydrogen and of coal-gas, the ignited
gun-cotton burned in the slow manner only a very short distance inside the
tube, the combustion ceasing altogether when not more than from half an
inch to one inch of the twist had burnt in the tube. The same result
was observed when the current of gas was interrupted at the moment that
the gun-cotton was inflamed. It was at first thought that this extinction
of the combustion of gun-cotton by hydrogen and coal-gas might be caused
by the very rapid abstraction of heat from the burning surface of gun-
cotton in consequence of the diffusive powers of those gases ; but when
the experiments were made in perfectly closed vessels, the piece of gun-
cotton-twist being ignited by means of a platinum wire, the combustion
also ceased almost instantaneously. These effects, therefore, can only be
ascribed to the high cooling-powers, by convection, of the gases in question.
It was found, by a succession of experiments, that when nitrogen was mixed
with only one-fifth of its volume of hydrogen the combustion of gun-cotton-
twist in the mixture was very slow and uncertain (being arrested after a
short time in some instances), and that a mixture of one volume of hydrogen
with three of nitrogen prevented its combustion, like coal-gas.
The slow kind of combustion of gun-cotton, in the form of twist, which
is determined by its ignition in currents or atmospheres of nitrogen, car-
bonic acid, &c. may also be obtained in a powerful current of atmospheric .
air, the thread of cotton being placed in a somewhat narrow glass tube.
If, however, the air is at rest, or only passing slowly, the result is uncer-
tain. In employing very narrow tubes into which the gun-cotton fits
pretty closely, the combustion passes over into the slow form when it
reaches the opening of the tube, and occasionally it will then continue
throughout the length of the tube. In that case, while the gun-cotton
214 Mr. Abel on the Combustion of [April 21,
burns slowly along the tube, with a very small sharp tongue of pale flame,
a jet of flame is obtained at the mouth of the tube, by the burning of
the gas evolved by the decomposition of the gun-cotton. Sometimes, and
especially when wider tubes are employed, the slow combustion will pro-
ceed only for a short distance, and then, in consequence of the ignition of
a mixture of the combustible gases and air within the tube, the gun-cotton
will explode with great violence, the tube being completely pulverized,
and portions of unburnt cotton scattered by the explosion. If still wider
tubes are employed, the cotton will flash into flame almost instantaneously
throughout the tube directly the flame reaches the opening : in these cases
the explosion is not violent ; sometimes the tube escapes fracture, and at
others is broken in a few places, or torn open longitudinally, a slit bemg
produced in the tube directly over the gun-cotton. By using narrow tubes
and gradually shortening the tube through which the gun-cotton was
passed, pieces of the twist being allowed to project at both ends, it was
found, upon inflaming the material which projected on one side, that the
slow form of combustion, induced in it as soon as it burned into the tube,
was maintained by that portion which burned in the open air on the other
side, when the combustion had proceeded through the tube. Eventually,
by the employment of a screen of wood or card-board containing a perfo-
ration of the same diameter as that of the gun-cotton-twist, through which
the latter was partially drawn, the alteration of the combustion of the
material from the ordinary to the slow kind was found to be invariably
effected. On the one side of the screen, the gun-cotton burned with the
ordinary flame and rapidity, until the combustion extended to the perfo-
ration, when the flame was cut off and the material on the opposite side of
the screen burned only slowly, emitting the small-pointed tongue of pale
yellow flame.
These results indicate that if, even for the briefest space of time, the
gases resulting from the first action of heat on gun-cotton upon its ignition
in open air are impeded from completely enveloping the burning extremity
of the gun-cotton-twist, their ignition is prevented; and as it is the com-
paratively high temperature produced by their combustion which effects
the rapid and more complete combustion of the gun-cotton, the momentary
extinction of the gases, and the continuous abstraction of heat by them as
they escape from the point of combustion, render it impossible for the
gun-cotton to continue to burn otherwise than in the slow and imperfect
manner, undergoing a transformation similar in character to destructive
distillation.
These facts appear to be fully established by the following additional
experimental results :-—
1. If, instead of employing in the above experiments a moderately com-
pact gun-cotton-twist, one of more open structure is used, it becomes diffi-
cult or even impossible to effect the described change in the nature of the
combustion, by the means described, because the gases do not simply burn
1864..] Gun-cotion and Gunpowder. 215
at, or escape from, the extremity of the twisted cotton, but pass readily be-
tween the separated fibres of the material, rendering it difficult or impos-
sible to divert them all into one direction; and hence they at the same
time transmit the combustion from particle to particle, and maintain the
heat necessary for their own combustion.
2. If a piece of the compactly twisted gun-cotton, laid upon the bres
be inflamed in the ordinary manner, and a jet of air be thrown against the
flame, in a line with the piece of cotton, but in a direction opposite to that
in which the flame is travelling, the combustion may readily be changed to
the slow form, because the flame is prevented from enveloping the burning
cotton, and thus becomes extinguished, as in the above experiment.
3. Conversely, if a gentle current of air be so directed against the gun-
cotton, when undergoing the slow combustion, that it throws back upon
the burning cotton the gases which are escaping, it will very speedily burst
into the ordinary kind of combustion. Or, if a piece of the gun-cotton-
twist, placed along a board, be made to burn in the imperfect manner, and
the end of the board be then gradually raised, as soon as the material is
brought into a nearly vertical position, the burning extremity being the
lowest, it will burst into flame.
By applying to the extremity of a piece of the compact twist a heated
body (the temperature of which may range from 135° C. even up to a red
heat), provided the source of heat be not very large in proportion to the
surface presented by the extremity of the gun-cotton, the latter may be
ignited with certainty in such a manner that the slow form of combustion
at once ensues, the heat applied being insufficient to inflame the gases
produced by the decomposition of the gun-cotton. By allowing the gun-
cotton thus ignited to burn in a moderately wide tube, closed at one end,
the inflammable gases produced may be burned at the mouth of the tube,
while the gun-cotton is burning in the interior; or they may be ignited
and the gun-cotton consequently inflamed, by approaching a flame, or a
body heated to full redness, to the latter, in the direction in which they
are escaping.
It need hardly be stated that these results are regulated by the degree
of compactness of the gun-cotton, the size of the twist, and the dimensions
of the heated body. Thus a small platinum wire heated to full redness,
or the extremity of a piece of smouldering string, will induce the slow
combustion in a thin and moderately compact twist; but. a larger body,
such as a thick rod of iron, heated only to dull redness, will effect the
ignition both of the gun-cotton and of the gases evolved by the combustion
of the first particles, so that the material will be inflamed in the ordinary
manner. Similarly the red-hot platinum wire, or a stout rod heated to
redness barely visible in the dark, if they are maintained in close proxi-
mity to the slowly burning surface of gun-cotton, will eventually cause the
gases evolved to burst into flame. The more compact the twist of the
gun-cotton, the more superficial is the slow form of combustion induced in
216 Mr, Abel on the Combustion of Gun-cotton. [April 21,
it, and a condition of things is readily attainable, under which the gun-
cotton-twist will simply smoulder in open air, leaving a carbonaceous
residue; and the heat resulting from this most imperfect combustion will
be abstracted by the gases evolved more rapidly than it is generated, so
that in a brief space of time the gun-cotton will cease to burn at all in
open air *.
The remarkable facility with which the nature of combustion of gun-
cotton in air or other gases may be modified, constitutes a most charac-
teristic peculiarity of this substance as an explosive, which is not shared
by gunpowder or explosive bodies of that class, and which renders it easily
conceivable that this material is susceptible of application to the produc-
tion of a comparatively great variety of mechanical effects, the nature of
which is determined by slight modifications in its physical condition, or by
what might at first sight appear very trifling variations of the conditions
attending its employment.
There is little doubt that the products of decomposition of aunts
vary almost as greatly as the phenomena which attend its exposure to heat
under the circumstances described in this paper. A few incidental obser-
vations indicative of this variation were made in the course of the experi-
ments. Thus, in the instances of the most imperfect metamorphosis of
gun-cotton, the products included a considerable proportion of a white
vapour, slowly dissolved by water, as also small quantities of nitrous acid
and a very large proportion of nitric oxide. The latter gas is invariably
formed on the combustion of gun-cotton im air or other gases; but the
quantity produced appears always to be much greater in instances of the
imperfect or slow combustion of the material. The odour of the gases pro-
duced in combustions of that class is powerfully cyanic, and there is no diffi-
culty in detecting cyanogen among the products. I trust before long to
institute a comparative analytical examination of the products resulting
from the combustion of gun-cotton under various conditions ; meanwhile
I have already satisfied myself, by some qualitative experiments, of the
very great difference existing between the results of the combustion of gun-
cotton in open air, in partially confined spaces, and under conditions pre-
cisely similar to those which attend its employment for projectile or de-
structive purposes. I have, for example, confirmed the correctness of the
statement made by Karolyi in his analytical account of the products of de-
composition of gun-cotton, that no nitric oxide or higher oxide of nitrogen
is eliminated upon the explosion of gun-cotton under considerable pressure,
as in shells. Coupling this fact with the invariable production of nitric
oxide when gun-cotton is exploded in open air or partially confined spaces,
there appears to be very strong reason for the belief that, just as the reduc-
* By enclosing in suitable cases solid cords, made up of two or more strands, and
more or less compactly twisted, I have succeeded readily in applying gun-cotton to the
production of fuses and slow-matches, the time of burning of which may be accurately
regulated.
1864.] Dr. Phipson on Magnesium. 217
tion of pressure determines a proportionately imperfect and complicated
transformation of the gun-cotton upon its exposure to heat, the results of
which are more or less essentially of an intermediate character, so, con-
versely, the greater the pressure, beyond the normal limits, under which
gun-cotton is exploded—that is to say, the greater the pressure exerted by
it, or the resistance presented at the first instant of its ignition, the more
simple are the products of decomposition, and the greater are the physical
effects attending its explosion, because of the greater energy with which the
chemical change is effected.
III. “On Magnesium.” By Dr. T. L. Pureson, F.C.S. Communi-
cated by Prof. G. G. Stoxzs, Sec. R.S. Received March 9,
1864.
(Extract.)
Iodine and Sulphur.—tI find that iodine can be distilled off magnesium
without attacking the metal in the least. In the same manner I distilled
several portions of sulphur off magnesium without the metal being at all
attacked.
Decomposition of Silicie Acid.—Heated for some time in a porcelain
crucible with excess of anhydrous silica, the metal burns vividly if the air
has access; and a certain quantity of amorphous silicium is immediately
formed. Magnesium is therefore capable of reducing silicic acid at a high
temperature. The reason why potassium and sodium cannot effect this is
simply because these metals are highly volatile and fly off before the
crucible has attained the proper temperature. Magnesium being much less
volatile than the alkaline metals, takes oxygen from silica before volatilizing.
If the silicic acid be in excess, a silicate of magnesia is formed at the same
time; if the metal is in excess, much siliciuret of magnesium is produced.
The presence of the latter is immediately detected by throwing a little of
the product into water acidulated with sulphuric acid, when the charac-
teristic phosphoric odour of siliciuretted hydrogen is at once perceived.
Decomposition of Boracie Acid.—With boracic acid the phenomena are
rather different ; the acid melts and covers the metal, so that it does not
inflame even when the crucible is left uncovered. A certain quantity of
boron is soon liberated, and the product forms a greenish-black mass, which
oxidizes and becomes white in contact with water, and disengages no
odoriferous gas in acidulated water.
Decomposition of Carbonie Acid.—I thought it would be interesting to
try a similar experiment with carbonic acid. Accordingly dry carbonate of
soda was heated with a little magnesium in a glass tube over a common
spirit-lamp ; and before the temperature had arrived at a red heat I observed
that carbon was liberated abundantly, and magnesia formed.
Action of Alkalies.—A solution of caustic alkali or ammonia has little
or no action upon magnesium in the cold.
218 Prof. Erman—Magnetic Elements at Berlin. [April 28,
Precipitation of Metallic Solutions.—Magnesium precipitates nearly
all the metals from their neutral solutions. When these are taken in the
form of protosalts, even manganese, iron, and zine are precipitated as black
powders. Aluminium and uranium (and perhaps chrome) are only pre-
cipitated as oxides.
Alloys of Magnesium.—I have examined only a few alloys of magnesium.
Unlike zinc, magnesium will not unite with mercury at the ordinary tem-
perature of the air. With tin 85 parts, and magnesium 15 parts, I formed
a very curious alloy of a beautiful lavender-colour, very hard and brittle,
easily pulverized, and decomposing water with considerable rapidity at
ordinary temperatures. If the air has access during the formation of this
alloy, the mixture takes fire; and if the crucible be then suddenly with-
drawn from the lamp, the flame disappears, but a vivid phosphorescence
ensues, and the unfused mass remains highly luminous for a considerable
time. A white powdery mass, containing stannic acid and magnesia, is the
result.
[With platinum, according to Mr. Sonstadt, magnesium forms a fusible
alloy ; so that platinum crucibles can be easily perforated by heating mag-
nesium in them. |
Sodium and potassium unite with magnesium, and form very malleable
alloys, which decompose water at the ordinary temperature.
It is probable that an alloy of copper and magnesium, which I have not
yet obtained, would differ from brass, not only in lightness, but by de-
composing water at the ordinary temperature with more or less rapidity.
Uses.—Magnesium will be found a useful metal whenever tenacity and
lightness are required and tarnish is of no consequence. The light fur-
nished by combustion of the wire has already been utilized in photography
at night. In the laboratory it will be found useful to effect decomposi-
tions which sodium and potassium cannot effect on account of their greater
volatility.
April 28, 1864.
Dr. W. A. MILLER, Treas. & V.P., in the Chair.
The following communications. were read :—
I. “On the Magnetic Elements and their Secular Variations at
Berlin,” as observed by A. Ekman. Communicated by General
SABINE, P.R.S. Received March 1, 1864.
All observations and results to be mentioned here relate to
Latitude 52° 31' 55” North.
Longitude 13° 23' 20" E. from Greenwich.
1. Horizontal Intensity.
Denoting by (1800+¢) the date of observation in tropical years of the
1864..] Prof. Erman—Magnetic Elements at Berlin. 219
Gregorian epoch, T the absolute value of horizontal intensity with milli-
metre, milligram, and the second of mean time as unities, w the same in
unities of the Gaussian constants; the two values of T for 1805°5 and
1828°31 have been deduced from observed w, by T=0°00349216. w.
r and 7! denote the observed time of oscillation of two magnets which,
since 1853°523 were carefully guarded from the influence of other magnets ;
and therefore, marking by C, a, 6, C’, a’, 6’ unknown constants, e the basis
of hyperbolic logarithms, and taking ¢,=¢—53°523, each value of r and
7 had to fulfil the equations
(2 See Le NR Sa ‘
(1+ae—84) . T° (l+q‘e—6'4) , T
In the following list of observed values, the first is due to Humboldt;
the twenty-eight following were obtained by Erman :—
Date of Horizontal intensity, Se iimes of apeillanon 08) is ae
observation. T. Magnet I. Magnet IT.
Ut vr’.
1800-+-2¢ | Observed. | Calculated.| Observed. | Calculated.| Observed. | Calculated.
1805:5 16452 G42 Px ay eieeeas Veet te ades ves eae
1828-31 1°7559 ST eer eSies ren ence ce arrcs We ME RCAM ECE a le le. Wyre ec he
1846-13 1-751 LIS 77 Cr EES One bang SSG) inl PMC CR CREME hs MENS on
1849°59 1-784 TELS TEA PNM TEL GD [sth cae cee eee OP eeewaceaen [ol wane uasie
LCS 0 8 ai eee hanes a ren a 3°1090 S VOB pees ee > Let
1854-59 1-7900 1:7904 3°1072 31141 8:0082 8:0056
1856°57 1:7900 1:7913 31168 3°1134 8:0954 81036.
1857°54 1-7879 17916 31105 31131 81193 8:1104
1858°53 1:8035 17917 3°1158 31130 8°1364 81126
185960 1°7933 1-79°.2 3°1229 3°1129 81223 81182
MERU srateeccus | becéine ss 3°1043 3°1129 8:0870 8°1135
1861:52 1°7972 Oe ly aie Nee St ocean buna Hache 81258 81138
1862-52 1:7900 a OLE ire de. srek. Guat. tirade 81100 81142 .
1863°80 1°7929 Lol) 31148 31135 8:0975 81151
The calculated values result from the following most probable expressions
for T, and for those values of r and 7’ which agree best with the contem-
poraneous T.
I. T=1°61892+0:0057689 ¢—0:000048119 2’.
a eA 17°3633
41+0°07892 ae ty. T with ¢,=f—53°523.
TE 117°956 |
{1+0°09733 . e— 1168274 T
The expression I. appears liable to the probable errors,
in first term, +0:00126
in coefficient of ¢, —+0°000065 | of a magnetic unity ;
in coefficient of 2”, -+0°00000074
220 Prof. Erman—Magnetic Elements at Berlin. [April 28,
and when brought under the form
(A) T=1-79183—0-000048119{¢—59-930}?,
identical with I., it shows that the horizontal intensity reached in 1859-930
the maximum of 1°79183.
_ It ought to be observed, that equal probability has been attributed to the
error
+l “in 20;
that is to say, equal errors to an intensity determined by each of the three
methods,—this supposition being at once the most simple and the most
conformable to my experience, by nearly contemporaneous repetitions of
each class of observation.
All my determinations of absolute intensity have been obtained either by
one of two, or by.two magnetometers ; the first of which is a Gaussian of
large size, by Meyerstein, the second my declination- and transit-instrument
by Pistor, completed by the usual graduated holders for pe te magnets,
and perfectly adapted to observations in the open air.
2. Inclination.
The values of inclination here employed are taken for 1806'0, 1832°5,
and 1836°87, from the observations of Humboldt, Rudberg, and Encke ;
for the ten other dates since 1825-0, they have been obtained by my own
applications of the methods exposed in my ‘ Reise um die Erde,’ Physikal.
Beob., tome il. pp. 8-42, to two different instruments—viz. till 1850 to
a large and highly perfect one by Gambey, and since that time to a
smaller dip-circle by Robinson. The methods of observation leave no
room for any constant error in the resulting inclination, as long as no di-
rective magnetic force is exerted upon the needle by the instrument itself.
In order to free my results from any influence from this improbable (but
not impossible) source, I compared, in 1860, three full determinations by
the last-mentioned apparatus, with an equal number which I obtained
under identical circumstances with a most perfect copy of Weber’s in-
ductive inclinometer. The result was an agreement of the two kinds
of determinations within the limits of accidental error of the first—that
is to say, far below one minute in the inclination; I venture, therefore, to
say hat the following numbers must give the absolute value of the element
in question with no less certainty than the rate of its secular variation :
1864. ] Prof. Erman—Magnetic Elements at Berlin. 221
Date of Inclination,
observation. j
1800+-¢. | Observed. | Calculated.
oO i jo} i
1806-0 69 53 69 52-99
1825:00 | 68 49:19 | 68 4462
1828-29 | 68 3455 | 68 34:17
1832-50 | 68 18:08 | 68 21:40
1836:87 | 68 743 | 68 8-84
1838°75 | 68 2:04 | 68 3°66
184620 | 67 43:25 | 67 44-46
1849°65 | 67 35-48 67 36:29
1853-78 67 29°81 67 27-09
185656 | 67 20°50 67 24:26
1857:55 | 67 20°30 67 19-25
1860:60 | 67 15°75 67 13°31
186255 | 67 763 67} 9:69
The system of the above calculated values, which best agrees with the
observed ones, results from the expression
(B) t= 70° 17!'-42—4"1854¢+0'-018931 2 ;
it leaves in each single equation a probable error of + 1'*42; and accordingly
in the expression itself the probable errors appear to be
in the absolute term +2'°17;
in the coefficient of £ +0'1211;
in the coefficient of 2? +0'°001591.
This expression can be brought under the form
(B*) i= 66° 26'09 + (¢?—110°543)’. 0'-018931,
which would prove that at the place in question the inclination will come,
in 1910°543, to a minimum of 66° 26°09. The aforesaid errors of terms
give +2°27 years for the uncertainty of the epoch of this minimum, and
+3'-9 for the uncertainty of its value; but as the expression (B) results
from observations between 1806 and 1863, its consequences ought not to
be extended as far as 1910.
3. Declination.
Four results of observations of this element, made by the late astrono-
mers Kirch in 1731, Bode in 1784 and 1805, and Tralles in 1819, have
been added to my own, which extend from 1825 to 1864. These latter
were obtained with the declination- and transit-instrument employed in my
voyage, which intermediately was frequently compared and found in per-
fect agreement with a large Gaussian magnetometer, whenever the indi-
cations of the latter were duly freed from the torsion of the suspending wires
and from the want of parallelism between the normal of the employed spe-
culum and the magnetic axis of the bar. My observations were all made in
the open air, with the exception of the two in 1849 and 1850, which, having
been executed in a room, were corrected for the influence of local attractions.
As the determination of this latter seemed exposed to a somewhat larger
222 Prof, Erman—Magnetic Elements at Berlin. [April 28,
error than the other declinations, in combining the two reduced values
with those obtained in the open air, I have given to the two first only
a fourth of the weight of the others. A similar allowance for larger pro-
bable errors should perhaps have been made in employing the four state-
ments of former observers ; but, for want of particulars about the operations
they are founded upon, it was more safe to neglect the difference between
their weight and that of the others, than to fix it by an arbitrary as-
sumption.
If, for the moment of observation, there were marked by 1800-+4, as
before, the tropical years elapsed since the Gregorian epoch, m the positive
excess of ¢ over the next integer, 2 the horary angle of mean Sun, each
observed west declination d' had to be brought under the form
d'=D+f(t)+9(m,2),
D denoting a constant, and f and ¢ two functions, the first of which was
to be determined here.
In order to form d'—¢(m, x)=d out of each d’, I put
o(m, v)=a+a.cosr+y.cos 24+ . cos 32,
+6 .sing+6.sin 27+. sin 32,
taking the values of a, a, 8, ..-... , £ by interpolation according to
m, from the following Table, derived from observations in the Russian
observatories at St. Petersburg, Catherinbourg, and Barnaoul in the year
1837 and 1838, and well agreeing with my own determinations of ¢(m, x)
for the years 1828 to 1830, and at eight places between latitude 50° and
62° North.
m a a. B y: ry € é
0042 | 445. | 54 | se Ibe | 27 | 90 15 Sok ee
o193°| = "62 | er | 46 | Soe) Tied 1 Pee ae
0-204 | — 43 | + 54 | 4135 | +411 | +173 | +22 | +62
0-288 |. —108 |} 46.64, [i++ 256] \. 4.14 44.199. it 2 eb eee
0373 | — 88 | 1104 | 4964 | +65 | +182 | +42 | Fae
0-455 | + 14 | +107 | +290 | 471 | +184 | +64 | +445
0-538 | +77 |.4082..) £975 1 a6: | 175 | eee
0623 | + 60 | + 8 |'4221 | +79 | 1187 | 166 >) sie
0-707 | +72 | +91 | 4139 | +51 | +156 | +57 | +34
0-790. | + 68 b+ 78 |ek-69. | pe Bb h1BF 29 «| oot
Oras oS ates ME get © yo a 76 “Po ee oe
0050) +) Bll BO) org 1/2074 -ae eg) aaae [eeeae
1042 [od We de 4 eee dbo | OR. GO. siaee a
When I supposed in this way that the parameters a,a,...., { of
the function ¢(m, x), or ¢ as I will call it for abbreviation, are the same for
all moments alike situated in different years, I was well aware that this
assumption is but approximative, and that all sufficiently extended and
direct investigations of ¢, as chiefly those of General Sabine, have shown
a periodicity of about 9:5 years in the total values of this function, But
as the laws of such dependence between T and each of the seyen para-
Prof. Erman—Magnetic Elements at Berlin, 223
1864. ]
meters of @ have not yet been perfectly exposed, I preferred in the pre-
sent to treat the latter as mere functions of manda. In the following
Table of employed mean declinations for the moments ¢, to each of them
is subjoined the value of ¢ by whose subtraction it has resulted from the
“momentary value furnished by observation. This arrangement will allow
us to appreciate (and, if wanted, to correct for) the influence exerted by
any periodical variation of @ upon the final result of my observations.
It may, too, be convenient to observe that for some of the following west
declinations (D), as well as for the before-mentioned intensities (T) and in-
clinations (1), the observations were made in latitude p— Ag, and longitude
1—A/ (where p and / mark the corresponding and above alleged values for
my ordinary place), and that then the directly obtained results, viz. d—Ad,
T—AT, or :— Ai, have been reduced by
Ad=—0-0940 . Ap—0°6103. AZ;
AT=—0°7480 . 10-3. Ap+0°2152. 10-3. Al;
Ai=+0°7405 . Ap—0°1861 . AZ;
the minute of arc being the unity for Ap, Ad, Az, and AJ.
These equations, which result from the Gaussian constants with the given
p and J, are sufficiently approximated when, as with us, Ap and A/ do
not exceed a few minutes. So then were obtained:
Mean declination,
Momentary
Date of declination. d.
observation. Mean
1800+. declination, By
. observation. Calculated.
ie) a i
1731-60 0 12 18:05 | 19 19-85
178400 0 17 59-65 17 46:09
1805-40 0 18 1:35 18 7:86
1819-00 0 17 36°50 17 48:06
1825-79 —1-80 17 24-46 17 28:37
1828-33 —4:08 17 21-35 17 19°34
1834-05 — 1-24 17 2-69 16 55-65
*1849-62 +2°74 15 21-55 15 24:39
*1850°63 +2-96 15 20-48 15 20-47
1853-81 +432 14 55°17 14 58:26
1854:36 — 2-86 15) E05 14 54:19
1856-58 JS) ES: 14 38:13 14 37:40
1857-49 —5°95 14 33°88 14 30:29
1858-54 —5°61 14 21-15 14 21:96
1859-58 —4:87 14 14:24 14 13°59
1861-50 +447 18 53°70 13 57°63
1862°55 +0:12 13 49-83 13 48°72
1863°79 +448 13 36°85 13 37:99
A fourth of the weight of each of the other observed values being given
to each of the two marked *, the whole is best represented by
d=18° 8':46+ 0'26820 ¢<—0'070665 47, . . . (IV).
224 Prof. Erman—Magnetic Elements at Berlin. A 28,
which furnishes the above calculated numbers; and by their corapurigen
with the observed ones, the probable errors are—
in the absolute term of d +1':94;
in the coefficient of in d +0':2932 ;
in the coefficient of ¢? in d+0':030669.
If, now, instead of employing the variations ¢ (m, x), or ¢ according to
observations in the years 1837 and 1838, we assume (1) that the periodi-
cal dependence between this function and the date ¢ consists in always
changing each parameter proportionally to its mean or primitive value,
and then (2) that, as General Sabine has proved, the whole function has
nearly reached a maximum in all moments marked by ¢=48-n. 9:5,
n being an integer, and (3) that, according to the same philosopher, the
least and the largest amount of corresponding variations are approximately
as 1: 1:°4, then, ® marking the function of ¢, m, x which in each case
must be substituted for ¢, and C a function of M and X, we shall have
d=c 12 20+0°20 . sin En C= —45-625)]] |
i
o=c | 1:20—0-20 . sin (8: 125) | = l3a8tl Ge:
To each of the preceding values of d must therefore be added
p= be% {0 1163—0:1472. sin E (¢—45°625)) \
By executing this operation, I found that the reduced observations are
best represented by
(C*) d=18° 8-43 -+-0°26831 . —0°070652. 2’,
and that, though scarcely differing from (IV.), this expression is preferable,
because the probable error of each of its terms is by nearly =); of its former
value smaller than the corresponding one in (IV.)
As the expression (C*) is identical with
(C) d=18° 8'68—0'-070652{¢—1-8991,
we see that, according to my observations, the west declination at the
place in question arrived in 1801-899 at a maximum of 18° 8'°68.
Putting off for a further article some more general observations on
the secular changes of terrestrial magnetism, I briefly resume, as results
of my nearly forty years’ observations, that for
latitude =52° 31' 55” North,
longitude = 13° 23’ 20” E. from Greenwich,
1864. | Action of Chlorine upon Methyl. 225
there have been—between 1805 and 1864,
Horizontal intensity =T=1°79183 —0°000048119 {¢—59-930}? ;
between 1806 and 1863,
Inclination =i=66° 26'-09 + 0':018931 {¢—110°543)? ;
and between 1731 and 1864,
West declination =d=18° 8'-68—0'-070652 {¢—1-899}?;
all results being meant to be just for the date 1800+¢ in years of the
Gregorian epoch.
N.B. It seems not unworthy of remark, that no evidence of the existence
of a third term in the expression for any one of the three phenomena
results from the above-mentioned observations; and this, though partly
due to the inevitable imperfections of the observations, makes it highly pro-
bable that a man’s lifetime, and even a century is but a very small part of
the secular period of terrestrial magnetism.
If. “ On the Action of Chlorine upon Methyl.” By C. Scuor-
LEMMER, Assistant in the Laboratory of Owens College, Man-
chester. Communicated by Professor Roscoz, F.R.S. Received
April 5, 1864.
In a paper published in the Journal of the Chemical Society, New Ser.
vol. 1. p. 425, I pointed out the great interest which attached to the study
of the lower terms of hydrocarbons, known by the name of the “ alcohol
radicals,” inasmuch as the question of the chemical constitution of these
bodies requires to be more definitely settled.
Having been aided in these researches by a grant from the Council, I
beg to lay before the Royal Society the results of an investigation on the
action of chlorine upon methyl, which are as unexpected as they are de-
cisive.
Equal volumes of chlorine and of methyl were exposed in strong well-
corked bottles, holding from two to three litres, to diffused daylight in the
open air at a temperature of about 5°C. The methyl was prepared
according to Kolbe’s method, by electrolysis of a concentrated solution of
acetate of potassium, and carefully purified by washing with a solution of
caustic potash and concentrated sulphuric acid. The colour of the chlo-
rine disappeared rather quickly ; colourless oily drops condensed on the
the sides of the bottles, and collected after some time on the bottom as a
mobile liquid, the greater part of which volatilized again when the bottles
were brought into a warm room. Hence it appears that by the action of
one volume of chlorine upon one of methyl, substitution-products are
formed, consisting chiefly of a volatile liquid, the boiling-point of which
ies between 5° and 15° C. In order to collect these products, the bottles
were heated till all the liquid had volatilized, and then opened, with the
mouth downwards, under a hot concentrated solution of common salt, to
which some caustic soda was added in order to quicken the absorption of
VOL. XIII. s
226 Action of Chlorine upon Methyl. [April 28,
the hydrochloric acid, of which half the volume of gas contained in the
bottles consisted. The bottles were then taken out of the liquid, placed in
an upright position, and the mouth provided with a doubly perforated
cork, into one opening of which a siphon fitted. Through this siphon a
hot concentrated solution of common salt slowly ran in, whilst the gas
thus displaced escaped by a bent tube and was condensed in a small tube
receiver, surrounded by a mixture of ice and salt. The liquid thus ob-
tained was ieft for some hours in contact with a piece of solid caustic
potash, in order to remove moisture and the last traces of hydrochloric
acid. Subjected to distillation, the liquid began to boil at 11° C., and the
boiling-point rose slowly to 30° C., at which temperature two-thirds of
the liquid had come over. On continuing the fractional distillation for
some time longer, the distillate yielded a few grammes of a colourless
mobile liquid, boiling between 11° and 13°C., which, as the following
analysis and vapour-density determinations prove, is chloride of ethyl,
C,H,Cl. The boiling-pvint of the liquid agrees with that of this com-
pound, and it possesses the strong peculiar smell and the property of
burning with a white, luminous, green-bordered flame, characteristic of the
chloride of ethyl.
I. Analysis :—
(1) 0°4245 grm. of the substance gave 0°5670 grm. of carbonic acid
and 0°3025 of water.
(2) 0°1810 grm. of the substance gave 0°3855 grm. of chloride of
silver and 0°0165 grm. of metallic silver.
Calculated for the formula C, H, Cl. Found.
2C 24 37°21 36°43
DEL co) Z:7D 7°92
Gi 3020 95°04 59°63
64°5 100-00 99°98
II. Determination of the vapour-density according to Gay-Lussae’s
method :—
Weight of substance employed........ 0°0893 grm.
Temperature of alr .........---.--- oC;
Height of barometer ................ 739 millims.
(1) Temperature of vapour.............. 50° C.
Volume of vapour
Difference of level
Vapour-density calculated from these numbers ....
(2) Temperature of vapour
Volume of vapour
Difference of level
Vapour-density calculated ....
(3) Temperature of vapour
Volume of vapour
Difference of level
eeerees ee e © © & © @ oe ©
coeeee ec eee 8B ew oe we oO
ee eeeevreereereeee ee
ose se eeeeeeeeeeeeeee
46°2 cub. centims.
140°5 millims.
2°24a%
70° C.
48:2 cub. centims.
130:0 millims.
2°244.
80°C.
49°45 cub. centims.
1250 millims.
1864. ] Mr. Russell on the Calculus of Symbols. 227
which numbers give the vapour-density 2°235, whilst the theoretical
vapour-density of chloride of ethyl is 2°233.
The boiling-point of the residue left after the first distillation rose
quickly up to 60° C., whilst nearly the whole distilled over between this
temperature and 70°C. By afew more fractional distillations of this latter
portion, monochlorinated chloride of ethyl, C,H, Cl,, boiling between
62° and 65° C., was isolated.
0°1270 grm. of this compound gave 0°3530 grm. of chloride of silver
and 0°0095 grm. of metallic silver, which corresponds to 71°43 per cent.
of chlorine, whilst the formula requires 71°71 per cent.
Hight litres of methyl yielded about 8 grammes of the mixed chlorides,
or only about one-third of the theoretical quantity of chloride of ethyl
which should have been obtained. This is easily explained by the vola-
tilization of the liquid, and its solution in large quantities of water, as well
as by the formation of higher substitution-products,. in consequence of
which a considerable quantity of methyl is left uncombined.
From these results it appears that the lowest term of the series of
alcohol radicals behaves with chlorine exactly in the same manner as I
have shown in the paper above referred to is the case with its homologues
ethyl-amyl, C, H,, (which gives chloride of heptyl, C,H,,Cl), and amy],
C,, H,, (from which chloride of decatyl, C,, H,, Cl, is obtained). If an
excess of chlorine is avoided, the principal products consist of the chlo-
rides of monatomic radicals containing the same number of atoms of
carbon as the original hydrocarbon contained, whilst at the same time
chlorine substitution-products of these chlorides are formed in smaller
quantities.
As there is no reason why those terms of the series which are placed
between C,H,, C,H,,, C,, H,, should show a different deportment, it
becomes obvious that, beginning with marsh-gas, C H,, the lowest term in
the series C,,Hon+42, the most simple of all hydrocarbons, and one which
can easily be obtained from its elements, we are now not only in a position
to prepare all the members of this series, but likewise to build up by
simple synthesis the series of mono-, di-, and polyatomic alcohols, acids,
compound ammonias, ethers, &c. &c. of which each of the marsh-gas hy-
drocarbons forms the starting-point.
III. “On the Calculus of Symbols (Fifth Memoir), with Applica-
tions to Linear Partial Differential Equations, and the Calculus
of Functions.” By W. H.L. Russexz, Esq., A.B. Communi-
cated by Professor Stoxss, Sec. R.S. Received April 7, 1864.
In applying the calculus of symbols to partial differential equations, we
find an extensive class with coefficients involving the independent variables
which may in fact, like differential equations with constant coefficients, be
228 Mr. Russell on the Calculus of Symbols. [April 28,
solved by the rules which apply to ordinary algebraical equations ; for there
are certain functions of the symbols of partial differentiation which com-
bine with certain functions of the independent variables according to the
laws of combination of common algebraical quantities. In the first part of
this memoir I have investigated the nature of these symbols, and applied
them to the solution of partial differential equations. In the second part I
have applied the calculus of symbols to the solution of functional equa-
tions. For ‘this purpose I- have worked out some cases of symbolical
division on a modified type, so that the symbols may embrace a greater
range. I have then shown how certain functional equations may be
expressed in a symbolical form, and have solved them by methods analo-
gous to those already explained.
The Society then adjourned to Thursday, May 12th.
1864. | Mr. Russell on the Calculus of Symbols. 227
which numbers give the vapour-density 2°235, whilst the theoretical
vapour-density of chloride of ethyl is 2°233.
The boiling-point of the residue left after the first distillation rose
quickly up to 60° C., whilst nearly the whole distilled over between this
temperature and 70°C. By a few more fractional distillations of this latter
portion, monochlorinated chloride of ethyl, C,H, Cl,, boiling between
62° and 65° C., was isolated.
0°1270 grm. of this compound gave 0°3530 grm. of chloride of silver
and 0:0095 grm. of metallic silver, which corresponds to 71°43 per cent.
of chlorine, whilst the formula requires 71°71 per cent.
Eight litres of methyl yielded about 8 grammes of the mixed chlorides,
or only about one-third of the theoretical quantity of chloride of ethyl
which should have been obtained. This is easily explained by the vola-
tilization of the liquid, and its solution in large quantities of water, as well
as by the formation of higher substitution-products, in consequence of
which a considerable quantity of methyl is left uncombined.
From these results it appears that the lowest term of the series of
alcohol radicals behaves with chlorine exactly in the same manner as I
have shown in the paper above referred to is the case with its homologues
ethyl-amyl, C, H,, (which gives chloride of heptyl, C,H,,Cl), and amyl,
C,, H,, (from which chloride of decatyl, C,, H,, Cl, is obtained). If an
excess of chlorine is avoided, the principal products consist of the chlo-
rides of monatomic radicals containing the same number of atoms of
carbon as the original hydrocarbon contained, whilst at the same time
chlorine substitution-products of these chlorides are formed in smaller
quantities.
As there is no reason why those terms of the series which are placed
between C,H,, C,H,,, C,, H,, should show a different deportment, it
becomes obvious that, beginning with marsh-gas, C H,, the lowest term in
the series C,,H2,+40, the most simple of all hydrocarbons, and one which
can easily be obtained from its elements, we are now not only in a position
to prepare all the members of this series, but likewise to build up by
simple synthesis the series of mono-, di-, and polyatomic alcohols, acids,
compound ammonias, ethers, &c. &c. of which each of the marsh-gas hy-
drocarbons forms the starting-point.
II. “On the Calculus of Symbols (Fifth Memoir), with Applica-
tions to Linear Partial Differential Equations, and the Calculus
of Functions.” By W. H. L. Russetx, Esq., A.B. Communi-
cated by Professor Stoxzs, Sec. R.S. Received April 7, 1864.
In applying the calculus of symbols to partial differential equations, we
find an extensive class with coefficients involving the independent variables
which may in fact, like differential equations with constant coefficients, be
VOL, XIII, Y
228 Mr. Gompertz on the Law of Mortality. [May 12,
solved by the rules which apply to ordinary algebraical equations ; for there
are certain functions of the symbols of partial differentiation which com-
bine with certain functions of the independent variables according to the
laws of combination of common algebraical quantities. In the first part of
this memoir I have investigated the nature of these symbols, and applied
them to the solution of partial differential equations. In the second part I
have applied the calculus of symbols to the solution of functional equa-
tions. For this purpose I have worked out some cases of symbolical
division on a modified type, so that the symbols may embrace a greater
range. I have then shown how certain functional equations may be
expressed in a symbolical form, and have solved them by methods analo-
gous to those already explained. .
The Society then adjourned to Thursday, May 12th.
May 12, 1864.
Major-General SABINE, President, in the Chair.
In accordance with the Statutes, the names of the Candidates recom-
mended by the Council for election into the Society were read, as follows :—
Sir Henry Barkly, K.C.B. William Jenner, M.D.
William Brinton, M.D. Sir Charles Locock, Bart., M.D.
T. Spencer Cobbold, M.D. William Sanders, Esq.
Alexander John Ellis, Esq. Col. William James Smythe, R.A.
John Evans, Ksq. Lieut.-Col. Alexander Strange.
William Henry Flower, Esq. Robert Warington, Esq.
Thomas Grubb, Esq. Nicholas Wood, Esq.
Sir J. Charles Dalrymple Hay, Bart.
The following communications were read :—
I, ‘Second Part of the Supplement to the two Papers on Mortality
published in the Philosophical Transactions in 1820 and 1825.”
By Bensamin Gompertz, F.R.S. Received March 30, 1864,
(Abstract.)
_ The objects of this paper are various; but the subject appears to the
author more especially important in consequence of the state of competition
among assurance establishments, which he holds to be injurious to the interest
of those valuable establishments, and to those of the assuring population.
The author’s purpose in this paper is greatly to extend the modes of cal-
culating valuations, and to improve the methods of calculation hitherto
used by actuaries, which are in many cases very laborious, and in some
almost impracticable. This part commences with observations on the inge-
1864.] Dr. Kopp on the Specific Heat of Solid Bodies. 229
nious plan of Barrett, which is shown to be capable of improvement and
extension. Parts of the excellent work of the late Mr. David J ones, ‘ Ta-
bles of Life Annuities,’ published under the care and suggestion of the
Society for the Diffusion of Useful Knowledge, founded on those ideas of
Barrett, are by the author here improved and extended so as to give methods
easier for common purposes, and capable of extension to almost all diffi-
culties which are likely to occur in the calculation of the value of property.
II. “ Investigations of the Specific Heat of Solid and Liquid Bodies.”
By Hermann Kopp, Ph.D. Communicated by T. GRAHAM,
Hsq., Master of the Mint. Received April 16, 1864. :
( Abstract.)
. In the first part the author discusses the earlier investigations on the
specific heat of solid bodies, and on the relations of this property to their
atomic weight and composition. In this historical report he gives a com-
plete analysis of the various opinions published on the subject.
In the second part the author describes the method he has used ies
determining the specific heat of solid bodies. This method is based on the
method of mixtures. The substance investigated is placed in a glass tube,
together with some liquid which does not dissolve it, and the tube is heated
im a mercury bath, and then rapidly immersed in a calorimeter containing
water. Equalization of temperature takes place rapidly, through the inter-
vention of the liquid in the tube. The thermal effect (increase of tempe-
rature in the water of the calorimeter) is determined. Preliminary expe-
riments give the means of allowing for the thermal effect due to the glass
and to the liquid in it, and of thereby obtaining the thermal effect produced
by the solid substance. The author gives a complete description of the
apparatus and of the mode of using it, and also of the means of determin-
ing the ancillary magnitudes which require to be taken into account. The
entire method is very simple, and it brings the determination of specific
heat out of the restricted sphere of the physical cabinet, with its compli-
cated apparatus, within reach of the ordinary appliances of the chemical
laboratory. It is also applicable to small quantities, and to such sub-
stances as cannot bear a high temperature. The author discusses the
possible deficiencies as well as the advantages of this method as compared
with those of Neumann and of Regnault.
In the third part the author gives his determinations of a very great.
number of solid bodies. The specific heat of many of them had been
determined by Neumann, or by Regnault ; and the almost universal agree-.
ment of the numbers found by their methods and by his own proved the
comparability of his results with those of other physicists. Where there
is a considerable difference, the cause is discussed. By far the greatest
T 2
230 Dr. Kopp on the Specific Heat of Solid Bodies. [May 12,
number of the author’s experiments are on substances whose specific heat
had not been previously determined ; they extend to all the more important
classes of inorganic compounds, and to a great number of organic com-
pounds.
In the fourth part the author gives a synopsis of the materials at pre-
sent available and trustworthy for considering the relations between specific
heat and atomic weight or composition. That is, he gives for solid bodies
of known composition the atomic formula, the atomic weight, the more
trustworthy determinations of specific heat, and (corresponding to these)
the atomic heats, or products of the specific heats and the atomic weights.
The relations between the atomic heat and the atomic weight or the
composition are discussed in the fifth part.
A discussion whether the specific heat of a body varies materially with
its different physical conditions forms an introduction to this part. The
influence which change of temperature of solid bodies exerts on the specific
heat is considered. This difference is inconsiderable, as is also the differ-
ence of specific heats found for the same substance, according as it is ham-
mered or annealed, hard or soft. With dimorphous varieties of the same
substance, even where the specific gravity is different, the same specific
heat is found in most cases. Great difference had been supposed to exist
in the specific heat of a substance, according as it was crystalline or amor-
phous. The author shows that, for a great number of substances, there is
no such difference, and that in other cases the apparent differences depend
on inaccurate determinations of the specific heat. He shows that three
sources of error more especially may give too great a specific heat for a
substance, or for one of its various modifications :—
1. When the substance is heated to a temperature at which it begins to
soften, and thus to absorb part of its latent heat of fusion.
2. If the substance is heated to a temperature at which it begins to pass
into another modification, and this change, with its accompanying deve-
lopment of heat, is continued in the calorimeter.
3. If the substance investigated is porous, and (as was the case in the
earlier methods) is directly immersed in the liquid of the calorimeter, in
which case the development of heat which accompanies the moistening of
porous substances comes into play.
The author arrives at the following result :—From what is at present
known with certainty, one and the same body may exhibit small differ-
ences with certain physical conditions (temperature, or different degrees of
density or porosity); but these differences are never so great as to furnish
an explanation of cases in which a body markedly deviates from a regu-
larity which might perhaps have been expected for it—always assuming
that the determination of the specific heat, according to which the body in
question forms an exception to the regularity, is trustworthy and free from
foreign elements.
The author then discusses the applicability of Dalong and Petit’s law.
1864.] Dr. Kopp on the Specific Heat of Solid Bodies. 23)
The atomic heats of many elements * are, in accordance with this law,
approximately equal; they vary between 6 and 6°8, the average being
about 64. The explanations attempted why this law only approximately
holds good, he considers inadequate. In any case there are individual
elements which do not obey this law. The atomic heat of phosphorus, for
instance, as deduced from direct determinations of its specific heat in the
solid state, is considerably smaller (about 5:4) ; and still more so are those
of silicium (about 4), of boron (about 2°7), and of carbon (1°8 for dia-
mond).
A regularity, to which attention has been already drawn, is, that the
quotient obtained by dividing the atomic heat of a compound by the
number of elementary atoms in one molecule, is approximately equal to
6:4; equal, that is, to the atomic heat of an element according to Dulong
and Petit’s law. Thus the atomic heat of the chlorides R Cl and RCl has
been found to be 12°8 on the average, and of the chlorides R Cl,=18°5.
Now ae and a =6'2. The same regularity is met with in
metallic bromides, iodides, and arsenides; and, according to the author’s
determinations, it is even found in the case of compounds which contain as
many as seven, and even of nine elementary atoms. The atomic heat of
Zn K, Cl, ig 43°4, and that of Pt K, Cl, is 55-2; now “246-2 and
a6. But the author shows at the same time that this regularity
is far from being general. For the oxides of the metals the quotient is less
than six, and is smaller the greater the number of atoms of oxygen in the
oxide. (From the average determinations of the atomic heats, it is for the
metallic oxides RO, =-—-=5°6; for the oxides R, 0, and RB, 0, 2”
5
==5°4; for the oxides RO,= i> oh) The quotient is still smaller for
compounds which contain borow as well as oxygen (for instance, it is
16'S 4-2 for the borates, RB 0,5 it is “{"=3°3 for boracie acid, B, ©,),
or which contain silicium (for silicic acid, Si®,, it is MBE say. or hydro-
v
gen (for ice, H,9, it is or = 2:9), or, finally, which contain carbon and hy-
aa : r «we 2029
drogen as well as oxygen (for succinic acid, €, H, O,, for instance, it 1s are
=2°6). It may be stated in a few words, in what cases this quotient
approximates to the atomic heat of most of the elements, and in what
* In accordance with recent assumptions for the atomic weights, H=1; Cl=35°5;
6=16; S=32; B=109; C=12; Si=28. R stands for a monequivalent atom, e. g.
As=75; Na=23; K=39'1; Ag=100; RB signifies a polyequivalent atom, e. g.€a=40 ;
Pb=207; Fe=56; Co=—63°4; Cr=52°2; Pt=184, &c.
232 Dr. Kopp on the Specific Heat of Sold Bodies. [May 12,
cases it is less. It is near 6’4 in the case of those compounds which only
contain elements whose atomic heats, in accordance with Dulong and
Petit’s law, are themselves approximately =6°4. It is less in those com-
pounds containing elements which, as exceptions to Dulong and Petit’s law,
have a considerably smaller atomic heat than 6-4, and which are found to
be exceptions, either directly, by determinations of their specific heat in the
solid state, or indirectly, by the method to be subsequently described.
After Dulong and Petit had propounded their law, Neumann showed
that a similar regularity existed in the case of compounds, that is, that the
atomic heats of analogous compounds are approximately equal. Regnault,
as is known, has confirmed Dulong and Petit’s, as well as Neumann’s law,
to a considerably greater extent, and for a larger number of compounds,
than had been previously done. And Regnault’s researches have more
especially shown that the elementary atoms, now regarded as monequivalent,
are, as regards the atomic heat of their compounds, comparable with the
elementary atoms which are to be considered as polyequivalent. Thus, as re-
gards atomic heat, arsenious acid, As, O,, and sesquioxide of iron, Fe, Q,, or
chloride of silver and subchloride of copper, Cu Cl, may be classed together.
Of the applicability of Neumann’s law, as hitherto investigated and found
in the case of chemically analogous compounds, the author’s experimental
determinations have furnished a number of new examples. But more
interest is presented by his results in reference to the applicability of this
law to compounds to which it had not hitherto been supposed to apply.
In comparing compounds as regards their atomic heat, their chemical
character has been taken into account, as represented by the formule
hitherto adopted. Sulphates and chromates, for instance, were looked
upon as comparable, but they would not have been classed with perchlorates,
or with permanganates. According to more recent assumptions for the
atomic weights of the elements, the following salts have analogous for-
mulze, and the adjoined atomic heats have been determined :—
C@hromate ot leade. 5 eee ae Ph€rO, 29-0
Solpuate of emt’). 2 Pbs 0, 25°8
Permanganate of potass ........ KMnO, = 28°3
Perchlorate of potass .......... K ClO, 26°3
The atomic heats of carbonates, R € O,, of silicates, R Si O,, of metaphos-
phates, RP O,, of nitrates, RN O,, are also very near.
But not even a common chemical behaviour, such as the bodies in this
group possess—that is, a common haloid character—is necessary in order
that compounds of analogous atomic composition shall show the same atomic
heat. No one would think of considering magnetic oxide of iron as analo-
gous to chromate of potass; and yet both have the same atomic structure,
and determinations of their specific heat have given approximately the
same atomic heat for both.
Mapneti¢ oxide of ifon *..:..:".'. 2° Be, ©, 37°7
Chromate of potass.............+. K,€rO 36:4
1864. ] Dr. Kopp on the Specific Heat of Solid Bodies. 239 |
And it is not less surprising that arseniate of potass, K As Q,, and chlorate
of potass have the same atomic heat as sesquioxide of iron, Fe, Q,, or ar-
senious acid, As, G,: with very different characters these compounds have
approximately equal atomic heat.
But comparability of chemical compounds, as regards the atomic heat,
is not limited to the cases in which, as far as can be judged, the individual
atoms have analogous construction. We do not regard the atom of binoxide
of tin or of titanic acid as analogous in construction to the atom of tung-
state of lime or of chromate of lead; nor to nitrate of baryta, or metaphos-
phate of lime. But if the formule of those binoxides are doubled or
tripled, they may be compared with these salts, and their atomic heats are
then approximately equal, as is,the case for compounds of analogous
chemical character. The atomic heats are for—
Binoxidé of tig. vse. a2.. Ze00 = SiO, 27°6
Witamie a€id's sis. ei eas eee =) Ey S, 27°3
Paneciare of lime ieee ay ah os CaW O, 27°9
Clromate of leadia icici de ce Pb Cr OQ, 29°0
Permanganate of potass .......... K Mn O, 28°3
Perchlorate of potass v1.0 sci eee es K ClO, 26°3
Binoxide of ti... 05. 62's 38n90,= 8n, 0, 41°4
Diane 401d vi vice cds es a PLO. =) 210, 41:0
Nitrate of barytas.c. 2... away. Ba N, 0, 38°9
Metaphosphate of lime .......... CaP,O, 39°4
These results seem to give to Neumann’s law a validity far beyond the
limits to which it had hitherto been considered to apply. But, on the
other hand, the author’s comparisons go to show that neither Neumann’s
nor Dulong and Petit’s law is universally valid.
Neumann’s law is only approximate, as is well known. For such analo-
gous compounds as, from what we know at present, are quite comparable
and,in accordance with this law, ought to have equal atomic heats, Regnault
found the atomic heats differing from each other by 745 to 4. In a few
such cases there are even greater differences in the atomic heats, for which
an adequate explanation is still wanting.
But there are other differences in the atomic heats of some compounds
which might have been expected to have equality of atomic heat in accord-
ance with Neumann’s law—differences which occur with regularity, and
for which an explanation is possible. Certain elements impress upon all
their compounds the common character that their atomic heats are smaller
than those of analogous compounds of other elements. This is the case, for
instance, with the compounds of boron: the atomic heat of boracic acid is
much less than that of the metallic oxides R, O, and R, O,; the atomic heat
of the borates R B Q, is much less than that of the oxides R, O,=(2 B®) ;
and the atomic heat of borate of lead, Pb B, 9,, is far less than that of mag-
netic oxide of iron, Fe, O,. The same is the case with compounds of carbon,
if the alkaline carbonates, R, © Q,, are compared with the metallic oxides
R, 0,=(3 BQ), or the carbonates B € O, with the metallic oxides R, O, and
234 Dr. Kopp on the Specific Heat of Solid Bodies. [May 12,
BR, O,. It is seen that the compounds of those elements which, in the free
state, have themselves a smaller atomic heat than most other elements, are
characterized by a smaller atomic heat.
This leads the author to discuss whether it is to be assumed that the
elements enter into compounds with the atomic heats which they have in
the free state. This assumption is only admissible provided it can be
proved that the atomic heat of a compound depends simply on its empirical
formula, and not on the chemical character or rational constitution. Much —
of what has previously been said favours this view of the case. It is also
supported by the fact, which the author proves, that similar chemical cha-
racter in analogous compounds, and even isomorphism, do noé presuppose
equality in the atomic heats, if in one compound an atomic group (a com-
pound radical) stands in the place of an elementary atom of another: for
instance, the atomic heat of cyanogen compounds is considerably greater
than those of the corresponding chlorine compounds, and those of ammo-
nium materially greater than those of the corresponding potassium com-
pounds. A further support for that assumption is found in the fact that,
regardless of the chemical character, the atomic heat of complex com-
pounds is found to be the sum of the atomic heats of simpler atomic groups,
the addition of which gives the formulze of those more complex compounds.
A few cases selected from the comparisons of the author may explain this.
The atomic heats have been found,— :
For the oxides..... eke i cast RO Liga i
For binoxide of tin.......... Sn 0, 13°8 j
Motalwforson2 cae «ee RRO, 24-9 .
For sesquioxide of iron ...... Fe, O, 26°8
Or,
For oxides 2B 0.2 .00600.% =o 222
For binoxide of tn 3 Sn 0,..= RB, 0, 41:4
etal fora 3 Pee R, 0, 63°6
For arseniate of lead,......... Pb, As, O, 65:4
Finally, the author shows, as supporting that assumption, that (as was
already maintained) water is contained in solid compounds with the atomic
heat of ice. The various determinations of the specific heat of ice give the
atomic heat of H, © at 8°6 for temperatures distant from 0°, and at 9:1 to
9-8 at temperatures nearer 0°. The atomic heat has been found (to adduce
again a few comparisons) be
For crystallized chloride of calcium.... €aCl,+6H,O 75°6
For anhydrous chlorides ............ R Cl, 18°5
Difference for .......0..2 6H,O 571 _ 9.5
For crystallized gypsum ............ CaS 0,+ 2H, 0 45°8
For anhydrous sulphates ............ RSO 264
Difference for’... . 82 H;O 19°7_9-9
2
,
.
1864.] Dr. Kopp on the Specific Heat of Solid Bodies. 285
The opinion that the elements enter into compounds with the atomic heats
they have in the free state has been already expressed ; but the view has
also been defended that the atomic heat of an element may differ in a com-
pound from what it is in the free state, and may be different in different
compounds. The author discusses the latter view, and criticises the reasons
_ which may be adduced for it; he comes to the result that it is not proved
and is inadmissible.
As the result of all these comparisons and observations, the author arrives
at the conclusion, Each element, in the solid state and at an adequate dis-
tance from its melting-point, has one specific or atomic heat, which may
indeed somewhat vary with physical conditions (different temperature, or
different density for example), but not so much as to necessitate such
variations being taken into account in considering the relation in which the
specific or the atomic heat stands to the atomic weight or composition.
For each element it is to be assumed that it has essentially the same
specific heat or atomic heat in the free state and in compounds. He then
passes on to determine what atomic heats are to be assigned to the indivi-
dual elements. As data for determining this he takes (1) the atomic heats
which follow from determinations of the specific heat of the elements in
the free, solid state; (2) the atomic heats obtained for an element if, from
the atomic heat of one of its compounds, which contains beside it only
elements of known atomic heat, the atomic heats corresponding to the
latter elements are subtracted ; (3) the difference found between the atomic
heats of analogous compounds of an element of unknown and of an ele-
ment of known atomic heat, in which case the difference is taken as being
the difference between the atomic heats of these two elements. The au-
thor dwells upon the fact that in the indirect deduction of an element by
(2) and (3) the result may be uncertain,—first, because the atomic heats
of compounds are frequently not known with certainty, as is seen by the
circumstance that analogous compounds, for which there is every reason to
expect equal atomic heat, are found experimentally to exhibit considerable
differences ; but secondly, because in such deductions the entire relative
uncertainty, in the atomic heats for a compound and for that to be sub-
tracted from its composition, is thrown upon a small number, viz. the
residue remaining in the deduction.
The details of the considerations by which the author deduces the
atomic heat of the individual elements cannot be gone into; the results
simply, which are not all attained with equal certainty, may be adduced.
The author adopts the atomic heat 1°8 for ©, 2°3 for H, 2°7 for B, 3:7 for
Si, 4 for O, 5 for Fl, 5:4 for P and 8S, 6°4 for the other elements for which
or for whose compounds the atomic heat is known in somewhat more
trustworthy manner, it being left undecided in the case of the latter ele-
ments, whether (in accordance with Dulong and Petit’s law) they have the
same atomic heats, or whether the differences in the atomic heats cannot
at present be shown with certainty.
236. Dr. Kopp on the Specific Heat of Solid Bodies. [May 12,
The author gives for all compounds, whose specific heat has been inves-
tigated in a trustworthy manner, a comparison of the specific heats found
experimentally with those calculated on the above assumption. The
atomic heat of a compound is obtained by adding the atomic heats of the
elements in it, and the specific heat by dividing this atomic heat by the
atomic weight. The calculated specific heat of chloride of potassium,
KCL, is 0172 ; of sulphide of lead, Pb 8, op = 00494 oo
borate of potass, K B 9,, it is
C,H, 0, it is (4x —— 2°3)+6x4
The Table, embracing 200 compounds, shows, on the whole, a sufficient
agreement between the calculated and the observed specific heats. The
author remarks that a closer agreement between calculation and observation
cannot be hoped for than that between the observed atomic heats of those
compounds for which, from all we know at present, the same atomic heat is
to be expected in conformity with Neumann’s law, to which im such eases,
of course, caleulation corresponds. In only a few cases are differences be-
tween calculation and observation met with which exceed these limits or
exceed the deviation between the results of different observers for the same
substance. The author states that be is far from considering the agree-
ment between his calculations and the experimental results as a measure of
the accuracy of the latter, since the bases of calculation ate too far from
being trustworthy. But he hopes that his Table of atomic heats will soon
acquire such corrections, and therewith greater trustworthiness, as was
the case with the first Table of atomic weights. Here, the data for
the Table were at first but little certain, and the differences between the
calculated and observed composition of chemical compounds very con-
siderable ; but the Table was the means of corrections being introduced
by which these differences were diminished.
If calculation ofthe specific heat does not supersede the necessity of
experimental determination in the solid state, and does not give a trust-
worthy measure for the accuracy of such determinations, it gives a rough
control for the experimental determinations, and it indicates sources of
error in the experiments which without it would not have been noticed.
An instance may be adduced. The author found for sesquichloride of
carbon, ©, Cl,, which, according to Faraday, melts at 160°, the specific
heat between 20° and 50° to be 0°276 in one series of experiments, and
0°265 in another. Hence the number 0°27 might from this be taken
to express the specific heat of the compound. But calculation gives
(2x 1°8)+(6 x oe
237
experiments with substance once more recrystallized, gave for the specific
heat between 21° and 49° 0°278, confirming the previous determinations.
6:442:74(2x4)_
ee
ad
0°209; of tartaric acid,
=0°300.
77, a very different number. A third series of
a
1864] Dr. Kopp on the Specific Heat of Solid Bodies. 237
It might here appear doubtful whether calculation was not refuted by
experiment. The discrepancy was removed by the observation that the
substance is distinctly more viscous at 50° than it is at lower temperatures,
and by the suspicion that it might at 50° (that is, 100° below its melting-
point) already absorb some of its latent heat of vitreous fusion. This was
found to be the case; two concordant series of experiments gave as the
mean of the specific heat the numbers :
Between 18° and 37°
Between 18° and 43°
Between 18° and 50° ...... 0°277
The first two numbers differ so little that it may be supposed the number
found for temperatures below 37° is very near the true specific heat of this
compound ; it also agrees well with the calculated number.
In the sixth part the author enters into considerations on the nature of
the chemical elements.
He calls to mind the discrepancy which has prevailed, and still prevails,
in reference to certain bodies, between their actual indecomposability, and
the considerations, based on analogy, according to which they were held to
be compound. kEven after Davy had long proclaimed the elementary
nature of chlorine, it was maintained that it contained oxygen. In regard |
both to that substance and to bromine and iodine, the view that they are
peroxides of unknown elements still finds defenders. That iodine, by a
direct determination of specific heat, and chlorine, by indirect deduction,
are found to have an atomic heat in accordance with Dulong and Petit’s
law, puts out of doubt that iodine and chlorine, if compound at all, are
not more so than the other elements to which this law is considered to
apply.
According to Dulong and Petit’s law, compounds of analogous atomic
composition have approximately equal atomic heats. In general, com-
pounds whose atom consists of a larger number of undecomposable atoms,
or is of more complex constitution, have greater atomic heat. Especially
in those compounds all of whose elements follow Dulong and Petit’s law,
is the magnitude of the atomic heat a measure of the complication, or of
the degree of complication. If Dulong and Petit’s law were universally
valid, it might be concluded with great certainty that the so-called ele-
ments, if they are really compounds of unknown simpler substances, are
compounds of the same order. It would be a remarkable result, if the
art of chemical decomposition had everywhere reached its limits at such
bodies as, if at all compound, have the same degree of composition.
Let us imagine the simplest bodies, perhaps as yet unknown to us; the true
chemical elements, to form a horizontal layer, and above them to be
arranged the more simple and then the more complicated compounds; the
general_validity of Dulong and Petit’s law would include the proof that
all the elements at present assumed to be such by chemists lay in the
same layer, and that, in admitting hydrogen, oxygen, sulphur, chlorine,
208 Dr. Kopp on the Specific Heat of Solid Bodies. [May 12,
and the various metals as elements, chemistry has penetrated to the same
depth in that range of inquiry, and has found at the same depth the limit
to its advance.
But with the proof that this law is not universally true, the conclusion
to which this result leads loses its authority. If we start from the ele-
ments at present assumed in chemistry, we must admit rather that the
magnitude of the atomic heat of a body does not depend on the number of
elementary atoms contained in a molecule, or on the complication of its
composition, but on the atomic heat of the elementary atoms which enter
into its composition. It is possible that a decomposable body may have
the same atomic heat as an element. Chlorine might certainly be the
peroxide of an unknown element which had the atomic heat of hydrogen ;
the atomic heat of peroxide of hydrogen, H ©, in the solid state or in
solid compounds, must be =2°3+4=6°3, agreeing very nearly with the
atomic heats of iodine, chlorine, and the elements which follow Dulong and
Petit’s law.
In a very great number of compounds the atomic heat gives more or
less accurately a measure for the complication of the composition. And
this is also the case with those compounds which, from their chemical
deportment, are comparable to the undecomposed bodies. If ammonium
or cyanogen had not been decomposed, or could not be by the chemical
means at present available, the greater atomic heats of the compounds of
these bodies, as compared with analogous potassium or chlorine com-
pounds, and the greater atomic heats of ammonium and cyanogen ob-
tained by indirect determination, as compared with those of potassium and
chlorine, would indicate the compound nature of those so-called compound
radicals. The conclusion appears legitimate, that, for the so-called ele-
ments, the directly or indirectly determined atomic heats are a measure for
the complication of their composition. Carbon and hydrogen, for exam-
ple, if not themselves actually simple bodies, are yet simpler compounds
of unknown elements than silicium or oxygen; and still more complex are
the elements which may be considered as following Dulong and Petit’s law.
It may appear surprising, and even improbable, that so-called elements,
which can replace each other in compounds, as for instance hydrogen and
the metals, or which enter into isomorphous compounds as corresponding
elements, like silicium and tin, should possess unequal atomic heats and
unequal complication of composition. But this really is not more sur-
prising than that undecomposable bodies and obviously compound bodies,
hydrogen and hyponitric acid, or potassium and ammonium, should, with-
out altering the chemical character of the compound, replace one another,
or even be present in isomorphous compounds as corresponding con-
stituents.
The author concludes his memoir with the following words :—‘“ I have
here expressed opinions, in reference to the nature of the so-called ele-
ments, which appear to depend upon allowable conclusions from well-
1864.] Messrs. Parker and Jones on Foraminifera. 239
demonstrated principles. It is of the nature of the case,{that with these
opinions the certain basis of the actual, and of what can be empirically
proved, is left. It must also not be forgotten that these conclusions only
give some sort of clue as to which of the present undecomposable bodies
are of more complicated, and which of simpler composition, and nothing
as to what the simpler substances are which are contained in the more
complicated. Consideration of the atomic heats may declare something
as to the structure of a compound atom, but can give no information as to
the qualitative nature of the simpler substances used in the construction of
the compound atoms. But even if these conclusions are not free from
uncertainty and imperfection, they appear to me worthy of attention in a
subject which is still so shroudedin darkness as the nature of the unde-
composed bodies.”
III. “On some Foraminifera from the North Atlantic and Arctic
Oceans, including Davis Strait and Baffin Bay.” By W.
Kircaen Parker, F.Z.8., and Professor T. Rupert Jonzs,
F.G.S. Communicated by Professor Huxtuy. Received April
26, 1864.
(Abstract. )
Having received specimens of sea-bottom, by favour of friends, from
Baffin Bay (soundings taken in one of Sir E. Parry’s expeditions), from
the Hunde Islands in Davis Strait (dredgings by Dr. P. C. Sutherland),
from the coast of Norway (dredgings by Messrs. M‘Andrew and Barrett),
and. from the whole width of the North Atlantic (soundings by Commander
Dayman), the authors have been enabled to form a tolerably correct esti-
mate of the range and respective abundance of several species of Foramini-
fera in the Northern seas; and the more perfectly by taking Professor
Williamson’s and Mr. H. B. Brady’s researches in British Foraminifera as
supplying the means of estimating the Foraminiferal fauna of the shallower
sea-zones at the eastern end of the great “‘ Celtic Province,” and the less
perfect researches of Professor Bailey on the North American coast, for the
opposite, or “ Virginian” end,—thus presenting for the first time the
whole of a Foraminiferal fauna as a natural-history group, with its internal
and external relationships.
The relative abundance or scarcity and the locations of the several species
and chief varieties are shown by Tables; and their distribution in other
seas (South Atlantic, Pacific, and Indian Oceans, and the Mediterranean
and Red Seas) is also tabulated; and in the descriptive part of the memoir
notes on their distribution, both in the recent and the fossil state, are care-
fully given.
In the description of the species and varieties there are observations
made on those forms which have been either little understood, hitherto
240 Dr. Phipson on the Variations of Density [May 26,
unknown, or mistaken; and the relationship, by structure or by imitation,
of the species and varieties is dwelt upon. For the description of the
better-known Foraminifera, the memoir refers to the works of Williamson
and Carpenter.
The authors enumerate 109 specific and varietal forms, most of which
receive descriptive comment, and all of which are figured in five plates
(two for the North Atlantic and three for the Arctic Foraminifera) with
upwards of 340 figures.
The relationships of the Lagene are specially treated of. Uvigerina,
Globigerina, and especially some of the Rotaline (Planorbulina, Discor-
bina, Rotalia, Pulvinulina) and Polystomella (including Nonionina) are
among those which are well represented in the fauna under description,
and have received much attention in the memoir.
The Society then adjourned over the Whitsuntide Recess to Thursday,
May 26.
May 26, 1864:
Major-General SABINE, President, in the Chair.
The following communications were read :—
I. “ Note on the Variations of Density produced by Heat in Mineral
Substances.” By Dr. T. L. Puirson, F.C.S., &c. . Communi-
cated by Professor Tynpatu. Received April 16, 1864.
That any mineral substance, whether crystallized or not, should diminish
in density by the action of heat might be looked upon as a natural con-
sequence of dilatation being produced in every case and becoming per-
manent. Such diminution of density occurs with idocrase, Labradorite,
felspar, quartz, amphibole, pyroxene, peridote, Samarskite, porcelain, and
glass. But Gadolinite, zircons, and yellow obsidians augment in density
from the same cause. This again may be explained by assuming that
under the influence of a powerful heat these substances undergo some per-
manent molecular change. But in this NoteI have to show that this mole-
cular change is not permanent but intermittent, at least as regards the
species I have examined, and probably with all the others. Such researches,
while tending to elucidate certain points of chemical geology, may likewise
add something to our present knowledge of the modes of action of heat.
My experiments were undertaken to prove an interesting fact announced
formerly by Magnus, namely, that specimens of idocrase after fusion had
diminished considerably in density without undergoing any change of com-
position: before fusion their specific gravity ranged from 3°349 to 3°45,
and after fusion only 2°93 to 2°945. Having lately received specimens of
this and other minerals brought from Vesuvius in January last by my friend
Henry Rutter, Esq., I determined upon repeating this experiment of
1864. ] produced by Heat in Mineral Substances. 241
Magnus. I found, first, that what he stated for idocrase and for a speci-
men of reddish-brown garnet was also the case with the whole family of
garnets as well as the minerals of the idocrase group ; secondly, that it is
not necessary to melt the minerals: it is sufficient that they should be
heated to redness without fusion, in order to occasion this change of density ;
thirdly, that the diminished density thus produced by the action of a red
heat is not a permanent state, but that the specimens, in the course of a
month or less, resume their original specific gravities.
These curious results were first obtained by me with a species of lime
garnet, in small yellowish crystals, exceedingly brilliant and resinous,
almost granular, fusing with difficulty to a black enamel, accompanied with
very little leucite and traces of grossular, and crystallized in the second
system.
Specimens weighing some grammes had their specific gravity taken with
great care, and by the method described by me in the ‘ Chemical News’ for
1862. ‘They were then perfectly dried and exposed for about a quarter of
an hour to a bright red heat. When the whole substance of the specimen
was observed to have attained this temperature, without trace of fusion, it
was allowed to cool, and when it had arrived at the temperature of the
atmosphere, its specific gravity was again taken by the same method as be-
fore. The diminution of density being noted, the specimens were carefully
dried, enveloped in several folds of filtering paper, and put aside in a box
along with other minerals. In the course of a month it occurred to me
that it would be interesting to take the specific gravity again, in order to
ascer‘ain whether it had not returned to its original figure, when, to my
surprise, I found that each specimen had effectively increased in density
and had attained its former specific gravity. Thus:—
Lime garnet (from Vesuvius).
Density after being heated Density determined in
red-hot for a quarter of an a month after the
Original density. hour and allowed to cool. experiments.
Meer tea RLS ee DPOT BR. PEW AG Se ale 3°344
eee Oe Ee ek ye BOBO Ole A aloe a 3°350
rere rr he S22 Pe 2977 9%, ONC a) eee iasoaa
The same experiments were made with several other minerals belonging
to the idocrase and garnet family, and always with similar results. Now
I ask, what becomes of the heat that seems to be thus shut up in a mineral
substance for the space of a month? The substance of the mineral is di-
lated, the distance between its molecules is enlarged, but these molecules
slowly approach each other again, and in the course of some weeks resume
their original positions. What induces the change? or how does it happen
that the original specific gravity is not acquired immediately the substance
has cooled ?* ‘Will the same phenomenon show itself with other families
of minerals or with the metallic elements ?
* Some minerais , like euclase, that become electric by heat, retain that state for a
a
242 Messrs. Huggins and Miller on Spectra [May 26,
Such are the points which I propose to examine in the next place ; in
the mean time the observations I have just alluded to are a proof that
bodies can absorb a certain amount of heat not indicated by the thermo-
meter (which becomes Jatent), and that this is effected without the body
undergoing a change of state; secondly, that they slowly part with this
heat again until they have acquired their original densities; thirdly, so
many different substances being affected by a change of density when
melted or simply heated to redness and allowed to cool, it is probable this
property will be found to belong, more or less, to all substances without
exception.
IT. “On the Spectra of some of the Fixed Stars.” By W. Hue.
cins, F.R.A.S., and Witi1am A. Mitier, M.D., LL.D., Trea-
surer & V.P.R.S., Professor of Chemistry, King’s College, London.
Received April 28, 1864,
(Abstract. )
After a few introductory remarks, the authors describe the apparatus
which they employ, and their general method of observing the spectra of
the fixed stars and planets. ‘The spectroscope contrived for these inqui-
ries was attached to the eye end of a refracting telescope of 10 feet focal
length, with an 8-inch achromatic object-glass, the whole mounted equa-
torially and carried by a clock-movement. In the construction of the
spectroscope, a plano-convex cylindrical lens, of 14 inches focal length, was
employed to convert the image of the star into a narrow line of light,
which was made to fall upon a very fine slit, behind which was placed an
achromatic collimating lens. The dispersing portion of the arrangement
consisted of two dense flint-glass prisms; and the spectrum was viewed
through a small achromatic telescope with a magnifying power of between
5 and 6 diameters. Angular measures of the different parts of the spec-
trum were obtained by means of a micrometric screw, by which the posi-
tion of the small telescope was regulated. A reflecting prism was placed
over one half of the slit of the spectroscope, and by means of a mirror,
suitably adjusted, the spectra of comparison were viewed simultaneously
with the stellar spectra. This light was usually obtained from the in-
duction spark taken between electrodes of different metals. The dispersive
power of the apparatus was sufficient to enable the observer to see the line
Ni of Kirchhoff between the two solar lines D; and the three constituents
of the magnesium group at 0 are divided still more evidently *. Minute
considerable time. The increase of density of Gadolinite and the decrease of density of
Samarskite by the action of heat are accompanied by a vivid emission of light, as mentioned
in my work on ‘ Phosphorescence’ &c., pp. 31 and 32, where H. Rose’s ingenious expe-
riment is described.
* Each unit of the scale adopted was about equal to -3,;th of the distance between
A and H in the solar spectrum. The measures on different occasions of the same line
rarely differed by one of these units, and were often identical,
1864. ] some of the Fixed Stars. 243.
details of the methods adopted for testing the exact coincidence of the
corresponding metallic lines with those of the solar and lunar spectrum,
are given, and the authors then proceed to give the results of their obser-
vations.
Careful examination of the spectrum of the light obtained from various
points of the moon’s surface failed to show any lines resembling those due
to the earth’s atmosphere. The planets Venus, Mars, Jupiter, and Saturn
were also examined for atmospheric lines, but none such could be disco-
vered, though the characteristic aspect of the solar spectrum was recognized
in each case; and several of the principal lines were measured, and found
to be exactly coincident with the solar lines.
Between forty and fifty of the fixed stars have been more or less com-
pletely examined; and tables of the measures of about 90 lines in Alde-
baran, nearly 80 in @ Orionis, and 15 in 6 Pegasi are given, with dia-
grams of the lines in the two stars first named. These diagrams include
the results of the comparison of the spectra of various terrestrial ele-
ments with those of the star. In the spectrum of Aldebaran coincidence
with nine of the elementary bodies were observed, viz. sodium, magnesium,
hydrogen, calcium, iron, bismuth, tellurium, antimony, and mercury; in
seven other cases no coincidence was found to occur.
In the spectrum of a Orionis five cases of coincidence were found, viz.
sodium, magnesium, calcium, iron, and bismuth, whilst in the case of ten
other metals {no coincidence with the lines of this stellar spectrum was
found.
( Pegasi furnished a spectrum closely resembling;that of « Orionis in
appearance, but much weaker: only a few of the lines admitted of accu-
rate measurement, for want of light; but the coincidence of sodium and
magnesium was ascertained; that of barium, iron, and manganese was
doubtful. Four other elements were found not to be coincident. In par-
ticular, it was noticed that the lines C and F, corresponding to hydrogen,
which are present in nearly all the stars, are wanting in @ Orionis and
( Pegasi.
The investigation of the stars which follow is less complete, and no
details of measurement are given, though several points of much interest
have been ascertained.
Sirius gave a spectrum containing five strong lines, and numerous finer
lines. The occurrence of sodium, magnesium, hydrogen, and probably of
iron, was shown by coincidence of certain lines in the spectra of these
metals with those in the star. In # Lyre the occurrence of sodium, mag-
nesium, and hydrogen was also shown by the same means. In Capella
sodium was shown, and about twenty of the lines in the star were mea-
sured. In Arcturus the authors have measured about thirty lines, and have
observed the coincidence of the sodium line with a double line in the star-
spectrum. In Pollux they obtained evidence of the presence of sodium,
VOL. XIII. U
244 Mr. Cayley on Skew Surfaces. [May 26,
magnesium, and probably of iron. The presence of sodium was also indi-
cated in Procyon and a Cygnt.
In no single instance have the authors ever ohsortid a star-spectrum in
which lines were not discernible, if the light were sufficiently intense, and
the atmosphere favourable. Rigel, for instance, which some authors state
to be free from lines, is filled with a multitude of fine lines.
Photographs of the spectra of Sirius and Capella were taken upon collo-
dion; but though tolerably sharp, the apparatus employed was not suffi-
ciently perfect to afford any indication of lines in the photograph.
In the concluding portion of their paper, the authors apply the facts
observed to an explanation of the colours of the stars. They consider that
the difference of colour is to be sought in the difference of the constitution
of the investing stellar atmospheres, which act by absorbing particular
portions of the light emitted by the incandescent solid or liquid photo-
sphere, the light of which in each case they suppose to be the same in
quality originally, as it seems to be independent of the chemical nature of
its constituents, so far as observation of the various solid and liquid ele-
mentary bodies, when rendered incandescent by terrestrial means, appears
to indicate.
III. “A Second Memoir on Skew Surfaces, otherwise Serolls.” By
A, Cayiey, Esq., F.R.S. Received April 29, 1864.
(Abstract. )
_ The principal object of the present memoir is to establish the different
kinds of skew surfaces of the fourth order, or Quartic Scrolls ; but, as preli-
minary thereto, there are some general researches connected with those in
my former memoir “On Skew Surfaces, otherwise Scrolls’? (Phil. Trans.
vol, 153. 1863, pp. 453, 483), and I also reproduce the theory (which may
be considered as a known one) of cubic scrolls; there are also some con-
cluding remarks which relate to the general theory. As regards quartic
scrolls, I remark that M. Chasles, in a footnote to his paper, ‘‘ Description
des Courbes de tous les ordres situées sur les surfaces réglées du troisiéme
et du quatricme ordres,’? Comptes Rendus, t. lili. (1861), see p. 888,
states, “les surfaces réglées du quatriéme ordre. . . . admettent guatorze
espéces.’”’ This does not agree with my results, since I find only eight spe-
cies of quartic scrolls; the developable surface or “‘torse”’ is perhaps in-
cluded as a “‘surface réglée;’’ but as there is only one species of quartic
torse, the deficiency is not to be thus accounted for. My enumeration ap-
pears to me complete, but it is possible that there are subforms which M.
Chasles has reckoned as distinct species.
1864,] — Prof. Boole on Differential Equations. 245
IV. “On the Differential Equations which determine the form of
the Roots of Algebraic Equations.” By Gzorez Bootg, F.R.S.,
Professor of Mathematics in Queen’s College, Cork. Received
April 27, 1864.
(Abstract.)
Mr, Harley* has recently shown that any root of the equation
y® —ay+(n—1)x=0
satisfies the differential equation
sssd =9 aed
(p 2n *) (D 3n ) " (D n 1)
n n n (n=)
D(D—1) .. (D—2+1) =O) ..f EP)
in which e?=2z, and D=-,, provided that x be a positive integer greater
d
de?
than 2. This result, demonstrated for particular values of m, and raised by
induction into a general theorem, was subsequently established rigorously
by Mr. Cayley by means of Lagrange’s theorem.
For the case of »=2, the differential equation was found by Mr. Harley
to be
1
me ee es
Solving these differential equations for the particular cases of n=2 and
n=3, Mr. Harley arrived at the actual expressions of the roots of the
given algebraic equation for these cases. That all algebraic equations up
to the fifth degree can be reduced to the above trinomial form, is well
known.
_ A solution of (1) by means of definite triple integrals in the case of n=4
has been published by Mr. W. H. L. Russell; and I am informed that a
general solution of the equation by means of a definite single integral has
been obtained by the same analyst.
While the subject seems to be more important with relation to diffe-
rential than with reference to algebraic equations, the connexion into which
the two subjects are brought must itself be considered as a very interesting
fact. As respects the former of these subjects, it may be observed that it
is a matter of quite fundamental importance to ascertain for what forms of
the function » (D), equations of the type
Ute AV eP ey hi) ng! Bas ent B)
admit of finite solution. We possess theorems which enable us to deduce
from each known integrable form, an infinite number of others. Yet there
is every reason to think that the number of really primary forms—of forms
the knowledge of which, in combination with such known theorems, would
enable us to solve all equations of the above type that are finitely solvable—
os
* Memoirs of the Literary and Philosophical Society of Manchester.
u 2
246 Prof. Boole on Differential Equations. [May 26,
is extremely small. It will, indeed, be a most remarkable conclusion,
should it ultimately prove that the primary solvable forms in question
stand in some absolute connexion with a certain class of algebraic equations.
The following paper is a contribution to the general theory under the
aspect last mentioned. In endeavouring to solve Mr. Harley’s equation by
definite integrals, I was led to perceive its relation to a more general equa-
tion, and to make this the subject of investigation. The results will be
presented in the following order :—
First, I shall show that if u stand for the mth power of any root of the
algebraic equation
y” — ay" + — 1 —0,
then uw, considered as a function of x, will satisfy the differential equation
[D]"u-+ “= so Ser ery —(),
in which e=27, D= = and the notation
[a]®=a (a—1) (a—2).. (a—6+1)
is adopted.
Secondly, I shall show that for particular values of m, the above equa-
tion admits of an immediate first integral, constituting a differential equation
of the n—1th order, and that the results obtained by Mr. Harley are par-
ticular cases of this depressed equation, their difference of form arising from
difference of determination of the arbitrary constant.
Thirdly, I shall solve the general differential equation by definite in-
tegrals.
Fourthly, I shall determine the arbitrary constants of the solution so as
to express the mth power of that real root of the proposed algebraic equa-
tion which reduces to 1 when 7=0.
The differential equation which forms the chief subject of these investi-
gations certainly occupies an important place, if not one of exclusive im-
portance, in the theory of that large class of differential equations of which
the type is expressed in (3). At present, I am not aware of the existence
of any differential equations of that particular type which admit of finite
solution at all otherwise than by an ultimate reduction to the form in
question, or by a resolution into linear equations of the first order. It
constitutes, in fact, a generalization of the form
a(D—2)’?+n? 2
DD Aycte e
given in my memoir “On a General Method i in Analysis’ (Philosophical
Transactions for 1844, part 2).
w+
1864.] General Sabine on Magnetic Disturbances. 247
Y. “A Comparison of the most notable Disturbances of the Magnetic
Declination in 1858 and 1859 at Kew and Nertschinsk, preceded
by a brief Retrospective View of the Progress of the Investiga-
tion into the Laws and Causes of the Magnetic Disturbances.”
By Major-General Epwarp Sasine, R.A., President of the
Royal Society. Received April 28, 1864.
(Abstract.)
The author commences this paper by taking a retrospective view of the
principal facts which have been established regarding the magnetic disturb-
ances, considered as a distinct branch of the magnetic phenomena of the
globe, from the time when they were first made the objects of systematic
investigation by associations formed for that express purpose, at Berlin in
1828 and at Gottingen in 1834, and dwelling more particularly on the
results subsequently obtained by the more complete and extended researches
instituted in 1840 by the British Government on the joint recommendation
of the Royal Society and of the British Association for the Advancement
of Science.
The Berlin Association, formed under the auspices of Baron Alexander
von Humboldt, consisted of observers in very distant parts of the European
continent, by whom the precise direction of the declination-magnet was
recorded simultaneously at hourly intervals of absolute time, at forty-four
successive hours at eight concerted periods of the year, which thence ob-
tained the name of “ Magnetic Terms.’ By the comparison of these hourly
observations it became known that the declination was subject to very con-
siderable fluctuations, happening on days which seemed to be casual and
irregular, but were the same at all the stations, consequently over the con-
tinent of Europe generally. This conclusion was confirmed by the Got-
tingen Association, established at the instance and under the superintendence
of MM. Gauss and Weber, by whom the ‘‘Term-observations ’’ were extended
to six periods in the year, each of twenty-four hours’ duration, the records
being made at intervals of five minutes. The number of the stations at
which these observations were made was about twenty, distributed generally
over the continent of Europe, but not extending beyond it. They were
continued from 1834 to 1841. The observations themselves, as well as the
conclusions drawn from them by MM. Gauss and Weber, were published in
the well-known periodical entitled ‘ Resultate aus der Beobachtungen des
magnetischen Vereins.’ The synchronous character of the disturbances,
over the whole area comprehended by the Association, was thoroughly con-
firmed: the disturbing action was found to be so considerable as to occa-
sion frequently a partial, and sometimes even a total obliteration of the
regular diurnal movements, and to be of such general prevalence over the
greater part of Europe, not only in the larger, but in most of the smaller
oscillations, as to make it in avery high degree improbable that they could
248 General Sabine—Comparison of Magnetic [May 26,
have either a local or an atmospherical origin. No connexion or correspon-
dence was traceable between the indications of the magnetical and meteoro-
logical instruments; nor had the state of the weather any perceptible in-
fluence. It happened very frequently that either an extremely quiescent
state of the needle or a very regular and uniform progress was preserved
during the prevalence of the most violent storm ; and as with wind-storms,
so with thunder-storms, as even when close at hand they appeared to exer-
cise no perceptible influence on the magnet. At some of the most active
of the Géttingen stations the fluctuations of the horizontal force were ob-
served contemporaneously with those of the declination-magnet, by means
’ of the bifilar magnetometer devised by M. Gauss: both elements were
generally disturbed on the same days and at the same hours. The
magnitude of the disturbances appeared to diminish as their action was
traced from north to south, giving rise to the conclusion that the focus
whence the most powerful disturbances in the northern hemisphere ema-
nated might perhaps be successfully sought in parts of the globe to the
north or north-west of the area comprehended by the stations. The imter-
comparison of the records obtained at the different stations showed more-
over that the same element was very differently affected at the same hours
at different stations; and that occasionally the same disturbance showed
itself in different elements at different stations. The general conclusion
was therefore thus drawn by M. Gauss, that ‘‘ we are compelled to admit
that on the same day and at the same hour various forces are contempo-
raneously in action, which are probably quite independent of one another
and have very different sources, and that the effects of these various forces
are intermixed in very dissimilar proportions at various places of observa-
tion relatively to the position and distance of these latter; or these effects
may pass one into the other, one beginning to act before the other has
ceased. The disentanglement of the complications which thus occur in
the phenomena at every individual station will undoubtedly prove very
difficult. Nevertheless we may confidently hope that these difficulties will
not always remain insuperable, when the simultaneous observations shall
be much more widely extended. It will be a triumph of science should
we at some future time succeed in arranging the manifold intricacies of the
phenomena, in separating the individual forces of which they are the
compound result, and in assigning the source and measure of each.”
In the British investigations, which commenced in 1840, the field of re-=
search was extended so as to include the most widely separated localities
in both hemispheres, selected chiefly with reference to diversity of geo-
graphical circumstances, or to magnetic relations of prominent interest.
Suitable instruments were provided for the observation of each of the three
magnetic elements; the scheme of research comprehended not alone the
casual and irregular fluctuations which had occupied the chief attention of
the German associations, but also “the actual distribution of the magnetic
influence over the globe at the present epoch in its mean or average state,
1864, | Disturbances at Kew and Nertschinsk. 249
together with all that is not permanent in the phenomena, whether it
appear in the form of momentary, daily, monthly, semiannual, or annual
change, or in progressive changes receiving compensation possibly, either
in whole or in part, in cycles of unknown relation and unknown period.”
