wees Speers tttec ten taiete fieterciche 4: i. ; HH ity rf i beth a TRANSACTIONS OF THE POW AL S0).C TY Y or EDINBURGH. VOL. XX. EDINBURGH: PUBLISHED BY ROBERT GRANT & SON, 82 PRINCES STREET. AND WILLIAMS & NORGATE, 14 HENRIETTA STREET, COVENT GARDEN, LONDON. MDCCCLIII. PRINTED BY NEILL AND COMPANY, EDINBURGH. CONTENTS. PART I. I. On the Volcame Geology of the Vivarais (Ardéche). By James D. Forzes, Esq., F.R.S., Sec. R.S. Ed., Professor of Natural Philoso- phy in the University of Edinburgh. (With Six Plates.) II. On a Process in the Differential Calculus, and its application to the So- — lution of certain Differential Hquations. By the Rev. P. K ELLAND, M.A., F.R.SS. L. & E., F.C.P.S., late Fellow of Queen’s College, Gg iptidees Professor “of Mathematics, &c., in the University of Edinburgh, III. On the Constitution of Codeine and its Products of LH ena By Tuomas ANDERSON, M.D., i : \ ; j IV. On the Equlbrium of Elastic Fluids. By Mr JAMES CLERK MAxwELL, V. Dissertation on a Peruvian Musical Instrument like the Syrinx of the Ancients. By Tuomas STEWART TRAILL, M.D., F.R.S.E., Profes- sor of Medical Jurisprudence in the University of Edinburgh. (With a Plate.) : ; ’ ; VI. Some Remarks on the Theories of Cometary Physics. By C. Pazzi SmytuH, Ksq., F.R.S.E., F.R.A.S., Professor of Practical Astrono- my in the University of Edinburgh, and Astronomer-Royal for Scotland, ; VII. On the Mechanical Action of Heat, especially in Gases and Vapours. By Wm. J. M. Rankine, Civil Engineer, F.R.S.E., F.R.S.S.A., . &e., VOL. XX. b PAGE 121 131 147 v1 CONTENTS. PART II. VIII. Note as to the Dynamical Equivalent of Temperature in Liquid Water, and the Specific Heat of Atmospheric Air and Steam ; being a Supplement to a Paper On the Mechanical Action of Heat. By Wo. J. M. RANKINE, Civil Engineer, F.R.S.E., F.R.S.S.A., &c., : 2 3 , , : IX. On the Power and Economy of Single-Acting Expansive Steam En- gines, being a Supplement to the Fourth Section of a Paper On the Mechanical Action of Heat. By Wm. J. M. Rankine, Civil En- gineer, F.R.S.E., F.R.S.8.A., &c., ; “X. On the Economy of Feat in Expansive Machines, forming the Fifth Section of a Paper On the Mechanical Action of Heat. By Wm. J. M. Rankine, Civil Engineer, F.R.S.E., F.R.S.S.A., &c. (With a Plate.) XI. Notes on the Geology of the Hildon Hills, in Roxburghshire. By JAMES D. ForsBss, F.R.S., Sec. R.S. Ed., Professor of Natural Philosophy in the University of Edinburgh. (With a Plate.) XII. On a new Source for obtaining Capric Acid, and Remarks on some of its Salts. By Mr THomas Henry Rowney, F.C.S. Communi- cated by Dr T. ANDERSON, XIII. On certain Salts and Products of Decomposition of Comenic Acid. By Mr Henry How. Communicated by Dr T. ANDERSON, XIV. On the Products of the Destructive Distillation of Animal Substances. Part II. By Tuomas AnpeErRson, M.D., F.R.S.E., XV. On the Dynamical Theory of Heat, with numerical results deduced from Mr Joute’s Equivalent of a Thermal Unit, and M. Rze- NAULT’S Observations on Steam. By WiLu1am Tuomson, M.A., Fellow of St Peter’s College, Cambridge, and Professor of Natural Philosophy in the University of Glasgow, XVI. On a Method of Discovering experimentally the Relation between the Mechanical Work spent, and the Heat produced by the Compression of a Gaseous Fluid. By Witti1aAM THomson, M.A., Fellow of St Peter’s College, Cambridge, and Professor of Natural ve in the University of Glasgow, : : PAGE 191 195 211 219 225 247 261 289 CONTENTS. XVII. On the Weight of Aqueous Vapour which is condensed on a Cold Surface, under given conditions. By JamMEs DatMAnoy, Esq., F.R.S.E., XVIII. On some remarkable Marine Invertebrata new to the British Seas. By Epwarp Forses, F.R.S., F.L.S., Professor of Botany, King’s College, London ; and J. Goopsir, F.R.SS.L. & E., Professor of Anatomy in the University of Edinburgh. (With Two Plates.) PART III. XIX. On the Total Intensity of Interfering Light. By Protessor STOKEs, XX. Some Observations on the Charr (Salmo umbla), relating chiefly to its Generation aud Early Life. By Joun Davy, M.D., F.R.SS. L. & E., Inspector-General of Army Hospitals, ; XXI. On the Total Eclipse of the Sun, on July 28, 1851, observed at Gote- borg ; with a Description of a new Position Micrometer. By Wi- LIAM Swav, F.R.S.E. (With a Plate.) XXII. Researches on some of the Crystalline ‘Constituents of Opium. By Tuomas ANDERSON, M.D., F.R.S.E., : 4 : XXIII. On a Necessary Correction to the Observed Height of the Barometer depending upon the Force of the Wind. By Captain HENRY J AMEs, R.E., F.R.S., M.R.LA., F.G.S., &c. ; ; XXIV. Defence of the Doctrine of Vital Afinty. By Witt1AM PULTENEY Autson, M.D., &c. &c., Professor of the Practice of Medicine in the University of Edinburgh, XXV. On Meconic Acid and some of its Derivatives. By Mr Henry How, Assistant to Dr ANDERSON. Communicated*by Dr T. ANDER- SON, XXVI. Notice of an Antique Marble Bust. By ANDREW CovENTRY, Esq., Vil PAGE » 299 307 317 335 347 385 401 417 Vill CONTENTS. XXVII. On the Centrifugal Theory of Elasticity, and its Connection with i the Theory of Heat. By Wa. J. M. Ranxine, C.E., F.R.S.E., ¥ RASS AG eee. : : ; F . 425 XXVIII. On the Computation of the Specific Heat of Liquid Water at various Temperatures, from the Experiments of M. REGNAULT. By Ws. J. M. Rankine, C.E., F.R‘S.E., F.R.S.S8.A., &e. 441 X XIX. On the Red Prominences seen during Total Eclipses of the Sun. Part I. By Witu1am Swan, F.R.S.E., . : . 445 XXX. On the Red Prominences seen during Total Eclipses of the Sun. Part II. By Witiiam Swany, F.R.S.E. (Witha Plate.) 467 XXXI. On the Dynamical Theory of Heat. Part V. On the Quantities of Mechanical Energy contained in a Fluid in Different States as to Temperature and Density. By W1LL1AM THomson, M.A.., Professor of Natural Philosophy in the University of Glasgow, 475. XXXIT. On two New Processes for the Detection of Fluorine when accom- panied by Silica ; and on the Presence of Fluorine in Granite, Trap, and other Igneous Rocks, and in the Ashes of Recent and Fossil Plants. By Grtorce W11son, M.D., : . 483 X XXIII. Contributions to a Knowledge of the Phenomena of the Zodiacal Light. By Professor C. Prazzi SmyTH. (With a Plate.) 489 XXXIV. On the Total Solar Eclipse of 1851. By Professor C. P1azzi SmytH. (With a Plate.) . : : : . 808 PART IV. XXXV_ Observations on the Speculations of Dr Brown and other recent Metaphysicians, regarding the Exercise of the Senses. By Professor W. P. ALISON, . é ‘ : ~ » ollie XXXVI. Summation of a Compound Series, and its Application to a Pro- blem in Probabilities. By Bishop TERROT, : 1 2) XXXVII. XXXVITII. XX XIX. Delis XLI. XLII. XLIII. CONTENTS. On the Optical Phenomena and Crystallisation of Tourmaline, Titanium, and Quartz, within Mica, Amethyst, and Topaz. By Sir Davin Brewster, K.H., D.C.L., F.R.S., and V.P.R.S. Edin. (With a;:Plate.) On the Production of Crystalline Structure in Crystallised Pow- ders, by Compression and Traction. By Sir DAviD BREWSTER, KOH. DC RS. VPA: Edin. On the Absolute Zero of the Perfect Gas Thermometer ; being a Note to a Paper on the Mechanical Action of Heat. By Wm. J. M. RANKINE, C.E., F.R.S.E., F.R.S.8.A., &c. , On the Mechanical Action of Heat. By Wm. J. M. RANKINE, CalieeE Reo bi, ERS SsA., ccs On Nitric Acid as a Source of the Nitrogen found in Plants. By GEORGE WILson, M.D., B ; 3 F Some Observations on [ish in relation to Diet. By Joun Davy, | M.D., F.R.S. Lond. & Ed., Inspector-General of Army Hos- pitals, 2 ; On Circular Crystals. By Sir Davin Brewster, K.H., D.C.L., F.R.S., and V.P.R.S. Edin. (With Two Plates.) Proceedings at Statutory General Meetings, §c., ‘ List of the present Ordinary Member's, in the order of thew Election, List of Non-Resident and Foreign Members, elected ander the Old Laws, | Honorary Fellows, Fellows Deceased, ened « or Goeatied oom 1349 to 1853, Public Institutions, Sc., entitled to receive the Transactions and Proceedings of the Society, List of Donations, continued from Vol. xX VI, page 648, Index, Laws of the See VOL. XX. ix PAGE 547 555 561 565 591 599 607 625 634 641 64] 643 645 647 665 Sion, Heddle Mea oe ‘ CONDITIONS OF THE KEITH PRIZE. This Prize, the interest of a sum which now amounts to about £800, left by the late ALEXANDER KEITH, Esq. of Ravelston and Dunnottar, will be awarded by the President and Council of the Royal Society of Edinburgh, on the following conditions :— I. The author of the best paper on a scientific subject (preference being, in all cases given to a paper containing an important discovery in science made in any part of the world), communicated in the first instance to the Royal Society during the sessions 1851-2, 1852-3, or any two succeeding sessions, shall be entitled to the biennial interest of the Kita Funp, accruing in the respective periods.” II. The form of the Prize shall be a Gold Medal, of not more than Fifteen Guineas value. The remainder of the sum shall be given in money, to be spent in Plate or other- wise, at the discretion of the receiver. Ill. The award being duly intimated to the receiver of the Prize, he is to apply forth- with to the Treasurer of the Society for payment of it; and, failing to do so within six months of the date of the intimation, he shall forfeit the money, but shall be entitled to re- ceive the Medal. * The proceeds of all preceding biennial periods have, in accordance with the decision of the President and Council, been either awarded to scientific individuals, or added to the capital sum, Lal ye ag She! » etl Ra aE te F eka al ot (halae ea ‘ ' my o*. Sie eS di oe Duiee =; a ‘S yo wy « somite Pr ‘ es out re st ag ey i PPh We Honk aed ‘es = ' J i : i ¥ { LA, 7 Pa 1 Me ia iy c “S| vw Ary we 4 i ¢ 4 ane . ‘ a 5A eee | . ‘a apy ly (% ahig? . j ‘ On) Sie e . * ¥ 1 , .\s * t j m Stale 20 : 4 ' 5 ? ad a Ps apagi al GTR eG Freier = vine tell POS Sia ie aha). Cala sad * fl ‘ A i ? hl: >, 5 4 . oF ah n > * 5 ‘ 7 c hia i a 1 s f 7 ' ~ i] = se ERRATA. pane 64, line 23, for 48 read 56. 71, as 7 from the bottom, for 215 read 216. 74, ... 7 from the top, for 20 read 21. 74, .... 10 from the top, for 5°23 read 8:23. 78, ... 18 from the top, for 8-662 read 8°62. PILATE 1 Royal Soc.trans Edin Vol XX p.1 . = Wz = WZ, Ny, Ss nee ras mK) E a a, or “A \\\ S LING th y ie { A Le, OF PART OF THE \\ ) VIVARAIS(ARDECHE) Showimg W ay) me Roxy THE LIMITS OF THE TRUE VOLCANIC ) WV Nye “ FORMATIONS. 2 Ss LA Ai q AUIIHY E‘— is dy fp GN IO Yy Yj il R . | \W " SF, Z WN wo aol ANS Z 6 Zan iy) ZA J < EG y, TH stourb = SS: : ‘ Bes ew AVA = i A. Nt! 7, \ Vie \"f pi) iy Wl \ , mall ir se = AME Ss ml] Wirrmwe =) HY SS LN Z GExX NH, aS zs : aw My S é WEAK Johnston, Ladin? Fur’ 765 ¢ az 2 2 4 3 Miles 8 Kilometres se AGED Se = s PLATE; [1 Royal Sac, Trans. Edun? Vol. XX tee Gig 2 Thee Wezenc fig 2 pll Near Pont de la Beaume ih i ; Ai aa ili eve, Trachyte and Phonolite _ —\ Basalt ba) 3 Tiachyte slightly Scoritied “ : 2 ee 5) Red Scorie ees Amorphous with ‘ (< 3) masses of Olwine i>, a Lava more or less Colunmnar ae b Score with occasional Ardéche Racin Coleman SAVIAC A! xy Wy Fig.8 p. Ly lig § pl6 Environs SP Jaujac LY ; Eaplanation A GT els wilh fae LCL. B Promlive, My med, wun Volcan /acing C Hill of Sandstone, +++ pouus YY marhing the continiuly of the Sandstone: —~ Course of CM the Lawa Wk AN Johnston lit, Ldn? PLATE TI kayal Soc. trans. Edin. vol XX Fig l. as Section at ee ae ih ae AVA if i ‘lit \\| h\\ ee y f Np a wd WKN, =e “h Le Vea if w Ay ir ti ual Bi Hy i / Fig. 3p 21 Superposition of Lava Q {| I) 6 ie ; Abin ‘a int yi” Z. fA WL is ty y an A / Cre yy iy, ey Ya | AN . Vy; iI, ’ gio Visas Wis, (Wet, L Fig. 4 p22 Gravenne of Montperat from the North. Ser ae Ne fig. © p23 Castle of Pourchivel. Lava from Gravenne = > 2 Finely “Strattied - ~ Bs EEE ~718 Giches 3S 4 Ss = 5S =. FoR ies > See large granite boulders | bas attic! Jara Older Basalt Acididlows Chalybeate Spring 0 led hloe hss 77 PB WY rm WHA Vy Wy, iy See WEAK Tolinslon We. Balin? Level of Forntaulier PLATE [V. hoyek Soe Trans kdink Wol’ XX Oo ep ann i i} I fig 2p 28. 26.27. Lava of Chambon => = YU = iil Ns \, i yin I) Sinan SECTION GE SECTION zz CC: LAVA :Grantte Debris lig L. p. 23 Superposition of Lavas w Valley of Montpezat. Voicano of Bauz0w L54 age of Crater of Pal = ! Fiighest powd of Lava ! Ee om AU 7 Gravatt’ ol Chambon (B arom Stat) : NY Grazute/ Bebris Second Mass of Lava ; Voteanie Si highest. bourdeaxzy of Crater - : Lava and Corgloveer ate’ & Pal (Barom Stat) ¥ 3 \ ve thick beds. Coreglomercahy OF Lal liq #4. p. 28. Crater of Pal \\ AANA iH - Cre HALO ii sini Hy SCOT? oe ( edi idles Fig. 9 Near Burzet. Pp: 29 ee aR Ly Bas, / | g GY Ge Wey / ian Dood y Z LPUSSAGH Of Pier Lontianer 4Dig wot of Ors at : wih Wem cay AN ‘id : tt BGeinbons ANN tee COMY LOMLET a Wk AK. Joanslon/ la Ean PLATE V. Royal Soc. trans. Fidin’ Vol. XX. a Vole, Conglomerate ; ; : 9. 2. p 34 Section in the course of the Volane - fig l p36 Pic de l Etoile ee : ye 5 as Fee 7 ~ a Se eytiat', aa F ai ¢ MAHL ON ) 1 HN hh i aie. SF ail @ r then uf eT gh —lyr(m—1) ar d a=|n |n ; a : L n=-1 ,—aax rr =f a G da, x or VOL. XX. PART I. lo 40 PROFESSOR KELLAND ON A PROCESS or, which is the same thing, iat 1 DR Gana, Va ff Gs da; from which it follows, by equation (1.), that & (S05) hfe “(carte aa aere =(-r)" an fe” eae [m+7 ey | r grt pela Consequently, (ar a = "So =(- yl at rt St) = Let w be a function, supposed to be capable of being represented under the . . Tr form of a series of functions, such as e-** ; then we shall have 1 d [-?+n r bi Verein! Rha: sesibae git (pT ae) u=(—7) D w (3.) |r . i ae du rdu 2. Since Fob eae ee ; LAN 2 eRe NE it follows that (— = u=r ie} u ae mr d #, == ie p 4 Mi or eae ag a rrr = 3. If we write d, « for ae = u; then from the last Art. it will be evident, x without demonstration, that . d, (uv) = vd. u + ndieod = u + a ad? sega on 4. Let @ (d,) be any function of d, capable of expansion in the form $ (d,)=2ad_; then, by the last Article ’(d,) wv=Safodutpd,v dy + &e.} =0(Sad")utd v(sapde )u+&e. IN THE DIFFERENTIAL CALCULUS. 4] =v (d,)u+d, 0 (d,) ut 5a, vp" (d,)u+be. where ¢’ (d, ) is the differential coefficient of @ (d,) with respect to d,. 5. In Art. 3, let o=e°” , then Bar Ba” é é —1 at u)= {d-u+pBra, u eee (d,+B ru; and hence, generally, as in Art. 1., p (d,) fer @ u} ey i Od, Poa 2. - (5.) 6. Let o(x)=3Be®”, then d (2) (d,)u=3Bee* (d,) u =I BY(d,—Gr) eu by (5) =3B{Y ,)-¥(G,) Br+¥ (a) CO bey Pu =) (d,) {3B ut —W (d,) fd,(2Be®)u} + de. = 4) {f (@) uh—¥ 4) {4 & @) 4 + 5 VG) {dt b (2) a} be. 7. It is easily seen that, if m be a whole number, —™m meg n/t ot 1 : d, log z= cS { log Eas (G+5+ee+ =) i, and that in other cases, TM d. log x Se ae a —m E, r—1 m 8. The operation denoted by 4. must not be confounded with (« I d x) : it is, in reality, ( je az) "The one expression can be deduced from the other, thus :— (a? da) “log gaa’ ge &-» log r=2 anne ge ee) 7 2) (il mami Fs 2d cal ee ae P [-e=2t | g—r+l1 r (r where 7, q, and : are indefinitely small. PROFESSOR KELLAND ON A PROCESS 42 [pte ita Hence (2 'faz) ” log PL wl Ne VON: he Ses “ pr | [Pam oe bm eal po aa Gtr sgl” ee ee a} ee og2— he gas “ees Tate ip) jet™ 9. To find the differential equation, on the solution of which depends the value of d* e&*. De = a” & Since e7“=1l+axr+ 7 5 + he. ax 4 —r | Cage fen an Ta | . r This equation can be made to depend on the solution of a differential equa- tion, when 7° is a whole number ; for, in that case, the terms will recur after the rth. To reduce the equation, we observe that j=@+)+rp j—l+rp = MLE end snien [ r+] ~ rtl—rp on ? E (he [Fe j—l+rp. | r+1lort+l1 a ee MN ie | __( oo ie abe ) ee sal ee prick wind r+l—rp jrt+l + & |r as f/—2+rp | r a x r+ 2 Greg t? ce i 2 (Gao jr+2 + &e.) + den &e, |... . (A) aoe = rprtl—rje Ee ee ee ie 7 ie Z lel (A+ Tre Ceti: 2mm Ge ONC ised 9 + ~ rth (r+ 1-7 pL) Qr+1—rp) AMOF a 6-oep oso ; then (eg / et Le ax’ **(r 41) (« oA a (G+moeiesm es dias dx =a" x Sy rrp CEEET! r r IN THE DIFFERENTIAL CALCULUS. 43 =H ere: { Ue Or penis ware te. Te x 2 Tpe2—rp [r+2 ce oe Gime (r +2) (27 +2) j2r+2 (P+ 2—r pf) (Qr+2—rp)” c.} i dy | , ae at ght? r+2 ——— Lf le = LF Se) (« ) ‘ io |r+2 r+2—T pe +&e. } =a ty eh ebere (B). The same process will give the same result for all the terms of this expan- sion except the last. But as ie ee is a factor cf that term, it is evidently 0. er a) Meee Consequently, the equation ee ( a” 7) =a'x'“y gives the complete value of y=d" ””, it being observed that one of the constants of integration is 0. The other constants must be determined by means of equation (A). 10. To find dr COS a 2. Since cos eral” ae — &e. } if —a*?=6, we shall have ee ; [=eite = ad a ce ae a 2—r (= =) cos az =(—7) \B 3 x be |r - See : othe 2 oe ss 49 be ee r 6—r "OO teres 1 Os a r a It remains to express this series in the form of a differential equation when 7 is a whole number. [/-2s+7r yh UE sd ABEL Let s be any whole number less than 7+1, S=(—7)“ 0° ee ; then the s Hee [~F series may be written eed, oY (r+2s)(2r+2s) aioe es ara [28° 7 ir as (r+2s—r pL) (Qr42s—r pl) Se ay Eh orton Bere em a ig oa ao) 2s j2s—r ica (at VOL. XX. PART I. ; M 44 PROFESSOR KELLAND ON A PROCESS as (r+2s)(2r4+2s)a472t3" : * s+8r—1 (r+2s—r ph) (2r+2s—r p) (Br+2s—7r py + &e. } eee Se aan dx te dx 28(2s—r) j2s—r—1 eS ee ber (7+2\s) (24428) a7*t3r-1—-rp al 25 [2s+3r—1l (r+2s—ryp)(27r+2s—r yp) S we. } ST re 8 gre SO guy _ g (Gee Crr—rp) esa. dz dx dx-! dz 2s (2s—r) [2s—2r WE Die ‘ed (r+2s)(2r+2s) 2s42r a * Brtle (r+2s—rp)(2r+2s—rp) + &e. | =s (2 s—1 pl) (2s—r—r pM), Pig tis 2s(Qs—r) Pe—2r AE ANS: 1 [f Sa, @e-ae7 ” a paee sue Ld, (2s—7 ph) (28—r—r HM) 25-27 _ eT eee aS oe ee 28(28s—r) /2s—2r (ni) regatere | | as pre, =(-f <0; gr—l , gd’ 1 ; dy Be a Tb Ae: A ee jel dee, gee ae ee or, if x"“ y=z, the equation may be written ao eid —r 3 =e "Ta? ‘ e=(—a?)z,.-.(C) a form which exhibits its relation with the differential equation resulting from ¢”. 11. There exist numerous relations between the differential coefficients of a - function ; such as the following :— /_D Since LS f) wa U; [or Wes 2 bar IN THE DIFFERENTIAL CALCULUS. 45 D ae Hence p (=) = — ane Die Cri eo —(u—1)r TD fr —D /—D j=F Hence at =” a) ~=(— 1) av io an) ps ayy, av a relation between differentials with positive and negative values of r. Section II. APPLICATION OF THE PRECEDING THEORY TO THE SOLUTION OF DIFFERENTIAL EQUATIONS. 12. The first example which I propose to give is the solution of equation (B), Art. 9. rp a rr ; Ex. 1. ph eee . =a’ x" y, where « may be anything whatever. Let a r—1 rs r—1 or Ye g | whl Pl_-Te gaaq"y"-lz dik or D(D-1). . (D—r+2) x x (D—rpt+l) Ba ee a" er? bate Let = or on ‘ >) v; then x r D D(D-1).. . . M=r+2)x(D—rpts (- =) °= a’ ef (- myeaa s(- 241) ey. 46 PROFESSOR KELLAND ON A PROCESS Which equation is reduced to DQ@M-1) .... M—7r4+1) v=a" ee"! v (1.) by the condition / (— _ +1)= — I (- >) (2.) 1 ee oa ee — Di, “ r r / 1 Dy 2 ror iP es ee ee nr ee ses ew whence . org * Wen Ee v z ; a Dew T Ye | ; bag dire Me es a—Ttly /_ D = (jean het eee Now ¢ is the solution of equation (1); or, which is the same thing, of d” v r = Gi F dx’ v=Ae** is a value of v; and hence, finally, —pt+tl1 -1 ee eel sm ere & ax =Bd,e , where B is an arbitrary constant. It is evident that any other of the 7 roots of the equation =a would aE satisfy the conditions, or that any one of the roots of a will produce the same result as a@ itself. This example affords an excellent illustration of the process. Let us take, in the next place, the equation which occurs in the theory of the Figure of the Earth; an equation which has been solved by Professor BooLe, in his admirable Memoir in the Philosophical Transactions for 1844, p. 251, but whose process is necessarily restricted to integral values of 7. The equation is— 2 . . Bx.) 2: a ee IN THE DIFFERENTIAL CALCULUS. 47 By the usual process, this equation becomes D (D—1) u—q2e24 u—i (é+1)u=0 or (D +2) (D—i-1) u—q? e?4u=0. Let wer (- >) v, then (D+7) (D—i-1) e-*"f (- x) 6 = gre?" f(— pt ey=0 or D@D-2-Ds (—F)e-P F(— pret v=0 an equation which, by omitting the function of 0, is reduced to D (D=1) v—¢ ec?’ v=0 ails) by the condition fog =e st (-3) DED —¢__9)-7t fl Wa \a v Se (= +) * But the solution of Equation (1.) is o=Aci*+ Be"; Hence the complete solution of the given equation is 1d x ax rela) ee ( Hi = (Ae*4+Be7?*) This solution is susceptible of another form by Art. 11; for by that Article, lL d\tv _7 4t -@it+2 (3 7@\' _v ( ) pn) 2 (« ia) a=) a dix e2i-1 ? , 4 qv —qa VOL. XX. PART I. N 48 PROFESSOR KELLAND ON A PROCESS in which form the solution has been given by Professor Boouz, when 7 is a whole number. Ex. 3. Solution of the Equation for Laplace’s Functions. This equation has been reduced by Professor BooLe, in the Cambridge Ma- thematical Journal, New Series, vol. i., p. 15, to the form a= wos y+ 2 (a1) wa + fn (24 1)—a (aD Jo=0... () where uw, the quantity sought, is aoe with v by the equation dik es (2). Putting w=e" and writing D for ,, oe we have {(e~?’-1)D (D—1) +2 (a—1) D+ (n+1)—a (a—1)}v=0 or e-24D (D—1) vp—(D—a+n) (D—a—n—1) v=0 or D (D—1) »—(D—a—n—2) (D—a+n—1) e?4v=0 Let, therefore, v=/ (-3) w (3), and this equation becomes D -vs(-3) m—~(D—a—n—2) (D—atn—1)f (5 +1)e" w=0 or D (D-1) w—(D—a—n—1) (D—a—n—2) e?4w=0 (4), provided D D—a-—n— D Neots if (- a D Greil ~ 5b ge gtp D See ee 1 eS an equation of which the solution is evidently Deen Ah r( 2a a aa 5.) 2 f SD Su mt a he D and by (3) v=s(-5)” [_ D am t ij. 2oo Eee Dee x i vort'o ors pees —e-(n—a-1)é (ae an gral 4, IN THE DIFFERENTIAL CALCULUS. 49 hn, Wossoide ly fells Qh \ ON meat Any ad ae ae Ie w (6) a result which is true, whether 7 be integral or fractional. The value of # from Equation (4.) is easily found, and is given by Mr BooLE in the form m= (1+ py? (p)+(1—m)"** x () whence that of w is found. Let us take, as our next example, the equation which has been discussed by M. Potsson in the Journal del’ Ecole Polytechnique, cah. 17, p. 614; and by Profes- sor Boor in the Philosophical Transactions for 1844, p. 254. ptl 2 Ex. 4. (—2) 75+ { ce Wat \-2n@n—p) u=0. seed Gl: The symbolical form of this equation is @O+2n— - (D+2n”—2—p) 2 DD+p) Oe) Let o— (-) Cee ise atau os)ee CHEM: i (-5)e ee ee a = iio (48 This last equation may be reduced to an integrable form in various ways: 1. By making = — prea >t (-F) DAs Davin ==, 2 Le Dips ap 3 ee ees see ee ( DY | Oe? hal ee or is -5) = a si eres E | ae ells OU ae OO eae DP pet (abe e ot bi per 2 2 2 -(@n p pe/ De VDe ED (2n—p—2) é ae /_D item oe ee a 2 # p -pfl d A= ons. cd 2 inp 2s 01 w= (—2)? 2 GC a) 2 ¢ 4) E and equation (4.) becomes D+2n—2)(D+2n—3) 2 ae free Me Rea... (5) which is a known form, and thus the given equation is completely solved. It is evident that our solution reduces the operation to that of ordinary dif- ferentiation or integration, when p is an odd integer, positive or negative. By varying the process, however, we can obtain other forms of the solution of this 50: PROFESSOR KELLAND ON A PROCESS equation, which are reduced to ordinary differentiation or integration in other cases. The other forms are as follow: : D D iM gH ‘ SS ee eee te hae 2. By making | ae ae i) D D eae or t(-3)=-p—— ae SaaS Hime) BY }—zptn-l1 —,p-(n—2)0/ 2 e(2n—2) 4 pea eo ld n—1 5 and, consequently, or a | ) z’"~? >; where v7 is found from the LAL . _D+2n—2—p ox (r/ 4) =a equation of the first order v =e gi ge | ees ) 0. This solution is of the ordinary form, whenever x is a positive or negative integer. : D D D By making Gaeta ree ee x) | \SB D Bi sonar Rar pide Zyl eee t22 | } SPse lise 9 [aioe —e—@n—2—p) | fe er" —2-p 1 Be 0 (ra P and u= _9)- @-§-D Ga) 3 Pt i dea v; xdx where v is found from the solution of the equation of the first order, D+2n—2 99 | D\. —= ee Ss a” v=s(-35) 0): This solution is of the ordinary form when x ~F is an integer. : D D 4. By making = at = ee LS 8 I (- =I D+2n—p—2 [_D_p or iso et ;-2 : ) opp aaa op -(2n—p—2)6 [-3 ie Ba (2n—p—2)6 IN THE DIFFERENTIAL CALCULUS. 51 Gis ei J MNP Ei ay hg and w=(—2)7 Pe eee bees Hm, where v is found from the solution of the equation of the first order, D+2n—2 96 | ID \ >) Dagens »=s(-3) © This solution is of the ordinary form when x —p is an integer. This last form appears to have been overlooked by Professor Boos. 2 The reason is, that equation (5) being of the second order, will contain two arbi- trary constants, and will thus render the solution of the given equation complete, without the introduction of eas other terms. —1 It may be remarked, that we have omitted / (- =) 0 in the first solution. Ex. 5. (1-2) 3 —(2 m+1) 25 —(n2—9) u=0. This equation has been solved by Professor BooLe ; but it is requisite to shew that his solution is not confined to integral values of m. The symbolical form of the equation is (D+m—2)? aa, ou-0 D(D-1) : UuUu— Let u=e—™ f(—D)v; then D—2)—¢? a) aaa dwar Oe ices a Dei’ 050. D (D-1) (D—m) (D—m— Dy or gp ew et By making f(—D)= —D+2); this equation is reduced to and a ae --"(4)" d\m a (32) {A cos (g sin—!x) + B sin (g sin} x) | This equation is, however, susceptible of a solution in a different form from that which we have just exhibited. Let = 7 (-3) v, then D D+m—2~— 9) (D+m-2 f(-3) Seer pon eee ee =) VOL. XX. PART I. O 52 PROFESSOR KELLAND ON A PROCESS (D—1) D f(-g+) = Dee 2497 (-3) a By making this equation is reduced to the equation of the first order -1 _ ee Pe v=1(-3) 0...(2) ee 2 Also Uf (-3) == — 272 —— Let OR | ie oe yer pee eee ea (m—2+9) 4 | 272 a 2 (m—249)¢ ee) 2 a Va ) m+q—1 gta =(—9)—™+-)) ( (+2) a x az which is of the ordinary form when m+q@ is a whole number The same is true if —q be substituted for g. Section III. CoMPAriIson OF PROCESSES We shall occupy this Section in the comparison of the different methods which may be employed in the solution of a given Differential Equation. 13. To find the value of [/—D . v. Suppose v expressed in the form =A e~"44 Be—@t 44 & then [=D . v=A [ne—"44+B |n+re~ + $4 &e. RO es x x “doth @ o ef ares (A a"+Ba"*” +&c Hence, if v= f(z) 2 —a“x da 1 Por aga =) IN THE DIFFERENTIAL CALCULUS. 53 14. All equations of the form y—m«’ —t=x can be converted into equations a ad: wv in ——. dx —D+n vol n|— _x For i =a Let y=/—D - Us then = : or ee aa /—Din v= xX D+r r—n ete = | or eer en aoe A e=(=D), Xx —(r—n) 7 ON a —— ot or v—m(—1) x a) “ "y=(/—-D) X or, if at" » = Z, ee en) se gern! 2 r—n (=D)~* X dx wherefore the above equation is reduced to an ordinary differential equation. whatever be a, provided 7 is an integer. As an example, let us take the simplest case, of which the solution will be found at pp. 257, 258 of my Memoir on General Differentiation, Part IIT. eens Rx. 1. y—-aV/—1e 7=0 x Suppose y=/[—D» then ee ee = (v Jz) = CV x or Z2—Aax qe UN where z=vJ/2; 2 2 as ave f A_o Lee alt a a x eee 2 ea NON WSO 1 Ae mG X aVvu a DAVE 24/p 2 Rs ee a eee Toe =| ie Vp a a p The constants A and C are not both of them arbitrary. In fact, it will be A : seen that C=» so that the final form of equation (1.) is 2 Spoke dy /O x 2 dd for a4 PROFESSOR KELLAND ON A PROCESS Ex. 2. To solve the equation 1. By the method employed at p. 269 of my previous Memoir, this equation becomes (—D+¥)y+a(—-1)' Daa ei ee /—D+4 : yo ae yt Me or a Be Fgh SE _1l fXdz wee: Pe; =P, suppose ; Tae (= a then zd, \dz + i an aa —are ae dip G=Awve oh we fe a2 (Teta) 2. By Professor BooLe’s method, given in the Philosophical Magazine for February 1847. The given equation when written a(d—a d)y—ky=Xa; may be thrown into the form f (ad) («F @))y=X2; provided f(a) F (d)=d-ad', and f’ (@E@ =-}. We have, therefore, _f(@)=(d?—a)~* F (d)=(a3—a) d? and y=a-3 (dt—a)—? {z—1 (dt—a) X21} 3. By Mr Harcreave’s method, given in the Philosophical Transactions for 1848, p. 31. By changing d into 2, and z into —d in the equation a(d—ad*)y—ty=Xz.... (1) it becomes d (x—ax*)yt+ty=dX.... (2) which, being an ordinary linear equation, gives, as its solution, if we write d—1 for fae, y=a-? (x? ~a)-2 d~ (wha) dX}... . (3) Now, since equation (2.) has been derived from equation (1.) by the change of d into x, and # into —d, equation (1.) may be derived from equation (2.) by changing 2 into d and d into —a#. Consequently (in some cases, at least, of which this form is an instance) the solution of equation (1.) may be derived from the solution of equation (2.) by the same change. Hencethe solution of the given equation is IN THE DIFFERENTIAL CALCULUS. 55 y=a-* (dt—a)~” fers (d? —a) x X}, which is precisely the solution given by Professor Boo.e’s process. We shall conclude the present Memoir by comparing the methods here exhi- bited in two particular cases of the second example. Casr 1. Let X—0; then the first method gives y=Axre*” : whilst the second and third methods give y=d—* (dt—a)~? . 0. Now, in a former paper (7'ransactions of the Royal Society of Edinburgh, vol. xiv., p. 252), I have shewn, in Cor. 1. to Example 3, that Com O=Ac™"+Bae** Hence yad-S{AeP*4 Ba e%} ee ate, Be ae Bax gant ~ 2a3 The condition B=2 Aa? reduces this solution to the former. i ii Cask 2. Let x=6(4r :) x? / w 2 then, by the first method, lf dee of TE aN ee Bread ue myelin Je} z Va N# __ 6 2ab/-1 1 ral Ni x a dP dtp ee dx dx =e 2 xt ue? 2 y=Ane”® + pee * fede 6 i x2 at oe a x b =Aze Vat By the second and third methods, Teese _,(V=1 1 a @V—T Also a-* (gt_g) 2? =P +2e+07 G@—aP y=(d—a?)~* (d§+2a+d~*) nea a ga = ) Be ek Nee Raa Garon oer a an ordinary linear differential equation, of which the solution is — ax aa 6b y=Axe “+Be Ars This agrees with the former solution by making B=0. VOL. XX. PART I. a ba rs rats MOS & HI: Ot, Soeeagh tile * srt, teat i oie (panies gl, it Whos obqranes, fywoecng ee Ty smb Ene ae Seay a a a bi , i » ° 1 # ( “ ~ s d im ® ae * * Pee: a Bat ® «a a hy aS oa ‘% : | : no: ake ‘ mn: ‘=’ ar! a ‘ , Po pag 7 As Py : : 4 a. abortiea Init) bon bates sed * ir e ‘> 1 Vee Wn tot ee eat ‘ =) ee j W oy Hee ingdce: Mtb melt ip be x ; : . ' ; - . d } =» F Y. Saya eae eo ae ee unio Swe wit iw Sonny vee 7 re wast pi alt ; a = a ah) I1l.—On the Constitution of Codeine and its Products of Decomposition. By THoMAs AnvErson, M.D. (Read 15th April 1850.) During the last few years, great progress has been made in the study of the organic alkalies, and the discovery of methods by which these substances can be artificially produced, and the long train of investigations by which it has been followed, has greatly extended our previous information, and afforded us some de- finite ideas regarding their constitution. The advance made has, however, related entirely to the volatile bases produced by artificial processes, and our knowledge of the natural fixed alkaloids stands very much where it did some years since, and is still very imperfect, and in regard to many entirely fragmentary; so much so, indeed, that of all the alkaloids of this class described in chemical works, there — are not perhaps a dozen of which the constitution can be considered as definitely fixed, and not half that number of which we know the products of decomposi- tion. The fact is, that the interest attaching to the artificial bases has altogether diverted the attention of chemists from the natural alkalies, which have not hitherto proved a very productive field of inquiry; at least the researches to which many of them were subjected ten or fifteen years since, proved compara- tively unfruitful in their results. The want of success which attended their in- vestigation at that time, however, is attributable, partly to the imperfections of the method of analysis of such compounds, and partly to our entire ignorance of the constitution of the nitrogenous substances generally. Neither of these diffi- culties can now be said to exist; and the investigation of the volatile bases has so far elucidated the constitution of these substances generally, that we are now in the condition to return to the examination of the far more complex natural bases with some prospect of ultimate success. Chemists are, accordingly, begin- ning to turn their attention to this field of inquiry, and during the last few months, several investigations have been published, by which the constitution and products of decomposition of several important bases have been established ; and in the present paper I propose communicating to the Royal Society the results of a series of investigations of codeine and its compounds, which has enabled me to add it to the number of those of which the constitution is definitely fixed. It will be unnecessary for me to premise any observations regarding the his- tory of codeine and its discovery, which are sufficiently well known, further than to refer to the analyses and formule given for it by the different chemists by VOL. XX. PART I. Q 58 DR ANDERSON ON CODEINE, AND whom it has been examined. Codeine has been analysed by its discoverer, RosiquET, and by CovERBE, REGNAULT, WILL, GREGORY, and GERHARDT. All the analyses of these observers I have brought together in the following table, in which, however, the per centage results are not those found in the original papers, but have been calculated from the analytical numbers according to the new equi- valent of carbon.* Anhydrous Codeine. ROBIQUET.f CovERBE.{ REGNAULT.§ GREGORY.|| WILL.4 Carbon, h 70-°363 71:59 72°10 73°31 72°93 73°18 73°27 Hydrogen, : 7-585 #12 7:17 T19 7:23 7°23 7°25 Nitrogen, 3 0'°353 5:23 tee 4:89 4:89 4°82 Oxygen, : 16-699 16-06 vee 14-61 14-95 14-77 100:00 100-00 100-00 100-00 100-00 Crystallised Codeine. GERHARDT.** Carbon, : : ; : : 67:77 67:87 Hydrogen, . : : ; : 7°59 7°33 Nitrogen, : : : : mat Aa Oxygen, From these analyses, four different formulze have been deduced. Two of these, however, those of RoziqueT and Covers, do not require particular mention, as they were unsupported by any accurate determination of the atomic weight of the substance, and are now certainly known not to represent its true constitu- tion. That which has been hitherto most generally adopted by chemists is the one founded by Recnavu.t upon his analysis, and represents codeine as C,, H,, NO., and the crystallised base as C,, H,, NO,+2 HO; the calculation of which gives Anhydrous. Crystallised. Carbon, . : 2 73°94 69°53 Hydrogen, ‘ : 7:04 7°28 Nitrogen, . ‘ ‘ 4-92 4-63 Oxygen, . : 5 14:10 18-50 100-00 100:00 The analyses of WiLL and Grecory have usually been quoted in confirma- tion of this formula. It is clear, however, that the agreement between the calcu- lated and experimental results is by no means satisfactory, either in them or in * In the case of Ropiquet and W111’s analyses, the details of the experiment are not given. I have, therefore, been obliged to convert the per centage of carbon into carbonic acid, according to the old equivalent of carbon, and recalculate it into carbon according to the new equivalent. + Annales de Chimie et de Physique, vol. li., p 265. t Ibid., vol. lix., p. 158. § Ibid., vol. lxviii., p. 136. | Annalen der Chimie und Pharmacie, vol. xxvi., p. 44. { Ibid. ** Revue Scientifique, vol. x., p. 203. ITS PRODUCTS OF DECOMPOSITION. 59 REGNAULT’S own results; the highest amount obtained for the carbon being 0°63 per cent. below the calculation, while the lowest differs by more than one per cent., and the mean of the whole four gives 0:77 too little carbon, involving a loss which could not possibly have occurred in carefully made analyses. Partly on account of this difference, and partly guided by his views regard- ing the divisibility of formule, GERHARD? was induced to doubt the exactitude of Reenavut’s formula, which presents three different deviations from his law ; the number of equivalents of carbon and of oxygen being uneven, and the sum of the equivalents of hydrogen and nitrogen also indivisible by two. He therefore repeated its analysis, using the crystallised codeine, and obtained the results contained in the table, and deduced from them the formula C,,H,, NO, for the anhydrous base, which gives the calculated results: Anhydrous. Crystallised, Carbon, . A A 72°24 68°13 Hydrogen, é , 7:02 7:25 Nitrogen, . 7 F 4°68 4:41 Oxygen, . 5 : 16-06 20°11 100-00 100-00 and tallies extremely well with his analysis. This formula has, however, been again called in question by Douurus,* who has endeavoured to determine the constitution and atomic weight of the alkaloids by the analysis of their hydro- sulphocyanates, and obtained from the codeine salt of that acid; results agree- ing with the formula C,, H,, NO,. Considering the known accuracy of REGNavLt, and of the chemists by whom his formula has been confirmed, I considered it an essential preliminary to my investigation to repeat its analysis with all possible care, so as to determine which of the two represents its true constitution. I. Preparation and Analysis of Codeine. I have little to add to the information we already possess regarding the pre- paration of codeine. I have obtained it, as usual, from the mother liquor from which morphia has been precipitated by ammonia. As the codeine forms only from a sixteenth to a thirtieth of the morphia, it is, of course, mixed in this fluid with a corresponding quantity of muriate of ammonia, which must be decomposed by potash, in order to obtain it. Much advantage is gained, however, by first. evaporating the fluid to crystallisation, and expressing the crystals deposited, as in this way the greater part of the muriate of ammonia, which is the more soluble salt of the two, is left in solution; and by repeating the crystallisation many * Annalen der Chimie und Pharmacie, vol. Ixv., p. 218. 60 DR ANDERSON ON CODEINE, AND times, it may be entirely removed, and crystals obtained which are pure hydro- chlorate of codeine. For the preparation of codeine, however, it would be worse than useless to carry the process thus far, as the solubility of hydrochlorates of codeine and ammonia differs so little that much of the former salt would be lost; but by carrying it a certain length, the greater part of the sal-ammoniac may be separated without any material loss of codeine, and the subsequent steps of the process much facilitated. The crystals so obtained being dissolved in boiling water, strong solution of caustic potash is added in excess, when codeine is in part precipitated as an oil, which by-and-by concretes into a solid mass, and is partly deposited in crystals as the solution cools. By evaporating the fluid, another crop of crystals is obtained; and, finally, when the mother-liquor has been concen- trated to a very small bulk, it becomes filled on cooling with long silky needles of morphia, which has been retained in solution by the excess of potash. A certain quantity of morphia appears always to remain in solution along with the codeine; at least I have found it in all the mother-liquors I have examined, although its quantity appears to vary considerably. Its presence in this solution has been observed before, and it has been stated that it exists in the form of a double salt with codeine; this, however, is not consistent with my own experience, at least the salt separated from the muriate of ammonia by successive crystallisations contained no morphia, but, as has been already stated, was pure hydrochlorate of codeine. The crystals of codeine precipitated by potash, in the manner described, are always more or less coloured. They are purified by solution in hydrochloric acid, boiling with animal charcoal, and reprecipitation with a slight excess of potash, and the precipitate obtained finally dissolved in ether, to separate any morphia which may adhere to it. For this purpose hydrous ether is best adapted; and it ought to be free from alcohol, as if any be present, the ether evaporates, and a syrupy fluid is left behind, which refuses to crystallise. When the ether is anhy- drous, it dissolves codeine with much greater difficulty, and by evaporation small crystals are deposited, which are anhydrous. The codeine employed for analysis was dried at 212°. The three first were made with codeine crystallised from hydrous ether, which lost two equivalents of water at 212°; the last was anhydrous codeine in small colourless crystals. 6-120 grains of codeine, with oxide of copper, gave I, < 16:185 ... of carbonic acid, and 3888 ... of water. 5°896 grains of codeine, with oxide of copper, gave II. < 15°616 ... of carbonic acid, and Oo (o0 es “Ol water. 4-688 grains of codeine, with chromate of lead, gave II. < 12:392 ... of carbonic acid, and 3°015 ... of water. ITS PRODUCTS OF DECOMPOSITION. 61 15485 _ ... of carbonic acid, and 5°858 grains of codeine, with chromate of lead, gave IV. 3°780 ... of water. 5°395 grains of codeine gave, by VARRENTRAP and WILL’s method, 3°79 grains of ammonio-chloride of platinum. 5°898 grains gave, by the same method, 4°32 grains of ammonio-chloride of platinum. I. II. III. LV. Carbon, . A é 71-91 72:02 72:09 72:09 Hydrogen, : : 7:05 7°04 714 Tlie Nitrogen, i F 4:4] 4:60 4:50 ach Oxygen, j : 16°63 16°34 16-27 100-00 100-00 100-00 These results confirm, in all respects, the formula C,, H,, NO,, the calculated results of which are given on a former page. The determination of the atomic weight of codeine by the analysis of its platinum salt, presented considerable diffi- culties, and at first gave extremely discordant results, the per centage of plati- num varying from 18°51 to 20°30. I found, however, that by precipitating in the - cold, a salt was obtained, to be afterwards described, which gave sufficiently uni- form results. This salt, dried at 212°, retained an equivalent of water. It gave, as the mean of seven experiments, the details of which will be afterwards given, 19-25 per cent. of platinum, while the calculation, according to the above formula, requires 19°19 per cent. These determinations leave no doubt as to the formula of codeine; and they are fully confirmed by the result of the analyses of the sub- stances to be described in the sequel of this paper. Codeine crystallised from water or hydrous ether is obtained in crystals, often of considerable size, belonging to the right-prismatic system, and presenting a considerable number of modifications. These crystals contain two equivalents of water of crystallisation, as determined by this experiment :— 7126 grains crystallised codeine lost, at 212°, 0:-454—5-°66 per cent. water. The calculated result gives 5:67. Codeine is an extremely powerful base, rapidly restoring the blue of reddened litmus, and precipitating oxides of lead, copper, iron, cobalt, nickel, and other metals, from their solutions. It is precipitated by potash from its salts; and is generally stated to be insoluble in that alkali, but this is true only of very highly concentrated solutions, as a considerable quantity of strong potash may be added to a saturated solution of codeine in water without producing precipitation; and even when a very large amount of potash is added, a certain quantity of the base is still retained in solution. Codeine is soluble in ammonia, but not more so than in water. 100 parts of a moderately strong solution of ammonia dissolved, at 60°, 1-46 parts of codeine; and according to Rosiquet, 100 parts of water, at 59°, dis- solve 1-26 parts. Contrary to what is usually stated, I have found that codeine VOL. XX. PART I. R 62 DR ANDERSON ON CODEINE, AND is precipitated from all its salts by ammonia; it does not, however, fall imme- diately, but is slowly deposited in small transparent crystals. Il. Salts of Codeine. Hydrochlorate of Codeine.—This salt is readily obtained by saturating hot dilute hydrochloric acid with pure codeine. If the solution has been sufficiently concentrated, it becomes nearly solid on cooling, but if more dilute, the salt is deposited in radiated groups of short needles, which, under the microscope, are found to be four-sided prisms terminated by dihedral summits. It is never ob- tained in large crystals, even when considerable quantities are crystallised. These crystals are soluble in 20 times their weight of water at 60°, and in less than their weight of water at 212°. Codeine is precipitated from the saturated cold solution immediately by potash; ammonia gives no precipitate, but after some time colourless crystals are deposited. The crystallised hydrochlorate of codeine con- tains water of crystallisation, and presents some curious anomalies in its rela- tions to that fluid. When dried in the air, it retains four equivalents of water, one of which escapes at 212°, but the remaining three are only expelled at 250°, and at the same time the salt loses acid, and acquires an alkaline reaction. It would appear, also, that under certain circumstances, the salt is deposited in anhydrous crystals, as one analysis of it dried at 212°, gave numbers corresponding to the an- hydrous salt. I could not, however, again succeed in obtaining it in this condition ; but many analyses were made which gave results lying between those of the anhy- drous and crystallised salts, and the only means of explaining the discrepancy is by supposing that the two sorts of crystals had been deposited simultaneously and in variable proportions. The following is the analysis of the salt dried at 212° :— 6-035 grains hydrochlorate of codeine gave 13:208 ... of carbonic acid, 3°830 ... of water. Experiment. Calculation, oo ee a=. Carbon, 2 j 59°68 59°58 C.. 216 Hydrogen, d ; 7:08 6.89 ee 25 Nitrogen, , ; oe 3°86 N 14 Oxygen, : : ws 19°88 0, 72 Chlorine, : Shs 9:79 Cl 35°5 100-00 362°5 10°735 grains of the salt lost, at 212°, 0°31 grains of water=2°88 per cent. One equivalent of water gives by calculation 2°42 per cent. The formula of the air-dried salt is therefore C,,H,, NO, H Cl+4HO. The anhydrous salt gave the following results. Of these, No. I. is the salt obtained by direct crystallisation from the morphia mother-liquor; No. II. is that ITS PRODUCTS OF DECOMPOSITION. 63 which was got anhydrous at 212°; and No. III. is a portion dried at 250°; it had become strongly alkaline, which accounts for the excess of carbon obtained. 6°171 grains dried at 250° gave I. <¢ 14:565 carbonic acid, and 3°795 water. 4-286 grains dried at 212° gave II. <¢ 10:014 carbonic acid, and 2°603 water. 5:740 grains dried at 250° gave III. < 13-667 carbonic acid, and 3:467 water. Experiment. Calculation. ile ; II. Til. Carbon, 64:37 64:56 64:93 64:38 Cx 216 Hydrogen, 6°83 6-74 6-71 6:55 He, 22 Nitrogen, v vee soe 4:17 N 14 Oxygen, 14°32 O, 48 Chlorine, 10-58 Cl 35°5 100:00 335°5 These results correspond to the formula C,, H,, NO, H Cl. Hydriodate of Codeine is obtained by dissolving codeine in hot hydriodic It is deposited in long slender needles, which fill the whole fluid, if it have been sufficiently concentrated. It is of rather sparing solubility in cold water, requiring about 60 times its weight, but is much more soluble in boiling water. Its saturated cold solution is precipitated by am- monia on standing. No difficulty was experienced in its analysis. acid, and allowing the solution to cool. 11-190 of carbonic acid, and 3°247 of water. | 5°801 grains dried at 212°, gave II. 6:336 grains hydriodate, dried at 212°, gave IC 10-347 of carbonic acid, and 2:977 of water. 5739 grains of hydriodate of codeine gave 2:994 grains of iodide of silver. Experiment. Calculation. —— —_—— aE II. Carbon, 48-1 48-64 48-60 C., 216 Hydrogen, 5-69 5-70 5-40 ies 24 Nitrogen, : 3°15 N 14 Oxygen, . Se 14:45 O, 64 Todine, 28-22 28:40 I 126-36 100-00 444°36 The formula of the salt, dried at 212”, is, therefore, C,, H,, NO, HI+2 HO. 64 DR ANDERSON ON CODEINE, AND Sulphate of Codeine.—Crystallises in radiated groups of long needles, or by spontaneous evaporation in flattened four-sided prisms. It requires for solution 30 times its weight of cold water, but it is very soluble in the heat. When pure, it is neutral to test paper, but it is very liable to retain a small quantity of acid, which can be got rid of by repeated crystallisations. The first analysis was made with the salt which had been only once crystallised, and has therefore given an excess of sulphuric acid. Analysis of the salt, dried at 212°, gave the following results :— 12°5386 ... of carbonic acid, and 5°564 grains sulphate of codeine gave i 3°270 ... of water. 5°677 grains of sulphate of codeine gave II. ¢ 12°831 ... of carbonic acid, 3°324 ... of water. I 9:540 grains of sulphate of codeine gave y 3°265 ... of sulphate of baryta. Il 10-826 grains of sulphate of codeine gave ; 3650 ... of sulphate of baryta. Experiment. Calculation. aS —_—_—_————— ee _ ia Ta: Carbon, : f : 61°44 61:64 62:07 C. 216 Hydrogen, : : : 6°52 6°50 6°39 Hs 22 Nitrogen, : : : on me 4:03 N 14 Oxygen, . ; : oo a 16:03 O, 48 Sulphuric Acid, : : 11°75 11-54 11°49 SO, 40 100-00 348 27-13 grains of the crystallised salt lost, at 212°, 3:068 grains of water=11°30 per cent. This corresponds to 5 equivalents of water, the calculated result for which is 11°45. The formula of the crystallised salt is therefore C,, H,, NO, HO SO, +5 HO. Mitrate of Codeine.—Is obtained by slowly adding nitric acid, of specific gra- vity 1-060, to powdered codeine, an excess of nitric acid being carefully avoided, as the base is rapidly decomposed by it with the formation of a product of sub- stitution to be afterwards described. The nitrate is readily soluble in boiling water, and is deposited on cooling in small prismatic crystals. Heated on plati- num, it melts, and on cooling, concretes into a brown resinous mass ; at a higher temperature it is rapidly decomposed, leaving a bulky coal, difficult of incineration. 13°854 --- of carbonic acid, 6-360 grains of nitrate of codeine, dried at 212°, gave 3°746 .-- of water. These results correspond with the formula C,, H,, NO, HO NO,,. ITS PRODUCTS OF DECOMPOSITION. 65 Experiment. Calculation. Carbon, . 59-40 59°66 ex 216 Hydrogen, 6:54 6:07 He 22 Nitrogen, ee 7:73 N, 28 Oxygen, 26°54 oF 96 100-00 362 Phosphate of Codeine.—Several phosphates of codeine appear to exist, but I have only examined that which is obtained by saturating tribasic phosphoric acid with codeine in powder. In this way a fluid is obtained, which, when concen- trated to a small bulk, refuses to crystallise, but from which crystals are imme- diately precipitated by the addition of strong spirit. The salt is thus obtained in small scales, or in short thick prisms. It is readily soluble in water, and cannot be obtained in crystals from the solution. Its analysis gave the following results, corresponding with the formula C,, H,, NO, HO 2 HO PO,. { 6:343 grains phosphate of codeine, dried at 212°, gave Carbon, . Hydrogen, Nitrogen, Oxygen, Phosphoric acid, 12°618 of carbonic acid, 3°708 of water. Experiment. 54°25 54:27 6°49 6:03 at 3°52 18-09 18-09 100-00 Calculation. Ce RTC H,, 24. N 14 0, 72 PO, 72 398 6911 grains of the crystallised salt lost, at 212°, 0:434 grains of water=6°27 per cent. Three equivalents of water correspond to 6°35 per cent. ; and the formula of the crystallised salt is, consequently, C,, H,, NO, HO 2HOPO+3 HO. Oxalate of Codeine.—This salt is deposited, on cooling its saturated hot so- lution, in short prisms, and sometimes in scales. It requires 30 times its weight ‘of water at 60° for solution, and about half its weight at 212°. Heated to 212° it loses water of crystallisation ; at 250° it becomes brown, and at a per tem- perature it is entirely decomposed. 6:073 grains oxalate of codeine, dried at 212°, gave 14-739 of carbonic acid, 3'608 of water. Experiment. Calculation. Carbon, . 66°19 66:28 Cus 228 ‘Hydrogen, 6:60 6°39 15 22 Nitrogen, Loe 4:07 N 14 Oxygen, 23°26 on 80 100:00 344 VOL. XX. PART I. S 66 DR ANDERSON ON CODEINE, AND 10:050 grains of the crystallised oxalate lost, at 212°, 0°704 grains of water = 7:00 per cent., corresponding to three equivalents of water, which re- quires 7:27 per cent. The formula of the crystallised salt is, therefore, C,, H,, NO, HO C,0,+3 HO. Hydrosulphocyanate of Codeine—This salt has been already examined by DotiFrus;* but I have prepared it, and repeated the analysis, with results differ- ing somewhat from those obtained by him. It is readily obtained by mixing _ solutions of hydrochlorate of codeine and of sulphocyanide of potassium, and is slowly deposited in beautiful radiated needles. 14:285 +. carbonic acid, and 6:164 grains of hydrosulphocyanate, dried at 212°, gave 3°543 ++ water, 7'444 grains, burnt with nitre and carbonate of soda, gave 4:899 grains of sulphate of baryta. These results correspond with the formula C,, H,, NO, HC,NS.,, as is shewn by the following per centage calculation, to which I have added the results obtained by DotiFus :— Experiment. Calculation. ae DoLirvs. Carbon, 5 ‘ : 62°30 63°20 63-68 Go 228 Hydrogen, ¥ : : 6°13 6°38 6°14 Ls Ge 29 Nitrogen, d eee ine 7°82 N, 28 Oxygen, 3 F ; nek =e 13°43 O, 48 Sulphur, ; : : ase 9°04 8:93 Ss, 32 100-00 358 11°613 grains of the crystallised salt, dried at 212°, lost 0°288 grains of water =2°47 per cent., corresponding to one equivalent of water, the calculation of which gives 2°45 per cent. In the analysis of Doutrus, there is manifestly a loss of carbon, as the results are quite incompatible with those of the base and its other salts. In the same paper Dottrus has also determined the amount of sulphocyanogen by precipitation with silver, and the results obtained agree better with the formula given above than with his own. Chloride of Platinum and Codeine.—When bichloride of platinum is added to a moderately concentrated solution of hydrochlorate of codeine, a pale-yellow, pulverulent precipitate is deposited. If this be allowed to stand for some time in the solution, or still better, if it be collected on a filter and kept moist, it begins to change in its appearance ; specks of darker colour appear in it, and it is gra- dually converted into a mass of crystalline grains of an orange-yellow colour. The fluid which filters off deposits, on standing, a small quantity of larger grains. * Annalen der Chimie und Pharmacie, vol. lxv., p. 218. ITS PRODUCTS OF DECOMPOSITION. 67 ‘ The change which takes place in this manner is not always complete, and the granular crystals are often mixed with unchanged yellow powder. When the chloride of platinum is added to a more dilute solution of hydrochlorate of co- deine, precipitation does not take place immediately, but in a short time the salt is deposited in minute tufts of silky needles. The salt is soluble in boiling water, and is deposited on cooling partly in grains, partly as a powder. By this process, however, it is partially changed ; and I have ascertained that by ebullition, with excess of chloride of platinum, it is completely decomposed. I have not as yet, however, followed up this observation. I at first attempted to purify the salt by solution in water and alcohol, in which it is also soluble; and a number of ana- lyses were made, which gave extremely contradictory results; but by precipita- tion in the cold, and without excess of platinum, sufficiently uniform results were obtained. When dried at 212’, the salt retains an equivalent of water, which is expelled at 250°, but not without occasioning partial decomposition of the substance, which evolves acid, and acquires a brownish colour. The following are the re- sults of analysis :— F 7°240 grains of platinum salt, dried at 212°, gave I. < 11:072 ... of carbonic acid, and 2°925 ... water. 9°394 grains of platinum salt gave II. < 14:593 .,. of carbonic acid, and 3°912 ... of water. 7648 grains of platinum salt gave ITI. < 11:694 ... of carbonic acid, and 3450 ... of water. 6°665 grains of platinum salt gave IV. ¢ 10-230 ... of carbonic acid, and 2°835 ... of water. 7°383 grains of platinum salt gave V 11:372 ... of carbonic acid, and 3°304 ... of water. 7247 grains platinum salt gave 1:400 grains platinum, =19-31 per cent. 10-030 en Be 920 hei ==) 0G) Cia 9°775 sat is 1:850 af = 18-92 10°471 si ak 2°020 54 = 19:32 8428 bp Siete 1-600 Os =18:98 6°790 atk dee 1-296 Esf. =19-08 5052 ats et 0-960 A =19-00 1 iT: III. IV. Vi VI. Vit: Carbon, 3 41:70 42:36 41:70 41°80 42-00 Hydrogen, . 4°49 4°62 5:01 4-72 4:97 Nitrogen, : Ae tee a6 ret fae Oxygen, Chlorine, Platinum, . 19:31 1914 1892 19:32 1898 19:08 19-00 68 DR ANDERSON ON CODEINE, AND These analyses correspond with the formula C,, H,, NO, HCl+ Pt Cl, +HO. of which the following is the calculated result compared with the mean of expe- riment :— : Mean. Calculation. ee Carbon, : - , 41-91 42:07 Ce 216: Hydrogen, . : 4:76 4:47 Lee 23° Nitrogen, : : z ae 2:72 N 14: Oxygen, : ; . eas 10°94 0, 56° Chlorine, ; ’ . es 20°61 Cl, 106°5 Platinum, P : é 19-25 19-19 Pt 98:7 100:00 514-2 The air-dried salt gave the following results, when dried at 212° :— 14-845 grains lost 0-770 grains of water, =5-11 per cent. 14:546 ae 0:758 3 = 5:20 This corresponds to three equivalents of water, the calculated result for which gives 4:99 per cent. The crystallised salt is therefore represented by the formula C,, H,, NO, HCl+ Pt Cl, +4 HO. Codeine forms many other crystallisable salts, none of which, however, have been examined. The chromate is easily obtained in fine yellow needles. With solution of bichloride of mercury, codeine gives a white precipitate, soluble in boiling water and alcohol, and deposited on cooling in stellated groups of crystals. With chloride of palladium a yellow precipitate is obtained, which is decomposed by boiling, with separation of metallic palladium. Tartrate and hydrocyanate of codeine are uncrystallisable. Propucts oF DECOMPOSITION OF CODEINE. Ill. Action of Sulphuric Acid. Amorphous Codeine-—When codeine is dissolved in an excess of moderately- concentrated sulphuric acid, and the mixture digested on the sand-bath, the fluid gradually acquires a dark colour, and after some time gives a precipitate with carbonate of soda, which the salts of codeine are incapable of doing. The preci- pitate so obtained is codeine in a modified or amorphous condition, similar to that in which quinine is obtained by a similar treatment with excess of acid. By carefully regulating the temperature of the mixture of codeine and sulphuric acid, the amorphous codeine may be obtained in a state of purity; but it is neither so definite nor so stable a substance as quinoidine. After the action has been pro- longed for some time, carbonate of soda is added to the fluid, and the gray preci- pitate obtained, collected on a filter, washed with water, dissolved in alcohol, and precipitated from the solution by means of water. As thus obtained, it is a gray powder, with a more or less green shade, insoluble in water, readily soluble in ITS PRODUCTS OF DECOMPOSITION. 69 alcohol, and precipitated by ether from the solution. It fuses at 212° into a black - resinous mass. In acids it is readily soluble, with the formation of salts which are amorphous, and dry up by evaporation into brown resins. Analysis gave the following results :— 14:240 .-. of carbonic acid, and 3°663 --- of water. 4°532 grains amorphous codeine gave II. { 5'400 grains amorphous codeine gave I 12-054 .--- of carbonic acid, and _ 2°781 «of water Experiment. Calculation. I. Il. Carbon, . , 2 4 : 71:92 72°53 72:94 Hydrogen, ; 4 ‘ ; 7:53 6°84 7:02 Nitrogen, ; ° 7 Lh ae 6:68 Oxygen, - : : 3 es aio 16:06 100-00 These results correspond sufficiently closely with those of codeine to shew that this substance is represented by the same formula. At the same time it is to be observed, that the action does not stop at the poit at which amorphous codeine is formed; for the excess of carbon and deficiency of hydrogen in the second analysis (which occurred also in another analysis from a different prepa- ration), appear to me to shew that some farther change had taken place. Indeed, by continuing the action of sulphuric acid, a deep-green powder was obtained, which contained sulphur, and agreed in its general properties with the sulpho- morphide described by Arpps, and the corresponding sulphonarcotide of LauRENT and GERHARDT. IV. Action of Nitric Acid. Nitrocodeine.—When strong nitric acid is poured upon codeine, and heat ap- plied, violent action takes place, nitrous fumes are abundantly evolved, and the solution acquires a red colour. If the fluid be evaporated on the water-bath, a yellow resinous acid is left, which dissolves in ammonia and potash solutions, with a red colour.* Ifthe nitric acid be employed in a sufficiently dilute state, a different result is obtained, and a nitrobase is formed, to which I give the name of nitrocodeine. The preparation of this substance is a matter of some nicety, as by the con- tinued action even of very dilute nitric acid it is rapidly destroyed. The opera- tion succeeds best when the acid employed is of a specific gravity of 1:060. Acid of this density is heated in a flask, but not to ebullition, and finely-powdered co- deine is added, and a moderate heat is sustained. In the course of a few minutes a small quantity of the fluid is poured out into a glass, and an excess of ammonia * The constitution and properties of this substance will be detailed in a future communication. VOL. XX. PART I. Ay 70 DR ANDERSON ON CODEINE, AND added ; if no precipitate appears, the heat is kept up for a short time longer, and another quantity is then taken out and tested; and this is repeated until the precipitate, which makes its appearance when the acid+is neutralised, ceases to increase. The fluid is then immediately saturated with ammonia, and stirred ra- pidly, when it becomes filled with a bulky precipitate of nitrocodeine. The action which takes place is extremely rapid, and the whole operation is complete in a few minutes; so that the experimenter requires to be carefully on the watch, in order to hit the right moment for precipitating the fluid. No red fumes are evolved; if they are seen, it is a sure sign that the action has gone too far, and that part of the codeine has been converted into the resinous acid already men- tioned. On this account it is better to stop the action before the whole of the | codeine is decomposed, the quantity left being easily recovered from the solu- tion; but even with the greatest possible care, the formation of a small quantity of the resinous acid cannot be avoided, and its presence is always indicated by the dark colour which the fluid acquires when saturated by ammonia. On the addition of ammonia, the nitrocodeine falls in the form of minute silvery plates, with a very slight shade of yellow. It is purified by solution in hydrochloric acid, boiling with animal charcoal_and a reprecipitation with ammo- nia, in order to separate colouring matter and any unchanged codeine which may have been precipitated along with the first crystals. The nitrocodeine is then crystallised by dissolving in dilute alcohol, or a mixture of alcohol and ether. Nitrocodeine crystallised from alcohol is deposited in the form of slender silky needles of a pale fawn-colour, which, on drying, mat together into a silky mass. From alcohol and ether it is obtained by spontaneous evaporation in small yellowish crystals, which, under the microscope, are seen to be four-sided prisms, terminated by dihedral summits. Nitrocodeine is sparingly soluble in boiling water, from which it is deposited in minute crystals on cooling. It dissolves abundantly in boiling alcohol, and but sparingly in ether. It is soluble in acids, with the formation of salts which are neutral to test-paper, and from which pot- ash and ammonia precipitate the base as a crystalline powder. When heated carefully, it melts into a yellow fluid, which concretes on cooling into a highly- crystalline mass. At a higher temperature, it suddenly decomposes without flame, leaving a bulky charcoal. Its analysis yielded the following results, of which No. 1 is from the base crystallised from the first precipitate by ammonia, before I had observed its ten- dency to carry down codeine with it, and which has therefore given a slight ex- cess; the others are from the pure base. Crystallised nitrocodeine is anhydrous. 5748 ae of nitrocodeine, dried at 212°, gave I 13°301 of carbonic acid, and _ 8128... of water. 5:523 ... of nitrocodeine gave II 12-724 ... of carbonic acid, and 2°887 ... water. ITS PRODUCTS OF DECOMPOSITION. 71 4-463 grains of nitrocodeine gave III. < 10-226 of carbonic acid, and a°377 of water. Experiment. Calculation. ee — eee Te Il. INOe Carbon, 63°10 62:83 62:49 62°79 Cae 216 Hydrogen, 6:04 5°80 a91 5°81 lo 20 Nitrogen, 8-11 N, 28 Oxygen, 23°29 Orn 80 100-00 344 These results correspond with the formula C,,H,,(NO,) NO,, derived from that of codeine by the substitution of NO, in place of an equivalent of hydrogen. It is confirmed by the analysis of its platinum salt, which was found to contain 17°88 per cent. of platinum, giving for the atomic weight of the base 345°8: the calculated atomic weight is 344. Hydrochlorate of Nitrocodeine.—Nitrocodeine dissolves readily in hydrochloric acid, and the solution on evaporation leaves the hydrochlorate in the form of a resinous mass, which cannot be made to crystallise. Sulphate of Nitrocodeine is obtained in a radiated group of short-pointed needles, which are neutral to test-paper, and very soluble in boiling water. 4-687 grains of the sulphate, dried at 212°, gave 1:383 sulphate of baryta. This corresponds to the formula C,, H,, (NO,) NO, HOSO,, which requires Experiment. Calculation. Soo Nitrocodeine, 344 Water, : the ee 9 Sulphuric acid, 10:18 10:17 40 393 Oxalate of Nitrocodeine.—Crystallises in beautiful yellow short prisms, readily soluble in water. Platinochloride of Nitrocodeine.—This salt is precipitated from the solution of the hydrochlorate as a yellow powder, insoluble in water and alcohol. Its ana- lysis gave the following results :— 8-113 grains of platinochloride of nitrocodeine, dried at 212°, gave 11-635 of carbonic acid, and 2.987 of water. 9:392 grains, dried at 212°, gave 1°68 grains platinum. Experiment. Calculation. Carbon, 39°11 39°25 Cy 215 Hydrogen, . 4:09 3°81 He 21 Nitrogen, aa 5:08 Ne 28 Oxygen, 14°58 OF; 80 Chlorine, Moe 19°35 Cl, 106-5 Platinum, 17:88 17:93 Pt 98°7 100-00 550°2 V2 DR ANDERSON ON CODEINE, AND 8'670 grains of the precipitated salt, dried by long exposure to the air, lost, at 212°, 0°569 grains of water=6°56 per cent. Four equivalents of water require 6-14 per cent. The formula of the salt is, therefore, C,, H,, (NO,) NO, HCl+Pt Cl, +4 HO. When nitrocodeine dissolved in alcohol is treated with hydrosulphuret of ammonia in the water-bath, the solution gradually acquires a dark colour, and sulphur is deposited. When the action is complete, the filtered fluid gives with ammonia a brown amorphous precipitate, which, when dissolved in hydrochloric acid, and boiled with animal charcoal, gives, on precipitation, a pale-yellow base. The substance so obtained is very different from nitrocodeine; it is extremely soluble in alcohol, and is deposited from it as an amorphous powder. Once only did I obtain definite crystals, which were brownish rhomboids, but in too small quantity to admit of examination. The amorphous base did not give satisfactory results; and as its preparation is extremely troublesome, I did not pursue its investigation further. Arguing from what we know of the other bases formed by the same process, its constitution ought to be C,, H,, N, O,, and it might be called azocodeine. | V. Action of Bromine on Codeine. Bromocodeine.—In order to obtain this substance, bromine-water is added in small successive portions to finely-powdered codeine. The base is rapidly dis- solved, and the solution loses its colour of bromine, but acquires a peculiar and characteristic red shade. After a certain quantity of bromine has been added, small crystals make their appearance, which are hydrobromate of bromocodeine ; but these are only observed if the bromine-water has been thoroughly saturated, and are deposited in small quantity only, the remainder being retained in solu- tion. When the whole of the codeine has been got into solution, ammonia is added, and bromocodeine is immediately thrown down as a silvery-white powder. In this state it contains a small quantity of unchanged codeine. It is collected on a filter ; washed several times with cold water, and redissolved in hydrochloric acid, from which it is reprecipitated by ammonia, and finally crystallised from boiling spirit. Bromocodeine is scarcely soluble in cold water; but by boiling, a somewhat larger quantity is taken up, and deposited again on cooling in minute prisms, terminated by dihedral summits. It is readily soluble in alcohol, parti- cularly on boiling, and is best crystallised from spirit diluted with its bulk of water. The crystals in which it is deposited are always very small, but bril- liantly white. It is scarcely soluble in ether. Exposed to heat, it melts into a colourless fluid, which is destroyed at a temperature slightly above its melting point. It dissolves in cold sulphuric acid, and the solution when heated becomes dark coloured. It is attacked by nitric acid, but much less rapidly than codeine itself. ITS PRODUCTS OF DECOMPOSITION. 73 Considerable difficulty was experienced in getting it absolutely free from co- deine; and the first of the following analyses has given an excess in the carbon :— 6-119 grains bromocodeine, dried at 212°, gave I 12:941 +. of carbonic acid, and 3:000 --- of water. 5°940 grains bromocodeine gave II 12°461 ... of carbonic acid, and 2:°910 --.- of water. 5268 grains gave 2°663 grains of bromide of silver. Experiment. — Calculation. ———— —_—_—_ oe — — a I, II. Carbon, . : 5 57°67 57:21 57-14 Cs, 216 Hydrogen, : : é 5°44 5:44 5:29 it 20 Bromine, . ; Z aes 21°50 21°16 Br 80 Nitrogen, . ; ; ie ay 3°70 N 14 Oxygen, . : 5 ee on 12-71 O, 48 100-00 378 The formula is therefore C,, H,, Br NO,. Bromocodeine is capable of uniting with water in two different proportions, as appears by the determination of the loss by drying. 11°784 Sears bromocodeine, lost at 212° 0-273, =2-32 per cent. 9-308 : Ace ac U:626,0—6'6905".. 7°707 at sap 0-512, = 6°64 The first of these results peers exactly to one equivalent of water, the calculated result for which gives 2°32 per cent. The other two give three equi- valents, for which the calculation is 6:66. I am unable now to recollect how the bromocodeine used in the first experiment was obtained, but my impression is, that it was prepared in exactly the same manner as the rest. Hydrochlorate of Bromocodeine is obtained in radiated needles closely re- sembling those of hydrochlorate of codeine. Hydrobromate of Bromocodeine.—The crystals, which have been mentioned as making their appearance during the preparation of bromocodeine, are this salt. It is sparingly soluble in cold water, readily soluble in boiling water, and is deposited from the solution in small prismatic crystals. It contains two equi- valents of water which are not expelled at 212°. 8-424 grains of hydrobromate, dried at 212°, gave 13:956 --- of carbonic acid, and 3°985 ++ of water. Experiment. Calculation. —— Carbon, : A rah ths 45:18 45°28 Cx 216 Hydrogen, . 4 : . 5°25 4°84 H,, 23 Bromine, é ; d ; see 33°04 Br, 160 Nitrogen, , : : : tee 2930 IN! 14 Oxygen, : A P : ste 13°41 OF 64 100-00 477 VOL. XX. PART I. U 74 DR ANDERSON ON CODEINE, AND The formula of the salt is therefore C,, H,, Br NO, H Br+2 HO. Platinochloride of Bromocodeine is precipitated as a pale-yellow powder, insoluble in water and alcohol. 8:126 grains, dried at 212°, gave 1-380 grains platinum. Experiment. Calculation. i Carbon, , é : : aes 36°97 tae 216 Hydrogen, . F 5 : oo 3°59 js 20 Bromine, : : : : wee 13-70 Br 80 Nitrogen, . . z : “ce 2°39 N 14 Oxygen, : : : : ot 5:23 O, 48 Chlorine, : ; ' Ao 18-23 Cl 106°5 Platinum, : : : i 16:98 16°89 lea 98-7 100-00 584:2 Tribromocodeine.—By continuing the addition of bromine water beyond the point at which bromocodeine is formed, a further action takes place, and a bright- yellow precipitate makes its appearance, which at first redissolves in the fluid, but after a time becomes permanent, and goes on gradually increasing until a very large quantity of bromine has been employed, when at length a point is reached at which no further precipitate is produced. If the solution be left till next day, however, bromine again causes a precipitate ; and if it be added, as long as anything falls, and the solution be again left standing, another precipitate is produced iden- tical in all respects with that before obtained, and this may be repeated day after day for a very considerable time. The yellow precipitate so obtained is the hydro- bromate of tribromocodeine. It is collected on a filter, and washed with water, in which it is very sparingly soluble. In order to obtain the base, this substance is dissolved in dilute hydrochloric acid and ammonia added, when the tribromoco- deine is immediately precipitated as a flocky powder, which is washed with water, and purified by solution in alcohol, and precipitation with water. Tribromocodeine is thus obtained as a bulky white precipitate, perfectly amor- phous, and when dry, more or less gray in its colour. It is insoluble in water and ether, but readily soluble in alcohol. It is sparingly soluble in hydrochloric acid in the cold, but much more so by boiling. In this process, however, it ap- pears to undergo a partial decomposition, as a small quantity is always left in- soluble. Heated on platinum foil it becomes brown, and is entirely decomposed at its melting point, leaving a coal difficult of incineration. The tribromocodeine employed for analysis was purified by a second solution in alcohol, and precipitation by ether. It gave the following results :— 8-014 grains of tribromocodeine, dried at 212°, gave 11-665 ... of carbonic acid, and 2:645 --- of water. 3°55 grains of tribromocodeine gave 3°727 grains bromide of silver. ITS PRODUCTS OF DECOMPOSITION. 15 a Experiment. Calculation. aE Carbon, ‘ : : 5 39-69 40-27 es 216 Hydrogen, . , - ; 3°66 3°35 H,. 18 Bromine, 5 5 5 : 44-68 44-72 B, 240 Nitrogen, : ; 5 on 2°61 N 14 Oxygen, : : : : te 9°00 O, 48 100-00 536 These results agree sufficiently well with the formula C,, H,, Br, O, pro- duced by the substitution of three equivalents of bromine; and this formula has been confirmed by the analysis of its platinum salt, which will be given below. In such cases as have been hitherto examined, the substitution of three equi- valents of bromine in a base, has entirely destroyed its basic properties, but tri- bromocodeine is still a base, though an extremely feeble one. Its salts are all sparingly soluble in water and amorphous; and as there is no possibility of ascer- taining their purity, I have not pursued their investigation to any extent. Hydrochlorate of Tribromocodeine.—It is obtained by dissolving the base in hot dilute hydrochloric acid, and is deposited on cooling as an amorphous powder. Hydrobromate of Tribromocodeine.—This is the substance deposited during the preparation of tribromocodeine. It is a bright-yellow powder, perfectly amorphous, and very sparingly soluble in cold water. On boiling, however, alarger quantity is taken up, and deposited unchanged on cooling. Its analysis gave the following results :— 7-501 grains hydrobromate, dried at Doe. gave I 8-868 ... of carbonic acid, and 1:915 --- of water. 6-840 grains hydrobromate, from another preparation, gave II 8-072 ... of carbonic acid, and 1-767 ... of water. 3°762 grains hydrobromate gave 4°865 grains bromide of silver. Experiment. Calculation. I Il Carbon, . : 32°24 82°18 32°84 €.; 4392 Hydrogen, . : 2°83 2°86 2:96 H,, 39 Bromine, . : tae 55:03 54:75 Br, 720 Nitrogen, . ‘5 ais bite 2712 N, 28 Oxygen, . F os ve 7:33 0, 96 100-00 1315 These results approach most nearly to the formula: 2(Cy, H,, Br, N O,) + 3H Br. They present, however, a certain deficiency, both in the carbon and hydrogen, and an excess in the bromine; but no other formula can be found at all approxi- 76 DR ANDERSON ON CODEINE, AND mating to the experimental numbers, and the recurrence of the results, in portions prepared at different times, leaves no doubt that this is their real constitution ; and, in aJl probability, the error may be due to the salt retaining a small excess of hydrobromic acid. The constitution is therefore remarkable, and I am not aware of any similar salt having been before observed. Platinochloride of Tribromocodeine.—Bichloride of platinum throws down from solution of tribromocodeine, in hydrochloric acid, this salt, in the form of a brownish-yellow powder soluble in water and alcohol. 5142 grains of platinum salt, dried at 212°, gave 0-669 grains of platinum. Calculation. Carbon, 29-10 C,., 216 Hydrogen, 2°55 a 19 Bromine, 32°33 Br, 240 Nitrogen, 1:88 N 14 Oxygen, 6°57 Ue 48 Chlorine, : see 14:34 Cl, 106°5 Platinum, : 13:07 13-29 Pt 98:7 100-00 742°2 I have reason to believe that the action of bromine upon codeine does not ter- minate with the production of the base now described; but its further action did not appear to afford any products of a sufficient interest to induce me to prose- cute the investigation in this direction. There must also no doubt exist a dibro- mocodeine, C,, H,, Br, N O,, but I did not meet with it in the course of my ex- periments, and have not made any special attempts to obtain it. VI. Action of Chlorine upon Codeine. We might anticipate that the action of chlorine upon codeine should be exactly similar to that of bromine; but this is not the case, as in place of a simple and definite action complex products are immediately obtained. When a current of chlorine is passed through an aqueous solution of codeine, the fluid immedi- ately acquires a brown colour, which soon becomes very deep, and eventually almost black. From this solution ammonia throws down an amorphous, resinous base. With chlorine-water the solution also becomes rapidly brown, and a similar precipitate is obtained. As there was no method of determining in either of these cases when the action was complete, I did not attempt to examine the product. I succeeded better, however, by the action of chlorate of potash, and obtained a base corresponding to bromocodeine. Chlorocodeine.—For the preparation of chlorocodeine a sufficient quantity of codeine is dissolved in an excess of dilute hydrochloric acid, at the temperature of about 150° or 160°. Finely-powdered chlorate of potash is then added, and the solu- tion agitated. In the course of a few minutes a small quantity of the fiuid is ITS PRODUCTS OF DECOMPOSITION. a tested with ammonia, in order to see whether a precipitate is formed ; and the action is allowed to go on until this is obtained, and the chlorocodeine is then pre- cipitated by a slight excess of ammonia. The successful performance of this expe- riment requires exactly the same precautions as the preparation of nitrocodeine ; and, unless the action is stopped at the right moment, further products of decom- position are obtained. The reaction which takes place is represented by this equation :— 3 (C,, H,, NO,, H Cl) +3 HC1+KO Cl0,=K Cl+6 HO+3(C,, H,, Cl NO, H Cl). The chlorocodeine is precipitated in the form of a silvery crystalline powder, closely resembling bromocodeine; it has generally a yellowish colour, and the fluid from which it has deposited is coloured dark-red by the presence of a small quantity of some products of the further action of chlorine. It retains also a small quantity of codeine, from which it is purified by dissolving in hydrochloric acid, boiling with animal charcoal, and reprecipitating with ammonia; and it is finally obtained in crystals from its solution in boiling spirit. In its general properties chlorocodeine closely resembles bromocodeine ; so much so, indeed, that they may be easily confounded with one another. It-is sparingly soluble in boiling water, and deposited, on cooling, in minute prisms exactly similar to, and apparently isomorphous with, those of bromocodeine. It is readily soluble in strong alcohol, especially with heat, and sparingly soluble in ether. It dissolves in sulphuric acid in the cold without change, but the solution is charred by heating. Nitric acid dissolves it, and the solution is decomposed. by boiling, but not by any means so readily as codeine. Red fumes are evolved along with a peculiar and excessively pungent vapour. Analysis gave the following results :— { 6:425 grains of chlorocodeine, dried at 212°, gave I 15°315 --. of carbonic acid, and 3°601 --- of water. 6°162 grains of chlorocodeine gave II. < 14:597 ... of carbonic acid, and { 3°372 ... of water. 5:030 grains of chlorocodeine gave 2°100 grains chloride of silver. Experiment. Calculation. — NL, I. II. Carbon, . : : 65-00 64:62 64-76 Ce 216 Hydrogen, : : 6:22 6:08 5:99 ee 20 Chlorine, ; . tae 10°32 10-64 Cl 85'5 Nitrogen, : - ay Bot 4:19 N 14 Oxygen, , , see aes 14:42 O, 48 100-00 333'5 VOL. XX. PART I. x 78 DR ANDERSON ON CODEINE, AND The crystallised base contains water which is expelled at 212°. 7°67 grains chlorocodeine lost 0°551 grains water, =7-18 per cent. 9°82 ae slag 0:740 Ss mate, The calculated number for three equivalents of water is 7°48 per cent.; and the formula of the crystallised base is therefore C,, H,, C1 NO,+3 HO. The salts of chlorocodeine are exactly similar in their properties to those of bromocodeine; so much so, that I have not thought it necessary to examine more than one or two of them. Hydrochlorate of Chlorodeine.—Crystallises in groups of needles, readily so- luble in water. Sulphate of Chlorocodeine is deposited from its hot solution in radiated groups of short prisms, which dissolve abundantly in boiling water and alcohol. 10°874 grains of the crystallised salt, dried at 212°, gave 0-953 grains of water, and 3:078 grains of sulphate of baryta. Experiment. Calculation. ite ete tt | ee Chlorocodeine, 3 : 79°34 79°63 Base. 333°5 Sulphuric acid, : ‘ HESY 11°75 HOSO, 49:0 Water, ‘ ‘ ‘ 8-76 8-662 4HO 36:0 100°00 100-00 418°5 Platinochloride of Chlorocodeine is obtained in the usual way, as a pale- yellow precipitate scarcely soluble in water. Its analysis gave the following results :— 10:658 «+. of carbonic acid, and 7:212 grains platinochloride, dried at 212°, gave 2-655 ++ of water. 8:793 grains platinochloride gave 1-608 grains platinum. Experiment. Calculation. a Carbon, a : 40°30 40:02 Co 216 Hydrogen, : ; : 4:09 3°89 Bh 21 Nitrogen, : ; : ae 2:59 N 14 Oxygen, : : 7 “ee 8°91 0, 48 Chlorine, ; : : be 26°31 Cl, 142 Platinum, : 5 ‘ 18:29 18:28 Pt 98-7 100-00 539°7 VII. Action of Cyanogen on Codeine. Dicyanocodeine.—When a current of cyanogen is passed into a solution of codeine in the smallest possible quantity of alcohol, the gas is rapidly absorbed, and the fiuid acquires, first a yellow, and, by continued action, a brown colour. If the solution be then left to itself for some time, the smell of cyanogen disappears, ITS PRODUCTS OF DECOMPOSITION. 79 and is replaced by that of hydrocyanic acid, and crystals are gradually deposited. In order to obtain the new compound in sufficient quantity, it is best to keep up a continuous slow current of cyanogen, by which means crystals are deposited during the action in considerable abundance. These are collected on a filter, and washed with a small quantity of alcohol; and the filtrate, on being again exposed to the action of cyanogen, yields an additional quantity of crystals inferior in purity to those obtained in the first part of the operation. The product is puri- fied by solution with the aid of heat, in a mixture of alcohol and ether, from which it is deposited in crystals, which are colourless, or slightly yellow. Ob- tained in this way, however, they are apt to retain a small quantity of codeine ; and it is, therefore, advantageous to pass cyanogen into the mixture to be used for their solution, by which means the last traces of codeine are converted into the new compound. The substance so obtained is a new base, to which I give the name of Dicyanocodeine. It is soluble in boiling absolute alcohol, or a mixture of al- cohol and ether, and is deposited on cooling in thin six-sided plates, with a bril- liant lustre. It is difficultly soluble in water, but on the addition of alcohol it is dissolved ; nothing, however, is deposited from the solution on standing, and by — evaporation it is decomposed, and crystals of codeine are left behind. With hy- drochloric acid, it is converted into a crystalline salt, but decomposition takes place immediately ; for on the addition of potash to the fluid, ammonia escapes, and if it be left for four-and-twenty hours, hydrocyanic acid is evolved. With sulphuric and oxalic acid, it likewise gives somewhat sparingly soluble compounds, which decompose rapidly with the evolution of ammonia and hydrocyanic acid. The crystals deposited from alcohol and ether are anhydrous. Their analysis gave the following results :— 11:388 ... of carbonic acid, and 4:552 grains, dried in vacuo, gave I 2:431 ~~... of water. 4-325 grains, dried in vacuo, gave Il. 10-790 --- of carbonic acid, and 2-405 ++ of water. 4-954 grains gave by WaRRENTRAP and Witt’s method 9-320 grains of pla- tinochloride of ammonium. . 5310 grains gave by the same method 9-890 grains of platinochloride. Experiment. Calculation. Carbon, ; : 68°22 68-04 63°37. ©), 240 Hydrogen, ‘ ; 593 6:17 OO[ ei 21 Nitrogen, : : 11°81 11:50 11:68 °N, 42 Oxygen, . - 14:04 14:27 LOE nO. 48 100-00 100-00 100-00 351 80 DR ANDERSON ON CODEINE, AND These results correspond exactly with the formula C,, H,, N,O,. The method of its formation, however, indicates unequivocally, that its rational formula must be C,, H,, NO, 2C, N, representing it as formed by two equivalents of cyanogen coupled with one of codeine, and belonging to the same class of compounds as cyaniline. It differs, however, from that substance, in containing two equi- valents of cyanogen; and owing to this circumstance, I was at first inclined to take a different view of its constitution, and to consider it as the hydro- cyanate of a cyanocodeine formed by substitution, and represented by the for- mula C,, H,, Cy NO, + H Cy, according to which its formation could obviously be equally well explained, and I considered the evolution of hydrocyanic acid, by treating it with acids, as favourable to this view. Attentive observation, however, convinced me, that though hydrocyanic acid always is produced by heating it with strong acids, it is never evolved immediately, as it necessarily must be, if it existed as such ; but that it only makes its appearance after the lapse of some time, and that only as the result of an advanced decomposition ; for long before it is observed, the addition of potash to the acid solution causes an abundant evolu- tion of ammonia. The ease with which dicyanocodeine is decomposed has prevented my ex- amining any of its compounds. I attempted to prepare a platinum salt by rapid solution in hydrochloric acid, and precipitation by bichloride of platinum ; but the instant the latter substance was added, evolution of hydrocyanic acid was observed, and the results obtained were, as might be expected, wholly incon- gruous and unsatisfactory. The decompositions of dicyanocodeine evidently afford several different substances; but I have not attempted to follow them out, as their investigation seemed to present some difficulties, among which, not the least was that of obtaining the base itself in sufficient quantity. VIII. Action of Alkalies on Codeine. Codeine, when treated at moderate temperatures with potash, yields more than one volatile base, according to the circumstances in which the experiment is made. I have found that similar results are obtained by the use of hydrate of potash, or of potash-lime, or soda-lime prepared in the usual way. The method employed in the experiment was to mix codeine with four or five times its weight of potash-lime or soda-lime, and introduce the mixture into a retort with a tubulated receiver, having a doubly-bent tube attached to its tubulature, the end of which passed into a small flask containing hydrochloric acid, in order to retain any of the very volatile base which might not be condensed in the receiver. The retort was introduced into an oil-bath, and kept at a uniform temperature of 250° Fahr. As soon as this temperature is reached, a slight peculiar odour is ob- served, which soon becomes more powerful, and a small quantity of water, retain- ITS PRODUCTS OF DECOMPOSITION. 81 ing the bases in solution, collects in the receiver. The decomposition at 250°, however, is excessively slow, and even after many days, bases are evolved appa- rently in undiminished quantity, but I retained the mixture steadily at this point, in hopes of obtaining the product free from ammonia, which my preliminary trials had shewn to be produced at higher temperatures; but I found that even with this low heat it was evolved always in appreciable, and, in some experiments, even in considerable quantity. I therefore gradually raised the temperature to about 350°, when a larger quantity of base was obtained; and after the heat had been sustained for some time, small crystals made their appearance, which deposited themselves in a line round the retort, just above the level of the oil in the bath, but which soon rose into and collected in the neck of the retort. These crystals resemble benzoic acid in their external appearance, and are at first perfectly colourless, but soon acquire a brownish shade by exposure to light and air. They are a base, and rapidly restore the colour of reddened litmus. They are sparingly soluble in water, but readily in acids, and give a precipitate with bichloride of platinum. The quantity of this substance obtained was exces- sively minute; and though considerable quantities of codeine were operated upon, all that was obtained served only to make the few qualitative experiments now detailed. The watery fluid which collected in the receiver possessed a pungent and peculiar smell ; it restored the colour of reddened litmus with great rapidity, and gave abundant fumes with hydrochloric acid. On the addition of solid potash, a highly volatile and pungent oily base collected as a layer on the surface of the fluid, and at the same time a gaseous base escaped along with ammonia. From the small quantity of these substances which I was able to obtain, I could not attempt to prepare either of them ina pure state. I was therefore under the necessity of determining their constitution by the analysis of their platinum salts, - which can be separated from one another, though not without difficulty. In order to prepare these salts, the basic fluid was saturated with hydrochloric acid, and evaporated to dryness in the water-bath, when it left behind a beautifully crystalline mass, highly soluble in water, and deliquescent in moist air. This was dissolved in absolute alcohol, to separate ammonia, and the filtered solution mixed with an alcoholic solution of bichloride of platinum, when the platinum salts were immediately thrown down as a pale-yellow powder, very sparingly soluble in absolute alcohol, but readily dissolved on the addition of water. The separation of the two bases is best effected by heating the washed precipitate with boiling absolute alcohol, and adding water in small quantities until the whole is dissolved. The crystals which deposit on cooling are one of the salts in a state of purity, if the process have been properly managed, or, at all events, only require a repetition of the process to make them absolutely pure. The salt thus obtained is scarcely soluble in absolute alcohol or ether, but is readily VOU. XX. PART! I. Y 82 DR ANDERSON ON CODEINE, AND soluble in water and dilute spirit, and is thrown down from the latter solution by ether in the form of fine yellow scales. Its analysis gave the following results :— 1°753 +.» of carbonic acid, and 8-723 grains, dried at 212°, gave 2090 ++. of water. 9:880 grains, dried at 212°, gave 4:100 grains of platinum. 7°784 <5 ioe 3196 Experiment. Calculation. a ———————— Ie | i Oe Carbon, . : : 5:48 eee 5:06 C, 12 Hydrogen, : ; 2:66 eee 2°52 E., 6 Nitrogen, : tee see 5:90 Ni 14 Chlorine, e wee se 44-91 Cl, 106°5 Platinum, ‘ : 41-49 41°32 41-61 Pi 98°7 100:00 237°2 The formula of the salt is therefore C,H, N H Cl Pt Cl,; and the base is, consequently, the methylamine of Wurrz, with whose description of that sub- stance and its platinum salt it perfectly agrees. The preparation of the platinum salt of the other base was attended with much greater difficulty ; and i did not succeed in obtaining it quite free from methylamine. In order to obtain it, the fluid which had deposited the methyla- mine salt was evaporated to a small bulk, the salt which separated filtered off, and ether added to the mother-liquor. Immediately a precipitate is obtained, generally in the form of minute yellow-needles, but sometimes in scales. It is sparingly so- luble in alcohol and ether, and highly soluble in water, from which it crystallises in long needles, and with such facility, that a few drops evaporated on a watch- glass leave the salt they contain in the form of five or six needles crossing the whole space occupied by the solution. The quantity of this salt which I had at my disposal was too small to admit of my carrying its purification by recrystal- lisation as far as was to be desired, and, consequently, a small quantity of methy- lamine remained in those subjected to analysis. 5°521 grains of platinum salt, dried at 212°, gave I 2-485 +.» of carbonic acid, and 1:800 --. of water. 10°475 grains platinum salt, gave 3°951 grains platinum. san 432. ors 6:475 an Experiment. Calculation. ee ——— ae I. ii. Carbon, . é : 12:27 de 13-57 C, 36 Hydrogen, ° : 3°62 as 3°77 i: 10 Nitrogen, ' ! ate oe 5:27 N 14 Chlorine, ; : tee see 40°18 Cl, 106°5 Platinum, ‘ 7 37°71 37°56 37°21 Pt 98-7 ITS PRODUCTS OF DECOMPOSITION. 83 These results approach most closely to the formula C, H, N H Cl Pt Cl,; and though the carbon is very deficient, and the platinum considerably in excess, there can be no doubt that this is due to the imperfect separation of the methy- lamine, and that this is its true formula; and that of the base itself C, H, N. The base, then, obviously belongs to the same series as methylamine, and forms the term of the series corresponding to metacetonic acid, and, in accordance with the system of nomenclature adopted by Wurtz, it receives the name of metaceta- mine. I have not attempted the examination of the salts of this base, as I did not obtain it in sufficient quantity for that purpose; but I take the opportunity of stating, that before I had obtained it from codeine I had ascertained its exist- ence among the products of destructive distillation of animal substances, and that I shall, at a future period, detail the properties of its compounds.* The residue in the retort after these bases have been evolved, is dark cinna- mon-brown, and slightly coherent ; it dissolves in water, with a dark-brown, almost black colour, and gives with acids a flocculent brown precipitate of a humus-like substance, and perfectly amorphous, which I have not thought it necessary to examine. It still contains nitrogen; and by exposure to a heat gradually raised to low redness, it gives an additional quantity of volatile bases, among which ammonia becomes more and more abundant as the temperature rises. A non- basic oil also makes its appearance, but only in very small quantity. Since these experiments were made, I have received the February number of the Annalen der Chimie und Pharmacie, which contains a preliminary notice of an investigation by WERTHEIM of the action of soda-lime on certain organic bases. He has obtained metacetamine from narcotine, and methylamine from morphia; and considering these substances to be directly eliminated from the bases, he ex- pects to obtain the residual atoms in the form of a definite compound. I enter- tained a similar idea with regard to codeine, until I detected the formation of two different bases, which seemed to me rather to indicate that these substances appear as the result of a true destructive distillation ; and that possibly by vary- ing the circumstances of the experiment, other bases may be obtained. I have also observed another remarkable decomposition of codeine, by which volatile bases are obtained. 1 have already mentioned the formation, by the action of nitric acid, of a resinous acid, with the examination of which I am still engaged. This acid, which is insoluble in water, dissolves readily in dilute potash, with a red colour; and the solution on boiling evolves a volatile base in * I may at the same time mention, that I have convinced myself that the petinine described by me two years since as existing in bone-oil, is represented by the formula C, H,, N, and not by C, H,, N, which I then gave for it. Indeed, my analysis of the platinum salt, which is most to be depended upon, tallies equally well with either formula. I have also ascertained the existence of ethylamine and me- thylamine in bone-oil. The details of these experiments will be contained in the second part of my paper on the Products of the Destructive Distillation of Animal Matters. 84 DR ANDERSON ON CODEINE, AND ITS PRODUCTS OF DECOMPOSITION. great abundance. I have not yet determined the whole circumstances under which this change takes place, but reserve this for a future communication.* I have likewise examined the action of iodine on codeine, which yields a mag- nificent crystalline compound presenting the phenomena of pleochroism in a re- markable manner. Difficulties connected with the analysis have, however, pre- vented my hitherto completing its investigation. The following is a Tabular View of the constitutions of the substances de- scribed in this paper :— Codeine, C); He NOS crydhalitweds C,, H,, NO, + 2 HO. Hydrochlorate, C, , H,, NO, HCl + 4 HO. | Hydriodate, Co NOPE | 2H Sulphate, C, PH NOSHO SO, + 5410: Nitrate, 6. H > NO, HO NO.,. Phosphate, (C,, H,, NO, HO) 2 HO PO, + 3G: Oxalate, Gs ie NOU HO CO.) 4 35H@: Bsdetvalpheayatite: C.. NO, HC, NS, aie «0 Platinum salt dried at 212", C. et NO, HCl Pt Cl, + HO. crystallised, Cee. NO, HCl Pt Cl, + 3 HO. Amorphous codeine, C.. LOS Nitrocodeine, C,H a (NO, PINOY Sulphate, . Ce NOS NO, HO SO.. Platinum salt, C. H,, (NO,) NO, HCl Pt Cl, + 4 HO. Bromocodeine, CT are hydrate, . C, jo Br WO. + HO. terhydrate, Cy, Hy be NO: 4. 3 HO: Hydrobromate,, . C,, By, Beno, HBr + 200: Platinum salt, C,, H,, Br NO, HCl Pt CL. Tribromocodeine, C. H,, Br; NO,. Hydrobromate, 2(C2 Ho) Br NO) ibe: Platinum salt, CH. Br, NO ier rs CL: Chlorocodeine, Cs EOUCE NGS terhydrate, C, be Cl NO, + 3 HO. Sulphate, . C, Pg: ina NO, HO SO, + 4 HO. Platinum salt, C,. He CaN 0. HCl Pt Cl, Dicyanocodeine, . Cy i, NO, 20, N. Metacetamine, Ce EAN. * The action of nitric acid on the organic alkalies, in this point of view, is now under investigation ? g in my laboratory. Narcotine has been found to undergo a precisely similar change, yielding a compound, which gives off a volatile base by ebullition with potash, and a whole series of other substances, the con- stitution of which will be detailed so soon as the investigations are completed. SUPPLEMENT. While engaged with the investigation of codeine, I sent to Professor MILLER, of Cambridge, some crystals of the base and its sulphate for crystallographic measurement. Owing to Professor MILLER’s other avocations, he was unable to furnish me with the results in sufficient time to admit of their being incorporated with the foregoing paper. I have, therefore, introduced them here in the shape of a supplement, as they form a valuable addition to the observations contained in the paper. Codeine.—Prismatic. The symbols of the simple forms are, c 001, s 011, 2101, w 102, #110. The angles between normals to the faces are: mc 90 0 Fig. 1. Se 38 37 ss! it te ec 39 46 ee 79 32 Uc 2235 uw 45 10 mm 87° 40°* em 63 42 sm 63 16 Se 53 3 Cleavage, c. The faces mm’ are usually of very unequal magnitude. The faces ss’ were not observed upon the same crystals. The form s is probably hemihedral. Fig. 1. Codeine crystallised from alcohol. Fig. 2. Codeine crystallised from water. The agreement of the different observations is not very good, so that the above measures must be considered as approximations only. Sulphate of Codeine.—Prismatic. Symbols of the simple forms, a 100, ¢ 101, m 110. The angles between normals to the faces are: ea 66 15 ed 46 30 ma 75 36 mm 28 48 Cleavage, a. VOL. XX. PART I. Z 5 ashe wasn init airy tin ry hy ei) | sina in ei} hie eLSer afelhes: vv t lar npe ar vu ane ‘ited HLdailong ai w easel ‘ed, ale 7 antne “ie . fotloale amo f Figsil inte bo al inl wide aH mort SN Se asi TT tod al B0AVS Pagel dr trcHih? sis Toit Vlite anon BITTE ONIGD ey hort bition Sl, + MDT Ww ergot aici tEE ortty a ta, otha (av : Vid 7 Fi SOMES ORES: Gal “up ; a - : en \ 08 ie oh an * wh -& a | | " a 1 ie am f ; : Shean p, ve at 5 e : At eet) oo he ‘rus hea i: oe | a ny ’ .* «hes Bist mt : . » iy. . ‘ 7 7 : nt ‘ AES ney ae ee ee CrSiee) IV.—On the Equilibrium of Elastic Solids. By JAMES CLERK MAXWELL, Esq. (Read 18th February, 1850). There are few parts of mechanics in which theory has differed more from experiment than in the theory of elastic solids. Mathematicians, setting out from very plausible assumptions with respect to the constitution of bodies, and the laws of molecular action, came to conclusions which were shewn to be erroneous by the observations of experimental philosophers. The experiments of GErstEp proved to be at variance with the mathematical theo- ries of Navier, Porsson, and Lams and CLapeyron, and apparently deprived this practically important branch of mechanics of all assistance from mathematics. The assumption on which these theories were founded may be stated thus :— Solid bodies are composed of distinct molecules, which are kept at a certain dis- tance from each other by the opposing principles of attraction and heat. When the distance betiveen tivo molecules is changed, they act on each other with a force whose direction is in the line joining the centres of the molecules, and whose magnitude is equal to the change of distance multiplied into a function of the distance which vanishes when that distance becomes sensible. The equations of elasticity deduced from this assumption contain only one coefficient, which varies with the nature of the substance. The insufficiency of one coefficient may be proved from the existence of bodies of different degrees of solidity. No effort is required to retain a liquid in any form, if its volume remain un- changed; but when the form of a solid is changed, a force is called into action which tends to restore its former figure; and this constitutes the difference be- tween elastic solids and fluids. Both tend to recover their volume, but fluids do not tend to recover their shape. - Now, since there are in nature bodies which are in every intermediate state from perfect solidity to perfect liquidity, these two elastic powers cannot exist in every body in the same proportion, and therefore all theories which assign to them an invariable ratio must be erroneous. I have therefore substituted for the assumption of Navier the following axioms as the results of experiments. If three pressures in three rectangular axes be applied at a point in an elastic solid,— 1. The sum of the three pressures is proportional to the sum of the compressions mhich they produce. VOL. XX. PART I. 2A 88 MR JAMES CLERK MAXWELL ON THE 2. The difference between tivo of the pressures is proportional to the difference of the compressions which they produce. The equations deduced from these axioms contain two coefficients, and differ from those of Navier only in not assuming any invariable ratio between the cubical and linear elasticity. They are the same as those obtained by Professor SroxeEs from his equations of fluid motion, and they agree with all the laws of elasticity which have been deduced from experiments. In this paper pressures are expressed by the number of units of weight to the unit of surface; if in English measure, in pounds to the square inch, or in atmo- spheres of 15 pounds to the square inch. Compression is the proportional change of any dimension of the solid caused by pressure, and is expressed by the quotient of the change of dimension divided by the dimension compressed.* Pressure will be understood to include tension, and compression dilatation ; pressure and compression being reckoned positive. Elasticity is the force which opposes pressure, and the equations of elasticity are those which express the relation of pressure to compression.+ Of those who have treated of elastic solids, some have confined themselves to the investigation of the laws of the bending and twisting of rods, without con- sidering the relation of the coefficients which occur in these two cases; while others have treated of the general problem of a solid body exposed to any forces. The investigations of Lrersnitz, BERNOULLI, EuLEeR, Varienon, Youne, La Hire, and LaGRrance, are confined to the equilibrium of bent rods; but those of Navier, Porsson, Lame and Cuapeyron, Caucuy, Strokes, and WERTHEIM, are principally directed to the formation and application of the general equations. The investigations of Navier are contained in the seventh volume of the Memoirs of the Institute, page 373; and in the Annales de Chimie et de Physique, 2¢ Série, xv., 264, and xxxviii., 485; L’ Application de la Mécanique, tom. i. Those of Poisson in Mém. de l’ Institut, viii., 429; Annales de Chimie, 2¢ Série, XXXvi., 3384; xxxvii., 337; xxxvili.,.338; xlii. Journal de l’ Ecole Polytechnique, cahier xx., with an abstract in Annales de Chimie for 1829. The memoir of MM. Lam& and Ciapeyron is contained in CRELLE’s Mathe- matical Journal, vol. vii.; and some observations on elasticity are to be found in Lame’s Cours de Physique. M. Caucuy’s investigations are contained in his Exercises de Analyse, vol. iii., p. 180, published in 1828. Instead of supposing each pressure proportional to the linear compression which it produces, he supposes it to consist of two parts, one of which is propor- * The laws of pressure and compression may be found in the Memoir of Lamé and Clapeyron. See note A. + See note B. EQUILIBRIUM OF ELASTIC SOLIDS. 89 tional to the linear compression in the direction of the pressure, while the other is proportional to the diminution of volume. As this hypothesis admits two co- efficients, it differs from that of this paper only in the values of the coefficients selected. They are denoted by K and 4, and K=p—1m, h=m. The theory of Professor SToKEs is contained in Vol. viii., Part 3, of the Cam- bridge Philosophical Transactions, and was read April 14, 1845. _He states his general principles thus :—-‘“‘ The capability which solids possess of being put into a state of isochronous vibration, shews that the pressures called into action by small displacements depend on homogeneous functions of those displacements of one dimension. I shall suppose, moreover, according to the general principle of the superposition of small quantities, that the pressures due to different displacements are superimposed, and, consequently, that the pressures are linear functions of the displacements.” Having assumed the proportionality of pressure to compression, he proceeds to define his coefficients.—“‘ Let —A 6 be the pressures corresponding to a uni- form linear dilatation 6 when the solid is in equilibrium, and suppose that it becomes m A 6, in consequence of the heat developed when the solid is in a state of rapid vibration. Suppose, also, that a displacement of shifting parallel to the plane zy, for which dr=ka, dy=—ky, and 6z=0, calls into action a pressure —Bé& on a plane perpendicular to the axis of v, and a pressure Bé on a plane perpendicular to the axis of y; the pressure on these planes being equal and of contrary signs ; that on a plane perpendicular to z being zero, and the tangential forces on those planes being zero.” The coefficients A and B, thus defined. when expressed as in this paper, are A=3 yw, B= os Professor Sroxes does not enter into the solution of his equations, but gives their results in some particular cases. 1. A body exposed to a uniform pressure on its whole surface. 2. A rod extended in the direction of its length. 3. A cylinder twisted by a statical couple. He then points out the method of finding A and B from the two last cases. While explaining why the equations of motion of the luminiferous ether are the same as those of incompressible elastic solids, he has mentioned the property of plasticity or the tendency which a constrained body has to relieve itself from a state of constraint, by its molecules assuming new positions of equilibrium. This property is opposed to linear elasticity; and these two properties exist in all bodies, but in variable ratio. M. WertHEIM, in Annales de Chimie, 3° Série, xxiii., has given the results of some experiments on caoutchouc, from which he finds that K=4, or uw=4m; and concludes that =K in all substances. In his equations, mw is therefore made equal to 4. 