The magnetic disturbances to which the notices in the present paper are
limited, form a small but important branch of this extensive inquiry, and are
referred to in the instructions prepared by the Royal Society in terms which
are recalled by the author on the present occasion, because they are ex-
planatory of the principles on which the coordination of the results ob-
tained in such distant parts of the world has been conducted, and the
conclusions derived from them established. In pages 2 and 3 of the
Report embodying the instructions drawn up by the Royal Society, it is
stated that ‘‘ the investigation of the laws, extent, and mutual relations of
the casual and transitory variations is become essential to the success-
ful prosecution of magnetic discovery .... because the theory of those
transitory changes is in itself one of the most interesting and important
points to which the attention of magnetic observers can be turned, as they
are no doubt intimately connected with the general causes of terrestrial
magnetism, and will probably lead us to a much more perfect knowledge
of those causes than we now possess.” In the opinion thus expressed, the
author, who was himself one of the committee by whom the Report was
drawn up, fully concurred; and having been appointed by Her Majesty’s
Government to superintend the observations made at the British Colonial
observatories, and to coordinate and publish their results, he has endea-
voured to show in this paper that the methods pursued have been in strict
conformity with these instructions, and also that the conclusions derived are
in accordance with the anticipations expressed therein.
Inferences regarding the ‘‘ general causes of terrestrial magnetism ”’
must be based upon the knowledge we possess of the actual distribution of
the magnetic influence on the surface of the globe, since that is the only
part which is accessible to us. In regard to this distribution, the Report
itself refers continually to two works, then recently published, as contain-
ing the embodiment of the totality of the known phenomena, viz. a
“Memoir on the Variations of the Magnetic Force in different parts of the
Earth’s Surface,” published in 1838 in the Reports of the British Associa-
tion, and M. Gauss’s ‘ Allgemeine Theorie des Erdmagnetismus,’ published
in 1839. In both these works the facts, as far as they had been ascertained,
were conformable in their main features to the theory, first announced by
Dr. Halley in his Papers in the Philosophical Transactions for 1683 and
1693, of a double system of magnetic action, the direction and intensity
of the magnetic force being, at all points of the earth’s surface, the -
resultants of the two systems. In both these works the Poles, or Points
of greatest force (in the northern. hemisphere) were traced nearly to the
same localities—viz. one in the northern parts of the American continent,
and the other in the northern parts of the Europso-Asiatic continent,—their
250 General Sabine—Comparison of Magnetic [May 26,
geographical positions, as taken from M. Gauss’s ‘ Allgemeine Theorie,’
being, in America, lat. 55°, long. 263° E., and in Siberia lat. 71°, long.
116° E. Combining then the expectation expressed in the Report of “a
probable connexion existing between the casual and transitory magnetic
variations and the general phenomena of terrestrial magnetism,’ with
M. Gauss’s conclusion from the Géttingen researches, that “the sources
of the magnetic disturbances in Europe might possibly be successfully
sought in parts of the globe to the north or to the north-west of the
European continent,” it seemed reasonable to anticipate that a connexion
might be found to exist between the “ points of origin” of the disturb-
ances, if these could be more precisely ascertained, and the critical locali-
ties of the earth’s magnetism above referred to. To put this question
to the test, the first step was to ascertain in a more satisfactory way
than had been previously attempted, the laws of the disturbances
themselves. The process by which a portion of the observations ex-
hibiting the effects of the disturbing action in a very marked degree
may be separated from the others, and subjected to a suitable analysis
for the determination of their general laws, has been fully described else-
where. The immediate effect of its application was to show that, casual
and irregular as the disturbances might appear to be in the times of their
occurrence, they were, in their mean effects, strictly periodical phenomena,
characterized by laws distinct from those of any other periodical phenomena
with which we were then acquainted, and traceable directly to the Sun as
their primary source, Inasmuch as they were found to be governed every-
where by laws depending upon the solar hours. To those who are familiar
with the theory by which the passage of light from the sun to the earth is
explained, an analogous transmission of magnetic influences from the sun
to the earth may appear to present no particular difficulty. It is when
the influences reach the earth that the modes of their reception, distribu-
tion, and transmission are less clearly seen and understood ; but these are
within our own proper terrestrial domain and sphere of research; and ac-
cordingly it was to these that the author’s attention was directed. Where-
ever the disturbances had been observed and were analyzed, it was found
that those of the declination were occasionally deflections to the east and
occasionally deflections to the west of the mean position of the magnet,
and those of the horizontal and vertical forces occasionally increased and
occasionally diminished the respective forces. The disturbances of each
element were therefore separated into two categories, according as they be-
longed to one or to the other class. Each category was found to present
diurnal progressions, of systematic regularity, but quite distinct from one
another, and so far in accordance with M. Gauss’s inference of the existence
of various forces contemporaneously in action, independent of one another,
and having different originating sources. Confining our view, for simplicity,
to one alone of the elements, viz. the declination, its two categories (of
easterly and of westerly deflection) presented, wherever they were examined,
1864. ] Disturbances at Kew and Nertschinsk. 251
the same distinctive features ; the local hours or maximum and minimum
varied at different stations, but the same two dissimilar forms were every-
where presented by the curves representing the two diurnal progressions.
Having thus traced apparently two sources in which the disturbances
might be supposed to originate, the possible connexion of these with the
points of maximum attraction in the two systems of the magnetic terrestrial
distribution presented itself as the next object of fitting research. It was
inferred that if two stations were selected in nearly the same latitude, but —
situated one decidedly on the eastern side and the other decidedly on the
western side of one of the points referred to, the curve of the easterly de-
flection at the one station would perhaps be found to correspond with the
curve of westerly deflection at the other station at the same hours of abso-
lute time, and vice versd. 'The Kew photograms in the five years 1858 to
1862 supplied the necessary data for one of the two stations, viz. the one
to the west of the point of maximum attraction of one of the two mag-
netic systems, whilst Pekin, where hourly observations from 1851 to 1855
inclusive are recorded in the ‘ Annales de l’Observatoire Central Physique
de Russie,’ might supply a station on its eastern side. As this comparison
might be regarded somewhat in the light ofa crucial experiment, the reliance
to which the Pekin observations were entitled was examined by the very deli-
cate test afforded by rewriting the observations recorded at solar hours in
hours of lunar time, and examining the lunar-diurnal variation thence
derived. When this is found to come out systematically and well, and
similarly in different years, the observations which have furnished it may
be safely regarded as trustworthy.. The Pekin observations corresponded
satisfactorily to this test, and in the Philosophical Transactions for 1863,
Art. XII., the comparison was made of the Kew and Pekin disturbance-
deflections, the result showing that ‘the conical form and single maximum
which characterize the curve of the easterly deflections at Kew, characterize
the curve of the westerly deflections at Pekin at approximately the same
hours of absolute time.”’ Fora further trial of this important result, a
second comparison of the same kind was made, being that of the curves of
the disturbance-deflections at Nertschinsk from 1851 to 1857, also re-
corded in the ‘ Annales de l’Observatoire,’ &c., with those from 1858 to
1862 at Kew. Nertschinsk is about 12° north of Pekin, and is nearly in
the same longitude as that station, whilst its latitude is almost identical
with that of Kew. The Nertschinsk observations were subjected to the
same test in respect to accuracy as those of Pekin, and with a similarly
satisfactory result. ‘The comparison of the disturbance-deflections showed
a still more perfect accord between the curves representing the easterly
deflections at Kew and the westerly at Nertschinsk at approximately the
same hours of absolute time.
The present paper contains a further comparison of the nearly synchro-
nous disturbances at Kew and at Nertschinsk on the days of most notable
disturbance at both stations in 1858 and 1859, the comparison being
252 General Sabine on Magnetic Disturbances. [May 26,
limited to those two years inasmuch as the Kew record did not commence
until January 1858, whilst the hourly observations at Nertschinsk for
1860 and subsequent years have not yet reached England. The deflections
at Nertschinsk from the normals of the same month and hour, on forty-four
days in 1858 and 1859, are given in a Table similar in all respects to the
Table, in the Philosophical Transactions for 1863, showing the deflections on
the most notable days of disturbance at Kew in the same years. The com-
parison of the two Tables is discussed in some detail ; but it is sufficient to
state here that the general conclusions are quite in accordance with those
arrived at in the previous comparisons.
The steps by which the author was led to a discovery of the decennial
variation in the magnetic disturbances, aud to its identification in period and
epochs with the variation in the magnitude and frequency of the sun-spots
resulting from the observations of M. Schwabe since their commencement in
1826, are too well known to need repetition on this occasion. But they
furnish the ground on which, in this paper, he has for the first time sug-
gested the possibility that a cosmical connexion of a somewhat similar
nature may be hereafter recognized as the origin and source of one of
the two magnetic systems which cooperate in producing the general
phenomena of the variations of the magnetic direction and force in dif-
ferent parts of the globe. The author’s suggestion is, that the one of
the two systems which is distinguished by its possessing a systematic
and continuous movement of geographical translation, thereby giving
rise to the phenomena of the secular change, may be referrible to
direct solar influence operating in a cycle of yet unknown duration. The
phenomena of the secular change in the earth’s magnetism have hitherto
received no satisfactory explanation whatsoever ; and they have all the cha-
racters befitting what we might suppose to be the effects of a cosmical
cause. Some of the objections which might have impeded the reception
of such an hypothesis before we had learnt to recognize in the sun itself a
source of magnetic energy, and to identify magnetic variations observed on
the earth with physical changes which manifest themselves to our sight in
the photosphere of the sun, are no longer tenable. It is true that we do
not yet possess similar ocular evidence of a solar cycle of the much longer
duration which would correspond to the secular change in the distribution
of terrestrial magnetism. But careful observations of the variable aspects
of the solar disk can only be said to be in their commencement, and it
would be premature to assume that no visible phenomena will be discovered
in the sun which will render the evidence of connexion as complete in the
one case as in the other. Such evidence, however, is not a necessary con-
dition of an existing connexion ; the decennial period would have been
equally true (though not so readily perceived by us) if the sun-spots had
been less conspicuous.
1864.] Archdeacon Pratt on Local Attraction in Geodesy, &c. 258
“Qn the degree of uncertainty which Local Attraction, if not
allowed for, occasions in the Map of a Country, and in the Mean
Figure of the Harth as determined by Geodesy; a Method of
obtaining the Mean Figure free from ambiguity by a comparison
of the Anglo-Gallic, Russian, and Indian Ares; and Speculations
on the Constitution of the Harth’s Crust.” By the Venerable J. H.
Pratt, Archdeacon of Calcutta. Communicated by Prof. G. G.
Stokes, Sec. R.S. Received October 5, 1863*.
1. In former communications to the Royal Society I have shown that Local
Attraction, owing to the amount it in some places attains, is a more trouble-
some element to deal with in geodetical operations than had generally been
supposed. The Mountains and the Ocean were shown to combine to make
the deviation of the plumb-line as much as 22'"71, 17°23, 21°05, 34'°16
(or quantities not differing materially from them) in the four principal sta-
tions of the Great Arc of India between Cape Comorin and the Himma-
layas—viz. at Punnce (8° 9! 31"), Damargida (18° 3' 15’), Kalianpur
(24° 7' 11"), Kaliana (29° 30’ 48"); and how much these might be in-
creased or lessened by the effect of variations of density in the crust below
t was difficult to say. Deviations amounting to at least such quantities as
7°61 and 7°87 were shown to exist in the stations of the Indian Are,
arising from this last cause (see Phil. Trans. 1861, p. 593 (4) and (5)).
M. Otto Struve has lately called attention to similarly important de-
flections caused by local attraction in Russia—and especially to a remark-
able difference of deflection at two stations near Moscow, only about eighteen
miles apart, amounting to as much as 18”, which is attributed to an invi-
sible unknown cause in the strata below (see Monthly Notices of the Royal
Astronomical Society, April 1862).
2. It is therefore an important inquiry, What degree of uncertainty does
Local Attraction, if not allowed for, introduce into the two problems of.
geodesy, viz. (1) obtaining correct Maps of a country, and (2) determining
the Mean Figure of the Harth. I have pointed out the effect on mapping
in India, as far as determining the latitudes is concerned, in a former paper.
I propose now to consider the subject generally with reference to any
country, and taking into account the longitudes as well as the latitudes.
The effect upon the determination of the mean figure of the earth I discuss
at greater length. Bya change, I venture to callit a correction, of Bessel’s
method of applying the principle of least squares to the problem, I obtain
formulze for the semiaxes and ellipticity of the Mean Figure involving ex-
pressions for the unknown local deflections of the plumb-line at the standard-
or reference-stations of the several arcs made use of in the calculation.
These formulze at once show the great degree of uncertainty which an ig-
norance of the amount of local attraction must introduce into the determi-
* Read November 26, 1863. See Abstract, vol. xiii. p. 18.
254, Archdeacon Pratt on the effect of
nation of the mean figure. After this I obtain formule for the mean
figures of the Anglo-Gallic, Russian, and Indian Arcs by the same method,
each involving the expression for the unknown local deflection of the plumb-
line at the reference-station of the arc concerned. I then show that values
of these three unknown deflections can be found which will make the three
ellipses which represent the three great arcs almost precisely the same.
These deflections are not extravagant quantities, but quite the contrary,
being small. I infer, then, that the mean of these three ellipses is in fact
the Mean Figure of the Earth, and in this way surmount what was the
apparently,insuperable difficulty which our ignorance of the amount of local
attraction threw in the way of the solution of the problem. The paper
concludes with some speculations on the constitution of the earth’s crust
flowing from the foregoing calculations.
§ 1. Effect of Local Attraction on Mapping a Country.
3. In determining differences of latitude and longitude between places
by means of the measured lengths which geodesy furnishes, the method of
geodesists is to substitute these lengths and the observed middle latitudes
in the known trigonometrical formule, using the axes of the MEAN FIGURE
of the earth. It might at first sight appear likely that this would lead to
incorrect results, as the actual length measured may lie along a curve dif-
ferent to that of the mean form. I propose now to show that no sensible
error is introduced by following this course, either in latitude or longitude,
if the are does not exceed twelve degrees and a half of latitude, or fifteen
degrees of longitude in extent.
4. First. An are of Latitude.—Suppose an ellipse drawn in the plane
of the meridian through the two stations, a and 6 being its semiaxes ; ¢
the chord joining the stations; s the length of the arc; r and 0, 7’ and 6’
polar coordinates to the extremities of the arc from the centre of the ellipse;
J and /' their observed latitudes; the amplitude of the arc; m its middle
latitude: then we have the following formule, neglecting the square of the
ellipticity (e),
s= 5 (at b)A— - (a—b) sin d cos 2m,
r=a(l—esin*/), 7'=a(1—esin’/’), tan0=(1—2e) tanJ,
tan 6’ =(1—2e) tan 7’.
Now
c= +r? — 2rr' cos (0—6') =2rr'{1— cos (@—8')} + (r—7')?
=2rr'{1—cos (0@—6')t.
By expanding the formule for tan 6 and tan 6’, we have
6=l—esin2/, 0’ =l'—e sin 2l',
“. O—6'=/—Il'~e (sin 2/— sin 2/') =1—1' — 2e sin (J—1’) cos (J+ 1’)
=)\—2e sind cos 2m;
.. 1—cos (0—6')=1— cosA—2e sin” A cos 2m
a sin’ {1—2c( + cos) cos 2m}.
Local Attraction on Geodetic Operations. 299
Also j
rr = a?4{1—e(sin?J-+ sin? 1!) } =a’ { 1— = (2— cos 2/— cos 27’) }
=a’{1—e(1—cosd cos 2m) ;
°, ado’ sin’ | 1—ef1+(2+ cos A) cos 2mt hs
ok c E
aa =] = | 2: >
sin 5 =i + 5 {1+ (2+ cos d) cos m} }
xr abe aC € c
aa TG | E+ C+ cos) ons 2m | ta,
=sin-! © ateye \ 1+(2-+ cos dA) cos 2m } nae
La 2 2
Hence by the first formula,
o=a( 1 — 5)\— = ae sin A cos 2m
=a(2—e) sin-} - +ae{1+(2+ cosd) cos 2m} tan% ~ S ae sinh cos 2m
a
=(a+6) sin-!—— +(a—b) { 1+ 1 (1—cos ) cos 2m tan >
2a 2 2
Taking the variation of s with respect to a and 4, considering ¢ as constant,
and and m also constant, occurring as they do only in small terms, we
shall have the difference in length of two arcs joining the stations and be-
longing to different ellipses, only having their axes parallel. Hence
sb ( WO a-BO cou
ds=(da+ 06) sin = Vp
-++ (da—66) { + 5( — cos i) cos 2m \ tan =
Since the terms are small, we may use the first approximate value for c
and 0;
oe ds= (Sa-+38) > —2tan ¥ da-+ (a—8) { 1+ 5 (1—c0s)) cos 2m | tan >
=(da-+2b) € —tan 5) +(da—20) 5 tan (1 — cos d) cos 2m
=(da+06)P+(da—<éb) Q cos 2m,
where
1
2
=(P+Q cos 2m)da+(P—Q cos 2m)éb.
J will find the values of éa and 06 which will satisfy this equation and
make da?+ 66” a minimum.
P= 5\—tan A, and Q= 5 tan 5 4(1— cos)
256 Archdeacon Pratt on the effect of
se (#—P4 Rem in
) = a minimum ;
P—Q cos 2m
-. {(P—Q cos 2m)’+ (P+ Q cos 2m)*}da=(P+Q cos 2m)éds ;
ase P+Qcos2m os vas P—Q cos 2m os
- P?+ Q? cos? 2m 2’ P?+ Q? cos? 2m 2’
1 os"
2 2
6a? +067= PQ cos Im 2"
This is least when m=O and 90°; then _
P+Q os _ P#Q os _ Qés
sa= PLO 9” 0b= PQ? 3° da ~ b= Pie
Let one of the two ellipses be equal to the mean ellipse of the earth’s
figure, a and 6 being the semiaxes, and ¢a and ¢é the excess (or defect, if
negative) of the semiaxes of the other ellipse. The first ellipse is not ne-
cessarily the mean ellipse itself, but is only equal to it in dimensions, and
parallel to it in position; for the actual are may lie above or below the
mean ellipse. The result of this is, that the arc of the mean ellipse which
corresponds with s of the actual arc will not necessarily have precisely the
same middle latitude, although the chord cis of the same length. But as
the middle latitude will differ only by a quantity of tue order of the ellip-
ticity, this difference will not appear in the result, because we neglect the
square of the ellipticity.
I will now make the extravagant supposition that the ellipse to which
the are actually belongs deviates from the form of the mean ellipse so much
that da ~ 66=13 miles, the whole compression of the earth’s figure. On
this supposition I will find how large the are may be so as not to produce
a difference in length greater than 1".
Put da ~ 6=13, ds=1'=0-0193 mile (1° being 69°5 miles),
-, (P?+Q?) +Q=0-0193+13=0-0015,
me — tan - + 5 tan’ * (1— eos d)*=0: 00075 tan > (1— cos A).
A slight inspection of this equation shows that \ must be small. Expand
in powers of A; then
: +)(3 x =0" 0015, or (5 :) =0-00135 ;
*, A=0°22 (in arc) =0°22 x 57°'3 (in degrees) =12°-6
This shows that in an arc of meridian as much as twelve degrees and a
half in length, it would require a departure from the mean ellipse equal to
the whole actual compression of the pole of the earth in order to produce
so slight a difference in the lengthas 1". Hence we may conclude that the
difference in length between the mean arc aud the actual are, joing any
two places on the same meridian, is an insensible quantity, since an extra-
vagant hypothesis regarding the departure of the form from the mean form
will not produce a difference in length of more than 1". This being the
Local Attraction on Geodetie Operations. 257
ease, the differences of latitudes calculated from the measured ares of meri-
dian with the mean axes, as is done in the Survey operations, will come out
free from any effects which local attraction can produce, as that attraction
can never be capable of causing so great a distortion in the measured arcs
as I have supposed for the sake of calculation. The absolute latitude,
however, of the station which fixes the arc on the map will be unknown to
the extent of the deviation of the plumb-line caused by local attraction at
that place.
5. Second. An Arc of Longitude.—Let S be the length of the are, 7 the
latitude, L the longitudinal amplitude or the difference of the longitudes of
its extremities, ec the chord. Then
S=Leosl{a+(a—6) snl}, e=2cosl{a+(a—S) sin* lt sin SL.
When a and @ vary, ¢ and J remain constant, but Sand L vary. Hence
dS=6cL cos / {a+(a—6) sin? 7+ +L cos 7 {da+ (da—dd) sin? Zt
O={a+(a—b) sin? 7} £08 LoL +2{3a-+ (aa—38) sin? 7} sin 5 Li.
By eliminating 6L from these,
S= (IL-2 tan 3 L) cos {3a-+(da—26) sin? Z} ;
Ho ohana rage a
(L—2 tan $ L) cos /
I will, as before, find the values of da and 980 which satisfy this equation,
and make 6a*+ 667 a minimum.
sin’ / da°+ {(1+ sin®/)da—n}?= a minimum ;
.. {sin*/+ (1+ sin*Z)?}da=n(1+ sin?Z) ;
“. da+ (6a—66) sin? /= =n, suppose.
caho (i+ sin? dn nen — sin’l.n
sin*/+ (1+ sin?/)?’ ~ sint7+ (1+ sin® 2)?’
ee es ani at Oe -
sin* 7+ (1+ sin? i? coslfsin'd + (1 + sin*/)?}{L—2tan3L}?
This is least when cos*/ {sin‘7+ (1+ sin?/)?} is greatest, or when J=0;
then
os
jan, ~Ob=0, Ja-—sbene i Oe
ay tea dat aye
Now put da ~ 66=13 miles, dS= arc 1" of a great circle =0°0193 mile;
“, L—2tan5L=0-0193 +13=0-0015.
This shows that L must be small: expanding, we have
L'=0°018, L=0-262 (in arc) =0-262 x 57°3 (in degrees) =15°,
We can reason from this, as before, that the differences of longitudes will be
accurately found by using the measured ares of longitude and the mean
axes, if the arcs are not longer than 15°. Now ares of this length, and of
258 Archdeacon Pratt on the effect of
the length determined in paragraph 4 for latitudes, are never used in sur-
vey operations: the great arcs are always divided into much smaller por-
tions. Hence the maps constructed from geodetic operations will always
be relatively correct in themselves; but the precise position of the map on
the terrestrial spheroid will be unknown by the amount of the unknown
deflection of the plumb-line in latitude and longitude at the place which
fixes the map. In India the effect of the Himmalaya Mountams and the
Ocean, taken alone, would throw out the map by nearly half a mile. The
calculations, however, which I give in the next two sections of this paper,
show that the effect of variations in the density of the crust below almost
entirely counteracts that of the mountains and ocean at Damargida in lati-
tude 18° 3’ 15”, and the displacement of the map is almost insensible if
fixed by that station. Iffixed by the observed latitude of any other station,
the map will be out of its place by the local deflection of the plumb-line at
that station. This, inthe Indian Great Arc, does not exceed one-thirteenth
of a mile at any of the stations where the latitude has been observed. It
appears also from those calculations, that, except in places evidently situated
in most disadvantageous positions, the local attraction is rarely of any con-
siderable amount.
§ 2. Effect of Local Attraction on the Determination of the Mean
Figure of the Earth.
6. The mean radius of the earth is nearly 20890000 feet, the ellipticity
i 1 ee :
is nearly 300° and it is found convenient to put the semiaxes of the earth’s
figure under the form
a+b 4) :
=f ] — Ait ts | .
2 ( sano) 20890000=20890000— 2089 xu feet,
a—b 1 u v [eyes ‘
2 “600 (1- 10000 =F = 20890000= =| 5; +4178000 5
(1)
u and v are quantities to be determined, and the squares and product ;
of these may be neglected.
ee a—b ] v
Also, ellipticity = aan (1 ++ ae
The arcs which are actually measured in geodesy do not necessarily
belong to precisely the same ellipse: in fact those arcs may not precisely
belong to any ellipse. Suppose one of these measured ares is laid along
the ellipse of which the axes are given above, and that, small corrections v
and a! being added to the observed latitudes of its extremities, the are
with its corrected latitudes exactly fits this ellipse. Then 2’—# may be
expressed in the form m+au+/3v, where m, a, and GB are functions of the
measured length, the observed latitudes, and numerical quantities. Let
this be done for all the arcs which have been measured and their subdivi-
sions. I shall take the eight arcs used in the chapter on the Figure of the
Karth in the Volume of the British Ordnance Survey ; viz. the Anglo-Gallic,
Local Attraction on Geodetic Operations. 259
Russian, Indian II. (or Great Arc), Indian I., Prussian, Peruvian, Hano-
verian, and Danish Arcs. Suppose
M+au+tEe+....%, m +e uth ete,
are the corrections of the latitudes of the extremities of the subdivisions of
the Anglo-Gallic Arc, 2, being the correction for the standard or reference
station inthis Arc. Similarly, let
mA-autBv+e, m,+e'u+p'wte,,....
M,+0UtB0+2, m',+a'utP' wa...
be the corrections for the divisions of the other Ares.
Then the values of uw and v which give the most likely form are those
which make the sum of the squares of all these corrections a minimum.
The sum of the squares will involve w and v, and also eight quantities
2,...&,. The usual course is to regard, not only u and v, but z,...2, as
independent variables, and to differentiate the sum of the squares with
regard to each of them in succession, and so obtain as many equations as
quantities to be determined.
7. This mode of proceeding is, I conceive, erroneous; as I shall now
endeavour to show. The corrections z,....«, are not properly indepen-
N N2 mm D
VOL, XIII. >.<
260 Archdeacon Pratt on the effect of
dent variables, but are functions of u and v, and of the deflections produced
by local attraction. In the preceding diagram the plane of the paper is
the plane of the meridian in which the arc, of which A B is one section,
has been geodetically measured. A is the reference-station of the several
portions of the whole arc. A Z is the vertical at A in which the plumb-
line hangs. The two curves, of which A’B’ and aé are portions, are a
variable ellipse and the mean ellipse having the same centre O and their
axes in the same lines, the mean ellipse being what the variable ellipse
becomes when the values are substituted for wu and v which make the sum
of the squares of the errors a minimum: Z’A A'N! and zAaN are nor-
mals through A to these two ellipses; AD, A’m', am are perpendicular
to OD.
Now, if the earth had its mean form, a plumb-line at A would hang in
the normal zA to the mean ellipse; but it hangs actually in ZA. Hence
ZAz is the deflection (northward in the diagram) which the plumb-line
suffers from the local attraction arising from the derangement of the figure
and mass of the earth from the mean. This angle is some constant but
unknown quantity ¢, ¢ being reckoned positive when the deflection is north-
ward, This quantity ¢ is part of the correction ZAZ', or x, added to the
observed latitude of A before applying the principle of least squares. "The
other part is zAZ', which I will now calculate: it is the angle between
the two normals drawn through A to the variable and the mean ellipses.
By the property of an ellipse of which the ellipticity is small,
ON=2e.Om, and ON'=2e'. Om’,
Also as Om, Om', OD differ only by quantities of the order of the ellip-
ticities, they may be put equal to each other in small terms, because we
neglect the square of the ellipticities.
, 2zAZ'= ZNAN’= ZAN’D— ZAND
cot AND—cot AN'D Laps (ND—N'D)AD
1+cot AND'cot AND ~"" AD?+ND.ND
(ON’—ON)AD 2(e’-—e)OD.AD , 4
: ~ AD?+D02 _ =tan-! AD?+ DO? =tan—l(e —e) sin 2/
—— fans
— Aion
Wy
. 1 : 5
=(e'—e) sin 2/ Sn 1” / being the observed latitude of A. -
Suppose that v and V are the values of v for the variable and the mean
ellipses. Then by the third of the formule (1),
F sin 2/7 pibeas tos
Zane = 5000 sn 17 (8 ~ V)=13""75 sin 21(v—V)=n(v— V) suppose..(2).
Hence
x==t+n(v—V).
Local Attraction on Geodetic Operations. 261
Therefore the sum of the squares of errors, which is to be differentiated
with respect to u and v to obtain a minimum, is
(n,(v—V)+ t, P+ (m,+a,u+B,v+n,(o—V)+ t,)’
+ (m', +a’ ut+'vt+n(o—V) +4)? +
(n,(v—V) + t.}? aa (m,+4,u-+ fv +n,(vo—V)+ Dy
+ (m',+a',ut B'v+n,(v—V) +t, )P+ ees
+ ; A : : : = a minimum.
Let U and V be the values of u and v which belong to the mean ellipse.
These values, then, must be put for wu and v in the two equations produced
by differentiating the above with respect to u andv, We have
a,(m,+aU+6,V+t,)+a,(m',+e,0+6',V+2)4+...
+a,(m,+a,U+B8,V+t,)+a,(m',+e,0+,',V+t,)+. : *
+ ; , 2 , : : ; 7 =0;
and
t, + (B,+2,)(m,+a,U+B8,V+t) + (6+) (m,+e'U0+6V+t)+..
Li + (6,-++2,)(m,+a,U +3,V +64.) +(B', ae +A ¥+i)+-!,
+ b 2 2 ry rt) e ° e tr e ay
Let (m) be a symbol representing the sum of all the m’s appertaining»
to the divisions of the same Arc; and let 2(m) represent the sum of all
these sums for all the Arcs; and similarly for other quantities besides m.
Then the above equations become
X(ma) +2(a7) U+ (eB) V+2t(a) =0
and 2(mB) | +228) | + 2G) | V+ 24(8)
+3n(m) { +32n(a) { ~ +3n(8){ + Bini
i being the number of stations on the representative Arc.
The numerical quantities involved in the first two lines of these equa-
tions have been already calculated in the article on the Figure of the Earth
in the British Ordnance Survey Volume, from which I borrow the results
in Table II. on the following page. The quantities involving z are calcu;
lated in Table I., and the results inserted in Table II. with the others.
x2
Archdeacon Pratt on the effect of
262
1
F8S2-Z1F—| PZSL-E8TL +] 0086-8FGI +} 80ST-28+ | 4894-601 —| 0916-6ES-+] 06L1-E81—| 9618-9671} “°° ahaa: Sees eet? ATEIO TF,
ZhEe-9% | G68hS-S —\|LL9%-4 +|ZgF9-9T —| 2620-0 +| 1760-0 —|8E08-0 +] 6912-0 +) 2969-0 —|} 8041-0 —|ZISS-0 + | 93-1 — |" Ystueg
1891-92 | 0067-2 —|0L24-6 +1648z-09 +] 9F£0-.0 +]O0SS1-0 —|FL29-0 +] 2928-0 —] 9892-6 +] 6981-0 — | 2924-0 + | 10%-% ***URTIOAOUR FT
1966-3 |81S9-1 t+iees9-1 +logtzo +] 69Gz-1 +]|29cz-1 +/96G¢-1 +)9291-0 +) 4291-0 +] TIZI-l +] €22t-T + | SFT-0 o"* URIAN IO
1zer-6¢ | zeere —|LPor6 +lzeze-62 +) 8990-0 +]| 9601-0 —| 4926-0 +) eS6r-0 —|O0e9F-L +} Z0FZ-0 — | 0122-0 + | 292-2 "rere UBISSNIg
8096-01123: +losz-e +/91480 +] 0492-0 +|+rF6z-0 +/9FZe-0 +)2280-0 +/9060-0 +] 4919-0 +] 4699-0 + | 6ST-0 seerereT UBIPUT
8428-79 | FOSL-1e —|12es-zl —| 660-71 +) 219€-62+ | F869-9E +] 0S29-9F +] 9E6F-01 —| 91S4-21 —| 6019-2 — | 9€8S-L — | F9L-T ““* sT] uerpuy
GLEL-8L1) GI8Z-61Z—| 61Es-6FZ +] 7986-666 +) SFL6-6E+ | IZFI-ZIT—| 81ES-SEst| S8rr-9ZI—| S29E-98ET| 2586-91 — | Se6r-FS+ | TE¢-69 = f“"""* UeIssny
©369-09F| LZE6-Z91—| Z98L-9LF +] 9F6S-F06 +] 9061-II+ | 6ESS-GE —| 1490-SSI+] $o9e-GF —| L0Z6-811+| 9868-21— | OST4-0€+ | 094-994 | “OlTeD-o[suy
od
—$———S|S§ —— —————— | — — |
m | je | -@e | ee | Ge) | -o) | w) | Om) | eM | -@ | -@ | -@ | vew
"T F[qey, wos pue ‘owunjor Aaaing souvupsG oY} WoAy posoyyed “T] ATAVY,
rie lorctra ee eal chemee | ierssscodl gy eae
apee.9z | |G68Pa-s —|ISLETSE-0| 2292-4 | ¥66L098-0| ZEF9-9I—| EZEZTZS-T| OLLIL-L1| ZOGPETT-T SLBTI8G-1/90-41 32 SG ["""* Bmquenvy |v" ysrueg
1992.92 | Z |006F-% —|600Z96E-0| OL22-6 | 44L6£86-0| 6282-09 | GOEZOSL-1|Ser6E-E1| G1Z69ZT-T) 8819886-1/98-2F TE 19 )""7* woSuMIQH | -UeHOAOUEHY
19¥6-2 |Z | 8199-1 +|Z9FGLIZ-0\SE99-1 | 80IFSIz-0| 9¢1z-0 _| g6996zE-T] FeELF-I | SLOEB9T-0| 1666620-1/40-2E F § fr" *S “MbaBy |" UeTANIOg
1ze-62 |e | ZeeLe —| GFSESGF-0|LF0F-6 | SLFLELG-0| ZSLE-6Z | LOSELIF-1| OPFO-LT| OLIFSII-1| G6OTLLE-ULP-TL ET HG | Zumay, |e" uerssnrg
8296-01 | z |ezeez | 1e9TacF-ol ogzT-¢ | S9L¢F6F-0/ 9128-0 | L4zE0P6-T| GSTSF-S | 90E68EL-0/ 64Z9009-1/66-2S FF TI; wmsodopueayry, |-***** TuerpUy
apzerg | 8 | POST-1@ —| SIFPSZe-1| 13e8-I—| S96ZBOT-1] 686-FI | 96FTSST-1| OLEOT-8 | 01S9806-0| S8FSOLL-T/6S-ST ¢ ST 77" ePIsxeureq |** “]] UeIpUy
GLEHBLT| EL | 18L-61Z—| ZIGGTFE-Z| 61ES-6FL | 919FL8-2| F986-S96 | L19h086-2| LO6PL-E1| SELZBET-T| 9046666-1| 8% 0% SP { i mans ie UeISsHY
€369-09F| FE | L286-L91—| SETSzs-z) L98T-91F | Z88Z619-2| 9F6S-F06 | OFSP9S6-2| S66FS-C1| LLEGTET-1] OSE9EEG-1/c6-Ee SS GP /-"* SoUsY “ag / OMTeD-O}suy
am |p | Gu | (o)uBor] “(mu | -@)u Bor | (wu [-(w)u Bop] ou | -wBor | puedo, | “OPUMET | prepung ‘SOxW
eo a a SIE
| | “WVL ZG UIs SOT + /ZOSSEL-1= “JL TUls So] +GZ.¢] sop =u do] focvd ysv] Ul 07 podtojod “T ATAV],
263
Local Attraction on Geodetic Operations.
a a em ee
GSc98TS-6— | £6660€0-€ L1V69F26-€ ‘on, ee Bed 9L0T-0€€ — 1886-CZ0T OTO8-GOLT [rrr *ee"** speqOT,
TV69L TPT EFECIVE-O— | ELETSS8-0 699SSTS-L— VE9T-9G 1616-6 — 9S9I-L. GAOL“). ) ope
ELC6PCF-L | €ZZ106E-0— | 2606186-0 LOOTPLL-T 8609-96 PoGh-S 0265-6 CLSh-6S sereee UBITOAOU
965¢609-0 | 6869¢9F-0 99FTF9P-0 881PSL5-1T 8490-P 1806-2 LI16-4 o9LE-0 *eneeeeeer’ UBTANIO J
669868¢-T TLS806F-0— | 162896-0 LG6S09F-1 6168-8¢ 4960-6 — 1662-6 6618-86 veeeeweoere’ UBISSNI
8096660-T 9L6616F-0 8S69CE¢S-0 €LGV6L6-1 CO8P-IT [660-¢ VLIP-< 8€56-0 Eee TEU IpRy
PL88E6L-1 0890716-0 1S8ZL26-1 6418625-0 616-69 8406-8 £998-S6 £008-€ “en ee LEAUCIPRT
G86SI16-6 | 9908FSZ-4— | L00ZF08-2 T9E88T6-2 LOGL-091 0£08-6£1 — 8680-269 9f6¢9-668 9 nen UeISSNY
€ELS199-6 9S8TS6L-6— | 06Z2608¢-2 I601PE6-2 L¥0E-8PhF 12FL-9ST— 8259-08E 620-668 |°"** ONTeD-opsuy
‘siaqumu ZuroSar0y 94} Jo suryyziaeRoy oy, “1u-+ (¢) “(gut (co) | *(#)u-+ (9) | *(w)u+ (gu) “sory
“TI aqe TL, uUlody PoeALtop “AT aTav 7,
G691S19-—|8096E40-€ |FL08682-E |8LL9F16-1 88Sh0F0-2—|Z9ZESEL-ZLSL489S-6—|L861969-2 | crt | cette aveeaeans ese U yO,
L0GS0CV-T|18461S€-0—|F664098-0 \es¢ez1z2-1— 6Z8EC9P-Z|9689EL6-4 —|BL8S8PF-L9CSCPEE-L |B8SPOSb8-1— 6L8h7E2-L—|Z60ETFZL-1 |IZPLZ101-0—|°"** asrued
9TS9622F-11600696¢-0—|4446486:0 |GOoez0gZ-1 [940689-2| 8ESS0ET-I —|LOFLZG4-1/8699606-1— |ST9EFIS-0 |F64269G-T—|Z9G0T98-L |0608E9-0 | UeItoAOURTT
6SEE69F-0\29FGL16-0 \801F812-0 869962€-L |4008660-0/46F2660-0 |ZeEc00T-O/SOZTLIZ-I (9L8E112-L |PPF9EFO-0 |06010G0-0 |OS9ETOT-T °°’ UetAndog
[E€S06S-1/6P86S6F-0—|ZZFEEL6-0 |E086L9F-T 8L48696-2 90186C0-1 — |L6VIVIS-1/€898F69-1—|\EPPcS9l-0 \O€LSO8E-I—|\€SE64G8-T |P89GsGE-0 |*°*""* UeIssnzg
TL966€0-T)16912SF-0 |B8949F6F-0 [L1E0F6-1 CLIGISH-T\SLE689F-L |SBPELTS-T8TZ8P16-4 |28014G6- (G8EZeTZ-L jO9P9GSL-L |LL6E10-T [°°] Werpuy
GIPLTIB-TiZLPPSSE-1 — |S967801-L—|96F1SS1-L |SEZLZ9F-1/LLZF9F9GT |6091899-1/SF260Z0-T —|LF9SS01-1 — ZOGL91F-0—|SSF9661-0—|986F9FG-0 |""* “IT weIpuy
LOLZSSZ-Z|Z1661FS-2—|S919FLB-¢ |\L1SF086-2 |1BZ109-1\L8926F0-2—|Z284S2%-2\4F16101-—|8h6698S-% lostseoe-T—|lereges-1 |seZztzPe-t |" uerssny
99TPE99-ZIZGE192Z-%—|Z88Z619-2 lOPSP9GG-Z |PESssF0-1/6zr90G9-T —|L61S061-2\8e22999-1—|czGzcL0-2 |ez61e60-1—|socezeF-t legTsrzs-1 |“omrep-osuy
"II [48], Ul stoquinu oy} Jo sMyIIIBsOT OY} SuIUTeJUOD “TTT ATAVY,
264 Archdeacon Pratt on the effect of
8. I will now apply the formulze just obtained to determine the Mean
Figure of the Earth from the (data afforded by the eight arcs. For conve-
nience I shall use the well-known symbol (2:6961987) to mean the number
of which 2°6961987 is the logarithm ; and so of other numbers. By sub-
stitution from the Table, the formule give
(2'6961987) + (2°7323262)U —(2:0404588)V + (1:4873505)é,
+-(1°7363431 )t,—(0°1996455 )t, + (1°7556462)¢, + (1'8579353)é,
+ (0:0501090)é, + (1°8610562)#,+(1°7413092)t,=0,.
(3'2469417) +(3:0309997)U —(2°5186555)V + (2°6515733)¢é,
+ (2°2115282)é, + (1°7938874 )é, + (1'0599608)¢, + (1°5898592)é,
+ (0°6093596)é, + (1°4249273)¢,+ (1°4176941)¢,=0.
Multiplying by the coefficients of V crosswise, and subtracting 80 as to
eliminate V, we have
(5*2148542) + (5°2509817)U + (4:0060060)¢, + (4°2549986)é,
= (2°7183010)z¢,
— (5°2874005) — (5:0714585) U — (4:6920321)#, —(4° 2519870)t,
— (3°834362)t,
++ (2°2743017)¢, + (2°2765908)¢, + (2°5687645)¢,+ (2° ort ae
+ (2°2599647 )é,
— (3°1004196)¢,—(3°6303180) é,— (2°6498184)¢,—(3°4653861)é,
— (3°4581529)t,=0.
Putting numbers in the place of logarithms,
164004+178230U+ 10139¢,+17989¢,— 523¢,
—193821—117885U— 49208¢,—178644,—6829¢,
= 29817+ 60345U— 39069¢,+ 1254,—7352¢,
4+ 188¢,+ 2384,+370¢,+ 240¢,4 1824,
— 1260¢,—4269¢,—446¢,—2920t,—2872¢,
—1072t,—4031t,— 76¢,—2680¢,— 2690¢,=0.
Putting logarithms in the place of numbers, _
— (4'4744639) + (4-7806413)U — (4°5918323)¢, + (2:0969100)¢,
= fo Secsobs 6 ds01ha8).,~(o ee
— (3°4281348)t,— (34297523) t,=0
Transposing and dividing by the coefficient of U,
U=(1-6938226) + (1-8111910)¢, —(3°3162687)#,+ (1-0857642)é,
+ (2:2495535 )t,+ (28247715)t,+ (5 1001723) + (2:6474933)¢,
+ (2°6491110)¢.
Local Attraction on Geodetic Operations. 265
Now 2089=(3'3199384),
-, 2089U =(3:0137610) + (3°1311294)é, —(0°6362071)#, + (2° crepe
_ +(1°5694919)¢, + (211447099 )é, + (0°4201107)¢,
+ (1:9674319)¢,+(1°9690494)¢,
= 1032'24-1352:42, —4°3t,+254°5t,+37°1t,+ as open :
+92-8t, + 93°1z,.
Transposing the term in V in the first UD of this paragraph and
dividing by its coefficient, we have
V=(0-6557399)+ (0°6918674)U + (1:4468917)é, + (1°6958843)é,
—(2'1591867)t, + (3°7151874)t, + (3°8174765)t, + (2°0096502)¢,
+ (3°8205974)z, + (3°7008504)¢,
= (0°6557399) + (1°4468917)¢, + (1°6958843)¢, — (2'1591867)#,+ (3°7151874)¢,
+ (0°3856900) + (0°5030584)¢,— (2:0081361)4,+ (1°7776316)#, + (2°9414209)¢,
+ (3°8174765)t,+ (20096502)t,+ (3'8205974)t,+ (3°7008504)¢,
+ (1°5166389)¢, + (3°7920397)t,+ (1°3393609)t,+-(1°3409784)z,.
Now 417800=(5°6209684),
» 417800V
=(6-2767083) + (5:0678601 )¢, + (5°3168527)t,—(3-780155 1 )t, +(3°3361558)z,
+ (6:0066584) + (6-1240268)z, —(3-6291045 )z, + (5°3986000)t, + (4:5623893)z,
+ (3°4384449)¢, + (3°6306186)¢, + (3°4415658)t,-+ (3°3218188)¢,
+ (5°1376073)t, + (3°4130081 )t, + (4:9602293)t, + (4:9619468)é,
=1891073+ 116912¢,+207421t,— 6028¢,+ 21682,
+1015450+1330537t,— 4257t,-+ 2503804, + 36508¢,
+ 2906523 + 14474492, + 203164¢, + 2443522, + 38676¢,
+ 2744¢,1+4272t,4 2764¢,+ 2098¢,
+ 137280f, + 2588¢,+ 91249¢,+4 91611¢,
+ 142024¢,+ 68602, + 940132, + 937092,
Substituting the values of 2089 U and 417800 V above deduced in the
formule (1) of paragraph 6, we have
24° — 20888968 —1352-4¢, + 4°3¢,—254-5f,—37°1,— 189-5t,— 268,
92°8¢,—93°1t,,
a—b- a+6
aoe “ao +417800 V }
= a $23795491 + 1446097¢, + 203168¢, + 244098¢, + 386392,
+ 139884¢,+ 6857t, + 93920¢,+ 93616¢,}
= 89659 + 2410°2¢, + 33862, + 406-82, + 64°44, + 233'1t, +1144,
4 156°5¢, + 156°0#, ;
266 Archdeacon Pratt on the effect of
+, a= 20928627 + 1057°8¢,+342°9¢, + 152°3t,4+27°3t,+93°6t,4-8'8f,.
+63°7t,+62°9t,,
6 == 20849309 —3762°6¢, —334°3t,—661° 3t, —101:5¢,—372°6¢,
—14-0¢,—249°3£,—249'1f,.
From these we may easily deduce the ellipticity
e= _— 7 {1+0°0608¢, + 0-0085¢,+ 0°0103¢,+ 0°00162,+0°00592,
+ 0:0003¢, + 0°0039¢, + 0:001639¢ a
These formule for the semiaxes and ellipticity of the mean figure of the
earth show us that the effect of local attraction upon the final numerical
results may be very considerable: for example, a deflection of the plumb-
line of only 5” at the standard station (St. Agnes) of the Anglo-Gallic are
would introduce a correction of about one mile to the length of the semi- :
major axis, and more than three miles to the semi-minor axis. If the de-_
flection at the standard station (Damargida) of the Indian Great Are be
what the mountains and ocean make it (without allowing any compensating
effect from variations in density in the crust below, which no doubt exist,
but which are altogether unknown), viz. about 17’24, the semiaxes will be
subject to a correction, arising from this cause alone, of half a mile and
two miles. This is sufficient to show how great a degree of uncertainty local
attraction, if not allowed for, introduces into the dekecdnatios of the mean
figure. As long as we have no means of ascertaining the amount of local
attraction at the several standard-stations of the arcs employed in the cal-
culation, this uncertainty regarding the mean figure, as determined by
geodesy, must remain.
§ 3. Comparison of the Anglo-Gallic, Russian, and Indian Arcs, with a
view to deduce the Mean Figure of the Earth.
9. The first three of the eight arcs which have been used in the calcula-
tion, viz. the Anglo-Gallic, Russian, and Indian, are of considerable length ;
and as the a priori probability appears to be that the earth nowhere departs
much from its mean form, it seems not unlikely that by the following de-
vice we may overcome the difficulty poimted out in the last paragraph. I
will deduce expressions for the semiaxes of the mean figure of each of
these three arcs by the method there given. If reasonable values can be
assigned to the expressions for the deflection of the plumb-line from the
normals to these three ellipses such as will make the axes the same, we
shall have a very strong argument in favour of those being the actual de-
flections in nature, and of the figure thus deduced, as common to the three
arcs, being in fact the mean figure of the earth.
10. In the previous calculation ¢ has represented the angle which the
plumb-line makes, in the plane of the meridian, with the normal to the
mean ellipse of the earth. I shall now use T as the angle which the plumb-
line makes, in the plane of the meridian, with the normal to the mean
Local Attraction on Geodetic Operations. 267
ellipse of the particular are under consideration. I shall begin with the
Anglo-Gallic are. Proceeding precisely as in paragraph 8, we have
(20752575) + (2°1905197)U, — (15506429) V, + (1°4873505)T, =0,
(2:9341091) + (2°5805290)U, — (2°1951856)V, + (2°6515733)T,=0,
(4:2704431) + (4°3857053)U, + (3°6825361)T,
— (4°4847520)—(4°1311719)U, —(4°2022162)T,=0,
18640 + 24306 U,+ 4814T,
— 30532—13526 U,— 15930 T,
—11892+ 10780 U,—11116 T,=0,
or
—(4°0752549) + (4:0326188)U, — (4:0459485)T, =0 ;
. U,=(0°0426361)+(0°0133297)T,, 2089=(3°3199384),
2089U, = (3°3625745) + (3°3332681)T, = 2304°5 + 2154°1T,.
By the first of the equations in V,, we have
V,=(0°5246146) + (0°6398768)U, +(1:9367076)T,
=(0°5246146)+(1:9367076)T,
+ (0°6825129)+(0°6532065)T,, 417800=(5°6209684) ;
-”.417800V,=(6°1455830) + (6°3034813) + {(5°5576760)+ (6:2741749)}T,
= 1398244 + 2011320+ {361140+1880074}T,
= 3409564 + 2241214 T, ;
a, +6,
*, 1 =20887695—2154"1 T,
uae
5 = Gq {24297259 + 2239060 T,} = 40495 + 3731°8 T, ;
» a,=2092819041577:7 T,, 6,=20847200—5885:9 T,,
1
ee a5e4 +0°0921 T,).
11. I proceed to the second, the Russian arc.
(2°5869948) + (2°5257337)U,—(2:0497688)V, + (1°736343])T,=0,
(2:9188361)+(2°8042007)U, — (2°2548066) V, + (2°2115282)T,=0,
(4°8418014) +(4°7805403)U,+ (3°9911497)T,
— (4'9686049)— (4°8539695)U,—(4°2612970)T,=0,
69471 +60331 U,+ 9798 T,
—93026—71445 U,—18251 T,
—23555—11114U,— 8453T,=0,
or 3
— (4°3720831)—(4:0458704) U,—(3'9270109)T,=0 ;
“. U,=—(0°3262127)—(1'8811405)T,, 2089=(3°3199384),
2089 U,= —(3°6461511)—(3°2010789)T,= —4427:4—1588°8 T,,.
é€
268 Archdeacon Pratt on the effect of — -
By the first of the equations in V,, we have
- -V,=(0°5372260)+(0:4759649)U,+(1- 6865743),
= (0°5372260)—(0°8021776) + {(1°6865743)—(0-3571054)}T,
417800 =(5-6209684) ;
-. 417800 V, =(6:1581944)—(6-4231460) + {(5°3075427)—(5:9780738)}T,
= 1439443— 2649391 + {203022—950766}T,
= — 1209948—747744 T, ;
. are = 20894427 + 1588-8 T,,
Mos = 5h {19684479 —746155 T,} =32807—1243°6 Ty,
a,=20927234+4+345:2T,, ,=20861620-+4 2832-4 T,,
—0-0379 T,).
12. The following is the calculation for the Indian are :—=
—(1:1055647) +(1°6681529)U,-+ (1°5646471)V,—(0°1996455)T,=0,
(0°5798179)-+(1°3777851)U,+(0°9140680)V, +(1°:7938874)T,=0, ~
—(2:0196327) + (2°5822209 )U,=(1°1137135)T,
— (2°1444650)—(2°9424322)U,—(3°3585345)T,=0,
= iO5-35920.—) 13 1
—139=876 U,—2283 T,
—244—494 U,— 2296 T,=0,
or
— (2°3873898) — (2°6937269)U,—(3'3609719)T,=0;
*, U;=—(1'6936629)—(0°6672450)T,, 2089=(3°3199384),
2089 U,=—(3-0136013) — (3°9871834)T, = —1031-8—97 09-2 T;.
By the first of the equations in V,, we have
V,= (15409176) — (0°1035058)U, + (2°6349984)T,
= (1°5409176) + (1°7971687) + {2°6349984) + Oe
417800= (56209684),
417800 V,=(5° 1618860) + (5-4181371) + {(4°2559668)+(6- si7iouaee
= 145173 +4 261901 + {18029 + 2464445}T,
_ = 4070744 2482474 T, ;
Local Attraction on Geodetic Operations. 269
” ae TORS
ft = oe ~~ {21298106 4+ 2492183 T,} =35497 +4153°6T, ;
o al T,, 6,=20855535-+5555'6 T,,
ST eri 70).
294°8
13. I have now, if possible, to find values of T,, T,, T, which will make
these three ellipses, which measure the Anglo-Gallic, the Russian, and the
Indian ares, the same; that is, a,=a,=a,, 6,=6,=0,. These give the
four following equations :—
15777T;— 345:2T,+ 956=0,) (3'1980244)T, —(2°5380708)T, + (29804579) =0,
5885°9T,+ 2832°4 mi1440040, bo. (3°7698129)T, + (3:4521546)T, + (4°1589653) =0,
1577-7 T; 138628 T,+ 1661=9,{ | (3:1980244)T, —(4:1418509)T,, + (32203696) =0,
5885°9T,+ 5555°6T,+ 8335=0,/ &(3-7698129)T, +(3°7447310)T,+(3-9209056) =0,
The most likely solutions of these four equations connecting the three
quantities T,, T,, T, which we are seeking are found by the method of least
squares. This leads to the three following equations :—
2(6°3960488) pa »— (7°3398753) \t T, + (61784823) + (6°4183940)
+-2(7°5396258)J +(7-2219675)) +4-(7-5145439)/ +.(7-9287782)+-(7-6907185)—0.
(5°7360952) } T,—(5°0761416) ) T,-+(5-5185287)
+ (72219675) +(6-9043092)) +(7-6111199)=0,
(7:3398753) | T, —(8°2837018) | T,+(7:3622205)
+(7°5145439)) +(7:4894620)/ +(7-6656366)=0,
or
2% 2489 = 545 —21871 + 1508 + 2621
4234644 +16671 32700 = 484875 449059
742667, +16126T, +10829T, -++138063 =0
(48707900) (4:2075267) (4:0345884) (5°1400773)
ip = 119 = 330 21871 =192177 +23026
+16671 +8022 440843 432700 + 30865 +46306
17216T, +7903T, +41173=0, 54571T, = 161312T; +69332=0
(42359323) (38977920) (4:6146125) (4°7369619) (5-2076667) (48409337) ;
T, = — (0°3381403)T, —(0-7168205), T= (1°5292952)T, + (16332670) ;
*. 16126T.= —(4-5456670)T, — (49243472), 108297, = (35638836), (3°6678554)-
= —35129T, —84013, =3663T +4654 ;
*. {74266 _ 35129-+36631T, + 138063 — 8401344654 =0,
42800T,+58704=0, T,=—1'37,
To= —2°18T, —5:2] = 42°99 —5°21 = —2'""22,
T3=0°338T, +-0°430 = —0°463-+0°430= —0'033.
270 Archdeacon Pratt on the effect of
When these are substituted in the semiaxes, they give
= 20928190—2161=20926029, a,=20927234—766 = 20926468,
a= 20926529 — 457 =20926072,
b, = 2084720048064 =20855264, %,—20861620—6288 — 20855332,
b,=20855535— 183=20855352.
These three results are remarkably near each other; they differ from
their average, 20926189 and 20855316, in no case by so much as 300 feet,
and in most cases by much less. I think, then, that we may safely infer
that this average ellipse is in fact the mean figure of the earth. This being
the case, T,, T,, T, are the same as z,, ¢,, ¢,; and therefore the deflections
of the plumb-line in the meridian at the standard stations of the Anglo-
Gallic, Russian, and Indian ares are 1'°37, 2''-22, 0-033, all in the south-
ern direction*.
14. The values, then, which I would assign to the semiaxes and ellipti-
_ city of the Mean Figure of the Earth are as follows :—
a=20926180, 6==20855316 fect, e=—! _.
295°3
If these are substituted in the formule (1) of paragraph (6), we have
U=—0°'3581 and V=0°8819.
§ 4. Speculations regarding the constitution of the Earth's Crust.
15. If the reasoning in the last section, which has led to so satisfactory
a result, be correct, I think we may draw some useful inferences regarding
the constitution of the earth’s crust.
By substituting the values of U, V, ¢,, ¢,, ¢, im the formule similar to
m+aU+6V-+¢ for the fifty-five stations of the eight arcs, which will be
found at p. 766 of the Ordnance Survey Volume, every one of the results
will be small. These results are the corrections of the latitudes of the
stations in referring them to the mean ellipse; that is, they are the deflec-
tions of the plumb-line in the meridian at those stations owing to local
attraction, or the attraction arising from the departure of the actual figure
of the earth from the mean figure.
Fifteen of these formulee I here select, adding one new one for Dehra
about 56 miles to the north of Kaliana, the northern extremity of the
Indian arc. They are as follows :—
* The numerical calculations in paragraphs 7 to 13 inclusive have been tested at the
Government Trigonometrical Survey Office in Calcutta,
es |
Local Attraction on Geodetic Operations. 271
From the Anglo-Gallie Are.
Detes-|Ctelate oe a
tions. |attractions. counted for.
(1) Barcelona...... +1:440—3°0644 U+0°0553 V—1°37= |+ 2:22
(2) Dunkirk ...... +0°767+0°4115 U—0-0765 V—1°37 = |—0°84
(3) High Port Cliff. +1:778 +0°2532 U—0:0450 V—1°37 = |+1°28| +3:29 | —2:01
(4) Week Down ...| +1°747+-0°2539 U—0°0452 V—1:37= |+0°25 | +1:98 | —1:°73
(5) Boniface Down) +1°967+0°2559 U—0:0455 V—1°37= |+0°46| +2°42 | —1:96
(6) Dunnose ...... — 0499+ .0°2613 U—0:0466 V—1°37= |—2:00| —0°54 | —1-46
(7) Blackdown ...| +4:279+ 0:2859 U—0-0513 V—1°37= |+2°76
(8) Burleigh Moor.| —1:814+1°6845 U—0°4137 V—1°37= |—4:15 | —4:°55 | +0°40
|
(9) Cowhythe ...... —6°915+42°8048 U—0°3340 V—1°37= |—9°31| —5:50?|} —3°81
(10) Ben Hutig ..... +0:095 +3°1173 U—0:9708 V—1:37= |—3°25| —2:01 | —1:24
(11) Saxavord ...... +4°403+3-°9370 U—1°3699 V—1°37 = |+0°41
From the Russian Are.
(i) Fornen: .....+.-. +11°826+7:3799 U—2°5821 V—2:22=
(13) Fuglenees ...... +10°008+9°1231 U—3°8418 V—2:22=
+4°69
+1:13
From the Indian Are.
(14) Panne. ......... + 0°625 —3°5622U —3°1853V —0°033=|—0°94 | +22°71 | —23°65
(15) Kaliana......... + 0°403+4°1251U +2°7756V —0°033 =|+ 1°34 | +34°16 | —32°82
(16) Dehra*......... +53°796+4:4215U —0°1010V —0:033=|+52°09
I have inserted the formula of Cowhythe from p. 771 of the Ordnance
Survey Volume. I have also added two columns, in one of which are given
the deflections of the plumb-line arising from attraction at those of the
stations for which it has been calculated. For those of the Anglo-Gallic
Are, I refer to the Ordnance Survey Volume, sect. xi. p. 625; and for
those of the Indian Arc to my paper in the Philosophical Transactions for
1861, p. 593. I would observe that not only in the two stations of the
Indian Arc, but in those I have selected from the Anglo-Gallic Are (all of
which are near the sea-shore), allowance is made for deficiency of density and
attraction of sea-water. In the stations (3), (4), (5), (6) the effect of the
sea for about 9 miles south of the coast is taken and estimated at +-0!!-27
(see Ordnance Survey Volume, p. 631); in station (8) for 36 miles north,
and estimated at —0!'"39 (p. 642); in station (9) for 50 miles north, and
estimated at —0'°70 (p. 664); in station (10) for 50 miles north, and esti-
mated at —0'-64 (p. 662). It is of importance to bear this inmind. For
stations (14) and (15) the effect of the sea the whole way to the south pole
* This is calculated by the formule at p. 737 of the Ordnance Survey Volume, from the
following data obligingly furnished me by Major Walker, Superintendent of the Govern-
ment Trigonometrical Survey of India, viz.
Astronomical latitude of Dehra 30° 19’ 19”.
Distance of parallels of Dehra and Damargida 4463510-7 feet.
The latitude of Damargida is 18° 3' 15",
272 Archdeacon Pratt on the effect of
is taken, and estimated at +1971 and +6"-18, the effect of the mountain
mass on the north being +3'-00 and 27-98.
16. The first thing I observe in the results given in the last paragraph
_is the very small amount of the resultant deflections at the two extremi-
ties of the Indian Are—Punnee close to Cape Comorin, and Kaliana the
nearest station to the Himmalaya Mountains; whereas the effect of the
Ocean and the Mountains has been shown to be very large. This shows
that the effect of variations of density in the crust must be very great, in
order to bring about this near compensation. In fact the density of the
crust beneath the mountains must be less than that below the plains, and
still less than that below the ocean-bed. If solidification from the fluid
state commenced at the surface, the amount of contraction in the solid
parts beneath the mountain-region has been less than in the parts beneath
the sea. In fact, it is this unequal contraction which appears to have
’ caused the hollows in the external surface which have become the basins
into which the waters haye flowed to form the ocean. As the waters
. flowed into the hollows thus created, the pressure on the ocean-bed would
be increased, and the crust, so long as it was sufficiently thin to be influ-
_enced by hydrostatic principles of floatation, would so adjust itself that the
pressure on any couche de niveau of the fluid shculd remain the same.
_ At the time that the crust first became sufficiently thick to resist fracture
under the strain produced by a change in its density—that is, when it first
eeased to depend for the elevation or depression of its several parts upon
the principles of floatation, the total amount of matter in any vertical
prism, drawn down into the fluid below to a given distance from the
earth’s centre, had been the same through all the previous changes. After
this, any further contraction or any expansion in the solid crust would not
alter the amount of matter in the vertical prism, except where there was
an ocean; in the case of greater contraction under an ocean than elsewhere,
the ocean would become deeper and the amount of matter greater, and in
ease of a less contraction or of an expansion of the crust under an ocean,
the ocean would become shallower, or the amount of matter in the vertical
prism less than before. It is not likely that expansion and contraction in
the solid crust would affect the arrangement of matter in any other way.
That changes of level do take place, by the rising and sinking of the sur-
face, is a well-established fact, which rather favours these theoretical con-
siderations. But they receive, I think, great support from the other fact,
that the large effect of the ocean at Punnce and of the mountains at Ka-
liana almost entirely disappear from the resultant deflections brought out
by the calculations. The formule of paragraph 15 show that when we
get close to the mountain-mass, as at Dehra, which is at the foot of the
mountains where they first rise rapidly above the plains, the resultant deflec-
tion is very great; the less density of the crust down below the sea-level
drawn under the mountain-mass has here a very trifling influence. This
is as it should be, if the depth of this less density is considerable ;
Local Attraction on Geodetic Operations. 273
whereas at Kaliana, and stations still further off, the attraction of the
mountain-mass above the sea-level, and the deficiency of attraction from
the crust below that level, would nearly counterbalance each other. Thus,
if the thickness of the crust below the plains is 100 miles, and the amount
of matter in the crust under the plains equals that of the crust and moun-
tains together in the mountain-region, then the deflections at Kaliana,
Kalianpur, and Damargida, instead of being 27°98, 12'°05, 6"°79, arising
from the mountains alone, are reduced to 1'°54, —0':06, —0':06 (see
Philosophical Transactions for 1858, p. 759), which are all insigni-
ficant compared with the large deflections caused by the mountains
alone.
This theory, that the wide ocean has been collected on parts of the
earth’s surface where hollows have been made by the contraction and
therefore increased density of the crust below, is well illustrated by the
existence of a whole hemisphere of water, of which New Zealand is the
pole, in stable equilibrium. ‘Were the crust beneath only of the same
density as that beneath the surrounding continents, the water would be
drawn off by attraction and not allowed to stand in the undisturbed posi-
tion it now occupies.
17. I have, in what goes before, supposed that, in solidifying, the crust
contracts and grows denser, as this appears to be most natural, though,
after the solid mass is formed, it may either expand or contract, according
as an accession or diminution of heat may take place. If, however, in the
process of solidifying, the mass becomes lighter, the same conclusion will
follow—the mountains being formed by a greater degree of expansion of
the crust beneath them, and not by a less contraction, than in the other
parts of the crust. It may seem at first difficult to conceive how a crust
could be formed at all, if in the act of solidification it becomes heavier
than the fluid on which it rests; for the equilibrium of the heavy crust
floating on a lighter fluid would be unstable, and the crust would sooner or
later be broken through, and would sink down into the fluid, which would
overflow it. If, however, this process went on perpetually, the descending
crust, which was originally formed bya loss of heat radiated from-the
surface into space, would reduce the heat of the fluid into which it sank,
and after a time a thicker crust would be formed than before, and the
difficulty of its bemg broken through would become greater every time a
new one was formed. Perhaps the tremendous dislocation of stratified
rocks in huge masses with which a traveller in the mountains, especially
in the interior of the Himmalaya region, is familiar, may have been brought
about in this way. The catastrophes, too, which geology seems to teach
hhaye at certaim epochs destroyed whole species of living creatures, may
have been thus caused, at the same time breaking up the strata in which
those species had for ages before been deposited as the strata were formed.
These phenomena must now long have ceased to occur, at any rate on a
‘very extensive scale, as Mr. Hopkins’s investigations on Precession appear
274 Archdeacon Pratt on the effect of
to prove that the crust is very thick, at least 800 or 1000 miles; and this
result, I understand, has been recently confirmed by Professor W. Thomson
in a paper “On the Rigidity of the Earth.”
18. These theoretical considerations receive, I think, some confirmation
from an examination of the calculated deflection of the plumb-line at sta-
tions near the sea-shore. It is for this reason that I have collected the
thirteen examples from the Anglo-Gallic and Russian Arcs in paragraph
15, all of which are near the coast. The evidence they furnish, however,
is not to be compared in weight with that of the Indian Arc, already con-
sidered. In some instances the local attraction of the surrounding country
and of the ocean for a certain distance has been calculated, as already
stated. These results I will take into account, except the allowances for
the ocean as noted at the end of paragraph 15, which I deduct in the fol-
lowing arrangement of the stations.
The Stations at which the Deflection is towards the Land.
: ad Ry Deflection. it
(1) Barcelona, lat. 41 23, S.E. coast of Spain, «as. wae ae +2:°22
(2) Dunkirk, .;, 51. 2, N.N.W. France, ~... 9h — 0°84
(7) Blackdown, ,, 50 41, S. Ss Dotsetcs.u+ eda ae ee +2°76
(9) Cowhythe, ,, 57 41, N. > ~bantf, —3°81+0:70=—3:1l
(10) BenHutig, ,, 58 33, N. sy Sutherland, — 1:24+0°64=—0°60
(12) Tornea, 65,50, Se is Lapland,>. 22% cee +4:69
The Stations at which the Deflection is towards the Sea.
Deflection.
(3) High Port Cliff, 50 36, S. coast of Isle of Wight, — 2-01 —0-27= —3-28
(4) Week Down, 50 36, _ a —1:73—0°27=—2:00
(5) Boniface Down, 50 36, —1°96—0°27= — 2:23
(6) Dunnose, —-50 37, \ ' —1-46—0-27=—1°73
(8) Burleigh Moor, 54 34, N. coast of Yorkshire, +0°40+0°39=-+0-79
(11) Saxavord, GO 50. ING 4 sass ones «0.2001» eee +0°41
(13) Fuglences, ZOrAO, Nee cvciat REMINISCE tec pee ones eed
The theory I have proposed, that contraction of the crust has formed the
basins in which the sea has settled, can hardly be expected to apply so
completely to such confined sheets of water as the Mediterranean south
of Spain, and the Gulf of Bothnia. Here there may be an actual defici-
ency of attracting matter in the water, not altogether compensated for by
increased density of the crust below. These hollows may have been formed
during the breaking up of the crust and subsequent removal of portions by
currents, and not chiefly by the contraction of the crust. Thus the deflec-
tions at the stations (1) and (12) towards the land may be sufficiently
accounted for, even if the land about Barcelona and Tornea does not rise
sufficiently high to produce them. The deflection at station (2) is small.
It seems probable that even if the North Sea hds been produced according
Local Attraction on Geodetic Operations. 275
to the theory of contraction of the crust, the parts near Dunkirk may
have been somewhat hollowed out by the scouring of the tide through the
Straits of Dover, so as to give the land, low as it is, every advantage in
deflecting the plumb-line south. I have no means of knowing the cha-
racter of the ground north of station (7) on the coast of Dorset.- There is
no difficulty, however, in accounting for the north deflection at that place,
and even for a greater deflection, if the attraction of the country north of
it is as much as the attraction of the land on Burleigh Moor on the north
coast of Yorkshire. To this station I shall revert. With regard to sta-
tions (9) and (10), I gather the following information from the Ordnance
Survey Volume. “At present there are no sufficient data for calculating
exactly the disturbance”’ at Cowhythe (p. 662). It is supposed not to
exceed 6" (p. 664); but the calculation is not made for any part of the
mountains further south than 50 miles. The south deflection to be ac-
counted for, viz. —3''11, may in part be thus explained; or, even if, as
before, the North Sea is supposed to have been formed by the contraction
of the crust, the confined portion between the north coast of Aberdeen and
the Orkney Islands*may have been formed by the removal of the superfi-
cial strata by currents so as to produce a deficiency of attracting matter.
So with respect to the other station, Ben Hutig, the unaccounted-for de-
flection, which is much smaller, viz. —0°60, may be easily explained, as
the effect of the land has not been calculated further off than about 3 miles
(pp. 660, 661). Thus, on the whole, the deflections at those coast-stations,
where itis towards the land, can be pretty well accounted for, without call-
ing in aid the deficiency of attraction of water and supposing that the crust
below the ocean is not condensed.
The seven coast-stations of the second list, where the deflection 1s towards
the sea, seem to bear individual testimony to the truth of the theory, that
the crust below the ocean must have undergone greater contraction than
other parts of the crust. The four stations (3), (4), (5), (6) on the south
coast of the Isle of Wight all have deflections southwards; and their mag-
nitudes diminish in the order that the distances from the sea increase,—that
order being (3) High Port Cliff, (5) Boniface Down, (4) Week Down, (6)
Dunnose (see the Contour Map of Isle of Wight in the volume of Plates
accompanying the Ordnance Survey Volume). The amounts of the deflec-
tion seem almost tc prove too much for the theory. Still they are all
in the direction of the ocean, and seem certainly to indicate that there is a
redundance of matter, and not a deficiency, in that direction. Blackdown
(7) is somewhat further inland than Dunnose is. If, then, the ocean and
crust together do really produce the outstanding deflection southward at
Dunuose, we shall have to suppose that the north deflection at Blackdown
in the first list of coast-stations, arising from the land, is not much less
than 2°76+1°73=4°49, which is a little less than the calculated deflection
at Burleigh Moor on the coast of Yorkshire, and is therefore not an unlikely
amount. The other three coast-stations, (8), (11), (13), all bear out the
VOL. XIII. Aa
276 Effect of Loeal Attraction on Geodetic Operations. -
theory: though the three deflections are all small, they are towards the
sea, the largest of them being at Fuglences, which is very near to the
North Cape, and has a large expanse of ocean above it.
19. The least that can be gathered from the deflections of these coast-
stations is; that they present no obstacle to the theory so remarkably sug-
gested by the facts brought to light in India, viz. that mountain-regions
and oceans on a large scale have been produced by the contraction of the
materials, as the surface of the earth has passed from a fluid state to a con-
dition of solidity—the amount of contraction beneath the mountain-region
having been less than that beneath the ordinary surface, and still less than
that beneath the ocean-bed, by which process the hollows have been pro-
duced into which the ocean has flowed. In fact the testimony of these coast-
stations is in some degree directly in favour of the theory, as they seem to
indicate, by excess of attraction towards the sea, that the contraction of the
crust beneath the ocean has gone on increasing in some instances still fur-
ther since the crust became too thick to be influenced by the principles of
floatation, and that an additional flow of water into the increasing hollow
has increased the amount of attraction upon stations on its shores.
Murree, Punjab,
August 20, 1863.
Local Attraction on Geodetic Operations. 275
to the theory of contraction of the crust, the parts near Dunkirk may
have been somewhat hollowed out by the scouring of the tide through the
Straits of Dover, so as to give the land, low as it is, every advantage in
deflecting the plumb-line south. I have no means of knowing the cha-
racter of the ground north of station (7) on the coast of Dorset. There is
no difficulty, however, in accounting for the north deflection at that place,
and even for a greater deflection, if the attraction of the country north of
it is as much as the attraction of the land on Burleigh Moor on the north
coast of Yorkshire. To this station I shall revert. With regard to sta-
tions (9) and (10), I gather the following information from the Ordnance
Survey Volume. “At present there are no sufficient data for calculating
exactly the disturbance”? at Cowhythe (p. 662). It is supposed not to
exceed 6" (p. 664); but the calculation is not made for any part of the
mountains further south than 50 miles. The south deflection to be ac-
counted for, viz. —3’'-11, may in part be thus explained; or, even if, as
before, the North Sea is supposed to have been formed by the contraction
of the crust, the confined portion between the north coast of Aberdeen and
the Orkney Islands may have been formed by the removal of the superfi-
cial strata by currents so as to produce a deficiency of attracting matter.
So with respect to the other station, Ben Hutig, the unaccounted-for de-
flection, which is much smaller, viz. —0°60, may be easily explained, as
the effect of the land has not been calculated further off than about 3 miles
(pp. 660, 661). Thus, on the whole, the deflections at those coast-stations,
where itis towards the land, can be pretty well accounted for, without call-
ing in aid the deficiency of attraction of water and supposing that the crust
below the ocean is not condensed.
The seven coast-stations of the second list, where the deflection is towards
the sea, seem to bear individual testimony to the truth of the theory, that
the crust below the ocean must have undergone greater contraction than
other parts of the crust. The four stations (3), (4), (5), (6) on the south
coast of the Isle of Wight all have deflections southwards; and their mag-
nitudes diminish in the order that the distances from the sea increase,—that
order being (3) High Port Cliff, (5) Boniface Down, (4) Week Down, (6)
Dunnose (see the Contour Map of Isle of Wight in the volume of Plates
accompanying the Ordnance Survey Volume). The amounts of the deflec-
tion seem almost to prove too much for the theory. Still they are all
in the direction of the ocean, and seem certainly to indicate that there is a
redundance of matter, and not a deficiency, in that direction. Blackdown
(7) is somewhat further inland than Dunnose is. If, then, the ocean and
erust together do really produce the outstanding deflection southward at
Dunnose, we shall have to suppose that the north deflection at Blackdown
in the first list of coast-stations, arising from the land, is not much less
than 2°76+ 1°73=4:'49, which is a little less than the calculated deflection
at Burleigh Moor on the coast of Yorkshire, and is therefore not an unlikely
amount. The other three coast-stations, (8), (11), (13), all bear out the
VOL, XIII. x
276 The Annual Meeting. [June 9,
theory: though the three deflections are all small, they are towards the
sea, the largest of them being at Fuglences, which is very near to the
North Cape, and has a large expanse of ocean above it.
19. The least that can be gathered from the deflections of these coast-
stations is, that they present no obstacle to the theory so remarkably sug-
gested by the facts brought to light in India, viz. that mountain-regions
and oceans on a large scale have been produced by the contraction of the
materials, as the surface of the earth has passed from a fluid state to a con-
dition of solidity—the amount of contraction beneath the mountain-region
having been less than that beneath the ordinary surface, and still less than
that beneath the ocean-bed, by which process the hollows have been pro-
duced into which the ocean has flowed. In fact the testimony of these coast-
stations is in some degree directly in favour of the theory, as they seem to
indicate, by excess of attraction towards the sea, that the contraction of the
crust beneath the ocean has gone on increasing in some instances still fur-
ther since the crust became too thick to be influenced by the principles of
floatation, and that an additional flow of water into the increasing hollow
has increased the amount of attraction upon stations on its shores. )
Murree, Punjab,
August 20, 1863.
June 2, 1864.
- The Annual Meeting for the Election of Fellows was held this day.
Major-General SABINH, President, in the Chair.
The Statutes relating to the Election of Fellows having been read,
General Boileau and Sir Andrew Scott Waugh were, with the consent of
the Society, nominated Scrutators to assist the Secretaries in examining the
lists. |
The votes of the Fellows present having been collected, the following
gentlemen were declared duly elected into the Society :—
Sir Henry Barkly, K.C.B. William Jenner, M.D.
William Brinton, M.D. Sir Charles Locock, Bart., M.D.
T. Spencer Cobbold, M.D. William Sanders, Esq.
Alexander John Ellis, Esq. Col. William James Smythe, R. A.
John Evans, Esq. Lieut.-Col. Alexander Strange.
Wilham Henry Flower, Esq. Robert Warington, Esq.
Thomas Grubb, Esq. Nicholas Wood, Esq.
Sir John Charles Dalrymple Hay,
Bart..
June 9, 1864. i
Major-General SABINE, President, in the Chair. —
Mr. W. Sanders; Mr: R. Warington; Dr. Jenner; Mr. J. Evans ;
1864.] Prof. Owen on the Cavern of Bruniquel. . oF
Lieut.-Col. Strange ; Mr. W. H. Flower ; Dr. Cobbold ; Col. W. J. Smythe ;
Sir J. C. Dalrymple Hay, Bart.; and Mr. A. J. Ellis, were admitted into
the Society.
Pursuant to notice given at the last Meeting, MM. Claude Bernard,
Jean Bernard Léon Foucault, and Adolph Wurtz, all of Paris, were balloted
for and elected Foreign Members of the Society.
The following communication was read :—
"i Description of the Cavern of Bruniquel, and its Organic Glonteriti
—Part I. Human Remains.” By Professor Richarp Owen,
F.R.S., &. Received May 12, 1864.
(Abstract.)
‘In sis communication the author gives an account of the Cavern of
Bruniquel, Department of the Tarn and Garonne, France, in the state which
it presented when visited by him in January 1864, and a description of the
human remains discovered therein by the proprietor, the Vicomte de Lastic
St. Jal, in 1863, and subsequently by the author in January 1864.
The circumstances under which these discoveries were made are minutely
detailed, and the contemporaneity of the human remains with those of the
extinct and other animals with which they are associated, together with the
flint and bone implements, is shown by the evidences of the plastic condition
of the calcified mud of the breccia at the time of interment, by the chemical
constitution of the human bones, corresponding with that of the other
animal remains, and by the similarity of their position and relations in the
surrounding breccia.
Among the principal remains of the men of the flint-period cesiciinGan are
the following :—1st, the hinder portion of the cranium, with several other
parts of the same skeleton, which were so situated in their matrix as to
indicate that the body had been interred in a crouching posture, and that,
after decomposition and dissolution of the soft parts, the skeleton had
yielded to the superincumbent weight ; 2nd, an almost entire calvarium,
which is described and compared with different types of the human skull,
shown to be superior in form and capacity to the Australian type, and more
closely to correspond with the Celtic type, though proportionally shorter
than the modern Celtic, and the form exhibited by the Celtic cranium from
Engis, Switzerland; 3rd, jaws and teeth of individuals of different ages.
After noticing other smaller portions of human cranium, the author
proceeds to describe minutely the lower jaw and teeth of an adult, and
upper and lower jaws of immature individuals, showing the characters of
certain deciduous teeth. The proportions of the molars are not those of
the Australian, but of other races, and especially those of ancient and
modern Europeans. As in most primitive or early races in which masti-
cation was little helped by arts of cookery or by various and refined kinds
of food, the crowns of the molars, especially of m 1, are worn down beyond
x2
278 Prof. Smith on Complex Binary Quadratic Forms. (June 16,
the enamel, flat and smooth to the stumps, exposing there a central tract
of osteodentine without any sign of decay.
The paper is illustrated by a view and plans of the cavern, and by
figures of the principal human remains, and of two implements of bone on
which the Vicomte de Lastic had discovered, on removal of the breccia,
outline figures of the head of a reindeer and the head of a horse in profile.
The description of the various remains of the animals killed for food,
and of the flint- and bone-implements applied to that and other purposes,
will be the subject of a future communication.
June 16, 1864.
Major-General SABINE, President, in the Chair.
Dr. Brinton; Professor Boole; Mr. T. Grubb; Sir Charles Locock, _
Bart.; and Mr. Nicholas Wood, were admitted into the Society. —
The followmg communications were read :—
I. “On Complex Binary Quadratic Forms.” By H. J. STEPHEN
Suir, M.A., F.R.S., Savilian Professor of Geometry m the
University of Oxford. Received May 18, 1864.
The purpose of this note is to extend to complex quadratic forms some
important investigations of Gauss relating to real quadratic forms. We
shall consider in order (I.) the definition of the Genera, (II.) the theory
of Composition, (III.) the determination of the number of Ambiguous
Classes, (IV.) the representation of forms of the principal genus by
ternary quadratic forms of determinant 1. For the comparison of the
numbers of classes of different orders, we may refer to a paper by
M. Lipschitz (Crelle’s Journal, vol. liv. p. 193); and for the principles
of the theory of complex numbers and complex quadratic forms, to Lejeune
Dirichlet’s Memoir, “‘ Recherches sur les formes quadratiques 4 coefficients
et 4 indétermindées complexes” (Crelle, vol. xxiv. p. 291).
I. The Definition of the Genera.
Let f=(a, 6, ec) be an uneven* primitive form of determinant D, and
m= ax+ 2bxy+cy?, m! =ax'?+2b2'y'+cy? twonumbers represented by /-
The generic characters of f are deducible from the equation
(ax? + 2bxy+ cy") (ax? + 2b2'y'+cy”) =
(ave! + Bf ay’ +2'y|+ cyy’P—D(ay'—2'y)’,
* A primitive form (a, 4, c) is uneven, semieven, or even, according as the peat
common divisor of a, 2b, c is 1, 1+, or (1+2)?; é.¢., in Lejeune Dirichlet’s nomencla-
ture, according as (a, b, c) is of the first, second, or third species. In this paper, when
we speak of an uneven, semieven, or even form or class, we shall always suppose the
ota or class to be primitive. A semieven number is a number divisible by 14-4, but not
y (1+4)%,
1864.] Prof. Smith on Complex Binary Quadratic Forms. 279
or, as we shall write it,
mv = P?— DQ?.
Thus, supposing that p is an uneven prime dividing D, and that m and
m’ are prime to p, the numbers prime to p, which are represented by f, are
either all quadratic residues of p, or else all non-quadratic residues of p ;
in the former case we attribute to f the character [4] = +1, in the latter
P
the character H =—],
Pp
Again, to investigate the supplementary characters relating to powers
of the even prime 1+7, let m=:-+7' be an uneven number, p and p’
representing real numbers, and for brevity, let
(a1 ee =o
c= ee + yp!)2— ny ee Bs
fe 1)5 =.
The values of the units, or characters, a, (3, y depend on the residue of
m for the modulus (1+7)’, as is shown in the following Table.
TABLE I.
m = a= p= y=
Se peer ae +1] +1 +1
a Myers oset See's +1 +1 —l
BE Bsa iccu big ens atalee ioe
BURG Ss as eae +1 —1 —1
+(1—2%) es As Kia). Dea
an ne) ee —l ae us
+ (142%) be lites ails en ol a
+(2—1).. | ia) |
An inspection of the Table shows that, of the sixteen uneven residues of
(1+2)’, eight have the character w=1, and eight the character w=—1,
-w representing any one of the seven characters a, 6, y, Py, ey, 4B, apy.
It will also be seen that any character of a product of two uneven factors
280 = Prof. Smith on Complea Binary Quadratic Forms. [June 16,
is found by multiplying together the corresponding characters of the
factors; so that, conversely, according as any character of a product of
two uneven factors is +1 or —1, the two factors agree or differ in respect
of that character.
The next Table assigns the supplementary characters proper to any
given determinant; they depend on the residue of the determinant for the
‘modulus (I+7)’.
TaBue II.
— Characters. = Characters.
+(1+42)... B ig | Y
+(1—2)... a [3 7 a
+ (3+7) apy +3 Y
a(3—2) By +31 a
Le tee ee a, Y + (1—27) y
RO ie wc ae' Y +(2+2) ay
2(1+3) ap, y + (1422) y
2(1—i) y + (2—i) ay
A, atslels a,
0. tO a, Bs Y |
Of the eighteen propositions contained in this Table, it will suffice to
enunciate and demonstrate one.
“Tf D=+(347), mod (1+7)’, and f is an uneven form of deter-
minant D, the uneven numbers represented by jf, all have the character
aQBy=-+1, or else all have the character aGBy=—1.”
In the equation P?—DQ?’=mm', let us suppose that m and m’ are un-
even ; then P is uneven because D is semieven ; also Q?==+1, +27, 4 or 0,
mod (1+7)’, according as the index of the highest power of 1 +7 dividing
Q is 0, 1, 2, or >2. If Q is uneven, mm'==+37 or +(2+2), mod
(1+72)’; if Q is semieven, mm! =+(1+27), mod (1+7)’; if Q is even,
mm! ==+1, mod (1+7)*; 7. e. in all three cases mm! has the character
ay=1, and mand m! both have the character aBy=-+1, or else both
have the character aBy=—1.
We add a third Table for the purpose of distinguishing between the
possible and impossible genera. In this Table S? is the greatest square.
dividing D, P is uneven and primary*, I is the index of the highest power
of 1+7 dividing 8S, @ represents an uneven prime dividing P, o an uneven
prime dividing S but not P. For brevity, the symbols w and o are written
instead of E ] and E |:
* By a primary uneven number we understand (with Lejeune Dirichlet) an uneven
number p+p’é satisfying the congruences p= 1, mod 4, pp’ =0, mod 2.
1864.] Prof. Smith on Complex Binary Quadratic Forms. 281
. Taste III.
(i) D=PS’*, P=1, mod 4.
I=0, lla 0, ¥
I=2 a a, Y,&
I>2 w a, 5 &, [.
(ii) D=PS*, P=1+ 22, mod 4.
f=) ae o
i —=2 @, ¥ o, a
I>2 @,¥ a, a,
Gi) D=7zPS’, P=1, mod 4.
Veal) Wy & o
it) 2 Dm, 0, Y
I>2 wD, & 6, y; B
(iv) D=7zPS’, P=1+2:, mod 4.
jfe=() BD, ay o
I=1,2)a,a,¥ o
[>2 WD, a, 7 GBs
(v) D=(1+7)PS’, P=1, mod 4.
I=0 w, [ o
a @, Pp 0,7
I>1 @, (3 Os Ys Be
(vi) D=(1+72)PS’, P=1-+ 22, mod 4.
1==0 a, By a
it @, 2, Y o.
I>1 @, 2s Oy Os
(vii) D=72(1+72)PS’, P=1, mod 4.
I=0 aw, a3 o
T=1 @, a3 o,Y
I>l |a,a, p G, Y:
(viii) D=i(1+72)PS*, P=1+ 2i, mod 4.
[=0 @,aGby |e
c=) a, a3, y |o
I>1 BD, a, ps Y|\G.
The characters preceding the vertical line by which the Table is divided
are not independent, but are subject to the condition (arising from the
laws of quadratic residues) that their product must be a positive unit. To
show that this is so, let D=:"(1 +i)? PS’, where @’ and 3’ are each
either 0 or 1; also let y’=0, or 1, according as P==1, or ==1+ 27, mod 4;
If m is a number prime to (1+72)D and capable of primitive representation *
- * If m=a2°+2b2y+cy?, the representation of m by (a, 3, c) is said to be primitive
when the values of the indeterminates are relatively prime.
282 Prof. Smith on Complex Binary Quadratic Forms. [June 16
by f, the congruence w=D, mod m, is resoluble ; and its resolubility im-
plies the condition [=| =| “|x a ]* E |=. But, by the
m 70
laws of quadratic residues, H =. [|= So [= |= "lS » and
the condition just written becomes a” cm y" = =1, which is coinci-
dent with that indicated in the Table.’ Thus (as in the real theory) one-
half of the whole number of assignable generic characters are impossible*
we shall presently obtain a different proof of this result, and shall also
show that the remaining half correspond to actually existing genera.
For the characters of a semieven form f, it is convenient to take the
characters of the numbers represented by 7 ; and for the characters of
}
an even form, the characters of the numbers represented by _ The
d
following Table will serve to form the complete generic character in each
case,
For a semieven form. |
(GG) PS, PL. nod.
1—0 | ze luc.
(i) D=PS’, P=1-+ 27, mod 4.
0 Pa, y |.
For an even form.
I=0 | w | Oo.
II. The Theory of Composition.
The theory of composition given in the ‘ Disquisitiones Arithmeticz’
is immediately applicable to complex quadratic forms. There are, how-
ever, a few points to which we must direct attention.
(1) If m,, m,, m, are the greatest common divisors of a, 2b, ¢; a, (1+7)b,
c; a, 6, c, we have
G) 7 =m—ms
(ii) m,=m,=(1+2)m,,
(il) m,=(1+72)m,=(1+7)?m,,
according as (a, 6, c) either is, or is derived from, (i) an uneven, (ii) a semi-
even, (ill) an even primitive. Hence the order of a form is given when ™,
and mm, are Meaty — if Fis compounded of f and 7’, and if M, M, M,,
mm, m,, m', m', m’, refer to F, f, f respectively, the order of F is com-
pletely penis oe the two theorems, “M, is the product of m, and
* The determinant is supposed not to be a square.
1864.] Prof. Smith on Complea Binary Quadratic Forms. 283
ue casei is the least common multiple of 1 and “2.” (Gauss’s 5th
M, M, nv,
and 6th conclusions, Disq. Arith. art. 235.)