90 MB JAMES CLERK MAXWELL ON THE The accounts of experimental researches on the values of the coefficients are so numerous that I can mention only a few. Canton, Perkins, CErstep, Aimt, CoLLADON and Sturm, and REGNAULT, have determined the cubical compressibilities of substances; CouLoms, DuLEav, and Giuio, have calculated the linear elasticity from the torsion of wires; and a great many observations have been made on the elongation and bending of beams. I have found no account of any experiments on the relation between the doubly refracting power communicated to glass and other elastic solids by com- pression, and the pressure which produces it;* but the phenomena of bent glass seem to prove, that, in homogeneous singly-refracting substances exposed to pres- sures, the principal axes of pressure coincide with the principal axes of double refraction; and that the difference of pressures in any two axes is proportional to the difference of the velocities of the oppositely polarised rays whose directions are parallel to the third axis. On this principle I have calculated the phenomena seen by polarised light in the cases where the solid is bounded by parallel planes. In the following pages I have endeavoured to apply a theory identical with that of Sroxss to the solution of problems which have been selected on account of the possibility of fulfilling the conditions. I have not attempted to extend the theory to the case of imperfectly elastic bodies, or to the laws of permanent bending and breaking. The solids here considered are supposed not to be com- pressed beyond the limits of perfect elasticity. The equations employed in the transformation of co-ordinates may be found in GrecoRY’s Solid G'eometry. I have denoted the displacements by dx, dy, dz. They are generally denoted by a, 6, y; but as I had employed these letters to denote the principal axes at any point, and as this had been done throughout the paper, I did a alter a notation which to me appears natural and intelligible. The laws of elasticity express the relation between the changes of the dimen- sions of a body and the forces which produce them. These forces are called Pressures, and their effects Compressions. Pressures are estimated in pounds on the square inch, and compressions in fractions of the dimensions compressed. Let the position of material points in space be expressed by their co-ordinates 2, y, and z, then any change in a system of such points is expressed by giving to these co-ordinates the variations 6x, dy, Oz, these variations being functions of «, y, 2. The quantities dz, dy, Oz, represent the absolute motion of each point in the directions of the three co-ordinates; but as compression depends not on absolute, but on relative displacement, we have to consider only the nine quantities— * See note C. EQUILIBRIUM OF ELASTIC SOLIDS. 9] doz déz doz dz dy dz ddy doy doy dx dy dz doz doz doz ax dy dz Since the number of these quantities is nine, if nine other independent quan- tities of the same kind can be found, the one set may be found in terms of the other. The quantities which we shall assume for this purpose are— oa 0B Oy FO. (ae in the directions of three principal axes 1. Three compressions, a, 2B, ¥. 2. The nine direction-cosines of these axes, with the six connecting equations, leaving three independent quantities. (See Grecory’s Solid Geometry). 3. The small angles of rotation of this system of axes about the axes of 2, y, 2, The cosines of the angles which the axes of 2, y, make with those of a, @, y are— cos (20 x)=a,, cos (80 2)=4,, cos (y02)=c,, cos (a 0y)=a,, cos (6 0 7)=8,, cos (V0 ¥)=c,, cos (a 0 z)=a,, cos (6 0 z)=6,, cos (y 0 z)=c;, These direction-cosines are connected by the six equations, 2 2 et oa a OF fe 2=1 a, a, +b, 6,+¢, c,=0 2 4 ? pa a,? + 6, +¢,2=1 a, a, + 6, 6, + €, ¢,=0 a,” + 6,7 +¢,7=1 a, a, + 6, 6, +¢, c,=0 The rotation of the system of axes a, @, y, round the axis of x, from y to z, =0 6,, y, from z to a, =0 8,, z, from x to y, =0 6,; By resolving the displacements 6 a, 68, Ory, 6,, 6,, 6, in the directions of the axes 2, y, z, the displacements in these axes are found to be Ox=a,0a+b, 0B +¢,0y—6,2+ Oy dy =a,0a+ 6,08 +¢,dy— 6,2 + 0,2 dz=a,0a+6,08+¢,0y — Ory + 0,2 5B 5 But Sa=a°4 9 = amdnocy = ry’. BO ae We VS gee and a=a,t+a,y+a,2, P=b,2+6,y+b,2, and y=c,2+c,y +0, 2. Substituting these values of 6a, 6, and dy in the expressions for d2, dy, VOL. XX. PART I. 2B 92 MR JAMES CLERK MAXWELL ON THE Oz, and differentiating with respect to «, y, and z, in each equation, we obtain the equations — doz aes eae doz do ) ) rr ay ady _ 8a, 38,2, be dy ee (1). do ) ) — = ee a = 5 5 es Equations of ab ae ra: Fi, cites: ey + Oe compression. a+ Pb, + he e, — 080, Araiet ape. “Bt, + Vege, + 88, » (2). Tages Po, b, + Vac 96, ae Rh ogate + 06, oe a+ “Po, b, ai. 7 wee, = OG dy Equations of the equilibrium of an element of the solid. The forces which may act on a particle of the solid are :— 1. Three attractions in the direction of the axes, represented by X, Y, Z. 2. Six pressures on the six faces. 3. Two tangential actions on each face. Let the six faces of the small parallelopiped be denoted by 2,, y,, ~,, @,, y,, and z,, then the forces acting on 2, are :— 1. A normal pressure p, acting in the direction of 2 on the area d y d z. 2. A tangential force g, acting in the direction of y on the same area. 3. A tangential force g,* acting in the direction of z on the same area, and so on for the other five faces, thus :— Forces which act in the direction of the axes of a y z On the face 2, —p,dydz | —9q,dydz —g,dydz ze C= 1dxz)dydz (q5+ ee Bda)dydn (y+ 2 aa) ay az n —q,\dzdu —p,dzdx —9,dzdu Y.| (Gt ve dy)dzdx (p+ Prdy)dedr (7, + Gh aydeda ~ EQUILIBRIUM OF ELASTIC SOLIDS. 93 On the face zy —q,dxdy —~gidxdy | —p,dxdy dq. ad p* d p. | (q+ Gu da) da dy (+h dz)dady (my + 3de)dady Attractions, pXdaxdydz pYdudydz pZduadydz Taking the moments of these forces round the axes of the particle, we find q,'=% 1 =% 73 = ee and then equating the forces in the directions of the three axes, and dividing by dx, dy, dz, we find the equations of pressures. d ik dei *, ag * Gd eee d 4 Equations of Pressures. Po dq dds = nigier Pee cn iy 4 (cee - + + (8) dps dq, dq es ae. ar pee ate dy ap fo) Li=0 The resistance which the solid opposes to these pressures is called Elasticity, and is of two kinds, for it opposes either change of volume or change of jigurre. These two kinds of elasticity have no necessary connection, for they are possessed in very different ratios by different substances. Thus edly has a cubical elasticity little different from that of water, and a linear elasticity as small as we please ; while cork, whose cubical elasticity is very small, has a much greater linear elasticity than jelly. Hooxe discovered that the elastic forces are proportional to the changes that excite them, or, as he expressed it, “‘ Ut tensio sic vis.” To fix our ideas, let us suppose the compressed body to be a parallelopiped, and let pressures P,, P,, P; act on its faces in the direction of the axes a, 8, y, which will become the principal axes of compression, and the compressions will gy The fundamental assumption from which the following equations are deduced is an extension of Hooxer’s law, and consists of two parts. I. The sum of the compressions is proportional to the sum of the pressures. Il. The difference of the compressions is proportional to the difference of the pressures. These laws are expressed by the following equations :— I. +P, +P) =8 mu (“+52 497) . (4) BY fe ne Equations of Elasticity. (Py ~ Py) = m ( “2 if, @,-P) =m (“2 — 29) . 6.) da a (P, — P,) =m ( 94 MR JAMES CLERK MAXWELL ON THE The quantity py is the coefficient of cubical elasticity, and m that of linear elasticity. By solving these equations, the values of the pressures P,, P,, P,, and the dB oy : Oa compressions ia B z may be found. Y P,=(u- 5m) (2 2 aes ae P,=(u-3 ) (Sa) + “Y 6) P,=(u-3m) (+P) = = G- —3;) (P,+P,+P,) + =P, “fe Gc 5a) (P,+P,+P,) += (7) oY (Gr - =) P, +P,+P,)+—P From these values of the pressures in the axes a, @, y, may be obtained the equations for the axes 2, y, z, by resolution of pressures and compressions.* For p=o PtP P, ek, and g—daP. + bbP, Peck, ba 1 doz doy doz moot usm) (F tah — es a doy a + mooy seer cee) P2=(H—3m) ( ax saps rere dy dz doz doy doz doz P= U3") (Fe tay + Te ) ae oe doz NTO Nae aaa | m (doz doz oral ane ) ue _m dézx d i) B=9 = + de doz 1 1 el ce (Pi +P.+Ds) ta do 1 1 ay (s5-sa) (P1 + P2+ Ps) + = Po - 10.) ata 1 1 ade > 9 8 - (Pr +P.+Ps) + eee * See the Memoir of Lamé and Clapeyron, and note A. EQUILIBRIUM OF ELASTIC SOLIDS. 95 ddx doy wh dy —96,=—~* + 06,=— 4% doy doz jegyl = — 00, = Tai +00,=—- Lr.) doéz doz 1 ae or = ae + 00, =~ % By substituting in Equations (3.) the values of the forces given in Equa- tions (8.) and (9.), they become (M+ a 5”) (+ — oe )) + (fades Foyt Fade) +pX=0 (+E Fn) (F a (ie2 dou o2)) ioc is geese?) PY = 05), 7 Ghz.) 1 d (dx doy doz m [{ a? 1), These are the general equations of elasticity, and are identical with those of M. Caucny, in his Exercises d’ Analyse, vol. iii., p. 180, published in 1828, when k stands for m, and K for ee and those of Mr Sroxes, given in the Cam- bridge Philosophical Transactions, vol. viii.” part 3, and numbered (80.); in his . ™ equations A= 3p, B=5 ; If the temperature is variable from one part to another of the elastic solid, the compressions a, a tues at any point will be diminished by a quan- tity proportional to the temperature at that point. This principle is applied in Cases X. and XI. Equations (10.) then become gee 1 1 r= (sn- gq) (Mt tp +e +P bay 1 f “dy (oa Fy) (PitPath) +60 Uti choy) Mog = MSCS; ) ddr (1 1 ae === Soy) (Pit Pat Pa) +e Oly Ds c, v being the linear expansion for the temperature v. Having found the general equations of the equilibrium of elastic solids, I proceed to work some examples of their application, which afford the means of determining the coefficients 4, m, and , and of calculating the stiffness of solid figures. I begin with those cases in which the elastic solid is a hollow cylinder exposed to given forces on the two concentric cylindric surfaces, and the two parallel terminating planes. VOL. XX. PART I. 2c 96 MR JAMES CLERK MAXWELL ON THE In these cases the co-ordinates 7, y, z are replaced by the co-ordinates a= X, measured along the axis of the cylinder. y=r, the radius of any point, or the distance from the axis. z=r 6, the arc of a circle measured from a fixed plane passing through the axis. ius os , p,=9, are the compression and pressure in the direction of the axis at any point. ddy dor h : d : : : f a we , P,=p, are the compression and pressure in the direction of the radius. g 2 =o* p=, are the compression and pressure in the direction of the . tangent. Equations (9.) become, when expressed in terms of these co-ordinates— m doO Se i m do % = 37S (14.) — wn Oa 13 = O° dr The length of the cylinder is 6, and the two radii a, and @, in every case. Case I. The first equation is applicable to the case of a hollow cylinder, of which the outer surface is fixed, while the inner surface is made to turn through a small angle 6 0, by a couple whose moment is M. The twisting force M is resisted only by the elasticity of the solid, and there- fore the whole resistance, in every concentric cylindric surface, must be equal to M. The resistance at any point, multiplied into the radius at which it acts, is ex- d00 pressed by 79, = 7? ae Therefore for the whole cylindric surface a0 mirrb= M dr M 1 1 Whence Dol Sane low re =, M 1 1 and m= own = " = eat (a) The optical effect of the pressure of any point is expressed by ee Seta (16.) Tr EQUILIBRIUM OF ELASTIC SOLIDS. 97 Therefore, if the solid be viewed by polarized light (transmitted parallel to the axis), the difference of retardation of the oppositely polarized rays at any point in the solid will be inversely proportional to the square of the distance from the axis of the cylinder, and the planes of polarization of these rays will be inclined 45° to the radius at that point. The general appearance is therefore a system of coloured rings arranged op- positely to the rings in uniaxal crystals, the tints ascending in the scale as they approach the centre, and the distance between the rings decreasing towards the centre. The whole system is crossed by two dark bands inclined 45° to the plane of primitive polarization, when the plane of the analysing plate is perpendicular to that of the first polarizing plate. A jelly of isinglass poured when hot between two concentric cylinders forms, when cold, a convenient solid for this experiment; and the diameters of the rings may be varied at pleasure by changing the force of torsion applied to the interior cylinder. By continuing the force of torsion while the jelly is allowed to dry, a hard plate of isinglass is obtained, which still acts in the same way on polarized light, even when the force of torsion is removed. It seems that this action cannot be accounted for by supposing the interior parts kept in a state of constraint by the exterior parts, as in unannealed and heated glass; for the optical properties of the plate of isinglass are such as would indicate a strain preserving in every part of the plate the direction of the original strain, so that the strain on one part of the plate cannot be maintained by an op- posite strain on another part. Two other uncrystallised substances have the power of retaining the polarizing structure developed by compression. The first is a mixture of wax and resin pressed into a thin plate between two plates of glass, as described by Sir Davin Brewster, in the Philosophical Transactions for 1815 and 1830. When a compressed plate of this substance is examined with polarized light, it is observed to have no action on light at a perpendicular incidence; but when inclined, it shews the segments of coloured rings. This property does not belong to the plate as a whole, but is possessed by every part of it. It is therefore similar to a plate cut from a uniaxal crystal perpendicular to the axis. I find that its action on light is like that of a positive crystal, while that of a plate of isinglass similarly treated would be negative. The other substance which possesses similar properties is gutta percha. This substance in its ordinary state, when cold, is not transparent even in thin films; but if a thin film be drawn out gradually, it may be extended to more than double its length. It then possesses a powerful double refraction, which it retains so strongly that it has been used for polarizing light.* As one of its refractive in- * By Dr Waicur, I believe. 98 MR JAMES CLERK MAXWELL ON THE dices is nearly the same as that of Canada balsam, while the other is very differ- ent, the common surface of the gutta percha and Canada balsam will transmit one set of rays much more readily than the other, so that a film of extended gutta percha placed between two layers of Canada balsam acts like a plate of nitre treated in the same way. That these films are in a state of constraint may be proved by heating them slightly, when they recover their original dimensions. As all these permanently compressed substances have passed their limit of perfect elasticity, they do not belong to the class of elastic solids treated of in this paper; and as I cannot explain the method by which an uncrystallised body maintains itself in a state of constraint, I go on to the next case of twisting, which has more practical importance than any other. This is the case of a cylinder fixed at one end, and twisted at the other by a couple whose moment is M. Case II. In this case let 6 6 be the angle of torsion at any point, then the resistance to torsion in any circular section of the cylinder is equal to the twisting force M. The resistance at any point in the circular section is given by the second Equation of (14.) m d00 GW = om 4 apg: This force acts at the distance 7 from the axis; therefore its resistance to torsion will be g,7, and the resistance in a circular annulus will be 06 d wd 3 gQr2nrdr=mTr da dr and the whole resistance for the hollow cylinder will be expressed by dd0 M="" —(a,t—a,4) . . (16) m=4M 30 z rss (a,*—a,*) 720 M b m= wileeca yah In this equation, m is the coefficient of linear elasticity; a, and a, are the radii of the exterior and interior surfaces of the hollow cylinder in inches; M is the moment of torsion produced by a weight acting on a lever, and is expressed by the product of the number of pounds in the weight into the number of inches in the lever; 6 is the distance of two points on the cylinder whose angular motion is measured by means of indices, or more accurately by small mirrors attached to EQUILIBRIUM OF ELASTIC SOLIDS. 99 the cylinder; x is the difference of the angle of rotation of the two indices in de- grees. This is the most accurate method for the determination of m independently of p, and it seems to answer best with thick cylinders which cannot be used with the balance of torsion, as the oscillations are too short, and produce a vibration of the whole apparatus. Case III. A hollow cylinder exposed to‘normal pressures only. When the pressures parallel to the axis, radius, and tangent are substituted for p,, p., and p,, Equa- tions (10) become dé Opals 1 dod Ey, stl _ om = (o+p+9) + =p ais d0(r0) Or ee 1 WeEeo ro Opes (o+ptg)+—q . . (20.) By multiplying Equation (20) by 7, differentiating with respect to 7, and comparing this value of ar with that of Equation (19.) i Jega (—- sa) (F dp dq 1 dq rm 9p 3m a rha rd kara m ar The equation of the equilibrium of an element of the solid is obtained by considering the forces which act on it in the direction of the radius. By equating the forces which press it outwards with those pressing it inwards, we find the equation of the equilibrium of the element, 7—P_4p r adr By comparing this equation with the last, we find 1 1 \ do il 2 dp. dqv _ one pea a) fae 1 1 il 2 = o+ ae (p+q) = C, Since 0, the longitudinal pressure, is supposed constant, we may assume (21.) Integrating, VOL. XX. PART I. 2D 100 MR JAMES CLERK MAXWELL ON THE q—-p=¢,—2p, therefore by (21.) dp 2p eC Z hie ae ee a linear equation, which gives pies que 3 2 The coefficients c, and c; must be found from the conditions of the surface of the solid. Ifthe pressure on the exterior cylindric surface whose radius is a, be denoted by #,, and that on the interior surface whose radius is a, by hs, then p=’, when r=a, and p=h, when 7 = a, and the general value of p is 2 2 272 iG; hy —a,* hy _ a" a," h,—h, ‘ - Se p= a? — ay? re @,? — ay (22.) rge=q-p= 29 by 21.) a, ast h ee oe ae 023.) I=bw (p—g)=b0 1 =a ee * Kae) This last equation gives the optical effect of the pressure at any point. The law of the magnitude of this quantity is the inverse square of the radius, as in Case I.; but the direction of the principal axes is different, as in this case they are parallel and perpendicular to the radius. The dark bands seen by polarized light will therefore be parallel and perpendicular to the plane of polarization, in- stead of being inclined at an angle of 45°, as in Case I. By substituting in Equations (18.) and (20.), the values of p and g given in (22.) and (23.), we find that when r=a,, Ox i a, h,—a,? h? 2 a,* h,—a,? h, ip (Cr) (0+2 a,” —a,? cael a,?— a," ) =f —a,° m EQUILIBRIUM OF ELASTIC SOLIDS. 105 3 a,? feet 21 Dah Se ee a oe : (= 7) h, a,° (7 3 ) = “| wale onees I sg oe ant 5 pa a>—a>\ mh 2m a>—a>\u 2m When the external and internal pressures are equal ois heh h,—h, 1 When rsa = = (39.) (40.) the change of internal capacity depends ee on the cubical elasticity of the vessel, and not on its thickness or its linear elasticity. When the external and internal pressures are inversely as the cubes of the radii of the surfaces on which they act, a? la? a,° hy =a," hy, ae ah g=— 273 hy OV 3 a,°h, V7 2 m - . GL) when r=a, Ee In this case the change of capacity depends on the linear elasticity alone. M. REGNAULT, in his researches on the theory of the steam engine, has given an account of the experiments which he made in order to determine with accuracy the compressibility of mercury. He considers the mathematical formulz very uncertain, because the theories of molecular forces from which they are deduced are probably far from the truth; and even were the equations free from error, there would be much uncertainty in the ordinary method by measuring the elongation of a rod of the substance, for it is difficult to ensure that the material of the rod is the same as that of the hollow sphere. He has, therefore, availed himself of the results of M. Lams for a hollow sphere in three different cases, in the first of which the pressure acts on the inte- rior and exterior surface at the same time, while in the other two cases the pres- sure is applied to the exterior or interior surface alone. Equation (89.) becomes in these cases,— 1. When 2,=h, = = = and the compressibility of the enclosed liquid being #,, and the apparent diminution of volume 0’ V, ce = hi (7 = a) Go) 2 OY On. gS 1 3 2 1 a OS ce 2. When =o, G-= y= tes Ga 5 =) buen 149.) 106 MR JAMES CLERK MAXWELL ON THE M. Lame’s equations differ from these only in assuming that pu = ? m. If this assumption be correct, then the coefficients pu, m, and y,, may be found from two of these equations; but since one of these equations may be derived from the other two, the three coefficients cannot be found when yp is supposed independent of m. In Equations (39.), the quantities which may be varied at pleasure are h, and h,, and the quantities which may be deduced from the apparent compressions are, C= GC + zs) and G- =) = therefore some independent equation between these quantities must be found, and this cannot be done by means of the sphere alone; some other experiment must be made on the liquid, or on another portion of the substance of which the vessel is made. The value of y,, the elasticity of the liquid, may be previously known. The linear elasticity m of the vessel may be found by twisting a rod of the material of which it is made; Or, the value of E may be found by the elongation or bending of the rod, and 1 plan KE 9p 38m We have here five quantities, which may be determined by experiment. 3 (48.) 1. (a fee (| + ra) by external pressure bo am (lee on sphere. (AD Ce.) Weg (Saae. equal pressures (81.) 3. = = (satan) by elongation of a rod. (17.) 4. m by twisting the rod. 5. By the elasticity of the liquid. When the elastic sphere is solid, the internal radius a, vanishes, and h,=p=g, j Ns an ie ie When the case becomes that of a spherical cavity in an infinite solid, the ex- ternal radius a, becomes infinite, and ae pHh,+ = (Ay — hy) vas gah, —5 a (fy hy) 46. Ors, - iia," ee ee ea “7 Op aie ls OV _h, pvt VW ae ae EQUILIBRIUM OF ELASTIC SOLIDS. 107 The effect of pressure on the surface of a spherical cavity on any other part of an elastic solid is therefore inversely proportional to the cube of its distance from the centre of the cavity. When one of the surfaces of an elastic hollow sphere has its radius rendered invariable by the support of an incompressible sphere, whose radius is a,, then ’) —=0, when r=a, a 3 a,° aa. 2m Poa 'msbanpee 2 re 24,2 m+3 a,° Uh Syanery Toye ee iY 2aeme sary) 2 re Zatmirsa, pe 2 Ahem (7. 110.) Ors a. el a,° a,° ae Sse r *2a3m+3a°p 7 £ 2a im+da pu OV _ 8a3—3a,3 When r=a, Vv 89a5mi3a, 5p CASE V. On the equilibrium of an elastic beam of rectangular section uniformly bent. By supposing the bent beam to be produced till it returns into itself, we may treat it as a hollow cylinder. Let a rectangular elastic beam, whose length is 27 ce, be bent into a circular form, so as to be a section of a hollow cylinder, those parts of the beam which lie towards the centre of the circle will be longitudinally compressed, while the op- posite parts will be extended. The expression for the tangential compression is therefore Or C.F r Cre, Comparing this value of ae with that of Equation (20.) e—r_ (1 1 q eet ca MOP d and by (21.) q=p+r—. By substituting for g its value, and dividing by r Gatsa) , the equation becomes dp 2m+3y Pp _Imp—(m—Bp)o_ Imp dr m+6u r (m+6p)r (m+ 6 fd) ¢ a linear differential equation, which gives ime 3mm r Ium—(m—3 p)o p=C,r # 7 _4 1 s,s (4B.) m+3[L ¢ 2m+3 ph VOL. XX. PART I. 2F 108 MR JAMES CLERK MAXWELL ON THE C, may be found by assuming that when r=a, p=4,, and g may be found from p by Equation (21.) As the expressions thus found are long and cumbrous, it is better to use the following approximations :— SE a cat lea) Ss ee EY 9mm\ 1 (e—-a@ a Spee +e+y) a In these expressions @ is half the depth of the beam, and y is the distance of any part of the beam from the neutral surface, which in this case is a cylindric surface, whose radius is ¢. These expressions suppose ¢ to be large compared with a, since most substances break when - exceeds a certain small quantity. Let } be the breadth of the beam, then the force with which the beam resists flexure =M. Z = SPUN ORs Ee on m= [oy ~m+6 fic 3 =e eis pus. es) which is the ordinary expression for the stiffness of a rectangular beam. The stiffness of a beam of any section, the form of which is expressed by an equation between 2 and y, the axis of x being perpendicular to the plane of flexure, or the osculating plane of the axis of the beam at any point, is expressed by Me=E fy da, BND M being the moment of the force which bends the beam, and ¢ the radius of the circle into which it is bent. Case VI. At the meeting of the British Association in 1839, Mr James Nasmytu de- scribed his method of making concave specula of silvered glass by bending. A circular piece of silvered plate-glass was cemented to the opening of an iron vessel, from which the air was afterwards exhausted. The mirror then became concave, and the focal distance depended on the pressure of the air. Burron proposed to make burning-miurrors in this way, and to produce the partial vacuum by the combustion of the air in the vessel, which was to be effected by igniting sulphur in the interior of the vessel by means of a burning- glass. Although sulphur evidently would not answer for this purpose, phos- phorus might; but the simplest way of removing the air is by means of the air- pump. The mirrors which were actually made by Burron, were bent by means of a screw acting on the centre of the glass. EQUILIBRIUM OF ELASTIC SOLIDS. 109 To find an expression for the curvature produced in a flat, circular, elastic plate, by the difference of the hydrostatic pressures which act on each side of it,— Let ¢ be the thickness of the plate, which must be small compared with its diameter. Let the form of the middle surface of the plate, after the curvature is pro- duced, be expressed by an equation between 7, the distance of any point from the axis, or normal to the centre of the plate, and « the distance of the point from the plane in which the middle of the plate originally was, and let ds =/(dz)+(d?). Let 4, be the pressure on one side of the plate, and 2, that on the other. Let p and qg be the pressures in the plane of the plate at any point, p acting in the direction of a tangent to the section of the plate by a plane passing through the axis, and g acting in the direction perpendicular to that plane. By equating the forces which act on any particle in a direction parallel to the axis, we find pe ot ate = = +irp aS + 7 (h, —h,) a =0 By making p=0 when r=0 in this equation, r ds p= ot aie (h, — hy) b . . (51.) The forces perpendicular to the axis are dr\ ? dp dr a’ r dx tp (=) ie eee te) Opens i a) Pg 9 6 0 Substituting for p its value, the equation gives h,—h dr dr ax hte & SOT AS 1874) Garr fesse aa) Fe Reem aijude wads) ) 22 ee The equations of elasticity become dds _ (<-s3) ( Pe ae tyes TSENG i Sim Jats 32) +2 On atic +1 hth \ 9 7 (Ga-as) (r+9* 834) +8 r m B ™m : Me) GOT). 2 (Oe aw ae Differentiating —~—=—- ( r) , and in this case d dr\r dor _,_ar ar dos r ds ads ds dor By a comparison of these values of —— dr 1 1 h,+h Gwar p 1 au dp a yee | Vier ea a ike Ae i abla ak a3 Sn ahaa ( =) - su) (p+o+ 2 \+ £45, ae za) dr ‘dr 110 MR JAMES CLERK MAXWELL ON THE To obtain an expression for the curvature of the plate at the vertex, let a be the radius of curvature, then, as an approximation to the equation of the plate, let 72 = By substituting the value of z in the values of p and q, and in the equation of elasticity, the approximate value of a is found to be pl py , Gy thy) = _2 ey i) 9 si Ga- -3,,) om t —18mp h,+h, m—dp a— Reh, loms5ip, (hm, ay Oey Since the focal distance of the mirror, or 5, “. depends on the difference of pressures, a telescope on Mr Nasmytu’s er. ae act as an aneroid baro- meter, the focal distance varying inversely as the pressure of the atmosphere. Case VII. To find the conditions of torsion of a cylinder composed of a great number of parallel wires bound together without adhering to one another. Let x be the length of the cylinder, a its radius, 7» the radius at any point, 66 the angle of torsion, M the force producing torsion, dx the change of length, and P the longitudinal force. Each of the wires becomes a helix whose radius is r,, its angular rotation 6 6, and its length along the axis z—0 6. Its length is therefore t, (rd OP +2 (a-* d2\? and the tension is 25 a- Ri ee. ) This force, ae aoa to the axis, is se Ty oP) : Ox _ 0 and since — and rv — are small, we may assume 4 Pak (S-5 )’ ) Park (7 ole Pity Marea a The force, when resolved in the tangential direction, is approximately 2g fen 22309) rt 00 Ox 76 aes EQUILIBRIUM OF ELASTIC SOLIDS. 111 By eliminating ox between (54.) and (55.) we have 2 r2 66 mo ee (56.) When P=0, M depends on the sixth power of the radius and the cube of the angle of torsion, when the cylinder is composed of separate filaments. Since the force of torsion for a homogeneous cylinder depends on the fourth power of the radius and the first power of the angle of torsion, the torsion of a wire having a fibrous texture will depend on both these laws. The parts of the force of torsion which depend on these two laws may be found by experiment, and thus the difference of the elasticities in the direction of the axis and in the perpendicular directions may be determined. A calculation of the force of torsion, on this supposition, may be found in Youne’s Mathematical Principles of Natural Philosophy ; and it is introduced here to account for the variations from the law of Case II., which may be observed in a twisted rod. Case VIII. It is well known that grindstones and fly-wheels are often broken by the centrifugal force produced by their rapid rotation. I have therefore calculated the strains and pressure acting on an elastic cylinder revolving round its axis, and acted on by the centrifugal force alone. The equation of the equilibrium of a particle (see Equation (21.)), becomes where g and p are the tangential and radial pressures, / is the weight in pounds of a cubic inch of the substance, g is twice the height in inches that a body falls in a second, ¢ is the time of revolution of the cylinder in seconds. By substituting the value of g and ~ in Equations (19.), (20.), and neglect- ing 0, Se i see d*p dp 4m? k d? p Pe a ee ae pe ae ; : Treas E which gives oe aes ) r+ ¢, Lak 25 FS peg (emeeye |. ary 1 ice 3 3 5 a ot ye spe If the radii of the surfaces of the hollow cylinder be a, and a,, and the pres- sures acting on them /, and 4,, then the values of ¢, and ¢, are VOL. XX. PART I. ZAG 112 MR JAMES CLERK MAXWELL ON THE a MR E a es Mig rats (2 +5) =a? a,? hurts 2907 m 2 a,7—a," : : rae (58.) _ ah, —a,7 h, re aye k (2 E og gee 1 2/99 P eS When a,=0, as in the case of a solid ae c,=0, and ¢,=h,—a,? _ 2 (2 +=) a +38 {2¢2+4,) + = Gr —a,°) | bath buey othiege When 2,=0, and r=a,, wT? ka’ (EK (2) sulle Gey When g exceeds the tenacity of the substance in pounds per square inch, the cylinder will give way; and by making g equal to the number of pounds which a square inch of the substance will support, the velocity may be found at which the bursting of the cylinder will take place. Since I=6 w (¢—p) = = (= -2) 6r°, a transparent revolving cylinder, when polarized light is transmitted parallel to the axis, will exhibit rings whose diame- ters are as the square roots of an arithmetical progression, and brushes parallel and perpendicular to the plane of polarization. CASE IX. A hollow cylinder or tube is surrounded by a medium of a constant temper- ature while a liquid of a different temperature is made to flow through it. The exterior and interior surfaces are thus kept each at a constant temperature till the transference of heat through the cylinder becomes uniform. Let v be the temperature at any point, then when this quantity has reached its limit, rav _ ana g=¢ Mogg te Pa. Moly Let the temperatures at the surfaces be 6, and 6,, and the radii of the sur- faces a, and a,, then 6,—0, _ log a, 6,—log a, 0, ~ Tog a, SEe ay oe log a, —log a, Let the coefficient of linear dilatation of the substance be c,, then the pro- portional dilatation at any point will be expressed by ¢, v, and the equations of elasticity (18.), (19.), (20.), become Lo =(5,- a =) (o+p+9)+ = =o EQUILIBRIUM OF ELASTIC SOLIDS. 113 dor 1 i p ip oe eee nga aar See 7) 1 1 ,= see (o+ptg)+ 5 ae The equation of equilibrium is d q=ptr= . . QL) and since the tube is supposed to be of a considerable length dog =c, a constant quantity. From these equations we find that 1, C,+¢, 0— ‘eo a) (Qp+r4 7) ih 2 On 3m and hence v=c, log r+c,, p may be found in terms of r. 2 1 \-1 1 p= (gn ae) CAN log r+ ¢; 5 + ¢, o—— 9 fe Hence I= (57 7) a c, log r—c eee a nee tsa)e om 9p 38m ye Sage Diet EB Spt MSGnye ee A 1 -1 1 Since Iau g+p)=ba (55 tam) os ¢,—2 bwe, the rings seen in this case will differ from those described in Case III. only by the addition of a constant quantity. When no pressures act on the exterior and interior surfaces of the tube h,=h,=0, and = | 2 BA a 2 = 9 gauss (= +3a) a e, {log r+ log a, —log a, +4 log a,—a, 8a} 9u 3m a,*—a,” a,”*—a," 2 a,” a,” a 2 log a,—loga, , a,? log a,—a,’ log a, 62. (¢g= (Gat 5; )o Cnc. { log r— ahaa + aman +1} 2 ry a, ane log a, — log a, r= Og aa a, 6,00 { 1— 2 hore \ There will, therefore, be no action on cae 3 light for the ring whose radius is r when pyees 1" a? cy (pet ae log - CASE X. Sir Davip Brewster has observed (Edinburgh Transactions, vol. viii.), that when a solid cylinder of glass is suddenly heated at the cylindric surface a polar- izing force is developed, which is at any point proportional to the square of the distance from the axis of the cylinder ; that is to say, that the difference of retarda- 114 MR JAMES CLERK MAXWELL ON THE tion of the oppositely polarized rays of light is proportional to the square of the radius 7, or T=de,wr=b 0 (g—p)=b aro? dp aia Cwxs Se eer +c, Since if a be the radius of the cylinder, =o when r=a, eh Coe: fe eS a Hence q=4 (3 r?— a?) By substituting these values of p and q in equations (19) and (20), and making 2c, 4 2 (63.) v= =a one aes) Pte, c, being the temperature of the axis of the cylinder, and c, the coefficient of linear _ expansion for glass. Case XI. Heat is passing uniformly through the sides of a spherical vessel, such as the ball of a thermometer, it is required to determine the mechanical state of the sphere. As the methods are nearly the same as in Case IX., it will be sufficient to give the results, using the same notation. pie SP ge hen aelantvn Aiea 6,—9, iF ae 6, a, aca a ag er alae 2 ear’: 1 2 1 ill 1 ata aa 9p een bi ee a When 4, =/,=0 the expression for p becomes 2 il a,> 1 cat a,?—a,” (08) 225g + 5m) MO tet tea From this value of p the other quantities may be found, as in Case IX., from the equations of Case IV. Case XII. When a long beam is bent into the form of a closed circular ring (as in Case V.), all the pressures act either parallel or perpendicular to the direction of the length of the beam, so that if the beam were divided into planks, there would be no tendency of the planks to slide on one another. But when the beam does not form a closed circle, the planks into which it may be supposed to be divided will have a tendency to slide on one another, and EQUILIBRIUM OF ELASTIC SOLIDS. 115 the amount of sliding is determined by the linear elasticity of the substance. The deflection of the beam thus arises partly from the bending of the whole beam, and partly from the sliding of the planks; and since each of these deflections is small compared with the length of the beam, the total deflection will be the sum of the deflections due to bending and sliding. Let A=Me=E fry? dy. . (65.) A is the stiffness of the beam as found in Case V., the equation of the trans- verse section being expressed in terms of 2 and y, y being measured from the neutral surface. Let a horizontal beam, whose length is 27, and whose weight is 2 7, be sup- ported at the extremities and loaded at the middle with a weight W. Let the deflection at any point be expressed by 0, y, and let this quantity be small compared with the length of the beam. At the middle of the beam, 6, y is found by the usual methods to be b9=— (Ge erZew) a 386) Let B= ady= % (sectional area), -. - . (6/.) B is the resistance of the beam to the sliding of the planks. The deflection of the beam arising from this cause is dy =5-5(@+W) - Wen Fie arhni(68) The quantity is small compared with 6, y, when the depth of the beam is small compared with its length. The whole deflection a y=6, ¥ +06, y 1 ta lea le fe LZ aya (satan) t W(gatan) + 69) Case XIII. When the values of the compressions at any point have been found, when two different sets of forces act on a solid separately, the compressions, when the forces act at the same time, may be found by the composition of compressions, because the small compressions are independent of one another. It appears from Case I., that if a cylinder be twisted as there described, the compressions will be inversely proportional to the square of the distance from the centre. VOL. XX. PART I. 2H 116 MR JAMES CLERK MAXWELL ON THE If two cylindric surfaces, whose axes are perpendicular to the plane of an indefinite elastic plate, be equally twisted in the same direction, the resultant compression in any direction may be found by adding the compression due to each resolved in that direction. The result of this operation may be thus stated geometrically. Let A, and A, (fig. 1.) be the centres of the twisted cylinders. Join A, A,, and bisect A, A, in O. Draw OBC at right angles, and cut off OB, and OB, each equal to OA,. Then the difference of the retardation of oppositely polarized rays of light passing perpendicularly through any point of the plane varies directly as the pro- duct of its distances from B, and B., and inversely as the square of the product of its distances from A, and A,. The isochromatic lines are represented in the figure. The retardaticn is infinite at the points A, and A;; it vanishes at B, and B,; EQUILIBRIUM OF ELASTIC SOLIDS. LEY, and if the retardation at o be taken for unity, the isochromatic curves 2, 4, sur- round A, and A,; that in which the retardation is unity has two loops, and passes through O; the curves = rare continuous, and have points of contrary flexure; the curve - has multiple points at C, and C,, where A,C,=A, A», and : : 1 two loops surrounding B, and B,; the other curves, for which I=7% = &c., con- sists each of two ovals surrounding B, and B,, and an exterior portion surround- ing all the former curves. I have produced these curves in the jelly of isinglass described in Case I. They are best seen by using circularly polarized light, as the curves are then seen without interruption, and their resemblance to the calculated curves is more apparent. To avoid crowding the curves toward the centre of the figure, I have taken the values of I for the different curves, not in an arithmetical, but in a geo- metrical progression, ascending by powers of 2. CaAsE XIV. On the determination of the pressures which act in the interior of transpa- rent solids, from observations of the action of the solid on polarized light. Sir Davip Brewster has pointed out the method by which polarized light might be made to indicate the strains in elastic solids; and his experiments on bent glass confirm the theories of the bending of beams. The phenomena of heated and unannealed glass are of a much more complex nature, and they cannot be predicted and explained without a knowledge of the laws of cooling and solidification, combined with those of elastic equilibrium. Tn Case X. I have given an example of the inverse problem, in the case of a cylinder in which the action on light followed a simple law; and I now go on to describe the method of determining the pressures in a general case, applying it to the case of a triangle of unannealed plate-glass. The lines of equal intensity of the action on light are seen without interrup- tion, by using circularly polarized light. They are represented in fig. 2, where A, BBB, DDD are the neutral points, or points of no action on light, and CCC, EEE are the points where that action is greatest; and the intensity of the action at any other point is determined by its position with respect to the isochromatic curves. The direction of the principal axes of pressure at any point is found by trans- mitting plane polarized light, and analysing it in the plane perpendicular to that of polarization. The light is then restored in every part of the triangle, except in those points at which one of the principal axes is parallel to the plane of polarization. A dark band formed of all these points is seen, which shifts its position as the triangle is turned round in its own plane. Fig. 8 represents these 118 MR JAMES CLERK MAXWELL ON THE Fig. 2. Fig. 4. Fig. 3. curves for every fifteenth degree of inclination. They correspond to the lines of equal variation of the needle in a magnetic chart. From these curves others may be found which shall indicate, by their own direction, the direction of the principal axes at any point. These curves of direc- tion of compression and dilatation are represented in fig. 4; the curves whose direction corresponds to that of compression are concave toward the centre of the triangle, and intersect at right angles the curves of dilatation. Let the isochromatic lines in fig. 2 be determined by the equation Pi (9) =12=0 (q—p)= where I is the difference of retardation of the oppositely polarized rays, and g and p the pressure in the principal axes at any point, z being the thickness of the plate. Let the lines of equal inclination be determined by the equation Pp. (% y) = tan 0 a 6 being the angle of inclination of the principal axes; then the differential equa- tion of the curves of direction of compression and dilatation (fig. 4) is $, (a, =F! By considering any particle of the plate as a portion of a cylinder whose axis passes through the centre of curvature of the curve of compression, we find = ee a deel ere (21.) Let R denote the radius of curvature of the curve of compression at any point, and let S denote the length of the curve of dilatation at the same point. Ps (% y)=R 4 (% Y=S d q—p=R EQUILIBRIUM OF ELASTIC SOLIDS. 119 and since (g—p), R and S are known, and since at the surface, where @, (x, y)=0, p=0, all the data are given for determining the absolute value of p by integration. Though this is the best method of finding p and q by graphic construction, it is much better, when the equations of the curves have been found, that is, when ¢, and ¢, are known, to resolve the pressures in the direction of the axes. The new quantities are p,, p,, and g,; and the equations are tan 0=—2_, (p—g=957+(P:—Po)*, Py t+P.=pt+¢ Pi —P2 It is therefore possible to find the pressures from the curves of equal tint and equal inclination, in any case in which it may be required. In the meantime the curves of figs. 2, 3, 4 shew the correctness of Sir Joun HERSCHELL’s ingenious explanation of the phenomena of heated and unannealed glass. Nore A. As the mathematical laws of compressions and pressures have been very thoroughly investi- gated, and as they are demonstrated with great elegance in the very complete and elaborate memoir of MM. Lame and Crapeyron, I shall state as briefly as-possible their results. Let a solid be subjected to compressions or pressures of any kind, then, if through any point in the solid lines be drawn whose lengths, measured from the given point, are proportional to the com- pression or pressure at the point resolved in the directions in which the lines are drawn, the extre- mities of such lines will be in the surface of an ellipsoid, whose centre is the given point. The properties of the system of compressions or pressures may be deduced from those of the ellipsoid. There are three diameters having perpendicular ordinates, which are called the principal ames of the ellipsoid. Similarly, there are always three directions in the compressed particle in which there is no tan- gential action, or tendency of the parts to slide on one another. These directions are called the principal axes of compression or of pressure, and in homogeneous solids they always coincide with each other. The compression or pressure in any other direction is equal to the sum of the products of the compressions or pressures in the principal axes multiplied into the squares of the cosines of the angles which they respectively make with that direction. Nore B. The fundamental equations of this paper differ from those of Navier, Porsson, &c., only im not assuming an invariable ratio between the linear and the cubical elasticity; but since I have not attempted to deduce them from the laws of molecular action, some other reasons must be given for adopting them. The experiments from which the laws are deduced are— 1st, Elastic solids put into motion vibrate isochronously, so that the sound does not vary with the amplitude of the vibrations. 2d, Reenauxt’s experiments on hollow spheres shew that both linear and cubic compressions are proportional to the pressures. 3d, Experiments on the elongation of rods and tubes immersed in water, prove that the elon- gation, the decrease of diameter, and the increase of volume, are proportional to the tension. VOL. XX. PART I. Aes | 120 MR JAMES CLERK MAXWELL ON THE EQUILIBRIUM OF SOLIDS. 4th, In Coutoms’s balance of torsion, the angles of torsion are proportional to the twisting forces. It would appear from these experiments, that compressions are always proportional to pressures. Professor Stoxes has expressed this by making one of his coefficients depend on the cubical elasticity, while the other is deduced from the displacement of shifting produced by a given tangential force. M. Caucuy makes one coefficient depend on the linear compression produced by a force acting in one direction, and the other on the change of volume produced by the same force. Both of these methods lead to a correct result ; but the coefficients of Stokes seem to have more of a real signification than those of Caucuy; I have therefore adopted those of Stokes, using the symbols m and p, and the fundamental equations (4.) and (5.), which define them. Nore C. As the coefficient #, which determines the optical effect of pressure on a substance, varies from one substance to another, and is probably a function of the linear elasticity, a determination of its value in different substances might lead to some explanation of the action of media on light. kk Fala a pide aa y 2 eae S| eee Pe ee ee bo . - ‘ ’ Aer ¥ fs . » f : ¢ ¥ ’ ) : : é i] ri . 4 \ at % oY) a i s t i i ‘ ; x : ; o m . x a y af ( se “ j ‘ « 2 “ has A ve . , “ nm as bs - “i eae PERUVIAN SYRINX. qe rien) V.—Dissertation on a Peruvian Musical Instrument like the Syrinz of the Ancients. By Taomas Stewart Trait, M.D., F.R.S.E., Professor of Medical Jurisprudence in the University of Edinburgh. (Read Ist April 1850.) The attention which has of late years been paid to the elucidation of the manners and arts of the ancient inhabitants of America, has been productive of the most convincing proofs of the communication between the Eastern and West- ern Continents at remote but unknown epochs. The learned and highly-interest- ing researches of Humsopt on the antiquities of the New World, have irresistibly led him to this conclusion, which has farther been strengthened by the researches of later travellers. The comparison of the idioms of the Asiatic and American tongues, has hitherto not afforded very direct proof; because the philologist has not yet been put in possession of a sufficient number of materials to make the comparison with advantage. Our ignorance of the languages and customs of Central Asia is a great bar to such studies, and needs not any other illustration than the fact that a highly-polished nation, with a literature and arts hitherto almost unknown in Europe, should have existed for ages in Central Asia. Our countryman, Dr GERARD, stimulated by the humane desire of extending the blessings of vaccina- tion to Thibet, has been for some time in that country, and has discovered in its language an Encyclopzedia in forty-four volumes, of which the medical part alone fills five volumes; and he finds, that the art of Lithography, so new in Europe, has been practised from time immemorial in Kinnaour, a principal city in Thibet, where he found it employed to display the anatomy of the human body. At- tempts have been made to supply such deficiencies in the knowledge of Asiatic languages, chiefly by the Germans; especially in the first volume of the Mithridates by ApELUNG, and in the Asia Polyglotta of Kitaprotu. When our acquaintance with Central Asia shall be more extensive, and the American languages more studied, we may be able to trace the origin of the nations of that continent with greater success ; and Humpotpr does not think it impossible, that traces may yet be discovered in America of tongues and nations that have disappeared from the older hemisphere. It would be curious if future inquirers should discover in America vestiges of those torments of the philologist and antiquary, the Median, Oscan, Phoenician, and Hetruscan tongues. “ Tf language supply,” says Humpoxpr, “ but feeble evidence of communica- tion between the two worlds, this communication is fully proved by the cosmo- VOL. XX. PART I. 2K 122 DR TRAILL ON A PERUVIAN MUSICAL INSTRUMENT gonies, the monuments, the hieroglyphics, and institutions of the people of Ame- rica and Asia.” It is impossible to consider the Mexican account of the Serpent-woman, To- nacacihua, or “ Woman of our Flesh,” the parent of mankind, with her fall from her state of pristine innocence and happiness; their traditions of a great inunda- tion, in which the human race perished, with the exception of a single family that escaped on a raft; their account of the building of a vast pyramid, which was intended to reach to the sky, and consequent dispersion of the sons of men, and the origin of different languages, caused by the anger of the gods, when they overthrew this monument of human presumption; without perceiving the proto- types of these traditions in the sacred writings of the Hebrews. The Mexican cosmogony notes jive epochs of the world; like the people of Thibet, and the Tatar tribes who have retained the ancient religion of the Llama. The first is the age of carth ; the second that of jive; the third the age of mind or air; the fourth that of water; we live in the fifth epoch. It was in the end of the fourth age that the deluge took place, and that a single family was preserved to repeople the earth. As might be expected, Cowcox (the Mexican Noah) is represented as the immediate ancestor of the inhabitants of that country. In the first four epochs we may trace the four ages of classical antiquity, with the Tatar addition of a fifth. Like the Chinese and Indians, the Mexicans supposed an enormous duration to our earth in all its cataclysms. The Mexican legends ex- tended the age of the world to upwards of 20,000 years. In the astronomical cycles of some of the American nations, we find strong analogies with the systems of the inhabitants of Thibet, and the various tribes of the Mantscheou Tatars. The Mexican division of the year into 365 days, distri- buted into 18 months, of 20 days each; the annual intercalation of five days to complete the year, and still more their curious cycle of 52 years, and great cycle of 104 years, in which they intercalated 25 days, to bring the commencement of the next cycle again to correspond with the winter solstice, shew so exact a deter- mination of the true length of the year, that the celebrated Lapiace is of opinion it could not have originated among a people in so rude a state of society as the Mexicans at their discovery by the Spaniards. The intercalation “ of 25 days in 104 years,” says he, ‘‘ supposes a more exact determination of the tropical year than that of Hrerarcuus, and, what is very remarkable, almost equal to the year of the astronomers of Al-Mamon. When we consider the difficulty of attaiming so exact a determination, we are led to believe that it is not the work of the Mexi- cans, and that it reached them from the Old Continent.” The vast pyramidal temples, accurately placed to the cardinal points, and constructed, as at Cholula, of swn-dried bricks, with interposed layers of clay; and occasionally, as at Papantla, with their successive stages neatly covered with hewn stone, sculptured with hieroglyphics, reminded us of the structures of the LIKE THE SYRINX OF THE ANCIENTS. 123 early ages of Babylonian and Egyptian architecture. The great pyramid of Cho- lula has a basis 1440 feet on each side, or twice as broad as the great pyramid of Giza; but its height is only 164 English feet. It is built in four stages, and had a small temple on its upper platform, while the interior contained sepulchral chambers ;—circumstances which still farther connect this American temple with the pyramids of Egypt, and the Chaldean monuments described by Ricu and others. The curious and systematic mode of hieroglyphic paintings of the Mexi- cans, which combined natural and conventional signs, and, according to Hum- BOLDT, also phonetic characters, bears a striking similarity to the hieroglyphical papyri of Egypt; and it may not be unworthy of notice, that the Mexican MSS. were folded up zigzag-wise, or something like a fan,—precisely almost as the Siamese papyri MSS. are folded to this day. The singular resemblance between the institutions of the Peruvian lawgiver Manco Capac and the systems of Hindostan, are not to be overlooked; the same exaltation of a theocracy, drawing its descent from heaven; the same exaction of passive obedience to the head of this theocracy, who, like the first legislator of India, traced his pedigree to the sun; the same division of the people into castes. The Peruvians, like the Hindoos, were, by such institutions, trained into a patient, laborious, little-intellectual people; and, like their Asiatic prototypes, have left behind astonishing monuments of patient industry in some of their public works. I have introduced this comparison between the people of both hemispheres, in order to shew that I do not assume too much in supposing an instrument in- vented by the ancient inhabitants of the eastern hemisphere, the ovzginal of the subject of this paper,—a musical instrument of stone found in a Huaca, or sepul- chral tumulus, which is said to have covered the body of an Inca of Peru. It was brought from South America by my friend Jossua Rawonon, Esq. He received it from General ParoisstEn, a native of England of French extrac- tion, who had obtained it as an article of value and great rarity in Peru. It was customary with the natives of South America to raise large tumuli over distinguished men; and in these were buried domestic utensils in wood, stone, and the precious metals, often with very considerable treasures, especially in Peru. It would seem that the contents of the rich Hwacas are still known to the Peruvian Indians, either from tradition or from some species of record. They appear to consider it a sacrilegious act for one of themselves to violate the tomb for the sake of its treasures; but there are more than one instance of their re- warding an European for kindness done them by revealing where he may dig with the certainty of obtaining a golden harvest. The vast Huaca near Truxillo, in the Plain of Chimu, was discovered to Juan GUTIERRES DE TOLEDO, in 1576, by an Indian, and the bars and utensils of gold it yielded to the fortunate Spaniard equalled 46,810 oz. of gold, or upwards of £181,288 sterling. It appears to have 124 DR TRAILL ON A PERUVIAN MUSICAL INSTRUMENT been customary to deposit with the dead the instruments they used, or articles they delighted in; and we may suppose that the Inca with whom this musical instru- ment was buried was not ignorant of its use. There is no figure of such an in- strument among any of the published remains of an American race, as far as my researches have extended; nor am I aware that it has been mentioned among the implements found among them by their Spanish conquerors. It therefore must be of considerably anterior date to the Spanish conquest; as we cannot suppose that since that era, so disastrous to the natives of America, any prince of a native race would have obtained the honours of a Hwaca, in regions held by the fierce and bigoted conquerors. Description of the Instrument. The Peruvian antiquity in question is, in form and principle, similar to the Syrinx of the Greeks and Romans, or Pan’s Pipe, well known in England by the somewhat barbarous name of Pandean Pipes ; and in the Italo-Helvetian cantons by the appropriate denomination of Organetto, a diminutive of Organo, of which it is most probably the prototype. The Peruvian instrument, however, is not constructed of unequal reeds bound together ; but it is cut out of a solid mass of a compact, softish stone, which appears to me to be a variety of Potstone (Lapis ollaris). It is cut with great neatness and precision. Its form will be best understood by inspection of the figure. Its sides are not parallel, but they slightly converge toward the upper part of the instrument, for the purpose, apparently, of rendering the orifices of the pieces thin, without endangering the solidity of the whole. The corners of the bottom of the instrument are smoothly and slightly rounded, as if by friction from the hand of the player. The surface seems to have been covered with a brownish shining varnish, similar to the vegetable varnish employed still by the natives on the Essequibo and Orinoco to cover their pottery. It has in part de- cayed, and in one place bears the impression of cloth of a coarse texture having adhered to it. The surface, which has evidently been intended for the outside when played, is ornamented with a very regular pattern. The volutes are very neatly executed, and the regular removal of the angular spaces on the right-hand side of the zig- zag lines, shews an attempt at variety not unpleasing. The horizontal band of what we would call Maltese crosses, is very well executed. The extreme breadth of the instrument, including the handle, is 6-2 ine its greatest depth 5:3; the thickness of the body of the instrument is from 0°7 to 05 of an inch. The handle projects 1:1 inch from one end, and is perforated by four holes, two of which appear at its extremity, and one on each of its edges, each of them communicating, in the thickness of the handle, with one of the other LIKE THE SYRINX OF THE ANCIENTS. 125 holes. Their obvious use is to receive a cord, for the convenience of holding the instrument more firmly, or of hanging it up. There are eight pipes or cylindrical tubes scooped out in the thickness of the stone: they have a diameter of about 0°3 inch, and rise in a sort of general neck three-fourths of an inch above the body of the instrument, forming a horizontal connected series of tubes, which, however, have no communication with each other. Their upper edges, on one side, are slightly thinned, which, no less than the orna- ments on the side, shew what part of the tube was pressed against the lips. These circumstances prove that the Peruvian instrument, like the organetto, was held by the player with the longest tubes, or lowest notes, toward his rzght hand. The depth of the tubes was carefully measured, and is as follows :— No, Inches. No. Inches. le = 4-90 5. = 2:45 a = 4-50 6. = 2:85 3. = 4:12 ite = 2:00 4. = 3°50 8. = 1:58 Though these measurements do not seem quite to accord with the usual propor- tionate length of pipes with regular musical intervals, they seem to have been adjusted from experimental trials by the maker; and I used every precaution in measuring them with a delicate instrument. In the common organetto, the tubes are portions of the Spanish reed (Av'wndo Donaz), of unequal lengths. These are usually 16 in number; and as each pipe differs from the next a note of the ordinary musical scale, the compass of the instrument, with the usual mode of blowing it, is two octaves. These tubes are open at both ends; and the instrument is tuned by the introduction of a piece of cork, which is pushed farther down when the tone of the note is too sharp, and pushed farther up when the tone is too flat. The key-note is first pitched from some other instrument, or by a tuning-fork; and the other pipes are adjusted by the ear from the key-note. In the Peruvian instrument the tone of the notes appears to have been ad- justed with considerable skill, by careful drilling of the stone; and this has been done by means of a circular drill with cutting edges and a hollowed centre, as the bottom of the holes still shews. The truth of the tones shews that this boring has not been done without repeated trials of the effect; and there is no reason to doubt that the Peruvian artist knew also how to amend the tone by stopping the bottom of the pipe when necessary. The Peruvian instrument has eight notes, in the ordinary way of blowing it ; but, by contracting the orifice of the mouth, and by pressing the orifice of the tube toward the lip, an octave to the first is obtained from each note, and if the force of the blast be very strong at the same time, a third octave may be ob- tained: so that, in the hands of an expert performer, the instrument had consider- able compass. In this paper, however, we shall confine our notice to what may VOL. XX. PART I. 21 126 DR TRAILL ON A PERUVIAN MUSICAL INSTRUMENT be termed the ordinary compass of eight notes, produced by moderate and easy blowing, and producing clear tones. The Peruvian instrument has a contrivance for giving variety to its notes, which appears to me very ingenious, and which, as far as I can learn, is peculiar to it. Four of its pipes, viz., Nos. 2, 4, 6, and 7, have each a ventilage, or small hole perforating its front, about an inch below its top, which must be covered with the fingers of the performer when these pipes are to be sounded. These holes are so near the top of the pipes, that, when open, the sound of the note is quite lost; so that if the performer does not mean to sound that particular note in a rapid movement, it is not necessary to avoid blowing into the pipe, but merely to uncover the ventilage, which effectually destroys its sound. From the peculiar adjustment of the instrument, an harmonious and pleasing tetrachord is produced by running up the scale with all the ventilages open. This description renders it evident that the Peruvian has considerable advan- tages over the simple Grecian syrinx, which is generally represented in sculpture with seven pipes, and occasionally with only s7z. In other respects, the Grecian instrument appears to differ little from the modern organetto; but it is, in some of its modifications, of very high antiquity, and perhaps preceded the invention of the single flute (wo«vA0c) with numerous ventilages. Lucretius describes Pan’s mode of playing to be the same as we now find it among the Italians: * Unco sepe labro calamos percurrit hianteis Fistula sylvestrem ne cesset fundere Musam.”’ Lib. iv., 592. The ancients ascribed the invention of the syrinx to the disappointed love of the god Pan, amid the hills of his favourite Arcadia. * Pan primus calamos cera conjungere plures Instituit.”’ Vinci, Eel, LT. Both Pan and the pipe, however, had probably an Egyptian origin, long before the groves of Greece were haunted by any deity; and, if I am not mistaken, we may trace the syrinx to an antediluvian patriarch. Jubal, the descendant of Carn, is in Genesis called “the father of all such as handle the harp and organ.” The English translators of the Bible have adopted the interpretation of the Latin Vulgate, in which the Hebrew bay, Yogel,* is rendered organum,—* ipse fuit pater canentium cithera et organo.” This passage, in the Septuagint, and in the famous Alexandrian MS., runs thus: éurog jy 6 xaladsZas parrngiov xal xdagav— ‘“* He it was who taught the psaltery and the harp.”+ * Or, with points, as in Watton’s Polyglott, sbarny: 4. + The Hebrew name is derived from the verb bY, which, in the Septuagint, is always rendered by eniridnus, I join together ; which would seem to indicate that it consisted of reeds or pipes put together. LIKE THE SYRINX OF THE ANCIENTS. 127 What the Yogel was has been disputed ; but Parxuursr explains it to be a wind instrument of several pipes. The arrngo of the Septuagint is, by several commentators, said to be a wind instrument, or “sort of flute used in churches ;” not the modern psaltery, which is a trapezoidal flat box, with 13 pairs of strings mounted on two bridges, and played with two crooked sticks. The invention of the modern organ is a subject of dispute; for few critics will receive S* Crcii1a as the inventor of that noble instrument, although Rar- FAELLO has introduced the syrinx in his grand picture of that saint in allusion to this fable. It is of considerable antiquity, however, and it will be sufficient here to remark, that the organ itself is only an adaptation of the more ancient syrinx to keys, and an artificial blast of air; and its pipes are tuned on the principle of its venerable prototype. The ancients seem, however, to have possessed an instrument somewhat in principle resembling the modern organ, in so far as it consisted of several pipes attached to a box, which contained compressed air. In the instrument briefly and obscurely noticed by Virruvius, who lived about the commencement or a little before the Christian era, the air seems to have been compressed by forcing mater into a brazen box, that communicated with the pipes. The instrument was termed by the inventor, Ceresesius of Alexandria, tégavac; and is attempted to be figured from the description in the Italian translation of Virruvius by BarBaTo, Patriarch of Aquileia. I am indebted to my friend Mr W. Cavett for the notice of a coin of NERo, in the British Museum, on which an ’ogyavy, or perhaps tagavac, is figured. It seems to be the instrument alluded to by Surronius, in the life of Nero—“ reliquam diei partem per organa hydraulica, novi et ignoti generis circumduxit.” There is a dissertation on the Hydraulis in the Gottingen Transactions. The organ or psaltery of the book of Genesis, I believe, then, to have been the syrinx ; an instrument with which we may reasonably suppose Mosss to have been familiar, as ancient authors generally agree in ascribing the invention of the weyré, and of the single flute, povrcs, to the Egyptians. Both flute and syrinx are mentioned by Homer as known to the Trojans— “AvAwy Sugiylav + evomny dmocdov 7 cvbewarwy ; so that, without doubt, the syrinx is an instrument of very great antiquity; and we know that it has been most widely diffused among ancient nations. Among the Arabs it is in use at the present day. In Kamprer’s History of Japan, two forms of a syrinx of twelve unequal reeds, used by that people, as also some singular Japanese flutes, are figured in Tab. xxxi., A. E. G. J. From time immemorial, it has been in use among the inhabitants of the Alps; and most of the performers on the organetio, who perambulate Europe, bring it from the Italian cantons in the vicinity of the Lake of Como. 128 DR TRAILL ON A PERUVIAN MUSICAL INSTRUMENT That it had been introduced into America, the instrument before you fully proves; and voyagers have discovered a musical instrument very like it in Am- sterdam Island, or Tongataboo, in the Pacific Ocean. In a letter which I received from the illustrious Humpotpr on this subject, he states, that he had found a rude sort of Pan’s pipe among the natives on the banks of the Orinoco.—“ Il est bien remarquable de vois les mémes formes se reproduire dans les regions les plus eloignées; j’avais deja été frappé de l’adresse avec laquelle les indigénes de ’Ori- noque savoient construire ses flutes de Pan, chaque fois que mes canots s’arréte- ment 1a, ot le rivage etoit couvert de roseaux.”’ Scale of the Instrument. The first attempts at obtaining an idea of the scale of the Peruvian instru- ment were imperfect, owing to my little skill in either the theory or practice of music. By means of Broapwoon’s C tuning-fork for concert pitch, compared to a piano, I discovered that the lowest note in the Peruvian syrinx was equivalent to E on the first line, and that the next three notes with that formed a tetrachord nearly corresponding to E, F, G, A; that the fifth ascending note was three notes higher than A, or equalled D; that the sixth note was a note ower than the pre- ceding; that the seventh was two notes higher than D; and that the eighth was four notes higher than D. These notes, however, differing from the piano by half a tone, it occurred to me, that, by obtaining the assistance of an accomplished musician on the violin- cello, the true scale might be ascertained far better than by my unskilful attempts. I employed an expert Italian performer on the organetto to play on the Peruvian instrument, on different evenings, and I was fortunate enough to obtain the assistance of three musical friends, who unite to fine taste great practical skill in music ; and to the aid of these gentlemen I am indebted for the following deter- mination of the true scale and powers of the Peruvian syrinx. The violincello was tuned to the pitch of the Peruvian instrument, and the value of each of its notes was repeatedly tried by this test. The result of these experiments convinced my musical friends, that the maker of that instrument had proceeded on just musical principles in its formation; and that its eight notes were resolvable into two distinct tetrachords, one of which is in a minor, and the other in a major key. When the ventilages are all shut, the following is the Scale. C) ry e r) ey oe oo Frenne dec es ————t ees @ +| — —— a =e ee ee P LIKE THE SYRINX OF THE ANCIENTS. 129 The division of this scale into two tetrachords in different keys is produced by opening the ventilages for the one, and sounding only the notes which were omitted by that process for the other. Tetrachord in the Key of K Minor. Or oO. OSs to “0- e— — ee ——@-— ee E G D A Tetrachord in the Key of F Major. a FE A Cc F The first tetrachord in the minor key is perfect, and is the most easily perform- ed ; for it only requires that all the ventilages be left open, and consequently those notes will not sound. This in all probability was the favourite Peruvian key, and must have imparted, as the minor key always does, a plaintive tone to their music. The second tetrachord in the major key is nearly perfect; but the instru- ment on this key is half a note above concert pitch, which throws the I’, into Fy, and the C4 into Cé. It is, however, to be noticed, that, by different modes of ordinary blowing, the tones may be varied nearly half a note; and it is not improbable that the notes now imperfectly pitched, were accurately adjusted by stujjing. The use of the ventilages now becomes very apparent. They enabled the performer to introduce several harmonious modulations, by opening one or more of the holes, without embarrassing him with the attention necessary to avoid the pipes not to be sounded. In this manner considerable variety is given to the succession of sounds, all of which are regulated by the fixed principle of present- ing agreeable successions or modulations to the ear. One of my friends was of opinion that some very simple modulations, produced by this means, as an accom- paniment to the songs or dances of the Peruvians, was one of the designs of the inventor of the Peruvian syrinx. The Peruvian performers probably used the succession of simple notes, often reiterated; and we might infer that they often delighted in slurring them, by sliding the instrument along the lip, instead of blowing each note distinctly allo staccato, as is usually done by modern performers on the organetto. It is worthy of remark, that the scale of the Peruvian instrument is founded on a system of tetrachords, as was that of a more refined people,—the ancient Greeks. The lyre, according to Dioporus, was invented by the Egyptian Herr- MES, and had originally only three strings,— ven» Te BUREN, ny woimoos reIgoedoy. The his- torian says that a fourth, “called jon, was added by the Muses; that Linus added VOL. XX. PART I. 2M 130 DR TRAILL ON A PERUVIAN MUSICAL INSTRUMENT, &c. the fifth string, named xyes; that ORPHEUS gave it a sixth, irar,; and that the seventh, cagirarn, was the addition of Taamyris.” Even in this improved state of their musical system, the fourth was still a favourite and important interval; for we find that their great musical system, as they termed it, ‘‘ extended to two octaves composed of five tetrachords ;” in the same manner that the scale of Gurpo of Arezzo, the inventor of the modern system of musical notation and of couwnter- point, is composed of different hexachords.—See Burney. The sagacity and profound investigations of the learned Sir WiLL1AM JoNEs have clearly proved that the same systems of literature and arts, which once gave lustre to Ethiopia and Egypt, prevailed in India; and more recent investigations, especially those of Humpotpt, AcLio, and several American travellers, have shewn, as we have already noticed, that the arts, the cosmogonies, and astrono- my, of the Peruvians, the Mexicans, and some of the other tribes of Central Ame- rica, betray, in some respects, an Asiatic origin. CCUST VI.—Some remarks on Theories of Cometary Physics. By C. Piazzi Smytu, Esq., F.RSE., Astronomer Royal for Scotland, and Professor of Practical Astro- nomy in the University of Edinburgh. (Read 1st April, 1850.) While the physical appearances of comets have ever excited such intense curiosity and interest, all the theories concerning them are generally confessed to be insufficient to explain them; and, certainly, if we may judge from the various views advocated by different writers, and the anomalous forces gratuitously brought in to support the different hypotheses—it is so. This unsatisfactory state of things, so different from that in which is the theory of the motions of comets,—seems to be owing partly to the difficulty of making the necessary observations by reason of the undefinable nature of the bodies themselves, and partly from the untoward circumstances under which the obser- vations must be made, as well as the rareness of any opportunities offering. Hence, theories are built upon accounts handed down from old astrological times, when men’s prejudices would have prevented them, even if their means had been ample, which they were not, from giving any satisfactory and trustworthy ac- counts of the phenomena displayed by the heavens of their day. Then, again, the theories appear to have failed from attempting too much, attempting things not legitimately within their reach; it would have been enough to determine the laws of the changes which the tail undergoes during the orbit of a comet; but in place of this, they attempted to shew why the tails were there, and how they came into existence. This is as much as in the planetary theory to attempt to determine why Saturn has rings; a problem which would have eluded the grasp even of Nrewron, and will for ever remain wrapped up in the mystery of creation; enough for us that the rings are there; we can measure their diameter and thickness, approximate to their weight, and determine the laws of their rotation, and alternate appearance and disappearance to the earth, and to their own planet; and something of the same sort we may expect to be able to do in the case now before us. It has been remarked that theory and fact sometimes unite, and that some- thing of theory is necessary to enable us to speak correctly of facts. Many in- stances of this occur in the history of most of the sciences, but in none have the facts been more misinterpreted by the vulgar feeling of the senses, in the absence of correct theory, than in the case of the physical characteristics of comets. No phenomena were so likely to be misinterpreted by reason of the strong pre- judices almost innate in men’s minds, as well as the specious and inexplicable character of the appearances themselves. Accordingly, because the tails of VOL. XX. PART I. 2N 132 PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. comets were seen chiefly at or about the perihelion passages, they were said to be produced then; to have been shot out, and then drawn in again, or dissipated ; and numerous have been the theories to explain this creation and extinction. And yet of all the facts that have been ascertained, if any of them can be so con- sidered, with regard to the physical appearances of comets, of none may we be more sure than that the tails of comets, in place of being largest, or existing only at the perihelion point of the orbits, are then the smallest. Comets of every size, (the distinction of those said to be with and without tails is visionary, or rather the tail is equally a part of the general body of the comet, as the so-called head, and obeys the same laws), when accurately observed, have always been found to decrease in coming to perihelion, and to increase in size in retreating therefrom ; this condensation of substance, producing more power to reflect light at that period of the orbit, when, from the closer proximity to the sun, there is more light to reflect. These two causes combining, and both increasing most rapidly with comets of great excentricity and small perihelion distance, occasions the sight, all of a sudden, of a long cometric ray in our skies, when the previous night, or at least the previous clear night, there was none bright enough to catch men’s eyes. As the comet leaves the sun, the tail or body expands, and partly from its consequent greater rarity, and the diminishing intensity of its solar illu- mination, is lost to our sight; and only the denser roundish portion about the head remains visible. This is likewise expanding, and is at length also lost sight of for the same reason. In like manner a comet reappears, first the oval mass about the head, and then the tail gradually strengthens; but its aspect will materially depend not only on its distance from the sun, but on our distance from it, and the direction of our line of sight with the longer axis of the body. Having had the good fortune to see a rather large number of comets, both great and small, and under circumstances favourable above the average, I hope that I may be of some service to theorists, by stating what data may be looked upon as well fixed with regard to these phenomena; by pointing out some cor- rections which are absolutely necessary to be made upon the observations, before any good and safe grounds for theorizing can be procured, but which corrections never have been made; and by pointing out the most probable method of im- proving the observations themselves, which, as at present conducted, are by no means satisfactory. With regard then to the physical nature of comets, we may take the follow- ing as axioms :— 1. A comet consists of a nucleus, and one or more gaseous envelopes. (1.) No instance has ever been recorded, at least since the fabulous days of astronomy, of a comet having ever been seen without some gaseous appendage, forming, indeed, a distinctive feature at a distance from every other body of the solar system; at a distance, because very close to one of the planets, especially one or two of the asteroids, something of its atmosphere might be ob- PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. 133 served; but, at the actual distances at which they are viewed, the most powerful telescopes never show these atmospheres in the same manner as those of a comet; they are indicated only by a very different order of phenomena. When Uranus was first discovered, and no one dreamt of planets beyond Saturn, it was called a comet; not because its form was like that of any recognised comet, but because it was expected that its orbit would prove similar; when, however, the real nature of its path was discovered, the appellation of comet was quickly retracted. So much for the necessity of a gaseous envelope; of the equal importance of a nucleus, it may be remarked, that although some comets are described as having nuclei, and others as having none ; this turns out to be but negative testimony, inasmuch as these latter bodies have always been the fainter, smaller, and more distant ones, in which the nucleus should have been so much the more difficult to distinguish ; and if it has not been actually observed itself, there has at least been in- variably noticed in every recorded comet, some one point where the gaseous matter was visibly more - eoncentrated than in other parts, indicating thus a virtual or a dark nucleus, if not an actual and a reflective one: while observation, combined with calculation, has satisfactorily shewn, that in comets of every degree of size and excentricity, the mass is so very nearly concentrated in this nucleoid centre, that that need alone be referred to in all determinations of the orbit. 2. The nucleus if solid and material, is exceedingly small. (2.) Every advance of our knowledge has tended to diminish the possible size of the solid nuclei of comets, planetary perturbation has shewn them to have no sensible mass, and telescopic observa- tion no sensible size; and in the cases of comets of all sizes, observers have witnessed them pass over stars in every position, except, perhaps, exactly centrically with the nucleus, without perceiving any obscuration of the stellar rays. The old observers have certainly spoken of very large nuclei, but they evidently meant rather the head, which, in some comets at certain parts of the orbit, presents in small] telescopes an ap- pearance of planetary opacity and definition. Such was the case with the great comet of 1843, for three or four days after having passed its perihelion ; in small_telescopes it was difficult to avoid believing in the existence of an actual planetary nucleus of very notable size; but the fourteen feet reflector of the Cape Observatory shewed the borders of this head to be filmy, and exhibited small stars shining through it ; day after day it expanded and became less defined, until at last it ceased to present a solid appearance in any telescope; and at no time was there anything larger than a stellar point, to which the attribute of hard or heavy matter might be expected to apply. 3. The nucleus is excentrically situated in the gaseous body. (3.) The nucleus actual or virtual, has never been observed in the middle of the envelope, but always nearer one end than the other, the envelopes too, never being round, but invariably more or less elongated. 4. Comets of longest period have the largest bodies. (4.) This is the general result of cometary statistics, but need not be any more strictly true, than that the largest planets are all at the greatest distances from the sun ; they are not strictly ranged in the order of distance agreeably with size, but as a general rule merely, the smaller are closer to the sun than the larger planets. In the same way the telescopic comets, when sufficiently numerous obser- vations have been obtained, have almost always been found to have short periods, and those very brilliant ones, with not only long but broad and dense tails, have invariably been found to be of long period. 5. Those comets whose orbits have the greatest excentricity, are the most excentrically situated in their envelopes, or, vulgarly speaking, have the longest tails. 134 PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. (5.) This may not be strictly true, but yet is assuredly a very marked feature in the statistics of the question. The great comet of 1843, whose orbit was the most excentric ever known, i. e., had the least perihelion, but great aphelion, distance,—had also the longest and narrowest tail, and the smallest head; consequently the nucleus situated near the centre of the latter was most excentrically situated in the gaseous envelope. Ha.izy’s comet, and that of 1811, of less excentricity of orbit, had shorter and broader tails and larger heads; and their nuclei, consequently, less excentrie : while the telescopic comets of short period, and aphelion not extraordinarily greater than their perihelion distances, exhibit merely somewhat oval masses of vapour. ~ 6. A comet revolves on an axis passing through the nucleus, and at right angles to the major axis of the envelope, in the same period of time that it takes to revolve about the sun: hence, the tail being turned away from the sun in the normal position, is turned away from him in all other parts of the orbit also. (6.) Every comet has invariably been observed to have its tail turned away from the sun in every part of its orbit; this was the first notable fact established in cometary physics, and the axiom is but a different statement of it. 7. This axis is not at right angles to the plane of the orbit, but variously in- clined in the case of different comets, as with the planets. (7.) There is no reason to expect the contrary; indeed, analogy rather leads us to this conclusion, and it may, if admitted, be sufficient to explain the apparent want of symmetry observed in the tail of Hartzry’s comet, that of 1819, and most, if not all, which have been the subject of special atten- tion ; and it may tend to account for some of the differences in the appearance of the former body in approaching and leaving its perihelion, at considerable but equal distances on either side of that point. 8. A quicker rotation round the longer axis of the body also appears to exist. (8.) This seemed to be almost proved by some of the changes which took place in the head of the great comet of 1843, night after night, in the earlier part of its apparition ; for instance, a double- winged head, laterally, one night, becoming a single and centrically winged, or rather a tailed-head the next night ; but when a body is seen for so very short a space of time, for a few minutes only in twenty-four hours ; and sometimes, perhaps, for several days, even that short glimpse is prevented by clouds,—it becomes extremely difficult to separate in such a body as a comet, in which there is nothing decided and tangible, and fixed either in size or brightness, any indications of revolution from those of the other motions and changes which are going on simultaneously. But it seems a point well worthy of attention, and to be proved or disproved. 9. A comet shines by reflected light, and shews a sensible phase; the quan- tity, form, and position, therefore, of its component matter, cannot be judged of by the eye alone. (9.) That comets shine by reflected light, is considered to have been proved by Araco’s polarizing experiment ; and was inferred before by every analogy in the planetary system; but all appearance of phase has been denied, this, therefore, requires a little explanation. The supposed absence of phase has been attributed to the excessive tenuity of the matter of the comet, and the case has been illustrated by reference to the thin clouds often seen in the west after sunset, or in the east before sunrise, glowing in the solar rays, literally drenched with light, and exhibiting no distinction of light and dark side, A little examination of this instance would have shewn that the conclusion is not so safe ; the whole of the cloud being so bright, the difference of illumination of the two sides of it is PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. 135 merely so much the more difficult to distinguish, by reason of the well-known optical or physiological law, that a small difference in the brightness of two objects is more difficult to perceive in proportion to their absolute brightness. If our sensation and means of measurement are not sufficiently accurate in this case of the thin cloud, we have only to turn to a thicker cloud (of the same species, and in a similar part of the sky with regard to the sun), and there we shall see the same law which must obtain in the former case now visibly developed ; and then we come to the necessary conclusion, that the illuminated side of every cloud must be brighter than the other, i. ¢., that it must shew some hase. ji The comets are undoubtedly far rarer than any description of cloud floating in our atmosphere, but they are seen under far more favourable circumstances for exhibiting a phase ; for, they are illuminated by the sun from one end, so that there must be a much greater difference of intensity of light at the two ends than there would be at the two sides, if transversely lighted, as with the long thin films of bright cloud alluded to; and, further, the comet being of the last degree of faintness, the eye is much better able to detect small differences of luminosity. Then again, comets, though they be exceedingly rare, are very voluminous, so that the rays of light have to traverse a great space of matter in passing through them; and if some is reflected in the anterior parts of the body, as we see is the case by the fact that the body is rendered visible to us, there cannot possibly be so strong an illumination on the posterior parts ; therefore, we shall either see them fainter than the others; or not at all, if the anterior portions themselves are but just visible. ; With these preliminaries then, we may ask, what comet has ever been seen without some phase ? for in every single instance, the anterior part of the head, or the denser portion of the envelope, has been brighter than the posterior, exhibiting sometimes the appearance of a luminous sector in front ; and the anterior half only, of the body, has been seen, the comet presenting as a general rule two diverging and slightly curved tails. This has been generally held to be merely the effect of looking transversely through a conical envelope of luminous matter, when the ray of light passing through the central portions would meet with less substance, and that part would therefore appear darker than the limbs. This, doubtless, prevails to a great extent, but then we must further remember, that the exterior coats of the envelope will be more strongly illuminated than the interior ; and the dark axis of the comet’s tail becomes therefore a particular character of phase. Further, as we procced to the posterior portions of even the outer coats of the envelope, they will be illuminated by a weaker light from the sun, by reason of their greater distance; and if any convergence of them towards the axis should occur, as has actually been observed in some cases, their illuminating rays being then still further diminished in intensity by absorption and reflection, they will hardly be enabled to make them- selves visible to us. Thus, the diverging limbs of the tail, and its forked or many-pointed termination, becomes an effect of phase on a body which may be of'a symmetrical and rounded, and complete character. This point, it is of the greatest importance to determine, for if the actual forms of comets be as we see them, they are altogether anomalous in the heavenly regions ; and merely on the score of the form of these supposed conical envelopes and diverging streamers, equally anomalous forces have been introduced to explain the phenomena; electricity and polarity, which have no place in any other department of astronomy, being allowed precedence here. _ Granting, that a comet is always a prolate spheroidal mass of vapour of different degrees of prolateness, and of actual length in various cases, but always illumined from one end, then we may expect in the larger and denser comets to see but the anterior half of the body ; the posterior half being so much further off from the sun, and the rays of light which reach it, being further so much weakened by having passed through the first half; consequently, in this description of comet, we might expect, and we absolutely do find, the phenomenon of the forked tail most marked. In the smaller and fainter comets, on the other hand, the rays of light which reach the posterior half of the body are not much dimmed either from having passed through the excessively tenuous anterior por- tion, or from having travelled through any notably greater distance from the centre of radiation; in such cases we may expect to see more completely the whole form of the comet; and in them we do actually find nearly, and sometimes quite oval forms, and all gradations from these, through truncated ovals to the forked tails. These facts induce us to admit the possibility of the bodies of comets being of a far more regular geometric form than has hitherto been suspected, if we allow that conclusions derived from small comets may be safely so extended, mutatis mutandis, to large ones ; but this view is further confirmed by a notable observation of one of the largest and most excentric of comets. As already observed, comets decrease in size and increase in density on approaching the peri- helion, and the reverse on receding therefrom ; hence the phase ought to be most evident, or the tail VOL. XX. PART I. 20 136 PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. most forked about the perihelion, both on account of the greater absorption and reflection of light in passing through the denser anterior half, and on account of the greater ratio which the difference of distance of the anterior and posterior ends bear to that of the former and the sun; and ata distance from the perihelion, the effects being reversed, we might expect to see less phase, a less dark axis in the tail, and something of a convergence in the limbs of it. Now, both of these phenomena were distinctly and markedly observable in the great comet of 1843; near the perihelion the tail being forked, the axis almost as dark as the sky round about, and the limbs intensely bright and sharp; but long before it was lost on its retreat to aphelion, the oval darkness was almost obliterated, the whole tail was diffuse, and the posterior portion for fully one-third of the whole visible length shewed a convergence inwards. But the notable phenomenon is still to come ; allowing the above increase of phase in approach- ing perihelion, it is also evident, that if the perihelion distance be very small, the sun may present a very large angle as viewed from the comet; and in this way rays of light may reach every part of the external coats of the body, and these may be also illumined to that intense degree, that as with the sunrise and sunset clouds already referred to, no phase may be seen; so that, with such comets the maximum of phase will occur a short distance on either side of the perihelion, at and very close to it there will be little or none. As the comet of 1843 almost touched the sun’s surface in passing round it, it must have pre- sented as satisfactory and conclusive a proof as man could have wished for. But although it must have been visible to the naked eye, and to nearly the whole world, in this critical part of its orbit, no mortal man is known to have seen it. Rather a melancholy fact of the imperfection of the astrono- mical watching of the present age; and it appears all the stronger, from Araco having, in his report to the Academy, descriptive of the discovery of a small comet, enlarged on the perfection of the system of search organized at the Parisian Observatory; by which it appeared that nothing could escape detection ; for the assistant who made the discovery, having purposely kept silence when he was relieved in his watch by another person, this one discovered the same comet before having been an hour at his post. But to return to the comet of 1843, it was seen while still not very far from the perihelion, when the sun was still subtending a very large angle, viz., on February 28, the perihelion passage being February 27, 1843; but then only by three persons, or rather parties, and none of them have given sufficiently accurate accounts of what they saw, or have attempted what would have been so invaluable, if effectually and faithfully executed, a drawing of the appearances; but their statements, as far as they go, decidedly confirm the views above enumerated. The first of these happy three, with whose account I became acquainted, was a person at the Cape of Good Hope, who (decidedly no scientific person, and having no prejudice in favour of any theory), described the comet as he and his shepherd boy saw it at noonday, a bright hazy star, with the hazy matter streaming off on one side, and collected into a focus about two feet behind it. Allowing him to have estimated the sun’s diameter at one foot, the apparent length of the comet’s tail is well given; and the comet itself being spoken of as a bright star in the hazy matter, which streamed off, and collected into a focus at a certain distance behind the head ; this certainly may be interpreted into a somewhat symmetrical elliptic figure, having the nucleus in the focus nearest the sun. The next testimony is from the ship Owen Glendower, the crew and passengers of which ship, when off the Cape on February 28, saw the comet plainly about sunset, “as a short dagger-like object close to the sun.” This is not particularly explicit, but yet we may certainly conclude from it, that the comet was broad in the middle of its length, and pointed towards each end, and had little or no axial darkness, which sufficiently conforms with our idea of the perfect shape of the envelope of a comet seen under such circumstances. The last witness is from the United States, where Mr Crarxe, of Portland, saw the comet at 3° p.M., on the same day, and examined it telescopically, and describes it in these words :—‘* The nucleus, and also every part of the tail, were as well defined as the moon on a clear day. The nucleus and tail bore the same appearance, and resembled a perfectly pure white cloud without any variation, except a slight change near the head, just sufficient to distinguish the nucleus from the tail at that point.” The first sentence well describes the increase of density and definition we have already insisted on as a consequence of so near an approach to the sun; and the second paragraph as perfectly describes the absence of axial darkness, a consequence partly of the increased brightness of the illumination of all the external portion, and partly of its being seen in daylight, and so close to the sun; for then, as every one knows, even the darkest shadows amongst the mountains, and in the craters of the moon, those which appear absolutely black at night, are, under those circumstances, barely distinguishable from the brightest portions. As to the shape, Mr Crarxe says,—that the PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. 137 whole body of the comet was seen, but what his idea of the true complete form of its body was, he does not give; but, as he states, that a slight change of brightness near the head was “ the only thing to distinguish the nucleus from the tail at that point ;” and, further, “ that every part of the tail was as well defined as the moon on a clear day ;”’ it would appear to be quite safe to infer, that the tail was not forked; and that the base, instead of a broad or forked, or many-pointed indistinct termination, was as well and sharply outlined as the limbs. A notable distinction this to every subsequent view obtained on succeeding days ; and, indeed, in the case of every other comet what- ever observed at a great distance from the sun,—when, whatever the definition of the limbs of the tail, the termination or the base has always been so excessively uncertain, that different persons have varied several degrees in assigning the place of it. Alas! indeed, that the practical astronomy of the present day did not take better account of this unique and critical instance which was offered by the skies of our times ; centuries may elapse before another such instance may occur, and this question of the real and complete form of a comet may be in abeyance as long. Something may, doubtless, be done by rigid examination of all the persons who did witness the phenomenon in the comparatively imperfect form of the day after the perihelion passage; but their answers would not be very safe now, so many years after the event, and after the promulgation of a particular theory. Something might also, perhaps, be done, by careful and photometrical observation of the faintest nebulz, while the darker part of a comet’s tail, if it exists, must be passing across them. But this is a very unpromising method, for comets, at all periods, attenuated, become so exceedingly diffuse by the time that they have reached a sufficient distance from the sun, to be viewed for any length of time in a dark sky, and contrasted therein with very faint nebule,—that we can hardly expect to obtain any certain indication in this manner. The only sure way is for the comet to be so very close to the sun, that rays from some part or other of his surface will reach every portion of the body of the comet directly, 7. ¢., without having to pass through any other part in order to arrive there. The fact of this great and invaluable opportunity having been lost, would seem to shew that it is highly desirable that extra meridian observations should be made and watched for by some public observatory in its official routine, instead of being abandoned altogether to amateurs. It is high time that our observatories should be placed in the clearer climates of some of the colonies, and that the most favourable geographical positions should be sought for, rather than the most convenient places in a social point of view ; for this results in smoky towns in our own beclouded country being selected as the places where the stars are if possible to be observed. 10. The gaseous envelope is of extreme tenuity, is elastic, and with regard to light is slightly reflective and imperfectly transparent ; it decreases in size, but increases in density, and light reflective power in approaching the perihelion, and the reverse when receding from it; and this occurs in a degree proportioned to the excentricity of the orbits of the comets. (10.) That the gaseous envelope of a comet is of extreme tenuity, and is elastic, slightly reflec- tive and imperfectly transparent, is apparently confessed on all hands, and is proved by the pheno- mena presented by every comet. That it increases in density and light-reflective power with its proximity to the perihelion, and that this occurs im a degree proportioned to the excentricity of the orbit, requires, at least the latter part does, that the instances on which it is founded should be men- tioned; for though the contraction in size of small comets on approaching the sun had been remarked, yet some had maintained it to be accompanied by a decrease in density, by an actual evaporation and disappearance at perihelio ; and no one that I am acquainted with had applied it to the larger comets also, or compared the degree of it, with the excentricity of the orbit. With regard to the effect of excentricity of orbit, a small proportion of it should make a comet visible for a long period on either side of the perihelion, from the lesser degree of attenuation and expan- sion of its substance at a distance therefrom ; and it should also be lost in the sun’s rays for a consi- derable time at and about the perihelion passage, from the matter never being compressed into a sufli- ciently dense body to be visible in the blaze of day. This rule appears well borne out by both small and large comets; the small ones, for instance Encke’s, Bieia’s, and Faye’s, which have for the ratio of the excentricity to the semiaxis major, the numbers respectively, 0-847, 0-755, 0:555, shew no very 138 PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. well marked changes or even characteristics at any part of their orbits, and are soon lost in the twilight even in their densest states ; there being little compression, and by axiom 4, little substance to compress, the mean distances being only 2:216, 3-502, and 3°812, the earth’s distance being unity. In the case of Hattzy’s comet, however, the appearances are very different, the excentricity being 0-967, and the semiaxis major 17-988 ; hence, on this large body approaching the sun and under- going such a much more intense degree of compression, distinctly marked changes were seen almost from day to day, and at a certain distance from the perihelion it was of great brightness. But the perihelion distance being still large, about half that of the earth, or near fifty millions of miles, the condensation was not sufficient to enable the comet to be seen in moderate twilight, and hence it was not seen after the perihelion passage for more than two months, but then remained visible for nearly four months, so that it was lost sight of at about six months after perihelion passage. The great comet of 1844-5 had a less perihelion distance, viz., about 25 millions of miles, and a mean distance probably much greater, hence it was sufficiently concentrated in the neighbourhood of the sun to force itself on the notice of men within a week after perihelion: which implies a very much greater degree of brightness, than if Hatiey’s comet had been seen as early, when powerful telescopes, directed by means of an accurate ephemeris, were employed in the search. This comet remained in sight between three and four months, and when last seen was a faint nebulosity with little or no apparent concentration in any part. But the great comet of 1843 is again the decisive test, as this had a perihelion distance of only half a million miles, 60,000 only from the surface of the sun: here, therefore, we might expect to see the brightness excessive at and about the perihelion ; but the subsequent expansion, on account of the great mean distance, would be so rapid that the comet would be soon lost sight of by reason of faintness. Accordingly, we find that this comet pressed itself on men’s attention one day only after the perihelion passage ; and from its being so very bright then, and yet seen by so few, there can be little doubt but that it might have been observed the day before, if it had been looked for ; and would have been so seen, were not staring into the sun’s face and immediate vicinity rather a trying, and, conse- quently, an unpleasant occupation to most eyes, and seldom indulged in, especially in the warmer countries of the south, when the sun might have been that day unveiled from cloud, and was high in the sky. But, however, even the day after the perihelion passage, when the comet must have been much less dense than at that epoch, it was quite bright enough to be seen throughout the day within two degrees of the sun, and was then about one degree in apparent length; four days after it had increased to 25 degrees, in a fortnight to double that ; in a month it was so faint and distended as to be lost to most person’s eyes, and powerful telescopes only kept it in sight a few days longer. Its meteor-like brightness and short ephemeral existence were subjects of general remark in the south, This instance may be considered to settle the matter, but Mr Hiyp’s interesting comet of 1847 as a later instance, and a well-marked one also, is very deserving of mention. He discovered this on February 6, 1847, as an exceedingly faint nebulous body approaching perihelion ; he observed the gradual condensation in the head and appearance of nucleus and tail, this last being about a degree long on March 9; and having computed the orbit and found the time of perihelion passage to be March 30'269, Gr. M. T., and that the distance from the sun was then only four millions of miles, he called general attention to the circumstance under the hope that, 1st, the comet might be seen in daylight on that day ; and, 2d, that a long tail might be visible in the evening after sunset. In the former he was borne out by the fact, for he observed the comet himself with a refractor of 7 inches aperture at 11 A.M., within two degrees of the sun, and three other persons are recorded to have witnessed it too. I examined that part of the sky myself on the occasion, but with a telescope of only 3°7 inches aperture could see nothing : Mr Hip himself found it a very difficult object to observe, so that the sizes of the two instruments may be taken as giving some measure of its visibility. In the latter supposition he was not confirmed; for no person saw a tail after sunset, and he himself says that the tail which he saw, exceedingly faint certainly, in the telescope in the day time, very nearly at the epoch of the peri- helion passage, was only 40” long,—but the 90th part of its length 21 days before. He was led to the first conclusion by the consideration, that the intensity of the light would vary as Za? (when r is the comet’s radius vector, and A its true distance from the earth), whence the comet should be at the time of perihelion 230 times brighter than that on March 8, when it was just perceptible to the naked eye. (Royal Astronomical Society’s Monthly Notices, vol. vii., p. 248.) But here it will be.seen that with regard to the distance from the sun and perihelion, the intensity of solar illumination alone is taken account of ; but the concentration of the comet at the perihelion must have greatly assisted the effect, and without this it seems pretty certain that the comet would not have PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. 