It will be found that Gauss’s proof of these theorems can be transferred to
the complex theory; only, when f and /’ are both semieven, or derived
from semieven primitives, the proof of the sixth conclusion is incomplete,
and, while showing that F cannot be derived from an uneven primitive,
fails to show whether it is derived from a semieven or from an even primi-
tive. But, in the same way in which Gauss has shown that M, is divisible
by m, xm’, it can also be shown that M, is divisible by m, x m',*; 7. @.,
in the case which we are considering, M, is divisible by M,, because
m,=m,, m',=m',, and m,m',=M,. Therefore M,=M,, and F is derived
from a semieven primitive in accordance with our enunciation of Gauss’s
sixth conclusion.
(2) In the real theory, when two or more forms are compounded, each
form may be taken either directly or inversely ; but, however the forms
are taken, the determinant of the resulting form is the same. In the
complex theory, not only may each of the forms to be compounded be
taken in either of two different ways, but also the determinant of the re-
sulting form may receive either of two values, differing, however, only in
sign ; and it is important to attend to the ambiguities which thus arise.
If a complex rational number 7 be written in the form (1 +7) = where
Ais 0, 1, 2, or 3, wis any positive or negative integer, and P, Q are primary
uneven complex integers, we may term 7’ the sign of x. Let F, of which
the determinant is D, be transformed into the product f, x f,x ... fa, by
a substitution [X, Y] linear and homogeneous in respect of h binary sets ;
we have, as in the real theory, / equations of the type
e& @YiiedX: d¥ine ede Y Et. Bie
de, dy, dy, de JD” Fy
d, representing the determinant of f,. Let
J (= dY dX d¥ 7
dx, dy, dy, dw, Fae
ke if A
so that x’, =i ift "is the sign of n,, we shall say that f, is taken with
the sign 7 ‘We can thus enunciate the theorem, “Forms, compounded
of the same forms, taken with the same signs, are equivalent.”” If f,
f,«--+fp are given forms which it is required to compound, the signs of
d,, d,,... 4, must be all real, or else all unreal; and the sign of D will be
real or unreal accordingly. The value of D (irrespective of its sign) is
ascertained as in the real theory; but it may receive at our option, in the
* Disq. Arith. art. 235. The proof that 2(4d'+A) and 2(4b'—A) are divisible by
m,xm',, may be employed ike mutandis) to show that (1 +7) (00'+A) and (1 4)
(b4'— A) are divisible by m, Xm’,
284 Prof. Smith on Complex Binary Quadratic Forms. [June 16,
one case, either of the two real signs, and in the other case either of the
two unreal signs. And whichever sign we give to D, the form f; may be
taken with either of the two real signs, if the sign of . is +1, and with
either of the two unreal signs, if the sign of = is —1. In the important
case in which d,, d,... all have the same sign, we shall always suppose D to
have that sign, and f,, f,... to be all taken with the sign +1. Adopting
this convention, we see that the class compounded of given classes of the
same determinant, or of different determinants having the same sign, is
defined without ambiguity.
(3) By the general formulee of M. Arndt (Crelle, vol. lvi. p. 69), which
on account of their great utility we transcribe here, we can always obtain
a form (A, B, C) compounded in any given manner of two forms (a, 6, ¢)
and (a’, b’,c’), of which the determinants d and d’ are to one another as
two squares. ,
q po sil
aM», meh
pe pe
Oia, te mod A
iu Be
bn’ +b'n_ __ bb’ + Dnn |
‘ BD
C— 7
In these formule D is the greatest common divisor of dm? and d’m?,
m and m’ representing the greatest common divisors of a, 2b, c, and a’, 2b’c’;
m and »’ are the square roots of = and pH is the greatest common divisor
of an’, a'n, and bn'+b'n. The signs of D, 2, and n’ are given, because the
manner of the composition is supposed to be given; to we may attribute
any sign we please, because the forms (A, B, C) and (—A, B, —C) are
equivalent.
(4) If F= (A, B, C) is compounded 2 two primitive forms f and .
and if M is the highest power of 1+7 dividing A, B, C (so that M is 1
or 1+2, or (1+7)*), the complete character of the primitive form a F is
obtained by the following rule :—
“Tf w is any character common tof and Oe vi F will have the cha-
racter w= +1, orw=—1, according as f and /” aan or differ i in respect of
that character.”’
In comparing the characters of f and 7’, it is to be observed that if w ie
w’ are two supplementary characters of 7, and w X w’ a supplementary cha-
racter of f’, w x w’ is to be regarded as a character common to f and 7.
1864.] ~ Prof. Smith on Complex Binary Quadratic Forms. 285
(5) Let us represent by (1), (c), and (2)* respectively the principal
uneven, semieven, and even classes of determinant D; 7. ¢. the classes con-
taining the forms (1,0, —D), ( aly a Ta) aad (2%, je _D-2 ).
the aa of the last two classes implying the congruences D==1, mod 2,
D==i" , mod 4, respectively. Employing the formule of M. Arndt, we
find ( f) x (1)=(f), if (f) is any class of determinant D; (f) x (c)
=(1+2)(f), if f is derived from a semieven or even ee i ROD
=2i(f), if f is derived from an even primitive; and, in particular,
(1) x ()=(), («) x (¢) =(1 +2) (e), (3) x (2) =22(2). Also, if (f) and
(f~') are two opposite primitive classes, (f) x ( f)*=(1), or (1 +%)(c), or
2i(3), according as f and f~* are uneven, semieven, or even. Hence the
three equations (/,) x (¢)=(/2), (A) X M=A +072), (K) x (@) = 2 fa)»
in which (f,) and (f,) are given primitive classes, uneven in the first, semi-
even in the second, and even in the third, are respectively satisfied by the
uneven, oo. and even classes (¢)=(f,) X ( hye (gy 2) XI; let
l4+2 °
(=X G7 (F2) X ae 2 ’, but by no other classes whatever. Again, let D=Am?’
and let the aa (mp, mq, mr), (L1+2]mp, mq, [1+7]mr), (2emp, mq, 2umr)
represent classes derived by the multiplier m from uneven, semieven, and
even primitives of determinant A; in all three forms we suppose p prime
to 2D; in the second and third we suppose q uneven, and A=1, mod 2;
in the third we suppose A=??*, mod 4. The formule of M. Arndt will
then establish the six equations, —
(m, 0, —Am) x (p, mq, mr) =(mp, mq, mr),
(0 +i}m, m, —m a ;) X(p, mg, Lim?r)=([1+i]mp, mg, i +i}mn),
72k
(2im, i'm, ume a x (p, mq, —4mr) = (2ump, mq, pitied
(a +i]m,m, —m +x ([1-+2]p, mq, [1 +7 ]mr)
=(1+7)X((1+2]mp, mq,[1+2]mr),
(zim vem, —m ie -) x (1 +7]p, mq, 2e[ 1-2 mr)
=(1 +2) x (2ump, mq, 2umr),
lel
20
2
(2m, vem, — ) X (Qip, mg, 2im?r) = 2i x (2ump, mq, 2mr).
* Tt is often convenient to symbolize a class by placing within brackets a symbol
representing a form contained in the class; thus (f) may be used to symbolize the
class contain ng the form /.
286 Prof. Smith on Complex Binary Quadratic Forms. [June 16,
From these equations, which contain a solution (for complex numbers)
of the problem solved for real numbers in art. 250 of the ‘ Disquisitiones
Arithmeticee,’ we may infer the following theorems (Disq. Arith. art. 25]
and 253) :—
«The number w of classes of any order © isadivisor of the number
» of uneven classes of the same determinant D; and, given any two classes
n . 3 °
of order ©, there are always — uneven classes which compounded with one
@
of them produce the other.”
«Tf D=1, mod 2, and if the classes of Q are derived from semievyen or
even primitives, w is a divisor of the number 7x! of semieven classes of
determinant D ; and, given any two classes of order Q, there are always
” semieven classes which compounded with one of them produce 1+7
‘,
times the other.” |
“Tf D=+1, mod 4, and if the classes of © are derived from even
primitives, w is a divisor of the number 7” of even classes of determi-
”
nant D; and, given any two classes of order Q, there are always ” even
7 aye
classes which compounded with one of them produce 2: times the other.”’
III. Determination of the number of Ambiguous Classes.
Any form (A, B, C), in which 2B==0, mod A, is called by Gauss an
ambiguous form; but in the investigation which follows we shall for
brevity understand by an ambiguous form an uneven form of one of the
four types :
+ (i) (A, 0, C),
(i) (1421 B, B, ©),
(11) (2B; i, ©), .
Gv)" > (27 BB: ©).
To determine the number of uneven ambiguous classes of any determi-
nant D supposed not to be a square, we shall determine, first, the number
of ambiguous forms of determinant D; and secondly the number of ambi-
guous forms in each ambiguous class.
(1) Let » be the number of different uneven primes Hee D. The
number of ambiguous forms of the type (1) is 4 x 2", or 8 x 2", according
as D is, or is not, uneven. For we may resolve —D into any two rela-
tively prime factors, and may take one of them (with any sign we please)
for A, and the other for C. There are no ambiguous forms of the
type (ii), unless D==7, mod 2, or =0, mod (1+7)*. For in the equation
D=B (B—[1+7] C), if Bis uneven, we have D=7, mod 2, because C
must be uneven; if B is semieven or even, we have D==0, mod (1+7)’.
If D=:, mod 2, we resolve D into any two relatively prime factors X and
Y, and writing B=X, B—(1+72) C=Y, we find bee a at
F ‘whieh is in-
a
1864.] Prof. Smith on Complex Binary Quadratic Forms. =——- 287
tegral because X and Y are uneven, and uneven because X is not —Y,
mod 2. Thus if D =z, mod 2, there are 4 x 2" ambiguous forms of the
type (ai). Again, if D=0, mod (1+7)*, we may resolve D in any way
we please into two factors having 1+2 for their greatest common divisor ;
we find in this way 8x2" ambiguous forms of the type (ii). There
are no ambiguous forms of the types (ili) or (iv), unless D=1, mod 2, or
== 2, mod 4, or =0, mod(1+7)’. Forif in the equation D=B(B—2C), we
suppose B uneven, we find D=1, mod 2; if B is semieven, B°=2/, and
2BC=2(1+7), mod 4, whence D==2, mod 4; lastly, if B is even, D=0,
mod (1+). The same reasoning applies to the equation D=B(B—2iC).
If D=1, mod 2, we resolve D in every possible way into the product of
two factors relatively prime; let D=XxY be such a resolution, then
D=7X x —7Y is another ; and it will be seen that according as the last
coefficient in the two forms
[2% X, <> *|- [ iX,
is uneven or not uneven, so the last coefficient in the two forms
| 20x = ae | E — 9% iX S|
5) 5) 9 2 9 3
is not, or is, uneven; 7. e. there are 2 x 2" ambiguous forms of each of the
types (il) and (iv). If D= 2, mod 4, we resolve D in every possible
way into two factors, of which 1+ is the greatest common divisor ; we
thus find 4 x 2» uneven forms of each of the types (iil) and (iv). Lastly,
if D=0, mod (1+7)’, we resolve D in every possible way into two factors
of which 1+2 is the greatest common divisor, and we obtain 8x2 forms
of each of the types (iii) and (iy).
The result of this enumeration is that if D be uneven, or semieven, or
= 2, mod 4, there are 8 x 2" ambiguous forms; if D==2, mod 4, or =0,
mod (1+7)*, but not mod (1+2)’, there are 16x 2"; and if D=0, mod
(1+7)’, there are 32x 2". On comparing this result with Table IIL., it
will be seen that in every case there are four times as many ambiguous forms
as there are assignable generic characters.
(2) Let f=(a, 6, c) be any form of an ambiguous class ; if (I)=
is an improper automorphic of /, X, p, v satisfy the equations
Be oe — heen st ak, ag sys 8 ey GN)
NL taatity 20% agen es [o-", |. tol. SUM)
- X—Y
i
¥, —}
and, conversely, if X, u, v satisfy the equations (1) and (2), (I)=
can
is an improper automorphic of f. Let a, y, p, g (of which a Ae y are
relatively prime) be a system of integral numbers satisfying the equations
pa=n, PUES 1, } ee (3)
qa=p+l, gy=y;
288 Prof. Smith on Complex Binary Quadratic Forms. [June 16,
and let 2=0, 1—i, 1, or —2, according as 0, 1—?, 1 or —i satisfies the
congruences
p+6a=0, mod 2,
q+6y=0, mod 2,
which are simultaneously resoluble, and admit of only one solution, because
a and y are relatively prime, while gza—py=2. Then it willbe found hea
by the proper transformation |
(= a, + (p+)
2 (qtby) |
fis transformed into an ambiguous form ¢, which will be of the type (i),
(ii), Gii), or (iv), according as §=0, 1—7, 1, or —7. It will also be seen
that, subject to the condition that a and y are relatively prime, there are
always four, and only four, solutions of the system (3), represented by the
formula
ta, id , ra inte,
There are thus four cee ee | included in the formula (J), two of
them transforming f into the same ambiguous form ¢, and the other two
transforming f into the same form taken negatively. The four transforma-
tions (J), and the two ambiguous forms ¢ and —¢, we shall term respect-
ively the transformations and the ambiguous forms appertaining to the im-
proper automorphic (I). If we now form the transformations appertaining
to every improper automorphic of f, it can be proved (A) that these trans-
formations will all be different, and (B) that they will include every proper
transformation of f into an ambiguous form.
(A) As the four transformations appertaining to the same improper au-
tomorphic are evidently different, it will be sufficient to show that if (J)
and (J') appertain to the improper automorphics (I) and ce the supposi-
tion (J)=(J’) he (1)=(I'). From the equations
axa, y=y, ptba=pl+O'a’, gqt+oy=q'+6'y'
(which are equivalent to the symbolic equation (J)=(J')), combined with
the system (3), and with a similar system containing the accented letters,
we find
(6—6')e?=r'—2r, (0-8 )ay=p'—p, (0-8) Y=v —r;
whence again (§—6’) (aa +2bay+ey*?)=0, by virtue of equation (2).
The coefficient of §—6' is not ZERO, for D=0°?—ac is nota square; there-
fore §— a'=0; i.e. = Ny p= py v= Y', oS Gee
(B) Let oS
form ; according as ¢ is of the type (1), (41), (iil), or (iv), let 6=0,
1—2, 1, or —t; let also A=2a3—Oa’, p=ad+Py—flay, y= 2yd—by’;
into an ambiguous
then \f we =(T) is an improper automorphic of f; for
pe —rv=(ad— —ByyY=1, and \a+2ub+re=0,
because of the ambiguity of the form into which / is transformed by
1864.] Prof. Smith on Complex Binery Quadratic Forms. 289
” B . Also ie Bp | appertains to (I); for, writing p and q instead of
a, | __|a, 3(p+0a) is '
Y> 3| F | Y> i(q-+6y) 9 Q, YY Ps q (of which
a and y are relatively prime) being four numbers which satisfy the system
a,
(3) 5, :2~.¢. ri i
It follows from (B) that, if we calculate the ambiguous forms ¢ and —¢
appertaining to every improper automorphic of f, we shall obtain all the
ambiguous forms to which fis equivalent ; it remains to see how many
of these. ambiguous forms are different from one another. If (1)
26—6a, and 26—6y, we have
appertains to (I), an improper automorphic of /.
= ? wt is any given improper automorphic of f, all its similar auto-
cant
morphics are contained in the four formule
(Tye x (I), (T)**1x (1), (Tx aay we | ore
=100
0, —1 | x),
where & is any positive or negative number, and (T)=
(Te 1 x
t, —u, 6, —u,c
u,a, t, +u, 6}?
[é,, u,] representing a fundamental solution of the equation ¢’—Dw’?=1.
Similarly, if (J) represent the four transformations, appertaining to (1), by
which f passes into ¢ or —¢, all the proper transformations of f into ¢ or
—g¢ are included in the formula (T)*x (J). We shall now show that the
four transformations included in the formula (T)* x (J) appertain to the
improper automorphic (T)**x(I). Writing
a= (t,— buy, )a—cupy, Pe=(4—bu,) p—eu,g,
ype auzat (t+ bu,)y, = auypt (t+ bu,)q,
Nop = (toy — Stlo,) A— Claes
rhc: es (toy —FUtg,) P—CUgyY = AU yA + (toy + ba, ps
Vo, = AUox et (toy, + Butgy.)¥5
we find immediately
L ba ) ky —A
Tye x (J) = | MF Pet k) |) (T)2 x (1) = | M2” 2k
( ) ( ) Vhs & (a+ 5 yx) ( ) \ ) V2k,» — P2k
Also attending to the equations (2) and (3), and to the relations
: ty =O,— Dury Uap = 2b; Uys
we obtain, after substitution and reduction,
Pp ye =Aoys Py Vor=Hor— 1,
We %e=Ho Tl, ge Ve=Vo
i.e. (T)*x (J) appertains to (T)?* x (1), if (J) appertains to (I), |
It follows from this result that the ambiguous forms appertaining to (1)
and to (T) x(I) are the same ; for fis transformed into the same forms
by (J) and (T) x (J); and conversely, if the ambiguous forms appertain-
290 Prof. Smith on Complex Binary Quadratic Forms. [June 16,
ing to two different automorphics (I) and (1’) are identical, an equation of
the form (I')=T™ x (I) will subsist ; for if (J) and (J’) are the transfor-
mations appertaining to (I) and (1’), smce by hypothesis (J) and (J’)
transform I into the same form, we must have an canny of the form
C= Cry" x (): nt (J') appertains to (1’), and (T)* x (J) to (Ee x (1) ;
therefore (1') = Ce x (I), by what has been shown above (A).
If then we calculate the eight ambiguous forms appertaining to the four
improper automorphics
(bo, )xO Dx@, (Th, \x xO
‘these eight forms will be the only ambiguous forms equivalent tof. Thus
every uneven ambiguous class contains eight ambiguous forms.
Combining this result with the preceding we obtain the Theorem,
“The number of uneven ambiguous classes is one > halt of the whole
number of assignable generic characters.”’
The number of semieven and even ambiguous classes is determined by
the two following Theorems :— ; 7
«When D= +1, mod 4, there are as many even as a ambiguous
classes.” BS Sie
«When D=1, mod 2, there are as many semieven as uneven ambiguous
classes, or only half as many, according as there at altogether as many
semieven as uneven classes, or only half as many
To prove the first of these theorems, let D==<", mod 4, and let
Meat
2=(24#, 5),
it is evident from the principles of the composition of forms that if (@) is
a given semieven ambiguous class, the equation (3) X (¢)=(1+2) x (/)
is satisfied by one and only one even ambiguous class (f) ; in addition to
this we shall now show that, if (/) is a given even ambiguous class, the
same equation is satisfied by one and only one semieven ambiguous class
(¢) ; from which two things the truth of the theorem is manifest. First,
let the whole number of even classes be equal to the whole number of semi-
even classes*; then the equation
(2) x (¢) =U. +2) x (/)
* That if D==-+1, mod 4, there are either as many semieven as even classes, or else
three times as many, is a theorem of M. Lipschitz (Crelle, vol. liv. p. 196), of which it is
worth while to give a proof here. The number of even classes is to the number of semi-
eyen classes, as unity to the number of semieven classes satisfying the equation
(2) x(@)=(+4) x(f),
f representing any given even form. ‘To investigate the semieven classes satisfying this
equation, apply to f a complete system of transformations for the modulus 1 +2, for
example, the transformations .
see | 1+2, 0 142, 1
0, 1+ |, DO divly 0, 1 >
1864.] Prof. Smith on Complexe Binary Quadratic Forms. 291
is satisfied by only one semieven class (@) ; and this class is ambiguous,
for the equation is satisfied by the opposite of (¢) as well as by (¢) itself ;
therefore (¢) and its opposite are the same class, or (@) is an ambiguous
class. Secondly, let the number of semieven classes be three times the
number of even classes ; then the equation
(2) x@=A+9 (Pf)
is satisfied by three and only three different classes (¢) ; but it is also satis-
fied by the opposites of these classes ; therefore one of them is necessarily
an ambiguous class. Let that class be (¢,) ; the other two are defined by
the equations
(+2) @)=(%) x (ho), A+2) (62) =) X (45);
and cannot be ambiguous classes; for by duplication we find
(G) x @)=A+9 (@), ) XG)=UA+4 (a) 5
whereas every semieven ambiguous class produces (1+7)o, by its duplica-
tion *,
The second theorem may he proved as follows. Let
S=(U1+¢]p, % [1 +¢]r)
be a semieven form of determinant D; and let
: D—1
a=((1+) ii, Ta)
we suppose that pis uneven. The equation (c,) X (¢)=(/) is satisfied by
one uneven class (¢,), or by two (¢,) and (¢,), according as the forms
d,=(p, q 2ir), and ¢,=(2ip, g, 7”), if 7 is uneven, or the forms
$= (p, q 2ir), and ¢,=(2ip, [1+7] p+q, p+[1—cz]q+7), if r is even,
are or are not equivalent}. If any one of the forms f, ¢,, ¢, is ambiguous,
the others are so too; the same thing is therefore true for the classes (/),
(%,), (¢,). Thus the number of semieven ambiguous classes is equal to or
and divide the resulting forms by 1+7; of the quotients, one, or three, will be semieven,
according as D==-++1, or -++-5, mod (1+7)°. It will be found that each of these semi-
even forms satisfies the equation 2X¢=(1+7)x/; and, conversely, every semieven
form ¢ satisfying that equation is equivalent to one of these forms; for, from any trans-
formation of (1+-2)f into =X ¢, we may (by attributing to the indeterminates of = the
values 1, 0) deduce a transformation of modulus 1-+72 by which / passes into (1+-2) ¢ ;
2.€., 6 is equivalent to one of the forms obtained by the preceding process. It only
remains to show that when there are three of these forms, they constitute either one or
three classes, but never two. For this purpose it is sufficient to consider the three semi-
even forms o,= (1 +2, 1, -75). g,, and o,, obtained by the preceding process from
the form >. These forms satisfy the equations o,Xo,=(1+2)o,, o,Xo,=(1+)e,,
6, Xo,=(1+7)o,, o,Xo,=(1+2)o,; from which it follows that any one of the suppo-
sitions 6,=0,, 6,=0), 6)=0, Involves the other two.
* For the definition of the classes («,), (o,), (¢,) see the preceding note.
t The forms ¢, and ¢, are obtained by applying to f a complete set of transformations
of modulus 1+, dividing the resulting forms by 1+-7, and retaining only those quotients
which are uneven forms,
VOL, XIII, Z
292 Prof. Smith on Complex Binary Quadratic Forms. [June 16,
is one half of the number of uneven ambiguous classes, according as the
classes (¢,) and (¢,) are identical or not; z.e., according as the whole
number of semieven classes is equal to or is one-half of the whole number
of even classes.
The demonstration in the ‘ Disquisitiones Arithmeticee,’ that the number
of genera of uneven forms of any determinant cannot exceed the number ~
of uneven ambiguous classes of the same determinant, may be transferred
without change to the complex theory. We thus obtain a proof (inde-
pendent of the law of quadratic reciprocity and of the theorems which
determine the quadratic characters of ¢ and 1+) of the impossibility of
one-half of the whole number of assignable generic characters ; and from
that impossibility, as we shall now show, the quadratic theorems are them-
selves deducible.
(1) If p is an uneven prime =1, mod 2, there are two genera of un-
even forms of determinant p: of these one is the principal genus, and has
the complete characters (4)=1, y=1; the other, containing the form
(7,0, +2p), has the particular character y= —1; whence it follows that
every uneven form of determinant p, which has the character y=-+1, is
a form of the principal genus, and has the character [- | =+1. Again,
1\. ‘
fp=1,mod 4, the form{ 2i, i, )is an uneven form of determinant p;
oad
20
this form has the particular character y= —1, because —Pte ==7, mod 2
Z
it is therefore not a form of the principal genus; but it has the character
(4) =1, because 2¢ is a square; therefore, if p==1, mod 4, every uneven
form of determinant p has the character E | =+1.
i
(2) There is but one genus of forms of determinant é, and its complete
character is a=-+1; there is also but one genus of forms of determinant
1+7, and its complete character is B=+1.
(3) Let » and g be uneven primes of which the imaginary parts are
even ; to prove the law of reciprocity, it will suffice to show that if an =I,
then rea =1. The equation fi =1 implies the existence of a con-
gruence of the type w°—p==0, mod gq, and consequently of an uneven
form of determinant p, and of the type @ Ww, nee ) This form has the
fi
character y=+1, because g==1, mod 2; it therefore has the character
l= ef]
(4) To prove the equatioa B == (— 1 sh) Me in which we may sup-
1864. | Prof. Smith on Complex Binary Quadratic Forms. 293
pose that the uneven prime p is primary, it will suffice to show (i) that
: 1 a (Np—1) oNiete h a (Np—1)
if =| PALA then (1) i aeting et) =1, then
a ‘ a 5 : w—7
—{!=1. (4) Let [= | =1; then, if w°—7=0, mod ( » W; )
fe @ p St Srenale
is a form of determinant 7; it therefore has the character a=1, Zz. é.
(cols pamela B (ai) Let Gay ine then p=1, mod 4, and
the form (7, 0,7) is an uneven form of determinant p; it therefore has
the character (Z)= +1; whence [= | =+1.
Pp P
(5) Similarly, if p=p,+¢p, is an uneven and primary prime, to prove
(potpi)?—1
the equation E& —(——1 8 we shall show, (1) that if Ee ills
(Potp1)?—-1
(po+p1)?—1 1+72
ene ol)—. © ..—=1; (ii) that if (—1). 8. =], then [-s*|=1.
(i) Let | =1; then there is a form of determinant 1+7 and of
]
d ;
the type (p, w,° —"—"); this form has the character B=+1; there-
ype | p p
(po+p1)?2—1 (po+p1)?—1
fore (—1) & =~ =+1. (ii) Let (—1) ® =-+1; then p is
either==1— 27, or==1, mod (1+2)’; if p=(1+2)"44+1—2, ([1+7]’, @
1—2/7) is an uneven form of determinant p; this form has the character
y=-+1, and consequently it also has the character E ] =-+1; there-
*\ 3
fore | = [Se] =+1; if p=(1+7)’£+1, one or other of the
forms ([1+7]’, 1, —#), and ({1+2]’, 1+[1+2]*, 1—4) is an uneven form
of determinant p, having the character [z | =]; therefore in this case
vo [14] = [C2]
IV. The representation of Binary Forms of the principal Genus by
Ternary Forms of Determinant 1.
The solution of the general problem, “To find the representations (if
any) of a given binary by a given ternary quadratic form,’’ depends, in the
case of complex as of real numbers, on the solution of the problem of equiva-
lence for ternary forms. Extending the methods of Gauss to the complex
theory, we find the necessary and sufficient condition for the primitive*
* If a matrix of the type
transforms a ternary into a binary quadratic form, the representation of the binary by
the ternary form is said to be primitive when the three determinants of the matrix are
relatively prime.
Z 2
294 Prof. Smith on Complex Binary Quadratic Forms. ! [June 16,
representation of a binary form f of determinant D by a ternary form of
determinant 1 to be, that f should be a form of the principal genus ; or,
if D= +1, mod 4, that f should be a form either of the principal genus,
or else of that genus which differs from the principal genus only in having
the character y= —1, instead of y=+1. Again, because the reduction
of Lagrange is applicable to complex binary forms, the reduction of Gauss*
is applicable to complex ternary forms. It is thus found that the number
of classes of such forms of a given determinant is finite ; and in particular
that every form of determinant 1 is equivalent to one or other of the forms
—2’?—y’—z2* and x? +iy’+ iz’, of which the former cannot represent num-
bers==2, or==1+7, mod 2; and the latter cannot primitively represent
numbers==2, or==2(1+7), mod 4. The method of reduction itself sup-
* If F=ax?+a'y?+a" 22+ 2bye+20'nz+2b’xy is a ternary form of determinant A,
and Aw?+ A’y?4 A’”22?+2Byz+2B/xz+2B’ ry its contravariant, by applying the reduc-
tion of Lagrange to the form ax?+2d’xy+a’y?, we can render N.a<2 VN. A”
(Dirichlet in Crelle’s Journal, vol. xxiv. p.348); and by applying the same reduction to
the form A’y?+2Byz+A”2?, we can render N.A”7<2/N.aA. The reduction of
Gauss consists in the alternate application of these two reductions until we arrive at a
form in which we have simultaneously N. a2 AGN. AONE AvN=2 YN.aA; and
consequently N.aX<44/N.A, N.A’<4 hy ee If A=l, we have N.aX4,
N.A”’=4; whence a and A” can only have the values 0, +1, +7, +(1+2), 4(1—2),
+2, +22; and it will be found, on an examination of the different cases that can arise,
that the reduction can always be continued until a and A” are either both units, or both
zero. In the former case, by applying a further transformation of the type
if es rtd
0, L ad 2
0; } Ose
the coefficients 5, 0’, b’’ may be made to disappear; and we obtain a form equivalent to
F, and of the type ex?+-e’y?+6’’2?, «, e’, e” representing units of which the product is
—l. In the latter case the form obtained by applying the reduction of Gauss is of the
type
ay? al 22 +-2byz+20'we2 ;
whence a’}’2=1, so that 0’ is a unit which we shall call ¢; and the form e7y
+a"z?-+4-2byz+2exy, by a transformation of the type
1, 0, p’
0, 1,
0, 0, 1
is changed into one of the four forms 6v?+2crz, e®%y2+-22+2exz, ey2+72? + 2enz,
e7y?-+-(1-+7)2?426xe; of which the first two by the transformations
67-12, B90; te 1 0, 0, —e
ei, «2, € . e—lz, 0, O
0, —7, —1 0, 7% &
are changed into the form —x?—yv?—z’; the last two by the transformations
0, -e O ée—1, e-1, e-1(1—2)
—e-l, 0, O ; —6, —6, 6
0, —te?, —1 0, —1, 7
are changed into #?-+-2y2+i22, (See Disq. Arith. art, 272-274.)
1864.] Prof. Smith on Complex Binary Quadratic Forms. ~. 295
plies a transformation of any given form of determinant | into one or other
of those two forms.
If D=z, or 1+2, mod 2, no binary form of determinant D can be re-
presented by —x*—y’—z’, because D cannot be represented by the con-
travariant of that form, 7.e. by the form —z2?—y’—z’ itself. Conse-
quently, if D==7, or 1+7, mod 2, the binary forms of its principal genus
are certainly capable of primitive representation by x?+ iy? +72”.
If D==1, mod 2, no form of the principal genus can be primitively
represented by 2*+72y’?+7i2°. Let f=(a, 4, c) be such a form, and let us
suppose, as we may do, that & is even, so that ac==1, mod 2, and
a=c=1, mod 2 (the supposition a==c=z is admissible, because f is of
the principal genus) ; if possible, let the prime matrix
a,
a! ; p!
all, Bl |
(of which A, B, C are the determinants) transform 2*+7y?+ 72’ into f; we
have the equations a=a’+ ia!’ + ia!”, c=6? +73 +73'", D=A’—7B’—:C’,
from which, and from the congruences D=a==c=1, mod 2, we infer the
incompatible conditions «! + 7a!'=/!' +76"=0, mod1+7, A=1, mod1 +27;
i.e. fis incapable of primitive representation by a?+7y’?+ 72°. If, there-
fore, D=1, mod 2, the forms of its principal genus are capable of primi-
tive representation by —a2*—y’—z*. We may add that when D= rl,
mod 4, the forms of that genus which differs from the principal. genus
only in having the character y=—1, instead of y=+1, are capable of
primitive representation by x*+?y?+72’, but not by —a’—y’—2’.
Lastly, let D=0, mod 2. If D=2, or=2(1+2), mod 4, D cannot be
primitively represented by «?—7iy?—iz*, the contravariant of x? +7y*+ 72’;
i.e. no form of determinant D can be primitively represented by 2? +2y? + 22’;
so that forms of the principal genus are certainly capable of primitive repre-
sentation by —2°—y’?—2*. But if D=2z, or=0, mod 4, the forms of the
principal genus are capable of primitive representation by both the ternary
forms —2*—y’—2* and w?+iy?+iz*. For if f=(a, 6, c) be a form of the
or =1, mod 2; so that a ternary form cf determinant 1 and of the type
Spe? + 2qye+ 2¢q' x2
will be equivalent to —x#’—y’— 2’, or ie x’ +iy?+i2*, according as p’==0,
or ==1, mod 2, on the one hand, or p!"==7, or =1++7, on the other hand.
Again, if (%, k') is a value of the expression / (a, —0, c), mod D, (in
which we now suppose a uneven and 6 semieven or even), des 7} 5 ae
is another value of the same expression; and it can be shown* that when
* If f+ p’2?+2qy?+2¢’xz is a ternary form of det. 1, derived from the value (4, k’)
of the expression 4/ (a, —%, c), mod D, & is the coefficient of yz in the contravariant
Observing that a==1, mod 2
form. Hence a=k*?—D(q’?—ap”), or ap” =y?4+= D
296 Prof. Smith on Complex Binary Quadratic Forms. [June 16,
D=2:, or 0, mod 4, one of the two forms of determinant 1, and of the
ype
f+ ple + 2qye+ 2q' 22,
which are deducible by the method of Gauss from those two values, satisfies
the condition p''==0, or ==1, mod 2, while the other satisfies the condi-
tion p=7, or 1+7, mod 2; that is, fis capable of primitive representation
by both the forms —a*—y’?—2’ and a°+iy?+i2°.
The preceding theory supplies a solution of the problem, “‘ Given a form
of the principal genus of forms of determinant D, to investigate a form
from the duplication of which it arises.’ Let f=(a, 6, c) be the given
form, and let us suppose (as we may do) that a and c are uneven. When
D=z, or 1+7, mod 2, let
a, f
i
al, 3
all, Bll
be a prime matrix (of which the determinants are A, B, C) transform-
ing a°+7y?+iz? into (a, —6, ce); and let @ represent the binary form
(C—iB, A, iC—B); then the matrix
B+i8", BB, ii) gy
a'+ia", a, a, —t(a! —ia!')
transforms f into ¢x@*; and is a prime matrix, for its determinants
-C—7B, 2A, and 7C—B are not simultaneously divisible by any uneven
prime (because A, B, and C are relatively prime), and are not simul-
¢7=0, or 1, mod 2, we see that p”=0, 1, or==¢, 1+2, mod 2, according as "=" =o, A,
D \2
oo )
Pada ed ance Bat nL an OLE erer 8 whieh aetaaene
gruous to 1+2, mod 2, if D=0, mod. 4, and to 7, mod 2, if D=2i, mod 4, since & is
a— k2
D
evidently uneven in either case. From this it appears that if
PD \2
(é+T)
then oe VARET
a
2q'az, p Lh or 1, mod 2, and in the other p” =z, or 1+7, mod 2.
* This assertion may be verified by means of the identity
(G19 Gos) ( Pot” +P LY! +PLY AD LY’ )Y
+(GoPs+Pods— Vi PoP Jo) (Po! LP BY +P.L'YAP LY’)
X (Jot! +9, 2Y' +9.2'Y +9,2'Y’)
+(P) P2—PoPs) (Go®L! FU 2Y +Q2'Y+G0'Y'P
= [(Po% PQ) £?+( Pods —P39o TP Yo Po )2Y + (2193 —P3)Y 7]
X [Pods Pio) 2” + ( Pods —PsVot Por — P1 Vo) 2Y + (Pos — Ps2)9"] 5
in which we have to replace the quantities
Po Pi Po Ps
% %1 G2 Vs
=0, 1, mod 2,
=7, 1+2, mod 2; that is, in one of the two forms f+ p"2?-+-2qyz+
by the elements of the matrix (Z).
1864.] Prof. Smith on Complex Binary Quadratic Forms. 297
taneously divisible by 1-+2, because (Z) is congruous, for the modulus 1 +2,
to the first or second of the matrices
OHO 1000.1
Ne FOO Ge ee a
& 0, ee) and tn i op (4)
according as a==2, c=1, or a=1, c=7, mod 2. Consequently ¢ is a
form the duplication of which produces f. When D==1, or=0, mod 2,
let the prime matrix
transform —2*—y’?—z<* into (a, —6, c). As we cannot have simultaneously
a=Bf, a'=Pf', a=", mod (1+72), we,may suppose that a and ( are
incongruous, mod (1+). If¢=(B+iC, 7A, B—7C), the matrix
Gala 22, ip, nna i (Z)
anal. wowace. eae yk ee cae
transforms f into ¢ xX ¢, and is a prime matrix, being congruous to one or
other of the matrices (Z') for the modulus 1+7, in consequence of the
two suppositions that a and ¢ are uneven, and that wand 6 are incongruous,
mod (1+z2): so that f arises from the duplication of ¢.
From the resolubility of this problem we can infer (precisely as Gauss
has done in the real theory) that that half of the assignable generic cha-
racters which is not impossible corresponds to actually existing genera.
We can also deduce a demonstration of the theorem that any form of de-
terminant D can be transformed into any other form of the same genus,
by a transformation of which the coefficients are rational fractions having
denominators prime to 2D. For every form which arises from the dupli-
cation of an uneven primitive form—that is, every form of the principal
genus—represents square numbers prime to 2D, and is therefore equivalent
to a form of the type (x. [ls p =} But (1, 0, —D) is transformed
Pees
into (x ii N
H
probable.
A mixture of diphenylamine and chloride of benzoyl, when heated, fur-
nishes a thick oil, which solidifies on cooling. Washed with water and
alkaii, and recrystallized from boiling alcohol, in which it dissolves with
difficulty, the new compound is obtained in beautiful white needles. Ana-
lysis has confirmed the theoretical anticipation,
C, H,
C,,H,,NO=C,H, {N.
| C,H, 0}
This substance has become the starting-point of some experiments which
I shall here briefly mention, but to which I intend to return hereafter.
On addition of ordinary concentrated nitric acid, the benzoyl-compound
liquefies and dissolves. From this solution, water precipitates a light-
yellow crystalline compound,
OF H., N, O, = C, H, (NO,) N,
C, HyQ: oon ht
7 5
which dissolves in alccholic soda with a scarlet colour, splitting on ebulli-
tion into benzoic acid_and reddish-yellow needles of nitro-diphenylamine,
C,H, ‘
C,, LB N,0,= be ee (NO,) N.
If, instead of ordinary nitric acid, a large excess of the strongest fuming
nitric acid be employed, the solution deposits, on addition of water, a crys-
1864.] Da Silveira on the Mean Declination of the Magnet. 347
talline compound of a somewhat deeper yellow colour, containing probably
C, H, (NO,)
C,, H,, N, 0, = C,H, (NO,) $
CHO
7 5
This substance dissolves in alcoholic soda with a most magnificent
crimson colour. Addition of water to the boiling liquid furnishes a yellow
crystalline deposit, benzoate (?) of sodium remaining in solution.
The yellow powder is dinitro-diphenylamine. From boiling alcohol, it
crystallizes in reddish needles, exhibiting a bluish metallic lustre. The
analysis of the compound has led to the formula
C, H, (NO,)
C,, H, N,0, = C, (HE (N03 |.
The chemical history of these compounds will be the subject of a special
communication.
XVI. “ A Table of the Mean Declination of the Magnet in each Decade
from January 1858 to December 1863, derived from the Observa-
tions made at the Magnetic Observatory at Lisbon; showing the
Annual Variation, or Semiannual Inequality to which that ele-
ment is subject.” Drawn up by the Superintendent of the
Lisbon Observatory, Senhor pa SitverRA, and communicated by
Major-General Sapine, R.A., President of the Royal Society.
Received June 6, 1864.
I have much pleasure in communicating to the Fellows of the Royal
Society a copy of a Table which I have received from the Superintendent
of the Magnetic Observatory at Lisbon, containing the mean values of the
Declination in each Decade from the commencement of 1858 to the close
of 1863, with corrections applied for the mean secular change, and showing,
in a final column, the difference in each decade of the observed from the
mean annual value derived from the 216 decades. This Table is a counter-
part of Table VII. in Art. XII. of the Philosophical Transactions for
1863, p. 292, differing only in the substitution in the Lisbon Table of de-
cades for weeks, and the addition of the year 1863.
This general confirmation by the Lisbon Observatory of the annual
variation to which the Declination is subject, “ the north end of the magnet
pointing more towards the East when the sun is north of the Equator,
and more towards the West when the sun is south of the Equator,”’ is very
satisfactory. Inthe Lisbon Table the disturbances have not been elimi-
nated.
io}
|
:
eo
ae | :
“ G-cO I— | £20 Fe | 22e0— | SFE Z | BFE 6 9-68 SI | 0-21 23 | 0-9 82 { Baz re | B.e2ze | “E
*S ¥8S O— | 60 72 | IF O— | 8-09 FZ | 3-0F 6 HES SI | F6222 | 99 82 | B82 SE | 39 Le | “gh jerreeeske~
& ITI | $99 86 | GOS O— | OL HZ | F-02 OL | BOF ST | 06 ZS | BIE 8B | 96 SE | Sar 9¢ Se
3 | j
s 0-66 O— | 881 72 | 4-69 0— | G81 ce | 9-Gh¥ OL | LE 9T | 8-66 e% | O-FG 82 | 0.46 FE | GIT LE ‘¢
. €-90 O+ | 1-71 9% | 6:80 I— | 0-€2 93 | 9-98 11 | 96 SI | FS Fo | FOZ 08 | FOG PE | Z-8T 62 4 meee THCY
= 1-20 O+ | 6-60 G2 | L-8I I— | 0-82.92 | 8-S¢ ZL | 3&2 ZI | 98h €@ | G29 08 | 0-6 FE | BLE 6E I
> 0c O+ | 8zP az | @421—| Lot Zz | o8r pt | 861 ZT | 80T Gz | 9-9¢ Te | 0.9% rs | ZLT 68 3
Ss 0-0F O+ | 8247 GS | FOE T— | ZFS L42 | BSS IL | O42 8I | HLE GS | Och ze | Os GSE | ZTE OF "Z “*°** UDICIN
$ 140 OF | GIT GS | 99h I- | GLE 9% | BIE IL | 29 BI | OSF Go | BOT Te | 208 FE | 9.99 6E ‘I
‘Ss 8:70 O+ | 9-21 G2 | 87S I— | FL L242 | 8-01 ZI | 0-42 81 | 80F 98 | 8-FE Te | £-OF Ge | O-IL 8g "e
> WIL OF | 2-61 GS | 0-70 2— | 3EZ 12 | F-2E ZI | 822 8l | 36192 | HB Te | £88 GE | G-ZT OF 4 *** ATenIQoyy
Q 948 O+ | SP GS | TEI 2—- | G86 22 | 9-6 FL | 0-81 6I | FES 9S | BOL OF Gr 9 | 9-FL IP “4
~
S 160 I+ | GIT 93 | €22 2— | BEE 82 | O-8F SL | FLT GL | HIF 6Z | 9-61 OG | FZI LE | 80 IP = :
= Ley 0+ | GOS G3 | GIE Z— | 0-32 84 | BSS SI | 9-81 06 | 82¢ 92 | 96G Of | £88 9f | GTS TF 43 ‘e+ Avenues
% VLE OF | 2SF GZ | L£0F c— | 6-66 8% | O-LZEL | 88002 | OF 92 | 2ze 08 | Gz Ze | 0-80 ZF gt
Ss 4 1 4 / 4 4 4s 4 4 / aA 4 Ww / 4 / aA J 4} /
S "srvak "sales te te +12 tol® + 12 = oie +o1@ +o1Z
g XIS 0q} ‘osueyy) 3 \ :
‘Do jo suvowl *poqoor | TeTHIIS LOF : : E = : i 4 . 2 / ‘opeoa(, “ST IUOTY
> ayy wory |-s09 suvayy| payvartog | “SUN S981 Z981 1981 0981 gest |} “saet
D sooualayiq, | 4
3
= "SO8T toquiesagy 0} gggy Arenuve wo. ‘10;earosqQ WOgsI'T 94} Je MOLeUITIEC] 48944 94} JO SULOTHT
349
\f the Magnet.
x
xi
ion O
rst
x2
=
—)
--
1864.] . Da Silveira on the Mean Declinat
©
i
GZ
GG
1G
GS
cG
G6
cZG
GZ
GG
cZ6
GG
GZ
io
GG
&Z
¥G
VG
VG
¥G
&G
&G
G-18 o+
€-26 Ot
Il 2+
0-40 2+
8-F¢ I+
9-Ch I+
-9§ I+
£6 I+
L810 I+
L0F t+ |
8-L0
0-0¢
6:01
9-9
v-0¢
9-FF
VLE
8-66
T-8¢
8-GZ
6-6
GGG
VE
LG
G-1G
G-GV
GFE
LGV
0-46
9-01
T-0¢
8-6
FiO iG
co
6G
&@
£%
6G
66
£3
63
&@
FG
VG
VG
VG
VG
VG
¥G
VG
ize
FG
GuiVE VG 9-,,8h 19 61:09 6-/BG iV Ouw4 PV
a fen aI SS ge ae
Gres OT v8 OT 0-29 2% G1 66 F-69 SE 5-90 8&
FES Z 0-SE ET 8-18 06 GGG 96 P-G6 GE VIP SE
0-0¢ 8 0-81 &T GL 16 VIP LZ 9-G1 €& 1-91 S&
68S f GSI SI 0-2F 16 0-66 £2 8-6) o£ GLI GE
9-6¢ L 0- B58
When hydrogen was passed through serum, after the lapse of a day or
two a tough elastic product was obtained.
In experiments tried by passing hydrogen through albumen greatly
diluted with water, I found, after the lapse of a few days, a floceulent de-
posit very similar in appearance to the deposit of mucus which often
takes place when urine is allowed to stand ashort time. This point, how-
ever, requires further investigation. I tried also the effect of passing
hydrogen through a portion of intestine inserted into an albuminous fluid.
I have not as yet been able to form either the dense hard or viscid frothy
substance by this method. I repeated the experiment for the formation of
fibrin from albumen, by decomposing the water of its composition by elec-
tricity. I must admit this is the most difficult, troublesome, and unsa-
tisfactory of all the methods I have employed. I find that the great ten-
dency of the poles to form different substances on them, and the great rapi-
dity with which they grow together, lead, without the greatest care, to
the belief that two different substances, differing only in density, are formed
at one and the same pole, so intimately blended are they together. Thus I
was led to believe at first sight that a dense hard substance was formed at
the oxygen end, and not until I had repeated the experiment many times
did I discover that the substance belonged to the hydrogen and not to
the oxygen pole, and had grown across from one pole to the other.
I have obtained on several occasions fibrin and chondrin at the same
time by conducting hydrogen and oxygen derived by the decomposition of
water by voltaic electricity through separate tubes. The oxygen passed
into slightly acid albumen formed fibrin ; the hydrogen passed into alkaline
albumen formed either the chondrin or else the frothy and viscid material.
The temperature was kept up at 98° F. in these experiments. On one
occasion, however, I happened accidentally to reverse the current (that
is to say, the hydrogen was passed into the acid, and the oxygen into the
alkaline albumen), when no chondrin or fibrin was formed.
The following conclusions I have arrived at after the study of the in-
fluence which oxygen and hydrogen gases exert upon albumen when sub-
mitted to their action separately at a temperature of 98° F., the normal
temperature of the living body. Albumen under the action of oxygen
forms, after the lapse of a longer or shorter period, fibrin. The fibrin thus
artificially produced is of three distinct varieties, viz., Ist, the granular
form; 2nd, a form allied to lymph incapable of being unravelled into
fibrils ; lastly, the true fibrillated fibrm. The law which appears to regu-
late the state into which the albumen is converted, as far as my observa-
tion has gone, is one of molecular aggregation, similar to the electric
deposit of metals, as the slower the fibrin is formed the more organized
is it in substance.
I have observed that when fibrin is rapidly formed it is almost always
produced in the granular state; this is particularly the case with fibrin
354 On Organic Substances artificially formed from Albumen. June 16,
formed from albumen by the decomposition of the water of its composition
by voltaic means.
Lymph I consider to be imperfectly formed fibrin more highly deve-
loped than the preceding or granular form. It is possible for this arti-
ficially formed lymph, under favourable circumstances, to assume a more
organized appearance.
I have no doubt that the fibrous outgrowths on the intestine would have
become larger and more developed if the experiment had been carried on
for a sufficient length of time. In fact almost all the fibrin formed round
a platinum wire inserted into albumen is at first covered by outgrowths of
a soft structure. These outgrowths, at the earliest period of their forma-
tion, do not under the microscope present any appearance of fibrils. After
the lapse of some time they appear to undergo condensation, and then to
organize to such an extent that it would be difficult at first sight to deter-
mine whether the substance might not be a portion of fibrous tissue.
The alkalies, with the exception of ammonia, prevent entirely the forma-
tion of fibrin. Ammonia, although it does not retard its formation, dis-
solves it after the lapse of ashort time. The acids and absence of alkaline
salts favour its formation. The opposite, however, is the case with the
hydrogen products, as an alkaline state favours their production.
The action of hydrogen on albumen, as far as my investigations have as
yet proceeded, forms substances analogous to chondrin and mucm. I
believe that the organic substances, chondrin and mucin, products formed
ina living organism, are very closely allied to one another, if not varieties of
the same substance, differing only in their mode of aggregation and stages
of development, and the amount of water in their composition.
Of the exact mode in which hydrogen acts on albumen we are at present
ignorant. I have noticed that in some experiments sometimes one, some-
times the other product was obtained, even when the same influences were
apparently acting on experiments conducted at the same time.
Considering the important physiological part that fibrin, chondrin, and
mucin play in the living body, the production artificially of substances
‘analogous in their behaviour with reagents to those products formed in a
living organism will, I trust, be taken as a sufficient excuse for submitting
to the Royal Society a paper so obviously deficient in many parts, but
which, nevertheless, it would require a vast amount of both time and labour
to carry one step further,
1864.] Reductionand Oxidation of the Colouring Matter of the Blood. 355
XVIII. “ On the Reduction and Oxidation of the Colouring Matter of
the Blood.” By G. G. Sroxus, M.A., Sec. R.S., Lucasian Pro-
fessor of Mathematics in the University of Cainbridge. Received
June 16, 1864.
1. Some time ago my attention was called to a paper by Professor
Hoppe *, in which he has pointed out the remarkable spectrum produced
by the absorption of light by a very dilute solution of blood, and applied
the observation to elucidate the chemical nature of the colouring matter.
I had no sooner looked at the spectrum, than the extreme sharpness and
beauty of the absorption-bands of blood excited a lively interest in my
mind, and I proceeded to try the effect of various reagents. The observa-
tion is perfectly simple, since nothing more is required than to place the
solution to be tried, which may be contained in a test-tube, behind a slit,
and view it through a prism applied to the eye. In this way it is easy to
verify Hoppe’s statement, that the colouring matter (as may be presumed
at least from the retention of its peculiar spectrum) is unaffected by alkaline
carbonates and caustic ammonia, but is almost immediately decomposed
by acids, and also, but more slowly, by caustic fixed alkalies, the coloured
product of decomposition being the hzematin of Lecanu, which is easily
identified by its peculiar spectra. But it seemed to me to be a point of
special interest to inquire whether we could imitate the change of colour
of arterial into that of venous blood, on the supposition that it arises from
reduction.
2. In my experiments I generally employed the blood of sheep or oxen
obtained from a butcher ; but Hoppe has shown that the blood of animals
in general exhibits just the same bands. To obtain the colouring matter
in true solution, and at the same time to get rid of a part of the associated
matters, I generally allowed the blood to coagulate, cut the clot small,
rinsed it well, and extracted it with water. This, however, is not essential,
and blood merely diluted with a large quantity of water may be used; but
in what follows it is to be understood that the watery extract is used unless
the contrary be stated.
3. Since the colouring matter is changed by acids, we must employ re-
ducing agents which are compatible with an alkaline solution. If to a
solution of protosulphate of iron enough tartaric acid be added to prevent
precipitation by alkalies, and a small quantity of the solution, previously
rendered alkaline by either ammonia or carbonate of soda, be added to a
solution of blood, the colour is almost instantly changed to a much more
purple red as seen in small thicknesses, and a much darker red than before
as seen in greater thickness. The change of colour, which recalls the dif-
ference between arterial and venous blood, is striking enough, but the
change in the absorption spectrum is far more decisive. The two highly
* Virchow’s Archiv, vol. xxiii. p. 446 (1862).
VOL. XIII. oD
356 Prof. Stokes on the Reduction and Oxidation [June 16,
characteristic dark bands seen before are now replaced by a single band,
somewhat broader and less sharply defined at its edges than either of the
former, and occupying nearly the position of the bright band separating
the dark bands of the original solution. The fluid is more transparent for
the blue, and less so for the green than it was before. If the thickness be
increased till the whole of the spectrum more refrangible than the red be
on the point of disappearing, the last part to remain is green, a little be-
yond the fixed line 6, in the case of the original solution, and dlue, some
way beyond F, in the case of the modified fluid. Figs. 1 and 2 in the accom-
panying woodcut represent the bands seen in these two solutions respec-
tively.
G
Fig. 2.
4. If the purple solution be exposed to the air in a shallow vessel, it
quickly returns to its original condition, showing the two characteristic
bands the same as before; and this change takes place immediately, pro-
vided a small quantity only of the reducing agent were employed, when the
solution is shaken up with air. If an additional quantity of the reagent be
now added, the same effect is produced as at first, and the solution may
thus be made to go through its changes any number of times.
5. The change produced by the action of the air (that is, of course, by
the absorption of oxygen) may be seen in an instructive form on partly
filling a test-tube with a solution of blood suitably diluted, mixing with a
little of the reducing agent, and leaving the tube at rest for some time in
avertical position. The upper or oxidized portion of the solution is readily
distinguished by its colour; and if the tube be now placed behind a slit
and viewed through a prism, a dark band is seen, having the general form
of a tuning-fork, like figs. 1 and 2, regarded now as a single figure, the
line of separation being supposed removed.
1864. ] of the Colouring Matter of the Blood. 357
6. Of course it is necessary to assure oneself that the single band in the
green is not due to absorption produced merely by the reagent, as is readily
done by direct observation of its spectrum, not to mention that in the
region of the previous dark bands, or at least the outer portions of it, the
solution is actually more transparent than before, which could not be occa-
sioned by an additional absorption. Indeed the absorption due to the
reagent itself in its different stages of oxidation, unless it be employed in
most unnecessary excess, may almost be regarded as evanescent in com-
parison with the absorption due to the colouring matter; though if the
solution be repeatedly put through its changes, the accumulation of the
persalt of iron will presently tell on the colour, making it sensibly yellower
than at first for small thicknesses of the solution.
7. That the change which the iron salt produces in the spectrum is due
to a simple reduction of the colouring matter, and not to the formation of
some compound of the colouring matter with the reagent, is shown by the
fact that a variety of reducing agents of very different nature produce just
the same effect: If protochloride of tin be substituted for protosulphate
of iron in the experiment above described, the same changes take place
as with the iron salt. The tin solution has the advantage of being colour-
less, and leaving the visible spectrum quite unaffected, both before and
after oxidation, and accordingly of not interfering in the slightest degree
with the optical examination of the solutions, but permitting them to be
seen with exactly their true tmts. The action of this reagent, however,
takes some little time at ordinary temperatures, though it is very rapid if
previously the solution be gently warmed. Hydrosulphate of ammonia
again produces the same change, though a small fraction of the colouring
matter is liable to undergo some different modification, as is shown by the
occurrence of a slender band in the red, variable in its amount of develop-
ment, which did not previously exist. In this case, as with the tin salt, the
action is somewhat slow, requiring a few minutes unless it be assisted by
gentle heat. Other reagents might be mentioned, but these will suffice.
8. We may infer from the facts above mentioned that the colouring
matter of blood, like indigo, 7s capable of existing in two states of oxida-
tion, distinguishable by a difference of colour and a fundamental difference
in the action on the spectrum. It may be made to pass from the more to
the less oxidized state by the action of suitable reducing agents, and re-
covers its oxygen by absorption from the air.
As the term hematin has been appropriated to a product of decomposi-
tion, some other name must be given to the original colouring matter. As
it has not been named by Hoppe, I propose to call it cruorine, as suggested
to me by Dr. Sharpey ; and in its two states of oxidation it may conveniently
be named scarlet cruorine and purple cruorine respectively, though the
former is slightly purplish at a certain small thickness, and the latter is of
a very red purple colour, becoming red at a moderate increase of thickness.
9. When the watery extract from blood-clots is left aside in a corked
2Dd2
308 Prof. Stokes on the Reduction and Oxidation (June 16,
bottle, or even in a tall narrow vessel open at the top, it presently changes
in colour from a bright to a dark red, decidedly purple in small thicknesses.
This change is perceived even before the solution has begun to stink in the
least perceptible degree. The tint agrees with that of the purple cruorine
obtained immediately by reducing agents; and if a little of the solution be
sucked up from the bottom into a quill-tube drawn to a capillary point, and
the tube be then placed behind a slit, so as to admit of analyzing the
transmitted light without exposing the fluid to the air, the spectrum will
be found to agree with that of purple cruorine. On shaking the solution
with air it immediately becomes bright red, and now presents the optical
characters of scarlet cruorine. It thus appears that scarlet cruorine is
capable of being reduced by certain substances, derived from the blood,
present in the solution, which must themselves be oxidized at its expense.
10. When the alkaline tartaric solution of protoxide of tin is added in
moderate quantity to a solution of scarlet crucrine, the latter is presently
reduced. If the solution is now shaken with air, the cruorine is almost
instantly oxidized, as is shown by the colour of the solution and its spec-
trum by transmitted light. On standing for a little time, a couple of minutes
or so, the cruorine is again reduced, and the solution may be made to go
through these changes a great number of times, though not of course in-
definitely, as the tin must at last become completely oxidized. It thus
appears that purple cruorine absorbs free oxygen with much greater avidity
than the tin solution, notwithstanding that the oxidized cruorine is itself
reduced by the tin salt. I shall return to this experiment presently.
11. When a little acid, suppose acetic or tartaric acid, which does not
produce a precipitate, is added to a solution of blocd, the colour is quickly
changed from red to brownish red, and in place of the vriginal bands (fig. 1)
we have a different system, nearly that of fig. 3. This system is highly
characteristic; but in order to bring it out a larger quantity of substance
is requisite than in the case of scarlet cruorine. The figure does not exactly
correspond to any one thickness, for the bands in the blue are best seen
while the band in the red is still rather narrow and ill-defined at its edges,
while the narrow inconspicuous band in the yellow hardly comes out till
the whole of the blue and violet, and a good part of the green, are absorbed.
The difference in the spectra figs. 1 and 3 does not alone prove that the
colouring matter is decomposed by the acid (though the fact that the
change is not instantaneous favours that supposition), for the one solution
is alkaline, though it may be only slightly so, while the other is acid, and
the difference of spectra might be due merely to this circumstance. As
the direct addition of either ammonia or carbonate of soda to the acid
liquid causes a precipitate, it 1s requisite in the first instance to separate the
colouring matter from the substance so precipitated.
This may be easily effected on a small scale by adding to the watery
extract from blood-clots about an equal volume of ether, and then some
glacial acetic acid, and gently mixing, but not violently shaking for fear
1864. | of the Colouring Matter of the Blood. 359
of forming an emulsion. When enough acetic acid has been added, the
acid ether rises charged with nearly the whole of the colouring matter,
while the substance which caused the precipitate remains in the acid watery
layer below*. The acid ether solution shows in perfection the characteristic
spectrum fig. 3. When most of the acid is washed out the substance falls,
remaining in the ether near the common surface. If after removing the
wash-water a solution, even a weak one, of ammonia or carbonate of soda
be added, the colouring matter readily dissolves in the alkali. The spec-
trum of the transmitted light is quite different from that of scarlet eruorine,
and by no means so remarkable. It presents a single band of absorption,
very obscurely divided into two, the centre of which nearly coincides with
the fixed line D, so that the band is decidedly less refrangible than the
pair of bands of scarlet crnorine. The relative proportion of the two parts
of the band is liable to vary. The presence of alcohol, perhaps even of
dissolved ether, seems to favour the first part, and an excess of caustic
alkali the second, the fluid at the same time becoming more decidedly
dichroitic. The blue end of the spectrum is at the same time absorbed.
The band of absorption is by no means so definite at its edges as those of
searlet cruorine, and a far larger quantity of the substance is required to
develope it.
This difference of spectra shows that the colouring matter (hematin)
obtained by acids is a product of the decomposition, or metamorphosis of
some kind, of the original colouring matter.
When hezematin is dissolved in alcohol containing acid, the spectrum
nearly agrees with that represented in fig. 3.
12. Heematin is capable of reduction and oxidation like cruorine. If
it be dissolved in a solution of ammonia or of carbonate of soda, and a little
of the iron salt already mentioned, or else of hydrosu!phate of ammonia, be
added, a pair of very intense bands of absorption is immediately developed
(fig. 4). These bands are situated at about the same distance apart as
those of scarlet cruorine, and are no less sharp and distinctive. They are
a little more refrangible, a clear though narrow interval intervening between
the first of them and the lime D. They differ much from the bands of
cruorine in the relative strength of the first and second band. With cruo-
rine the second band appears almost as soon as the first, on increasing the
strength or thickness of the solution from zero onwards, and when both
bands are well developed, the second band is decidedly broader than the
first. With reduced hematin, on the other hand, the first band is already
black and intense by the time the second begins to appear; then both
bands increase, the first retaining its superiority until the two are on the
* Jf I may judge from the results obtained with the precipitate given by acetic acid
and a neutral salt, a promising mode of separation of the proximate constituents of blood-
crystals would be to dissolve the crystals in glacial acetic acid and add ether, which pre-
cipitates a white albuminous substance, leaving the hematin in solution.
360 Prof. Stokes on the Reduction and Oxidation [June 16,
point of merging into one by the absorption of the intervening bright band,
when the two appear about equal.
Like cruorine, reduced hematin is oxidized by shaking up its solution
with air. I have not yet obtained hematin in an acid solution in more
than one form, that which gives the spectrum fig. 3, and which I have
little doubt contains heematin in its oxidized form; for when it is with-
drawn from acid ether by an alkali, I have not seen any traces of reduced
heematin, even on taking some precautions against the absorption of oxygen.
As the alkaline solution of ordinary hematin passes, with increase of thick-
ness, through yellow, green, and brown to red, while that of reduced
hematin is red throughout, the two kinds may be conveniently distin-
guished as brown hematin and red hematin respectively, the former or
oxidized substance being the heematin of chemists.
13. Although the spectrum of scarlet cruorine is not affected by the addi-
tion to the solution of either ammonia or carbonate of soda, yet if after such
addition the solution be either heated or alcohol be added, although there
is no precipitation decomposition takes place. The coloured product of de-
composition is brown hzematin, as may be inferred from its spectrum. Since,
however, the spectrum of an alkaline solution of brown hematin is only
moderately distinctive, and is somewhat variable according to the nature of
the solvent, it is well to add hydrosulphate of ammonia, which immediately
developes the remarkable bands of red hematin. This is the easiest way
to obtain them; but the less refrangible edge of the first band as obtained
in this way is liable to be not quite clean, in consequence of the presence
of a small quantity of cruorine which escaped decomposition.
Some very curious reactions are produced in a solution of cruorine by
gallic acid combined with other reagents, but these require further study.
14. Hoppe proposed to employ the highly characteristic absorption-
bands of scarlet cruorine in forensic inquiries. Since, however, cruorine
is very easily decomposed, as by hot water, alcohol, weak acids, &c., the
method would often be inapplicable. But as in such cases the coloured
product of decomposition is hematin, which is a very stable substance,
the absorption-bands of red hematin in alkaline solution, which in sharp-
ness, distinctive character and sensibility rival those of scarlet cruorine
itself, may be employed instead of the latter. The absorption-bands of
brown hematin dissolved in a mixture of ether and acetic acid, or in acetic
acid alone, are hardly less characteristic, but are not quite so sensltiye, re-
quiring a somewhat larger quantity of the substance.
15. I have purposely abstained from physiological speculations until I
should have finished the chemico-optical part of the subject; but as the
facts which have been adduced seem calculated to throw considerable light
on the function of cruorine in the animal economy, I may perhaps be
permitted to make a few remarks on this subject.
It has been a disputed point whether the oxygen introduced into the
blood in its passage through the lungs is simply dissolved or is chemically
1864. | of the Colouring Matter of the Blood. 361
combined with some constituent of the blood. The latter and more natural
view seems for a time to have given place to the former in consequence of
the experiments of Magnus. But Liebig and others have since adduced
arguments to show that the oxygen absorbed is, mainly at least, chemically
combined, be it only in such a loose way, like a portion of the carbonic acid
in bicarbonate of soda, that it is capable of being expelled by indifferent
gases. It is known, too, that it is the red corpuscles in which the faculty
of absorbing oxygen mainly resides.
Now it has been shown in this paper that we have in cruorine a substance
capable of undergoing reduction and oxidation, more especially oxidation,
so that if we may assume the presence of purple cruorine in venous blood,
we have all that is necessary to account for the absorption and chemical
combination of the inspired oxygen.
16. It is stated by Hoppe that venous as well as arterial blood shows
the two bands which are characteristic of what has been called in this
paper scarlet cruorine. As the precautions taken to prevent the absorption
of oxygen are not mentioned, it seemed desirable to repeat the experiment,
which Dr. Harley and Dr. Sharpey have kindly done. A pipette adapted
to a syringe was filled with water which had been boiled and cooled without
exposure to the air, and the point having been introduced into the jugular
vein of a live dog, a little blood was drawn into the bulb. Without the
water the blood would have been too dark for spectral analysis. The
colour did not much differ from that of scarlet cruorine; certainly it was
much nearer the scarlet than the purple substance. The spectrum showed
the bands of scarlet cruorine.
This, however, does not by any means prove the absence of purple cruo-
rine, but only shows that the colouring matter present was chiefly scarlet
cruorine. Indeed the relative proportions of the two present in a mixture
of them with one another and with colourless substances, can be better
judged of by the tint than by the use of the prism. With the prism the
extreme sharpness of the bands of scarlet cruorine is apt to mislead, and
to induce the observer greatly to exaggerate the relative proportion of that
substance.
Seeing then that the change of colour from arterial to venous blood as
far as it goes is in the direction of the change from scarlet to purple cruo-
rine, that scarlet cruorine is capable of reduction even in the cold by sub-
stances present in the blood (§ 9), and that the action of reducing agents
upon it is greatly assisted by warmth (§ 7), we have every reason to believe
that a portion of the cruorine present in venous blood exists in the state
of purple cruorine, and is reoxidized in passing through the lungs.
17. That it is only a rather small proportion of the cruorine present in
venous blood which exists in the state of purple cruorine under normal
conditions of life and health, may be inferred, not only from the colour,
but directly from the results of the most recent experiments *. Were it
* Funk’s Lehrbuch der Physiologie, 1863, vol. i. § 108.
362 Prof. Stokes on the Reduction and Oxidation [June 16,
otherwise, any extensive hemorrhage could hardly fail to be fatal, if, as
there is reason to believe, cruorine be the substance on which the function
of respiration mainly depends; nor could chlorotic persons exhale as much
carbonic acid as healthy subjects, as is found to be the case.
But after death there is every reason to think that the process of reduc-
tion still goes on, especially in the case of warm-blooded animals, while
the body is still warm. Hence the blood found in the veins of an animal
some time after death can hardly be taken as a fair specimen as to colour
of the venous blood in the living animal. Moreover the blood of an animal
which has been subjected to abnormal conditions before death is of course
liable to be altered thereby. The terms in which Lehmann has described
the colour of the blood of frogs which had been slowly asphyxiated by
being made to breathe a mixture of air and carbonic acid seem unmistake-
ably to point to purple cruorine*.
18. The effect of various indifferent reagents in changing the colour of
defibrinated blood has been much studied, but not always with due regard
to optical principles. The brightening of the colour, as seen by reflexion,
produced by the first action of neutral salts, and the darkening caused by
the addition of a little water, are, I conceive, easily explained; but I have
not seen stated what I -feel satisfied is the true explanation. In the former
case the corpuscles lose water by exosmose, and become thereby more
highly refractive, in consequence of which a more copious reflexion takes
place at the common surface of the corpuscles and the surrounding fluid.
In the latter case they gain water by endosmose, which makes their refrac-
tive power more nearly equal to that of the fluid in which they are con-
tained, and the reflexion is consequently diminished. There is nothing in
these cases to indicate any change in the mode in which light is absorbed
by the colouring matter, although a change of tint to a certain extent, and
not merely a change of intensity, may accompany the change of conditions
under which the turbid mixture is seen, as I have elsewhere more fully
explained +.
No doubt the form of the corpuscles is changed by the action of the
reagents introduced ; but to attribute the change of colour to this is, I ap-
prehend, to mistake a concomitant for a cause, and to attribute, moreover,
the change of colour to a cause inadequate:to produce it.
19. Very different is the effect of carbonic acid. In this case the ex-
istence of a fundamental change in the mode of absorption cannot be ques-
tioned, especially when the fluid is squeezed thin between two glasses and
viewed by transmitted light. I took two portions of defibrinated blood ; to
one I added a little of the reducing iron solution, and passed carbonic acid
into the other, and then compared them. They were as nearly as possible
alike. We must not attribute these apparently identical changes to two
totally different causes if one will suffice. Now in the case of the iron
* Physiological Chemistry, vol. ii. p. 178.
+ Philosophical Transactions, 1852, p. 527.
1864. ] of the Colouring Matter of the Blood. 363
salt, the change of colour is plainly due to a deoxidation of the cruorine.
On the other hand, Magnus removed as much as 10 or 12 per cent. by
volume of oxygen from arterialized blood by shaking the blood with car-
bonic acid. If, as we have reason to believe, this oxygen was for the most
part chemically combined, it follows that carbonic acid acts as if it were a
reducing agent. We are led to regard the change of colour not as a direct
effect of the presence of carbonic acid, but a consequence of the removal
of oxygen. There is this difference between carbonic acid and the real re-
ducing agents, that the former no longer acts on a dilute and comparatively
pure solution of scarlet cruorine, while the latter act just as before.
If even in the case of blood exposed to an atmosphere of carbonic acid
we are not to attribute the change of colour to the direct presence of the
gas, much less should we attempt to account for the darker colour of
venous than arterial blood by the small additional percentage of carbonic
acid which the former contains. The ascertained properties of cruorine
furnish us with a ready explanation, namely that it is due to a partial re-
duction of scarlet: cruorine in supplying the wants of the system.
20. Iam indebted to Dr. Akin for calling my attention to a very in-
teresting pamphlet by A. Schmidt on the existence of ozone in the blood*.
The author uses throaghout the language of the ozone theory. If by
ozone be meant the substance, be it allotropic oxygen or teroxide of hy-
drogen, which is formed by electric discharges in air, there is absolutely
nothing to prove its existence in blood; for all attempts to obtain an oxi-
dizing gas from blood failed. But if by ozone be merely meant oxygen in
any such state, of combination or otherwise, as to be capable of producing
certain oxidizing effects, such as turning guaiacum blue, the experiments of |
Schmidt have completely established its existence, and have connected it,
too, with the colouring matter. Now in cruorine we have a substance ad-
mitting of easy oxidation and reduction ; and connecting this with Schmidt’s
results, we may infer that scarlet cruorine is not merely a greedy absorber
and a carrier of oxygen, but also an oxidizing agent, and that it is by its
means that the substances which enter the blood from the food, setting
aside those which are either assimilated or excreted by the kidneys, are
reduced to the ultimate forms of carbonic acid and water, as if they had
been burnt in oxygen.
21. In illustration of the functions of cruorine, I would refer, in conclu-
sion, to the experiment mentioned in § 10. As the purple cruorine in the
solution was oxidized almost instantaneously on being presented with free
oxygen by shaking with air, while the tin-salt remained in an unoxidized
state, so the purple cruorine of the veins is oxidized during the time, brief
though it may be, during which it is exposed to air in the lungs, while
the substances derived from the food may have little disposition to combine
with free oxygen. s the scarlet cruorine is gradually reduced, oxidizing
thereby a portion of the tin-salt, so part of the scarlet cruorine is gradually
* Ueber Ozon im Blute. Dorpat, 1862.
364 Sir W. Snow Harris on the Laws and Operation [June 16,
reduced in the course of the circulation, oxidizing a portion of the sub-
stances derived from the food or of the tissues. The purplish colour now
assumed by the solution illustrates the tinge of venous blood, and a fresh
shake represents a fresh passage through the lungs.
XIX. “ Further Inquiries concerning the Laws and Operation of Elec-
trical Force.” By Sir W. Snow Harris, F.R.S., &c. Received
June 8, 1864.
(Abstract.)
1, The author first endeavours to definitely express what is meant by
quantity of electricity, electrical charge, and intensity.
By quantity of electricity he understands the actual amount of the un-
known agency constituting electrical force, as represented by some arbi-
trary quantitative ‘electrical’ measure. By electrical charge he under-
stands the quantity which can be sustained upon a given surface under a
given electrometer indication. lectrical intensity, on the contrary, is
‘the electrometer indication’ answering to a given quantity upon a given
surface.
2. The experiments of Le Monnier in 1746, of Cavendish in 1770, and
the papers of Volta in 1779, are quoted as showing that bodies do not take
up electricity in proportion to their surfaces. According to Volta, any
plane surface extended in length sustains a greater charge,—a result which
this distinguished philosopher attributes to the circumstance that the elec-
trical particles are further apart upon the elongated surface, and conse-
quently further without each other’s influence.
3. The author here endeavours to show that, in extending a surface in
length, we expose it to a larger amount of inductive action from surround-
ing matter, by which, on the principles of the condenser, the intensity of
the accumulation is diminished, and the charge consequently increased ; so
that not only are we to take into account the influence of the particles on
each other, but likewise their operation upon surrounding matter.
4. No very satisfactory experiments seem to have been instituted showing
the relation of quantity to surface. The quantity upon a given surface has
been often vaguely estimated without any regard to a constant electro-
meter indication or intensity. The author thinks we can scarcely infer from
the beautiful experiment of Coulomb, in consequence of this omission, that
the capacity of a circular plate of twice the diameter of a given sphere is twice
the capacity of the sphere, and endeavours to show, in a future part of the
paper (Experiment 16), that the charge of the sphere and plate are to each
other not really as 1:2, but as 1:/2, that is, as the square roots of
the exposed surfaces; so that we cannot accumulate twice the quantity of
electricity upon the plate under the same electrometer indication.
5. On a further investigation of the laws of electrical charge, the quan-
tity which any plane rectangular surface can receive under a given intensity
1864.) of Electrical Force. 365
is found to depend not only on the surface, but also on its linear boundary
extension. Thus the linear boundary of 100 square inches of surface under
a rectangle 37°5 inches long by 2°66 inches wide, is about 80 inches ;
whilst the linear boundary of the same 100 square inches of surface under
a plate 10 inches square is only 40 inches. Hence the charge of the rec-
tangle is much greater than that of the square, although the surfaces are
equal, or nearly so.
6. The author finds, by a rigid experimental examination of this question,
that electrical charge depends upon surface and linear extension conjointly.
He endeavours to show that there exists in every plane surface what may
be termed an electrical boundary, having an important relation to the group-
ing or disposition of the electrical particles in regard to each other and to
surrounding matter. This boundary, in circles or globes, is represented by
their circumferences. In plane rectangular surfaces, it is their linear ex-
tension or perimeter. If this Joundary be constant, their electrical charge
(1) varies with the square root of the surface. If the surface be constant,
the charge varies with the square root of the boundary. Ifthe surface and
boundary both vary, the charge varies with the square root cf the surface
multiplied into the square root of the boundary. Thus, calling C the charge
S the surface, B the boundary, and » some arbitrary constant depending
on the electrical unit of charge, we have C=p S.B, which will be found,
with some exceptions, a general law of electrical charge. It follows from
this formula, that if when we double the surface we also double the boun-
dary, the charge will be also double. In this case the charge may be said
to vary with the surface, since it varies with the square root of the surface,
multiplied into the square root of the boundary. If therefore the surface
and boundary both increase together, the charge will vary with the square
of either quantity. The quantity of electricity therefore which surfaces can
sustain under these conditions will be as the surface. If/ and 6 represent
respectively the length and breadth of a plane rectangular surface, then
the charge of such a surface is expressed by p ¥ 216 (1-6), which is found
to agree perfectly with experiment. We have, however, in all these cases
to bear in mind the difference between electrical charge and electrical
- intensity (1).
7. The electrical intensity of plane rectangular surfaces is found to vary
in an inverse ratio of the boundary multiplied into the surface. If the sur-
face be constant, the intensity is inversely as the boundary. If the boun-
dary be constant, the intensity is inversely as the surface. If both vary
alike and together, the intensity is as the square of either quantity ; so that
if when the surface be doubled the boundary be also doubled, the intensity
will be inversely as the square of the surface. The intensity of a plane
rectangular surface being given, we may always deduce therefrom its elec-
trical charge under a given greater intensity, since we only require to de-
termine the increased quantity requisite to bring the electrometer indica-
tion up to the given required intensity. This is readily deduced, the
366 Sir W. Snow Harris on the Laws and Cperation [June 16,
intensity being, by a well-established law of electrical force, as the square of
the quantity.
8. These laws relating to charge, surface, intensity, &c., apply more
especially to continuous surfaces taken as a whole, and not to surfaces
divided into separated parts. The author illustrates this by examining the
result of an electrical accumulation upon a plane rectangular surface taken
as a whole, and the results of the same accumulation upon the same sur-
face divided into two equal and similar portions distant from each other,
and endeavours to show, that if as we increase the quantity we also increase
the surface and boundary, the intensity does not change. If three or more
separated equal spheres, for example, be charged with three or more equal
quantities, and be each placed in separate connexion with the electrometer,
the intensity of the whole is not greater than the intensity of one of the parts.
A similar result ensues in charging any united number of equal and similar
electrical jars. A battery of five equal and similar jars, for example, charged
with a given quantity =1, has the same intensity as a battery of ten equal
and similar jars charged with quantity =2; so that the intensity of the
ten jars taken together is no greater than the intensity of one of the jars
taken singly. In accumulating a double quantity upon a given surface
divided into two equal and separate parts, the boundaries of each being
the same, the intensity varies inversely as the square of the surface. Hence
two separate equal parts can receive, taken together under the same electro-
meter indication, twice the quantity which either can receive alone, in
which case the charge varies with the surface. Thus if a given quantity be
disposed upon two equal and similar jars instead of upon one of the jars
only, the intensity upon the two jars will be only one-fourth the intensity
of one of them, since the intensity in this case varies with the square of the
surface inversely, whilst the quantity upon the two jars under the same
electrometer indication will be double the quantity upon one of them only ;
in which case the charge varies with the surface, the intensity being con-
stant. If therefore as we increase the number of equal and similar jars
we also increase the quantity, the intensity remains the same, and the
charge will increase with the number of jars. Taking a given surface
therefore in equal and divided parts, as for example four equal and similar
electrical jars, the intensity is found to vary with the square of the quantity -
directly (the number of jars remaining the same), and with the square of
the surface inversely (the number of jars being increased or diminished) ;
hence the charge will vary as the square of the quantity divided by the
square of the surface; and we have, calling C the charge, Q the quantity,
2
and S the surface, ta which formula fully represents the phenomenon
of a constant intensity, attendant upon the charging of equal separated sur-
faces with quantities increasing as the surfaces ; as in the case of charging
an increasing number of equal electrical jars. Cases, however, may possibly
arise in which the intensity varies inversely with the surface, and not in-
—
Se
1864.] of Hlectrical Force. 367
versely with the square of the surface. In such cases, of which the author
gives some examples, the above formula does not apply.
9. From these inquiries it is evident, as observed by the early electricians,
that conducting bodies do not take up electricity in proportion to their sur-
faces, except under certain relations of surface and boundary. If the breadth
of a given surface be indefinitely diminished, and the length indefinitely in-
creased, the surface remaining constant, then, as observed by Volta, the
least quantity which can be accumulated under a given electrometer indi-
cation is when the given surface is a circular plate, that is to say, when
the boundary is a minimum, and the greatest when extended into a right
lime of small width, that is, when the boundary is a maximum. In the
union of two similar surfaces by a boundary contact, as for example two
circular plates, two spheres, two rectangular plates, &c., we fail to obtain
twice the charge of one of them taken separately. In either case we fail
to decrease the intensity (the quantity being constant) or to increase the
charge (the intensity being constant), it being evident that whatever de-
creases the electrometer indication or intensity must increase the charge,
that is to say, the quantity which can be accumulated under the given in-
tensity. Conversely, whatever increases the electrometer indication de-
creases the charge, that is to say, the quantity which can be accumulated
under the given intensity.
10. If the grouping or disposition of the electrical particles, in regard to
surrounding matter, be such as not to materially influence external induc-
tion, then the boundary extension of the surface may be neglected. In all
similar figures, for example, such as squares, circles, spheres, &e., the elec-
trical boundary is, in relation to surrounding matter, pretty much the same
in each, whatever be the extent of their respective surfaces. In calculating
the charge, therefore, of such surfaces, the boundary extensions may be
neglected, in which case their relative charges are found to be as the square
roots of the surfaces only ; thus the charges of circular plates and globes
are as their diameters, the charges of square plates are as their sides. In
rectangular surfaces also, having the same boundary extensions, the same
result ensues, the charges are as the square roots of the surfaces. In cases
of hollow cylinders and globes, in which one of the surfaces is shut out
from external influences, only one-half the surface may be considered as
exposed to external inductive action, and the charge will be as the square
root of half the surface, that is to say, as the square root of the exposed
surface. If, for example, we suppose a square plate of any given dimen-
sions to be rolled up into an open hollow cylinder, the charge of the cylinder
will be to the charge of the plate into which we may suppose it to be ex-
panded as 1: 72, In like manner, if we take a hollow globe and a circular
plate of twice its diameter, the charge of the globe will be to the charge of
the plate also as 1: ¥ 2, which is the general relation of the charge of closed to
open surfaces of the same extension. The charge of a square plate to the
charge of a circular plate of the same diameter was found to be 1: 1°13;
368 Sir W. Snow Harris on the Laws and Operation [June 16,
according to Cavendish it is as 1: 1°15, which is not far different. It is
not unworthy of remark that the electrical relation of a square to a circular
plate of the same diameter, as determined by Cavendish nearly a century
since, is in near accordance with the formules C= /S above deduced.
11. The author enumerates the followimg formule as embracing the
general laws of quantity, surface, boundary extension, and intensity, prac-
tically useful in deducing the laws of statical electrical force.
Symbols.
Let C= electrical charge ; Q= quantity ; E= intensity, or electrometer
indication ; S= surface, B= boundary extension, or perimeter ; A= direct
induction; 6= reflected induction; F= force; D= distance.
Formule.
C «8S, when §S and B vary together.
C « Q, E being constant, or equal 1.
Ca wh S, B being constant, or equal 1.
Ca VA B, S being constant, or equal 1.
C «,/S.B, when S and B vary together.
Ea = (Q being constant), for all plane rectangular surfaces.
1
B’
E« = B being constant, or equal 1.
E « _,S being constant, or equal 1.
Ea 2. when S and B vary together.
S?
|
Ca WA
E « Q’, S being constant, or equal 1.
Q?
Ca sr
In square plates, C « with side of square.
In circular plates, C « with diameter.
In globes, C « with diameter.
A, or induction « S, all other things remaining the same.
The same for 6, or reflected induction.
In circular plates, globes, and closed and open surfaces,
E x4; oras a
S’ A
F (=E) « Q’.
ForEa =, S being constant.
2
Generally we have F « D™
1864. | of Electrical Force. 369
12. The author calculates from these laws of charge for circles and
globes, a series of circular and globular measures of definite values, taking
the circular inch or globular inch as unity, and calling, after Cavendish, a
circular plate of an inch in diameter, charged to saturation, a circular inch
of electricity ; or otherwise charged to any degree short of saturation, a
circular inch of electricity under a given intensity. In like manner he de-
signates a globe of an inch in diameter a globular inch of electricity.
In the following Table are given the quantities of electricity contained in
circular plates and globes, together with their respective intensities for dia-
meters varying from °25 to 2 inches; a circular plate of an inch diameter
and 4th of an inch thick being taken as unity, and supposed to contain
100 particles or units of charge.
Diameters, Circle. Globe.
or 7 | Se
units of charge. || Particles. | Intensity. || Particles. | Intensity.
0:25 25 0:062 39 0:124
0:50 50 0:250 70 0-500
0-75 75 0-560 105 1:120
1:00 100 1-000 140 2°000
1:25 125 1560 175 3°120
1:40 140 1-960 196 3°920
1:50 150 2250 210 4-500
1:60 160 2°560 224 5120
1:75 175 3060 245 6:120
2:00 200 4-000 280 8:000
13. The experimental. investigations upon which these elementary data
depend, constitute a second part of this paper. The author here enters
upon a brief review of his hydrostatic electrometer, as recently perfected
and improved, it being essential to a clear comprehension of the laws and
other physical results arrived at.
In this instrument the attractive force between a charged and neutral
disk, in connexion with the earth, is hydrostatically counterpoised by a
small cylinder of wood accurately weighted, and partially immersed in a
vessel of water. The neutral disk and its hydrostatic counterpoise. are
freely suspended over the circumference of a light wheel of 2°4 inches in
diameter, delicately mounted on friction-wheels, so as to have perfectly
free motion, and be susceptible of the slightest force added to either side
of the balance. Due contrivances are provided for measuring the distance
between the attracting disks. The balance-wheel carries a light index of
straw reed, moveable over a graduated quadrantal are, divided into 90° on
each side of its centre. The neutral attracting plate of the electrometer is
about 14 inch in diameter, and is suspended from the balance-wheel by
a gold thread, over a similar disk, fixed on an insulating rod of glass, placed
in connexion with any charged surface the subject of experiment. The
least force between the two disks is immediately shown by the movement
370 Sir W. Snow Harris on the Laws and Operation [June 16,
of the index over the graduated arc in either direction, and is eventually
counterpoised by the elevation or depression in the water of the hydrostatic
cylinder suspended from the opposite side of the wheel. The divisions on
the graduated quadrant correspond to the addition of small weights to
either side of the balance, which stand for or represent the amount of
force between the attracting plates at given measured distances, with given
measured quantities of electricity. This arrangement is susceptible of very
great accuracy of measurement.
The experiment requires an extremely short time for its development,
and no calculation is necessary for dissipation. The author carefully de-
scribes the manipulation requisite in the use of this instrument, together
with its auxiliary appendages. He considers this electrometer, as an in-
strument of electrical research, quite invaluable, and peculiarly adapted to
the measurement of electrical force.
14. Having fully described this electrometer, and the nature of its indi-
cations, certain auxiliary instruments of quantitative measure, to be em-
ployed in connexion with it, are next adverted to.
- First, the construction and use of circular and globular transfer measures
given in the preceding Table, by which given measured quantities of elec-
tricity may be transferred from an electrical jar (charged through a unit-
jar from the conductor of an electrical machine) to any given surface in
connexion with the electrometer. The electrical jar he terms a guantzty-
jar, the construction and employment of which is minutely explained ; as
also the construction and employment of the particular kind of unit-jar he
employs.
15. Two experiments (1 and 2) are now given in illustration of this
method of investigation.
Experiment | developes the law of attractive force as regards quantity ;
which is found to vary with the square of the number of circular or glo-
bular inches of electricity, transferred to a given surface in connexion with
the fixed plate of the electrometer, the distance between the attracting sur-
faces being constant.
Experiment 2 demonstrates the law of force as regards distance between
the attracting surfaces, the quantity of electricity being constant ; and by
which it is seen that the force is in an inverse ratio of the square of the
distance between the attracting plates, the plates being susceptible of per-
fect inductive action. From these two experiments, taken in connexion
with each other, we derive the following formula, F « as calling F the
force, Q the quantity, and D the distance. It is necessary, however, to
observe that this formula only applies to electrical attractive force between
a charged and neutral body in connexion with the earth, the two surfaces
being susceptible of free electrical induction, both direct and reflected.
16. The author now refers to several experiments (3, 4, 5, and 6), show-
ing that no sensible error arises from the reflected inductive action of the
1864. ] of Electrical Force. 371
suspended neutral disk of the electrometer, or from the increased surface
attendant on the connexion of the surface under experiment with the fixed
plate of the electrometer; as also, that it is of no consequence whether the
suspended disk be placed immediately over the fixed attracting plate of the
electrometer, or over any point of the attracting surface in connexion
with it.
17. Having duly considered these preliminary investigations, the author
now proceeds to examine experimentally the laws of surface and boundary
as regards plane rectangular surfaces, and to verify the formule C=,/ S.B,
and B=: in which C=charge, E=intensity, S=surface, and B=
boundary. :
For this purpose a series of smoothly-polished plates of copper were em-
ployed, varying from 10 inches square to 40 inches long by 2°5 to 6 inches
wide, and about 3th of an inch thick, exposing from 100 to 200 square
inches of surface.
The charges (1) of these plates were carefully determined under a given
electrometer indication, the attracting plates being at a constant distance.
Experiment 7. In this experiment, a copper plate 10 inches square is
compared with a rectangular plate 40 inches long by 2°5 inches wide.
In these plates the surfaces are each 100 square inches, whilst the boun-
daries are 40 and 85 inches, The boundaries may be taken, without sen-
sible error, as 1 ; 2, whilst the surfaces are the same.
On examining the charges of these plates, charge of the square plate
was found to be 7circular inches, under an intensity of 10°. Charge of the
rectangular plate 10 circular inches nearly, under the same intensity of 10°,
The charges therefore were as 7: 10 nearly, that is, as 1: 1-4 nearly ; being
the square roots of the boundaries, that is, as 1: V2.