139 been visible : then the introduction of the distance from the earth does not appear correct, for although this may change the apparent diameter of the body, it does not at all alter the intrinsic brightness of the surface. The second conclusion he was led to, by the old erroneous idea (to use his own words) that ‘“ the close approach of the comet to the sun would be likely to produce a tail of considerable length :” but in place of so doing it was contracted in size to a very small compass. This additional instance of the prevalence of an idea so completely the reverse of the fact, will, I hope, excuse me from having attempted in so very crude a manner to establish what appears to me the grand statistical truths of cometary physics. But if I have not been able to agree with Mr Hrnn in his physical ideas, I must express my testimony of his high standing in the more important question of the motions of comets ; here he has indeed filled an honourable niche, which had been long, if not always, unfilled in the cometary credit and fame of this country. A general result in cometography, certainly following the establishment of this axiom, is, that when the length of the tail of any comet of celebrity is described in millions of miles, a very favourite method with most writers, it will be absolutely necessary to accompany it with an account of the part of its orbit, where the comet is supposed to have been at the time: without this, the statement of an actual length, is as absurd as the fixation of the place of the magnetic pole, without a date being attached, 11. The axis of the tail of a comet is straight at the perihelion, but at any point between this and the aphelion is curved, and is concave toward the latter, the radius of curvature being inversely as the excentricity. (11.) This I will not attempt to lay much stress upon ; but certainly the tails of the comets of Hatey, of 1843, and of 1844—5, were sensibly straight near the perihelion; and the two latter became curved after it, the former more than the latter, and they were concave to the direction in which they wete proceeding ; precisely the reverse of the general belief, which states them to bend backwards at the extremity of the tail, as if experiencing some resistance, when whirled round the perihelion with such exceeding velocity. The direction in which those two comets were proceeding at the time was towards the aphelion ; and I have not had any opportunity of examining a large comet coming up to the perihelion. The great comet of 1843 would have been sufficient to settle the question, but I have only heard of one person (a Commissariat officer voyaging from New South Wales to the Cape), who saw it in the eastern skies before sunrise and the perihelion passage ; and he had made no observations. 12. The molecules composing the envelope of a comet are only held together by their mutual gravitation, each constituting almost a separate projectile, and describing its own parabola about the sun. The 12th axiom is Sir Joun Herscuet’s, and taken in conjunction with the others, seems generally to explain all the principal variations in appearance, and affords ground for testing each exactly by calculation, and thereby of ascertain- ing what residual phenomena may be due to laws others than those of gravita- tion, mechanics, and optics. After alluding to the observed concentration of ENcKE’s comet near perihelio, and the error of attempting to account for it by the pressure of a supposed ether in the vicinity of the sun, Sir Joun says (Royal Astrononucal Society’s Memoirs, vol. vi.), ‘« It appears to me that the phenomenon is (if not wholly, at least par- tially) explicable on a much less gratuitous supposition, viz., that of the extremely feeble attractive force by which the matter of a comet must be held together, VOL. XX. PART I. ZP 140 PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. owing to the probable minuteness of its mass. Cohesion can hardly be supposed to exist in a gaseous or nebulous body of such tenuity; so that the only bond of union between its molecules must be their fecble gravitation to each other, which is hardly more than mere juxtaposition in space. Hence we must regard each molecule as constituting almost a separate, independent projectile, describing its own parabola about the sun. Now, the interval between two or more parabolas described about a common focus, and having their axes coincident, is a minimum at the perihelion, and increases as we recede from it” in the sesquiplicate ratio of the radius vector. The obervations of ENckE’s comet, which Sir Joun treated by this theory, shewed rather a more rapid rate of increase and decrease; which might, he thought, be readily accounted for by the effect of the brighter back- ground of sky on which the comet was projected as it approached its perihelion, and vice versd. But whether any other forces may have part in the entire pheno- menon presented, he concludes that the property above pointed out, cannot but be allowed to be a vera causa, and to have some share in the production of the effect. To the latter part of this opinion every one must assent; and with respect to the want of agreement between theory and observation, in the case quoted by Sir Joun of a small comet, in addition to the observations themselves requiring cor- rection, for the cause he has mentioned, the theoretical quantity requires it also on account of the greater attraction of the molecules upon each other at the perihelion, by reason of their increased proximity; while, moreover, the figure of the comet, and the direction in which it is seen, require also to be taken into consideration. With regard to large comets, which seem generally to have been thought to be under the dominion of absolutely different laws, the decrease and concentration of the tail at perihelio, is fully accounted for by this 12th axiom, as well as some other pheno- mena, the perplexing nature of which, when viewed by the light of any other theory, may be gathered by the account given by Sir J. Herscue. himself, at the conclusion of the chapter on comets in his work of last year (Outlines of Astronomy.) “ It is in a physical point of view that these bodies offer the greatest stimulus to our curiosity. There is, beyond question, some profound secret and mystery concerned in the phenomena of their tails. Perhaps it is not too much to hope that future observations, borrowing every aid from rational speculation, grounded on the progress of physical science generally (especially those branches of it which relate to the ethereal or imponderable elements), may ere long enable us to penetrate this mystery, and to declare whether it is really matter, in the ordi- nary acceptation of the term, which is projected from their heads with such extra- vagant velocity, and if not impelled, at least directed, in its course by a reference to the sun, as its point of avoidance. In no respect is the question as to the materiality of the tail more forcibly pressed on us for consideration, than in that of the enormous sweep that it makes round the sun in perihelio, in the manner of PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. 141 a straight rigid rod, in defiance of the law of gravitation, nay, even of the received laws of motion, extending (as we have seen in the comets of 1680 and 1843)* from near the sun’s surface to the earth’s orbit, yet whirled round unbroken; in the latter case through an angle of 180° in little more than two hours. It seems utterly incredible that, in such a case, it is one and the same material object which is thus brandished.” This and much more to a similar effect might be quoted from Sir J. HrEr- SCHEL, and other authors, as to the difficulties experienced in the usual method of viewing a comet, as a planetary body at the nucleus, with an appendage attached to, and whirled along with it and by it. No wonder that doubts were expressed as to the attractive force of the small nucleus being able to retain within its grasp portions of matter thrown out to such distances; and that fears’ were expressed as to the breaking off of the tail; and, because some thought that it ough to bend backwards from the resistance experienced in its course, there- fore they said that they did see it bend. Other difficulties also follow from the usual mechanical view of the production of the tail at perihelio, as has been stated by many, from the heat of the sun causing the nucleus to throw out jets of vapour on the side of that luminary, which again has the power to bend them back, and sending them streaming past the nucleus once more, forms the tail. These jets of vapour ought to drive the nucleus away from the sun; for though it may be said that the vapour, being nearly imponderable, should not produce any sensible or visible effect on the nucleus,—yet the nucleus itself is, for any- thing we know, as imponderable; indeed, if we judge of the masses of the two by the quantity of light reflected, which is almost the only indication we have, and perhaps not a very bad one, then the mass of the tail in most cases exceeds that of the nucleus, 2. ¢., if the quantity of light reflected by the whole envelope were to be concentrated into a single point, it would be brighter than the nucleus. Iience with the extravagant rapidity and the enormous quantity of vapour rush- * This is not stated with perfect correctness, at least with regard to the comet of 1843, which might have had a tail of that length some days after the perihelion passage, when it had grown with the rapid increase of its radius vector; but the first day after the perihelion passage, the tail was observed to be only double the sun’s diameter (excluding inclination), and its distance must then have been 100 times greater than at the perihelion; so that if the sesquiplicate ratio holds good, we shall have for that epoch a size not very different from planetary bodies. (A curious meet- ing this must be of the molecules brought for an instant into such close proximity, after having been separated for ages by distances so vast and inconceivable as they must be at the aphelion ; and when separating for their diverse orbits, what speculations on their next meeting, not in thunder, lightning, and in rain, but in light and heat unspeakable. On the last occasion, February 18438, the heat was equal (according to Sir J. Hurscuer) to 47,000 of our suns, 1900 whereof are sufficient to melt the very rocks. Such, at least, must have been the heat, if the comet travelled at that part of its orbit only at the mean rate of the earth; but the velocity was really vastly greater, and the heat much modified thereby. The degree to which velocity in the heavenly spaces may modify distance, in respect of heat, is one still open for inquiry; and the result, in the case of our own earth, as far as it may have been very imperfectly examined into, would lead us to expect that the above proportion would be greatly reduced.) 142 PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. ing forth from one side only of the nucleus, that body should be driven far in the opposite direction: but by comparing its observed daily places during the peri- helion passages with the computed, we find that no deviations from any such anomalous causes are ever experienced. . All these difficulties, however, vanish on considering the envelope of a comet to consist of separate molecules, each constituting an independent projectile, and bound together only by their mutual gravitation and the laws mentioned above ; for then the size, character, and position of a comet being given at the perihelion, which we must look on as the normal state, all its principal variations of appear- ance during the rest of the orbit may be readily computed; and the return of every particle of the envelope to perihelion, or, vulgarly speaking, the retention of the tail by the nucleus, will be no more surprising, nor deviating from ordinary laws, than the return of the nucleus itself: certainly there is nothing “in defiance of the laws of gravitation, and even of the received laws of motion,” as. stated by a supporter of the other theory to be the case with that. But following this principle further, we may expect that, in the multitude of molecules moving about amongst each other, occasional conglomerations may occur, after passing the proximity of some large planet, whose attraction acting much more strongly on one part of the envelope than the other, will so much alter the motion of the particles therein, that they will, after some revolutions, gradually collect together at a distance from the nucleus, and at length separate and become a distinct comet. Such a case having actually occurred under our own eyes, four years ago, with BreLa’s comet, when it was not at the time under the immediate influence of any planet in particular, nor in any trying part of its orbit round the sun, adds much additional weight to this view of the constitution of such bodies. This brings us to the second portion of the subject, viz., the corrections which should be applied to apparent observations to deduce the real phenomena. A comet being an elongated, gaseous, elastic, and semitransparent body, varying in size and density with its distance from the sun, evidently requires many different corrections, according to the point of view and the distance from which it is seen, to give an idea of its real nature at the instant of observation ; and needs other corrections, to reduce it from that instant to some other in which itis in a normal condition. This normal condition is plainly in perihelio (though a better general comparison of the volumes of different comets would be obtained by reducing each to its mean distance, as they would then be all of much more nearly equal density), and viewed at right angles to the line of its larger axis. This is a position which seems generally to have been taken for granted, though it never oc- curs evel approximately. If we could see a comet at the instant of its perihelio, the plane of its orbit being inclined 90° to that of the ecliptic, and the radius vector being infinitely small, the above view would be nearly obtained, but would gradually PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. 143 be altered as the comet proceeded in its orbit. As seen from the sun, the comet should always present a circular body, and be equally illuminated on all sides, except in so far as the longer axis is inclined to the plane of the orbit: when the comet retreats towards the aphelion, the point of view from the earth becoming more nearly the same as that from the sun,—the comet should become rounder and rounder, as well as larger; and this is found actually to be the case,—the tails of HALLeEy’s and those of 1843 and 1844-5, having been, at and about the perihelion passage, narrow, and intense, and becoming at the last instant in which they were seen, wide, round, and diffuse. This, perhaps, together with the facts of phase and imperfect transparency (axioms 9 and 10), is sufficient to shew the importance of correcting the observa- tions for both the terrestrial and the solar elements of effect on the appearance of a comet, and be able to deduce its normal condition. That there may be other changes operating is very probable, but be that as it may, these effects of geometry, mechanics, and optics, actually exist to a very sensible amount, and their corrections must be applied before we can expect to discover any of the residual causes. I ought, doubtless, to apologize for having formed opinions different from Sir J. Herscuer’s last, as he is confessedly the person, above all others, entitled to paramount weiglit in cometary physics; and it may be that I have not properly understood, and unintentionally have not here sufficiently represented the reasons upon which his old conclusions have been altered, and on which he has thought it allowable to introduce electrical and other forces, to explain phenomena amongst the celestial bodies ; and I would therefore refer inquirers to his works themselves. But while on the one side, I hope that what has been here brought for- ward with regard to the complete body of a comet and its symmetrical and geome- trical form, when freed of the effects of phase, may remove one of the objections which he felt to allowing the all-sufficiency of gravity acting on a group of inde- pendent molecules ; on the other side, I not only allow, but think it extremely pro- bable, that some other effects besides those already mentioned, may legitimately occur; and if heat and rotation on the earth produce our trade-winds and hur- ricanes, much greater effects may follow the more violent alterations of tempera- ture and velocity of motion in a comet. Further, as confirming a curious feature noticed in HALLEy’s comet, by Sir Joun, after the perihelion passage, viz., a long thin ray posterior to the nucleus, to which it might perform the office, he suggest- ed, of conveying back the vapour driven off in front at perihelion; I would men- tion, that a ray of the same sort was seen posterior to the nucleus of the great comet of 1843, of extravagant length and excessive thinness, appearing as a very fine line of light, and traceable for many degrees up the tail: in these particu- lars, bearing some relation, perhaps, to the excentricity of the orbit, and to the VOL. XX. PART I. 2Q 144 PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. great length and small breadth of the comet itself. The first day that I saw the comet, three days after perihelio, it was not visible; but, clearly seen on every sub- sequent day, it existed until the whole was lost in faintness. The observation of these bodies is not, however, as hinted above, in a suffi- ciently satisfactory state for rigidly testing any calculable theory. This depends not only on the rarity of the appearance of comets (a matter beyond our control) ; but also on the insufficient means with which, and the untoward circumstances under which they are generally observed. The telescopes usually turned upon them, have been of so small an optical power, that they would have been considered utterly incompetent for ascertaining the nature of nebulee high up in the sky ; how much more so, when employed on nebulous objects close to the horizon, as the comets usually are, flickering and faint in vapour and smoke, and almost over- powered by the strength of the twilight. But a sufficiently powerful telescope need not any longer be a difficulty, since the publication of the inventions of the EArt of Rosse, and Messrs LAssEL and NaAsmytTuH ; and the effect of the vapour of the horizon, and the glare of twilight, might be successfully overcome, by establishing an observatory on high land within the tropics, where the geographical position renders the twilight short even to the plains; and the rarity of mountain air would still further reduce the reflective power of the atmosphere. Micrometrical measures, with such instru- ments, and under such circumstances, should be combined with photometrical deter- minations of the brightness of the various parts of the comet, and of the background of the sky. The former observations are easy and straight forward enough, but the latter are difficult and new; the zero must inevitably be taken from a stellar scale, but none such exists at present; for the telescope measure has invariably failed whenever employed for the purpose, and the eye is still thought the best available mean. Hence, none but the brightest stars have had their magni- tudes determined, and that but coarsely, while the great question still remains in much the same state as that in which the application of the telescope to divided instruments was in, before men had learnt how to determine the error of colli- mation. They knew that there were vast powers of accuracy in the optic tubes, but were afraid of great and mysterious errors, which they neither exactly understood, nor saw how to correct. Similarly in photometry, a telescope of large aperture, is confessed to have a larger scale and range than the unassisted eye, but is suspected of misleading to a greater extent. This is hardly the place for entering into such an experimental branch of practical astronomy ; for pointing out what appears to be the error of the methods adopted by others; and for shewing the correctness and efficacy, as I believe, of another plan, which might be adapted to telescopes of any size. But there can PROFESSOR PIAZZI SMYTH ON COMETARY PHYSICS. 145 be little doubt, from the pressing nature of the demand for advance in this depart- ment, that those who are more fortunately situated, must, before long, perfect and employ some method by which the great desideratum for inquiry into cometary physics may be obtained, viz., drawings, wherein every feature represented shall be accompanied by numerical statements of its dimensions and brightness, with the probable error of each determination. Until this shall have been done, the necessary corrections to reduce the apparent to the real phenomena cannot be undertaken, and I shall therefore hope to return to the subject if it should not be taken up in the meantime by any one better able to conduct it to a successful issue. Qld) VII.—On the Mechanical Action of Heat, especially in Gases and Vapours. By WituiaM Joun Macquorn Rankine, Civil Engineer, F.R.S.E., F.R.S.S.A., &c. (Read 4th February 1850.) INTRODUCTION. SUMMARY OF THE PRINCIPLES OF THE HYPOTHESIS OF MOLECULAR VORTICES, AND ITS APPLICA- TION TO THE THEORY OF TEMPERATURE, ELASTICITY, AND REAL SPECIFIC HEAT. The ensuing paper forms part of a series of researches respecting the conse- quences of an hypothesis called that of Molecular Vortices, the object of which is, to deduce the laws of elasticity, and of heat as connected with elasticity, by means of the principles of mechanics, from a physical supposition consistent and con- nected with the theory which deduces the laws of radiant light and heat from the hypothesis of undulations. Those researches were commenced in 1842, and after having been laid aside for nearly seven years, from the want of experimental data, were resumed in consequence of the appearance of the experiments of M. REGNAULT on gases and vapours. The investigation which I have now to describe, relates to the mutual con- version of heat and mechanical power by means of the expansion and contraction of gases and vapours. In the introduction which I here prefix to it, I purpose to give such a sum- mary of the principles of the hypothesis as is necessary to render the subsequent investigation intelligible. The fundamental suppositions are the following :— First,—That each atom of matter consists of a nucleus, or central physical point, enveloped by an elastic atmosphere, which is retained in its position by forces attractive towards the nucleus or centre. Suppositions similar to this have been brought forward by FraNKLIN, PI- nus, Mossortt, and others. They have in general, however, conceived the atmo- sphere of each nucleus to be of variable mass. I have treated it, on the contrary, as an essential part of the atom. I have left the question indeterminate, whether the nucleus is a small body of a character distinct from that of the atmosphere, or merely a portion of the atmosphere in a highly condensed state, owing to the mutual attraction of its parts. — According to this first supposition, the boundary between two contiguous atoms of a body is an imaginary surface at which the attractions of all the atomic VOL. XX. PART I. 2k 148 MR W. J. M. RANKINE ON THE centres of the body balance each other; and the elasticity of the body is made up of two parts: First, the elasticity of the atomic atmospheres at the imaginary boundaries of the atoms, which I shall call the superficial-atomic elasticity ; and, secondly, the force resulting from the mutual actions of distinct atoms. If the atmospheres are so much condensed round their nuclei or centres, that the super- ficial-atomic elasticity is insensible, and that the resultants of the mutual actions of all parts of the distinct atoms are forces acting along the lines joining the nuclei or centres, then the body is a perfect solid, having a tendency to preserve not only a certain bulk, but a certain figure ; and the elasticity of figure, or rigid- ity, bears certain definite relations to the elasticity of volume. If the atmospheres are less condensed about their centres, so that the mutual actions of distinct atoms are not reducible to a system of forces acting along the lines joining the atomic centres, but produce merely a cohesive force sufficient to balance the superficial-atomic elasticity, then the condition is that of a perfect liquid; and the intermediate conditions between this and perfect solidity consti- tute the gelatinous, plastic, and viscous states. When the mutual actions of distinct atoms are very small as compared with the superficial-atomic elasticity, the condition is that of gas or vapour ; and when the substance is so far rarefied that the influence of the atomic nuclei or centres in modifying the superficial elasticity of their atmospheres is insensible, it is then in the state of perfect gas. So far as our experimental knowledge goes, the elasticity of a perfect gas at a given temperature varies simply in proportion to its density. I have therefore assumed this to be the law of the elasticity of the atomic atmospheres, ascribing a specific coefficient of elasticity to each substance. The second supposition, being that from which the hypothesis of molecular vortices derives its name, is the following :—That the elasticity due to heat arises Srom the centrifugal force of revolutions or oscillations among the particles of the atomic atmospheres ; so that quantity of heat is the vis viva of those revolutions or oscillations. This supposition appears to have been first definitely stated by Sir Humpury Davy. It has since been supported by Mr Joutz, whose valuable experiments to establish the convertibility of heat and mechanical power are well known. So far as I am aware, however, its consequences have not hitherto been mathema- tically developed. To connect this hypothesis with the undulatory theory of radiation, I have introduced a third supposition:—That the medium which transmits light and radiant heat consists of the nuclei of the atoms, vibrating independently, or almost independently, of their atmospheres ;—so that the absorption of light and of radiant heat, is the transference of motion from the nuclei to their atmospheres, and the MECHANICAL ACTION OF HEAT. 149 emission of light and of radiant heat, the transference of motion from the atmo- spheres to their nuclei. Although in all undulations of sensible length and amplitude, such as those of sound, the nuclei must carry their atmospheres along with them, and vibrating thus loaded, produce a comparatively slow velocity of propagation; yet in all probability the minute vibrations of light and radiant heat may be performed by the atomic nuclei in transparent and diathermanous bodies, without moving the atmospheres more than by that amount which constitutes absorption; and those vibrations will therefore be transmitted according to the laws of the elasticity of perfect solids, and with a rapidity corresponding to the extreme smallness of the masses set in motion, as compared with the mutual forces exerted by them. This supposition is peculiar to my own view of the hypothesis, and is, in fact, the converse of the idea hitherto adopted, of an ether surrounding ponderable particles. The second and third suppositions involve the assumption, that motion can be communicated between the nuclei and their atmospheres, and between the different parts of the atmospheres; so that there is a tendency to produce some permanent condition of motion, which constitutes equilibrium of heat. It is now to be considered what kind of motion is capable of producing increase of elasticity. and what are the conditions of permanency of that motion. It is obvious, that the parts of the atomic atmospheres may have motions of alternate expansion and contraction, or of rectilinear oscillation about a position of equilibrium, without affecting the superficial atomic elasticity, except by small periodical changes. Should they have motions, however, of revolution about centres, so as to form a group of vortices, the centrifugal force will have the effect of increasing the density of the atmosphere at what I have called the bounding surfaces of the atoms, and thus of augmenting the elasticity of the body. In this summary, I shall not enter into the details of mathematical analysis, but shall state results only. The following, then, are the conditions which must be fulfilled, in order that a group of vortices, of small size as compared with the bulk of an atom, and of various diameters, may permanently coexist, whether side by side, or end to end, in the atomic atmospheres of one substance, or of various substances mixed. First, The mean elasticity must vary continuously ; which involves the condi- tion, that at the surface of contact of two vortices of different substances, side by side, or end to end, the respective densities at each point of contact must be inversely proportional to the coefficients of elasticity. Hence the specific gravities of the atmospheric parts of all substances, under precisely similar circumstances as to heat and molecular forces (a condition realised in perfect gases at the same pres- sure and temperature), are imversely proportional to the coefficients of atmospheric elasticity, Therefore let 4 represent the mass of the atmosphere of one atom of 150 MR W. J. M. RANKINE ON THE any substance, 6 its coefficient of elasticity, and m the number of atoms which, in the state of perfect gas, occupy unity of volume under unity of pressure at the temperature of melting ice ;—then nip'e! Pn! Qos, sine tatty is a constant quantity for all substances. Secondly, The superficial elasticity of a vortex must not be a function of its diameter: to fulfil which condition, the linear velocity of revolution must be equal throughout all parts of each individual vortex. Thirdly, \n all contiguous vortices of the same substance, the velocities of revolution must be equal; and in contiguous vortices of different substances, the squares of the velocities must be proportional to the oe of elasticity of the molecular atmospheres. The second and third conditions are those of equilibrium of heat, and are equivalent to this law :— TEMPERATURE ts a function of the square of the velocity of revolution in the mo- lecular vortices divided by the coeficient of elasticity of the atomic atmospheres ;—or Temperature = > (7) - aitounc hod exugi( BD where ww represents that velocity. The mean elasticity which a vortex exerts endways is not affected by its motion, being equal to OG ED Taree eee ae (Aes) where @ is its mean density. The superficial elasticity at its lateral surfaces, however, is expressed by - Ww Til errs at VIN The additional elas ticity “ a, bie being that which is due to the motion, is independent of the diameter. The divisor g (the force of gravity) is introduced, on the supposition of the density e being measured by weight. Supposing the atmosphere of an atom to be divided into concentric spherical layers, it may be shewn that the effect of the coexistence of a great number of small vortices in one of those layers whose radius is 7, and mean density @, is to give it a centrifugal force, expressed by a gr which tends to increase the density and elasticity of the atmosphere at the sur- face, which I have called the boundary of the atom. The layer is also acted upon by the difference between the mean elasticities at its two surfaces, and by the attraction towards the atomic centre; and these three forces must balance each other. (V.) : MECHANICAL ACTION OF HEAT. 151 I have integrated the differential equation which results from this condition, for substances in the gaseous state, in which the forces that interfere with the centrifugal force and atmospheric elasticity are comparatively small; and the result is : P=6ED (S25 +1) 0-H) +s) aI P is the entire elasticity of the gas, and D its mean density. M represents the total mass of an atom, measured by weight, and p that of its atmospheric part ; so that FD is the mean density of the atomic atmospheres. J (D) denotes the effect of the mutual actions of separate atoms. The first term represents the superficial-atomic elasticity. F denotes the effect of the attraction of the nucleus in modifying that elasticity, and can be represented approximately by a converging series, in terms of the negative powers 2 w . e 5 i : of mae z+ 1, commencing with the inverse square, the coefficients being functions of the density D. By using the first term of such a series, and determining its coefficient, and the quantity /(D) empirically, I have obtained formule agreeing closely with the results of M. REGNAULT’s experiments on the Expansion of Atmospheric Air, Carbonic Acid, and Hydrogen. In a perfect gas, the above expression is reduced to pagip (so 5+ 1) i leg va) Let », as before, denote the number of atoms of a substance which, in the state of perfect gas, occupy unity of volume under unity of pressure at the tem- perature of melting ice, so that ” M is its specific gravity in that state: then D id P= mpd (s-471) tad ACVLEL) The factor by which ate is here multiplied fulfils the condition of being a function of e, and of constants which are the same for all substances, and is therefore fitted for a measure of temperature. It obviously varies proportionally to the pressure of a perfect gas of a given density, or its volume under a given pressure. Let 7, therefore, denote temperature, as measured from an imaginary zero, C degrees of the scale adopted, below the temperature of melting ice, at which no Bg VOL. XX. PART I. 28 1=0; ie MR W. J. M. RANKINE ON THE Then for all substances Ww and in perfect gases ta ies Me tmay be termed absolute temperature, and the point from which it is measured, the absolute zero of temperature. This, as I have observed, is an ima- ginary point, being lower than the absolute zero of heat by the quantity Cn, which is the same for all substances. The value of C, or the absolute temperature of melting ice, as determined from M. REGNAUL?’s experiments, is | 274°6 centigrade, being the reciprocal of 0:00364166 per centigrade degree, the value to which the coefficients of dilatation of gases at the temperature of melting ice approximate as they are rarefied. For FAHRENHEIT’S scale C=494°28. In the sequel I shall represent temperatures measured from that of melting ice by ae =—T— C We have now to consider the absolute quantity of heat, or of molecular vis viva, Which corresponds to a given temperature in a given substance. It is obvious that bw? 29 represents, in terms of gravity, the portion of vs viva, in one atom, due to the molecular vortices ; but besides the vortical motion, there may be oscillations of expansion and contraction, or of rectilinear vibration about a position of equili- brium. The velocity with which these additional motions are performed will be in a permanent condition, when the mean value of its square, independent of small periodic changes, is equal throughout the atomic atmosphere. We may there- fore represent by me ee ig tog eee the total vis viva of the atomic atmosphere. To this we have to add that of the nucleus, raising the quantity of heat in one atom to Mee vi 29 ate While the quantity of heat in unity of weight is (XL) ue ra MECHANICAL ACTION OF HEAT. 153 The coefficient & (which enters into the value of specific heat) being the ratio of the vis viva of the entire motion impressed on the atomic atmospheres by the action of their nuclei, to the vs viva of a peculiar kind of motion, may be conjec- tured to have a specific value for each substance depending in a manner as yet unknown on some circumstance in the constitution of its atoms. Although it varies in some cases for the same substance in the solid, liquid, and gaseous states, there is no experimental evidence that it varies for the same substance in the same condition. In the investigation which follows, therefore, I have treated it as sen- sibly constant. The following, then, are the expressions for quantity of heat in terms of temperature. In one atom :— v 3kM 129° 2Cnp In unity of weight :— (XIL.) v? 3k Or a DOnp ( (rf —Cnpb) r—Cnypb) Real specific heat is consequently expressed by the following equations :— For one atom :— dq _ 3kM dr 2Cnp For unity of weight :— dQ_ 3k dr 2Cnp ee (XIII) For so much of a perfect gas as occupies unity of| | volume under unity of pressure at the temperature of melting ice :— nag 3kM dr 2Cp The laws established experimentally by Dutone, that the specific heats of simple atoms, and of certain groups of compound atoms, bear to each other simple ratios, generally that of equality, and that the specific heats of equal volumes of all simple gases are equal, shew that the specific factor ie depends on the che- mical constitution of the atom, and thus confirm the conjecture I have stated respecting the coefficient k. As I shall have occasion, in the investigation which follows, to refer to and to use the equation for the elasticity of vapours in contact with their liquids, which I published in the Edinburgh New Philosophical Journal for July 1849, 1 shall here state generally the nature of the reasoning from which it was deduced. 154 MR W. J. M. RANKINE ON THE The equilibrium of a vapour in contact with its liquid depends on three con- ditions. First, The total elasticity of the substance in the two states must be the same. Secondly, The superficial atomic elasticity must vary continuously ; so that if at the surface which reflects light there is an abrupt change of density (which seems almost certain), there must there be two densities corresponding to the same superficial-atomic elasticity. Thirdly, The two forces, which act on each stratum of vapour parallel to the surface of the liquid, namely, the preponderance of molecular attraction towards the liquid, and the difference of the superficial-atomic elasticities at the two sides of the stratum, must be in equilibrio. Close to the surface of the liquid, therefore, the vapour is highly condensed. The density diminishes rapidly as the distance from the liquid increases, and at all appreciable distances has a sensibly uniform value, which is a function of the temperature and of certain unknown molecular forces. The integration of a differential equation representing the third condition of equilibrium, indicates the form of the approximate equation. Log P=a—2— ¥ oo, REN S) The coefficients of which have been determined empirically by three experi- mental data for each fluid. For proofs of the extreme closeness with which the formule thus obtained agree with experiment, I refer to the Journal in which they first appeared. I annex a table of the coefficients for water, alcohol, ether, turpentine, petro- leum, and mercury, in thé direct equation, and also in the inverse formula, 1/2 wee -£ eh, BORN.) by which the temperature of vapour at saturation may be calculated from the pressure. In the ninth and tenth columns are stated the limits between which the formule have been compared with experiment. For turpentine, petroleum, and mercury, the formula consists of two terms only, Lene Re 0.6) T the small range of the experiments rendering the determination of impossible. 155 MECHANICAL ACTION OF HEAT. 366% °F 9FOO: “soqouy 092 4 ELL-0 *SoTJOUL] [TI 09:9 % 00-08 FG-G9 00-08 00:08 %% 06-9 LG-€91T %} 00-08 8G-GOL %} TLF-0 $9-F68 9 FL0-0 *soqouy GP60G %}F GE-0 ‘SOLPOUITTT TI ‘soanssoedg JO osueiy Cov) F-o9L9 0) £6691 “qloquo1g ey o8E8 9} FLL, ‘epeasryuay) oG LE OF of I 6 0698 9} FOE oFO il 04 oVS oO 1G 9} GOT oF 9G 9} GE + oIVh t+ 0 .66— “yloquerqe 086+ OF .08— ‘epersyuen ‘sounqededwiey, Jo oduey (6) FLIELO000: 841900000: 6&6&00000- F9EGT0000- 90070000: eecees 9669800: 9G87600- 866L100- S91G800- F6G8900- 4G “¢ , (Cp) ~ 9EG8EGL-E ig og TLEGsor-€ * O6F8F9G- os 1OL08E¢-§ O9FGIGE-G | GISTLES-E €68611E-G | SLEF806- 60LZ09L-E | OGGE9TE-E 9G9GE6S-G | OISEOFFE 9111680-¢ | LGOTS8I- ‘A “Bory ‘J ‘Bory (9) (‘g) 6S61-9 c0ee-L ISF61-9 L8186-¢ O8SPP-G 06G8E-G O0Z99T-9 LGP9IGF-9 LEGTES-L (‘¥) “‘qloy Uo e ‘ape.Lstyuay “op ‘op ‘op ‘op ‘op ‘POY UoLYe ‘ape.is1yuay ‘sounyeaod way, jo a[evog (-¢) *AIMOIO TAL jo soyouy { “AINIIOT FO } SoTPQUITT LAL ‘op ‘Op ‘op ‘op ‘op { “KMOIO PT } jo soyouy { “AIMOIOT[ JO \ Sor} QUAL] [TTA ‘soinssatg JO ayev0g (3) ‘spmbuT ayn yun qowjuos m sunodn, fo somwusnpy yy lof apnusog oy2 ur spunjsuon oy? fo FTAVAL tm ee evasoe umMe][o1}eg ] MICK GOUD ourjuodan J, ‘H oFOT Ye StnTOg |v gees = se alese yy eon sutylog pee ee Oud Gy { “"eTR.0 "13 ‘ds serereses ss TOUOOT VW ee eer eeeees "'T9V8 AA ‘spINTA oY} JO soureNy (Go) VOL. XX. PART I. 156 MR W. J. M. RANKINE ON THE The following are some additional values of the constant a for steam, corre- sponding to various units of pressure used in practice. Units of Pressure. Values of «a. ArmospueErss of 760 millimétres of mercury, = 29-922 inches of mercury, = 14-7 Ib. on the square inch, =1-0333 kilogrammes on the square centimétre, . 4 4:950433 ArtMmosPHERES of 30 inches of mercury, =761-:99 millimétres, = 14-74 lb. on the square inch, = 1-036 kilogrammes on the square centimétre, . : 4:949300 Kilogrammes on the square centimétre, . 5 : : : : 4:964658 Kilogrammes on the circular centimetre, : : : . é 4859748 Pounds avoirdupois on the square inch, 5 : : : 5 6:117662 Pounds avoirdupois on the circular inch, ; : : - : 6012752 Pounds avoirdupois on the square foot, : : : ‘ : 8276025 All the numerical values of the constants are for common logarithms. Section I.—Or tue Mutua. ConvERSION OF HEAT AND EXPANSIVE POWER. (1.) The quantity of heat in a given mass of matter, according to the hypo- thesis of molecular vortices, as well as every other hypothesis which ascribes the phenomena of heat to motion, is measured by the mechanical power to which that motion is equivalent, that being a quantity the total amount of which in a given system of bodies cannot be altered by their mutual actions, although its distribu- tion and form may be altered. This is expressed in Equation XII. of the Intro- duction, where the quantity of heat in unity of weight, Q, is represented by the height - , from which a body must fall in order to acquire the velocity of the molecular oscillations. This height, being multiplied by the weight of a body, gives the mechanical power to which the oscillations constituting its heat are equivalent. The real specific heat of unity of weight, as given in Equation XIII. of the Introduction, dQ Ltadk dr 20np represents the depth of fall, which is equivalent to one degree of rise of temperature in any given weight of the substance under consideration. We know, to a greater or less degree of precision, the ratios of the specific heats of many substances to each other, and they are commonly expressed by taking that of water at the temperature of melting ice as unity; but their actual mechanical values have as yet been very imperfectly ascertained, and, in fact, the data necessary for their determination are incomplete. (2.) Mr Jouve, indeed, has made several very interesting series of experi- ments, in order to ascertain the quantity of heat developed in various substances MECHANICAL ACTION OF HEAT. 157 by mechanical power employed in different ways, viz., by electric currents excited by the rotation of a magnet, by the forcing of water through narrow tubes, by the agitation of water and oil with a paddle, by the compression of air, and by the fric- tion of air rushing through a narrow orifice. The value of the depth of fall equiva- lent to a rise of one degree of FanreNuE!t’s scale in the temperature of a mass of water, as determined by that gentleman, varies, in the different series of experi- ments, between the limits of 760 feet and 890 feet, the value in which Mr JouLE appears to place the greatest confidence being about 780 feet. Although the smallness of the differences of temperature measured in those experiments renders the numerical results somewhat uncertain, it appears to me that, as evidence of the convertibility of heat and mechanical power, they are unexceptionable. Nevertheless, there is reason to believe that the true mecha- nical equivalent of heat is considerably less than any of the values deduced from Mr Jou.e’s experiments; for in all of them there are causes of loss of power, the effect of which it is impossible to calculate. In all machinery, a portion of the power which disappears is carried off by waves of condensation and expansion, along the supports of the machine, and through the surrounding air: this portion cannot be estimated, and is, of course, not operative in producing heat within the machine. It is also impossible to calculate, where friction is employed to produce heat, what amount of it has been lost in the production of electricity, a power which is, no doubt, convertible into heat, but which, in such experiments, pro- bably escapes without undergoing that conversion. To make the determination of the mechanical equivalent of heat by electro-magnetic experiments correct, it is necessary that the whole of the mechanical power should be converted into magnetic power, the whole of the magnetic power into what are called electric currents, and the whole of the power of the electric currents into heat, not one of which conditions is likely to be exactly fulfilled. Even in producing heat by the compression of air, it must not be assumed that the whole of the mechanical power is expended in raising the temperature. (3.) The best means of determining the mechanical equivalent of heat are furnished by those experiments in which no machinery is employed. Of this kind are experiments on the velocity of sound in air and other gases, which, according to the received and well-known theory of Lapuacg, is accelerated by the heat developed by the compression of the medium. The accuracy of this theory has lately been called in question. There can be no doubt that it deviates from absolute exactness, in so far that the magnitude of the displacements of the particles of air is neglected in comparison with the length of a wave. It appears to me, however, that the Astronomer-Royal, in his remarks on the subject in the London and Edinburgh Philosophical Magazine for July 1849, has shewn, in a satisfactory manner, that although the effect of the appreciable magnitude of those displacements, as compared with the length of a 158 MR W. J. M. RANKINE ON THE wave of sound, is to alter slowly the form of the function representing the wave, still that effect is not sufficiently great to make Lapuace’s theory practically erro- neous. I have, therefore, in the sequel, adhered to the experiments of DuLone, and to those quoted by Poisson, on the velocity of sound, as the best data for determining the mechanical equivalent of heat. (4.) The expression already given for the real specific heat of unity of weight of a given substance may be resolved into two factors, thus :— PQ INy Si 3kM dct) Onlin v2 ode The first factor, .—, ae may be considered in general as a known quantity; for C represents, as already stated, 274-6 centigrade degrees, the absolute temperature of melting ice, and 2 M the theoretical weight, in the perfectly gaseous state, of unity of volume of the substance, under unity of pressure, at that temperature ; or what is the same thing, = is the height of an imaginary column of the sub- stance, of uniform density, and at the temperature of melting ice, whose pressure by weight upon a given area of base is equal to its pressure by elasticity, sup- is neces- posing it to be perfectly gaseous. The determination of the ratio a fa sary, to complete the solution of the problem. (5.) The relation now to be investigated between heat and mechanical power, is that which exists between the power expended in compressing a body into a smaller volume, and the increase of heat in consequence of such a compression, and conversely, between the heat which disappears, or, as it is said, becomes latent, during the expansion of a body to a greater volume, and the mechanical power gained or developed by that expansion. Those phenomena, according to che hypothesis now under consideration, as well as every hypothesis which iscribes heat to motion, are simply the transformation of mechanical power from one shape into another. It is obvious, in the first place, without the aid of algebraical symbols, that the general effect of the compression of an oscillating atomic atmosphere, or molecular vortex, must be to accelerate its motion, and of its dilatation, to retard its motion; for every portion of such an atmosphere is urged towards the nucleus or atomic centre by a centripetal force equal to the centrifugal force arising from the oscillation; so that when, by compression, each portion of the atmosphere is made to approach the centre by a given distance, the vis viva of its motion will be increased by the amount corresponding to the centripetal force acting through that distance; and conversely, when by expansion each portion of the atmosphere is made to retreat from the centre, the vis viva of its motion will be diminished by a similar amount. It is not, however, to be taken for granted, that all the power expended in MECHANICAL ACTION OF HEAT. 159 compressing a body appears in the form of heat. More or less power may be consumed or developed by changes of molecular arrangement, or of the internal distribution of the density of the atomic atmospheres; and changes of molecular arrangement or distribution may develope or consume heat, independently of changes of volume. (6.) We shall now investigate, according to the Hepotiosis of molecular vortices, the amount of heat produced by an indefinitely small compression of one atom of a body in that state of perfect fluidity which admits of the bounding surface of the atom being treated as if it were spherical: its radius being denoted by R, and the radius of any internal spherical layer of the atmosphere by multi- plying R by a fraction w. I shall denote by the ordinary symbol of differentiation d, such changes as depend on the various positions of portions of the atomic atmosphere relatively to each other, when changes of volume and temperature are not taken into con- sideration; while by the symbol 6 of the calculus of variations, I shall represent such changes as arise from the variations of volume and temperature. Let us consider the case of an indefinitely thin spherical layer of the atomic atmosphere, whose distance from the nucleus is Rw, its thickness Rdw, its area 4m R?u?, and its density & D¥ (w, D, 7). The weight, then, of this layer is 47 RL Du? p(w, D, tT) du. Its velocity of oscillation is v, and having, in virtue of that velocity, a mean cen- trifugal force, as explained in the Introduction (Equation V.), equal to eh hed gkRue and 3-—=M is equal to =e oD Ou +QM. uw YD; T) a? (5 ~ 3") au. We must suppose that the velocity of oscillation is equalised throughout the atomic atmosphere, by a propagation of motion so rapid as to be practically instantaneous. Then if the above expression be integrated with respect to du, from w=0 to w=1, the result will give the whole increase of heat in the atom arising from the con- densation 6D; and dividing that integral by the atomic weight M, we shall obtain the corresponding development of heat in unity of weight. This is expressed by the following equation :— sq=207t Lif Daf 1 du . u? ) (u, D, 7) -3 [du vduy(ud.7)} Hs) RB) The letter Q/ is here introduced to denote, when negative, that heat which is consumed in producing changes of volume and of molecular arrangement, and when positive, as in the above equation, the heat which is produced by such changes. The following substitutions have to be made in Equation (1.) of this Section. For Q is to be substituted its value, according to Equation XII. of the Intro- duction ; or abbreviating C nd into «:— 3k san) B The value of the first integral in Equation (2.) of this Section is pt du . wb (u, D, ")=5 0 The value of the second integral -3f" du. udu (u, D, 7) | remains to be investigated. The first step in this inquiry is given by the condition, that whatsoever changes of magnitude a given spherical layer undergoes, the por- tion of atmosphere between it and the nucleus is invariable. This condition is expressed by the equation d d d VopwEs ST, = (dur +87 g-+8D a5) du.wb@D,7).... & from which it follows that bu=— reps (87 oy du. w(u, D, 7) MECHANICAL ACTION OF HEAT. 161 and consequently that -3f- au . udu (u,D,7)= d d 1du 5 +(d7. 5 + ODF) SF ais ‘e | du. wah (u, D, 7) Hence, making 1du se on es du.wWyuD7r)=U... 6) 0 The second integral in Equation (2.) is transformed into 1 d +3 (Orgy + OD zp) U- By means of those substitutions we obtain, for the mechanical value of the heat developed in unity of weight of a fluid by any indefinitely small change of volume or of molecular distribution— Se=gan (8D-(F +5) +875) dD or taking v=> to denote the volume of unity of weight of 6.) the substance, dees gaz (av (2-20) —ae80) tT—K OD T—K OV Cpl. DD. CaM. y., riation of heat arising from mere saree of volume. oi : al OV av = chi i spo! ap” U denotes the variation of heat produced by change of molecular distribution dependent on change of volume. oa spe’ expresses the variation of heat due to change of molecular dis- nM at tribution dependent on change of temperature. (7.) The function U is one depending on molecular forces, the nature of which is as yet unknown. The only case in which it can be calculated directly is that of a perfect gas. Without giving the details of the integration, it may be sufficient to state, that in this case Of this expression, represents the va- and therefore that Bide ob Daas) Gr, Ka anes aN In all other cases, however, the value of this function can be determined indirectly, by introducing into the investigation the principle of the conservation of vis viva. 162 MR W. J. M. RANKINE ON THE Suppose a portion of any substance, of the weight unity, to pass through a variety of changes of temperature and volume, and at length to be brought back to its primitive volume and temperature. Then the absolute quantity of heat in the substance, and the molecular arrangement and distribution, being the same as at first, the effect of their changes is eliminated ; and the algebraical sum of the vis viva expended and produced, whether in the shape of expansion and compression, or in that of heat, must be equal to zero :—that is to say, if, on the whole, any mechanical power has appeared, and been given out from the body, in the form of expansion, an equal amount must have been communicated to the body, and must have disappeared in the form of heat; and if any mechanical power has appeared and been given out from the body in the form of heat, an equal anount must have been communicated to the body, and must have disappeared in the form of compression. This principle expressed symbolically is ATS A = 0", oa eee fas Boe Where nu, when positive, represents expansive power given out, when negative, compressive power absorbed ; and Q/ represents, when positive, heat given out, when negative, heat absorbed. To take the simplest case possible, let the changes of temperature and of volume be supposed to be indefinitely small, and to occur during distinct intervals of time, so that 7 and V are independent variables. Let the initial absolute tem- perature be 7, the initial volume V, and the initial total elasticity P; and let the substance go through the following four changes. First, Let its temperature be raised from + to 7+67, the volume remaining unchanged. Then the quantity of heat absorbed is dQ t-K dU -$r (52-GoM ae) and there is no expansion nor compression. Secondly, Let the body expand, without change of temperature, from the volume V to the volume V+¢0V. Then the quantity of heat absorbed is 7+07T-—K/1 dU —8v ar (yay - 0+, 2) while the power given out by ae is oV(P = 8 T) Thirdly, Let the temperature fall from 7+67 to its original value 7, the volume V+06V continuing unchanged; then the heat given out is dQ TK +87(52- oe a7 OV) and there is no expansion nor compression. MECHANICAL ACTION OF HEAT. 163 Fourthly, Let the body be compressed, without change of temperature, to its original volume V; then the heat given out is 1 €&U a mv d cv) while the power absorbed in compression is = OV 12 The body being now restored in all respects to its primitive state, the sum of the two portions of power connected with change of volume, must, in virtue of the principle of vis viva, be equal to the sum of the four quantities of heat with their signs reversed. Those additions being made, and the sums divided by the common factor 6 V 67, the following equation is obtained :— dP 1 br dW, ae ee Ge The integral of this partial differential equation is U=¢.7+ fav (--Cum =) nasa 6106 Now ¢ .7 being the same for all densities, is the value of U for the perfectly gaseous state, or =3 for in that state, the integral = 0. The values of the partial differential coefficients are accordingly— COA | dP ayy MER ys ite (ia: dU K a FT eT COM av. aes and they can, therefore, be determined in all cases in which the quantity k=Cnypb, and the law of variation of the total elasticity with the volume and temperature are known, so as to complete the data required in order to apply equation 6 of this section to the calculation of the mechanical value of the varia- tions of heat due to changes of volume and molecular arrangement. The total elasticity of an imperfect gas, according to Equations VI. and XII. of the introduction, being T aa a (1-¥ (pz) ) + f(D) its first and second partial differential coefficients with respect to the tempera- ture are,— dP ar =tanv(1- (147 in) F (, i) d?P 1 d d? T GRE ae: at 7 a3) ¥ (D2) VOL. XX. PART I. ZX 164 MR W. J. M. RANKINE ON THE Consequently, for the imperfectly gaseous state, at roy (Gets F (0,7) bahle,) 102 8s (af sgh) fv 08 (8.) It is to be observed that the process nine in ascertaining the nature of the function U is analogous to that employed by M. Carnér in his theory of the motive power of heat, although founded on contrary principles, and leading to different results. Carnot, in fact, considers heat to be something of a peculiar kind, whether a condition or a substance, the total amount of which in nature is incapable of increase or of diminution. It is not, therefore, according to his theory, con- vertible into mechanical power; but is capable, by its transmission through substances under particular circumstances, of causing mechanical power to be developed. He supposes a body to go through certain changes of temperature and volume, and to return at last to its primitive volume and temperature, and con- ceives, in accordance with his view of the nature of heat, that it must have given out exactly the same quantity of heat that it has absorbed. The transmission of this heat he regards as the cause of the production of an amount of mechanical power, depending on the quantity of heat transmitted and on the temperature at which the transmission has taken place. According to these principles, a body, having received a certain quantity of heat, is capable of giving out not only all the heat it has received, but also a quantity of mechanical power which did not before exist. According to the theory of this Essay, on the contrary, and to every con- ceivable theory which regards heat as a modification of motion, no mechanical power can be given out in the shape of expansion unless the quantity of heat emitted by the body in returning to its primitive temperature and volume is less than the quantity of heat originally received: the excess of the latter quantity above the former disappearing as heat, to appear as expansive power, so that the sum of the vis viva in those two forms continues unchanged. MECHANICAL ACTION OF HEAT. 165 Section IJ.—Or Reat AND APPARENT SpEciIFIC HEAT, ESPECIALLY IN THE STATE oF PERFEcT GAs. (9.) The apparent specific heat of a given substance is found by adding to the real specific heat (or the heat which retains its form in producing an elevation of one degree of temperature in unity of weight) that additional heat which disap- pears in producing changes of volume and of molecular arrangement, and which is determined by reversing the sign of Q’ in equation 6 of Section I. (so as to transform it from heat evolved to heat absorbed), and taking its ¢ota/ differential coefficient with respect to the temperature. Hence, denoting total apparent spe- cific heat by K,— d.Q' dQ dQ dQ av a Sain. Sar aN ar = Gam) on * (gy av) az) | oO) Another mode of expressing this coefficient is the following :— . 2p Denote the ratio sau bY N, and the real specific heat by & Viere@k2) te 1 —CnMN Then GI jf lbs GH dU Kat {1+N-) (7 (7-Zy) ~ az) } 08) The value of = is to be determined from the conditions of each particular case; so that each substance may have a variety of apparent specific heats, accord- ing to the manner in which the volume varies with the temperature. If the volume is not permitted to vary, so that = = 0, there is obtained the following result, being the apparent specific heat at constant volume :— 1 1 dU Ky = ony (w -C- Zz) dU = (1-N (@-) 5—) ede) (10.) When the substance under consideration is a perfect gas, it has already been stated (Eq. 7), that au - > = = 0; and because the volume of unity of weight is directly as the absolute temperature and inversely as the pressure, ravi is 2 1dP ei a Bias ho oa ae 166 MR W. J. M. RANKINE ON THE Hence the following are the values of the apparent specific heats of unity of weight of a theoretically perfect gas under different circumstances :— General value of the total apparent specific heat :—_ K dV AL 1 : K= orm wt-0 (5 + yas) oe le wt (S+: GP } omen ri eS Apparent specific heat at constant volume :— 1 { i Doge s «} K,=———. Sa = No ors? (18.)- Apparent specific heat under constant pressure :— 1 1 K? = ona (x 1-2) K?2 The ratio of the apparent specific heat under constant pressure to the appa- rent specific heat at constant volume is the following :— 2 1in(i-% foes LF fs (19.) The value of « is unknown; and, as yet, no experimental data exist from which it can be determined. I have found, however, that practically, results of sufficient accuracy are obtained by regarding x as so small in comparison with 7, 2 that ~, and a jortiort _ may be neglected in calculation. Thus are obtained the following approximate results, for perfect gases, and gases which may without material error be treated as perfect. General value of the total apparent specific heat :— 1 tT aed dV K= cau (nty ar) =#+P a alee (5 1 TadP = OnM\N* -375) Apparent specific heat at constant volume :— (20.) i ; a> Oa being equal to the real specific heat. Apparent specific heat under constant pressure :— ey? = oom (x i 1) —% (1+N) MECHANICAL ACTION OF HEAT. 167 Ratio of those two specific heats :— z = Toni Ce ON) This ratio is the quantity called by Porsson ¥, in his researches on the pro- pagation of sound. (11.) It is unnecessary to do more than to refer to the researches of Porsson, and to those of Lariace, for the proof that the effect of the production of heat by the compression of air is the same as if the elasticity varied in proportion to that power of the density whose index is the ratio of the two specific heats; so that the actual velocity of sound is greater than that which it would have if there were no such development of heat, in the proportion of the square root of that ratio. The following is the value of the velocity of sound in a gas, as given by Poisson, in the second volume of his T7aité de Mécanique :— a= Jy. 7. + E1)™ Pn Pere ‘where a denotes the velocity of sound, g the velocity generated by gravity in unity of time, E the coefficient of increase of elasticity with temperature, at the freezing point of water, T the temperature measured from that point, m the spe- cific gravity of mercury, 4 that of the gas at the temperature of melting ice, and pressure corresponding to a column of mercury of the height 2. It follows that the ratio y is given by the formula a* A gmhdsET «°° (23) Calculations have been made to determine the ratio y from the velocity of sound; but as many of them involve erroneous values of the coefficient of elasti- city E, the experiments have to be reduced anew. The following calculation is founded on an experiment quoted by Poisson on the velocity of sound in atmospheric air, the values of E, m, and a being taken from the experiments of M. REGNAULT. a = 340-89 metres per second. g = 980896. h = 0™-76. T = 15°-9 Centigrade. E = 0:003665; = = 0519: y=1+N nearly = Consequently, for atmospheric air, ry = 1-401. The results of a reduction, according to correct data, of the experiments of DvuLoneG upon the velocity of sound in atmospheric air, oxygen, and hydrogen, are as follows :— Atmospheric air, : : : : y = 1-410 Oxygen, ; : F p : ‘ : 1-426 Hydrogen, . : : - ; : : 1426 ViOlAOOXL PART 1, ZY 168 MR W. J. M. RANKINE ON THE Thus it appears, that for the simple substances, oxygen and hydrogen, the ratio N is the same, while for atmospheric air it is somewhat smaller.* (12.) The ordinary mode of expressing the specific heats of gases is to state their ratios to that of an equal volume of atmospheric air at the same ghee and temperature. When “ is a very small fraction, specific heats of wnity of volume of a perfect gas are given by the equations nM Ky=oy | (24.) nMK= 5 (y+), | That is to say, the specific heat of unity of volume at constant volume is inversely proportional to the fraction by which the ratio of the two specific heats exceeds unity; a conclusion already deduced from experiment by Dutone. The following is a comparison of the ratios of the apparent specific heats under constant pressure, of unity of volume of oxygen and hydrogen respectively, to that of atmospheric air, as deduced from Equation (24.), with those determined experimentally by Dr 1a Rocue and Berarp. ; nM K, (Gas gare ie Roan Gas. By Theory. By Experiment. Oxygen, . é ' : 0-973 0:9765 Hydrogen, . ; : : 0:973 0:9033 This comparison exhibits a much more close agreement between theory and expe- riment than has been hitherto supposed to exist, the errors in the constants employed having had the effect of making the ratio 1+ N seem greater for atmo- spheric air than for oxygen and hydrogen, while in fact it is smaller. To treat the other substances on which both M. Dutone and MM. De 1a * The following are some additional determinations of the value of y for atmospheric air, founded upon experiments on the velocity of sound :-— T a x Observers. Centigrade. Métres per second. Bravais and Martins: mean of several experiments at temperatures varying from 5° to 11° centigrade, 0° 332°37 1-40955 reduced to 0° (Comptes Rendus, xix.) Moll and Van Beek: reduced to : : . 0° 332°25 1°40853 pti and Myrbach : reduced to 0° (not corr eeea } 0° 339-96 1:41456 or moisture) 5 : : Académie des Sciences, 1738: ach corrected for } 6°1 337-10 1-418 moisture) : . : A variation of c one métre per second in the velocity of sound at 0° corresponds to a variation of 0085 in the value of y. ; MECHANICAL ACTION OF HEAT. 169 RocuE and Brrarp made experiments as perfect gases, would lead to sensible errors. I have, therefore, confined my calculations for the present to oxygen, hydrogen, and atmospheric air. (13.) The heat produced by compressing so much of a perfect gas as would occupy unity of volume under the pressure unity, at the temperature 0° centigrade, . as . . . : : from its actual volume x MV, =; into a volume which is less in a given ratio s (when « is neglected as compared with 7), is expressed by the following motion :— nMQ=-— Suna yao aMy, ["Pas Men Yo 1 1 being, in fact, equal to the mechanical power used in the compression. When the temperature is maintained constant, this becomes T C o a log, os aMQ = (26.) which is obviously independent of the nature of the gas. Hence equal volumes of all substances in the state of perfect gas, at the same pressure and at equal and constant temperatures, being compressed by the same amount, disengage equal quantities of heat; a law already deduced from experi- ment by DuLone. (14.) The determination of the fraction N affords the means of calculating the mechanical or absolute value of specific heat, as defined by Equation 1, Sec- tion First. The data for atmospheric air being taken as follows :— Ne 0-4, C = 274°6 centigrade, = = height of an imaginary column of air of uniform density, at the tempera- ture 0° cent., whose pressure by weight on a given base is equal to its pressure by elasticity, . . . . =7990 métres, =26214 feet :— the real specific heat of atmospheric air, or the depth of fall equivalent to one centigrade degree of temperature in that gas, is found to be i 1 ~ Cra MN The apparent specific heat of atmospheric air, under constant pressure, according to Dr na Rocue and Berarp, is equal to that of liquid water at 0° centigrade x 0:2669. The ratio of its real specific heat to the apparent specific heat of water at 0° centigrade, is, therefore, 10 2669 x Ti 1906, K =72°74 métres=238'66 feet . . . (27.) And, consequently, the mechanical value of the apparent specific heat of liquid water, at the temperature of melting ice, is 170 MR W. J. M. RANKINE ON THE & Gt alt) 381-64 métres=1252 feet per centigrade ae 28. or 6956 feet per degree of Fahrenheit’s scale, er This quantity we shall denote by K,,._ It is the mechanical equivalent of the ordinary thermal unit. I have already pointed out (in Article 2. of the First Section) the causes which tend to make the apparent value of the mechanical equivalent of heat, in Mr Joutn’s experiments, greater than the true value. The differences between the result I have just stated, and those at which he has arrived, do not seem greater than those causes are capable of producing, when combined with the un- certainty of experiments, like those of Mr JouLE, on extremely small variations of temperature. (15.) Besides the conditions of constant volume and constant pressure, there is a third condition in which it is of importance to know the apparent specific heat of an elastic fluid, namely, the condition of vapour at saturation, or in con- tact with its liquid. The apparent specific heat of a vapour at saturation, is the quantity of heat which unity of weight of that vapour receives or gives out, while its temperature is increased by one degree, its volume being at the same time compressed so as to bring it to the maximum pressure corresponding to the increased temperature. It has been usually taken for granted, that this quantity is the same with the variation for one degree of temperature, of what is called the total heat of evapor- ation. Such is, indeed, the case according to the theory of Carnot; but I shall shew that, according to the mechanical theory of heat, these two quantities are not only distinct, but in general of contrary signs. I shall, for the present, consider such vapours only as may be treated in prac- tice as perfect gases, so as to make the first of the Equations (20.) applicable. Tt has been shewn that the logarithm of the maximum elasticity of a vapour in contact with its liquid may be represented by the expression log Pag The coefficients a, G, y, being those adapted for calculating the common loga- rithm of the pressure, I shall use the accented letters a’, @’, y, to denote those suited to calculate the hyperbolic logarithm, being equal respectively to the for- mer coefficients x 2°3025851." Then for vapour at saturation, ae a = A 2 5 (29.) Making this substitution in the general Equation (21.), we find the following value for the apparent specific heat of perfectly gaseous vapour at saturation :— MECHANICAL ACTION OF HEAT. Pet : K,=k+P oY (Q+N. £ <) d Vi dt 7 aP i mae ve hal ef. .2730° {1+N(1 EB zz) } (30.) ieee / 1 Bo 2+ =oau wt) (16.) For the vapours of which the properties are known, the negative terms of this expression exceed the positive at all ordinary temperatures, so that the kind of apparent specific heat now under consideration is a negative quantity :— that is to say, that if a given weight of vapour at saturation is increased in tem- perature, and at the same time maintained by compression at the maximum elas- ticity, the heat generated by the compression is greater than that which is required to produce the elevation of temperature, and a surplus of heat is given out; and on the other hand, if vapour at saturation is allowed to expand, and at the same time maintained at the temperature of saturation, the heat which disappears in producing the expansion is greater than that set free by the fall of temperature, and the deficiency of heat must be supplied from without, otherimise a portion of the vapour will be liquefied, in order to supply the heat necessary for the expansion of the rest. This circumstance is obviously of great importance in meteorology, and in the theory of the steam-engine. There is as yet no experimental proof of it. It is true, that, in the working of non-condensing engines, it has been found that the steam which escapes is always at the temperature of saturation corresponding to its pressure, and carries along with it a portion of water in the liquid state; but it is impossible to distinguish between the water which has been liquefied by the expansion of the steam, and that which has been carried over mechanically from the boiler. The calculation of the proportion of vapour liquefied by a given expansion, requires the knowledge of the latent heat of evaporation, which forms the subject of the next section. Section [1J.—Or tue Latent anp Tota HEAT or EvAPoRATION, ESPECIALLY FOR WATER. (17.) The latent heat of evaporation of a given substance at a given tempe- rature, is the amount of heat which disappears in transforming unity of weight of the substance from the liquid state, to that of vapour of the maximum density ' for the given temperature, being consumed in producing an increase of volume, and an unknown change of molecular arrangement. It is obvious, that if the vapour thus produced is reconverted into the liquid state at the same temperature, the heat given out during the liquefaction must be VOL. XX. PART I. 22 172 MR W. J. M. RANKINE ON THE equal to that consumed during the evaporation; for as the sum of the expansive and compressive powers, and of those dependent on molecular arrangement during the whole process, is equal to zero, so must the sum of the quantities of heat absorbed and evolved. The heat of liquefaction, at a given temperature, is therefore equal to that of evaporation, with the sign reversed. (18.) If to the latent heat of evaporation at a given temperature, is added the quantity of heat necessary to raise unity of weight of the liquid from a certain fixed temperature (usually that of melting ice) to the temperature at which the evaporation takes place, the result is called the total heat of evaporation from the fixed temperature chosen. According to the theory of Carnot, this quantity is called the constituent heat of vapour ; and it is conceived, that if liquid at the temperature of melting ice be raised to any temperature and evaporated, and finally brought in the state of vapour to a certain given temperature, the whole heat expended will be equal to the constituent heat corresponding to that given temperature, and will be the same, whatsoever may have been the intermediate changes of volume, or the tem- perature of actual evaporation. According to the mechanical theory of heat, on the other hand, the quantity of heat expended must vary with the intermediate circumstances ; for otherwise no power could be gained by the alternate evaporation and liquefaction of a fluid at different temperatures. (19.) The law of the latent and total heat of evaporation is immediately deducible from the principle of the constancy of the total vs viva in the two forms of heat and expansive power, when the body has returned to its primitive density and temperature, as already laid down in Article 7. That principle, when applied to evaporation and liquefaction, may be stated as follows :— Let a portion of fluid in the liquid state be raised from a certain temperature to a higher temperature: let it be evaporated at the higher temperature: let the vapour then be allowed to expand, being maintained always at the temperature of saturation for its density, until it is restored to the original temperature, at which temperature let it be liquefied :—then the excess of the heat absorbed by the fluid above the heat given out, will be equal to the expansive power generated. To represent those operations algebraically,—let the lower absolute tempe- rature be r, :—the volume of unity of weight of liquid at that temperature, v,, and that of vapour at saturation, V,: let the pressure of that vapour be P,: the latent heat of evaporation of unity of weight, L,; and let the corresponding quantities for the higher absolute temperature 7,, be v,, V,, P,, L,. Let K, represent the mean apparent specific heat of the substance in the liquid form between the tem- peratures 7, and 7,. Then,— MECHANICAL ACTION OF HEAT. Iba First, Unity of weight of liquid being raised from the temperature 7, to the temperature 7,, absorbs the heat, Ky, (7,—7)) and produces the expansive power, v *dv.P % Secondly, It is evaporated at the temperature r,, absorbing the heat | te and producing the expansive power, P, (V,—%) Thirdly, The vapour expands, at saturation, until it is restored to the origi- nal temperature 7. In this process it absorbs the heat, Ty -f/ Figina T 9 and produces the expansive power, Vv) se ave Vv, Fourthly, Xt is liquefied at the original temperature, giving out the heat L, and consuming the compressive power, Py (Vo—%): The equation between the heat which has disappeared, and the expansive power which has been produced, is as follows :— if L,-y+K, (4 -7))—[ Meh K, a ie (31.) =P, (V,-4)—P,(Vi—a) + fay P+ Ha all 0 . 1 If the vapour be such that it can be regarded as a perfect gas without sen- sible error, the substitution of k+ Boe for K,, and of oi =k N + for PV, trans- forms the above to L,—L, + {K,—k 1+N)} (7,—7,) | 0 Jey mete wees . (82.) 2 —P, 0, + Pi H+ dv.P=— aP.» : U P, In almost all cases which occur in practice, v is so small as compared with V, that —far .» may be considered as sensibly = 0; and therefore (sensibly) L, + K,(7,-—7)=L, + #(1+N)(7,-—7,)- . - (83.) 174 MR W. J. M. RANKINE ON THE Now this quantity, which I shall denote by H, is the total heat required to raise unity of weight of liquid from +, to 7, of absolute temperature, and to evapo- rate it at the latter temperature. Therefore the total heat of evaporation, where the vapour may be treated as a perfect gas, increases sensibly at an uniform rate with the temperature of evaporation ; and the coefficient of its increase with temperature is equal to the apparent specific heat of the vapour at constant pressure, & (1+N). (20.) There have never been any experiments from which the apparent spe- cific heat of steam under constant pressure can be deduced in the manner in which that of permanent gases has been ascertained. The experiments of M. Reanautt, however, prove that the total heat of evaporation of water increases uniformly with the temperature from 0° to 200° centigrade, and thus far fully confirm the results of this theory. The coefficient of increase is equal to Ky, x 0°305 Its mechanical value is consequently (34.) 116-4 metres=382 feet per centigrade degree, or 212 feet per degree of Fahrenheit. Although the principle of the conservation of vis viva has thus enabled us to ascertain the law of increase of the total heat of evaporation, it does not enable us to calculate @ priori the constant L, of the formula, being the latent heat of eva- poration at the fixed temperature from which the total heat is measured; for the changes of molecular arrangement which constitute evaporation are unknown. When the fixed temperature is that of melting ice, M. REGNAULT’s experi- ments give 606°5 centigrade degrees, applied to liquid water as the value of this constant; so that H=K,, (606°-5 + 305 T°) } For the centigrade scale, (35.) H=K,, (1091°7 +-305 (T°—32°) ) J For Fahrenheit’s scale. is the complete expression for the heat required to raise unity of weight of water from the temperature of melting ice to T’ above the ordinary zero, and to evapo- rate it at the latter temperature. This formula has been given by M. ReGnaut as merely empirical; but we have seen that it closely represents the physical law, when quantities depending on the expansion of water are neglected. It must be remarked, that the unit of heat in M. REGNAvLT’s tables is not precisely the specific heat of water at 0° centigrade, but its mean specific heat between the initial and final temperatures of the water in the calorimeter. The utmost error, however, which can arise from this circumstance, is less than 3459 of the total heat of evaporation, so that it may safely be neglected. MECHANICAL ACTION OF HEAT. 175 The coefficient -305 K,,=382 feet per centigrade degree is the apparent specific heat of steam at constant pressure; that is to say, for steam,— 1 \ K+ CnM = 882 feet per centigrade degree, 1 Therefore the real specific heat of steam is 1 ee er ee Oe) Cn MN 279 feet per centigrade degree, =127-4 feet per deg. of Fahrenheit, =K,, x 183 L5SdHan 42 i The quantity — Ss Hi dP . v has been neglected, as already explained, in these , calculations, on account of its smallness. When 7,=6, or the fixed point is 0° centigrade, this integral is nearly equal to ee er eae ae oP - ogy EN yn: + + OD) which, for steam, is equal to v = Ky x 12255 7, For a pressure of eight atmospheres, v= 053 nearly, t,=445°5 (T=170°9 cent.) consequently, —v P,=—K,, x 0°22 cent. a quantity much less than the limit of errors of observation in experiments on latent heat. This shews that in practice we are justified in overlooking the influence of the volume of the liquid water on the heat of evaporation. Section 1V.—Or THE MrEcHANICAL ACTION OF STEAM, TREATED AS A PERFECT Gas, AND THE POWER OF THE STEAM-ENGINE. x (21.) In the present limited state of our experimental knowledge of the den- sity of steam at pressures differing much from that of the atmosphere, it is desir- able to ascertain whether any material error is likely to arise from treating it as a perfect gas. For this purpose the ratio of the volume of steam at 100° centi- grade, under the pressure of one atmosphere, to that of the water which produces it at 4°-1 centigrade, as calculated theoretically on the supposition of steam being a perfect gas, is to be compared with the actual ratio. VOL. XX. PART I. 3A 176 MR W. J. M. RANKINE ON THE The weight of one volume of water at 4°:1 centigrade being taken as unity, that of half a volume of oxygen at 0° centigrade, under the pressure of one atmo- sphere, according to the experiments of M. ReGNAULT, is 0-000714900 That of one volume of hydrogen, . ; : ; 0-:000089578 The sum being ; ‘ : é 4 ; 0000804478 a. aad 3746 Li ae The reciprocal of this sum being multiplied by 5774 = 1364166 the ratio of dilatation of a perfect gas from 0° to 100° centigrade) the result gives, for the volume of steam of saturation at 100° centigrade as compared with that of water at Ave : : : : : 1695°72 And for its density, : ; 0:00058972 The agreement of those results with the known volume and density of steam is sufficiently close to shew, that at pressures less than one atmosphere, it may be regarded as a gas sensibly perfect; from which it may be concluded, that in the absence of more precise data, the errors arising from treating it as a perfect gas at such higher pressures as occur in practice, will not be of much importance. Representing, then, by v the volume of unity of weight of water at 4-1 cen- tigrade, that of unity of weight of steam at any pressure and temperature will be given by the formula 1696 va oT vey pe eB) a representing the number of units of weight per unit of area in the pressure of one atmosphere, and (r) the absolute temperature at which the pressure of satura- tion is one atmosphere; being for the centigrade scale 374'-6, and for Fahren- heit’s scale 674-28. The mechanical action of unity of weight of steam at the temperature 7 and pressure P, during its entrance into a cylinder, before it is permitted to expand, is represented by the product of its pressure and volume, or by Bye ee (7) : 1696 vw . The coefficient waGEEA represents a certain depth of fall per degree of abso- lute temperature, and is the same with the coefficient = already referred to. By taking the following values of the factors :— v=0-016 cubic foot per pound avoirdupois, @ =2117 pounds avoirdupois per square foot, we find this coefficient to be 153°35 feet=46'74 métres per centigrade degree, \ 40. 85°19 feet per degree of Fahrenheit ; al MECHANICAL ACTION OF HEAT. 177 this determination may be considered correct to about z395 part. When French measures are used in the calculation, the following is the result :— v=1 cubic centimetre per gramme, @=1033'3 grammes per square centimetre, 1 < : On Ma 46-78 metres per centigrade degree, =153-48 feet ewe ur, (AL) or 85:27 feet per degree of Fahrenheit. The difference, which is of no practical importance in calculating the power of the steam-engine, arises in the estimation of the density of liquid. water. (22.) Unit of weight of steam at saturation, of the elasticity P, and volume V, corresponding to the absolute temperature 7,, being cut off from external sources of heat, it is now to be investigated what amount of power it will produce in expanding to a lower pressure P, and temperature r.,,. It has already been shewn. at the end of the second section, that if vapour at saturation is allowed to expand, it requires a supply of heat from without to main- tain it at the temperature of saturation, otherwise a portion of it must be liquefied to supply the heat required to expand the rest. Hence, when unity of weight of steam at saturation, at the pressure P, and volume V,, expands to a lower pressure P, being cut off from external sources of heat, it will not occupy the entire volume V corresponding to that pressure, according to Equation (38.), but a less volume S=mV, where m represents the weight of water remaining in the gaseous state, the por- tion 1—%m having been liquefied during the expansion of the remainder. The expansive action of the steam will therefore be represented by wile aes SS api . 1 The law of variation of the fraction m flows from the following considera- tions :— Let 6 m represent the indefinitely small variation of m corresponding to the indefinitely small change of temperature 7; L, the latent heat of evaporation of unity of weight ; K,, as in Equation (30.), the specific heat of vapour at satura- tion, which is a negative coefficient varying with the temperature; then we must have —Lom=mK,67r, or om _ 12a 6 m L in order that the heat produced by the liquefaction of dm may be equal to the heat required to expand m. Hence making, according to Equation (30.)— K, d7=8 (O+N— OV) 178 MR W. J. M. RANKINE ON THE iL Bf ee a eo we obtain , m Kr il V m- Sagat: Q+y V (43.) hi oalseiie ; : OV and denoting the coefficient of — by —», dlogm_ _ .dlogS _, dlog Vi... ? dlogV +H! bd tony. 1 and because nies Bo, gee Th dlogm _ Sent (1 1 (44.) dlog P ~ eB aa TT T dlog S 1 oe) ee eee) ee d log P ( ( tac = pie As the mean temperature of the liquid thus produced more or less exceeds that of the remaining vapour, a small fraction of it will be reconverted into vapour, if the expansion is carried on slowly enough; but its amount is so small, that to take it into account would needlessly complicate the calculation, without making it to any material extent more accurate. (23.) The extreme complexity of the exponent oc, considered as a function of the pressure P, would render a general formula for the expansive action / Pd S very cumbrous in its application. For practical purposes, it is sufficient to consider the exponent ¢ as constant during the expansion which takes place in any given engine, assigning it an average value suitable to the part of the scale of pressures in which the expansion takes place. For engines in which the steam is intro- duced at pressures not exceeding four atmospheres, I conceive that it will be suffi- ciently accurate to make c= are while for engines in which the initial pressure lies between four and eight atmo- spheres, the suitable value is are The utmost error which can arise from using these exponents is about 749 of the whole power of the engine, and that only in extreme cases. Making, therefore, 1 Sa eie p=, (+) MECHANICAL ACTION OF HEAT. 179 we obtain for the value of the expansive action of unity of weight of steam, 1 S, c Sey nea a8. P=P,V,;77(1- (=) ) Ss, 2a LE eee 45) i —— Lp yi me(- ‘) = s being used to denote es or the ratio of the volumes occupied by steam at the 1 end and at the beginning of the expansion respectively. A table to facilitate the computation is given in the Appendix. The gross mechanical action of unity of weight of steam on one side of the piston is found by adding to the above quantity the action of the steam before it begins to expand, or P, V,, and is therefore a 1 Gane PV, (a-G F °) ‘any nedig) The values of the coefficients and exponent being 1 o eo 1 1l-o 1—¢ o For initial pressures between 1 and 4 atmospheres, . : : : 7 6 =; - 4and 8 atmospheres, . Z f 3 6 5 =: (24.) The following deductions have to be made from the gross action, in order to obtain the action effective in overcoming resistance. First, For loss of power owing to a portion of the steam being employed in filling steam-passages, and the space called the clearance of the cylinder at one end. Let the bulk of steam so employed be the fraction cS, of the space filled by steam at the end of the expansion ; then the loss of power from this cause is P,cS,=csP, Vy. Secondly, For the pressure on the opposite side of the piston, of the steam which escapes into the condenser, or into the atmosphere, as the case may be. Let P, be the pressure of this steam; the deduction to be made for its action is P, S, (1—c)=P, V, (1—c)s. These deductions having been made, there is obtained for the effect of unity of weight of water evaporated, Vv, {Pi (pile yr ac08s) ai (1-2) «} ol 47) (25.) The effect of the engine in unity of time is found by multiplying the VOL. XX. PART I. 3B 180 MR W. J. M. RANKINE ON THE above quantity by the number of units of weight of water evaporated in unity of time. If this number be denoted by W, WS, (l—c)=WV, (1-c)s=Au .. . (48) will represent the cubical space traversed by the piston in unity of time, A denot- ing the area of the piston, and w its mean velocity. Now let the whole resistance to be overcome by the engine be reduced by the principles of statics to a certain equivalent pressure per unit of area of piston, and let this pressure be denoted by R. Then, RA wR WV, (ela. so ao) expresses the effect of the engine in terms of the gross resistance. We have now the means of calculating the circumstances attending the work- ing of a steam-engine according to the principle of the conservation of vis viva, or, in other words, of the equality of power and effect, which regulates the action of all machines that move with an uniform or periodical velocity. This principle was first applied to the steam-engine by the Count pe Pam- Bour; and accordingly, the formulee which I am about to give only differ from those of his work in the expressions for the maximum pressure at a given tempe- rature, and for the expansive action of the steam, which are results peculiar to the theory of this essay. In the first place, the effect, as expressed in terms of the pressure, is to be equated to the effect as expressed in terms of the resistance, as follows :— 1 RAw=RWV,(1—c)s=WV, +P ieee ae seal ec — P,(1-c)s . a ee 1: 1 i\Pagnie- 3 This is the fundamental equation of the action of the steam-engine, and corresponds with Equation A. of M. pz Pamgour’s theory. (26.) Dividing both sides of Equation (50.) by the space traversed by the piston in unity of time W V, (1—c) s, and transferring the pressure of the waste steam, P.,, to the first side, we obtain this equation :— 1 ¢ +e 1267 16 fo Se (l—c)s BaP .= 2, vi (Ons) which gives the means of determining the pressure P, at which the steam must enter the cylinder, in order to overcome a given resistance and counter-pressure with a given expansion; or supposing the expansion s to be variable at pleasure, and the initial pressure P, fixed, the equation gives the means of finding, by approximation, the expansion best adapted to overcome a given resistance and counter-pressure. The next step is to determine, from Equations XV. of the Introduction and. MECHANICAL ACTION OF HEAT. 181 (33.) of this section, the volume V, of unity of weight of steam corresponding to the maximum pressure P,. Then Equation (48.) gives the space traversed by the piston in unity of time, which, being multiplied by the resistance R per unit of area of piston, gives the gross effect of the engine. (27.) If, on the other hand, the space traversed by the piston in unity of time is fixed, Equation (48.) gives the means of determining, from the evaporating power of the boiler W, either the volume V, of unity of weight of steam required to work the engine at the given velocity with a given expansion, or the expansion $ proper to enable steam of a given initial density to work the engine at the given velocity. The initial pressure P, being then determined from the volume V,, the resistance which the engine is capable of overcoming with the given velocity is to be calculated by means of Equation (51.) (28.) This calculation involves the determination of the pressure P, from the volume V, of unity of weight of steam at saturation, which can only be done by approximation. The following formula will be found useful for this purpose :— 12 Peo ) Pah T aa Boy where @ represents the pressure of one atmosphere, V, the volume of steam of saturation at that pressure (being 1696 times the volume of water at 4°:1 cent., or 27:136 cubic feet per pound avoirdupois), and V, the volume of steam of satu- ration at the pressure P,. This formula is only applicable between the pressures of one and eight atmospheres: that is to say, when the volume of steam is not greater than 27 cubic feet per pound, nor less than 4, and the temperature not lower than 100° centigrade, nor higher than 171° centigrade (which correspond to 212° and 340° Fahrenheit). The greatest error in computing the pressure by means of this formula is about #5 of an atmosphere, and occurs at the pressure of four atmospheres, so that it is 3} of the whole pressure. This is sufficiently accurate for practice, in calculating the power of steam-engines; but should a more accurate result be required, the approximate value of the pressure may be used to calculate the temperature by means of Equation XV.; and the temperature thus determined (which will be correct to. 3 of a centigrade degree) may then be used in conjunc- tion with the volume to compute a corrected value of the pressure, according to Equation (38.) The pressure, as thus ascertained, will be correct to 3999 of its amount, which may be considered the greatest degree of accuracy attainable. The most convenient and expeditious mode, however, of computing the pres- sure from the volume, or vice versd, is by interpolation from the table given in the Appendix to this paper. (29.) The resistance denoted by R may be divided into two parts; that which arises from the useful work performed, and that which is independent of it, being, 182 MR W. J. M. RANKINE ON THE in fact, the resistance of the engine when unloaded. Now it is evident, that the maximum useful effect of the steam has been attained, as soon as it has expanded to a pressure which is in equilibrio with the pressure of the waste steam added to the resistance of the engine when unloaded; for any further expansion, though increasing the total effect, diminishes the useful effect. Therefore if we make R=R +f, R’ being the resistance arising from the useful work, and / the resistance of the engine when unloaded, both expressed in the form of pressure on the piston, the expansion corresponding to the maximum of useful effect will take place when P,=P34+/ the corresponding ratio of expansion being aie ey ee ae ( ae The maximum useful effect with a given pressure on the safety-valve has been so fully discussed by M. pe Pamsour, that it is unnecessary to do more than to state that it takes place when the initial pressure in the cylinder is equal to that at the safety-valve: that is to say, when it and the useful resistance are the greatest that the safety-valve will permit. (30.) Annexed is a table of the values of some of the quantities which enter into the preceding equations in the notation of the Count pE PamsBour’s works. Expression in the Notation Equivalent Expression in of this paper. M. DE PamMBouR’s Notation. RoR ad ly cag en: (1+0)r4f Au : : , : av W ‘ “ 2 . Sx weight of one cubic foot of water. Jes 4 : : : Pp I+e $ : . . . Tie Ute c c . . ° ° == U+e (31.) As an illustration, I shall calculate the maximum useful effect of one pound, and of one cubic foot of water, in a Cornish double-acting engine, in the circumstances taken by M. pE Pamsour as an example for that kind of engine: that is to say,— t Clearance one-twentieth of the stroke, or c=5 72 lb. per square foot. 576 lb. ve os Resistance not depending on the useful load, Pressure of condensation, i= Pye MECHANICAL ACTION OF HEAT. 183 Consequently to give the maximum useful effect, Py= Py +f = 648 lb. per square foot. Total pressure of the steam when Ad admitted, P,=7200 lb. “ Volume of 1 |b. of steam V, =8°7825 cubic feet. Therefore P, V, =63234 lbs. raised one foot. Pie (200 P. = Gis and consequently, 6 Expansion to produce the maximum useful effect s= (=) 7 On th 2 Space traversed by the piston during the action of one pound of steam, =V, (1—c) s=65°886 cubic feet. Gross effect of one pound of steam, in pounds raised one foot high, =P,V, (7-608 -7) -P,V,d-os . . = 112004 Deduct for resistance of engine when unloaded fV,(1—c)s = 4744 Effect of one pound of steam in Syereomine resistance mer 107260 on useful load, : : This being multiplied by 623, gives for the effect of one cubic foot of water evaporated, in pounds raised one foot, ‘ F ; 4 6,703,750 It is here necessary to observe, that M. pp Pampour distinguishes the useful resistance into two parts, the resistance of the useful load independently of the engine, and the increase in the resistance of the engine, arising from the former resistance, and found by multiplying it by a constant fraction which he calls 0. In calculating the net useful effect, he takes into account the former portion of the resistance only ; consequently, Net useful effect as defined by M. DE PAMBOUR = Grass oe y pe?) sy dh (54.) The value of 6, for double acting steam-engines generally, is considered by M. DE Pamsour to be 4; consequently, to reduce the effect of one cubic foot of water as calculated nite to that which corresponds with his definition, we must deduct i, which leaves, 5,865,781 lb. raised one foot: M. DE PamBour’s own calculation gives, 6,277,560 being too large by about one-fifteenth. (32.) In order to shew the limit of the effect which may be expected from the expenditure of a given quantity of heat in evaporating water, and also to verify the approximate method employed in calculating the expansive action of the steam, I shall now investigate the maximum gross effect, including resistance of all kinds, producible by evaporating unity of weight of water at a higher tem- perature and liquefying it at a lower, and compare, in two examples, the power produced, with the heat which disappears during the action of the steam, as calculated directly. VOL. XX. PART I. onG 184 MR W. J. M. RANKINE ON THE To obtain the maximum gross effect, the steam must continue to act expan- sively until it reaches the pressure of condensation, so that P,=P,. The clear- ance must also be null, or c=0. Making those substitutions in the formula (47.), we find, for the maximum gross effect of unity of weight of water, evaporated under the pressure P, and liquefied under the pressure P,, EE l-o 1 ( hs) vs (52) Pipes l-—s o == a Vi a ae oe a . (55.) In order to calculate directly the heat which is converted into power in this operation, let r,, 7,, respectively represent the absolute temperatures of evapora- tion and liquefaction, and L, the latent heat of evaporation at the lower tempera- ture 7,; then the total heat of evaporation at 7,, starting from 7, as the fixed point, by Equation (33.), is H,, ,=L, +°305 Ky (r,—7,). This is the heat communicated to the water in raising it from 7, to 7, and evapo- rating it. Now a weight 1—m of the steam is liquefied during the expansion at temperatures varying from 7, to 7,, so that it may be looked upon as forming a mass of liquid water approximately at the mean temperature a5, and from which a quantity of heat, approximately represented by Ky (1—m) aS at must be abstracted, to reduce it to the primitive temperature r,. Finally, the weight of steam remaining, m, has to be liquefied at the tem- perature r,, by the abstraction of the heat m Ly. The difference between the heat given to the water, and the heat abstracted from it, or 7,—T,; H,, , —Ky (l—m) — mL, (56.) =(1-m) Ly +Ky (:805-75") (7,-7) is the heat which has disappeared, and ought to agree with the expression (55.) for the power produced, if the calculation has been conducted correctly. . As a first example, I shall suppose unity of weight of water to be evaporated under the pressure of four atmospheres, and liquefied under that of half an atmo- sphere; so that the proper values of the coefficients and exponent are 1 : 1 == a l-o =H MECHANICAL ACTION OF HEAT. 185 The data in this case for calculating the power, are, P, = 8468 lb. per square foot. V,=7584 cubic feet for one lb. of steam. P, V,=64221 Ib. raised one foot. P, rod rah er p =g Whence s=8 = 5944. Maximum possible effect of one pound of water, SB Vin X & (1 = (3) 7) =115600 lb. raised one foot. Being the mechanical equivalent of 92°:3 centigrade degrees applied to one pound of liquid water at 0° C. ; or, 92°-3 K,, Maximum possible effect of one cubic foot of water, 7,225,000 lb. raised one foot. In order to calculate directly the heat converted into power, we have, T,=C+144"1 cent. 7, =C+81°7 L,=549°7 Ky H,, ,=568°-7 K,, = heat expended in the boiler. ; 1—m='14 nearly = proportion of steam liquefied during the expansion. The heat converted into mechanical power, as calculated from these data, is found to be, JL OK, differing by only 0°:7 from the amount as calculated from the power produced. The direct method, however, is much less precise than the other, and is to be regarded as only a verification of the general principle of calculation. The heat rendered effective, in the above example, is sae or less than one- siath of that expended in the boiler, As a second example, I shall suppose the steam to be produced at a pressure of eight atmospheres, and to expand to that of one atmosphere. In this case, P, =16936 lbs. per square foot. V,=4-08 cubic feet per lb. of steam. P, V,=68252 lbs. raised one foot. rs 9=5-657=8° Maximum possible effect of one pound of water, 1 =P, V,x6(1- (5) &) =119,042 Ib. raised one foot: Being the equivalent of 95°°8 K,, (Centigrade). Maximum possible effect of one cubic foot of water = 7,496,375 lb. raised one foot. The data for calculating directly the heat rendered effective are, 7,=C+170°9 cent. +, =C+ 100° y—5o1 Kk. H,, ,=558"6 K,, = heat expended in the boiler. 1—m='148 nearly = steam liquefied during the expansion. 186 MR W. J. M. RANKINE ON THE Whence, the heat converted in power, as calculated directly, is, 95°'S K,, agreeing with the calculation from the power produced. In this example, the heat rendered effective is a or somewhat more than one-sixth of that expended in the boiler. (33.) The results of the calculations of maximum possible effect, of which examples have just been given, are (mits which may be approached in practice by Cornish and similar engines, but which cannot be fully realised; and yet it has been shewn, that in those theoretical cases only about one-sixth of the heat expended in the boiler is rendered effective. In practice, of course, the propor- tion of heat rendered effective must be still smaller; and, in fact, in some unex- pansive engines, it amounts to only one-twenty-fourth, or even less. Dr Lyon PLAYFarR, in a memoir on the Evaporating Power of Fuel, has taken notice of the great disproportion between the heat expended in the steam- engine and the work performed. It has now been shewn that this waste of heat is, to a great extent, a necessary consequence of the nature of the machine. It can only be reduced by increasing the initial pressure of the steam, and the extent of the expansive action; and to both of those resources there are practical limits, which have already in some instances been nearly attained. APPENDIX TO THE FOURTH SECTION, CONTAINING TABLES TO BE USED IN CALCULATING THE PRESSURE, VOLUME, AND MECHANICAL ACTION OF STEAM, TREATED AS A PERFECT GAS. The object of the first of the annexed tables is to facilitate the calculation of the volume of steam of saturation at a given pressure, of the pressure of steam of saturation at a given volume, and of its mechanical action at full pressure. The pressures are expressed in pounds avoirdupois per square foot, and the volumes by the number of cubic feet occupied by one pound avoirdupois of steam, when considered as a perfect gas; those denominations being the most convenient for mechanical calculations in this country. The columns to be used in determining the pressure from the volume, and vice versd, are the third, fourth, sixth, and seventh. The third column contains the common logarithms of the pressures of steam of saturation for every fifth degree of the centigrade thermometer from —30° to + 260°: that is to say, for every ninth degree of Fahrenheit’s thermometer from — —22° to +500’. The fourth column gives the differences of the successive terms of the third column. MECHANICAL ACTION OF HEAT. 187 The sixth column contains the common logarithms of the volume of one pound of steam of saturation corresponding to the same temperatures. The seventh column contains the differences of the successive terms of the sixth column, which are negative; for the volumes diminish as the pressures increase. By the ordinary method of taking proportional parts of the differences, the logarithms of the volumes corresponding to intermediate pressures, or the loga- rithms of the pressures corresponding to intermediate volumes, can be calculated. with great precision. Thus, let X+/ be the logarithm of a pressure not found in the table, X being the next less logarithm which js found in the table; let Y be the logarithm of the volume corresponding to X, and Y—£ the logarithm of the volume corresponding to X+h; let H be the difference between X and the next greater logarithm in the table, as given in the fourth column, and K the corre- sponding difference in the seventh column; then by the proportion | sh Ged eR either Y—% may be found from X +, or X+h from Y—A. In the fifth and eighth columns respectively, are given the actual pressures and volumes corresponding to the logarithms in the third and sixth columns, to five places of figures. In the ninth column are given the values of the quantity denoted by P, V, in the formule, which represents the mechanical action of unity of weight of steam at full pressure, or before it has begun to expand, in raising an equal weight. Those values are expressed in feet, being the products of the pressures in the fifth column by the volumes in the eighth, and have been found by multi- plying the absolute temperature in centigrade degrees by 153:48 feet. Interme- diate terms in this column, for a given pressure or a given volume, may be approxi- mated to by the method of differences, the constant difference for 5° centigrade being 767°4 feet ;, but it is more accurate to calculate them by taking the product of the pressure and volume. When the pressure is given in other denominations, the following logarithms are to be added to its logarithm, in order to reduce it to pounds avoirdupois per square foot :— For Millimétres of mercury, : ; 3 ; : : : 0:44477 Inches of mercury, : : : : : 5 : : 1:84960 Atmospheres of 760 millimetres, . : ; , 4 ; 3°32559 Atmospheres of 30 inches, . ; : : 4 ‘ : 3°32672 Kilogrammes on the square centimetre, , 5 , b 3°31136 Kilogrammes on the circular centimetre, : : ‘ 3°41627 Kilogrammes on the square métre, ; ; : : 1:31136 Pounds avoirdupois on the square inch, : : ; : 2°15836 Pounds avoirdupois on the circular inch, ; ; , : 2:26327 VOL. XX. PART I. 3D 188 MR W. J. M. RANKINE ON THE To reduce the logarithm of the number of cubic métres occupied by one kilo- gramme to that of the number of cubic feet occupied by one pound avoirdupois, add 1:20463. The logarithms are given to five places of decimals only, as a greater degree of precision is not attainable in calculations of this kind. The second table is for the purpose of calculating the mechanical action of steam in expansive engines. The first column contains values of the fraction of the entire capacity of the cylinder which is filled with steam before the expansion commences (being the quantity + a of the formule), for every hundredth part, from 1:00, or the whole cylinder, ie to 0°10, or one-tenth. If / be the entire length of stroke, /’ the portion performed at full pressure, and ¢ the fraction of the entire capacity of the cylinder allowed for clearance, then 1 oie K 1 if pias 1 gee roast The entire capacity of the cylinder is to be understood to include clearance at one end only. The second column gives the reciprocals of the quantities in the first, or the values of the ratio of expansion s. The third and fourth columns, headed Z, give the values of the quantity 1 a - a sof Article 23, which represents the ratio of the entire gross action of the steam to its action at full pressure, without allowing for clearance. The third column is to be used for initial pressures of from one to four atmospheres ; and the fourth for initial pressures of from four to eight atmospheres. The deduction to be made from the quantity Z for clearance is cs, or the product of the fraction of the cylinder allowed for clearance by the ratio of expan- sion. Hence, to calculate from the tables the net mechanical action of unity of weight of steam, allowing for the counter-pressure of the waste steam P,, as well as for clearance, we have the formula P, V, (Z—es)—P, V, (l—c)s being equivalent to the formula (47.) of this paper. 189 MECHANICAL ACTION OF HEAT. d its Action at Full Pressure. d Volume of Steam, an TABLE I.—Pressure an 8. .) (3.) (4) ©.) ie oe x“ ight of Steam in Q.) (2) Toners aaaproe (i odie on ee , : of vo ' P eight in feet, a ra- | Tempera- alee Differences. ee Si ars bape cteien "ieetL cto ae ture Cen- | in ‘ibs. per BAHASEREAO: ey feet, eae: renheit. tigrade. square foot. aoopie 38171 ee ee | 0-9835] 4.58173 | 9 19694 24260 38309 —22° | —30° | 1:99278 | 9.9563 15791) 4-38489 | 9 ie741 15757 oe O-19841 | 6 19600 2-4799) 4.19748 | 4 iegs 10443 39843 0:39443 | 9 13719 3-8153) 4.01883 | 9 12936 7054.6 40611 0-58153 | 4 17964 5-7567 | 3-84847 | 9 1979 4850-1 41378 0:76017 0-17085 8-5314| 3-68575 0-15550 3390-4 42146 0-93102 0-16348 12-431 | 3.53025 0-14877 2407-0 42913 1:09450 | 9.15661 17-828 | 3-38148 | 9 14049 1734.0 43680 1-25111 0-15012 25-190 | 3-23906 0-13648 | j066.4 44448 1-40123 | 5.14404 35-097 | 3-10258 | 9 13993 936-81 45215 1:54527 0-13836 48-265 | 2-97165 0-12553 701-65 45983 1-68363 | 9 13984 65-535 | 284612 | 4 15081 531-51 46750 181647 | 4 15x89 87-957 | 2-72551 | 6.11599 407-01 47517 194427 | 9 15097 116-75 | 260961 | 9.11146 314.88 48285 eee ovitaea.|| Ere alo peas O80 25) | oneigg so008 2-18566 0-11410 199.42 2:39090 0-10328 193.92 49820 2-29976 | 9.11002 256-91 | 2-28762 | 9 o9950 154-21 50587 2.40978 | 9 10614 328-04 | 218812 | 9 aoz93 123.65 else 2:51592 | 9 10947 415-33 | 2:09219 | 9 ggo53 99-922 peuee peirag pomseey: | Geren, todas 0-08931 | 31/349 a2) 2-71736 | 9 n9566 650-16 | 1-91035 | 9 gg¢as 66-696 aaood 281302 | 0 o9950 804-49 | 1:82410 | 9 oesa¢ 55-048 54424 290552 | 9 9953 988-67 | 1-74074 | 9 og050 45.734 voile Bee ea gb108058) | Gaee cae ligeeegia 007788 | 35 906 Bose 3-08163 | 9 99398 1463.9 158236 | 9 97538 32.135 56726 3.16551 008129 | jre5 5 1-50698 0.07295 27.166 57494 3-24680 | 9 gze79 2116-4 1-43403 | 9 97064 23.088 ao 332559 | 9 o7640 9593.4 136339 | 9 96847 19.721 59028 3-40199 | 0 o2415 2993-2 | 1-29492 | 9 esas 16.927 59796 3-47614 | 9 97196 3532-6 122857 | 9 96434 14.596 60563 3-54810 | | goss 4149-3 | 1-16423 | 5 ogo4a1 12.642 61331 361798 | 9 peze8 4851-3 110182 | 9 o¢957 10.996 62098 3-68586 | 9 96397 5647-2 | 1-04125 | 9 osgs1 9.6037 62865 3-75183 0-06414 | 6545.9 0-98244 | 9.95711 8.4204 Babes See INES Witeee ob laideras 0.05548 7.4105 64400 3.87835 | 4 n6069 8690-4 | 0-86985 | 9 45393 6-5452 woe 3-93904 | 0 ns07 9956-6 | 0-81592 | 4 oso45 5.8010 65935 399811 | 9 o5a51 11366 0:76350 | 9 o5099 5.1583 66702 4.05562 | 9 55601 12931 On2>1 || 9104959 4.6017 SG 4-11163 | 9 5456 14662 0-66292 | 9 04898 4.1176 68237 4.16619 0:05319 16572 0-61464 0.04698 3.6954 | 69005 421938 | 9 05184 18673 0-56766 | 9 94576 3-3258 69772 Peo iae (NORO6" | 5a on5 0-52190 | 9 94457 30014 | 70539 4.32178 0-04932 | 53-09 0:47733 | 9 94349 2-7159 71307 pi eon na4s 12 26256 Oe En194031 2.4638 72074 4-41922 | 9 j4696 29254 0-39160 | 9 94196 2.2405 72842 4:46618 | 9 4596 39512 0-35034 | 9 94093 2.0423 73609 451204 | 9 pag 36043 0-31011 | 9.93994 1-8663 74376 4.55682 0:04375 | 39963 0-27087 | 9.93899 1-7084 75144 4-60057 0-04274 43986 | 0-23258 0-03734 1-5676 75911 B6A0l Maia hos 0-19524 | 9 na64g 14413 | 76679 468507 | 9 o4085 53201 0-15875 | 9.93561 1.3278 77446 472592 | 0 03994 58326 0-12314 | 9 93478 1.2256 78213 4-76586 | 9 93006 2nGiE 0-08836 | 9 93395 1-1335 78981 4-80492 | 9 93819 69680 0-05441 | 9 3390 1-0501 79748 484311 | 9 93749 75947 0-02121 | 9 93044 0-97447 80516 4-88051 | 4 93660 82625 198877 | 9.93170 0-90588 81283 ee 0-03582 | gor98 Ee 0-03099 0-84349 eeunt 4- : 7 1-92 4.98800 | 2°03507 | g7ov5 1 190 MR W. J. M. RANKINE ON THE MECHANICAL ACTION OF HEAT. TABLE II.—Eapansive Action of Steam. (l.) (2.) (3.) (4.) (1, (2.) (3.) (4) Fraction of Cy- Coefficient of gross action — z, || Fraction of Cy- Coefficient of gross action — Z, linder filled Ratio of linder filled Ratio of with Steam at] Expansion {Initial Pressure |Initial Pressure || Wit Steamat| Expansion. Initial Pressure [Initial Pressure full pressure Ist one to four four to eight full pressure. es one to four four to eight = 1 Atmospheres. | Atmospheres. — L Atmospheres, | Atmospheres. 1:00 1:000 1-000 1:000 64 1:852 1:586 1-580 “99 1-010 1:010 1:010 63 1-887 1:602 1-596 98 1:020 1-020 1:020 92 1:923 1-620 1:613 97 1:031 1:030 1:030 “ol 1-961 1637 1:630 “96 1:042 1:041 1:041 -60 2-000 1:655 1°647 95 1:0538 1051 1:051 “49 2°041 1-673 1:665 “94 1:064 1:062 1°062 ‘48 2°083 1691 1°683 93 1:075 O72 1:072 47 2133 1-709 1:701 ‘92 1:087 1-083 1:083 “46 2-174 1°728 1-719 ool 1:099 1:094 1:093 | 45 9-222 1-748 1°738 “90 Wei 1:104 1-104 “44 2-273 1-767 1°757 *89 1:124 1-115 1115 43 2-326 1°787 I a a 88 1:186 1:126 1126 “42 2:381 1:808 1-796 87 1:149 1:138 iT3y ) “41 2-439 1:829 LSLy 86 1163 1149 P43 | -40 2-500 1°850 1°837 85 1:176 1:160 1'160 39 2-564 1:871 1°858 “84 1:190 1172 Heilteft “38 2-632 1°894 1°880 83 1:205 1:183 1183 37 2:703 i: SiG 1‘902 *82 1-220 1:195 1195 36 2-778 1°939 1-924 81 1:235 1:207 1°206 i. OD 2-857 1:963 1°947 ‘80 1:250 129 1-218 “34 2-941 1°987 1°970 “79 1:266 1-231 1'230 33 3:0380 2°012 1°994 7(c8 1:282 1:243 1°242 *32 3-125 2°038 2°019 17 12299 1:256 1°255 31 3:220 2:064 2°044 0 1:316 1:268 1°267 -30 3:333 2:091 2070 ‘75 1:333 1:281 1°280 “29 3:448 2119 2°097 “74 1351 1-294 1-292 -28 3-571 2°147 2:124 “13 1-370 1°307 1°305 27 3704 2°176 2°152 “ies 1:389 1:320 1°318 26 3-846 2207 |}. 2teL “heal 1-408 1:3338 1331 25 4-000 2:238 2211 ‘70 1:429 1:346 1:344 "24 4-167 2:270 2°249 69 1-449 1-360 1°358 23 4-348 2°304 2°:273 68 1-471 1:374 1-371 -22 4-545 2°338 2°306 67 1-493 1:387 1°385 “21 4-762 2°374 2°341 66 1:515 1-401 1°399 20 5:000 2-412 2°376 65 1:538 1:416 1°413 ail) 5-263 2°451 2°413 64 1:5638 1:430 1:427 als} 5-556 2:492 2°452 63 1:587 1:445 1:441 le 5-882 2°534 2°492 62 1613 1:459 1:456 16 6:250 2°579 2°434 ‘61 1-640 1-474 1-471 15 6-667 2°626 2°579 “60 1:667 1-490 1:486 14 7143 2:676 2°626 “59 1°695 1-505 1:501 alte 7692 2-730 2:675 58 1:724 T5211 1-516 ld 8°333 2-786 2-728 57 1°754 1-537 1-532 oT 9-091 2°847 2°784 “56 1-786 1-553 1°547 10 10-000 2-912 2°845 55 1:818 1:569 1-563 (194 > VIII.—WNote as to the Dynamical Equivalent of Temperature in Liquid Water, and the Specific Heat of Atmospheric Air and Steam, being a Supplement to a Paper On the Mechanical Action of Heat. By WitttamM JoHn Macquorn RankINE, Civil Engineer, F.R.S.E., F.R.S.S.A., &c. (Read 2d December 1850.) (33*.) In my paper on the Mechanical Action of Heat, published in the 1st Part of the 20th Volume of the Z’ransactions of the Royal Society of Edinburgh, some of the numerical results depend upon the dynamical equivalent of a degree of temperature in liquid water. The value of that quantity which I then used, was calculated from the experiments of De La Rocue and Bérarp on the apparent specific heat of atmospheric air under constant pressure, as compared with liquid water. The experiments of Mr ou.e on the production of heat by friction, give, for the specific heat of liquid water, an equivalent about one-ninth part greater than that which is determined from those of De La RocuE and Berarp. I was for- merly disposed to ascribe this discrepancy in a great measure to the smallness of the differences of temperature measured by Mr Jouue, and to unknown causes of loss of power in his apparatus, such as the production of sound and of electri- city; but, subsequently to the publication of my paper, I have seen the detailed account of Mr Jouxe’s last experiments in the Philosophical Transactions for 1850, which has convinced me, that the uncertainty arising from the smallness of the elevations of temperature, is removed by the multitude of experiments (being forty on water, fifty on mercury, and twenty on cast iron); that the agree- ment amongst the results from substances so different, shews that the error by unknown losses of power is insensible, or nearly so; and that the necessary con- clusion is, that the dynamical value assigned by Mr JouLz to the specific heat of liquid water, viz. :—772 feet per degree of Fahrenheit, does not err by more than two, or, at the utmost, three feet; and therefore, that the discrepancy originates chiefly in the experiments of De 1a Roce and Brrarp. I therefore take the earliest opportunity of correcting such of my calculations | as require it, so as to correspond with Mr JouLer’s equivalent. They relate to the specific heat of atmospheric air as compared with liquid water, and to that of steam, and are contained in the second and third Sections of my paper, Articles 14 and 20; Equations 28, 34, and 36. . VOL. XX. PART II. f | 3 E 192 MR W. J. M. RANKINE ON THE SpEcIFIC HEAT OF ATMOSPHERIC AIR AS COMPARED WITH Liquip WATER.—(Section II Article 14.) The dynamical values of the specific heat of atmospheric air are calculated independently from the velocity of sound, without reference to the specific heat of liquid water; and from the closeness of the agreement of the experiments of M.M. Bravais and Martins, Mott and Van Beek, STAMPFER and Myrpacu, WERTHEIM and others, it is clear that the limits of error are about 5%) for the velocity of sound, 735 for the ratio, and from 4 to 35 for the dynamical values of the specific heat of air, at constant volume and constant pressure. Those values, as given by Equation 27, are— ; Real specific heat,— k =238°66 feet =72°74 metres per centigrade degree. =132°6 feet per degree of Fahrenheit. Apparent specific heat under constant pressure,— K,=334 feet =101°8 metres per centigrade degree. =185°6 feet per degree of Fahrenheit. The ratio of these two quantities being taken as ee eg’ A TItN=14 The dynamical equivalent of the specific heat of liquid water, as determined by Mr JouLg, is Ky =1889°6 feet =423'54 metres per centigrade degree. =772 feet per degree of Fahrenheit. The specific heat of air, that of liquid water being taken as unity, has there- fore the following values :— Real specific heat,— 132°6 K.. = 772 = 0 1717. Apparent specific heat under constant pressure,— K, _185:6_, K. = 772 =0-2404 This last quantity, according to Dr La Rocue and BERAaRD, is 0:2669 The discrepancy being, : : 0:0265 or one-ninth of the value according to Mr Jour’s equivalent. Sprciric Heat or STEAM. (Section III. Art. 20.) The apparent specific heat of steam (Eq. 34 and 36) as a gas under constant MECHANICAL ACTION OF HEAT. 198 pressure is equal to that of liquid water x 0:305. Its dynamical value is therefore 1 phe Gn ~ 1389 6 x 0°305 = 422-83 feet=129-18 metres per centigr. degree. But — 15348 feet= 46°78 metres per centigr. degree. Therefore the real specific heat is k = 269-35 feet= 82:40 metres per centigr. degree. Or, that of liquid water being taken as unity, Kk 269-35 jesisspe 1 The ratio of these two values of the specific heat of steam is Pee IN = 1-54. Their dynamical equivalents for FaAHRENHEIT’S scale are k = 149-64 feet . . . K, = 235-46 feet. Neither the formule in the fourth Section, respecting the working of the steam-engine, nor the tables at the end of the paper, require any alteration ; for the action of steam at full pressure being calculated from data independent of its specific heat, is not at all affected by the discrepancy I have mentioned; and the expansive action is not affected to an extent appreciable in practice. ( 195 ) IX.—On the Power and Economy of Single-Acting Expansive Steam-Engines, being a Supplement to the Fourth Section of a Paper On the Mechanical Action of Heat. By Witt1am Joun Macquorn Ranking, Civil Engineer, F.R.S.E., F.R.S.S.A., &c. (Read 21st April 1851.) (34.) The objects of this paper are twofold: First, To compare the results of the formule and tables relative to the power of the steam-engine, which have been deduced from the Dynamical Theory of Heat, with those of experiments on the actual duty of a large Cornish engine at various rates of expansion ; and, Secondly, To investigate and explain the method of determining the rate of expan- sion, and, consequently, the dimensions and proportions of a Cornish engine, which, with a given maximum pressure of steam in the cylinder, at a given velocity, shall perform a given amount of work at the least possible pecuniary cost, taking into account the expense of fuel, and the interest of the capital re- quired for the construction of the engine. This problem is solved with the aid of the tables already printed, by drawing two straight lines on a diagram annexed to this paper. The merit of first proposing the question of the economy of expansive en- gines in this definite shape, belongs, I believe, to the Artizan Club, who have offered premiums for its solution; having done so (to use their own words), ‘with a view to enable those who, from their position, cannot take part in the discussions of the various scientific Societies to give the profession the benefit of their studies and experience.” The 5th of April is the latest day fixed by them for receiving papers; and as this communication cannot possibly be read to a meeting before the 7th April, nor published until some months afterwards, I trust I may feel confident that it will not be considered as interfering with their design. Formule applicable to the Cornish Engine. (35.) The equations of motion of the steam-engine, in this and the original paper, are the same in their general form with those of M. pr Pamspour. The differences consist in the expression’ for the pressure and volume of steam, and for the mechanical effect of its expansion; the former of which were deduced from a formula suggested by peculiar hypothetical views, and the latter from the dynamical theory of heat. Those equations are Nos. (50) and (51) of the original paper. I shall now VOL. XX. PART II. 3 F 196 MR W. J. M. RANKINE ON THE POWER AND ECONOMY express them in a form more convenient for practical use, the notation being as follows :— Let A be the area of the piston. /, the length of stroke. n, the number of double strokes in unity of time. c, the fraction of the total bulk of steam above the piston when down, allowed for clearance, and for filling steam-passages; so that the total bulk of steam at the end of the effective stroke is — : : Eh 4 - (@) i’, the length of the portion of the stroke performed when the steam is cut off. s, the ratio of expansion of the steam, so that il Hf =i ire | 1 : : : ; . (6) pes lc Let W be the weight of steam expended in unity of time. P,, the pressure at which it enters the cylinder. V,, the volume of unity of weight of steam at saturation at the pressure P, ; which may be found from Table I. of the Appendix to the original paper. F, the sum of all the resistances not depending on the useful load, reduced to a pressure per unit of area of piston; whether arising from imperfect vacuum in the condenser, resistance of the air-pump, feed-pump, and cold-water pump, fric- tion, or any other cause. R, the resistance arising from the wseful load, reduced to a pressure per unit of area of piston. Z, the ratio of the total action of steam working at the expansion s, to its action without expansion. Values of this ratio are given in the second Table of the Appendix to the original paper. ; Then the following are the two fundamental equations of the motion of the steam-engine, as comprehended in equation (50) of the original paper. First, Equality of power and effect,— RAln=WV, {P, (Z—cs)—F (1~c) s} : L Ke) Secondly, Equality of two expressions for the weight of steam expended in unity of time,— Aén Weyag ss) Siew (02) woh me OF SINGLE-ACTING EXPANSIVE STEAM-ENGINES. 197 From these two equations is deduced the following, expressing the ratio of the mean load on the piston to the initial pressure of the steam :— R+F ZL—cs “P, = (—o)s . . . . (e) being equivalent to equation (51). In computing the effect of Cornish engines these formule require to be modi- fied, owing to the following circumstances. The terms depending on the clearance c have been introduced into equations (c), (Z), on the supposition that the steam employed in filling the space above the piston at the top of its stroke is lost, being allowed to escape into the condenser, without having effected any work; so that a weight of steam Wes is wasted, and an amount of power WV, (P,—F)cs lost, in unity of time. But in Cornish engines this is not the case; for by closing the equilibrium-valve at the proper point of the up or out-door stroke, nearly the whole quantity of steam necessary to fill the clearance and valve-boxes may be kept imprisoned above the piston so as to make the loss of power depending on it insensible in practice. This portion of steam is called a cushion, from its preventing a shock at the end of the up- stroke; and as Mr Pots in his valuable work on the Cornish engine has observed, its alternate compression and expansion compensate each other, and have no effect on the duty of the engine. The proper moment of closing the equilibrium- valve is fixed by trial, which is, perhaps, the best way; but if it is to be fixed by theory, the following is the proper formula. Let /" be the length of the portion of the up-stroke remaining to be performed after the equilibrium-valve has been closed : then— ; rh as cae uae) A slight deviation from this adjustment will produce little effect in practice, if the fraction ¢ is small. In forming the equations of motion, therefore, of the Cornish engine, we may, without material error in practice, omit the terms denoting a waste of steam and loss of power due to clearance and filling of steam-passages ; and the results are the following :— Equation of effect and power in unity of time :— Useful effect E=RAln=WV,{P,Z—-F} . (57.) Weight of steam expended in unity of time :-— Alu Wesag s 1 (58.) From those two fundamental equations the following are deduced :— Ratio of mean load on piston to maximum pressure,— Seles B= (59.) x 198 MR W. J. M. RANKINE ON THE POWER AND ECONOMY Duty of unity of weight of steam,— AO 2 anh te Sp al Cl which, being multiplied by the number of units of weight of steam produced by a given weight of fuel, gives the duty of that weight of fuel. Weight of steam expended per stroke,— Wal a In fact, it is clear that if any five quantities out of the following seven be given, the other two may be determined by means of the equations: R+F, the mean load on unit of area of piston. P,, the maximum pressure of steam in the cylinder. s, the ratio of expansion. W, the weight of steam produced in unity of time. A, the area of the piston. i, the length of stroke. n, the number of strokes in unity of time. The other quantities, E, V,, Z, are functions of those seven. (61.) Comparison of the Theory with Mr WickstEED’s Experiments. (36.) In order to test the practical value of this theory, I shall compare its results with those of the experiments which were made by Mr WicksTEED on the large Cornish pumping engine built under the direction of that eminent engineer by Messrs Harvey and West, for the East London Water-Works at Old Ford, and which were published in 1841. The dimensions and structure of the engine, and the details of the experiments, are stated with such minuteness and precision, that there is none of that uncertainty respecting the circumstances of particular cases, which is the most frequent cause of failure in the attempt to apply theoretical principles to practice. The engine was worked under a uniform load at five different rates of ex- pansion successively. The number of strokes, and the consumption of steam during each trial, having been accurately registered, Mr WickSTEED gives a table shewing the weight of steam consumed per stroke for each of the five rates of expansion. I shall now compute the weight of steam per stroke theoretically, and compare the results. Throughout these calculations I shall uniformly use the foot as the unit of length, the avoirdupois pound as that of weight, and the hour as that of time. Pressures are consequently expressed in pounds per square foot for the purpose of calculation ; although in the table of experiments I have reduced them to pounds per square inch, as being the more familiar denomination. OF SINGLE-ACTING EXPANSIVE STEAM-ENGINES. 199 The data respecting the dimensions and load of the engine, which are constant throughout the experiments, are the following :— Area of piston, : : 4 A=34-854 square feet. Stroke, . : s ‘ § Z =10 feet. Cubic space traversed by piston during one down stroke, = A /=348°54 cubic feet. Clearance and valve-boxes, : ; : ’ : ; 18-00 Sum, : 366:54. Therefore, c=0:05 R=useful load of piston, . : : =1597: lb. per square foot. F= additional resistance, . § f = 2666 Ae ft R+F= total mean pressure on piston, =1863°6 The mode of calculation is the following :— Mr WicxsTEep states the fraction . of the stroke performed at full pressure in each experiment. From this the ratio of expansion s is computed by equation (6), giving in this case ES esi nis Ss l ‘ The value of Z corresponding to s is then found by means of the third column of Table second ; that column being selected because the initial pressures were all below four atmospheres. This affords the means of determining the initial pressure of the steam by equation (59), viz. :— P,=7 (R+F)=18636 5 By using Table first according to the directions prefixed to it, the volume of one pound of steam at the pressure P,, in cubic feet, is calculated, and thence, by equation (60), the weight of steam per stroke, according to theory, which is com- pared with the weight as ascertained by experiment. Further to illustrate the subject, the useful effect, or duty of a pound of steam, is computed according to the theory and the experiments respectively, and the results compared. The following Table exhibits the results. VOL. XX. PART II. oe 200 MR W. J. M. RANKINE ON THE POWER AND ECONOMY Comparison of the Theory with Mr WICKSTEED’s Lxperiments on the Cornish Pumping Engine at Old Ford. Bere petenll| Steam ent : Maximum | Lb. of Steam expended Duty of one Ib, of Number th eS, ay Vv Ratio of | Pressure in per stroke, Steam, of Expe- eee off at L of | Expansion | the Cylin- Difference. as Difference. Sar bata | abt | a eR ee ee ¥ A y etapa, | facta 13} 30°45 | 0°6038 | 1:605 | 14:27 | 7-781 | 7-536 |—0-245| 71530 | 73860} +2330 C. 33°20 | 0-477 | 1:988 | 15°59 | 6:963 | 6-463 |—0-°500| 79936 | 86123] +6187 108 39:2 0°397 | 2-342 | 16:9 6:236 | 6-200 |—0:036| 89275 | 89776/ + 501 EK. 41-2 0°352 | 2°605 | 17°89 | 5:905 | 5:985 |+0°085) 94258 | 93002) —1256 Be 45-7 0313 | 2-882 | 18:93 | 5-626 | 5-470 |—0-156| 98940 | 101756 | +2816 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) This comparison sufficiently proves that the results of the theory are practically correct. It is remarkable, that in every instance except one (experiment E) the expe- rimental results shew a somewhat less expenditure of steam per stroke, and a greater duty per pound of steam, than theory indicates. This is to be ascribed to the fact, that although the action of the steam is computed theoretically, on the assumption that during the expansion it is cut off from external sources of heat, yet it is not exactly so in practice; for the cylinder is surrounded with a jacket or casing communicating with the boiler, in which the temperature is much higher than the highest temperature in the cylinder, the pressure in the boiler being more than double the maximum pressure of the steam when working, as columns (2) and (5) shew. There is, therefore, a portion of steam, of whose amount no computation can be made, which circulates between the boiler and the jacket, serving to convey heat to the cylinder, and thus augment by a small quan- tity the action of the steam expended; and hence the formule almost always err on the safe side. Supposing one pound of the best Welsh coals to be capable (as found by Mr WIcKSTEED) of evaporating 9°493 lb. of water at the pressure in the boiler during the experiment F, then the duty of a Cornish bushel, or 94 lb. of such coals, in the circumstances of that experiment would be— By theory, | = B8ibaeinon Fe ap. By experiment, : - 90,801,000 «.. Difference, . + 2,513,000 --- OF SINGLE-ACTING EXPANSIVE STEAM-ENGINES. 201 Economy of Single-Acting Expansive Engines. (37.) By increasing the ratio of expansion in a Cornish engine, the quantity of steam required to perform a given duty is diminished; and the cost of fuel, and of the boilers, is lowered. But at the same time, as the cylinders and every part of the engine must be made larger, to admit of a greater expansion, the cost of the engine is increased. It thus becomes a problem of maxima and minima to determine what ratio of expansion ought to be adopted under given circum- stances, in order that the sum of the annual cost of fuel, and the interest of the capital employed in construction, may be the least possible, as compared with the work done. That this problem may admit of a definite solution, the following five quanti- ties must be given :— P., the initial pressure in the cylinder. F, the resistance not depending on the useful load. in, the amount of the length of the effective strokes made in unity of time. h, the annual cost of producing unity of weight of steam in unity of time, which consists of two parts; the price of fuel, and the interest of the cost of the boilers. k, the interest of the cost of the engine, per unit of area of piston. Hence the annual expenditure to be taken into consideration, reduced to unity of weight of steam, is A Vis And the useful effect of unity of weight of steam being V, (P, Z—Fs) The problem is to determine the ratio of expansion s, so that V, (P, Z—Fs) h+k nas ln shall be a maximum. Dividing the numerator of this fraction by V,P,, and the denominator by kV ; : ‘ TR both of which are constants in this problem, we find that it will be solved by making the ratio Z——s] P Se 3 ONG) EV a maximum. The algebraical solution would be extremely complicated and tedious. The 202 MR W. J. M. RANKINE ON THE POWER AND ECONOMY graphic solution, on the other hand, is very simple and rapid, and sufficiently accurate for all practical purposes ; and I have therefore adopted it. In the annexed diagram, Plate VIII. fig. 1, the axis of abscisse, —XO+X, is graduated from O towards +X into divisions representing ratios of expansion, or values of s. The divisions of the axis of ordinates, O Y, represent values of Z. The curve marked “locus of Z,” is laid down from the third column of Table II. of the Appendix to the original paper, being applicable to initial pressures not exceeding four atmospheres. Through the origin O draw a straight line BOA, at such an inclination to —X0O+X that its ordinates are represented by my Then the ordinates measured ul from this inclined line to the locus of Z represent the value of the numerator — s, of the ratio (62), corresponding to the various values of s. 1 Take a point at C on the line BOA, whose abscissa, measured along O—X, re- presents — ies Then the ordinates, measured from BOA, of any straight line 1 drawn through C, vary proportionally to the denominator it s of the ratio (62). Through the point C, therefore, draw a straight line CT, touching the locus of Z: Then the ratio (62) is a maximum at the point of contact T, and the abscissa at that point represents the ratio of expansion required. Example. (38.) To exemplify this method, let us take the following data. Greatest pressure in the cylinder P,=20 1b. per square inch, =2880 lb. per square foot. The corresponding value of V, is 20248 cubic feet per pound of steam. To obtain this initial pressure in the cylinder, it will be necessary to have a pressure of about 50 lbs. per square inch in the boiler. F, resistance not depending on the useful load =2 Ib. per square inch, =288 lb. per square foot, =z, P,. Zn, amount of down strokes, =4800 feet per hour; being the average speed found to answer best in practice. To estimate h, the annual cost of producing one pound of steam per hour, I shall suppose that the engine works 6000 hours per annum; that the cost of fuel is one penny per 100 1b. of steam ;* that the cost of boiler for each pound of steam per hour is 0°016 ton, at £27, =£0°432; and that the interest of capital is five per cent. per annum. Hence / is thus made up— * This estimate is made on the supposition that coals capable of producing nine times their weight of steam are worth about 16s. 9d. per ton. OF SINGLE-ACTING EXPANSIVE STEAM-ENGINES. 203 Fuel for 6000 lb. of steam at 0:01d., : ; . £0°2500 Interest on £0°432, at 5 per cent., . P : ; 0:0216 h = £02716 Estimating the cost of the engine at £250 per square foot of piston, we find k= 5 per cent. per annum on £250 = £12'5, and * = 00217 ; Lh z V, = 9°144 The line BOA, then, is to be drawn so that its ordinates are Fs= DD 6 1 The point C is taken on this line, at a= — 5'144 divisions of the axis of 1 abscissze to the left of O Y. The tangent C T being drawn, is found to touch the locus of Z at 2-800 divi- sions to the right of O Y. Then s=2°800 is the ratio of expansion sought, corresponding to the greatest economy. If we make c=0'05 as in Mr WIcKSTEED’s engine, then the fraction of the stroke to be performed at full pressure is iq! being nearly the same as in experiment F. The mean resistance of the useful load per square foot of piston is |e _ P, —F=1713°6 lb. The duty of one square foot of piston per hour,— Rin = 8,225,300 foot-lb. And one horse-power being 1,980,000 foot-lb. per hour, the real horse-power of the engine is 4-154 per square foot of piston. The duty of one pound of steam is RV,s = 97,154 foot-lb. To give an example of a special case, let the duty to be performed be 198,000,000 foot-pounds per hour, being equal to 100 real horse-power, for 6000 hours per annum. This being called E, we find from the above data that the area of piston required is A= — =24:072 square feet. The consumption of steam per hour is E SR Mise = 2038 lb. which requires 2038 x 0:016=32°608 tons of boilers. VOL. XX. PART II. 3H 204 MR W. J. M. RANKINE ON EXPANSIVE STEAM-ENGINES. The expenditure of steam per annum is 2038 x 6000 =12,228,000 lb. Hence we have the following estimate :— Cost of engine, 24:072 square feet of piston at £250, : £6018-000 Cost of boilers, 32:608 tons at £27, 5 F , ~ 880°416 Total capital expended, £6898-416 Interest at five per cent. per annum, : . £344:921 Cost of fuel per annum, 12,228,000 lb. of steam a 0-01d., 509°500 Annual cost for interest and fuel, £854-421 I wish it to be understood that the rates I have adopted in the foregoing calculations, for interest, cost of fuel, and cost of construction, are not intended as estimates of their average amount, nor of their amount in any particular case, but are merely assumed in order to illustrate, by a numerical example, the rules laid down in the preceding article. It is of course the business of the engineer to ascertain those data with reference to the special situation and circumstances of the proposed work ; and having done so, the method explained in this paper will enable him to determine the dimensions and ratio of expansion which ought to be adopted for the engine, in order that it may effect its duty with the greatest possible economy. X.—On the Economy of Heat in Expansive Machines, forming the Fifth Section of a Paper On the Mechanical Action of Heat. By Witiiam Jonn Macquorn Ran«IneE, Civil Engineer, F.R.S.E., F.R.S.S.A., &c. (Read 21st April 1851.) (39.) A machine working by expansive power consists essentially of a portion of some substance to which heat is communicated, so as to expand it, at a higher temperature, being abstracted from it, so as to condense it to its original volume, at a lower temperature. The quantity of heat given out by the substance is less than the quantity received; the difference disappearing as heat to appear in the form of expansive power. The heat originally received by the working body may act in two ways: to raise its temperature, and to expand it. The heat given out may also act in two ways: to lower the temperature, and to contract the body. Now, as the conver- sion of heat into expansive power arises from changes of volume only, and not from changes of temperature, it is obvious, that the proportion of the heat re- ceived which is converted into expansive power will be the greatest possible, when the reception of heat, and its emission, each take place at a constant tem- perature. : (40.) Carnov was the first to assert the law, that the ratio of the maximum me- chanical effect, to the whole heat expended in an expansive machine, is a function solely of the two temperatures at which the heat is respectively received and emitted, and is independent of the nature of the working substance. But his investigations not being based on the principle of the dynamical convertibility of heat, involve the fallacy that power can be produced out of nothing. (41.) The merit of combining Carnoét’s Lam, as it is termed, with that of the convertibility of heat and power, belongs to Mr CLausius and Professor W1LL1AM THomson ; and in the shape into which they have brought it, it may be stated thus:— The maximum proportion of heat converted into expansive power by any ma- chine, 1s a function solely of the temperatures at which heat is received and emitted by the working substance ; which function, for each pair of temperatures, is the same Jor all substances in nature. This law is laid down by Mr Cuausius, as it originally had been by Carnot, as an independent axiom; and I had at first doubts as to the soundness of the reasoning by which he maintained it. Having stated those doubts to Professor Txomson, I am indebted to him for having induced me to investigate the subject thoroughly; for although I have not yet seen his paper, nor become acquainted with VOL. XX. PART II. 3 I 206 _ MR W. J. M. RANKINE ON THE ECONOMY OF the method by which he proves Carnot’s law, I have received from him a state- ment of some of his more important results. (42.) I have now come to the conclusions,—First: That Carnov’s Law is not an independent principle in the theory of heat; but is deducible, as a consequence, Jrom the equations of the mutual conversion of heat and expansive power, as given in the First Section of this paper. Secondly: That the function of the temperatures of reception and emission, which expresses the maximum ratio of the heat converted into power to the total heat received by the working body, is the ratio of the difference of those temperatures, to the absolute temperature of reception diminished by the constant, which I have called k=Cnb, and which must, as I have shewn in the Introduction, be the same for all substances, in order that molecular equilibrium may be possible. (43.) Let abscissee, parallel to OX in the diagram, Plate VIII. fig. 2, denote the volumes successively assumed by the working body, and ordinates, parallel to OY, the corresponding pressures. Let 7, be the constant absolute temperature at which the reception of heat by the body takes place: 7,, the constant absolute temperature at which the emission of heat takes place. Let AB be a curve such that its ordinates denote the pressures, at the temperature of reception 7,, cor- responding to the volumes denoted by abscissee. Let DC be a similar curve for the temperature of emission 7,. Let AD and BC be two curves, expressing by their co-ordinates how the pressure and volume must vary, in order that the body may change its temperature, without receiving or emitting heat; the former corresponding to the most condensed and the latter to the most expanded state of the body, during the working of the machine. The quantity of heat received or emitted during an operation on the body involving indefinitely small variations of volume and temperature, is expressed by adding to Equation (6.) of Section Fourth the heat due to change of tempera- ture only, in virtue of the real specific heat. We thus obtain the differential equation hee aU) dU Je Serene —k Or In which the negative sign denotes absorption, and the positive emission. aU aU ‘ i : If we now put for 747, 7; their values according to Equation (11.), we find 8q—8Q=-(7—0& . dv -{ ®t gg (SS) +e-o fav jar. 3) The first term represents the variation of heat due to variation of volume only; the second, that due to variation of temperature. Let us now apply this HEAT IN EXPANSIVE MACHINES. 207 equation to the cycle of operations undergone by the working body in an expan- sive machine, as denoted by the diagram. First operation. The body, being at first at the volume V, and pressure P,, is made to expand, by the communication of heat at the constant temperature 7,, until it reaches the volume V, and pressure P,, AB being the locus of the pressures. Here 67=0; therefore the total heat received is H,=-Q,=(7, fs Baba | (a) =(7,—K) [P(Va; oe — (Vas ™)} Second operation. The body, being prevented from receiving or emitting heat, expands until it falls to the temperature 7,, the locus of the pressures being the curve BC. During this operation the follbwing condition must be fulfilled,— 0=0Q —0Q Which, attending to the fact that V is now a function of 7, and transforming the integrals as before, gives the equation J= Pe (G- <) + (7 — K) (AT. a) p (V,7) This equation shews that P (Va, 1)—P (Vor T)=¥ (Ts To) . . . (6) Third operation. The body, by the abstraction of heat, is made to contract, at the constant temperature 7,, to the volume V, and pressure P,, which are such as to satisfy conditions depending on the fourth operation. CD is the locus of the pressures. The heat emitted is evidently Hy=Qo=(T)—K){P (Ver T)-P(Vo T)} - . (c) Fourth operation. The body, being prevented from receiving or emitting heat, is compressed until it recovers its original temperature 7,, volume V , and pres- sure P,; the locus of the pressures being DA. During this operation, the same conditions must be fulfilled as in the second operation; therefore P (Vas 1) —P (Von T)=V (Ty To) , ° . . (d) _~) being the same function as in Equation (6). By comparing Equations () and (d), we obtain the relation which must sub- sist between the four volumes to which the body is successively brought, in order that the maximum effect may be obtained from the heat. It is expressed by the _ equation — (Va, 7,)-P (Va, 7)= P (Vor Th)? CVartos : (64.) From this, and Equations (a) and (c), it appears that Jal TK pers Oh fe ee ONES BAe aie (7 7) Fab uparyinplane 22) 208 — MR W. J. M. RANKINE ON THE ECONOMY OF \ That is to say: when no heat is employed in producing variations of tempera- ture, the ratio of the heat received to the heat emitted by the working body of an expansive machine, 1s equal to that of the absolute temperatures of reception and emission, each diminished by the constant x, which is the same for all substances. Hence let m= —Q,—-Q,=H,—-H, denote the maximum amount of power which can be obtained out of the total heat H,, in an expansive machine working between the temperatures 7, and 7,. Then Hi ee AD Se ¥ A aiey ees being the law which has been enunciated in Article 42, and which is deduced entirely from the principles already laid down in the Introduction and First Section of this paper. The value of the constant x is unknown; and the nearest approximation to accuracy which we can at present make, is to neglect it in calculation, as being very small as compared with +. (44.) This approximation having been adopted, I believe it will be found that the formula (66.), although very different in appearance from that arrived at by Professor Tomson, gives nearly the same numerical results. For example: let the machine work between the temperatures 140° and 30° centigrade: then 7,=414°6, 7, =304°6, and nl H, = 0:2653 Professor THomson has informed me, that for the same temperatures he finds this ratio to be 0:2713.* (45.) To make a steam-engine work according to the conditions of maximum effect here laid down, the steam must enter the cylinder from the boiler without diminishing in pressure, and must be worked expansively down to the pressure and temperature of condensation. It must then be so far liquefied by conduc- tion alone, that on the liquefaction being completed by compression, it may be restored to the temperature of the boiler by means of that compression alone. These conditions are unattainable in steam-engines as at present constructed, and different from those which form the basis of the formule and tables in the Fourth Section of this paper; hence it is found, both by experiment and by calculation * Prom information which I have received from Professor THomson subsequently to the com- pletion of this paper, it appears that his formula becomes identical with the approximate formula here proposed, on making the function called by him p= ve J being Jouxe’s equivalent. : T Mr Jovze also, some time since, arrived at this approximate formula in the particular case of a perfect gas. HEAT IN EXPANSIVE MACHINES. 209 from those formule, that the proportion of the total heat converted into power in any possible steam-engine is less than that indicated by Equation (66.) The annexed Table illustrates this :— | Heat trans- | Total heat | formed into Nearui ; } expended in| expansive | Proportion proportion CASE Absolute temperature in the Absolute temperature in the | centigrade | power, in | of heat ren- teehee | boiler —+7; centigrade. condenser =p centigrade. degrees ap- | centigrade | dered effec- ea plied to degrees ap- tive. Tae liquid water.| plied to liquid water. ee) Prample a 144°-1 4.2746 = 418°7 | 81°7 +274°6=356"3| 568°7 | 832 | 01463 | 0-1490 Section 4, Art. 32, Second Ideal Example, |170°9+274°°6 = 445°°5| 100°+274°'6=374°°6| 558°°6 86°°3 071545 | 0°1592 Mr WicksteED’s En- gine, Experiment F, \ |135°-2 + 274°6 = 409°°8| 30°+.274°-6 = 304°6| 617°7 | 71°2 | 0°1153 | 0°2567 by calculation, . . Do., by observation, . . Ditto. Ditto. Ditto. 73°23 | 0°1185 | Ditto (1) (2) (3) (4) (5) (6) (7 The heat transformed into power, as given in the fifth column, has been reduced to centigrade degrees in liquid water, by dividing the duty of a pound of steam by Mr Joue’s equivalent, 1389°6 feet per centigrade degree. Hence the first two numbers in that column are less than those given in Art. 32, which were com- puted from too small an equivalent. The first two cases fulfil the conditions required by Carnot’s law in every respect except one, viz.:—that the steam remaining at the end of the stroke, instead of being*partially liquefied by refrigeration, and then reduced to water at the tem- perature of the boiler by compression, is supposed to be entirely liquefied by refrigeration. This occasions the loss of the heat necessary to raise the water from the temperature of the condenser to that of the boiler; but at the same time, there is a gain of the power which would be required to liquefy part of the steam by compression, and those two quantities partially compensate for each other’s effects on the ratio of the power to the heat expended, so that although it is below the maximum, the difference is small. In the third and fourth examples, founded on the calculated and observed duty of Mr WicxsTEEp’s engine during experiment F, the actual ratio is less than half the maximum. This waste of heat is to be ascribed to the following causes. First, The mode of liquefaction, which has already been referred to. Secondly, The initial pressure in the cylinder is but 18°93 lb. on the square inch, while that in the boiler is 45:7; so that although the steam is produced at 135°-2 centigrade, it only begins to work at 107°26. This great fall of pressure is VOL. XX. PART II. 3K 210 MR W. J. M. RANKINE ON EXPANSIVE MACHINES. accounted for by the fact, that the steam for each stroke, which is produced in the boiler in about seven or eight seconds, escapes suddenly into the cylinder in a fraction of a second. Thirdly, The expansive working of the steam, instead of being continued down to 30° centigrade, the temperature of the condenser, stops at a much higher temperature, 74°°66. This is the most important cause of loss of power. If we now take for 7, and 7, the absolute temperatures at the beginning and end of the expansive working, and calculate the maximum duty of one pound of steam by Carnot’s Law between those temperatures, we find,— T, =107°-26 + 274°-6 =381°'86 7, = 74°66 +2746 = 349-26 iat or H, =564°5 ; teh). Aa To this aed to a added the aaty, at full pressure, of steam at 7,, dimi- nished by one-third for back-pressure and friction, and by one-fifteenth for liquefaction in the cylinder, = . - : . ‘ : : 23°14 The whole amounting to 71°:36 Which agrees very nearly with 73°23, the observed duty, and almost exactly with 71°-2, the duty as calculated by the formule and tables of Section Fourth. These examples shew clearly the nature and causes of the waste of heat in the steam-engine. ‘deay, ongedspy ip) TESTSeqo d' Lf JOT Aq S'TTIH NoQTIa = \ re = er ue ey jo Jo UonraLp Mays RaaVipo sry ay) pup suaupods a4) 0) Ldfad SLIQUINAT IY J %& ‘otLoys peg p?yl al ‘en, deal pam) Peaaye ATySupog | ‘oyUMsory (om TWOIDO'TONDS © EL Pf POS 28 URDU LOMO PELE ME APRS vs ; SPUDUTUDAS DUPE QYOUNS U2 UOISUDALT JO BPDd TRORUOUOI2 P80 AY) BUND pp oy Umisho todd “LVaL H 10 NOILOV TVOINVHOAW oy} wo QNIMNVA [ \i tb iN eta es we t | T a ++ ane eee LL XX PAIN 20s oho XI.—WNotes on the Geology of the Eildon Hills, in Roxburghshire. By James D. Forses, Esq., F.R.S., Sec. R.S. Ed., Professor of Natural Philosophy in the University of Edinburgh. (Read 7th April 1851.) The following remarks, being the result of a careful examination of a small district of country characteristic of the relations of the trap formations, are per- haps worthy of being recorded; although the general features of the county of Roxburgh have been very clearly stated in a paper by Mr Mine, published in the 15th volume of the Edinburgh Transactions. The outburst of porphyritic trap forming the conspicuous small group of the Eildon Hills, may be stated to be surrounded by the characteristic greywacke of the south of Scotland. It forms an elongated patch on the map, extending from the west end of Bowden Muir in the direction of the town of Selkirk, and running from west-south-west to east-north-east (true) towards Bemerside Hill, on the north bank of the Tweed. The breadth is variable, probably less than is generally sup- posed ; but it cannot be accurately ascertained, owing to the accumulated diluvium | which covers the whole south-eastern slope of this elevated ridge. On this ac- count, my observations on the contact of rocks have been almost entirely confined to the northern and western boundaries of the trap, although the other side was examined with equal care. The character of the greywacke strata near Melrose is in general that of the surrounding country. The strike is nearly due east and west, the position nearly vertical, rather declining to the north; and these features are remarkably uniform and uninterrupted. In the excellent sections exhibited by the course of the rail- way, immediately to the east of Melrose, where the greywacke is not far distant from the trap of the Eildon Hills, the strike of the strata inclines more to the south-west, the strata are thinner and more undulating, mixed with more numer- ous clayey strata, and including many veins of calcareous spar. If we follow the greywacke strata to the eastward, we find them exposed near the village of New- stead, and along the south bank of the Tweed towards Drygrange Bridge. Be- tween these two points they are so much altered as to be scarcely recognisable, yet having the usual stratification from east to west. There is every appearance of a real barrier having crossed the present course of the river, which still runs in a very uneven channel; and behind this barrier is an enormous accumulation of debris of all sorts, forming the eminences through which the railway passes, beyond the village of Newstead, which have no nuclei of solid rock, as far as can be seen. Among these debris, boulders of the trap tufa of Melrose are conspicu- VOL. XX. PART II. 3 L 212 PROFESSOR FORBES ON THE GEOLOGY ous, which appear to be derived more immediately from boulders of that rock imbedded in the drift formation. It is also evident that the partial or complete removal of the barrier of altered rock just mentioned has changed the course of the Tweed, which appears once to have swept over the site of the present village and abbey of Melrose, forming the well-marked cliffs at Newstead, which may also have been the boundary of a fresh-water lake, whose depth depended on the height. of the rocky barrier. The remarkable promontory of Old Melrose, nearly three miles below the present village, and the picturesque site of the orzginal abbey of that name, founded, as is stated, in the end of the sixth century, is unquestionably owing to the prolongation of the trap-formation of the Eildons, which here becomes very narrow, crossing the Tweed just below Gladswood, and probably uniting itself to the trap of Bemerside Hill. The greywacke strata may easily be traced on each side of the narrow belt of trap on which the mansion- house of Old Melrose stands. If we now return to the little basin of the village of Melrose, close under the north foot of the Eildon Hills, we find the following arrangement of the rocks, the understanding of which will be facilitated by the inspection of the map, Plate VIII., fig. 3, where the outlines of the formations are marked, and reference is made by numbers to the principal specimens, and by lines to the strike of the strata, where it has been observed. In the course of a little stream passing through the town of Melrose, called Matty’s or Dingleton Burn, the greywacke strata may with care be observed almost continuously; and it is remarkable that they exhibit the east and west strike* and vertical dip with scarcely any alteration until we approach the farm-house of Dingleton Mains, when they become suddenly much confused at the point marked 3. In the field above Dingleton farm occurs a quarry of felspar porphyry, including much quartz (specimen M. 4a.+). This seems to be an offset from the trap of the north-east Eildon Hill, the greywacke appearing higher up (at 5 and 6) nearly unaltered, and may be traced almost to the head of the small streams which rise between the Eildons, and afterwards join the Dingleton Burn. It has probably not been suspected that so large a portion of this face of the Eildons is formed of the rock of the surrounding country. The ereywacke skirts the base of the principal Eildon Hill, the portion with the por- phyry passing a little to the south of a water-tank on the moor, near the point marked 17 on the map, where the position of the strata is east by north, and vertical. From this point the junction trends round the north slope of Bowden Muir, until we reach Cauldshiels Loch, on the Abbotsford property, where the junction is well marked on the eastern bank. * The deviation from true east and west is less than 5°. + The collection of specimens referred to in this paper has been placed in the Museum of the Royal Society of Edinburgh. OF THE EILDON HILLS, IN ROXBURGHSHIRE. 213 In the little basin to the south of Melrose, which has been so far described, we farther find a local and nearly concealed deposit of the red or Dryburgh sand- stone, which possesses considerable interest. It lies between the back of the “Quarry Hill,” which is a remarkable eminence of trap tufa close to the railway station at Melrose, and the strata of greywacke which we have seen to skirt con- tinuously the north-west slopes of the Eildons. This curious deposit may be easily detected in the wood inclosing a very small ravine with the local name of “ the Duke’s Glen,” and whose position will be best indicated by the numbers 28 and 29 onthe map. Itis here very nearly in contact with the trap tufa just mentioned. The strata absolutely resemble those at Dryburgh, four miles lower down the banks of the Tweed. They are purplish-red and white alternating, consisting of sandstone mixed with much slate-clay, and are here occasionally very much altered in tex- ture; the soft sandstone becoming very white and crystalline, and the slate-clay becoming extremely hardened, without losing its power of being diffused in water by steeping. ‘The strata are horizontal; and they are intermixed in some places with trap rock, intermediate between trap tufa and felspar rock. The altered sandstones and shales extend up both branches of the little stream until they touch the greywacke between the numbers 18 and 19, the former being iron- shot strata of greywacke, vertical and running north-east by east, the latter is the altered slate-clay of a pearl-grey colour, which can here only form a narrow strip dividing the red sandstone from the Eildon trap. I have not succeeded in tracing this patch of red sandstone farther west, at least with any certainty. I now come to speak of the trap tufa of Melrose, a rock always interesting in its geognostic relations, and on which my repeated examinations throw some light. It is a very perfect rock of its kind; including numberless fragments of felspar porphyry, usually rather small, and united by an earthy basis, which is either of a yellowish-brown or of a leaden-grey colour. It also contains many small frag- ments of a pearl-grey hue and uniform texture. These I believe to be portions of the altered slate-clay already spoken of. It is rather extensively quarried as a building material, for which it is exceedingly well adapted, as it is soft’ at first, and hardens on exposure. In the Dingleton Burn, already mentioned, it may be seen that the vertical strata of greywacke run towards the “Quarry Hill,” without the slightest discon- tinuity or swerving ; and though we cannot trace the junction, it is all but certain that the mass of trap tufa must cut off the greywacke strata abruptly. I was able to detect traces of the greywacke in a very imperfect section immediately behind the Melrose Station, which is within a short distance of the lofty escarpment of trap tufa, so that the transition is probably extremely abrupt. The trap tufa is separated throughout from the Eildon trap by greywacke strata. I imagine that it is more recent than the Eildon trap. It has unquestionably succeeded the deposit of the Dryburgh sandstone, as is also manifested by the alterations which 214 PROFESSOR FORBES ON THE GEOLOGY we observe on the same sandstone by another patch of trap tufa on the south bank of the Tweed, opposite Dryburgh Abbey, to which I was directed by Mr MILNE’s map, and which perfectly resembles the Melrose tufa; but it is evidently separated from it by the entire mass of the Eildon Hills and the adjoining grey- wacke rocks.* The Melrose tufa is completely lost to the north, in consequence of the ancient excavations occasioned by the river Tweed as already mentioned ; it sinks under flats and mounds of débris. But it may be traced to the eastward in the bed of the Huntly Burn, close to the house of that name, and to the villa of Chiefswood. It also extends to the Rhymer’s Glen, forming evidently a tongue, which runs up be- tween the narrow belt of greywacke which continues to fringe the trap of Bowden Muir and the well-marked greywacke ridge parallel to it on the north, which stretches to Faldonside. The section in the Rhymer’s Glen is not without inte- rest. Characteristic trap tufa (No. 26) first appears from under the detritus of the valley in the bed of the small stream. This unquestionably belongs to the same mass as the Melrose tufa. It may be traced up the stream of the Rhymer’s Glen, until it passes into a yellowish felspar rock in a gradual manner, which is probably in contact with the greywacke strata which succeed in almost vertical strata. Some of these strata are exceedingly hard, and form the barrier at the - first waterfall. It is here in contact with a singular bed of a coaly-appearance, which I believe has been mistaken for an indication of the coal formation, which, however, it cannot be, as it is interstratified with the hardened strata of ereywacke just mentioned, which, it may be added, include traces of common galena (No. 24), and are traversed by calespar veins (No. 25). The dark bed is a shale (No. 23) resembling alum shale, mechanically diffusible in water, and in- cluding soft whitish fragments resembling steatite. At the highest waterfall in the Rhymer’s Glen, the greywacke strata (which here run in a direction of east by north) are interrupted by a dyke of felspathic trap, sometimes of a purplish, sometimes of a yellow colour, and which I have no doubt is the same vein as may be discovered in the greywacke on the east side of Cauldshiels Loch (No. 20), not far from its contact with the main mass of the porphyry of Bowden Muir, of which this vein may be an offset. The waterfall above mentioned is unquestion- * The deposit in question occurs at the house of Holmes, exactly opposite to Dryburgh Abbey. The course of the Tweed is here north-north-west to south-south-east. The strata on both sides of the tufa mass are red and white sandstone, stratified nearly horizontally with some slate-clay. At the north junction the strata cannot be distinctly traced to within 50 or 60 yards of the trap; but, when the river is low, a better view might be had. The tufa rock, however, is modified and com- pacted, including large and small nodules of rounded quartz, and, in one place, includes soft angular fragments (perhaps of slate-clay), which give it almost a porphyritic appearance (specimen No. 30). The characteristic tufa rock (No. 31) may be traced 100 yards or so up a little side ravine, but is then completely lost under diluvium. The southern part of the tufaceous mass becomes very com- pact, and assumes the character of a very tough felspar porphyry (No. 32). The sandstone strata in contact with it are hardened and bleached in a remarkable manner. OF THE EILDON HILLS, IN ROXBURGHSHIRE. 215 ably very near the mass of Bowden trap. The purple and yellow trap-dyke may probably be identified also with one (No. 29) cutting the new red sandstone in the “ Duke’s Glen,’ behind the Quarry Hill at Melrose, already referred to. - I shall conclude with some observations on the structure of the Eildon Hills themselves. We have seen that the greywacke formation rises to within 200 feet or thereabouts of the level of the col or neck which unites the two principal emi- nences. At this very level occurs a tolerably marked shelf of diluvium, which has strongly the appearance of having been caused by a temporary sojourn of stag- nant water at that height. Mr Minne has very correctly remarked, that the drat on the Eildon Hills includes fragments of bright red sandstone. This phenome- non is better marked, however, on the south side of the col or neck above referred to. It is an inquiry of some interest whence these fragments could possibly have been derived so as to have been transported by water or otherwise to so high a level. The last visible greywacke strata (at 5 or 6) are not much altered (whilst nearer the farm of Dingleton the alteration is very marked, the strata being iron- shot and hardened, and the direction of strike in some places changed). Here the rock is sandy and of natural hardness, the strata nearly vertical, and running almost due east and west; in short, in almost exact parallelism to the general stratification of the country. Yet this must be very close to the contact with the great mass of porphyry of the Eildons, though the junction can no where be _perceived. In ascending slopingly to the top of the highest Eildon by its north- west acclivity, I found many blocks, apparently of altered greywacke, having a singular character, some quite injected (as it appeared to me) with felspar, yet distinguishable almost by the touch from felspar rock, having a peculiar gritty feel. These blocks appeared to have fallen from small cliffs above, which, having ascended, I found to display a progressive alteration or metamorphosis from the trap rock of the hill into a rock having in one place almost the character of | gneiss, and which I take to be a portion of indurated greywacke caught up by the | trap, and forming the greater part of the summit of the Eildon, whose bold form | arises in part from the excessive resistance of such metamorphic rocks to the | action of the weather. The real trap which has effected this metamorphosis is a | porphyritic claystone, and the whole somewhat resembles the well-known features | of the geology of the Pentland Hills at Habbie’s How.* : Repeated visits and a careful selection of specimens confirmed this view. | Specimens of the brick-red felspar passing into claystone porphyry are found in | Nos. 7, 11, 15. As we approach the top it becomes slaty, and the direction of | cleavage shifts round, dipping towards the centre of the cone, the summit being | what appeared to me the altered rock. The slaty felspar acquires green dots | (Nos. 8 and 9.) Then we have the slaty rock shot with red felspar (12), before * Mr Mie describes the top of Eildon as composed of a very hard clinkstone with a grey | basis, which strikes fire with steel. But true clinkstone could not do so, being a pure felspar. VOL. XX. PART II. 3M (219i) XII.—On a New Source for obtaining Capric Acid, and Remarks on some of tts Salts. By Mr Tuomas Henry Rowney, F.C.S. (Read March 17, 1851.) The following examination of capric acid and some of its salts, was made in the laboratory of Dr T. ANDERson, to whom I am much indebted for his kindness in procuring for me the materials to work upon, and also for advice during the progress of this investigation. Capric acid has been found by CHEvreEuL and Lercu in the butter of the cow and goat; by REDTENBACHER,* amongst the vola- tile oily acids he obtained by acting on oleic acid with nitric acid; by GerHarpt and Canours,{ by the action of nitric acid on the oil of rue; and by GorcEy,t in cocoa-nut oil ;—from all these sources it has been obtained only in small quan- tities, and always along with other acids of the series to which capric acid belongs. In the present paper I have to point out a new source for obtaining it, namely, the fousel oil or grain oil of the Scotch distilleries. The principal constituents of grain oil are water, alcohol, and the hydrated oxide of amyl.. The proportions of these constituents vary in the oils obtained from different distilleries ; in some cases it is soluble in water, and then consists chiefly of water and alcohol, with a sma"! quantity of the hydrated oxide of amyl; generally, it is an oily liquid lighter than, and insoluble in, water. Besides the three above-mentioned constituents, other compounds have been found in it in small quantities. MutpEr§ found cenanthic acid, and Koise|| found margaric acid. In the oil examined by myself, an acid was found, which analysis proved to be capric acid. In what state it exists in the oil, 1 am not able to say, but I think it most probable that it is in com- bination with the hydrated oxide of amy]. To obtain the capric acid, the grain oil was distilled with a thermometer placed in the tubulure of the retort, and the distillate collected in separate re- ceivers. ‘The first portion consisted of water, alcohol, and the hydrated oxide of amyl; the second portion was the hydrated oxide of amyl, and a dark-coloured residue was left. This residue was oily, it had a very disagreeable smell, and was insoluble in water and KO,CO,, even when boiled with a solution of the latter; when boiled with a strong solution of caustic potassa it is rendered so- luble in water. Whilst boiling, a strong smell of the hydrated oxide of amyl is * Journal of the Chemical Society, Part 19. + Annalen de Chemie und Pharmacie, Band 56. ¢ Annales de Chemie et de Physique, 3d § Liebeg’s Annalen, Bd. 24, p. 248. Series, Tome 24. || Idem, Bd. 41, p. 35. VOL. XX. PART II. 3N 220 MR THOMAS HENRY ROWNEY ON A NEW SOURCE given off; and if the operation be performed in a retort with a receiver attached, this compound is found floating on the water that passes over during the opera- tion. It is also rendered soluble by being digested with a strong solution of caustic potassa for two or three days on the sand-bath. On adding HCl or HO, SO, to the cold alkaline solution, a dark oily mass rises to the surface; this was filtered and washed with cold water. I found that the best way to obtain the acid pure, was to dissolve it in a dilute solution of NH,0O, and then to add Ba, Cl until it ceased to give a precipitate; this precipitate was filtered and washed with cold water, then dissolved by boiling with water, filtering whilst hot, and allowing the filtrate to crystallize. It is sometimes dissolved with difficulty by boiling water, owing to its forming hard soapy masses during the boiling; by crys- tallizing the baryta salt two or three times, it becomes nearly colourless. It was then decomposed by boiling with NaO,CO,, and filtered from the precipitated BaO, CO,, dilute HO, SO, was added to the filtrate to separate the capric acid, and by these means it was obtained nearly colourless, and in a solid state. To obtain it perfectly pure, it was dissolved in alcohol, and a large quantity of water was added to the alcoholic solution, the mixture becomes turbid, and after stand- ing for some hours capric acid crystallizes out; and by repeating this process it may be obtained perfectly pure and colourless. The mother liquors from the baryta salt were concentrated by evaporation and then boiled with NaO, CO,, filtered from the BaO, CO,, and the filtrate decomposed by HO,SO,; the capric acid obtained from this portion was mixed with a small quantity of an oily acid, the quantity was so small that I was not able to ascertain its constitution. Caprice Acid. Capric acid, as obtained in the manner I have described, is a solid, white, and crystalline compound, having a faint odour, and fuses readily when taken be- tween the fingers. It is very soluble in cold ether and alcohol, and does not crys- tallize from these solutions. It is insoluble in cold water, but dissolves sparingly in boiling water, and crystallizes from this solution on cooling in the form of scales. It is also soluble without decomposition when boiled with concentrated nitric acid, and is precipitated from this solution by the addition of water. It is obtained in a mass of needle-shaped crystals by the addition of water to the alco- holic solution. Its specific gravity is less than that of water. The crystallized acid commences to fuse at 81° Fahr., and the mercury of the thermometer conti- nues to rise to about 116° Fahr. before the whole is completely fused. When allowed to cool, it becomes solid at 81° Fahr. The fused acid is slightly coloured, and has a faint smell; it becomes crystalline on cooling. This fusing point differs from that generally given. Gorey gives it at 86° Fahr., and others have stated it to be from 60° to 66° Fahr. These differences probably arise from im- pure acids having been used. For analysis the crystallized acid dried 7 vacuo over sulphuric acid was employed. FOR OBTAINING CAPRIC ACID. 221 9558 of carbonic acid, and 3759 grammes of substance gave I *3930 of water. -3176 grammes of substance gave II. < -8080 of carbonic acid, and 3330 of water. Theory. Experiment. — oJ — ————————S—_ ep LBls Mean. C5, 120 69°76 69°35 69°38 69°36 leis 20 11:62 11-61 11:65 11-63 A 32 18°62 172 100-00 Caprate of Silver. This salt is formed when AgO, NO, is added to a slightly ammoniacal solu- tion of capric acid. It is insoluble in cold water, sparingly soluble in boiling water, and is deposited again on cooling in needle-shaped crystals. It is more soluble in boiling alcohol, but the solution becomes dark-coloured, and the crystals deposited from it are also dark-coloured. GorG&y also observed this change. It is very soluble in ammonia, and if the ammoniacal solution be kept in a warm place, so as to drive off the ammonia, a crystalline salt is obtained; but not hav- ing a sufficient quantity, no examination of this compound was made. The silver salt whilst moist is rapidly blackened, if exposed to bright daylight; but after drying it may be exposed to the light without undergoing any change. The silver salt for analysis was precipitated and washed during the evening, dried 7 vacuo over sulphuric acid, the receiver being covered with a cloth, to prevent the access of light to it; it was then dried in a water-bath at 212° Fahr. r. {2485 grammes of silver salt gave " (0951 of silver. iz { 3050 grammes of silver salt gave | 175 of silver. Ill ‘2715 grammes of silver salt gave ~ {+1050 of silver. ‘4265 grammes of silver salt gave IV. < -6650 of carbonic acid, and 2617 of water. -3402 grammes of silver salt gave V. < °5282 of carbonic acid, and ‘2062 of water. Theory. Found. ———— Fr Se a Te II. III. IV. VE Mean. Ca 120 43°01 42°52 42°34 42°43 His 19 6°81 6°81 6-73 6°77 0, 32 11-47 Sek Bee sj ss aa Ag 108 38°71 38:27 38°52 38°67 38°49 279 100-00 222 MR THOMAS HENRY ROWNEY ON A NEW SOURCE Caprate of Baryta. The baryta salt was obtained by adding Ba Cl to an ammoniacal solution of capric acid, the precipitate was filtered and washed with cold water. It is soluble both in water and alcohol when boiled with these liquids, and crystallizes out from these solutions, on cooling, either in needle-shaped or prismatic crystals; the crystals obtained from the alcoholic solution are sometimes of considerable size. This, as also the other salts of the alkaline earths, and the silver salt, are insoluble in water after having been dried, as they float on the surface of the water and repel it; but by first moistening the salt with alcohol, they may be again rendered soluble in boiling water. They are also very difficult to powder and mix for analysis. The salt analyzed was crystallized from water, and dried in the water-bath at 212° Fahr. The baryta was determined as BaO,SO,, and the combustion was made with chromate of lead. I -2935 grammes of baryta salt gave * (1415 of BaO, SO,. II -4375 grammes of baryta salt gave > \5<2a1 95 of BaO, SO,. ‘2411 grammes of baryta salt gave III. < -4410 s of carbonic acid, and "1750 of water. -2335 grammes of baryta salt gave IV. < °4245 of carbonic acid, and 1732 of water. Theory Found. I LE III. VES Mean. Cor 120 50°08 49-88 49°58 49-73 GG 19 7:93 8:06 8:24 8°15 Otani gett ae 10-08 » re we 2 Re BaO 76°6 31:97 31°65 31:88 31-78 239-6 100-00 Caprates of Lime and Magnesia. These salts crystallize and have similar properties to the baryta salt, but they are more soluble both in alcohol and boiling water. No analysis was made of the lime salt, but the base of the magnesia salt was determined. The salt em- ployed for this purpose was crystallized from water, and dried at 212° Fahr. The magnesia was determined as 2 MgO, PO.. ‘3687 grammes of caprate of magnesia gave 1145 of 2 MgO, PO,. The formula C,, H,, O,, MgO requires 11:25 per cent. of MgO, and the per-centage obtained by analysis was 11:37 MgO. FOR OBTAINING CAPRIC ACID. 223 I endeavoured to obtain some other salts of capric acid, but as only the salts of the alkaline earths are readily crystallizable, I did not succeed in doing so. The salts I tried were the soda, copper, and lead salts. The copper salt is insoluble in water and alcohol, but soluble in ammonia. The analyses of these salts always gave an excess of base; this was caused by my not being able to obtain a neutral ammoniacal salt of capric acid. The lead salt is insoluble in water, and very sparingly soluble in boiling alcohol; the solution, on cooling, deposits the lead salt in rounded grains. The soda salt is exceedingly soluble both in cold water and alcohol, and does not crystallize from these solutions. When evaporated to dryness, it dries up to a horny mass, partially crystalline on the surface. It is soluble in absolute al- cohol when warmed, and the solution when allowed to cool becomes an opalescent mass. I could not obtain it free from NaO,CO,, even by means of absolute alcohol, consequently the analysis gave an excess of base. From the analyses made of the soda and copper salts, they appear to be neutral salts; the formula of the soda salt being NaO,C,,H,,0,, that of the copper salt being CuO, C,, H,, O,. Capric Ether. This ether I obtained by dissolving capric acid in absolute alcohol, and passing dry hydrochloric acid gas into the solution to saturation. The addition of water to the solution caused the capric ether to rise to the surface as an oily liquid. It was separated from the acid liquid and washed with cold water, and then dried by digesting it with fused Ca, Cl: its specific gravity is 862. It is insoluble in cold water, but readily soluble in alcohol and ether. As the quantity of the ether was too small to allow of an analysis of it being made, I converted it into the following compound :— Capramide. The capric ether was dissolved in alcohol, and a strong solution of ammonia was added to it in a stoppered bottle; after a few days the solution became turbid ; this turbidity increased after allowing it to stand for a longer period, and crystals began to make their appearance. The digestion was continued until the whole of the ether had disappeared. The crystals were then filtered off, and the filtrate evaporated to dryness on a water-bath ; the residue was dissolved in alcohol, and the addition of water caused the capramide to crystallize from the solution; the whole was dissolved in warm dilute alcohol, and allowed to crystallize. As ob- . tained in this manner it is quite colourless, and crystallizes in brilliant scales, which, when dry, have a bright silvery lustre. It fuses below 212° Fahr., and is insoluble in water and ammonia. It is very soluble in cold alcohol, and in dilute alcohol when warmed in it. Its other properties I could not examine, as I had only suf- VOL. XX. PART Il. 3 0 224 MRT. H. ROWNEY ON A NEW SOURCE FOR OBTAINING CAPRIC ACID. ficient substance for one combustion. For analysis it was dried in vacuo over sulphuric acid, and the combustion was made with oxide of copper. 5407 ~~... of carbonic acid, and 2088 grammes of substance gave 2287 =... of water. The numbers correspond to the formula C,, H,, 0, N, which requires C 70:17, H 12-28. The numbers obtained are C 70°62, H 12-17. XIL.—On certain Salts and Products of Decomposition of Comenic Acid. By Mr Henry How. Communicated by Dr T. ANDERsoN. (Read 7th April 1851.) The study of the organic acids appears scarcely to have advanced of late years pari passu with the other branches of organic chemistry. It seems, indeed, as if the development of each of the different departments of the science had been, to a certain extent, periodical; each engrossing the labours of investigators to the temporary exclusion of the others, themselves to be renewed when some new experiments should reawaken an interest in them. However this may be, the subject of the natural and artificial bases has proved so productive of interesting results as to have recently become the chosen and almost exclusive field of inquiry, notwithstanding several investigations which have thrown much light on one class of organic acids, namely, that represented by the general formula C,H, O,. With the exception of this section, the his- tory of the organic acids remains very imperfect, and in many cases we have but a meagre account of a few of their salts. These remarks apply with peculiar force to the polybasic acids; and it was with a view to add something to the existing information respecting this import- ant class of bodies that I undertook an examination of the acid which forms the subject of the present paper. Although this is not among those which have been least investigated, many gaps existed in its history which seemed to me worthy of being filled up. I first gave my attention to those of its salts, which had hitherto remained undescribed or been but imperfectly examined, not from their possessing any very marked interest in themselves, but with the idea of obtaining points of comparison between acids likely to occur in the course of the proposed investigation. My experiments were performed in the laboratory of Dr T. ANDERSON. Comenic acid was discovered by RosiquEet,* who observed that meconic acid undergoes a change of properties when boiled with water, carbonic acid being evolved, and a product obtained to which he gave the name Parameconic Acid, indicative of isomerism with the original substance. Lizpic,+ however, pointed out that there was also difference in composition, and proposed the provisional name Metameconic Acid for the new substance, whose composition he represented by the formula C,, H, O,,, derived from the analysis of the acid itself and of a silver salt. In a subsequent paper{ he shewed its bibasic nature, and entered * Annales de Chimie et de Phys., Tome 51, p. 244. + Ibid., 54, p. 26. t Annalen der Chemie und Pharmacie, Band 26. VOL. XX. PART Il. 3 P 226 MR HENRY HOW ON CERTAIN SALTS AND fully into the relations between it, which was now named Comenic Acid, Meconic Acid, and Pyromeconic Acid, the product of dry distillation common to both the former bodies. The subject was further discussed by Dr Srenuovuse,* in a paper, to some of the details of which I shall have occasion to refer. I employed for the preparation of comenic acid the process of RoBiquET as modified by GRrEGoryY, which consists in boiling crude meconate of lime (or, still better, the acid salt obtained by once treating this substance with boiling water and hydrochloric acid) with a quantity of pretty concentrated hydrochloric acid suffi- cient to dissolve it. For the purification of the acid which is deposited in the form of very dark-coloured hard crystalline grains, SrenHousE recommends solu- tion in a slight excess of caustic potass or soda, and recrystallization of the salt deposited from the boiling fluid. I preferred, however, to use ammonia, since, if certain precautions are adopted, a salt is obtained as readily deprived of colour as the potass salt, and much more insoluble in cold water than the corresponding salt of soda; while the mother liquors afforded a convenient means of trying the action of various chemical agents upon the acid. The process I employed consists in boiling the dark-coloured grains in water, with gradual addition of caustic ammonia, till the whole is in solution. The fluid is then immediately filtered. The addition of an excess of ammonia, and the continuance of a boiling heat are to be avoided, as there ensues, if this be not attended to, a curious decomposition, attended with the production of much colouring matter, the explanation of which will be entered into subsequently. The ammonia salt obtained as above, deposits from the black fluid in yellow hard crystals if the solution is left at rest, but in soft silky prisms when it is agi- tated; in the latter state the salt is not so readily washed free of the coloured mother liquor. By two or three crystallizations from boiling water, a salt of dazzling whiteness, in fine radiated four-sided prisms, is obtained. From solutions of this salt, which, when even quite pure, have a faint shade of straw-colour, the addition of concentrated hydrochloric acid throws down co- menic acid in the form of a white heavy crystalline powder adhering to the sides of the vessel, which, when dissolved in boiling water, in which it is not very so- luble, is deposited from a saturated solution in grains and crusts, almost colour- less; but as the solution cools, groups of short prismatic, or sometimes leaf-like, crystals appear, always possessing a characteristic yellowish-red tinge of colour. The general chemical and physical properties of comenic acid have been already too well described to require any special remarks on my part; I shall therefore proceed at once to the details of the salts I have examined. Bicomenate of Ammonia. This salt was obtained and analysed by SteNHovsgE, who formed it by solution * Mem. and Proc. Chem. Soc., vol. i. PRODUCTS OF DECOMPOSITION OF COMENIC ACID. 227 of the acid in a slight excess of ammonia, and subsequent concentration in vacuo over sulphuric acid. He describes it as “ partly amorphous, partly crystalline ;” he found that it lost two equivalents of water on drying at 212°. As obtained by the process above given, it is in the form of square prismatic crystals, white and of great brilliancy, presenting when in mass a beautiful appearance. It is very soluble in boiling water, very little soluble in alcohol. It has a strong acid re- action, and is deposited even from a solution of the acid in an excess of hot caustic ammonia, if the boiling has not been continued. It is represented by the formula NH,0, HO, C,, H,0, + 2aq. My own analyses agree with this, which is the result of the analyses of Dr StenHousE; but a salt containing an additional single atom of water is obtained when strong alcohol is added to cold saturated alkaline solution of comenic acid in ammonia. It falls in groups of radiated prisms. 5-193 grains of the air-dried salt lost at 212° Fahr. O-713 - ..7)) water. The per-centage calculated from the number is 13°73, while 13°50 is that corre- sponding to the formula NH,O, HO, C,, H,O, + 3 aq. Bicomenate of ammonia, in the dry state, sustains a temperature of 350° Fahr. without decomposition or loss of weight. When heated to 390° Fahr. in a closed tube, it blackens and fuses, and on examination it is found to have undergone a change, an acid substance being produced, which I shall describe fully hereafter. Bicomenate of Potass. When comenic acid is boiled with a slight excess of caustic potass, it dissolves readily, and the fluid on cooling deposits a salt, which, when washed with cold water, and subsequently recrystallized from the same menstruum boiling, presents itself in groups of short, square, prismatic needles. They are not very readily deprived entirely of colour. They have a strongly acid reaction, and are the an- hydrous bicomenate of potass. They gave the following results on analysis; the potass was determined by ignition with a few drops of strong sulphuric acid. 6:250 grains air-dry salt gave 8-497 ... carbonic acid, and 0-987 ..... water. 5291 grains gave 2°335 ... sulphate of potass. Experiment. Calculation. Pe emmeniaemmiaemmmeantintemeammenememaeme Carbon, : 37:07 37:07 Oe 1? Hydrogen, . 1°75 1:54 ld 3 Oxygen, ; bp 37-09 0, 72 Potass, : 23°88 24°30 Ko 47:2 100-00 100-00 194-2 The formula of the above salt is therefore KO, HO, C,, H, 0,. 228 MR HENRY HOW ON CERTAIN SALTS AND Bicomenate of Soda. Comenic acid was dissolved in a tolerably strong solution of caustic soda by boiling ; the fluid on cooling deposited two forms of crystals, one in mammillated masses, the other in transparent prisms half an inch in length. On washing the mixture with a little cold, and resolution in boiling, water, no deposit was obtained on cooling, even after the lapse of some hours; but on evaporation of the fluid to about two-thirds of its bulk, groups of mammillary crystals appeared, which when magnified were found to consist of four-sided elongated prisms. From this it appears that the salt is much more soluble than either the potass and ammonia salt, and cannot be employed with advantage in the preparation of comenic acid. It has an acid reaction, and is anhydrous; its analysis is subjoined. The soda was determined by simple ignition, and subsequent weighing of the carbonate of soda produced { 6-020 grains dried at 212° gave 1:753 ... carbonate of soda. The per-centage of soda calculated from this experiment is 17:09 : 17-41, being that corresponding with the formula NaO, HO, C,, H, 0,. It is obvious, from the foregoing experiments, that neutral salts of comenic acid with the fixed alkalies or with ammonia do not exist in the dry state. That this is not the case with reference to the alkaline earths, I shall now proceed to shew. Salts of Lime with Comenic Acid. Finely-powdered comenic acid, mixed with water and an excess of carbonate of lime, decomposes the earthy salt with effervescence, in the cold. When the liquid is boiled for some time, then filtered and allowed to stand, a few rhombic crystals appear; but by far the larger proportion of the acid remains on the filter in combination with the lime, mixed with the excess of carbonate employed. The crystals were in very small quantity; they consisted doubtless of the acid salt, which I obtained more conveniently in another way. Bicomenate of Lime-——When a cold, saturated, aqueous solution of bicomenate of ammonia is added to a solution of chloride of calcium, brilliant crystals soon begin to appear which gradually increase in quantity. They are, though small, perfectly defined transparent rhombs; they dissolve readily in boiling water, and are deposited on cooling of a larger size than when first obtained. In the follow- ing analysis the substance was dried at 250° Fahr., as it was found that the whole © water of crystallization was not expelled at 212°, or only after the lapse of a very long time. The lime was determined as sulphate, by ignition with a few drops of sulphuric acid, as the salt swelled up inconveniently when heated by itself. 4-512 grains dried at 250° Fahr. gave 6-755 ... carbonic acid, and 0:788 ... water. PRODUCTS OF DECOMPOSITION OF COMENIC ACID. 229 { 6-475 grains dried at 250° gave 2520 ... sulphate of lime. Experiment. Calculation. SS Carbon, . , 40°83 41:14 Gis 72 Hydrogen, 2 1:94 17a) H, Oxygen, . : a 41-15 0, 72 Lime, : ‘ 16:02 16:00 CaO 28 100:00 100-00 175 Hence the composition of the salt dried at 250° is represented by the formula CaO HO, C,, H, 0,. The crystals contain seven equivalents water of crystallization. 7177 grains air-dry salt lost at 250° Fahr. 1893 ... water. { 8°757 grains air-dry salt lost at 250° Fahr. 2°270 ... water. these numbers, when calculated for per-centage, give i i, Mean. 26°37 25:92 26°16 and 26°47 is that corresponding to the formula CaO, HO, C,, H, 0,+7 aq. Neutral Comenate of Lime.—This salt is obtained in the form of crystalline grains, when a solution of the acid ammonia salt, to which an excess of ammonia has been added, is poured into a solution of chloride of calcium. According to the state of dilution of the fluids employed, salts containing different amounts of water of crystallization are obtained, and the appearance of the product varies accordingly. They are all insoluble in water. The well-washed substance gave the following results; the lime being estimated as sulphate, because the salt when dried blows up in a cloud on ignition. { 9-670 grains dried at 250° gave 6-270 ... sulphate of lime. 6-015 grains dried at 250° gave 7:545 ... carbonic acid, and 1-280). ony o water. Experiment. Calculation. OO Carbon, . : 34:20 33°96 OR Ue Hydrogen, 3 2°36 1:88 H, 4 Oxygen, : a 27°75 OF, 80 Lime, F é 26°59 26:41 2CaO 56 100-00 100-00 212 The formula of the salt, dried at 250°, is therefore 2Ca0, C,, H, 0,+2 H,. two equivalents of water being retained at this temperature. VOL. XX. PART II. 3 Q 230 MR HENRY HOW ON CERTAIN SALTS AND As before mentioned, salts containing various amounts of water of crystalliza- tion are formed in more or less concentrated solutions. The crystals of that one whose analysis in the dry state is given, were in the form of groups of minute prisms. They were deposited in a tolerably dilute fluid, and lost five atoms of water in drying. 11-785 grains lost at 250° { 2-145 water. which number gives a per-centage of 18°20: 17°50, being that corte to the formula 2 CaO, C,, H, O,, 2Ho+5 aq. By employing very dilute solutions, a salt was got in very well-defined, small, brilliant crystals, which lost, at 250° Fahr., 31:27 per cent. of water: now the number 31°82 is that required by the formula 2 CaO, Cie Hi, OF 2 Ho+11 aq. This dried salt gave 26°35 per cent. of lime, which agrees perfectly well with the results obtained in the former case. All these neutral salts are converted into basic compounds by simple ebulli- tion in water. Salts of Baryta with Comenic Acid. Carbonate of baryta is partially decomposed by comenic acid in the cold, and completely so when heated with an excess in water, the acid comenate of baryta being produced. On the other hand, when a mixture of the acid and an excess of carbonate of baryta is boiled with water, effervescence ensues, but the comenic acid remains undissolved, being in combination with the earth in form of a basic salt. I readily obtained both an acid and a neutral salt by double decomposition. Bicomenate of Baryta.—A cold saturated aqueous solution of bicomenate of ammonia gives, with a solution of chloride of barium, an immediate precipitate of a crystalline nature. With more dilute solutions, the salt appears more slowly in well-defined transparent rhombs. It is readily soluble in boiling water, and has a strong acid reaction. It loses its water of crystallization at 212°, but very slowly; the dried salt fuses on ignition. 5°878 grains dried at 212° gave 6-874 ... carbonic acid, and 0:905.... ‘water. { 5-797 grains dried at 212° gave, on ignition, 2:525 ... carbonate of baryta. . Experiment. Calculation. —— Carbon, . . ~— 31-89 p19) \eelh a 4 Hydrogen, ; cg | 1-34 Hy 3 Oxygen, . t in 32°21 O,, yes Baryta, . : 33°81 34:26 BaO 76°64 100-00 100-00 223°64 PRODUCTS OF DECOMPOSITION OF COMENIC ACID. 231 Hence the composition of the salt dried at 212° is expressed by the formula BaO HO C,, H, 0,. In the crystals, as appears from the following experiments, two equivalents of this substance are combined with thirteen of water. { 14-815 grains air-dry substance lost at 212° 3°105 ... water. 10-721 grains air-dry substance lost at 212° 2°228 ... water, The per-centage calculation from which, ile JOM Mean. 20:95 20-78 20:86 agrees well with the number, 20°73, required by the formula | 2 (BaO, HO, C,, H, 0,) +13 aq. Neutral Comenate of Baryta.—An alkaline ammoniacal solution of comenic acid causes an immediate precipitate in chloride of barium, of minute radiated crystals. In dilute solutions these do not appear immediately, but in a very short time they commence forming, and their quantity increases till the whole fluid is filled. Under these circumstances they present a very beautiful appearance, being in individual groups, whose silky needles radiate regularly from a centre. Under the microscope these needles are seen to be square prismatic crystals. This salt is insoluble in boiling water, and does not lose its water of crystalli- zation at a temperature of 212°. When dried at 250°, it is almost pyrophoric on ignition, blowing up in a light fiery cloud; for this reason the base was deter- mined as sulphate in the analysis which follows, by ignition with a little sul- phuric acid. 5-418 grains dried at 250° Fahr. gave 4-584 ... carbonic acid, and 0-721 ... water. 5°556 grains dried at 250° Fahr. gave 4:194 ... sulphate of baryta. Experiment. Calculation. CES ae Le Carbon, . 2 23°07 23:27 Cie 12 Hydrogen, 5 1-47 1:29 tay 4 Oxygen, . ; as 25°89 Or 80 Baryta, . , 49-54 49-55 2BaO 153-28 100-00 100-00 309-28 From the above it appears that this salt, like the corresponding one of lime, retains two equivalents of water at this temperature, its formula being 2 BaO, C,, H, 0,+2 HO, 232 MR HENRY HOW ON CERTAIN SALTS AND The crystals contain in addition eight atoms of water. { 14-380 grains air-dry salt lost at 250° —2TT6. . \... water, and 11-665 grains air-dry substance lost at 250° 27180 ... water. the mean of these numbers, when calculated on 100 parts, It «II. Mean. 19-29 18°77 19-03 agrees perfectly with that,—18'88,—corresponding to the formula 2 BaO, C,, H, 0,, 2 HO +8 aq. The crystallized salt when boiled in water is converted into a basic com- pound, which loses no water at a temperature of 250°. A portion, which had been so dried, gave on analysis 54°5 per cent. of baryta; this is considerably more than would correspond with a normal neutral salt entirely free from water. Salts of Magnesia with Comenic Acid. Acid Comenate of Magnesia.—This salt is much more soluble than the corre- sponding salts of lime and baryta; it crystallizes out after some time, in perfect small rhombs, when strong cold solutions of bicomenate of ammonia and sulphate of magnesia are mixed. When obtained from dilute solutions, by spontaneous or very slow artificial evaporation, these crystals are of very large size, and when possessing the yellow colour so apt to adhere to salts of comenic acid, they very much resemble regular crystals of ferrocyanide of potassium. They are readily soluble in hot water, and react strongly acid. The following is the analysis, the magnesia being estimated as sulphate, by ignition with sulphuric acid :— 7-426 grains dried at 240° Fahr. gave 10-517. ... carbonic acid, and 1988 ... water. 5-613 grains dried at 240° Fahr. gave 1-863 ... sulphate of magnesia. Experiment. Calculation. —————_— Carbon, . s 38°62 38:77 Cr 72 Hydrogen, . 2°97 2°69 ELE 5 Oxygen, . ; ae 47-41 On 88 Magnesia, : 11eh0 11-13 MgO 20°67 100-00 100-00 185:67 from which it appears that two atoms of water are retained in combination at the temperature of 240° Fahr.; the composition of the so-dried salt being ex- pressed by the formula MgO, Ho, C,, H, O,+2 HO. PRODUCTS OF DECOMPOSITION OF COMENIC ACID. 233 The crystals contain further six atoms of water, according to one experiment, { 16-794 grains air-dry substance lost at 240° Fahr. 3-709 <:.: water, which gives for 100 parts, 22-08 ; the number 22°53 is that required by the formula MgO, HO, C,, H, O,, 2 HO + 6 aq. Neutral Comenate of Magnesia.—When an alkaline ammoniacal solution of comenic acid is added to a solution of sulphate of magnesia, a salt is precipi- tated, especially on stirring the fluid, in the form of hard crystalline grains, adhering very much to the sides and bottom of the vessel. Under the microscope, those grains are found to be made up of groups of short prismatic needles. They are insoluble in boiling water. They lose their water of crystallization at 212°, but only after long exposure to that heat; thus dried they give the following results on analysis :— 5°680 grains dried at 212° gave 7°305 ... carbonic acid, and 1387 ... water. . 5:422 grains dried at 212° gave 3°115 ... sulphate of magnesia. Experiment. Calculation. anes Carbon, . : 35°07 34:89 Cr a2, Hydrogen, 2°53 2-42 Hi, 5) Oxygen . : aa § 42°66 OF 88 Magnesia, : 19°53 20°03 2MgO 41:34 100-00 100-00 206°34 from which it appears that the formula expressing the composition of the salt, dried at 212°, is 2 MgO, C,, H, 0,+3 HO. I endeavoured, by employing a higher temperature, to obtain a salt corre- sponding with the neutral salts of lime and baryta, in the amount of water retained at the same heat; but in the experiment I made, the substance lost weight at 250° gradually through a space of four days, and then the loss between each weighing was very small. It yielded 21:3 per cent. of magnesia, which ‘is more by a half per cent. than is required by a salt of the constitution sought for. The neutral comenate of magnesia, precipitated as above mentioned, has the com- position expressed by the formula 2Mg0, C,, H, 0,,3HO+8 aq. the eight atoms aq. being lost at 212”. 15-103 grains air-dry substance lost at 212° 4:003 ... water. This experimental number, calculated for 100 parts, gives 26:50; the number calculated from the above formula is 25:86. VOL. XX. PART II. 3R 234 MR HENRY HOW ON CERTAIN SALTS AND The salts of strontian somewhat resemble in appearance those of baryta, but are more soluble. It is curious that this acid does not form an acid salt with oxide of copper; the salt with two equivalents of base being obtained both by the addition of comenic acid itself and of acid comenate of ammonia to a solution of sulphate of copper. This salt was analysed by Srennouse, who also examined some others, the details of which will be found in the paper already referred to. Products of Decomposition of Comenic Acid. By Oxidation.—The conversion of comenic into carbonic, oxalic, and hydro- cyanic acids, by the agency of nitric acid, was noted among the first facts con- nected with the subject. It takes place with very dilute acid. When tolerably strong nitric acid is employed, the action is very rapid and violent, and when once commenced by application of a gentle heat, is completed in very few minutes, though the heat be withdrawn. Dr STENHOUSE, in the paper before mentioned, states that when comenic acid is kept for some hours at a temperature of 150° Fahr. in a solution of persulphate of iron, yellow crystals are formed, which contain protoxide of iron, and an acid which is not comenic acid. I did not succeed in obtaining a similar result on a repetition of his experiment, possibly because the circumstances were not strictly the same. I think it possible, however, that these crystals consisted of oxalate of protoxide of iron, from the ease with which comenic acid is oxidized, when boiled in a solution of persulphate of iron. I treated a quantity of comenic acid in this way, effervescence of carbonic acid ensued strongly, and the fluid was found to contain much protoxide of iron and oxalic acid. I identified the latter by a pre- paration and analysis of its lime salt in a pure state, after the removal of the iron and sulphuric acid by appropriate means. I could not succeed in producing any change by the action of sulphurous acid or of sulphide of hydrogen upon comenic acid. Action of Chlorine on Comenic Acid. Chlorocomenic Acid—When a current of moist chlorine is passed through water holding powdered comenic acid in suspension, a portion of the acid is dis- solved, and the clear liquid deposits, after the lapse of some time, long, brilliant, and colourless prismatic needles of the new acid. The same effect is produced when a solution of the ammonia salt is employed, and as, from the more ready solubility of this substance, results were more conveniently obtained, I used it in preference in my experiments. If an alkaline ammoniacal solution of comenic acid be exposed to the action of chlorine, the first result is a precipitation of the acid comenate of ammonia; but if a cold, saturated, coloured solution of the latter salt be employed, and the PRODUCTS OF DECOMPOSITION OF COMENIC ACID. 235 gas be passed through it for some time, the whole of the colour disappears, or the liquid only retains the faint yellowish-green characteristic of an aqueous solution of chlorine, without the formation of an immediate precipitate. After the lapse of some hours, groups of long, colourless, prismatic needles are deposited, the quantity of which is increased by the addition of hydrochloric acid. The mother liquor, on gentle evaporation, gradually acquires a brownish shade of colour, which passes ultimately into a very dark brown, and there deposited a further quantity of the new acid in prismatic crystals, separate and in groups, of a brown, nearly black, lustrous appearance. In this second mother liquor, in addition to the colouring matter, oxalic acid is to be detected. The colourless crystals at first obtained, after washing with cold water, were recrystallized from boiling water, in which they are readily soluble: they acquired, in this process, a slight shade of yellow, and presented themselves in the form of short, thick, square prisms. They gave the following results on analysis :— 5°240 grains dried at 212° Fahr. gave 7210 ... carbonic acid, and 0-847 ... water. 3°877 grains dried at 212° Fahr. gave, after burning with lime, 2:940 ... chloride of silver. Experiment. Calculation. oo Carbon, . : 37°53 37°79 OF; 72 Hydrogen, : erie) 1:57 H, 3 Oxygen, . ; ah 42:01 or 80 Chlorine, . , aS Vi 18°63 Cl 35:5 100:00 100-00 190°5 The above shews this substance to be an acid, obtained by the substitution of an equivalent of hydrogen in comenic acid, by an equivalent of chlorine, accord- ing to the following equation :— 2HO, C,H, 0,+2Cl=2H0, C,, { G Cl It crystallizes with three equivalents of water, which are readily expelled at 212° Fahr., as the following experiment proves :— 10°528 grains air-dried substance lost at 212° Fahr. I-Slsy We swater; \ O, + HCl. giving for per-centage 12°47, the number 12°41 being that corresponding to the formula 2 HO, Cio { Gy } Os + 324. This acid, as before mentioned, is readily soluble in hot water, less so in cold, but under both circumstances its solubility is much greater than that of the parent acid; it is very soluble in alcohol when warm. It imparts to persalts of iron the same deep red colour as meconic and comenic acids. When a piece of granulated zinc is placed in its aqueous solution, hydrogen is slowly evolved, and both zinc 236 MR HENRY HOW ON CERTAIN SALTS AND and hydrochloric acid are found in the liquid. Nitric acid rapidly decomposes it, with formation of hydrochloric, hydrocyanic, carbonic, and oxalic acids. Sub- mitted to destructive distillation it fuses and blackens, hydrochloric acid is evolved in large quantity, and towards the end of the process a small quantity of a crys- talline sublimate appears. This product I obtained in too small quantity to examine thoroughly. I imagine it, however, to be pyrocomenic acid, and attri- bute the presence of the traces of chlorine I detected to the impossibility of com- pletely purifying the little matter I had at my disposal. Chlorocomenic, like comenic acid, is bibasic, forming two series of salts. The salts I chose for controlling the analysis, and establishing the saturating power of the acid, were those of silver. Bichlorocomenate of Silver—A warm aqueous solution of the acid gives, with nitrate of silver, a white precipitate, in feathery crystals. When freed from the excess of solution of silver and nitric acid by washing with cold water, in which it is sparingly soluble, it may be recrystallized from boiling water, from which it separates on cooling in brilliant, short, prismatic needles. It is not at all, or very slightly, decomposed by boiling in water when no free nitric acid is present. The silver, in the following analysis, was determined by precipitation with hydro- chloric acid; the ordinary process of burning the salt and weighing the residuary silver being inapplicable, since a portion of the chlorine of the acid remains in combination with the metal upon ignition. { 5:157 grains dried at 212° gave 2-490 ... chloride of silver. Experiment. Calculation. —— Carbon, . ‘ see 24:19 Crs 72 Hydrogen, : oe 0-67 Er 2 Oxygen, . ; ade 24-19 0; 72 Chlorine, . : se 11-94 Cl 85°5 Oxide of silver, 39:03 39°01 AsO N1Gt 100-00 100-00 297°6 The composition of the salt, when dried at 212°, is therefore represented by the formula Ag0, HO, C,, {Gi } 0,. The crystallized salt appears to be a combination of the above with water, in the proportion of three equivalents of the latter to two of the former; the two specimens of the salt giving this indication were of different preparations. 5674 grains air-dry salt lost at 212° ona sen Wabers 5-428 grains air-dry salt lost at 212° 0-253 ... water. PRODUCTS OF DECOMPOSITION OF COMENIC ACID. 237 The per-centage calculated from these numbers are, I. ie Mean. 4:22 4:66 4:44 the mean of which agrees well enough with the number 4°33, corresponding to the formula 2 (AgO, HO, C,, HCl O,) +3 aq. Neutral Chlorocomenate of Silver.—This salt is obtained in the form of a yellow, flocky, amorphous substance, on the addition of a solution of the acid in a slight excess of ammonia to nitrate of silver. It is insoluble in boiling water, and acquires, in the process of drying, the consistence and adhesiveness of clay, which it also closely resembles in appearance. Considerable difficulty was experienced in the analysis of the salt; since, for the reason mentioned with regard to the acid salt, it cannot be burned, and it is, moreover, insoluble in water. When boiled with hydrochloric acid, a part of it escapes decomposition ; and if the attempt be made to dissolve it by aid of nitric acid, and precipitate the silver by hydrochloric acid, care must be taken to prevent the formation of cyanide of silver, which readily takes place when either of the silver salts is kept warm with even dilute nitric acid. The number I obtained was by carefully employing this process, and, though not accurate, comes suffi- ciently near to prove the composition of the salt. tere grains dried at 212° gave 5:457 ... chloride of silver. The per-centage of oxide of silver calculated from this is 56°85, and 57°37 is that corresponding to the formula H 2 Ag, C,, { a } 0,. The other salts of chlorocomenic acid, as might be anticipated, present close analogies with those of comenic acid; the former are generally more soluble than the latter. I have been unable to prepare neutral salts of the alkalies. The acid salts of potass, soda, and ammonia, crystallize readily ; a solution of the latter salt gives, with chlorides of calcium and barium, radiated groups of needles, appearing more or less quickly according to the state of concentration of the fluids; with sulphate of magnesia, a few crystals after some time; with sulphate of copper, a rapidly-appearing crystalline salt. The neutral salts of these bases appear to be insoluble amorphous substances generally. Action of Bromine on Comenic Acid. Bromocomenic Acid.—As might be expected, the behaviour of comenic acid towards bromine is closely similar to that which it exhibits when submitted to the influence of chlorine. It dissolves readily in aqueous bromine, yielding a colourless fiuid if the bromine is not in great excess. In the course of a few hours VOL. XX. PART II. 38 238 MR HENRY HOW ON CERTAIN SALTS AND the new acid is deposited in fine, square, prismatic crystals, often of considerable length, and presenting a very beautiful appearance, from their high refractive power. It may also be obtained by addition of bromine water to solution of acid comenate of ammonia, but I found it more convenient to employ the acid itself. I may mention that in one instance, when operating upon a solution of the am- monia salt, a considerable excess of bromine failed to yield any new acid, even after the lapse of many hours. The solution remaining colourless, more bromine was added, and as no crystals appeared, the fluid was evaporated, but still without any signs of bromocomenic acid; and it was not until the liquid was reduced to a very small bulk, that any substance crystallized out. On pouring off the liquid, which had now become nearly black, there were found some considerable-sized transparent crystals, together with a little bromocomenic acid in groups. The crystals became perfectly colourless on washing with a few drops of water; they proved to be oxalic acid. This acid always appears in the mother liquors from which chloro and bromo comenic acids have been separated by evaporation, result- ing probably from a secondary decomposition. The crystals, as obtained by the action of bromine water upon comenic acid, after being washed, and recrystallized from boiling water, gave the following results :— 6-001 grains dried at 212° Fahr. gave 6:767 ... carbonic acid, and 0-806 ... water. 4-330 grains dried at 212° gave, when burned with lime, 3:475 ... of bromide of silver. Experiment. Calculation. TFT Carbon, . : 30°75 30°63 Cs 2 Hydrogen, : 1-49 1-27 iD 3 Oxygen, . : pera 34:06 OF, 80 Bromine, . : 34°15 34:04 Br 80 100-00 100-00 235 which shew that they consist of an acid precisely analogous with chlorocomenic acid; an equivalent of bromine taking the place of one of hydrogen in the comenic acid. In the hydrated state it contains, like the chlorine acid, three atoms of water. 