Experiment 8. A rectangular plate 37:5 inches long by 2°7 inches wide,
surface 101 square inches, boundary 80°5 inches, compared with a rect-
angular plate 34°25 inches long by 6 inches wide, surface 205 square
inches, boundary 80:5 inches.
Here the boundaries are the same, whilst the surfaces may be taken as
5:2.
On determining the charges of these plates, charge of the rectangular
plate, surface 101 square inches was found to be 8°5 circular inches under
an intensity of 8°. Charge of the plate with double surface =205 square
inches, was found to be 12 circular inches under the same intensity of 8°;
that is to say, whilst the surfaces are as 1: 2, the charges are as 85: 12
nearly, or as the square roots of the surfaces, that is, as 1: 4/ z,
Experiment 9. A rectangular plate 26°25 inches long by 4 inches wide,
surface 105 square inches, boundary 60°5, compared with a rectangular
plate 40 inches long by 5 inches wide, surface 200 square inches, boundary
90 inches.
Here the surfaces are as 1: 2 nearly, whilst their boundaries are as 2:3.
VOL, XIII. 25
372 Sir W. Snow Harris on the Laws and Operation [June 16,
Charge of the rectangular plate surface =105 square inches, 7 circular
inches under an intensity of 10°. Charge of rectangular plate surface 200
square inches, 12 circular inches, under the same intensity of 10°. The
charges therefore are as 7:12 nearly, or as 1: 1°7, being as the square
roots of the surfaces multiplied into the square roots of the bouneaee#
very nearly.
Experiment 10. A square plate 10 inches square, surface 100 square
inches, boundary 40 inches, compared with a rectangular plate 40 inches
long by 5 inches wide, surface 200 square inches, boundary 90 inches.
Here the surfaces are double of each other, and the boundaries also
double each other, or so nearly as to admit of their being considered
double of each other. Charge of square plate 6 circular inches, under an
intensity of 10°. Charge of rectangular plate 12 circular inches, under
the same intensity of 10°. The charges, therefore, are as the square roots
of the surfaces and boundaries conjointly, according to the formula
C=‘ S.B, as also verified in the preceding experiment 9.
A double surface, therefore, having a double boundary, takes a double
charge, but not otherwise. Neglecting all considerations of the boundary,
therefore, the surface and boundary varying together, the charge in this
case will be as the surface directly.
18. The author having verified experimentally the laws of surface and
boundary, as regards plane rectangular surfaces, proceeds to consider the
charges of square plates, circular plates, sphéres, and closed and open sur-
faces generally.
Experiment 11. Plate 10 inches square, surface 100 square inches,
boundary 40 inches, compared with a similar plate 14 inches square, sur-
face 196 square inches, boundary 56 inches. Here the surfaces are as 1:2
nearly, whilst the boundaries are as 1: V 2 nearly.
In this case charge of square plate, surface 100 square inches, was found
to be 8 circular inches under an intensity of 10°. Charge of the plate,
surface 196 square inches, 11 circular inches, under the same intensity of
10°. Here the charges are as 8:11, whilst the surfaces may be taken as
1: 2, that is to say (neglecting the boundary), the charges are as the a
roots of the surfaces, according to the formula C= VS.
On examining the intensities of these plates, they were found to be
inversely as the surfaces ; thus 8 circular inches upon the plate, surface 100,
evinced an intensity of 10°; 8 pace inches upon the plate, surface 196,
evinced an intensity of 5° only, or 3 the former, according to the formula
ai et
E=<.-
Experiment 12. A circular plate of 9 inches diameter, surface 63-6
square inches, compared with a circular plate of 18 inches, or double that
diameter, surface 254 square inches. Here the surfaces are as 1: 4, whilst
the boundaries or circumferences are as | : 2.
Charge of 9-inch plate, 6 circular inches, under an intensity of 10°.
ee
1864. ] , of Electrical Force. . 373
Charge of 18-inch plate, 12 circular inches, under the same intensity of 10°.
Here the charges are as 1 : 2, whilst the surfaces are as 1:4; neglecting
the difference of boundary, therefore, the charges, as in the preceding ex-
periments, are as the square roots of the surfaces.
On examining the intensities of these plates, they were found to be in-
versely as the surfaces; thus 6 circular inches upon the 9-inch plate
evinced an intensity of 10°, as just stated; 6 circular inches upon the
18-inch plate had only one-fourth the intensity, or 2°5; beimg inversely
: ]
as the surfaces, according to the formula Be
Experiment 13. A circular plate of 9 inches diameter, surface 63°6
square inches, compared with a circular plate of 12°72 inches diameter,
surface 127-2 square inches. Here the surfaces are as 1: 2.
Charge of 9-inch plate (surface 63°6 square inches), 5 circular inches,
under an intensity of 8°. Charge of 12°72-inch plate (surface 127°2
square inches), 7 circular inches, under the same intensity of 8°. The
charges here are as 5:7, whilst the surfaces are as 1:2; that is to say
(neglecting the boundaries), the charges are as the square roots of the
surfaces.
On examining the intensities of these plates, they were found to be, as
in the preceding experiments, inversely as the surfaces.
Experiment 14. Comparison of a sphere of 4°5 inches diameter, viene
63°5 square inches, with a sphere of 9 inches, or double that diameter,
surface 254 square inches.
Charge of sphere of 4°5 inches diameter (surface 63°5 square inches),
4 circular inches, under an intensity of 9°. Charge of sphere of 9 inches
diameter (surface 254 square inches), 8 circular inches, under the same
intensity of 9°. Here the charges are as 1: 2, whilst the surfaces are as
1:4. The charges, therefore, are as the square roots of the surfaces, or
as 1:44.
On examining the interieities of these spheres, they were found to be as
the surfaces inversely, or very nearly ; being as 2°°5 and 9° respectively.
Experiment 15. Circular plate of 9 inches diameter compared with a
sphere of the same diameter. Here the actual surfaces are 63:6 square
inches for the plate, and 254 square inches for the sphere, being as 1: 4.
We have to observe, however, that one surface of the sphere is closed or
shut up, consequently the exposed surfaces, electrically considered, neglect-
ing one-half the surface of the sphere as being closed, are as 1:2; and the
exposed surface of the plate is exactly one-half the exposed surface of the
sphere.
Charge of plate 8 circular inches, under an intensity of 12°. Charge of
sphere 11 circular inches, under the same intensity of 12°, The charges,
therefore, are as 8: 11, or sa 1:1°4; the exposed surfaces being as 1:2,
The charges, therefore, are as the square roots of the exposed surfaces.
On examining the intensities of the plate and sphere, they were found
2E2
B74 On the Laws and Operation of Electrical Force. [June 16,
to be in an inverse ratio of the exposed surfaces, as in the former expe:
riments.
Haperiment 16. Comparison of a sphere of 7 inches diameter with a
circular plate of 14 inches, or double that diameter. In this case the
inner and outer surface of the sphere, taken together, are actually the
same as the two surfaces of the plate. The inner surface of the sphere
being closed, however, as in the last experiment, the surfaces of the sphere
and plate, electrically considered, are therefore not equal, and the surface
of the plate is twice the surface of the sphere. The surfaces, therefore,
open to external induction are as 2: 1.
On examining the charges of the plate and sphere, they were found to
be as 10: 14, or as 1:1°4; charge of sphere being 10 circular inches,
under an intensity of 20°, and charge of plate being 14 circular inches,
under the same intensity of 20°. The charge of the sphere, therefore, as
compared with the charge of the plate, is as 1: ¥ 2, that is, as the square
roots of the exposed surfaces.
On examining the intensities of the sphere and plate, they were found to
be, as in the preceding experiments, in an inverse ratio of the exposed sur-
faces. We cannot, therefore, conclude, as already observed (4), that the
capacity of the plate is twice that of the sphere.
19. The following experiments are further adduced in support of the
preceding :—
Experiment 17. A copper plate 10 inches square, compared with the
same plate rolled up into an open hollow cylinder, 10 inches long by 3:2
inches diameter. Here, as in the last experiments, although the surfaces
are actually the same, yet, electrically considered, the plate has twice the
surface of the cylinder, one surface of the cylinder being shut up.
_ On examining the charges of the cylinder and plate, they were found to
be, as in the preceding experiments, as 1: V2; that is, as the square roots
of the exposed surfaces, and the intensities in an inverse ratio of the sur-
faces, which seems to be a general law for closed and open surfaces.
Experiment 18. A hollow copper cube, side 5:7 inches, surface 195,
compared with a hollow copper sphere of diameter equal side of cube,
surface 103 square inches nearly.
On examining the charges of the sphere and cube, they were found to
be as 9: 10 nearly ; charge of the sphere being 9 circular inches, under an
intensity of 10°, and charge of cube being 10 circular inches, under the
same intensity of 10°. The charges of a cube, and of a sphere whose dia-
meter equals the side of the cube, approach each other, notwithstanding
the differences of the surfaces, owing to the six surfaces of the cube not
being in a disjointed or separated state.
20. The author observes, in conclusion, that the numerical results of the
foregoing experiments, although not in every instance mathematically exact,
yet upon the whole were so nearly accordant as to leave no doubt as to the
law in operation. It would be in fact, he observes, assuming too much to
1864. ] My. P. Griess on a New Class of Compounds. 375
pretend in such delicate experiments to have arrived at nearer approxima-
tions than that of a degree or two of the electrometer, or within quantities
less than that of ‘25 of a circular inch. If the manipulation, however, be
skilfully conducted, and the electrical insulations perfect, it is astonishing
how rigidly exact the numerical results generally come out.
XX. “Ona New Class of Compounds in which Nitrogen is substituted
for Hydrogen.” By Prrrr Griess, Esq. Communicated by Dr.
Hormann. Received June 2, 1864.
(Abstract. )
All the bodies in which nitrogen is substituted for hydrogen which I
have discovered during the last few years* may be divided into two dis-
tinctly different classes. The first class comprises those bodies which are
obtained when three atoms of hydrogen in two atoms of an amido-com-
pound are replaced by one of nitrogen from nitrous acid. The members of
the second group are formed by the action of nitrous acid upon one equi-
valent of an amido-compound only. The following equations will best
show these various reactions :—
a 2(C, H, NO,) + NHO,=C¢,, H,, N,9,+2H,0
en —~— OE =
Amidobenzoic Nitrous Diazoamido-
acid. acid. benzoic acid.
II. 6, H, N, 0, +NHO0,=C, H, N, 0,42H,0.
Picramic acid Diazo-dinitro-
(amidonitrophenylic phenylic acid.
acid).
I have hitherto chiefly examined into the constitution of the bodies that
form according to the first equation (diazoamidobenzol, diazoamidobenzoic
acid), and have only incidentally explored the field of bodies which equa-
tion II. opens up. I have had occasion since to study more closely several
representatives of the latter class of compounds, which are derived from
aniline (amidobenzol) and analogous organic bases; and since the results
which I obtained cannot but excite some interest, I may be permitted to
submit them briefly to the Royal Society.
Nitrate of Diazobenzol, C,H, N,, NHO,.
This compound is most readily obtained by passing a rapid current of
nitrous acid gas through a solution of nitrate of aniline, saturated in the
cold, until aniline ceases to be separated by the addition of solution of
caustic potash to the liquid. On diluting the solution then with three
times its volume of alcohol, and adding a sufficient quantity of ether, nitrate
of diazobenzol separates in long white needles. In order to remove a trace
of a colouring substance, the crystals are redissolved in a small quantity of
* Ann. der Chem. und Pharm. vol. exiii. p- 201; vol. cxvii. p. 15 vol. cxxi. p. 257.
Proceedings of the Royal Society, vol. x. p. 591; vol. xi. p. 263; vol. xii. p. 418.
376 Mr. P. Griess on a New Class of Compounds | [June 16,
cold dilute alcohol and precipitated by ether. The following equation
expresses the reaction :—
©, H,N, NHO,+ NHO,=€, H,N,, Be 3+2H, 9.
we —<— A Ms ; ~~
Nitrate of aniline. Nitrous Nitrate of oe
acid. benzol.
Nitrate of diazobenzol may also be prepared from diazoamidobenzol, a
substance described by me on a former occasion*, by treating an etherial
solution of the latter with nitrous acid,
C,, H,, N, +NHO,+2NHO,=2(G, H, N,, NHO,)+2H, 9.
Cente Oe | __9 Se — —S
Diazoamido- Nitrate of diazobenzol.
benzol.
The new compound dissolves very readily in water, more difficultly in
alcohol, and is almost insoluble in ether. On heating, the solutions are
decomposed with evolution of gas. The dry substance explodes with the
greatest violence when gently heated, and it is necessary to observe great
precautions whilst working with it. ‘The chemical analysis could not, for
the same reason, be performed by the usual methods. Its composition
was, however, readily established by studying the products of decomposi-
tion to which boiling with water gives rise, according to the equation
ey EN Lee. + H,O=C,H,O + N, + NHO,.
“Nite ate of diazo- Phenylic Nitro- Nitric
benzol. acid. gen. acid.
Sulphate of Diazobenzol, C,H, N, SH, 9,,.
This salt forms when a highly concentrated aqueous solution of the
former compound is treated with a sufficient quantity of cold sulphuric
acid diluted with its own bulk of water. ‘The solution is treated, as before,
with three times its volume of alcohol, and ether added, which causes the
sulphate of diazobenzol to separate in a layer of a very concentrated aqueous
solution at the bottom of the vessel. On placing this latter solution over
sulphuric acid, crystallization ensues after a short time. The crystals are
freed from the mother-liquor by washing with absolute alcohol. In this
manner large white prisms, which rapidly deliquesce in moist air, are ob-
tained, and which are decomposed with slight deflagration when heated by
themselves.
Hydrobromate of Diazobenzol, C,H,N,, HBr.
This compound is obtained in small white soft plates when an etherial
solution of diazoamidobenzol is mixed with an etherial solution of bromine,
(C,, H,, N,+6Br=C, H,N,, HBr+ C, H, Br, N+2(HBr).
—-,-—" SS + —— 7 ——_~,- --
Diazoamido- Hydrobromate of Tribromaniline.
benzol. diazobenzol.
* Ann. der Chem. und Pharm. vol. cxxi. p- 258.
1864. | in which Nitrogen is substituted for Hydrogen. B77
Hydrobromate of diazobenzol is very unstable. The beautifully white
erystals change so rapidly that in a few moments they acquire a reddish
colour, and in a few days the decomposition is almost complete. They
explode on heating almost with the same violence as was experienced with
nitrate of diazobenzol. |
Dibromide of Hydrobromate of Diazobenzol, ©, H,N,, HBr, Br,.
On adding excess of bromine-water to an aqueous solution of any one of
the compounds previously described, an orange-coloured oil is obtained which
rapily solidifies, after the mother-liquor has been removed, to small orange-
coloured plates. The crystals of dibromide are obtained in a perfectly pure
state by washing with a little alcohol. This compound is rather difficultly
soluble in cold alcohol and ether ; and the solutions are rapidly decomposed,
particularly on the application of heat.
Platinum-salt of the Hydrochlorate of Diazobenzol, ©, H, N,, HCl, PtCl,.
This salt forms beautiful yellow prisms which are almost insoluble in
water. The gold-salt, C,H, N,, HCl, AuCl,, can be recrystallized from
alcohol, and is obtained in very fine golden-yellow brilliant plates.
It has thus been sufficiently shown that diazobenzol deports itself like
an organic base, being capable, like aniline, of forming salts with various
acids. It possesses, however, also the property of combining with the
hydrates of the metals, thus playing the part of a weak acid.
Compound of Hydrate of Potassium with Diazobenzol, C,H, N,, KHO.
This body is obtained when a concentrated aqueous solution of nitrate of
diazobenzo] is treated with excess of concentrated aqueous potassa. By
evaporating on the water-bath, the liquid solidifies, when sufficiently eon-
centrated, to a magma of yellow crystals consisting of nitre and the com-
pound of hydrate of potassa with diazobenzol. The crystalline mass is
pressed between porous stones, and thus partly freed from moisture. By
dissolving in absolute alcohol and treating with ether, the new compound
of hydrate of potassium with diazobenzol is obtained in a pure state,
crystallizing in small soft white plates, which rapidly become reddish,
especially in the moist condition. It is very readily soluble in water and
alcohol; the solutions, however, decompose slowly, and deposit a reddish
amorphous body. Heat does not seem to accelerate this decomposition
materially.
Compound of Hydrate of Silver with Diazobenzol, C,H, N,, AgHO.
This substance is obtained in the form of an almost white precipitate
when a solution of silver is added to an aqueous solution of the former
compound. It is verystable. Similar compounds are obtained with lead-
and zinc-salts. ue
378 Mr. P. Griess on a New Class of Compounds [June 16,
Diazobenzol, ©, H, N,.
This substance is obtained when an aqueous solution of the compound
of hydrate of potassium with diazobenzol is neutralized with acetic acid.
It separates as a thick yellow oil of very little stability. After a few
moments an evolution of gas ensues, and the diazobenzol is rapidly con-
verted into a reddish-brown viscid mass. Diazobenzol is soluble in acids, as
well as bases, with formation of the saline compounds previously described.
By acting in the cold with aniline upon nitrate of diazobenzol*, the
following change takes place :—
G, H,N, NHO,+2¢, H, N= Ga HAN, +, H, N, NHO,.
NOE -TREIAS bs. Vecesy, adceite ghOEy 5Get Tia
Nitrate of diazo- Aniline. PRON ea Nitrate of aniline.
benzol. benzol.
ee
I was formerly of opinion that diazoamidobenzol must be viewed as a
double compound of diazobenzol and aniline. The above equation seems
to confirm this view.
New compounds analogous to diazobenzol-amidobenzol are obtained by
the action of other organic bases upon nitrate of diazobenzol, viz. diazo-
ici ele wh
benzol-amidobromobenzol, C be NP? by the action of bromaniline.
°\ Br
Naphthalidine and nitrate of diazobenzol combine directly and form nitrate
of diazobenzol-amidonaphtol, crystallizing in magnificent large green prisms.
The action of amido-acids upon nitrate of ee: is analogous to
that of the aniline; ez. g7.,
6, H,N,
C,H,N,, NHO,+2C,H,NO,= 1é ee 4+. HI, NO,, NHO,.
—— -+- W- -~-— +e — Ss =a
Nitrate of diazo- Amido-acid. Diazobenzol- Nitrate of amido-
benzol. amidobenzoic acid. benzoic acid.
Diazobenzol-amidobenzoic acid separated quickly as a yellow crystalline
mass on mixing the aqueous solutions of both substances. It is purified
by recrystallization from ether in the form of small yellow plates. It
combines with bases and forms saline bodies. Bichloride of platinum
precipitates from an alcoholic solution a yellowish-white crystalline pla-
tinum-salt of the composition C,, H,, N, O,, 2HCl, 2PtCl,.
Similar double acids to the one just described are obtained by the action
of amidodracylic acid, amidoanic acid, &c., upon nitrate of diazobenzol.
Fwedeen Compounds of Diazobenzol.
These peculiar compounds are formed when aqueous ammonia, as well as
certain organic bases, are made to act upon the dibromide of diazobenzol.
* It is self-evident that for this and similar experiments sulphate and hydrobromate of
diazobenzol may also be employed.
1864.] in which Nitrogen is substituted for Hydrogen. 379
Diazobenzolimide, C,H, H ie) N, is obtained according to the equation
C, H, N, HBr,+4NH,=C, H, N,+3NH, Br.
— ae SS —>_-—" —__-—~+---—_—“
Dibromide. Ammonia. Diazoben- Bromide of
zolimide. ammonium.
It forms a yellowish oil, Which must be distilled zz vacuo with the aid of
a current of steam. Exposed by itself to a higher temperature, it decom-
poses with detonation. It is remarkable for its stupefying ammoniacal-
aromatic odour.
Ethyldiazobenzolimide, Ce! i: } N, is analogous in its properties, and
is formed in a similar manner.
Products of Decomposition of Diazobenzol Compounds.
The transformations which the molecule of diazobenzol undergoes under
the influence of various reagents are numerous. The products often re-
present some peculiar classes of entirely new compounds; more frequently,
however, they belong to the phenyl- and benzol-group. I will describe a
few of them somewhat more fully.
It has already been mentioned that, on boiling with water, nitrate of
diazobenzol is broken up into nitrogen, phenylic acid, and nitric acid.
Hydrobromate of diazobenzol undergoes an analogous decomposition, viz.,
C,H,N, HBr+H, O=N,+4€, H, O+ HBr.
Treated with alcohol, nitrate of diazobenzol is decomposed in the fol-
lowing manner :—
2(C,H,N, NHO,) + C,H,O=C,H,+C,H,(NO,),0+€,H,O+N,+H,0.
——— ecak eee ter >—————-+-—- ——
“Nitrate of diazo- Alcohol. Benzol. Dinitrophenylic Aldehyde.
benzol. acid.
On dissolving sulphate of diazobenzol in a small quantity of concentrated
sulphuric acid, it gives rise to the formation of a new sulpho-acid which I
propose to call disulphophenylenic acid,
©, H, N, SH, 0,4+SH, 0,=C, H,, 8, H, O,+N,,.
SS —— ———+-
Sulphate of diazo- Disulphophenylic
benzol. acid.
The excess of sulphuric acid may be removed from the new acid by
means of carbonate of barium. The new barium-salt crystallizes in
beautiful prisms. Its composition must be expressed by the formula
€,H,S,H,Ba,@,. The free acid obtained by the addition of sulphuric
acid to the barium-salt is deposited in warty masses of radiating crystals
which deliquesce in the air. Disulphophenylenic acid is four-basic, and is
capable of forming four series of salts. The silver-salt forms, however, an
exception, its composition being expressed by the formula C, H, 8, Ag, ..
Disulphophenylenic acid, like phosphoric acid, appears to be capable of
existing in different modifications, possessing different powers of basicity.
380 Mr. P. Griess on a New Class of Compounds [June 16,
Diazobenzolimide in alcoholic solutions is decomposed by nascent hydro-
gen, generated with zinc and sulphuric acid in the following manner :—
GC ,H,N,+8H=€, H,N+2NH,.
+
Diazoben- Aniline.
zolimide.
On adding to an aqueous solution of nitrate of diazobenzol levigated
carbonate of barium, a feeble evolution of gas ensues, which lasts for several
days, until the original compound has been completely decomposed.
Two new substances are formed, which are very differently soluble in aleo-
hol, and can thus readily be separated. ‘The easily soluble compound,
which I will call phenyldiazobenzol, crystallizes from alcohol in yellowish
warty masses; from water (in which it dissolves very difficultly) in small
rhombic prisms. The difficultly soluble one, which I propose to call phe-
nyldidiazobenzol, crystallizes in reddish-vellow needles. The following
equation expresses the formation of these two bodies :—
I 2(6,H,N,, NHO,)+H, O=C,, H,,N,O+N,+2NHO,.
~~ ——4--
Nitrate of diazobenzol. Phenol-
diazobenzol.
Il. 3(C,H,N,, NHO,)+H, 0=G,, H,,N,O+N,+3NHO,.
* MM —+-----—"
Phenoldidiazo-
benzol.
On looking at these formule, it becomes evident at a glance that both
compounds contain phenylic acid and diazobenzol ; viz
€,H,N,+6,H,0= leet
CE te eC), Cree —_-—
Diazobenzol. Phenol. a i
diazobenzol.
2(, H, NS +, H, of, H,, ay 0
—— Ly, ee eS)
Diazobenzol. Phenol. Phenol-
diazobenzol.
Both compounds are weak acids; the first being capable of forming a
well-characterized silver-salt, which is obtained in the form of a blood-red
precipitate when an ammoniacal solution of phenoldiazobenzol is treated
with nitrate of silver.
On heating the platinum-salt of diazobenzol mixed with carbonate of
sodium in a retort, chlorobenzol is obtained, the formation of which may
be expressed as follows :-—
GC, H, N,, HCl, PtCl,=6, H, Cl+N,+PtCl,.
Niel ee ee sey
rc
=
Platinum-salt. Chlorobenzol.
A similar decomposition ensues when the dibromide is heated with carbo-
1864. | in which Nitrogen is substituted for Hydroyen. 381.
nate of sodium,
6, H,N, HBr,=€, 0, Br + N,+ Br,.
SEALS aan
Dibromide. Bromobenzol.
The same change may also be effected by simply boiling an alcoholic
solution of the dibromide.
The peculiar and often remarkable properties of the diazobenzole-com-
pounds have induced me to try whether analogous bodies could not be pre-
pared also from bromaniline, nitraniline, dibromaniline, &c. Experiment
has fully borne out theory. These analogous diazo-substitutions exhibit,
however, so much resemblance to the normal diazobenzol compounds, that
I should frequently have to repeat almost literally what has already been
said of the latter, were I to describe these compounds in detail. I may be
permitted, however, to mention a remarkable and interesting fact which their
investigation prominently brought out. There are, as is well known, two
isomeric nitranilines—the alphanitraniline of Arppe, and the betanitraniline
of Hofmann and Muspratt. This isomerism, I found, extends itself to
their respective nitrogeri-substitution compounds, and even to their pro-
ducts of decomposition. On heating, ev. gr., the dibromide of alphadiazo-
nitrobenzol with alcohol, the following change takes place :-—
©, H, (NO,) N, HBr,=6, H, (NO,) Br+N,+Br,.
poyiee |
G VST
a-dibromide. Bromonitrobenzol.
The bromonitrobenzol thus obtained is identical with ‘that prepared by
Cooper from benzol derived from coal-tar. It crystallizes in the same form,
and fuses, like the latter, at 126° C.; sulphide of ammonium converts it
imto bromaniline, which crystallizes in octahedra, and is identical with the
bromaniline of Hofmann obtained from bromisatine. Bromonitrobenzol,
prepared in a perfectly similar manner by the decomposition of the dibro-
mide of betadiazonitrobenzol, possesses, however, widely different properties.
The e-bromonitrobenzol just described crystallizes in long needles, whilst the
new benzol-derivative, which I will designate by the name of 6-bromonitro-
benzol, forms well-developed prisms, the fusing-point of which lies at 56°C.
Sulphide of ammonium converts it likewise into bromaniline; but this
base differs in its physical properties entirely from the bromaniline obtained
by Hofmann. It forms a colourless oil, which combines with acids, and
gives rise to a series of beautiful salts, which in their turn differ greatly
from the ordinary bromaniline salts in their physical properties. I will
distinguish this bromaniline by calling it 3-bromaniline from that obtained
by Hofmann, which I will call a-bromaniline.
It deserves to be mentioned briefly that there exist likewise two isomeric
chloronitrobenzols (alpha and beta) obtained by heating the platinum-salts
of the respective diazonitrobenzole with carbonate of sodium,
C,H, (NO,) N,, HCl, PtCl,=C, H, (NO,) Cl+ N,-+ PtCl,.
io Tar AIS Ce ys
a, B Platicame salt, a, B Chloronitrobenzol.
382 Mr. P. Griess on a New Class of Compounds [June 16,
Alpha-nitrochlorobenzol furnishes, when reduced by means of sulphide of
ammonium, the ordinary (alpha-) chloranilme; beta-chloronitrobenzol
yielding a new base of like composition (beta-chloraniline), distinguished
from the former by its oily nature.
Corresponding diazo-compounds can readily be prepared from the homo-
logues of aniline and other analogous bases by submitting them to a treat-
ment exactly similar to that which in ease of aniline yielded diazobenzol.
Thus I have obtained the diazo-compounds from toluidine, naphthalidiue,
and nitranisidine, C,H,(NO,)9. I have abstained from entering more
fully into a description of their physical and chemical habitus, as well as
the respective products of decomposition to which they give rise, since they
offer nothing characteristically new *.
All compounds already described have been derivations from monoatomic
amido-bases.* I have on a former occasiont had an opportunity of pointing
out that the action of nitrous acid upon diatomic bases, such as nitrate of
benzidine, is perfectly analogous to that which gives rise to the formation
of nitrate of diazobenzol from nitrate of aniline. Whilst, however, in the
last-mentioned reaction only one atom of nitrous acid exchanges its nitrogen
for three atoms of hydrogen of the original compound, six atoms of hydrogen
are exchanged for two atoms of nitrogen when nitrous acid reacts upon
nitrate of benzidine. Respecting these compounds I shall only briefly
describe a few general properties and a few products of decomposition.
Sulphate of Tetrazodiphenyl, 2C,, H, N,, 38H, Q,, crystallizes in white
or slightly yellowish-coloured needles, which are very soluble in water, and
almost insoluble in strong alcohol and ether. On boiling the alcoholic
solution, the following decomposition takes place :—
26,,H,N,, 39H, 0,44H, 0=26,, H,,0,+N,+39H, 9,.
as Nagy oe 8
Sulphate of tetrazodi- Diphenylenic acid
phenyl. (diphenylene-alcohol).
I have already had occasion to describe diphenylenic acid (diphenylene-
alcohol) obtained by decomposition, analogous to that of nitrate of tetrazo-
diphenyl with water, and I have therefore only to refer to what has been
stated on that occasion.
The decomposition which tetrazodiphenyl undergoes on boiling with
* In a former notice (Proceedings, Jan. 22, 1863) I briefly described the formation of
nitrate of naphthol, which by its decomposition with water gave rise to the long-sought-
for naphthyl-alcohol, €,, H, 9.
+ Proceedings, Jan. 22, 1863.
1864. | in which Nitrogen is substituted for Hydrogen. 383
alcohol differs from the previous one, and takes place according to the
equation
2C,,H,N,, 38H, 0,+4¢, H, O= 26H +40, H, +38 H,0,+8N.
a Eye)
(eee Bisse
Sulphate of tetrazodiphenyl. Alcohol. Diphenyl. one
The dipheny] which results from this reaction is identical with the com-
pounds obtained by Fittig from bromobenzol. A comparative examination
of the two demonstrates this most unmistakeably.
The transformation which sulphate of tetrazodiphenyl undergoes when
it is heated with a small quantity of strong sulphuric acid is likewise of
great interest. Two new sulpho-acids are formed, which I shall call
tetra- and tri-sulphodiphenylenic acid. The following equation explains
their formation in the most natural manner :—
C,H, N, +48 H, Ss), = Ea Ho §, H eOrnt Ny
Tale aaa
Tetrazodi- Tetiasnlphediane:
phenyl. nylenic acid.
G,, H, N,+38H, 0,=¢,, H,, 8, H,0,,+N,.
NE
aa
Trisulphodiphenylic acid.
The separation of these two acids is based upon the unequal solubility
of their barium-salts. The process is, however, somewhat complicated,
and I therefore abstain from describing it. Both acids are capable of com-
bining with bases in various proportions. Tetrasulphodiphenylenic acid is
octobasic. The lead-salt crystallizes in beautiful needles, and has the com-
position €,, H,, S, Pb, O,,. Trisulphodiphenylenic acid appears to be hexa-
basic. I have as yet only prepared the former acid in a free state. It
crystallizes in white needles, which are readily soluble in water and alcohol.
Tetrabromide of the Tetrazodiphenyl, C,, H,N,, 2HBr, Br,,
This compound forms crystals of an orange colour with curved faces.
On heating with alcohol, it splits up according to the equation
©, H, N, H, Lar =€,, H, Br,+N,+Br,.
cee ioe ey) = ae
Tetrabromide. Bromodipheny]l.
Bromodipheny] crystallizes from alcohol and ether (in which it is rather
difficultly soluble) in beautiful prisms which fuse at 164°C. This sub-
stance can be distilled without undergoing decomposition. Bromodiphenyl
has also been obtained by Fittig (according toa private communication) by
the action of bromine upon diphenyl.
The platinum-salt of tetrazodiphenyl, C,,H, N,,H, Cl, (PtCl,),, forms
small yellow plates, which furnish, when heated with carbonate of sodium,
chlorodipheny] closely resembling the analogous bromine-compound.
384, Dy. L. S. Beale on the Minute Anatomy [June 16,
: 1 H,N,
Tetrazodiphenyl-amidobenzol, € H. N a
C H, N 3
This complex body is formed when an aqueous solution of nitrate of
tetrazodiphenyl is mixed with aniline. It is deposited in a yellow crystal-
line mass, which can be recrystallized from alcohol or ether (in which it is
but slightly soluble), and is obtained in lancet-like plates. When heated in
a dry state, it is decomposed with slight explosion. Its formation is ex-
pressed by the equation
C,H, N,, 2NHO,+46, H, N=G,, H, oN,+ 2G, H,N, NHQ,.
| : ees
Va
pee
Nitrate of tetrazodi- Aniline. New compound. arn of aniline.
phenyl.
Pere daphien ne Oo A \n,.
This body is obtained in the form of slightly yellowish-tinged lustrous
plates, which are very difficultly soluble in cold, readily, however, in hot
alcohol and in ether. It combines neither with acids nor with bases.
Heated by itself it explodes. The following equation explains its forma-
tion :—
C,, H, N, H, Br,+8NH, eo , H,N,+6NH, Br.
ay Set ay fact pm,
Tetrabromide. , Tetrazodi-
phenylimide.
I have not succeeded in preparing tetrazodiphenyl in a free state, nor
have I been able to obtain compounds of tetrazodiphenyl with bases in any-
thing like a well-characterized condition. I pass over the abortive experi-
ments made by me in this direction.
Many of the experiments just described have been carried on in the
laboratory of the Royal College of Chemistry, London, others in that of the
University of Marburg ; and I take this opportunity of returning my thanks
to Prof. Hofmann of London, and Prof. Kolbe of Marburg, for allowing
me the use of these institutions.
XXI. “New Observations upon the Minute Anatomy of the Papillee
of the Frog’s Tongue.” By Lionex 8. Beare, M.B., F.R.S.,
F.R.C.P., Professor of Physiology and of General and Morbid
Anatomy in King’s College, London; Physician to the Hospital,
&e. Received June 16, 1864.
(Abstract.)
After alluding to the observations of Axel Key, whose results accord
with his own more closely than those of any other observer, the author
refers particularly to the drawings of Hartmann, the latest writer upon the
structure of the papillee. According to the author, Dr. Hartmann, owing
1864.] | of the Papille of the Frog’s Tongue. 385
to the defective method of preparation he employed, has failed to observe
points which had been seen by others who had written before him, and
which may now be most positively demonstrated. Hartmann’s process
consisted in soaking the tissue for three days in solution of bichromate of
potash, and afterwards adding solution of caustic soda. It can be shown
by experiment that many structures which can be most clearly demon-
strated by other modes of investigation, are rendered quite invisible by this
process. Hartmann’s observations, like those of the author, have been
made upon the papillee of the tongue of the little green tree-frog (Hyla
arborea).
With reference to the termination of the nerves in the fungiform papillee
of the tongue of the Hyla, the author describes a plexus of very fine nerve-
fibres, with nuclei, which has not been demonstrated before. ‘ Fibres re-
sulting from the division of the dark-bordered fibres in the axis of the
papilla can be traced directly into this plexus. From its upper part fine
fibres, which interlace with one another in the most intricate manner,
forming a layer which appears perfectly granular, except under a power
of 1000 or higher, may be traced into the hemispheroidal mass of epithe-
lium-like cells which surmounts the summit of the papilla. This hemi-
spheroidal mass belongs not to epithelial, but to the nervous tissues. It
adheres to the papilla after every epithelial cell has been removed; the
so-called cells of which the entire mass consists cannot be separated from
one another like epithelial cells; fibres exactly resembling nerve-fibres
can often be seen between them; and very fine nerve-fibres may be traced
into the mass from the bundle of nerves in the papilla.
The fine nerve-fibres which are distributed to the simple papille of the
tongue, around the capillary vessels, and to the muscular fibres of these
fungiform papillz, come off from the very same trunk as that from which
the bundle of purely sensitive fibres which terminate in the papille are
derived. ‘The fine nucleated nerve-fibres of the capillaries which the author
has demonstrated have been traced into undoubted nerve-trunks in many
instances, so that it is quite certain that many of the nuclei which have
been considered to belong to the connective tissue (connective-tissue cor-
puscles) are really the nuclei of fine nerve-fibres not to be demonstrated
by the processes of investigation usually followed*. ‘These nerve-fibres in
the connective tissue around the capillaries are considered by the author to
be the afferent fibres of the nerve-centres of which the efferent branches
are those distributed to the muscular coat of the small arteries.
The author’s observations upon the tissues of the frog convince him that
the nervous tissue is distinct in every part of the body from other special
tissues. For example, he holds that nerve-fibres never pass by continuity
of tissue into the ‘ nuclei’ (germinal matter) of muscular fibres, or into those
* See “On the Structure and Formation of the so-called Apolar, Unipolar, and Bi-
polar Nerve-cells of the Frog,” Phil. Trans. 1863, plate 40, fig. 44.
386 Dr. L. S. Beale on the Paths [June 16,
of tendon, of the cornea, or of epithelium. He advances arguments to
show that the epithelium-like tissue upon the summit of the papilla is not
epithelium at all, but belongs to the nervous tissues. Hence it follows
that nerves do not influence any tissues by reason of continuity of tissue,
but solely by the nerve-currents which pass along them*.
The author states that the so-called ‘ nuclei’ (germinal matter) of the
fine muscular fibres of the papille are continuous with the contractile
material, as may be demonstrated by a magnifying power of 1800 linear;
and he holds the opinion that the contractile matter is formed from the
nuclei. He adduces observations which lead him to the conclusion that
these nuclei alter their position during life, and that, as they move in one
or other direction, a narrow line of new muscular tissue (fibrilla) is as it
were left behind+. This is added to the muscular tissue already formed,
and thus the muscle increases.
XXII. “Indications of the Paths taken by the Nerve-currents as they
traverse the caudate Nerve-cells of the Spinal Cord and Ence-
phalon.” By Lionet 8S. Beatz, M.B., F.R.S., F.R.C.P.,
Professor of Physiology and of General and Morbid Anatomy
in King’s College, London; Physician to the Hospital, &c. Re-
ceived May 18, 1864.
Although the caudate nerve-vesicles, or cells existing in the spinal cord,
medulla oblongata, and in many parts of the brain, have been described
by the most distinguished modern anatomists, there yet remains much to
be ascertained with reference to their internal structure, connexions, and
* The author feels sure that the conclusions of Kihne, who maintains that the axis
cylinder of a nerve-fibre is actually continuous with the ‘ protoplasm’ (germinal matter)
of the corneal corpuscle, result from errors of observation. The prolongations of the
corneal corpuscles, on the contrary, pass over or under the finest nerve-fibres, but are
never continuous with them, as may be distinctly proved by examining properly pre-
pared specimens under very high magnifying powers (1000 to 5000 linear). The
corneal tissue results from changes occurring in one kind of germinal matter—the
nerve-fibres distributed to the corneal tissue from changes occurring in another kind of
germinal matter. If the connexion is as Kihne has described, a ‘nucleus’ or mass of
germinal matter would be producing nervous tissue in one part and corneal tissue in
another part; and since it has been shown that the ‘nuclei’ of the corneal tissue are
continuous with the corneal tissue itself, the nerve-fibres must be continuous, through
the nuclei, with the corneal tissue itself ; and if with corneal tissue, probably with every
other tissue of the body. But such a view is opposed to many broad facts, and not
supported by minute observation. The nuclei of the nerve-fibres are one thing, the
nuclei of the corneal tissues another ; and the tissues resulting from these nuclei, nerve-
tissue, and corneal tissue are distinct in chemical composition, microscopical characters,
and properties and actions.
t “New Observations upon the Movements of the Living or Germinal Matter of
the Tissues of Man and the higher Animals,” Archives, No, XIV. p. 150.
er aS ee eee ee ae ee =
PROCZEDINGS OF THE ROYAL SOCIATY.
Scale, 7¢43 of an Bnéglish Inch [+++ s1+s+ss+s 1 X 700.
Large candate nerve cell, with smaller cells and nerve fibres, from a thin transverse section of the lower
part of the grey matter of the medulla oblongata of a young dog. The specimen had been soaked for
some weeks in acetic acid and glycerine. The lines of dark granules resulting from the action of the acid
are seen passing through the very substance of the cell in very definite directions. Thus the cell is
the point where lines from several distant parts intersect (Diagram. Fig.2). It is probable that each
of these lines is but a portion of a cornplete circuit (see Diagram in Fig. 3). A,A,A, large fibres which
leave the cell. B, a fibre from another cell, dividing into finer fibres, exhibiting several lines of granules.
c,C,C, fibres from a youn¢er candate nerve vesicle. D, fine and flattened dark-bordered fibres. E, three
fine nerve fibres running together in a matrix of connective tissue. F, F, F, capillary vessels.
i, 3, B. del. 1863.
1864. ] of Nerve-currents in Nerve-cells. 387
mode of development. In this paper I propose to describe some points of
interest in connexion with their structure. In the first place, however, I
would remark that there are neither ‘cells’ nor ‘ vesicles’ in the ordinary
acceptation of these words, for there is no proper investing membrane,
neither are there ‘cedl-contents’ as distinguished from the membrane or
capsule ; in fact the so-called cell consists of soft solid matter throughout.
The nerve-fibres are not prolonged from the nucleus or from the outer part
of the cell, but they are continuous with the very material of which the
substance of the ‘cell’ itself is composed, and they are, chemically speaking,
of the same nature. So that in these caudate cells we have but to recog-
nize the so-called ‘nucleus’ (germinal matter) and matter around this
(formed material) which passes into the ‘ fibres,’ which diverge in various
directions from the cell: see Plate III. (fig. 1).
At the outer part of many of these ‘cells,’ usually collected together in
one mass, are a number of granules. These are not usually seen in the
young cells, and they probably result from changes taking place in the
matter of which the substance of the cell is composed. But it is not pro-
posed to discuss this question in the present paper.
My special object in this communication is to direct attention to a pecu-
liar appearance I have observed in these cells, which enables me to draw
some very important inferences with reference to the connexions and action
of these very elaborate and most important elements of the nervous
mechanism.
In some very thin sections of the cord and medulla oblongata of a young
dog, which had been very slowly acted upon by dilute acetic acid, the ap-
pearances represented in Plate III. (fig. 1) were observed. Subsequently,
similar appearances, though not so distinct, have been demonstrated in the
caudate nerve-vesicles of the grey matter of the brain of the dog and cat,
as well as of the human subject. I have no doubt that the arrangement is
constant, and examination of my specimens will probably satisfy observers
that the appearance is not accidental. ach fibre (a, a, a) passing from
the cell exhibits in its substance several lines of granules. The appearance
is as if the fibre were composed of several very fine fibres imbedded in a
soft transparent matrix, which fibres, by being stretched, had been broken
transversely at very short intervals. At the point where each large fibre
spreads out to form the body of the cell, these limes diverge from one
another and pursue different courses through the very substance of the cell,
_ in front of, and behind, in fact around the nucleus. Lines can be traced
__ from each fibre across the cell into every other fibre which passes away from
it. The actual appearance is represented in Plate III. ; and in the diagram,
fig. 2, a plan of a ‘cell,’ showing the course of afew of the most important
___ of these lines which traverse its substance, is given.
| I do not conceive that these lines represent fibres structurally distinct
from one another, but I consider the appearance is due to some difference
in composition of the material forming the substance of the cell in these
VOL. XIII. 2F
388 Dr. L. 8. Beale on the Paths [June 16,
particular lines ; and it seems to me that the course which the lines take
permits of but one explanation of the appearance. Supposing nerve-cur-
rents to be passing along the fibres through the substance of the cell,
A diagram of such a cell as that represented in Plate IIT. (fig. 1), showing the prin-
cipal lines diverging from the fibres at the point where they become continuous with
the substance of the cell. These lines may be traced from one fibre across the cell,
and may be followed into every other fibre which proceeds from the cell.
they would follow the exact lines here represented ; and it must be noticed
that these lines are more distinct and more numerous in fully-formed than
in young cells. They are, 1 think, limes which result from the —— ;
passage of nerve-currents in these definite directions.
Now I have already advanced arguments in favour of the existence of
complete nervous circuits, based upon new facts resulting from observations
upon a, the peripheral arrangement of the nerves in various tissues* ; 4,
the course of individual fibres in compound trunks, and the mode of
branching and division of nerve-fibrest ; and ce, the structure of ganglion-
cellst. I venture to consider these lines across the substance of the cau-
date nerve-cells as another remarkable fact in favour of the existence of
such circuits ; for while the appearance would receive a full and satisfactory
explanation upon such an hypothesis, I doubt if it be possible to suggest
another explanation which would seem even plausible.
Nor would it, I think, be possible to adduce any arguments which would
so completely upset the view that nerve-force passes centrifugally from one
* Papers in the Phil. Trans. for 1860 and 1862. Lectures on the Structure of the
Tissues, at the College of Physicians, 1860.
t “On very fine Nerve-fibres, and on Trunks composed of very fine Fibres alone,” Ar-
chives of Medicine, vol. iv. p.19. ‘ On the Branching of Nerve-trunks, and of the sub-
division of the individual fibres composing them,” Archives, vol. iv. p. 127.
¢ Lectures at the College of Physicians. Papers in Phil. Trans. for 1862 and 1863.
1864. | of Nerve-currents in Nerve-cells. 389
cell, as from a centre, towards its peripheral destination, as this fact. So
far from the fibres radiating from one cell, or from the nucleus as some
suppose, in different directions, all the fibres which reach the cell are com-
plex, and contain lines which pass uninterruptedly through it into other
fibres. Instead of the cell being the point from which nerve-currents
radiate in different directions along single fibres, it is the common point
where a number of circuits having the most different distribution intersect,
cross, or decussate. The so-called cel/ is a part of a circuit, or rather of
a great number of different circuits.
Diagram to show the possible relation to one another of various circuits traversing
a single caudate nerve-cell. @ may be a circuit connecting a peripheral sensitive sur-
face with the cell; & may be the path of a motor impulse; ¢ and d other circuits
passing to other cells or other peripheral parts. A current passing along the fibre a
might induce currents in the three other fibres, 4, c, d, which traverse the same cell.
i
I conclude that at first the formed material of the cell is quite soft and
almost homogeneous, but that as currents traverse it in certain definite
lines, difference in texture and composition is produced in these lines, and
perhaps after a time they become more or less separated from one another,
and insulated by the intervening material.
It may perhaps be carrying speculation upon the meaning of minute
anatomical facts too far to suggest that a nerve-current traversing one of
these numerous paths or channels through the cell may influence all the
lines running more or less parallel to it (fig. 3).
I have ascertained that fibres emanating from different caudate nerve-
cells situated at a distance from one another (fig. 4, a, a) at length meet
and run on together as a compound fibre (4, 6, 6), so that Tam compelled
to conclude (and the inference is in harmony with facts derived from ob-
servations of a different kind) that every single nerve-fibre entering into the
formation of the trunk of a spinal nerve, or single fibre passing from a
282
Lie
390 Dr. L. S. Beale on the Paths [June 16,
ganglion, really consists of several fibres coming from different and probably
very distant parts. In other words, I am led to suppose that a single dark-
bordered fibre, or rather its axis-cylinder, is the common channel for the
passage of many different nerve-currents having different destinations. It is
common to a portion of a great many different circuits. The fibres which
result from the subdivision of the large fibre which leayes the cell become
exceedingly fine (the ath of an inch in diameter or less), and pursue a
very long course before they run parallel with other fibres. As the fibres
which have the same destination increase in number, the compound trunk
becomes gradually thicker and more distinct. The several individual fibres
coalesce and form one trunk, or axis-cylinder, around which the protective
white substance of Schwann collects. At the periphery the subdivision of
the dark-bordered fibre again occurs, until peripheral fibres as fine as the
central component fibres result *.
Diagram to show the course of the fibres which leave the caudate nerve-cells. a, a
are parts of two nerve-cells, and two entire cells are also represented. Fibres
from several different cells unite to form single nerve-tibres, 6, 6,5. In passing towards
the periphery these fibres divide and subdivide; tne resulting subdivisions pass to dif-
ferent destinations. The fine fibres resulting from the subdivision of one of the-caudate
processes of a nerve-cell may help to form a vast number of dark-bordered nerves, but
it is most certain that no single process ever forms one entire axis-cylinder.
Although it may be premature to devise diagrams of the actual arrange-
ment, if I permit myself to attempt this, I shall be able to express the in-
ferences to which I have been led up to the present time in a far more
intelligible manner than I could by description. But I only offer these
schemes as rough suggestions, and feel sure that further observation will
* “ General Observations upon the Peripheral Distribution of Nerves,” my ‘Archives,’
iu. p. 234. “* Distribution of Nerves to the Bladder of the Frog,” p. 248. ‘‘ Distribution
of Nerves to the Mucous Membrane of the Epiglottis of the Human subject,” p. 249.
1864. ] of Nerve-currents in Nerve-ceils. 391
enable me to modify them and render them more exact. The fibres would
in nature be infinitely longer than represented in the diagrams. The cell
below ¢ (fig.5) may be one of the caudate nerve-cells in the anterior root
of a spinal nerve, that above & one of the cells of the ganglion upon the
posterior root, and a@ the periphery. I will not attempt to describe the
course of these fibres until many different observations upon which I am
now engaged are further advanced, but I have already demonstrated the
passage of the fibres from the ganglion-cell into the dark-bordered fibres
as represented in the diagram.
Fig. 5.
Diagram to show possible relation of fibres from caudate nerve-cells, and fibres from
cells in ganglia, as, for example, the ganglia on the posterior roots. @ is supposed to
be the periphery ; the cell above 6 one of those in the ganglion. The three caudate
cells resemble those in the grey matter of the cord, medulla oblongata, and brain.
The peculiar appearance I have demonstrated in the large caudate cells,
taken in connexion with the fact urged by me in several papers, that no
true termination or commencement has yet been demonstrated in the case
of any nerve, seems to me to favour the conclusion that the action of a
nervous apparatus results from varying intensities of continuous currents
which are constantly passing along the nerves during life, rather than from
the sudden interruption or completion of nerve-currents. So far from any
arrangement having been demonstrated in connexion with any nervous
structure which would permit the sudden interruption and completion of a
current, anatomical observation demonstrates the structural continuity of
all nerve-fibres with nerve-cells, and, indirectly through these cells, with
one another.
392 Mr. A. J. Ellis on Musical Chords. [June 16,
I venture to conclude that the typical anatomical arrangement of a ner-
vous mechanism is not a cord with two ends—a point of origin and a
terminal extremity, but a cord without an end—a continuous cireuit.
The peculiar structure of the caudate nerve-cells, which I have described,
renders it, I think, very improbable that these cells are sources of nervous
power, while, on the other hand, the structure, mode of growth, and indeed
the whole life-history of the rounded ganglion-cells render it very pro-
bable that they perform such an office. These two distinct classes of
nerve-cells, in connexion with the nervous system, which are very closely -
related, and probably, through nerve-fibres, structurally continuous, seem
to perform very different functions,—the one originating currents, while the
other is concerned more particularly with the distribution of these, and of
secondary currents induced by them, in very many different directions. A
current originating in a ganglion-cell would probably give rise to many
induced currents as it traversed a caudate nerve-cell. It seems probable
that nerve-currents emanating from the rounded ganglion-cells may be
constantly traversing the innumerable circuits in every part of the nervous
system, and that nervous actions are due to a disturbance, perhaps a varia-
tion in the intensity of the currents, which must immediately result from
the slightest change occurring in any part of the nerve-fibre, as well as
from any physical or chemical alteration taking place in the nerve-centres,
or in peripheral nervous organs.
XXIII. “On the Physical Constitution and Relations of Musical
Chords.” By Arexanper J. Exuis, F.R.S., F.C.P.S.* Received
June 8, 1864.
When the motion of the particles of air follows the law of oscillation of
a simple pendulum, the resulting sound may be called a simple tone. The
pitch of a simple tone is taken to be the number of doudle vibrations
which the particles of air perform in one second. The greatest elongation
of a particle from its position of rest may be termed the extent of the
tone. The intensity or loudness is assumed to vary as the square of the
extent. The tone heard when a tuning-fork is held before a proper re-
sonance-box is simple. The tone of wide covered organ-pipes and of flutes
is nearly simple.
Professor G. S. Ohm has shown mathematically that all real tones
whatever may be considered as the algebraical sum of a number of simple
tones of different intensities, having their pitches in the proportion of the
numerical series 1, 2, 3, 4, 5, 6, 7, 8, &c. Professor Helmholtz has esta-
blished that this mathematical composition corresponds to a fact in nature,
that the ear can be taught to hear each one of these simple tones separately,
and that the character or quality of the tone depends on the law of the
intensity of the constituent simple tones.
These constituent simple tones will here be termed indifferently partial
* The Tables belonging to this Paper will be found after p. 422.
1864. | Mr. A. J. Ellis on Musical Chords. 393
tones or harmonics, and the result of their combination a compound tone.
By the pitch of a compound tone will be meant the pitch of the lowest
partial tone or primary.
When two simple tones which are not of the same pitch are sounded
together, they will alternately reinforce and enfeeble each other’s effect,
producing a libration of sound, termed a beat. The number of these beats
in one second will necessarily be the difference of the pitches of the two
simple tones, which may be termed the beat number. As for some time
the two sets of vibrations concur, and for some time they are nearly oppo-
site, the compound extent will be for some time nearly the sum, and for
some time nearly the difference of the two simple extents, and the zntensity
of the beat may be measured by the ratio of the greater intensity to the less.
But the beat will not be audible unless the ratio of the greater to the
smaller pitch is less than 6:5, according to Professor Helmholtz. This
is a convenient limit to fix, but it is probably not quite exact. To try the ex-
periment, I have had two sliding pipes, each stopped at the end, and having
each a continuous range of an octave, connected to one mouthpiece. The
tones are nearly simple; and when the ratio approaches to 6:5, or the
interval of a minor third, the beats become faint, finally vanish, and do
not reappear. But the exact moment of their disappearance is difficult to
fix, and indeed seems to vary, probably with the condition of the ear. The
ear appears to be most sensitive to the beats when the ratio is about
16:15. After this the beats again diminish in sharpness ; and when the
ratio is very near to unity, the ear is apt to overlook them altogether. The
effect is almost that of a broken line of sound, as i
the spaces representing the silences.
Slow beats are not disagreeable; for example, when they do not exceed
3 or 4 in a second. At 8 or 10 they become harsh; from 15 to 40 they
thoroughly destroy the continuity of tone, and are discordant. After 40
they become less annoying. Professor Helmholtz thinks 33 the beat
number of maximum disagreeableness. As the beats become very rapid,
from 60 to 80 or 100 in a second, they become almost insensible. Pro-
fessor Helmholtz considers 132 as the limiting number of beats which can
be heard. They are certainly still to be distinguished even at that rate,
but become more and more likea scream. Though /*¢ and g* should give
198 beats in a second if ce=264, and the interval is that for which the ear
is most sensitive, I can detect no beats when these tones are played on two
flageolet-fifes. Hence beats from 10 to 70 may be considered as discord-
ant, and as the source of all discord in music. Beyond these limits they
produce a certain amount of harshness, but are not properly discordant.
When the extent of the tones is not infinitesimal, Professor Helmholtz
has proved that on two simple tones being sounded together, many other
tones will be generated. The pitch of the principal and only one of these
combinational tones necessary to be considered, is the difference of the
pitch of its generating tones. It will therefore be termed the differential
394 ‘Mr. A. J. Ellis on Musical Chords. » [Sunee;
tone. Its intensity is generally very small, but it becomes distinctly
audible in beats. The differential tone is frequently acuter than the lower
generator, and hence the ordinary name ‘‘ grave harmonic”’ is inapplicable.
As its pitch is the beat number of the combination, Dr. T. Young attri-
buted its generation to the beats having become too rapid to be distin-
guished. This theory is disproved, first, by the existence of differential
tones for intervals which do not beat, and secondly, by the simultaneous
presence of distinct beats and differeutial tones, as I have frequently
heard on sounding f*, f*4, or even f”, ft together on the concertina, when
the beats form a distinct rattle, and the pa tone is a peculiar pene-
trating but very deep hum.
The object of this paper is to apply these laws, partly physical and
partly physiological, to explain the constitution and relations of musical
chords. It is a continuation of my former paper on a Perfect Musical
Scale*, and the Tables are numbered accordingly.
Two simple tones which make a greater interval than 6:5, and there-
fore never beat, will be termed disjunct. Simple tones making a
smaller interval, and therefore generally beating, will be termed pulsative.
The unreduced ratio of the pitch of the lower pulsative tone for which the
beat number is 70 to that for which it is only 10, will be termed the range
of the beat. The fraction by which the pitch of the lower pulsative tone
must be multiplied to produce the beat number, will be termed the beat
factor. The ratio of the pitches of the pulsative tones, on which the
sharpness of the dissonance depends, will be termed the beat enterval.
A compound tone will be represented by the absolute pitch of its primary
and the relative pitches of its partial tones, as C (1, 2, 3, 4,....)2 As
generally only the relative pitch of two compound tones has to be con-
sidered, the pitches will be all reduced accordingly. Thus, if the two
primaries are as 2: 3, the two compound tones will be represented by 2, 4,
6, 8, 10,...., and 3, 6,9, 12,15 .... The intensity of the various
partial tones differs so much in different cases, that any assumption which
can be made respecting them is only approximative. In a well-bowed
violin we may assume the extent of the harmonics to vary inversely as the
number of their order. Hence, putting the extent and intensity of the
primary each equal to 100, we shall have, with sufficient accuracy—
danmonies.. Me 262 3 A ne OT Te 8) Oat?
Latent...» 100, 50, 33, 25, (20,17, 145° ° 2 ee
Intensity... 1003.5 25, 11-86, 45352
It will be assumed that this law holds for all combining compound
* Proceedings of the Royal Society, vol. xiii. p.93. The following mis-
prints require correction :—P.97, line 7 from bottom, for c? read 6. Table L.,
p- 105, diminished 5th, example, read f:B; minor 6th, logarithm, read :20412;
Pythagorean Major 6th, read 27:16, 3°:2*; Table V., col. VL, last line, read
felt tot tk.
1864. ] “Mr. A.J. Ellis on Musical Chords. 395
tones, the intensity of the primary in each case being the same. The
results will be sufficient to explain the nature of chords on a quartett of
bowed instruments, but may be much modified by varying the relative
intensities of the combining tones.
On examining a single compound tone, we may separate its partial tones
into two groups: the first disjunct, which will never beat with each other ;
the second pulsative, which will beat with the neighbouring disjunct tones.
Thus.
Wisunce.. 1, 2, 3, 4, 5,'6, = 8, -, 10, —, 12, —, —, —, 16,
Pulsative. -,-,-, -, -,-, 7, -,9, -—, 11, -—, 13, 14, 15, -
Disjunct. . TT are) ese 20, are Seppe. Sh cannys 24, SEED s age Sia 30.
Pulsutive. 17, 18,19, —, 21, 22, 23, —, 25, 26, 27, 28, 29, —
When any compound tone therefore developes any of the harmonics
above the 6th, there may, and probably will, be beats, producing various
degrees of harshness or shrillness, jarring or tinkling. These, however,
are all natural qualities of tone, that is, they are rooted at once by the
natural mode of vibration of the substances employed. But if we were to
take a series of s¢mple tones having their pitches in the above ratios, and to
vary their intensities at pleasure, we should produce a variety of artificial
qualities of tone, some of which might be coincident with natural qualities,
but most of which would be new. This method of producing artificial
qualities of tone is difficult to apply, but has been used with success by
Professor Helmholtz to imitate vowel-sounds, &c.
If, however, instead of using so many simple tones, we combine a few
compound tones, the pitches of which are such that their primaries might
be harmonics of some other compound tone, then the two sets of partial
tones will necessarily combine into a single set, which may, or rather must
be considered by the ear as the partial tones of some new compound tone,
having very different intensities from those possessed by the partial tones of
either of the combining compound tones. That is, an artificial quality of
tone will have been created by the production of these jovn¢ harmonics.
Such an artificial quality of tone constitutes what is called a musical chord.
The two or more compound tones from which it is built up are its consti-
tuents. ‘The primary joimt harmonic is the real root or fundamental bass
of the chord, which often differs materially from the supposititious root
assigned by musicians.
If the primaries of the constituents are disjunct, and all their partial
tones are disjunct, then the joint harmonics will be also disjunct, unless
some pulsative differential tones have been introduced. If, however, the
constituents have pulsative partial tones, the chord will also have them.
Such chords, which are generally without beats, and are only exceptionally
accompanied by beats, are termed concords, and they are unisonant or dis-
sonant according as the beats are absent or present. Their character
therefore consists in having the pitches of their constituents as 1, 3, 5, oras
396 Mr. A. J. Ellis on Musical Chords. [June 16,
these numbers multiplied by various powers of 2, that is, as 1, 3, 5, or their
octaves.
If any of the constituents is pulsative the chord will generally have
beats, but may be exceptionally without beats. Such chords are termed
discords. ‘Their character consists in having ¢wo or more of the pitches of
their constituents as 1, 3, 5, or their octaves, and at least one of them as
7, 9, or some other pulsative tones, or their octaves. What pulsative tones
should be selected depends on the sharpness of the dissonance which it is
intended to produce, and therefore on the interval of the beat which is
created. Thus, since 7: 6=1:'16667 and 8: 7=1°14286 are both near the
limit 6: 5= 1-2, the discord arising from 7 would be slight. Some writers
have even considered the chord 1, 3, 5, 7 to be concordant. Again,
9: 8=1°'125 is rather rough, but 10: 9=1-11111 is much rougher. Hence,
if 9 is introduced, 10 should be avoided, that is, the octave of 5 should be
omitted, which generally necessitates the omission of 5 itself, as in the
chord 1,3,9. But 11: 10=1°'1 and 12:11=1-09091 are both so sharply
dissonant, that if 11 is used neither 10 nor 12 should be employed. Now
10 is the octave of 5, and 12 is both the 3rd harmonic of 4 and the 4th
harmonic of 3, and would therefore be produced from 3 and 4. Hence
the use of 11 would forbid the use of 3, 4, and 5, that is, of the best disjunct
tones. Hence 11 cannot be employed at all. Similarly, 13 : 12=1-08333
and 14: 13=1:07692 are both extremely harsh. The latter is of no con-
sequence, because 7 can be easily omitted. But even 15: 13=1°15384 is
more dissonant than 7:6. Hence 13 would also beat with the harmonics
of 3, 4, and 5. Consequently 13 must be also excluded. All combina-
tions in which the differential tones 11 and 13 are developed will also be
extremely harsh. As we therefore suppose that 14: 13=1°07692 never
occurs, and as 14:12=7:6, the mildest of the dissonances, 14 may be
used if 15 is absent, and thus 15: 14=1°'07143 avoided. When 14 and 15
are developed as harmonics of 7 and 5, and not as the primaries of con-
stituent tones, their intensity will be so much diminished that the discord
will not generally be too harsh. When 15 is used as a constituent, 14
and 16 should be avoided; that is, 7, and 1, 2 and 4, of which 14 and 16
are upper harmonics, should be omitted to avoid 15: 14=1-07143 and
16: 15=1:06667, which may be esteemed the maximum dissonance. By
omitting 16 and 18, and thus avoiding 17:16=1°0625 and 18:17=
1:05882 (that is, by. not using 4, 8, or 9 as constituent tones), 17 becomes
useful ; for 17 : 15=1°13333 is milder than 9: 81-125, which is by no
means too rough for occasional use. The other pulsative harmonics, which
are represented by prime numbers, are not sufficiently harmonious for use ;
but those produced from 2, 3, 5 (such as 25, 27, 45) may be sometimes
useful, provided that the tones with which they form sharp dissonances are
omitted.
The result of the above imvestigation is that the only pulsative tones
suitable for constituents are 7, 9, 15, 17, 25, 27, 45, and their octaves.
1864. ] Mr, A. J. Ellis on Musical Chords. 397
The introduction of any one of these tones in conjunction with 1, 3, 5 and
their octaves will therefore form a discord, the harshness of which may be
frequently much diminished by the omission of 1 and its octaves for the
constituents 7, 15, 17, by the omission of 5 for the constituent 9, and by
the omission of 24 for the constituents 25, 27, 45.
Using the notation of my former paper, where gz=63: 64, and putting
in addition vij=84:85, xj=33: 32, xij =39:40, 17=255:256, and
Xv1j=135 : 136, the tones 1 to 18 may be represented by the following
notes in terms of C* :—
TD 2. 3, 4, 5, 6, rips 8, 9, 10,
Pye Gc, e, OG, GOD or vy a” oct
1], We 13, 14, Los 4-16, 17,
Meo) Xe, coDorvjat, (6, c', gd) or xviy ct,
18, 20, 24, 29, 27; 45,
a’, e, I ee Sh:
This notation will show what are the musical names of the constituents
of musical chords, and how they may be approximately produced on an
organ, harmonium, or pianoforte.
- By the ¢ype of a musical chord is meant the numbers which express the
relative pitches of its constituents, after such octaves below them have been
taken as to leave only uneven numbers, which are then called the elements
of the type. By the form of the chord is meant the numbers before such
reduction. Thus the type 1, 3, 5 embraces, among others, the forms
I, 3, D5 l, 2, 3, D5 2, 3, D5 4, 3, 35 3, 8, LO’; 6, 10, 16 ; 2, Qo; 6, 8,
and so on; hence the types of musical chords consist of groups of the
elements 1, 3, 5, 7,9, 15, 17, 25, 27, 45. The type of a concord is 1, 3, 5,
and of a discord 1, 3, 5, P, or 1, 3, 5, P, P’, where P, P! are any of the
numbers 7, 9, 15, 17, 25, 27, 45. Discords may be divided into strong
and weak, according as those disjunct tones with which the pulsative tones
principally beat are retained or omitted. These discords again may be dis-
tinguished into those which have one or two pulsative constituents. The
chords may also be grouped according to the number of elements in their
type, dyads containing two, triads three, tetrads four, and pentads five.
The number of elements in the type by no means limits the numbers of
constituents, as any octaves above any of the elements may be added.
Hence it is possible to classify all the suitable chords of music according
to their type, as in Table VI., where the notes corresponding to each type
are added in the typical form only. A simple systematic nomenclature is
proposed in an adjoining column, and the names by which the true chords
or their substitutes are known to musicians are added for reference. Occa-
sionally two forms of substitution are given, as they are of theoretical im-
portance, although confounded on some tempered instruments. A mode of
symbolizing the chords is subjoined, in which several types are classed
under one family. A capital letter shows the root of major chords, either
398 Mr. A. J. Ellis on Musical Chords. [June 16,
complete or imperfect, and of strong discords, and a smaller letter gives the
root of weak discords, a number pointing out the family. In the minor
triad the characteristic number is omitted; thus ¢ is written for 15e,
meaning the minor triad g e 6, which is the major tetrad 15 C, or CG EB,
with its root C omitted, and is usually called “the minor chord of e,” a
nomenclature which conceals its derivation.
Although chords of the same type have the same general character, this
is so much modified by the particular forms which they can assume, that
it is necessary to examine these forms in detail. They may be distinguished
as simple and duplicated. In the former the number of constituents is the
same as in the type; thus 4, 5, 6; 2, 3, 5 are simple forms of the type
1, 3, 5. In the latter, the number of constituents is increased by the
higher octaves of some or all of them; thus 1, 2, 3, 5; 2, 4, 5, 6 are dupli-
cated forms of 1, 3, 5 and 2, 5, 6, as they contain the octaves 1, 2 and 2, 4.
The mode in which the effect of any or all of these combinations may be
calculated is shown in Table VII., which consists of two corresponding
parts, each commencing with a column containing the “ No. of J. H.,” or of
the joint harmonics resulting from the combination of the harmonics of the
constituent compound tones. ‘The next columns are headed by the relative
pitch of the constituent tones, and contain their harmonics, never extending
beyond the 8th, arranged so that their pitch is opposite to the corresponding
number of the joint harmonic. It is thus seen at a glance which harmonics
of the constituents are conjunct or tend to reinforce each other, and produce
a louder joint harmonic, and also which are disjunct and pulsative. In the
second part of the Table the extent of each harmonic of each constituent is
given on the assumptions already explained. To find the extent of the
joint harmonic, we add the extents of the generating conjunct harmonics,
and thence find the intensity by squaring and dividing by 100. The dif-
ferential tones must then be found by subtracting the pitches of the pri-
maries (or in exceptional cases of higher and louder harmonics). The in-
tensity of these differential tones may be called 1 for a single tone, and 4
for two concurrent tones, and this number may be subscribed to the inten-
sity of the corresponding joint harmonic, as 0,, 25,.
The beat intervals have next to be noted, and the beat factors, which are
usually the reciprocal of the relative pitch of the lower pulsative harmonic.
Thus for the dyad 3, 4 the beat interval is 2, and the beat factor 4. From
this factor, or 1:f, we calculate the range P: p=70f: 10f/=210: 30 mm
the present case. This must not be reduced, as‘it shows that the interval
is dissonant when the pitch of the lower tone is between 30 and 210. To
find the intensity, we add and subtract the extents of the pulsative joint
harmonics; in this case 50 and 33 are the extents of the 8th and 9th
joint harmonics, and their sum and difference are 83 and 17. Then we
take the ratio of their squares, each divided by 100, which gives 69: 3.
This result must not be reduced, as it gives not only the relative loudness
of the swell and fall, but also the loudness of these in relation to the other
1864. | Mr. A. J. Ellis on Musical Chords. 399
jomt harmonics. It must be remembered that when there are several dis-
junct harmonics, their unbroken sound tends to obliterate the action of the
beats. There is no sensible silence between the beats unless the tones are
- simple and the intensities nearly equal. The intensities of the beats be-
tween joint harmonics and differential tones cannot be reduced to figures.
It is not large. The history of a beat is therefore given by four fractions,
which in this case are the interval 9 : 8, the factor 1: 3, the range 210: 30,
and the intensity 69:3.
These calculations have been made for concordant dyads in Table VIII.,
and for concordant or major triads in Table IX. An attempt has been
made to arrange the 13 forms of the first, and the 20 forms of the second
in order of sonorousness, by considering the distribution of the intensities
among the several joint harmonics, the development of pulsative differential ©
tones, and the nature of the beats, omitting those due to the seventh har-
monic of an isolated constituent. It has not been thought necessary to
give the history of every beat. The intervals of all the beats are seen at
a glance by the list of intensities of the joint harmonics.
By Table VIII. we see that the only unisonant dyad is the octave 1, 2*,
which will be as unisonant as the constituents themselves. All other dyads
are occasionally dissonant. Thus the fifth itself is decidedly dissonant
when the pitch of the lower constituent lies between 20 and 140. Ona
bass concertina tuned justly, I find the fifth, C*G*, quite intolerable, the fifth,
C G, rough, but D +d nearly smooth, and at higher pitches there isno per-
ceptible dissonance. The beat interval of the major third is 16:15, and
the range of dissonance is much greater. The roughness can be distinctly
heard as high ase e; in the lower octaves CH is quite discordant, and C*E*
intolerable. This Table VIII., therefore, establishes the fact that con-
cordance does zo¢ depend on simplicity of ratio alone; but when the de-
nominator of the beat factor is small the range is lower, and therefore the
dissonance less felt. Dissonance also arises from the pulsative differential
tones 7 and 11, so that if the relative pitches are expressed in terms high
enough to differ by 7 and 11, the combination will be dissonant. The ear
is also not satisfied with forms in which great intensities of joint harmonics
are widely separated by many small intensities. The four last forms in
Table VIII., namely, the minor tenth 5, 12, the eleventh 3, 8, and the
two thirteenths 3, 10 and 5, 16, should therefore be treated as discords.
The Table also suggests how defects may be remedied by introducing new
constituents to fill up gaps, or by duplications.
Similar observations apply to the triads in Table IX. None of them can
be unisonant at all pitches. Some of them, as the last seven, are really
discordant. The gaps may be generally filled up by duplication. Thus
* That is, within the limits of the Table. Dyads such as 1, 2; 1,3; 1,4;
1, 5; 1, Gare all unisonant; but when the interval is very large, the want of con-
nexion between the tones renders them unpleasant. The dyad 1, 8 which
developes the differential tone 7 is dissonant.
400 Mr. A. J. Ellis on Musical Chords. [June 16,
1, 3, 5 may be converted into 1, 2, 3, 5, and by thus strengthening the 2, 4,
and 8 joint harmonics the finest form of concord is produced. In this
way the series of duplications in Table X. was produced. In this Table an
example has been added to each form to facilitate trial ; but the great im-
perfection of the major third in the ordinary system of tuning pianos and
harmoniums materially deteriorates the effect of the chords, which ought
to be taken on some justly tuned instrument.
The discords may be deduced from Tables VII. and VIII., when pro-
perly extended, by supposing 7, 9, 15, 17, 25, 27, 45 to be used in the first,
and their effect allowed for in the second. The additional discordant effect
of 7 will be necessarily least felt where 7 occurs as a differential tone, but
these are not the best forms of either triad or tetrad. In the better forms
the dissonances 6, 7 and 7, 8 will always be well developed, and as the
latter is sharper, the omission of 8, at least as a constituent tone, is
suggested. If 71 is used instead of 7, the omission of 8 becomes more
urgent, while 6, 74 will beat less sharply than 6, 7, and therefore almost
inaudibly. The real beats of the constituents 6, 74 arise from the har-
monics 6.6, 5.74, or 36, 352, which are, however, not so much felt as
those of 6.6, 5.7 arising from 6, 7, because 36 : 353=1-0125 is further
from 16 : 15=1:°0667 than is 36: 35=1:0286. Hence, when 8 is omitted,
the dissonance arising from 7} is less than that arising from 7 itself.
When 8 is present, 7 or 7/5 is superior to 74. The use of 17,4 for 17
would hardly create any perceptible alteration of roughness when 18 is
absent, and when 18 is present 18: 17;—=1-:0548 is further from 16:15
than is 18: 17=1-0588, and therefore the roughness is not quite so great.
Of all discords the least dissonant is the minor triad 3, 5, 15, which is
formed from the tetrad 1, 3,5, 15 by omitting the root 1, to avoid the dis-
sonance 15,16. When the differential tones derived from the primaries
of the constituents are deeper than the primaries, and therefore merely
indicate the presence of a pulsative tone, which is only faintly realized by
the differential tones derived from the upper harmonics of the primaries,
and when the dissonant intervals of the minor tenth and major thirteenth
5, 12 and 3,10 are not present in the constituent tones, this chord may
be treated as a concord. But in most positions the minor triad is sensibly
dissonant, as shown in Table XI., where an attempt has been made to
arrange its 20 forms in order of sonorousness. ‘The pitches of the differ-
ential tones are added, and examples. subjoined. The effect of the minor
chord is very much injured by the usual tuning of harmoniums, &c. A
peculiar character of these and other discords, when the pulsative con-
stituent is not the highest, consists in the quality of tone being due to very
high joint harmonics, except such as are due to differential tones. The
root will be consequently extremely deep when the constituent tones are
taken at a moderate absolute pitch. This great depth renders its recogni-
tion by the ear difficult. Hence probably the disputes of musicians con-
cerning the roots of certain discords, and their error in considering 5 to be
1864. ] Mr. A. J. Ellis on Musical Chords. 401
an octave of the root of the minor triad, so that e, g, 6 or 10, 12, 15 is con-
sidered by them as derived from * instead of C*.
Chords will evidently be related to each other when one or more of their
constituents are identical, and natural qualities of tone will be related which
have one or more identical harmonics, or which form parts of related chords.
Transitions between related chords and compound tones will be easy and
pleasing. Hence, in forming a collection of compound tones for use either
as natural qualities of tone (in melody) or as constituents of artificial
qualities of tone, that is, chords (in harmony), it is important to select such
as will have numerous relations, and will produce the concordant dyads
and triads, and the least dissonant discord, the minor triad. Hence, taking
the concordant major triad 1, 3, 5 as a basis, we must possess its products
by 2, 3, and 5. There must be abundant multiples by 2 in order to take
the several forms of the triad and to introduce the duplications. The
products by 3 and 5 give 3, 9,15 and 5,15, 25. We have then the
tones 1, 3, 5, 9, 15, 25, and their octaves. These give three concordant
major triads, 1, 3,5; 3, 9, 15; and 5, 15, 25, each of which has one con-
stituent in common with each of the others. We have also the major
pentad 1, 3, 5, 9, 15, the nine-tetrad 1, 3, 5, 9, the major tetrad 1, 3, 5,
15, and the minor tetrad 3, 5, 9, 15, whence, by omissions, result the nine-
triad 1, 3, 9 and minor triad 3, 5, 15. Each of these triads is related to
two of the three major triads. The minor triad is intimately related to all
three major triads by having two constituents in common with each of
them. The discords involving 7 and 17 would evidently require 1, 3, 5,
7, 17 to be taken as a basis. Neglecting these discords for the present,
the above results show that we should obtain a useful series of tones by
multiplying 1, 3, 5 successively by 3, and each product by 5, taking octaves
above and below all the tones thus introduced. We thus find
| MAJOR. Menor. Mid rust NEAT OR Asi | eons lea sane
nl ee
|
i ie Ass
Bee Set lolS, 4.9; 45 EK je ae | AK {Cy
a 27, 45) 9, 15, 45 B ig ¢.6 | KB. ta
FE | d 6 ff) BREID
27, 81, 135/27, 45, 135|
81, 243, 405 tA TECH
128, 256, in order to compare them with the larger numbers. Such mul-
tiplications are presumed to have been made in the columns of notes.
Hence +4:A=81: 5.16, or F=81 : 80,
Be: F—135: 1.128, or #=135 : 128,
tCi: C=25: 3.8, or {#=—25 : 24, whence E—S07 or.
And in the same way the other ratios in ‘ Proceedings,’ vol. xii. p. 95, are
reproduced.
402 Mr. A. J. Ellis on Musical Chords. [June 16,
In addition to the chords already noticed, we have now the twenty-seven
tetrad, 1, 3, 5, 27, or F CAD, and the twenty-seven triad, 1, 5, 27, or
F AD, and all the discords derived from 1, 3, 5, 9, 15, 25, 27, 45. But
for those derived from 7 and 17 substitutes must be employed. These are
obtained as follows. The chord 9, 27, 45, 1.64 is 9 times 1, 3, 5, 74, so
that GD BF approximates to 1, 3, 5, 7 in a manner already tested.
Again, 1. 32, 3.32, 5.32, 225 is 32 times 1, 3, 5, 73\,, whence FC A {DE
gives the second and closer approximation to 1, 3, 5, 7 already considered.
When 7} is used for 7 it will be better to use 1, 3, 5, 74, 88, or one-ninth
of 9,27, 45, 1.64, 5.16, that is G B D F A, in place of 1, 3, 5, 74, 9 or
one-ninth of 9, 27, 44, 1.64, 81, that is G B D F +A, to avoid the disso-
nance 5.74, 4.9, or 352, 36. This will therefore replace the seven-nine
pentad 1, 3, 5, 7, 9. .
The chord 45, 135, 225, 5.64,3.256 is 45 times 1, 3, 5, 74, 1774, or
B Ft {Dz AC, and it forms an excellent substitute for the seven-seventeen
pentad 1, 3,5, 7,17. Again, the chord 3.16, 5. 16, 15. 16) 135)or 6
times 3, 5, 15, 164, that is C 4 # F, is a sufficiently close approximation
to the rough discord 3, 5, 15, 17.
It has already been shown that the alterations in the discords thus pro-
duced will be slight, and, under certain circumstances, improvements. The
omission of 7, 17 in the base 1, 3, 5 is therefore justified. Their insertion
would embarrass the performer and composer by an immense variety of
tones very slightly differing from each other, as 64, 63; 135, 136; 255, 256.
As it is, the distinction between 81, 80 is the source of much difficulty,
- and separates chords such as 81, 243, 405, and 5.16, 15.16, 25. 16, or
80, 240, 400, that is, td +H CZ and 4 # {C¥#, which composers desire to
_ consider as identical. It was shown in my former paper (Proceedings,
vol. xill. p. 98) that the use of 1, 3, 5as a basis requires 72 different tones,
exclusive of octaves. The introduction of 7 in the base would increase this
number by 45, and the introduction of 17 by 30, while the mental effect
produced would be very slightly different. On the other hand, if instead
of 1, 3, 5 as a base, we took 1, 2v, 47, where v, T' are ratios differing
slightly from 3: 2 and 5:4, we might avoid the ratio 81: 80, reduce the
number of tones to 27, and greatly increase the relations of chords. How
to effect this important result with the least dissonant effect will be con-
sidered in the following paper on Temperament.
The three major triads 1, 3,5; 3,9,15; 9, 27, 45 are so related as to
form two major pentads, 1, 3, 5, 9, 15 and 3.1,3.3,3.5,3.9, 3.15.
Hence the middle triad forming part of both pentads connects the three
triads into a whole, closely related to the middle triad, and therefore to its
root. These are called the tonic chord and fonic tone, and the connexion
itself is termed tonality. If octaves of these tones be taken, thus,
Ligroes 3:2 83 5.8 or FC A,
Sus Sy 9 Awe Noe 2 CGE,
9.4, Dies 45 GD B,
1864.] Mr. A. J. Ellis on Musical Chords. 403
and the results be taken in order of pitch, we find, on supplying the second
octave 3.16,
2A 27, (OO) 32," 30,40, 45,4 (48
ON Ds CE, ce Gy As BS &
In this series any two consecutive tones, except 40, 45 or 4, B, belong to
the same major pentad, and these are therefore eminently adapted for suc-
cessions of chords. Even 40, 45, or 5.8, 45, belong to two related discords ;
for 1, 3, 5, 9, or F, C, A, G, and 1, 3, 5, 27, or F C AD, have each two
constituents in common with 9, 27,45, 1.64,or GDBF. The discord
3, 5, 15, 45, or CA EL B, contains both the tones in question. These con-
siderations justify the major diatonic scale.
~The last discord contains a minor triad, 3, 5, 15. These minor triads,
from their relations to three major triads, are evidently peculiarly adapted
to introduce successions of harmonies. ‘Taking then the three minor triads
and forming their octaves, thus
3. 64, Dad, 15.8 or c2 ae,
ger 10, Eas 8s 454 g eb,
27 .8, 45.2, 1385 @&bf4,
we may extend them into a scale,
120% 13552. 144, 160, 180, 192, 216, 240
é; St ip I> a; b, c?, d*, e*,
where the chordal relations are even more intimate than before, and by
means of the chord 45, 135, 225, 5.64, 3.256, or B Ft {D# ac, already
noticed, the major triad, 45, 135, 225, or B F¢ {D, is brought into close
connexion with the minor triad, 3, 5, 15, or cae. Practically the use of
the minor scale consists of a union of four major triads, 1, 3, 5; 3, 9, 15;
9, 27, 45; 27, 81, 135, forming two major scales, with three other major
triads, 5, 15, 25; 15, 45, 75; 45, 135, 225, forming a third major scale,
by means of three minor triads, 3, 5,15; 9, 15, 45; 27, 45, 135, the roots
of which, 1, 3, 9, are the same as the roots of the first three major triads.
There are therefore seven roots to all the chords introduced, namely 1, 3,
9, 27, and 5, 15, 45, or F, C, G, D and A, EH, B, and these seven roots
form a major diatonic scale. From these relations spring all the others
which distinguish the minor scale together with all its various forms and
its uncertain tonality, which is generally assumed to be the relation of the
chords to 15 or £, the tonic of the last three major triads, but which evi-
dently wavers between this and 3, 9 or C, G, the tonics of the first four
major triads, and these three tonics, 3, 9, 15, or CG H, form a major triad.
By extending this system of chords up and down, right and left, we
arrive at the perfect musical scale in Table V. (Proceedings, vol. xii. p. 108),
which is therefore entirely justified on physical and physiological grounds,
without any of those metaphysical assumptions or mystical attributes of
numbers which haye hitherto disfigured musical science. In that Table the
VOL, XIII. 2G
404 Mr. A. J. Ellis on the Temperament [June 16,
chords have been arranged in the forms 4, 5, 6 and 10, 12, 15, im accord-
ance with the usual practice of musicians. In the present paper the typical
1, 3, 5 and 3, 5, 15 have, for obvious reasons, been made the basis of the
arrangement. ;
XXIV. “On the Temperament of Musical Instruments with Fixed
Tones.” By Atexanper J. Exxis, F.R.S., F.C.P.S.* Received
June 8, 1864.
In the preceding paper on the Physical Constitution of Musical Chords
(Proceedings, vol. xiii. p. 392), of which the present is a continuation, I
drew attention to the importance of abolishing the distinction between
tones which differ by the comma 81:80, on account of the number of
fresh relations between chords that would be thus introduced. The con-
trivances necessary for this purpose have long been known under the name
of Temperament. I have shown that the musical scale which introduces
the comma consists of tones whose pitch is formed from the numbers
1, 3, 5, by multiplying continually by 2, 3, and 5. Hence to abolish the
comma it will be necessary to use other numbers in place of these. But
this alteration will necessarily change the physical constitution of musical
chords, which will now become approximate, instead of exact representa-
tives of qualities of tone with a precisely defined root. It is also evident
that all the conjunct harmonics will be thus rendered pulsative, and that
therefore all the concords will be decidedly dissonant at all available
pitches. The result would be intolerable if the beats were rapid. Tem-
perament, therefore, only becomes possible because very slow beats are not
distressing to the ear. Hence temperament may be defined to consist in
slightly altering the perfect ratios of the pitch of the constituents of a
chord, for the purpose of increasing the number of relations between
chords, and facilitating musical performance and composition by the re-
duction of the number of tones required for harmonious combinations.
The subject has been frequently treated +, but the laws of beats and
* The Tables belonging to this Paper will be found after p. 422.
+ I have consulted the following works and memoirs. Huyghens, Cosmo-
theoreos, lib. i.; Cyclus Harmonicus. Sauwvewr, Mémoires de l’Académie, 1701,
1702, 1707, 1717. Henfling, Miscellanea Berolinensia, 1710, vol. i. pp. 265-294.
Snuth, Harmonics, 2nd edit. 1759. Marpurg, Anfangsgruende der theoretischen
Musik, 1757. Estéve, Mém. de Math. présentés a l’Acad. par divers Savans,
1755, vol. ii. pp. 113-136. Cavallo, Phil. Trans. vol. lxxviii. Romieu, Mém.
de l’Acad., 1758. Lambert, Nouveaux Mém. de l’Acad. de Berlin, 1774, pp.
55-73. Dr. T. Young, Phil. Trans. 1800, p. 143; Lectures, xxxiii. Robison,
Mechanics, vol. iv. p. 412. Farey, Philosophical Magazine, 1810, vol. xxxvi.
pp. 89 and 374. Delezenne, Recueil des Travaux de la Société des Sciences, &c.
de Lille, 1826-27. Woolhouse, Essay on Musical Intervals, 1835. De Morgan,
On the Beats of Imperfect Consonances, Cam. Phil. Trans. vol. x. p. 129.
Drobisch, Ueber musikalische Tonbestimmung und Temperatur, Abhandlungen
1864. ] of Instruments with Fixed Tones. 405
composition of tones discovered by Prof. Helmholtz have enabled me to
present it in an entirely new form, and to determine with some degree of
certainty what is the best possible form of temperament.
Let the compound tones P and Q, of which P is the sharper, form the
concordant interval p:g. Then P: Q=p: gq, or gP=pQ, that is, the gth
harmonic of P and the pth harmonic of Q are conjunct. Now let P be
changed into P.(1+72), where ¢ is small, and rarely or never exceeds
go 0125. Then the gth harmonic of P.(1+¢) will be gP.(1+¢) and
will no longer=pQ. The difference between the pitch of these harmonics
is gP. (1+4)—pQ=qt.P=pt.Q. Hence the number of beats in a
second produced by this change in P will be found by multiplying the
lower pitch Q by pé, which is therefore the beat factor, and will be positive
or negative according as the pitch of P is increased or diminished, or the
interval is sharpened or flattened. The other beats which existed between
the joint harmonics of the dyad P, Q may be increased or diminished by
this change, but in either case so slightly that they may be left out of
consideration in comparison with the beats thus introduced. But the dif-
ferential tone which was P—Q becomes Pt+ P—Q, and is therefore a
tone which is entirely unrelated to the original chord, and which may be-
come prominently dissonant. This is an evil which cannot be avoided by
any system of temperament, and is about equally objectionable in all
' systems. It may therefore be also left out of consideration in selecting
a temperament.
The melody will also suffer from the alteration in the perfect ratios.
An interval is best measured by the difference of the tabular logarithms of
the pitches of the two tones which form it. ence the interval error
e=log [P. (1+¢)+Q]—log [P: Q]=log (1+¢)=n#, if the square and
higher powers of ¢ be neglected, and » be the modulus. Hence the beat
factor which =pt, will =pe+p, or ape. I call pe the beat meter, and
represent it by (3.
We may assume that the dissonance created by temperament « 3”. Hence
for the same just interval p: g, variously represented in different tempera-
ments, the dissonance «e*. That is, the harmony varies inversely as }’,
and the melody varies inversely as e*. Hence for the same interval the
harmony and melody both vary inversely ase*. The general harmony and
melody may be assumed to be best when 3° and Xe” are minima, which will
not happen simultaneously.
The following contractions for the names of the principal intervals will
der k. Sachsischen Gesellschaft der Wissenschaften, vol. iv. Nachtrage zur
Theorie der musikalischen Tonverhaltnisse, ibid. vol. v. Ueber die wissen-
schaftliche Bestimmung der musikalischen Temperatur, Poggendorn’s Annalen,
vol. xc. p. 353. Nawmann, Ueber die verschiedene Bestimmung der Tonver-
haltnisse und die Bedeutung des Pythagoreischen oder reinen Quinten-Systems
fiir unsere heutige Musik, 1858. Helmholtz, Die Lehre von den Tonempfin-
dungen, 1863. I am most indebted to Smith, Drobisch, and Helmholtz.