11:14 grains air-dry acid lost at 212° 1:15 .... water; which corresponds to 10-32 per cent.; 10-30 is the number required by the formula 2HO C,, ea O, +3 aq. This acid so closely resembles the chlorocomenic in its general properties and products of decomposition, that a very few words will suffice to describe it. It is PRODUCTS OF DECOMPOSITION OF COMENIC ACID. 239 rather less soluble in hot water and in alcohol than the former acid; it is de- posited from alcohol in fine rhombic crystals. It is decomposed by zinc. With nitric acid it gives hydrobromic, hydrocyanic, carbonic, and oxalic acids. The acid ammonia salt crystallizes in fine long needles; the acid salts of potass and soda also crystallize. I could obtain no neutral alkaline salts. The acid salts of the alkaline earths are very soluble; the neutral salts are insoluble and amorphous. The acid silver salt was obtained by adding warm aqueous solution of bromo- comenic acid to an aqueous solution of nitrate of silver; the flocky precipitate which fell was well washed with cold, and subsequently dissolved in boiling water. This fluid deposited the salt, on cooling, in brilliant, short, prismatic crystals. The silver was determined, in the following analysis, by solution of the salt in boiling water, and the subsequent addition of hydrochloric acid— { 6-435 grains dried at 212° gave 2678 --- chloride of silver. which, calculated for per-centage, gives 33°64 oxide of silver; the number 33:93 being that corresponding with the formula AgO, HO, C,, ee } 0,. A neutral silver salt was also obtained as a yellow amorphous precipitate, by adding solution of the acid in slight excess of ammonia to nitrate of silver in excess; it presented, on drying, the clayey character I remarked in the corre- sponding salt of chlorocomenic acid. As there could exist but little doubt of its composition, I thought it useless to occupy time with an analysis of it. Iodine appeared, from some experiments I made, to be without the power of decomposing comenic acid. , Acid Comenic Ether. Comenovinic Acid.—From the bibasic nature of comenic acid, and a consider- ation of the fact that Dr Srennovsse* failed in a special attempt to obtain a neutral ether of this acid, I was led to seek it in its combination with ether, a compound of an acid nature analogous to sulphovinic, tartrovinic, and the other acids similarly constituted. I did not succeed in my endeavour to form such a substance by action of sulphuric acid on alcohol and comenic acid; but was more successful in a slight modification of the method usually adopted for the production of organic ethers. Comenic acid in the state of fine powder was suspended in abso- lute alcohol, in which it is insoluble per se, and a stream of dry hydrochloric acid | gas was passed through the fluid. After some time the whole or the greater , part of the acid was taken up, the last portions disappearing very slowly. The | clear solution gave no deposit, even on standing at rest for many hours, nor was any precipitate produced by the addition of water, but when it was evaporated to * Mem. and Proc. Chem. Soc., vol. i. 240 MR HENRY HOW ON CERTAIN SALTS AND dryness, at a heat somewhat below 212’, a crystalline residue remained, which was evidently not comenic acid. This was kept at the same heat till it ceased to smell of hydrochloric acid ; it was then dissolved in water under the boiling point; the fluid, on cooling, deposited well-defined, square, prismatic needles of considerable size. A portion, dried in vacuo, gave the following results on analysis. 5:625 grains, dried in vacuo, gave I. ¢ 10-740 ... carbonic acid, and 2-260... . water. 4-110 grains, dried in vacuo, gave st 7°865 ... carbonic acid, and L755: oye Ul eaters Calculation, eet ee a 1: Carbon, . . 52:07 52-18 [OT Ae RR Hydrogen, ‘ 4-50 4:63 4:34 aa 8 Oxygen, . . oe Sits 43°49 OF; 80 100-00 100-00 100-00 184 From which it will be seen that this substance has the composition of an acid ether, or true vinic acid, and is represented by the formula HO, C, H, 0-C,, H, 0, and I shall presently shew, that the atom of water is capable of being replaced by bases. The acid crystallizes, like the corresponding compound of tartaric acid, without water. Comenovinic acid is readily soluble in hot water, and may be boiled a short time without undergoing decomposition; but if long kept at this temperature, comenic acid is reproduced. It is extremely soluble in alcohol. It commences to volatilize, when kept in the dry state, at 212°; it fuses at 275° Fahr. into a transparent brownish liquid, which becomes, on cooling, a crystalline striated mass. When kept at about its fusing point, it sublimes, unaltered in composi- tion, in brilliant, long, flattened prisms, of great beauty; the second analysis above given is that of the sublimed product. It gives a strongly acid reaction with test- papers ; its aqueous solution readily coagulates the white of eggs; it imparts to persalts of iron a deep red colour. Though of so stable a nature per se, this substance rapidly decomposes in contact with fixed bases; so that I have been unable to obtain any of its salts in the dry state. All those I have attempted to prepare gave, upon analysis, results closely agreeing with the composition of salts of comenic acid, with which their general properties were also identical, notwithstanding that I carefully avoided application of heat. I obtained a salt of ammonia by passing the dry gas into a solution of the acid in absolute alcohol. Under these circumstances a precipitate soon forms, in small silky tufts of a yellow colour. They preserve their silky appearance on being PRODUCTS OF DECOMPOSITION OF COMENIC ACID. 241 dried, but soon commence to lose ammonia in a dry atmosphere. A portion of the substance which had been exposed one night was placed 7m vacuo over sul- phuric acid; it was found to lose less weight by about half a per cent. than would correspond to the ammonia in a salt of the composition. NH, 0, ©, H, 0, C,, H, 0,. As the residue was found to consist of pure comenovinic acid, there can be little doubt that the above is a true ammonia salt. Its other salts, with the alkalies and alkaline earths, are very soluble. Its silver salt is gelatinous, and rapidly decomposable even in the dark. Decomposition of Comenate of Ammonia. Comenamic Acid.—I mentioned, in a former part of this paper, that bicomenate of ammonia is decomposed, when subjected to a temperature of 390° Fahr. in a sealed tube. The contents of the tube were a black coaly mass, which partially dissolved in boiling water. The filtered solution gave, with hydrochloric acid, a white scaly precipitate, separating on cooling. I did not endeavour to procure more of this substance in this manner, as I considered it to be the comenamic acid, which a more convenient process enabled me to obtain in sufficient quantity. When a solution of comenate of ammonia, containing an excess of the alkali, is boiled, it soon becomes coloured, and after some little time a black-red fluid is obtained ; if the boiling be continued till the whole or the greater part of the excess of ammonia is expelled, and the fluid be then allowed to cool, a grey sedi- ment falls to the bottom of the vessel. This, when thrown upon a filter, is found to have a most peculiar, clayey, tenacious character ; it is the ammonia salt of co- menamic acid, very impure, from adhering colouring matter. It dissolves, though sparingly, in boiling water; and hydrochloric acid added in just sufficient quan- tity to decompose it, precipitates very dark bronze-coloured scales of comenamic acid, which separate completely when the liquid cools. Excess of hydrochloric acid is to be avoided, as the new acid is extremely soluble in this reagent. ‘The dark crystals are readily deprived of their colour by two or three crystallizations from boiling water, and very easily by the aid of animal charcoal, which must, however, for this purpose be entirely free from iron, as the least quantity of this substance imparts a purple colour to solutions containing the acid. When pure, comenamic acid presents itself in the form of brilliant colourless plates, the following is its analysis :— 5:540 grains dried at 212° gave I. ¢ 9:345 ... carbonic acid, and 1685 ... water. 5-585 grains dried at 212° gave II. ¢ 9-487 ... carbonic acid, and I 7loe ... water, 6-505 grains dried at 212° gave 9500 ... platinum salt of ammonia. VOL. XX; PART It, 37 242 MR HENRY HOW ON CERTAIN SALTS AND Calculation. Nn I. ie. Carbon, . . 46:00 46-32 46-45. C,. 72 Hydrogen, ; 3°37 3°41 3°22 iE 5 Oxygen, . ‘ eae Ss! 41-30 oF 64 Nitrogen, : 9-17 AA 9-03 N 14 100-00 100-00 155 It is obvious that this substance is an acid amide, analogous to oxamic acid, and that its constitution is expressed by the formula of acid comenate of ammonia minus two atoms of water = HO, NH,C,, H, 0,.* It crystallizes with four equivalents of water. { 10-250 grains air-dry acid lost at 212° 1-955... water. 7°810 grains air-dry acid lost at 212° 1-450 ... water. Te i Mean. Per-centage, 19-07 18-56 18°81 The number 18°84 is that corresponding to the formula BOL NE, Ce OF aa Comenic acid, as obtained above, is in brilliant scales, very slightly soluble in cold water; the crystals effloresce, and partially lose their lustre in a dry atmosphere. It is soluble in boiling spirit, but very slightly in absolute alcohol. It has a powerful acid reaction; dissolves readily in excess of alkalies; also with * extreme facility in the strong mineral acids. From a solution in any of these, ammonia, added in quantity not quite sufficient to neutralize the whole of the solvent, throws down a granular precipitate of the ammonia salt. Its aqueous solution imparts to salts of peroxide of iron a magnificent and deep pure purple colour, which is destroyed by a few drops of a mineral acid, but reappears on dilution of the fluid with water. It is decomposed by boiling with caustic potass, with evolution of ammonia and production of comenic acid. It forms readily crystallizable salts with a certain proportion of ammonia, potass, and soda; these have an acid reaction. The acid remains completely in solution in a small quantity of water, when supersaturated with any alkali; if ammonia be employed, and the fluid be evaporated to dryness at 212°, the salt with acid reaction remains. It dissolves the earthy carbonates with effervescence, when heated with them in water; if the acid be in excess, a crystalline salt, with an acid reaction, is obtained ; if the carbonate predominate in quantity, almost the whole acid remains undissolved as some basic compound. * T have also obtained this substance from meconate of ammonia; the details of my experi- ments will be given in a future paper on the subject of some derivatives of meconie acid. PRODUCTS OF DECOMPOSITION OF COMENIC ACID. 243 A solution of the crystalline ammonia salt gives, with nitrate of silver, a white gelatinous precipitate, which partially decomposes in boiling water. The same solution made alkaline gives, with nitrate of silver, a yellow flocky precipitate, which almost instantly passes through deepening shades of colour into a heavy, black, amorphous precipitate. The same solutions give, with acetate of lead, heavy insoluble precipitates; the acid solution gives, with sulphate of copper, a grey precipitate. I have examined more fully and analyzed two or three of the salts of come- namic acid. Comenamate of Ammonia.—Comenamic acid dissolves readily in ammonia, when the alkali is added in excess, and such a fluid deposits no salt on standing ; but if ammonia be added to a boiling aqueous solution of the acid, in such quan- tity that the reaction remains slightly acid, the ammonia salt crystallizes out on cooling of the fluid in small grains, which, when magnified, are found to consist of bundles of needles radiating from a centre. They are difficult of solution in boiling water, but do not always reappear quickly when the liquid is cold. Their solution shews the phenomenon of epipolic dispersion very beautifully, when ren- dered alkaline by ammonia. They are anhydrous. 5°623 grains dried at 212° gave 8-570 carbonic acid, and 2°446 ... water. 4:945 grains dried at 212° gave 12°715 ... platinum salt of ammonia, Experiment. Calculation. Oe _ Carbon, . ‘ 41:56 41°86 Cis 12 Hydrogen, ; 4:83 4:64 HL, 8 Oxygen, ; “te 37°23 OF 64 Nitrogen, . ; 16:14 16-27 ING 28 100-00 100-00 100 The above analysis leads to the formula NH, 0, NH, C,, H, 0,. Comenamate of Baryta.—The salt I analyzed was obtained by adding a solu- tion of the ammonia salt to chloride of barium; a precipitate was obtained in radiated groups, which, on crystallization from boiling water, assumed the form of separate prisms. It had an acid reaction. 5055 ... carbonic acid, and 4-565 grains dried at 212° gave P0500!) © water. 4-425 grains dried at 212° gave, when ignited with SO,, 2°190 ... sulphate of baryta. 244 MR HENRY HOW ON CERTAIN SALTS AND Experiment. Calculation. Carbon, 30-20 29-92 Cy, 72 Hydrogen, 2°68 2°82 F Oxygen, 30°62 us 12 Nitrogen, ry 5°81 N 14 Baryta, 32-02 31°83 BaO 76°64 100-00 100-00 240-64 The formula deduced from the analysis of this substance, supposing it to be the neutral salt of a monobasic acid will be BaO, NH, C,, H, 0,+2 HO. Comenamate of baryta, precipitated in an alkaline solution of the ammonia salt by chloride of barium, falls as a heavy white powder, insoluble in boiling water. Its analysis is subjoined :— 6-023 grains dried at 212° gave 5-065... carbonic acid, and 0-989... .... water. 5-247 grains dried at 212° gave 4:020 ... sulphate of baryta. Experiment. Calculation. TT Carbon, . ; 22-93 23°35 Gs (Pe: Hydrogen : 1:80 1:62 : Oxygen, . ; ay 20°77 0, Cat Nitrogen, . : Be 4:54 N 14 Baryta, . ; 50:29 49-72 2BaO 153:28 100-00 100-00 308-28 From this analysis it follows, that, to assimilate this salt to the last, it must be considered as a basic compound, in which one of the equivalents of water re- tained at 212°, is replaced by an atom of baryta, according to the formula BaO, NH, C,, H, 0,+Ba0 HO. As precipitated from water, it contains an additional equivalent of water :— | { 11-720 grains air-dry lost at 212° O°362. .., ‘water. the per-centage calculation from the experiment is 3°08; and the number 2°83 corresponds to the formula BaO, NH, C,, H, 0,, BaO HO + aq. The salts of lime are very similar in appearance to the above, and with every base this acid seems to form two salts, which is a curious fact, since, reasoning from analogy, a substance originating as it does, should be monobasic in its nature. I am not at present able to afford any further information on the subject of its constitution and products of decomposition; but I may mention that I have observed, in its behaviour under certain circumstances, phenomena which I believe may prove of sufficient interest to encourage investigation. I append a list of the salts, &c., mentioned in this paper. PRODUCTS OF DECOMPOSITION OF COMENIC ACID. Salts of Comenic Acid. NH, O, HO, C,, H, 0, +2 aq., : ; crystallized from water. thrown down from alkaline solution by eae HOC, BH, Os +3.a4., { strong alcohol. Ne, ©; HO, C,, H, 0O,, : i : dried at 212° Fahr. MO” HO, C,, H, 0, : : : - crystallized from water. Na0, HO, C, aah Orr 2 (a0, HO, C,, H, O an ae ‘ : as Bs CaO, HO, C,, H, 0. : : ; dried at 250° Fahr. 2 CaO, C,, H, 0, 2 HO +5aq., . é deposited in concentrated cold fluids. 2 CaO, C,, H, 0O,,2HO+11laq, . ; ; dilute ce 2 CaO, C,, H, O,, 2 HO, : : ; dried af 250° Fahr. 2 (BaO, HO, C,, O,) +13 a Nias : crystallized from water. BaO, HO, C,, ii, 0 8 ‘ ; dried at 212° Fahr. 2 BaO, C,, H, O,,2 HO+8aq., . 3 deposited in cold water. Y Bao, Cc, H, On 2 HO, , ; : dried at 250° Fahr. MgO, HO, C,, H, O,, 2HO+6 3 as : crystallized from water. MgO, HO, C,, H, HO,A: 3 dried at 240° Fahr. 2 MgO, C,, H, 0, 3 HO +8aq., : deposited in concentrated cold fluids. 2 MgO, C,, H, O, 3 HO, : : 5 dried at 212° Fahr, Acids derived from Comenic Acid. Chlorocomenic acid, crystallized, é : 2 HO, C, a aa | O, + 3 aq. : & - H- deine” HOC, { a | 0, acid, silver salt, dried at 212°, AgO, HO, C,, e \ 0; H neutral bre = ae 2 AgO, C,, nae Os Bromocomenic acid, crystallized, : : 2 HO, C,, { ea O,+3 aq : é H dried at212°, . 34. 2HO,C, | 0, acid, silver salt, dried at 212°, AgO, HO, C,, ae O, Comenovinic acid, crystallized, F ’ : HOC HO, C, 4, 0, ... ammonia salt, . : 2 NET ORC HS ONC. He O, Comenamic acid, crystallized, ‘ f : HO, C,, H, NO, +4 HO. cM dried at 212°, . } ‘ HO, C,, ENO} ammonia aalt, , : NEO, Cr NO, baryta salt, with acid reaction, dried at 219°, BaO, C,, H, NO, +2 HO. neutral ditto, BaO, C,, H, NO, + BaO HO. w q VOL. XX. PART II. XIV.—On the Products of the Destructive Distillation of Animal Substances. Part II. By Tuomas AnpErson, M.D. (Read 21st April 1851.) I propose in the following pages to communicate to the Society the progress of my investigation of the products of the destructive distillation of animal sub- stances, the first part of which was published in the 16th volume of the Trans- actions. Since that period, partly owing to my numerous avocations, and partly to the inherent difficulties of the subject, less progress has been made than I had hoped or expected, but still I have accumulated some facts of considerable inte- rest, which I think deserving of the attention of the Society. It may be remembered that, in the paper just referred to, I announced the discovery, among those products, of picoline, which I formerly obtained from coal- tar, and of a new base, to which I gave the name of Petinine; and I entered pretty fully into the method adopted for the preparation of these substances, and of certain other bases, the existence of which I merely indicated, without at the time attempting to characterize them. On proceeding to the more minute investigation of these bases, I soon found that the quantity of material at my disposal was much too small to admit of satisfactory or complete results, although I had employed for their preparation above 300 pounds of bone-oil. I found it necessary, therefore, to begin ab initio with the preparation of the bases from another equally large quantity of the oil; and after going through the whole of the tedious processes described in my previous paper, with the expenditure of the labour of some months, I found my object again defeated by deficiency of mate- rial. After various experiments, which, though they led to no definite or con- clusive results, served to familiarize me with the nature and relations of the products obtained, I made up my mind once more to begin again; and being ~ resolved on this occasion not to be foiled in the same way as before, I used for my new preparation no less than 250 gallons of crude bone-oil, the weight of which was somewhat above a ton. The result of this process, though involving an immense amount of labour, has been satisfactory, not only in supplying me with a large amount of material, but has also enabled me to obtain many substances, some of . them possessed of very remarkable properties, which had escaped my observation when operating on a smaller scale. The employment of so large quantity of material has, as might be expected, led to some modification of the process described in the first part of this paper, VOL. XX. PART II. 3x 248 DR ANDERSON ON THE PRODUCTS OF THE which, though convenient enough on the small scale, was too tedious for the large quantities on which I now operated. The preliminary process of rectifying the oil, which was quite beyond the resources of a laboratory, was effected at a manufactory. The whole oil was introduced at once into a cast-iron retort, fur- nished with a good condenser, kept cool by an abundant current of ice-cold water. A very gentle heat was applied, and the first twenty gallons which passed over were collected apart ; they consisted of about equal bulks of a highly volatile oil, and of water charged with sulphide of ammonium, hydrocyanate and carbonate of ammonia, and a small quantity of very volatile bases. . The oil which distilled over after this fraction had been separated was collected in a succession of casks, which were numbered as they were filled. In the after treatment of the oil, a process was employed similar to that which I had formerly made use of, with this exception, that the watery fluid, which had formerly been rejected, was employed for obtaining any bases which might have been dissolved in it along with the ammonia. For this purpose it was separated from the oil, and dilute sulphuric acid gradually added, when carbonic, hydro- cyanic, and hydrosulphuric acids escaped with violent effervescence. When acid enough had been added to communicate a powerfully acid reaction to the fluid, it was put into a large copper boiler and boiled for some time, water being added at intervals, so as to keep up the bulk. After the ebullition had been sufficiently prolonged, the fluid was allowed to cool, and slaked lime added in excess. A copper head was then fitted to the boiler and luted down with clay, a condenser attached, and heat applied. The distillate was collected in a large glass receiver, which, in order to prevent the escape of ammonia and any very volatile products which might be carried along with it, was connected by a doubly-bent tube with a second receiver containing water, through which the gaseous products were allowed to stream. The fluid which distilled was coloured blue by the solution of small quantities of copper from the condenser; it had a powerfully ammoniacal and putrid odour, and when treated with sticks of caustic potass, in the manner described in the first part of this paper, ammonia was rapidly evolved with effervescence, and a small quantity of very volatile and pungent bases collected on the surface of the potash. These bases were separated from the potash fluid, which was preserved along with the ammoniacal solution obtained by the absorp- tion of the gaseous products in the second receiver. The treatment of the oil was conducted in a manner very similar to that already described, and as I desired to have only the more volatile products, I em- ployed the first half of the oil only. It was agitated with dilute sulphuric acid in casks about half full, and after two or three days, during which the agitation was frequently repeated, more water was added, and the solution of the bases sepa- rated from the oil. To this fluid acid was added, so as to have a distinct excess; and it was then boiled for the separation of Runex’s pyrrol, to which reference DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 249 has been made in the first part of this paper. As, however, I observed that a very powerful and pungent odour was evolved when the fluid began to boil, and the vapours presented the characteristic reaction of pyrrol in a very high degree, the head of the boiler was luted on, and the condenser attached, for the purpose of endeavouring to obtain that substance, which in my previous experiments I had not done. The fluid which distilled over carried with it a small quantity of oil, which, at the moment of distillation, was perfectly colourless, but soon acquired a reddish shade, and in the course of a few days became almost black. The sreater part of this oil passed over with the first portion of water; but the last traces adhered with great obstinacy to the acid fluid, and could only be separated by very protracted distillation. The substance thus obtained proved to be a mixture of an oil insoluble in acids, and which appeared to be merely a small quantity of the crude oil, mechanically mixed with the fluid, and of a series of bases of very remarkable properties, and obviously related to one another, to which I shall afterwards refer under the provisional name of pyrrol bases. When these substances had entirely distilled, the fluid was allowed to cool, excess of slaked lime added, and the distillation again commenced, in order to obtain the bases which had been retained by the sulphuric acid. The separation of these was conducted in a manner in all respects similar to that employed in the former preparations, solid caustic potash being added in sufficient quantity to cause the separation of the bases held in solution in the water. The potash fluid, however, retained a certain proportion of ammonia, another gaseous base, and of the most volatile bases, which could be separated only by a very large excess of potash. The fluid was therefore distilled in glass vessels, and the product collected in a succession of three receivers, the first of which was kept cold by water, the second by a freezing mixture, and the third contained hydrochloric acid, for the purpose of condensing the gaseous products. The first receiver now contained the bases dissolved in a small quantity of water, from which they were readily separated by potash; the second receiver contained only a drop or two of liquid; but in the third the hydrochloric acid was rapidly saturated, and required repeated renewal — during the progress of the distillation. The hydrochloric solution thus obtained contained a very large quantity of chloride of ammonium, along with a small proportion of another base, in order to obtain which the fluid was slowly evaporated, allowed to cool at intervals, and the sal-ammoniac which deposited was separated by straining through cloth and expression. After the separation of several crops of crystals, a dark-brown mother liquor was left, which refused to crystallize by evaporation on the water- bath, but on cooling solidified into a mass of long foliated crystals, which soon deliquesced in moist air. These crystals still contained traces of sal-ammoniac, for the separation of which they were evaporated to complete dryness on the water-bath, and dissolved in the smallest possible quantity of absolute alcohol, 250 DR ANDERSON ON THE PRODUCTS OF THE with the aid of heat. The filtered fluid, on cooling, deposited a few tabular crystals mixed with a little sal-ammoniac, which was got rid of by a second filtra- tion; and the filtrate, when treated with animal charcoal and further concen- trated, solidified, on cooling, into a mass of large foliated crystals. These crystals are long, transparent, and colourless plates, entirely without odour, and with a pungent and bitter taste. In moist air they deliquesce rapidly. Solid potash added to their concentrated solution causes the immediate escape of a gaseous base resembling ammonia, but distinguished by its peculiar putrid odour. This gas dissolves readily in water, and gives a powerfully alkaline solu- tion. It gives with corrosive sublimate a fine white precipitate, soluble in hot water or spirit, and deposited on cooling in fine silvery plates; and its hydro- chlorate gives, with bichloride of platinum, a soluble salt, depositing from its hot saturated solutions in beautiful golden-yellow scales. I selected this salt as a means of determining the constitution of its base. 6-885 grains of the platinochloride, dried at 212°, gave uf 1:243 ... of carbonic acid, and 1648 ... of water. II 6-189 grains of the salt gave ; 2°565 ... of platinum. Ilr 11-531 grains of another preparation gave , 4-764 ... of platinum. Experiment. Calculation. ————————_ ro Carbon, : y 4:92 Le 5:06 C, 12 Hydrogen, . : 2°67 es 2:52 H, 6 Nitrogen, . : ae = 5°92 N 14 Chlorine, . : sh Ss 44°89 Cl, 106°5 Platinum, . ; 41°31 41:44 41°61 Pt 98-7 100-00 237°2 These analyses, then, correspond exactly with the formula C, H, N HCl Pt Cl, ; and the base is consequently methylamine, with which it and its salts agree in all respects. The oily bases which had been separated from their solution in water by means of potass, were dried by the addition of successive portions of that sub- stance, as long as it continued to become moist. The dry oil, which was very dark coloured, was then introduced into a large retort, furnished with a thermo- meter and a tubulated receiver kept cold by ice, and connected first with a U tube immersed in a freezing mixture, and then with a large vessel of water, in order to collect the gaseous bases which began to escape with effervescence almost as soon as heat had been applied. Ata temperature under 150° Fahr. drops began to condense in the neck of the retort, and the fluid entered into rapid ebullition. At 212° the receiver was changed, and the oil distillmg above that temperature was collected in receivers, which were changed at every ten degrees. The quantity of bases which distilled under 212° was much less than I had anti- DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 251 cipated, and proportionably much smaller than that obtained when operating on a much smaller scale before; and I consequently found myself compelled to proceed very carefully, so as to avoid loss in the purification. By distilling the product which boiled under 212°, I collected fractions nearly equal in bulk at every five degrees, all very similar in their general properties. They were all limpid and colourless fluids, with high refractive power, and pungent odour, remarkably similar to that. of ammonia in the lower fractions. They fumed strongly when a rod moistened with hydrochloric acid was brought near them, and presented all the properties of powerful bases. Exposed in the anhydrous ‘state to a mixture of snow and salt, they remain perfectly fluid, but if a small quantity of water be added, beautiful white crystals of a hydrate are deposited. I attempted, by several successive distillations, to obtain fixed boiling points; but the quantity I had to work with was too small for an operation involving so much loss of material, and I therefore converted portions of the fractions which I had reason to suspect corresponded with particular bases into platinum salts. I selected, in the first place, the lowest fraction of all, that, namely, which boiled under 150°. It was dissolved in water, saturated with hydrochloric acid, and evaporated to dryness on the water-bath. The highly crystalline residue obtained was dissolved in water, and mixed with a solution of bichloride of platinum, when a yellow crystalline salt was slowly deposited, which dissolved readily in water even in the cold, and still more abundantly on boiling; and the solution on cooling deposited fine golden scales, scarcely to be distinguished in their appear- ance from those of methylamine or of petinine. These crystals were separated, and as the salt was highly soluble, and much remained in the mother liquor, a mixture of alcohol and ether was added, when the fluid rapidly filled with small shining scales. The analysis of this salt dried at 212° gave the following results :— 3°392 ... of carbonic acid, and 6-970 grains of platinochloride gave 2-434 ... of water. 6:475 grains of the salt gave 2422 grains platinum. 8-257 Kae be 3°047 ne Experiment. Calculation. aaa ee Carbon, 13°27 13°57 OF 36 Hydrogen, 3°88 3°77 Ee) te Nitrogen, as. 5:27 N 14 Chlorine, ‘* 40-18 Cl, 106-5 Platinum, 37°56 37°21 Pt 98-7 100-00 265°2 From these results we arrive at the formula C,H,N HCl Pt Cl,, which is that of the platinum salt of a base C,H, N. The base is therefore the substance I have VOL. XX. PART II. 3 Y 252 DR ANDERSON ON THE PRODUCTS OF THE before described* as a product of the action of alkalies upon codeine, under the name of Metacetamine, but which I now prefer calling Propylamine, in accord- ance with the name now usually applied to the acid with which it corresponds. Unfortunately the quantity of propylamine obtained was too small to admit of my examining either its compounds or itself with accuracy. It is, however, a perfectly limpid and colourless fluid, with a strong pungent odour resembling that of petinine, but more ammoniacal. It gives an abundant white cloud when a rod dipped in hydrochloric acid is brought near it, and unites with the con- centrated acids, with the evolution of much heat. Its hydrochlorate crystallizes in large plates closely similar to those of methylamine and petinine. The discovery of methylamine and propylamine among these products natu- rally directed my attention to the probable presence of ethylamine, the interme- diate term of the same series; but as I had not employed any very particular precautions in condensing the more volatile products during the successive recti- fications to which I had subjected the crude oil, almost the whole of it appears to have escaped. By collecting, however, the first few drops passing over in the rectification of the portion boiling under 150° in hydrochloric acid, and forming a platinum salt, I obtained the following result :— 6-930 grains of platinochloride gave 2°649 grains platinum. This corresponds to 38°22 per cent. Now the per-centage of platinum in the ethylamine salt is 39°60, and the result obtained, which is much too high for the propylamine salt, shows that I must have had a mixture of the two, which might have been separated had I possessed a sufficient quantity of the salt. It will readily be understood that a result of this kind could not in general be produced as evidence of the existence of ethylamine, but under the particular circumstances of the case, the next term of the same series on either side of it having been detected, it may be considered as sufficiently conclusive of its presence. The occurrence of these bases enables us to establish, on satisfactory grounds, the constitution of petinine. In the first part of this paper, an analysis of that base is given, which agrees in the most perfect manner with the formula C, H,, N, which was also confirmed by that of its platinum salt. It cannot, however, for a moment be doubted that it is homologous with the bases with which I have now shewn it to be associated, that its true formula is C, H,, N, and that it is really butylamine, the corresponding base of the butyric group. The analysis of the platinum salt given in my former paper agrees equally well with this formula, and though that of the base differs from it to some extent, much less reliance is to be placed upon it, as it is scarcely possible, when operating upon so small a scale as that upon which I was compelled to work, to subject the bases to a sufficient number of distillations to effect their complete separation. * Edinburgh Philosophical Transactions, vol. xx., p. 82. DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 253 I have thus then established the existence, among the products of destructive distillation, of ammonia, and the first four members of the series of bases homo- logous with it. I have every reason, however, to believe that the series does not end with petinine, for the fraction boiling about 200° yields a platinum salt in fine scales, and having all the characters of the salts of the same series of bases, and in all probability contains valeramine. I am not without hope also of obtaining caprylamine; but this I expect will be the last of the series, for when we reach the temperature of about 240°, the character of the bases changes, and we enter upon an entirely different. series. In the separation of the bases boiling above 240°, I have encountered very great difficulties. After the trial of many different processes, such as converting them into salts, exposing them to cold, partial saturation, and every other plan which appeared likely to answer, I have been compelled to return to fractionated distil- lation, as the method most likely to answer the end [had in view. But even with this process the difficulties are great, and I have been by no means so successful in obtaining fixed boiling points as I was when operating on a smaller scale in my former preparations. I subjected the whole of the oils boiling above 212° to a sys- tematic course of fractionation, each fraction being distilled alone, and the product collected in a fresh series of bottles, and the receivers changed at every ten de- grees. In the earlier rectifications each fraction spread itself over a very large num- ber of degrees, and shewed little tendency towards concentration to fixed points. The distillations were repeated no less than fourteen times, but even after all this the indications of boiling points were extremely indistinct. Sometimes in one dis- tillation certain fractions appeared larger than others, but their pre-eminence disap- peared again in succeeding rectifications. Still a certain improvement was manifest, some of the fractions being confined more nearly to the range of degrees within which they had boiled at the previous rectification. It was obvious, from the whole phenomena of the distillation, that the separation of the different bases was going on, although with extreme slowness; and at this point I endeavoured, by the examination of the platinum salts obtained at different temperatures, to deter- mine the constitution of the bases which these fractions contained ; and as I knew from previous experiment, that the quantity boiling between 270° and 280° con- sisted of picoline, I had from this fact indications of the temperatures at which bases were likely to be found, and I have thus been enabled to determine the existence of two substances belonging to the same homologous series with that substance. Pyridine. The first of these bases, to which I give the name of pyridine, occurs in the fraction boiling about 240°. This fraction has an odour precisely similar to that of picoline, but more powerful and pungent. It is perfectly transparent and colour- 254 DR ANDERSON ON THE PRODUCTS OF THE less, and does not become coloured by exposure to the air. It dissolves in water in all proportions, and is also readily soluble both in the fixed and volatile oils. It dissolves in the concentrated acids, with the evolution of much heat, and the formation of highly soluble salts. When bichloride of platinum is added to a solution of its hydrochlorate, a double salt is slowly deposited in flattened prisms, which are tolerably soluble in boiling water, less so in alcohol, and entirely insoluble in ether. When these crystals are boiled for a considerable time in water, they appear to undergo decomposition, with the formation of a platinum salt, crystal- lizing in golden scales. Two analyses of this salt were made, one upon the sub- stance simply precipitated from the hydrochlorate; the other was the same salt redissolved in hot water, so as to leave a considerable proportion undissolved. In | the last analysis the salt was mixed with the chromate of lead when still rather hot, and it immediately evolved a strong smell of the base, which accounts for the loss of carbon obtained in the experiment. 8234 grains of the platinochloride gave I. < 6:486 ... of carbonic acid, and 1705 ... of water. { 5:396 grains of the platinochloride gave Ly. 4:015 ... of carbonic acid, and (1-091... of water. 8-138 grains platinochloride gave 2-792 grains platinum. 4:956 sa cig oo 1-708 ee Experiment. Calculation. a , iia a Se Carbon, . . 21-48 20-29 21-08 C160 Hydrogen, . : 2°30 2°24 2°10 lays 6 Nitrogen, . ‘ oak er 4:93 N 14 Chlorine, : 2 nes ae 37°34 Cl, 106°5 Platinum, . 5 34:30 34°56 34:60 Pt 98°7 100-00 285:2 The formula C,, H, N, HCl, Pt Cl, agrees very closely with these analyses ; and the salt is consequently that of a base having the formula C,, H, N, which forms a term of the picoline series. I have not as yet directed further attention to this base, as the phenomena observed in the examination of the next base served to shew that, notwithstanding the correspondence of the salt with theory, much difficulty would be experienced in obtaining the base itself in a state of purity. Lutidine. In the fraction boiling about 310°, a base occurs which possesses precisely the constitution of toluidine, and to which I give the name of lutidine. When in the distillation of the mixed bases the temperature rises to about 305° to 310°, more — distinct indications of a fixed boiling point are obtained than at any other tem- perature, and the base which distils presents sufficiently distinct characters from those obtained at lower points. The product is now much less soluble in water ; DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 255 when dropped into a small quantity of that fluid it floats on the surface, and is only slowly dissolved on agitation. It possesses the remarkable property of immediately separating from its solution on the application of a gentle heat, and collecting on the surface in the form of an oily layer which dissolves again as the temperature falls. Its smell is less pungent and more aromatic than that of picoline, and it is also more oily in its characters. It unites with the acids and forms salts, all of which are highly soluble. Analyses were made of the different portions of oil boiling about the tempera- ture of 310°, with the following results :— 3°840 grains of the base, boiling between 310° and 315°, gave I. ¢ 11:007 ... of carbonic acid, and 3°060 ... of water. 4:012 grains of the base, boiling between 315° and 320°, gave II. ¢11:516 ... of carbonic acid, and 3160 ... of water. 4-319 erains of the base, boiling between 316° and 320°, gave III. 4 12°480 ... of carbonic acid, and 3:576 ... of water. 4-430 grains of the base, boiling between 320° and 324°, gave IV. 4 12°812 ... of carbonic acid, and 3°405 ... water. I, II. III. IV. Carbon, . 78-17 78-28 78-48 78-87 Hydrogen, . 8°85 8°75 9-10 8°54 Nitrogen, . 12:98 12:97 12°42 12°59 100-00 100-00 100-00 100-00 These results agree very closely with the formula C,, H, N, as is shewn by the following comparison of the mean experimental and calculated numbers. Mean. Calculation. PE oT Carbon, . : 78°45 78°50 Cin, 1 oe Hydrogen,. °. 8°81 8:41 H, Nitrogen, . 3 12°54 13°09 N 14 100-00 100-00 LOT: Notwithstanding the close correspondence of these results, however, further experiment shewed that some of the fractions, especially those of lower boiling points, contained appreciable quantities of picoline, the presence of which was established by the analysis of the platinum salts. When, for instance, a portion of any of these fractions was saturated with dilute hydrochloric acid and bichloride of platinum added, fine prismatic crystals were slowly deposited, which, as the result of numerous experiments, were found to contain about 32°8 per cent. of platinum, which is exactly the quantity present in the picoline salt, of which the theoretical per-centage is 32°92. On evaporation of the mother liquor, crystals were deposited which gave quantities of. platinum varying from 32°5 to 32:0 per VOL. XX. PART II. 3 Z 256 DR ANDERSON ON THE PRODUCTS OF THE cent., and which were obviously mixtures of the picoline and lutidine salts. When the last mother liquor, however, was evaporated to a small bulk, and alcohol and ether added, another salt altogether distinct from that of picoline, and crystal- lizing in flattened tables, was deposited, which analysis proved to have the con- stitution of the lutidine salt. This platinum salt crystallizes from its solutions in square tables, sometimes very distinct, at other times confused and irregular. It dissolves very readily in cold water, and still more abundantly in boiling, and appears also to be very easily soluble in excess of hydrochloric acid. Numerous analyses of this salt were made, of which the following are the results :— No. 1. This was the analysis of the salt prepared from the oil distilling between 315° and 325° in the seventh rectification. 6:°187 ... of carbonic acid, and 6°377 grains of the platinochloride gave 1915 ... of water. 6-810 grains platinochloride gave 2:146 grains platinum. 6:476 ch Poe 2-051 ie No. 2. Portion of the oil distilling between 295° and 300° in the fourteenth. rectification ; the platinum salt of picoline was separated by crystallization, and the salt analysed precipitated by alcohol and ether. 7906 grains gave 2°491 grains platinum. 7:835 ... of the salt recrystallized gave 2470 ... of platinum. No. 8. Another preparation from the same portion of oil. 7°330 grains of platinochloride gave 7-070 ... of carbonic acid, and 2:090 ... of water. 6°830 grains gave 2°155 grains platinum. No. 4. Portion of the oil boiling between 300° and 305° in the thirteenth recti- fication. 7401 grains gave 2°328 grains platinum. No. 5. Portion boiling between 325° and 335° in the seventh rectification. 7°194 grains gave 2:256 grains platinum. ie II. III. Ve WV: ——— Se ———_—————— Carbon, - 26°41 oe ore are 26:30 Hydrogen, . 3°33 Bes Zale son 3°16 Bis ud Platmum, . 31°51 31°67 31°50 31:52 31:55 31°45 31°35 These results correspond very closely with the formula C,, H, N HCl Pt Cl,, of which the following is the calculated result compared with the mean of experi- ment. iw) Or ~J DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. Mean. Calculation. Carbon, . P 26°35 26°81 Cra 84 Hydrogen, : 3°23 3°19 Ey LO Nitrogen, . , ie 4°49 N 14 Chlorine, . ; 404 34°00 Ci, 1065 Platinum, . : 31-50 ol-do1 1B 98-7 100-00 3132 It is clear, from these analyses, that the salt obtained is that of the base of which the analysis is given above; but it is equally evident, from the presence of small quantities of picoline, that the base itself was not obtained in a state of absolute purity, notwithstanding the close approximation of the experimental results with those required by theory. I have been struck throughout the whole course of the investigation by the fact, that when the fraction corresponding to the boiling point of any particular base has been analysed, results very nearly correct were obtained, even when the substance was very far from being pure. [ found, for instance, in the earlier part of the investigation, that the fraction boil- ing between 270° and 280°, after one or two rectifications, gives precisely the results obtained from pure picoline, although on further rectification the fluid will begin to boil about 250°, and a small portion will still remain in the retort when the thermometer has risen to 300°. It is, however, readily intelligible, that this should be the case when we have to deal with a series of homologous bases, in which the per-centage of carbon goes on increasing as the boiling point rises, so that, as in this particular case, we have the excess of carbon in the less volatile base exactly counterbalancing the deficiency in the more volatile. Thus lutidine, containing 78°5 per cent. of carbon, and pyridine only 75-9, and each successive rectification removing equal quantities of the more and less volatile substances of _ which the boiling points are equidistant from that of the intermediate member of | the series, must always leave a substance in which the quantities of the two im- purities must be exactly sufficient to counterbalance the error which each will / occasion. Hydrargo-chloride of Lutidine.—I directed my attention to this compound, | which is sparingly soluble and crystallizable, in hopes that it might be adapted | to the purification of the base itself. I soon, however, abandoned it, as it turned | out that it was not possible, in repeating its preparation, to obtain invariably the | same substance, each base appearing, like aniline, to form different compounds with | corrosive sublimate. When a solution of corrosive sublimate in alcohol is added to | an alcoholic solution of lutidine, a curdy white precipitate falls immediately, unless the solutions be highly dilute, in which case it is slowly deposited in groups of radiated crystals. This salt dissolves in boiling water, with partial decom- | position; it is still more soluble in spirit, and is deposited unchanged as the solution cools. The following analysis corresponds exactly with the formula 12 He Cl+C,, H, N. 258 DR ANDERSON ON THE PRODUCTS OF THE 6°373 ... of carbonic acid, and 7°850 grains dried in vacuo gave 1:905 ... of water. 3°112 grains gave 2°32 grains of chloride of silver. 7684 ... gave 4-090 grains mercury. Experiment. Calculation. Oe Carbon, . : 22-14 22°05 Ci 84 Hydrogen, . f 2°69 2°36 H, 9 Nitrogen, . : . 3°69 N 14 Chlorine, . - 18-43 18°64 Cl, 71 Mercury, . : 53°22 53°26 Hg, 202 100-00 380 On another occasion results were obtained more nearly corresponding with the formula 3 Hg Cl+C,,H, N; and intermediate results were also obtained, but as the existence of these different compounds appeared to me to be fatal to their employment as a means of purifying the base, I did not attempt to pursue the subject further. The separation of lutidine from the other bases was also at- tempted by forming other salts, but none were found to answer, all being highly soluble except the carbazotate, which crystallizes in beautiful, long, yellow needles, a property which, however, is unfortunately possessed by the carbazotates of all the other bases. From all these experiments, it appears that I have been able to substantiate the existence of two bases, pyridine and lutidine, although it has been as yet impossible to obtain the bases themselves in a state of satisfactory purity. J am inclined, however, to think that the platinum salts, from their greater stability, and the ease and regularity with which they crystallize, will afford means of purification, but I have been hitherto deterred from trying this method on the large scale by the enormous quantity of platinum which would be requisite for the purpose. . It appears, then, that DiprEt’s oil contains two series of bases, one that is homologous with ammonia, the other a series peculiar to that oil, homologous with one another, and remarkable for their isomerism with the series of which aniline is the type. Thus we have— Pyridine, . : : Ce a | Picoline, : 2 C7 Hem 5 d : Aniline. Lutidine, . . : Coaatta IN| : 5 ‘ Toluidine. And it is probable that the series existing in Dippet’s oil does not cease here, as I have found that the bases, with higher boiling points, give a steadily decreasing per-centage of platinum. It is impossible, in the present state of the investiga- tion, to give any opinion as to the intimate constitution and relations of these two groups of what I may call isohomologous bases. The most obvious explanation, however, would be to suppose the new bases to be imidogen or nitrile bases, DESTRUCTIVE DISTILLATION OF ANIMAL SUBSTANCES. 259 which would enable us to understand why they differ from the aniline series, which we know to be amidogen bases. If, however, they belong to either of these classes, they must differ remarkably from any of those hitherto examined, all already formed being extremely unstable, and decomposed even by very feeble affinities, while picoline and its congeners are extremely stable, and resist even the action of nitric acid. Into these points, however, I shall not now enter, but reserve their discussion for a future part of this paper. Pyrrol Bases. I have already referred, at the commencement of this paper, to another series of bases, to which I have given the provisional name of pyrrol bases, and which distil away from the acid fluid by which the others are retained. They are obtained in the form of an oil, which is transparent and colourless at the moment of distillation, but rapidly acquires first a rose, then a reddish-brown, and finally an almost black colour, and the mixture gives, with hydrochloric acid and a piece of fir wood, the purple-red colour which Runee describes as characteristic. of pyrrol. In fact, I imagined that I had at length obtained this substance, which had escaped-me in my previous experiments, but I soon found that the product was really a mixture of several different bases. When distilled with the thermo- meter it began to boil at about 212°, and the temperature gradually rose to above 370°, and during the whole of the distillation pretty large fractions were obtained at every ten degrees, but those between 280° and 310° were decidedly larger than the others. These oils were all bases, with a peculiar and disgusting odour, quite different from, and much more disagreeable than, that of the picoline series of bases. They all acquire colour on standing, although more slowly than the crude oil. These substances dissolve easily in a small quantity of hydrochloric acid, and give, with bichloride of platinum, a precipitate which is at first yellow, but is rapidly converted into a black substance. When dissolved in an excess of acid, and heated along with it, they present a very remarkable character ; the solution at a certain temperature becomes filled with red flocks, so abundant and bulky, that, if not too diJute, the fluid becomes perfectly solid, and the vessel can be inverted without anything escaping. The same change takes place, though more slowly, in the cold, and the substance deposited is then of a pale orange- colour, but becomes darker by boiling or exposure to the air. When this substance is collected on a filter, washed, and dried, it forms a reddish-brown and very light and porous mass. It is insoluble in water, acids, and alkalies, but soluble in alcohol, and the solution on evaporation leayes a dark resinous mass. When subjected to dry distillation, it leaves a bulky charcoal, while an exceedingly dis- gusting oil distils. The acid fluid which has been separated from this substance by filtration, when supersaturated by an alkali, evolves the odour of the bases of the picoline VOL. XX. PART Il. ; ; 4A 260 DR ANDERSON ON THE DISTILLATION OF ANIMAL SUBSTANCES. series. These pyrrol bases I conceive, therefore, to be substances formed by the coupling of the picoline series with some substance which yields the red matter — to which I have alluded. I have not as yet, however, pursued the investigation of these bases, but shall communicate the result of their examination in a future paper. The Non-basic Constituents of Bone Oil. I have as yet directed very little attention to this branch of the subject. I have found, however, that when the most volatile part of the oil, after sepa- ration of the bases, is repeatedly rectified, it improves in odour, and at length there is obtained a substance which, when acted upon by nitric acid, and then by sulphide of ammonium, gives the reaction of aniline,—indicative of the presence of benzine in the oil. It is probable, therefore, that this series of homologous carbo- hydrogens forms a part of the oil, but not the whole of it, for I have found that when the oil is boiled for some time with potass, ammonia is evolved, and on supersaturating the potash solution with sulphuric acid, the odour of butyric acid, or at all events of one of the fatty acids, becomes apparent ; from which phenomena I draw the conclusion that it also contains the nitriles of these acids. ( 261 ) XV.—On the Dynamical Theory of Heat, with numerical results deduced from Mr JouLE’S equivalent of a Thermal Unit, and M. Reenaurt’s Observations on Steam. By Witiiam Tuomson, M.A., Fellow of St Peter’s College, Cam- bridge, and Professor of Natural Philosophy in the University of Glasgow. (Read 17th March 1851.) INTRODUCTORY NOTICE. 1. Str Humpnrey Davy, by his experiment of melting two pieces of ice by rubbing them together, established the following proposition :—“ The phenomena of repulsion are not dependent on a peculiar elastic fluid for their existence, or — caloric does not exist.” And he concludes that heat consists of a motion excited among the particles of bodies. ‘To distinguish this motion from others, and to signify the cause of our sensation of heat,” and of the expansion or expansive pressure produced in matter by heat, “the name repulsive motion has been adopted.’ * 2. The Dynamical Theory of Heat, thus established by Sir Humpurey Davy, is extended to radiant heat by the discovery of phenomena, especially those of the polarization of radiant heat, which render it excessively probable that heat propagated through vacant space, or through diathermane substances, consists of waves of transverse vibrations in an all-pervading medium. 3. The recent discoveries made by Mayer and Jou.e,} of the generation of heat through the friction of fluids in motion, and by the magneto-electric excita- tion of galvanic currents, would, either of them be sufficient to demonstrate the immateriality of heat; and would so afford, if required, a perfect confirmation of Sir Humpurey Davy’s views. * From Davy’s first work, entitled “ An Essay on Heat, Light, and the Combinations of Light,” published in 1799, in “ Contributions to Physical and Medical Knowledge, principally from the West of England, collected by Tuomas Bzppors, M.D.,”.and republished in Dr Davy’s edition of his brother’s collected works, vol. ii. Lond. 1836. + In May 1842, Maver announced in the “ Annalen” of Wouter and Lizzie, that he had raised the temperature of water from 12° to 18° cent. by agitating it. In August 1843, JouLe announced to the British Association, ‘‘ That heat is evolved by the passage of water through narrow tubes;” and that he had “ obtained one degree of heat per lb. of water from a mechanical force capable of raising 770 Ibs. to the height of one foot;’ and that heat is generated when work is spent in turning a magneto-electric machine, or an electro-magnetic engine. (See his paper ‘‘ On the Calorific Effects of Magneto-Hlectricity, and on the Mechanical Value of Heat.” Phil. Mag. vol. xxiii. 1843.) VOL. XX. PART II. 4B 262 PROFESSOR WILLIAM THOMSON ON THE 4. Considering it as thus established, that heat is not a substance, but a dynamical form of mechanical effect, we perceive that there must be an equiva- lence between mechanical work and heat, as between cause and effect. The first published statement of this principle appears to be in Mayer’s “ Bemerkungen tber die Kriafte der unbelebten Natur,” * which contains some correct views regarding the mutual convertibility of heat and mechanical effect, along with a false analogy between the approach of a weight to the earth and a diminution of the volume of a continuous substance, on which an attempt is founded to find numerically the mechanical equivalent of a given quantity of heat. In a paper published about fourteen months later, ‘‘ On the Calorific Effects of Magneto- - Electricity and the Mechanical Value of Heat,’+ Mr Jove of Manchester expresses very distinctly the consequences regarding the mutual convertibility of heat and mechanical effect which follow from the fact, that heat is not a sub- stance but a state of motion; and investigates on unquestionable principles the “ absolute numerical relations,’ according to which heat is connected with mechanical power ; verifying experimentally, that whenever heat is generated from purely mechanical action, and no other effect produced, whether it be by means of the friction of fluids or by the magneto-electric excitation of galvanic currents, the same quantity is generated by the same amount of work spent, and determining the actual amount of work, in foot-pounds, required to generate a — unit of heat, which he calls “ the mechanical equivalent of heat.” Since the publication of that paper, Mr JouLe has made numerous series of experiments for determining with as much accuracy as possible the mechanical equivalent of heat so defined, and has given accounts of them in various communications to the British Association, to the Philosophical Magazine, to the Royal Society, and to the French Institute. 5. Important contributions to the Dynamical Theory of Heat have recently been made by RanxineE and Ciausius; who, by mathematical reasoning ana- logous to Carnot’s on the motive power of heat, but founded on an axiom con- trary to his fundamental axiom, have arrived at some remarkable conclusions. The researches of these authors have been published in the Transactions of this Society, and in Poccenporrr’s Annalen, during the past year; and they are more particularly referred to below in connection with corresponding parts of the investigations at present laid before the Royal Society. 6. The object of the present paper is threefold,— (1.) To shew what modifications of the conclusions arrived at by Carnor, and by others who have followed his peculiar mode of reasoning regarding the motive * « Annalen” of WéoHLER and Lizzie, May 1842. + British Association, August 1843, and Philosophical Magazine, September 1843. DYNAMICAL THEORY OF HEAT. 263 power of heat, must be made when the hypothesis of the Dynamical Theory, contrary as it is to Carnor’s fundamental hypothesis, is adopted. (2.) To point out the significance in the Dynamical Theory of the numerical results deduced from REGNAULT’s Observations on Steam, and communicated about two years ago to the Society, with an account of Carnor’s Theory, by the author of the present paper; and to shew that by taking these numbers (subject to correction when accurate experimental data regarding the density of saturated steam shall have been afforded), in connection with JouLE’s mechanical equivalent of a thermal unit, a complete theory of the motive power of heat, within the temperature limits of the experimental data, is obtained. (3.) To point out some remarkable relations connecting the physical properties of all substances, established by reasoning analogous to that of Carnot, but founded in part on the contrary principle of the Dynamical Theory. Part I.—FUNDAMENTAL PRINCIPLES IN THE THEORY OF THE MOTIVE PoweER oF HEAT. 7. According to an obvious principle, first introduced, however, into the theory of the motive power of heat by Carnot, mechanical effect produced in any process cannot be said to have been derived from a purely thermal source, unless at the end of the process all the materials used are in precisely the same physical and mechanical circumstances as they were at the beginning. In some conceiv- able “ thermo-dynamic engines,” as for instance Farapay’s floating magnet, or Bartow’s “wheel and axle,” made to rotate and perform work uniformly by means of a current continuously excited by heat communicated to two metals in contact, or the thermo-electric rotatory apparatus devised by Marsu, which has been actually constructed; this condition is fulfilled at every instant. On the other hand, in all thermo-dynamic engines, founded on electrical agency, in which discontinuous galvanic currents, or pieces of soft iron in a variable state of magnetization, are used; and in all engines founded on the alternate expansions and contractions of media; there are really alterations in the condition of mate- rials; but, in accordance with the principle stated above, these alterations must be strictly periodical. In any such engine, the series of motions performed during a period, at the end of which the materials are restored to precisely the same condition as that in which they existed at the beginning, constitutes what will be called a complete cycle of its cperations. Whenever in what follows, the work | done, or the mechanical effect produced, by a thermo-dynamic engine is mentioned | without qualification, it must be understood that the mechanical effect produced, | either in a non-varying engine, or in a complete cycle or any number of complete | cycles of a periodical engine is meant. 264 PROFESSOR WILLIAM THOMSON ON THE 8. The source of heat will always be supposed to be a hot body at a given constant temperature, put in contact with some part of the engine; and when any part of the engine is to be kept from rising in temperature (which can only be done by drawing off whatever heat is deposited in it), this will be supposed to be done by putting a cold body, which will be called the refrigerator, at a piven constant temperature, in contact with it. 9. The whole theory of the motive power of heat is founded on the two following propositions, due respectively to JouLE, and to Carnot and Ciaustus. Prop. I. (Joutz).—When equal quantities of mechanical effect are produced by any means whatever, from purely thermal sources, or lost in purely thermal effects, equal quantities of heat are put out of existence, or are generated. Prop. II. (Carnor and CiAusius).—If an engine be such that, when it is worked backwards, the physical and mechanical agencies in every part of its motions are all reversed; it produces as much mechanical effect as can be pro- duced by any thermo-dynamic engine, with the same temperatures of source and refrigerator, from a given quantity of heat. 10. The former proposition is shewn to be included in the general “ principle of mechanical effect,” and is so established beyond all doubt by the following demonstration. 11. By whatever direct effect the heat gained or lost by a body, in any con- ceivable circumstances, is tested, the measurement of its quantity may always be founded on a determination of the quantity of some standard substance, which it or any equal quantity of heat could raise from one standard temperature to another; the test of equality between two quantities of heat being their capa- bility of raising equal quantities of any substance from any temperature to the same higher temperature. Now, according to the dynamical theory of heat, the temperature of a substance can only be raised by working upon it in some way so as to produce increased thermal motions within it, besides effecting any modi- fications in the mutual distances or arrangements of its particles which may accompany a change of temperature. The work necessary to produce this total mechanical effect is of course proportional to the quantity of the substance raised from one standard temperature to another; and therefore when a body, or a group of bodies, or a machine, parts with or receives heat, there is in reality mechanical effect produced from it, or taken into it, to an extent precisely pro- portional to the quantity of heat which it emits or absorbs. But the work which any external forces do upon it, the work done by its own molecular forces, and the amount bywhich the half zs viva of the thermal motions of all its parts is diminished, must together be equal to the mechanical effect produced from it; and consequently, to the mechanical equivalent of the heat which it emits (which will be positive or negative, according as the sum of those terms is positive or e DYNAMICAL THEORY OF HEAT. 265 negative). Now, let there be either no molecular change or alteration of tempe- rature in any part of the body, or, by a cycle of operations, let the temperature and physical condition be restored exactly to what they were at the beginning; the second and third of the three parts of the work which it has to produce vanish; and we conclude that the heat which it emits or absorbs will be the thermal equivalent of the work done upon it by external forces, or done by it against external forces; which is the proposition to be proved. 12. The demonstration of the second proposition is founded on the following axiom :— Jt is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects.* 13. To demonstrate the second proposition, let A and B be two thermo-dynamic engines, of which B satisfies the conditions expressed in the enunciation ; and let, if possible, A derive more work from a given quantity of heat than B, when their sources and refrigerators are at the same temperatures, respectively. Then, on account of the condition of complete reversibility in all its operations which it fulfils, B may be worked backwards, and made to restore any quantity of heat to its source, by the expenditure of the amount of work which, by its forward ac- tion, it would derive from the same quantity of heat. If, therefore, B be worked backwards, and made to restore to the source of A (which we may suppose to be adjustable to the engine B) as much heat as has been drawn from it during a certain period of the working of A, a smaller amount of work will be spent thus than was gained by the working of A. Hence, if such a series of operations of A forwards and of B backwards be continued, either alternately or simultaneously, there will result a continued production of work without any continued abstrac- tion of heat from the source; and, by Prop. L., it follows that there must be more heat abstracted from the refrigerator by the working of B backwards than is de- posited in it by A. Now, it is obvious that A might be made to spend part of its work in working B backwards, and the whole might be made self-acting. Also, there being no heat either taken from or given to the source on the whole, all the surrounding bodies and space, except the refrigerator, might, without interfering with any of the conditions which have been assumed, be made of the same tem- perature as the source, whatever that may be. We should thus have a self-acting machine, capable of drawing heat constantly from a body surrounded by others at a higher temperature, and converting it into mechanical effect. But this is contrary to the axiom, and, therefore, we conclude that the hypothesis that A * If this axiom be denied for all temperatures, it would have to be admitted that a self-acting machine might be set to work and produce mechanical effect by cooling the sea or earth, with no limit but the total loss of heat from the earth and sea, or, in reality, from the whole material world. VOL. XX. PART II. 4c 266 PROFESSOR WILLIAM THOMSON ON THE derives more mechanical effect from the same quantity of heat, drawn from the source, than B, is false. Hence no engine whatever, with source and refrigerator at the same temperatures, can get more work from a given quantity of heat intro- duced than any engine which satisfies the condition of reversibility, which was to be proved. | 14. This proposition was first enunciated by Carnot, being the expression of his criterion of a perfect thermo-dynamic engine.* He proved it by demonstrat- ing that a negation of it would require the admission that there might be a self- acting machine constructed which would produce mechanical effect indefinitely, without any source either in heat or the consumption of materials, or any other physical agency ; but this demonstration involves, fundamentally, the assumption that, in “a complete cycle of operations,” the medium parts with exactly the same quantity of heat as it receives. A very strong expression of doubt regard- ing the truth of this assumption, as a universal principle, is given by CArNnor himself ;+ and that it is false, where mechanical work is, on the whole, either gained or spent in the operations, may (as I have tried to shew above) be considered to be perfectly certain. It must, then, be admitted that Carnot’s original demon- stration utterly fails, but we cannot infer that the proposition concluded is false. The truth of the conclusion appeared to me, indeed, so probable, that I took it in connection with JouLn’s principle, on account of which Carnor’s demonstration of it fails, as the foundation of an investigation of the motive power of heat in air-engines or steam-engines through finite ranges of temperature, and obtained, about a year ago, results, of which the substance is given in the second part of the paper at present communicated to the Royal Society. It was not until the commencement of the present year that I found the demonstration given above, by which the truth of the proposition is established upon an axiom (§ 12) which I think will be generally admitted. It is with no wish to claim priority that I make these statements, as the merit of first establishing the proposition upon correct principles is entirely due to CLaustus, who published his demonstration of it in the month of May last year, in the second part of his paper on the Motive Power of Heat.t I may be allowed to add, that I have given the demonstration exactly as it occurred to me before I knew that Ciausius had either enunciated or demonstrated the proposition. The following is the axiom on which Ciausius’ demonstration is founded :— It is impossible for a self-acting machine, unaided by any external agency, to convey heat from one body to another at a higher temperature. It is easily shewn that, although this and the axiom I have used are different * “ Account of Carnot’s Theory,” § 13. + Ibid., § 6. + Pocgesnporrr’s Annalen, referred to above. DYNAMICAL THEORY OF HEAT. 267 in form, either is a consequence of the other. The reasoning in each demonstra- tion is strictly analogous to that which Carnor originally gave. 15. A complete theory of the motive power of heat would consist of the ap- plication of the two propositions demonstrated above, to every possible method of © producing mechanical effect from thermal agency.* As yet this has not been done for the electrical method, as far as regards the criterion of a perfect engine. implied in the second proposition, and probably cannot be done without certain limitations ; but the application of the first proposition has been very thoroughly investigated, and verified experimentally, by Mr Jouz, in his researches “ On the Calorific Effects of Magneto-Electricity ;’ and on it is founded one of his ways of determining experimentally the mechanical equivalent of heat. Thus, from his discovery of the laws of generation of heat in the galvanic circuit,f it follows that, when mechanical work by means of a magneto-electric machine is the source of the galvanism, the heat generated in any given portion of the fixed part of the circuit is proportional to the whole work spent; and from his experimental demonstration that heat is developed in any moving part of the circuit at exactly the same rate as if it were at rest, and traversed by a current of the same strength, he is enabled to conclude— (1.) That heat may be created by working a magneto-electric machine. (2.) That if the current excited be not allowed to produce any other than thermal effects, the total quantity of heat produced is, in all circumstances, exactly proportional to the quantity of work spent. 16. Again, the admirable discovery of PELTIER, that cold is produced by an electrical current passing from bismuth to antimony, is referred to by JouLE, as shewing how it may be proved that, when an electrical current is continuously produced from a purely thermal source, the quantities of heat evolved electrically in the different homogeneous parts of the circuit are only compensations for a loss from the junctions of the different metals, or that, when the effect of the current is entirely thermal, there must be just as much heat emitted from the parts not affected by the source as is taken in from the source. 17. Lastly,{ when a current produced by thermal agency is made to work an * «There are [at present known] two, and only two, distinct ways in which mechanical effect can be obtained from heat. One of these is by the alterations of volume which bodies experience through the action of heat, the other is through the medium of electric agency.”—Account of Car- nor’s Theory, § 4. (Transactions, Vol. XVI., Part V.) . . - . . > > > > : sos The experiments contained in the twelfth co- 3 05°49 lumn of the first Table are omitted, as 03-97 affording no definite results. The fifty- 7 249 sixth experiment is also omitted, having 8 Pree 3 obviously been spoiled. 9 es 18:38 16-02 18°37 15-63 The average values of M and m for a surface of 11:8 square inches and five minutes of time. 06-5 The average values of M and m for a surface of 100 square inches and one minute of time. Forbes de? ce — ———. —— LO ———xx<—a el rt Roval Sve. rans. Ldin® Vol. XX Part 2 MARINE INVERTIBRATA. a j ~~ a ne , , a _- Ai a. 3 ; - (4 3070) XVIII.—On some remarkable Marine Invertebrata new to the British Seas. By Epwarp Forsgs, F.R.S., F.L.S., Professor of Botany, King’s College, London : and J. Goopsir, F.R.S.S.L. and E., Professor of Anatomy, University of Edin- burgh. (Read 20th January and 3d February 1851.) The animals, either wholly new, or new to Britain, described in the following communication, were taken during a yachting cruise, with our indefatigable friend Mr Macanprew, among the Hebrides, in the month of August 1850. During this voyage, which lasted three weeks, a series of observations were con- ducted by means of the dredge and the towing-net. Not a single new form of testaceous mollusk was procured ; our exertions were amply rewarded, however, by the discovery of several remarkable Ascidians and Radiata, some of them so curious in themselves, and so important in their zoological bearings, that we have thought it desirable to lay an account of their characters and anatomy before the Royal Society of Edinburgh. . The most remarkable of them is the largest of compound Ascidians yet dis- covered in the Atlantic. Its nearest described ally is the genus Diazona of Savieny, between which animal and Clavellina it constitutes a link; one of con- siderable zoological importance, since it binds together more closely the truly compound Ascidians or Botryllide, with the social Ascidians or Clavellinide, which latter in their turn pass into the family of Ascidiade, through the anomalous Cynthia aggregata. The discovery of a creature thus filling up a gap in the animal series, was of itself a sufficient harvest from our autumn tour; in this instance our pleasure was enhanced by the beauty and singularity, as well as novelty, of the remarkable animal we have first to describe. The Syntetuys, for so we propose to designate the Ascidian, presents itself in the form of a compact gelatinous mass of half a foot, and sometimes more in diameter, and very nearly an equal height. It is affixed to the rock or stone by a short slightly spreading base of various breadth, whence rises as an inverted pyramid the body of the mass, irregularly circular and slightly lobed, spreading out at its summit. It is of a translucent apple-green hue; the surface is nearly smooth. The whole of the expanded disk is thickly studded with individual ascidians growing out, as it were, from the common mass. They are arranged in irregular rows, witha tendency to concentric order. Each individual measures, when full grown, nearly two inches in length, and has the shape of an elongated ampulla, with two terminal orifices, set well apart, but not very prominent, and VOL. XX. PART II. 40 308 PROFESSORS EDWARD FORBES AND J. GOODSIR ON SOME nearly on the same level. The outer tunic is a smooth and transparent softly cartilaginous sac of a pale emerald green tint, slightly swelling out above the centre, and contracted, but not pedunculated at the base. The inner tunic is clearly seen through the walls of the outer; it is rather less in dimensions than the outer, and its shape is plainly indicated by the opaque white lines which mark its boundaries. The orifices of the outer tunic are both quite plain; the branchial one is rather longer than the anal, as is also the case with the openings of the inner tunic. The branchial orifice of the latter is fringed with a circle of pointed tentacula more than twelve in number; its anal orifice is at the end of a short tube, and has no tentacula, but six conspicuous white ocelli. Beneath the branchial orifice are two crescentic white lines, at the summit of a single white line which runs down the branchial side of the body; under the anal orifice there is a short oblique central white line running from the neighbourhood of a large ganglion to the summit of two white lines uniting in a loop at the point of junction, and running down the visceral side of the body. The chief visceral mass is seen at the base of this line imbedded in the common pedicle. When the entire mass was first dredged up, many of the tests appeared as if emptied of their contents, or as if the inner tunic and viscera had not become developed. After it had for some time remained at rest in a vessel of sea-water, to our great surprise we found all the sacs filled up again. On closer examina- tion, we found that the inner tunic is exceedingly irritable, and can withdraw itself like the finger of a glove, entirely independent of the outer tunic, and hide itself in the common mass or peduncles. This is done very rapidly sometimes, at other times rather slowly; most rapidly when the ganglionic mass between the orifices is pinched or otherwise irritated. When-we squeezed it with the forceps, the withdrawal of the common branchial sacs was almost instantaneous. The genus Syntethys differs from Diazona in the structure of the branchial and anal orifices, which, instead of being six-rayed, as in the latter genus, are simple and even-edged as in Clavelina ; moreover, instead of having a peduncu- lated, it has a sessile abdomen. The structure and form of the common mass is similar, making a strong distinction between it and Clavelina. The following summary of the characters of Syntethys will serve to compare them with those of the genera described by Savieny. Common mass sessile, gelatinous, forming a single orbicular system. Jndivi- duals very prominent, arranged subconcentrically. Branchial and anal orifices simple, and not cut into rays. Thorax oblong and cylindrical. Branchial chamber with thirteen transverse rows of oblong openings, fringed with ciliated epithelium ; hooked fleshy tubercles at the intersections of the branchial meshes, each mesh presenting one of the ciliated openings; the tubercles give the internal surface of the chamber a dotted appearance. REMARKABLE MARINE INVERTEBRATA NEW TO THE BRITISH SEAS. 309 Gsophagus elongated, situated on the left side. Stomach cubical, spongy, or glandular. Intestinal loop large and open, reaching to the bottom of the muscu- lar tunic; its ascending portion glandular, probably hepatic; the rectum passes from the ventral to the right side of the cesophagus; the anus is on the dorsal edge of the sac about its middle. The ovary is in the loop of the intestine, but was not in season in the specimens taken. Testis white, ramifying on the surface of the ovary; the vas deferens runs up on the oesophagus and rectum to the side of the anus. The heart is in the loop of the intestine and ovary. Sp. Syntethys hebridicus—All the specimens were dredged in thirty fathoms water, close to Croulin Island, near Applecross. The locality in which they occurred is remarkable for the assemblage of boreal mollusca there congregated, so that we may reasonably expect that this extraordinary ascidian will be found hereafter in the Norwegian seas. It is probably a member of the boreal type of the British fauna. Holothuria intestinalis. Ascan.and RatHkKE.—From a depth of thirty fathoms in the Minch, and from the same depth off Croulin Island, we dredged a twenty- tentaculated Holothuria, undescribed as a member of the British fauna. It has an elongated cylindrical body of a pinkish-grey colour, and very soft in texture of skin. The tentacula are short and orbicular, compactly frondose, and of a dark orange colour. The surface of the body is thickly covered with slender suckers, dilated at their bases, and rather more numerous on the ventral than on the dorsal aspect. By means of these suckers, the animal invests itself with fragments of shells and stones in the manner of Thyone. It grows to the length of half a foot. Judging from the description given in the “ Ofversigt af Skandina- viens Echinodermer,” by Dusen and Koren, this appears to be the Holothuria intestinalis of Ascanius and RatuKe, H. mollis of Sars. We have not been able to compare it with the original figures. It constitutes a second British species of Hlolothuria proper ; the first being the animal described by Mr Peacu, under the name of “ Nigger,” given to it by the Cornish fishermen. Sarcodictyon agglomerata. Sp. nov.—Examples of a new species of this curious genus of Asteroid zoophytes were dredged in thirty fathoms water off Croulin Island, and also between Rasa and Scalpa. Like its congener the Sarcodictyon catenata, it invests the surface of stones and shells, and is also found adhering to corallines. It differs essentially, how- ever, in having the polype cells, instead of being arranged in single file, grouped together in assemblages of from three to five, each group connected with its neighbour by a stolon-like extension of the polypidom. The texture of its surface is not so smooth, and the colour invariably ochraceous yellow. The polypes are _ white, and exactly resemble those of Sarcodictyon catenata. Each polype cell measures about two-tenths of an inch across. 310 PROFESSORS EDWARD FORBES AND J. GOODSIR ON SOME In the synopsis of the genera of zoophytes, by Minne Epwarps and Haine, the genus Sarcodictyon is placed in the family Cornularine, among the Alcy- onaria. Wecan hardly assent to its removal from the immediate neighbourhood of Alcyonium, for it differs merely in the stoloniferous method of growth. The new species now announced, goes far to confirm our view of its affinities. This genus may be said to bear much the same relation to Alcyoniwm, which our new genus Syntethys (among the Ascidians) bears to Clavelina. Arachnactis albida. Sars.—In the first part of the very beautiful and valu- able work by M. Sars, entitled “ Fauna Littoralis Norvegiz,” published at Chris- tiania in 1846, a new genus and species of Helianthoid zoophytes is described at length, and figured in detail, under the name of Arachnactis albida. In the “ Travels in Lycia,” by Professor E. Forpes and Captain Spratt, R.N., published in 1847, a swimming Actinea is noticed and figured from the Egean. This was clearly a species of Arachnactis. When Dr Batrovur visited the Island of Lewis with his pupils in August 1841, they procured a number of mutilated specimens of a radiate animal found floating in the Minch. These were too imperfect for determination at the time. This year, however, we have discovered a species of Arachnactis evidently identical with the Norwegian one in the Minch, and the remains of Dr BaLrour’s animal have proved identical with it. The definition of the genus given by Sars is,;—‘‘ Animal liberum, molle, natans; corpus breviter cylindricum, parvum, basi rotundata, disco suctorio carente; os seriebus tentaculorum non retractilium duabus circumdatum, exte- rioribus longissimis, interioribus brevibus.” The number of the larger tentacula were eight to ten, of the smaller, accord- ing to SARs, twelve; we have observed them as many as sixteen. The shape of the body is pyriform; its colour dusky white, tinged with tawny. The outer tentacula are very long, tawny and white; the inner, much shorter. The length of the body is about one inch. The outer tentacula can be extended to three or four times the length of the body. The creature swims freely, and habitually in the manner of a medusa. There is a point, however, of consequence which Sars did not observe, 2 can convert its posterior extremity into a suctorial disk, and fix itself to bodies im the manner of an Actinea. ARistotLE states in several places in his History of Ani- mal, that the Actinea (ax«anpn) can detach itself from the rock and swim. Thus, in Book iv. 6, speaking of these animals, he writes,—* apoorépuxe wer yap ros sergous donee tna ruv doreanodeguav, cmodvercu 8 évore.” Commentators have supposed that he confounded Actineze with Medusz. But he mentions the latter animals under another name. The discovery of the Avachnactis, and its abundance in the Grecian seas explain the difficulty, and shew the accuracy of his observations. Plancia. New Genus.—Umbrella hemispherical ; radiating vessels four, REMARKABLE MARINE INVERTEBRATA NEW TO THE BRITISH SEAS. 311 simple; no conspicuous genital glands; two long marginal tentacles, and numerous intermediate rudimentary tubercles, all with ocelli at their bases ; stomach at the end of a very long, extensile, cylindrical tubular proboscidiform peduncle, with a simple or obscurely lobed orifice. We have deemed it necessary to constitute this genus for a very curious little naked-eyed medusa of the family Sarscade@, so distinct in its characters, as not to be referable to any of the defined groups. We have dedicated it to Janus PLANcus, who, in his tract “ De Conchis Minus Notis,” published in 1739, was the first naturalist who figured a naked-eyed medusa. Plancia gracilis. Sp. Nov.—Disk hemispherical, depressed, colourless, smooth, its margin furnished with two long tubular tentacula, one on each side opposite the terminations of gastrovascular canals; at the origin of each of these is asmall fixed tentacular process, connecting the umbrella with the subumbrella, as in the genus Steensirupia. The remainder of the margin is occupied by about sixty minute tubercles or rudimentary tentacula, beside each of which on an oblong process is a minute black ocellus. Four simple gastrovascular canals, connected with a marginal canal, divide the disk into as many equal segments. The entrance of the cavity is protected by a broad veil. The peduncle is very long and extensile, resembling in shape that of Sarsia; it is very acute at its base, and is of a general pink hue, with darker lines, as if of genital glands lining its tube. It is terminated by a short orange-coloured campanulate stomach, opening by an irregularly four-lobed orifice. This is an active and elegant little creature. Its disk measures rather less than a quarter of an inch across. When swimming, it carries its two tentacula streaming behind it for a great length. We procured several examples in the Sound of Mull and off Staffa. Oceania ducalis. Sp. Nov.—Umbrella campanulate, subglobose, round above, smooth, colourless, transparent. Subumbrella rather small in proportion, its orifice protected by a conspicuous veil; its margin edged with rose-colour, and bearing 16 (3 x 444) pinkish tentacula, springing from bulbous bases, each of which is marked by a conspicuous crimson or purple crescentic ocellus: between each pair of tentacles is a minute tubercular process. Down the sides of the subumbrella run the four simple gastrovascular canals, tinged with red. From its centre depends the oblong, massive, reddish-tawny peduncle, in the upper part of which are obscurely seen the convoluted reproductive glands. The orifice of - the peduncle is campanulate, and bordered by four slightly-fimbriated lips. The height of the body is less than a quarter of an inch. It was taken at Tobermory. We had previously met with the same species on the coast of Dorsetshire. Slabberia catenata.—Hitherto only a single species of the genus-Slabberia, one of the most curious types of the Medusa Gymnopthalmata, has been met with, VOL. XX. PART Il. 4p 312 PROFESSORS EDWARD FORBES AND J. GOODSIR ON SOME namely, the S. halicrata, a native of the coasts of Cornwall. We have the pleasure of adding a second and very distinct species, to which the name of Slabberia catenata may be applied. , It differs from the former, among other characters, most conspicuously in having its poiser-like marginal tentacula thickened for half their length by a series of rings or bulbs, charged with pigment cells, and ranged in succession above the terminal bulb with a dark nucleus, so characteristic of the genus. The umbrella is deeply campanulate or subglobular, smooth and colourless. The subumbrella is much less in proportion than in its described ally; it is divided into equal portions by four canals, which open into a central marginal vessel. The very minute linear genital glands can scarcely be traced on the upper part of these vessels. The border of the general cavity is provided with a shelf-like veil. The tentacula are stout, four in number, colourless, and cylindrical in their upper, nodulose and annulated in their lower half. There are five or six ring-like or bulbous thickenings, besides the terminal bulb. Each is of an orange hue, and the lower ones are larger than the upper. The next above the terminal bulb is largest. The terminal bulb is also orange, but has a dark nucleus. The tentacula spring from ocellated bulbs. These are somewhat trian- gular in shape, pale yellow above, marked across the centre by a band of dark orange, below which, on a pale yellow ground, is the small black ocellus. The peduncle, or stomach, is longer than the tentacula when expanded to its full dimensions. It is highly contractile, and is of a dull olive hue, with indicaticns of darker cylindrical bands. The height of the umbrella was about two-tenths of an inch. This curious medusa was taken off Tobermory, and afterwards near Loch Laigh in Mull. Hippocrene pyramidaia. Sp. Nov.—During our cruise, we had the good fortune to add no fewer than three new and very distinct species to the beautiful and singular genus Hippocrene or Bougainvillia. They, like their congeners, were all exceedingly minute. The first of which we name /7. pyramidata, is distinguished conspicuously by the form of the ovarian lobes of the peduncle; instead of being quadrate, as in all known species, they are triangular, so that the entire peduncle assumes the shape of an inverted pyramid. The umbrella is transparent, smooth, colourless, and subglobular. The sub- umbrella is comparatively small and quadrately campanulate; its opening is protected by a four-lobed veil. At the four angles are the groups of connate eye- tubercles. Each group forms an oblong mass, the general colour of which is yellowish below and orange above. From four to six tubercles go to a mass, and the orange-coloured portion is lobed according to their number. On the lobed yellowish part below is a black eye-speck, one to each tubercle. One, or at most two transparent tentacula, were seen to protrude from each of the masses. The REMARKABLE MARINE INVERTEBRATA NEW TO THE BRITISH SEAS. 313 peduncle is pyramidal, and composed of four triangular lobes, corresponding with the four gastrovascular canals. Each lobe is of a tawny-yellow colour, with a dark orange centre, and as it is narrow, the four combined, when seen from above, appear as a small yellow cross, with an inner cross of orange. From the dependant apex of the peduncle hangs a short and narrow colourless stomach, the lips of which are produced into bifurcated tentacular processes of no great length. Several examples of this animal were taken off Loch Laigh in Mull. Hippocrene crucifera. Sp. Nov.—This new form of Hippocrene differs from all its congeners in the very long genital lobes springing from the peduncle, and running down one-half the length of the canals, so as to remind us of the ovaries of the Thaumantias. It was taken off Tobermory. The umbrella is globular, colourless, and smooth; the subumbrella rather large. The four fascicles of tentacular bulbs are each of an oblong and some- what crescentic shape, tawny-orange above and colourless below. Each is com- posed of six bulbs, bearing black ocelli on their pale portions, and corresponding to as many short transparent colourless tentacula. The peduncle is rather short, but its lobes, which are of a tawny-yellow colour, with a double line of orange in their centres, are very long and narrow, somewhat undulated, and prolonged for half the length of the subumbrella, appearing like so many arms. The anal lobes are colourless; they are produced into short and proportionally minute labial tentacula, each of the four presenting a simple bifurcation. Hippocrene simplex. Sp. Nov.—This species is more nearly allied to the H. britannica than the others, and connects that well-known form with AH. nigriiella, but is very distinct from both. The umbrella is globular, colourless, and smooth; the subumbrella large in proportion. The four fascicles of tentacular bulbs are each oblong, yellow below and orange above ; each is composed of four bulbs, and is acutely four-lobed, bearing four black ocelli on as many projections. Only one yellowish tentacle (as in H. nigritella) springs from each mass. The peduncle resembles that of fH. britannica, is quadrate, massive, four-lobed, and of a dull orange hue. ‘The stomach is short and wide, terminating in four colourless labial tentacles, which twice bifurcate. Several specimens were taken at Tobermory. Thaumantias undulata. Sp. Nov.—When sailing through the Minch on a very warm day, when the sea was very calm, we met with a number of small medusz, each measuring about an inch and a-half in diameter, and conspicuous in the water, owing to the undulated pink cross which marked their subumbrella. On capturing some, they proved to belong to an undescribed, and very curious form of the genus Thawmaniias. The umbrella is hemispherical, smooth, and colourless. Its margin is fringed with very numerous slender coloured tentacula, which are often carried coiled up 314 PROFESSORS EDWARD FORBES AND J. GOODSIR ON SOME spirally. Their formula is 40 x 4+ 4. Each of these springs from a bulbous base, bearing a small but distinct black ocellus. Between each pair of tentacula is a minute transparent mobile pedunculated tubercle. Down the four gastrovas- cular canals, very nearly from their divergence, to the margin of the umbrella, run the four linear genital glands, tinged with rose colour. They are very pecu- liarly formed, each hanging from the surface of the subumbrella in the shape of a pair of undulated membranous curtains, strikingly reminding us of the appear- ance presented by Stawrophora (so well described and figured by Professor Acassiz in his Memoir on the Naked-Eyed Medusze of Massachusetts), but differ- ing in their nature; for, in the animal we are describing, they are assuredly quite distinct from the stomach-lobes. The stomach is rather large and quadrangularly campanulate, rose coloured, and slightly fimbriated at the margins. Thaumantias confluens—To find a new species of the genus Thawmantias sufficiently distinct from the numerous and very similar described forms, was scarcely to be looked for. In the one before us, however, we have found such a desideratum. The Thaumantias confluens differs from all its British allies in having the genital glands continued so high up on the gastrovascular canals, that they all meet on the vertex of the umbrella, and form an unbroken cross. The umbrella is hemispheric, smooth, and colourless. Its margin is fringed with pale pinkish tentacula; the formula of their number being 14 x 4 + 4. Their bases bear very minute black ocelli; the intertentacular spaces have minute tubercle-like bodies on each, some of them being shortly pedunculated. The marginal veil is broad. The genital glands are of a pale pink colour, very narrow and linear, confluent at their bases, and continued down the upper third of each of the four gastrovascular canals. When the creature is in the water, they present the appearance of a pink cross. The stomach is very short and narrow, and terminates in four lanceolate acute lips. The disk measures nearly half-an-inch across. This delicate and pretty animal was met with not unfrequently off Tober- mory, and afterwards near Skye. Fig. Fig. Fig. Fig. Fig. REMARKABLE MARINE INVERTEBRATA NEW TO THE BRITISH SEAS. 2315 EXPLANATION OF THE PLATES. PLATE IX. 1. Holothuria intestinalis, natural size. 2a. Arachnactis albida, natural size; and 2 6, the same with some of the outer tentacula removed in order to shew the inner circle and the globular form at times assumed by the body. 3a. Sarcodictyon agglomerata, natural size; 3 b. the same magnified ; and 3c. the polypes. 4a. Syntethys hebridicus, less than the natural size; 4. one of the individual Ascidians of the size of nature; 4c. the same with the ner tunic retracted ; 4 d. the orifices of the inner and outer tunics much magnified, PLATE X. . la. Plancia gracilis, three times the natural size, seen in profile; 16. the same, seen from above; 1c. its peduncle; 1 d. orifice of the peduncle; 1 ¢. extremity of a tentacle. . 2a. Oceania ducalis, much magnified, and seen in profile; 2b. the peduncle, ovaries, and mouth ; 2 ¢. one of its tentacula. . 3a. Slabberia catenata, natural size; 3 b. the same, magnified; 3c. its peduncle; 3 d. genital glands on the side of a gastro-vascular canal ; 3 ¢. one of the tentacula. . 4a. Natural size of Hippocrene pyramidata; 4 6. the same, magnified; 4 c. as seen from above ; 4d. the genital lobes and peduncle; 4 ¢. genital cross; 4. one of the tentacular fascicles. . 5a. Natural size of Hippocrene cruciata ; 5 b. lateral view, magnified ; 5c. view from above: 5 d. genital lobes and peduncle ; 5 e. one of the tentacular fascicles. . 6 a. Natural size of Hippocrene simplex ; 6 b. lateral view magnified; 6 c. the view from below ; 6 d. one of the tentacular fascicles ; 6 e. genital lobes and peduncle. . 7a. Thawmantias, natural size; 7 b. diagram of same, seen from above; 7 c. section shewing the genital folds and stomach ; 7d. margin and tentacula. 8a. Thaumantias confluens, side view magnified; 8 6. diagram of view from above; 8c. pe- duncle and buccal lobes ; 8 d. margin and tentacula. VOL. XX. PART II. 4Q Vihar ded fe m at 4 Fr tay Na Pot. te ee Tyan rlgines we ie es a e na ei one yon ' ‘bulged. pia ’ as ¥ ie bah only rath, | as yo ars a8; Ht welty | sche eT ‘ b Sey Saamk, o eee & d ~ : a’ 7 Lo Ae 5 , hq ah ia) (~ My eX ’ ._ ' 7 Pron % «eee YG aS aeRO 9 Peat sage 244 pee oe i Lae ik Le , , i ; ; ; , Aes hy Lape i? Olan ite S, " ; w y Lag aed y 7 oe Alapaha? dO. ei fo ince thw bite es AE , xy ders Mann Fadl "ioe aha oa 7 ‘es r “rt { 4 Misia Vie hey > : % | oi} rH A Belihens esi tn aeat Fi : Dy Pits Bria isu b i yi) iN ‘ad Way wi Pte Wh how i hin 1 7 at . >t} : ‘its ae 7 iathiny Gauie ® se : haa, | dA ‘Owe seit WA ete i : re wil H ae. bar ( han? 4 ‘ sie WH we haya PS. j Py | te { ah, Hived aur eA ais voi A _ ' = \ \ “ ; am Te Ask = Wh a Lean 7 iy tig anh Li ne rT at tad ere) he "i i ' if i oO inne bs Ayo wehtwes x fi 7 Maru tve, mgr j JiPigt iy gi al gy. runes ' lity ng wie mer wiped beeen h) y, F { , . a " rs | i ‘ . “a ne - ‘ +9 > hs ’ . P | N i fr ? fr ‘ : Mia ilergssert NE Gu sete Mon 1 ir J ye Wyle 5 GE it rat et ® ; : e ii if 4 a | ADS ae 4 * 1 h J ¥ ( , ' ’ ’ * ‘ 1 ‘ ' * Pi Be ‘ ta APG XIX.—On the Total Intensity of Interfering Light. By Professor SToKEs. | Eatracted from a Letter addressed to Professor Kelland. | PEMBROKE COLLEGE, CAMBRIDGE. My DEAR SiR, * * * * In reading your paper in the Transactions of the Royal Society of Edinburgh, vol. xv., p. 315, some years ago, it occurred to me to try whether it would not be possible to give a general demonstration of the theorem, applying to apertures of all forms. I arrived at a proof, which I wrote out, but have never published. As I think it will interest you I will communicate it. You may make any use you please of it. Case I. Aperture in front of a lens; light thrown on a screen at the focus, or received through an eye-piece, through which the luminous point is seen in focus. The expression for the intensity is given in Airy’s Tract, Prop. 20. If the in- tensity of the incident light at the distance of the aperture be taken for unity, and D be the quantity by which any element of the area of the aperture must be divided in forming the expression for the vibration, that expression becomes 1 12 ATT; prtqy pt fain == (ve—B+ part) ax dy, the integration being extended over the whole aperture. If it should be neces- sary to suppose a change of phase to take place in the act of diffraction, such change may be included in the constant B. If, then, I be the intensity, 2 pets ( ffein “Pee Maedy) + ( ffoose P2744 andy) and if I be the total illumination, T= f f- tapag. Now, { [[renazay\ =ff[[frapse.y) az dy de ay, the limits of 2’, y’ being the same as those of 2, y. Hence, Dp? t= ff foos <5 (vi=a+ay=y) ae dy dx dy’. VOL. XX. PART III. 4R 318 PROFESSOR STOKES ON THE In the present shape of the integral, we must reserve the integration with respect to p and gq till the end; but if we introduce the factor e+«» +47, where the sign — or + is supposed to be taken according as p or q is positive or nega- tive, we shall evidently arrive at the same result as before, provided we suppose in the end a and @ to vanish. When this factor is introduced, we may, if we please, integrate with respect to p and q first. We thus get pt i= limit of ff fff fer? ** cos 5 (pia +9 y/=9) dz dy da! dy dp dy. ice) io 0) Now, uf e*“P cos (kp—Q) d p= cos Qf eT“? coskpdp — oo —o + sin Qf eT“? sin kp dp —o ao =2 cos af, e “” coskp dp en A similar formula holds good for g, whence D? I = limit UST ag nice i a 2EY=Dy") dxdydx dy. bx bAv Let now 2 1 (a —x) :? é yd bAa aaa > Waal whence da’= aq ah and the limits of w are ultimately —« and +o, since a ultimately vanishes. Hence 2adrx ON f2-) “dia limit of a ol ae ae Tee Ps br A similar formula holds good for vy’, and we have, therefore, DI =e rf dx dy=B A, if A be the whole area of the aperture or apertures. Now I ought to be equal to A, and, therefore, D=6X. Case II. Aperture in front of a screen. The formula for the illumination is given in Arry’s Tract, Art. 73. We have as before, D? 1 = limit of [Lf ff femrr | (v- a — (#- i) + +(y ogy. -( ae jax dy ay ay dp ag +b Wane a+b =] imit of [fff fereres cos {nie [2222 4 y'2?—y?] TOTAL INTENSITY OF INTERFERING LIGHT. 319 ia ae (a/—x) — — = -y)} de dy dz dy dpdgq = limit ot fil eme=9)" : an erw=n)" T (a+b) cos (?—2 +y7?%—y*)dxdydx dy. Aab Now, when a vanishes, the whole of the integral he 2adzx' ae 2 —o a? + (7 x) is ultimately comprised between limits for which a’ is infinitely close to x, and similarly with respect to 7’; so that ultimately 5 7(a+ 4) Nabe within the limits for which the quantity under the integral sign does not vanish. Hence, passing to the limit, we get D? I =r? vf fax ay= é? A, as before. Sey’ —y)=1 Cass III. Everything the same as in Case II., except that the phase of vibra- tion is retarded by p, where p is some function of x and y. This case is very general. It includes, as particular cases, those numbered I. and Ii. The experiment with FrEsNEL’s mirrors or a flat prism is also included as a particular case.* From what precedes, it is plain that we should have in this case peT = limit of {fff Cea a OG A 6b cos — [x2 — x2 +y?7-y"]-p’+e } dx dy da dy’, where p’ is the same function of 2 and y’ that p is of z and y. The same reason- ing as before leads to the same result. I do not regard the preceding demonstration of a result which you were the first to announce, as of any physical interest after what you have yourself done. Still it may not seem wholly uninteresting, in an analytical point of view, to de- monstrate the proposition for any form of aperture. * Thus, in the case of the flat prism, if P, Q be the virtual images corresponding to the halves AB, BC, if we produce A B to D, we may suppose the light D which falls on B C, instead of coming from Q, to come from P, and to have been accelerated by the passage through the wedge DB Cr B =e of air instead of the same wedge of glass. 320 ON THE TOTAL INTENSITY OF INTERFERING LIGHT. Of course, by comparing the result A’ 6’ A with that obtained, in particular cases, by integrating in the straightforward way, we may arrive at the values of various definite integrals. I am, dear Sir, Yours very truly, G. G. STOKES. (apelin XX.—Some Observations on the Charr (Salmo umbla), relating chiefly to tts Generation and Early Stage of Life. By Joun Davy, M.D., F.R.SS., L. & E., Inspector-General of Army Hospitals, &c. (Read 15th March 1852.) The natural history of the Charr, especially as regards its generation and the early period of its life, is admitted to be very defective, partly, no doubt, arising from the peculiar habits of the fish withdrawing it from observation, and in part, and more, to the circumstance that it is comparatively of rare occurrence, being found only in a limited number of the deepest lakes of this country, and, with few exceptions, seldom taken by the angler, and consequently a good deal removed from the notice of the naturalist. Residing for several years in the neighbourhood of Windermere,—a fee in which this fish, though decreasing in number, is still pretty abundant,—I en- deavoured to collect information respecting its breeding, the time required for the hatching of its ova, and the peculiarities of the young fish after its exclusion, but in a great measure in vain. The fishermen of the lake were acquainted with its spawning season and the spawning localities; but none of them had ever seen a young charr after its quitting the egg, nor till it had attained a notable size. Artificial breeding—that process of fecundation which was first tried by Count GosreEIN in the middle of the last century, and has since been so success- fully employed both in propagating some of the more valuable species of the Salmonidee, and in illustrating their history—occurred to me as the only likely means of affording the information desired. About the same time, viz., in the autumn of 1850, a gentleman, Morris Rey- NoLps, Esq., living near thé lake,—through whose garden a small stream of good water descends from the hill above, very favourably circumstanced for carrying on the process of artificial breeding,—commenced the attempt, after the manner recommended by Jacozi. This process is now so well known as hardly to require description. I may briefly mention, that two wooden boxes, communicating, were used, through which a small current of water was allowed to pass by a grating of perforated zinc, over a bed of gravel laid on the bottom of each compartment. In these boxes the roe of the fish, for trial, after admixture with the fluid milt, was deposited, each obtained from individuals in the act of spawning, or mature for that act, as denoted by both the roe and milt being yielded under gentle VOL. XX. PART III. 4s 322 DR DAVY’S OBSERVATIONS ON THE CHARR. pressure applied to the abdomen, soon after the fish were taken from the water,— the roe in detached ova, the milt in the state of a milk-like fluid. It was from these boxes that I obtained, through the kindness of their pro- prietor, most of the subjects of the following observations; and to him, too, I was indebted for exact particulars, without which the observations would have been almost valueless. 