262
406. Mr. A. J. Ellis on the Temperament [June 16,.
be used throughout this paper. See also the last columns in Tables XII.
and XIV.
Sign. Interval. Example.|| Sign. Interval. Example.
Ist. Unison!) ta CE
Mind.“ Major second... ¢5) ic a 2nd. | Minor Second....| ef
Ilird. | Major Third Gie ord. | Minor Third ....| eg
IVth. | Augmented Fourth} fb Ath. | Perfect Fourth Cr
Vth. Pertect Pifth |...) 7 eg 5th. | Diminished Fifth..| bf?
Vith. | Major Sixth ca 6th. | Minor Sixth e ¢?
VIlth. | Major Seventh ch 7th. | Minor Seventh g PP
Willie, | Oenave sce. enc?
IXth. | Major Ninth cd? || 9th: | Minor Nimth Saye
t= = 56 = oe Da et
E (a eal @ aa mals
P) —=— er —o« bok ee ae —~ pe
Whence m=#/, l=dt, m=iot, mm ?=2.
1864. ] of Instruments with Fixed Tones. — 407
Hence all intervals and pitches can be expressed in terms of v. This
further appears from arranging the 27 different tones required in tempered
scales, in order of Vths, thus
app, epP, bb, SO; Oo, 9 d), a), ed, bp,
fee. Ga a, ay! ey -0;
SH, ch, oF, Up, af, et, b¢, fX, eX, 9X.
It will be obvious from Table V. (Proceedings, vol. xiii. facing p. 108),
when the signs +{ are omitted, that these 27 tones suffice for all keys from
Cp to CH. This also appears from observing that the complete key of C
requires 7 naturals, 3 flats and 3 sharps, or 13 tones, and that one flat or
sharp is introduced for each additional flat or sharp in the signature of the
key. Hence for 7 flats and 7 sharps in the signature 14 additional tones
are required, making 27 in all. The rarity of the modulations into dd, 9?
or c) minor enables us generally to dispense with the three tones a)b, e)b,
690, and thus to reduce all music to 24 tones. The system of writing
music usually adopted is only suitable to such a tempered scale, and there-
fore requires the addition of the acute and grave signs (+ {) to adapt it for
a representation of the just scale founded on the numbers 1, 2, 3, 5.
To calculate the value which must he assigned to v so as to fulfil the
conditions supposed to produce the least disagreeable system of tem-
perament, it will be most convenient to use logarithms, and to put log
v=log3—a#='1760913—w. The above arrangement of the requisite 27
tones in order of Vths, therefore, enables us to calculate the logarithms of
the ratios of the pitches of all the tones to the pitch of c in terms of x, by
continual additions and subtractions of log »v, rejecting or adding log 2
='3010300, when necessary, to keep all the tones in the same VIIlve.
The result is tabulated in Table XII., column T. From this we imme-
diately deduce
log m=log d —log ce °0511526— 2x
log 7 =log f —log e °0226335+ 5x
log # =log ft—log f °0285191— 7x
log 6 =log gd —log fy=— 0058851 + 12a.
To find the interval errors, the just intervals must be taken for the
commonest modulations into the subdominant and dominant keys, as ex-
plained in my paper on a Perfect Musical Scale (Proceedings, vol. xiii.
p- 97). Asthe method of determining temperament here supposed makes
the errors the same for the same intervals in all keys, that is, makes
the temperament equal, it is sufficient to determine the interval errors for
a single key. Hence the just intervals are calculated in Table XIL.,
column J, for the key of C, and the interval error is given in column e, in
terms of x and k=log $1, the interval of a comma. From these interval
errors the beat meters for the six concordant dyads are calculated in
column (3. To these are added the values of 3 e? and = £’, also in terms
408 Mr. A. J. Ellis on the Temperament [June 16,
of wandk. If for k we put its value ‘0053950, these last expressions
become
Se?="0009314 —1°1437400x2+4+ 4202?
2° = 00043659 — 5:8158100x+ 19982".
Hence Table XII. suffices to give complete information respecting the
effect of any system of temperament when wv is known. The following are
some of the principal conditions on which it has been proposed to found
a system of temperament. I shall first determine the value of w and log v
on these conditions, and then compare the results.
A. Harmonic Systems oF Equa TEMPERAMENT.
I. Systems with two concords perfect.
No. 1 (45)*. System of perfect 4ths and Vths.
Here x=0, log v=°1760913.
This is the old Greek or Pythagorean system of musical tones, more
developed in the modern Arabic scale of 17 tones. No nation using it has
shown any appreciation of harmony. 7
No. 2 (2). System of perfect [IIrds and 6ths.
Here e for III, or s—4v=0, vx=14=:00134875, log v="17474255.
Hence log m=log d=‘0484551=3% log 3=3 (log 3+1 42), so that
the tempered mean tone is an exact mean between the just major and
minor tones. Hence this is known as the System of Mean Tones, or the
Mesoftonic System, as it will be here termed. It was the earliest system
of temperament, and is claimed by Zarlino and Salinas. See also Nos.
13 and 19.
No. 3(23). System of perfect 3rds and VIths.
Here e for 3, or —k+32=0, «=3 k=:0017983, loz v=-1742930.
Il. Systems in which the harmony of two concords is equal.
No. 4 (20). The I1Ird and Vth to the same bass; beat equally and in
opposite directions tT.
Here @ for L1L+ 6 for V=0, or (54—20 x) —34=0, «=, k=:0011725,
log v=1749188.
No. 5 (15). The 6th and Vth beat equally, and in the same direction +.
Here 6 for 6=£ for V, or —84+4+324=—3z, v= k=:0012381,
log v='1748582.
* The number preceded by No. points out the order of the system in the
present classification. The number in a parenthesis shows the position of the
system in the comparative Table XV., which is explained hereafter (p. 418).
+ That is, one interval is too great, or “beats sharp,” and the other too
small, or “ beats flat.”
+ That is, both “beat sharp ” or both “ beat flat.”
1864. ] | of Instruments with Fixed Tones. 409
No. 6 (21). The IIIrd and 4th beat equally, and in the same direction.
Here 6 for III=6 for 4, or 54—20e=40, w=3, k=:0011239,
log v="1749674.
No. 7 (18). The 6th and 4th beat equally, and in opposite directions.
Here 6 for 6+ for 4=0, or (—84432x) +4x7=0, w=2 4=:0011989,
log v= 1748924.
No. 8 (16). The 3rd and Vth beat equally, and in the same direction.
Here 6 for 3=( for V, or —64+18v=—3x, w=? x=-0015414,
log v="1745199. See No. 20.
No. 9 (13). The VIth and Vth beat equally, and in opposite directions.
Here 6 for VI+ for V=0, or (54—152x) —3a=0, v= 3,k='0014986,
log v="1745927.
This coincides with Dr. Smith’s system of equal harmony, as contained
in the Table facing p. 224 of his ‘ Harmonics,’ 2nd ed.
No. 10 (9). The 3rd and 4th beat equally, and in opposite directions.
Here G for 3+ for 4=0, or (— 64+ 18x) + 4e=0, v=, h=:0014713,
log v="1746200,
No. 11.(2). The VIth and 4th beat equally, and in the same direction.
Here 2 for VI=f for 4, or 54—1l5e=—4a, x=; k=:0014197,
log v="1746716.
III. Systems in which the harmony of two concords is in a given ratio.
No. 12 (24). The beats of the IIvd and Vth are as 5: 3, but im opposite
directions.
Here G for III: B for V= — 5: 3, or 154—602= 15x, ex=Lh4=:0010790,
log v= "1750123.
M. Romieu gives this temperament under the title of “ systeéme tempéré
de + comma,” Mém. de Acad. 1758. See No. 18.
No. 13 (2). The beats of the 3rd and Vth are as 2: 1, and in the same
direction.
Here 6 for 3: 6 for V=2, or —64+ 18e=— 62, v=zh, as in No. 2.
No. 14 (12). The beats of the 3rd and Vth are as 5: 2, and in the same
direction.
Here G for 3:3 for V=5:2, or —12h+4 36a= — Lda, a= 74,k= "0012694,
log v=1748219. See No. 29.
IV. Systems of least harmone errors.
No. 15 (7). The harmonic errors of all the harmonic intervals conjointly
are a minimum.
This is determined by putting the sum of the squares of the beat meters,
410 Mr. A. J. Ellis on the Temperament [June 16,
or (by Table XII.) 1504°—1078A4x+19982°=a minimum, which gives
r= Pe k='0014554, log v=:1746359.
Tf we had used the sum of the squares of the beat factors, we should
have obtained an equation of 16 dimensions in», which gives logu=*1746387.
The difference between the two values of log v is not appreciable to the ear.
No. 16 (14). The harmonic errors of the 3rd, IIIrd, and Vth conjoiatly
are a minimum.
Here (( for 3)?+(G for IIT)?+(G for V)’, or
(6k—182x)?+ (54—202)? + 92° =a minimum, which gives
2=298 f=-0015309, log v=:1744404.
No. 17 (6). The harmonic errors of the Vth and IIIrd conjointly are a
minimum.
Here (6 for V)?+(6 for IID’, or 9a°+(54—20x2)=a minimum,
x=ti) k='0013190, log v="1747723.
AO9
B. Mrxropic Systems or Equa TEMPERAMENT.
V. Systems of equal or equal and opposite interval errors.
No. 18 (24). The interval errors of the I1Ird and Vth are equal and
opposite.
Here e for IJI+ e for V=0, or 4—4v=4, x=Hf, as in No. 12.
No. 19 (2). The interval errors of the 3rd and Vth are equal.
Here e for 3 =e for V, or —k+3v=—a, =H, as in No. 2,
No. 20 (16). The interval errors of the [[Ird and 3rd are equal.
Here e for []T=e for 3, or k—4a=—k+3x, r=2h, as in No. 8.
e e a e e
VI. Systems in which the interval errors of two intervals are in a
given ratio.
No, 21 (17). The errors of the IIIrd and Vth are as 5: 3, but in opposite
directions.
Here e for II]: e forV =—5: 3, or 34—124=5ea, v=}, k='0015750,
log 8= "1745163.
This is the theoretical determination of M. Romieu’s anacratic tempera-
ment (Mém. de l’Acad. 1758, p. 510), to which, however, he has in
practice preferred No. 22.
No. 22 (29). The errors of the IIIrd and Vth are as 2: 1, but in opposite
directions.
Here e¢ for III : e« for V=—2, or 4—4v=2e, x=1k=:0008975,
log v='1751938.
This is M. Romieu’s anacratic temperament. See No. 21.
No. 23 (26). The errors of the I1Ird and Vth are as 1:94: 1, and in
opposite directions,
1864:.] of Instruments with Fixed Tones. 41]
Here e for IIT :¢ for V=—1°94, or kK—4v=1°94a, z=195 £=-0009683,
log v="1751830.
This is the temperament calculated by Drobisch (Nachtriige, § 10)
from Delezenne’s conclusion (Rec. Soc. Lille, 1826-27, pp. 9 and 10),
that the ear can detect an error of ‘2844 in the [1Ird, and -1464 in the
Vth, which gives the comparative sensibility as -284 : -146=1°94.
No. 24 (20). The errors of the IIIrd and 3rd are as 2 : 5, but in opposite
_ directions.
Here e for IIT : for e 3=—2: 5, or 5k—20e%=2h—6a, w=3, kh
=°0011561, log v="1749352. See No. 27.
No. 25 (46). The errors of the 3rd and IIIrd are as 2: 1, but in opposite
directions, or the errors of the Vth and 3rd are equal and opposite.
Here e for3: efor IIJ=—2, or 2k—6x=h—4z, or else r= —4+32;
both give e=4 k=:0026975, log v='1733938.
Here the error of the Vth reaches the utmost limit of endurance.
VII. Systems of least melodic errors.
No. 26 (1). The interval errors of all the melodic intervals conjointly are
a minimum.
Here the sum of the squares of the 23 interval errors in Table XII., or
32k? —212kae+4202° =a minimum, 2=~7;3, k= 0013616, log v="1747297.
No. 27 (20). The melodic errors of the IInd, IlIrd, 4th, Vth, VIth, and
Vilth conjointly, are a minimum.
Here (e for II)*+(e for IIT)?+(e for 4)*+(e for V)?+(e for VI)?+
(ce for VII)’, or 4x°+ (A—42)’ + 22° + (k—3x)?+(k—5e0)’= a minimum,
x= 3h, as in No. 24.
This is Drobisch’s ‘‘ most perfect possible” (mdglich reinste) tempera-
ment (Poggendorff’s Annalen, vol. xc. p. 353, as corrected in Nachtrige,
§ 7). It is only the “most perfect possible”’ for the major scale.
No. 28 (5). The melodic errors of the 3rd, II[Ird, and 4th conjointly are
a minimum.
Here (e for 3)’+(e for IIT)’+(e for 4)’, or (—k+43x)?+(k— 4a’)
+2°=a minimum, c= 75 k=:0014525, log v="1746388.
This is Woolhouse’s Equal Harmony (Essay on Musical Intervals,
p- 45).
No. 29 (12). The melodic errors of the [IIrd and Vth conjointly are a
minimum.
Here (e for IIl)’+(e for V)’, or 2° +(k—4z)’= a minimum, r= 44,
as in No. 14.
This is given by Drobisch (Nachtrige, § 8) as ‘‘ the simplest solution
of the problem.”
412. Mr. A. J. Ellis on the Temperament — [June 16,
C. CoMBINED SystTEeMs or Equa TEMPERAMENT.
No. 30 (4). The combined harmonic and melodic errors are a minimum.
By combining the equations of No. 15 and No. 26, we have (539+ 106) &
= (1998+ 420)a, or o= 3845, k=-001444, log v="1746439.
No. 31 (32). The tones are a mean between those of No. 1 and No. 2.
Here e=3 (sum of the two values of w in No. 1 and No. 2)=:0006744,
log v="1754169.
This is proposed by Drobisch (Nachtriage, § 9).
No. 32 (42). The errors occasioned by using the tempered c,d, f, f, g,
bbb, ¢), & for the just c, d, e, f, g, a, 6, c are a minimum.
Using s for *0004901, and forming the values of these errors by
Table XIT., we have42” + (s—8z)?+27+(s—9zx)?+(s—/7z)’=a minimum,
r= 24, s='000059084, log v=1760322.
This is proposed by Drobisch as a system of temperament adapted to
bowed instruments (Mus. Tonbestim. § 57), allowing them to use a system
of perfect fifths, and yet play the perfect scale very nearly by substitution.
Such a system would be more complicated than the just scale for any in-
strument, and would require many more than 27 tones. It is, therefore, un-
necessary for the violin, and impossible on instruments with fixed tones.
D. Cycuic Systems or EquaL TEMPERAMENT.
When it was supposed that the number of just tones required would be
infinite, importance was attached to cycles of tones which by a limited
" number expressed all possible tones. Hence Huyghens’s celebrated Cyclus
Harmonicus, which he proposed to employ for an instrument with 31
strings, struck by levers and acted upon by a moveable finger-board
(abacus mobilis), acting like a shifting piano or harmonium. The condi-
tion of forming a cycle is not properly harmonic or melodic ; it is rather
arithmetic. If log v:log 2 be converted into a continued fraction for any
of the preceding values of log v, and y: 2 be any of the convergents, then,
putting log 2=2.h, we shall have log v=yh, which is commensurable
with log 2, and consequently the logarithms of all the intervals will be
multiples of 4, and therefore commensurable with log 2. A cycle of z
tones to the octave will thus be formed. If z is less than 27, the number
of tones otherwise necessary, the cycle may be useful, otherwise it can only
be judged by its merits as an equal temperament. As an historical interest
attaches to several of these cycles, I subjoin a new method for deducing
them all, without reference to previous calculations of log v.
Since log vu=y.h, and log 6=7 log 2—12 log v=(7z—12y) . h, we
have only to put 7z—12y= ... —2,—1, 0, 1, 2,...and find all the positive
integral solutions of the resulting equations. This gives for
13 27 41 55 69
2— =——?2 ih csi SS SS SP SSS
lpia! > g~«29? 46 70’ 94 118
eo
1864. ] of Instruments with Fixed Tones. 413
eal [a oe
eu i729: A ge Ge a Sa
a ioye LEE
7e—l2y= 0, La
Pi 1 = yl4 1 18 25 32 90 46/58)
ba
15 29 43 57
f2 19 i=
te Ao, gue 96? 50). 7a' 08’
7z—12y= 3 y 5 12 19 26 33 40 47 54
SS tS ro eee) —=9
9.2133 Ab: 47 69" 61.93.
Many of these cycles are quite useless. The following selection is ar-
tanged in order of magnitude, from the greatest to the smallest cycle.
No. 33 (38). Cycle of 118; A="0025511, log x= 69h="1760259.
This is Drobisch’s cycle (Mus. Ton. § 58) representing No. 32.
No. 34 (8). Cycle of 93; h=-0032368, log vx=54h='1747872.
This may represent No. 2.
No. 35 (3). Cycle of 81; A=:0037164, log v=47h='1746708.
This may represent No. 11 (2).
No. 36 (39). Cycle of 77; h=:0039095, log vu=45h='1759275.
This is the same as No. 52.
No. 37 (19). Cycle of 74; h=:004068, log v=434="1749200.
This is another of Drobisch’s cycles (Nachtrage, § 7) representing No. 27.
No. 38 (22). Cycle of 69; h=-004363, log x=404=°1745200.
No. 39 (28). Cycle of 67; #= "004493, log v=394="1752270.
No. 40 (40). Cycle of 65; h=-0046123, log v=38h=°17598674.
No. 41 (27). Cycle of 57; A=-0052812, log x=33h='1742796.
No. 42 (30). Cycle of 55; A=:0054733, log v=32h=°1751456.
_ This is mentioned by Sauveur (Mém. de l’ Acad. 1707) as the commonly
received cycle in his time. Estéve (Joc. cit. p. 135) calls it the Musicians’
Cycle.
No. 43 (11). Cycle of 50; A=*0060206, log x=29h=:1745974.
This is Henfling’s cycle (loc. ect. P- 281), and is used by Dr. Smith to
- represent No. 9.
No. 44 (43). Cycle of 53; h=-0056798, log vx=31h="1760800.
This is the cycle employed by Nicholas Mercator (as reported by Holder,
‘Treatise on Harmony,’ p. 79) to represent approximately the just scale.
He did not propose it as a system of temperament as has been recently
done by Drobisch (Musik. Tonbestim. Einleit.). It was the foundation of
A414 Mr. A. J. Ellis on the Temperament [June 16,
the division into degrees and sixteenths adopted in my previous paper
Proceedings, vol. xii. p. 96.
No. 45 (37). Cycle of 45; h="006689, log vu=26h='1738940.
No. 46 (25). Cycle of 43; A=°0070007, log x=25h=:1750175.
This is Sauveur’s cycle, defended in Mém. de l’Acad. for 1701, 1702,
1707, and 1711.
No. 47 (10). Cycle of 31; A=*009711, log v= i8h=:1747900.
This is Huyghens’s Cyclus Harmonicus, which nearly represents No. 2
(2). It was adopted, apparently without acknowledgment, by Galin (De-
lezenne, loc. cit. p. 19).
No. 48 (44). Cycle of 26; A=-011578, log vx=15h=-1736700.
No. 49 (25). Cycle of 19; h=-0158437, log v=11h='1742807.
This is the cycle adopted by Mr. Woolhouse (Essay on Beats, p. 50) as
most convenient for organs and pianos. It may therefore go by his name,
although it is frequently mentioned by older writers. It is almost exactly
the same as No. 3 (23).
No. 50 (35). Cycle of 12; 4=°0250858, log u=7h=:1756008.
As this is a cycle of twelve equal semitones, it may be termed the Hemi-
tonic temperament. It is the one most advocated at the present day, and
generally spoken of as ‘‘equal temperament” without any qualification,
as if there were no other. It was consequently referred to by that name
only in my former paper (Proceedings, vol. xiii. p. 95). For its harmonic
character see No. 53.
E. DEFECTIVE SYSTEMS oF EQuAL TEMPERAMENT.
It has been from the earliest times customary to have only twelve fixed
tones to the octave, on the organ, harpsichord, piano, &c., and to play the
other fifteen by substitution, as shown below, where the tones tuned, ar-
ranged in dominative order, occupy the middle line, and the tones for which
they are used as substitutes are placed in the outer lines, and are bracketed.
[Abb, Hob, Bob, Fb, Cb, Gp, Dp, Ar]
Eb, Bp, F, 0, Gy) D,- Ay BB, FR On ee
[Dy, At, FH, BE, Fx, Cx, Gx].
The consequence was, that while the Vths in the middle line were uni-
form, the Vths and 4ths produced in passing from one line to the other
(as GED for ADE or GED) were strikingly different. Similar errors
arose in the other concordant intervals. It is evident that the interval
error thus produced must be the usual interval error of the system increased
or diminished by the logarithm of the diesis, where log 6=log 9) —log ft=
1864. | of Instruments with Fixed Tones. 415
—°0058851 +12%—=—k—s+127, where s=:0004901*. Such interval
errors are termed wolves, from their howling discordance. In Table XIII.
will be found an enumeration of all the wolves, with a notation for them, and
an expression of their interval errors and beat meters in terms of 4, s, and 2.
No. 51 (33). System of least wolf melodic errors.
The sum of the squares of the wolf interval errors, or
2h? + 2ks + 6s*—4 (1144 28s) «+ 2662’,
isaminimum. Hence 224+ 56s= 2662, or e=:0005495, log v=: 1755418.
No. 52 (39). System of least wolf harmonic errors.
The sum of the squares of the wolf beat meters, or
25k? + 175s’ + 50ks— (5504+ 3072s) 2+ 136622" ,
is a minimum. Hence 2754+ 1536s=13662z2, or r=:0001638, log v
="1759275, as in No. 36 (39).
No. 53 (35). The wolf interval errors are equal to the usual interval errors,
that is, there are no wolves, or there are none but wolves.
In this case log 5=0, or, since 6=9) : ft=2": v”, 7 log 2=12 log v.
Hence this system is the cycle of 12, No. 50. Wyle . is greater than 1,
g? is sharper than f¥, and log v is less than + 15 log 2 eGt, Fares But
if dis less than 1, y) is flatter than 7%, and ihe v is less than {5 log 2, or
"1756008. The lattes case is, according to Drobisch, fadisfencaule for
musical theory and violin practice (Musik. Tonbestim. Einleit.). Since
this temperament thus forms the boundary of the two other classes, distin-
guished by g? being flatter or sharper than /#, Drobisch terms it the
“mean”? temperament (ibid. § 51). It is this property of making g) =/+
which renders this temperament so popular, as the ear is never distressed
by the occurrence of intervals different from those expected, and the whole |
number of tones is reduced to 12.
No. 54 (31). The wolf interval error of the ILIrd is to its usual interval
error as 14: 5.
This gives —s+8r7: k—4rv=14: 5, or 962=144+5s8, c='0008123,
log v="1752790. This is Marsh’s system of temperament ; see Phil. Mag.
vol. xxxvi. p. 437, and p. 39 segq. Schol. 8.
No. 55 (36). The wolferrors of the IIIrd and Vth conjointly are a minimum.
Here (—s+8v)?+(—A—s+llz) is a minimum, whence 114+19s
=1852, 2="0003712, log v=:1757201.
No. 56 (37). The wolf errors of the Vth and IIIrd are equal and opposite.
Here —k—s+lla=s—8za, 192=h+ 2s, e=:0003356, log v= "1757557.
No. 57 (34). There is no Vth wolf.
Here —k—s+11e=0, r=-0005351, log v=-1755562.
* It appears from Proceedings, vol. xiii. p. 95, that s must be nearly the loga-
rithm of the schisma or log J. Actual calculation shows that s and log 4 agree
to 14 places of decimals,
416 Mr. A. J. Ellis on the Temperament [June 16,
No. 58 (41). There is no IIIrd wolf.
Here —s+8x=0, =0000613, log v=-1760300. This is almost ex-
actly No. 32 (42).
No. 59 (42). There is no 3rd wolf.
Here s—9x=0, x='0000545, log v="1760368.
F. Systems or UnequaL TEMPERAMENT,
In a defective equal temperament the same just concordance is represented
by two different discordances. As performers limited themselves to twelve
tones to the octave, those who found the Hemitonic temperament No. 50
(35) too rough, accepted this variety of representatives of the same con-
cordance as the basis of a temperament, hoping to have better IIIrds in
the usual chords, without the wolves of the defective temperament. Others
conceived that an advantage would be gained by altering the character of
the different keys. Thus arose wnequal temperament, properly so called,
which must be carefully distinguished from any defective equal temperament
with which it is popularly confused.
Arrange the twelve unequally tempered chords as follows, where the
identical numbers indicate identical chords with different names :—
LG kesG, 7. Fe At cet. 7. Go Bp dp.
2.GB d. 8. Ot Ee GH. 8. D? F Ab.
3. D Ft A, 9. Gt BE dy. 9. .c op.
4, A cH e. 10. Dy Fx A. 10. Ep G Bp.
5. E Gt B. ll. At ex et. 11. JB) og gage
6. B dt ft. 12. He Gx By. 12, Fee
Let 7, ¢,, Y, be the ratios of the IIIrd, 3rd, and Vth in the nth chord,
so that, for example, in the 6th chord dg=T7T,.B, fg=t,.dt, ft=v,. B.
Then it is evident from the above scheme that there exist 12 pairs of
equations between these 36 ratios, of the form
fm ° ‘ Vy and Ato ° Ont4 ° Unto e Un43
(where, when the subscript numbers exceed 12, they must be diminished
by 12), and one condition,
Vy + Das Uy 6 Uy 0 Oy + Uy 2 Vy + Vy + Vy # Vo = yy» Vig =A"
Put log T,,=log $+y,; log ¢,=log $—z,, log v,=log 3—2,, then the
above equations become
Ln=ULn t+ Yn ’
Yn=h—(Xy+G nti tenpotXn4s)s
0, +0, +0,+0,+4, 44,14, +8, 1% +2,,+%,,+%,,='0058851,
which represent 25 equations, where the second set of 12 may be replaced
by the following, which are readily deduced from them and the last con-
dition :—
1864.] of Instruments with Fixed Tones. 417
WAFYst+Yo=YotYot Y= Yat Yr FY = Yt Yot Yir= '0103000...... (2)
Uy= H+ Y1— Yo» Ly =X,+Yy— Yoo
Ue=L,+ Y2— Yo Ly y= % FY —Yros
Ly =U, Ys— Yas Ly =%y+Ypo— Yip
C=", FYs—Y 59 Lyy=L,+Y, —Yro
A system of unequal temperament may therefore be determined by arbi-
trarily selecting eleven different Vths, or else eight different IIIrds and
three Vths. The equations (a) show that if the temperament is not equal
(in which case all the y’s are equal, and the interval error of the IIIrd is
4 xX ‘0103000 =0034333, as in the Hemitonic temperament), at least four
IiIrds must have their interval errors greater than 3 x ‘0103000, that is,
there must be at least four IIIrds in every unequal temperament which are
inferior to the very bad IIIrds of the Hemitonic system. Kirnberger,
Dr. T. Young, and Lord Stanhope*, in the unequal systems they propose,
have each seven IlIrds sharper, and therefore worse than the Hemitonic
IlIrds. In one of Prof. de Morgan’s unequal temperaments, six IIIrds
are sharper than the Hemitonic; in another four are sharper and four the
same; in a third all are the same, but the Vths differ+. Hence nothing
is gained over the Hemitonic system in the way of harmony, while the
uniformity in the representation of the uniformity of just intonation is
entirely lost.
In selecting a temperament, therefore, we may dismiss all unequal tem-
peraments, as they must be inferior to the Hemitonic in both harmony and
melody, and will have no advantage over it in the relations of chords or the
number of tones required. Also, if it is considered necessary to play in all
keys with only twelve tones, any system of defective equal temperament
will be inferior to the Hemitonic, on account of the various and distressing
wolf intervals which occur when the music is not confined to the six major
scales of Bp, F, CO, G, D, A, and the three minor scales of g, d, a. Hence
the two conditions of having only twelve tones (exclusive of octaves) and
of playing in all keys, at once exclude all temperaments but the Hemitonic.
As, however, organs, harpsichords, and pianofortes with 14, 16, 17, 19, 21,
22, and 24 tones to the octave have been actually constructed and used {,
as Mr. Liston used 59§, Mr. Poole used 50, and Gen. T. Perronet Thomp-
* Kirnberger, Kunst des reinen Satzes in der Musik. Dr. T. Young, loc. cit.
_ Charles Earl Stanhope, Principles of the Science of Tuning, 1806.
+ De Morgan, loc. cit. p. 129, temperaments Q, R, S.
¢ Mr. Farey (Phil. Mag. vol. xxxix. p. 416) gives the particulars of their scales,
builders, and localities.
§ The following account of Mr. Liston’s organ is deduced from the data of
Mr. Farey (Phil. Mag. vol. xxxix. p.418). Scale: ¢ te tet cit d) tet td) tex
td cx d td tat & dt te tte .c f) te tfd ttfD tet ct f tet tf tt A
P tft to? tfx tg Fx 9 to tok @ gh ta? ttad a ta oD tod tak of wD
tat +0) tb bc th +) tot te bY. Chords: Table V. col. ILL, lines 4 to 13;
418 Mr, A. J. Ellis on the Temperament [June 16,
son now uses 40 tones to the octave on their justly intoned organs, the
condition of having twelve tones and no more, does not seem to be inevit-
able. It will therefore be necessary to determine what would be the best
system of temperament for the complete equally tempered scale of 27 tones,
and how great a sacrifice of musical effect is required by the use of the
Hemitonic system.
In Table XV. I have calculated for each of the 59 (reducing to 51)
systems of equal temperament already named, the interval errors of the
Vths, IIIrds, and 3rds, and the sums of the squares of the 23 interval
errors and the 6 beat meters of Table XII. I have then arranged the
temperaments in order according to each of these five results, and numbered
the order. Finally, I have added the five order numbers together and ar-
ranged the whole in the order of these sums. The smallest number would
therefore clearly give the best temperament, supposing that all the five
points of comparison were of equal value. Now the first and second tem-
perament on the list, or No. 26 and No. 2, only differ from each other in
the fifth, sixth, or seventh place of decimals with respect to these five re-
sults, a difference which no human ear, however finely constituted by nature
or assisted by art, could be taught to detect. As No. 2, or the Mesotonic
system, is determined in the simplest manner, I consider it as the real head
of the list. There is, however, little to choose between it and any one of
the ten or twelve systems which follow, except in simplicity of construction
and comparative ease in realization. The Hemitonic system, however, comes
35th in the list, and the old Pythagorean, recently defended by Drobisch
and Naumann (op. cit.), and asserted to be the system actually used by
violinists, is the 45th. No one who has heard any harmonies played on
the Pythagorean system will dispute the correctness of the position here
assigned to it, which fully explains the absence of all feeling for harmony
among the nations which use it—the ancient and modern Greeks, the old
Chinese, the Gaels, the Arabs, Persians, and Turks. No modern quartett
players could be listened to who adopted it.
The contest lies, therefore, between the Mesotonic and the Hemitonic
systems. The Mesotonic is that known as “ the old organ-tuning,”’ or, since it
was generally used as a defective twelve-toned system, as the ‘‘ unequal tem-
perament.” Within the limits of the nine scales already named, the superiority
of the Mesotonic to the Hemitonic system has long been practically acknow-
ledged. But the extremely disagreeable effect of the wolves (more espe-
cially to the performer himself) has finally expelled the system from Ger-
many altogether, and from England in great measure. On the pianoforte
IV.,5 to 14; V.,5to16; VI, 6%015; VIL,7to16; VIIL, 7 to 17; IX.,9 to
13; X.,9 to 13. Tones not forming part of any chord and required chiefly by
the system of tuning : +d) tte +f0 +t/p +g) tta? Bp +b) +2. Complete
keys: F, C,G, D, +A; E, B, Ft. The keys of £7, BD had their synonymous,
and +£, +B their relative minors perfect,
1864. | of Instruments with Fixed Tones. 419
the Hemitonic system is universally adopted in intention. It is, however,
so difficult to realize by the ordinary methods of tuning, that “equal tem-
perament,” as the Hemitonic system is usually called, has probably never
been attained in this country, with any approach to mathematical precision.
In Table XIV. I have given a detailed comparison of the Mesotonic and
Hemitonic temperaments with each other and with just intonation, for the
system of C (Proceedings, vol. xiii. p. 98), from which the great superiority
of the Mesotonic over the Hemitonic both in melody and harmony becomes
apparent. But this comparison rests upon the preceding calculations, which
were founded upon the beats that arise from rendering the conjunct har-
monics pulsative. It was therefore assumed that the qualities of tone em-
ployed were such as to develope these beats. The result will consequently
be materially modified when the requisite harmonics either do not exist or
are very faint. Now
for the Vth the conjunct harmonics are 2 and 3,
Bert Ath v3 5 3 and 4,
geo Vith a sdf s 3 and 5,
3 Wed ay x 4 and 5,
sj eord is iss 5 and 6,
sp Oth 36 53 5 and 8.
If then only simple tones are used, as in the wide covered pipes of organs,
or such qualities as develope the second harmonic only, such as tuning-forks,
to which we may add flutes, which have almost simple tones, no beats will
be heard, and any system of temperament may be used in which the ear
can tolerate the interval errors. Now Delezenne’s experiments show (Joc.
cit.) that a good ear distinguishes
in the unison an interval error of 0°28074,
» VIlIve bs A 0:31h,
33 Vth 39 99 0°14614,
x Ld ird FF if 0°2844,
aL 4 i 0°2994,
and an indifferent ear perceives an error of 0°561% in the VIIIve, and
0°292k in the Vth. We may say, therefore, generally that the ear just
perceives an interval error of 74 in the Vth, and 44 in the other intervals.
Now in the Mesotonic system the interval error of the Vth is —14, and
therefore just perceptible, but in scarcely any other interval does it exceed
tk. Thus it is —14 in the VIIth, 0 in the ITIrd, and +1 in the VIth,
and it is therefore in those intervals imperceptible. In the Hemitonic
system the error of the Vth is —;/,A, and hence quite imperceptible, but
the errors of the VIIth, I1Ird, and VIth are respectively 6-4, Jk, and
7, and therefore perfectly appreciable. It is only in the VIIth that this
error is at all agreeable. The sharpness of the IIIrd and VIth is univer-
sally disliked. Hence in those qualities of tone which are most favourable to
the Hemitonic system, it is much inferior to the Mesotonic. In Table XV.
VOL. XIII. 2H
420 Mr. A. J. Ellis on the Temperament [June 16,
the Mesotonic stands 2nd in order of melody, inappreciably different from
the Ist, and the Hemitonic 39th.
If the 3rd harmonic only is developed in the qualities of tone combined,
the beats of the Vth are heard, but those of the other intervals are not
‘perceived. The beats of the IIIrd and VIth, which are so faulty on the
‘Hemitonic system, will not be perceived at all unless the 5th harmonic be
developed, and will not be much perceived unless it be strongly developed.
‘Now the 5th harmonic is comparatively weak on all organ pipes and on
pianofortes, and hence the errors are not so violently offensive on these
instruments. If, however, the ‘mixture stops,’ which strengthen the upper
harmonics by additional pipes, are employed on the organ, the effect is un-
mistakeably bad, unless drowned by din or dimmed by distance. On the
pianoforte, however, these intervals, and even the still worse 3rd and 6th,
depending on the 6th and 8th harmonics, which are undeveloped on piano-
forte strings, are quite endurable.
Hence the Hemitonic system, except as regards melody, will not be
greatly inferior to the Mesotonic on a pianoforte and on soft stops of organs,
but will only become offensive on loud stops. But for harmoniums and
concertinas, violins and voices, where harmonics up to the Sth, and even
higher, are well developed, the Hemitonic temperament is offensive. The
roughness of harmoniums is almost entirely due to this mode of tuning.
The beats of the VIth, IIIrd, and 3rd are distinctly heard, and the develop-
ment of differential tones is so strong as frequently to form an unintelligibly
inharmonious accompaniment*. Concertinas having 14 tones to the octave
are indeed generally tuned mesotonically (or intentionally so), thus ¢ cf,
d di, e€), Tig ga, aa), bb). They are, however, occasionally tuned hemi-
tonically (or intentionally so) to accompany pianofortes, thus ¢ cf, d dq,
* The three recognized forms of the common major triad 4, 5,6; 5,6,8; 3,4, 5,
or CEG, E Gc, Gce, have the pitches of their tones as 4n,5n, 6n ; 5n, 6n, 8n, and
dn, 4n, dn respectively. They produce, therefore, the differential tones n, n, 2n ;
Nn, 2n, 3n, and n, n, 2n respectively. If the chords are tempered, the altered
unisons 7, x become pulsative, and the other tones disjunct. Now if in Table XIE
we put «=log (1+7) and Spe as t?, we shall have very nearly £=#1 -d— At) .C;
G=2.(-12).C; e=2C, e=31. Ges At).C; g=3.(1-2).C. The la of pul
sative diterencell tones are ae efore H— C=(44—22).C, G—C=(#343H).¢G,
and c— G=(3+3t).C, e-—c=(L2-8 S¢)- C. The numbers of beats are a abso-
lute Sk of the eee of these pairs of numbers, or of (-,4+“2).C,and
(—34+%2).C. The squares of these expressions, and the sum of their squares,
will be minima respectively for t=54,, r=00157070, log v=+1745206, which is
nearly No. 38 (22); ¢=,4,, c= 0011658, log v= 1749255, which is heey No. 24
(20); and t=,,4,,, e='0013096, log p= 1747817, ae is nearly No. 34 (8).
These beats, though perfectly distinct in some octaves, do not appear to be suffi-
ciently prominent to serve as a criterion of the relative value of different systems
of temperament, or to form the basis of a system, and they have consequently
not been introduced into the text. They were noticed and used by H. Scheibler
(Der So a a und musikalische Tonmesser, p. 15).
1864.| of Instrumenis with Fixed Tones. | 421
e dt, f ft, g ot, «gt, bag. Hence it is easy to compare the different effects
of the two systems as applied to the same quality of tone, for harmonies
which are common to both. Having two concertinas so tuned, and a third
tuned to just intervals, I have been able to make this comparison, and my
own feeling is that the Mesotonic is but slightly, though unmistakeably,
inferior to the Just, and greatly superior to the Hemitonic.
There are two other points in which the complete Mesotonic system
possesses advantages over the Hemitonic. The Mesotonic VIIth is rather
flat, but by using the flat VIIIth in its place, when the harmony will allow,
the effect of an extremely sharp VIIth is produced, which is sometimes de-
sirable in melodies. Thus log Mesotonic VIII? =-28195, which is sharper
even than log Pythagorean VII[=°27840. The ordinary and flatter VIIth
can be used when necessary for the harmony. Again, by using the
German sharp VIth in place of the dominant 7th, that is, by using the
chords G? By Dy ce, Dp F Ap b, Ad C Eb ft, ED G BD ck, Bb D F gt,
HACd, CHGo, GBD, DAM ACRES x, HGE Bex,
B Dt Ft g x, in place of G) B? Dd fo, Do F Ad, Ad CO ED gh,
NG Bd, BDFd, FACY, CEGh, GBD, DihAs,
ACZ Eg, EGE Bd, B Dz Fx a, when the progression of parts will allow,
an almost perfect natural seventh, better than that obtained by using the
corresponding just tones, will result, producing beautiful harmony ; for
log Mesotonic VIF=°24228, log i=-24304, and log Just VI =-24497.
The ordinary sharper 7th can be used when necessary. Neither of these
effective substitutions is possible on the Hemitonic system.
Considering that singers and violinists naturally intone justly (Delezenne,
foc. cit.), and that the interval errors of the Mesotonic system seldom
exceed the natural errors of intonation which may be expected from the
inability of the ear to appreciate minute distinctions of pitch, it appears
desirable to tune harmoniums at least, and perhaps organs, mesotonically.
Except as an instrument for practising singers, however (for which purpose
it would be superseded by a Mesotonic harmonium), it would be unnecessary
to alter the Hemitonic tuning and arrangement of the piano. But it would
be best to teach the Mesotonic intonation on the violin in preference to the
Hemitonic, as proposed by Spohr*. As, however, it would be useless to
tune mesotonically with only 12 tones to the octave, it is necessary to have
some practical arrangement for 27, 24, or 21 tones at least. I propose the
following plan for 24 tones, and as these are exactly twice as many as on
pianos, &c. of the usual construction, I call my arrangement the
* “Unter reiner Intonation wird natiirlich die der gleichschwebenden [ Hemi-
tonic | Temperatur verstanden, da es fiir moderne Musik keine andere giebt. Der
angehende Geiger braucht auch nur diese eine zu kennen ; es ist deshalb in dieser
Schule von einer ungleichschwebenden [defective equal, or unequal] Temperatur
eben so wenig die Rede, wie von kleinen und grossen halben Ténen [¢ cf & ¢ d? =
Gc, that is, = 7), weil durch beides die Lehre von der véllig gleichen Grosse
aller 12 halben Tone nur in Verwirrung gebracht wird.”—Violinschule, p. 38.
422 On the Temperament of Instruments with Fixed Tones. [June 16,
DurpLex FINGER-BOARD.
PLON.
FX g9©éX
cb dbx eb hb gx abx bp ch ab Oclours
et ot ee t ee White Black.
Lront€ Llevation. FellowRea
Let the black and white manuals remain as at present, and let a yellow
manual, of the same form as the black, be introduced between B and C, and
E and F. Cut out about the middle third of each black and yellow manual,
up to half its width, on the right side only, and introduce a thin red manual
rising as high above the black or yellow as these do above the white. Over
G, A, and D, each of which lies between two black manuals, introduce three
yellow metal manuals (lacquered or aluminium-bronze) shaped like flute
keys, and standing at the height of a red manual above the white one, which
can therefore, when necessary, be reached below it. ‘The 7 white manuals
are the 7 naturals; the 5 black manuals are the 5 usual sharps, ch dz f¥
gt at; the 2 long yellow manuals are the unusual sharps et 62, and the 3
metal yellow manuals are the double sharps f/x gx cx ; and the 7 thin
red manuals are the 7 flats, 2), db, 9, f0, 97, a), 69. The shapes of the
red and metal manuals were suggested by those of General T. Perronet
Thompson’s quarrils and flutals. The 24 levers opening the valves on the
organ or harmonium would li side by side, being made half the width of
those now in use, and metallic, if required for strength. The organ pipes
or harmonium reeds would be arranged in two ranks of 12 for each octave,
the first rank containing the 7 naturals and 5 usual sharps, and the back
rank containing the 7 flats, 2 unusual and 3 double sharps. The use of
this finger-board is accurately pointed out by the ordinary musical notation
which distinguishes the sharps from the flats, and is therefore in no respect
adapted to the Hemitonic fusion of sharps and flats into mean semitones.
‘(epour
‘Tar) 136 poppe “ “ | peneLay | ogF, F199] GF ‘cL ‘eg
"Tg ae apy “ @ | peyeL ee | 09% $499] 9G ‘el ‘eT
r 9pour
Tox) W9 poppe “ “ | peor JT ‘GT | OLE ‘eT #0 fax qe) LT ‘er ‘e ‘g
Com py ta “ “ | pegey rourpy | 9, qP9°H| g1'6 ‘G's
TL peysmurog | peter 2 “L | LT GP2T 29D] 212 ‘G'S
UW “BUr "TA, TAL OY} FOTO | pear e‘s | 26, eP dp 9) 6° ‘9 "8
*SJUONYTISUOL) OATPESTO OMT, oS
‘(qooproduar) 139
Poppe “BT OY} Jo "GO| pvuty, 1g 16 are) 1 ‘QT
‘penty, snongiodng | prny, gg GG foto 9 Go ‘@ ‘T
‘(qoogroduat)
(9 peppetourm =“ “| per, JT 9,11 #,9 [tax 0 9 LI ‘a ‘g
‘Cduar) yz MH em}JO'YO) — PRL LT OLT GP2T 99 LL'G'¢
LOU) LOULTAT MOUMUOD | PLL, OUTTA, Qs lebi qa GT 39 1G.
‘STUOONOD ‘T
’
eure Ny Areurprg ‘oure ny “yskg | ‘Toquikg ‘op durexny | ‘od XT,
el ee ee eee
(*26¢ ‘d 909) "SployyQ [vorsnyy jo TONvoyIsse[Q—'TA XIAVy,
Taste VI.—Classification of Musical Chords.
(See p. 397.)
Type: Example, Symbol. | Syst. Name. Ordinary Name.
I. Concorps.
1,1 C4 C4 Cc 1 Dyad | Unison (Octaye 1, 2).
765) OG C 3Dyad |Twelfth (Fifth 2, 3;
Fourth 3, 4).
1,5 Cle Cc 5 Dyad | Majorl/7#h(Ma. 10th2,5;
Ma, 31d 4,5; Mi. 6th5,8).
3, 5 Ge c | 8,5 Dyad |Ma. 6th (Mi. 8rd 5, 6).
1, 3,5 C'Ge C | Major Triad |Common Major Chord.
Ii. Strone Discorns.
1, One Pulsatiye Constituent.
ii C! gb? 7C 7Dyad |Perfect 7th 4,7; Ex-
tended tone 7, 8.
3, 7 G gb) 70 3, 7 Dyad | Contracted 3rd 6,7; Ext.
6th 7, 12.
5, 7 e gb? 70 5,7 Dyad | Contracted 5th 5, 7.
iL, 8, af CG gb 7C | 3,7 Triad |Imp.Ch.of Dominant7th.
MO C1 e gb? 70 | 5,7 Triad . in
1, 5, 7 C* e yvij att 70) 5, 7'Triad | Chord of the Italian 6th.
1, 5,9 Cred 9C | 5,9 Triad | Imp. Ch. of the 9th.
1, 3, 15 OG b 15C | 3,15 Triad || Imp. Ch. of the Mi. 6th,
1,5,15 * Ct eb? 15C | 5,15 Triad inor mode;
TL, BY ili 0! G Iga'b 17C | 3,17 Triad pa Ch, of the Minor
1, 6, 17 Cte Iga? 17C | 5, 17 Triad 9th.
1, 3,5, 7 0 Ge gb) 70 7 Tetrad | Ch. of the Dominant 7th.
Wy By By 1 C* G e vij att 7'C 7'Tetrad | , 4, German 6th.
1, 3,5, 9 CGed 9C 9Tetrad | ,, 4, 9th.
1, 3,5, 15 Ct Ge hb? 15C | Major Tetrad| ,, 4, Ma. 7th.
1,3,5,17 |C*Ge 1ga 17C | 7 Tetrad |, 4, Mi. 9th imp.)
1, 3, 5, 27 Ot Ge tat 27C | 27 Tetrad | ,, ,, add.Gth,ma.m,
2. Tio Pulsative Constituents.
1,8,5,7,9 |C!Ge cb) @ 79C | 7,9 Pentad | Ch, of the added 9th.
1, 3, 5,7, 17 | C*Ge zbD gdb 170 17,17 Pentad | ,, ,, Mi. 9th,
1, 3, 5,9, 15 |C'Ge db! "15C | Major Pentad| ? ” Ma, 9th.
1, 3, 5, 15, 17) C* Ge b’xvij cf} 15,170 | 15,17 Pentad| ,, ,, augmented 8th.
I. Wax Discorps.
1, One Pulsative Constituent.
M37 Ge cb) Te 7 Triad | Ch.ofthe See
1, 3,9 LORE 9c 9Triad | 4, 4, 9th (im
3, 5, 15 Geb =G Minor Triad |Common Minor Da
3, 5, 17 Ge 1gay 17c 17 Triad | Ch. ofthe Dim. 7th (imp .).
8, 5, 17 G e xvij cit 17'c 17’ Triad » » Minoradded bth
(amperfect),
1, 5, 25 Ce tet 25¢ 25 Triad Superfluous Triad.
1, 5, 27 Cte ta 27e 27 Triad Ch. of the Ma. added
6th (imperfect),
2. Two Pulsative Constituents.
38, 5, 7,9 Ge gb) d? 9c 7, 9 Tetvad | Ch, of the Mi. 7th, ma. m.
8, 5, 7, 17 Ge gb? gdb 17e | 7,17 Tetrad | ,, ,, Diminished 7th,
3, 5, 9, 15 Gedb ‘ec | Minor Tetrad | ,, ,, Mi.7th(mi.m.).
8, 5,15,17 | Geb xvij cf 15,17¢ | 15,17 Tetrad| ,, ,, added 6th (mi.
mode),
1,5,15,25 |Ceb te 25¢ 25 Tetrad » 4, augmented 5th,
3,5, 15,45 |Gebf ’45e | 45 Tetrad » _» added 9th (mi,
mode).
~ is iS iS
ON
NRK AAR KS
oD oD
NOOO HWDOMODNGO
= ==
nid oD 6 SHS
v
‘ApISMOYUT
‘QdUvyy]
"1OJOB
‘TRALOYUT
H Jatoe oy} Jo serpisuozUy
*SOTUOTHAIV
Py li
ae
L L & &
ve vé 69 69 1z
9G Ov OF OF 0
Sree ores le cotre, |) conte sl) 20
g ¥ £ &
% L L T th
8L gL 6 8 8B
oz | 9 Ot 6 6
9 $ G 6 G
eet e eee G 6 G
9 0G 9 Vv ates
IL eeees g g 8
eee 9g eee 9 ° ee
6e (9 eo
ae ag ore ik tes les a ae
oS NeGs Sal 8G 4G
OOT | OOL QOL | OOL SS alee
QOOT|‘*°'' | OOT| 9
| | a | nr |
——— EE oa Enel a |e | | RR |
QOL | ,OOT | ,
Bboy “svy) “RIUOT PUNOAWIOD Wo SproYy [woIsNY Jo UoNONIySU0Q— "TTA T1avy,
a | RS ee at al ta aed gee GE ar |
RET.
eas
ae oa
ear ee
SLE
| F
leer alse
a lea
oalee
69 | a
7
og | 99
OOr| TI
O66
0 | ‘oot
dla eat
|
Index.
p:
be
‘SOMMOULIVTT JULIO JO AjIstoyUT
0;
“ae
100 | 100
10
10
1
2
3
i
5
) ee eae
1900 | 100
ae
Tasie VII.—Construction of Musical Chords from Compound Tones. (See p. 398.)
of the Constituent Tones.
onics
Extent of the Harm
Harmonies of the Constituent Tones,
CO) S
a=)
al aint io io:
al | aaawtioon@
(See p. 399.)
Taste VIII.—Qualities of Concordant Dyads.
-zequinyy | AHARDWOAANDROD
re
a
cs AMMDOAWODOWOONDNS
4 ECL || 1c: Ey CC eC ae ar Oe
ott ND 09 09 OD HD 19 10 1
di | Bega
e|& “eure Ny ‘SOTUOMLIV]T JULOL Oy} JO SorzIsuOzUT § 3 a8
FA | Re feay-ftc|
“qyueOPIL, a
N : :
he . “as . . . . cle le
“W700 care - cre S -O -tH -O 10NN Ce Ae
5 ja oom | DiGi: ja cas] : : | easy Es
SES iS lis tom Hope acs! Sev} 6 re
SH | ao yqueayg | 2 iS Q ion c 5 a: a ne Pans
2 ga 8 ; : : : op Pee
es
. =
e WHS TW) 2:9 1B) 13g: zi aReegece
2 | ox | peur in |S: 2 38 al ae | ae.
é |-~ | a an | S 38 | [1:8 | ie e Sus | ie
———— en ne Pe
e[oo| msm] i598 ig|8 : ine | io: ia| i ie jenn [onze
e[se| -wma[S gg [a ose || ie 2 |e ie tee [>
ay len | wean |SSR°* jares | = fois | 100 5 NN | ose
[worth] ae8e|= = 3 [males =
|
|__| gga :| | |
Jans | |
| | |
i
Index.
1D © O 10
ro ro
COI IS oO
ONS PS ION UES
hn fs I FK
PE Cee ONL EN
Index.
Taste [X.—Qualities of Concordant Triads. (See p. 399.)
log eae
l| - x Ex sa
yz, | ‘uO T SOTMOULIEPT quIor Jo AjtsuoyUy aS Be Fi
28
as
aS
spe eaee Eis 6 =
o lonw S65 3S) S 16 | SS Lani =) 19 219 | we Soh
a Ee | :: s | a Ss = E SS mtowles
a loow|o ; =) o|co Sim 30 10 St
a [ace |? i: g|g:iis|9s tials ia © = aoe:
7S °@ ].9 2 iene | oO i ; :
ey eee | ce) 5S [8 Se || OS E ace ooo t
- a ed rao Ct .
mlood]|] - Oo : : jid ia EX) 100 “ec
n|a2°| jig i]s uns| eg: Eee
© |nNaWm 5 EIS Soo 20 aS) Ned EOF
2|5 lee g | Eats E Eetegeae
= Sura i z y
S eo Oro =10 ok See omns
| jae= | ss | Ara} Of [e Theo
ne . - in| ol
6 | 295
[E9100 | HOO 1G it c ar 2
ay Inee | “97> ANS E a Bian) siGN ardaalS
| 1 a 3 no A
= 7 ao 5 ae
Seon ROO F Jes) 3 o,4
S| ieee | Ssa E Sait oS N er) aH | ote
a4 Sh ilee 3 aa
5
© loda |S (eo FI] SSweHO |] fx © ia ee oat
a{4 SS = 1A AHS | 209 : Reiter
a = 3 = ap tae
mi 5 A a oa, Bho
es Sr 19 | hie Sei CN lO
@ loon | Sand /SNS :a! :& ics piste
a a] 5 a aie Ce
gro | oeanso ce) to
o);onre 2 P Se Scene
SOR Sasa eS |e oes
SeTey = S 3 ve ho 1 Id 2
ay |eex | 7S E 16 ia | ia a is Sle teuel22In
i | F 5 o
SS io : : =
© |oox seigizig| ie 2 ig et
aa] e 2 al
ISS IS J1o tone | io c eee
DW} WIOMD! I~ SIS|A SHA] = ai? n-Pnls
oth ote! a c on ae,
a Zn
Teen : 5 :
19 Je : @| 9 : 2
st Joon | “gose RiP Gl] ik In | seHeo-
| = |- > 5 3 ri!
oS F, 3 =
19 419 5 z : Seo
Ee) jew |°°sgs a > Tea lley | ia ©) oCe) reels
i E = PS
aon 5 r
o [oon [S855 [97738 ‘0 ies gent 202
oo | 5
ane 5 5 5 : z
= e& | "esas E Be CK |e GShei2 Soave tigs | andes
— | q .
5 i Oa a onx j
HA rye on [FOS Re OS a 4 SoSSana | seo
No.| sue XII.—General Table of Equal Temperament. (See p. 407.)
Tf,
log of tem-
pered pitch.
0000000
0285191 — 7x
0226335 5x
0570382 — 14x
‘0511526 — 2x
0452670-+10x
0796717 — 9x
0737861-+3x
1023052 —4x
‘0964196+-8x
1308245 — 11x
-1249887-+x
1534578 —6x
14757224.6x
1819769 — 13x
|
J, é,
log of just
pitch. i
0000000 | 0
0053950] —k
‘0177287 | 2k—7x
0280285 | —k-+5x
0457574| k—2x
0511526] —2x
0688813 | 2k—9x
0791812} —k+8x
1249386] x
1503338
"1426675
1480626
B,
beat meter.
Inter-
val.
—ooooooor* | ee rr rr |
me | | | ee
Hig
—6k+418x| 3
5k — 20x seal
a | a a | A | A |
a | | er | eR ce | RTS ee |
1760913 —x
1702057 -+-11x
2046104 —8x
198724844
2331295 —15x
|
‘1706961
‘1760918
1938200
2041199
i | | re ee | ee een | REESE
ee | eee
1 (
Pel peme |
3 - peted
4 i note.
5
Saree
7\|t | @
|? dp
9 cx
10
Ses
12 |.
13/2 | 42
ja |? | te
Tb eee
Sony it as
16
17, eq
18
19 bi £
20 |.
; fi
ry)
#x
t]
ab
‘|g
gx
7
ppb
) ap
. bp
b
oy
bt
‘2272459 — 3x
2213583-49x
2557630 — 10x
‘24987744 2x
‘2783965 — 5x
'2725109-+-7x
0058851 —12x
3010300
|
|
|
2218486
2272438
‘2498773
‘2552725
‘2676061
‘27300138
3010300
ee. ee ee eee
—1078kx
+1998x?
Where k=:0053950 and = is arbitrary.
¢
J. Just Intonation i
M. Mesotonic Temp
H, Hemitonic Temp
Wolves of
——
00810
Gee ae 00270
2 00270
—
Miner
3a |-90135
3 ihe
©, 00000
6th W onarn
0.4 =e A 00
Bye — De HOS?
B) ft =At f 2
Beh = Es cf 00270
ere ay F002 TO
TOW cet
BD ct = At c
B GE = EEG oo405
Ae el
FE eb =F ay00876
cf B= Chad ;
GEE =GF et ooo00
(00539
Where & 100000
100675
00135
00405
00270
Beat Factor. _ |
+ -00638
— ‘00392
-- ‘018605 | — 053965
+ 00343
— 00197
000000 |-+--059684
+-00490 |
— -00589 |
+ 00686
4.00195 |
— 00344 |
+ 00932 |
+ 00589 |
+ -00098 |
— 00441}
010547
Taste X.—Duplicated Forms of the Concordant Triad. (See p. 400.)
No.| Simple. Duplicated. Simple. Duplicated. Tasie XII.—General Table of Equal Temperament. (See p: 407.)
1/2, 3, 5/2, 8 4, 5/2, 3, 5, 8|2,3,5,61C Ge |C Geel Ge @|O Geg Tem-
2/1, 3, 5/1, 2 3 5/1, 3 4, 5/135, 61C'Ge |O'CGe |O'Gce |O'Ge g Just | pered | log vies. ie Geral eae Bl Inter.
3/3, 4, 5) 3, 4, 5, 6) 3, 4, 56, 8) 3,4,.5,10]G ce|/G ceg |G cee’?!Gce e& note. | ote. pered pitch aan T—J. |beat meter.) yal,
4|2 5, 6|2, 4, 5, 6) 2, 5, 6 8 Ceg/iC ceg |G eg @ [else aitee eael Rale
5 | 3, 5, 8) 3, 5, 6, 8] 3, 5, 8,10 GeceiG ege’|G eee? ce 0000000! 0 T
— : 5 te } = || Seendeo 10088980 =k H
6| 4, 5, 6) 4, 5, 6, 8) 4, 5, 610) 45,6,12)c¢ eg |c egelc eg elceg g te ef | 0285191—7x | -0177287| 2k—7x tt
7 | 5, 6, 8/5, 6, 8,10) 5, 6, 8,12 e BS e g cele g cg’ dd | -0226335-+-5x | -0280285] —k+5x 2
8| 1, 3,10] 1, 2, 3,10] 1, 3, 4,10/1,3,6,10]C'Ge|C'CGe2|C'Ge &|C'Gg e& ex | -0570882_ 14x
9/1, 5, 6)1, 2, 5, 6/1, 4, 5, 6 Cteg |C'Ceg |Ciceg
10 | 3, 4,10] 8, 4, 6,10 G ce? |G ec ge? ; z
Yiledess|28. 9D : Sues if d | -0511526—2s 10511598 are a
11 | 2, 3,10| 2, 3, 4,10] 2, 8, 8,10 CGe|C Gee|O0 Gee ebb | -0452670+10x ge
12 | 2, 6,12 | 2, 4, 5,12 | 2, 5 812 C e g. Ce eg C e cg? tat dt | -0796717—9x | -0688813| 2k—9x {Ut
FO Ps UO A te Ae cdligu bes alg te? | eb | -073786148x | -0791812| —k+3x | —6k+18x| 3
14] 1, 5,12] 1, 2, 5,12) 1, 4, 5,12 | 1,5,8,12] 0% e o2/0'G e 2|C'ce g?| Cre og?
15 | 4, 5,12 | 4, 5, 8,12) 4, 5,10,12 | 4,5,8, 10} ¢ e g*)c¢ e cg?) c ecep?!c e ee 6 é -1023052—4x 0969100] 1—4x 5k —20x oat
aaa fp | 0964196-+8x ;
16 | 5, 8,12 | 5, 8,10,12 e c?o?]e ce? p? x
17 | 3,10,16 | 3, 6,10,16 | 3, 10, 12,16 G ec|G g eG eg? ct pint sgees =
18 | 8, 5,16 | 8, 5, 6,16 | 3, 5, 10,16 G ectiG eg ctlG e ect 949¢ :
19 | 5, 616 | 5, 6,10,16 | 5, 6,12, 16 Bee ils coalie a cea ai fey | 124087 | 112 Pela ar a
20 | 5,12) 16 | 5,10, 12, 16 e pect|e e% pct t SRD EET EW ook "lity
| -1702057+4-11x an
j -2046104—8x | -1988200| 2k—8x
Forms of the Minor Triad. ig at 1987248+4x | -2041199] —k+4x | —8k+82x| 6
ox | 2331295 — 15x
No.| Form. | Diff. Tones. No. = 9918486| k—3x Bk—15x VI
TR ES fa t BO BEEP SOS | 3072488 —8x tVI
BS a bob | -2218583+49x
2 | 12, 15, 20 g 8 7
; 2557630 — 10x
8 | 10, 2, ib 6 12 al at 2498778 7
12, 15 _ | -2498774-42
5| 610,15 G 1s oy | O8774-+25 | 9559795 47
6 | 15, 20, 24 9] > eg? th = ouge fv
7| 6,15,20| 5, X14|G be 16| BIE | Oe eee | 12780018 wat
8| 3,10,15| 5, 7,121/Ge b 19 e) | 2725109-+7x
9 | 12,15,40| 3,25,28]¢ bet 5 | | be | 0058851—12x
10 | 10,15,24 | 5, 9,14] b g 7 e ce? | -3010300 *3010800| 0 vol
| 5, 6,15 10]E G 7 ze 28
12 | 8,15, 20 17 |G*b 3 =32k? | =1501°
13 | 15, 20, 48 33] b & 10 —212kx | —1078kx
14 | 15, 24, 40 25} b g? d, c*, tet 10,15, 48 | 20 +420x? | +1998x?
15 | 15,40, 48 83 | b et gt] o tee, sje! 12) 15,90 | “3 SE ee eee ee SS
16] 5,15, 24 E 9 Where £=:0053950 and z is arbitrary.
17 | 615,40 G 6
18] 38,15, 40 G 13
19 | 5,15, 48 E 14
20 ae 15, e 15
J. Just Intonation i
M. Mesotonic Temp
H, Hemitonic Temp
Wolves of Coe
ee tN
PGE! 4 90135
Gee = Fn
C
ip Cr EK
tg 0st ors
BiH, = Di pote
Bie Att
Bee = EF et ooa70
00270
3rd w s
BD Fe= De F00270
Des Ate,
BGS = EL G4 og405
th w'00185
ee mee
GZf =GP eZ oo000
aero 100589
Where eye
100675
Comparative Tab
. (continued).
Interval Errors.
+:00981
+ °00441
— ‘00098
+ 00638
— ‘00392
+ 00348
— ‘00197
+-00784 |
+ 00245 |
— 00246 |
+0040 |
— 00049 |—-009304
— 00589 |
+ 00686
+-00195 |
— 00344 |
+ 00932
+ 00392 1+ -015553
— 00147 |
Beat Factor. |
‘000000
H
‘010547
Taste XIV. (continued).
Notes. Logarithms, Interval Errors, Beat Factor,
J M J M H M-J | H—-J M
c @ 00000 ‘00000 | -00000] -00000} -00000
Tasie XII te 00540 —-00540 |— -00540
; tet | | cy 01773 | | 01908 + 00135 |-++ 00786
Wolves of Defective Equal Temperaments. (See p. 415.) ¢ 02312 ‘02509 |— 00404 toota7
db | ab 02803 | 02938 +-°00135 |— 00294
Wolves. Interval erzor, «| Beat meter, 8, ex 03816
a ee eee tid ‘04036 + 00981
b Vth ee td d nee 04846 | ~-05017 |+:00: + ‘00441
Gie=AD g=GH dt........ —k—s+llx | —3k—38s+33: d 05115 —00098
u ye awe eee a ebb ‘05876 I
: 4th wolf=4w.
ED GE=B) Ab=D# Gt...... lets—Ilx | 4k-4-ds—ddx tat Jat || ax] 06888 | 06753 +-00638
ted |e 07918 | 07783 — ‘00392 }---018605
IUhd wolf= Iw. =| —S
GZ s =ADe e { e ‘09691 09691 + 00343} ‘000000
Be? =B dt e te 10231 —'00197
F# B) =F Wile abeosoonune —s-+8x —5s+40x fb 10721
CLF =Cz i
ef 11599
6th wolf=6y. tf 11954 + 00599
C Git =C Al f fi 12494} | 12629 + ‘00049
P = . eat ¢
is B att poOoHSTOOLGeD s—8x 83— 64x is 18033 00491
Pet =D ct tf fit 14267 | | 14537 + 00784
fq 14806 15051 |— 00270 |+ 00245
; 3rd wolf= 3vw. a) |g? 15297 | 15567 — 00246
ED Fe= De Fe
Beh = Atiet yoo. ees seen s—9x 63—54x fx 16444
FG? = Ee Gt te 17070 +-00490
g g 17609} | 17474 — 00049
VIth wolf= VIw. tg 18149 — 00589
FH e) =F d abb 18504
CHBDS= CHAT Yee eee —s+9x —5s+45x 3
Git =GH ed tet | et 19382 | -19382 + 00686
ap 19873 + 00195
2 tad { | ap 20412( | 20412 — 00344] -000000 |—:062995
Where &=-0053950, s=:0004901, and a is arbitrary. — pce
8x 21290
fa 1645 +-00932
a a 2185 \ | 22320 + 00392
ta 22724 5 | — 00147
bob ‘23350
at at 24497 | -24998 | ae
. 24988 | | 25258 4
Tasiz XIV. (See p. 419.) + 25507 * O0441
Comparative Table of the Mesotonic and Hemitonic Temperaments. ina —— eatin acne CH : 0 00883 8
b (|b 273 ‘27165 |\ * — 00135 |+-'00295
J. Just Intonation in the keys of B), F, C, G, D, or System of C; 33 tones. Fe) 7300 eee
M. Mesotoniec Temperament in all keys. No. 2 (2); 27 tones. ———_|—_ arora os cara|
H. Hemitonic Temperament in all keys. No. 50 (35); 12 tones, te? by moet 29073 30103 [4+--00540 | +-00540
2 {|e 301034 30103 ‘ 00000 ya
Sum of squares........---+ '0004735 |:0008748 i
rT eae
aments.
Error of 3rd.
el
fi
12
er. Error.
7 | —:0013102
3 | —-0013488
5 | —°0011359
t | —-0011385
3 | —-0010528
2 | —°:0010375
9 | —:0014380
1 | —:0010288
0 | —:0014833
0 | —-0009811
1 | —:0014911
9 | —:0009133
2 | —-0015868
8 | —:0008992
7 | —:0008023
4 | —-0016957
6 | —-0007707
5 | —:0006700
5 | —:-0017983
8 | —:0018811
9 | —-0019267
7 | —:0018775
10 |} —:0020233
‘3 | —-0016811
1 0
}1 | —:0020580
oat (36
2 | +-0000368
33 | —-0026901
3 | +-0000401
36 | —-0028021
35 =| —-0027025
4 |+-0004421
37 ~=«| — 0029581
38 «=| — 0083718
39 | —-0037465
10 | —-0037897
41 | —:0039235
49 | —-0042814
16 | +-0011969
43, | —-0043882
48 | —-0051988
44. | —-0049036
45 | —-0050812
46 | —:0052111
49 | —:0052177
47 \ —-0052315
50 | —:00538611
26 | —:0018689
51 | —:0053950
34 |+-0026975
Melodic Errors.
0001597
(See p. 418.)
Se.
0001527
‘0001528
(0001541
0001542
0001559
‘0001562
‘0001535
0001564
0001541
0001578
‘00015438
0001601
0001563
‘0001606
‘0001648
‘0001664
0001719
0001639
‘0001679
‘0001705
0001983
‘0001764
‘0001706
0002329
0001863
‘0001875
0002375
0002177
0002378
0002563
0002432
0002961
0002794
0003511
0004297
0004897
0004714
0004461
0005939
‘0009584
0007554
‘0008164
0008651
0008703
0009185
0006244
‘0009314
| 0009028
0005648
0008628
|
Order.
0001513
‘0001565 |
0001363
‘0001361
‘0001339
0001338
Harmonic Errors.} Comparison.
=P.
‘0001709
0001337
0001718
0001542
‘0001812
‘0001367
0002029
0001375
0001451
0002525
‘0001485
0001625
0002625
0002950
0003127
‘0002936
0003533
0001589
0003587
0004168
0004247
0003858
‘0006077
0003873
0008306
0007556
‘0006140
0009600
0013524
0017734
‘0018255
0019940
0024829
0012335
0026391
‘0039960
‘0034669
0037795
0040169
0040292
0040549
"0043004
‘0019977
0043659
0032183
1864.] Mr. W. H. L. Russell on the Calculus of Symbols. 423
“On the Calculus of Symbols.—Fourth Memoir. With Ap-
plications to the Theory of Non-Linear Differential Equa-
tions.” By W.H. UL. RussExz, Esq., A.B. Received July 31,
1863%*.
In the preceding memoirs on the Calculus of Symbols, systems have
been constructed for the multiplication and division of non-commutative
symbols subject to certain laws of combination ; and these systems suffice
for linear differential equations. But when we enter upon the consideration
of non-linear equations, we see at once that these methods do not apply.
It becomes necessary to invent some fresh mode of calculation, and a new
notation, in order to bring non-linear functions into a condition which
admits of treatment by symbolical algebra. This is the object of the fol-
lowing memoir. Professor Boole has given, in his ‘ Treatise on Differential
Equations,’ a method due to M. Sarrus, by which we ascertain whether a
given non-linear function is a complete differential. This method, as will
be seen by anyone who will refer to Professor Boole’s treatise, is equivalent
to finding the conditidns that a non-linear function may be externally
divisible by the symbol of differentiation. In the following paper I have
given a notation by which I obtain the actual expressions for these con-
ditions, and for the symbolical remainders arising in the course of the
division, and have extended my investigations to ascertaining the results
of the symbolical division of non-linear honedare by linear functions of the
symbol of differentiation.
Let F (a, y, Ys Yoo Y3 + + + + Yn) be any non-linear function, in which
Yis Yo, Ys, ++» + Y, Aenote respectively the first, second, third, .... th
differential of y with respect to (a).
Let U, denote fdy,, ¢.e. the integral of a function involving 2, y, 445 Ya ++
with reference to y, alone.
Let V, in like manner denote 4 when the differentiation is supposed
YY
effected with reference to y, alone, so that V, U, F=F.
The next definition is the most important, as it is that on which all our
subsequent calculations will depend. ‘Ve may suppose F differentiated.
(m) times with reference to Y¥,) Yn—1) OF Yn—25 &C., ANA Yn, Yn—1y OF Yn—os
&c., as the case may be, afterward equated to zero. We shall denote
this entire process by Z™, Z), Z}, &e.
The following definition is also of importance: we shall denote the ex-
pression
d
Yr-1
f+, © yt! te aS a a eee as
by the is b
* Read Feb. 11, 1864; see Abstract, vol. xiii. p. 126.
VOL. XIII, 21
&
Taste XV.—Comparative Table of Equal Temperaments. (See p. 418.)
Error of Vth.
Error of Iird.
rror of 3rd.
Melodic Errors. | Harmonic Eyrors.
0001513
0001565
0001363
0001389
0001338
0001709
0001337
0001718
0001342
0001812
0001367
0002029
0001375
0001451
0002325
=p.
0001361
0001485
0001623
0002625
0002950
0003127
0002936
0003533
0001589
0003587
0004168
0004247
0002375 0003858
Name. Log »v.
Envor. Exror. Enror. Order.
Least Errors.............-.. 1747297 — ‘0013616 2 | —-0000514 — 0013102 1
M&EsSOTONIC ......-eseeeees 1747426 — 0013488 1 0 —:0013488 2
Equal beats of Vi and4...... 1746716 —'0014197 6 | —:0002838 —*0011359 4
Cycle of 81 ...----..sssseee 1746703 —:0014205 7 | —:0002870 — 0011385 6
Least Errors and Beats ...... 1746439 — 0014474 9 | —:0003946 — 0010528 8
Woolhouse’s Equal Harmony . .| 1746388 —'0014525 | 10 | —-0004150 —0010375 9
Least Beats of V and IIT .| 1747723 —'0013190 3 | +:0001190 — 0014380 3
Least Beats ........++-0000s 1746359 —:0014554 | 11 | —-0004266 —:0010288 } 11
Cycle of 93 ....... ee ee eee 1747872 —:0013039 4 |+-0001794 — ‘0014833 5
Equal and opp. Beats of 3 and 4} 1746200 —:0014713 | 13 | —-0004902 — 0009811 12
Huyghens’s Grate iol scanod ‘1747900 — ‘0013013 5 | +:0001898 —‘0014911 7
Henfling’s Cycle of 50........ 1745974 — 0014939 — ‘0005806. — 0009133 | 14
Drobisch’s Simplest it OTRO 1748219 — 0012694 —‘0003174 —:0015868 | 10
Dr. Smith's Equal Harmony . .} 1745927 — 0014986 — ‘0005994 — 0008992 | 16
Least Beats of 8, Il, V...... 1744404 — ‘0015309 —-0007286 —0008023 | 18
BWqual Beats of 6 and V ...... 1748582 — 0012331 + 0004626 — 0016957 | 13
Equal Errors of Ii and 3 ....}+1745199 — "0015414 —:0007707 —0007707 | 19
Romieu’s Theoretic ........-. 1745163 — ‘0015750 —:0009050 —:0006700 | 16
Equal and opp. Beats of 6 and 4) -1748924 — 0011989 + 0005994 —0017983 | 17
Drobisch’s Cycle of 74.......5 1749200 — 0011713 + :0007108 —‘0018811 20
Drobisch’s least Evrors........ 1749352 —‘0011561 + 0007706 — ‘0019267 21
Bqual and opp. Beats of IIT & Vj 1749188 —'0011725 -+:0007050 —‘0018775 | 26
Hqual Beats of IIT and 4 1749674 — 0011239 + 0008994 — 0020233
Qycleiof 22) 6. cues .| 1745200 — 0015713 — 0008902 —-0016811
Perfect 3rds and VIths 9 f — ‘0017983 — ‘0017982 0
Enrors of III and V eq. and op.}* —‘0010790 +:0010790 — ‘0020580
Sauveur’s Cycle of 43 ........ 1750175 — ‘0010738 +-0011008 —0021736
Woolhouse's Cycle of 19 ,,.... ‘1742807 —‘0018106 — 0018474 +-0000368
Drobisch after Delezenne ...... 1751830 —:0019683 +:0015218 — 0026901
OMOEA, ahoon nao mninccg 1742796 —:0018117 —‘0018518 +:0000401
Oy clevoniG 7a vrniicicanrirsiet 1752270 — ‘0008643 + 0021378 —-0028021
Romiew’s Anacratic ........4+ 1751938 — 0008975 +:0026050 — 0027025
Musicians’ Cycle of 55 ...... 1751456 —‘0019457 --'0023878 +:0004421
Marahisia vein cnieisttaietes wast tsk: 1752790 — ‘0008128 +:0021458 — ‘0029581
Drobisch’s V and III combined] 1754169 — 0006744. +:0026974 — 0033718
Least Wolf Errors .......... 1755418 —°0005495 +:0031970 — ‘0037465
No Vi WiOolBiSscaccreeue tees 1755562 — ‘0005351 + 0032546 —:0037897
FEBMOTONTIC: \torssranteratermatriaess *1756008 — 0004905 + 0034333 — ‘0039235
Least [iL and V Wolves...... 1757201 —:0003712 +-0039102 — ‘0042814
Gyelelof 46) os. vedieicetc esate 1788940 | —:0021973 — 0033942 +:0011969
III and V Wolves eq. and opp. | 1757557 — ‘0003356 + 0040526 — ‘0043882
Drobisch’s Cycle of 118 ...... 1760259 — 0000654 +:0051334 — 0051988
Least Wolf Beats............ 1759275 —:0001638 +:0047398 — ‘0049036
Cycle of65 ....0....0. 6.4.5 1759867 — ‘0001046 + 0049766 —:0050812
INORUISW VOLE rae trcterearee nae 1760300 5 | —:0000613 +:0051498 —-0052111
Drobisch's Violin ...........- “1760322 4 | —:0000591 + 0051586 — 0052177
No 8rd Wolf .............. 1760368 3 | —-0000545 +:005177 —-0052315
N. Mercator and Drobisch ....| ‘1760800 2 | —:0000113 +:0053498 —-0053611
Oycle of 26 .............05- ‘1786700 | 50 | —:0024213 — 0042902 —:0018689
PYTHAGOREAN..... 0... 0000s 1760913 1 0 +:0053950 — 0053950
Error of V and 8 eq. and opp.. .|-1733938 | 51 | —:0026975 —:0053950 +-0026975
0006077
0003873
0008306
‘0007556
0006140
0002177
0002378
0002563
0002432
0002961
0009600
0013524
0017734
0018255
0019940
“0002794
0003511
0004297
0004397
0004714
0005648
0004461
0005939
0009584
0007554
0008164
0024829
0012335
0026391
0039960
0034669
0037795
0040169
0040292
0040549
0043004
0019977
0043659
0032183
0008628
0008651
0008703
0009185
0006244
0009314
0009028
a
1864.] Mr. W. . LU. Russell on the Calculus of Symbols. 423
“On the Calculus of Symbols.—Fourth Memoir. With Ap-
plications to the Theory of Non-Linear Differential Equa-
tions.” By W.H.L. Russexz, Esq., A.B. Received July 31,
1863%*.
In the preceding memoirs on the Calculus of Symbols, systems have
been constructed for the multiplication and division of non-commutative
symbols subject to certain laws of combination ; and these systems suffice
for linear differential equations. But when we enter upon the consideration
of non-linear equations, we see at once that these methods do not apply.
It becomes necessary to invent some fresh mode of calculation, and a new
notation, in order to bring non-linear functions into a condition which
admits of treatment by symbolical algebra. This is the object of the fol-
lowing memoir. Professor Boole has given, in his ‘ Treatise on Differential
Equations,’ a method due to M. Sarrus, by which we ascertain whether a
given non-linear function is a complete differential. This method, as will
be seen by anyone who will refer to Professor Boole’s treatise, is equivalent
to finding the conditidns that a non-linear function may be externally
divisible by the symbol of differentiation. In the following paper I have
given a notation by which I obtain the actual expressions for these con-
ditions, and for the symbolical remainders arising in the course of the
division, and have extended my investigations to ascertaining the results
of the symbolical division of non-linear functions by linear functions of the
symbol of differentiation.
Let F (a, ¥, Ys Yoo Y3 + + ++ Yn) be any non-linear function, in which
Yrs Yr, Yo » +» + Yn Aenote respectively the first, second, third, .... mth
differential of y with respect to (a).
Let U, denote fdy,, 7.e. the integral of a function involving 2, ¥, 445 Ya 00+
with reference to y, alone.
Let V, in like manner denote = when the differentiation is supposed
Yy
effected with reference to y, alone, so that V,U,F=F.
The next definition is the most important, as it is that on which all our
subsequent calculations will depend. We may suppose F differentiated.
(m) times with reference to ¥,5 Yp_1, OY Yn—2> &C., AND Yn, Yn—1» OF Yn—2s
&c., as the case may be, afterward equated to zero. We shall denote
this entire process by Z), 2}, Z,0%, &c.
The following definition is also of importance: we shall denote the ex-
pression
d d d d d
eee dy? a 7 a ee ae
by the symbol Y,.
* Read Feb. 11, 1864; see Abstract, vol. xiii. p. 126.
VOL. XIII. 21
a ee o * eS ED Ear, oc ee a ee
AQ4 Mr. W. H. L. Russell on the Calculus of Symbols.
Having thus explained the notation I propose to make use of, I proceed
to determine the conditions that F may be externally divisible by = or,
in other words, that F may be a perfect differential with respect to (7).
It will be seen that the above notation will enable us to obtain expressions
for the conditions indicated by the process of M. Sarrus. )
It is obvious that if we expand F in terms of y,, in order that the sym-
bolical division with reference = may be possible, the terms involving
Yn>o Yrs &C. must vanish. |
Hence V,? F=0, and consequently
| FH=ZF+y,0!,F,
where, of course, Z2F, Z',F do not contain y,,
Hence we have
£U,a2.E) =Y. -1U,12',F =e YnL',F,
and therefore F becomes
£ (U,30,F) Ste epee a
and if R, be the first remainder,
R,=Z,F—Y,,_,U,12',F.
The condition that this may be divisible by = will be, as before,
C—O hence R, becomes
Lia Zn —Z)_1Y,1U,12Z',F + Yn (Z'_,ZoF — 2, 1¥n-1 naan) :
Now
2 p-1(En POEL, Nn sUya8'yB) =
Yn-2U of n a ZF — Y¥_2U non 1 n1U, il). F
+ Yn (Zins ZnF —Zi, YU, aZ'nF) ;
and if R. be the second remainder, we find
R.=Z)_:Z),F —Z)_1Y,.U,.1Z),.F
= Y¥,-2U pn 2Z'n_1 ZF + Y,-2U,-24naYn aU, ZF :
the next condition is V,,_,.R.=0, and therefore
R,=Z)_ LZ) ZF
— Zyoin 1X nO 1h’, F — Zn_2¥n—2U 2, a ZF
+2) oY n—2U 28’ n_1Vn1U ns Z' nF
+ Yn Z,-2L, ZF —Z', LZ 4 Me Pee AGS *s
Diy 2X p20 pod nr ZF + Zn _2¥n—2QU ya 2Z'n-1 nL pr nF).
Mr. W. H. L. Russell on the Calculus of Symbols. 425
But :
fF VUca(2hy sh COP 2',_ 2h SY Uy ali
— Zi, 2X n—2U 2’ ys ZnF + Zin 2V ns nL! ny 1Yn—1 ra Zik) }
=Yj-3Un_3(Z'n—2Ln1Z,F — 2’, Ln iY n1U, 1Z',F
— Din 2Xy—2U Lin LF + Z'n_2¥n2U py 2L'n1YnUnaZ',F)
+Yn-9(Z'n—2Lp_10),F —Z',_ LZ) 1 Y,-1U,_1Z',F
— Dn 2X n—2U nl’ ZF + L'n-2¥ n—2U p-2n_1¥ n—1U, 12 ) 3
whence we find
R3=Z,_2Ln_1Z,F —Z)_oLn_1Y,1U,1Z',F
—Zi-2¥n—2U y_2L'y_1ZnF + Zp_o¥n—2U y_2Z'n 1 Vn 10, Zi nF
—Y,,-3U yn 3Z'n2LZn a ZnF + Yn 3U n2Z'n—2Zn—1 Yn1U np 1Z oF
+ Y,,-3Uy3Z'n2¥n2U 2 Z'n a ZnF
a nan aL nan 2 noi na Una ak.
Hence we infer the following rule for the formation of R,.
Construct the term
MUA a opcik _,4U, Li Gee peep) ee oA ne ce
wee SN pea ete Dre ee ss Ue eZ
In any symbol Z’,, the accent may be changed into a zero, 7. e. we may at
pleasure substitute Z?, anywhere for Z’,,; but in such case the previous
symbolical factor Y,,_,U,,_; must be omitted. This term is positive or
negative according as the symbol Z’ occurs an even or an odd number of
times in it; the aggregate of all the terms thus formed constitute the re-
mainder R,, and the conditions that F may be externally divisible by
a are
dz
Ve R06; Vio —0; Vion; Wael t= 0, &e.
We shall now investigate the conditions that < +P may externally
a
divide F where P is a function of (7) and (y).
As before, V,F=0, and in consequence
F=2AF+y,Z',F.
Now
‘ a PU, 2,F=Yo1 pond we
+PU,2,.F+y,2/2.
Hence we shall have
R,=2.F—Y,,_,U,,_,Z',F—PU,_,Z',F.
We have V7,_,R,=0 in order that this remainder may contain only the
first power of y,_,, and
R,=Z)_:Z2)F—Z)_, n—1U y1Z',F —Z)_,PU,,_1Z',F
y. n~i(Z Ze —Z ith dU pik oe Z',PU,1Z "nk )s
212
426 Mr. W. H. L. Russell on the Calculus of Symbols.
since
= 2 P) U2 Din aZnF — Zi, natin iA ae
—Z', ,PU,4Z',F) =
Yo 0U 24, 2a Te YU, 24, 59,50, 52,8 =
Y,,2U,, 52’, 4PU,,_,Z',.F +9. (2), ZOE
—Z',4Y,1U,:Z',F —Z',_,PU,_,Z',F) +
PU Ay OE — PU, 7 2eN, Wn e
—PU,,-2Z',-1PU, 1Z',F.
Whence we find that = +P divides R, with a remainder,
ny
R=) {7h Rey, Uae
—fi ,PU,G7,.F“Y;_.U, 57, Ze
Vp $25, a Mini Un _iZink 4 YU ee) os Pee
— PUL F(Z PU. 6A N21 py es
+ PU Aaa eU, 3a ak:
Putting V;_.R,=0, we find in like manner,
Rs=Z)_oZ) ZF —Z)_oZn_iV,1U0,1Z',.F
DP Fe a PU Lin — Leno \ pio eae
+2i2Y, Up Ao V,aU, 17,8 +2, 2%, 2, eee
= Zi2PU, f'n Z¥ + APU, 24, 4¥, 50, aa
=F ZpeePUpsHi, a. PU, «Zi re Nis Uy hy of) Znk
SEN LU 557, eo Leia NG, 4 Uplate ae
SY UA ol oagletle Ae
te Kg Upeg hl grate Voge quod nv,
cath ier OR AR Oo UP ai ee UL aya Ie
me Uy A, SY, pU nA PU ak
V2 U p2sZ no Pn Un eA Ze
mee Ge Oe Ae dl US A ec DINE EE! ©
—¥ U7, ol Uae Zi Palo Ane
— PU,_34', oF, Zn? + PU, sf aoZn a
+ PU, 24’, oft _-4PU,1Z',F + PU; 7 Ye U2 ee
=P eT Sa ee 7). Von ae ke
ae Uy eel) oN noe Shi Ua
See: UP Sy GaaN 2! Opt oy filam Seal Si
PM Zia NO ok Zi yn N yep eed
= PU, a oP eA PU aA
We see at once that the value of R, in this case can be formed from that
calculated in the last example, by writing Pat pleasure for any one or
Mr. W. 8. L. Russell on the Calculus of Symbols. 427
more of the symbols Y, and taking the aggregate of the terms so formed.
The conditions of division will be, as before,
VEE =e Vt 0 Vokes ee
Let us now investigate the conditions that F may be externally divisible
ad
by a
We see at once that F, as before, must take the form Z°F+y,Z',F, and
also that Z’,F can contain neither y, nor y,_;. Hence we shall have
V2F=0, and also V,,_,V,F=0.
Now
Ee 7) 2 be Ven UE
des B® dnt "2 Yn-1¥ n-26 Un-24 n
=XY,,_.U,_.Z',.F +y, XZ) nF + ynZ' nF.
Hence we shall have
R,=2F—XY,,_.U,,_2Z',F —y, 1 XZ',F;
when we must introduce the conditions
v2, — O07 ani V5 ¥, 2, —0:
consequently we shall have
RZ! _,7oE— Zo XY, U3 FF +
(Z', :Z0F —Z',_ yXY,,-2U nL, F —Z9_ XZ, F )yn_1
Now
5 U,-s(Z'ns2RE ci Zi ya XX n-2U, 2’ .F
—Z°_,XZ',F)=
XY, 30 n-3Z'n ZF ae XY, 30, 3Z'n_-1 XY n_2U,, FF
“Ee a XY,,_3U,,_3Z5 :XZ',F == (XZ, 1Z,F a
A ee Ve UAE ere XZ XZ )yn—2 ae
(Z',, Zi F— Zin XX n_2U ZF — To XL Ey,
Hence
Ro=Z)_ ZF —Z)_,XY,,_2U,_2Z’,F
SON a aU GA yp Oy Pe OY Wh pA 1 Nagy ee gk
= €Y,,U,. 42 ZF + (XZ, XY, UU, 4 4¥
+XZ°_,XZ',.F—XZ', ZF )y,_>.
Introducing the conditions
Vii-2R.=0, V,_3Vn-2R,=0,
we find
R, — (jae Soca SM or
PE oie GRY 4g U 2 2 — De RN GO eng ZOE
=fZe ok Vn 3U gM peek Yn oA aE
+2 2X Vn 3Un_3Zn XZ) F + (Zi!) 2Zin Zak
—Z', of XY ,_.U,_.Z', F—Z',_oXY,3U,,_-3Z', 1Z2F
SPL oO gig Un Fie RY SU pe Fie k
4+Z', oX¥,_-3U,_3Z_1XZ',F +20 _,XZ',_ XY,,_2U,_.Z’,F
+ Zi-gXZ)_)XZ',,F—Zo_ XZ", DOF )yy_2
428 Mr. W. H.L. Russell on the Calculus of Symbols.
Now
a? ' 0 70
qin n—2Lin1Lnk —
Zi, -2L, XY n_2QU yp 2Z',F — Zi n_2XV,_3Un_3Z, sZAF
+Z', 2X Vp -3Un_sZ'n_1 XY n_2U,_20',,F |
+ Zi, 2X Y,3U n-sZn1XZ',F + Zh 9 XZ", XV n_2Uy20'F
+ Z)_oXZn_:XZ',F —Z)_.XZ',_ ZhP)
= XY, 10, 4Z'n_2Zn 1 ZF
—XY,,_ 0,2 p22, s1XY,2U, 20, F
—XY,,_,U, 12, 2XY,_3U,,_3Z', ,Z,F
+XY,,_,U,,4Z',_2XY,,_3U,,-3Z', 1X Y,,2Uy_2Z'.F
+XY,,4U,,4Z',, 2X Y,,_3U,,_sZ)_.XZ',.F
+XY, U, 2) XZ, XY, U..78
+XY,,_,U,,_,Z20_.XZ7_,XZ'F
—XY,,_,U,,_, 2 2XZ', s ZF
+ (XZ, oF), ZF —XZ', Zi XY, .U,_.Z',F
—XZ',,_.XY,,3U,-3Z',aZF
+XZ',_2XY,_3U,_34', 1XY,_2U,,_24',F
+XZ', oXY,3U,sZ,1XZ',F
+XZi_-2XZ', :XY,,2U, 20", F
+XZ0_,XZ°_,XZ',F—X2Z_,X7', ,22F)y,-s
(45 2, 54,0 Zi, 0, sk, ee
— Zin 2X ¥n_sUy_3Z!naZ¥ + Z',_2X Yn_3U ng Z'n1& Vn-2U p24 F
+ Zn 2X VY, -3U yn _3Zn1XZ',F +2) XZ, XV n-2U yf nk
+2_,XU2:KU/,B—2, XU, OR) y yo
We thus find
R3= Zio, ZF — ZZ, XY »2U no, F —
Zi, 2&V,-3Un-3Z', 1ZnF + Z,_2XY,3U,_3Z/,1X VY, 2U no EF
+ Zi XY, 3Un 34, 1X2, —XY,_,U,,_ 4, 2A gee
+XY,,,U,_,4', 24 XY, 2U,,_ 22", F
+XY,,_,0,_,4'n2XYn_3U,3L'n ZF
— XY ,,1,U, 2 2X, U2 RV BU neo
—XY,,_,U,_,4/n 2X Yn3U,_sZ,_ XZ), F
—XY,,_,U,_,27-2X0', aXY,_2U, 20) EF
—XY,_,U,_,27_.X 2) _,XZ' EF
=F DG Gc, Ula, nary OA pa Ze
+ (XZ",_oZ) sXY,2U,_2Z', F—XZ',_.Z) sZ0F
“eh, SON ee, 52,
—XZ', oY, sUy_sf'n1XV,2U p22 ,F :
— XZ’, 2X V¥,_3U,-s4,1¥4Z',F —XZ)_ XZ! XY, _2U p20), F
+ XZ) XZ XZ', B+ XZ) XZ ‘nn LB Yn—s) :
Mr. W.H. L. Russell on the Calculus of Symbols. 429
Let us now assume
; R,=M,+N,yn->
Then M, is formed according to the following rule :—Form the term
ON Wie Ae 6, Ay ao RN gery eee pas
eaiviveive DEY ea ee VD’ E.
Z',, may in any place be changed into Z',; but in this case either the
preceding XY,, .U,,-. must be omitted, or the succeeding XY,,_,U,,_1
changed into X. The signs of the terms follow this law. A term not
containing X introduced in place of XYU is positive if Z' occurs in it an
even number of times, negative in the contrary case. But every X in-
troduced in place of XYU occasions a change of sign. The aggregate
of all the terms thus formed will give M..
We form N thus: construct the term
et ONG Ur Unt p iy see a VIA
and a precisely similar rule holds good. R, is subject to the condition
Ve Oe 2” hu == 0.
Let us now investigate the criterion that F may be divisible by
dl” d
ait P+
where P and Q are functions of () and (y).
Proceeding as before, we have
a? d P ie
Wie aa PS == Q)U, 2 r=
(z P) (Y,,-2+Yn—1Vn—2) Un_2Z' nF + QU, 20’, F
= (XY,-2+ PY; 2+ Q)U, 2ZnF + ynaA(X+ PZ F+ yn ZF.
The form of this equation gives us the following rule to ascertain the
successive remainders. Construct the remainder in the last ease as before,
and substitute at pleasure Q in any place where XY is found, P in any
place where X is found. The aggregate of the term thus formed will give
the remainder in this case.
We now investigate the condition that ie may be an external factor
of F.
We put, as before, F=Z)F+y,Z’,F, where Z',F must contain neither
Yn—1 NOY Y,_2, Which gives the conditions
ViF=0, ViaVAL=0, V,,-2Vr,H=0.
Now we have
a? a?
beth ZF) =
dix® (U,,-4' nF) dic”
@? , If
=F Yn 24 nt ar Yn—h iby)
= XY ,,-3U,_34',F oe ¥ nad Z a te 2y n-1 XZ H sf Yn aes
(¥), —3 a Yn— oVa =) U,_34 ful
430 Mr. W. H. L. Russell on the Calculus of Symbols.
And we consequently obtain
R= Zlk— KYU, Se Fy JEU 9y, F.
Introducing the conditions
Ven 0; Veo hi — 0; Vee
and expanding in terms of y,_,, we have
B= (22_2F— 20 XY, 5U,22',F) +
(Zi Pgh fy i XY 523 U nisl Ya 1 Ena
Yn Yn nL, F— 2y,_sZ>_ 1 XZ" EB.
As the coefficient of y,_, in this cannot contain Yn—2, We may write this
expression,
R,=(Z) sa — Be XY, 30,34, Yn ot
4 (Zn, ZF —Z)_ LZ", ~X7Y, 30,32", F 22) _2Ln_ 1 XZ! nb) Yn
Let us now assume
Rn=L,+ MiYn—-m—1+ NnYn—ms
where R,, is the mth remainder, and N,, does not contain ¥,,_ 1 OT Yn_m—2
Hence, expanding in terms of y,_,,, we have
RS Za ae Ze ls,
a5 (2) _,,.M.,, + Una ‘nm ML) Yn—m-1
ae (Zire Ne Vil Nn Un
=) Aaery Lites ay Spain| Da ae
gl Skee ey Arman, Ui eS AO DI
Now
B}
= : Us CAE APN Op == Vipera pee) t
aaa a fay —m—s s+ (Speeaietir | io i Urs
ST a: ie pla Le ol aio, Nowe
22 KW) OU) 5(Z) o's oi at Zi ig ie ee
== RA iat pees te Di iphy Dea ND - Yn—m—2
DR TE NDGA GP AD ae a INA eae
BELG step Lg = Lit oN gc
Hence (R= (Biome Mncm—sU fa, nolan,
UG in (fe eames Fa
SL ga ma at gare egg Ny
SDR! eh SM Le My + 2X2) Zin Nn )Yn—m=i*
Now consider for a moment the equations
Lnu=G,L, + HM, + K,Niw
a Gi lin == H’,,M., == I< Ns
Nru=G",L,,+ HH", M,+tK,Niw
Mr. W. H. U. Russell on the Calculus of Symbols. 431
and suppose that
Dinas = ee Sal iM,,i+ N41
=) Lot poM 2+ v2N,_2= &e.
= Ee Ee Ne
—— ee.
Then we find
dy = Gn.Gnr—1 == EG: a= KG
A, — G36, 1G. 5 te HB, GaGa. =i K rns et Ogee
1G be Got A. iG yo K, EE oe Gee
+G,,K,,1G@", 2+ H,K' ni G' not K,,.K",-1G"'m
7. G.G.,_.G, .G,.,+ H, GG, Gs
See RG iG oa, Gb Ge GC...
eee 5G Gs Kk HG G's
eG, kG) Gee Ke GG.
SP Ee yO tat Og 9 Ae gy Oe EN yg oF ass
ee GE Ge aK Gr on Gs
+ GH EG ee-+ HW ng Bak oG ses
SP a, 2G ae EK, LH 2G ies
eG. Red Ee |G BW KRY Ae Ges
Stes Or Crea Ke Gy ample, one ns
11 ONS id SGA 8 sre SM Coe i WEN read GS eters
SN Ee es ier curt ED AR ecg ake
pee Ke Ge ee WA, le a oss
ripe, Mer pea Rigo sass
Hence we obtain the following rule for the determination of X,.:— Write
down the term G,,,G,,_:G,,......G,_,. Wemay substitute H and K at
pleasure for G anywhere except in the last factor, which is always G.
Whenever we put H for G, the succeeding letter is to receive a single
accent ; whenever K for G, the succeeding letter receives a double accent.
The aggregate of all the terms thus formed will be A,, and we may of
course obtain similar expressions for p,, &c.
Now if we put
-Q?
G,,, = ae
(22-4-y2) sin—1 —_" __
Vere $, (@® +9"),
— (20° + 2ay’ iE
ABA: Mr. W. H. 1. Russell on the Calculus of Symbols.
This equation may be written
ad a : 2 2 d ad 2 2\2 44
(05 Vas) 20 +Y) (#5, age) + HIE,
ile iO Saas yb ft bo es 5 tae
1% Vg MOTI)? Gy ag
which may be treated as before.
In order to find the most general form of equation to which the symbols
@
dy
d d\” d d Ne ae : :
Ge —y a) a UA zy +y a and z°—y’ likewise combine according to
the laws of algebraical symbols, we shall take (oF +y = y"to avoid the
a Bart, : A
fe ae and x°+y” give rise, we must determine the expansion of
negative sign.
Now the expansion of (es +y <\ will consist of all the terms of the
(+a) (va) (a) (a)
C464 .0. bebe onan,
<, and dy for 7 g —, where it is to be understood that
dz and dy do not apply to the aha
Moreover we shall use, as in the third memoir,
a—l a—2 a—r+l] ;
form
in which
We shall write 6, for
a, for @.—5—* B+ +s 7
Then we shall have, if a+a=7,
d\& d \@ gq Goa gd’ —2
ests, — ) mre ye od Cae ues xe?
(3) (vz) OY ye dga WN" Gat dae)
ia
+a,0% 0, y% yd ee
Again, a+a+6=n,
(yaa)
I Te ( dy (vz,
a dn aot an a+b ce Ore
digas TO Oe a gatia t a Oa Te gato
$5, y2t? Fae Oo"
dy* datto—3 **
Mr. W.H. 1. Russell on the Calculus of Symbols. 435
+a,xry? 6 aaa wee +a,b, y? 3 xb, y% ie aol
1 ] dy*- yet b« att y dy*—deute—"
—3
+4, b, y? Py vt by" d”
dy*— 1 dayats—2
qd—2 qd-3
6b 2 7,0 b
HY 0x6 v4 dy*— 2 yat 6 a oe by On U2 0y ge dy* 2 yet o— 1
Bde ss q2-3
PON OS aps dear t
+ &e.
And again, if a+a+6+ (=n, we shall have
yay a2)
( =) (9-55 ( dy Te
=yttb pee et +6, y2*? x8 a fe an}
dy**B dete dy*tB daets—1
n—2
PR gah aes TRO ye a 0
qd—3
dy +B yats—3 Hits
g?-) : a qd”-2
a, vatBy? dy dy2+B—1 agate + a,b, xB y? dna Oy Y dyttB-X dageto=1
qd»—-3
9/0
+ 0,6, xP y On wo Oyu" Ger dee +...
n—2 d™—3
ae eee
b ~a+B e2
+ ay ¢ y dy*+b—2 daets—i
qdn—-3
dy*+B—8 datt 6
claerele
=F ay? wotB O°, y@
q”-) ‘ x dn—-2
+ Bert Poy pate deat TBE eye at Tarai gat i=
qd2—3
+B, 6,0 byy2t? Orn, 0 dypP) dato
qn—2 qd’—-3
+ fa, wtb by, y?dyy% dyrtP—2 qcats + a,b, 8, byy? d,* 0 yy" dy? *B-2qlpetb-1
2-3
+ 2,3, 2 t8 0,4? Oy y" dy*tb—3 datto—]
Op tet
436 Mr. W. H. L. Russell on the Calculus of Symbols.
“eee 4.5, 8, 08 5,ce%82, 248 ee
dy* +82 duets 101M: yd dyB=2 qyato-1
q”2-3
dye BS dogo
+024 3%, ye?
+ a, 3, oyy? yo yy
Heo:
+B, x8 tB§, yate ee
Dy ee dxete
We are consequently able to see that the bis term of
(2 =) (vz) e a (a)
is
qy> q! 8 xp! got ais
By Cr Byte By Spee OLY? Py. .0L 08 SP la pai igo
where
pte +o. -=7, 0 . 6. 8
Pte + sey vw is 2 es 5
and
r+s Me ig 2 es
d NP i 8
Hence the general term of (« iy +y aE ) will be
q2-m
> PP ae S Ont st* Bg Gy one OLY? RYO, OO ho 7 ea ee
under the ‘ohteLEE (1), (2), (8), and also
a+64+...+ta+6+...=n.
Calling the expanded form of (95+ y za): An, it is easily seen that we
can resolve all linear partial differential equations of the form
S(e—y)Anit+f,(a?—y)An-1 Uu+f,(e—y)An-1u+ &. =F (a, y).
The same property is possessed by a great number of other symbols.
Let us examine the condition that ,
(ax + by +c) *. —(a'ae+b'y+c') =
and
Az’ +2Bay+ Cy’+ 2Kv+2Fy+H
may combine according to the algebraical law. The condition is easily
seen to be
(Av+ By+ E) (z+ by+¢)—(Cy+ Be+F) (e+ o'y+c')=0,
from whence we have
Aa —Ba'=0, Bod—Cd'=
Ab +Ba =Ca'+ Bo’,
Be +Ed =Cc!+ Fd’,
Ea +Ac =Fa'+Be',
and
Ec =Fe’.
ha pile teat Fa
Mr. W. H.L. Russell on the Calculus of Symbols. 437
We may consider B=1, which gives the following conditions: a'/b=a0',
a=b'. Also
!
A= ee C=] —— =-_,
a a
And the symbols may be written
d 1, &
b(ax + by +c) ae meee | tyere ay
and.
a+ 2ab xy + by? + 2acle+ 2cby+H.
It fallow: hence me in order to find the form of the differential equa-
tions to which these symbols give rise, we must know the expansion of
d d\” :
(x are +Y a) , where X and Y are functions of # and y.
The expanded form will be a series of terms like
d \B d \? d \* d\*
(rq) Ga) ("a) (a).
We must consequently find an expression for (x =) in powers of Le It
must be remembered that X is a function of x and y, in which (y) during
the present process is considered as constant, and therefore X may be looked
upon as a function of (x) only.
Now we shall find after a few differentiations, that
d 5 ae a’
(x dz} = dx’?
+ (X6X* + X°5X3 + X°SK24 X*9X) =
+ (XdXOX? + XSX7SX?+ X*IXOX?
+ Xo
+ (XdXOX6X?+ XOXdX*5X + Bs a8 =
+ Xoxexaxex 2,
dx
Now let
x xy ee ae
( Z) = =iG ee da" nase di"?
ee
Then
X=, X*OXFOXY...
where there are 7 0’s, and a+(B+y+....=n. Hence we shall have
CHa CH Cs
438 Mr. W. H. L. Russell on the Calculus of Symbols.
dp dB
= ( )
1% eget ae as grat}
Le p-2
be ee Oo A= Stag
pee See 8 4. ee
4 aye dy*— —2
eae (2) d4—2
“teh Foy XO Fh
oe it : obvious that the general expression for the expansion of
(x< <+¥ =) will depend upon principles not materially differing from
oo one considered.
The symbols we have already considered are only of the first order of
differentiation ; we shall show that there exist symbols of the second order
which combine with certain algebraical quantities as if they were themselves
algebraic.
Let us take the symbols '
a a? d’ ,@ , a
oe 5 Aen” dor dy ay a ap + 2a rn +26 a +e,
and
Az’? + 2Bay+Cy?+ 2A'r+ 2Bly+H.
Proceeding as before, we arrive at the following conditions :
Ab +Be =0,0 0.0."
Bé +Ce-=0; 2 2 ee
A+ Ble=0) 4. he
Ac@!+- Bb! = 0, yer wc yuk ie 2 ee ar
Be! +Co'=0,.. . 6
Aa +Bé o ay 't oo Deke)
Bas = sg be oh
Ala+ een oo Ss Se
DA ABB 42004 doll 4 40H c= 0 . 0. ee
Whence we have, putting B=1,
A=—
and with the following conditions,
ac=—6*?, ac—bd'=0
4a! A'+ 40'B/+e=0
the condition a!e— 6d! may be otherwise written a'6—ab'=0, in consequence
of the equation ac=0’.
It will be observed that several of the nine above equations are not inde-
pendent of the rest ; so that the result is much simplified.
p) C=—
Mr. W. H. L. Russell on the Calculus of Symbols. 439
I now proceed to apply the calculus of symbols to the solution of func-
tional equations.
daz
i =X.
Let
Then the following formule are known:
d
MODS =f Xe +1)
Gone
(EY) =x +2)}-
&e.
(cP a) -f0) =fyUy(@) +1)}-
These formule may ee thus expressed in the notation of the calculus of
symbols: if p= a ms m=, § a functional symbol acting on f(7) in such
a manner as to convert f(r) into fy—'(yr +1); then
pf (=) =Ofr .p,
a general law of symbolical combination due to Professor Boole.
We will now consider two cases of internal and external division in which
the symbols combine according to this law. The results, as will appear
afterward, will be found useful in the solution of functional equations.
And, first, for internal division. We shall determine the condition that
pv, (7) +,(7) may divide p”$,(7) +p” dn—1(7) +. oe es The process will
be, mutatis mutandis, the same as in my former memoir. The symbolical
quotient is
p2-} ont n—2 Qn-17 Wot p Ont .
of +p oe a Soe ee:
and the required condition is cea by equating the symbolical final re-
mainder to zero, and we have
| QT bx Yor pom Wor ve 9 Pat —
o,7—wW,70 We +W,78 Wis ee te —&.twv, Wee 0 : Pee
6 affecting every part of the term which succeeds it.
I shall now give the corresponding condition for an external factor. The
symbolical quotient is
. Vie ae oe ar}
n—2 4 2Q—(m—-1) 1—2 —(1=2) 4, -A—(—2)_—_ =!
. yr z! { oe eee yr ae Ga TR a
The required condition is found by equating the final remainder to zero;
we have
Wor Wom WoT py Wor Por=0
oT — Gut +9 ~ Be. + gg HoT g~1 YOR g—1 YO g~1 YoR= 9
As ae Ee ame aaah
6-1 in each term affecting ever ything which comes after it.
I conclude with some examples of functional equations.
Let the functional equation be
f(0) of Fs FO):
VOL. XIII. 2
4.40 Mr. W..H. L. Russell on the Calculus of Symbols.
this may be written ©
d
f(a) —ae* fe) =F (2),
or
K(2)= see hh
1 —qede-?
Afi fo gy bil
={1 oo ieee Re a C2)
=F a ee
(2) +aF 7 ate OTe hE
To make this solution ee we must add a complementary function,
and we have
C C,
(Va) (— Va)”
&
+F eta aE ot Ch. eee
Ore V1+ ne i poe es
As an tpi of te put F(2)=a, and the series becomes
Oa an
Bee 2 et
* Tiga * Vicar 2 vise
= ae Mg e (lee ae oe
: NV x 0
_ 22 3) @seedp
REN a é 1— ae—2202
As a second example, we will take the equation
f(=<5) ar ( a) tYO=FO).
This equation may be written
g,4_ ee
Fe die 2h
d —
(e Be aL ye) Fa
(= 22) =y@).
and the functional equation resolves itself into the two,
(54) -FO=x
Now let
and.
x (se) -x@=FC).
which are known forms.
Mr, W. H. L. since onthe Calculus of are Add
As a last example, we will take the equation ~
32—2 v+3a—1 .2a—1:
es Ue i on otetfe)= F(a); 4
or putting
Seis 2 :
(e—1) is = 0, wv=n,
d
ze
= hel : ; ¢——
we can write the equation (since p=e *—*)
2n*—7r—3
\ep (==) 4 +m (741) \ u=F(2).
Applying the method of divisors, we see that if the symbolical portion of
the first member admit of an internal factor, it must be either p—* or
p—(r-+1).
Now in this case
oft )=f(— )p.
ll )
Wherefore the meres ¢
Po™ — oer i ~ + bor io ae —&e. +70 =
becomes, if we A the factor p—7, and put
Yea], syn —m,
Cea @(=— 5) - ae ery
Hence
afte) =f (=
Wor Wet Var _
ie aati
an identical equation if we put for the symbol 0 its equivalent as given
above. .
Hence p—z is an internal factor of the symbolical portion of the first
member. Effecting the internal division, we have
(o—@+1))(p—a flo) =F).
(e i f(z) = x(x),
and the equation resolves itself into the two,
(ep—(7+ 1))x(@) =F@)
Let
and
r (p—m) f(x) = x(2) ;
x (= = F(z)
and
AAA )-A@ =x
2K 2
442 My. Warren De la Rue—Comparison of De la Rue’s {| Recess,
forms which I have considered in my memoir on the Calculus of Functions
published in the Philosophical Transactions for 1862, in which the general
solution of the equations |
at+be
go) —x(w)g | Eb =I),
where ¢ is the unknown function, has been obtained.
COMMUNICATIONS RECEIVED SINCE THE END OF THE SESSTON.
I. “ Comparison of Mr. De la Rue’s and Padre Secchi’s Hclipse
Photographs.” By Warren De ta Ruz, F.R.S. Received
August 8, 1864.
T have stated, in the Bakerian Lecture read at the Royal Society on
April 10, 1862, that the boomerang (prominence E)* was not depicted on
Senor Aguilar’s photographs. This is true of the prints which came into
my hands in England. A visit to Rome in November 1862, however,
afforded an opportunity for the examination of the first prints which had
been taken in Spain on the day of the eclipse, previous to those printed off
for general distribution by Senor Aguilar. I was agreeably surprised to
find that the photograph of the first phase of totality showed not only this
prominence very distinctly, but also other details, presently to be described,
which were quite invisible in Sefior Aguilar’s copies. I had in fact experi-
enced some difficulty in comparing measurements of my photographs with
those of Senor Aguilar’s, on account of the indistinctness (woolliness) of the
latter, which I have attributed to Padre Secchi’s telescope not having fol-
lowed the sun’s motion perfectly. A careful examination of the prints in
Padre Secchi’s possession has, however, convinced me that this was not the
case during the period of exposure of the first negative ; for I have been able
to identify with a magnifier many minute forms which could only have been
depicted by the most perfect following of the sun’s apparent motion. For
instance, my statement that the prominence H (the fallen tree) was not seen
from having been mixed up with the prominence G, is not applicable to
Padre Secchi’s copy of the first phase of totality, for in it every detail of
the fallen tree can be made out. 7
On expressing to Professor Secchi my surprise at the great discordance
between the copy of the first phase of totality sent to me by Seftor Aguilar
and that of the same phase in his possession, I was informed that after a
few positive prints had been taken from the then unvarnished negative, it
was strengthened by the usual photographic process with nitrate of silver.
This I look upon as an unfortunate mistake, as the images of the promi-
nences were increased and their details hidden, and the beauty of the
negative for ever lost.
It occurred to Padre Secchi and myself that although there was no hope
* See Index Map, Plate XV. Phil. Trans, Part I. 1862.
1864.] and Secchi’s Kelipse Photographs. 443
of procuring more satisfactory prints from the original negative of the first
- phase of totality, yet some advantage would arise from taking an enlarged
negative from the positive print in his possession, although it could not
be expected to yield as perfect an impression as might have been obtained
by enlarging from the original photograph. The enlargement has been
successfully accomplished in my presence ; and although Professor Secchi
will take such means as he may think proper to make known the results
of comparisons he may make between my photographs and his own, it
will not be out of place for me to add a few remarks by way of appendix
to my paper.
Taking the prominences in the order in my index map, Plate XV. :—
Prominence A (the cauliflower or wheatsheaf) has the same form in
Padre Secchi’s photograph as in mine. It extends considerably less in
height above the moon’s edge in this copy than in that printed off from the
strengthened negative (Senor Aguilar’s copy); the bright points of the
two branching streams which issue from the summit towards the North are
well depicted in the Secchi photograph, but not the fainter parts.
’ There exists a faint indication of the minute prominence B in the §,
photograph.
The convolutions of the prominence C (the floating cloud) are seen in
the S. photograph, and its form coincides absolutely with that of mine; it
is a little nearer the moon’s edge at the point c, probably because the
telescope was uncovered relatively a little later than at Rivabellosa.
The prominence D cannot be clearly traced in the S. photograph.
The boomerang HE is distinctly visible in the 8. photograph ; the point e
is apparently prolonged ; but this I attribute to an accidental photographic
stain, for the bright part ¢’ can be well made out.
The long prominence F cannot be made out in the 8S. photograph, pro-
bably from the cause explained in reference to C.
The fallen tree (Hi in the S. photograph) corresponds in its minutest
details with its picture in my own. The articulated extremity f, the
round points h' h”, the point 4”, and the connecting branch joining it with
the stem are clearly seen.
The prominence G from g_to g’ corresponds precisely in the S. photo-
graph with its image in my own, and a dark marking near g also is seen ;
the narrow portion of this prominence, from g to the point immediately
below A, is not seen in the S. photograph.
The prominence I (the mitre) agrees in form in the S. photograph with
its image in my own, even the faint point zis there seen. This prominence
in the 8. photograph extends further from the edge of the moon than in
mine; and whereas in my photograph the convex boundary next the moon
is cut off by the moon’s limb, in Padre Secchi’s the convex boundary is
complete, and hence in all probability the prominence I presented another
case of a floating cloud.
About midway between G and I there is a small round prominence visi-
AAAs ~~ Prof. Guthrie on Drops. [Recess,
ble in the S. photograph not seen in mine, which may be accounted for from
our different positions in respect to the central line of the eclipse.
Between I and K, at a distance from I equal to about two-thirds the
angular interval, there is in the S. photograph a prominence consisting of
two round dots, which extend beyond the moon’s limb to precisely the
same extent as the prominence K protrudes in Professor Secchi’s photo-
graph beyond the moon’s limb in excess of what it does in my own.
The prominence K has precisely the same form in every respect in the S.
photograph as in mine, so far as mine shows it ; but on account of parallax,
more of it is seen in the S. photograph than in mine.
Beyond K is another prominence, visible in the S. photograph about 17°
distant from K, a small round prominence which could not have been
visible from my station. |
Of the remaining prominences, L, M,N, O, P, Q R, none were visible at
the epoch of the photograph.
In conclusion, the photographic images of the prominences, so far as they
are common to the two photographs taken at Miranda and Desierto de las.
Palmas, accord in their most minute details. The photographs must, from
the difference of position of the two stations, have been made at an abso-
lute interval of about seven minutes; and this fact, while it strongly sup-
ports the conclusion that the protuberances belong to the sun, at the same
time shows that there is no change in their form during an interval much.
greater than the whole duration of an eclipse.
I. “On Drops.” By Freprrick Gururiz, Esq., Professor of Che-
mistry and Physics at the Royal College, Mauritius. Communi-
cated by Professor Stoxss, Sec. R.S. Received July 15, 1864,
In the following investigation, the word drop is used in a rather more
definite sense than that which is usually attached to it.
In common speech a drop signifies any mass of liquid matter whose form,
is visibly influenced towards the spherical by the attraction of its parts, and
whose sensible motion or tendency is towards the earth. This definition
both includes drops with which we are not here concerned, and excludes
others which we shall have to consider; for we shall; have to measure the
size of drops; and it can only be of avail to measure the size of ss drops
as are formed under fixed and determinable conditions.
How many drops, according to the usual scope of the term, are formed
under indefinite conditions. For instance, a rain-drop depends for its size’
upon such circumstances as the quantity of vapour at the time and place
of its formation, the tranquillity and electrical condition of the air, its rate
of motion, the number and size of the drops it meets with in its course,
&c., all of which are fortuitous, or, at least, immeasurable conditions.
With such drops we have here nothing to do, but only with those
which are. formed under fixed circumstances. On the other hand, we
e
1864.] Prof. Guthrie on Drops. AAS
shall have to consider drops which move upwards*. “Drops of this kind
are so seldom. met with that no distinguishing name has been given to
them. We shall find it convenient to include them in the Benet term
drop, though it may appear at first inapplicable to them. —
Without attempting to give an exhaustive definition, it will be sufficient
to define a drop as a mass of liquid collected and held together by the
attraction of its parts and separated from other matter by the attraction
of gravitation. This definition will exclude such drops as those of mist or
rain, and will include the upward-moving drops mentioned above.
It follows that the size of a drop may depend upon and be influenced by
variation in—
(1) The self-attraction and cohesion of the drop-generating liquid ;
(2) Its adhesion to the matter upon which the drop is formed ;
(3) The shape of the matter from which the drop moves ;
(4) The physical relation of the medium through which the drop moves,
on the one hand, to the liquid of which the drop is formed, and on the
other, to the matter on which it is formed ;
(5) The attraction of the earth, or gravitation, upon the drop-forming
liquid and upon the medium, as influenced by their respective and relative
densities, and by variation in the attracting power of the earth.
In order to study systematically the influence which each of these factors
exerts, each must be varied in succession while the others remain con-
stant.
Denoting the three states of matter, solid, liquid, and gaseous, by the
symbols 8, L, G respectively, and considerimg the symbols in the order
in which they are written to denote respectively the matter from which
the dropping takes place, the drop and the medium, we get a convenient
notation.
As we are speaking at present exclusively of liquid drops, L must
always hold the middle place in the symbol.
Of the eight symbolically possible variations, Bid Baten
Q) (2) (3) (4) (5) (6) (7) (8)
SLS, SLL, SLG, LLS, LLL, LLG, GLS, GLG,
(1), (4), and (7) are physically impossible on account of the superior
cohesion of solids over liquids, (6) and (8) are physically impossible on
account of the superior density of liquids over gases.
SLL, SLG, and LLL are therefore the only cases we have to consider.
That is,
* Owing to the numerical preponderance of downward-moving drops, we are prone to
associate the ideas of “drop” and “down.” How far I may be justified philologically
in using the expression ‘‘ drop up,”’ must depend upon the relative primitiveness of the
noun and verb “drop.” Once for all, I beg permission to use the term drop in this more
extended sense.
Of course, in the absence of positive levity, an upward drop can only be caused by the
downward motion of the medium in which the drop moves.
446 Prof. Guthrie on Drops. [ Recess,
SLL, from a solid a liquid drops through a liquid.
SLG, from a solid a liquid drops through a gas.
LLL, from a liquid a liquid drops through a liquid.
Of these three cases, two, SLL and LLL, may be inverted ; that is, the
motion of the drop may be towards or from the earth. ‘The gravitation
of the drop may be greater than and overcome the gravitation of the
medium, the drop descends; or the gravitation of the medium may over-
come that of the drop, the drop ascends. ‘The case SLG cannot be in-
verted, because, at all events, at the same pressure every known gas is
lighter than every known liquid.
It will be convenient to consider the case SLG first, because instances
of it come more frequently under our notice than of the other two, and
because it will be convenient to consider together those cases which are
capable of inversion.
' As we are considering the physical aspect of the question, we will only
discuss those cases where no chemical action takes place between the terms,
and where either no solution takes place, or where it is so small as to be
negligible, or of such a kind as to admit of experimental elimination. This
limitation of course excludes a vast number of combinations, but it must
be made in order to study the purely physical and definite influences which
determine the size of a drop.
SLG. From a Solid a se drops through a Gas.
The variable factors are
1. The self-attraction and aneaod of the liquid :
A. Dependent on its purely chemical constitution. -
B. Dependent on the proportion and physical relation between its
heterogeneous parts, when a mixture.
C. Dependent on temperature.
2. The adhesion between the solid and the liquid:
A, B, C asin 1.
D. Dependent upon the shape of the solid.
3. The adhesion of the gas to the solid.
4. The adhesion of the gas to the liquid.
The factors 3 and 4 may be neglected, as we shall at present only con-
sider the case where the gaseous medium is air at the ordinary barometric
pressure.
One of these factors, namely temperature, though varying in different
cases, may be supposed in the same case to be the same for the different
kinds of matter present. Another factor in the same predicament is the
locally constant gravitation at the place where the dropping occurs. Lastly, —
a condition of great influence is the length of the time-interval between the
successive drops. This interval we shall call, for brevity, the growth-time,
and denote by gt.
If the above conditions are exhaustive, we may assert that a drop of
1864.] Prof. Guthrie on Drops. 447
liquid will always be of the same size, if it is formed of the same liquid
substance and falls from a solid of the same substance, size, and shape,
provided that the temperature remain the same, and the growth-time be
constant.
The size of the drops may be most conveniently determined by weighing
a noted number of them. We are concerned rather with the relative than
with the absolute sizes of the drops. The sizes of drops formed of the
same liquid are proportional to their weights; of different liquids, to those
weights divided by the specific gravities of the liquids.
In the first series of experiments the apparatus, fig. 1, was employed.
The globe A, full of the liquid under experiment, is inverted into the
cylinder B, containing the same. The mouth of A is supported just in
contact with the surface of the liquid in B, by means of the tripod stand
D. A and B are carried on a table, which may be raised or lowered at
pleasure. A siphon, E, leads from the reservoir B, and is firmly held by
the clamp F, The longer limb of E, from which the liquid flows, is
ee
448 Prof, Guthrie on Drops. [Recess,
turned up at the end, and touches a plug of cotton wool at G. The
sphere H, from which the dropping takes place, is hung by three thin
wires from the ring of a retort-stand. The upper half of the sphere is
clothed in cotton wool, which reaches up to the plug at G. The whole
arrangement is placed upon a separate table from that which supports the
balance, so as to avoid the vibration caused by opening and shutting the
balance case. The drops which fall from H enter the funnel L, whose
lower end is somewhat bent, so that the drops are thrown out of the ver-
tical, and all upward splashing avoided. The rapidity of the flow through
the siphon, and consequent dropping from H, is regulated by raising or
lowering the table C. The vessel A acts as a regulator for keeping the
level of the liquid in B at a constant height.
The first series of experiments was made with the double object of
determining how far the rapidity of dropping influenced the size of the
drops, and to establish the uniformity of the size of the drops which drop
at equal intervals of time.
In these experiments cocoa-nut oil was taken as the liquid, an ivory
sphere as the solid, and atmospheric air as the gas. The ivory sphere was
washed in hydrochloric acid, so as to deaden its surface. Immediately
before and after each batch of drops, the same number of drops were
counted, and their time of fallmg compared with the time which elapsed in
the actual experiment. In no case, however, was there a difference between
the two of a single second, so that g¢ may be considered in each case to be
exactly given.
TasiE 1.—Cocoa-nut oil.
T =28°:5 C.
ge— Al
Radius of ivory sphere = 22:1 millims.
Numb
tae gt. Weight of drops.
Mu gramme.
60 1 3-9817
60 1 3984]
; 60 1 3-9784
| 60 1 3°9742 |
bee alge 3:9730 |
| 60 1 3°9735
60 1 3-9682
gt. | Mean weight of single drop.
a” 0:066279
Preliminary experiments having shown that the size of a drop is greatly
affected by the rate at which the dropping takes place, that is, by the time
occupied by the drop in its formation, the following experiments were per-
formed to establish the connexion between the two.
It may be here remarked that with some liquids, of which cocoa-nut oil
1864.] Prof. Guthrie on Drops. 449
is one, a continuous stream of liquid by no means implies a faster delivery
of it than may be achieved by a succession of drops. On the contrary,
just as by walking more rapid progress may be made than by running, so
may dropping deliver more liquid than passes ina stream. A uniformly
rapid series of drops may be converted into a stream, and reconverted into
drops under certain restrictions, at pleasure, without altering the quatiniy
of liquid delivered. We shall return to this point.
TaBLE IT.—Cocoa-nut oil.
devas Soy ad
Radius of ivory sphere =22°1 millims.
|
Time between fall : | Time between fall ‘
Te ber of first but one and Weight Number of first but one and Weight
of drops. last drop. of drops. || of drops. last drop, of drops.
. gramme. || 7 gramme.
60 26 45212 || 60 38 4:3678
60° 26 45173 60 38 43628
60 26 45265 || 60 38 43682
60 26 45316 120 76 87403
60 | 30 43676 || 60 38 43646
60 30 43668 || 60 42 4-23.42
60 30 | 43593 60 | 42 4:2357
60 30 43665 || 60 42 42362
60 34 4°4827 60 42 4:2368
60 34 44731 60.6. 42 4-2330
60 34 44643 60 | 42 4-9378
60 34 44779 60 46 41487
60 | 34 44681 || 60 | 46 4-1438
60 | 34 44752 60 | 46 4:1499
60 | 38 43778 | 60 | 46 4147)
!
From this Table is constructed the followmg Table III., which shows g#
in seconds and the corresponding drop-weights in grammes, the latter
values being the mean of the resultsin Table II. g# is got by dividing
the time-lapses of Table II. by the number of drops.
TaBLeE III.—Cocoa-nut oil.
‘E=28?*7
Radius of ivory sphere = 22°] millims.
‘ Mean weight of
y single drop.
j | grm.
0-433 | 0:07540
0-500 0:07275
| 0-567 0°07456
| 0-633 0:07281
| 0-700 0-07059
0°767 0:06912
| 1-000 0:06628*
* Table I. T=2875 C.
450 Prof, Guthrie on Drops. [ Recess,
Hence it appears that, within the above limits, on the whole, the weight
or size of a drop diminishes as its growth-time increases. Further, it seems
that between the rates gi =°433 and gt=°567 a minimum occurs, that is,
instead of there being a continuous diminution in the weight as the growth-
time increases, there is at first a diminution, then an increase, and finally
a continuous diminution, so that drops of the rate gf=*500 have sensibly
the same size as those of the rate gé="633.
In order to establish more precisely the position of this minimum and
the general relation between rate and size, the observations must be both
more minute and more extended. For this purpose a fresh sample of oil
was taken, and the time-intervals extended from 25" per 60 drops to 240"
per 20 drops; as before, four experiments were made at each time-interval.
The mean results are given in Table IV.*, in which the values of gé are
obtained by dividing the time-intervals by the number of drops. The
mean weights of the single drops are got as in Table III. The weights of
oil passing in one second are found by dividing the terms of column 2 by
those of column 1, which correspond to them.
TaBLe 1V.—Cocoa-nut oil (specific gravity =0°9195).
T=29° C.—29°4 C.
Radius of ivory sphere=22°1 millims.
1 | Mean weight Weight of oil
es of single drop. |passing per second.
hy grm. erm.
(0°333) (009264) (0:27792)
0°417 0:08265 0°19837
0:433 0:08074 0°186381
0-450 0:08185 0:18189
0467 0-07918 0:16968
0°483 0:07932 0-16412
0:500 0:08017 0:16035
0°517 0:08017 0:15518
0533 0-:07961 0:14927
0:550 0:07698 0:13985
0-567 0:07664 0:138524
0-583 0:07558 0°12957
0600 0:07334 0:12221
0-617 0 07820 0:11871
0633 0:07821 0°11560
0-667 007260 0:10891]
0-750 0:07102 0:09469
0°833 0:06902 0:08283
1-000 0:06605 0-06605
1:500 006215 004144
2-000 0:05986 0:02993
3000 0:05710 0-01903
4°000 0:05561 0:01432
5000 0:05469 0:01094
12-000 0 05201 0:00433
* A Table exhibiting the details is given in the MS., which is preserved for reference
in the Archives.
x
1864. } Prof, Guthrie on Drops. 451
It was found impossible to arrest an exact number of drops when the
rate was faster than 60 drops in 25". A few rather discordant results, got
at the rate of 60 drops in 20", gave a mean of 0°09264 grm. as the weight
of a single drop; this tends to show that at this high rate the drops were
considerably larger than at any lower rate.
Towards the end of the Table, at the slower rates, the error of time be-
comes so exaggerated (the least alteration in the adjustment of the instru-
ment makes so sensible a change in the entire time-lapse) that it is nearly
impossible to avoid an error of about 0”*5 in the whole time of several
minutes. Although the time-error thus becomes palpable, it nevertheless
remains, relatively to the whole time-lapse, as immaterially small as the
inappreciable errors of the swifter rates of dropping.
The numbers of Table IV. present us with several interesting and im-
portant facts.
From gf='333 to gé= 433 there is diminution.
ss 9 == 433.5. 5,—= “490 5, __,, mMerease.
wees a AD, oo ag CIINTL IOI,
33 oe) =°*467 3) ae °900 3 -, Icrease.
Be a "00 7g. 55. 12-000- ,, ,5,continual dimination.
The most prominent fact is that, on the whole, the drops undergo a
continuous diminution in weight or size as gé increases. To such an
extent is this the case, that the most rapidly falling drops of the above
Table are nearly twice as heavy as the most slowly falling ones. The cause
of this is probably to be sought for in the circumstance that when the
flowing to the solid is more slow, the latter is covered with a thinner film
of liquid, so that, as the drop parts, the solid reclaims by adhesion more
of the root of the drop than is the case when the adhesion of the solid to
the liquid can satisfy itself from the thicker film which surrounds the drop
‘in the case of a more rapid flow. The influence of rate is seen to extend
even to the exceedingly slow rate of gf=12".
This connexion between rate and weight (or quantity) should not be lost
sight of by prescribers and dispensers of medicine. A pharmacist who
administers 100 drops of a liquid drug at the rate of three drops per
second, may give half as much again, as one who measures the same
number at the rate of one drop in two seconds, and so on.
For our present purpose the effect of rate upon the size of a drop is of
great moment, because it proves that there is no such thing as a drop of
normal size. At no degree of slowness of dropping do drops assume a size
unaffected by even a slight change in the rate of their sequence. Hence,
whenever a comparison has to be made between the sizes of different drops,
we shall have to eliminate this source of difference by taking drops which
follow at exactly the same rate.
About the rate at which the diminution of size takes place for equal
increments of gf, the Table gives us little information beyond the fact that,
452 Prof. Guthrie on Drops. [Recess,
on the whole, the sizes of the drops at the slower rates are less influenced
by equal increments of g¢ than are those of the quicker rates. This, how-
ever, ouly appears distinctly at and below the rate of about gé=1"-00.
_ If the connexion between gt and the drop-size be represented by a curve
(fig. 2, A), the abscissee being the values of gt, and the ordinates the
corresponding drop-weights, there is apparently no asymptote parallel to
the axis of X. The curve presents, however, in its course two cecmnane
maxima and minima:
‘Secondary maxima. Secondary minima.
(1) “gt “= "450" ot="435a"
= 500! |
(2) at} Le pit , gt= "467"
Although at these minima the drops are less than at the immediately
succeeding rates, yet the quantity of liquid passed in a given time is, at
every rate of dropping, greater than the quantity passed in the same time
at every slower rate. The decrease of rate more than counterbalances the
temporary increase in the drop-size. This is seen on comparing the num-
bers of column 3, Table IV., with one another. They are found to de-
crease continually, though by no méans uniformly, as the rate of dropping
decreases.. ‘The same fact is shown graphically in fig. 2, B.
The second maximum (at gf ='500 and gt = 517) is in remarkable
connexion with the rate at which a series of drops may be converted into
a continuous stream. At all rates of dropping, from gt=°333 to gt='517
inclusive, the drops may be converted into a permanent stream by pouring
a little additional oil upon the sphere as the drops are falling from it. A
stream is thus established which remains for any length of time, if it be
protected from all currents of air and vibration. At the rate gf=+519
the stream may be established by the same means for a few seconds (about
30"), but the continuous part inevitably begins to palpitate, becoming
alternately longer and shorter, thinner and thicker, until at last it draws
up and is converted into a succession of drops. At the immediately slower
rates of dropping the same effect follows, but in each case in a shorter
time, so that the slowest rate of dropping, which may be converted into
permanent running, coincides with the rate which gives the second maxi-
mum size of drops (gé=°500 and gt=°517). ‘The appearance of a drop-
convertible stream is peculiar, the narrowing which it undergoes on leaving
the solid beg remarkably sudden.
iad #In many liquids such secondary maxima are entirely wanting. They —
appear in liquids of the physical nature of oils, whether those oils be che-
mically fatty (adipic salt’of glycerine), or whether they be miscible with
water, as syrups, glycerine itself, &c.
In order to avoid the influence of variations in rate, we shall for the
future take the same rate of dropping in all cases, and, unless the contrary
be stated, the rate adopted will be gt=2".
1864. | Prof. Guthrie on Drops. 453.
_ The factor, the influence of whose variation on the size of the drop
we have next to consider, is the constitution of the liquid.of which the
drop is formed. For the foregoing experiments concerning the influence
of rate, cocoa-nut oil was employed on account of its non-volatility. On
allowing a quantity of it, having an exposed surface of about two square
inches, to stand for 70 hours, it was found to have increased about 2 milli-
grammes in weight, probably in consequence of oxidation, Its fixedness,
therefore, and its perfect liquidness at the temperature of 28°-30° C., make
it well adapted for this special purpose. Chemically. and physically, how-
ever, it is of little interest for our immediate purpose, because it is a mix-
ture of several substances, the proportion between which is indefinite.
The constitution of a ‘liquid may vary in two ways. A liquid may be a
mixture of two or more simple liquids, or a solution of one or more solids
in a single or mixed liquid; or secondly, the liquid being single, may vary
in the sense of its chemical constitution. It would be clearly impossible
to exhaust experimentally the countless variations which might thus arise.
We must be satisfied with taking a few simple examples of the two
cases. : 2
With the more mobile liquids the apparatus, fig. 1, fails to give a
strictly uniform flow. As the liquid descends in B, it adheres by capillary
action to the lip of A for some time after the level of B is below the lip.
The air at last separates the two, enters the flask A, displaces the liquid
there, and restores the level to B, so that although the average height of
B is constant, yet it undergoes a series of slight but ceaseless variations.
As even such slight irregularities sensibly affect the rate of flow through
the siphon, and consequently the rate of dropping from the sphere, the
apparatus is slightly modified as follows, fig. 3. Between the reservoir,
B, fig. 1, and the dripping sphere, a second reservoir, M, is placed. This
is kept in a state of continual overflow. The overflow is regulated by means
of a few filaments of cotton wool hanging over the edge of the overflowing
vessel, and so fashioned that the end in the overflowing vessel tapers to a
point. Finally, the rate of flow is in many instances so sensitive, that it
is impossible to procure exactly a predetermined rate by the ordinary
screw-adjustment of the holder which carries the siphon. For the final
adjustment, it is convenient to depend upon the elasticity of the siphon.
A heavy ring is passed over the siphon, which is then firmly fixed so:
as to deliver the liquid at nearly the required rate. The ring slipped back-
wards and forwards, bends the siphon more or less, and regulates the flow
through it.
Solution of Chloride of Calcium in water.—A. solution of chloride of
calcium, nearly saturated at 28° C., was taken as the starting-point or
solution of maximum saline contents. Half of this solution was mixed
with an equal volume of water (solution 2). Half of solution 2 was mixed
with its own volume of water, giving solution 3, and so on. In this
manner, without knowing the absolute strength of solution 1, we know.
45 4: Prof. Guthrie on Drops. : [ Recess,
that the successive strengths of the saline solutions, whether there be loss
S 8
Pee ey
These numbers give exactly the relative quantity of solid matter in a
unit of volume of the liquid. As, however, solution 1 on dilution evolves
heat and therefore probably contracts, the sizes of the drops cannot be
derived directly from their weights. The specific gravity of each solution
has to be determined experimentally.
TasLe V.—Solutions of Ca Cl.
of volume owing to chemical union or not, areas s,
j6=—2
Radius of ivory sphere=22°1 millims.
T= 28°.
Solution; Mean weight | Specific | Relative size
of CaCl.| of single drop*.| gravity. | of single drop.
Wateror; stm.
2 0185166 | 1-0000| 0-18517
= 0:168137 | 1-0039 016750
= 0172907 | 1.0084 0-17147
5 0:172593 | 1-0172 0-16967
= 0:167222 | 1.0383 0-16105
- 0:191008 | 1-0720 0:17817
: 0195839 11721 0-16742
2 0-211396 1:2786 0-16533
S 0:225558 | 1-4939 015098
The column of the relative sizes of the single drops (which is got by
dividing the mean weights by the corresponding specific gravities) shows
that, under like conditions, a drop of water is larger than a drop of solution
of chloride of calcium of any strength whatever. The comparatively small
quantity of solid matter in me causes the drop to diminish about 3th of its
volume.
We must bear in mind that the successive increments of solid matter
may affect the size of the drop in opposite directions,—by affecting the
* The first number from six, the following numbers from four determinations of the
weight of 30 drops.
1864..] Prof. Guthrie on Drops. 455
cohesion of the water, by asserting its own cohesion, by increasing the
gravity of the liquid and thereby determining an earlier separation of the
drop, and, in this particular case, by the chemical affinity of the solid to
the liquid, and the probable formation of hydrates. It is seen that these
influences cause an irregularity in the diminution of the size of the drop
as it acquires more solid matter. In fact, it is only when the liquid has
the considerable strength of 3 that the diminution in drop-sizé becomes
continuous.
In fig. 2, C shows graphically the relation between drop-size and strength.
The abscissee represent the strengths of the solution progressing in geometric
ratio; the ordinates show the corresponding comparative drop-sizes. It
may be remarked that the curve C bears a striking resemblance to the
curve A, as though increase in solid constituent produced a similar effect
upon the drop-size as increase in the time-interval on the drops of a
homogeneous liquid. We may also notice the great difference in size between
a drop of water and a drop of oil under the same conditions. From
Table IV. we find that a drop of oil of specific gravity 9195 has the weight
05986 when gt=2". Hence the comparative sizes of the two are,— —
} Radius of T Comparative
ui: sphere. i sizes.
Water 2! 22°1 mm. 237... 0°18517
Oil oe 22°] mm. 29°-29°°4 C. 0:06510
Or a drop of water is nearly three times as large as the drop of oil, the
only difference in the circumstances being that the oil was 1°-1%4 C,
warmer. We shall have to study this point more especially hereafter.
On account of the chemical union which takes place on dissolving Ca Cl
in water, it would be useless to give the absolute strengths of the various
solutions.
VOL. XIII. 21
a a
456 . Prof. Guthrie on Drops. [Reces,
Solution of Nitrate of Potash in water.—Nitrate of potash was the next
solid examined, on account of the probable non-existence of hydrates.
Seven solutions of nitrate of potash were made of the following eye
by weight :— :
(1) 22 of water to 1 of nitrate of potash.
(2) 99 9 29 2 29 29 9
- (3) cy) De DS 3 93 9 oy)
(4) oy) 29 29 4 239 29 29
(5) ry) oy) 23 5) 9 29 ”
(6) 29 99 99 6 29 39 23
(7) 99 99 9 7 29 99 33
These solutions were made to drop from the ivory sphere at the rate of
gt=2", Ineach instance four batches of drops, of 30 each, were weighed.
In the following Table the mean results only are given.
TaBLe VI.—Solutions of Nitrate of Potash.
Gi—2
T =28° C.
Radius of sphere =22°1 millims.
1. 2. 2 4, 5.
a Mean weight | Specific gravity | Relative size | Weight of KNO,
of single drop. | by experiment. | of single drop. in a drop.
KNO, :
Water
= 0:18517 1-0000 0:18517 -00000
= 0-18613 1-0164 0:18314 00846
= 0:17908 10341 0:17318 01628
= 0717714 10511 016853 02411
= 0-16917 1-0680 0-15840 03075
— 0:17805 1:0832 0-16439 04047
22 018254 1:0987 0:16618 04978
6
22 0-18611 1/1130 0°16723 05921
7
Hence it appears that on the addition of the first quantities of nitre
22 22 22 22 22 22 22
(=, elec =) the size of the drop is diminished. Afterwards (= 5” rae =)
1864. | Prof. Guthrie on Drops. 457
the size of the drop is partially recovered. There is a stage of dilution
when the specific gravity is 1-0680, where the drop-size is a minimum.
_ Further, it is seen from column 5 that the quantity of nitre in a drop in-
creases continually as the strength of the solution increases, although both
the weight and the volume of the drop vary.
Inversely, the regularity of the variation of drop-size, in the case of nitre,
points to the absence of hydrates of that body.
It would be delusive to endeavour to construct a formula connecting the
specific gravity with the drop-size or drop-weight of the solution, but, as
before, a graphic representation serves to show the connexion between the
variables. In curve D, fig. 2, the abscissee represent the quantity of
nitrate of potash in solution, the ordinates show the corresponding drop-
sizes. As with chloride of calcium, it is seen that the drop-size of water is
larger than that of any solution of nitre. Curve H, fig. 2, having the
same abscissz as D, has ordinates which represent the drop-weights.
It is confessedly a matter of great interest, and still greater difficulty, to
determine exactly the relation which exists between a dissolved solid and
its solvent; that is, to find out whether or when a solid should be viewed
as being in combination with a portion of the liquid in which it is dissolved.
Such questions may perhaps receive additional light from experiments
similar to the above, but more extensive, and performed with this special
object in view. Comparing the curves C and D, for instance, there can be
little doubt that the secondary maxima and minima of C are owing to the
existence of hydrates of chloride of calcium in solution. The only known
hydrates of chloride of calcium are Ca Cl, 2HO and Ca Cl, 6 HO, the latter
of which contains 50-7 per cent. of CaCl. Solution S contains about 42°5
per cent. It is noteworthy that, while the six-water chloride in the solid
state absorbs heat on solution, the solution S evolves heat on dilution, as
already mentioned. In the case of nitre we have in the drop-sizes evidence
only of the opposite efforts of two cohesions, that of the water and that of
the nitre. By pursuing this direction of experimental inquiry, evidence
may probably be got concerning the truth of Berthollet’s hypothesis of
reciprocal recomposition in the case of the mixture of the solutions of two
salts, AX and BY, where AY and BX are also soluble in water.
frm
ie
Peasy:
-
®
a
»
»
+
a
see
So ae
“sere Se
1864. ] Prof. Guthrie on Drops. 457
the size of the drop is partially recovered. There is a stage of dilution
when the specific gravity is 1:0680, where the drop-size is a minimum.
Further, it is seen from column 5 that the quantity of nitre in a drop in-
creases continually as the strength of the solution increases, although both
the weight and the volume of the drop vary.
Inversely, the regularity of the variation of drop-size, in the case of nitre,
points to the absence of hydrates of that body.
It would be delusive to endeavour to construct a formula connecting the
specific gravity with the drop-size or drop-weight of the solution; but, as
before, a graphic representation serves to show the connexion between the
variables. In curve D, fig. 2, the abscissee represent the quantity of
nitrate of potash in solution, the ordinates show the corresponding drop-
sizes. As with chloride of calcium, it is seen that the drop-size of water is
larger than that of any solution of nitre. Curve H, fig. 2, having the
same abscissze as D, has ordinates which represent the drop-weights.
It is confessedly a matter of great interest, and still greater difficulty, to
determine exactly the relation which exists between a dissolved solid and
its solvent —that is, to fnd out whether or when a solid should be viewed
as being in combination with a portion of the liquid in which it is dissolved.
Such questions may perhaps receive additional light from experiments
similar to the above, but more extensive, and performed with this special
object in view. Comparing the curves C and D, for instance, there can be
little doubt that the secondary maxima and minima of C are owing to the
existence of hydrates of chloride of calcium in solution. The only known
hydrates of chloride of calcium are Ca Cl, 2HO and Ca Cl, 6 HO, the latter
of which contains 50°7 per cent. of CaCl. Solution S contains about 42°5
per cent. It is noteworthy that, while the six-water chloride in the solid
state absorbs heat on solution, the solution S evolves heat on dilution, as
already mentioned. In the case of nitre we have in the drop-sizes evidence
only of the opposite efforts of two cohesions, that of the water and that of
the nitre. By pursuing this direction of experimental inquiry, evidence
may probably be got concerning the truth of Berthollet’s hypothesis of
reciprocal recomposition in the case of the mixture of the solutions of two
salts, AX and BY, where AY and BX are also soluble in water.
III. “On Drops.’—Part If. By Frepverick Guturiz, Esq., Pro-
fessor of Chemistry and Physics at the Royal College, Mauritius.
Communicated by Professor Stokes, Sec.R.S. Received October
17, 1864.
We have next to consider the influence which variation in the chemical
nature of the drop-forming liquid may exercise upon the drop-size in the
case SLG.
The liquids which were selected for this purpose were chosen as being
VOL, XIII, 2M
458. Prof. Guthrie on ‘Drops. [ Recess,
typical of extensive classes, rather than as being connected mee one another
in immediate chemical relation. They were—
Water. | Oil of turpentine (turpentol).
Alcohol. ~~. Benzol.
Acetic acid.’ Glycerine.
Acetic ether. Mercury.
Butyric acid.
These several liquids were allowed to drop under the same conditions,
from the bottom of a hemispherical platinum cup. The arrangement of the
apparatus was quite similar to that described in Part I., the ivory ball being
replaced by the platinum cup, and the overflow of the cup being deter-
mined by strips of paper bent over its edge. The case of mercury is the
only one which requires some explanation. A few years ago I noticed the
fact that mercury which holds even a very little sodium in solution has
the power of “ wetting” platinum in a very remarkable manner. The
appearance of the platinum is quite similar to that presented by amalga-
mable metals in contact with mercury. But the platinum is in no wise
attacked. Further, the amalgam may be washed off by clean mercury,
and the latter will also continue to adhere equally closely to the platinum.
All the phenomena of capillarity are presented between the two. The
surface of the mercury ina platinum cup so prepared is quite concave; and
a basin of mercury may be emptied if a few strips of similarly prepared
platinum foil be laid over its edge—just as a basin of water may be emptied.
by strips of paper or cloth, and under the same condition, namely that the _
external limb of such capillary siphon be longer than the internal one.
I generally use this curious property of sodium-amalgam for cleaning
platinum vessels. It enables us now to examine the size of drops of mer-
cury under conditions similar to those which obtain in the case of other
liquids*. After the cup had been used for the other liquids, its surface
* In regard to the above-mentioned property of sodium, the following observations
may be of interest. At first the explanation naturally suggests itself, that the effect
wrought by the sodium may be due to an absorption of oxygen, in consequence of the
oxidation of the sodium, the consequent diminution of the gaseous film between the
two metals, and the resulting excess in the superior pressure of the air. This, however,
cannot be the true explanation, because it is found that the perfect contact between the
two, or “ wetting,” takes place equally well in an atmosphere of nitrogen, carbonic acid,
or in vacuo. Hence, if I may venture upon a guess, unsupported by experimental evi-
dence, I should be rather disposed to assign the phenomenon to the reducing action of
nascent hydrogen derived from the contact of sodium with traces of water. Perhaps —
even the least oxidizable metals are covered with a thin film of oxide, which is reduced
by the nascent hydrogen at the same moment that the mercury is presented to the re-
duced metal. It is found that iron, copper, bismuth, and antimony are also wetted by
mercury if their surfaces are first touched with sodium amalgam. Not only do -the
latter metals lose this power on being heated (as we might expect, in consequence of
their superficial oxidation), but platinum, from which the adhering mercury film has
been wiped by the cleanest cloth, or from which it has been driven by heat, also loses
the power. It is true that the surface of clean platinum is supposed to condense a
1864.] | Prof. Guthrie on Drops. 459:
was rubbed with sodium-amalgam and washed with clean mercury. A
few strips of similarly prepared platinum foil being bent over the edge and
pressed close to the sides of the cup: the mercury could be handled simi-
gee to the other liquids.
The following Table VII. shows,—
1. The liquids examined.
2. The number of drops which were weighed.
3. The weights found.
4. The mean weights of single drops.
5. The observed specific gravity at the given temperature.
6. The relative sizes of single drops.
Tasxe VII.
2 0,
gt=2"
Radius of curvature of platinum cup=11°4 millims.
1. 2, 3. 4, b. 6.
Name and formula] Number | Weight | Mean weight of | Specific | Relative size of
of liquid. of drops.| of drops.| single drop. | gravity. | single drop.
erm. grm
20. | 2:9703
20 | 2:9923
‘AGE Sh a Ae ae ne 20 | 29472 0:14828 1:0000 0°14828
HO. 20 | 29603
20 | 29533
20 | 2:5496
Glycerine ......... 20 | 2:5576 | 0:12804 1:2452 0:10280
C, H, O,. 10 | 1-2877
20 | 1:1616
Butyric acid ...... 20 | 1°1630 | 0:05813 1:0017 005803
, H, O,. 20 | 11634
20 | 7:9655
Meroury ....+sseses. Br Noeeee i. Overos. |1eare8. |) won7ee
8 20 | 7:8197
20 | 0°9514
Benzol ...sesssee a een +| 04778 | 08645 | 0-05527
ei | 579
12 “"6" 20 | 0-9644.
20 |0°8675 é
Turpentol ......... 20 | 0:8656 | 0:04331 0:8634 0:05016
ia 20 | 0:8653
20 |0°7890
J G5) 10) ree 20 |0°7910 | 003949 08163 0:04960
6, H,.0, 20 | 07896
20 | 08214
Acetic-ether .....: 20 | 0:8300 | 0:04149 08930 - 0:04647
C,H, 0,C,H,0,.) [20 |0-8384
30 | 1:3636
Acetic acid ....:.... 20 |0°9055 | 0:04540 1:0552 0:04302
HO C,H, 0,. 20 | 0:9095 |
film of oxygen ; and the removal of this might alter the adhesion between the mercury
and platinum ; but such a film could scarcely exist 7 vacuo or in another gas, ved
2m 2
460 Prof. Guthrie on Drops. [ Recess,
The experimental numbers obtained are given without omission. The
liquids are arranged in the order of magnitude of their drop-sizes. It
appears from column 5 (of the specific gravities) that some of the liquids
employed were not perfectly pure. This, however, is quite immaterial in
the present direction of examination, provided that in all cases where the
liquids named are in future employed and compared with those of Table
VII., identically the same liquids are meant.
The numbers of column 6, with which we are now exclusively concerned,
present several points of great interest. In the first place, it appears that
the specific gravity of a liquid is not by any means the most powerful de-
terminant of the drop-size. Thus-butyric acid, which has sensibly the
same specific gravity as water, gives rise to a drop less than half the size
of the water-drop ; while mercury, of singular specific gravity, has no ex-
ceptional drop-size. Lastly, it may be observed how that remarkable body
water asserts here again its preeminence. ‘The first impression which
these numbers make is, that there are three groups of magnitude, n, 2 n,
3n. But it is possible that a change in the nature of the solid might
throw these drop-sizes into a different order of magnitude; and certainly
until a very much greater number of bodies is examined in this sense, it
would be premature to attempt to establish anything like a law.
It is sufficient for the present to poimt out that the drop-size is not
directly dependent upon either the specific gravity or boiling-point ; nor
does it stand in any obvious relation to what is sometimes called the liqui-
dity, mobility, or thinness of a liquid. For we find that glycerine and
(from former experiments) cocoa-nut oil both form smaller drops than
water, the one being heavier and the other lighter than that body, and
both being viscid or sluggish. On the other hand, alcohol and acetic acid,
both perfectly mobile liquids, give rise to drops about half as large as those
of glycerine*.
Hence it is clear that we are still ignorant of that property of a liquid
upon which its drop-size mainly depends. We are not yet in a position
to connect the drop-size with any of the known physical or chemical pro-
perties of liquids. We approach the solution of the problem by studying
the effects of change in some others of the variables.
The adhesion between the liquid which drops and the solid from which
it drops is also affected by the curvature and general geometric distribution
of the solid at and about its lowest point. And the variation in the adhe-
sion between the solid and liquid, caused by the variation in the geometric
distribution of the solid, may and does in its turn affect the size of the
drop. Yd
From this aspect, one of the simplest kinds of variation is that offered
* The evaporation of the more volatile of these liquids is a source of slight error ;
not so much on account of the direct loss in weight of the drop in falling, as by reason
of the cooling which it causes, and the consequent variation in density and adhesion.
Such source of variation we shall examine in the sequel, and find insignificant.
1864. | Prof. Guthrie on Drops. 46]
by a system of spheres of various radii, but made of the same material.
And this case is an important one, because it undoubtedly offers the key
to all drop-size variation arising from a similar cause. ‘To study this point
we may make use of any one convenient liquid, such as water, and cause
it to drop at a fixed rate from spheres of various radii, including the ex-
treme case of a horizontal plane. This extreme case, however, presents
certain practical difficulties. From a plane it is almost impossible to get
a series of drops uniform in growth-time and in position. A ripe drop
hanging from a horizontal plane will seek the edge thereof. Several drops
may form upon and fall from the same plate at the same time and inde-
pendently of one another. It is only by employing a plate not absolutely
flat, that an approximation to the required conditions can be made. Taking
ry for the radius of curvature, the first numbers for 7 =o can therefore be
considered only as an approximation. The arrangements for the other
cases were quite similar to that described in Part I., fig. 3.
No. 1. A glass plate, fastened to and held by a vertical rod.
Nos. 2, 3, 4. Selected globular glass flasks.
Nos. 5, 6, &c. Perfectly spherical glass spheres.
TaBLe VIII.—Water.
ge 2)
T—22°5 ©.
ae | 9, 3, 4, F
Number} Radius of | Weight Mean weight
and relative size
of drops.| curvature. | of drops. of single drop.
———
erm.
5.229
1. {50} a { ae \ 026549
° 20 mm. 49296 .
2, 130} 1131 { oie \ 0:24808
3. { a \ 70-1 | 45018 1) 022619
4 | {So} |] 472 |{a5o4q}| 021257
20 | £35055 .
Be { 50} 175 | { 34733 \ 0-17497
6. {50} 15-1 {33600 | 0-16765
m7. {30 | 115 { 3.0206 \ 0:15122
8. { 5 \ 11-2 { ae \ 0:14896
20 Py | (9-8665 a.
9. { 50 10:0 | 5-8619 | 0-14321
20 29-6765 So
10. | 30} TD { 26660 \ 0:13356
. 7)
1, {*o} ral 111001 | 0:12877
It appears, therefore, that the drop increases in size according as the radius
462 Prof. Guthrie on Drops. [Recess,
of the sphere increases from which the drop falls, and, further, that the
difference of drop-size brought about by this cause alone may easily amount
to half the largest drop-size. For dispensers of medicine this fact is as im-
portant as that pointed out in Part I., where it was shown that the growth-
time so materially influenced the drop-size. The lip of a bottle from which
a drop falls is usually annuloid. The amount of solid in contact with the
dropping liquid is determined by the size of two diameters, one measuring
the width of the rim of the neck, the other the thickness of that rim. In
most cases the curvature and massing of the solid at the point whence the
liquid drops is so irregular as not to admit of any mathematical expression.
The reason why drops which fall from surfaces of greater curvature are
larger than those which fall from surfaces of less curvature is surely
this :—In the case of a surface of greater curvature the base of the drop
has more nearly its maximum size; the centre of gravity of the liquid film
from which the drop hangs is nearer to the centre of gravity of the hang-
ing drop ; the contact between the two is more extensive and intimate ; so
that the drop is held for a longer time and therefore grows more.
On comparing columns 3 and 5 of Table VIII., there does not appear
to be any obvious law of connexion between the two; nor indeed can the
numbers of column 4 pretend to such a degree of accuracy as would justify
us in attempting to establish one. This is seen on comparing znter se the
numbers of column 4. Especially with the spheres of longer radu, there
is so much difficulty in getting a uniform wetting of the surface whence
the drop falls, and this so materially influences the drop-size, that the
numbers found are seen to vary considerably. Greater accord is obtained
with spheres of less radii. As we might expect, the same absolute increase
in length of radius takes less effect upon the drop-size in the case of longer
than in that of shorter radii. The infinite, or at least indefinitely great
difference between the radii 1 and 2 produces about the same effect upon
the drop-size as the difference of 43 millims. between the radii 2 and 3,
and so on. |
The following Table of first differences shows this more strikingly :—
Trti—Tn Wyti1—Wn. |
(oe) 0-01854
43° 0:02189
22'9 0:01862 |
29-7 0:03760
2-4 0:00732
36 0:01643
0:3 0:00226
1:2 0:00575
2°5 0:00965
0-4 0:00479
The relation exhibited in this Table supports the supposition that the
size of the drop varies inversely as the contents of a figure bounded below
by a circular horizontal plane of constant diameter (less than that of the
1864.] - . Prof. Guthrie on Drops. 468
sphere) tangent to the sphere, laterally by a cylinder of vertical axis stand-
ing on the tangent plane and cutting the sphere, and above by es convex
surface of the sphere itself (Plate IV. fig. 4).
As the diameter of the sphere still fabithiee diminishes, the size of the
drop is limited by the possible size of its base, until finally the sphere is
completely included in the drop.
It would be interesting, but it would take us too far, to consider the vari-
ous cases of liquids dropping from cones, edges, solid angles, cylinders,
rings, &c. We must content ourselves in this direction with the fact that
the size of a drop is greater the more nearly plane is the surface from
which the dropping takes place. If it were possible for a drop to fall from
a concave surface, we should anticipate a still further increase in its size.
The relation between drop-size and curvature may be more strikingly
shown by arranging the spheres one above the other in the order of mag-
nitude.
Plate IV. fig. 5.—Each sphere receives the drops from the higher one.
The quantity of water which drops in a given time, from every sphere, is the
same. Hence in all cases the number of drops is inversely as the drop-
TABLE [X.—Water.
er
TJ GC,
E, 2. 3. 4,
Radius | Number| Weight Mean weight
i nd relat:
of disk. | of drops.| of drops. a ees
in. orm.
(20 | 33682
5 | 90 | 31193 |
5 90 | 325934 | 0-16895
20 20 | 3:3256 |
20 | 32594)
; 20 | 2-9693
| 90 | 29-9854
0 20 a O'14915
20 | 30031
: 20 | 1-9333
90 | 1-9244
0 20 A 009666
90 | 1-9248
: 20 | 1-4618 |
20 | 1-4672
0 20 | 1-4688 007332 |
20 | 1-4682 |
: 20 | 0:8250 |
20 | 0:8212 me |
50 90 | 08208 0-04107
20 | 0:8190
size; so that by counting the number of drops which fall from any two
spheres in the same time, we get at once the relative sizes of the respective
nnn nen a
464: Prof. Guthrie on Drops. [ Recess,
drops. For several reasons, this plan of comparison is not sufficiently ac-
curate to measure drop-sizes ; but it offers a method of making the differ-
ence of drop-size visible to any number of persons at once.
The only other variation in the geometrical relation between the solid
and the liquid, which we shall consider, is the variation in the size of a cir-
cular horizontal plane from which drops fall.
Five disks of copper foil were cut of the radii 35, 35, 3 o> soth of an
inch respectively. These were fastened horizontally to vertical wires, and,
having been thoroughly cleaned by momentary immersion in nitric acid
and washing, water was made to drop from them at the rate gf= 2".
Table IX. shows the influence of this kind of variation upon drop-size.
The want of accord in the numbers of the largest disk is owing to a pecu-
liar tremor which the drops exhibit at the moment of delivery. The same
phenomenon was noticed, but to a less extent, with the next smaller disk.
With the remainder it was not noticed.
The curvature and shape of the solid, and its consequent massing towards
the liquid, is intimately connected with the next phase of variation which
we shall consider, to wit, the variation in the chemical composition of the
solid from which the drop falls. The influence of this kind of variation is
to be studied by examining the size of drops formed under like circum-
stances, from spheres of the same size, but made of different material. Since
in this case the liquid remains the same, we must limit the solids examined
to such as the liquid completely wets. In this case, variation in the drop-
size implies a variation in the thickness of the liquid film covering the
solid. The latter must be caused by variation in the adhesion between the
solid and liquid. Finally, such adhesion can only vary through one or both
of two causes—namely, variation in the density of the solid, or in its spe-
cific adhesion dependent upon its chemical nature.
The first qualitative experiment was made upon three equal spheres of
brass, glass, and cork. They were hung one above the other im the manner
before described, so that the drop from one sphere fell upon the lower
one*, It was found that, in whatever order the spheres were arranged,
when the flow was uniform and not quicker than gi= 2", the dropping from
the cork took place with the greatest rapidity, that from the glass next,
and that from the brass most slowly—showing that the brass gives rise to
the largest, the glass to the next largest, and the cork to the least drops.
From this it would seem that the drops are in the same order as to size as
are the solids as todensity. We shall find, however, that this is not always
the case, and that some other property as well as density is at work to in-
fluence the drop-size. The quantitative experiment, the results of which
are given in Table X., confirms the result of the qualitative experiment
given above, but shows, at the same time, that the joint influences of den-
* Jn this kind of experiment there should be a considerable mass of cotton wool on
each sphere to receive the drops from the higher one, and, by acting as a reservoir, to
regulate the flow.
1864. Prof. Guthrie on Drops. 4.65,
sity and chemical diversity of the solid have only a small effect upon the
drop-size. The conditions of the experiment were similar to those pre-
viously described.
TABLE X.—/VVater.
GEE
ae
7=7'1 millims.
Number of drops=20.
Weight of Mean weicht
Substance. 20 ga rere: of single drop.
erms. grm.
72-4846
e 4848
cohecaas aale 2 oe 012418
2: 2821
‘A877
+ 5930)
2:5985 |
j 25980
(CC ROMA Oreo 92-5949 (
25953
( 2-5900
26295
9-629
9-626
oe eee ee 0-13118
92-6296
| 26116
0712975
When a liquid drops from a solid it is not always that the adhesion be-
_ tween the solid and liquid is overcome. The phenomenon of “ wetting ”’
implies a superiority of the adhesion between the solid and liquid over the
cohesion of the liquid ; and in all cases where a liquid drops from a solid
which it wets, the act of separation is a disruption of the liquid, and not a
separation of the liquid from the solid ; that is, the separation of the drop
is a failure of cohesion and not of adhesion. We are not, however, justified
on this account in anticipating that the size of a drop is unaffected by the
chemical nature of the solid from which it drops, even in those cases where
the adhesion between the solid and liquid is greater than the cohesion of
the liquid (that is, where the liquid completely wets the solid), because,
although it is the liquid which is broken, yet the size of the broken-off
part, or drop, depends in great measure upon the thickness of the residual
film, as we have seen in examining the influence of the growth-time (in
Part I.) and of the radius of curvature.
Adhesion may also exist between a solid and a liquid which does not wet
it, as when a drop of mercury hangs from a glass sphere. But the cohe-
sion of the liquid in such a case, by its effort to bring the liquid to the
spherical form, and the weight of the drop so modify the adhesion between
466 Prof. Guthrie on Drops. [Recess,
the solid and liquid, by altering the size of the surface of contact between
the two, that the size of the drop gives no direct clue to the cohesion of
the liquid. -
We may now examine a. few cases in which, the size of the sphere re-
maining the same, and its density in some instances nearly so, the matter
of the solid varies, but the liquid wets it in all cases. This will show
whether the differences of Table X. are due wholly to differences of density
of the solid, or also or wholly to differences of chemical constitution.
TaBLe XI.—Water.
Gt=2,
A leas dst By
Radius of curvature==7 millims.
iL 2. 3. 4.
Weight of | Mean weight | Specific gravity
Bubshance: 20 drops. | of single drop. of solid.
germs. m.
011984 6°80
012021 2-00
0°12246 6°86
012264 11-44
Phosphorus 0°12274 2:08
Bismuth......... 0°12285 990°
SarG 012425 7-29
Equal spheres of the substances were made by casting them in the same
‘bullet-mould. The surfaces of the metals were roughened by momentary
immersion in acid; tin and antimony in hydrochloric, the rest in nitric
acid. Without this precaution a metallic surface is apt to be wetted only
locally, the base edge of the drop is irregular and inconstant, and the drop-
, 1864.] Prof. Guthrie on Drops. 467
weight varies. Indeed with some metals, such as tin, a smooth and bright
surface is scarcely wetted by water.
As the bodies examined have different coefficients of expansion by heat,
and one of them expands on solidification, it was necessary to test the
equality of their size and remedy any inequality. ‘This was done by ar-
ranging three of them, one at each angle of a small equilateral triangle
drawn on a large piece of plate glass. Another piece of plate glass was
then placed upon the spheres so as to rest on them all three, and slightly
loaded. On passing a gauge between the plates, at their edges, the slightest
inequality of the spheres could be detected, because the gauge lifted the
plate off the smallest of the three balls, which could then be moved. The
larger spheres were then reduced im size by brisk agitation in acid. The
sulphur and phosphorus were, for the same purpose, washed in ether.
Although there is only a slight difference between the consecutive terms
of column 3, yet between the extremes of antimony and tin a well-marked
difference exists. |
This Table shows that the drop-size stands in no simple relation either to
the equivalent density or chemical character of the solid, and establishes
the existence of a specific adhesion independent of these. Although the
differences of Table IX. may be partly owing to the differences of density
of the solids cork, glass, and brass, yet we see from Table X. that there
is about half as great a difference between the sizes of drops from antimony
and tin as between those from cork and brass, although the difference of
density between the first two is small compared with that between the last.
Again, sulphur gives rise to drops intermediate between those of antimony
and cadmium. Without, therefore, venturing to assert that density is with-
out influence on drop-size, it is clearly proved that it does not exert the
most powerful influence.
We have finally to examine the direction and extent of variation in drop-
size caused by change of temperature. By altering the density of the
liquid, a change in its temperature may affect the drop-weight without
altering the drop-size. It may further alter the drop-size by altering the
size and therefore the curvature of the solid. Any error introduced by
the first of these sources is eliminated by dividing the observed weight by
the specific gravity at the proper temperature, as in the case of different
liquids at the same temperature. Errors from the second source may be
certainly safely neglected, being far within the errors of observation.
In the place where these experiments were made, the range of natural
atmospheric temperature is very small. From the coldest to the hottest
season the difference scarcely exceeds 10°C. This circumstance made an
extended and minute study of the influence of temperature impossible, by
preventing more than one observation at each temperature being made.
The liquid taken was water, and the solid was glass. The water was heated
to the boiling-poimt and placed in the apparatus (Part I. fig. 3). The
sphere from which the water fell was the bulb of the thermometer which
468 Prof. Guthrie on Drops. [ Recess,
measured the temperature. Fully the upper half of the sphere was covered
with cotton-wool, so that the whole of the sphere was kept wet. The con-
siderable mass of mercury in the bulb of the dropping sphere or thermo-
meter itself served to make more uniform the temperature of the drops;
while the actual contact between the drops and the spherical bulb ensured
a tolerably close approximation between the actual temperature of the drops
and that indicated on the stem of the instrument. Although, therefore,
the temperatures observed cannot pretend to any even approximate positive
accuracy, yet they are certainly in the actual order of magnitude. The
arrangement is seen in Plate IV. fig. 6. :
TasLe XII.—Water.
oe
r=7°A millims.
Number of drops=20.
Relative mean
Temperature,| Weight of | Weight of | size of single drop
Centigrade. | 20 drops. | single drop. (corrected for
temperature).
ie germs. erm.
ao 2:5564 0:12782
40°35 40 25795 012897 0°12985
37° 25826 012913
35° 26083 0:13041
339 26105 0138052
32°6 26161 0:13080
31:2 25960 0:12980
30°64 306 26065 0:13032 0-13066
29: 26044 0-13022
| 28-2 25983 0:12992 |
28° 26078 0°13029
(27-5 2:6032 0:13016 )
20°4 20-4 26480 0-13240 0:13262
In the above Table the temperatures are so grouped together that the
means of the groups differ from one another by about 10°C. The single
drop-weights are correspondingly grouped, and the mean of each group is
then divided by the specific gravity of water (0°=1) at the mean tempe-
rature of the group.
It appears then that, for a range of 20° Centigrade, or 36° F., the dif-
ference in drop-size effected by change of temperature in the liquid is in-
appreciably small, not being more than 0:00277, a quantity almost within
the limits of experimental error ; for on referring to Table X. we find that
the greatest difference between the numbers for glass, which should be
equal, amounts to 0°00044 grm., or a sixth of the greatest difference due
to variation in temperature.
On the whole, then, we may conclude that the temperature has very little
influence on the drop-size in the case of water between the above limits.
No doubt, near the point of solidification, where liquids have an incipient
1864. ] Prof. Guthrie on Drops. 469
structure, the drop-size would be subject to sudden changes of magnitude.
A few experiments with other liquids, namely turpentol, acetic acid, and
alcohol, showed that with them the drop-size was almost equally insensible
to change of temperature; and in all cases, as with water, the lower the
temperature, on the whole, the larger the drop.
We have now examined seriatim all the chief causes upon which the
drop-size depends in the case SLG. They are, J. Rate of delivery;
2. Solids held in solution; 3. Chemical nature of liquid; 4. Geometric
relation between solid and liquid; 5. Density and chemical nature of solid ;
6. ‘Temperature.
Our data, however, are still insufficient for us to predict, under all cir-
cumstances, the relative sizes of the drops of liquids under known external
conditions. Clearly the missing term is closely related to the specific co-
hesion of the liquid. But what is cohesion ? and how can it be measured ?
It lies perhaps in the nature of things—it seems at least inevitable—that
the nomenclature of elementary properties should be vague and unsatisfac-
tory. The properties of solids—hard, soft, brittle, tough, tenacious, elastic,
malleable—do not stand in any definite relation to one another. Even the
hardness which resists abrasion, the hardness which resists penetration, the
hardness which resists crushing are by no means identical; so that one
body may possess more of the one sort of hardness than a second body
does, while the second body exceeds the first in another sort of hardness.
Nor do any of the above-mentioned properties of solids stand in any simple
relation to that resistance to the separation of the contiguous parts which
is called cohesion. Thus, by no attribution of this single property of co-
hesion could we define ice or shell-lac, bodies which are at the same time
tough, brittle, elastic, and soft.
We are forced to the conception of two distinct kinds of cohesion—séub-
born and persistent. These may coexist, but are not identical. The one
is strong to assert, the other pertinacious to maintain. The four following
substances may serve to illustrate the possession of these two cohesions in
various quantity.
Talc has little stubborn and little persistent cohesion.
Glass has much stubborn and little persistent cohesion.
Gold has little stubborn and much persistent cohesion.
Tron has much stubborn and much persistent cohesion.
The necessity for such a discrimination exists in a yet higher degree in
liquids. If we conceive two liquids of different nature dropping from the
same substance which they both wet, and if there be only one kind of co-
hesion, the one which has the greatest cohesion will tend most strongly to
assume the spherical form ; and this would tend to cause it to drop sooner,
or have a smaller drop-size than the other. Ona the other hand, the liquid
of stronger cohesion will cling most strongly to the film of liquid adhering
to the solid ; this will keep it longer from falling, and thereby increase its
drop-size.- Hence an increase of cohesion tends to produce two contrary
4.70. Prof. Guthrie on Drops. | Recess,
effects. But if there be a similar distinction between the two kinds of co-
hesion of liquids, as above pointed out in the case of solids, we have the
following consequence. It is the persistent cohesion which causes the as-
sumption of the spherical form, the stubborn which resists the separation
of the drop. The former tends to diminish, the latter to increase its size.
As one or other predominates, the size of the drop varies.
Accordingly the drop-size is by no means a measure of what is generally
called the cohesion of the liquid, but rather a measure of the difference
between the two cohesions, stubborn and persistent ; and the law is, that
the drop-size varies versely as the persistent, and directly as the iilicin
cohesion of the liquid.
In mercury, water, and glycerine the stubborn cohesion is greater in
proportion to the persistent cohesion than in the other liquids examined ;
but it by no means follows that persistent cohesion is wanting in mercury
or stubborn in alcohol.
When a drop is in the act of falling its stubborn cohesion is in equili-
brium with the resultant of two forces—the one, the persistent cohesion,
tending to produce a spherical form, the other the weight of the drop.
Since the former of these component forces is, for the same liquid, constant,
it seems as though the weight of the drop might be taken as a measure
and expression of the stubborn cchesion. But such is not the case, because
we have no ground for supposing that the diameter of the drop where the
separation occurs is of constant size; on the contrary, it must be conceded.
that in larger drops this hypothetical surface of stubborn cohesion is larger —
than in smaller drops. Further, unless we know the exact shape of a drop
in all cases, we are not in a position to deduce the size of the surface of
cohesion from the drop-size or drop-weight.
_ In the cases where it has been tried, it has not been found that the nature
of the gaseous medium in the case of SLG exerts-any appreciable or defi-
nite influence upon the drop-size. Taking glass for the solid and water
for the liquid, the medium was changed from air to nitrogen, hydrogen,
and carbonic acid. The exceedingly slight variation wrought in the
drop-size by this change may probably have been due to the different solu-
bility of the gases in water, and the consequent alteration in the cohesion
of that liquid.
Having now traced the effect of variation in the conditions which deter-
mine the size of a drop in the general case SLG (or where from a solid a
liquid drops through a gas), we come to the case SLL (that is, where from
a solid a liquid drops through a liquid). As in the cases of SLG, we must
here also take the three terms of such chemical nature as to be without
action upon one another.
SLL. From a Solid a Liquid drops through a Liquid.
A preliminary quantitative experiment was made under the following
conditions :—Water was made to drop from a glass sphere at the rate
1864.] _ Prof, Guthrie on Drops. 471.
gt=5". The drops were collected in a tube bearing an arbitrary mark.
The number of drops required to fill the tube up to this mark was noted.
Then the sphere was surrounded by turpentol, and the rate having been
brought again* to gt=5", the number of drops of water necessary to fill
the tube up to the same mark was counted. The turpentol being replaced
by benzol, the same operation was performed. The entire arrangement of
the Stalagmometer+ is seen in Plate V. fig. 7.
X, Y¥ are contrivances described in Part I. for giving a uniform flow of
water.
_ The siphon A rests upon the cotton-wool covering half of the dropping
sphere and thermometer-bulb G. The sphere is held by its stem B in the
clamp H. C is half a globular 1-lb. flask, supported by the filter-stand K..
Through the neck of C passes the tube D. C and D are joined liquid-
tight by the caoutchouc collar L. A few arbitrary marks are made at E.
The lip of C is turned down to a beak at M above the vessel F.
In adjusting the instrument, to get the required value of gé, the holder
K is slipped along the table so that the drops from G fall between C and
D, and not into D. When the required rate is obtained, it is slipped back
again. When such liquids as turpentol are used as media, a little water
is poured between D and C to protect the caoutchouc. In all cases where
a liquid medium is employed C is filled till it runs over.
In the first experiment, of which the results are given in the following
Table XIII., the numbers are subject to two sources of error. The volume
filled is rather small, and no allowance is made for meniscus. In this, as
in all cases of SLL, great care must be taken not to shake the instrument.
Tas.Le XIII.—Water.
Cue"
D227 €:
Radius of glass sphere=7°4 millims.
i, 2. 3. a.
Number of drops of) aroan of Relative size of
Medium. water required to | Gojimn 2. single dro
fill a given volume.
(through air=1).
DS cole ee ee ; { oe \ 57-0 1-0
28
Purpentol ......... - | 26°7 2:14
26
13-2440) By aoe aS { é \ 7:0 8:14
There is therefore a ereater difference between the drop-sizes of water in
benzol and turpentol than between those in turpentol and air. The tur-
* A diminution of g¢ is observed. Sita T Sradaypos, a drop.
472 Prof. Guthrie on Drops. [Recess,
pentol and benzol here employed had the specific gravities of 0-863 and
0:864 respectively ; they may therefore be considered of equal density.
Hence variation in the liquid medium, independent of variation in its den-
sity, produces an enormous effect upon drop-size. We shall have occasion
to return to this case. .
The influence which the liquid medium exerts on the drop-size, and the
share of that influence due to the specific gravity of the medium, will be
well seen on comparing the drop-sizes of mercury which falls through
various liquid media.
The arrangement of the apparatus for this purpose is seen in Plate V.
fig. 8. As far as A it is similar to fig. 7. The siphon A, fig. 8, is a capillary
tube; its lower end, which is turned vertically downwards, rests upon a sphere
of bees: R, which has been washed with nitric acid and sodium- amalgam, and
allowed to soak for some days under mercury. Mercury adheres perfectly
to such a sphere. In every case the sphere was immersed just halfway
in the liquid. A small capsule S is supported in the liquid on a stand T
about half an inch lower than the bottom of the sphere. As soon as gé
becomes constantly =5", the vessel V is moved so that S comes under R.
Five drops of mercury having been caught, the cup is moved horizontally
as before, taken out and replaced by a fresh one, and so on. The batches
of five drops are washed, dried, and weighed. The results are given in
Table XV.
We may, however, previously notice here with advantage a phenomenon
which attends the separation of drops under several circumstances, but
which can be watched most narrowly in the cases of SLL, because in a
liquid the separation of a drop is less abrupt than in a gas.
When water falls from glass through air, immediately after the drop
separates, a very minute drop is frequently projected upwards from the
upper surface of the drop*. I have not traced the conditions under which
this supplementary drop is formed; indeed it is sometimes formed, and
sometimes not, under apparently similar circumstances. No doubt the
proximate cause is that the drop at the instant of separation is not sphe-
rical; the persistent or retentive cohesion, which brings it almost imme-
diately to its normal shape, does not allow time for its more excentric parts
to collect to the main mass ; they are therefore by the motion of the main
drop flung off and projected upwards.