1. Of the Roe and Milt of the Charr. The ova of the charr, at their full time, that is, when they are detached from their ovaries, and are loose in the cavity of the abdomen, ready for expulsion, are, like those of the other Salmonidee, almost, if not quite, spherical. Those I have examined, I have found to vary in diameter from ‘16 to °18 and 20 of an inch; and in weight (after the removal of adhering moisture by wiping) from ‘7 grain to 1 grain each. Their colour is a light yellow, lighter than that of the ova of the salmon or lake trout with which I have compared them, and thus distinguish- able, as well as by their somewhat smaller size. The matter of which they con- sist may be described as an almost colourless, transparent, viscid fluid, contain- ing suspended in it very many oil globules of various sizes, hardly distinguishable without the aid of the microscope, of a yellow colour, to which the colour of the egg is principally owing. This matter may be considered as corresponding to the yolk of the egg of the bird: it is more than doubtful that the ova of the charr have any part corresponding to the albumen of the bird’s egg. The matter of the charr’s egg, I may remark, like that of the ova of the Salmonide generally, is peculiar in some of its properties; being coagulable on admixture with water, as I believe was first pointed out by M. Voer, in the instance of the Coregonus of the Lake of Neuchatel,*—in being, as I have found, not coagulable by heat, even at a temperature of 212° Fahr., if water be excluded,—in being, after coagulation by water, soluble in a solution of common salt and in other saline solutions, and also in such cf the vegetable acids as were tried, for instance, the tartaric, acetic, oxalic, and citric. For a fuller account of these experiments, I may refer to a paper expressly on this subject, which has been communicated to the Royal So- ciety of London, the results of which would seem to Show that the substance of the egg of the Salmonidze may be viewed as a distinct species of albumen,—as much so, perhaps, as the coagulable lymph of the blood compared with the serum of that fluid. The shell of the egg of the charr may be briefly noticed. Nearly transparent and colourless, it is of considerable strength, and until thinned and weakened in the process of hatching, is not easily ruptured. Five emptied of their contents, but not deprived of their moisture by drying, weighed one-tenth of a grain; tho- * See ‘‘ Embryologie des Salmones. Par C. Voer.” Neuchatel, 1842, 4to, p. 11. DR DAVY’S OBSERVATIONS ON THE CHARR. o20 roughly dried, so as to expel this moisture, they were reduced from ‘10 to ‘07 of a grain, thereby denoting a large proportion of solid matter, viz., 70 per cent. Whether this shell in its sound state, before putrefaction has commenced, is pervious to water, seems to me questionable; and also, whether the internal vitelline membrane, after fecundation, is altogether impermeable by it. M. Voer holds that the shell is at all times so permeable, but the vitelline membrane, after impregnation, never, so long as the ovum retains its vitality ; losing which, the membrane, he infers, no longer resists the transmission of water, and the coagulation of the fluid yolk takes place as an unavoidable consequence. I might assign reasons for the doubts I venture to entertain on these points; but not sure that they would be considered satisfactory, or that the points themselves, though not without interest, require here to be discussed, I shall avoid bringing them forward. That the death of the impregnated ovum, as pointed out by M. Voar, is clearly indicated by the coagulation of the yolk, from the penetration of water into its substance, is certain. But there is another indication of the event, and not less certain, viz., the adherence of the lighter oil globules to the vitelline membrane, preventing thereby their change of place with a change of position of the ovum, and that tendency to ascend in the heavier yolk fluid which is observable whilst vitality lasts, and which may perhaps be considered as a characteristic of it. The adhesion of the oil globules alluded to, not unfrequently takes place in eggs which retain their transparency. In no instance have I observed any traces of foetal development after these have become fixed, or, if commenced, any further pro- eress. Why these ova do not become opaque, why their membranes should re- main impervious to water, I am ignorant; but that they are so, must be inferred from the circumstance, that when ruptured, and their contents mixed with water, coagulation is immediately effected. Relative to the milt or spermatic fluid of the charr, I have but ee observa- tions to offer, the examination I have hitherto made of it not having been minute, except very partially. Like that of the Salmonide generally, in its mature state when ready to be shed, it is a milk-like fluid, slightly viscid, heavier than water, and containing, diffused through it (the cause of its milkiness) a vast number of granules (spermatozoa). These minute bodies are nearly spherical in form, are about wth of an inch in diameter, and seem to move spontaneously, as seen under the microscope, for a short time after the expulsion of the fluid from the live fish. Though they are of greater specific gravity than water, yet, owing to their minuteness, they are easily diffused and suspended in this fluid. After a rest of two hours, water rendered turbid by the addition of a small quantity of spermatic fluid had not become clear, even towards its surface. A drop placed under the microscope was found to abound in spermatozoa. Another property of the spermatic fluid, not unworthy of mention, is the remarkable manner in which it resists putrefaction. Whether the spermatozoa are capable or not of impreg- 324 DR DAVY’S OBSERVATIONS ON THE CHARR. nating the ova after they have lost their power of spontaneous motion, I cannot offer any decided opinion ; from the few trials I have made, I am led to believe that the one quality or power is distinctive of the other, and that, ceasing to move, they become inert. In a charr weighing about half a pound I have found the number of ova to be 1230, all nearly of full size. As the volume of the mature and distended testes is about the same as that of the ripe ovaries, the number of spermatozoa belong- ing to them must almost baffle calculation ; and if, as there is reason to believe, a single one may suffice to impregnate an ovum, the whole from one male may, it is presumed, be more than adequate to effect the impregnation of the entire eggs of many females, especially taking into account how readily these minute bodies are suspended and diffused in water. 2. Of the time required for the hatching of the Ova; and of the young Charr in their early stage. The principal spawning season of the charr in the several lakes of the Lake District in which this fish occurs, is the beginning of winter, from about the first week in November to the first in December, when the water over the spawning- beds has become comparatively cool, reduced from about 60° Fahr. to about 50°. Whether this is the only season is somewhat doubtful; the fishermen of Winder- mere speak of a later one, in which it is believed by them that fish of the larger size and few in number deposit their spawn, viz., in February and March.* Be this as it may, all the observations I have recorded were made on spawn obtained during the first period mentioned. From analogy, it might be inferred that the time required for the hatching of the charr would be a variable one, depending on the degree of temperature of the water and on other less appreciable circumstances. In 1850-51, Mr Reynoxps, as he informs me, found none hatched in a shorter period than 60 days; the ereater number on the 70th, and from that to the 75th day; some few as late as the 90th. The average temperature of the water in the breeding boxes was about 40°. Ata higher temperature, viz., an average one of about 55°, I have wit- nessed the completion of the process in the short period of 41 days. In this in- stance the milt and the roe were mixed as soon as they were taken from the fish on the 29th of last October; a certain number of the ova were put into a glass vessel and covered with water to the depth of about an inch, which was changed twice daily, and kept in a room the temperature of which was very uniform,— * T am disposed to think that the breeding-time of the charr in Windermere is even less limited than is stated above, having found in the latter end of February individuals with the testes nearly of their full size, and this not in large fish; and others with ovaries containing eggs varying in size from a mustard to a millet seed. These fish were all from the lake; I have never heard of one being taken or seen in the Brathay (a river flowing into the lake, to be mentioned hereafter) after Decem- ber. DR DAVY’S OBSERVATIONS ON THE CHARR. 325 seldom below 54° and never above 56°. On the 10th of December two young fish left their shells, and on the following day a third. They were all three feeble, as if their development had been premature; in a few days they died. Some eggs from the same fish which had been placed in Mr Rreynoxp’s breeding boxes were not hatched till the 90th day, or more than double the time. What the other circumstances are—other than that of mere difference of tem- perature—which influence the acceleration or retardation of the hatching process, are deserving of being investigated experimentally. Something may, perhaps, - depend on the size and quality of the egg; something on the contact of the sper- matozoa, their number and activity ; and other conjectures might be offered. In illustration of the growth of the young fish, after quitting the egg, I shall briefly describe what I witnessed in the instances of three that I observed with some care from the time of their escape from the shell to the attainment nearly of their perfect form. It was on the 17th of January that they were hatched. Some days previously the embryos were very active, frequently changing their position by sudden jerks, effected by the tail and the posterior portion of the body. One I saw in the act of bursting the shell, now become very thin and tender. The rupture took place suddenly at a spot where there was a little prominence,—an evident yielding of the shell to the pressure from within,—and simultaneously the coiled-up foetus became liberated; the effort, it may be inferred, made by the tail, by which the opening was made, sufficing to extricate it. The instant the young fish entered the water, it darted about wildly for a few seconds ; then rested, lying on its side. It was most easily disturbed ; on the slightest touch, even if merely applied to the water near it, it fled from the touching body, moving with wonderful rapidity, and in such an irregular, devious course as was well adapted to promote its escape from a pursuing enemy. These fish varied in length from about six-tenths to seven-tenths of an inch ; the yolk attached was about -25 of an inch in length, and about 15 of an inch in depth, of an oval form. They were transparent and almost colourless, allowing the circulation of the blood to be seen distinctly with the microscope, using even a low power, such as a glass of one-inch focal distance. Their eyes appeared to be perfect, the lens visible and apparently prominent, the iris coloured; and, in accordance, the vision seemed to be acute, even the approach of a moving body, without coming in contact with the water, exciting alarm, indicated by a sudden change of place. The pectoral fins were distinct and almost constantly in action ; the single embryonic fin including the rounded tail, extended inferiorly to the yolk sac, and superiorly a little beyond the spot where the dorsal fin was to be. On the 30th of January, a very slight increase in their length was observable, about -02 of an inch. ‘The several fins, the dorsal, the abdominal, and anal, were beginning to appear in the form of slight projections from the single fin, especially the dorsal, in which rays were noticeable. The gill-covers now were somewhat VOL. XX. PART III. 4p 326 DR DAVY’S OBSERVATIONS ON THE CHARR. projecting, resembling fins, and were in constant motion over the branchial arches, in which the blood corpuscles were to be seen circulating in looped vessels. On the 4th of February, it is noticed that the fish were acquiring colour, dark colouring matter being deposited in stelliform specks; that the embryonic fin was diminishing, and that the adipose fin was beginning to appear, marked by a slight elevation. On the 14th of the same month, they were found to have increased to about ‘8 of an inch in length, and the yolk to have diminished to -2 of an inch, and to have become narrower. On the 22d, the water in which they were kept was frozen over: they were seen swimming actively under the ice, and restlessly, as if in search of a passage to deeper and less cold water. On the 13th of March, the dorsal fin was almost apart, the other fins advan- cing, the single one receding from absorption; the tail still rounded; the abdo- minal integument extending over the diminishing yolk, but not yet entirely covering it. One died on the 18th of this month; the others on the following day. In these there was an appearance of sooty matter about the gills, which probably was the cause of their death, by obstructing respiration. One of them, weighed, was found to be little more than half the original weight of the egg; merely wiped, it was equal to 58 of a grain; thoroughly dried, at a temperature of 100’, it was reduced to ‘16 of a grain. From the time of their hatching to that of their death, | am not aware that they had taken any food other than that provided for them by nature in the attached yolk, a period of sixty and sixty-one days. Pro- bably had they been favourably situated, where they could have found suitable food in the water, their growth would have been more rapid. One taken from the breeding-boxes on ‘the 22d of March, hatched about the same time as the preceding, viz., the 17th of January, and when, consequently, about sixty-five days old, may be adduced in proof; premising that, from the manner in which the boxes were supplied with water, and their being shaded with trees, and some aquatic plants having been introduced, brought from the bed of the Brathay—that part of the river where the charr is known to spawn—there was probably no want of the proper food of the young fish, minute insects and infusorial animalcules, traces of which, indeed, were detected in its excrements, when seen under the microscope using a high power. The young fish of the age mentioned was perfect in its form. The embryonic fin had entirely disappeared, with the exception of a slight vestige of it between the anal and the abdominal fins. All the permanent fins had become distinct, even the adipose, though it was rather more extended and less elevated than in the full-grown fish. The caudal had lost its rounded form, and had become not forked but square. No vestige remained externally of the yolk-vesicle, the abdomen being entirely closed, covered uniformly with a DR DAVY’S OBSERVATIONS ON THE CHARR. B20 silvery integument. The back and sides, of a light greenish-brown, were marked by two rows of spots of a dark hue, almost black, the inferior the largest, remind- ing one of the bars of the parr and the marking of the young trout. Measured, its length was found to be one inch; its width or depth, where greatest, about ‘16 of an inch. It was very active, and disposed to feed, darting often with avi- dity at any minute body thrown into the water, but only whilst in motion; and often after taking it into its mouth, casting it out. Fed daily, chiefly with finely- erated dried beef, it was kept alive till the 21st of June, when it was increased in length only to 1:06 inch, so inconsiderable had been its growth. The water in which it had been kept, and which was changed daily, was about the temperature 50°, sometimes two or three degrees higher, seldom lower. The young fish was fre- quently to be seen in a restless state, as if seeking to escape. Those of the same brood, left in the breeding boxes, effected their escape about the middle of April, when, in consequence of a flood, the water overflowed. They were then from 1:25 to 1°5 inch in length. In the cartilaginous fishes, the yolk is found in the cavity of the abdomen long after it has disappeared externally. In the torpedo I have detected it there as late as the fifth month from the time of hatching.* That the same happens in the young charr, I cannot entertain a doubt. In one instance,—that of a fish hatched six weeks, kept the whole of the time in the breeding-box, and which was nearly perfect in its form,—though no trace of the vesicle remained exter- nally, it was visible within, seen through the transparent parietes of the abdomen, distinguishable both by its form and under the microscope by the oil globules belonging to it. 3. Of some Agencies and Circumstances supposed likely to influence the Ova and Young Fish. These, so far as I have tested them by experiment, I shall briefly notice. From the best information I have been able to obtain, the charr in the Lake District, with few exceptions, chooses for its breeding-place stony and gravelly shallows in the lakes in which it is found, and never, after the manner of the trout, ascends the small streams towards their source to deposit its spawn. The exceptions alluded to, which have come to my knowledge, are in the instances of the charr of Windermere and that of Ennerdale. The former, it is known, not only breeds in the lake, but also in the river Brathay; but it deserves to be kept in mind, that that part of the river which it selects for the purpose has a good deal the character of a lake, the water there being expanded, forming a small lake or pool, where, in parts out of the actual current, it is little more disturbed by the wind than the shallows of Windermere itself. The charr of the lake of Ennerdale—the other exception—I am assured on good authority, that of Dr * See Researches, Physiological and Anatomical, vol. i., p. 73. 328 DR DAVY’S OBSERVATIONS ON THE CHARR. Liztcu of Keswick, frequents in the spawning season a pool of a little mountain river, called, from the circumstance, the “Charr Dub,” about 300 yards from the head of the lake; itself (the pool) about 120 yards in length, and about 6 or 7 yards in width, with a sandy, gravelly bottom, and large stones here and there interspersed. In this pool, it is said that the fish congregate, with great regu- larity as to time, about the 7th or 8th of November, and remain there usually about a fortnight, when, having performed the function for which they came, they return to the deep water of the lake. I make this statement in consequence of some naturalists, guided by the ana- logy of the best-known species of the Salmonidz, having inferred that, like them, the charr can breed only in running water, and that its being seen in large numbers in the spawning season in shallow water in lakes, was only preparatory to ascending the streams. The weight of evidence against this conclusion is such, that I think it cannot be maintained; nevertheless, it appeared to me worth while to make a few experiments for the purpose, if possible, of testing it. With this intent, portions of roe, after having been mixed with liquid milt, were put into vessels, some of earthenware, some of glass, with a limited quantity of water (not changed during the trial); some in the open air, some within doors. This was done on the 4th of November, using the roe that had been obtained on the 30th of October, the same as that from which three ova, as already mentioned, had been hatched in forty-one days. None of these trials were perfectly success- ful: excepting in one, no progress towards development was observable. This was in the instance of ova contained in a glass bottle of eight ounces capacity, the water about two inches deep, and kept in a room, the temperature of which was commonly about 55°. On the 26th of the same month, marks of progress were observable in one of these ova; the eyes of the embryo were apparent as black specks, and vessels carrying red blood were to be seen ramifying in the vitelline membrane. The development went no farther. Even imperfect as this result is, is it not in favour of the conclusion that running water is not’ essential to the hatching of the fish ? Mr Reynotps mixed together the roe of a lake trout and the fluid milt of a charr, which he placed in his breeding-boxes in November. In 70 days some of the ova were hatched, and the young fish had a hybrid character, the fish them- selves having much the appearance of the charr of the same age, whilst the yolk attached, with its few large richly-coloured oil globules, was exactly similar to that of the trout. Is not, I would ask, this fact that the ova of the one species can be fertilized by the spermatic fluid of the other, in favour also of the conclu- sion that the breeding-places of the two are different? Were they not so, as the breeding season of the two is the same, a constant crossing would be almost unavoidable, and a confusion and loss of species would be an almost necessary consequence. DR DAVY’S OBSERVATIONS ON THE CHARR. 329 As a solution of common salt has the property not only of keeping liquid the fluid of the yolk, but also of dissolving its coagulum, it seems well adapted as a medium for the purpose of examining the foetal structure. Using it thus, I found that an ovum in which the embryo was active on the 42d day, immersed in a solution of salt of the specific gravity 1033, kept therein about half an hour, retained its vitality ; and that, excluded by an opening artificially made in the shell, the young fish remaining in the solution, continued active for another half hour. This result led me to try the effect of keeping the ova in solutions of com- mon salt, and also the young fish, to ascertain whether the former would be hatched, and what would be the effects on the latter. One trial was made with the ova, using salt water of the specific gravity mentioned, 1033 ; another with water just perceptibly impregnated with salt, confined in glass bottles and kept in the room of the average temperature of about 55°. In the stronger solution, the ova remained transparent, but no marks of development appeared. In the weaker solution, on the 26th of November,—-the trial was begun on the 4th,— black specks denoting eyes, in the act of forming, were observable in four ova, and vessels carrying red blood in the vitelline membrane. In this stage, further progress was arrested by death. The first experiment on a young fish was made on one that had been hatched about 22 days. Put into sea-water, diluted with spring-water so as to be of specific gravity 1020, it was found dead three hours after ; it was contracted in length from ‘68 to ‘46 of an inch. The next was on a young charr of the same age: this, immersed in a solution of the specific gravity 10036, after 24 hours, seemed as active as before. More salt was then added so as to increase the specific gravity to 10068, but still without marked effect. After other 24 hours the specific gravity, by another addition of salt, was raised to 10098 ; now the fish became more restless, as if seeking to escape. After the same interval a fresh portion of salt was introduced, raising the specific gravity to 10153: the effect now was strongly marked ; in about six hours the fish was found motionless, except the lower jaw, which, under the microscope, exhibited a tremulous movement, and except the heart, which still acted pretty vigorously, and which continued to act, but with decreasing force, for about 20 hours, reckon- ing from the time that the fish first appeared motionless and moribund. The next trials I shall mention were made with the intent to endeavour to ascertain how long young charr might be kept alive in the same portion of water, and that a small quantity, such as might be used in conveying the fish from place to place at an early age, when, before the yolk is exhausted, it stands in no need of a supply of food from without. Two experiments were made, one with a portion of pure oxygen over the water, the other with common air. The volume of water and air in each instance was nearly equal—about four ounce measures,—the capacity of the containing bottle being about eight ounces. The bottles, after the introduction of the young fish, were closed with a glass stopper and inverted VOL. XX. PART III. 4U 330 DR DAVY’S OBSERVATIONS ON THE CHARR. in water ; they were kept part of the time in the open air, and part of it in the room of equable temperature: each fish had been hatched about six weeks. The one in water, with oxygen, put in on the 28th of January, was very active till about the middle of February ; about the 24th of that month it began to appear lan- guid, and it was more so on the 26th, when it was taken out and transferred to a vessel fully exposed to the air, and the water in which was changed daily. Though it lived till the 18th of March it did not recover its activity. Its growth whilst under oxygen was much the same as if it had been kept in water exposed to the air and changed daily. The oxygen used was not tested for carbonic acid ; by the taper-test its purity did not appear to be impaired. The trial with com- mon air was commenced on the 7th of February ; on the 13th, the young fish was found dead. As there was a small spot of stagnant blood in the vitelline mem- brane, its death might be owing to disease unconnected with the peculiarity of circumstances in which it was placed. On the 28th of March I repeated the ex- periment with a young fish which was vigorous and active. Taken out on the Ath of April, its activity seemed unimpaired ; it fed greedily. This fish had been hatched about seven weeks. The only other trials I have made have been on the effects of temperature,— an infiuence that this fish appears to be peculiarly sensitive of, as indicated in all its habits, and in the circumstance that it is only found in those lakes in which, in consequence of their great depth, it can find a retreat in summer and winter in water of about 40° Fahr. On the 28th of March I transferred into water, of the temperature of 83°, a young charr that had been hatched not quite seven weeks. It rushed about for a second or two, then turned on its back and rose almost in- animate to the surface. The heart and gill-covers being still in motion, it was instantly put back to the water from which it had been taken of 52°. It made one or two efforts as if reviving, swimming for a few seconds in a natural posi- tion ; but in less than a minute it was dead, the heart having ceased to act: thus, compared with the effects of a solution of common salt, offering a remarkable con- trast. On the 29th of the same month, a young charr of about the same age as the preceding was put into water of 75°: it immediately became very restless ; its gill-covers moving rapidly. After a quarter of an hour, when the temperature of the water had fallen to 70’, it lay still at the bottom and not apparently dis- tressed, except that the movement of the gill-covers and the action of the heart were unduly quick. In an hour and a-half, when the water was 60°, it was still at rest: some hours later, when the water was 54°, it seemed well; and, on the following day, put into fresh water, it appeared as active as before. I have now to conclude. This I shall do without entering on the embryology of the charr,—a vast subject, which, in the instance of one of the family of the DR DAVY’S OBSERVATIONS ON THE CHARR. 351 Salmonidee (Coregonus Palewa), M. Vocer has so ably and elaborately treated of in the work already referred to. The observations I have described are fewer than I could have wished. and the results more imperfect; I can offer them only in the manner in which I trust they will be received, viz., as a contribution to the history of the charr. I may notice some of the facts which they seem to establish, and some of the inferences which they appear to me to warrant. 1. That the time required for hatching the ova of the charr is variable, de- pending on the degree of temperature of the water and other influences: that 70 days may be considered about the average, and 40 and 90 about the extremes. 2. That after exclusion from the ege the young fish can live at least 60 days without taking food, deriving the material required for its support and growth from itself, and chiefly from the store that nature has supplied in its yolk. 3. That under favourable circumstances, it attains its perfect form in about from 60 to 70 days, when it becomes dependent for its subsistence chiefly on food which it has to seek and to procure from without; though even then it is pro- bable the whole of the yolk is not expended, so that external food failing, the privation can be borne and life maintained, and that for no inconsiderable time, by means of the residual yolk contained within the abdominal cavity. 4, That running water is not essential to the hatching of the ova; and, in consequence of its breeding-place being distinct from that of the trout, it is exposed to little risk of being lost as a species by repeated crossings with the trout. 5. That salt water, even of greater saltness than sea-water, is not imme- diately fatal to the embryo, even when not included in its shell; moreover, that in slightly brackish water a partial development of the ovum may take place; and that the young fish can exist some days in such water, rendering it probable that the adult may be capable of existing in a tidal stream, or even in the sea, for a time, where it is stated that the Welsh charr has been caught.* 6. That in water of small bulk, such as may be used for transporting fish from place to place, with common air, the young charr may endure confinement for several days without impairment of its vigour ; and that substituting oxygen, it may endure such confinement for a much longer time, at least quadruple that period. 7. That the young fish can bear, without any immediate injury that is appa- rent, a temperature removed only a degree or two from the freezing-point of water; and also a higher temperature, ranging from 60° to 70°, but not above 83°, which, in the single instance tried, was almost instantly fatal to it. The application of these facts to the breeding and transporting of the charr * See Mr Yarrexu’s History of British Fishes, vol. i1., p. 71. 1st Kdit. 302 DR DAVY’S OBSERVATIONS ON THE CHARR. hardly requires any comment. Whilst they shew how easily it may be introduced into any lake or body of water, they are of no. significancy in relation to the establishing it for a permanency in such water. What appears to be most requi- site for the purpose is deep and pure water. In no body of water in the Lake District is the charr found, which is not of this character. The attempts to esta- blish it in some not possessed of the qualities named, have repeatedly failed ; and in others, in which the fish once abounded, it has become either entirely or almost extinct, since mines have been opened in their vicinity, by which the purity of the water, it may be inferred, has been impaired. Whether the quality of the food is of much importance, seems to be doubtful in relation to this its main- tenance. There are circumstances that seem to warrant the conclusion, that, like the trout, its condition rather than its existence depends on the kind of food, and the quantity it can obtain. This we know, that it is taken with the same baits as the trout, and also that it exhibits varieties like the trout, though hardly so strongly marked, according to, asis believed, its manner of feeding; for in- stance, the charr of Hawes Water, which is known to feed a good deal on insects, is a small and slender fish in comparison with the charr of Windermere, which feeds more at the bottom, and has a less precarious supply, especially of squillee, which abound in that lake.* These remarks are offered with hesitation. The subject is one that is not without obscurity, and in need, for the better under- standing of it, of further and minute inquiry specially directed to it. Lesxetu Howe, AMBLESID=, February 28, 1852. P.S. Reflecting on the effects of sea-water on the ova of the charr and its young, shortly after quitting the egg, as described in this paper, I venture to offer the conjecture, that the action of sea-water may be similar on the impregnated egg of the salmon and its fry; and that it is on this account (looking to the final cause), rather than for the purpose of seeking water cooler and more aerated, that the salmon, impelled by instinct, quits the sea for the river, preparatory to breed- ing; and also, that the young remain in fresh water till they have acquired not only a certain size and strength, but also additional scales, fitting them, in their smolt stage, to endure without injury the contact of the saline medium. * The charr of the Lake District, though occasionally taken with the artificial fly and minnow, like the trout, on the whole, I believe, may be considered a more delicate feeder, and, in consequence, of superior quality for the table ; its organization is in accordance with this, viz., its smaller teeth, and smaller stomach and intestines. The charr of Upper Austria is said to have a thick stomach, approaching in its character to that of the Gillaroo trout. (See Salmonia, p. 55, ed. 4th.) In most instances that I have examined this organ in the charr of the Lake District, I have found it as thin, and often even thinner in its coats than that of the trout inhabitmg the same water. DR DAVY’S OBSERVATIONS ON THE CHARR. 393 I have had no opportunity to try the effect of sea or salt water on the impreg- nated ova of the salmon. The few experiments I have been able to make on the young fish have given results favourable to the above conjecture. I shall briefly relate them. - On the 10th of April, a young fish, about an inch in length, its permanent fins fully formed, taken from a small pool in the bed of the Leven (the river that flows out of Windermere, and then unusually low) was put into a half-pint of salt water, of the specific gravity 10277. It lived about thirty-three minutes. Shortly after, a smolt, the instant it was taken was put into the same water ; it was about seven inches in length, and its head was not constantly under water. It lived about an hour. From comparative experiments with fresh water, I am led to infer that in the same limited quantity of river water, it might have lived two hours; the limit being probably the exhaustion of the air. When a stronger so- lution of salt was used—that in the preceding experiments being nearly the same as sea-water—the effects were far more decided. Thus a fish of the same size as that first mentioned, put into a saturated solution of common salt, died in two minutes; and a parr taken on the 10th of October, measuring about four inches in length, put into a solution of common salt of the specific gravity 1047, died in a few minutes. April 12, 1852. VOL. XX. 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It had interesting historical associations connected with eclipses ; and there was something pleasing in the prospect of seeing the red prominences, which excited so much attention at the eclipse of 1842, at the very spot where they were observed, probably for the first time, in 1733 ;* but a more import- ant ground of preference, was its proximity to the central line of the moon’s shadow, and its being directly accessible from England. I accordingly sailed from Hull on the 19th July, by the Courier Steamer, and reached Goteborg on the 24th. Among the passengers were Mr Lasse, Mr Apams of Cambridge, Mr Carrineron of Durham Observatory, Mr Robert CHAm- BERS and Mr Joun Avie of Edinburgh, Mr Dunxin of Greenwich Observatory, and the Astronomer-Royal. Mr Arry had determined to observe the eclipse at Goteborg, and at his request a meeting was held there on the 26th July, when it was agreed by those who were present to separate as much as possible, in order to increase the chance of at least some one seeing the eclipse, in the event of the weather proving cloudy,— a precaution which its unfavourable aspect at that time rendered the more advis- able. Professor CHEVALLIER of Durham and Mr Joun Apiz, had previously de- termined to observe the eclipse from the roof of their hotel in town. Lieutenant PETTERSSON of the Navigation School of Goteborg, kept by the Observatory of that institution. The Astronomer-Royal selected a station to the east of the town, and Mr CHaMBeErs, one about three miles to the west. I chose for my station a hill named Ramberget, situated about a mile to the north of Goteborg, and on the op- posite bank of the river. This, being the highest eminence in the neighbourhood of the town, commanded an extensive view of the country on every side, and was therefore a very favourable station for witnessing the effects produced on the land- scape during the eclipse. I referred its position to that of Lieutenant PErrrErs- son’s Observatory, by the magnetic bearings of several conspicuous objects, taken by means of a prismatic compass. (See Table I., page 345.) The observations, when * See Observatio Eclipsis Solis totalis cum mora facta Gothoburgi Svecie, &c., a Dom. Birgereo Vassenio.—Phil. Trans., vol. xxxviii. VOL. XX. PART III. 4Y 3936 MR WILLIAM SWAN ON THE protracted on a trustworthy map of the environs of Goteborg,* are very well satisfied by a point, which, from the known latitude and longitude of the Observa- tory, I find to be in latitude 57° 42’ 57’:3 N. and longitude 0° 47™ 45*2 E.+ So many phenomena occur at the total phase of a solar eclipse, that I wished to avoid having my attention distracted by my being obliged to count the beats of the chronometer in taking observations for time. I therefore gladly availed myself of the assistance of Mr Epwarp W. Lanz, Advocate, of Edinburgh, who kindly undertook to read the chronometer, and mark the times at a preconcerted signal. His co-operation proved quite invaluable; and it is with the greatest pleasure I avail myself of this opportunity of acknowledging my obligations to him. The telescope I employed in observing the eclipse was furnished by Mr Antz. It has avery good object-glass{ of about 2°3 inches aperture, and 31-5 inches focal length, and was mounted on a rough equatorial stand. Of the eye-pieces be- longing to this instrument, I chose that of the lowest power, magnifying 28 times, as it was necessary for some of the observations I purposed to make, to have the entire disc of the sun within the field of view at once. I also then thought, and I am still of the same opinion, that any advantage gained by using a higher power would be more than counterbalanced by the time lost, during the short duration of the total phase of the eclipse, in directing the telescope from point to point of the moon’s limb, instead of seeing the whole at once. In effect, the power I had chosen proved very convenient, and apparently quite sufficient for observing the interesting phenomena of the total phase; while the definition of the corona and the red prominences seemed as perfect as could be wished. I had prepared some slips of smoked plate-glass, gradually increasing in depth of tint from one end to the other, for the purpose of observing the sun before the period of total obscuration; but Professor CHEVALLIER kindly lent me a dark glass, by TRoucHTon and Sms, consisting of wedges of coloured glass achroma- tised by a colourless prism.) This combination of glasses made the sun appear yellow, slightly tinged with green, and I willingly adopted it in preference to the smoked glasses, as the definition of the sun was decidedly sharper when it was used instead of them. ‘This dark glass slid in a groove in front of the eye- piece, so as to admit of being instantly removed. From the conflicting accounts which were given regarding the red prominences * This map, published by A. Hanr, is entitled Topograjisk Karta éfver Gétheborgs Omgifning Jemte plan éfver Staden med dess nya Hambyggnad. 1844. + Since this paper was read, Lieutenant Perrmrsson has kindly verified my calculation, and assigns, as the position of my station, lat. 57° 42’ 58”-0 N., long. 05 47™ 45-3 KE. + As the value of the following observations must depend greatly on the character of the instru- ment with which they were made, I may mention that this telescope shews bright stars, with per- fectly round, well-defined discs; and, with a power of 75, the two stars in Castor are seen com- pletely separated. § To Professor CuEvauisr, and especially to Lieutenant Perrersson, my warmest thanks are also due, for their kind assistance and advice. a: (os Noms a AL Rava Soc. trans, Lid Vd XXp PLATE a ETI TT TY TTT) Loe “= - =5 io * A TT iT TL tba =< Fig, 6 Fig 4 Fig 3 X. Johnston: Ein? Lith? by WEA, TOTAL ECLIPSE OF THE SUN, JULY 28, 1851. 337 seen on the moon’s limb at the eclipse of 1842, it seemed very desirable to have some means of noting with accuracy the positions of any objects of a similar nature that might appear at the approaching eclipse; and in a letter in the Atheneum of 12th July 1851, I suggested a species of position micrometer suitable for that purpose. The instrument there described, with a slight addition, was constructed for me by Mr Joun Ante, and its performance proved very satisfactory. It consists of a circular plate of metal, AB, fig. 1, (Plate XI.) 8 inches in diameter, attached to the sliding tube of the telescope by a split collar with a tightening screw, not seen in the figure, so as to prevent it from turning round. The face of this plate, next the eye-end of the telescope, was covered with a disc of card, attached to it by four screws, ¢e¢ee. Inside the tube carrying the plate, another tube carrying the eye-piece slid smoothly, so as to admit of being freely turned round. To this were attached, by another split collar and clamping screw, two springy arms, FC, FD, bearing steel points, by which holes could be pricked in the card disc, and a small level, G, was fixed at right angles to one of the arms. In the eye-piece were three equidistant parallel spider-lines, ab, cd, ef, fig. 2; the two outer, ab, cd, being placed at an interval equal to the apparent diameter of the moon, calcu- lated for the time of the total phase of the eclipse; so that when they were made to embrace the moon’s disc, gh, the middle wire would pass through its centre, o. The instrument was adjusted for observation by making the middle wire coincide with a plumb line, seen at a distance of about 150 yards, while at the same time the bubble of the level was brought to the middle of its tube; and the arms with the level were then clamped to the tube carrying the eye-piece. When this adjustment was completed, it is obvious that the wires in the eye- piece would point vertically whenever the bubble of the level was again brought to the middle of the tube. If now the bubble were brought to the middle of the tube, while the outer wires were made to embrace the moon’s disc, the middle wire would pass through its vertex, g; and two holes being pricked in the card, the line joining them would represent the moon’s (or, with sufficient accuracy, the sun’s) vertical diameter at the moment of observation. If next, while the moon was still kept between the outer wires, the middle wire were made to bisect any object, /, near its limb, the wires now having the positions a’0’, cd’, #7’, and holes were again made in the card, the angle between the lines joining the respective pairs of holes would measure, goh, the angular distance of the object from the sun’s vertex. It is easy to see how, in this manner, the positions of the red prominences seen during a total eclipse, could be rapidly registered on the card without ever removing the eye from the telescope. In order to repeat the observations, the steel points admitted of being moved in longitudinal slits in the arms. so as to describe circles of different radii on the card; and the reading point was distinguished from the other by being placed a little farther from the centre. 398 MR WILLIAM SWAN ON THE It is evident that if the telescope were mounted equatorially, the level could be dispensed with, and the objects might be referred to a parallel of declination, by causing a spot on the sun to travel along the wires; but my stand was too rade to allow this method to be adopted with safety.* In order to ascertain the times of the different phases of the eclipse, I used a box chronometer by Apams of London, which was obligingly furnished by Lieute- nant Perrersson. It was compared with his standard chronometer about 3" 15™ before the commencement of the eclipse, and again the following day after an in- terval of 24 hours. The error and rate of the standard chronometer had been de- termined by observations made with a small transit instrument at the Observa- tory. For several days before the eclipse the weather was variable, with little sun- shine; and it became gradually worse, until at length the morning of the 28th arose as gloomy as the most unfavourable foreboding could have anticipated. But about noon, to the great delight of every one, the sun shone brilliantly, and the sky soon became nearly cloudless towards the zenith. This state of things, however, did not last long; for shortly after the commencement of the eclipse, an extremely thin cirrous cloud began to overspread the sky. I was apprehensive that this might interfere with the observation of the eclipse; but it produced no sensible effect in impairing the definition of the sun, which was remarkably good, and unusually free from tremulous motion. All the minute spots and facule, which were visible before the cirrous cloud had formed, were seen until they were covered by the moon; and it was only after the total phase of the eclipse had passed that the definition was perceptibly injured. Towards the horizon, espe- cially in the east, the sky was pretty thickly studded with detached cumulous clouds; and a strong south-west breeze continued to blow during the eclipse, ex- cept about the period of the totality, when the wind almost entirely subsided. I determined the places of the only spots I saw near the sun’s limb by means of the position micrometer. There was a patch of small spots 96° 30’ to the west of the sun’s vertex, and about 1:5’ from its limb; and a considerable spot, evi- dently round, but much foreshortened, 62° to the east of the vertex, and less than 1’ from the limb of the sun. This spot was surrounded by conspicuous facule : and after two days, when it had advanced on the sun’s disc, it proved, as it had seemed at first, to be circular. At the commencement of the eclipse, my eye was directed to the point at which the moon’s limb entered the sun’s disc; but, although I distinctly saw the first impression of the moon, I did not feel perfectly sure of this until about two * The chief inconvenience I found in using this instrument, arose from being obliged to point the telescope by the hand. A slow rack motion would have been very useful. In observing a total solar eclipse, every moment is so valuable, that too much care cannot be bestowed beforehand in having everything adapted to save time. From my own experience, I should recommend observers to have their telescope mountings as commodious and firm as possible. TOTAL ECLIPSE OF THE SUN, JULY 28, 1851. 339 seconds had elapsed. The time stated as the commencement of the eclipse, is, therefore, probably two seconds too late. This was 2° 53™ 4°4 Goteborg mean time. There were numerous mountains on the moon’s limb, which gave it a sensibly serrated appearance, and it was much more sharply defined than that of the sun. The gradually decreasing brightness of the sun’s disc from the centre to- wards the edges, which is pointed out by Mr Arry in his account of the eclipse of 1842, was best seen when the sun was about half covered by the moon. Repeated attempts were now made with the naked eye, with the telescope, and with a French opera-glass of 1:9 inches aperture, and 5:8 inches focal distance, to ascertain whether the moon’s disc was sensibly illuminated, and whether any part of its limb was visible beyond the sun. But although in every trial, the sun’s light was as little diminished by the dark glasses as the eye could bear, the face of the moon looked quite black, and no part of its limb was visible beyond the sun’s disc. During the progress of the eclipse, the cusps continued perfectly sharp, as re- presented in fig. 3, until the sun was reduced to an extremely narrow crescent of 90°, or less, when they began to assume a decidedly rounded appearance (fig. 4). It seemed as if the light had flowed beyond its proper boundary, so as to invade the province of darkness; the cusps becoming disfigured, much as they would have been had one attempted to draw their outline in ink upon blotting paper, where the ink flowed slightly beyond the limit traced by the pen.* Daylight had now greatly diminished, and the air felt chilly. Towards the west, in the direction of the approaching shadow of the moon, the sky looked ex- tremely black and frowning, and the whole landscape wore a peculiarly cold and desolate air. The light had much of the ordinary gray tint of morning, and less than I expected of the peculiar greenish hue [remember to have observed at Edinburgh, in the eclipses of May 1836 and July 1842; and as the totality ap- proached, the sky assumed a more cloudy appearance than it had at the com- mencement of the eclipse, either from the actual formation of clouds, or as I could not help thinking, from something in the altered state of the light render- ing the existing clouds more visible. The sun was now nearly gone, and darkness was coming on with a degree of rapidity which was quite startling. From the accounts of previous eclipses, I was prepared to anticipate something very awful; but I certainly did not expect that this part of the phenomenon would have affected me so much. An instan- * SHAKESPEARE makes Hecate say :— “‘ Upon the corner of the moon There hangs a vaporous drop profound.” This odd fancy forms no unapt description of the rounded appearance of the cusps, which certainly looked very much as if a drop of liquid were depending from them, VOL XX. PART III. 47 342 MR WILLIAM SWAN ON THE anything like concentric rings. Its light was brightest next the moon’s limb, and gradually shaded off into darkness at a distance of about half the moon’s diameter. The most striking feature in the corona was the appearance of brilliant beams of light which shone out in various directions. They were sharply defined, and much brighter than the rest of the corona; and, probably owing to their supe- rior illumination, they were visible a little beyond its general outline. One of these beams (see Plate XII.), I found was situated 28° 35’ to the east of the sun’s vertex. It constituted by far the brightest part of the corona, and had a sort of conoidal figure. I had not time to ascertain the positions of the other beams ; but there was a remarkable one about 35° or 40° to the west of the sun’s vertex, and two others which I have ventured to represent in the figure from memory. The three latter beams were quite different in form from the first. They resembled the narrow sunbeams which shine through broken clouds; or the inverted cone of light visible in the dark over a blast-furnace fed by coke. Their sides were beautifully rectilinear, apparently converging to the centre of the sun, so that their forms were those of very acute cones. In one at least, the light increased in brilliancy from the centre towards the sides, as if the cone were hollow; its edges appearing brightest owing to the lumimous stratum, constituting the hollow cone, being there presented to the eye more obliquely, and therefore acting on it with a greater depth of lucid matter. The first object that attracted my attention on looking at the corona through the telescope was a remarkable hook-shaped red prominence (represented in Plate XIL., and in Plate XI., figs. 7 and 8) 110° 30’ to the west of the sun’s vertex. The next moment I thought there was the trace of a red prominence in the middle of the bright beams of light to the east of the sun’s vertex; but in another instant my attention was withdrawn from this by the appearance of a second prominence a little below the hook-shaped one, and on looking back I saw no farther trace of red light to the east of the sun’s vertex. As considerable doubt had been expressed whether the red prominences exist in the sun or moon, or are only optical phenomena, I was prepared to look for faint objects of variable and indistinct appearance, requiring, perhaps, consi- derable attention to see them at all. I was therefore agreeably surprised to find the prominences objects of perfectly definite outline, and of permanent form so long as they continued visible. The hook-shaped prominence, especially, had a remarkably smooth, sharp outline, and its rose tint became darker towards the edges, suggesting the idea of a convex surface. At the risk of offering what may be deemed: a whimsical comparison, I may mention, that, at the moment, it seemed to me very like the Eddystone, or Bell Rock lighthouse transferred to the sun, with its top beginning to fuse and bend over like a half melted rod of glass. The other prominence was of less height, but of greater lateral extent ; and its top was deeply serrated, so as to bear a strong resemblance to a chain of peaked ‘VWI. Roval Soc. Trans. Edin. Vol XN pe Vertex W. Swan, Delt 7 Johnston. Kd As seen towards the end of the totalty, by MW.Swan at Goteborg 9 in Sweden, with a telescope magnifying 28 times TOTAL ECLIPSE OF THE SUN, JULY 28, 1851. 345 eranite mountains. Both prominences were remarkably distinct from the co- rona, so as almost to appear standing in front of it; and their outlines seen upon it were at least as definite as that of the illuminated edge of a detached cumulous cloud projected against the clear blue sky. But as the sharp definition of such a cloud isan illusion, depending as much on its distance, as on the density of the vapour composing it, I do not mean to draw from this comparison any inference regarding the density of the matter composing the red. prominences. Notwithstanding their definite outlines, they may, like the tails of comets, be of extreme rarity, and indeed, as Sir Jonn Herscuet remarks,* their faint illumi- nation clearly proves them to be “ cloudy masses of the most excessive tenuity.”’ The colour of the prominences was a full rose-tint, and the light of the corona in their neighbourhood seemed brighter than elsewhere, with the exception of the brilliant beams already mentioned. The appearance of the prominences as they were seen shortly after the com- mencement of the totality is represented in figure 7. By means of the microme- ter | determined their positions as well as that of the bright rays to the east of the sun’s vertex, and then quitted the telescope for a little to make some other ober- vations. On returning to the telescope I found that the bright rays to the east of the sun’s vertex appeared shorter than before, while the red prominences to the west had increased sensibly in height; and while I watched them, they continued to increase still more in size, as if rising from behind the moon’s limb. I should almost say their motion was sensible; but however doubtful this may be, its cumulative effect was strikingly apparent, for before the end of the totality they had assumed the appearance presented in figure 8. All this was exactly what would have happened on the supposition that the prominences belonged to the sun; for objects on the eastern limb would gradually suffer occultation by the ad- vancing moon, while those on the western limb would be simultaneously exposed. While, then, the definite outlines and permanent forms of the prominences satisfied me that they were real objects, and not mere optical phenomena, their gradually increasing altitude convinced me that they belong to the sun and not to the moon. The observed angles of position of the red prominences and spots on the sun’s disc, referred to the sun’s vertex, and also their angles of position reckoned eastward from the sun’s vertex are given in Table II., p. 346. The data for reducing their positions to the sun’s vertex are the known latitude of the station, the sun’s declination, and the hour angle from apparent noon, assuming the observations to be made at the middle of the totality. The prominences were distinctly visible to the naked eye by the strong red tinge they imparted to the adjacent portions of the corona; but I could neither distinguish their outlines nor see them as separate objects. I wished to compare the shadow cast by the corona with that formed by a -* Outlines of Astronomy, 1851, par. 395. VOL. XX. PART III. DA 344 MR WILLIAM SWAN ON THE candle; but upon a rapid trial it was found that the corona cast no sensible sha- dow, its feeble light being evidently overpowered by the diffuse illumination de- rived from the horizon.* I also lcoked at the corona for an instant with a Nicol’s prism, and thought its outline was slightly distorted, so as to appear somewhat four-cornered ; but as there was no time to repeat this observation I regard it as extremely doubtful. I was so much occupied during the totality with more important observations that I found no time to look for stars; but Venus was too conspicuous an object to escape detection. It appeared shining brilliantly a little to the west of the sun. I now prepared to observe the end of the total phase, and I had not the slight- est difficulty in finding the point of greatest brightness on the moon’s limb where the sun actually emerged. THis re-appearance was preceded by something like a gradually brightening twilight ; and the red prominences had vanished, before the formation of Baily’s beads announced the end of the totality. The beads were not now so numerousas at the moment of total obscuration, but their appearance was otherwise the same. The end of the totality was observed at 3" 59" 8°1 Goteborg mean time, mak- ing its duration 3" 15°5, and the eclipse ended at 4° 57" 57°8; but by that time the clouds had become so much thicker as to impair the definition of the sun’s limb, which rendered it difficult to observe the end of the eclipse with accuracy. The observations of the different phases of the eclipse, along with Lieutenant PETTERSSON’S observations, which he has kindly placed at my disposal, will be found at p. 346. After the totality, the appearance of the sky was greatly altered. Its warm tint before the commencement of the eclipse had given place to a cold gray; and the cumulous clouds in the horizon had changed to stratous clouds, which now overspread the whole of the sky. At about 4" 55™ a large halo formed round the sun, and everything indicated a great change in the meteorological condi- tions of the atmosphere. The weather gradually became more gloomy, and there was heavy rain in the evening. The observations of temperature contained in Table V., (p. 346), were made by means of two small thermometers by Apiz. Their scales are trustworthy; and on comparison with Mr Apre’s standard thermometer, were found correct to the 10th of a degree. The thermometers were hung on pieces of wood stuck in the ground, and were sheltered from the sun by a rock. Neither Mr Lane nor myself had any opportunity of witnessing the effects of the eclipse on the lower animals; as there were no cattle or birds on the hill near our station. * If this experiment be ever repeated, it should be performed in an apartment, or by means of a box adapted to exclude the general light of the atmosphere. The candle should be carefully preserved in order to compare its light with that of the moon. TOTAL ECLIPSE OF THE SUN, JULY 28, 1851. 345 One reason which induced us to select a station on the opposite side of the river from Goteborg, was to avoid what HAu.ey in his account of the solar eclipse of 1715, quaintly terms, being “ opprest by too much company.” We were, therefore, not a little disconcerted at finding a large number of people resorting to the hill we had chosen. But the fears we entertained of being interrupted proved quite groundless, for with much propriety of feeling, every one kept at a respect- ful distance during our observations. When the eclipse was over, a venerable Swedish clergyman came up and shook hands with us; an example which was followed by a good number of his countrymen who were present. We did not understand each other’s language, but it was not necessary that we should. Our mutual congratulation, although silent, was quite intelligible, and I am sure it was warmly felt on both sides. TABLE I. Magnetic Bearings from Ramberget, the station from which the Eclipse was observed. =, | Mag. Azimuth, reckoned STATION. | from North, Eastward. Lejonet, . ihe, curse se 107° 45’ Christine Kyrkan, ; ; | 135 46 Domkyrkan, : . : 140 30 Kronan, . ; . 168 45 Carl Johan’s Kyrkan, : : 216 15 Nya Warfvet Telegraph, ; 227 53 Elfsborg, . j 257 00 As the station, E//sborg is not included in my map, I could not employ its azimuth in my calculation. The position of Ramberget was determined from the remaining six azimuths along with the following data kindly furnished by Lieu- tenant Perrersson from his own observations. The Navigation School is situated in lat. 57° 42’ 62 N.; long. 0" 47™ 51° E. The true azimuth of a telegraph shewn in the map, on a hill named Stzgbergsasen, as seen from the Navigation School, is 108° 56° 55" NW. The variation of the compass at Goteborg on the Ist April 1851, was found to be 17° 15’ W. ' 346 MR WILLIAM SWAN ON THE ECLIPSE OF THE SUN, 1851. TABLE II. Observations of Red Prominences and Spots on the Sun. Calculated angle from Sun’s north point, Goteborg M. T. Onspar angle from un’s vertex. Group of spots, 15 from Sun’s limb, 12 37™ | 96° 30’ west. 288° 47’ Single spot, 1’ from limb, . : 1 40 62 00 east. - 87 17 Hook-shaped red prominence, . | About 3 58 | 110 30 west. 282 Serrated prominence, ? . | About 3 58 | 132 40 west. 259 Bright rays in corona, ; . | About 3 58 28 30 east. 61 TABLE III. Phases of the Eclipse observed by MM. Swan and Lane, in Lat. 57° 42’ 573 N.; Long. 08 47™ 458-2 E. First external contact, 2h 53m 454 About 28 late. Beginning of totality, 3 55 562°6 End, 3 59 8-1 , Last external contact, 4 57 57°8 Probably too late. TABLE IV. Phases of the Eclipse observed by Lieutenant Pettersson, in Lat. 57° 42' 6-2 N. Long. 0» 47™ 51s E. First external contact, Qh 53m _ 389 Beginning of totality, 3 55 58-2 Too late. End, 3 59 82 Last external contact, 2 ye 518) 2-6 Difficult to observe. TABLE V. Thermometrical Observations. Times. Dry Ther. Wet Ther. on 45m 66° 60° 2 53 ahs. 5h First external contact. 3 0 64 59 3 15 62 57°5 3 30 61 56°6 3 45 60 57 3 50 57°8 55:5 3 56 | ne BS Beginning of totality. 3 59 igs End of totality. 4 10 57 55 4 30 58:5 56 4. 45 60 57 4 55 62°3 59:5 4. 58 | i we Last external contact. 5 5 | 62 58°5 5 30 62 57:5 pnt XXII.— Researches on some of the Crystalline Constituents of Opium. By Tuomas AnDErRSON, M.D., F.R.S.E. (Read 5th April 1852.) Since the year 1803, when DEesrone discovered the substance which afterwards received the name of Narcotine, the chemical investigation of opium has engaged the attention of many skilful and distinguished chemists, and in their hands has proved the source of a series of substances, unprecedented in their number and the variety of their properties. Up to the present time, there have been de- tected in it no less than eleven different substances,* one acid, and ten, either basic or indifferent, all presenting definite characters and crystalline form, besides various imperfectly characterised substances, described under the names cf caoutchouc of opium, resin of opium, extractive, and the like. With these facts before us, the chemistry of opium may appear at first Sight to be almost exhausted, and that little remains to be done, except to fill up the minor details of former investigations. But when we come to inquire more minutely into its history, the meagre and even conflicting statements of different investigators, sufficiently indicate the imperfections of their researches, and the necessity of revising and greatly extending their inquiries before our knowledge can be considered as either definite or satisfactory. The most remarkable con- stituents of opium were detected a number of years since, at the time when at- tention was first directed to the existence of peculiar constituents on which the active properties of vegetables depended ; and since their discovery. compara- tively little has been done to confirm the original observations, which are often unsatisfactory, and serve not so much to supply definite facts, as to indicate the direction in which they are to be sought for. Some conception of the limited extent of our information regarding opium may be formed by a few preparatory statements as to our present knowledge of its basic and indifferent constituents, amounting, as has been already mentioned, to ten in number. Of these, four have been repeatedly examined within the last few years, and their constituents may now be considered as conclusively esta- blished. These are:—. * Since this paper was written, two new substances have been added to the number of the constituents of opium ; these are methylonarcotine and propylonarcotine, which have been recently described by WERTHEIM. ~ VOM pe PART Tit: 0. B 348 DR ANDERSON’S RESEARCHES ON SOME OF THE Morphine, : : : : : Ce, NO: Codeine, . : 3 5 : Cae i. NO. Papareine, : : : ; : Cee, NO, Narcotine, : F . : ; Op aks eas (0 Fy And the products of decomposition have been entered upon in some detail in the case of narcotine and codeine, but are still entirely unexamined in the other two. : Of the remaining six, porphoroxine is as yet unanalysed ; opianine is only of recent discovery, and the details of its analysis not having yet been published, the formula given for it must still be considered doubtful. The other four have been submitted to analysis, most of them at the time of their discovery, but the results obtained are very imperfect, and not of a character to inspire much confidence in their accuracy. The following are the formulze which have been most generally adopted for these substances :— Thebaine, . : F : ‘ : Gams | Pseudomorphine, : : : ‘ Ce ca N 0, Narceine, . 3 , : : : oe tay ee Opianine, . : : ; ; : Coakit: NOs Meconine, . : , : : : CO aektn O These formule are very far from being satisfactory ; indeed, most of them are purely empirical, and even in those instances in which the atomic weight has been determined, it has been done according to some of the older methods, on which much dependence could not at any time be placed, and which are now entirely superseded by more accurate and satisfactory methods of experiment. As far as their physical properties are concerned we have tolerably—though only tolerably—accurate information ; but of their products of decomposition absolutely nothing is known except in the case of meconine, on which we have just sufficient information to shew how much interesting matter lies ready for investigation. The following paper contains the result of a pretty extended investigation of ‘some of the constituents of opium, to which my attention has been directed by the facilities afforded, by an extensive morphia manufactory, of obtaining products which, though commercially little better than refuse, are of much interest in a scientific point of view. For the preparation of the bases which form the subject of my investigation, I have made use of the mother liquors of the preparation of muriate of morphine by the process of Rosertson and Grecory. This method, as is well known, con- sists in precipitating the aqueous infusion of opium with a solution of chloride of calcium, filtering from the meconate of lime and evaporating the solution to a small bulk. On cooling, crystals of muriate of morphine are deposited, which are separated by expression, and the mother liquor again evaporated. A fresh crop of crystals is thus obtained. and the evaporation is continued as long as muriate of CRYSTALLINE CONSTITUENTS OF OPIUM. 349 morphia is deposited. As the final result of these processes there is obtained a thick fluid, perfectly black, and of the consistence of tar, which formed the raw material for my investigation. I. Preparation of the Bases. The black mother liquor just referred to is diluted with water, and filtered through cloth in order to separate a small quantity of a brown flocky matter which is deposited. To the filtered fluid ammonia is added as long as a precipitate is obtained, and the whole is strained through a cloth filter, and the precipitate subjected to strong pressure. The precipitate thus obtained is of a rather dark- brown colour, and granular, but if left in the press for any length of time, is apt to run together into a resinous mass. It must, therefore, be rapidly removed before this change has taken place, broken up with the hands in a fresh quantity of water, and again expressed ; and this is repeated several times, until the fluid which runs off is no longer dark-coloured. The precipitate consists principally of narcotine, along with a considerable quantity of resin and a small quantity of thebaine; the filtrate contains narceine, and must be preserved for the prepara- tion of that substance. A portion of the precipitate is boiled with rectified spirit and filtered hot ; on cooling, impure and very dark-coloured crystals of narcotine are deposited, which are collected on a cloth washed with a small quantity of cold alcohol and ex- pressed. The mother liquor of these crystals is then employed for the solution of a fresh quantity of the precipitate, the crystals obtained washed and expressed as before, and the operation repeated until the whole precipitate has been treated in the same way. The impure crystals of narcotine are then reduced to powder and rubbed into a paste with a concentrated solution of caustic potash. After standing for some time a large quantity of water is added, and the narcotine is deposited in a much less coloured state, the resinous impurities being retained in solution by the potash. The solution is then poured off, the precipitate of narco- tine washed with water, and finally purified by several crystallisations from boil- ing alcohol. The alcoholic solution from which the first dark-coloured crystals of narcotine were deposited, on being distilled in the water-bath, leaves behind a considerable quantity of a dark amorphous mass containing much resin mixed with a little narcotine and the whole of the thebaine present in the original precipitate. This residue is treated with hot dilute acetic acid, which leaves behind a large quan- tity of resinous matter, and dissolves the two bases, along with a certain quantity of resin. After several trials, I found that subacetate of lead afforded the best means of obtaining the thebaine in a state of purity from this solution. When subacetate of lead is added to the acetic solution until the reaction becomes dis- 300 DR ANDERSON’S RESEARCHES ON SOME OF THE tinctly basic, the whole of the resin and narcotine are precipitated, while the the- baine remains in the solution. The fluid is filtered from the precipitate, and the excess of lead thrown down by means of sulphuric acid, the sulphate of lead separated by filtration, and ammonia added, when there is immediately obtained a more or less brown precipitate of thebaine, which is collected on a filter, washed, dried, and dissolved in boiling alcohol. The solution, which is generally very dark-coloured, becomes filled, on cooling, with flattened crystals of thebaine. The mother liquor is separated by expression, and the crystals, after boiling with animal charcoal and several crystallisations from boiling spirit, constitute pure thebaine. The mother liquor of the original ammonia precipitate, as has been already mentioned, contains narceine, for the separation of which I have found it most convenient to proceed in the following manner. A solution of acetate of lead is added to the fluid, and the dirty brownish precipitate which appears is separated by filtration through cloth. The excess of lead is removed by means of sulphuric acid, and the fluid filtered from the sulphate of lead, after being saturated with ammonia, is set to evaporate on the sand-bath at a moderate temperature. If the operation has been properly conducted, a film appears on the surface at a certain degree of concentration, and on cooling, a quantity of a crystalline matter is deposited in the thick brown mother liquor, which increases somewhat on being allowed to stand for some days. When this substance is collected on a cloth, and washed with a small quantity of water, it is sometimes obtained perfectly colourless at once, but more generally has a brownish colour. By farther evapo- ration of the mother liquor an additional quantity of crystals is obtained. The crystals are then boiled with a large quantity of water, and the solution, filtered hot, becomes filled on cooling with fine silky needles of narceine, while a large quantity of sulphate of lime and other impurities remain on the filter. The crys- tals of narceine have generally a slight shade of colour, and retain traces of sul- phate of lime, from which they are purified by solution in alcohol, boiling with animal charcoal, and again crystallising from water. II. Narceine. Narceine was discovered by PELLETIER,* about the year 1832, and to his own and CouERBE’s} researches we owe all our present information regarding it. Both these observers have analysed it, but with results quite incompatible with one another, and from which they have deduced entirely different formule. Their analyses, when recalculated with the corrected atomic weight of carbon, gave the following results :— * Annales de Chimie et de Physique, vol. 1., p. 262. + Ibid., vol. lix., p. 151. CRYSTALLINE CONSTITUENTS OF OPIUM. 351 PELLETIER. COUERBE. —_—_—— Carbon, 54:02 56°42 56:00 Hydrogen, 6°52 6°66 6:62 Nitrogen, 4:33 4:76 Oxygen, 35°13 32°16 100-00 100-00 From which PELLetier has deduced the formula C,, H,, NO,,, and CovERrBE that of C,, H,, NO,,, PELLETIER’S Formula. Carbon, 53°63 Hydrogen, 6:70 Nitrogen, a9 Oxygen, 35°76 100-00 of which the respective calculations are given below. CovUERBE’s Formula. 56°37 6-71 4-69 32°23 100-00 CouERBE’s formula agrees extremely well with his analytical results, but it, as well as PELLETIER’S, is entirely unsupported by determination of the atomic weight, which neither of them seem to have attempted, owing to the impression they derived from their experiments, that narceine does not possess basic proper- ties, an opinion which I have found to be altogether incorrect. III. Analysis of Narceine. The analysis of narceine was made upon a quantity which had been purified by repeated solution both in water and alcohol, and which was absolutely white. It loses its water with great difficulty at 212°, and it is most convenient to dry it at 230°. 10:130 2°660 L { 1 water. 7°236 grains of narceine gave 3°845 Experiment. ’ —_—_—_—_— I. Agi Carbon, 59:64 59:08 Hydrogen, 6:38 6:45 Nitrogen, 3°10 3°30 Oxygen, 30°88 31°22 100-00 100-00 VOL. AX. PART III. 4'632 grains of narceine gave carbonic acid, and 4-861 grains of narceine gave 10-522 carbonic acid, 2°824 water, 5°650 grains of narceine gave 2°790 and platinochloride of ammonium. platinochloride of ammonium. Calculation. TTY = a 59-63. 6,0) o7e 628 H,, 29 3:02 N 14 S100) Ome 1a 100-00 463 5 352 DR ANDERSON’S RESEARCHES ON SOME OF THE These results correspond exactly with the formula C,, H,, NO,,, as is obvious from their comparison with the calculated numbers given above. The atomic weight was determined by the analysis of its platinum salt, which is a very cha- racteristic compound, and which gave, as the mean of three experiments, 14-56 per cent. of platinum, giving, for the atomic weight of the base, 4648, and cor- responding perfectly with 463, the calculated number. IV. Properties of Narceine. Narceine crystallises in delicate needles which mat together into avery light and bulky mass, with a brilliant silky lustre. These crystals are always extremely white; indeed, narceine is remarkable for the facility with which it is obtained colourless, and while all the other crystalline principles of opium retain colour with considerable obstinacy, it may, with ordinary care, be obtained colourless by a few crystallisations, and in some cases is deposited in that state even from the highly-coloured mother liquor of the ammoniacal precipitate. In cold water it is sparingly, but in hot readily, soluble, and the solution on cooling becomes filled with a network of bulky crystals. In alcohol it is still more soluble, and is depo- sited from the hot fluid in needles which are generally shorter, thicker, and less silky, than those obtained from water. It is insoluble in ether. Ammonia and dilute solutions of potash and soda dissolve it in larger proportion than water, but the addition of a large quantity of concentrated potash to the dilute solution, pre- cipitates it, even in the heat, in the form cf an oily mass, which remains fluid for some time under the solution. The potash fluid. on standing for some time, depo- sits unchanged narceine, in the form of shining plates, which, by recrystallisation, again acquire the acicular form. It dissolves in dilute sulphuric, nitric, and hy- drochloric acids, without undergoing any change, and the solutions if sufficiently concentrated, deposit crystalline salts of narceine. When boiled with dilute nitric acid, the solution acquires a yellow colour, which on saturation with potash becomes reddish-brown, and the odour of a vola- tile base is immediately evolved. Concentrated nitric acid acts violently in the cold with copious evolution of nitrous fumes; after boiling for some time it gives on dilution a whitish precipitate, soluble in ammonia. and the fiuid contains oxalic acid. Strong sulphuric acid dissolves it in the cold with an intense red colour, which on the application of heat passes into a dark green. Strong hydrochloric acid dissolves it entirely, and without producing the blue colour which is de- scribed by PELLETIER as characteristic of narceine. I did obtain a blue colour on one occasion, but it was when operating on a very small scale, and when the nar- ceine was not absolutely pure; but on repeating and varying the experiment in every possible way with the pure base, I have never again succeeded in producing it. Ihave been equally unsuccessful with a quantity of narceine which I obtained CRYSTALLINE CONSTITUENTS OF OPIUM. 353 direct from the establishment of Messrs RopiquEetT, PELLETIER, and CAVENTOU, in Paris; but I am informed by Professor HEInricu Rose of Berlin, that he possesses a specimen from the same source, which shews a feeble blue.* The specimen of narceine which I obtained from Paris, though closely agree- ing in character with that which I had myself prepared, presented some minor differences, and analysis shewed that its constitution was entirely different. 4'458 grains of Ropiquer’s narceine gave 10-2505 carbonic acid, and 2: 620M Gee, water, 3°340 grains of Ropi@veET’s narceine gave 2°245-—... platinochloride of ammonium. Experiment. Calculation. oe Carbon $ 62-70 62:95 C- 192 Hydrogen : 6:53 6-23 Ee 9 Nitrogen : 4:22 4.58 oN 14 Oxygen é 26°45 26°24 OF 80 100-00 100-00 305 These results correspond exactly with the formula C,, H,, NO,, of which, however, I have no means of confirming the correctness. I attempted to form a platinum salt, but the fluid, in place of depositing a crystalline salt, solidified into a thin jelly, which I did not think deserving of analysis. The high price of the substance (nine francs per gramme), has deterred me from attempting a more ex- tended examination. V. Salts of Narceine. According to PELLETIER and CovUERBE, narceine, though dissolved by the acids, is deposited unchanged from the solutions. In this, however, their results do not agree with mine. Though incapable of restoring the blue of reddened litmus, narceine is a feeble base, and its solutions in acids deposit crystalline salts of well- marked characters. Hydrochlorate of Narceine.—When narceine is mixed with water, and hydro- chloric acid is added, it rapidly dissolves, and on standing deposits large groups of radiated silky needles. These needles, if collected on a filter and left for some time, occasionally pass into a congeries of short, thick, irregular prisms, and si- milar crystals are deposited by spontaneous evaporation in dilute solutions. These crystals are readily soluble in water and alcohol, and their solution has a * Dr Trart has since informed me that a specimen in his collection gives a fine blue with hy- drochloric acid; so that the product sold in Paris as narceine, would appear to be very variable in its properties, 354 distinctly acid reaction. analysis :— DR ANDERSON’S RESEARCHES ON SOME OF THE Dried at 212° the salt gave the following results to 4-692 grains of hydrochlorate of narceine gave 9-520 carbonic acid, and 2°710 water. 4-477 grains hydrochlorate of narceine gave 1:274 chloride of silver. Experiment. Calculation. Carbon aso 55-25 Cu 276 Hydrogen 6°41 6:00 i 30 Nitrogen 2°80 N 14 Oxygen af 28°85 0% 144 Chlorine 7-04 7:10 Cl 35:5 100-00 499-5 And the formula of the salt is consequently C,. H,, NO,, H Cl. Sulphate of Narceine is deposited from its solution in tufts of silky needles, not differing much in appearance from the base itself. It is of rather sparing so- lubility in cold water, but dissolves abundantly in hot. Nitrate of Narceine.—The nitrate is deposited in radiated groups from a hot solution of narceine in dilute nitric acid. It is sparingly soluble in the cold. Chloride of Platinum and Narceine.—When a solution of chloride of platinum is added to hydrochlorate of narceine, the double compound is deposited sometimes in prismatic crystals of small size, and sometimes as a crystalline powder, of a dark orange colour. ing results :— The salt was dried for analysis at 212° and gave the follow- : nf 9-713 grains of platinochloride 7°685 grains of platinochloride of narceine gave 11:576 carbonic acid, and 3°188 water. 6448 grains of platinochloride of narceine gave 9°698 carbonic acid, and 2°675 water. gave 1:392 grains of platinum. 6:829 1-008 6:195 0°907 Experiment. Calculation. Co ae ee Ae II. III. Carbon, 41:08 41:01 41:24 OF 276 Hydrogen, 4:60 4:60 4-48 15s 30 Nitrogen, 2°09 N 14 Oxygen, 21°51 O,, 144 Chlorine, ans at ee 15:94 Cl, 106-5 Platinum, 14:33 14:76 14:64 14-74 Pt 98°7 100-00 669-2 The formula C,,H,, NO,, H Cl PtCl, expresses completely the results of ex periment. CRYSTALLINE CONSTITUENTS OF OPIUM. 309 VI. Thebaine. Thebaine was discovered in 1832, and was examined and analysed by PELLE- TIER,* who gave to it the name of Paramorphine, expressive of its isomerism with morphine, which he supposed to be established by his analysis. It was after- wards examined by CoversEf and by Kanez,t} with results differmg widely from one another and from PELLETIER, and each has deduced from his analysis a dif- ferent formula, none of which can be considered as agreeing in a satisfactory manner with the analytical numbers, as is obvious from the following tabular view of their analyses, recalculated according to the corrected atomic weight of carbon, and compared with the formula deduced from them and the theoretical numbers which they ought to give. PELLETIER, CovuERBE. KANE. 1 eerie mia ora ae aS Carbon, 71:09 71:07 70:96 73°39 (6x0) Hydrogen, 6:29 6:47 6-44 6-78 6°85 Nitrogen, 4-40 6°38 oe 6:94 Goz Oxygen, 17:22 16:08 a 12-89 100-00 100-00 100-00 PELLETIER’S formula, : Cit, INO: CovERBE’s, ‘ : z Ohi aie O) Kane’s, : E : CPaL, NO, Calculation— PELLETIER’S COUERBE’S KANE’S Formula. Formula. Formula. Carbon, 71:83 71-59 74:25 Hydrogen, 6°34 6:44 6:93 Nitrogen, 4:93 6:68 6:93 Oxygen, 16-90 15:29 11-89 100-00 100-00 100-00 The atomic weight has been determined by Coverse and Kane by ascertaining the amount of hydrochloric acid absorbed by the dry base. Their results, how- ever, differ in a very remarkable manner, and do not admit of any conclusion or satisfactory deductions being made from them. CovurERBE, who does not give any particulars as to the method in which his experiment was made, found that 100 parts of base absorb 8°35 of the acid. Kane, on the other hand, found that when the hydrochloric acid was passed into thebaine, at the temperature of 212°, it absorbed as the mean of two experiments, which, however, do not agree very well, 16°96 per cent. of the dry gas; but that when the absorption took place at * Journal de Pharmacie, vol, xxi., p. 569. + Annales de Chimie et de Physique, vol. lix., p. 155. ¢{ Annalen der Chemie, vol. xix., p. 9. VOL. XX. PART III. 5D 356 ordinary temperatures, 33:28 per cent. was taken up. These results are very un- intelligible, and certainly cannot be employed as the foundation of an atomic weight. It is, however, worthy of observation, that they are very nearly in the ratio of 1, 2, and 4, but this relation must be purely fortuitous, as I have found that thebaine is very easily decomposed by hydrochloric acid, and none of the results agree at all with the actual atomic weight, as deduced from the experiments which DR ANDERSON’S RESEARCHES ON SOME OF THE I am about to detail. The thebaine employed for analysis was prepared by the process already de- scribed, and purified by repeated crystallisation ; it was burned with oxide of cop- VIL Analysis of Thebaine. per, and is very easily combustible. carbonic acid, and 5-475 grains of thebaine, dried at 212°, gave I.< 14-675 37500 water. 4-990 grains of thebaine gave II. ¢ 13-383 carbonic acid, and 3°135 water. 5-089 grains of thebaine, of another preparation, gave III, ¥ 13°621 carbonic acid, and 3228 water. 5:336 grains of thebaine gave 3°735 platinochloride of ammonium. 6:332 grains of thebaine gave 4-515 platinochloride of ammonium. Le II. Carbon, 73°10 fo 14 Hydrogen, 7:10 6:98 Nitrogen, 4:39 4:47 Oxygen, 15°41 15:41 100-00 100-00 III. 73°01 7:04 These results correspond exactly with the formula, differing from that of codeine by two equivalents of carbon, as is seen from the following comparison of the experimental mean with the calculated result of that formula. C5, H,, NO, Mean. Carbon, 73°08 Hydrogen, 7:04 Nitrogen, 4°43 Oxygen, 15:45 100-00 Calculation. 73°31 6°75 4°50 15:44 100-00 Cae, ee H,., 21 N 14 0, 48 311 CRYSTALLINE CONSTITUENTS OF OPIUM. Bye Some difficulty was at first experienced in the determination of the atomic weight of thebaine by the analysis of its platinum salt, until it was ascertained that that salt, when dried at 212°, retains two equivalents of water. The mean of three determinations of platinum gave 18°70 per cent. of the metal, and the calcu- lated result for the formula, C,, Hp, NO,, HCl, Pcl, + 2HO is 18°44. These results were also confirmed by the analysis of the hydrochlorate, of which the details will be given in their proper place. Properties of Thebaine. Thebaine crystallises from its alcoholic or ethereal solution in brilliant square plates with a silvery lustre. It is insoluble in water, but very soluble in alcohol and ether, especially on boiling. It dissolves readily in acids, and forms salts which are not obtained in crystals from aqueous solutions. It is insoluble in potash and ammonia. Strong sulphuric acid reacts upon it, and produces a deep-red colour, even when it is free from nitric acid. Concentrated nitric acid acts violently in the cold, with copious evolutions of red fumes, and formation of a yellow solution, which becomes dark coloured on the addition of potash, and evolves a volatile base. In hydrochloric acid it dissolves readily, and the solution on evaporation becomes dark coloured, and leaves behind a resinous matter, which does not dis- solve completely in water. Sulphuric acid, of specific gravity 1:300, dissolves it in the cold; and on gently heating a resinous or semisolid matter is thrown down, which, on boiling with water, slowly dissolves, and deposits, on cooling, a rather sparingly soluble salt, in microscopic crystals, which appears to be a product of decomposition, but of which I must defer the examination until I have obtained an additional quantity of thebaine. Chlorine and bromine rapidly decompose thebaine with the formation of resinous compounds. VIII. Salts of Thebaine. The small quantity of thebaine which I had at my disposal has prevented my extending the examination of its salts as far as I could have wished, and I have only examined such as are necessary for the determination of its atomic weight, and must reserve further details for a future paper. Hydrochlorate of Thebaine.—In order to prepare this salt, thebaine is mixed with a small quantity of strong spirit, and an alcoholic solution of hydrochloric acid gas is gradually added until the thebaine is dissolved, an excess being care- fully avoided. On standing for some time, the hydrochlorate is deposited in extremely brilliant rhomboidal crystals, often of considerable size, or as a crys- talline powder if the solution be agitated. These crystals are purified by resolu- tion in absolute alcohol. They are extremely soluble in water, and the solution, on evaporation, gives only a resinous mass. In alcohol, especially if absolute, 358 DR ANDERSON’S RESEARCHES ON SOME OF THE they are rather sparingly soluble, and in ether they do not dissolve. 212°, their analyses gave 93984 0988 carbonic acid, and 4-108 grains of hydrochlorate of thebaine gave iE OA OA Se ois water. 5°356 grains of hydrochlorate of narceine gave 1 ame a U5 lye carbonic acid, and 3192 ... hydrogen. 3°620 grains of hydrochlorate of narceine gave 1517 °... ‘chloride of silver. 5°356 grains of hydrochlorate of narceine gave 2085 ... chloride of silver. Experiment. Calculation. a SSS i, 1BE Carbon, . 62:39 6219 62:38 Cy, 228 Hydrogen, : 6°80 6:62 6:56 i: 24 Nitrogen, : i ra 3°83 N 14 Oxygen, : da sh 17:52 O, 64 Chlorine, é 10°36 9°63 9°71 Cl 35-5 100-00 365-5 Dried at The salt, dried at 212°, contains, therefore, two equivalents of water, and is represented by the formula, C,, H,, NO, H Cl + 2 HO. Platinochloride of Thebaine.—The platinum compound is thrown down as a yellow crystalline precipitate on the addition of bichloride of platinum to the preceding compound. It is sparingly soluble in boiling water, and the solution deposits a salt which appears to be a product of decomposition. 8-735 ... carbonic acid, and 5:555 grains of platinochloride of thebaine, dried at 212°, gave I 2-180 --. ‘water. carbonic acid, and 5°418 grains of platinochloride of thebaine, dried at 212°, gave II. < 8593 2315... sia.» aOR: 5:037 grains of platinochloride of thebaine gave 0-927 grains of platinum. 4-998 ¥ Bet 0-936 5°793 — a ase 1-100 Experiment. Calculation. oa —__ eee I. itt III. Carbon, ‘ 42°88 43:25 ee 42°60 Cy, 228 Hydrogen, . 4-36 4-74 See 4-48 eis 24 Nitrogen, . ae A oe 2°61 N 14 Oxygen, : At a wht 11:98 0, 64 Chlorine, : sic ya ce 19-89 Cl, 106°5 Platinum, , 18°43 18°72 18-98 18-44 Pt 98°7 CRYSTALLINE CONSTITUENTS OF OPIUM. 359 The formula of the salt is therefore C,, H,, NO, H Cl Pt Cl, + 2 HO. Deficiency of time and material have prevented the full examination of any other salts of thebaine. The sulphate was prepared by adding sulphuric acid to an ethereal solution of thebaine; it was deposited partly in crystals, partly as a resinous mass which became crystalline on standing. This was dissolved in ab- solute alcohol, and thrown down by ether as a white powder. A determination of sulphuric acid gave 16°53 per cent., which is not far removed from the quantity required by theory for a sesquisulphate. Hydrochlorate of thebaine gives, with a spiritous solution of corrosive subli- mate, a fine white crystalline precipitate of a double salt, and the alcoholic solu- tion of the base itself gives a bulky precipitate insoluble in water and alcohol; neither of these substances, however, could be got of constant composition. Terchloride of gold gives a fine reddish-orange precipitate, which, at 212°, fuses into a resinous mass. IX. Action of Nitric Acid on Narcotine. Narcotine has been already repeatedly analysed, and its constitution sa- tisfactorily determined. I have not, therefore, attempted to repeat its analysis, or to add any confirmatory evidence of the correctness of its formula, but have directed my attention to the action of nitric acid upon it, which I had found, by previous experiments, to give a series of products varying with the circumstances of the action and the concentration of the acid. When proper precautions are taken, the whole series of products which Wouter discovered by the action of peroxide of manganese and sulphuric acid upon narcotine, are obtained along with several new substances, which stand in very intimate relation to these compounds, and are peculiarly remarkable, both in their chemical relations and the circumstances under which they are produced. When concentrated nitric acid is added to narcotine, a very violent action ensues, even in the cold; red fumes are copiously evolved, and a thick resinous- looking red matter is left behind. With somewhat weaker acid and a gentle heat, a similar action takes place, and a red fluid is obtained, which, by evapora- tion, yields an amorphous orange residue. In both cases, the action was much too violent, and the product obtained obviously the result of several complex ac- tions. The action of nitric acid in a more dilute state was therefore tried and after several experiments, the following was found to be the most advantageous method of treatment. Six hundred grains of narcotine are mixed with two-and- a-half ounces, by measure, of nitric acid, of specific gravity 1-400, diluted with ten ounces of water, and exposed in the water-bath to an uniform temperature of 120° Fahr. The narcotine fuses into a yellowish mass, which, by continuous agitation, slowly dissolves without the evolution of red fumes. When the solution is nearly complete, a small quantity of a white deposit begins to make its appear- VOL. XX. PART III. 5 E 360 DR ANDERSON’S RESEARCHES ON SOME OF THE ance in the solution, and gradually increases in quantity until the fiuid becomes filled with bulky crystalline flocks. The quantity of this substance produced appears to depend, to a great extent, upon the rapidity of the oxidation, being sometimes extremely minute, and always bearing a very small proportion to the quantity of narcotine employed. When these flocks have ceased to increase in quantity, they are separated from the fluid by filtration through asbestos, washed with water, in which they are insoluble, and purified by solution in a consider- able quantity of boiling alcohol, from which they are deposited on cooling in minute needles. To this substance I give the name of Teropiammon, for reasons which will be immediately apparent. Teropiammon.—As obtained by the process just described, teropiammon is in the form of extremely small colourless needles. It is insoluble in water, both hot and cold, and undergoes no decomposition by boiling with that fluid. It is -very sparingly soluble in cold alcohol, more so in boiling; and it is also very little soluble in ether. Concentrated sulphuric acid dissolves a small quantity in the cold, with a yellow colour, and on heating a fine crimson colour is produced. Nitric acid dissolves it readily in the cold ; and on heating, red fumes are evolved, and on dilution with water, a white precipitate of teropiammon in an altered condition is obtained. It is insoluble in hydrochloric acid and in ammonia. Boiled with caustic potash, it dissolves with evolution of ammonia, and opianic acid is found in the fluid. At my first examination, I considered this substance to be identical with WoutEr’s* opiammon, but the entire absence of xanthopenic acid in this reaction, as well as various other differences in its properties, con- vinced me that it was actually different,—a conclusion which has been confirmed by analysis. 10:960 ... — earbonic acid, and 5-052 grains of teropiammon, dried at 212°, gave i 2-262... 2.) Speer: 5-090 grains of teropiammon gave TI. ¢11:020 ... carbonic acid, and 2-290 .... . water, I 4-358 grains of teropiammon gave ; 1515 ... _ platinochloride of ammonium. Il 7°312 grains of toropiammon gave : 2405 ... _ platinochloride of ammonium. Experiment. Calculation. ee ae (Fee Carbon, . 59-16 59-04 58-91 Cari 360 Hydrogen, . 4:97 4-99 4:74 ie tes 29 Nitrogen, é 2°18 2:06 2:29 N 14 Oxygen, . 33°69 33-91 34.06 0,, 208 100-00 100-00 100-00 611 * Annalen der Chimie und Pharmacie, vol. 1., p. 6. CRYSTALLINE CONSTITUENTS OF OPIUM. 361 These numbers correspond very closely with the formula C,, H,, NO,,, as is obvious from the comparison of the calculated results of that formula given abov e That it is actually different from Won rr’s opiammon, of which the formula is C,, H,, NO,,, is very obvious, but it bears a very interesting relation to it. The latter substance is derived from two equivalents of opianic acid and one equiva- lent of ammonia, by the removal of the elements of four equivalents of water as thus represented :-— 2 eq. opianic acid, : : , Coo ay One 1 eq. ammonia, . é 5 Jas Ri Cy) H,, N On, 4 eq. water, : : 2 - EIA 1 eq. opiammon, F ; : yp eslen SP Oar and the new compound is derived in a precisely similar manner from three equi- valents of opianic acid :— 3 eq. opianic acid,~ . : é Osho 3 Dre nae a 1 eq. ammonia, ; P ; EL oe) Ceo H,, N 035 4 eq. water, : : bhi fied ieee eOde leq. teropiammon, . : j CP Ne Os. Both these substances may therefore be considered as a sort of nitriles of opianic acid, at least they bear to the opianates of ammonia a similar relation to that which the nitriles hitherto examined do to the ammonia salts from which they are obtained. That this is actually the constitution of teropiammon, is _ proved by the action of potash, which, when boiled with it, produces an abundant evolution of ammonia, while the fluid contains an acid, which was found by its properties, as well as by an analysis, of which the details will be given under another head, to be opianic acid. It is in consideration of this constitution, that I give to the substance the name of teropiammon, while I should propose that of binopiammon for the substance described by WontER, reserving that of opiam- mon for the corresponding compound derived from one equivalent of opianic acid and ammonia, should that substance be discovered, which is by no means impro- bable. The production of teropiammon in a highly acid fluid must be considered as an extremely remarkable phenomenon, and one of which, so far as I know, we have no similar example. It is obviously the result of a secondary decomposition, produced by the further action of nitric acid on narcotine, which, as we shall immediately see, yields a great variety of curious and complex products; but it has appeared to me that the quantity obtained was largest when the action was most moderate, at least I have never succeeded in obtaining it more abundantly by continuing the action for a longer time, but rather the reverse. 362 DR ANDERSON’S RESEARCHES ON SOME OF THE The fluid from which teropiammon has been separated is pale yellow. When supersaturated with potash, it acquires a more or less dark colour; and on stand- ing, and still more rapidly on agitation, deposits a quantity of pale-yellow crys- talline grains. The mother liquor, which contains a large excess of potash, is separated by filtration, and the precipitate washed with water. It then presents all the characters of cotarnine, dissolves in the acids, with a red colour, gives highly-soluble salts, and is precipitated by potash and soda, but not by ammonia. Its identity was further determined by the following analysis of its platinum salt :— { 5-436 grains of platinochloride of cotarnine gave 1242 ... platinum. Experiment. Calculation. ee _ Carbon, : . £8: 35°68 Cas 156 Hydrogen, : : sab 3°20 Hy 14 Nitrogen, ; ; so 3°20 N 14 Oxygen, ‘ ; - 10-98 O, 48 Chlorine, : oe 24°37 Cl, 106°5 Platinum, : . 22°84 22°57 Pt 98-7 100-00 437-2 In this way cotarnine is obtained with extreme facility, and the process is greatly to be preferred to WouLER’s method of preparation. The sole precaution necessary is to avoid the application of too high a temperature during the action of the nitric acid, and to arrest the action as soon as the whole of the narcotine is dissolved. Ifthe heat be too great or too long continued, the cotarnine itself undergoes decomposition, and yields products which will be described afterwards. X. Examination of the Potash Solution. In the alkaline fiuid from which the cotarnine had been separated, it was natu- ral to look for the opianic acid of Lizsig and WouLER, which, as the simultaneous product of the oxidation of narcotine, must almost of necessity be present. Its ex- istence was accordingly soon ascertained ; but it was also found that it was by no means the only or the invariable product of the action, but that different substances were obtained in different operations, even when the nitric acid was caused to act under what were supposed to be perfectly identical conditions. In some instances, opianic acid was entirely absent, and its place was taken by hemipinic acid, which was invariably obtained in greater or less quantity, even when opianic acid was present; and in other cases, substances appeared which could not be produced at will, and were only obtained when the conditions of the oxidation were very successfully fulfilled. In order to obtain these substances, the alkaline fluid is evaporated on the sand-bath to a small bulk, and the nitre, which deposits on cooling, is separated CRYSTALLINE CONSTITUENTS OF OPIUM. 363 by filtration, and the evaporation repeated until as much as possible is separated. The remaining syrupy fluid, which contains a large quantity of carbonate of potash, is then boiled with successive quantities of rectified spirit, as long as anything is extracted, the alcohol is distilled off, and the residue mixed in the ‘cold with an excess of hydrochloric acid. A precipitate makes its appearance, with characters differing according to the substances which happen to be present, and is sometimes crystalline, and sometimes a syrupy mass, which passes into the crystalline state on standing. This precipitate contains opianic acid, hemipinic acid, and in some instances two other substances, to one of which I give the name of Opianyl], and to the other that of Hydrate of Opiany]. Opianyl.—This substance is only formed when the oxidation has been extremely gentle, and, though repeated trials have been made, it has been found impossible to moderate the action in such a way as to produce it at will. In order to obtain it in a pure state, the precipitate by hydrochloric acid, which has just been referred to, is dissolved in a large quantity of boiling water, and the solution allowed to cool. A crop of crystals is deposited which consists of opianyl along with some opianic acid, if the quantity of water employed have not been suffi- ciently large. These crystals are purified by solution in boiling water and in alcohol. In one instance opianyl was obtained along with hemipinic acid, and with only traces of opianic acid, and in that case its purification was conveniently effected by dissolving in boiling water, precipitating hemipinate of lead with a solution of neutral acetate of lead, washing the precipitate in boiling water, and evaporating to a small bulk, when opianyl was deposited in colourless crystals, which were purified by solution in boiling water. Opianyl is thus obtained in long delicate needles, which, when pure, are per- fectly colourless. They are sparingly soluble in cold water, and more soluble in boiling. When a quantity is boiled with a smaller amount of water than is re- quired to dissolve it, the residue melts under the fluid; but it does not fuse at 212° in the water-bath, requiring, when dry, a temperature of 230° to produce its fusion, and, on cooling, it resolidifies at about 220°. In alcohol it is easily soluble. Ether takes it up readily, and, on evaporation, deposits it in brilliant groups of radiated needles. Concentrated sulphuric acid dissolves it in the cold, and forms a perfectly colourless solution, which, when heated, becomes of a beautiful and characteristic purple colour. Nitric acid, of specific gravity 1°400, dissolves it in the cold, and on dilution with water it is deposited unchanged. By boiling, red fumes are evolved, and the fluid no longer gives a precipitate on being diluted. Hydrochloric acid dissolves it in somewhat larger quantity than water. Solutions of potash, soda, and ammonia, do not dissolve it more abundantly than water. It is incapable of forming compounds with the metallic oxides, and con- tains no nitrogen. VOL. XX. PART II. i pects 364. DR ANDERSON’S RESEARCHES ON SOME OF THE carbonic acid, and 5-590 grains of opianyl, dried at 212°, gave I, < 12°605 26B0 "P.. Waler. f 5°895 grains of opianyl gave II. ¢ 13°350 ... carbonic acid, and 2°885. =... water. 5°886 grains of opianyl gave III. < 138:307 ... ~—_ carbonic acid, and 2160), <8 » opwater. r. 28 LW ii Carbon, . s : 61:49 61:76 61:65 Hydrogen, : 4 5°32 5°43 5:21 Oxygen, . : 33°19 32°81 33°14 100-00 100-00 100-00 These results correspond exactly with the formula C,, H,, O,, as is obvious from the following comparison of the calculated numbers with the experimental mean :— Mean. Calculation. Carbon, : é 61:63 61°85 Us 61 Hydrogen, . : 5°32 5°15 Doe 10 Oxygen, ‘ : 33°05 33°00 OF 64 100-00 100-00 194 Opianyl thus bears a very interesting relation to opianic and hemipinic acids, provided we assume for the former the formula as corrected by Berzetius, and, for the latter, an atomic weight twice as high as that assigned to it by WoHLER, both of which assumptions are consistent with analyses which will be detailed in the sequel. The three substances then stand as follows :— Opianyl, , : : . 2 : Oat Ben Oe Opianic acid, : : : é 4 Loa: Hemipinic acid, CG) te and appear as three successive degrees of oxidation of the same radical. I have not attempted to convert opianyl into opianic acid by oxidation, as the quantity at my disposal was not sufficiently large to admit of an accurate experiment, but no reasonable doubt can be entertained on that subject. The derivation of opianyl from narcotine is abundantly simple. Two equiva- lents of hydrogen are oxidised by the nitric acid, and the narcotine splits up into opianyl and cotarnine, as is expressed in the following scheme :— 1 eq. of narcotine : : ‘ Z Cy eNO 2 eq. of oxygen, CRYSTALLINE CONSTITUENTS OF OPIUM. 365 Yield 1 eq. of cotarnine, : : ; Coa NO « 1 eq. of opianyl, : 4 A : Used 5 eam 0 2 eq. of water, d : ; : Ee 2O; Cy, Hy; NOx, The same scheme, with the addition of two or four equivalents of oxygen, re- presents also the mode in which opianic and hemipinic acids respectively are derived from narcotine, much more simply than it has been by Bryru* in his paper on the action of bichloride of platinum on narcotine, who gives a scheme involving the evolution of carbonic acid. ‘The appearance of this gas, which was actually observed by Bryru during the action, has, however, always appeared to me to be the result of a secondary decomposition ; and this view, I think, receives confirmation from the production of teropiammon, where nitric acid acts even in the most feeble manner on narcotine, and the formation of which must, of neces- sity, be attended by the evolution of carbonic acid. If we pursue the relations of opianyl to narcotine, we shall find that these also are of a very interesting nature. By subtracting an equivalent of cotarnine from one of narcotine, Narcotine, : : ; P : Ce NO. Cotarnine, : s : : ; Co in Ole Ore O we find that the substance coupled with cotarnine to form narcotine may be con- sidered as a hydruret of opianyl, or a substance bearing to opiany! a relation simi- lar to that which alloxantin bears to alloxan, and the preparation of which in a separate form would be most interesting. The attempts which I have made to obtain it have, however, as yet proved abortive. I have tried the action of sul- phuretted hydrogen upon opianyl, but no change took place, and also the fer- mentation of narcotine, but with equally little success. Although this hydruret of opianyl has not been obtained in a separate form, we have a corresponding compound in the sulphopianic acid of WouLer, which may be considered as hydru- ret of opianyl, in which the two equivalents of hydrogen are replaced by sulphur. Hydruret of opianyl, , ; . C,, H,, 0,+H Sulphopianic acid, . : : , Cr ety Oak By and in this point of view the latter substance deserves a further investigation. It bears certain analogies in properties to opianyl, and especially gives a purple colour when heated with sulphuric acid ; but it appears to possess acid proper- ties, although they are certainly very feeble. Hydrate of Opianyl.__On one occasion, in acting upon narcotine with nitric acid, there was obtained a substance which closely resembled opianyl, but differed * Annalen der Chimie und Pharmacie, vol. 1., p. 29. 366 DR ANDERSON’S RESEARCHES ON SOME OF THE from it in fusing readily when introduced dry into the water-bath, which opianyl does not. Its fusing point is 205°. In all its other properties, however, it is quite identical with opianyl. It gives the same purple with sulphuric acid, and shews the same relations to solvents. Its analysis gave the following results :— 9-265 ... carbonic acid, and 4-295 grains of hydrate of opianyl, dried at 212°, gave st {528 a water. 5°955 grains of hydrate of opianyl, dried in vacuo, gave, II. < 12-840 nga carbonic acid, and 2:905 soc, Warten. Experiment. Calculation. BS a i. le 1S Carbon, . s 58°83 58°84 59:11 Coy), 120 Hydrogen, : fu ler 5:42 B41 i Tt Oxygen, 36:00 35°74 35°48 0, 72 100-00 100-00 100-00 203 These numbers correspond with the formula C,, H,,0O,+HO. The quantity of this substance which I obtained was too small to admit of any detailed examina- tion of its chemical relations. Opianic Acid.