The same phenomenon is seen much more distinctly when water drops
at this rate (gé=5'') through benzol or turpentol. In these cases the per-
sistent cohesion of the liquid medium comes also into play.
But the most striking example of supplementary drops is seen when
* The secondary drop may be well shown by holding a plate containing anhydrous
cupric sulphate about two inches below the dropping solid. The white salt is smoothened
by pressure under a plate, and its surface, being porots, absorbs the water-drops instantly
and without splashing. The blue spots of hydrated sulphate show where the water
has fallen, ~
re, Lith.
SL
2
.
iC
Proc. Roy. Soc. Vol AM FU LV.
UA) AOS0T 7
Proc. Rey-Soe. VLXIIELVI
1864..] Prof. Guthrie on Drops. 473
glycerine forms the medium through which mercury drops. In this case,
when gé=5", there are always two supplementary drops of mercury formed.
It is impossible to determine whether they both have their origin at the
same moment and from the same drop. The probability, however, is that
they have not, but that one is first separated from the main drop, and the
second from the first; for there is always a great disparity between the
sizes of the two supplementary drops, whereas, if they were both formed
at the same time and for the same reason, we should be justified in expect-
ing greater equality. The drops soon separate in falling, in consequence
of the difference of their surfaces. The relative sizes of the main and sup-
plementary drops in the case of mercury falling from copper through gly-
cerine were determined as follows:—A number of porcelain cups (fig. 9)
were arranged at the bottom of a shallow dish full of glycerine ; when the
rate of dropping was uniform at gé=4", the dish was shifted horizontally
so that every drop with its two supplements was caught in a separate cup.
The globules of mercury in each cup were removed by a little scoop of
copper foil. Ten of each kind were collected. After washing and drying,
they were weighed, with the following result :—
Taste XIV.—Mercury.
gt 4."
P=2103,C.
Radius of sphere= 12:8 millims.
grms.
10 principal drops weighed ............ 6°3447
10 first supplementary drops weighed .... 0°1242
10 second do. do. G0; te. Or0229
10 complete drops weighed ........ 6°4918
In all cases of SLL the supplementary drop or drops were collected and
weighed or measured with the main drop.
In Table XV.—
Column 1 shows the medium through which the mercury dropped.
Column 2. The number of drops weighed.
Column 3. The weight of the drops. The weight of every batch of drops
is given, in order that the approximation between the figures for each liquid
may be compared with that between the separate liquids. In two cases
only, marked by an asterisk, are the numbers probably erroneous. They
are not reckoned in taking the mean.
Column 4. Mean weight of single drop, from column 3.
Column 5. Specific gravity of medium.
Column 6 shows the weight of the drop of mercury in the liquid. Since
the falling of the drop is determined in part by its weight, and since the
weight depends not only upon the size of the drop, but also upon the den-
sity of the medium in which it ig formed, it is interesting to see how the
VOL. XIII, 2N
A7 4 Prof. Guthrie on Drops. , [Recess,
size of the drop is affected by the diminution in its we = by the
density of the medium.
If W,=weight of drop of mercury in air,
W,=required weight of drop of mercury in liquid,
A=specific gravity of liquid, |
B=specific gravity of mercury ;
then W,=W —$W,
The values of W, form column 6.
The liquid media are arranged according to the order of rinecetiGllle of the
numbers of column 4. The salient points of Table XV. are chiefly these :-—
1. The drop-size of a liquid which drops under like conditions through
various media does not depend wholly upon the density of the medium and
consequent variation in the weight, in the medium, of the dropping liquid.
Thus glycerine, whose density is above that of all the other liquids ex-
amined, does not, as a medium, cause the mercurial drop to assume either
its minimum or maximum size.
2. The liquids in Table XV. are in the same order as in Table VII.
In other words, if there be two liquids, A and B, which drop under like
conditions through air, and the drop-size of the one, A, be greater than
that of the other, B; then of a third liquid, C, be made to drop through A
and through B, the drop-size of C through A is greater than the drop-size
of C through B.
3. Further, on comparing Tables XIII. and XV. it appears that, whether
water or mercury drops through turpentol and benzol, the drop through
benzol is greater than the drop through turpentol. This we shall after-
wards find confirmed in other instances into the law, If the drop-size of
A through B be greater than the drop-size of A through C, then the drop-
size of D through B is also greater than the drop-size of D through C.
It is further observed that, while mercury exhibits its largest drop when
falling through air, water assumes its smallest drop-size under this condition.
This method of the examination of liquids by drop-size in the case SLL,
which brings so prominently forward a comparatively slight difference be-
tween similar liquids, may be used, not only to detect commercial adulte-
rations of one liquid by another, but perhaps to distinguish between those
remarkably-related isomeric liquid bodies (the number of which is quickly
increasing) between whose terms the difference has until lately escaped
detection. Of these bodies perhaps the first most remarkable instance was
furnished by the two amylic alcohols ; but the greatest number at present
known is amongst the hydrocarbons.
We may take an example illustrating the use of the stad osiniottielee in
approximately measuring the proportion, in a mixture, of its two chemically
and physically similar, but not isomeric constituents.
Suppose we had a liquid which we knew to consist wholly of a mixture
of benzol and turpentol, and we wished to find the propor in which
1864.] . Prof. Guthrie on Drops. 475
TaBLE XV.—WMercury.
ge— a
P21 sc.
Radius of sphere=12°8 millims.
i, 2. 3. 4, 5. 6.
Medium Mean weight in| Specific | Weight of
through which pies Weight air and gravity | single drop in
the mercury of drops. | relative size of of respective
dropped. single drop. _|medium. medium.
———— = | — |
drops.
germs. m. grm.
0°76545 0-00 0°76545
3°5047 0°69750 1:00 0:64619
35066)
Glycerine ...... 3-4088 0:61508 1245 0:55793
2
—
(sy)
(J)
Or
Ean oe 29637 059822 0-364 | 056014
Turpentol ...... 043497 0°863 040715
|
pene eysrerenv anor |
i)
=
&
\—
476 Prof. Guthrie on Drops. [ Recess,
these two ingredients were present. We could scarcely approach to an
answer by any of the means hitherto employed. The specifie gravities of
the two liquids are so close (864, °863) that the density of the mixture
would give us no substantial aid. Though there is a considerable differ-
ence (80° C.) in their boiling-points, no one who is familiar with the diffi-
culties of fractional distillation would place any reliance upon a quantita-
tive separation based upon volatility. heir refractive indices are nearly
the same*. Their vapour-densities, 2°77, 4°76, though comparatively
different, are not absolutely very wide apart. They are active and passive
towards most of the same chemical reagents, and interfere with one another’s
reactions. If we have recourse to chemical analysis (C,, H,, C,, H,,), a very
small experimental error would point to a great difference in the proportion
of the two.
To find how far the stalagmometer (Plate V. fig. 7) is applicable in this
case, it was filled with five liquids in succession :—
Ist, with benzol: ioe. wal east eee ae o's aft ey =e
2nd, with two volumes benzol and one of turpentol =B,T.
3rd, with one volume benzol and one of turpentol.. = BT.
4th, with one volume benzol and two of turpentol =BT,.
Sth, with, turpentol
°
4
prasad)
Financial Statement.
518
"WOANSDOLT,
‘UATIIN NATIV WVITIIM
b L 966hF
G 0 g eee eee eee eee eee ee ee ee ee ry 74 yser Ayo 6é
I wf i! 0 eile ccm 2 a ne aman To LOLI Yr en co) tg) 6c
2D GLQ teen sumer ge OOURTeE
€ L Ghar
T SI C pot EES SME Se STO RR Plryoare ip ‘SUIGGo4C Id "AON
g QT VA Pere ee eee r ese eer eeeeassenes odN4OorT UBIUOOID WAY COLL (2) 8 9 ‘JOlg
0 0 - cht ue Aa eee ebro mpg UVLO ‘Trepud gy, "JOLT
G 61 $ SANE I CDR neti cee ESE NCS « ser [8p Koy dog
0 91 Fe SERB MORSE sess ERDAS banies tas nig nee Tino ULVY.GULLYUL AA
0 0 09 itt eseseeeseeseresrees Dug HOTBUOCL
9 14106 “""''' oFeysqy odaorjortqey Jo Loaang ‘KoyyeO pue yyrTag
g re 6e Ce ecrnccenneettececeese eee sosuod xn dANSOTOUT UojoV ‘KoTYVO “f
0 Zw Ve eeattccccennececece Cuses sTooyog odlcoyyoTquyL (73
00 GQ CC yomyg uojoy surprmqoy—: suorydraosqne
9 61 0g AOR COO OC TOR TOCIOTEICE FOr sodavyO Ayqog pue ‘s]001e ‘90R4SOq
9 91 y) CCIOIOCICICRCICIC NC ICTC NCTC RCH NC eC) Oieyehextyelyaneieiece aie lesalelaaceiereuaieigcesCeelersinie lela tern AaouUoTy~49
02 2 asataareter cieteratathirecsiale sista vial sais atareietatieve stemware waleniiclals sosuodxty AUT
9 2 GL ies Bi mine aEie tran eee itn, SI TS cs “0 SOXUT.
G LI OT falblaxeielaiarey stuta eeveneccence GUT Tete e cece eee enees sosuodxm ourddrys
9 1 Gp occu titeveseeeeeesseveeesserseeeresreerseererts QOUIBINSUT OAL
OL 61 t+ Desens ennnne POE SRE itn Nee alt it Soro ees OSTIOCNGT eo,
0 I CIl COCO OOO OCIA OMT OO CIO LAC DAOCOr Coecccccecece SuUlyYSrT pue [v09
ILO O08 ‘"''''"' sosuodxpp snoourjoostpy pus ‘ourureg ‘Axoyspoyd a,
g ST CQET eleieisiefaleialatatuleleiaveta Rie acnietetereteretarararetnieie Aydeasoyywy pue ‘OUIABLOUTT
‘Suipurg ‘1odeg ‘SSUIpOODOIg pue suOTjoLsULAT, SUUIT
g To Gin iajulelels ejsiciehsiniels sle:slarelaisis vaiare sutpurg, pue Axeaquy ony TOF syoogy
OL GOG arieett ee rereenee nnn teerteees ensoyeye9 OYMUOIOG OUT,
GI 868 “""' $68 98 qysnoq ‘sonmuUuy yueg poeyeprposuoy’) OOOLF
Moors
Il SIOL Oo eee eee rere res ovi cesossvasessvece mwoIsudg pure ‘S008 AA ‘solde[Rg
‘s
F
Boy 9eors
"MOojg "yuoy tod TZ MONT "pg 8G ETCH
‘SOMMUUY YU PoyEpl[OsUoH "PL SCT 696'LGF
‘sormuUy ‘yuey aod ¢ psonpoy ONO FF
‘unuue sod EF ‘suvrorskyg Jo odoT[o9 omy
WOdF “TILET TJOQuv'y 4v oyeyso UB Jo yUat aBozo OYY Jo YIFy-0uO
‘unuue dod ‘sp ETF Kossng up quer wtey 09,7
‘unUuUe
tod “PO 80 OLTF ‘Ca IT YS 'V FE) Xoso~ppINT ‘Wop 4x oyvys7q
‘umuuUe zed
P20 80 921F “Ca Ge G “V GG) oatysupooury ‘edaoyyorquyy 4x oyeysoy
‘spun psig] Hueprjour hparaog yohoy ayp fo hywadoug pup sagnasy
g GT G eoeee eect eeee eeeeee COO iC iii ii iri ir iy potoaodox SOIRYO yoo gy
9 CG e eee ee reese eees SON OOOO ng ncn iris predox ‘se pue sosuodxop voy,
0 0 OL, Sa ee eceeeee SOOO ii iii iris asonbogy “Qrars y ‘pjorog Ye
0 0 08 { ee cceeee Peewee oor are eereeeesseves siodeg s Ajjosuog “LIN pus
8 109FT “A(T 0} SoqyvTq JO°4soo FeyP—s}nog yyopang_ sstyy
0 0 0¢ SININOSIOnICn Ui seveeee F9-EOLT ‘soulpoo00rg ‘Ayoro0g [woruteyg,
e CI COF we .ee eee eeee Cee eee essere rane “ON ‘sduIpo0001g ‘SUOTJOVSULAT, jo ce) RS
0 ih E5G eee eereee ee eeeeeeee eee aeeeeeee seer ‘ysonbog UWOSTIOADIG ‘oI ‘ov
L 0 08G eeeesosons eee esenecersce Peer eee reese nsee spun iy qsnay, ‘OWE ‘ONL
5G eae Sicriie onise Nibbana se ersaite a dteoreeiey caicate ste yoo}g Uo spuapLAtcT
Q GL peg ces Sina stto a Sas atu tis grt sty ccusataanan Sete Capito syuoyy
O OL SZOL suorisodutog pur suorydtzosqng jenuuy
il 0 8cg CH Ome eee er ease ee seeeseresesoesvesesy puey uo pues ‘yueg 4v QOUBTET
SS ad
"POST ‘OG taquanoay pun “EQeT ‘T waquiasage waamjag hzowog yohoay ay fo syuawhng pun spdraooy
519
Financial Statement.
"LOANSDOLT,
EE ee Cece eeeserceastsss Cescese.scesssssesecorssseees ¢ “AO
9 O PECEF ‘WHTIIN NATIV WVITIIM 6 0 P90F { SuIpue woz oy} UI oAMyIpuedxT t0A0 ie an
9 61 0g eoeccese eecsceoce SEEING) AyVog pue ‘sjoor1e gd ‘95RjSs0q :
9 OT y weer cre resco reece see eseereressssosoesseeesersssssseseseneses Arauoye49
0 VA CG eee c osc rreceeveseseerseseeesessese eee escecevcscen ecco sosuodxqy MOT
rs Se coo. GaN Sos caste aaoaeecoeee Samat’ paren eehtes doe
ee os ae Oe eo ee
Q Ft OZ eer O4B987 adaomjorqeyy Jo Aoaang ‘AopyeOQ pues TUG
@ € €6& RGIS! GCG Co eae sosuodxiy] OINSOpOUT UOJ HIRES, “pe
ee ee spoorpg adr0ToTqe TL Di SpeZen es PORT ‘oe “AON Surpue IeaX oy} Ul ammyipuedxay
eee Ga oo gear yomyy uoyoy sutplinqey—: suondraosqng 8 0 S68& “FIST ‘OG ‘AON Surpue cveX olf} OF o[qutteav ommoouy
iy il yg SuedeeGe out Occer Gee ece ect abe ae etc scan aouvanstry oats os
OL 61 eT Tote oter cle ee siarotevaisiaisiatareiovelaieieioicteveleiclelela\stslatsieelaleleisyele sosuadxqy VOT, @ CLG alnlelntaratavoleteleteitorereVateravereforatetateisveleteyets do * paxoaooar soSaeqy jooreg,
OYE a 0 OS en ce ey ea Sunysry pue [vog 6) BQO DUCE 90G BUGS 20E 9 9 ‘SOB 8091009 "49
Fr 79 nooegeoad sosuadxqy snoouryaostpy pure ‘s aredoyy cK ‘roysjoyd a { osgoans0caoud guopanboodnoedci90700050000 sSU00 TI
oy Dn yO RIC noa err toe ecco cet Surely pue Suyureg 9 6 32 8 F 8 | Sumosq ye seg ‘Kyorog eorydeasoay
IM eOG TEs: Eee kydeasoyyry pue Suravasugy (tol 6 Fs ol fae **sosuodxnp vay, ‘Ajoro0g uveuury
CG). lds aC ea aIR le aioe O4jIp SuypoyyG pue sutpurg Ge Oleyls * sosuodxm vag, ‘Ajoro0g [eolmeyg
0 8 SSI °° ssuIpesoorg pur suorjoesueay, 107 1odeg 0:20 0G) =o ee ee " 79 S981 ‘sSuIpoo001g OF ‘£yer00g jeormeyg
g ST CSS 1 0 9 SPL orc oes eer sess sreoseosessseene SNODULTIOSTI oI 0 0 OL COP eee ss OoSseentFseeerosciossese "= -qsonbaq— o Wa ‘ppoyqog. eS i
6 cl HG ceeceee eececece 19-8¢ "SON ‘seuTpos001g ory e cI COP eo ccecsccccoes eccccsece ° “ON ‘ssulpooo0d ‘suOTjoRSUBL, jo a[eg
oo fe ee eae capes ee 28 0 FORT TL T sqleg 0 L EGG mislalatereleteveleloleteteloiniels\eloleistarsvalaieleters qsonbog, TOSTIAAO}C mo 3
TT GI cP pue ‘eget ‘IT Wee ‘sUOTORSURLT, SUUTIG BeOS Ona tae ee * (spun ysnay, Jo oATsn]oXe) Yoojg WO spuepLATy
"3 ¥ QT $2 peer reer eres eres seas eesssereeeseeace 0771p Ssurpulg, 9 Zl $GG Coo e eee w neces cece eee en see sesseceessceseserssecsorsesese-ssneee . S}U94,
S 8 I) Il 6 987 “Cues aeaqyy oy} toy syoog, 0 0 GEG irreeseeereeeeeees ofesenaenenena “++ suortsodurog
J) SITE Gi tee a veeececens aretatareteiesieiscereleterels ongoyeye9 oyUeIOY oy, 0 0 OSE sansa escestocscecconcsccsecss te eeseeeesceee sees ‘+ goog UOISSIUpY
9 a SIOT eecrccrcecees eecceecece ecvecceves uoIsuag pue ‘S058 AA. ‘SOLABTBG | a) OL IStl oem oreo reece rere ssecesevosersoseesecsacees suoljdizosqng yenuuy
DS OF eS es
‘EQQT “OR waquianoar burpua wnax oy2 buunp (spun ysni7, wows undo) ounprypuadaug pun amoouy fo quowamnrg
_———— a ne
Il & Gor IL & Gore
Il 2 008 seer eracecceresesesevececs eases eeecnee ecevcceres ec eececes "* gouvyeg
0 0 CZI eee eee eco e een sere eee ere esseresasessrerasesasesssseenee sjuvag Ag Il @ CaP Ooo cesecccssseeses spuoplLicy pus suordrazosqug ‘gouvleq OF,
Pp’ F pe FF
70) 0 0 o0sex “
0 0 O0gcF’ Cees ro ber earenseasee see eaeene ats "qua Jod € MON ‘e991 one 07 du s]U9TSOAUT
520 Statement of the number of Fellows. [Nov. 30,
The following Table shows the progress and present Hite of the Society
with respect to the number of Fellows :—
Patron Having | Paying | Paying
and | Foreign.) com- £2 12s. £4 =| Total.
Honorary. pounded. | annually. | annually.
November 30, 1863. 6 49 324 4 274 657
Since compounded..|..... ie heer hd ee —3
Since elected ...... +3 +4 +11 +18
Since deceased ....|....<. —2 | —11 —] —6 | —20
November 30, 1864. 6 50 320 3 276 655
Financial Statement. 519
1864.]
"LOLNSD OAT,
i
9 0 FECEF ‘WaT NATIV WVITTIM
9 61 0& Be NSS aVERS SS 8s SE SOAR O Anog pue ‘sjoorg ‘oseyso7
9 91 L e COOCOCNOONOLGODOOCODDOGOCOnDODOGOCOOUCUUODOUEEBOODDGGdD “+ KTATIOTIRIG
0 G CG SS SPS gS i a ie aes baat: anaes 2)5)0 (2100 er ng |
9 2 &I W cieeeaees Br Lc Meese Bes 5 eS eee Ene aR SOXRT,
G LI OL ececcccceccee Coeeneeoseoe eases eccece eeecccvccccce sosuod xq suiddiyg
9 1102 srreeess-oneisiy odsoujotqeyy, Jo Aoaang ‘AopyeQ pue Laphavitsl
g e 6e Peeve cencceccccececavess sosuodxqy QINSOTOUT u0pO_y ASRIEO “p
0 G G eceeeoseec reser er oesesece sjooyog edzoyyeTqe yr
(eon en. ce OORT OR BREE “youn uoJOY SutplInqoy—: suordriosqng
9 1 op occ eee AeA ANE ESRC RRR eke oa ie soueansuy ort
OL 6I $F Cvererrcesccccece oh erases nsccce eceeccore ercccceccce oo sosuodxny vol,
0 T CIl OIIOOIOICIOCIOIOIOICICTOICICN TC ICRCICICACIC Coeacccrcescsoscecnr * SuTYSIT pue [R09
IL LI ¥9 ROSES sosuodxm SnooweyT[OOSIPT pue ‘suredoyy ‘Aroystoyd q,
0 g GI eescecs Coecece verses ees eeoeseesescn eoceecce SUIURITO pue Sure g
[ESCH YC aii pas * Aydeasoyyry pue surmessug
9 L 96 letelolelstelelelsiclelaiete eoecones 0391p Ssurtoyy9 pue SsuIpurg:
0 8 SSI °° sdurpeooorg pue suortjoesueay, toy rodeg
g ST CQeT 1 0) 9 OPI aie ejelalelaleleietle/slclelslofelalelelelotefe/aistereve snoouvy] [ost] OIC.
GGT tee "19-89 “SONI ‘sBurposoorg onnt¢
daelste Tucan qaeceeeien sqrt
IT GT Ler ee ‘e08T TI 410 onic eNO
@ 8 TL TOE POM La cay es ee ceo ae "*-onaTp Surpurg
it 6 98F addocagsooBdacoDO nodagooace Axeaqvy aly} OF syoog
Me co | £06 ee eee recor eevee see eseeseessecs Cece rccsceces onsojeye9 OFIWUSIOG oud
9 IL SIOL ee ecccncvccscceccccece elelslcleicie ecoe Osu pue ‘so5e AA. ‘SOLIBTRS
6 © poeer
9 0 ECE
8 0 868¢
‘5 EY
os)
o>
8&
BOOO8NOCOMOS
NA
me
SH
Yen)
N
{ Core eresesecersce voeseee.soee Bia OGILEO: 4 (oy ‘og ‘AON
“POST ‘OG “AON Surpue reaxX oy AoF oqeteav oumoouy
eee ccocscveeccrccvscece ce ccecacccee ocee petdAooex sosreyy) [eae
0 9 0 eeoeccece @sceceesccccone 0491p ‘Soptyy g 8109 “40
cece ees rcsosescoce Cocccccesccsessceres SdU1I90 TAT
ee { sumoay ye sex ‘Ayor00g eorydeaSoex
GGlvleso oes sosuedxq vay, ‘Ajeto0g UvouUTT
GC Glare aes sosuedxap vay, ‘Ayoto0g TeoruLey{D
SSancnacoSDORd T9- 6981 ‘ssuIpoooorg IOF ‘Ayot00g [eoTUTEYD
Per oeeseoceeaearesccsoceccoresceoses gsonbobq—'s"a7uy ‘ ppwog “ay
eee eeossccsrcsccssccseesce
‘on ‘SduIpoo001g ‘suoTjORsUBIT, JO OTeO
Poe oreesccccarcoreeecnecesce qsonbogy WOSU9AR}G) uO 66
(spun ysnaq, Jo eATSnOXO) 40010 MO SpuapIATCL
S}U9 yy
Oe eee e cree ccessccccene eee reccccrscccerccceesscsscses suoTyIsodur0g
weer w error sess eeesee weer reosoeoseoeseesesoeeceresenese $997 UOISsSIUpYy
"rere" sTOTIdLIOsqny [eNUuLy
eeercccserce
"FOST ‘OG laquianoyy burps umag ay) bump (spunyy psniy, woul zundv) aimppucdag pun awoouy fo yuawaynrg
Il € Gover
Gevceceegaeasesnesesencoe
It &: o0@ ter eseeseeeereeeeeeereeeererres QUT EET
OO GGL ttt eeees goueg Sep
a lapel
“0 0 0 O0EcF
0 0 O0geF
IL & GCF
Il & cP
ye
@eereeroeesocegece
SpuepLAIg, pue suordraosqng ‘sourpeg Oo,
“uC
"* sormuauy yuop sod ¢ mony ‘gogT Ame 07 dn squomsoauy
‘pung Joyo oyfauarogy
Fa
F981 ‘0G “AON SUIpUS Iva OY} UL omNyIpUodxT SV
VOL, XITI.
520. —~Prof. A. H. Church on certain Ethylphosphates. [Dec. 8,
The following Table shows the progress and es state of is saad
with respect to the number of-Fellows :— ,
Patron Having | Paying | Paying
Seco aes 4 ; UN and | Foreign.| com- |. £2 12s. £4 Total. .
Borae Honorary. pounded. | annually. | annually.
November 30, 1863.) 6 49 | 324 4 .| (274) a eae
Since caripbiindell TS ne eae eet ee peeon —3 :
Since elected ...... to ees. | PO $4.60. 1y| 2
Since deceased ....|...... —2 | —11 —1 —6 | —20
November 30, 1864.) 6 | 50 | 320 3° | 976 | Gas
December 8, 1864.
Dr. WILLIAM ALLEN MILLER, Treasurer and Vice-President,
in the Chair.
It was announced from the Chair that the President had pp the
following Members of the Council to be Vice-Presidents :—
The Treasurer.
Mr. Gassiot.
Sir Henry Holland. —
The following communications were read :—
1. “ Researches on certain Ethylphosphates.” By ArrHur HERBERT
Cuurcu, M.A. Oxon., Professor of Chemistry, Royal Agricul-
tural College, Cirencester. Communicated by A. W. Hormann,
Ph.D., LL.D. Received October 21, 1864.
The constitution, properties, and derivatives of the so- »-called conjugated
sulphurous and sulphuric acids have been made.the subject of numerous
researches, and have led, in the hands of Gerhardt and others, to very
interesting results. I have examined at different times* several members
* On the Benzole Series, Parts 1 & 2. Phil. Mag. April and June 1855.
On the Spontaneous Decomposition of certain Sulphomethylates. Phil. Mag.
July 1855.
On the Action of Water upon certain Sulphomethylates. Phil. Mag. Jan. 1856.
On Parabenzole, Parts 1&2, Phil. J ae June 1857, pad Dec. 1859.
—_______________. :
1864.] Prof. A. H. Church on certain Ethylphosphates. 521
of the methylsulphuric, phenylsulphurous, nitrophenylsulphous and other
series, but have lately turned my attention to the analogous compounds of
the phosphoric series. Some remarkable substances have been thus made,
their constitution seeming to have a direct. bearing upon the important
question of the atomicity and equivalency of certain of the metallic elements.
Several substances might have served as starting-points for these new
Inquiries. A curious compound, phenylphosphorie acid, C, H, H, PO,,
was prepared ; but its instability, and the oxidation to which it and its salts
are liable, rendered it unsuited for the present purpose. I intend to
describe in the present paper but one series of salts, formed from Pelouze’s
ethylphosphorie acid, C, H, H, PO,. This compound, containing two atoms
of easily replaceable hydrogen, appeared admirably adapted for the pur-
pose in view. It is readily prepared by digesting (for 48 hours) finely:
crushed glacial phosphoric acid with alcohol of 90 per cent.:—
C,H,
oe i | O+HPO,= H | Po,
H
From the ethylphosphoric acid thus formed the barium salt was prepared
in large quantity and of perfect purity. This compound, C,H,, Ba,, PO,
+6H, 0, is remarkable for being less soluble in boiling water than in
water at 70° C., or even at 15°—a characteristic property of several other
ethylphosphates. Boiling water, in fact, affects this barium salt in a peculiar
manner. If to its boiling saturated solution a quantity of the ordinary
crystallized salt be added, the crystals instantly assume a pearly aspect,
and are found, after having been filtered off, washed once with boiling
water, and dried im vacuo over sulphuric acid, to have lost 5H,O, and
thus to have the formula
C,H,, Ba,, PO,+ Aq.
_ They thus contain the proportion of water found in the majority of the
ethylphosphates. _ When, on the other hand, cold water is poured on these
crystals, or on the salt dried at 100°, the lost water is regained, the nacreous
aspect of the dried salt disappears, while a great increase in its bulk occurs.
From the barium salt the lead and silver compounds are readily made.
To a solution of ethylphosphate of barium nearly saturated at 70°, acetate
of lead or nitrate of silver is added in slight excess, the liquid allowed
to cool and then filtered. The collected precipitate is to be washed with
cold water. The lead salt may be obtained anhydrous by heating it to
130°-150°: it is almost insoluble in cold water, but is slightly soluble in
hot water, from which it may be crystallized. The silver salt dissolves to
some extent in hot water, and separates in pearly plates as the liquid cools.
It is blackened, especially when moist, on exposure to daylight. | Dried in
* The following are the atomic weights adopted :—C=12, O=16, Hg=200; T have
provisionally retained for Ag, Ba, Ph, &c. the lower atomic eae till lately in
general use.
Dee
522 Prof. A. H. Church on certain Ethylphosphates. [Dee. 8,
the water-oven, it retains one atom of water of crystallization, and has the
formula C,H, Ag, PO,+Aq. It was chiefly by double decomposition with
the barium, lead, and silver salts that the compounds presently to be
described were formed. ‘The perfect purity of the substances used was
established by rigorous experiment ; a silver-determination, for instance, in
the argentic ethylphosphate used in many of the reactions to be detailed
further on, gave the following numbers :—
10°27 grains of the salt dried at 100°C. gave 8:22 grains of Ag Cl.
This result corresponds to 60°24 per cent of Ag, while the percentage
required. by the formula C, H,, Ag,, PO,+ Aq is 60°33. The other analyses
were equally satisfactory.
I give, in the present communication, a selection of the most interesting
of the numerous results obtained during the course of my experimental
inquiry. Many points of departure for other researches have occurred—
the investigation, for example, of the products, volatile and fixed, of the
destructive distillation of the ethylphosphates, and the determination of the
varying amount of water of crystallization in several of the salts prepared.
I may cite the barium salts as illustrations. Not only do the salts already
mentioned exist, namely one containing 6 Aq and the other 1 Aq, but a third
compound may be obtained by evaporating at about 50° or 60°C. a saturated
solution of the ordinary barium salt, and filtering off the deposited crystals
rapidly. The slender pearly plates thus formed are perfectly definite and
constant in composition ; they probably consist of equal equivalents of the
two former salts. Analysis gave the following numbers :—
7°04 grains g gave 5°01 grains of Ba, SO,,.
12°88 grains lost at 130° C. 2°5. grains of H, O.
These results correspond to 41° 85 per cent. ne Ba, and 19°407 per cent.
of H,O; the formula 2 (C, H, Ba, PO,)+7 Aq demands 42°28 per cent. of
Ba, wl 19°44 per cent. of HOO:
Ferrie Ethylphosphate.—Equivalent proportions of argentic ethylphos-
phate and pure crystallized anhydrous ferric chloride were weighed out.
The silver salt was mixed with some quantity of hot water, and the ferric
chloride, previously dissolved in hot water, then added, the liquid being
kept warm for some time. On filtering, a pale yellow liquid was obtained
which contained no silver, and the merest trace of chlorine. On heating
this liquid to the boiling-point, pale straw-yellow films separated from it:
a quantity of these was collected, washed with cold water and with alcohol,
and, after having been dried in the water-oven, analyzed with the following
results :—
I. °6115 grm. of the ferric salt gave on combustion with chromate of
lead 296 grm. of CO, and ‘22 grm. of H, O.
TI. °475 grm. gave 142 germ. of Fe, O,.
III. °393 grm. gave ‘115 grm, of Fe, O,.
IV. °475 grm. gave 294 grm. of Mg, P, O,.
V. 1°317 grm, lost at 150°C. -134 grm. of H, O.
1864. ] Prof. A. H. Church on certain Ethylphosphates. 523
These numbers correspond to the formula (C,H,), Fe,3PO,+3 Aq, as
may be seen in the comparison given below of the theoretical and experi-
mental percentages. |
Theory. Experiment.
— ~~ K, TI. III. IV.
Weiaee 5 72°. 13°38 SEO Ch etter eed bayeeet
Ele igi). 21 3°91 BGO le fe cyst) Ret an ae
ewe, UI. 20°82 = / 20°82, 20°56)
eee 4 93). 17-28 os) poboeteenelel tein alge
2240. 44-61 Sat) y: ves, Ning
938 100°00
In analysis V. 10°17 per cent. of water were lost by drying the air-dried
salt at 150°: the formula above given requires 10°03 per cent. If we
allow the formula fe Cl to express the molecule of ferric chloride, giving to
the iron in it the atomic weight a a2 18°67, then the ferric ethylphos-
phate may be written
C,H,
ie! | PO,+ Aq.
fe!
Few chemists would now admit such an expression to be anything more
than what may be termed an equivalent formula, comparable with that of
ethylphosphoric acid itself, yet representing one-third only of the true
atomic weight of the iron compound. It may, however, be worth while to
consider whether there be any mode of arriving at a decision concerning
the formula of the ferric ethylphosphate—whether the above simple ex-
pression be admissible, or the more complex form
(C, H,), )
Fet’
Fe™’ >3PO,+3 Aq.
Fert’ |
It appeared to me that, if the latter expression be the true one, we ought
to be able to replace +th or 3ths of the iron present by another metal: if
the simpler formula be correct, then any other replacement but that of
4 would be impossible, unless indeed we suppose that the very chemical
process made use of to effect the replacement causes a coalescence of three
atoms of the original salt, in order that one more complex atom of the new
mixed compound may be thereby constructed.
With this object in view, several experiments were devised. A solution
saturated at 60° and containing a known proportion of ferric and aluminic
ethylphosphates was brought to the boiling-point, and the salt thus
separated removed by filtration. In other cases absolute alcohol was
added to the warm concentrated solution till a part only, often but a small
part, of the salt was precipitated. By these methods, and by the action of
524 Prof. A. H. Church on certain Ethylphosphates. [Dee. 8,
mixed ferric and aluminic chlorides upon argentic ethylphosphate, several
salts were obtained of constant as well as of definite composition. For in
the majority of experiments where the same or slightly varied proportions
were employed, the same compound was obtained, even where but a very
small portion of the new compound, compared with the quantity formed,
was allowed to separate or be precipitated. This observation applies to
the salts obtained by ebullition and evaporation, by precipitation with
alcohol, and by the action of the mixed ferric and aluminic chlorides upon
the argentic ethylphosphate.
When the proportion of aluminium to iron in the mixed ethylphosphates
ranged near the ratio 13-7 : 84, the salt first formed gave on analysis results
corresponding to the formula
(C, rf
Fe, + 3P0,+3 Aq.
Al
In_ an analysis where both Al and Fe were determined, the following
results were obtained :—
1-056 grm. gave °241 germ. Fe, O,, and :0515 grm. AJ, O,.
A comparison of these results with theory gives—
Theory. Experiment.
Percentage of Fe.... 16:04 15°97
Percentage of Al..,. 2°62 2 At
When the ratio 27:4: 56 was attained, there was no difficulty im obtain
ing a salt having the formula
|
e, > 3 PO,+3 Aq.
eee
In one analysis
*83 grm. gave °1305 grm. Fe, O,, and -081 grm. Al, O,.
A comparison of these results with theory gives—
Theory. Experiment.
Percentage of Fe.... 11°18 11°01
Percentage of Al.... 5°38 5°21
But on further increasing the proportion of aluminium to iron up to
41-1: 28, no other definite compound could be obtained, though the salt
(C, re
Fe -3P0,+3Aq
Al,
might be reasonably supposed to exist. Yet the two compounds obtained,
if from their constancy of composition when prepared in diverse manners
(volumetric determinations of iron in both salts were made with nearly
the same results as those just given) I am justified in deeming them definite
salts, not mixtures, may lead one to conclude the formula for the ferric
ethylphosphate
1864. ] Prof, A. H. Church on certain Ethylphosphates. 525
C,H, ae
a fol PG. BAG
fe
inadmissible, and the expression
CoH ye
( Bee | 3P0,+3Aq :
correct, since we can replace not half only of its iron, but one-fourth also
by aluminium—a replacement manifestly impossible with the simpler ex-
pression. I am submitting this matter to further scrutiny by an investi-
gation of the mineral phosphates containing not only aluminium and iron,
but also calcium &c.
The higher atomic weights of iron still remain to be considered in con-
nexion with these complex salts. Ifthe atom of ferricum be triatomic and
therefore =56, then the normal ferric ethylphosphate already Bes Go is
readily represented thus,
(C, H,),
Fe!” | 3P0,43Aq,
Kell!
a compound which equally well admits the expression
C,H
eaeeeth 3P0,+3 Aq,
where Ffe=112. But with the mixed ferric-aluminic ethylphosphates
the case is altered. The compound (C,H,), Al, Fe,3PO,+3Aq allows
us indeed to assume the triatomicity of ferricum and aluminium,
(C, ria
Fell! +} 3P0,+3Aq,
Aq
though excluding the supposed hexatomic value of these metals ; while the
other salt described, (C, H,),, Fe,, Al, 3PO,+3Aq, does not allow their
triatomicity even ; we return in fact to the oldest view, where Fe=28, and
is sesquiatomic. _
Ferroso-ferric Ethylphosphate.—By acting upon a warm saturated so-
lution of basic ethylphosphate with a solution of mixed ferrous and ferric
sulphates, filtering rapidly, and adding to the filtrate strong alcohol till a
precipitate begins to separate, a solution is obtaimed which, after filtration
and standing, soon deposits a greenish-white precipitate, slightly crystalline.
This salt is.constant in composition when prepared under rather widely
varied conditions; but if in its preparation the ferric salt preponderate, the
normal ferric ethylphosphate will be first precipitated. Perhaps a better
way of preparing the new compound than that above given consists in
warming a strong solution of ethylphosphoric acid with ferrous hydrate,
filtering and adding strong alcohol. The precipitate produced by either
method is to be washed with weak alcohol, and dried as rapidly as possible
im vacuo over sulphuric acid. It contains iron in both conditions, and
526 Prof. A. H. Church on certain Ethylphosphates. [Dec. 8,
gave results, according to the subjoined analytical details, agreeing with
the formula
rer $8PO,+3Aq,
Fe
An identical compound may also be obtained by following the several plans
adopted in preparing the ferric ethylphosphate ; it is, however, very diffi-
cult to prevent a partial oxidation of the ferrosum in the salt. It will be
noted that the atomic weight 28 is indicated by the constitution of this
compound.
In order to analyze the ferroso-ferric ethylphosphate, the following
methods were adopted. In a preliminary examination of the salt it was
found that strong mineral acids did not effect the separation of phosphoric
acid from it: it was also seen that its acid solution gave the ordinary
reactions of both conditions of iron. For analysis a weighed amount of
the salt was dissolved in dilute sulphuric acid, and the amount of standard
permanganate solution decolorized by it ascertained; this gave the amount
of ferrosum in the salt taken. A second experiment was then made, in
which the total amount of iron in both forms was determined by perman-
ganate after reduction of the sulphuric solution with pure zinc; the differ-
ence between the two percentage results gave the percentage of iron existing
as ferricum in the original compound. The numbers thus obtained were
on the whole satisfactory ; the total amount of iron agreed nearly with that
demanded by theory, though the amount of ferrosum in the salt was never
less than °5 per cent. below the required proportion. It was in fact impos-
sible entirely to prevent oxidation of the salt; but it will be perceived that
the ferric oxide thus produced, not being lost, introduced but an inconsi-
derable error into the determinations. Nor did any inconvenience arise
from the presence of phosphovinic acid, which, curiously enough, was found
to be without reducing action on the permanganate, even in the presence
of sulphuric acid. The following results were obtained in the analysis of
the ferroso-ferric ethylphosphate.
The ferroso-ferric ethylphosphate was dried in vacuo over sulphuric acid.
In each experiment with the permanganate solution -5 gramme of the iron
salt was taken. ach cubic centimetre of the permanganate solution cor-
responded to ‘00492 grm. of Fe. The following are the results obtained
by this method of analysis, three different preparations of the ethylphos-
phate being used :—
I. 14:4 cub. centims. permang. = *070848 Fe
II. 14:2 cub. centims. permang. = *069864 Fe
III. 14:0 cub. centims. permang. = *06888 Fe
IV. 14:4 cub. centims. permang. = *070848 Fe
After reduction of va V. 25:0 cub. centims. permang. = ‘123 Fe
ethylphosphate VI. 24°6 cub. centims. permang. = ‘121032 Fe
Before reduction of the
ethylphosphate with
zinc.
1864. ] Prof. A. H. Church on certain Ethylphosphates. 527
The mean of the first four experiments gives 14-022 as the percentage
amount of ferrosum in the compound. The theory (C, H,), (Fe!), (Fe’),
3PO,+3Aq demands 14°841.
The mean of the last two experiments gives 24°402 as the total percentage
of iron in the compound, ‘The theoretical percentage is 24°745. If the
experimental mean percentage of ferrosum be deducted from the total mean
percentage of iron arrived at by experiment, thus, 24°402— 14:022=10°38,
the number arrived at gives the percentage of ferricum in the compound ;
the formula above given requires 9°894 per cent.: thus the experimental
percentage exceeds the theoretical by 486 per cent.—a small error, consi-
dering the very great difficulties attending the manipulation of this easily
oxidized salt.
Uranylic Ethylphosphate.—Some pure uranic oxide, Ur,O,, was pre-
pared by repeatedly acting on uranic nitrate with alcohol, the pasty mixture
being heated ona water-bath. When the separation of the oxide was com-
plete, it was mixed at a temperature of about 60° or 70° with a weak solu-
tion of ethylphosphoric acid. After dilution with hot water and digestion,
the solution was filtered and evaporated. As soon as the boiling-point
was attained, the solution almost solidified from the separation of clear
yellow gelatinous masses of the newsalt. These were collected by filtration
of the boiling liquid after a portion of the water had evaporated. Sub-
mitted to analysis, they gave results leading to the formula C, H,, U, O,,
PO,+Aq. This uranic salt thus agrees in constitution with the inorganic
uranic phosphates already known, and lends additional support to Péligot’s
Uranyle theory. The following list gives the formulee of various uranylic
phosphates, uranyle being represented by the expression U,O :—
DAO EH PO,--Aq..... ... Monuranic phosphate.
2U,0, H, PO,+3 Aq
2U,0, H, PO,+4 Aq
UO WhO, (i) rite ie eat Triuranic phosphate.
2U,0, Ca, PO,+4Aq .... Diurano-calcic phosphate (lime-uranite).
C, H,, 2U,0, PO,+Aq .. Diurano-ethylphosphate.
This new uranic salt, like many other ethylphosphates, is less soluble in
water at 100° than in water at 60° or 70°. It separates from its solutions
in pale yellow flocks, which dry up in the water-oven into amorphous brittle
masses of a bright lemon-yellow colour. Attempts to replace a portion of
the uranyle in this salt by calcium and by silver led to no definite results.
The following are the analyses of the uranylic ethylphosphate dried at 100° :
I. +517 grm. gave ‘106 grm. of Co, and ‘0835 grm. of H, O.
Il. °375 grm. gave ‘254 germ. of protosesquioxide of uranium, U, O,.
III. -3335 grm. gave °226 grm. of U, O,.
IV. 6645 grm. gave °1735 grm. of Mg, P, O,.
V. +1 grm dried at 100° lost at 150° -044 grm. of H,O.
These results correspond to the following percentages :—
} .. .. Diuranic phosphate.
528 Prof. A. H. Church on certain Ethylphosphates. [ Dee.3;
Theory. Experiment.
——— 7 I. ir, III. IV.
TOS OA ays 550) ee
Ao 1:69 179°
Wie a ee 57°97 — $733 5754 —
| Bae ah aa 31 Zoe — gules pal 7°29
Oe ag G2 eh) 27°01 — — — —
414 100°00
_ The loss of water in analysis V. amounted to 4°4 per cent.; the theory
C, H,, 2U,O, PO,+Aq requires 4°35 per cent. |
_ Arsenious Ethylphosphate.—The replacement of the basic hydrogen of
ethylphosphoric acid by such an element as arsenic appeared to present
some features of interest. The experiment was thus made. Toa weighed
quantity of pure arsenious chloride in a small flask, an equivalent quantity
of anhydrous ethylphosphate of lead was added (in one experiment ethyl-
phosphate of silver). The mixture became warm, and after moderate
heating solidified. It was extracted with warm water, and the filtered
extract evaporated. Beautiful feathery crystals separated in considerable
quantity. Once crystallized from a solution, they appeared to dissolve less
readily a second time in water. The cause of this phenomenon was soon
discovered. Water gradually decomposes this salt, giving arsenious anhy-
dride and ethylphosphoric acid. Although the analysis of the first crop
of crystals was tolerably satisfactory, the original method of preparing the
compound was abandoned, and another plan adopted. It was found that
ethylphosphoric acid readily dissolves arsenious acid at the boiling-point,
and that on heating and evaporating the solution, beautiful crystals of the
arsenious ethylphosphate separate. In order to study this reaction more
closely, the experiment was repeated, substituting, however, common ortho-
phosphoric for the ethylphosphoric. The arsenious anhydride readily
dissolved in considerable quantity on ebullition; and after filtration and
cooling, an abundant crop of brilliant crystals was deposited from the filtrate.
These crystals were not perceptibly affected by washing with cold water,
and proved to be completely volatile when heated in a test-tube over a
spirit-lamp. In fact they were nothing but octahedra of arsenious anhy-
dride. Further experiments showed that it was not possible in this manner
to form an arsenious phosphate ; so that the statement in Gmelin’s Hand-
book, referring to this salt as probably obtaimable by the process above
given, would seem to require correction. ‘The normal arsenious phosphate,
As PO,, remains to be discovered ; a peculiar interest consequently attaches
to the salt now under review, as the only arsenious phosphate known.
Prepared. by either of the processes above given, pressed between folds of
filtered paper, and dried in vacuo, it gave on analysis numbers very nearly
agreeing with the expression
C,H
(C, re } 3PO,.
1864.] Prof. A. H. Church on certain Ethylphosphates. 529
The arsenic in the arsenious ethylphosphate was determined as sulphide,
the precipitation being effected according to the directions given by Fre-
senius. The salt was dried by pressure between folds of filter-paper, it
was then placed im vacuo over sulphuric acid, and finally heated for a short
time in the water-oven. The arsenious sulphide obtained on its analysis
was dried at 100° C.
I. 1°347 grm. gave °639 grm. of As, 8,.
II. -591 grm. gave ‘29 grm. of As, §,.
The formula (C,H,), As, 3PO, requires 28°74 per cent. of arsenic:
analysis I. gave 28:95, while II. gave 29°58, the specimen of salt sub-
mitted to analysis in the latter case having been partially decomposed by
washing, ethylphosphoric acid being thus removed, and consequently an
excess of arsenious anhydride remaining in the residual salt.
The ease with which the arsenious ethylphosphate is formed induced me
to hope that similar success would attend experiments made with another
triatomic element, phosphorus. When an action is established between
terchloride of phosphorus and ethylphosphate of silver, an oily product
may be removed from the mass by means of anhydrous ether, but it yields
on analysis results less definite than could be wished. Yet the reaction is
a promising one: I hope to recur to it shortly, and to experiment in a
similar manner with antimony and bismuth compounds.
Ditetrethyliac Kthylphosphate.—The ordinary ethylphosphate of ammo-
nium is very readily made; its aqueous solution becomes acid on evapora-
tion, but the salt may be obtained in a semicrystalline form by drying its
saturated solution 7m vacuo over sulphuric acid. The salt heated carefully
in an oil-bath for some time loses ammonia as well as water, but yet appears
to yield, among other products, ethylphosphamic acid. A different and
much more definite kind of decomposition takes place with the compound
next to be described.
When a hot solution of argentic ethylphosphate is mixed with a solu-
tion of iodide of tetrethylinum, a change occurs expressed by the equation
C, H,, Ag,, PO,+2((C, H,),NU=C, H,, (C,H), NJ, PO,+2AgT.
If the two salts be employed in the exact proportions indicated by this
equation, it will be found that after boiling them together the new com-
pound is contained in the filtrate. On evaporating this liquid first of all
at 100°, and then in vacuo over sulphuric acid, a syrup, and finally a
mass of confused crystals will be obtained; by long drying, these crystals
lose their transparency, most probably because they have thus parted with
some of their water of crystallization. The salt is intensely soluble in cold
water, and deliquescent. The analyses of this salt were not exact, but
corresponded sufficiently with the formula of an ethylphosphoric acid in
which two atoms of hydrogen had been replaced by two atoms of tetrethy-
lium. This view of its constitution is amply confirmed, not only by the
mode in which the salt is prepared, but also by a singular decomposition
530 Prof. A. H. Church on certain Ethylphosphates. [Dec. 8,
which it undergoes when heated. It begins indeed to decompose, though
- very slightly, at 100°, even when water is present, giving off a distinct
odour of triethylamine. But on heating the salt itself to a temperature
exceeding 100°, decomposition becomes more rapid, and the substance is
finally resolved into triethylamine and triethylic phosphate,
C,H, ((C, H;), NJ, PO,=(C, H,), PO,+ 2 (C, H,), N.
The triethylamine was analytically identified by a platinum-determination
in the double chloride made from it by addition of hydrochloric acid and -
platinic chloride. 'The metamorphosis of this ethylphosphate is perhaps
more easily seen by means of the following arrangement of its formula :—
C,H, |
C, Ht,
»H,;N
C, |
C,H, +N
0, H,
CHENG
Several ethylphosphates have been prepared besides those described in
the present paper; most of these salts, however, presented no marked
features of interest. The ammonium, nickel, chromic, mercurous, and
platinic compounds were investigated more particularly. ‘The mercurous
ethylphosphate is somewhat difficult to prepare; it is best made by adding
a few drops of mercurous nitrate to a strong solution of potassic ethylphos-
phate, filtermg off the grey precipitate first formed, and then adding a
further quantity of the mercurous nitrate in solution ; if the solutions are
not too concentrated the salt gradually separates in pearly plates. Hot
water partially dissolves this salt, the residue becoming yellow, and the
solution acquiring a distinct acid reaction. It is slightly soluble in cold
water, though not altogether without decomposition; it is insoluble in
alcohol. Dissolved in dilute nitric acid and precipitated by chloride of
sodium, the air-dried crystals of this salt gave the following result :—
236 grm. gave ‘191 grm. of Hg" Cl.
This corresponds to 71-09 per cent. of mercury; the formula C,H, Hg", PO,
+2 Aq requires 71°45 per cent. The more probable formula, C,H, Hg", PO,
+ Aq, requires 73°82 per cent.
In offering the foregoing results to the Society, I do not wish it to be
supposed that I consider them conclusive so far as regards the theoretical
considerations introduced into the present paper. It is possible that the
various aluminium and iron salts described may be mixtures only, in spite
of their apparent constancy of composition ; or, again, it may be that their
formulee ought to be doubled or quadrupled. Moreover the constitution
of ethylphosphoric acid itself has not been made out: I trust that the study
of diethyl-, ethylpyro-, and ethylmeta-phosphoric acids, and of the pro-
1864. | Dynamical Theory of the Electromagnetic Field. 531
ducts of the action of heat on the ethylphosphates, may aid in determining
this question. Meanwhile the observation, already recorded, as to the
stability of ordinary ethylphosphoric acid and its salts in the presence of
permanganate of potassium requires a word or two of further comment.
When argentic diethylphosphate is acted upon with iodine, the silver and
one atom of ethyl may be removed, and after treatment with finely divided
silver and a little oxide of silver to remove any iodine and hydriodic acid,
and then with excess of carbonate of barium, an ethylphosphate of barium
is obtained, which, unlike the ordinary salt, immediately reduces perman-
ganate of potassium ; perhaps the ethyl in this salt exists in a different and
less intimate form of combination. I am inclined to think that the per-
manganates will afford, in some cases, criteria for the detection of slight
differences in isomeric compounds, although it would be premature at
present to hazard an exact interpretation of the phenomena to which they
give rise. I may add that treatment of an ethylphosphate with strong
nitric acid fails to decompose the ethylphosphoric acid ; so that phosphoric
acid cannot thus be separated from this remarkably stable body.
If. “ A Dynamical Theory of the Electromagnetic Field.” By Pro-
fessor J. Crerk Maxwe nt, F.R.S. Received October 27, 1864.
(Abstract.)
The proposed Theory seeks for the origin of electromagnetic effects in
the medium surrounding the electric or magnetic bodies, and assumes that
they act on each other not immediately at a distance, but through the
intervention of this medium.
The existence of the medium is assumed ag probable, since the investi-
gations of Optics have led philosophers to believe that in such a medium
the propagation of light takes place.
The properties attributed to the medium in order to explain the propa-
gation of light are—
Ist. That the motion of one part communicates motion to the parts in
its neighbourhood.
2nd. That this communication is not instantaneous but progressive, and
depends on the elasticity of the medium as compared with its density.
The kind of motion attributed to the medium when transmitting light is
that called transverse vibration.
An elastic medium capable of such motions must be also capable of a
yast variety of other motions, and its elasticity may be called into play in
other ways, some of which may be discoverable by their effects.
One phenomenon which seems to indicate the existence of other motions
than those of light in the medium, is that discovered by Faraday, in which
the plane of polarization of a ray of light is caused to rotate by the action
532 Prof. J. C. Maxwell on a Dynamical Theory _— [Dee. 8
of magnetic force. Professor W. Thomson* has shown that this pheno-
menon cannot be explained without admitting that there is motion of the
luminiferous medium in the neighbourhood of magnets and currents.
The phenomena of electromotive force seem also to indicate the elasticity
or tenacity of the medium. When the state of the field is being altered by
the introduction or motion of currents or magnets, every part of the field
experiences a force, which, if the medium in that part of the field is a con-
ductor, produces a current. If the medium is an electrolyte, and the elec-
tromotive force is strong enough, the components of the electrolyte are
separated in spite of their chemical affinity, and carried in opposite direc-
tions. Ifthe medium is a dielectric, all its parts are put mto a state of
electric polarization, a state in which the opposite sides of every such part
are oppositely electrified, and this to an extent proportioned to the intensity
of the electromotive force which causes the polarization. If the intensity
of this polarization is increased beyond a certain limit, the electric tenacity
of the medium gives way, and there is a spark or “disruptive discharge.”
Thus the action of electromotive force on a dielectric produces an elec-
tric displacement within it, and in this way stores up energy which will re-
appear when the dielectric is relieved from this state of constraint.
A dynamical theory of the Electromagnetic Field must therefore assume
that, wherever magnetic effects occur, there is matter in motion, and that,
wherever electromotive force is exerted, there is a medium in a state of con-
straint; so that the medium must be regarded as the recipient of two kinds
of energy—the actual energy of the magnetic motion, and the potential
energy of the electric displacement. According to this theory we look for
the explanation of electric and magnetic phenomena to the mutual actions
between the medium and the electrified or magnetic bodies, and not to any
direct action between those bodies themselves.
In the case of an electric current flowing in a circuit A, we know that
the magnetic action at every point of the field depends on its position rela-
tive to A, and is proportional to the strength of the current. If there is
another circuit B in the field, the magnetic effects due to B are simply
added to those due to A, according to the well-known law of composition
of forces, velocities, &c. According to our theory, the motion of every part
of the medium depends partly on the strength of the current in A, and
partly on that in B, and when these are given the whole is determined.
The mechanical conditions therefore are those of a system. of bodies con-
nected with two driving-points A and B, in which we may determine the
relation between the motions of A and B, and the forces acting on them, by
purely dynamical principles. It is shown that in this case we may find two
quantities, SLE, the ‘reduced momentum” of the system referred to A
and to B, each of which is a linear function of the velocities of A and B.
The effect of the force on A is to increase the momentum of the system
* Proceedings of the Royal Society June 1856 and June 1861.
1864. ] of the Electromagnetic Field. — 533
referred to A, and the effect of the force on B is to increase the momentum
referred to B. The simplest mechanical example is that of a rod acted on
by two forces perpendicular to its direction at A and at B. Then any
change of velocity of A will produce a force at B, unless A and B are
mutually centres of suspension and oscillation.
Assuming that the motion of every part of the electromagnetic field is
determined by the values of the currents in A and B, it is shown—
Ist. That any variation in the strength of A will produce an electromo-
tive force in B. .
2nd. That any alteration in the relative position of A and B will produce
an electromotive force in B.
3rd. That if currents are maintained in A and B, there will be a mecha-
nical force tending to alter their position relative to each other.
Ath. That these electromotive and mechanical forces depend on the valué
of a single function M, which may be deduced from the form and relative
position of A and B, and is of one dimension in space ; that is to say, it is a
certain number of feet or metres. ; :
The existence of electromotive forces between the circuits A and B was
first deduced from the fact of electromagnetic attraction, by Professor Helm-
holtz* and Professor W. Thomson+, by the principle of the Conservation
of Energy. Here the electromagnetic attractions, as well as the forces of
induction, are deduced from the fact that every current when established
in a circuit has a certain persistency or momentum—that is, it requires the
continued action of an unresisted electromotive force in order to alter its
value, and that this ‘“‘ momentum”’ depends, as in various mechanical pro-
blems, on the value of other currents as well as itself. This momentum is
what Faraday has called the Electrotonic State of the circuit.
“It may be shown from these results, that at every point in the field there
is a certain direction possessing the following properties :—
A conductor moved in that direction experiences no electromotive force.
- A conductor carrying a current experiences a force in a direction per-
pendicular to this line and to itself. A
A circuit of small area carrying a current tends to place itself with its
plane perpendicular to this direction.
A system of lines drawn so as everywhere to coincide with the direction
having these properties is a system of lines of magnetic force ; and if the
lines in any one part of their course are so distributed that the number of
lines enclosed by any closed curve is proportional to the “ electric momen-
tum ”’ of the field referred to that curve, then the electromagnetic pheno-
mena may be thus stated :—
The electric momentum of any closed curve whatever is measured by the
number of lines of force which pass through it.
* Conservation of Force. Berlin, 1847: translated m Taylor’s Scientific Memoirs,
Feb. 1853, p. 114.
+ Reports of British Association, 1848, Phil. Mag. Dec. 1851.
534 Prof. J.C. Maxwell on a Dynamical Theory _— [Dee. 8,
If this number is altered, either by motion of the curve, or motion of
the inducing current, or variation in its strength, an electromotive force acts
round the curve and is measured by the decrease of the number of lines
passing through it in unit of time. |
If the curve itself carries a current, then mechanical forces act on it tend-
ing to increase the number of lines passing through it, and the work done
by these forces is measured by the increase of the number of lines multi-
plied by the strength of the current.
A method is then given by which the coefficient of self-induction of any
circuit can be determined by means of Wheatstone’s electric balance.
The next part of the paper is devoted to the mathematical expression of
the electromagnetic quantities referred to each point in the field, and to the
establishment of the general equations of the electromagnetic field, which
express the relations among these quantities.
The quantities which enter into these equations are :—Electric currents
by conduction, electric displacements, and Total Currents; Magnetic
forces, Electromotive forces, and Electromagnetic Momenta. Each of
these quantities being a directed quantity, has three components; and be-
sides these we have two others, the Free Electricity and the Electric Poten-
tial, making twenty quantities in all.
There are twenty equations between these quantities, namely Equations
of Total Currents, of Magnetic Force, of Electric Currents, of Electro-
motive Force, of Electric Elasticity, and of Electric Resistance, making
six sets of three equations, together with one equation of Free Electricity,
and another of Electric Continuity.
These equations are founded on the facts of the induction of currents as
investigated by Faraday, Felici, &c., on the action of currents on a magnet
as discovered by Oersted, and on the polarization of dielectrics by electre-
motive force as discovered by Faraday and mathematically developed by
Mossotti.
An expression is then found for the intrinsic energy of any part of the
field, depending partly on its magnetic, and partly on its electric polari-
zation.
From this the laws of the forces acting between magnetic poles and
between electrified bodies are deduced, and it is shown that the state of
constraint due to the polarization of the field is:such as to act on the bodies
according to the well-known experimental laws.
It is ae shown in a note that, if we look for the explanation of the force
of gravitation in the action of a surrounding medium, the constitution of
the medium must be such that, when far from the presence of gross matter,
it has immense intrinsic energy, part of which is removed from it wherever
we find the signs of gravitating force. This result does not encourage us
to look in this direction for the explanation of the force of gravity.
The relation which subsists between the electromagnetic and the electro-
static system of units is then investigated, and shown to depend upon what
1864. ] of the Electromagnetic Field. 535
we have called the Electric Elasticity of the medium in which the experi-
ments are made (7.e. common air). Other media, as glass, shellac, and
sulphur have different powers as dielectrics; and some of them exhibit the
phenomena of electric absorption and residual discharge.
It is then shown how a compound condenser of different materials may
_be constructed which shall exhibit these phenomena, and it is proved that
the result will be the same though the different substances were so intimately
intermingled that the want of uniformity could not be detected.
The general equations are then applied to the foundation of the Electro-
magnetic Theory of Light.
Faraday, in his “‘ Thoughts on Ray Vibrations” *, has described the effect
of the sudden movement of a magnetic or electric body, and the propaga-
tion of the disturbance through the field, and has stated his opinion that
such a disturbance must be entirely transverse to the direction of propaga-
tion. In 1846 there were no data to calculate the mathematical laws of
such propagation, or to determine the velocity.
The equations of this paper, however, show that transverse disturbances,
and transverse disturbances only, will be propagated through the field, and
that the number which expresses the velocity of propagation must be the
same as that which expresses the number of electrostatic units of electricity
in one electromagnetic unit, the standards of space and time being the same.
The first of these results agrees, as is well known, with the undulatory
theory of light as deduced from optical experiments. The second may be
judged of by a comparison of the electromagnetical experiments of Weber
and Kohlrausch with the velocity of light as determined by astronomers
in the heavenly spaces, and by M. Foucault in the air of his laboratory.
Electrostatic units in an electromag-
mete Ant... .".. . - vee.
Velocity of light as aad be M. aS 314,858,000.
Velocity of baht by M. Foucault...... 298,000,000.
gale” of light deduced from ser 308,000,000.
At the outset of the paper, the dynamical theory of the electromagnetic
field borrowed from the undulatory theory of light the use of its lumini-
ferous medium. It now restores the medium, after having tested its powers
of transmitting undulations, and the character of those undulations, and
certifies that the vibrations are transverse, and that the velocity is that of
light. With regard to normal vibrations, the electromagnetic theory does
not allow of their transmission.
What, then, is light according to the electromagnetic theory ? It consists
of alternate and opposite rapidly recurring transverse magnetic disturbances,
accompanied with electric displacements, the direction of the electric dis-
placement being at right angles to the magnetic disturbance, and both at
right angles to the direction of the ray.
* Phil, Mag. 1846. Experimental Researches, yol, iii, p. 447.
VOL, XIII. 28
a 310,740,000 metres per second.
586 A Dynamical Theory of the Electromagnetic Field. (Dee. 8
The theory does not attempt to give a mechanical explanation of the
nature of magnetic disturbance or of electric displacement, it only asserts
the identity of these phenomena, as observed at our leisure in magnetic and
electric experiments, with what occurs in the rapid vibrations of light, 1 ina
portion of time inconceivably minute.
This paper is already too long to follow out the application of the elec-
tromagnetic theory to the dlirerent phenomena already explained by the
undulatory theory. It discloses a relation between the inductive capacity —
of a dielectric and its index of refraction. The theory of double refraction
in crystals is expressed very simply in terms of the electromagnetic theory.
The non-existence of normal vibrations and the ordinary refraction of rays
polarized in a principal plane are shown to be capable of explanation; but
the verification of the theory is difficult at present, for want of accurate
data concerning the dielectric capacity of crystals in different directions.
The propagation of vibrations in a conducting medium is then considered,
and it is shown that the light is absorbed at a rate depending on the con-
ducting-power of the medium. This result is so far confirmed by the
opacity of all good conductors, but the transparency of electrolytes shows
that in certain cases vibrations of short period and amplitude are not ab-
sorbed as those of long period would be.
_ The transparency of thin leaves of gold, silver, and platinum cannot be
explained without some such hypothesis.
The actual value of the maximum electromotive force which is called
into play during the vibrations of strong sunlight is calculated from
Pouillet’s data, and found to be about 60,000,000, or about 600 Daniell’s
cells per metre.
The maximum magnetic force during such vibrations is ‘193, or about >
of the horizontal magnetic force at Tignes
Methods are then given for applying the general oe. to the calcu-
lation of the coefficient of mutual induction of two circuits, and in parti-
cular of two cireles the distance of whose circumferences is- small eine?
with the radius of either.
The coefficient of self-reduction of a Jeoil of Petal section is found
and applied to the case of the coil used by the Committee of the British
Association on Electrical Standards. The results of calculation are com-
pared with the value deduced from a comparison of experiments in which
this coefficient enters as a correction, and also with the results of direct
experiments with the electric balance.
1864.] = =-Dr. Bence Jones on the production of Diabetes. 537
December 15, 1864:
J. P. GASSIOT, Hsq., Vice-President, in the Chair.
A letter addressed to the President by Dr. William Farr, F.R.S., was read,
as follows :—
General Register Office, Somerset House,
Dec. 2, 1864.
My pear Sir,—The Registrar-General requests that you will do him
the favour to present the accompanying copy of the English Life Table to
the Royal Society.
It contains some work by Scheutz’s Machine, on which a Committee of
the Royal Society reported ; and the Table is the first national Table which
has been constructed, except one for Sweden.
_ The method I employed I described in the paper which you did me
the honour to print in the Transactions. I have extended the method, and
have described its application to life and other risks.
Tam, &c.,
| ' W. Farr.
The President of the Royal Society.
The following communications were read :—
I. “On the production of Diabetes artificially in animals by the
external use of Cold.’ By Henry Bence Jonzs, M.D., F.R.S.
Received November 16, 1864.
In 1789 Lavoisier wrote :—‘‘ La respiration n’est qu’une combustion
lente de carbone et d’hydrogéne qui est semblable en tout a celle qui s’opére
dans une lampe ou dans une bougie allumée; et sous ce point. de vue les
animaux qui eee sont des yéritables corps combustibles oe brilent et
‘se consument.”’ Bie
The different degrees of oxidation of different substances in the different
parts of the body at different times, forms still, and will long continue to
form, one of the largest and most important parts of the animal chemistry
of health and of disease.
_ Notwithstanding all that Professor Liebig has done, the knowledge of
the phenomena of oxidation in the body is only at its commencement.
Take, for example, a grain of starch. It enters into the body, becomes
sugar, is acted on by oxygen, and ultimately passes out as carbonic acid
and water. This is the final result of the perfect combustion ; but what
are the different stages through which the starch passes? what happens if
the oxidation stops at any of these stages—that is, when imperfect com-
bustion occurs ?
282
538 Dr. H. Bence Jones on the production [Dec. 15,
The combustion may be made imperfect in at least three different ways :
—First, by insufficient oxygen. Secondly, by overwhelming fuel. Thirdly,
by reducing the temperature so low that chemical action is checked.
From each of these causes the following scale of the combustion of starch
in the body may be formed.
When there is perfect combustion, then carbonic acid and water are
produced. With less perfect combustion, oxalic and other vegetable
acids are formed. With the least possible combustion sugar results.
Between perfect combustion and the most imperfect combustion (that is,
between carbonic acid and sugar) there are probably many steps, formed by
many different acids; and as in a furnace one portion of the coal may be
fully burnt, whilst other portions are passing through much less perfect
combustions, or are not burnt at all, so different portions of starch may
reach different steps in the scale of combustion, and sugar, acetic acid,
oxalic acid, carbonic acid, and many other acids between acetic and oxalic
acid may be simultaneously produced.
From this account of the oxidation of starch, it follows that sugar should
always be found in the urine whenever any of the three causes mentioned
reduce the oxidation in the system to its mimimum. In other words, by
stopping the combustion that occurs in the body, diabetes should be pro-
duced artificially.
It has long been known that an excess of sugar taken into the blood by
injection causes temporary diabetes. This is imperfect combustion from
excess of the combustible substance. |
The diabetes of old age, of pregnancy, and after the inhalation of
chloroform, may be considered as arising from imperfect combustion in
consequence of a deficiency of oxygen. Bernard’s diabetes from injury of
the floor of the fourth ventricle probably belongs to this cause.
The third mode of checking the chemical actions in the body is by re-
ducing the temperature. This has not yet been proved to cause diabetes,
though it ought as surely to stop oxidation as excess of fuel or insufficiency
of oxygen.
The simplest experiment consists in placing an animal in ice. The cold
soon deprives it of feeling, and perfect insensibility is produced. My friend
Dr. Dickinson undertook to give me the urine of rabbits before they were
placed in ice, and after they had died from the effect of the cold. —
Experiment 1.—This lasted one hour and twenty-three minutes. The
cold was very carefully applied; fresh ice was added from time to time.
The temperature in the rectum fell from 103° F. to 73° F. In the liver
immediately after death the temperature was 76° F. The urine made im-
mediately before the application of cold gave no perceptible trace of sugar
with sulphate of copper and liquor potassee. The urine collected after death
gave marked reduction with these reagents, and when boiled with liquor po-
tassee alone it deepened in colour. The acid reaction also was distinctly more
1864. ] of Diabetes artificially by Cold. 539
marked in this urine than in that made before the application of cold.
The total quantity of urine obtained after death was between two and three
drachms.
Experiment 2.—This lasted seven hours and a half, in consequence of
an interruption caused by the melting of nearly all the ice surrounding the
rabbit. The temperature fell from 101° F. in the mouth to 69° F. after
death. The urine made before the application of cold contained no sugar.
The quantity of urine obtained after death was so small that I was unable
to prove to my own satisfaction that sugar was present in it.
Experiment 3.—This lasted four hours and five minutes. The tempe-
rature at the commencement was 101° F. in the mouth. The urine made
before the icing was alkaline from fixed alkali. It did not give any trace
of sugar, and when mixed with yeast and put in a warm place it rapidly
putrefied. Its specific gravity was 1014. The urine obtained after death
was strongly acid, and contained crystals of oxalate of lime. It gave a plen-
tiful reduction of oxide of copper when boiled with sulphate of copper and
liquor potassee. When boiled with liquor potasse alone, it deepened
markedly in colour. When mixed with yeast it quickly fermented most
distinctly. The specific gravity was 1020.
I sent my results to Professor Briicke, and I asked him to repeat my ex-
periments, and I have received from him the following account written in
June 1864.
« +p’.
These two expressions are equivalent to each other, and any number which
is of the one form is also of the other form; and if they be doubled and
1 be added to each, they will become
2a°+ 2a+1+26°+4 2c*?+ 2c, 2m?+ 2m+ 1+ 2n? + 2p,
ue either of them will represent pny odd number whatever. For a?+a+
—(m?+m-+n?) not only equals p?—(c?+c), but it also equals p*— (c*
ihe ; and if both be doubled and 1 be added,
2m? + 2m+ 1+ 2n*+ 2p?4+ 2q=2a?+ 2a+1+4 267420? +4 2c;
if therefore to either form any even number (2q) be added, it is still of the
form of the other, and therefore still of its own form, that is,
2m? + 2m+ 1+ 2n?+ 2p? + 2q
is still of the form 2m?+2m+1+2n?+ 2p’, and that form therifare repre-
sents any odd number.
It is shown in the paper that when 2a?+ 2a-+ 1, 267, 2c?+ 2c is expanded,
2a°+2a+1 becomes a series (by the addition of 4, 8, 12, &c.) whose
terms will be 0, 0, 0, 1; 0, 0, 1, 2; 0, 0, 2, 3, &c., and may be considered as
a line whose general expression is 0, 0, a, (+1).
When 26? is added to each term by the addition of 2, 6, 10, 14, &c. it
becomes a square whose general term is 6, 6, a,a+1 (these being roots
whose squares added together form the term in the square). Lastly, when
2c’-+ 2c is added (by decreasing a and increasing a+1, 1 each time) and
the square:becomes a cube, every term has two roots equal, but is composed
of not exceeding 4 square numbers; and as on the addition to any term of
any even number (2q) the term so increased will still be within the cube
(extended indefinitely), the cube will contain every odd number; but if
2m’ + 2m-+1-+ 2n? be formed into a square, and then by the addition of 2p”
be raised into a cube (the terms 7,7 in each term being one increased,
and the other diminished by 1), every term in the cube will have two
roots differing by 1, and will be composed of not exceeding 4 square num-
bers; and ‘this cube also will contain every odd number for the same
reason that the other will.
_ Supplement.
Lastly, a +a+6?— Us +m-+n”) will (as it equals any number) equal
either p” i or p” Be +4, and therefore 2a +2a+1, +20?+e’+e
will equal 2m’ rae 1+ 2n?+ 2p? with or without 2q.
In raising a,a+1, 2,6 to a cube by adding c?+c, it must be by the
1864.] On the Structure and Affinities of Kozoon Canadense. 545
addition of 2, 4, 6, 8, 10, &c., which must be added alternately to each; 2,
6, 10, 14, &e. to 6, 6, and 4, 8, 12, 16, &c. to a, a+1; but the effect of this
alternate addition of 2,6, 10, &c. to 4, 6, by increasing one of them by 1
and diminishing the other, and of 4,8,12, &c. to a,a+1 by decreasing
each time by 1 and increasing a+1 by 1, is to make the algebraic sum
of the four roots at all times equal to 1, as is distinctly shown in the paper ;
and if 2a?+2a+1+420’+c?+e will represent any odd number, then
2a? 4+ 2a+ 14 26?+¢’?+c=2n+1, deducting 1 and dividing by 2.
2
C+taty+s =n and as a°+a+6* equals the sum of 2 triangular
2
numbers and ¢ ae is a triangular number therefore every number is
- composed of not exceeding three triangular numbers,
LV. “On the Structure and Affinities of Hozoon Canadense.’ In a
Letter to the President. By W. B. Carpenter, M.D., F.R.S.
Received December 14, 1864.
I cannot doubt that your attention has been drawn to the discovery
announced by Sir Charles Lyell in his Presidential Address at the late
Meeting of the British Association, of large masses of a fossil organism re-
ferable to the Foraminiferous type, near the base of the Laurentian serics
of rocks in Canada. The geological position of this fossil (almost 40,000
feet beneath the base of the Silurian system) is scarcely more remarkable
than its zoological relations; for there is found in it the evidence of a most
extraordinary development of that Rhizopod type of animal life which at
the present time presents itself only in forms of comparative insignificance
—a development which enabled it to separate carbonate of lime from the
ocean-waters in quantity sufficient to produce masses rivalling in bulk and
solidity those of the stony corals of later epochs, and thus to furnish (as
there seems good reason to believe) the materials of those calcareous strata
which occur in the higher parts of the Laurentian series.
Although a detailed account of this discovery, including the results of
the microscopic examinations into the structure of the fossil which have
been made by Dr. Dawson and myself, has been already communicated to
the Geological Society by Sir William KE. Logan, I venture to believe that
the Fellows of the Royal Society may be glad to be more directly made ac-
quainted with my view of its relations to the types of Foraminifera which I
have already described in the Philosophical Transactions.
The massive skeletons of the Rhizopod to which the name Hozoon Cana-~
dense has been given, seem to have extended themselves over the surface of
submarine rocks, their base frequently reaching a diameter of 12 inches, and
their thickness being usually from 4 to 6 inches. A vertical section of one
of these masses exhibits a more or less regular alternation of calcareous and
546 Dr. W. B. Carpenter on the Structure [Dec. 15,
siliceous layers, these being most distinct in the basal portion. The speci-
mens which the kindness of Sir William E. Logan has given me the oppor-
tunity of examining, are composed of carbonate of lime alternating with
serpentine—the calcareous layers being formed by the original skeleton of
the animal, whilst the serpentine has filled up the cavities once occupied
by its sarcode-body. In other specimens the carbonate of lime is replaced
by dolomite, and the serpentine by pyroxene, Loganite, or some other
mineral of which silex is a principal constituent. The regular alternation
of calcareous and siliceous layers which is characteristic of the basal por-
tion of these masses, frequently gives place in the more superficial parts to
a mutual interpenetration of these minerals, the green spots of the serpen-
tine being scattered over the surface of the section, instead of being col-
lected in continuous bands, so as to give it a granular instead of a striated
aspect. This difference we shall find to depend upon a departure from the
typical plan of growth, which often occurs (as in other Foraminifera) in the
later stages—the minute chambers being no longer arranged im continuous
tiers, but being piled together irregularly, in a manner resembling that in
which the cancelli are disposed at the extremities of a long bone.
The minute structure of this organism may be determined by the micro-
scopic examination either of thin transparent sections, or of portions which
have been submitted to the action of dilute acid, so as to remove the cal-
careous shell, leaving only the siliceous casts of the chambers and other
cavities originally occupied by the substance of the animal. ach of these
modes of examination, as I have shown on a former occasion*, has its peculiar
advantages; and the combination of both, here permitted by the peculiar
mode in which the Hozvon has become fossilized, gives us a most complete
representation not only of the skeleton of the animal, but of its soft sarcode-
body, and its minute pseudopodial extensions as they existed during life.
In well-preserved specimens of Hozoon, the shelly substance often retains
its characters so distinctly, that the details of its structure can be even more
satisfactorily made out than can those of most of the comparatively modern
Nummulites. And even the hue of the original sarcode seems traceable in
the canal-system ; so exactly does its aspect, as shown in transparent sections,
correspond with that of similar canals in recent specimens of Polystomella,
Calcarina, &c. in which the sarcode-body has been dried.
This last circumstance appears to me to afford a remarkable con-
firmation of the opinion formed by Mr. Sterry Hunt upon mineralogical
grounds—that the siliceous infiltration of the cavities of the Hozoon was
the result of changes occurring before the decomposition of the animal.
And the extraordinary completeness of this infiltration may be the result
(as was suggested by Professor Milne-Kdwards with regard to the infiltra-
tion of fossil bones and teeth, in the course of the discussion which took
place last year on the Abbeville jaw) of the superiority of the process of
* Memoir on Polystomeila in Phil. Trans. for 1860, pp. 538, 540.
1864.] and Affinities of Kozoon Canadense. 547
substitution, in which the animal matter is replaced (particle by particle)
by some mineral substance, over that of mere penetration.
The Zozoon in its living state might be likened to an extensive range of
building made up of successive tiers of chambers, the chambers of each tier
for the most part communicating very freely with each other (like the
secondary chambers of Carpenteria*, so that the segments of the sarcodic
layer which occupied them were intimately connected, as is shown by
the continuity of their siliceous models. The proper walls of these
chambers are everywhere formed of a pellucid vitreous shell-substance
minutely perforated with parallel tubuli, so as exactly to correspond with
that of Nummulites, Cycloclypeus, and Operculina+; and even these minute
tubuli are so penetrated by siliceous infiltration, that when the calcareous
shell has been removed by acid, the internal casts of their cavities remain
in the form of most delicate needles, standing parallel to one another on
the solid mould of the cavity of the chamber, over which they form a
delicate filmy layer.
But, between the proper walls of the successive tiers of chambers, there
usually intervene layers of very variable thickness, composed of a homo-
geneous shell-substance ; and these layers represent the “intermediate” or
*‘supplemental”’ skeleton which I have described in several of the larger
FoRAMINIFERA, and which attains a peculiar development in Calcarina tf.
And, as in Calearina and other recent and fossil FoRAMINIFERA, this ‘‘in-
termediate skeleton’ is traversed by a “‘ canal-system’’§ that gave passage
to the prolongations of the sarcode-body, by the agency of which the calca-
reous substance of this intermediate skeleton seems to have been deposited.
The distribution of this canal-system, although often well displayed in
transparent sections, is most beautifully shown (as in Polystomella ||) by
the siliceous casts which are left after the solution of the shell, these casts
being the exact models of the extensions of the sarcode-body that origi-
nally occupied its passages.
In those portions of the organism in which the chambers, instead of
being regularly arranged in floors, are piled together in an “ acervuline ”
manner, there is little trace either of “intermediate skeleton”? or of
*‘canal-system”’; but the characteristic structure of their proper walls is
still unmistakeably exhibited.
Whilst, therefore, I most fully accord with Dr. Dawson in referring the
Hozoon Canadense, notwithstanding its massive dimensions and its zoophytic
mode of growth, to the group of Foraminirera, I am led to regard its
immediate affinity as being rather with the Nummuline than with the
Rotaline series—that affinity being marked by the structure of the proper
wall of the chambers, which, as I have elsewhere endeavoured to show 4,
* Phil. Trans. 1860, p. 566. + Ibid. 1856, p.558, and pl. xxxi. figs. 9 & 10.
¢ Ibid. 1860, p. 553. § Ibid. 1860, p. 554, plate xx. fig. 3.
| Ibid. 1860, plate xviii. fig. 12.
# Introduction to the Study of the Foraminifera, chap. ii,
548 On the Structure and Affinities of Fozoon Canadense. [Dee. 15,
is a character of primary importance in this group, the plan of growth and ~
the mode of communication of the chambers being of secondary value, and
the disposition of the ‘‘ intermediate skeleton” and its ‘ canal-system”’
being of yet lower account. ;
I cannot refrain from stopping to draw your attention to the fact, that
the organic structure and the zoological affinities of this body, which was
.at first supposed to be a product of purely physical operations, are thus
determinable by the microscopic examination of an area no larger than a
pin-hole—and that we are thus enabled to predicate the nature of the
living action by which it was produced, at a geological epoch whose
remoteness in ¢ime carries us even beyond the range of the imagination,
with no less certainty than the astronomer can now, by the aid of ‘spectrum
analysis,” determine the chemical and physical constitution of bodies whose
remoteness in space alike transcends our power to conceive.
The only objections which are likely to be raised by paleontologists to
such a determination of the nature of Hozoon, would be suggested by its
zoophytic mode of growth, and by its gigantic size. The first objection,
however, is readily disposed of, since 1 have elsewhere shown* that a
minute organism long ranked as zoophytic, and described by Lamarck
under the designation Millepora rubra, is really but an aberrant form of
the Rotaline family of ForAMINIFERA, its peculiarity consisting only in
the mode of increase of its body, every segment of which has the charac-
teristic structure of the Rotaline; and thus, so far from presenting a
difficulty, the zoophytic character of Fozoon leads us to assign it a place im
the Nummuline series exactly corresponding to that of Polytrema in the
Rotaline. And the objection arising from the size and massiveness of
Eozoon loses all its force when we bear in mind that the increase of Fora-
MINIFERA generally takes place by gemmation, and that the size which
any individual may attain mainly depends (as in the Vegetable kingdom)
upon the number of segments which bud conéinuously from the original
stock, instead of detaching themselves to form independent organisms; so
that there is no essentia] difference save that of continuity, between the
largest mass of Hozoon and an equal mass made up of a multitude of
Nummulites. Moreover there is other evidence that very early in the
Paleeozoic age the Foraminiferous type attained a development to which we
have nothing comparable at any later epoch; for it has been shown by
Mr. J. W. Salter + that the structure of the supposed coral of the Silu-
rian series to which the name Receptaculites has been given, so closely
corresponds with that which I have demonstrated in certain forms of the
Orbitolite typet, as to leave no doubt of their intimate relationship,
although the disks of Receptaculites sometimes attain a diameter of 12
inches, whilst that of the largest Orbitolite I have seen does not reach
* Introduction to the Study of the Foraminifera, p. 235.
+ Canadian Organic Remains. Decade i. + Phil. Trans. 1855,
1864.] — Mr. Lee on the Functions of the Fetal Liver, &c. 549
{ths of an inch. And it is further remarkable in this instance, that the
gigantic size attained by Receptaculites proceeds less from an extraordinary
multiplication of segments, than from such an enormous development of
the individual segments as naturally to suggest grave doubts of the charac-
ter of this fossil, until the exactness of its structural conformity to its
comparatively minute recent representative had been worked out.
_ In a private communication to myself, Dr. Dawson has expressed the
belief that Stromatopora and several other reputed corals of the Paleeozoie
series will prove in reality to be gigantic Zoophytic Rhizopods, like Zozoon
and Receptaculites; and I have little doubt that further inquiry will
justify this anticipation. Should it prove correct, our ideas of the imports
ance of the Rhizopod type in the earlier periods of geological history will
undergo a vast extension; and many questions will arise in regard to its
relations to those higher types which it would seem to have anticipated.
In the present state of our knowledge, however, or rather of our igno-
rance, I think it better to leave all such questions undiscussed, limiting
myself to the special object of this communication—the application of my
former Researches into the Minute Structure of the Foraminifera, to thé
determination of the nature and affinities of the oldest type of Organic
Life yet known to the geologist.
December 22, 1864.
Dr. WILLIAM ALLEN MILLER, Treasurer and Vice-President,
in the Chair.
The following communications were read :—
I. “On the Functions of the Foetal Liver and Intestines.” By
Rozert James Lez, B.A. Cantab., Fellow of the Cambridge
Philosophical Society. Blocreuinicites by Rozerr Lrz, M.D,
Received November 1, 1864.
(Abstract. )
After some introductory remarks, the author observes that the intes-
tines of the foetus, between the fifth and ninth months of intra-uterine life,
“contain a flocculent substance of orange-pink colour in the duodenal
portion, a slimy green substance (the meconium) in their lower portion.
‘The nature of the former was ascertained by Dr. Prout to be highly
albuminous and nutritious. The nature of the latter, of which Dr. John
Davy has given a complete analysis (Trans. Med. Chir. Soc.), is simply
excrementitious. In the intermediate portion of the intestine the substance
is of intermediate character; the more nutritive its property, the higher its
position in the intestine.”’
He next points out that the mesenteric glands which belong to ie
550 Mr. Lee on the Functions of [ Dec. 22,
duodenum are most numerous, and that they diminish towards the lower
portion of the intestine; so that they are in greatest number where the
intestine contains most nutritive substance.
«From this examination,” the author continues, ‘‘ no further proof is
required that digestion and absorption are performed, as Harvey believed,
during foetal life.
«The origin of the albuminous substance in the intestine was supposed
by Harvey to be the liquor amnii, which he attempts to prove is swallowed
by the foetus in utero.
“In the Bird, as will be seen, the origin of this albuminous substance
was ascribed by John Hunter to the eels sac.
“In the year 1829 it was shown by Dr. Robert Lee, in a paper ale
lished in the Philosophical Transactions, ‘On the Functions of the Feetal
Liver and Intestines,’ that Harvey’s explanation was not correct, and that
there is satisfactory evidence to prove that the Liver is the source of this
albuminous substance.”
In the foetal bird on the twelfth day of incubation, or later, “the liver
is seen to occupy both sides of the abdomen, as in the human feetus. The
yelk-sac is seen fixed to the small intestine; the white more than half
absorbed. ‘The umbilical vein receives blood from the chorion membrane,
in which it has been exposed to the influence of the oxygen of the atmo-
sphere; it receives blood also from the yelk-sac and from the white. So
that the nature of the blood in the portal vein of the fcetal bird is both
highly nutritious and arterial in character.
‘«‘ The intestines are in the same condition as in the human feetus.
« The origin of the albuminous substance may be ascertained to be from
the same organ, namely, from the liver.
“That John Hunter was mistaken in supposing that albumen passed
through the vitelline duct (that part of the yelk-sac which is connected
with the intestine), is generally allowed ; and his supposition may be almost
disproved by the fact that it is not possible to inject any fluid into the
yelk-sac from the intestine. Besides, Hunter states that it passes through
only at the time of hatching, which is not the case, as the intestines
are full long before the bird is hatched. The lacteals of the fcetal bird
cannot be seen.
«<'To take another class of animals, the Marsupialia. The liver in the
foetal kangaroo at the time of birth (that is, in the sixth week of utero-
gestation), in the words of Professor Owen, ‘consisted of two equal and
symmetrically diposed lobes’ (Art. ‘ Marsupialia,’ Cyclopeed. Anat. and
Physiology). As soon, however, as the mode of life is changed and the
umbilical vein closed, the liver begins to diminish in size. Yet there is
this resemblance between a Marsupial animal five or six months old, and
a human foetus of the same age in utero, that, although the source of
nutrition is different, yet the intestines are supplied with nutritive sub-
Stance, and digestion proceeds in both cases alike, the nutritive substance
1864.] Letter of Capt. Skogman on the Spitzbergen Survey. 551
in one case being derived from the placenta, in the other from the
mamma of the mother kangaroo.
‘From the foregoing facts certain conclusions may be drawn.
**1. With regard to the placenta.
“Since the organs of the foetal bird are in the same condition as in the
human feetus, the nature of the blood supplied to them is probably the
same. If so, the umbilical vein of the human fcetus contains blood highly
nutritious and arterial in character, and therefore the function of the
placenta corresponds to that of the chorion membrane, yelk, and white
combined ; it is in fact the means of absorption, as the veins absorb
the yelk and white, and the substitute of the lung in adult life. There is
no need of lymphatic vessels in the placenta.
‘© 2, With regard to the liver.
‘That the function of this organ is to separate a highly nutritious sub-
stance from the blood of the portal vein ; and this is true both of the liver
of the foetal bird and of the human feetus.
«3. That this albuminous substance is not in a condition to be directly
absorbed from the umbilical vein, but is elaborated and separated for
absorption by the lacteal vessels.
“4, That there is reason to believe that this function of the liver con-
tinues to a great extent during adult life; for the portal vein in that state
receives veins which correspond to the umbilical vein in the fact that they
proceed from the source of nutrition. That the liver must be actively
engaged after the introduction of food into the intestinal canal, and its
secretion then more plentiful than at other times.”
II. “Completion of the Preliminary Survey of Spitzbergen, under-
taken by the Swedish Government with the view of ascer-
taining the practicability of the Measurement of an Arc of the
Meridian.” In a letter addressed to Major-General SaBine
by Captain C. Skoeman, of the Royal Swedish Navy: dated
Stockholm, Nov. 21, 1864. Communicated by the President.