—The fluid which has deposited opianyl yields, on evaporation. a crop of crystals of opianic acid, which are readily purified by solution in water or alcohol. Its properties are already so well known, that I have not thought it necessary to examine them further; but as the formula given by Wouter is different from the one I have adopted, which is that of Berzexius, the following analyses, in which every care was taken to dry the substance thoroughly, may be of value as confirming the correction of the latter chemist :— 11:170 ~~... ~~ earbonie acid, and 5:343 grains of opianic acid, dried at 212°, gave I 2-440 ... water. 9-485 ... carbonic acid, and 4°528 grains of opianic acid gave 1 2-013 9... water. 4-883 grains of opianic acid gave III. < 10-200 ..... _—_ carbonie acid, and 2-190 We water. Experiment. Calculation. te it: III. Carbon, 56°99 57°12 56:96 57:14 Coy gl Hydrogen, 5:07 4-93 4-98 4:76 Bee sue Oxygen, 37°94 37°95 38-06 38°10 O},/ #80 100-00 100-00 100-00 100-00 210 The opianic acid of the last of these analyses was prepared by the decomposition of teropiammon by potash. CRYSTALLINE CONSTITUENTS OF OPIUM. 367 Wouter’s formula, C,, H, O,,, requires 4:30 per cent. of hydrogen, which is much too low for the experimental result. Opianic Ether.—According to WoHLER, opianic ether cannot be obtained by the action of sulphuric or hydrochloric acids upon a mixture of opianic acid and alcohol. I have found the reverse of this to be the case, and obtained it by chance on one occasion when hydrochloric acid had been added to the alcoholic solution of the opianate of potash, which had been separated from the excess of carbonate in the preparation of the acid itself. It is obtained in the form of colourless needles which are insoluble in water, but dissolve readily in alcohol and ether. It melts under water, and also dry, at the temperature of 198° Fahr. Its analysis gave— 5615 grains of opianic ether gave 12°325 ... carbonic acid, and DOG) as | Rvater: Experiment. Calculation. Carbon, 3 : 59-86 60-50 C,, 144 Hydrogen, . ; 5:90 5:88 Hey 14. Oxygen, j ; 34:24 33°62 OF 80 100-00 100-00 238 Hemipinic Acid.—By further evaporation of the solution which has deposited opianic acid, hemipinic acid is obtained, and it may be purified by several crystal- lisations. It is, however, in this case frequently more or less yellow-coloured, but may be readily obtained colourless, and is also effectually separated from any traces of opianic acid which may chance to adhere to it, by precipitating the solu- tion with acetate of lead, and decomposing the washed hemipinate of lead by a cur- rent of sulphuretted hydrogen. The characters of the acid corresponded in all respects with WouLER’s description, and the analysis gave the same results as his. 5°445 grains of hemipinic acid gave 10603 ... carbonic acid, and 2210 4... . swater. Experiment. Calculation. Carbon, : : 53:17 53:14 C, 120 Hydrogen, . : 4-64 4:42 ine 10 Oxygen, : - 42-19 42:44 OF 96 100-00 100-00 226 It will be observed that the formula above given, C,, H,, O,., is exactly double of that attributed to hemipinic acid by Wouter. The examination of some of the salts of hemipinic acid leave no doubt that it is a bibasic acid, and that its con- stitution is correctly expressed by the higher formula, which its relations to opianyl and opianic acid would also lead us to consider as extremely probable. VOL. XX. PART III. 5G 368 DR ANDERSON’S RESEARCHES ON SOME OF THE Acid Hemipinate of Potass——This salt was met with at first accidentally in an experiment in which, during the preparation of the acid, a sufficient quantity of hydrochloric acid was not added to the original alkaline solution; but it may be readily prepared by dividing a quantity of hemipinic acid into two equal quan- tities, neutralising one half with potash, then adding the other and evaporating. It is deposited in thick six-sided tables sometimes of considerable size. It is readily soluble both in cold and hot water and in alcohol, but not in ether, which throws it down from its alcoholic solution in shining plates. It is highly acid to test paper. Dried at 212° it gave the following results: 10:245 ees carbonic acid, and 6-203 grains acid hemipinate of potass gave 1935 ... ‘water. 5:330 grains acid hemipinate of potass gave 1-763 ... sulphate of potass. Experiment. Calculation. Carbon, ; f 45°04 45:42 Crap hy EB _ Hydrogen, . : 3°46 3°40 Hi, 9 Oxygen, : . Si 33°32 o. 88 Potass, : ; 17:88 17:86 KO 47:2 100-00 13°505 grains of the crystallised salt lost, at 212°, 1:950 grains =14-43 per cent., and corresponding to 5 equivalents of water, the calculated result for which is 14°55 per cent. The formula of the crystallised salt is consequently, KO HO C,, H, 0,,+5 HO. Neutral Hemipinate of Potass is a highly soluble salt, and crystallises only with difficulty. Neutral Hemipinate of Silver is obtained as a white precipitate, insoluble in water. Dried at 212° and burned, it gave the following results :— 6:278 grains hemipinate of silver gave o096" 4... silver: Experiment. Calculation. Carbon, : : ee 27°27 Ct) Hydrogen, . t a 1:81 He 8 Oxygen, : A 21°83 oD 96 Silver, 5 5 49°34 49-09 Ag, 216 100-00 440 Acid Hemipinic Ether—Hemipinovinic Acid.—When hemipinic acid is dis- solved in absolute alcohol, and a current of hydrochloric acid gas passed through the solution, hemipinovinic acid is formed. It is obtained in the pure state by CRYSTALLINE CONSTITUENTS OF OPIUM. 369 evaporating to dryness in the water-bath and crystallising the residue from alco- hol or water. It is thus obtained in the form of tufts of extremely light and bulky crystals, sparingly soluble in cold water, but more so in boiling. It fuses when dry at the temperature of 270° Fahr., but melts easily under boiling water into a transparent fluid. It is strongly acid to test paper. Its aqueous solution does not precipitate the salts of lead or silver, but gives with perchloride of iron a bulky, pale brownish-yellow precipitate. It dissolves readily in potash, and the solution, on boiling, evolves alcohol. 5-445 grains hemipinovinic acid, dried at 212°, gave 10-603 ... carbonic acid, and 2275. 15..8 water. Experiment. Calculation. > Carbon, : 3 56°45 56°69 Cos 144 Hydrogen, . j 5:67 5°51 15 14 Oxygen, : } 37:88 37°80 OFS 96 100-00 100-00 254 This corresponds exactly with the formula Cpt) OTOL Ons but the crystallised substance contains, in addition, three equivalents of water of crystallisation. 5°74 grains lost 0°570 grains at 212°, corresponding to 9:93 per cent., and the calculation for three equivalents gives 9°60. Crystallised hemi- pinovinic acid has, therefore, the formula C, H, 0 HO C,, H, 0,,+3 HO. Although hemipinovinic acid possesses distinctly acid properties, and is capable of combining with bases, I have failed in obtaining its compounds in a state of purity. Its baryta salt was obtained in tufts of minute needles, by digesting the solution of the acid with carbonate of baryta, or baryta water, evaporating, dis- solving in water and recrystallising. But the compound could not be obtained in a state fitted for analysis, and appears to be very liable to undergo decomposition. The existence of an acid potass salt, and an acid ether, appear to me to esta- blish, in the most conclusive manner, the bibasic character of hemipinic acid, and to connect it most closely with opianic acid. It is, however, very remarkable, that by the simple addition of two equivalents of oxygen, the latter acid, which is unequivocally monobasic, should acquire bibasic properties. The compounds and products of decomposition of both acids are deserving of further study, but want of time has prevented my pursuing this part of the investigation further. XI. Action of Nitric Acid on Cotarnine. I have already mentioned that narcotine, when treated with strong nitric acid, undergoes a very powerful oxidation, in which products of further changes are 370 DR ANDERSON’S RESEARCHES ON SOME OF THE obtained ; and as these changes are obviously not confined to the non-nitrogenous component of narcotine, but extend to the cotarnine also, I proceeded to the examination of the action of nitric acid upon that substance in a pure, or at least in a nearly pure, state. The products of the action of nitric acid on cotarnine are extremely complex, and several different actions appear to occur simultaneously, in each of which a different decomposition is produced. When concentrated nitric acid is employed, an extremely violent and tumultuous action takes place on boiling, and the fluid contains a large quantity of oxalic acid. When, however, the acid is more dilute, the action goes on more steadily, red fumes are abundantly developed and an acid substance is produced, which remains in solution in the nitric acid. The preparation of this substance is a matter of considerable nicety, and it is particu- larly important that the nitric acid be not employed in too large an excess, partly on account of the risk of carrying the action too far, and partly on account of the difficulty of separating the product from a very large excess of acid. As the new product is liable to undergo a further oxidation with production of oxalic acid, it is not safe to attempt its separation by evaporating the nitric acid solution. The best method is to dissolve the cotarnine in nitric acid diluted with about twice its bulk of water, and then adding strong nitric acid to raise the mixture to the boiling-point. Red fumes are copiously evolved, and after some time a small quantity of the fluid is taken out and mixed with a considerable quantity of alco- hol and ether. Ifon standing for a short time crystals are deposited, the whole fluid is treated in the same manner ; but, if they do not appear, the digestion is continued somewhat longer, and it is tried again, and so on, until the right point is hit. The fluid, mixed with alcohol and ether, is allowed to stand for twenty- four hours, and the precipitated crystals are separated by filtration. This sub- stance agrees in all respects with the apophyllic acid obtained by Wout er as a product of the action of bichloride of platinum upon cotarnine, and which he obtained in too small a quantity for examination and analysis. Apophyllic Acid—The crude crystals of the acid deposited from the alcohol and ether are purified by solution in boiling water, and, if necessary, by digestion with animal charcoal and crystallisation. It then presents all the characters at- tributed to it by WouLER, and is obtained with ease, either in hydrated or anhy- drous crystals, as described by him. It dissolves in water, but not in alcohol and ether. Concentrated sulphuric acid dissolves it readily, and the solution remains colourless even when pretty strongly heated. Strong nitric acid oxidises it. When heated on the platinum knife it fuses, and, on cooling, solidifies into a crystalline mass. Its fusing point is 401°. It dissolves in large quantity in potass and soda, also in ammonia, and the latter solution, on evaporation, gives very soluble crys- tals of an ammonia salt. Its salts are ail very soluble, and are not easily obtained in a satisfactory state for analysis. CRYSTALLINE CONSTITUENTS OF OPIUM. 371 10:995 ... . carbonic acid, and 5.690 grains of apophyllic acid, dried at 212°, gave i £990)..." ‘water. 10:055 ... carbonic acid, and 5'185 grains of apophyllic acid gave oe HEO15 1) ia qracent { 3°983 grains of apophyllic acid gave 4-675 ... platinochloride of ammonium, Experiment. Calculation. ——S SS it TI. Carbon, - ; 52-70 52°88 53:04 Cie 96 Hydrogen, : 3°88 4:12 3°86 Jule fi Nitrogen, : (caw ee 7°73 N 14 Oxygen, 2 36-05 ag, 35°37 0, 64 100-00 100-00 181 The formula of the acid is, therefore, C,, H, NO,, and this has been confirmed by the analysis of its silver salt, to be given below. Its derivation from cotarnine cannot be distinctly understood, and is attended by the formation of several other substances which I have not examined. If we compare its formula with that of cotarnine, however, we shall see that if we add to the latter two equivalents of oxygen, and subtract from it the formula of apophyllic acid, the difference is GP H,. Cotarnine +2 eq. 0, . : : ; Geet eNO; Apophyllic acid, . : : : : Cre NO® C,H, I have, however, been unable to determine whether this group of atoms passes into any particular form of combination, or whether it be entirely oxidised into carbonic acid and water, which I suspect it is. Apophyllic acid differs from anthranilic acid by the elements of two equiva- lents of carbonic acid. Apophyllic acid, . ; 4 ‘ ; Crk INO; 2 eq. carbonic acid, * O, Anthranitic acid, : : A : Cy, Ap NOY According to WouLER, when apophyllic acid is distilled, it gives a quantity of chinoline. From our knowledge of its constitution, however, we should rather anticipate the production of aniline, or, at least, of an isomeric of it, particularly if distilled with excess of lime or baryta, thus :— C,, H, NO,—400,=C,, H, N. By distillation I obtained a small quantity of an oily base with a somewhat aromatic odour ; but it did not give the reaction of aniline with chloride of lime, VOL. XX. PART III. oH 372 DR ANDERSON’S RESEARCHES ON SOME OF THE and I did not obtain it in sufficiently large quantity for analysis. Chinoline, I conceive, it cannot possibly be, but whether it is aniline, or a base isomeric with it, I shall for the present leave an open question. My impression certainly is, that it is not aniline, and it is quite conceivable that the decomposition may be very different, and that during distillation only two equivalents of carbonic acid are separated, as is the case in every other instance if the production of a volatile base; and in that case we should have a substance isomeric with anthranilic acid, and possessing basic properties. Apophyllate of Silver.—This salt can only be obtained by digesting apophyllic acid in solution upon moist carbonate of silver, filtering from the excess of car- bonate, and precipitating the solution with a mixture of alcohol and ether. The salt is thrown down as a perfectly white powder, of a more or less crystal- line appearance, and which colours slightly by exposure to the light. It is ex- tremely soluble in water, sparingly soluble in alcohol, and insoluble in ether. It does not explode when heated, and undergoes a slow decomposition, leaving behind metallic silver. As precipitated from the original solution it is lable to retain excess of oxide of silver, and requires to be purified by a second solution in water and reprecipitation with alcohol and ether. 8:005 ... carbonic acid, and 6:685 grains of apophyllate of silver gave I300%_ *,.... 1 Waller. { 5°802 grains of apophyllate of silver gave 2-882 moe silver. { 6-425 grains of apophyllate of silver gave 25395 ... silver. Experiment. Calculation. ES eee it 5 Carbon, . : 32°65 oe 33°22 Gi 96 Hydrogen, 5 2°30 pe 2-08 H, 6 Nitrogen, : =f ote 4:85 N 14 Oxygen, : oe ext 22°33 O; 64 Silver, . : 37°39 37°27 37°52 Ag 108-1 100-00 288-1 The formula is therefore AgO C,, H, NO.. Apophyllate and Nitrate of Silver—When a solution of nitrate of silver is added to one of an alkaline apophyllate, a rather sparingly soluble crystalline salt is deposited, which has been described by WouHLER as the apophyllate of silver. It is, however, a double compound of that salt with nitrate of silver. It explodes violently when heated, and the silver must be determined as chloride. 4-785 ... carbonic acid, and 6-238 grains of the double salt gave 1-800 4) 23.))) “water: CRYSTALLINE CONSTITUENTS OF OPIUM. 373 { 4-522 grains of the double salt gave 2-984 silver. Experiment. Calculation. Carbon, 20:92 20:95 Cr 96 Hydrogen, 3°20 1:30 H, 6 Nitrogen, 6-11 NG 28 Oxygen, LA 24:44 Oren 22 Silver, 49-70 * 47-20 Ag, 216-2 100-00 458-2 This analysis, though far from correct, gives a sufficient approximation to theory to shew that the substance actually is a double compound, and the presence of nitric acid in it can be easily demonstrated. Apophyllate of Ammonia.—When apophyllic acid is digested with ammonia, and the solution evaporated, this salt is left in small prismatic crystals. Of this, a nitrogen determination gave a number too low for the formula of a neutral apo- phyllate, but approximating to it. Apophyllate of Baryta is obtamed by digesting the acid with carbonate of baryta. It is highly soluble in water, and is precipitated by strong alcohol in wart- like crystals. Associated with apophyllic acid, another substance was obtained on one occa- sion in small quantity. It occurs in the form of yellow needle-shaped crystals, which have an acid reaction and are readily soluble in water. They fuse on the application of heat into a yellow fluid, which solidifies on cooling into a crystalline mass. Its analysis gave these results :— carbonic acid, and water. 4°857 grains, dried at 212°, gave , 10:907 1-723 { 4-755 grains, dried at 212°, gave 3°155 platinochloride of ammonium. Experiment, Calculation. Carbon, 61:24 60°85 CEANQNG Hydrogen, 3°94 3°66 lee 13 Nitrogen, 4:16 3°94 N 14 Oxygen, 30°66 31:55 Oo 62 100-00 100-00 355 The formula approximating most nearly to these numbers is C,, H i WOE but I have been unable, from want of material, to confirm them by additional analyses or determinations of atomic weight. On another occasion, a substance was obtained which presented no marked differences from the last, but which contained 55:80 of carbon and 3:94 of hydro- gen. There was not a sufficient quantity for a nitrogen determination. These matters will require a further investigation, and I only refer to them here for the 374 DR ANDERSON’S RESEARCHES ON SOME OF THE purpose of indicating the great complexity of the decomposition which nitric acid produces. When the solution containing alcohol and ether, from which the apophyllic acid has been precipitated, is distilled, a syrupy residue of a more or less dark- brown colour is left, which, on the addition of caustic potass, immediately evolves the odour of a volatile base. In order to obtain this substance a considerable excess of potass was employed and the liquid distilled. A highly alkaline fluid passed into the receiver which gave abundant fumes with hydrochloric acid, and rapidly restored the blue of reddened litmus. In this fluid, ammonia and one or two other bases are always present. For the separation of the former the fluid is supersaturated with hydrochloric acid evaporated to dryness, and extracted with absolute alcohol at the boiling temperature. The filtered solution deposits on cooling traces of sal ammoniac, which are dissolved even in absolute alcohol. The alcohol, on distillation, leaves a salt in fine scales, which gives, with bichloride of platinum, a yellow precipitate soluble in boiling water, and deposited, on cooling, in fine golden-yellow scales, and sometimes needles. 9-375 grains of platinum salt, dried at 212°, gave 1-492 ... carbonic acid, and 27098 ... water. ina grains of platinum salt gave 3878 ... platinum. Experiment. Calculation. See ae eee Carbon, ; : 4°34 5°05 C, 1 Hydrogen, . ; 2-48 2:52 i, 6 Nitrogen, : ; eee 5°93 N 14 Chlorine, . : =H 44-89 Cl, 106-5 Platinum, . : 41-81 41-61 Pi 98:7 100-00 237°2 These results correspond with the formula C, H, N HCl Pt Cl,, and indicate the presence of methylamine. In another experiment a platinum salt was obtained which gave,— 2°615 ... carbonic acid, and 9-075 grains of platinum salt gave 2098 aa. 9 Gwaiter. { 8-475 grains of platinum salt gave 3°360 ... platinum. Experiment. Calculation. i Carbon, b ‘ 7°84 9-55 GC; 24 Hydrogen, . : 2°84 2°78 Lala 8 Nitrogen, . : Ai 5-99 N 14 Chlorine, . ‘ Aaa 42°39 Cl, 106-5 Platnum, . : 39-64 39-29 Pt 98-7 100-00 251-2 CRYSTALLINE CONSTITUENTS OF OPIUM. 375 I have placed these results in juxtaposition with the calculated numbers of ethylamine for the purpose of shewing that it consisted of a mixture of the pla- tinum salts of that base and of methylamine. The presence of the latter base was also determined, in this case, by dissolving the salt in water and twice crystallising, when the small quantity obtained gave 40°32 per cent. of platinum, indicating that in this way a separation of the two might have been effected if the quantity of material had been sufficiently large to admit of additional crystallisations. Some observations lead me to suppose that these are not the only bases formed, but that others with much higher atomic weights are occasionally produced. Pt Oe0) oT - yea , a “ py ral * i hal Ps ¥ » « ‘ . ay 7. ‘4 & iy i STi 1 sare aoe 4 ' 7 1 - ‘ . he ‘a : ’ 1 7 ? » - * P : rs as bP AP pay h) & y revi. ues eae (iar ’ erm F a i i iat a P. \ Fide Te ‘ jt i 74 ; } Ee J Hh eens + oath ‘ . 7 * i : , “ 1 ® ha S zi a 4 _ wth » : i F Nolin 4 ' v1 E ’ ¢ @ “as i fie ik » / hes ib Ww ASA ee Beal di ¢ Pt ' "s ‘ 4 9 t% ep io , ee de ee Loh oes oe ” Te } ai i - : Ps ‘ ow a? N a ‘. . 7 mie! ys ’ i [or > Ai, ae Uy, ¥ i Pei G es - | = mn ’ ) , i i da ‘ cas pita Crary XXII.—On a Necessary Correction to the Observed Height of the Barometer de- pending upon the Force of the Wind. By Captain Henry James, R.E., F.R.S., M.R.LA., F.G.S., &e. (Read 15th March 1852.) The oscillations of the barometer during gales of wind must have been noticed soon after the invention of the instrument by TorricELLI 200 years ago. Every observer is familiar with the fact, that the barometric column is continually rising and falling during gales; and we frequently meet such observations as “ Barometer very unsteady,” in Meteorological Registers. In Sir Witi1am ReErp’s work on the Law of Storms, he says, “during the hardest part of the gale (the Bermuda hurricane of 1839) several persons ob- served remarkable oscillations of the mercury in the tubes of the barometers ;” and in a letter which I had the honour to receive from the Astronomer-Royal, Professor Arry, in reply to one from myself on this subject, he says, “ I think (but am not certain) that the depression of the barometer at every gust of a gale of wind is an ordinary phenomenon, without reference to the position of the barometer with regard to the direction of the wind. Many years ago I was in the observatory of Marseilles during the blowing of the Mistral (a wind well known there), and there I saw the drop of the barometer at every gust in great perfection. I do not remember the position of the barometer.” I am not aware that the cause of this unsteadiness of the barometer has been hitherto investigated by any one, or that the amount of the depressions has been shewn to depend upon the force of the wind. My attention was particularly drawn to this subject last December, by observ- ing that during the heavy gale of wind which we had on the 7th and 8th of that month, the barometer was always depressed at each gust of wind, and that, as far as I could judge by the ear, by listening to the rush of the wind round my cottage at Granton, the amount of the depression was in some proportion to the force or velocity of the wind. My cottage, which stands alone on a height overlooking the Forth, is pecu- liarly well situated for investigating this question; and the succession of gales from the south-west which we had during the months of January and February, afforded me the opportunity for following up this inquiry, to confirm my previous impressions, and to give approximately the depression of the barometer corre- sponding to the different amounts of the pressure of the wind. The barometer used in these experiments was an aneroid, which from its being so portable, and requiring no other adjustment than to be laid horizontal, was VOL. XX. PART III. 5K 378 CORRECTION TO BAROMETER FOR FORCE OF WIND. best suited for the purpose.* The wind-gauge was of a very simple construction, and on the same principle as the instrument used for weighing letters, the weight or pressure being indicated by the compression of a spiral spring in a tube. Fig. 1. Lufra Cottage, Grafton, The wood-cut, fig. 1, represents my cottage (~~) and an open summer-house (~~) near it. The table in my room in the cottage, the seat of the summer-house, and the surface of the ground (~) close to the summer-house, are all on the same level ; T could thus very readily compare the indications of the barometer in these three different situations—that is, as sheltered by the cottage, as sheltered by the back only of the open summer-house, and as laid on the ground without any shelter whatever. During calm weather I found that the indications of the barometer were iden- tically the same in all three positions; but that when the wind blew with any considerable force, the barometer in the two sheltered positions, that is, in the cottage and in the summer-house, were depressed as compared with the indica- tions of the instrument on the open ground, and that in the two sheltered posi- tions the depressions were in proportion to the force of the wind; and further, * The correction for temperature to my aneroid between 56° and 92°, is 0025 for every degree of increase or decrease of temperature, but the barometer is more immediately affected by a change of temperature than the enclosed thermometer. CORRECTION TO BAROMETER FOR FORCE OF WIND. 379 that every gust of wind was indicated by a corresponding depression of the baro- meter, whilst the barometer on the open ground remained stationary during all the changes in the amount of pressures of the wind, whether arising from the in- creased force of the gale, or from the intermittent gusts. It was, therefore, obvious that the cause of the depressions of the barometer was owing solely to the screened position of the instrument in the cottage and in the summer-house; and that all barometers in detached houses, or observatories in exposed situations, must be similarly affected ; and that a ship’s barometer, which is always hung in the cabin, and therefore also in a screened position, must be affected in a like manner. The cause of this phenomenon may be explained by the pneumatic experiments made by Hawkesser and Lestiz, and by the hydrodynamic experiments of Brr- NOUILLI and VENTURI, though the former were made to illustrate a different sub- ject from that which is now under investigation.* “ Dr Hauiey sought to account for the depression of the barometer before a storm, to the withdrawing of the vertical pressure of the atmosphere, when borne swiftly along the surface of the globe by a horizontal motion.” —Encyc. Brit. The experiment of HaAwkEsBEE was made with the view of illustrating and supporting the above hypothesis, whilst the experiment of LEsLIz was made with the view of refuting it; but they each serve admirably to explain the cause of the depressions of the barometer in a screened position during a gale of wind. In HaAWKESBEE’s experiment, two barometers are enclosed in boxes which are Fig. 2. connected by a pipe, as shewn in the wood-cut. A globe of compressed air is screwed to a tube leading horizontally into the upper part of one of the boxes, whilst a larger tube is placed opposite to it, for the escape of the air. When the * I am indebted to my friends Professor Kentanp and Professor: Priazz1 Smytu, for drawing my attention to these experiments. 380 CORRECTION TO BAROMETER FOR FORCE OF WIND. cock which confines the compressed air is turned, the air rushes out by the larger tube, drawing with it part of the air which was in the two boxes, and causing a partial vacuum—as is demonstrated by the fall of the barometers in each box. Sir Joun Lesuie’s experiment is of a more simple nature, and will be under- stood at once by reference to the wood-cut. By blowing through a cylinder, to the lower sides of which a glass syphon, partially filled with water, is attached, he found that if the eduction-pipe was larger than the ene through which he blew, that a partial vacuum was formed in the cylinder, as indicated by the rise of the water in the leg of the syphon attached to it; but by reversing the instrument and blowing through the larger tube, he found that the air was compressed in the cylinder, and caused a depres- sion in that jeg of the syphon. In the experiments of Bernourtii and VENTuRI, the rush of a stream of water through a horizontal tube made wide at the end by which the water escapes, is shewn to have the effect of drawing up water through a smaller pipe leading into it. ° In fig. 4. it is shewn that the water is drawn up and carried away by the rush Fig. 4. SSIS SSTSECC—C-_ CT. ''C FT. i SSS SESEEE EERE CORRECTION TO BAROMETER FOR FORCE OF WIND. 381 of water through the larger tube; and, in No. 5, that the water descending ver- tically in the large tube, draws up the water vertically through the smaller. Fig.5. Whilst these experiments illustrate each other, they also serve to illustrate the cause of the depression in the barometer during gales of wind ; for the rush of a stream of wind over and around any house or ship, as shewn in figs. 6 and 7, Fig. 6. Fig, 7. must have the same effect of drawing out the air and producing a partial vacuum VOl.. XX. PART II. 5 L 382 CORRECTION TO BAROMETER FOR FORCE OF WIND. in them, as in the above experiments ; and this view is further confirmed by the fact, that if a window or door exposed to the wind is opened in any room in which there is a barometer, the mercury is raised, shewing that the air is compressed in the room, as it is in Lesuie’s cylinder, when we blow through the larger tube. So also the barometer is elevated by the compression of the air on the windward side of the summer-house, whilst it is depressed on the leeward in proportion to the force of the wind and the intermittent gusts; but the effect in a room, the doors and windows of which are usually closed on the windward side, is to produce a depression. We may also infer, but I know of no experiments to support the opinion, that during gales of wind the barometer would stand at a higher level on the windward side of a hill than on the leeward, the points of observation being at the same altitude. The known discrepancies between the heights deduced from the indications of the barometer during high winds and calms, are, however, most probably due to this cause. Professor DANIELL, indeed, suggests this very question, ‘‘ Whether local cur- rents of air, and those deflections of the wind which are caused by the different directions of different valleys, may not produce various partial adjustments of density which may have an influence upon barometrical measurements ;’ and in the experiments which he made for determining the altitude of Hedley Heath, by observation at different stages of the height, he found an error of 7°5 feet in 157 in the height of the station in a ravine ; he says, “ omitting the second result (the one in the ravine) all the rest are correct, and the third is deficient ex- actly the quantity which is in excess in the second ;” it is, therefore, obvious that the configuration of the ground was the cause of this anomaly. It is much to be regretted that Professor Daniett had not followed up the inquiry; but he concludes his remarks by putting the following question :—‘* What is the effect of wind upon barometrical mensurations? If I had the means of prosecuting these inquiries in the complete manner which the nicety of the subject requires, I would not have suffered them to retain the form of crude speculation.” By a repeated series of comparisons at Granton, I obtained the following results; but I wish them to be considered as merely approximate results, to which I desire to draw the attention of meteorologists, that those who are stationed in countries subject to violent storms and hurricanes, may supply us with the amount of the depressions, corresponding to higher velocities of the wind than I have been able to supply, and that thus the law connecting the amount of depression with the velocity or pressures at different stations may be established. ‘The effect of the wind when blowing from different quarters will also have to be studied, that the amount of the corrections necessary to be applied to the observed height of the barometer at any particular station, when the wind blows from any quarter, may be known. CORRECTION TO BAROMETER FOR FORCE OF WIND. 383 Velocity in Miles Pressure in Pounds Depression per Hour. per Square Foot. in Inches. 14-2 1 ‘010 20-0 2 015 | 24:5 3 -020 28°3 4 “025 31-6 5 ‘030 7 Observed. 34°6 6 035 37°4 7 ‘040 40:0 8 045 42°4 9 -050 44:7 10 055 .61°6 19 ‘100 In this table, I have distinguished the observed depressions corresponding to the observed pressures, and have extended the table, shewing that the depression would be one-tenth of an inch for a pressure of 19 Ib. per square foot, supposing the depressions follow the same law; but I do not assert that they do, and rather think it probable that they do not, with the higher velocities ; but this is a mat- ter for further investigation. It is not, therefore, correct to speak of these depressions as oscillations in the level of the mercury, above and below a sort of mean tidal line; they are simply: caused. by diminished pressure, and the barometer resumes its original position without passing it, when the gale or gust of wind passes away. With a pressure of 2 lb. per square foot during the lulls in a gale, and, with gusts, giving a pressure of from 6 to 7 lb., we find the barometer is ‘015 always below what it should be, and the effect of the gust is indicated by a further depression of ‘035 and -040; so that by the indications of barometer alone, we are able approximately to estimate the additional force of the gust without reference to the anemometer, and by com- paring the readings of the barometer in an exposed and in a sheltered position, we mnay estimate the force of the wind at the time of observation. In applying the correction for the force of the wind, the depression due to the force during the lulls, should be added to the reading of the barometer when at its highest point. Now the corrections hitherto considered absolutely necessary to the readings of the barometer, with the view of having the results in a form strictly com- parable from different places of observation, are, for barometers with cisterns, without zero-points, 1st, For the capillary action of the tube. 2d, For temperature to reduce the readings to what they would be at 32’. 3d, For capacity, depending on the relation of the area of the surface of the mercury in the cistern to the area of that in the tube. And, 4th, For altitude above the level of the sea. Now, if we assume the observed height of the barometer to be 29-500 inches at the temperature of 40°, the size of the tube to be ‘35 inches, and its capacity asth of the cistern, and the neutral point of the instrument at 29-750, the height 384 CORRECTION TO BAROMETER FOR FORCE OF WIND. above the mean level of the sea 25 feet, the wind blowing with a force of 6 Ib. per square foot, the value of the corrections will be, Capillarity, . : : : ? : +°021 Temperature, 2 : : - 3 —°023 Capacity, . : : 3 : : —°007 For altitude, ‘ : : 5 ; +°034 Force of wind, : : : : : +°035 it will thus be seen that the correction for the force of the wind, in the sup- posed case, would be greater than any of those hitherto considered absolutely necessary for a strict comparison, and, consequently, that it is an element which cannot properly be neglected ; but I beg to repeat that I do not give the depres- sions corresponding to the force of the wind as absolutely determined, even for the short range I have observed; and it is possible that in towns and other shel- tered places, the results would be different. My object is to draw the attention of meteorologists to the facts stated, in the hope that by more extended observations we may obtain more accurate data; and it is important that their attention should be drawn to this subject at this time, when I trust we are on the eve of seeing established a uniform system of observation and registry for the world, under the sanction of the several governments, and promulgated by the authority of a congress of the most eminent men in meteorological science, from all parts of the world. The practical importance of the study of meteorology is daily becoming more evident by the results obtained by Mr Reprietp and Colonel Sir W. Rerp from the study of the law of storms, by the results obtained by the wind and current- charts of Lieutenant Maury, the astronomer at Washington, and in the true in- dications, as I believe, which the isothermal lines give of the most accessible route to the open Polar Sea, and the pole itself, as explained by Mr PETERMANN, not to speak of the accurate data which meteorology gives us for understanding the peculiarities of the climates of the different parts of the world, the causes favour- able or otherwise to the health of man, or the necessary conditions for the suc- cessful cultivation of the different products of the earth, or the high interest which must ever attach to the purely scientific branch of this inquiry; but we can never arrive at a full understanding of these important subjects without that combined and uniform system which has been proposed. T cannot terminate these remarks better than by quoting the words of Pro- fessor DaNTELL in “an urgent recommendation to meteorologists to use standard instruments, to observe them with care, and to make all necessary corrections for accidental differences ; and, above all, to keep their tables on the same scheme. Much curious information is dependent upon such an extensive plan of compara- tive observation ; and, without it, the observer does little more than accumulate an overwhelming mass of crude and incorrect materials.” ( 385 ) XXIV. — Defence of the Doctrine of Vital Afinity. By Wii11am PuLTENEY Auison, M.D., &c. &c., Professor of the Practice of Medicine in the University of Edinburgh. (Read 15th March 1852.) Having expressed a decided opinion that there are, in all living bodies, che- mical as well as mechanical phenomena, which, in the present state of our knowledge, ought to be designated as Vital, and referred to the operation of laws, distinct from those that regulate the chemical changes of inanimate matter, and observing that this opinion is controverted, and that the view of the chemical phenomena of life which I have maintained, is rejected as unphilosophical and delusive by two authors of high scientific reputation—Baron Humsoutpr and Dr Dauseny,—and that the judgment of other authors of acknowledged character on this subject is not clearly expressed, and seems to me to involve it in unneces- sary obscurity, I am led to hope that some farther explanations may be of some use in establishing the first principles of a Science which, as it appears to me, has suffered, in several instances, not so much from want of facts, as from hypo- thetical and erroneous inferences, drawn from facts that are already known. When I first undertook, above thirty years ago, to deliver lectures on Phy- siology, I ventured to express an opinion, that “a discovery would be made, connecting the zngesta into the animal body with the nourishment of the different textures, and with the nature of the different excretions, equally important as illustrating the obscure chemical phenomena of the living body, and the intention of the different secretions, as the discovery of the circulation of the blood was, in illustrating the movements going on in its interior, and the use of the organs con- cerned in effecting them.” It did not occur to me, nor do I know that any one had then conjectured, that these chemical phenomena, like the movements of the animal fluids, partook of the nature and formed part of @ circulation, but of one of such extent and complexity, that the atmosphere, the soil, and the vegetable kingdom, furnish the other great links in the circuit, and that all the elements of the ancients, fire, air, earth, and water, are literally and essentially concerned as agents in maintaining it. It appears, however, from the following passage in one of the earlier writings of Sir Humpury Davy, that he was aware of, and had duly reflected on, the most VOL. XX. PART III. 5M 386 PROFESSOR ALISON’S DEFENCE material facts on which this important discovery is founded:—‘“ Nature has catenated together organic beings, and made them mutually dependent on each other for their existence, and all dependent on light. A privation of light would be immediately destructive to organic existence; vegetation would cease; the supply of oxygen gas would be quickly cut off from animals; the lower strata of the atmosphere would become composed of carbonic acid; and perception and volition would exist no longer.” * The following description of the circulation, in which all the matter destined by Nature to the maintenance of organised creation on the earth’s surface is con- tinually engaged, is merely an amplification of the expressions of Dumas; and although part of the statements contained in it are liable to objection, its general import is such as amply to fulfil the expectation of a great discovery which I had expressed. Vegetables, under the influence of light and of a certain temperature, are continually abstracting from the atmosphere, directly or indirectly, a part of its constituents, in the form of water, carbonic acid, a little nitric acid, and ammonia. The radicals of this inorganic matter (matiere brute) are gradually organised in vege- tables, which are a true reducing apparatus, while a part of its oxygen is set free; and, after being formed into organic principles, those radicals are yielded directly or indirectly to animals. This matter is applied, without farther change, to the maintenance of the functions of animal life; particularly it furnishes the condi- tions, and becomes the instrument, of mental acts; after which, as if exhausted by the effort which it has made, it falls again under the influence of oxygen, in the animal body, which is a true apparatus of combustion ; and either before or after the death of the animal structure, returns as inorganic matter, under the name of manure, to the great reservoir from which it came. In this eternal circuit, life is the chief agent, and by these changes it makes itself known; but the matter that is thus employed undergoes only a change of place. I apprehend we must add, that the properties as well as the position of this matter are conti- nually altered and resumed, and that it is the modification which the properties of this matter undergo, in the course of this circulation, which constitutes the pre- cise object of all physical inquiries, both in vegetable and animal physiology, so far as the organic functions of animals are concerned. The final cause of all these changes is already obvious. We know that it has pleased the Author of our being to connect with a world previously existing, and consisting of matter already long endowed with all its physical properties, an in- finite number and variety, and eternal succession, of sensitive creatures, and ulti- mately a race of beings “formed after his own image.” The acts of sensation and thought which characterise these, he has placed in immediate connection * Works, vol. i, p. 106. OF THE DOCTRINE OF VITAL AFFINITY. 387 with that peculiar structure, endowed with still more peculiar properties, to which we give the name of a living Nervous System; and he has established laws, in the execution of which the vegetable as well as the animal kingdom bears its part, according to which infinite varieties and endless successions of nervous systems shall be engendered and supported from a limited quantity of the matter originally contained in the atmosphere surrounding our globe,—shall be nourished, lodged, protected, and enabled to satisfy the wants and to obey the will of their immaterial inhabitants; but all this innovation on the laws regu- lating the matter previously existing on the earth’s surface is only transient. The same portions of matter which are thus employed, whether they pass through vegetable structures only, or minister to the support both of vegetables and ani- mals, are restored unchanged to the reservoir whence they came,—in the latter case more rapidly and frequently, and during the life of the structures thus main- tained,—and are ready to run the same course again when again placed in pre- sence of living beings. Like the figures of snow into which the imagination of Souruey figured the magician Oxsa, breathing the breath of life every morning, that they might people the surrounding wilderness, and charm the solitude of his daughter Lema, they all receive vitality only for their day, and “ ver when night closes, They melt away again ;” and such of them as have served as the habitations of mental acts or feelings then “restore the spirit to Him who gave it.” The provisions for the temporary maintenance, for the protection and comfort, for the sentient and mental enjoy- ments, and the eternal reproduction, of this infinite number and variety of sensi- tive beings, out of a limited quantity of certain chemical elements contained in the earth’s atmosphere,—and for the progressive development of the human mind, as the destined lord of this Creation,—are the great Laws of Life, the investiga- tion of which is the object of this science. The power of perceiving their adapta- tion to their object, and of appreciating the grandeur of the design, is one of the highest privileges of our nature; and without pretending to be qualified to assign the respective merit of the different physiologists, geologists, and chemists, who have illustrated the different parts of this general view of life,—of Cuvier, Dat- TON, Prout, Lizsic, BROoNGNIART, PREvost, Dumas, and Bousineauut, and their numerous friends and followers,—we may all congratulate ourselves on having lived in the age when so much of the designs of Infinite Wisdom for the regula- tion of this world has been made manifest to mankind. But when we inquire a little more minutely into the nature of the changes constituting this great vital circulation, I think it must appear obvious, that the most essential of all are and must be strictly chemical; and it seems to me that the grandeur of the design is not clearly perceived, unless we fix atten- 388 PROFESSOR ALISON’S DEFENCE tion on the alteration of al/ the qualities of matter which are here implied, and shew that the Power which has introduced living beings upon earth has had at its command, and has actually modified, all the laws of nature. The water, car- bonic acid, and ammonia, which form the chief and essential constituents of the ingesta of vegetables, are there thrown into combinations, differing from any which they form, or which can be formed from the elements composing them, in any other circumstances. This is fairly admitted by Dr Dauseny, who says,— “ We are still far from imitating Nature in those processes by which she continues to bring about the wonderful products of organic life, and must admit that, judging from what is yet known, there would seem to be a power residing in living matter, distinct, at least in its effects, from ordinary chemical and physical forces.* Now, before going farther, let us observe how essential to everything living, and how peculiar in its effects (from which alone it is known to us), is this power residing in living matter, and distinct from ordinary chemical forces, but which Dr Davupeny must regard as producing chemical effects, because he himself ascribes to it the formation of “the wonderful products of organic life.” Let us remember, that the very first requisite to the commencement of this great vital circulation, the decomposition of the carbonic acid of the atmosphere, fixing the carbon which is to serve as the basis of all organised structures, and setting free the oxygen, producing therefore a change which is unquestionably both peculiar and chemical, ‘‘is done by a power,” as stated by LieBiG, “ surpassing that of the strongest galvanic battery, to which the strongest chemical action cannot be com- pared.” Next, let us observe, that the compounds formed in living bodies under the influence of this acknowledged power, of which the first indications are so striking, possess peculiarities (which I formerly noticed) quite sufficient to distin- guish them from all compounds formed by chemical affinities, under any other circumstances in nature. They have a uniform complexity of constitution, even in the minutest particles, not seen in inorganic solids; they assume perfectly de- finite forms, varying, not according to their chemical constitution, but according to their living progenitors, or the particles of living matter with which they come in contact. These forms, as long as they belong to living structures, never be- come crystalline; although the same elements, after escaping from the imme- diate contact and influence of living structures, even within the excretory ducts by which they are to be thrown out of the body, fall into compounds which take the crystalline arrangement. Above all, these organic compounds, thus influenced by place, are equally liable to an influence of time. They are all of transient duration, and particularly in the case of animals, we know that at the same time, at the same points, and in presence of the same agents, in which the * On the Atomic Theory, p. 370. OF THE DOCTRINE OF VITAL AFFINITY. 389 matter originally introduced from vegetables is applied to the nutritive assimila- tion and formation of the living textures, other portions of the same elements, previously used in the same process, are continually yielding to the influence, previously resisted, of the oxygen of the air, and are forming another set of com- pounds, by the process of destructive assimilation, which are ready to take the form of crystals; which either already possess, or rapidly tend to, the composi- tion of the inorganic matter whence all these compounds originate ;—which are poisonous if retained in the body, and for which, therefore, outlets are provided in the organs of excretion, so as to justify the striking expression of Cuvisrr, that all living animal matter, although the depository of force which will compel other matter to follow the same course as itself, will soon occupy its own place no longer. This is a series of chemical changes quite distinct from anything seen in any other circumstances of Nature. And farther, we know, in regard to the power exciting these, that it is obedient to certain laws of animal life, to which nothing analogous is seen in other chemical operations; nutrition and secretion being liable to sudden and important change, as living movements are, by living changes in nervous matter, ¢. g., by those which attend certain acts of mind; and farther, every such action being liable to diminution or exhaustion by the degree in which’ it is itself exercised. It will be observed, that all these are peculiarities in the chemical nature and constitution, even of the minutest particles of all living structures; and that without reference to them nothing living can be characterised. These phenomena are just as distinctly peculiar to living bodies, and characteristic of their living state, as the contraction of muscles, whether produced by irritations of their own fibres or of the nerves entering them; and they are muc/: more general in all classes of living beings. If anything in the economy of living beings demands explanation, or is deserving of being made the object of scientific research, it must be these, their most essential characteristics. If they are not of such importance as to demand special investigation,—if it is only the movements of the particles concerned either in the development of vegetables, or the varied functions of animals, that we ought to regard as peculiar to living bodies,—then Physiology, so far as these properties of living bodies are concerned, has no claim to the title of a separate science, it is only a branch of Chemistry. But it is just as probable, a priori, that the laws of chemistry should undergo a modification in living bodies, as that the laws of motion should be made subordinate in certain parts of living animals, to the vital property of Irritability of muscles, as explained by Hauer; and the very peculiar changes which are observed in tracing the course of the elements of water, carbonic acid, and ammonia, which are absorbed by vegetables, until they pass out in the form of water, carbonic acid, and am- monia (or in compounds immediately resolvable into them), in the excretions of VOL. XX. PART Il. DN 390 PROFESSOR ALISON’S DEFENCE animals, and resume their office as manures, afford a manifest presumption that such modification takes place. The chief consideration which seems to have prevented Dr Daupeny from acknowledging that the power which he himself supposes to exist in living beings, and to regulate chemical changes there, is deserving of a separate name and a separate inquiry, is thus stated :—“ If it is asserted that this power is to be directly ascribed to the vital principle itself, we pause for further information.” Here it seems to me manifest, that there is a misapprehension as to the correct meaning of words, and one which may be traced in many other speculations in the elementary departments of physiology,—investing the term Vital Principle with a meaning much more mysterious and formidable than is needful. Accord- ing to the only idea which I can form of what is properly termed the vital prin- ciple, Dr DausBeny has already admitted, in the words above quoted from him, that, so far as we can yet see, we must regard the vital principle as concerned in forming the “wonderful products of organic life; because he says, that these result from a power residing in living matter, producing physical effects, yet distinct in its effects from ordinary chemical and physical forces. The only correct way of defining what we call Vitality, or the vital principle. as I have always maintained, and as I think the best authorities now admit, is this :—First, we describe what we call living beings. They are those, as Cuvier states, which originate by a process of generation, which we can describe,—are maintained by a process of growth and nutrition, which we can describe,—and ter- minate by death and decomposition, which we can describe. Then, having thus dis- criminated those bodies which we call living, we say that, in so far as we can satisfy ourselves, that any part of the phenomena which they present are inexplicable by, and inconsistent with, the laws regulating the changes of any other matter, we call them effects of the vital principle, or vitality; and that is our definition of those terms. Those who object to the use of the substantive noun Vitality, or the Vital Principle, as a general expression for such phenomena, constantly use the adjective Vital, or Living, which conveys the very same meaning, and can be defined, as I apprehend, in no other way. ‘The real efficient cause of these, as of all other phenomena in nature, is the Divine Will, and is inscrutable; but we know, that in all departments of Nature, this all-powerful cause acts according to laws which we can understand, and the discovery and application of which is the object of all science. When we see that any phenomena in nature take place according to the same law as others more familiar, we are said to explain them, or to assign their physical cause; but until that is clearly ascertained, we obey the dictates of science in declining to arrange them along with those de- pending on any law otherwise known to us, and endeavouring to apply the me- thod of induction to themselves,—and to any such isolated phenomena as may OF THE DOCTRINE OF VITAL AFFINITY. 391 seem analogous to them,—so as to ascertain laws peculiar to this set of phe- nomena. Dr Davseny refers also to a passage in the writings of Dr Bostock, in which he speaks of reference to the operation of the vital principle, or to any vital affi- nities, “‘as one of those delusive attempts to substitute words for ideas, which have so much tended to retard physiological science;” or, as it may be more simply expressed, as only a reference to an occult cause, or a confession of ignorance on the subject. On this I would observe, that if, by merely using the term Vital Affinity, we were to suppose that we offered a sufficient explanation of any pheno- mena, I would agree with Dr Bosrocx. But I use the term only as defining the department of human knowledge to which these phenomena are to be refer- red, and in which the explanation of them (7. ¢., the law according to which they take place), is to be found; and thus using it, I maintain that there is nothing delusive or unscientific in thus limiting and fixing the object of our inquiries. The investigation of the law or laws by which vital affinities are distinguished from the affinities of inorganic matter, is a subsequent inquiry, in which we may add, that some progress has been made. It is something, for example, to say that vital affinities shew themselves in living beings in two distinct ways; jirst, by the formation of new compounds, found nowhere else in nature; secondly, by the selection and attraction of these compounds, at different points, out of a very complex fluid, so as to form organised structures ; and to point out the circum- stances in which these powers act. It is something to say, with Dr Prout (if that principle is to be held as established), that in the formation of new com- pounds in living bodies, the elements employed by nature are not subjected to any new affinities, but only hindered from obeying certain of those which actuate them in other circumstances; while others are allowed to act. It is some- thing to say, that the compounds thus formed perish many times during the life of the structure in which they are contained,—-the more rapidly as their vital pro- perties have been more energetically exercised; and by perishing furnish the poi- sonous matter which continually circulates in every living animal, and for the expulsion of which the organs of excretion are provided. It is something to say that Carbon, fixed from the atmosphere by plants, is the substratum of all the organic compounds of which living beings are composed ; and that Oxygen, taken in by the lungs or gills of animals, is the great agent in forming the excretions by which they are constantly worn down. And I think we define and limit all these inquiries satisfactorily, when we say, that we seek to ascertain the laws, according to which ordinary chemical affinities are modified in living bodies; or according to which that power acts, which, by Dr Dauseny’s own admission, resides in living bodies, and produces chemical effects, ‘ but is distinct from or- dinary chemical forces.” Dr Davseny goes on to say, that Nature has at her command an apparatus 392 PROFESSOR ALISON’S DEFENCE of a more refined and subtle description than any which we can command, and may therefore accomplish effects by purely chemical and physical agency, which may for ever lie beyond the reach of the coarser manipulations of art; and here he refers to HumBoip?, who says, that, as we do not understand all the conditions under which ordinary chemical and physical forces act in living beings, we are not entitled to assert that they may not produce all the chemical changes that we seein them : to what conditions he here alludes does not appear, but he gives this as a reason for renouncing, or, at least, expressing doubts as to the theory of vital affinity, which he had formerly espoused, and illustrated by an allegory under the name of the Rhodian Genius. Dr DAuBENY says more precisely, that “‘ the peculiar structure of parts, arising out of the Movements induced by a vital principle, may be found competent to bring about these phenomena in question, and that it is incumbent on us to in- vestigate to the full the extent to which such physical causes can be supposed to operate, before pronouncing whether there may not, after all, be some residual phenomenon, inexplicable by the common principles of science, and which we must, therefore, refer to vital affinity.” But even in regard to movements, from his ex- pressions at p. 379, he does not seem to admit that any others are to be ascribed to the vital principle, than those which result from Contractility. In thus admitting that the movements which take place in living animals, at least those which can be referred to contraction of solids, arise out of the vital principle (which, I apprehend, means only that they are an ultimate fact,—so far as yet known exemplified in no other department of nature); and in as- cribing to the peculiarity of those movements the peculiar structure of living parts, and through the intervention of that structure the peculiar chemical changes of living beings, Dr DauBEny has stated what I believe to be the general idea of those physiologists who reject the doctrine of vital affinity. They think that having allowed that movements, and particularly contractions of living solids, are truly vital phenomena, they have furnished a possible explanation of all chemical changes which seem peculiar to life, and that they are entitled to throw on us the burden of disproving this theory, before they can be called on to admit any such principle as vital affinity modifying chemical laws in the living body. To this I reply, jist, that this theory in explanation of the chemical pheno- mena of life is distinctly znadequate. I do not think it can be more distinctly stated, or more plausibly supported, than it was by the late Dr Murray, in treat- ing of Secretion, who, at the same time, however, distinctly admitted that it was ““ hypothesis supported by little direct proof. The cause of production of the new combinations which constitute secretion,” he says, “‘ may be the simple approxima- tion of the elements which constitute the blood. That fiuid is propelled byt he vis a tergo into canals of the most astonishing minuteness, the diameters of which are OF THE DOCTRINE OF VITAL AFFINITY. 393 still farther diminished from their alternate contraction from the stimulus of the blood. There can be no doubt that in compounds the force of attraction subsist- ing among their constituent particles, is modified by the distance at which these are placed; and in compounds especially, which consist of four or more prin- ciples, the slightest -alteration in their relative situation is sufficient to change entirely their existing attraction, and induce new combinations. The blood is a compound of this kind ; its ultimate principles, too, are capable of entering into an innumerable variety of combinations with each other; we may conceive, therefore, that when subjected to the contraction of the extremely minute vessels through which it is forced to circulate, the relative position of its elements will be changed, and new combinations formed. And if we suppose a fluid thus passing through tubes of different diameters, and undergoing successive decompositions, we may easily conceive that very different products may be formed from the same original compound. This affords a very simple view of the nature of Secre- tion. No complicated apparatus is requisite; all that is necessary being the pro- pulsion of the blood through extremely minute vessels capable of contraction. And it is easy to account for the variations to which secretion is liable, as the contraction of the vessels must vary from variations in the state of their irritabi- © lity and of the stimuli acting on them.” [Murray's System of Chemistry, vol. iv., p. 518.] In regard to the Nutrition of solids, Dr Murray says merely that they appear to attract immediately from the blood the materials which it contains ready formed, as there is probably ‘“‘no solid in the animal body, of which the imme- diate principles do not exist in the blood.” [J0id., p. 516.] But I need hardly say that subsequent researches have not only completely demonstrated the insuf- ficiency of this explanation, but have shewn that the cause of the difference of products formed apparently from the same blood must be essentially different from that here assigned; and I would say farther, have shewn that the pecu- liarity of the compounds formed in living bodies cannot be reasonably ascribed to any modification of those movements of fluids, which Dr Daupeny regards as the only results of the vital principle. To shew this, I need not go into the question of the mode of action of arteries on the blood, or the portion of the changes essen- tial to secretion, which takes place in cells, exterior to vessels, and, of course, can- not be ascribed merely to the pressure to which the blood passing along the vessels may have been subjected; which had certainly been misapprehended by Murray, as by most other physiologists of that day. It is sufficient to quote a brief state- ment from Cuvier, which seems to me quite conclusive as to the question, whether difference of secreted fluids in the animal economy can be ascribed to difference in the structure of, and therefore of the movement of the blood through, the organs in which they appear. “The same organ,” he says, 7.¢., the organ secreting the same fluid from the blood, “ presents in different classes of animals, sometimes in the same class, perfectly distinct structures. This is true of the VOL. XX. PART III. 50 394 PROFESSOR ALISON’S DEFENCE salivary glands, of the testes, even of the liver, of which the organisation is the most uniform, and likewise of the kidneys.” “It would be interesting also,” he adds, ‘‘to compare the secreting organs with their secreted fluids, and observe whether the organs that have a similar structure afford similar products. But experience will sanction no such theory. Nothing, for example, can be more various than the matter furnished by ‘crypts’ in different animals, from a simple mucus to the most odoriferous compounds.” “The simplest secreting organs,” he observes elsewhere, “are in insects, where they are merely tubes which float in the general nourishing fluid, which is in contact with their outer surface, while their inner surface contains the secreted fluid. Secretion there can be only a kind of filtration; but how different from that which can take place where there is no life, through ‘an inorganic solid!” (Lecons sur? Anat. Comp. Lect. xxx., Art. 1.) But farther, not only is the complex vascular structure and the varying pres- sure from contracting solids, which was regarded by Murray as the main cause of the formation of new compounds out of the blood, shewn by the examination of other animals, to be quite unnecessary for that purpose; but we now know, that where these conditions exist, that formation is never effected—the most com- pound fluids of the animal economy, which appear in the different glands, being really not formed there, but in the course of circulation, and appearing in the blood or in other parts of the body when the organs where they usually appear have been extirpated, or rendered useless by disease; that is, when the cause to which their origin is here ascribed has been absolutely withdrawn. The mere selection and attraction out of the blood at different places, of dif- ferent compounds already existing and circulating in it, is certainly the chief, and, according to many, and particularly according to Dr Dauseny himself, the sole office. performed by any parts 9f animals by which any new organic products are exhibited; and the office of forming those organic compounds, the origin of which is the great chemical change effected by living beings, is performed by no organ capable of exerting a varying power of contraction and pressure, but simply by the cells of vegetables, where the fluid introduced from without is usually not con- veyed in vessels at all, and is clearly not subjected to any such pressure from contracting solids, as is exerted on the blood in most animals; nor to any such peculiar cause of movement as can be ascribed to the living property of contrac- tility, the only one which Dr Davuseny admits to be strictly vital. I have formerly stated, and notwithstanding the opposition of Dr DauBeny and others, still think, that the judgment of various authors on the respective offices of vegetables and animals as to vital affinities,—the supposition that no organic compound can be formed in animals, and that their office is merely the selection and appropriation of the compounds formed in vegetables, and after- wards the destructive assimilation by which these are restored, through the excre- tions, to the inorganic world, is too hasty. It appears from the experiments of OF THE DOCTRINE OF VITAL AFFINITY. 395 Liesic himself, that the infusory animals decompose the carbonic acid of the air, and exhale oxygen in like manner as vegetables ; and the evidence of the forma- tion of oily out of saccharine or amylaceous matters in many animals appears to be unequivocal. The two distinct powers, therefore, of forming and of jixing, or appropriating the organic compounds, are not so accurately divided between the vegetable and animal world as has been thought. But the more that any physio- logist is convinced, as Dr Dauseny is, that the formation of organic compounds is peculiar to vegetables, certainly the less reason can he have for supposing that this great change can be due to any mechanical movements, on the principle of contraction and impulse, arising out of the vital principle; the provisions for such movements being so striking a part of the economy of animals, and never having been proved to exist at all in vegetables. But, secondly, In maintaining the scientific correctness of the doctrine of vital affinity, as I have defined it, I think it quite unnecessary to go into these details. I maintain that the objections made to this doctrine, both by Dav- BENY and Humspouprt, are logically incorrect, because, in dealing with a set of facts so extraordinary, so important and characteristic as the chemical changes of living beings have been shewn:to be, they hold it to be incumbent on us to prove the negative proposition, that these may not ultimately be referred to those laws which regulate the chemical changes in dead matter, which may be acting under conditions not yet known, and of which they say nothing. The rule of sound logic is,—“ afirmantibus incumbit probatio.” It is admitted on all hands, that the phenomena of life in general are so peculiar and important as to be properly ranked together as a separate science; and we have shewn that of these phenomena, the most essential and characteristic are certain chemical changes, which are admitted to be so distinct from any that can be observed any- where else in nature as to “indicate the existence of a power distinct from any simply chemical or physical forces.” It is clearly incumbent on those who main- tain that, nevertheless, these ordinary chemical forces, acting under conditions not yet understood, may be found adequate to this explanation, to give evidence in the way of observation and experiment of this proposition, otherwise their doctrine is only a hypothesis. If the subject is not thought worthy of scientific inquiry at all, then Physiology is not a separate science. If it is regarded asa separate science, of equal interest and importance as any other, then it is the duty of physiologists, acting on the strict method of induction,—because ascend- ing from facts to principles, instead of descending from principles to facts,—to examine these individual phenomena themselves, arrange and classify them as they present themselves in the different classes of living beings, and consider how far laws deduced from the observation of dead matter can go in the explanation of them ; but wherever we find that there is a difficulty in that explanation,—in- 396 PROFESSOR ALISON’S DEFENCE stead of straining the principles of other sciences formerly ascertained, to make them include phenomena admitted to be distinct from any of those to which they have formerly been applied,—it becomes our duty to attempt the investigation and determination of laws peculiar to this department of nature. If these laws shall ultimately resolve themselves into any previously known and more general laws of nature, science will be simplified, and a great advance made ; but it is assuredly mistaking the right order of inquiry to assert that, because such simpli- jication may ultimately be effected, therefore we are now to decline giving these phenomena an appropriate name, and endeavouring to reduce them to general laws by an induction limited to this department of nature itself. This is the principle which has been successfully followed in other departments of science. Speculations have been hazarded as to the cause of the principle of Gravitation itself. I recollect that the late Mr PLAyrair used to say a few words in favour of one of these, the theory of Ultra Mundane Particles continually moving in all directions through all space, although not making themselves known to the human senses; which, if admitted, would resolve the principle of gravitation into that of motion communicated by impulse. But no one will main- tain that it was incumbent on Nrewron to prove, that this theory would not ex- plain the phenomena, before asserting the principle of gravitation, and determin- ing, by observation and experiment, the laws according to which that principle acts, or by which the phenomena coming under that head are regulated. It is, indeed, observed in many departments of science, that one great difficulty in the early inquiries is, to keep the inquirers from deviating into lines of research which they may think analogous to their own, and applying prematurely principles which have been established by an induction of very different facts. This is the error which Dr Rem made an object of special remark when speaking of the ‘‘enumeration of the original powers and laws of our mental constitution.” ‘Success in an inquiry of this kind it is not in human nature to command ; but perhaps it is possible, by caution and humility, to avoid error or delusion. The labyrinth may be too intricate to be traced through all its windings; but if we stop when we can trace it no farther, and secure the ground we have gained, there is no harm done;-a quicker eye may in time trace it further.” —(Hamulton’s edition of Reid, p. 40.) In physiology itself, it is a similarly just and comprehensive obser- vation of Mr Lawrence, “ that although organised bodies are subjected in many respects to physical laws, yet, as regards their own peculiar phenomena, the refer- ence to gravity, to attraction, to chemical affinity, to electricity or galvanism, can only serve to perpetuate false notions in physiology, and to draw us away from the proper point of view in which the nature of living phenomena, and the properties of living beings, ought to be considered.” —(Zwo Introductory Lectures, p. 161.) It was the same idea, not, perhaps, so accurately conceived, but more graphically announced, which prompted Dr Witt1am HunTer’s remark, in com- OF THE DOCTRINE OF VITAL AFFINITY. 397 mencing the subject of Digestion in his anatomical lectures. “Some tell you that we have here a fermenting vat, and some tell you we have a stewpan, but I tell you we have a stomach.” And when we remember how little has been done to elucidate the function of digestion by likening the changes in the stomach either to fermentation or to chemical solution (although both are principles which appear to act to a certain extent), and how much comparative anatomists and physiologists have done, by extending their inquiries into other classes of ani- mals, and studying in all, the changes which commence in the stomach and ter- minate in the different organs of excretion—to establish laws peculiar to physio- logy, under which so many forms of structure, and so many vital operations may be arranged,—we can hardly fail to admit that this distinction was wisely drawn. Indeed, the whole science of Morphology, or of the analogies of the structures formed by living action—as it is certainly a branch of knowledge strictly sui generis—may be said to furnish an illustration of the advantage of keeping the investigation of the laws of living action entirely separate from all other scientific inquiries. But the authority to which I would wish particularly to refer, as sanctioning and authorising the view of the chemical phenomena of the living body which I here advocate, is that of Hatter, whose great achievement in physiology was simply that of establishing the strictly vital nature, and laying down the most important laws, of the living property of Contractility; the only property con- cerned in organic life which is expressly admitted by Dr Dauseny to be truly vital, but to the assertion of which the mechanical physiologists of that age were opposed, on grounds, as it appears to me, exactly analogous to those on which the doctrine of vital affinity is now opposed, because 7 had not been proved how far the mechanical properties of matter were, or were not, adequate to explain the move- ments of living bodies. « As all physiology,” says Harr, “involves a history of motions by which the animal machine is agitated, and as all motions have their own laws, we can perceive why, about the end of last century, the principles of hydraulics, hydro- statics, and mechanics, were transferred to physiology. There is a difficulty in this matter, however, and if we reckon up all the good, and all the evil, which has been done to physiology, by the cultivation of these sciences, some may think that we might gladly renounce all the good, for the sake of escaping the evil. There are certainly many things in the animal economy very different from the effects of ordinary mechanical laws; great movements excited by slight causes ; the flow of fluids hardly diminished by causes which, according to established mechanical laws, ought to arrest them entirely ; motions excited by unperceived causes ; vigorous movements produced by the contraction of weak fibres, &c. ; from which I do not infer, that simply physical laws are to be repudiated in phy- siology ; but this I maintain, that they are never to be transferred to the explana- VOL. XX. PART III. 5P 398 PROFESSOR ALISON’S DEFENCE tion of phenomena of living bodies, unless their application 4 as confirmed by experi- ment.” —(Phys. Prin., p. 6.) It might have been perfectly fairly argued at that time, that physiologists did not understand all the conditions, under which the laws of mechanics and of hy- draulics (admitted to have a certain influence) act in a living body, and that until it was ascertained that these would not suffice for the explanation,—that there was some residual phenomenon of life not capable of being so explained,—the exposition of any laws of motion peculiar to living bodies was premature. But Hauer did not think it incumbent on him to prove this negative proposition, before announcing the laws of muscular irritability as distinguished from any merely physical cause of motion; and I believe we shall all now admit, that if he had thought this incumbent on him, the greatest impulse which the science of physiology received during the last century, would have been long, and perhaps indefinitely, post- poned. Fortified by these authorities, as well as by some formerly quoted, I again assert, that the only truly scientific view to be taken of this department of Phy- siology is, that its object is to ascertain, by the method of induction, to use again the expressions of Professor WHEWELL, “ when, and in what manner and degree, chemical as well as mechanical agencies are modified, overruled, or counteracted in living bodies, by agencies which must be hyper-chemical as well as hyper- mechanical ;” and I farther maintain, that the term Vital Affinity is as accurate a term as can be employed as a general expression for these agencies; that, like all other general principles in nature, we may expect it to act according to general laws, and that several of these laws, to which I have referred in this and former papers, are already ascertained, at least, in so far as to shew that the subject is one of legitimate inquiry. I am aware that it may be still said that this dispute is only a verbal one, and can have no practical or even strictly scientific application. But in answer to this I would observe, that so long as we adhere to the supposition, that there is nothing truly vital or peculiar to living bodies in their economy (as regards their organic functions), except motion, and that motion derived from contraction of solids and impulse, the notions that we can form of the nature of these functions in health, and of the deviations from that state in disease, must necessarily be erro- neous, because we shall always be looking in the wrong direction for the cause of these phenomena; and that at this precise point the most plausible medical theories of the last, and even of the present age, have gone astray. This, I think,, is sufficiently illustrated by the example already given, of the ingenuity of Dr Murray wasted in the invention and defence of the hypothesis which ascribed the secretions of animals to varying impulse on their fluids from contracting solids; and I shall only add a single illustration of the same kind drawn from the science of Pathology, and from the most fundamental of all inquiries in it, OF THE DOCTRINE OF VITAL AFFINITY. 399 the theory of Inflammation. It being sufficiently obvious, that inflammation is strictly a vital process, and one in which the flow of blood through the affected part is materially changed, it was naturally supposed that the vital powers by which that movement is affected in the natural state, must be those which undergo modification in this diseased state; when, therefore, it was believed that the only truly vital power concerned in the organic functions of the living body is one form or other of contractility, the only explanations of the phenomena of inflammation that were attempted turned on the possible modifications of the contractile powers of vessels, as influenced by their contents or through their nerves. But I believe it is now pretty generally admitted, that all this was nearly lost labour; and if phy- siologists had earlier seen that the most fundamental and characteristic of all strictly vital actions,—those by which nutrition and secretion are effected, and which have always more or less of a chemical character, take place, not in vessels, but in cells, independently of any contractions of the organs containing the fluids —that they are most obvious in those living beings which have neither heart, arteries, nor veins ;—and that, as occurring in the higher animals, they are carried en partly in the interior of the fluids contained in the vessels, and partly in the matter that has exuded from the vessels and lies exterior to them,—they would — sooner have perceived, that all the changes of action of the organs of circulation, heart, arteries, or capillaries, in the case of inflammation, are to be regarded as effects of the truly essential, fundamental, and strictly vital changes, which take place in the fluids of an inflamed part, and in the relation between the fluids and solids there; 7.¢. in matter which is apparently at rest, and much of which, being outside the vessels of the part, has escaped from all influence of the vital contractions either of heart or vessels. I do not say that we have a satisfactory explanation of inflammation merely by taking this view of it,—regarding it as fundamentally a perversion of nutrition or secretion, and the circulation as only secondarily affected; but I maintain that in this way we can understand, and so far explain, by reference to more general facts, known in the history of the sound as well as the diseased body, many facts as to it, which we never understand at all so long as we think only of altered action of vessels,—but which are easily arranged along with others previously known, when we regard them only as indications of changes in vital actions that are con- stantly going on in living fluids, both those contained in vessels, and those recently delivered from them, into the cellular structure of living parts. Thus, we can perceive how inflammation should spread, asit does, not along the course of vessels, but from a point as from a centre,—not only along continuous surfaces, but to con- tiguous surfaces lying beside them, but supplied from other vessels, the larger branches of which frequently undergo little or no change in the process ; thus we can perceive how the amount of effusions and exudations from the blood in in- flamed parts should bear no fixed proportion to any action of the heart, or of 400 DEFENCE OF THE DOCTRINE OF VITAL AFFINITY. any contractile organ by which it is propelled into those parts,—the most copious effusions sometimes taking place when the impulse of the blood, passing along the larger arteries, is distinctly feebler than natural during the whole disease; thus we can understand how the blood passing through an inflamed part should undergo a change in its own constituents, and how the fluid, which escapes from the vessels there, should possess a peculiar composition, and be peculiarly fitted for certain vital actions, and thereby for repairing some of the injuries resulting from the inflammation itself. Thus, also, we can understand and admit a prin- ciple which has been confidently disputed, but which I have long thought, and now find to be maintained, as fairly established, viz., that matter exuding asa re- sult of simple inflammation, may afterwards degenerate, according to the state of the constitution, into various forms of heterologous deposit. (See e.g. Copland and Quain, in Medico-Chirurgical Transactions, vol. xxxiii., p. 144.) Still more, if we regard it, as I think we may, as an established fact, that the vital properties of living fluids, as well as solids, are of temporary duration only, and are subject to the general law, of increased action being followed by diminished action, or accelerated loss of vitality, we can understand how the most important con- sequences of inflammation, both beneficial and injurious, should be produced,—how the matter that was concerned in it being peculiarly excited, and, therefore, quickly rendered effete, should be peculiarly liable to Absorption, which we know to be the agent by which its injurious effects are chiefly effaced,—how the increased absorption should, under certain circumstances, extending to the ad- joining sound parts, effect that destruction of texture which we call Ulceration ; and how, in other circumstances, either of peculiar violence of the inflammation, or depressed vitality of the organ inflamed, this form of diseased action should, by the established laws of vitality, lead to premature death of the diseased part, 7. ¢., either to partial Sloughing or more extensive Gangrene. All these are facts of the highest practical importance, of which we have explanations so far satisfactory, on the strict principles of induction, when we look to the changes that take place in inflamed parts in those living actions which I have referred to the heads of Vital Attractions and Repulsions, and Vital Affinities ; but I will ven- ture to say, that we never shall have any explanation of them consistent with the supposition, that the contractions of living solids are the only changes in organic life which are truly vital, 2. ¢., dependent on laws essentially distinct from those that regulate the changes of inorganic matter. ( 401 ) XXV.—On Meconic Acid, and some of its Derivatives. By Mr Henry How, Assistant to Dr ANDERson. Communicated by Dr T. ANDERsoN. (Read 5th January 1852.) In a paper on Comenic Acid, read before this Society in April of last year, and since honoured with a place in its Transactions, I mentioned my being engaged in an investigation on Meconic Acid; the details of the experiments referred to form the matter of the present communication. My object in undertaking this subject was to ascertain if products correspond- ing to those described as derived from comenic acid were formed under similar circumstances in the case of meconic acid. I also thought it probable, that as the former is itself a derivative of the latter, the changes undergone by meconic acid in some reactions, would be found to result in substances apparently the imme- diate derivatives of comenic acid. This remark refers to the action of heat on | meconate of ammonia; and it will be seen that the expectation was realised. A similar result was found in other instances, where it had not been anticipated. The experiments I am about to detail were performed in the laboratory of Dr T. ANDERSON. The process employed for the purification of meconic acid was that given by Grecory in his “Outlines,” excepting that ammonia was substituted for potass as the solvent of the crude acid. As in the case of comenic acid the vola- tile alkali was preferred, because, although in both cases a great deal of acid remains in the highly coloured mother liquors, from which it can only be reco- vered in a pure state at the expense of much time and labour, it was found that if ammonia was used, the whole of the mother liquors could be employed under circumstances where their impure state did not affect the results of the experi- ment. A considerable saving was thus effected. This point is of some import- ance, because the numerous solutions requisite for the purification of meconic acid occasion so much loss, that seldom much more than a fourth part of the weight of the crude acid started from, is obtained as the result of a careful pre- paration. The process consists in dissolving crude meconic acid in hot water by aid of caustic ammonia. The crude acid is obtained from meconate of lime by treating it three successive times with twenty parts boiling water and three parts strong muriatic acid. The mixture of the acid so obtained, and about twice its weight of water, is kept hot in a water-bath and constantly agitated, till, by the addition of caustic ammonia, solution is complete ; the salt formed is extremely soluble in hot water, and the fluid cools to a solid mass. The black mother liquor is squeezed VOL. XX. PART III. 2 Q 402 MR HENRY HOW ON MECONIC ACID, out by strong pressure, and the cake of salt redissolved twice or thrice in as smali a quantity of boiling water as is found sufficient, the mother liquors being always pressed from the crystallised salt. By proceeding in this manner a perfectly white salt is obtained, from whose solution in hot water an excess of strong hy- drochloric acid throws down the meconic acid in colourless brilliant scales; these require but a little washing with cold water, and one resolution in the smallest pos- sible quantity of hot water, to be obtained on cooling of the fluid absolutely pure. This is another advantage in the use of ammonia, for the potass salt requires, at the least, three treatments with acid to abstract the alkaline base entirely. Bibasic Meconate of Ammonia.—The ammonia salt obtained in the above given process, crystallises from tolerably dilute fluids left at rest, in groups of radiated fine silky needles: they have an acid reaction. In the following analysis the nitrogen was determined by adding hydrochloric acid to a solution of the salt, evaporating the filtrate with some bichloride of platinum, collecting the residue on a filter, and washing with alcohol and ether; the per-centage of nitrogen was | calculated from the platinum remaining on ignition of the undissolved ammonia salt. This method was preferred in one or two other cases of ammonia salts, as more convenient than a combustion with soda lime, and less liable to loss; for it is not easy always to mix these salts with soda lime so quickly as to avoid the escape of ammonia. 6°732 ... carbonic acid, and 5-170 grains, dried at 212°, gave 27201)... water. 5:285 grains, dried at 212°, gave 4:505 ... metallic platinum. Calculation. Carbon, f : 35°51 35°89 Ca 84 Hydrogen, . : 4:73 4:27 Ht, eae G Oxygen, ; ‘ OM 47°88 OF rig Nitrogen, . : 12:09 11:96 N, 28 100-00 100-00 234 The hydrogen is rather above the calculated result, but the substance, when dried at 212°, is extremely hygroscopic: the numbers lead to the formula HO, 2 NH,0, ©,, HO,, as representing the constitution of bimeconate of ammonia in the dry state; the crystals appear to contain varying amounts of water of crystallisation, as num- bers were obtained in drying different specimens indicating a loss of between six and sixteen per cent. of water. An aqueous solution of this salt may be boiled without any change; but when kept for a considerable time boiling with an ex- cess of ammonia, it becomes altered. AND SOME OF ITS DERIVATIVES. 403 Action of Heat on Meconate of Ammonia. Comenanuc Acid.—Some of the highly-coloured mother liquors of the purify- ing process, were retained at or near the boiling temperature for some hours, ammonia being kept present in excess. The addition of hydrochloric acid to the cooled fiuid caused copious evolution of carbonic acid, and when added in proper quantity, a considerable precipitate. By repeated crystallisations from boiling water, and the use of pure animal charcoal, the precipitated substance was obtained in colourless shining scales; the following is its analysis before being rendered absolutely pure :— 4-335 grains, dried at 212°, gave 7°287 ... carbonic acid, and 1:370 ... water. 6-295 grains, burnt with soda lime, gave 8-700 ... ammonio-chloride of platinum. Calculation. —— eee ee Carbon, / 45-84 46°45 Chee 12 Hydrogen, : f 3°51 3°22 H, 5 Oxygen, : : en 41-30 OF 64 Nitrogen, 5 : 8°67 9:03 N 14 100-00 100-00 155 The results of which are sufficient to shew this body to have the composition of comenamic acid; the characters and reactions of the acid left me no doubt as to its identity with that derived from comenate of ammonia under similar circum- stances. It may be considered as formed from the bibasic meconate of ammonia, in the presence of an excess of ammonia, by the elimination of two eq. carbonic acid, two of water, and one of ammonia, as in the equation HO, 2 NH,O, C,, HO,,=C,, H, NO,+NH,+2HO+20C0,. This offers a convenient source of comenamic acid, as very impure meconic acid may be employed. Action of Chlorine on Bibasic Meconate of Ammonia. A current of chlorine gas passed through some of the coloured mother liquor of the above salt deprived it of colour considerably, and caused a speedy deposit of hard granular crystals adhering to the sides of the vessel. This was collected, and recrystallised from boiling water; it was found to be not very soluble, and the fluid on cooling deposited the substance in hard crystals, which, on being mag- nified, were seen to consist of thick needles radiating from a centre. It contained no chlorine, and proved to be an ammonia salt of meconic acid containing one equivalent of alkaline base. I am not aware that this salt has been obtained before, I therefore subjoin an analysis of it. 404 MR HENRY HOW ON MECONIC ACID, 4-708 grains, dried at 212°, gave 6659 ... carbonic acid, and 1;505 ,..,..... water: pgs grains, dried at 212°, gave, by H Cl, &., 1780... platinum. Calculation. ae Carbon, . : 38°57 38°70 Gi 84 Hydrogen, : 3°55 3°22 Oxygen, . : sae 51°63 Oy eriZ Nitrogen, . 6-21 6°45 N 14 100-00 100-00 217 which gives as the formula of the monobasic meconate of ammonia, as dried at 212’, 2 HO, NH,O, C,, HO,, The crystallised salt contains two equivalents of water ; 9-535 grains lost, at 212°, 0-735 .:. water. which is equal to 7°70 per cent. ; 7:65 is the number corresponding to the for- mula 2 HO, NH,O, C,, HO,, +2 aq. The original mother liquor of this salt:deposited a further quantity of the same on being concentrated ; and by continued evaporation a few crystals of a different appearance were obtained ; when these were separated, and recrystallised from boiling water, they presented themselves in the form of long square prismatic needles. In their appearance, and a few reactions, they shewed the characters of chlorocomenic acid. A determination of the chlorine is, I think, sufficient to prove that the crystals really consist of this acid. ( 3°315 grains, dried at 212° gave, after burning with lime, | 2:505 ... chloride of silver; the per-centage of chlorine calculated from this experiment is 18°69, which agrees very closely with 18°63, the number corresponding to the formula of chloroco- menic acid in the dry state. H 2 HO, C,, fa } 0, Oxalic acid is found in the last mother liquors of this process. Action of Bromine on Meconic Acid. Bromocomenic Acid ; Carbonic Acid.—\ had no doubt of finding the action of bromine closely similar to that of chlorine on meconate of ammonia; but it occurred to me it would be more readily learned from employing the acid itself, whether it gave a substitution product, or whether its molecule, under these cir- cumstances, split up at once into carbonic acid and a substitution acid of comenic AND SOME OF ITS DERIVATIVES. 405 acid. Accordingly, bromine water was poured upon powdered meconic acid ; lively effervescence took place, which was found to result from the evolution of carbonic acid, and complete solution subsequently ensued. The fluid, when left at rest a considerable time, deposited a few long prismatic crystals of great beauty, a much more copious product was obtained by gentle evaporation. Recrystallisation from hot water gave groups of brilliant square prismatic crystals, of which, { 6°787 grains, dried at 212°, gave, when burnt with lime, 5-480 ... bromide of silver. This experiment gives a per-centage of 34°36 bromine: 34:04 is that corre- sponding to the formula of dry bromocomenic acid, 210, C,, fae} 0, The nature of the reaction is seen in the equation C,, H, 0,,42Br=C,, { is } 0,, + HBr +2 CO, Crystals of oxalic acid were obtained by evaporating the original mother liquors to a small bulk. Ethers of Meconic Acid. When absolute alcohol is poured upon meconic acid, and the mixture is agi- tated, partial solution takes place, accompanied by a considerable fall in tempe- rature, amounting to about 10° or 12° Fahr.: application of a gentle heat causes complete solution. A stream of hydrochloric acid gas passed through the fluid is attended by the usual result observed in these cases, the formation of an ether compound; but in this instance more than one of such substances are pro- duced, and the relative proportion of the individual products depends on the amount of acid gas and the strength of the alcohol employed ; I say the strength of the alcohol, because rectified spirit serves to produce etherification, and I have employed it, but have found it disadvantageous, because whenever I did so, I observed the formation of an uncrystalline compound which very much impeded the purification of the other substances. The large amount of water of crystal- lisation of meconic acid, amounting to fully 25 per cent., tends to dilute the alco- hol, and I have sometimes dried the acid at 212° Fahr. before using it, and found this a good plan when working with rectified spirit. The results I have observed may be stated in a few words as preface to the description of the individual products; when a current of dry hydrochloric acid gas is passed through an alcoholic solution of meconic acid till it fumes strongly, and the fluid is set aside to cool, there appears, after a shorter or longer time, according to the circumstances above referred to, a deposit in feathery crystals ; the fluid filtered from this, where absolute alcohol has been used, gives no further deposit ; but, in the case of rectified spirit, another less crystalline substance ap- VOL. XX. PART III. DR 406 MR HENRY HOW ON MECONIC ACID, pears after some little time. On evaporating the liquid which has ceased to give deposits to complete dryness, the chief constituent of the residue is found to be a substance fusing under boiling water ; it is more or less accompanied by the other bodies according to the said conditions. Ethylomeconic Acid. The first deposit I have usually found to be so nearly a pure and uniform sub- stance, that one recrystallisation from hot water, after a little washing, was suf- ficient to render it completely so; it then appeared as highly crystalline in bril- liant short needles. The following is its analysis :— 9558 ... carbonic acid, and 5:500 grains, air-dry, gave I 1°860. ..., water. 5°110 grains, dried in vacuo, gave Il. < 8-830 ... carbonic acid, and 1-685 ... water. Calculation. SS —EEEEEe Le i Carbon, . 47°39 47-12 47-36 Cig, 108 Hydrogen, . 3°75 3°66 3°50 158 8 Oxygen, sae oe 49°14 ON AI2 100-00 100-00 100-00 228 from which it is obvious that we have here an acid ether, analogous to phospho- vinic acid, in which one atom of water of a tribasic acid is replaced by an equiva- lent of ether; its rational formula is, therefore, 2 HO, C,H,0 C,, HO 11’ according to which it is a bibasic acid: this I shall presently shew to be the case. I propose to call this the ethylomeconic acid, in preference to meconovinic acid, both as more expressive of one of its constituents, and to facilitate its comparison with another ether, to be described shortly, which I should hardly know how to name otherwise than by calling biethylomeconic acid, containing, as it does, two equivalents of ether. Ethylomeconic acid, when pure, crystallises from boiling water in brilliant small crystals, which, when magnified, are seen to be square prismatic needles. It is very readily soluble in this menstruum, also in ether and common alcohol when warmed, less soluble in absolute alcohol. It separates from concentrated solutions in these three fluids in groups of stellate crystals, and when they are left to spontaneous evaporation, in long needles. It is anhydrous, its crystals lose no weight either in vacuo or at 212° Fahr. It fuses at about 316-318" Fahr. to a transparent yellowish liquid, with the formation of a sublimate in very bril- liant rhombic crystals. AND SOME OF ITS DERIVATIVES. 407 Its aqueous solution reacts strongly acid, and readily coagulates the white of eggs. It imparts to persalts of iron a deep red colour. It decomposes carbonates with effervescence. It is bibasic, forming two series of salts, the acid ones are readily crystal- lisable ; its salts are very stable, the acid being recoverable from them by decom- position with stronger acids. Acid Ethylomeconate of Baryta—When carbonate of baryta is added in suc- cessive small quantities to water covering solid ethylomeconic acid, lively effer- vescence ensues and the acid quickly disappears; there is formed at the same time a small amount of an insoluble yellow salt. If the fluid be filtered imme- diately on the cessation of the effervescence, and the vessel be placed under the receiver of an air-pump and a vacuum made, a considerable deposit of carbonate of lime, which had been held in solution by the carbonic acid now liberated, takes place. By a second filtration a clear yellowish fluid is obtained, which yields, on evaporation in vacuo or at a gentle heat, very well-defined brilliant rhombic crys- tals of a yellow colour. A specimen prepared in this way gave the following results :— 5-058 grains, dried at 212°, gave 6:708 ... carbonic acid, and 1:198 ... water. 5-455 grains, dried at 212°, gave on ignition with HO SO,, 2175 ... sulphate of baryta. Calculation. Carbon, . : 36:20 36°53 Cre 208 Hydrogen, . ; 2°63 2°36 Hy, 7 Oxygen, .— . a catomy OL. 04 Baryta, : 26°17 25°92 BaO 76°64 100-00 100-00 29564 which lead to the formula, for the dried ethylomeconate of baryta, of BaO, HO, 0,H,0 C,, HO,,. The crystals contain water which they lose on drying, but I missed ascertaining the quantity. Acid Ethylomeconate of Silver.—I obtained this salt by adding an aqueous solu- tion of the former to nitrate of silver; a precipitate was immediately formed, which, upon resolution in boiling water, after washing, crystallised out on cooling of the fluid in groups of fine small stellate crystals, brilliant and white. This salt is remarkably stable, remaining perfectly unchanged in appearance when exposed a long time to the diffused daylight of summer; it gave the following results on analysis :— 6:°215 ... carbonic acid, and 5°310 grains, dried at 212°, gave 1:°053 ... water. 408 MR HENRY HOW ON MECONIC ACID, { 4595 grains, dried at 212°, gave, on ignition, 1468 ... silver. Calculation. Carbon, . . 31:92 S209" | Ln 1t08 Hydrogen, . ; 2°20 2:08 H, | Oxygen, : 5 ase 33°45 Oi hi? Silver, 4 ; 31:94 32°25 Ag 108-1 100-00 100-00 335°1 which lead to the formula AgO, HO, C,H,0O C,, HO,, for the dried salt ; the crystals contain two equivalents of water, { 10: 40 grains lost, at 212°, 0545 ... water. This number gives for per-centage 5°24; 5:08 is that corresponding to AgO, HO, C,, H, 0,. +2 aq. An aqueous solution of acid ethylomeconate of baryta gives with acetate of lead a yellowish white, with sulphate of copper a pale green, and with perchloride of iron a red-brown precipitate ; this last is readily soluble in an excess of the iron salt, forming with it a dark red fluid. Neutral Salts of Ethylomeconic Acid.—I have not been successful in procuring these salts absolutely pure, although I have tried many. On one occasion I obtained, by saturating ethylomeconic acid as nearly as possible with carbonate of baryta at a temperature of 212°, and subsequent filtering of the fluid, a salt which deposited on cooling in small short yellow needles; of this { 3°442 grains, dried at 212°, gave 2:197 ... sulphate of baryta. The per-centage of baryta calculated from this is 41:89: 42°19 is the number cor- responding to the formula 2 BaO, C,H,0 C,, HO,,. Although this result is satisfactory, I could not succeed upon repetition of the experiment in obtaining an analytical number sufficiently close to confirm it. Those I obtained by heating ethylomeconic acid with excess of carbonate of baryta, varied from 42 to 44:5 per cent. baryta, which lead to the conclusion that the acid forms basic combinations in addition to acid and neutral salts. The other alkaline earths shewed similar deportment with the acid, and when it is heated with an excess of carbonate of silver, it remains almost entirely undissolved,—in some basic combination. When ethylomeconic acid is heated with an excess of caustic potass or soda, meconates of these bases are produced. An excess of caustic ammonia decom- poses it very readily. AND SOME OF ITS DERIVATIVES. 409 Meconamidic Acid. When ethylomeconic acid is dissolved in warm water or alcohol, and an excess of strong aqueous or alcoholic solution of ammonia is added, the fluid assumes a deep yellow colour, and becomes very soon filled with a yellow semi-gelatinous- looking substance, which after being washed with dilute spirit, dries up in the air to an amorphous mass, which powders with some difficulty to a very fine yellow powder. This substance, when dissolved in hot water, smells of ammonia, and the solution gives, with dilute fixed alkalies, abundant evidence of its contain- ing this body as a base. I was at first of the opinion that it was the neutral salt of an amide acid corresponding to ethylomeconic acid, and formed from it in the manner characteristic of the action of ammonia in these cases, in which one atom takes the place of an equivalent of alcohol. Upon submitting it to analysis, however, I found this not to be the case; and it appears to me to be the result of a complicated decomposition, which is, so far as I am aware, without analogy. Upon adding to its solution in hot water some hydrochloric acid, a white precipitate is obtained, which I presume to be the acid of the compound. I will first give its analysis, and the formula I deduce from it, to render more clear the only constitution I can assign to these two bodies. The following ana- lyses were performed on specimens of different preparations, the acid was recrys- tallised from boiling water, it then appeared as a white crystalline crust or rind : 5°972 grains, dried at 212°, gave 8-700 ... carbonic acid, and He Lengo). n+,» Water. 5623 ... dried at 212°, gave, when burnt with soda lime, 7:020 ... platinum salt of ammonia. 5°884 grains, dried at 212°, gave 8555 ... carbonic acid, and TL. 4 0-760) See. water. 5655 ... dried at 212°, gave, with soda lime, 7:250 ... platinum salt. 5°205 grains, dried at 212°, gave III. ¢ 7:540 ... carbonic acid, and 1530 ... water. IV 7°925 grains, dried at 212°, gave, with soda lime, ‘ (9°728 ... platinum salt. Mean. Calculation. ee I. Ville ITI. IV. Carbon, BN) a7ic) 39°65 39°50 ce 39°62 39°84 C,, 504 Hydrogen, . 3°30 3°32 3:26 og 3°29 3°08 Laie 39 Oxygen, . “al 2%: oy sae sie 49°34 O,, 624 Nitrogen, . 7°84 8-05 2 7:70 7-86 7:74 N, 98 100-00 100-00 100-00 100-00 100-00 100-00 | 1265 VOL. XX. PART III. oS 410 MR HENRY HOW ON MECONIC ACID, The first glance at the above formula reveals a very complex atom, yet in the following scheme its derivation seems at least possible. Seven atoms of ammonia react on six of the acid ether, 6 atoms ethylomeconic acid, - a, HOT ee On, 27> 2) ammonia) 0: ; : ; 4 r, N, Cys Heo Oss Nz —6 ... alcohol, : : : . : Caan ie Cs, H,; 0,. N, +6 ... water, 1 ig © C 84 Hy, O75 N, If we consider the above as its derivation, and the six atoms of water as water of crystallisation retained at 212°, the acid will be C,, H,, N, 0,,3 upon examining this, it is found to contain the elements of six atoms of normal amidomeconic, corresponding to ethylomeconic acid, plus an equivalent of am- monia, C,, H,, N, 0 ».