Received December 15, 1864.
‘On the receipt of your letter of the 12th of November, I started
immediately in quest of Professor Nordenskjold, to obtain from him the
materials for the fulfilment of your wishes in respect to the Spitzbergen
Expedition. The Professor, with his usual obliging frankness, at once
complied with my request, and communicated to me the Minutes from
which I have compiled the subjoined brief Report of his proceedings. You
must excuse the hasty manner in which the Report itself, as well as the
accompanying map, has been put together, as time presses if my letter
has to reach you before your Anniversary on the 30th. The map has no
pretensions to exactness, but must be viewed merely in the light of a dia-
VOL, XIII. 2T
552 Letter of Capt. Skogman on the Spitzbergen Survey. , { Dee. 22,
gram to-show the extent and shape of the triangles, which may also have
to undergo future minor modifications.
“« Report on the Swedish Expedition to Spitzbergen in 1864.
- During the expedition of 1861 several attempts were made to penetrate
into the Storfjord, or Wide Jaws Water; but from ice and calms (the
_ Expedition not being provided with a steamer) they all proved ineffectual.
As it was evident, however, that the firth in question is, beyond com-
parison, the best locality in the island for carrymg on the measurement of
an arc of the meridian, provided only that it is accessible to vessels, it was
resolved that a fresh attempt should be made; and the Estates of the
Kingdom having liberally granted the necessary means, another Expedi-
tion was fitted out, though on a smaller scale than that of 1861. Mr.
Chydenius, who in 1861 had been particularly occupied in selecting and ~
determining the stations for the Survey, unfortunately died in the begin-
ning of 1864. His place has been supplied by Professor Nordenskjold
of the Academy of Sciences at Stockholm, and Mr. Dunér, Professor of
Astronomy in the University of Lund, both having been in the Expedi-
tion of 1861.
‘A small vessel having been chartered at Tromsoe in Norway, they
started in the first days of June, and made Bear Island on the 17th, having
been detained by gales and adverse winds. Shortly afterwards they
reached the opening of the Storfjord; and there appeared to be a good
chance of getting in; but the ice soon packed, and, after several ineffectual .
attempts to force the vessel through, they had to bear up to the western
side of Spitzbergen. On June 23rd they were off Bell Sound, but ice and
calms prevented their getting in. On June the 25th they anchored at
Safe Haven in Ice Sound. Here they remained shut in by the ice until
July 16th, making the best use they could of their time by examining the
greater part of the Sound, which was found to be considerably larger in
extent than is laid down in the charts. Having got out, and returning
to the southward, they were met by a heavy southerly gale, which obliged
them to run for Bell Sound, where they were detained until July 27th,
meanwhile completing the survey of the coasts of that Sound. Being
again delayed by head-winds and calms, they did not reach South Cape
until August the 7th, and on the 9th had succeedéd in getting past the
Thousand Islands to Whalers’ Point, close to which is one of the south-
ernmost stations within the firth* [marked v on the Map, from which, at
a height of 12C0 feet, the summits of the three stations, w, 7, and p, were
seen against the sky]. On the 10th they reached Foul Point, on the
opposite land [where a mountain, 1600-feet high (7), was ascended, from
which the summits v, p, £, and o were seen projected against the sky, with
the exception of o, which was backed by land]. On the 16th the third
* The sentences within brackets are supplied from a letter of a still more recent
date, from Dr. Otto Torell and Professor Dunér, written from Lund.
1864.] Prof. Cayley—Sezxtactic Points of a Plane Curve. 558
Station, p, was visited [and, from a height of 1100 feet, the summits 9, 7,
a, €, and z were observed projected against the sky, and o against other
mountains]. On the 21st, after having ridden out a heavy gale, they
-sueceeded in climbing Mount Walrus [marked 7], a mountain 1100 feet
high, surrounded by glaciers, and laid down as an island on the existing
charts. [From this mountain the station marked A in Mr. Chydentias S
map (Royal Society Proceedings, vol. xii. Plate IV.) was seen. |
‘Proceeding in the boats they reached, on the 22nd, and ascended a
mountain 2500 feet high, situated near the channel which joins the Stor-
fjord with the southern opening of Hinlopen Straits. This was named
White Mountain [and is marked y on the Map]. From this summit they
saw on a clear bright day the South Cape of North-east Land (u), Mount
Loven about the middle of Hinlopen Straits on the west shore, and the
station marked « on the eastern shore. Having thus ascertained satisfac-
tory points in the Storfjord, they proceeded again to the west coast of
Spitzbergen, with the intention of pushing to the northward as far as
possible, but had not proceeded far when they fell in with several boats
with the crews of wrecked sealing vessels. Of course they were obliged
to take these men on board; and being short of provisions for the increased
number of hands, and the season drawing towards its close, they put back
to Tromsoe. The sealing vessels had been wrecked on the east side of
North-East Land, having got there by the north of the island. The men
had afterwards made their way in the boats through Hinlopen Straits,
_having thus circumnavigated North-East Land—a feat said never to have
been accomplished before. ;
‘The shores of the Storfjord are mountainous. ‘The glens and valleys
between the ridges are for the most part filled by glaciers, especially on
the western shore. The mountains average from 1000 to 1500 feet in
height, and belong in general to the Jura formation, which is here and
there broken through by basaltic rocks (hyperite). In the Jura have been
found skeletons, dhonel not complete, of an Ichthyosaurus, closely resem-
bling the species found in Arctic America by Sir Edward Belcher’s Expe-
dition. Mr. Malmgren, of the University of Helsingfors in Finland,
accompanied the Expedition in the capacity of zoologist.”
Il. “On the Sextactic Points of a Plane Curve.” By A. Cay.ey,
F.R.S., Sadlerian Professor of Mathematics, Cambridge. Re-
ceived November 5, 1864. ee
(Abstract.)
. It is, in my memoir ‘‘ On the Conic of Five-pointic Contact at any Point
of a Plane Curve”? (Phil. Trans. vol. exlix. (1859) pp. 371-400), remarked
that as in a plane curve there are certain singular points, viz. the points of
inflexion, where three consecutive points lie in a line, so there are singular
PA ay
554 Prof. Cayley—Sextactic Points of a Plane Curve. [Dee. 22,
points where six consecutive points of the curve lie in a conic; and such a
singular point is there termed a “ sextactic point.” The memoir in question
(here cited as ‘‘ former memoir ’’) contains the theory of the sextactic points
of acubic curve ; but it is only recently that I have succeeded in establish-
ing the theory for a curve of the order m. The result arrived at is that
the number of sextactic points is =m(12m—27), the points in question
being the intersections of the curve m with a curve of the order 12m—27,
the equation of which is
(12m?—54m +57) H Jac. (U, H, OF)
+ (m—2) (12m—27) H Jae. (U, H, QF)
+40 (m—2)? Jac. (U, H, ¥)=0,
where U=0 is the equation of the given curve m, H is the Hessian or
determinant formed with the second differential coefficients (a, 6, ¢,f, 9, h)
of U, and, (A, 38, ©, F, C,H) being the inverse coefficients (A=be—/, &e.),
then
QA= (A, 45, C, S, Gi, HY. Oy, 0.) H,
v=(A, 2, C, F, Gi, 3 (0. H, 0, H, 0, H)? ;
and Jac. denotes the Jacobian or functional determinant, viz.
Jac. (U, H, ¥)= 0, U, dy U, 0, U
0. H, 0, H, 0, H
Or ¥, 0, ¥, 0. ¥
and Jac. (U, H, ©) would of course denote the like derivative of (U, H, Q) ;
the subscripts (H, U) of © denote restrictions in regard to the differentia-
tion of this function, viz. treating © as a function of U and H,
O= (4, 8, C, F,&, HC’, b,c, If", 29', 2h' );
if (a', b',c’', f', g', h') are the second differential coefficients of H, then we
have
0, 2=(0, A,. Le, y Ag " (=0, OR)
(Boas XBed ea) ca, (one
viz. in 0, Qg we consider as exempt from differentiation (a’, 6’, c', 7’, 9’, h')
which depend upon H, and in 0, Q% we consider as exempt from differen-
tiation (A, 13, ©, F, G, H) which depend upon U. We have similarly
0, A=0, OF +0, Og, and 0,Q=0,05+0,0,; and in like manner
Jac. (U, H, Q)=Jac. (U, H, OF) + Jac. (U, H, OF),
which explains the signification of the notations Jac. (U, H, Q3), Jae.
(U, H, Q5). |
The condition for a sextactic point is in the first instance obtained in a
form involving the arbitrary coefficients (A, u,v); viz. we have an equation
of the order 5 in (A, p, v) and of the order 12m—22 in the coordinates
(z,y,2). But writing S=Axr+py+z, by successive transformations we
1864.] Registration of the Chemical Action of Daylight. 555
throw out the factors 3°, 3,5, 5, thus arriving at a result independent of
(A, #, v); viz. this is the before-mentioned equation of the order 12m—27.
The difficulty of the investigation consists in obtaining the transformations
by means of which the equation in its original form is thus divested of these
irrelevant factors.
IV. “On a Method of Meteorological Registration of the Chemical
Action of Total Daylight.”” By Isenny HE. Roscos, B.A., F.R.S.
Received November 8, 1864.
(Abstract.)
The aim of the present communication is to describe a simple mode of
measuring the chemical action of total daylight, adapted to the purpose of
regular meteorological registration. This method is founded upon that
described by Prof. Bunsen and the author in their last Memoir* on Photo-
chemical Measurements, depending upon the law that equal products of the
intensity of the acting light into the times of insolation correspond within
very wide limits to equal shades of tints produced upon chloride-of-silver
paper of uniform sensitiveness—light of the intensity 50, acting for the
time 1, thus producing the same blackening effect as light of the intensity
] acting for the time 50. For the purpose of exposing this paper to light
for a known but very short length of time, a pendulum photometer was
constructed ; and by means of this instrument a strip of paper is so exposed
that the different times of insolation for all points along the length of the
strip can be calculated to within small fractions of a second, when the
duration and amplitude of vibration of the pendulum are known. The
strip of sensitive paper insolated during the oscillation of the pendulum
exhibits throughout its length a regularly diminishing shade trom dark to
white; and by reference to a Table, the time needed to produce any one of
these shades can be ascertained. The unit of photo-chemical action is
assumed to be that intensity of light which produces in the unit of time
(one second) a given but arbitrary degree of shade termed the standard
tint. The reciprocals of the times during which the points on the strip
have to be exposed in order to attain the standard tint, give the intensities
of the acting light expressed in terms of the above unit.
By means of this method a regular series of daily observations can be
kept up without difficulty ; the whole apparatus needed can be packed up
into small space ; the observations can be carried on without regard to wind
or weather ; and no less than forty-five separate determinations can be made
upon 36 square centimetres of sensitive paper. Strips of the standard
chloride-of-silver paper tinted in the pendulum photometer remain as the
basis of the new mode of measurement. Two strips of this paper are
exposed as usual in the pendulum photometer ; one of these strips is fixed
* Phil. Trans. 1863, p. 139.
556 Prof. Roscoe—Registration of Action of Daylight. [Dee. 95;
in hyposulphite-of-sodium solution, washed, dried, and pasted upon a
board furnished with a millimetre-scale. This fixed strip is now graduated
in terms of the unfixed pendulum strip by reading off, by the light of a
soda-flame, the position of those points on each strip which possess equal
degrees of tint, the position of the standard tint upon the unfixed strip
being ascertained for the purpose of the graduation. Upon this com-
parison with the unfixed pendulum strip depends the subsequent use of the
fixed strip. A detailed description of the methods of preparing and gra-
duating the strips, and of the apparatus for exposure and reading, is next
given. The following conditions must be fulfilled in order that the method
may be adopted as a trustworthy mode of measuring the chemical action of
light :—
ist. The tint of the standard strips fixed in hyposulphite must remain
perfectly unalterable during a considerable length of time.
- 2nd. The tints upon these fixed strips must shade regularly into each
other, so as to render possible an accurate comparison with, and gra-
duation in terms of, the unfixed pendulum strips. |
3rd. Simultaneous measurements made with different strips thus gradu-
ated must show close agreement amongst themselves, and they must
give the same results as determinations made by means of the pendu-
lum photometer, according to the method described in the last
memoir.
_ The fixed strips are prepared in the pendulum apparatus, and after-
wards fixed in hyposulphite of sodium. A series of experiments is next
detailed, carried out for the purpose of ascertaining whether these fixed
strips undergo any alteration by exposure to light, or when preserved in the
dark. ‘Two consecutive strips were cut off from a large number of different
sheets, and the point upon each at which the shade was equal to that of the
standard tint was determined. One half of these strips were carefully pre-
served in the dark, the other half exposed to direct and diffuse sunlight for
periods varying from fourteen days to six months, and the position of
equality of tint with the standard tint from time to time determined. ~ It
appears, from a large number of such comparisons, that in almost all eases an
irregular, and in some cases a rapid fading takes place immediately after
the strips have been prepared, and that this fading continues for about six
to eight weeks from the date of the preparation. It was, however, found
that, after this length of time has elapsed, neither exposure to sunlight nor
preservation in the dark produces the slightest change of tint, and that, for
many months from this time, the tint of the strips may be considered as
perfectly unalterable.
The value of the proposed method of measurement entirely depends
upon the possibility of accurately determining the intensities of the various
shades of the fixed strip in terms of the known intensities of the standard
strips prepared in the pendulum photometer. The author examines this
question at length, and details two methods of graduating the fixed strips,
£
1864.] Prof. Roscoe—Registration of Action of Daylight. 557
giving the results obtained in several series of determinations, in order that
the amount of experimental error may be estimated. Curves exhibiting
the graduation of several strips are also given; and from these the author
concludes that the determinations agree as well as can be expected from
such photometric experiments, the mean error between the positions 40
and 80 min. on the strip in one series of graduations not exceeding | per
cent. of the measured intensity. To each fixed strip a Table is attached,
giving the intensity of the light which must act for 1 second upon the .
standard paper, in order to produce the tints at each millimetre of the
length of the strip.
The methods of exposure and reading are next described. The exposure
of the paper is effected very simply by pasting pieces of standard sensitive
paper upon an insolation band, and inserting the band into a thin metal
slide having a small opening at the top and furnished with a cover, which
can be made instantly to open or close the hole under which the sensitive
paper is placed. When one observation has thus been made, and the time
and duration of the insolation noted, the remaining papers can be similarly
exposed at any required time; and thus the determinations can be very
easily carried on at short intervals throughout the day.
The reading-instrument consists of a small metallic drum, furnished
with a millimetre scale, and upon which the graduated strip is fastened.
The drum turns upon a horizontal axis, and the insolation band, with the
exposed papers upon it, is held against the graduated strip, so that by
moving the drum on its horizontal axis the various shades of the strip are
made to pass and repass each of the papers on the insolation band, and the
points of coincidence of tint on the strip and on each of the exposed
papers can be easily ascertained by reading off with the monochromatic
soda-flame.
In the next section of the paper the author investigates the accuracy
and trustworthiness of the method. This is tested in the first place by
making simultaneous measurements of the chemical action of daylight by
the new method and by means of the pendulum photometer, according to
the mode described in the last memoir, upon which the new method is
founded. Duplicate determinations of the varying chemical intensity
thus made every half-hour on four separate days give results which agree
closely with each other, as is seen by reference to the Tables and figures
showing the curves of daily chemical intensity which are given in the
paper. Hence the author concludes that the unavoidable experimental
errors arising from graduation, exposure, and reading are not of sufficient
magnitude materially to affect the accuracy of the measurement. As a
second test of the trustworthiness and availability of the method for actual
measurement, the author gives results of determinations made with two
instruments independently by two observers at the same time, and on the
same spot. The tabulated results thus obtained serve as a fair sample of
the accuracy with which the actual measurement can be carried. out ; and
558 Prof. Roscoe—Registration of Action of Daylight. [Dec. 22,
the curves given represent graphically the results of these double observa-
tions. From the close agreement of these curves, it is seen that the method
is available for practical measurement.
In order to show that the method can be applied to the purposes of
actual registration, the author gives the results of determinations of the
varying intensity of the chemical action of total daylight at Manchester on
more than forty days, made at the most widely differmg seasons of the
year. These measurements reveal some of the interesting results to which
a wide series of such measurements must lead. They extend from August
1863 to September 1864; and Tables are given in which the details of
observations are found, whilst the varying chemical intensity for each day
is expressed graphically by a curve.
As a rule, one observation was made every half-hour ; frequently, how-
ever, when the object was either to control the accuracy of the measure-
ment or to record the great changes which suddenly occur when the sun
is obscured or appears from behind a cloud, the determinations were made
at intervals of a few minutes or even seconds.
Consecutive observations were carried on for each day for nearly a
month, from June 16th to July 9th, 1864; the labour of carrying out
these was not found to be very great, and the results obtained are of great
interest. By reference to the Tables, it is seen that the amount of chemi-
cal action generally corresponds to the amount of cloud or sunshine as
noted in the observation; sometimes, however, a considerable and sudden
alteration in the chemical intensity occurred when no apparent change in
the amount of light could be noticed by the eye. The remarkable ab-
sorptive action exerted upon the chemically active rays by small quantities
of suspended particles of water in the shape of mist, or haze, is also clearly
shown. For the purpose of expressing the relation of the sums of all the
various hourly intensities, giving the daily mean chemical intensities of the
place, a rough method of integration is resorted to: this consists in deter-
mining the weights of the areas of paper inscribed between the base-line
and the curve of daily intensity, that chemical action being taken as 1000
which the unit of intensity would produce if acting continuously for
twenty-four hours. ‘The remarkable differences observed in the chemical
intensity on two neighbouring days is noticed on the curves for the 20th
and 22nd of June 1864: the integrals for these days are 50°9 and 119,
or the chemical actions on these days are in the ratio of 1 to 2°34.
The chemical action of light at Manchester was determined at the winter
and summer solstices, and the vernal and autumnal equinoxes: the results
of these measurements are seen by reference to the accompanying curves.
The integral for the winter solstice is 4°7, that of the vernal equinox 36°8 ;
that of the summer solstice 119, and that of the autumnal equinox 29°1.
Hence, if the chemical action on the shortest day be taken as the unit,
that upon the equinox will be represented by 7, and that upon the longest
day by 25.
1864.] Prof. Roscoe—Registration of Action of Daylight. 559
The results of simultaneous measurements made at Heidelberg and
Manchester, and Dingwall and Manchester, are next detailed.
From the integrals of daily intensity the mean monthly and annual
chemical intensity can be ascertained, and thus we may obtain a know-
ledge of the distribution of the chemically acting rays upon the earth’s
surface, such as we possess for the heating rays.
Figure showing curves of daily chemical intensity at Manchester, in
spring
, summer, autumn, and winter.
OBITUARY NOTICES OF FELLOWS DECEASED
Between 30TH Nov. 1862 ann 30TH Nov. 1863.
ArtTHuR CONNELL was the eldest son of Sir John Connell, Judge
of the Admiralty Court of Scotland and author of a well-known work on
the law of Scotland respecting tithes. He was born in Edinburgh on the
30th of November 1794. Having received his early education at the High
School of that city, he (in 1808) entered the University, where he studied
under Playfair, Leslie, Dugald Stewart, and Hope. Mr. Connell then be-
came for a time a student in the University of Glasgow, and having there
obtained a Snell Exhibition, he went to Balliol College, Oxford, in 1812.
In 1817 he passed Advocate at the Scotch Bar, but never practised ; follow-
ing a decided turn for science which had early shown itself, he devoted
himself to the pursuit of chemistry, which became his main occupation,
and in 1840 he was appointed to the professorship of that science in the
University of St. Andrews. In St. Andrews Mr. Connell continued to
study and teach his favourite science till 1856, when the fracture of a limb,
and its effects upon a constitution already long enfeebled, completely in-
eapacitated him for active duty.
Mr. Connell was chosen a Fellow of this Society at the annual election
in 1855; from 1829 he had been a Fellow of the Royal Society of Edin-
burgh, in whose ‘ Transactions’ or in the ‘ Edinburgh Philosophical Journal ;
his various scientific memoirs and communications have appeared. Most
of his published researches belong to the province of mineral analysis, in
which he justly attained a high reputation for skill and accuracy. To him
is due the merit of Pa ablohine several new mineral species, and of showing
_that in certain minerals baryta exists in combination with silicic acid; and
as an example of his nicety as an analyst, we may refer to his determination
of the constitution of Greenockite from a single grain of that mineral. But
Mr. Connell’s labours as a chemist were not confined to a single field of
inquiry; he was the author of valuable researches on voltaic decompositions,
published in the Transactions of the Royal Society of Edinburgh; and he
contrived an instrument for ascertaining the dew-point, which is superior
in some respects to that generally used.
Mr. Connell died on the 31st of October 1863. He was of a modest,
retiring nature and gentle disposition. To those who enjoyed his private
friendship, it was well known that the merit he evinced as an earnest and
faithful worker in science was but the manifestation, in that special direction,
of the excellent qualities which belonged to his natural character.
Epwarp JosHua Cooper, one of our most distinguished amateur
astronomers, received the first impulses which made him pursue that
science from his mother’s early teaching, and from his visits to the Armagh
Observatory while at the endowed school of that city. Thence he passed
to Eton, and from it to Christ Church, Oxford, where it may be feared
that in those days he met little encouragement in his favourite pursuit.
VOL. XIII. b
il
After leaving Oxford he travelled extensively, with a sextant, chronometer,
and telescope as his inseparable companions. While at Naples in 1820
he met Sir William Drummond, some of whose wild inferences from the
Denxdera Zodiac he showed to be inconsistent with sound astronomy. Sir
Willam replied that these objections were based on the inaccuracy of the
existing drawings ; and Mr. Cooper met that by going to Egypt, securing
the services of an accomplished Italian artist, and brmging home correct
plans of the Dendera ceiling, which, with many other drawings, he printed
for private distribution under the title ‘Egyptian Scenery. He thence
visited Persia, Turkey, Germany, and Scandinavia as far as the North
Cape, accumulating a great mass of observations of latitude and longitude,
which unfortunately remain unpublished. Shortly after his return to
Ireland the death of his uncle placed him in possession of a large estate,
and enabled him to carry out ona great scale the plan which he had formed
of determining some portion of the small stars which were in general
neglected by the great observatories. In the year 1831 he purchased, from
Cauchoix of Paris, an object-glass of 13°3 inches aperture and 25 feet
focus, the largest then existing, which in 1834 was mounted with perfect
success at his magnificent mansion of Markree, on an equatorial constructed
by Mr. Grubb of Dublin. It is of cast iron (the first application of that
material to astronomical instruments), and stands in the open air, encircled
by the buildings of a first-rate observatory, which contain, among other
chefs-d cewvres, a fine meridian-circle by Ertel, with eight microscopes, and
an 8-inch object-glass. ‘These instruments were at once applied to active
work, in which he had a most able cooperator, his first assistant, Mr. A.
Graham ; and the Memoirs of the Royal Astronomical Society and of the
Royal Irish Academy (of both which he was a member) bear ample
testimony of their diligence. One result of their labours was the discovery
of the planet Metis; but his greatest work is his ‘Catalogue of Kcliptic
Stars.’ This (which was published by aid from the Government grant
placed at the disposal of the Royal Scciety, and which the Royal Irish
Academy honoured with their Cunningham Medal) contains upwards of
60,000 stars down to the 12th magnitude, of which very few had been
previously observed. The places are reduced to 1850, and though only
approximate, possess a sufficient degree of precision for the use to which
they were destined. Their probable error is +2'°6, both im right ascen-
sion and in declination. The value of this Catalogue to future astronomers
can scarcely be overrated, for many facts tend to show that much is to be
learned by studying these minute stars. As an instance, it may be stated
that fifty stars of his own Catalogue and twenty-seven of others’ were
found to have disappeared during the progress of the observations. Many
of these, no doubt, are variable; many probably are unknown planets ;
some perhaps have great proper motion. But when shall we have such a
survey of the whole sky as that of this comparatively small zone!
He promised a fifth volume, the materials for which are nearly complete,
ill
as is also the case with a set of star-charts, in which, besides all the stars
actually observed, as many are inserted as could be interpolated by the eye.
Tt is much to be desired that these should not be lost to astronomy; and
all who love that science will express a hope that his representatives will
complete a work which has done such honour to their name.
Mr. Cooper continued to observe almost up to his death, which occurred
on April 23, 1863, shortly after that of his wife, to whom he was deeply
attached. The date of his election into the Royal Society is June 2, 1853.
He represented the county of Sligo in Parliament for many years, and was
a kind and good landlord, making great exertions to educate and improve
his numerous tenantry. His personal qualities were of a high order,
blameless and fascinating in private life, a sincere Christian, no mean poet,
an accomplished painter and linguist, an exquisite musician, and possessing
a wide and varied range of general information.
JosHuA FreLp was a member of a well-known firm of Civil Engineers
at Lambeth. The chief occupation of his life was mechanical engineering,
and he had an important share in the improvements which have been made
during his time in the construction of marine steam-engines. Mr. Field.
was one of the founders of the Institution of Civil Engineers, and one of
its earliest Vice-Presidents. In 1848 he was elected President, on which
occasion he, in his inaugural address, gave a sketch of the progress of
improvement in steam navigation. He became a Member of the Royal
Society in 1836. His death took place on the llth of August 1863,
at the age of 76.
Ricwarp Fow.er, M.D., the oldest Fellow of the Royal Society, died
at his residence, Milford, near Salisbury, April 13, 1863, in his 98th
year. He was born in London, November 28, 1765, and at an early
age was so feeble in health, that it was thought necessary to send him to
reside with a relation in Staffordshire. He was thence sent to Edinburgh
for his education. While yet a youth he was entered for the medical pro-
fession, and while pursuing his studies he eagerly embraced the oppor-
tunity of attending the lectures on Moral and Political Philosophy of
Dugald Stewart, to whose influence he ever afterwards referred with grati-
tude. From Edinburgh he proceeded to Paris, at a time when Louis XVI.,
Marie Antoinette, and the Dauphin were yet to be seen in their regal state ;
and Dr. Fowler was fond of telling how he saw them thus, and also of
having exchanged greetings with Talleyrand while yet the young and
courtly Bishop of Autun. He remained long enough in Paris to witness
much of the strife of the first French Revolution. He was personally ac-
quainted with Mirabeau, and often listened to his eloquence in the National
Assembly. On his return to Edinburgh he was admitted, in Nov. 1790, a
Member of the Speculative Society of that city, which had been founded in
1764, and has numbered among its members some of the most eminent
b 2
iv
men of Great Britam. Dr. Fowler was an active member, and brought
forward questions on politics and social economy for discussion. He early
adopted the Liberal side in politics, and that of complete toleration in reli-
gion, and throughout his long career he was a steady supporter of Liberal
principles. In 1793 he published a work entitled ‘ Experiments and Ob-
servations relative to the influence lately discovered by M. Galvani, and
commonly called Animal Electricity... The work consists of 176 pages,
and contains an account of numerous experiments with different metals on
frogs, the earthworm, the hearts of cats and rabbits, &. The work also
contains a letter from Professor Robison giving an account of some ex-
periments with dissimilar metals. Dr. Fowler took his medical degree at
the University of Edinburgh, Sept. 12, 1793; he was admitted Licen-
tiate of the Royal College of Physicians of London in March 1796, about
which time he settled at Salisbury, and was elected Physician to the In-
firmary of that city, an office which he filled during forty years; after
which he continued to be one of its consulting physicians to the time of
his death. In 1802 he was elected a Fellow of the Royal Society. In
1805 he married the daughter of William Bowles, Esq., of Heale House.
He had an extensive medical practice during many years, and a still more
extensive acquaintance with the leading men of the day, for which he was
partly indebted to his early friendship with the Marquis of Lansdowne and
Lord Holland, and also to his own social qualities and conversational
powers, the latter being enlivened by anecdote, apt quotation, and varied
knowledge, which enabled him to say something agreeably and well on
almost every subject; at the same time his kindly nature mellowed and
improved everything he said and did. In 1831 he became a Member of
the British Association, and during a number of years made frequent com-
munications to it on subjects in mental philosophy and their relation to
physiology. The last communication was in 1859, when Dr. Fowler, then
m his 94th year, made the journey to Aberdeen for the purpose of being
present at the Congress. He took great interest in the mental condition
of the deaf, dumb, and blind, and was fond of inquiring how it was that
persons so afflicted displayed a higher intelligence than that of the most
sagacious of the lower animals, and how by touch alone the meaning of
others can be communicated to the blind and deaf, and instantly iter-
preted. During the later years of his life, Dr. Fowler was himself afflicted
with loss of sight. Indeed, in his work published in 1793, he complains
(page 76) that the weak state of his eyes did not permit him to look in-
tently at minute objects. Nevertheless his mental activity was so great,
that when he could no longer see to read he kept employed two men and
two boys in reading to him, and writing down from his dictation memo-
randa for future papers. One of his latest acts, in conjunction with Mrs.
Fowler, was to purchase and endow a suitable home for the Salisbury and
South Wiltshire Museum, in which he took a great interest, and bestowed
on it a large portion of his books and collections. Dr. Fowler was also a
Vv
Fellow of the Antiquarian Society, and a member of the Zoological Society,
and of the Kdinburgh Medical and Speculative Societies.
Peter Harpy (born Dec. 17, 1813, died April 23, 1863) was the son
of an officer in the artillery, and the brother of Mr. T. Duffus Hardy of
the Record Office and Mr. William Hardy of the Duchy of Lancaster.
He was educated for an actuary, was placed in the Equitable Office in 1829,
was appointed actuary of the Mutual Assurance Office in 1837, and of the
London Assurance Office in 1850. The details of his professional life,
active and well employed as it was, offer nothing to record. He distin-
guished himself in 1839 by the publication of a sound mathematical work
on interest, containing tables subdivided into quarter rates per cent. In
1840 he published a system of notation for life contingencies, which, besides
its ingenuity, was of a practicable character. In 1848 he was one of the
founders of the Institute of Actuaries. He was elected Fellow of the Royal
Society in 1839, immediately after the publication of his first work.
Mr. Peter Hardy possessed that talent for research which has contributed
to render both his brothers eminent in their several walks of life. His
walk, indeed, did not offer any opportunities; but the taste found vent in
the collection of old books and the study of early printing. In this he
would have been eminent, had it been anything but an employment of
leisure. His library, very large for that of an actuary, contained rare
specimens, of which he knew the history and the literary value.
JoHN Taytor was born at Norwich, on the 22nd of August 1779,
and died in London on the 5th of April 1863. He was the eldest of five
brothers belonging to a well-known and respected family in his native city.
In early youth Mr. Taylor showed a natural turn for mechanical contrivance,
and a decided bent towards the profession of an engineer ; but as his native
district afforded but little scope for engineering work, he was brought up
to land-surveying, as the employment within reach which seemed to fall in
most nearly with his natural taste. From this occupation, however, he
was called off at the early age of nineteen, to take the management of the
Wheal Friendship Mine in Cornwall, Inexperienced as he then was in
all that specially concerned mining work, he was, nevertheless, appointed
to that charge, in reliance on his ability to master the task he was to
undertake, and on his diligence and integrity in the performance of it.
Soon after he became thus engaged, Mr. Taylor published, in the ‘ Phi-
losophical Magazine’ (for 1800), an article ‘On the History of Mining in
Devon and Cornwall ;” and in succeeding years he communicated to the
world, in that and other journals, the results of his experience concerning
the operations and processes followed in mining, and the means of im-
proving them, and on the general economy of mines.
But whilst his daily occupation was in directing practical work, it was
Mr. Taylor’s constant aim to elevate the art of mining and place it on a
vil
scientific basis. With this purpose he (in 1829) undertook the editorship,
and, to a considerable extent, the cost of a publication which he hoped
would conduce to the end in view. This work, which was entitled ‘ Re-
cords of Mining,’ did not meet with the support he had looked for, and was
not continued; but the part published contains four contributions from
his own pen. One of these, which deserves especial notice, is an excel-
lent and well-digested paper, in which he advocates the establishment of a
School of Mines in Cornwall, and presents a “‘ Prospectus,”’ setting forth
the details of a plan for the foundation, government, and maintenance of an
institution of that kind, and for regulation of the instruction it should
afford. This proposal did not meet with encouragement at the time, but
the establishment of the present School of Mines, although he had no
active share in it, may be traced to Mr. Taylor’s earnest and judicious
representations.
In 1812 Mr. Taylor settled in London, and engaged with his brother in
a chemical manufactory at Stratford in Essex; but although he had long
applied himself to chemistry as a scientific pursuit, and attained a high
reputation as a metallurgic chemist, he was compelled to relinquish it as a
profession in consequence of the increased extent and importance of his
mining business.
Throughout his eminently practical life Mr. Taylor strove constantly to
maintain a healthy reciprocity between science and practice; and while
availing himself of his scientific knowledge for the improvement of tech-
nical processes, he was no less earnest in turning to account his experience
and opportunities as a mining engineer and metallurgist for the promotion
of the sciences of geology, mineralogy, and chemistry. We accordingly
find his name enrolled as a member of various scientifie bodies, both British
and Foreign. He was one of the earliest Fellows of the Geological Society,
and from 1816 to 1844 filled the office of its Treasurer. In 1825 he was
elected a Fellow of the Royal Society, and repeatedly served on the Council.
But of the several Societies to which he belonged, the British Association
for the Advancement of Science has been the most indebted to Mr. Taylor’s
useful cooperation, both scientific and administrative. He was, indeed,
present at its birth, and the first meeting of its first Council was held at
his house. This was on the 26th of June 1832. He was also the first
Treasurer, and held that office till September 1861, when the infirmities
of age constrained him to retire from it. On relieving him from the
duties he had so long and so well discharged, the Council of the Associa-
tion joined in a unanimous expression of respect for his character and
gratitude for his long and valuable services to the cause of science. The
Council of University College, London, expressed themselves in no less
respectful and grateful terms when, for the same reason, he retired from
the Treasurership of that Institution, which he had held for many years.
Wixui1aM Tooke was born on the 22nd of November 1777, at St. Peters-
Vil
burg, where his father was then Chaplain to the factory of the Russian
Company. Mr. Tooke was a solicitor by profession, but amidst the calls
of business he was able to devote much time and attention to public
affairs, and took part in the formation of various public institutions which
were established during the active period of his life. He was long a lead-
ing member and Vice-President of the Society of Arts, and was elected
President on the vacancy caused by the death of His Royal Highness the
Prince Consort. His election to the Royal Society was in 1818. From
1832 to 1837 he sat in Parliament for the borough of Truro. Besides
a compilation on French history, in two volumes, which appeared in 1855,
and occasional contributions to magazines, Mr. Tooke, when a young man,
published, anonymously, an edition of Churchill’s Poems, with notes and a
Life of the Author, which was favourably reviewed by Southey. He died
in London on the 20th September 1863.
Rear-Admiral Joun WASHINGTON was born on the Ist of January 1801.
He entered the Navy in1812, on board the ‘Juno,’ fitting for the American
station, where he served for the next two years, and took part in various
active and successful operations against the enemy. In i814 he returned
to England, and entered the Royal Naval College at Portsmouth. During
the two years he spent as a student in that Institution he applied himself
diligently to the scientific study of his profession, and laid the foundation
of that skill and accomplishment which he afterwards attained in nautical
surveying and hydrography, and through which in the after course of his
life he was able to render much valuable service to the maritime interests of
this and other countries.
After serving at sea for some years, and rising to the rank of Com-
mander, he returned home for a time, but in 1841 he was appointed to
continue the Survey of the North Sea, in which duty he was employed
until the close of 1844. In 1842 he was promoted to the rank of Post
Captain.
This Survey was Captain Washington’s last service afloat; but his ex-
perience and judgment were turned to public account at different times,
when he acted as a Royal Commissioner on important questions affecting
the interests of navigation and of our maritime industry. In 1853 he
visited some of the Russian fortresses in the Baltic, and the results of his
observations proved of the greatest value in the conduct of the warlike
operations which soon followed.
On the retirement of Sir Francis Beaufort, Captain Washington was
appoimted Hydrographer to the Admiralty, and was promoted to the rank
of Rear-Admiral in 1862. His anxious and unremitting application to the
various duties of his otfice is believed by his friends to have shortened his
valuable life, which was closed at Frascati, near Havre, on the 16th of
September 1863. He was a member of various learned Societies at home
and abroad, and was Secretary of the Royal Geographical Society from
vill
1835 to 1841. His election into the Royal Society is dated February 13,
1845. .
César Mansurte Desprerz was born at Lessines in Belgium, on the
13th of May 1789. At an early age he came to Paris for the purpose of
devoting himself to the study of chemistry and physics. His intelligence
and industry soon attracted the attention of Gay-Lussac, who appointed
him répétiteur of his course of lectures on Chemistry at the Ecole Poly-
technique. He became the Professor of Physics at the Sorbonne in 1837,
having previously held a similar office in the Ecole Polytechnique and the
Collége Henri IV. In 1822 the Academy awarded him the prize for the
best memoir on the causes of animal heat. In 1825 he published an
elementary treatise on Physics, which in 1836 reached a fourth edition ;
and in 1830 the Elements of Theoretical and Practical Chemistry. He was
the author of numerous memoirs published in the ‘Annales de Chimie’
and in the ‘Comptes Rendus,’ dating from 1817 up to 1858. These
memoirs give an account of researches on the specific heat and conductivity
of metals and various mineral substances; on the propagation of heat in
liquids; on the transmission of heat from one solid body to another; on
the heat absorbed in fusion ; on the elastic force of vapours; on the density
and latent heat of vapours; on the compressibility of liquids; on the
density of gas under different pressures; on the displacement and oscilla-
tions of the freezing-point of the mercurial thermometer; on the heat
developed during combustion ; on the expansion of water, and the tempera-
ture at which water and saline solutions attain a. maximum density ; on the
modifications which metals undergo under the joint action of heat and
ammoniacal gas; on the chemical action of voltaic electricity, the light and
heat of the voltaic arc, and the intensity of the voltaic current; on the
electricity developed by muscular contraction ; on chloride of boron; on
the decomposition of water, carbonic acid, and acetic acid; on the decom-
position of salts of lead; on the limits of high and low musical notes; on
the fusion and volatilization of some refractory substances under the triple
action of the voltaic battery, the sun, and the oxyhydrogen blowpipe.
Though not successful in making any brilliant theoretical discoveries, the
important scientific facts he has observed and arranged bring his name
perpetually before the reader of any modern treatise on Physics. He
laboured hard to fulfil to the utmost his duties as a Professor at the Sor-
bonne; and his lectures, being carefully prepared and well illustrated by
experiments, attracted a numerous auditory. He was elected a Foreign
Member of this Society in 1862.
His character was upright and benevolent, his tastes simple, and his
habits regular 1 in the extreme. It was his custom every year to make a
long excursion in England, Germany, or Italy, by himself, and without
letting any one know the day of his departure from Paris.
His last illness was preceded by several slight attacks of cerebral con-
1X
gestion. These were followed by congestion of the lungs, of which he died
on the 15th of March 1863.
Einuarpt Mritscnernicn was born on the 7th of January 1794, in
the village of Jever in Oldenburg. His father was pastor of Neuende; his
uncle, the well-known philologer, was Professor in Gottingen. He was
educated at the Gymnasium of Jever, under the historian Schlosser.
Following the example of his uncle, and encouraged by Schlosser, he
devoted himself to the study of history, philology, and especially the
Persian language. In order to prosecute these studies, he went in 1811
to the University of Heidelberg, and in 1813 to Paris. He had hoped to
be allowed to accompany an embassy to Persia, but was prevented by the
fall of Napoleon. In 1814, on his return to Germany, he commenced
writing a history of the Ghurides and Kara-Chitayens, compiled from
manuscripts in the Gottingen Library, and of which a specimen was
published in 1815 under the title ‘“‘ Mirchondi historia Thaheridarum.”’
Unwilling to renounce his favourite project of travelling in Persia, he de-
termined to accomplish it without any extraneous assistance. The only
way in which it appeared possible to travel was in the character of a phy-
sician; accordingly he resolved to study medicine. He went to Gottingen
for this purpose, and first applied himself to the introductory sciences,
especially to chemistry, which so fascinated him that he gave up philo-
logy and his intention to visit Persia. In 1818 he went to Berlin for the
purpose of obtaining license to lecture. Link allowed him to carry on his
researches in the laboratory of the University. Here he undertook the
examination of the phosphates and arseniates, and confirmed the accuracy
of the latest conclusion arrived at by Berzelius, viz. that phosphoric and
arsenic acid contain each five equivalents of oxygen, while phosphorous
and arsenious-acid contain three equivalents. He noticed at the same
time that the similarly constituted phosphates and arseniates crystallized
in similar forms. Up to this period he had never paid any especial atten-
tion to crystallography, but the conviction that he was on the eve of a
great discovery allowed him no rest; he studied the laws of crystallo-
graphy, learned the method of measuring the angles of crystals, and soon
satisfied himself that the phosphates and arseniates are not merely similar
but identical in form, and that, consequently, bodies exist of dissimilar
composition having the same crystalline form, and that these bodies are
compounds containing respectively the same number of equivalents. Many
minerals appeared to confirm this law, viz. the carbonates, dolomite, chaly-
bite, diallogite and calcite, and the sulphates, baryte, celestine, and Angle-
site. In confirmation, however, of this discovery he considered it neces-
sary to appeal to artificial salts which crystallize readily and distinctly, and
are easily obtained of sufficient purity, so that his conclusions might be
confirmed by any one without difficulty. The neutral sulphates of prot-
oxide of iron, oxide of copper, oxide of zinc, and magnesia, which all con-
x
tain water, mostly in different proportions, appeared peculiarly well fitted
for this purpose. He found that the following were similar in form :—
(1) sulphate of copper and sulphate cf protoxide of manganese; (2) sul-
phate of protoxide of iron and sulphate of oxide of cobalt; (3) sulphate
of magnesia, sulphate of oxide of zine, and sulphate of oxide of nickel. He
also found that the salts which had dissimilar forms contained a different
number of equivalents of water, and that those which had similar forms
contained the same number. He then mixed the solutions of the different
sulphates, and found that the resulting crystals had the form and the same
number of equivalents of water as some one of the unmixed sulphates.
Lastly, he examined the combinations of these sulphates with sulphate of
potash, and showed that the double salts had all similar forms belonging to
the oblique system, and that they were composed of one equivalent of the
earthy or metallic sulphate, one equivalent of sulphate of potash, and six
equivalents of water. The memoir in which these observations are recorded
was presented to the Berlin Academy on the 9th of December 1819. In the
course of the preceding August Berzelius came to Berlin, on his way from
Paris to Stockholm. He became acquainted with Mitscherlich, and con-
ceived such an opinion of his talents, that he suggested him to the
Minister Altenstein as the most fitting successor to Klaproth in the chair
of Chemistry in the University of Berlin. Altenstem did not at the
moment act upon this suggestion, but consented to the proposal that
Mitscherlich should perfect his chemical education by working for some
time under the guidance of Berzelius. In Stockholm he continued and
extended his researches on the phosphates and arseniates, and wrote a
memoir on the subject, which appeared in the Transactions of the
Swedish Academy. In it he described with great care the forms of the
acid and neutral phosphates and arseniates of potash, soda, and ammonia,
the neutral double salts of potash and soda, and of ammonia and soda, and
the phosphates and arseniates of oxide of lead. He showed in every case
that the phosphates and arseniates have similar forms and analogous com-
positions. Urged by Berzelius to give a name to this newly detected
property of the chemical elements, he designated it by the term iso-
morphism. 'This discovery was of the highest importance to the theory of
chemical equivalents, inasmuch as it explained the exceptions to the law
of definite proportions in the mineral system of Berzelius. It appeared
moreover, from the crystallization of the mixtures of the different sulphates,
that isomorphous substances combine in all proportions; and that they re-
place one another in indefinite proportions in the composition of minerals
was proved by Mitscherlich’s fellow-students, Heinrich Rose and Bons-
dorff, in the cases of augite and amphibole.
The doctrine of isomorphism, moreover, was an admirable test of the
determination of the equivalents of the different elements, whilst the
smallness of the number of changes in the equivalents of the simple sub-
stances that followed the discovery of isomorphism, is an indication of the
xi
admirable sagacity with which they had been determined by Berzelius.
Mineralogists and chemists had long been occupied with researches on the
relation between chemical composition and crystalline form; they had
discovered a number of important facts bearing upon the subject, but no
one had discovered the basis upon which the phenomena rested. Fuchs
had already observed that some of the constituents of a mineral might be
replaced by others without any change of form, and had called these con-
stituents vicarious, but by adducing the sesquioxide of iron and lime as
vicarious constituents in Gehlenite, he showed that the true explanation
had eluded his grasp. Fuchs had moreover remarked the close resemblance
of the mineral sulphates to one another, as well as that of the rhombohedral
carbonates. He also showed that strontianite was not rhombohedral as
Hauy supposed, but prismatic, and that it resembled Aragonite in form.
The small percentage of strontian detected in Aragonite by Stromeyer was
regarded by Fuchs as the cause of the resemblance of the forms of the
two minerals, as the very small quantity of carbonate of lime in chalybite
had been supposed the cause of its resemblance to calcite. The only con-
clusion which Fuchs drew from the resemblances of these minerals was, that
certain substances possess such an overpowering force of crystallization,
that, even when present in small quantity, they constrain other substances
to assume their form.
In November 1821 Mitscherlich returned to Berlin, was elected a Mem-
ber of the Academy of Sciences and appointed Professor extraordinary
in the University, and remained in that position till 1825, when he became
Professor in ordinary. Inthe summer of 1822 he gave his first lecture on
Chemistry to a large audience. He also continued his researches on isomor-
phism, and those which he had commenced in Stockholm, especially those
which bore upon the artificial formation of mmerals. He exhibited to the
Academy a collection of about forty crystallized substances, which he had
found in the slag-heaps surrounding the copper-smelting furnaces of
Fahlun during a visit he paid to that place in 1820, im the company of
Berzelius. Of these, however, he described only two, a silicate of prot-
oxide of iron isomorphous with olivine, and a mica, the composition of
which approximates closely to that of a black mica of Siberia. He re-
sumed these researches along with Berthier in the winter of 1823 and
1824, which he passed in Paris, and by fusing the mineral constituents
together in proper proportions, succeeded in producing diopside, idocrase,
and garnet.
In the course of his examination of the phosphates and arseniates he
had observed that the acid phosphate of soda crystallizes in two totally
different forms, both of which belong to the prismatic system, but cannot
be referred to the same parameters. From this he inferred that the
ultimate atoms of crystallized bodies by change of circumstances may ad-
mit of a change in their arrangement, and hazarded the opinion that, as
Aragonite resembles strontianite and cerussite in form, and calcite re-
xi
sembles dolomite, chalybite, and diallogite, it is possible for the substances
isomorphous with Aragonite to crystallize in the form of calcite, and the
substances isomorphous with calcite to crystallize in the form of Aragonite,
and so greatly enlarge each group of isomorphous bodies. This opinion
was looked upon with great distrust by chemists and mineralogists. All
the examples he had brought forward were taken from compound bodies,
which possibly might have contained admixtures which analysis had failed
to detect, and the substances assumed to have the same composition might
after all be different. These doubts were suggested by the analyses of
Aragonite, which had been pronounced by some of the most eminent che-
mists of the time to be pure carbonate of lime; then Stromeyer detected
strontia in it, which, notwithstanding that its amount was very small, and
different in Aragonite from different localities, was immediately regarded as
the cause of the difference of its form from that of calcite; lastly, Buch-
holtz proved the existence of a variety of Aragonite absolutely free from
any admixture of strontia, to which, therefore, the difference of form could
not by any possibility be due. At this conjuncture Mitscherlich made the
remarkable discovery that sulphur also takes different forms under different
circumstances. The crystals obtained from solutions belong to the pris-
matic system, and are identical in form with those which occur in nature ;
but when sulphur is fused and allowed to cool, with proper management
distinct crystals are obtained, but they are entirely different from the
former, inasmuch as they belong to the oblique system. This observation
was of great importance, because sulphur being a simple substance crystal-
lizable at pleasure in either of its two forms, the difference of form could
not be attributed to a difference of composition. He had already proved
that the acid phosphate of soda and carbonate of lime possessed the same
property of crystallization in two different forms, which he now considered
as appertaining to all simple substances and their chemical combinations,
and to which he gave the name of dimorphism. He regarded it, more-
over, as affording an explanation of the fact that bodies possessing analo-
gous chemical constitutions are not always isomorphous. The memoir on
the dimorphism of sulphur was presented to the Academy on the 26th of
July 1826.
It was found that the forms of isomorphous substances are not absolutely
identical, except, of course, when they belong to the cubic system, but
exhibit some differences, showing that the chemical nature of the substance
is not altogether without influence on the form. In order to determine
the difference between the angles of isomorphous bodies with greater
accuracy than was attainable by the use of the ordinary Wollaston’s gonio-
meter, he caused a goniometer to be constructed by Pistor, provided with
four verniers, each reading to 10", and with a telescope magnifying twenty
times for viewing the reflexions of the signal in the faces of the crystal.
With this instrument, in the summer of 1823 he began to measure the
angles of calcite from Iceland, and was surprised to find differences in the
Xill
angle between the same pair of cleavages amounting to 20", a difference
which, though small, was too large to be attributed to errors of pointing
or reading. The observations were made in the morning and in the after-
noon in a room facing the south. The morning observations differed from
those made in the afternoon, but the observations made at the same period
of the day agreed well with one another ; also the temperature of the room
in the afternoon was nearly 4° C. higher than in the morning. He there-
fore concluded that the variation of the angle could only be due to the un-
equal expansion of the crystal in different directions. He increased the
difference of temperature by immersing the crystal in a bath of heated
mercury, and found that the cleavages became more nearly at right angles
to one another, by 8! 34", for an increase of temperature of 100° C. In
dolomite from Traversella, Breunnerite from Pfitsch, chalybite from Ehren-
friedersdorff similar changes occurred amounting to 4!’ 6", 3! 29!, and
2! 22" respectively, for a change of temperature of 100° C. A large
number of other crystals examined by him afforded like results. In the
winter of 1823-1824, during his stay in Paris, he measured the expan-
sion of calcite in volume by Dulong’s method, and found it equal to
0:001961 for 100° C. Hence it appears that by an increase of tempera-
ture of 100° C. the crystal expands 0°00288 in the direction of its axis,
and contracts 0°00056 in a direction at right angles. to its axis. He con-
firmed the accuracy of this most unexpected result by comparing, at
different temperatures, the thicknesses of two plates of calcite of nearly
equal thickness, bounded by planes parallel and at right angles to the axis
respectively, and the thickness of a plate bounded by planes parallel to the
axis with that of a plate of glass of nearly the same thickness, the expan-
sion of which was known. His memoir on this important discovery was
presented to the Academy on the 10th of March 1825.
The large goniometer which he employed in these observations being too
cumbersome, and also too costly to be used by mineralogists in measuring
the angles of crystals, he contrived an instrument more convenient for
ordinary use, reading to half a minute, and provided with a telescope
having a magnifying power of not more than three. ‘The signal consists of
cross wires in the focus of a collimator, as in the goniometers of Rudberg
and Babinet. The adjustment of the crystal is effected by a very ingenious
contrivance due to M. Oertling, by whom many of these instruments have
been constructed. By the invention of this goniometer, which has come
into general use under the name of Mitscherlich’s goniometer, he conferred
a great boon on mineralogists. A minute description of it appeared in the
Memoirs of the Berlin Academy for 1843, a considerable time after it was
originally contrived, and not till its value had been tested by long use.
Of his observations on the effect of heat on the double refraction of
crystals, little is known beyond a notice in Poggendortf’s ‘ Annalen’ of the
remarkable changes which occur in gypsum when heated. At the ordinary
temperature of the atmosphere the optic axes lie in a plane at right angles
X1V
to the plane of symmetry, and make angles of about 60° with a normal to
the plane of symmetry. On warming the crystal the optic axes approach
the plane of symmetry, and at about 92°C. they coincide, exhibiting the
phenomena of a uniaxal crystal, and on further 1 meet the temperature
they open out in the plane of symmetry.
In 1827 Mitscherlich discovered selenic acid, and ae isomorphism of
seleniate of potash with sulphate of potash, and afterwards of other
seleniates with the corresponding sulphates. In 1830 he observed the
isomorphism of manganate of potash with sulphate of potash. This led
him to a further examination of manganese, and to the discovery of the
isomorphism of the permanganates with the perchlorates, and to the
isolation of the hydrate of permanganic acid. At a later period (1860) he
repeated, by new and more accurate methods, the analysis of permanganate
of potash, which had been called in question, confirming the exactness of
the earlier analysis; he succeeded at the same time in isolating the
anhydrous permanganic acid.
The crystallographic researches he carried on about the time of the
discovery of the new acids were extremely numerous, yet very little has
been made known respecting them. He prepared a large number of
salts in his laboratory, determined the systems to which they belonged,
measured some of the angles, and drew by hand the figures of their
principal combinations. But this, though it satisfied his own curiosity,
was manifestly insufficient for publication, and the new discoveries that
presented themselves were much more attractive than the wearisome and
time-consuming task of preparing his researches for the press. He made,
however, an attempt-to carry out his intention of describing the forms of
the most important simple and compound bodies. He commenced with
the sulphates, seleniates, and chromates, because these salts present almost
all the phenomena on which the laws of crystalline form and chemical
composition are founded. He described the sulphates and seleniates of
soda and of oxide of silver; the sulphate, seleniate, and chromate of oxide
of silver and ammonia; the sulphate and seleniate of oxide of nickel, and
the seleniate of oxide of zinc; the anhydrous and hydrous chloride of
sodium ; iodide of sodium and bromide of sodium; sulphate, seleniate,
and chromate of potash, and sulphate of ammonia. Unfortunately these
were his last regular contributions to crystallographic chemistry. Long
afterwards he described the forms of the chloride and iodide of mercury,
the latter of which is dimorphous, and the forms of phosphorus, iodine, and
selenium crystallized from solution in bisulphide of carbon, which proved
to be in an isomeric state differing in density from fused selenium.
In 1833 his crystallographic labours were interrupted by the publication
of his ‘Treatise on Chemistry.’ For this work he had been long preparing
himself by original researches, by associating with the most eminent
chemists of Europe, by visiting their laboratories, and the most important
chemical manufactures and smelting-furnaces. A large number of original
XV
observations of his own are embodied in this work, which had never
appeared in any scientific journal. A fifth edition was commenced in 1855,
but left unfinished. In this year he commenced his important labours on
the density of the vapour of bromine, sulphur, phosphorus, arsenic, and
mercury, nitrous acid, nitric acid, sulphuric acid, &c., and on the relation
of the density of vapours to their chemical equivalents. In the same year
he commenced his researches on benzoyl, which suggested to him a simple
theory of the constitution of those organic combinations in which compound
radicals are assumed to exist. His experiments on the formation of ether
led him to the doctrine of chemical combinations and decompositions by
contact, whereby dormant affinities in mixtures, or compounds held together
by feeble affinities, become active by mere contact with a substance
chemically inactive. These labours in the domain:of organic chemistry
wholly occupied him for nearly twelve years. At the conclusion of
this period he turned his attention to geology. Indeed, ever since
he had engaged in researches on the artificial production of minerals,
he used to theorize on the formation of rocks, and on the existence
of mineral springs and volcanos. In his earlier travels, while his main
object was the examination of chemical manufactures and smelting-
furnaces, his attention was also directed to the geology of the countries
through which he passed. He frequently devoted the concluding lectures
of each half-year’s course to a sketch of the geological structure of the
earth, and the changes which its surface had undergone. Year after year
he made systematic journeys in the Kifel, with the intention of publishing
a complete description of the extinct volcanos of that district, and
connecting it with a theory of voleanic action. And, as the study of this
region made a comparison with the volcanos of other countries desirable,
he visited in succession the principal voleanic districts of Italy, France, and
Germany. But, notwithstanding all this preparation, the description of
the Eifel was never printed, with the exception of some pages distributed
among the hearers of lectures of a popular character given by him in the
winter of 1838 and 1839. Im these he states the views of the nature of
voleanic processes which he then entertained. They appear to have been
founded on a very careful study of voleanic phenomena. He supposes the
explosive action to be caused by the vapour of water. The only hypothesis,
however, by which the presence of water in an active volcano could at that
time be accounted for, was beset by serious difficulties. These have since
been removed by the beautiful experiment made by Daubrée, which shows
that when one side of a stratum of porous rock is heated, water in contact
with the opposite side makes its way through it, in the direction of the
heated part, notwithstanding the high pressure of the vapour generated on
that side.
During the autumnal vacation of 1861 he made his last geological
excursion in the Eifel; in December of that year he began to suffer from
disease of the heart, the complaint increased in severity in the summer of
Xvl
1862, and he had much difficulty in completing his course of lectures. In
the autumn of this year he went again to the Rhine, but only to stay ma
country-house near Bonn, the home of his son-in-law, Professor Busch.
Here his health appeared to revive, and he returned to Berlin feeling so
much better that he commenced his winter lectures; a fortnight before
Christmas, however, he was obliged to give them up, never again to be
resumed. In the spring of 1863 he retired to a country-house at
Schoneberg, near Berlin, and here, on the morning of the 28th of August,
his valuable life was closed by a painless death. His name will ever be
cherished in the annals of that science which he had so greatly enriched.
Few philosophers have ever united such a versatility of genius with a mind
so severely disciplined, or who, possessing such a talent for observing, were
able to deduce such important results from their observations.
He was member of probably every Academy in Europe. He was elected
Foreign Member of the Royal Society in 1828; the Royal Medal was
awarded to him in 1829, ‘‘for his Discoveries relating to the Laws of
Crystallization, and the Properties of Crystals.”
In 1852 he was elected Foreign Associate of the French Institute, in the
place of Cirsted. |
The greater part of the preceding notice is extracted from an Address
to the German Geological Society by Professor G. Rose, Mitscherlich’s
successor as President of the Society.
Cart Lupwic Curistian RUMKER was born on the 28th of May 1788,
at Neubrandenburg in Mecklenburg-Strelitz, in the service of which State his
father held an important position. After a careful preparatory education
at home, he was sent to the Graue Kloster at Berlin, and later to the
Engineering Academy of that place. In 1807 he passed the Government
examination for qualification as an engineer and architect.
In consequence of the gloomy aspect of affairs in Prussia after the peace
of Tilsit, he endeavoured to establish himself in Hamburg; but here also,
finding no prospect of occupation in the profession he had adopted, he
resolved in 1808 to go to England with the intention of devoting himself
to a seafaring life. Accordingly, in the 21st year of his age, he began the
world anew, under the most unfavourable circumstances, in a strange coun-
try, without friends, and entirely cut off from his home by the continental
blockade. With an energy and strength of character peculiarly his own, he
overcame the difficulties of his situation, and obtained an appointment as
Midshipman in the Navy of the East India Company. Feeling dissatisfied
with this service, he entered into that of the German house of Riicken in
London, and visited many parts of the world in their ships. In 1811 or
1812 he obtained admission into the Royal Navy, and served during the
latter part of the war on board various ships of the Mediterranean fleet.
He was first appointed to the ‘Benbow’; afterwards he became Naval In-
structor on board the ‘ Montague,’ Captain Peter Heywood (formerly of the
XV1i
* Bounty’), of whom he used to speak in terms of the greatest regard, as the
most kind-hearted and excellent man he had ever known. He was then
transferred to the ‘Albion,’ and on his passage out from England to join Sir
Charles Penrose, fought at the battle of Algiers.
During a visit to Genoa Rimker became acquainted with the Baron v.
Zach, to whom he submitted the results of various astronomical observations
in order to obtain his opinicn of their value. The Baron soon discovered his
talent for astronomy, encouraged him to cultivate that science, and aided
him with his advice and the use of his astronomical library. Rumker’s
first observations, occultations, and the determination of the latitude and
longitude of Malta, where he was stationed for a considerable time, were
published in vy. Zach’s ‘ Correspondance Astronomique.’
In 1817, when the Fleet returned to England, he quitted the Naval
Service and went to Hamburg, carrying with him the friendship and
esteem of his comrades of all ranks, which he had won by his ability and
energy, combined with a peculiar suavity of manner: Here he was ap-
pointed Principal of the School of Navigation. In the society of Schu-
macher, the Director of the Observatory of Altona, Repsold, and Woltmann,
his taste for astronomy was strengthened, and he found many opportunities
of extending his knowledge of the subject. As at that time Hamburg did
not possess an Observatory, he built one at his own expense on the Stint-
fang.
In 1821 he resigned his post at the School of Navigation in order to
accompany Sir Thomas Brisbane, Governor of New South Wales, to whom
he had been introduced by Captain Heywood, and to take charge of the
Observatory which Sir Thomas purposed founding in that colony.
Rumker’s labours in the Observatory of Paramatta are well known to
astronomers. _ In 1822 he observed the first calculated reappearance of
Encke’s comet, which was invisible in Europe, and thereby first confirmed
the shortness of its periodic time. He afterwards cbserved and discovered
many other comets, some of which were not seen in Europe. He observed
the sun in the solstices, made many observations with Kater’s pendulum,
and determined the magnetic declination and inclination. These and other
observations were published in a separate volume of the Transactions of
the Royal Society for 1830. His observations of the stars of the southern
hemisphere are in part contained in the ‘ Brisbane Catalogue,’ and in the
‘Preliminary Catalogue of Fixed Stars in the Southern Hemisphere,’ pub-
lished by himself at Hamburg in 1832. In after years, however, he was
never able to find leisure for continuing the work, and the greater part of
the observations remain still unpublished.
In 1829 he returned to Europe to resume his post as Principal of the
School of Navigation, and to undertake the Direction of the New Obser-
vatory built by the Senate of Hamburg. He devoted himself with the
most unwearied diligence to the duties of these two offices. After nights
passed im observing, he made his appearance at the School of Navigation at
VOL, XIIT. €
XVIll
eight both in summer and winter, and remained there teaching for five and
even seven hours, regardless of his failing health, which was unable to sus-
tain so severe a trial.
Under his care the school attained an unexpected prosperity. It pro-
duced the most distinguished sailors of the German merchant navy, and
the teachers of almost all the Schools of Navigation on the coast of the
North Sea have been his pupils. The number of students, which at the
time of his appointment to the school was only 60, amounted to 250 in
1857. He possessed in an unusual degree the art of teaching. By the
clearness of his methods, and a singular patience and mildness which encou-
raged the self-respect of his pupils and gained their confidence, and espe-
cially by his power of adapting his teaching to the comprehension of each
individual, he succeeded in preparing the most uncultivated sailor for the
examination in navigation often in a surprisingly short time, so as to enable
him to pass it with credit.
His ‘ Handbook of Navigation,’ which appeared in 1843, and has gone
through three large editions, is used as a text-book in most of the Schools
of Navigation on the shores of the North Sea, in Austria, and in Russia.
He devoted himself with equal or even still greater energy to his duties
in the Observatory. The principal instruments consisted of an equatorially
mounted refractor of 5-feet focal length by Fraunhofer, and a meridian
circle constructed by the brothers Repsold, which was mounted in 1836.
The observations made with the refractor are published in Schumacher’s
‘ Astronomische Nachrichten,’ and in the Menthly Notices of the Astro-
nomical Society. With the meridian circle he undertook the determination
of the places of all the fixed stars visible through its telescope,—a work of
many years’ duration, the results of which he published in the years
1843-59 under the title of a Catalogue of 12,000 fixed stars, but in reality
containing upwards of 15,000.
In speaking of the observations made with the refractor, at the Anniver-
sary Meeting of the Astronomical Society in 1854, when the medal of the
Society was awarded to M. Riimker, the Astronomer Royal, President of
the Society, expressed himself in the following terms :— 3
“For a very long time M. Rimker has been known as furnishing extra-
meridional observations of comets and newly discovered planets, possessing
the highest degree of accuracy, and extending to times when the objects
which he could successfully observe were lost to other astronomers fur-
nished apparently with much more powerful means. I have myself visited
the observatory and inspected the instruments which have been devoted to
these observations, and I have inquired, How is it that with instruments
so insignificant you have been able to see so much more than others could
see who are so much better equipped? The answer was very simple.
Energy, care, patience,—in these, I believe, is contained the whole secret,
M. Rimker perhaps possesses in perfection the sensibility of eye and the
acuteness of ear which are required for the most delicate observations; but.
x1X
these powers, which might seem at first to be original gifts of nature, have,
I do not doubt, acquired very much of their activity from their careful and
energetic use.”
Adverting to the Catalogue of fixed stars, for which more especially the
medal was bestowed, Mr. Airy observes,—
** Had this Catalogue proceeded from an observatory of which the per-
sonal establishment was charged with no other labours, we should have
considered it as a highly meritorious work... .. What, then, shall we say
to this work in the circumstances under which it has reached us? It has
come, the voluntary enterprise of an individual, who could not, by any con-
struction of his connexion with the Hamburgh Observatory, be supposed
to owe to the world a hundredth part of the labour which it has cost. It
is the fruit of observations made in the watches of the night, and calcula-
tions made in the leisure hours of the day, by a person who would seem,
to vulgar eyes, to be engrossed to the limits of human endurance by an
onerous professional office. Well may we consider it as a remarkable
instance of voluntary labour, undertaken under difficult circumstances, not
for public display, but as an aid to science, and skilfully and steadily
directed to that purpose alone.”
M. Rimker was,a Member of the Royal Academies of Minich and Got-
tingen, the Batavian Society of Rotterdam, the Royal Astronomical and
many other English and Foreign learned Societies. He was elected Foreign
Member of the Royal Society in 1855.
After having laboured long and profitably, repeated attacks of illness,
accompanied by an asthmatic cough which increased in severity at each
relapse, forced him at length (in 1857) to rest from his labours, and to
seek a milder climate for the benefit of his shattered health.
At his suggestion the care of the Navigation School was entrusted to
M. Niebour, who had been his assistant for many years, and that of the
Observatory to his only son, George Riimker, at that time the Astronomer
of the Durham Observatory, and now his successor as Director of the
Observatory of Hamburg.
He had visited and been pleased with Lisbon during his earlier voyages,
and was induced to select that place for his retreat. There, after a residence
of six years, tenderly watched over by his wife, a lady of English birth, and
the discoverer of the comet VI of 1847, retaining full possession of his
faculties, he died on the 21st of December 1862.
Having served in the British Navy, and received the medal given to those
who shared in the battle of Algiers, he was followed to the grave by officers
of the British fleet in the Tagus, and by his German friends. He lies
buried in a spot chosen by himself, close to Fielding’s grave in the cemetery
of the church of Estrella.
INDEX tro VOL. XIIi.
————<———-
ABEL (EF. A.) on some phenomena ex-
hibited by gun-cotton and gunpowder
under special conditions of exposure to
heat, 204.
Acid, liquid stannic and metastannic, on
the preparation of, 340.
, liquid titanic, on the preparation of,
340.
——, liquid tungstic, dialysis of, 340.
——, molybdic, decomposition of, 341.
, on a colloid, a normal constituent of
human urine, 314.
, silicic, and other analogous colloidal
substances, on the properties of, 335.
Acids derivable from the cyanides of the
oxy-radicals of the di- and tri-atomic
alcohols, 44.
of the lactic series, notes of re-
searches on, 140.
’ Admission of Fellows, 276, 278.
Aérial tides, 329.
Air-pump, description of a new mercurial,
321.
Airy (G. B.), first analysis of 177 mag-
netic storms, registered by the magnetic
instruments in the Royal Observatory,
Greenwich, from 1841 to 1857, 48.
Albumen, on organic substances artificially
formed from, 350.
Alcogel, 337.
Alcosol, 337.
Algebraic equations, on the differential
equations which determine the form of
the roots of, 245.
Alizarine, 87, 150.
Alkaloids, researches on isomeric, 303.
Amyloid substance met with in the animal
economy, further observations on, 317.
Anesthetics, effect of, upon blood, 159.
Aniline-blue, on, 9.
Aniline-yellow, on, 6.
Anniversary Meeting, November 30, 1863,
21; November 30, 1864, 494:
Annual Meeting for election of Fellows,
_ June 2, 1864, 276.
Arc of meridian, at Spitzbergen, on th
measurement of, 83.
, preliminary survey for the measure-
ment of an, at Spitzbergen by the Swe-
dish Government, 551,
Attraction, local, uncertainty occasioned
by, in the map of a country, 18, 253.
Auckland (Harl of), letter from, concern-
ing Sir J. South’s experiments on the
vibrations occasioned by railway trains,
68.
Barometer, description of an improved
mercurial, 160.
Bayma (Rev. J.) on molecular mechanics,
126.
Beale (L. 8.), new observations upon the
minute anatomy of the papille of the
frog’s tongue, 384.
, indications of the paths taken by
the nerve-currents as they traverse the
caudate nerve-cells of the spinal cord
and encephalon, 386.
Berkeley (Rev. M. J.), Royal Medal
awarded to, 35.
Bernard (C.), elected foreign member, 277.
Biliverdin, on the supposed identity of,
with chlorophyll, 144.
Binocular vision, on the normal motions
of the human eye in relation to, 186.
Blood, on the influence of physical and
chemical agents on, 157.
, on the reduction and oxidation of
the colouring-matter of the, 355.
Blood-vessels, on the distal communication
of the, with the lymphatics, 327.
Boole (G.) on the differential equations
which determine the form of the roots
‘of algebraic equations, 245. a
Bruniquel, description of the cavern of,
and its organic contents (Part I.), 277.
Calculus of symbols, on the, (fourth me-
moir) 126, 423; fifth memoir, 227,
. 432.
Candidates for election, list of, March 3,
1864, 153.
, list of selected, May 12, 1864, 228.
Capello (Senhor) and Stewart (B.), results
of a comparison of certain traces pro-
duced simultaneously by the self-record-
ing magnetographs at Kew and at Lis-
bon; especially of those which record
the magnetic disturbance of July 15,
1863, 111.
562
Carpenter (W. B.) on the structure and
affinities of Hozoon Canadense, 545.
Carter (T. A.) on the distal communica-
tion of the blood-vessels with the lym-
phatics ; and on a diaplasmatic system
of vessels, 327.
Cayley (A.), a second memoir on skew
surfaces, otherwise scrolls, 244.
—— on the sextactic points of a plane
curve, 553.
Cerebellum, on the functions of the, 177,
334.
Chase (P. E.), aérial tides, 329.
Child (G. W.), experimental researches on
spontancous generation, 313.
Chinoline, on the higher homologues of,
dll.
Chlorine, action of, on methyl, 225.
Chlorophyll, remarks on the constitution
of, 144.
Chrysaniline, 7.
Church (A. H.), researches on certain
ethylphosphates, 520.
Clarke (J. L.), Royal Medal awarded to,
512.
Coal-tar, colouring-matters derived from,
6, 9, 341, 485.
Cold, its effect in producing diabctes, 537.
Connell (A.), obituary notice of, 1.
Cooper (E. J.), obituary notice of, 1.
Copley Medal awarded to Rev. A. Sedg-
wick, 81; to C. Darwin, 505.
Creosote, on the chemical constitution of
Reichenbach’s, 484.
Croonian Lecture, April 14, 1864.—On
the normal motions of the human eye
in relation to binocular vision, 186.
Curve-plane, on the sextactic points of, 553.
Darwin(C.), Copley Medalawarded to, 505.
Daylight, total, on a method of meteoro-
logical registration of the chemical ac-
tion of, 555.
De la Rue (W.), comparison of Mr. De la
Rue’s and Padre Secchi’s eclipse photo-
graphs, 442.
, his photograph of the moon, 491.
, Royal Medal awarded to, 510.
Density, variations of, in mineral sub-
stances produced by heat, 240.
Despretz (C. M.), obituary notice of, vili.
Diabetes, on the production of, artificially
in animals by the external use of cold,
537.
Diazobenzol, compounds of, 378.
Dickinson (W. H.) on the functions of
the cerebellum, 177, 334.
Dietary, inquiries into the national, 298.
Diphenylamine, 341.
Drops, on, 444, 457.
Earth’s crust, speculations on the consti-
tution of the, 18, 253.
INDEX.
Eclipse photographs, comparison of Mr.
De la Rue’s and Padre Secchi’s, 442.
Electrical force, further inquiries concern-
ing the laws and operation of, 364.
Electromagnetic field, a dynamical theory
of, 5381.
Ellis (A. J.) on the conditions, extent,
and realization of a perfect musical
scale on instruments with fixed tones,
93.
on the physical constitution and re-
lations of musical chords, 392.
on the temperament of musical in-
struments with fixed tones, 404.
Eozoon Canadense, on the structure and
affinities of, 545.
Equations of rotation of a solid body
about a fixed point, 52.
Erman (A.) on the magnetic elements and
their secular variations at Berlin, 218.
Etherogel, 338.
Ethylphosphates, researches on certain,
520.
Hye, on the normal motions of the human,
in relation to binocular vision, 186.
Fairbairn (W.), experiments to deter-
mine the effects of impact, vibratory
action, and a long-continucd change of
load on wrought-iron girders, 121.
Farr (W.), life tables printed by Scheutz’s
calculating machine, 537.
Field (J.), obituary notice of, ii.
Figure of the earth, a method of obtaining,
free from ambiguity, 18, 253.
Feetus, description of the pneumcgastric
and great sympathetic nerves in an
acephalous, 90.
Foraminifera, on some, from the North
Atlantic and Arctic Oceans, 239.
Forchhammer (G.) on the composition of
sea-water in different parts of the ocean,
493.
Foreign members elected: Bernard (C.),
Foucault (J. B. L.), Wurtz (A. C.), 277.
Foucault (J. B. L.), elected foreign mem-
ber, 277.
Fowler (R.), obituary notice of, iii.
Frankland (R.) and Duppa (B. F.), notes
of researches on the acids of the lactic
series: No. I. action of zine upon a
mixture of the iodide and oxalate of
methyl, 140.
Frog, tongue of, new observations upon
the minute anatomy of the papille of,
384, .
Gases, respiratory, mutual action of the
blood and the, 157.
and vapours, on the spectra of
ignited, 153.
Gasometer, description of a new mercu-
rial, 321.
INDEX.
Gassiot (J. P.), description of a train of
eleven sulphide-of-carbon prisms ar-
ranged for spectrum analysis, 183.
, Royal Medal awarded to, 36.
Glaisher (J.) on the meteorological re-
sults shown by the self-registering in-
struments at Greenwich, during the ex-
traordinary storm of October 30, 1863,
1:
Glycerogel, 338.
Glycerosol, 338.
Glyptodon, on the osteology of the genus,
108.
Gompertz (B.), second part of the supple-
ment to the two papers on mortality
published in the Philosophical Trans-
actions in 1820 and 1825, 228.
Graham (T.) on the properties of silicic
acid and other analogous colloidal sub-
stances, 335.
an ee magnetic variations observed
at, 87.
Griess (P.) on a new class of compounds
in which nitrogen is substituted for
hydrogen, 375.
Gun-cotton, on some phenomena exhibited
by, under special conditions, 204.
» remarks on, 29.
Gunpowder, on some phenomenaexhibited
by, under special conditions, 204.
Guthrie (F.) on drops, 444; Part II. 457.
Haig (Capt. R. W.), account of magnetic
observations made between the years
1858 and 1861 inclusive in British
Columbia, Washington Territory, and
Vancouver Island, 15.
Hardy (P.), obituary notice of, v.
Harley (G.) on the influence of physical
and chemical agents upon blood; with
special reference to the mutual action of
ee blood and the respiratory gases,
157,
Harris (Sir W. 8.), further inquiries con-
cerning the laws and operation of elec-
trical force, 364,
Hartnup (J.) on the great storm of De-
cember 3, 1863, as recorded by the self-
registering instruments at the Liverpool
Observatory, 109.
Haughton (Rey. 8.) on the joint-systems
of Ireland and Cornwall, and their me-
chanical origin, 142.
Heat, specific, of solid and liquid bodies,
229.
, variations of density produced by,
in mineral substances, 240.
Helmholtz (H.) on the normal motions
of the human eye in relation to binocu-
lar vision, 186.
Hennessy (H. G.) on the synchronous
distribution of temperature over the
earth’s surface, 312,
563
Herschel (Sir J.), a general catalogue of
nebulee and clusters of stars for the year
1860°0, with precessions for 1880-0, 2.
Hicks (J.), description of an improved
mercurial barometer, 169.
Hofmann (A. W.), note on kinone, 4.
, researches on the colouring-matters
derived from coal-tar : No. I. on aniline-
yellow, 6; No. II. on aniline-blue, 9;
No. III. diphenylamine, 341; No. IV.
phenyltolylamine, 485.
Huggins (W.) on the spectra of some of
the chemical elements, 43.
on the spectra of some of the ne-
bule, 492.
Huggins (W.) and Miller (W. A.) on the
spectra of some of the fixed stars, 242.
Hulke (J. W.), a contribution to the mi-
nute anatomy of the retina of amphibia
and reptiles, 138.
Huxley (‘T. H.) on the osteology of the
genus Glyptodon, 108.
Hydrogel, 337.
Hydrosol, 337.
Ibbetson (L. L. B.), readmitted, 15.
Tmaginary roots, an inquiry into Newton’s
rule for the discovery of, 179.
Integral numbers of the indeterminate
equation, on the criterion of resolubility
in, 110.
Intestines, foetal, on the functions of the,
549.
Iodine, action of chloride of, upon or-
ganic bodies, 540.
Treland and Cornwall, mechanical origin
of the joint-systems of, 142. ;
Joint-systems of Ireland and Cornwall,
on the, 142.
Jones (H. Bence) on the production of
diabetes artificially in animals by the
external use of cold, 537.
Kew curves, comparison of, 111, 115,
Kinone, note on, 4.
Kopp (H.), investigations of the specific
heat of solid and liquid bodies, 229,
Lee (R. J.), a description of the pneumo-
gastric and great sympathetic nerves in
an acephalous foetus, 90.
on the functions of the footal liver
and intestines, 549.
Life tables, printed by Scheutz’s caleulat.
ing machine, 537.
Lisbon curves, comparison of, 118, 115.
Liver, foetal, on the functions of the, 549,
Lutidine, physical properties of, 305.
M‘Donnell (R.), further observations on
the amyloid substance met with in the
animal economy, 317.
564:
-Madder, Rubia munjista, examination of,
86, 145.
Magnesium, on, 217. ingedh
Magnet, table of the mean declination of
the, at Lisbon, from January 1858 to
December 1863, 347.
Magnetic elements and their secular varia-
tions at Berlin, 218.
declination, comparison of the most
notable disturbances of, at Kew and
Nertschinsk, 247.
, results of hourly observations
made at Port Kennedy, 84; compari-
son of, with observations made at Point
Barrow, 8d.
, semiannual inequality of, 347.
disturbance, comparison of certain
’ traces produced simultaneously by the
self-recording magnetographs at Kew
and at Lisbon, July 15, 1863, 111.
disturbances, retrospective view of
the progress of the investigation into
the laws and causes of, 247.
observations made in British Co-
lumbia, Washington Territory,and Van- -
couver Island, 15.
—— storms, first analysis of 177 regis-
tered by the magnetic instruments in
the Royal Observatory, Greenwich, 48.
variations observed at Greenwich,
Marcet (W.) on a colloid acid, a normal
constituent of human urine, 314.
Mauve, or aniline-purple, on, 170.
Maxwell (J. C.), a dynamical theory of
_ the electromagnetic field, 531.
Meteorites, on the microscopical struc-
ture of, 333.
Meteorological registration of the chemi-
cal action of total daylight, 555.
Methyl, action of chlorine on, 225.
Mitscherlich (E.), obituary notice of,
1x.:
Molecular mechanics, on, 126; principles
of, 127;. mathematical evolution of prin-
ciples of, 131; application of the prin-
_ciples of, 135.
physics,
memoir, 160.
Mortality, second part of supplement to
“two papers on, 228.
Miiller (H.) on the chemical constitution
of Reichenbach’s creosote, 484.
Munijistine, 86, 147; tinctorial power of,
148.
Musical currents, on the physical consti-
tution and relations of, 392.
instruments with fixed tones, on
the temperament of, 404.
scale, on the conditions, extent, and
realization of a perfect, 93.
Myology, on some varieties in human,
299.
contributions to, fifth
INDEX,
Nebule and clusters of stars, catalogue
of, 2. .
, on the spectra of some of the, 492:
Nerve-currents, indieations of the paths
taken by, through the caudate nerve-
oe of the spinal cord and encephalon,
86.
Nerves, pneumogastric and great sympa-
thetic, in an acephalous foetus, deserip-
tion of, 90.
Nitrogen substituted for hydrogen in a
new class of compounds, 375.
Nitropurpureine, 150.
Obituary Notices of deceased Fellows :—
Arthur Connell, i.
Edward Joshua Cooper, i.
Joshua Field, iii.
Richard Fowler, M.D., iii.
Peter Hardy, v.
John Taylor, v.
William Tooke, vi.
Rear-Admiral John Washington, vii.
César Mansuéte Despretz, yiil.
Eilhardt Mitscherlich, ix.
Carl Ludwig Christian Riimker, xvi.
Owen (R.), description of the cayern of
Bruniguel, and its organic contents.—
Part I. Human remains, 277.
Parker (W. K.) and Jones (T. R.) on
some foraminifera from the North At-
lantic and Arctic Oceans, including
Davis Strait and Baffin Bay, 239.
Perkin (W. H.) on mauve or aniline-
purple, 170.
Phenyltolylamine, 485.
Phipson (T. L.) on magnesium, 217,
, note on the variations of density
produced by heat in mineral substances,
240.
Plane water-lines, on, 15.
Plicker (J.) and Hittorf (J. W.) on the
spectra of ignited. gases and vapours;
with especial regard to the different
spectra of the same elementary gaseou
substance, 153. “=
Point Barrow, magnetic observations
made at, 85.
Pollock (Sir F.) on Fermat’s theorem of
the polygonal numbers, 542.
Polygonal numbers, on Fermat’s theorem
of the, 542.
Port Kennedy, observations of the mag-
netic declination made at, 84.
Pratt (Ven. J. H.) on the degree of un-
certainty which local attraction, if not
allowed for, occasions in the map of a
country, and in the mean figure of the
earth as determined by Geodesy; a
method of obtaining the mean figure
free from ambiguity, from a comparison
of the Anglo-Gallic, Russian, and In-
INDEX.
dian ares; and speculations on the con-
stitution of the earth’s crust, 18, 253.
Prestwich (J.) on some further evidence
. bearing on the excavation of the valley
of the Somme by river-action, as ex-
hibited in a section at Drucat near
Abbeville, 135.
Purpureine, 87, 148.
Purpurine, action of bromine on, 152.
Quadratic forms containing more than
three indeterminates, on the orders and
genera of, 199.
forms, on complex binary, 278.
Radiant heat, researches on, (fifth me-
moir) 160.
Railway trains, experiments on the vibra-
tions occasioned by, in a tunnel, 65.
Rankine (W. J. M.) on plane water-
lines, 15.
Retina of amphibia and reptiles, contri-
bution to the minute anatomy of, 138.
Robinson (Rev. T. R.), description of a
new mercurial gasometer and air-pump,
321.
Rosaniline, methylic, ethylic, and amylic
derivatives of, 13.
Roscoe (H. E.) on a method of meteoro-
logical registration of the chemical ac-
tion of total daylight, 555,
Royal Medal awarded to Rev. M. J.
' Berkeley, 35; to J. P. Gassiot, 36;
W. De la Rue, 510; J. L. Clarke, 512.
Rubia munjista, the Kast-Indian madder,
* or munjeet of commerce, examination
of, 86, 145.
Rumford Medal awarded to J. Tyndall,
515.
Riimker (C. L. C.), obituary notice of,
XVi.
Russell (W. H. L.) on the calculus of
symbols (fourth memoir). With ap-
plications to the theory of non-linear
differential equations, 126, 423.
(fifth memoir), with applications
to linear partial differential equations
and the calculus of fanctions, 227, 482.
Russian arc, remarks on, 24.
Sabine (Gen. E.), anniversary address,
497.
, a comparison of the most notable
disturbances of the magnetic declina-
tion in 1858 and 1859 at Kew and -
Nertschinsk, preceded by a brief retro-
spective view of the progress of the in-
vestigation into the laws and causes of
the magnetic disturbances, 247.
, results of hourly observations of
the magnetic declination made by Sir
Francis Leopold M‘Clintock, R.N., and
the officers of the yacht ‘ Fox,’ at Port
565
Kennedy, in the Arctic Sea, in the
winter of 1858-59; and a comparison
of these results with those obtained by
Captain Maguire, R.N., and the officers
of H.MLS. ‘ Plover,’ in 1852, 1853, and
1854, at Point Barrow, 84.
Schorlemmer (C.), on the action of chlo-
rine upon methyl, 225,
Scientific relief fund, first report of, 495.
Sea-water, composition of, in different parts
of the ocean, 493.
Renate (Rey. A.), Copley Medal awarded
to, 31.
Silveira (Senhor da), a table of the mean
~ declination of the magnet in each de-
cade from January 1858 to December
1863, derived from the observations
made at the magnetic observatory at
Lisbon ; showing the annual variation
or semiannual inequality to which that
element is subject, 347.
Simpson (M.) on the acids derivable from
the cyanides of the oxy-radicals of the
di- and tri-atomic alcohols, 44. ;
on the action of chloride of iodine
upon organic bodies, 540.
Skew surfaces, otherwise scrolls, second
memoir on, 244.
‘Skogman (Capt. C.), completion of the
preliminary survey of Spitzbergen, un-
dertaken by the Swedish Government
with a view of ascertaining the practi-
cability of the measurement of an arc
of the meridian, 551.
Smee (A. H.) on organic substances arti-
ficially formed from albumen, 350.
Smith (E.), inquiries into the national
dietary, 298.
Smith (H. J. S.) on complex binary qua-
dratic forms, 278.
on the criterion of resolubility in
integral numbers of the indeterminate
equation f= aa?+a'e'?+a"'z'242b2'x"!
+ 26'var"+26"x'x =0, 110.
on the orders and genera of qua-
dratic forms containing more than three
indeterminates, 199. -
Somme, valley of the, on the excavation
of, by river-action, 135.
Sorby (H. C.) on the microscopical strue-
ture of meteorites, 333.
South (Sir J.), experiments, made at Wat-
ford, on the vibrations occasioned by
railway trains passing through a tun-
nel, 65.
Spectra of ignited gases and vapours, on,
3.
of some of the chemical elements, 43.
—— of some of the fixed stars, 242.
Spectrum analysis, description of a train
of eleven sulphide-of-carbon prisms
arranged for, 183.
Spitzbergen, preliminary survey by the
566
Swedish Government for the measure-
ment of an are of meridian at, 551.
Spontaneous generation, experimental re-
searches on, 313.
Spottiswoode (W.) on the equations of
rotation of a solid body about a fixed
point, 52.
Squalls, sudden, of 30th October and
November 21, 1863, on, 51.
Stars, clusters of, catalogue of, 2.
, spectra of some of the fixed, 242.
Stenhouse(J.),examination of Rubia mun-
jista, the Hast-Indian madder or mun-
jeet of commerce, 86, 145.
Stewart (B.) on the sudden squalls of 30th
October and 21st November 18683, 51.
, remarks on sun-spots, 168.
Stokes (G. G.) on the supposed identity
of biliverdin with chlorophyll, with re-
marks on the constitution of chloro-
phyll, 144.
, on the reductionand oxidation of the
colouring-matter of the blood, 355.
Storm, on the great, of Dec. 3, 1863, 109.
Storms, magnetic, first analysis of 177,
48. -
Sulphagel, 338.
Sun-spots, remarks on, 168.
Sylvester (J.J.), an inquiry into Newton’s
rule for the discovery of imaginary
roots, 179.
Taylor (J.), obituary notice of, v.
Telescope, southern, remarks on, 23.
Temperature, on the synchronous distri-
bution of, over the earth’s surface, 312.
- INDEX.
Tetrazodiphenyl, 382.
Tides, aérial, 329.
Tooke (W.), obituary notice of, vi.
Torell (Dr. Otto), extract of a letter fo |
General Sabine from, dated Copenhag
Dec. 12, 1863, 83.
Triangulation, on the we ag
84.
Triphenylic leucaniline, 12.
rosaniline, 12.
Tyndall (J.), researches on radiant heat.—
Fifth memoir. Contributions to mole-
cular physics, 160.
, Rumford Medal awarded to, 515.
Urine, physiological relations of the col-
loid acid of, 316.
Vessels, on a diaplasmatic system of, 327. i
Washington (J.), obituary notice of, vii.
Williams (C. G.), researches on isomeric
alkaloids, 303.
Wolf (Prof.) on the magnetic variations
observed at Greenwich, 87.
Wood (J.) on some varieties in human
myology, 299.
Wrought-iron girders, experiments to de- —
termine the effects of impact, vibratory
action, and a long-continued change of
load on, 121.
Wurtz (A. C.), elected foreign member, —
277.
Zinc, action of, upon a mixture of the
iodide and oxalate of methyl, 140.
END OF THE THIRTEENTH VOLUME.
a
3
*
Fs
Printed by Taylor and Francis, Red Lion Court, Fleet Street, London.
VAR 475 LA
ju 1/5 dal
A heh we & ANWR see *
’
|
: , SMITHSONIAN INSTIT' UTION LIBRARIES
“NAITO
: 3 9088 01305 9712