=6(2 HO, NH, C,, HO,,) +N. A comparison of the numerical per-centages required by the formula of the normal amidomeconic acid, with those really obtained, is here given to shew how widely they differ, Mean of Calculation of Amido- Experiment. meconic Acid. ——————— eee Carbon, : ‘ 39°62 42:21 Cy 84 Hydrogen, . : 3°29 2°51 ini 5 Oxygen, 3 ; a 48°25 OT 96 Nitrogen, . : 7°86 7:03 N 14 100-00 100-00 199 Yet that the acid in question is really an amidogen compound resulting from meconic acid, is to be inferred from the fact, that when it is heated with solution of potass, ammonia is evolved in quantity, and the fluid gives, with hydrochloric acid, a crystalline precipitate to be recognised as bimeconate of potass, which, upon subsequent treatment in the same manner, furnishes the characteristic scales of meconic acid. This is the deportment of an acid amide. The appropriation of the atom of ammonia among the six atoms of amido- meconic acid, if, indeed, this be the constitution of the compound acid produced, seems to have much diminished the basicity of the complex atom, or else the yel- low salt is not a neutral one: the amidomeconic acid being bibasic, six of its atoms should, in forming a neutral salt, take up twelve equivalents of ammonia, but a considerably less amount is found in the yellow ammonia salt: this is AND SOME OF ITS DERIVATIVES. 411 shewn in the following analyses; they were performed on specimens prepared at different times, 8395 ... carbonic acid, and ' 6:277 grains, dried a day at 212°, gave I 2°60 ... water. 6:150 grains, dried in vacuo, gave 8-205 ... carbonic acid, and Is \ 2°7504 5%, “awater. | 5-751 ... dried in vacuo, gave, burnt with soda lime, 14650 ... platinum salt of ammonia. Wt 4-912 grains, dried in vacuo, gave, burnt with soda lime, “(12580 ... platinum salt. IV 4-925 grains, dried in vacuo, burnt with soda lime, gave* " (12445 ... platinum salt. Calculation. Le tite Te 1 a : Carbon, . 36-47 36°38 oN 1m 36°23 Cy, 504 Hydrogen, . 4:60 4:96 as my 4:59 13 63 Oxygen, . Ae a bhi Ah 43°01 Oe 600 Nitrogen, . z 15:99 16:08 15:86 16°24 Ni, 224 10000 100:00 100-00 100-00 100-00 1391 The formula expressive of the constitution of this substance as an ammonia salt of the above acid, is, SENT OSC.) Hp N 0. 4.3 aq: And the acid itself, considered with regard to its amount of basic water as indi- cated in the salt, is represented thus, 9 HO, Cy) Hog Nn Og, +6:aq. I attempted to determine directly the amount of nitrogen existing in the yellow salt as ammonia, but, upon reflection, I despaired of success, because the only method at my disposal being to decompose by hydrochloric acid, and evaporate the solution filtered from the precipitated amidic acid with bichloride of platinum, I saw that if this acid behaved as amidogen acids are known to do in concentrated acid fluids, namely to regenerate the parent acid and ammonia, I should inevitably obtain an excess. Nevertheless I made the experiment, and the lowest result I obtained was 10-4 per cent. nitrogen: now, 9:08 corresponds to 9 atoms of nitro- gen. I also attempted to form other salts by precipitation of solutions by that of the ammonia salt, but the results were unsatisfactory and inconstant. The silver salt, a yellow gelatinous precipitate, dried up to a black mass; and the baryta compound, a yellow amorphous precipitate, insoluble in boiling water, gave vary- ing numbers on analysis. * T am indebted for this analysis to my friend Mr Rowney. He performed it on the substance mixed with sugar. 412 MR HENRY HOW ON MECONIC ACID, I have nothing to add descriptive of the acid to what little has been men- tioned. It is a white powder as precipitated by acids from the yellow compound, crystallising from concentrated solution in hot water in a crystalline crust. The yellow salt has a peculiar appearance. It does not present the least crys- talline structure even under the microscope, but consists of round translucent granules ; when deposited slowly from dilute fluids these have the appearance of small yellow vesicles or air-bubbles. It is readily soluble in hot water with a decided smell of ammonia; it is very sparingly soluble in hot, insoluble in cold, alcohol. It gradually loses ammonia when heated in the dry state at 212° Fahr. ; at a higher temperature it blackens and fuses. I have adopted the name of Meconamidic Acid for the acid of this salt, as simply expressive of its constituents, without any reference to the molecular arrangement of its elements. Coupled Acid Ether of Meconic Acid. The substance I have described as occurring in the process of making the ethers of meconic acid, when rectified spirit is employed, is deposited generally after the first product of ethylomeconic acid is filtered off. I have sometimes observed it also falling from the mother liquor, from which the first deposit had been crys- tallised, and also in the course of purification of the residue left on evaporation of the original acid mother liquor. Its constant occurrence induced me to examine if it were a substance of determinate composition; I accordingly redissolved some of it in hot water, it which it is extremely soluble, twice or thrice, and obtained, on cooling of the liquid, a white amorphous powder. I select the analyses of two specimens treated in this manner :— {ras grains, dried at 212°, gave I. 7655 ... carbonic acid, and 1311 ... water. 5-335 grains, dried at 212°, gave II. <¢ 8-712 ... carbonic acid, and 1:315 .... . water. Calculation. le IL. ——————— Carbon, . e 44:80 44°53 44°85 Cr Loe y Hydrogen, 5 3°12 2°73 2°80 His 12 Oxygen, won 52°35 OF a ee 100-00 428 I am inclined to think the approximation of the above numbers to the per-cent- ages corresponding to the formula given, in a substance purified from different preparations, is too close to be accidental, and that the body in question is a de- terminate compound. The formula given contains the elements of one atom of meconic and one of ethylomeconic acid, C,, Hy, 0,,=8 HO, C,, HO,, +2 HO, C,H;0 C,, HO,,. AND SOME OF ITS DERIVATIVES. 413 A substance of such constitution may be easily imagined to occur, when an insuf- ficient quantity of acid gas had been employed to remove all the water from the meconic acid, or its power had been diminished in this respect by the ready formed water existing in the fluids. That the substance is something more than an accidental mixture, is to be inferred from the action of ammonia. When its warm aqueous solution is super- saturated by strong ammonia, the fluid becomes yellow, but none of the yellow amidic salt is deposited, as might be expected in a mixture containing ethylo- meconic acid. If, however, to a concentrated aqueous ammoniacal solution strong alcohol be added, a deposit in small radiated yellow silky tufts appears; and when such an aqueous solution is evaporated to dryness at 212°, a crystalline residue remains, part of which is extremely sparingly soluble in boiling water ; the more soluble portion gives, with hydrochloric acid, a crystalline precipitate in the form of needles. I have not followed out the changes which these few experiments seem to indicate, for my material was small in quantity, and I had no means of readily preparing it tolerably pure at will. I have called this substance Meconoethylomeconic Acid, as the name expresses . most distinctly the constitution deduced from analysis, and represented by the formula given. I was anxious to have substantiated its constitution as such by a determination of its saturating capacity, but was unable to effect my purpose, owing to the impossibility I experienced of obtaining its salts. When it is treated with bases, the salts produced decompose into meconates with greater facility than those of ethylomeconic acid. Meconic Ether containing tivo Equivalents of Ether. LBiethylomeconic Acid.—This substance is found in considerable quantity in the acid mother liquors from which the bodies before described have deposited, especially when absolute alcohol has been employed; its proportionate amount appearing to depend on that of the hydrochloric acid gas employed. It remains, on evaporation of the liquid, till acid ceases to be evolved at 212° Fahr., as a thick oil or viscid mass, becoming a solid crystalline mass on cooling. It may be ren- dered pure by two or three crystallisations, these serving to remove any of the former-mentioned bodies, of which small quantities are generally present in the residue left on evaporation. It is thus obtained in colourless flattened prisms: the analysis is as follows :— 8-932 ... carbonic'acid, and 4-745 grains, dried in vacuo, gave if 2055 ... water. 9:160 ... carbonic acid, and 2°120 ... water. VOL. XX. PART III. 57 {2288 grains, dried in vacuo, gave II. 414 MR HENRY HOW ON MECONIC ACID, Calculation. ti if ae Carbon, . : 51°33 51°35 51-56 Cal lee Hydrogen, “ 4°81 4:84 ~ 4°68 Le 12 Oxygen, : ‘es iv 43°76 7-112 100-00 100-00 100-00 256 These numbers lead to the formula, HO, 2 C,H,0, C,, HO,,- Having thus far succeeded in replacing one and two of the atoms of basic water of meconic acid by corresponding equivalents of ether, | was in hopes of being able to go still further and obtain a neutral compound. For this purpose I dis- tilled some meconic acid with absolute alcohol and strong sulphuric acid. By application of a gentle heat, tranquil ebullition was commenced and sustained. The distillate consisted of alcohol and ether, and the contents of the retort gra- dually acquired a syrupy consistence ; at this period they were poured into a comparatively large quantity of cold water; in a short time a crystalline precipi- tate of a delicate rose-pink colour was formed, which gradually increased in quan- tity. On recrystallisation from water it was obtained in colourless flattened prisms, which gave, on analysis, the following numbers :— 9:128 ... carbonic acid, and 4-860 grains, dried at 212°, gave 2°135 ... ‘water. which, when calculated for per-centages, are equal to Carbon, ; ; : 51-22 Hydrogen, . : ; 4°88 and shew the substance to be identical with that obtained in the former process. This method obviously furnishes a ready source of the pure ether. I may men- tion, that I have not been able to produce it this way by employing rectified spirit in place of absolute alcohol. Biethylomeconic acid, in its pure state, as crystallised from water, occurs in the form of long, flattened, colourless, prisms; it fuses under boiling water before dissolving. It is very soluble in alcohol. In the dry state it fuses at about 230° Fahr. to a yellowish transparent liquid. Its aqueous solution readily coagulates the white of eggs, has an acid reaction, and decomposes carbonates with effervescence. It imparts to persalts of iron a red colour. As the above formula indicates, it is a monobasic acid ; I add the analysis of two salts which shew this fact. When subjected to the action of ammonia in the cold, biethylomeconic acid does not undergo decomposition ; the substances simply enter into combination. AND SOME OF ITS DERIVATIVES. 415 Biethylomeconate of Ammonia.—Some of the ether was dissolved in strong, nearly absolute, alcohol, and dry ammoniacal gas was passed into the fluid ; the whole soon became a nearly solid yellow mass. When this was freed by pres- sure from the ammoniacal alcohol, it was found to crystallise from hot spirit in tufts of radiated silky yellow needles. From its analysis, 5:140 grains, dried in vacuo, gave 9:055 ... carbonic acid, and 27610 ... water. 5825 ... dried in vacuo, gave, on burning with soda lime, 5065 ... platinum salt of ammonia. Calculation. Carbon, . . 48-04 4635). Cy, 132 Hydrogen, . fF 5°64 5:49 “if 16 Oxygen, : ; Dis 41:04 OF, y 112 Nitrogen, . ; 5°46 5:12 N 14 100-00 100-00 273 Its constitution is evidently represented by the formula, NH, 0; 20,10, Cy, HO,,); it crystallises without water. Biethylomeconate of ammonia is readily soluble in cold water to a yellow fluid ; acids precipitate from this the unchanged ether. Its aqueous solution gives the following reactions :—with nitrate of silver a yellow gelatinous precipitate in- soluble in boiling water, and apparently unaltered by the elevation of tempera- ture; with sulphate of copper, a green gelatinous precipitate; with acetate of lead, a heavy yellowish white, and, with sulphate of magnesia, a crystalline precipi- tate ; with the chlorides of barium, strontium, and calcium, it produces pale yel- low semi-gelatinous precipitates, insoluble in boiling water, but readily soluble in excess of the earthy salts; a determination of the base in the baryta salt was made, 5°533 grains, dried at 212°, gave { 1:985 ... sulphate of baryta. Calculation. Carbon, 7," i Asien, | C,, 132) Hydrogen, . ; Hes 3°39 la Be 11 Oxygen, : oe 32°15 Ode 104 Baryta, ; : 23°54 23°68 BaO 76°64 100-00 100-00 323°64 which leads to the formula for biethylomeconate of baryta, of BaO, 2 C,H,0, C,, HO,,. I believe, from an experiment made on a small scale, that biethylomeconic acid, when heated with ammonia, undergoes a change; the result is probably an 416 MR HENRY HOW ON MECONIC ACID. acid amide; want of material, however, has prevented me as yet from arriving at a satisfactory conclusion on this point. I subjoin a list of the substances described in this paper. Salts and Compounds of Mecomic Acid. Bibasic meconate of ammonia, dried at 212°)“ ELO, 2 NEO SC HEOF Monobasic ye a fa 2 HO, NH,O, C,, HO,, Aas ei crystallised, 2 HO, NH,0, C,, HO,, +2 aq. Ethylomeconic acid, Ae os 2H0;C 0.0 CAO) ‘ Acid ethylomeconate of baryta, dried at 212°, BaO, HO, C,H,O C,, HO,, silver, ne AgO, HO, C,H,O C,, HO,, tee Be crystallised, AgO, HO, C,H,O C,, HO,, +2 aq. Neutral a) baryta, dried at 212°, 2 BaO,C,H,O C,, HO,, Meconamidic acid, . : pe. 9 HO, C,, H,, N, 0,,+6 aq. Meconamidate of ammonia, dried in vacuo, 9NH,O, C,, H,, N, 0,,+3 aq. Meconoethylomeconie acid, dried at 212°, 3HO, C,, HO,, +2 HO, C,H,O C,, HO,, Biethylomeconic acid, Se HOT 2 CHONG ae, Biethylomeconate of ammonia, crystallised, NH,0; 2°00; C,, HO, baryta, dried at 212°, BaO, 2 C,H,O, C,, HO,, Products of Decomposition. Comenamic acid, ‘ : { : : - ; . : HO;C), i NO? Chlorocomenic acid, . : 3 4 ‘ : : : ; 2 HO, C,, ‘a } UE Bromocomenic acid, . : ‘ . ; : : ; : 2 HO, C,, { i } 0, (eraalinncyy XXVI.—WNotice of an Antique Marble Bust. By ANpREw Coventry, Esq. (Read February 16, 1852.) Having had the good fortune last autumn to get an antique marble bust of extreme beauty, the question naturally arose, of whom it might be the portrait, if, indeed, it was a portrait at all, and not an ideal head. I had proceeded some way in this inquiry, when it was suggested to me one day that it might interest the Society to know something of it, and that, though a little foreign no doubt to its usual topics, the change would be agreeable, and that ancient art was not without its charms. So urged I yielded,—perhaps too easily ; but of this you will judge when I have done. Unfortunately the history of the bust, before it became mine, is altogether un- known to me, further than that it belonged to a gentleman in Westmoreland, who, there is reason to think, picked it up whilst travelling in Italy. And Iam sorry . that owing to his absence once more abroad, wandering about with uncertain health, and often changing his residence, I have been unable as yet to learn any- thing of its early history. Before going further, I may mention that the bust would have been here to-night for exhibition if I had found it possible to remove it from my house with any safety. It would have been attended, however, with considerable risk, as there are several joinings, particularly in the back of the shoulders, and it is altogether a little crazy. But in its place [ have brought some photographs executed by my friend Captain Scott, R.N., and one or two very deli- cate photographs, with collodion upon glass, by Mr Tunny of Newington. These really leave no room for disappointment or regret. In truth, they shew the fea- tures more perfectly than an exhibition of the bust itself, in the full blaze of gas light, without shadows or relief, could possibly have done. A single light, no doubt, from a torch, or day-light entering by a side-window and casting shadows, shews it to most advantage; and I only hope this may induce any gentleman present, who feels so far interested, to call at my house. when it will give me the greatest pleasure to shew it him. The bust is that of a young woman of serene and pensive beauty. The head is of Parian marble, but the drapery of Carrara, and seemingly of a later age. Probably at an early period some accident befel it, for the Carrara marble extends from the drapery upwards a little way to a crack in the neck, and the nose and the knot of the hair have been slightly injured and restored with Carrara marble. It was not unusual, as we know,* for the head to be wrought separately from the * Burron’s Rome, 2. 2038. VOL. XX. PART III. Su 418 MR ANDREW COVENTRY’S NOTICE OF rest of a statue; such was the case with the Niobe and her children. Fre- quently, also, the original head was displaced for another to save expense.* ‘Pliny tells us, that in his time it was a common custom to change the heads of illustrious persons and fit on new ones; and Chrysostom reproaches the Rho- dians with their economy in dedicating the same statues to different persons, de- facing the original inscriptions.” But in the present instance it is more probable that the circumstance of the bust being in two pieces must have been owing to a fall, as the junction is clumsily executed, and advantage has not been taken of the drapery to conceal it. Still the drapery cannot be referred to any recent period. It is too simple, and has suffered too much from the action of the weather to be modern. I think the bust must have lain for ages with the face down, and the shoulders, which have chiefly suffered, exposed ; and, when it came into my possession, the folds of the drapery were full of what seemed garden mould. It is difficult to resist the impression that we have here a specimen of high Greek art. There is the wonderful repose which baffles modern skill, the fine short upper lip, the flat pupil of the eye, and the delicate line of junction of the lips admirably given. My belief, too, is that it is a portrait. It has an air of individuality about it ; and it has none of the emblems of mythology, such as the diadem or the ivy chaplet. Further, there is a dimple on the chin, which would appear to be de- cisive. For Winckelmann} informs us, that there exist only three fine statues of an ideal character (the Venus de Medici, a bronze Apollo, and a Bathyllus at Samos) with a dimpled chin, it not being a feature which the Greeks admired. I may mention that the ears are pierced, as was not unusual. The ears of the Venus de Medici are also pierced. Of whom, then, have we here the portrait? At first sight this would seem a hopeless inquiry ; and if the Greeks had been in the habit, as we are, of decorating their mansions with the images of their friends, it certainly would be hopeless now, among the ruins and remains of so many families, to trace the likeness of a bust. But it was not so in Greece. There sculpture had high and public aims. There were, as Heeren}{ tells us, no private galleries and no private collections. Sometimes, indeed, an Athenian, out of piety or patriotism, commissioned a statue ; but, in all cases, it was to adorn a temple or a portico, or some place of public resort: and we read§ of a person who had spent between £600 and £700 in certain votive statues, whose heir was reproached with having let them lie in the sculptor’s hands unconsecrated. In this way it came that persons only of some public mark were honoured with statues; and we now have not so bound- less and discouraging a field as it might have been. * Burton’s Rome, 2. 307; Puiny, 35. 2. { WinckLemann on Greek Art, p. 220. { Hesren’s Greece, pp. 284-9. § Miitier’s Ancient Art, p. 65. AN ANTIQUE MARBLE BUST. 419 At Rome I believe with Heeren that it was much the same during the Re- public, and private galleries were unknown. After the taking of Corinth,* how- ever, a passion seems to have sprung up in Italy for possessing works of art, the generals and governors of provinces vieing with each other in having them. Verres plundered in Sicily and Achaia; yet, with one exception (if it be one), it was statues which had graced some temple, or had been the pride of a city, that he was charged with having carried off.t And with his rapacity Cicero + contrasts the conduct of Marcellus and Mummius, who, with the whole spoils of Syracuse and Corinth at their command, had appropriated not a picture or statue, but given all to their country. But Verres soon had many followers; and by the time of Juvenal) we find that ancestral busts, but still of men who had filled some curule office, were objects of ambition with the degenerate nobles having the jus imaginum, the more opulent devoting a room in their houses to their reception, or using them to ornament their gardens.|| Yet the possession of works of art long survived as a matter of municipal pride in cities, casting private galleries, we may believe, into the shade. And thus it happens, that long after the Roman arms had swept the land, we find a town in France purchasing a statue of Mercury from a Greek artist at no less a sum than £320,000 (forty mil- lions of sisterces), as Sir James Stephen relates. And the same spirit lingers in Rome and Florence to the present day. The conclusion to which this little digression leads us is, that among the Romans as among the Greeks, statues of private persons were unknown; and such statues as did exist were rarely private property till near the age of Augus- tus, which is the period, as it will appear, that interests us. To return to the bust ;—its resemblance to the young Augustus was remarked to me very soon by several friends. I discovered, however, on comparing it with casts of his daughter, that it was not the profligate Julia; and much in the same way I satisfied myself that it was not Livia, of whom there is a beautiful portrait in the Dactyliotheca Smithiana.** But in my search I came upon a certain amount of evidence for its being his sister Octavia, the grandniece of Julius Czesar, whose affecting history is too well known to require more than a passing allusion here. She was, as many may remember, the mother of the young Marcellus,—Vireil’s friend too,—married young to the faithless Antony, yet did it ‘“‘never taint her love,”—and who, through her whole life, toiled for her brother and her country, without one thought of self, till, as Shakspeare +f tells us, “each heart in Rome did love and pity her.” In all the three English dramas * Smiru’s Dictionary of Greek and Roman Antiquities, p. 908; and Miitxer, pp. 124-5. { Cicero in Verrem, II. I., 19 and 23; Herren, p. 288. tTbid) Tih, 212 § Juvenat, Satire VIIT., 1-19. || Smrrx’s Dictionary, voce ‘‘ Pinacotheca ;” and Apam’s Antiquities, p. 460. { Lectures on French History, I., 21. FRVGH, te Gae tt Antony and Cleopatra, Act III., Scene 3. 420 MR ANDREW COVENTRY’S NOTICE OF founded on Antony and Cleopatra (Shakspeare’s “‘ Antony and Cleopatra,” Dry- den’s “ All for Love,” and “ The False One” of Beaumont and Fletcher), we find Octavia brought little upon the stage, as if so much worth and beauty must have robbed Cleopatra of dramatic interest. But to proceed. The jirst thing that struck me in reference to the bust was the very great resemblance, as I have said, which it has to the young Augustus. It is really most remarkable. The same gentle rise of the nose,—the same breadth of forehead, in contrast with a tapering chin—the same small mouth,— and the same low setting of the ears,—these are points of which any one may satisfy himself by inspecting the antique casts in the adjoining room. Sue- tonius,* to whom we owe the full description of Augustus’s appearance, spe- cially dwells upon the delicacy of his features and the singularly tranquil and serene look he always had; and Mr Merivale (2. 465) following him, speaks of “ the graceful beauty of his mouth, and chin of almost feminine delicacy.” Now, curiously enough, these are the most obvious peculiarities of this bust. The pre- cise features of Octavia herself are nowhere given that I can find; and I have searched Dion Cassius, Seneca, Aurelius Victor, and Plutarch, besides Sue- tonius, being curious to trace to some authentic source, if it were possible, the round face and the low brow which Shakspeare has given to his Octavia. 2d, Of Octavia there was, some years ago, a bust at Rome in the Capitol, as I am informed. ‘Two friends cf mine who had often seen it and admired it, upon visiting the bust in my possession, immediately recognised the resemblance be- tween the two. What has become of it I cannot say; but it would appear that it must have changed either its local habitation or its name, there being no bust of Octavia there now. So I have been given to understand by a young friend at present in Italy (Mr James Swinton) ; but, of course, it is a matter to be further inquired into. 3d, In the “Signorum Veterum Icones’’ of Gerard Reynst, p. 26, there is an engraving which professes to be of Octavia; and it certainly is not of Oc- tavia Augusta, the unfortunate wife of Nero, of whom a portrait follows at page 36. Now, it has the hair parted in the middle, as in the bust in my posses- sion,—the same short upper lip,—the same dimpled chin,—and, I should say, the same low brow. The engraving, indeed, gives the idea of a fuller and rather a coarser face, perhaps the fault of the draftsman, but the general likeness is con- siderable. 4th, In the Dactyliotheca (1., 67), there is a portrait which possesses a peculiar kind of interest, not that it represents Octavia, but Antonia Augusta, her second daughter by Mare Antony ; and in it I think one may see a great resemblance to the bust. This was her favourite daughter, the one that inherited her virtues and * SuEToNIus, voce ‘ Octavius ; and Arnotp’s Roman Commonwealth, II., 406. AN ANTIQUE MARBLE BUST. 42] her misfortunes ; and, what is more pertinent, her looks, as I find mentioned in the Life of Octavia, which is generally ascribed to the Abbé St Real.* With regard to coins and medallions, | have not found them of much use. Through the kindness of friends in the British Museum, | have had casts from the unique gold coin there, and from some copper coins of Thessalonica. I have also consulted an engraving of the Vienna medallion in the “ Numismata Aus- triaca,” but all with little benefit. Without going into details, I may mention that I have not spared myself a weary pilgrimage through Spanheim, Rashe, Golzius, Aneas Vicus, King, Pelerin, Mionnet, Ackerman, Smith, and Eckhel,— with this result, that the greatest uncertainty attaches to the coins of Octavia. In the copper coins of Thessalonica, for instance, the female head is generally thought to be one of Liberty, and not of Octavia. Again, the only coin which bears the name “‘ Octavia” on it, is considered by many (Mr Burgon of the British Museum among others) to be false, the true one giving Livia; and as to the coins (Cistophori) with Antony’s head beside a female head, there is great reason to suppose that it is not Octavia’s, but Cleopatra’s. Indeed, I have been shewn by my friend Mr William Scott, an engraving of one with the name “Cleopatra” actually occurring on it. For our purpose, it is enough, perhaps, that not two of — the coins agree in their representation of Octavia, if it be Octavia that they give. 5th, Will it be thought fanciful if I add, as some corroboration, though trifling, that the bust is in perfect harmony with all we know of the history and character of Octavia. I think we may trace in it that wonderful beauty which we know was not eclipsed by her rival Cleopatra—that gentleness which made her so forgiving of her unworthy lord,—that serenity which was unruffled amidst countless wrongs,—that affection which tied hert to the last to his house and kindred,—and that pensive look, the ‘‘/rons leta parum,” even in youth, which foreshadowed in her case a broken heart.{ Iam not sure that all these things could be said of any other individual of those times. As it seems to me, the bust has, for example, too much feeling for Livia, the hard step-mother, as Tacitus§ calls her, and too much purity for either of the Faustinas ; and so of many Bee if we cared to follow out this view. 6th, and lastly. In looking over the Florentine gallery the other day, I was struck by an observation which I could scarcely avoid making, of the simple way in which it was usual for ladies to dress their hair in the time of Augustus, much as in our bust. I might refer to the heads of Livia and Antonia Augusta in that collection, as instances. But very soon the taste for that simplicity declined, and then we have Agrippina, Messalina, Nero’s Octavia, Plautina, Poppzea, and a host of others, all revelling in most fantastic locks, some of them artificial, or * (Kuvres de S. Reat, III., 295. t+ Merivate’s Roman Empire, 3. 283-4. { Seneca, “ Ad Marciam.” § Tacitus, Annals, I., 10. “Gravis in rempublicam mater, gravior domui Cesarum noverea.” VOL. XX. PART III. dy de 422 MR ANDREW COVENTRY’S NOTICE OF with a fillet of hair bound round the head. If this observation be correct (and I have since found it in Muller),* then it furnishes us with one presumption more for the bust being that of Octavia; since, if it must belong to her age, it is no stretch to say that it may more fairly be given to her than to any other, when we take into account its perfect accordance with her character, and its resem- blance to her brother, Augustus. Such are the various grounds on which I should be disposed to rest. That they amount to proofs I do not pretend, for well I know the difficulty in all such matters of getting more than presumptions. Uncertainty hangs over too many of the finest remains of antiquity, making the Clite of one person the Isis of another, and raising a question, whether the beautiful Ariadne in our adjoining room is not, after all, a Bacchus, as Visconti and the latest editor of Winckel- mann} maintain. Enough, then, if I may be thought to have adduced reasonable grounds of belief, and all that could be hoped for at the end of nineteen cen- turies, with no contemporary record of the features, and scarce a relic left to guide us. The bust may have been made at Rome by some of the numerous Greek artists who flocked there, encouraged by Cicero and Atticus. Octavia{ was more than once at Athens, the idol and the charm of it, but this was as a married woman,—and the bust must have been made before her marriage, if we may safely judge by the hair tied behind in a knot, and not as matrons were in the habit of wearing it. There is no reason for supposing that the drapery may not be of high antiquity. The Carrara, or, as they were then termed, the Luna marble quarries, were open before her day, in the time of Julius Ceesar. § Since preparing this notice, I received by to-day’s post the following very in- teresting communication from Mr Burgon of the British Museum, which was sent me by Sir David Dundas. “ Mus. Brit., Feb. 14, 1852. “ Dear Sir Davin, “ T beg to return my best thanks to your friend for his very kind compliance with my suggestion, in sending me two new photographs. I hope they may be thought to have been productive of some fruit. I have done my best in coming to a conclusion, and have made up my mind to suggest that the bust represents Antonia, the daughter of M. Antonius and Octavia. She was the wife of Drusus, and the mother of Germanicus and of Claudius, who struck coins in her honour. She was a personage of high celebrity and a very likely person to have a fine bust, having had the honour of numismatic deification at least. * Miitier’s “ Ancient Art and its Remains,” pp. 169-70. t+ WincKELMANN, p. 96. t Merivate’s Roman Empire, III., 309. § Burron’s Rome, I., 22; and II., 303. AN ANTIQUE MARBLE BUST. 423 “ In adopting this opinion I have been led by the best of all guides, an in- scribed coin, of the second brass series, not very uncommon. “ My colleague, Mr Oldfield, agrees with me in thinking, that the coins and the photographs are as similar as could possibly be expected. ‘ T have the honour, &c., “ T. BurGon.” How interesting this revelation at the eleventh hour, and how curiously it dovetails into what I had written! It may be remembered that I had mentioned the likeness of Octavia to Augustus,—the treatment of the hair peculiar to that age,—and the accordance of her character with the bust; but all these remarks are quite as applicable to her daughter. They were both of them singularly beautiful, singularly amiable, and singularly unfortunate, as I had remarked ; and what IJ regretted as wanting for Octavia, the evidence of coins, has been found for Antonia Augusta by the industry of Mr Burgon and his colleague. On their authority we may safely say, that the scale preponderates for ANTONIA Aveusta ; and so the question may be considered as set at rest, and the riddle of | the bust solved. » ra ns amy © i DP j s nid, om aba vig ib ahd.’ tp ; 2, * oe i be Pa rr nig {thae’bn: dues at yea) 14 reine no nol gta ah rine nsioeholll wis ail VidehaiRam : din. TNT. whoa ic . ha Rea roo . n rm a” “s : Ae aa eee it a8 Wy ‘% ie 2 Wi Suge FF HV enn rinueared ban xinoitt emewatalhas diakshitel wre a Troi tie tnditel read arp Addgnan 42d cern (wh piled o Jind, seh ~ see did, wari oil isourrt net bh: iy. Fite) FLIG boul bi hiaw, aphoiruade friagl a . si _ r , _ iat A i v 3 mF = q hepa rt , phalitytte comeeta ul a ones Watt oe rytdacdidyiredadh, cient 7 > boohepenat ded | a aacetioding vitalogal+)tuts ean ‘Stay : tedium. eet! erp thts brew) tated Te ws bat ord 4 wh: osrgaylios ethene ten wth lala odie atuirqeds unpre des . . wily weet. wi) peterson uy. SiBDe os tal) ete y Lote (BATT 0 raim ets ; ° . a P hsggl in ihre? Lae tedden a6 Dope Rie ae e AULD dite TAY Orta paren * [ ai ° { t ; . - M " } “ - aL “ “se ‘ iE ? Ps a e 4 | i. td ny + Stat ne ‘ ~ = , a i . ( 425 ) XXVII.—On the Centrifugal Theory of Elasticity, and its Connection nith the Theory of Heat. By Wituiam Jonn Macquorn Rankine, C.E., F.R.S.E., F.R.S.S.A., &c. (Read December 15, 1851.) Section First.—Relations between Heat and Expansive Pressure. (1.) In February 1850, I laid before the Royal Society of Edinburgh a paper, in which the laws of the pressure and expansion of gases and vapours were de- duced from the supposition, that that part of the elasticity of bodies which depends upon heat, arises from the centrifugal force of the revolutions of the particles of elastic atmospheres surrounding nuclei, or atomic centres. A summary of the results of this supposition, which I called the Hypothesis of Molecular Vortices, was printed in the Transactions of this Society, volume xx., as an introduction to a series of papers on the Mechanical Action of Heat; and the original paper has since appeared in detail in the Philosophical Magazine. In that paper, the bounding surfaces of atoms were defined to be imaginary surfaces, situated between and enveloping the atomic nuclei, and symmetrically placed with respect to them, and having this property—that at these surfaces the attractive and repulsive actions of the atomic nuclei and atmospheres upon each particle of atomic atmosphere, balance each other. The pressure of the atomic atmospheres at those imaginary boundaries is the part of the total expansive pressure of the body which varies with heat; the effect of the centrifugal force of molecular vortices being to increase it. In the subsequent investigation it was assumed, that owing to the symmetrical action of the particles of gases in all directions, and the small amount of those attractive and repulsive forces which interfere with the elasticity of their atmo- spheres, no appreciable error would arise from treating the boundary of the atmo- sphere of a single atom, in calculation, as if it were spherical; an assumption which very much simplified the analysis. An effect, however, of this assumption was, to make it doubtful whether the conclusions deduced from the hypothesis were applicable to any substances except those nearly in the state of perfect gas. I have, therefore, in the present paper, investigated the subject anew, without making any assumption as to the arrange- ment of the atomic centres, or the form of the boundaries of their atmospheres. The equations deduced from the hypothesis, between expansive pressure and heat, are therefore applicable to all substances in all conditions; and it will be seen that they are identical with those in the original paper; shewing that the assump- VOL. XX. PART III. BY 426 MR W. J. M. RANKINE ON THE CENTRIFUGAL THEORY OF ELASTICITY, tion, that the atomic atmospheres might be treated in calculation as if spherical, did not give rise to any error. By the aid of certain transformations in those equations, I have been enabled, in investigating the principles of the mutual transformation of heat and expansive power, to deduce JouLe’s law of the equivalence of heat and mechanical power directly from them, instead of taking it (as I did in my previous papers) as a con- sequence of the principle of vis-viva. Carnot’s law is also deduced directly from the hypothesis, as in one of the previous papers. (2.) Classification of Elastic Pressures.—The pressures considered in the present paper are those only which depend on the volume occupied by a given weight of the substance ; not those which resist change of figure in solids and viscous liquids. Certain mathematical relations exist between those two classes of pressures; but they do not affect the present investigation. To illustrate this symbolically, let V represent the volume occupied by unity of weight of the substance, so that = is the mean density; Q, the quantity of heat in unity of weight, that is to say, the vis-viva of the molecular revolutions, which, according to the hypothesis, give rise to the expansive pressure depending on heat ; and let P denote the total expansive pressure. Then, P=F.(V,'Q) +f @) othe bow eeied Mice In this equation, F (V, Q) is the pressure of the atomic atmospheres at the sur- faces called their boundaries, which varies with the centrifugal force of the mole- cular vortices as well as with the mean density; and /(V) is a portion of pressure due to the mutual attractions and repulsions of distinct atoms, and varying with the number of atoms ina given volume only. If the above equation be differentiated with respect to the hyberbolic logarithm of the density, we obtain the coefficient of elasticity of volume 1 Pp d d m po cave cmavEUO-wWslM e AD Finseh ie Vv where 3 denotes the cubic compressibility. The latter portion of this coefficient, -“ J (V), consists of two parts, one of Vv which is capable of being resolved into forces, acting along the lines joining the atomic centres, and gives rise to rigidity, or elasticity of figure, as well to elas- ticity of volume, while the other, which is not capable of being so resolved, gives rise to elasticity of volume only. The ratio of each of those parts to their sum must be a function of the heat, the former part being greater, and the latter less, as the atomic atmosphere is more concentrated round the nucleus; that is to say, AND ITS CONNECTION WITH THE THEORY OF HEAT. 427 as the heat is less; but their sum, so far as elasticity of volume is concerned, is a function of the density only. That is to say, as in equation (12) of my paper on the laws of the elasticity of solids (Cambridge and Dublin Mathematical Journal, February 1851), let the total coefficient of elasticity of volume be denoted thus 1 Ces) ay CON RNa coy.) BD C,, C,, C,, being the coefficients of rigidity round the three axes of elasticity, and J a coefficient of fluid elasticity ; then d d J=— me (V, Q)—+¥ (V, Q). avi) Vv a ‘ (1 C.) ? CO, C,, C,) =— (1-4 (V, Q) ) avif™) ae * For the present, we have to take into consideration that portion only of the expansive pressure which depends on density and heat jointly, and is the means of mutually converting heat and expansive power ; that is to say, the pressure at the boundaries of the atomic atmospheres ; which I-shall denote by p=F (V, Q) Pressures, throughout this paper, are supposed to be measured by units of weight upon unity of area; densities, by the weight of unity of volume. (3.) Determination of the External Pressure of an Atomic Atmosphere.—Let a body be composed of equal and similar atomic nuclei, arranged in any symmetrical manner, and enveloped by an atmosphere, the parts of which are subject to attrac- tive and repulsive forces, exercised by each other, and by the nuclei. Let it further be supposed, that this atmosphere, at each point, has an elastic pressure proportional to the density at that point, multiplied by a specific coefficient depending on the nature of the substance, which I shall denote by h. (This coefficient was denoted by 0 in previous papers). Let ¢ and p’ denote the density and pressure of the atomic atmosphere at any point ; then p=he d® d® d® Let—g Fei dae ee be the accelerative forces operating on a particle of atomic atmosphere, in virtue of the molecular attractions and repulsions, which I have made explicitly negative, attractions being supposed to predominate. The property of the surfaces called the boundaries of the atoms is this d@® d@® d® (7) =o eae ES Pe en 428 MR W. J. M. RANKINE ON THE CENTRIFUGAL THEORY OF ELASTICITY, The suffix , being used to distinguish the value of quantities at those surfaces. Hence ©, isa maximum or minimum. Those surfaces are symmetrical in form round each nucleus, and equidistant between pairs of adjacent nuclei. Their equation is o—o,=0. Let M denote the total weight of an atom; u that of its atmospheric part, and M~—v that of its nucleus; then M V is the volume of the atom,— a= the mean density of the atmospheric part, measured by weight, the nucleus being supposed to be of insensible magnitude ;— and we have the following equations MY = Vf az aya (2.) bas te ay te= fff, oar ay az ; The suffix (,) denoting that the integration is to be extended to all points within the surface (®—#,=0). According to the hypothesis now under consideration, //eat consists in a re- volving motion of the particles of the atomic atmosphere, communicated to them by the nuclei. Let v be the common mean velocity possessed by the nucleus of an atom and the atmospheric particles, when the distribution of this motion has been equalised. I use the term mean velocity to denote, that the velocity of each particle may undergo small periodic changes, which it is unnecessary to consider in this investigation. Then the quantity of heat in unity of weight is vw ae, being equal to the mechanical power of unity of weight falling through the height i The quantity of heat in one atom is of course MQ, and in the atmospheric part of an atom, » Q. I shall leave the form of the paths described by the atmospheric particles in- determinate, except that they must be closed curves of permanent figure, and in- cluded within the surface (e—2,=0). Let the nucleus be taken as the origin of co-ordinates, and let a, 8, y, be the direction-cosines of the motion of the particles at any point (2, y, 2). Then the equations of a permanent condition of motion at that point, are AND ITS CONNECTION WITH THE THEORY OF HEAT. 429 ldp do d d Nea me ces Seas haga 2-9 ldp do d d d ee Rotary = ast aa tere . ‘a ldp do d d aan 0 den Bh Oa VO Let 7 be the radius of curvature of the path of the particles through (a, y, z) ; and a’ 3 ¥, its direction-cosines; then the above equations obviously become ldp d® Gt Tita gala Bed =O Ldp de _ Gat etme eee ee Nee et es Cw) ldp 4@® og,%_ Sodas dae eS If these equations are integrable, i dz oe dx+ ee dy+ — r r r must be an exact differential. Let —@ be its primitive function; the negative sien being used, because a’, (’, y’ must be generally negative. Then the integral of the equations (3) is log. O= 2 = = : (2 Q @—4)+ constant ; or taking ¢, to denote the pressure at the bounding surface of the atom :— 22 e=0,¢" Our present object is to determine the superficial-atomic density, o,, and thence 1 Cs eae aes 4 ' ; (4). the pressure p=/ @,, in terms of the mean density is and heat Q. For this pur- pose we must introduce the above value of @ into equation (2), giving 2Q a ge n=afffyer oP CaN it a a ae paho=hps fff e MEE A arayaz well 1 Let the volume of the atom be conceived to be divided into layers, in each of which ? has a constant value. Then we may make the following transforma- tions. VOL. XX. PARTI, DZ whence 430 MR W. J. M. RANKINE ON THE CENTRIFUGAL THEORY OF ELASTICITY, k(9—9) Lf [axay azar fe Vad yy ss 6) SL f- he C9 gedydz=kMV f iii e at ad. - k being a specific constant, and . and w functions of ¢, and of the nature and density of the substance. The lower limit of integration of @ must be made—~, that it may include orbits of indefinitely small magnitude described round the atomic centre. The nature of the function ¥ is limited by the following condition, p k (— 1) =i f ; é ig — 1 (7.) 2Q Let ae +1=0 Then these transformations give the following result for the pressure at the bound- ing surface of an atom :— Aw , £9, on@-9) PTT any si fod Piel sage _ fp Oo » Poa V 7 u um ‘i a, — St +s — ah + &e. p=, w’,, &c. being. the successive differential coefficients of w with respect to sp, when (4.) The following transformation will be found useful in the sequel. Let » be the indefinite value of log. V, and A, its actual value in the case under consideration. Let G be the same function of A which w is of & @, and let G’, G”, &c. be its successive differential coefficients with respect to A. Let oot e-é 1) Then a hip Ge ‘7 MY H, 2 |S The function H has the following properties, which will be afterwards referred Lo nana patna AND ITS CONNECTION WITH THE THEORY OF HEAT. 431 (5.) Case of a Perfect Gas.—As a substance is rarefied, it gradually approaches a condition in which the pressure, under like circumstances as to heat, varies pro- portionally to the density. This is because the effect of the molecular attrac- tions and repulsions on the pressure diminishes with the density, so that 4, «, and G approximate to constant quantities. In the limiting or perfectly gaseous condition, therefore, H,= 9 and pith 2Q p=atv=ay (Get!) ides lage Said ely SE (6.) Equilibrium of Heat: Nature of Temperature and Real Specific Heat.— When the atmospheres of fae of two different substances are in contact at their common bounding surface, it is necessary to a permanent condition, that the pres- sure in passing that surface should vary continuously. Let (a) and (6) be taken as characteristics, to distinguish the specific quantities peculiar to the two media respectively. Let dm denote the volume of an indefinitely - thin layer, close to the bounding surface. Then the following equations must be fulfilled, to ensure a permanent condition :— p (a)=p (6) ;sx ae a= - ar b) when p’=p . : ; ; (12.) By making the proper substitutions in equation (4), it appears, that k 8 (9-9) p=pe igh see aw Hence Pea us d (ko) p 75, (e'=p)= p (02E® 5 = 1 9) — —($—4)) —=—| @ av Now p is the same for both media: st I “is either a maximum 1 or a minimum, so that its differential is null; and dm is a continuous function d(k d(k of k ?, so that f ae oD) (a= Y ae (6). There remains only the function of heat 6= 2 Qe 1. Therefore the condition of a permanent state of molecular motion, that is to say, the condition of equilibrium of heat, is that this function shall be the same for the two substances ; or that h,k = h, i, . . : 6 - ° A 5 ° (13.) 432 MR W. J. M. RANKINE ON THE CENTRIFUGAL THEORY OF ELASTICITY, Hence, temperature depends on the above function only; for the definition of temperature is, that bodies at the same temperature are in a permanent condition as to heat, so far as their mutual action is concerned. The ratio of the real specific heat of (a) to that of (b) is obviously hk, 2 hy, &, ; : : : : : : : : (14.) (7.) Measure of Temperature and Specific Heat—The function 4 is proportional to the pressure of a perfect gas at a constant density. That pressure, therefore, is the most convenient measure of temperature. Let 7 denote absolute temperature, as measured by the pressure of a perfect gas at constant density, and reckoned from a certain absolute zero, 274°-6 Centi- grade, or 494°:28 Fahrenheit below the temperature of melting ice. Let x be a constant which depends on the length of a degree on the thermometric scale, and is the same for all substances in nature. Then T=K O= ne +K f ; , / : : : | (15.) hk Q= (T—K) IK ' : - “ fe 2 - and the real specific heat of the substance, that is to say, the depth of fall, under the influence of gravity, which is equivalent to arise of one degree of temperature in the body, is represented by hk eee ere en er en 6 ee The pressure of a perfect gas is represented in terms of temperature by _ Apt = MVkK : : : , 3 : F : ‘ (17.) It may also be expressed thus: let +, denote the absolute temperature of melt- ing ice in degrees of the scale employed, and V, the volume of unity of weight of the substance in the theoretical state of perfect gas, at the temperature of melting ice and pressure unity :—then Vier pe Sete EAR eee On comparing this with equation (17) we see that hfe ONE sae | (19.) et hut, hm _K- PeMVe MV ur, Now / is the specific elasticity of the atomic atmosphere of the substance ; L v 0 is the mean specific gravity of that atmosphere, when the body is in the theoretical state of perfect gas; and « and 7, are the same for all substances in nature. There- AND ITS CONNECTION WITH THE THEORY OF HEAT. 433 fore, for every substance in nature, the mean specitic gravity of the atomic atmosphere in the theoretical state of perfect gas is inversely proportional to the specific elasticity of that atmosphere. Real specific heat may also be thus expressed :— WV, eM = , 20. RD) (20.) SMT. oe 2p Soon The latter factor appears to depend on the chemical constitution of the sub- stance, being the same for all simple gases. ; BAN iy kM in which = corresponds to Gnu 12 my former papers, and 2p to (8.) Total Pressure of Substances in general, expressed in terms of temperature. In equation (9) let - be put for 0: then Aut KG’ K?G” P=p+f(V)=/(V) + HO G+{6,- =a a mege we } Woe A A Aé =fW)+ 37 {1-3-9 - he} ery ai) WO where —k G’ K? Ag 3s AD (GG St Gi 2 Gal 1 i) 3 A,=- es (G,?— 2 Gy G."+G,”"); &e. This formula is identical with that which I employed in my former paper, to represent the pressure of an imperfect gas, and which I found to agree with M. REGNAULT’S experiments, when the coefficients A and the function f (V) had been calculated empirically. SEcTION SEconD.—Relations between Heat and Expansive Power. (9.) Variations of Sensible and Latent Heat: Fundamental Equation of the Theory.—lIf the forms, positions, and magnitudes of the paths described by the revolving particles of the atomic atmospheres be changed, whether by a variation of mean density, or by a variation of temperature, an increase or diminution of the vis-viva of their motion, that is to say, of the heat of the body, will take place in virtue of that change of the paths of motion; an increase when they are con- tracted, and a diminution when they are dilated. Let 6 . Q represent, when positive, the indefinitely small quantity of heat which must be communicated to unity of weight of a substance, and when negative, that which must be abstracted from it, in order to produce the indefinitely small variation of temperature 6 7 simultaneously with the indefinitely small variation VOL. XX. PART III. 6A 434 MR W. J. M. RANKINE ON THE CENTRIFUGAL THEORY OF ELASTICITY, of volume 6 VY. Let 6. Q be divided into two parts ) Q+ ) Y= é. Q of which 6 Q, being directly employed in varying the velocity of the particles, is the variation of the actual or sensible heat possessed by the body; while 6 Q’, being employed in varying their orbits, represents the amount of the mutual transformation of heat with expansive power and molecular action, or the varia- tion of what is called the /atent heat ; that is to say, of a molecular condition con- stituting a source of power, out of which heat may be developed. (6 Q’ in this paper corresponds to — 06 Q/ in my former papers. ) The variation of sensible heat has evidently this value OQ=kdr Sl elk mA joo ties Let 62, dy, 62, be the displacements of the orbit of the particles of atomic atmosphere at the point (z,y, 2.) A molecule edxdydz is acted upon by the accelerative forces (see equation 3 A.) 299%; 293?; 2q%#, parallel to the three axes respectively. The sum of the actions of those forces on the molecule ed adyd z during the change of temperature and volume, is —2Q (2 Oa+ oe d+ a) odxdydz =—2Q0poedzrdydz The sum of such actions upon all the particles in unity of weight is equal in amount and opposite in sign to the variation of latent heat: that is to say, 8q= ELT] 9 ob arayas | - og Pen To determine the value of the variation 6 ¢, let it be divided into two parts, thus :— re) co) = re) P, + re) A co) where a p=$—9, First, With respect to 6 ¢,, it is obvious that because, according to equations (6, 7) pr kae MV=kMV af oe vag Sedum we must have OV=kV 09g, and 6 ¢,= on Hence the first part 4 the integral (23) is Ot [ff edrayas = SS Sate AND ITS CONNECTION WITH THE THEORY OF HEAT. 435 . =F on De |, eHORIMBI ES aT To determine the second part of the integral we have the condition, that the quantity of atomic atmosphere enclosed within each surface at which a @ has some given value, is invariable; that is to say 9) ~° (0. %755 46S an 7) (veuv fee Hence (0 ae oy 2) (teste pt) Bite ® ko,MVe x 1 The value of the second part of the integral (23) is now found to be:— OAag= ay at Af ¢babandyae ap ray fe my OS Pa =-79 (ov Arde) foamy aie se In the double integral, let >A = log. V be put for £ ¢, G for w, and H for the single integral, as in equation (9.) Then the double integral becomes dH, aT” Han -& <5" by Eq. (10) aa ag? | 20 = zd Ek) the second part of Also because e, MV = the integral (23) is found to es h H. qe rw) (Or x hia ea a ase RA Oa E8 Hence, adding together (23 A.) and (23 B.) we find for the total variation of latent heat i Pilon El 2 log H dQ= Thorn {dr- part tov: (+ See) |} oe To express this in terms of quantities which may be known directly by expe- riment, we have by equations 10 and 9 :— dH, G, EN is ar cites O, that is to say, MloggBin +G, fete! ME T avn HV KV hp’ KV 436 MR W. J. M. RANKINE ON THE CENTRIFUGAL THEORY OF ELASTICITY, and, therefore, Log, H,,= raf Pey - “log. V + f (7) + constant. f (7) is easily found to be =— log. t for a perfect gas, and being independent of the density, is the same for all substances in all conditions; Hence we find (the integrals being so taken that for a perfect gas they shall = et " Sitges M dp dv Se ee @log,H, M ap 4 1 at hp av T? d?log, H, _ Mdp_ 1 dtdV hpdt KV and, therefore, d? d 0Q= (T—K) {Or (Gen + [Taty) +dv. oP} . > (25.) is the variation of latent heat, expressed in terms of the pressure, volume, and temperature ; to which if the variation of sensible heat, 6 Q=% 07, be added, the complete variation of heat, 6Q+dQ=6. Q, in unity of weight of the substance, corresponding to the variations 6 V and 67 of volume and temperature, will be ascertained. It is obvious that equation (25), with its consequences, is applicable to any mixture of atoms of aoe substances in equilibrio of pressure and temperature ; for in that case 7, oe and 54 ? are the same for each substance. We have only to substitute for — the following expression :— y/ y/ n, Mt “Mr, + &. where 7,, 2,, &c., are the proportions of the different ingredients in unity of weight of the mixture, so that n,+n,+&c.=1. Equation (25) agrees exactly with equation (6) in the first section of my original paper on the Theory of the Mechanical Action of Heat. It is the funda- mental equation of that theory; and I shall now proceed to deduce the more important consequences from it. (10.) Equivalence of Heat and Expansive Power. JovuiE’s Law.—From the variation of the heat communicated to the body, let us subtract the variation of the expansive power given out by it, or POV={p+sf(V)} OV The result is the variation of the total power exercised upon or communicated to * This coefficient corresponds to — iz in the notation of my previous paper on the Mechanical K Action of Heat. AND ITS CONNECTION WITH THE THEORY OF HEAT. 437 unity of weight of the substance, supposing that there is no chemical, electrical, magnetic, or other action except heat and pressure ; and its value is :— dv=0Q4dq-Pdvadr. {w+ 58 (Z- 4) a0 f hav } + dv. {@-93-p-s™) | (06. This expression is obviously an exact differential, and its integral is the follow- ing function of the volume and temperature :— vat (r—«) +50 (Jog. 7 a ‘i + fr-#) eee -frmav 2%) Accordingly, the total amount of power which must be exercised upon unity of weight of a substance, to make it pass from the absolute temperature 7, and volume V, to the absolute temperature 7, and volume V.,, is 2 (VY t= FY Ver Fo) This quantity consists partly of expansive or compressive power, and partly of heat, in proportions depending on the mode in which the intermediate changes of temperature and volume take place; but the total amount is independent of these changes. Hence, if a body be made to pass through a variety of changes of temperature and volume, and at length be brought back to its primitive volume and temperature, the algebraical sum of the portions of power applied to and evolved from the body, whether in the form of expansion and compression, or in that of heat, is equal to zero. This is one form of the law proved experimentally by Mr Jouts, of the equiva- lence of heat and mechanical power. In my original paper on the Mechanical Action of Heat, I used this law as an axiom, to assist in the investigation of the Equation of Latent Heat. I have now deduced it from the hypothesis on which my researches are based ;—not in order to prove the law,but to verify the correct- ness of the mode of investigation which I have followed. Equations (26) and (27), like equation (23), are made applicable to unity of weight of a mixture, by putting =» & for &, and =x oa for ae The train of reasoning in this article is the converse of that followed by Pro- fessor WiLLIAM THomson of Glasgow, in article 20 of his paper on the Dynamical Theory of Heat, where he proves from JouLe’s law, that the quantity correspond- ing to 6 ¥ is an exact differential. (11.) Mutual Conversion of Heat and Expansive Power. Carnot’s Law of the Action of Expansive Machines.—If a body be made to pass from the volume V, and absolute temperature 7, to the volume V, and absolute temperature 7,, and be then brought back to the original volume and temperature, the total power exerted VOL. XX. PART III. 6B 438 MR W. J. M. RANKINE ON THE CENTRIFUGAL THEORY OF ELASTICITY, (¥) will have, in those two operations, equal arithmetical values, of opposite signs. Each of the quantities ¥ consists partly of heat and partly of expansive power, the proportion depending on the mode of intermediate variation of the volume and temperature, which is arbitrary. Ifthe mode of variation be different in the two operations, the effect of the double operation will be to transform a portion of heat into expansive power, or vice versa. Let (a) denote the first operation: (6) the reverse of the second. Then Ye The terms of ¥ which involve functions of 7 only, or of V only, are not affected by the mode of intermediate variation of those quantities. The term on which the mutual conversion of heat and expansive power depends, is therefore fo-9Zvo = [o-oPav@ or, es ) dV (b)= SGP ) dV (a) Hence, ge av (a) ao aV (6) = [vav@) - foavy which last quantity is the amount of the heat transformed into expansive power, or the total latent heat of expansion in the double operation. Let DD an 1 4Q ow_ a) ee et Then because ad / tv av= (T—k) d¥ fre Are dF @fe-9 dF (6) = / (7,-7)dF=/ 1.—74Q, | -fe es 7 "dV : ; E - (8) In which 7, and 7, are the pair of absolute temperatures, in the two operations respectively, corresponding to equal values of F. This equation gives a relation between the heat transformed into expansive power by a given pair of operations on a body, the latent heat of expansion in the first operation, and the mode of variation of temperature in the two opera- tions. It shews that the proportion of the original latent heat of expansion finally transformed into expansive power, is a function of the temperatures alone, and is therefore independent of the nature of the body employed. Equation (28) includes Carnor’s law as a particular case. Let the limits of we have AND ITS CONNECTION WITH THE THEORY OF HEAT. 439 variation of temperature and volume be made indefinitely small. Then = dQ dpadV=-— -aV av and dividing by dtadV i ee d ( dt T—K' dV This differential pear is also an immediate consequence of equation (25.) ff f be put for — and J M for a it becomes identical with the equation by ae Professor WILLIAM mee expresses Carnor’s law, as deduced by him and by Mr Crausius from the principle, that 7 is impossible to transfer heat from a colder to a hotter body, without expenditure of mechanical power. The investigation which I have now given is identical in principle with that in the fifth section of my paper on the Mechanical Action of Heat; but the result is expressed in a more comprehensive form. Equation (28) like (25), (26), and (27), is applicable to a mixture, composed of any number of different substances, in any proportions, provided the temperature, 2 the pressure, and the coefficients ae = are the same throughout the mass. (12.) Apparent Specific Heat.—The general value of apparent specific heat of unity of weight, is dQ. dQY dQ dV _ hp 9 ae sgl oa al : aS Sa Fie Pragee Fie wa eck {a Mot aa aia dias - (29.) agreeing with equation 13 of my previous paper. The value in each particular case depends on the mode of variation of volume with temperature. Specific heat at constant volume, is h d” p iie—% +(T—K) (sr + aie av ) ; A 3 5 (30.) When the pressure is constant, we must have dP ae 2 av d V + ne d i, == O and, consequently, dp dV dt at ie, ae dV therefore specific heat at constant pressure, is dp K =K,+ (7— kee) A Te MIE 1 737) aV This agrees with equation (16) of Professor THomson’s paper, if J u in his notation = 7T— K. 440 MR W. J. M. RANKINE ON THE CENTRIFUGAL THEORY OF ELASTICITY. If the body be a perfect gas, then Ka“ KIM Kk, K* “Sk aV Tao tin aca emg) K,= <9 (50+ *-S) Ty ee oF NV; Na fe NE pie K =K += (1 - *) - (sp +1-s) 0 The fact that the specific heats of all simplé gases for unity of weight are in- (32.) versely proportional to their specific gravities, shews that — is the same for them all. (13.) Velocity of Sound in Fluids.—Let a denote the velocity of sound in a fluid, and d. P the total differential of the pressure. Then rag Oe ee - dP ibaa aav(y. raw {9% Ce sae, } dv (33.) If it were possible to maintain the temperature of each particle of the fluid in- variable during the passage of sound, this velocity would be simply : aP “ (y i‘ dl ) Vv But we have reason to believe, that there is not time, during the passage of sound, for an appreciable transfer of heat from atom to atom; so that for each particle . dQ+dQ=O0; or, K=O in equation (29). To fulfil this condition, we must have OT >~tTK\ d ip dN YH [dis Consequently, safer (Ee (2) or, by equation (31) Ge KG. a= nif (95 . = . > . . . . . (34). Vv That is to say, the action of heat increases the velocity of sound in a fluid, beyond what it would be, if heat did not act, in the ratio of the square root of the specific heat at constant pressure, to the square root of the specific heat at constant volume. This is Lapiacr’s law of the propagation of sound; which is here shewn to be applicable, not only to perfect gases, but to all fluids whatsoever. ( 447) XXVUI.—On the Computation of the Specific Heat of Liquid Water at various Temperatures, from the Experiments of M. Regnault. By Wit11aM JoHn Macquorn Rankine, Civil Engineer, F.R.S.E., F.R.S.S.A., &e. (Read December 15, 1851.) Correction of M. Regnaults Experiments for the Effect of Agitation. The discovery by Mr Joute of the fact, that mechanical power expended in the agitation of liquids is converted into heat as the visible agitation subsides, renders a certain correction necessary in calculating the results of experiments on specific heat in which such agitation has occurred. Of this kind are the experiments of M. ReaNavutt on the apparent specific heat of liquid water at different temperatures. Water at a high temperature, T,, was emitted from a boiler into a calorimeter containing water at a low tempera- ture, T,, and the resulting intermediate temperature of the whole mass, T,, was used as the means of calculating the ratio of the mean specific heat of water be- tween T, and T,, to its mean specific heat between T, and T,. Now, the upper part of the boiler contained steam at a high pressure, so that the hot water was expelled with great force. The vis-viva thus communicated to the water, having been converted by fluid friction into heat, ought to be allowed for in computing the results of the experiments, Let W, be the weight of water originally contained in the calorimeter, at the temperature T, : W,, The weight of water introduced into the calorimeter from the boiler, at the temperature T, ; T,, the resulting temperature, corrected, as has been done by M. Ree@nauttr, for the effect of conduction. Let K,, , be the mean dynamical specific heat of water between the tempera- tures T, and T,,— K,, ,, its mean dynamical specific heat between T, and T,. Let P be the pressure of steam of saturation at the temperature T,,— a, the pressure of the atmosphere,— And 2, the volume of unity of weight of water at the temperature T.,,. Then the following equation must be fulfilled ;— W,K, (T,—T,)—W, K,, ; 1,-T,)-—W, (P-@)v=0: Consequently, K,, yee W, (T, —T,) 2 (Eo) Y : . \ (1.) K,, 2 W,; (T,—T,) K,, 2 (T;—T,) VOL. XX. PART III. 6c 442 MR. W. J. M. RANKINE ON THE COMPUTATION The first term of this expression corresponds to the formula employed by M. Reanautt. To correct the results given in his table of experiments, we must, therefore, subtract from each of them the quantity (P—@) v K,, 2 (T, - T,) As T, and T, were always low temperatures, I have treated K,, , as a con- stant quantity in computing the corrections, its value being N Common umber. E Logarithm. In feet per degree of Fahrenheit, . : : ‘ 772 2-8876173 In feet per centigrade degree, : : ; : 1389°6 3°1428898 In métres per centigrade degree, . ; : 423-54 2-6268944 In the following table, the numbers in the first column refer to certain groups of experiments in M. Reenavtr’s table, the mean results of which are given in the succeeding columns. The correction, which is scarcely appreciable for temperatures near the ordi- nary boiling point, increases rapidly as the temperature in the boiler rises. The temperatures are all stated according to the scale of a centigrade air ther- mometer. TABLE I. Ky,3 Reference to kK. : Ko, 3 M. REGNAULT’S T, T, 1; 1,2 = Correction to Kis Experiments. aa eee be subtracted. Oona ae 10,237 11-97 20-77 107-79 | 1-00384 0:00009 | 1:00375 Aes Oeane 8°39 17:70 109-29 1:00665 0:00010 1:00655 Nos rly OX8), DG. 12:96 26°31 159-74 1:00871 0-:00092 1:00779 30; Sle 32, a3. 8:95 23°94 172:°69 1:01140 0:00121 1:01019 SOMONOOF 12:97 28:69 18651 1:01581 0-00162 1:01419 Empirical Formule. The results of experiment, as thus corrected, agree very nearly with those of the following empirical formula, in which K is the apparent specific heat of liquid water at the temperature T, and K,, its apparent specific heat at the tempera- ture T,, which is that of the maximum density of water; viz., 4°-1 centigrade, or 39°°4 Fahr. a is a constant coefficient, whose value is, For the centigrade scale, : ; : : é 0-000001 For Fahrenheit’s scale, . j J ‘ < : 0:000000309 OF THE SPECIFIC HEAT OF LIQUID WATER. 443 Rated Ty = eon ff Kat 20 od TORE RE.) K, K, (,—T)) ibs =1+ : { (Eye Dei th) (T,—T,) + (1, —T,)? } The following Table exhibits a comparison between the results of equation (3.) and those of the five groups of experiments already referred to :— TABLE IT. K Kas x. Ty T, Ts 12 by the Empi- Difference. by Experiment. cal Formula. 11:97 | 20:77 107-79 1:00375 1:00409 + 0:00034 3:39 Le (azo 109-29 1:00655 1:00414 — 000241 12:96 [> 96°31 159°74 1:00779 1:00959 + 0:00180 8-95 | 9394 172:69 1:01019 | * 1:01055 + 0:00036 12°97 | 98-69 186-51 1:01419 1-01248 —0-00171 A third Table is annexed, which may be found practically useful. It contains the results of the empirical formule (2.) and (3.), for every tenth degree of the centigrade scale from 0° to 260°. The column headed 4 shews the ratio of the specific heat at T to the specific 0 Beaeat 0°. That headed = m 0 0° and T to the specific heat at 0°. shews the ratio of the mean specific heat between 1 Ad The column headed y- i) K dT shews the ratio of the heat required to raise °F 0 a given weight of water from 0° to T, to the heat required to raise the same weight of water from the temperature of maximum density to one degree above it. t44 100 110 120 ON THE SPECIFIC HEAT OF LIQUID WATER. 1:0000 1:0000 1:0001 1:0002 1:0004 1:0006 1:0010 1:0014 1-:0018 1:0023 1:0029 1-0036 1:00428 1:0051 Ay | Centigr. 140 150 160 170 180 190 200 210 220 230 240 250 260 ( 445 ) 4 XXIX.— On the Red Prominences seen during Total Eclipses of the Sun. Part lI. By Wiuttam Sway, F.R.S.E. (Read April 5, 1852.) The red prominences seen during total solar eclipses, are conspicuous rose- coloured objects which appear round the dark edge of the moon, as soon as the last rays of the sun have disappeared. In preparing my account of the total eclipse of the 28th July 1851, it was at first my intention to have stated some hypothetical views which I had formed regarding those remarkable objects, and other appear- ances I had observed during the total phase of the eclipse. I found, however, that the mere description of phenomena extended to so great a length, as to render such a course inexpedient; and I have since delayed resuming the subject, in order that by comparing a number of other observations with my own, I might be enabled, either to confirm or to modify my views. The object of the first part of this paper is, To discuss the evidence afforded by the observations of the late eclipse to which I have obtained access, as to the nature and locality of the red prominences; and, of the second part, To state the views which I have been led to form regarding the cause of those singular objects, and their probable connexion with other solar phenomena. In inquiring into the nature of the red prominences, I shall examine in suc- cession different opinions, which have either been formally announced, or are likely to be entertained, regarding them, in order to ascertain which of those hypo- theses is most accordant with actual observation. The hypotheses I shall discuss are the following, namely, 1st, That the prominences are optical phenomena, caused by the telescope used in viewing the eclipse,—by the unequally heated state of the earth’s atmosphere,—or by the action of the moon’s edge on the rays of light ; and, 2d, That they are material objects, existing in the sun or in the moon. I. On the Hypothesis that the Red Prominences are Optical Phenomena. “1. On the Visibility of the Red Prominences to the Naked Eye. 1. It may be supposed that the red prominences are optical phenomena caused by the telescope used in viewing the eclipse; but this opinion is at once disproved by the fact, that they are visible to the naked eye. At the late eclipse, although I was unable to distinguish the /orms of the prominences with the naked eye, I had no difficulty in seeing the position of at least one of them, by the strong red tinge it imparted to the adjacent portions of the corona. It was also seen by Mr Lane, who observed the eclipse along with me. Mr Apir saw the same pro- VOL. XX. PART III. 6D 446 MR WILLIAM SWAN ON THE minence “ distinctly,” “ with its marked colour;”* and it was seen by so many persons at Goteborg, that its visibility to the naked eye was a common subject of conversation for some days after the eclipse. Mr Witiams observes, that “ the largest red prominence was visible by the unaided eye;”+ and Mr Arry states, in his Account of the Total Eclipse of 1842, that an observer who accompanied him saw these objects with the naked eye.t The only observer of the late eclipse who formally states that he could not see the prominences without using a telescope, is Lieutenant Krac;) but such nega- tive evidence cannot affect the concurring testimony of so many observers who saw them distinctly by unaided vision; and we must therefore reject the idea that they are caused by the telescopes used in observing the eclipse. || 2. On the Hypothesis that the Red Prominences are Phenomena arising from the Action of unequally heated Strata of Air on the Sun’s rays. Another opinion regarding the red prominences is that advanced by M. Fave, who conceives them to arise from a species of mirage, occasioned by the unequally heated state of the atmosphere during a total eclipse. The air all round the moon’s shadow is heated by the sun, while that within the shadow is sheltered from his rays. This he conceives occasions a reduction of temperature in the air within the shadow; and the warm air without, communicating its heat to that within, gives rise to a succession of concentric layers gradually decreasing in tem- perature, from the surface of the shadow inwards. These layers of unequal den- sity, acting on the rays proceeding from the edge of the moon to the observer’s eye, will, it is assumed,—like the unequally heated strata of air which sometimes exist near the horizon,—produce the well known phenomena of mirage. The red prominences, he supposes, are then merely the magnified and distorted images of Junar mountains, illuminated obliquely by the sun.4] * Edinburgh New Philosophical Journal, Oct. 1851, p. 375. t+ Royal Ast. Soc. Notice, Jan. 1852, p. 54. t Royal Ast. Soc. Notice, for Nov. 1842, p.220. § Royal Ast. Soc. Notice, Jan. 1852, p. 47. || M. Araco’s highly interesting Account of the Total Eclipse of July 1842, in the Anniaire for 1846, contains ample evidence of the visibility of the red prominences to the naked eye. The following are some of the testimonies to that fact. M. Araco says, “ A Perpignan, plusieurs per- sonnes virent les protubérances & Vail nu. Le fait n’est pas douteux.” (p. 412.) M. Fravcurrcugs, who observed at Toulon, remarks, ‘“ Je n’avais point encore repris le télescope, lorsque je fus surpris par Vapparition d’un point lumineux rouge; puis, d’un second point semblable.” (p. 418.) M. Santrnt, who observed the eclipse at Padua, relates that several persons saw the prominences with the naked eye, (p. 427.) I did not obtain access to M. Araco’s admirable Memoir until after this paper had been read ; otherwise I should have gladly availed myself more fully of its valuable contents than is now possible. PS Cette atmosphére conique [‘ le céne d’ombre’] doit produire, dans ses couches succes- sives, concentriques et de plus en plus froides, les phénoménes analogues aux réfractions qui s’opérent rés de l’horizon, en un mot, des phénoménes de mirage.” “ Les montagnes roses qui apparurent alors [8 Juillet 1842], ne seraient autre chose que les images démesurément agrandies et déformées de quelques parties des montagnes lunaires, éclairées obliquement par le Soleil, et visibles 4 travers des vallées qui se trouvent ¢a et la, dans une direction favorable, sur le bord apparent de la Lune.”— Comptes Rendus de ? Academic, 4 Nov. 1850, p. 648. RED PROMINENCES SEEN DURING TOTAL ECLIPSES OF THE SUN. 447 In reference to this opinion, Mr Airy has observed, “that in the rapid passage of the moon’s shadow he conceived it impossible to find air in the state required for the explanation”’* proposed by M. Fayr. But even if the atmosphere exist in the state he has supposed, it is evident that the inequality of tempera- ture in the successive layers of air, must decrease rapidly from the surface of the shadow inwards, and hence the phenomena of mirage must vary, according as the observer is situated near the edge of the shadow or near its centre. If then, the prominences are caused by the unequal heating of the air, on the two sides of the path of light ; we might expect them to attain their maximum size and distinctness near the beginning and end of the total phase of the eclipse, and about those times, they ought to vary rapidly in appearance: for the light passing near the surface of the shadow then traverses, in succession, strata of air of rapidly decreasing temperature. Near the middle of the totality, on the contrary, the phenomenon ought to be almost insensible, as the rays then traverse air far removed from the heating action of the sun, and of nearly uniform tem- perature. Let us inquire how this agrees with what was actually observed at the late eclipse. Mr Dunxin remarks, that one of the prominences “was most curiously formed, having something of a horned shape;” that his “eye was intently fixed upon it for about a minute of time, and during that interval not the slightest change took place in its form.”+ Lieutenant Perrersson “ observed no change [in the form of the prominences] that was not due to the motion of the moon.” According to Mr Apre, “no change was observed in the form or position of the prominences, or - in the position of the detached mass of light [relatively] to that of the crescent, farther than that due to the motion of the moon; nor did there appear any insta- bility or wavering, in their colour or intensity.” Mr Carrineron “ cannot depose to have seen the slightest change” of outline in the large prominence: and he afterwards states, that the prominences had “hard and well-defined outlines.”’| Mr LassEuu states, that “ the prominences were of a most brilliant lake colour, a splendid pink, quite defined and hard. They appeared to him ‘ not quite quiescent, but the moon by her movement might cause an idea of motion.’”4{ With refer- ence to the largest prominence, Mr Hrnp says he “ perceived no change of form or motion, and it was visible four seconds after the sun reappeared, but detached from the sun, the strong white light of the corona being visible between it and the sun.”’** Mr Dawes observes, regarding the same prominence, that “ its apex was paler than the base, and of a purplish tinge; and it certainly had a flicker- * Lecture by Mr Arry on the Total Solar Kclipse of 1851, July 28, p. 6.—Atheneum, No. 1230, p. 559. + Ast. Soc. Notice, p. 46. t Ibid., p. 58. § Edin. New Phil. Journal, 1851, p. 375. || An Account of the late Total Kclipse of the Sun, by R. C. Carrineton, Hsq., pp. 7, 10, @ Ast. Soc. Notice, p. 53. ** Thbid., p. 67. 448 MR WILLIAM SWAN ON THE ing motion. Its base was from first to last sharply bounded by the edge of the moon.” ‘To my great astonishment,” he adds, “ this marvellous object con- tinued visible for about five seconds, as nearly as I could judge, after the sun began to reappear, which took place many degrees to the south of the situation it oc- cupied on the moon’s circumference. It then rapidly faded away, but it did not vanish instantaneously.’’* . These observations seem quite inexplicable, on the hypothesis that the pro- minences result from mirage occasioned by the unequal heating of the air. For not only did they preserve their forms unchanged during a period at which little or no unequal heating of the air could have taken place; but according to the very important observations of Mr Dawes and Mr Hrnp, they continued visible, apparently without change of form, even after the reappearance of the sun. Now, at the reappearance of the sun, the air in the path of light would rapidly pass through the three states, of being first entirely protected from the sun’s rays, then heated on one side at the moment of reappearance, and finally heated on both sides.t| About that time, then, if phenomena of the nature of mirage ex- isted, we might expect the most rapid and conspicuous changes of form to occur; but instead of this being the case, the prominences retained their forms unal- tered, until they vanished before the direct light of the sun. On these grounds, we must therefore regard the hypothesis which would refer them to the unequal heating of the air, as quite untenable. * Ast. Soc. Notice, p. 69; or Astronomische Nachrichten, No. 777. M. Mayerte at the eclipse of 1842, saw one of the red prominences after the sun had reappeared (quelques instantes apres l’emersion du Soleil.\—Annuaire, for 1846, p. 411; see also p. 421. M. ContTI saw the prominences for a long time (per lungo tempo), after the reappearance of the sun ; and M. Brera for some seconds, pp. 428,429. The statement of the latter observer is particularly explicit. “ Les premiers rayons du Soleil se montrerent en divers points séparés. Bientdt ces points se réunirents et formerent une lunule tres-déliée. Quelques secondes aprés la formation de cette lunule, les pyramides rougeatres cessérent de se voir.” + May not the unequal heating of the air on the two sides of the path of the solar rays be the chief cause of the remarkable fluctuations in the sun’s light, which have been observed at the be- ginning and end of the total phase of a solar eclipse? M. Savourntn, an observer of the eclipse of July 1842, relates, “ On a vu ici des ombres et des taches Iumineuses courir les unes aprés les autres, comme paraissent le faire les ombres produites par de petits nuages qui passent successivement sur le Soleil. Ces taches n’étaient pas de la méme couleur; il y en avait de rouges, de jaunes, de bleues, de blanches. Les enfants les poursuivaient et essayaient de mettre la main dessus. Ce phénoméne extraordinaire fut remarqué quelques instants seulement avant Ja disparition compléte du Soleil.” —Annucire for 1846, p. 393. The strata of illuminated and dark air at the surface of the moon’s shadow, if their temperatures, and consequently their densities differ, cannot fail to mingle irregularly, and occasion fluctuating movements in the transmitted rays of light, similar to those which cause the dancing motion of objects seen through an ascending current of heated air, or through liquids of unequal densities which are in the act of mixing. This may also serve to ex- plain the flickering appearance of the prominences noticed by some observers ; which, from the terms used in describing it, was evidently not a permanent change of outline, but merely a fluctuation of their forms about a mean condition, Thus Mr Dawers and Mr Goon, who saw on the moon’s southern limb a long range of low prominences, both describe it as in motion. Mr Dawes, however, says, its irregularities appeared permanent, and he ascribes its undulation to our own atmosphere, RED PROMINENCES SEEN DURING TOTAL ECLIPSES OF THE SUN. 449 3. On the Hypothesis which would refer the Phenomenon of the Red Prominences to the Action of the Moon’s Limb on the Sun’s Rays. If we suppose the prominences to be caused by some action of the moon’s limb on the rays of light, whatever hypothesis we form regarding the precise nature of that action, it is evident, that the effect produced will depend in some way upon the relative positions of the luminous object,—of the body acting on its light,—and of the observer's eye. Any change in the position of the observer relatively to the sun and moon, would seem to necessitate some change in the appearance of the red prominences, supposing them optical phenomena of the nature of reflexion or diffraction; and these are the only known species of phenomena which the action of the moon’s limb on the sun’s light would occasion. Now, as the moon and earth are in rapid motion, the position of an observer relatively to the line joining their centres is continually changing; and in order to see the supposed optical phenomena always from the same point of view, it would literally become necessary for him to run a race with the moon’s shadow. It thus seems difficult to avoid the conclusion, that if the red prominences were caused by the action of the moon’s limb on the sun’s light, their appearance should rapidly change during the progress of the eclipse. But it has already been seen, that their forms remained unaltered; and it is therefore in the last degree improbable that they are optical phenomena, caused by the action of the moon’s limb on the sun’s light. II. On the Hypothesis that the Red Prominences eaist in the Sun or Moon. On these grounds it seems impossible to regard the prominences as mere optical phenomena. Let us now inquire whether equal difficulties attend the sup- position that they are objects really existing in the sun or moon. 1. On the Discrepancies in the Observed Positions of the Red Prominences. The observers of the late eclipse seem frequently to have adopted no better means of ascertaining the angles of position of the red prominences, than estima- tion by the eye, with reference either to the sun’s vertex or north point; and in many cases the point of reference is confessedly only roughly estimated. In some instances also, the angles have been merely guessed by the editor of the Royal Astronomical Society’s Transactions, from the drawings furnished by the ob- servers ;* and in such circumstances, we may be prepared to expect notable dis- crepancies in the observations. In other cases, however, greater care was taken to ensure accuracy. Thus Mr Dawes observed the eclipse with a telescope equatorially mounted, having cross * Royal Ast. Soc. Notice, p. 43. VOL XX. PART III. 6 E 450 MR WILLIAM SWAN ON THE spider-lines in the eye-piece, which were carefully adjusted to polar and equatorial directions.* By this arrangement, the moon’s limb could be readily divided into four quadrants, so as to facilitate the estimation of angles of position. I employed a position micrometer, expressly devised for the purpose of re- gistering the places of the red prominences;} and although we witnessed the eclipse under very different circumstances, and I failed to see a number of promi- nences which Mr Dawes has figured, yet our observations of the objects which we both saw, agree so closely, as to render it probable, that if some efficient means of ascertaining angles of position had been generally adopted, the observations would usually have been accordant. On comparing the different observations, it appears that at least two isolated red prominences were seen to the east of the sun’s north point; a long sierra or range of red prominences on the sun’s southern limb; two detached prominences towards the west of the sun’s vertex ; a large hook-shaped prominence also to the west ; a small prominence detached from the moon’s limb, a little to the south of the hook-shaped prominence; and two prominences between the large one and the western end of the sierra. These objects were by no means equally remarkable in appearance; and, ac- cordingly, they did not all receive the same share of attention. Probably on this account, differences, so great, occur among the observed angles of position, in the case of some of the less conspicuous prominences, as to render it impossible, in some instances, to determine with certainty to which of them the observations refer. I think it then sufficient, to select the hook-shaped prominence already noticed, as the object which, on the whole, excited most attention,—whose place may thus be assumed to have been the best ascertained,—and of which the ob- served angles of position are therefore the most likely to throw light on the nature of the red prominences. In the absence of information regarding the manner in which the different ob- servers ascertained their angles of position, I have given all the observations equal weight; and the following table exhibits the several positions assigned to the hook-shaped prominence, with the difference of each from the mean of the whole. Such of the angles as were reckoned from the sun’s vertex, I have reduced to his north point, by means of the latitudes of the stations, and the times of , obser- vation, supposing the observations to be made at the middle of the total phase of the eclipse. As, however, those data are sometimes only approximately known, the reduction of the observed angle is not always quite correct; yet, I believe, the error in no case will be found to amount to 1°, so that the comparison of the ob- servations is sufficiently exact for the purpose intended. * Astronomische Nachrichten, No. 777. 7 Plssk RED PROMINENCES SEEN DURING TOTAL ECLIPSES OF THE SUN. 451 Observed Angles of Position of the Hook-shaped Red Prominence. OBSERVER. ee . see Ch Difference. Adie, 4: ’ 293°6 417°5 Airy, i ; 302°6 +26°5 Carrington, . 222 — 39 Dawes, . ‘ 282°5 + 6-4 Dunkin, . ; 245°3 — 30°8 Good, : , 287-1 +11-0 Gray, ; : 255 —21:1 Hind, : ; 275 — iL Humphreys, . 259-9 = NG Jackson, 3 280-5 + 4:4 Lassell, . é 270 — /6:1 Pettersson, ; 282°6 + 6:5 Snow, : : 265°3 —10°8 Swan, : , 282°1 + 6:0 Wichmann, : 984 tL '9/c(9) Williams, : 280 a5, Bg) Mean ofall, . 276-1 0-0 I believe the discrepancies exhibited by these observations are fairly within the limits of error, when it is considered that the angles of position were roughly estimated during the haste and excitement unavoidably attending observations of a total solar eclipse.* If, on the other hand, they are regarded as too great to arise from mere errors of observation,—and it be attempted to reconcile the obser- vations, by supposing that the prominences are merely optical phenomena, which actually appeared differently at different stations,—it can easily be shewn, that nothing is gained by such a course. Granting, for the sake of argument, that the prominences are optical pheno- mena, it would still follow, that they should have appeared in exactly the same positions to observers situated at precisely the same point on the earth’s surface. Yet we find Mr Lasset and Mr Wititams differ by 10°, in assigning the position of the hook-shaped prominence, although they observed from the same house.t * M. Araco observes, “ Admettons un moment que les flammes étaient des parties in- tégrantes du Soleil,’—“ Deux queleonques de ces flammes ayant été visibles dans deux stations différentes, a Montpellier et 4 Turin par exemple, ne purent manquer de s’y présenter dans les mémes positions relatives et avec des formes identiques. Or les relations ne s’accordent pas toutes avec ce principe. Je m’empresse d’ajouter que la briévéte du temps dont les astronomes purent disposer pour mesurer les protuberances, pour determiner leurs assiette, et par-dessus tout, que la surpris que chacun éprouva au moment d’une apparition si inattendue, durent beaucoup nuire a |’exactitude des observations.” —Annuaire for 1846, p. 453. The observers of the late eclipse, certainly cannot plead the surprise occasioned by an unforeseen appearance as areason why their accounts of the red promi- nences are not more consistent. But I believe they will agree with me in thinking, that a closer coinci- dence cannot be expected in observations so hastily conducted, and where the phenomenon observed. was one whose novelty and grandeur were fitted to excite the most powerful emotions. t Ast. Soc. Notice, pp. 53, 54. 452 MR WILLIAM SWAN ON THE Mr Dunxin and Mr Snow, who were both stationed near the observatory in Christiania, differ by 20° in their observations of the same remarkable object. Lieutenant Perrersson, Mr Apis, Mr Airy, and myself, were all situated within a circle of about two miles radius, yet while Lieutenant PETTERSsoN’s observation of the hook-shaped prominence agrees almost exactly with mine, Mr Apig, and Mr Airy differ from us by 13° and 22° respectively. Here then, where, even on the hypothesis that the prominences are merely optical phenomena, we should expect identity of position, we meet with alarming discrepancies. On the other hand, although Mr Dawes was stationed above 100 miles from Goteborg, the position he assigns to the hook-shaped prominence, agrees almost exactly with that given by Lieutenant Perrersson and by me; and Mr Hinp also, who was near Mr Dawes, differs from us by less than 8°. Now, as Goteborg was near the middle of the moon's shadow, while Ravelsberg, where Mr Hinp and Mr DaweEs observed, was near the southern edge of the shadow, the eclipse was seen at the two stations under widely different circumstances; and on the optical hypothesis, we might expect great discrepancy in the angles of position. The coincidence in the observations is therefore strongly in favour of the view that the prominences are material objects; and this conclusion is strengthened, when it is borne in mind that the hook-shaped prominence being seen near one of Mr Dawes’s cross-wires, its position could be estimated with great accuracy, and my angles of position were actually measured ; so that the close agreement of our observations is by no means to be attributed to chance. The only other person, so far as lam at present aware, who has determined the position of the hook- shaped prominence by actual measurement, is M. WicumMann, who observed the eclipse with the Konigsberg heliometer. He states his determination as some- what doubtful; but it agrees so well with that of Mr Dawes, and with my own, as to render it highly probabie that the positions of that prominence, as seen from stations nearly 400 miles distant, were identical. The following table con- tains the observations to which I have now referred; and I have added those of the spots on the sun, in order that it may be seen that the discrepancies in the observed positions of the prominence scarcely exceed those in the positions of the spots. As the spots are objects which, while they last, have their positions, if not permanent, at least subject only to small and slow changes, we cannot attribute the variations in their observed positions to change of place. We must therefore refer these discrepancies to errors of observation ; from which it follows inevitably, that the variations in the observed positions of the prominence, as they scarcely exceed those in the positions of the spots, are also within the limits of errors of observation. The agreement of the measured angles of position of that object appear, in- deed, sufficiently close, when we advert to the circumstance that it must have * Astron,, Nachrichten, No. 787, p. 328. RED PROMINENCES SEEN DURING TOTAL ECLIPSES OF THE SUN. 453 subtended an angle of not less than 4°°5 on the moon’s limb ;* and its figure being irregular, the different observers may have estimated the position of points in it whose places varied considerably. . Angles of Position of the Hook-Shaped Prominence. Angle of Position of Hook- OBSERVER. Station. Shaped Prominence from Sun’s North Point. Angles of Position of Spots near the Sun’s Limb. Dawes, Ravelsberg, 282° 30’ 88° 0 Swan, Goteborg, 282 8 One lf 288° 47’ Wichmann, Konigsberg, 284 0 86 40 Parsee 87) It thus appears, that the discrepancies in the angles of position, cannot be explained on the hypothesis that the prominences are merely optical phenomena which appeared differently at different stations; for as great differences occur be- tween observations made at the same place, as between those made at stations widely removed from each other. It has also been seen, that where the angles of position were carefully ascertained, the places of prominences seen at distant stations, situated very differently in the moon’s shadow agreed closely; which is unfavourable to the idea that these objects are merely optical phenomena. 2. On the Discrepancies in the Forms assigned to the Red Prominences by different Observers. The forms assigned by different observers to the red prominences exhibit, as might be expected, considerable diversity. The large hook-shaped promi- nence, to which reference has been so often made, was seen by every one, and engrossed a large share of attention. Several drawings of this remarkable object by different observers, are given in fig. 9, Plate XI.+ In its neighbourhood wasa small red spot, completely detached from the sun’s limb, and also a low promi- nence, neither of which was seen by all the observers. ~The drawings of this group differ in the occasional absence of the smaller detached prominence, or of the low one, and also in the form assigned to the hook-shaped prominence ; but all agree in giving the latter a form curved in the same direction. Considering the hasty nature of the observations, the various powers possessed by different indi- viduals of delineating objects, and the fact that the drawings must either have been _ * In this estimation it is supposed that the breadth of the prominence was about two-thirds of its height, or 80”; an assumption which seems fully warranted by the drawings of the prominence given by most of the observers, _{ The drawings of the hook-shaped prominence in fig. 9, are all taken from the Royal Astro- nomical Society’s Notice for January, with the exception of Mr Apix’s, which is enlarged from the plate accompanying his account of the eclipse in the Edinburgh New Philosophical Journal. VOL. XX. PART III. OF 454. MR WILLIAM SWAN ON THE made from memory, or hastily sketched during the totality ; there seems suffi- cient resemblance between them, to shew that they all represent the same object.* But here again, if the differences in the drawings are thought sufficient to shew that the objects were optical phenomena,—differently delineated by the observers, because their forms actually varied when seen at different stations,—it will be found that the difficulties are as great as before. If the figures given by Mr Lassetit, Mr Wiuuiams, and Mr SrannisTREET (See fig. 9, Nos. 1, 2, 3), who observed from the windows of the same house, be compared, it will be found that they exhibit as great inconsistencies as any of the other drawings: for all assign to the hook-shaped prominence different forms; and while Mr WiuuiaAms did not see the detached prominence, nor Mr LassELL the low one, Mr STaNNISTREET saw both. Again, Professor CHEVALLIER and Mr Avie (See fig. 9, Nos. 4 and 5), who observed from the roof of the same house, differ greatly in the delineation of the hook-shaped prominence ; for while the latter saw the detached prominence, the former did not see it. Lieutenant Perrersson also, who was scarcely a mile distant from them, gives a figure of the hook-shaped prominence totally unlike their drawings (See No. 6). Contrasted with this, we have Mr Arry’s and Mr CHEVALLIER’S drawings agreeing well with that of Mr Wiuuiams (See Nos. 7, 4, and 2), who was distant 40 miles from them; and Mr Hinp’s and Mr Dawes’ resemble closely my own (fig. 9, Nos. 8 and 9, and fig. 8), although we observed at a distance of nearly 100 miles. In this case, then, as formerly, the optical hypothesis is of no service in reconciling discrepancies between the observations; for we have the observations agreeing, where on that hypothesis we should expect them to differ, and differing where they ought to agree. It thus appears, that any objections to the hypothesis, that the prominences are objects existing in the sun or moon, founded on a want of agreement in the observed angles of position, and in the: forms assigned to those objects, apply with at least equal force to the hypotheses that they are optical phenomena ; while it has already been shewn, that the latter hypotheses labour under insur- mountable difficulties peculiar to themselves. The objections to the idea, that the prominences are material objects being thus more than neutralised, the coin- cidence in the observations of position at tolerably distant stations in cases where the angles were carefully ascertained, affords the undiminished weight of * While the causes now enumerated account sufficiently for much of the general diversity in the representations of the hook-shaped prominence, there are at the same time certain different types of form which may be observed among the drawings, and which can scarcely be referred to these causes. On comparing Nos. 2, 4, 7 with Nos. 8, 9, fig. 9, and also with fig. 8, it will be seen that the first three drawings are very like each other, as are also the last three, while there is little resemblance between the two sets. The first three represent the hook-shaped prominence as seen through rather large telescopes; the second, through small ones; and, as it is well known that certain telescopic objects vary greatly in appearance according to the instrumental power brought to bear on them, it may be worth inquiry, whether the same is not also the case with the red prominences. RED PROMINENCES SEEN DURING TOTAL ECLIPSES OF THE SUN. 455 its evidence in favour of that hypothesis. That they really are material objects, and that they are situated in the sun, and not in the moon, is rendered still more evident by the following facts. 3. On the Different Appearances of the Red Prominences, as seen at Different Stations, compared with the Effects which Parallax would produce, if the Prominences existed in the Sun. If the prominences were in the moon, they ought to have been seen almost precisely in the same positions, and of the same forms by all the ob- servers. If, on the other hand, they belong to the sun, when seen at all, their positions, and the forms of such parts of them as were visible, ought to have been identical in every case:—but owing to parallax, the moon would overlap the sun more on one side or the other, according to the observer’s position with reference to the line of central eclipse; and thus a low prominence near the sun’s north point might be hidden from an observer on the southern edge of the shadow, while a prominence near his south point might, in like manner, be invisible to an observer at the northern edge of the shadow. It follows from this, that while differences in the angles of position, or forms, assigned to the prominence by different observers, are equally unfavourable to the supposition that they are real objects existing in the sun, or in the moon ; differences in the number and magnitudes of the prominences, although unfavour- able to the supposition that they exist in the moon, may admit of explanation on the hypothesis that they belong to the sun. If, then, the prominences existed in the sun, the effect of parallax, to observers situated near the edge of the moon’s shadow, would be to disclose the prominences on one side of the moon, while it hid those on the other side. Accordingly, we find that Mr Hinp, Mr Dawes, and Mr Goop, who were situated near the southern edge of the moon’s shadow, saw a long sierra of prominences extending over about 120° of the moon’s southern limb, while they all failed to see the prominences, situated near the sun’s north point.* Even after making allowance for the effect of irradiation, which would diminish the apparent diameter of the moon, and thus increase the apparent height of the prominences, it appears that if their estimated height be correct, the parallax would be insufficient to hide any of them com- pletely. Still, however, it might diminish their apparent heights so much, that in the haste with which the observations were necessarily made, they might be overlooked; and the discrepancy noticed above is therefore so far in favour of the hypothesis that the prominences belong to the sun. 4. On the Occultation of the Red Prominences by the Moon. That the prominences belong to the sun, seems to be proved most decidedly * Ast. Soc. Notice, pp. 67, 69; Edin. New Phil. Journal, Oct. 1851, pp. 365, 366. 456 MR WILLIAM SWAN ON THE by the fact, that the moon was seen by degrees to cover those which were situated on the side towards which it was moving, while it as gradually exposed those on the other side. Of all the phenomena of the eclipse, there is none on which the testimony of the observers is more unanimous, than it is regarding this; and there is certainly none which, at the time, seemed to me more striking and beautiful, or which is now more strongly impressed on my memory. The only observer whose testimony is decidedly opposed to the fact, that the moon occulted the prominences on one side, and disclosed them on the other, is Mr Dunkin, who watched the hook-shaped prominence for more than a minute, without perceiving the slightest change in its appearance. ‘‘ It seemed to me,” he remarks, ‘‘ from the excessive steadiness of this prominence, and from the fact that I had zealously watched it for so long an interval without its undergoing any change, that this object had some connexion with the moon.” He adds, however, ‘‘as my observations have been all made under rather difficult circum- stances, it is possible | may be deceived.” * In opposition to this observation, we have the testimony of a large number of persons who saw the moon gradually occult those prominences which were situated on the sun’s eastern limb, while those on the western limb were gradually elongated; and, in some instances, additional ones were seen on the west side, towards the end of the eclipse, which were not visible at the beginning. Thus Mr Jackson states, that “on a second view, a little before the sun re- appeared, a fourth prominence shewed itself at about 45° from the vertex towards the west, and the other prominences, especially the hook-shaped one, were elon- gated.”+ Mr SrepHenson remarks, that the large hook-shaped prominence “ in- creased in size very rapidly, and then, other two rose-coloured prominences, one on the right and the other on the left, started out.” “These red prominences began as red specks, which almost immediately became summits, by the extension below into bases.{” Mr Lasse. says, the prominences “ were evidently belonging to the sun; for, especially on the western side, I observed that the moon passed over them, leaving them behind, and revealing successive portions as she advanced. I observed only the summit of one on the western side, although my friends in the adjoining room had seen two. The moon had covered one, and probably three fourths of the other, while I was engaged in registering the time, and making my observations with the naked eye.”§ Mr Wittams saw “ two conical redpromi- nences on the following or east limb;” and, “as the moon advanced, she speedily covered these.” He again states, that “as the moon progressed and left it be- hind,” the hook-shaped prominence on the west side “increased in size and brilliancy.”|| Mr SranNnisTREET says, the same prominence “ appeared to alter * Ast. Soc. Notice, p. 46. + Ib., p. 49. t Ib., p. 50. § Ib., p. 53. || Ib., p. 54. RED PROMINENCES SEEN DURING TOTAL ECLIPSES OF THE SUN. 457 its shape rapidly, unfolding more and more of the curve, as the phase proceeded.’’* Mr CarRINGTON saw a small pink prominence at an angle of 100° from the upper limb reckoned towards the east ; it was of the form of a hay-rick, and rapidly di- minished,” so that “in 10° it was no longer seen ;” on the other hand, he had “no manner of doubt” that the prominences to the west of the sun’s vertex “ increased in size so as to be five times as large” as when they first appeared. He afterwards adds, “that these changes are fully accounted for by the moon’s motion ;” and he concludes, that “ the prominences are appendages to the sun.”+ Lieutenant PETTERSSON says, that the movement of the prominences relatively to the limb of the moon, and above all, the successive removal of a detached prominence, which was at first in contact with it, convinced him that they belong to the sun. According to Mr Arry’s observations, a prominence at first seen to the east “‘ disappeared, the moon having overlapped it, and the two to the west, which touched the moon, were lengthened ; the moon evidently having uncovered more of their bases ;” while the detached mass “ was further removed from the moon’s limb,” and “now a conical prominence came into sight” at about 60° to the west, measured from the sun’s vertex.” ‘Just before the sun reappeared all these objects were still further lengthened from the moon’s motion,” while a sterra or range of serrated eminences came into view.” § Professor CHEVALLIER, who ob- served the eclipse with the high power of 180, is of opinion that the promi- nences “ were certainly connected with the sun, for the separation of the edge of the moon from them, as she moved onwards, could be distinctly seen.” || Mr Hinp estimated the height of the hook-shaped prominence at 45", about 20° after the sun disappeared, and towards the end of the totality at 2’; “the moon having apparently left more and more of it visible, as she travelled across the sun.” There was no change in the form of this object ; and while the moon moved away from the detached prominence, the latter “‘ preserved its relative position” to the hook-shaped one. Mr Apis says, that “as the moon advanced, the crescent,” or hook-shaped prominence “ increased in altitude,’ as did another prominence below it; while that “ to the eastern side diminished to less than one-half the altitude it had when first observed ;” and these changes, he thinks, afford the most satisfactory proof “that the prominences belong to the sun and not to the moon.’’** Mr Dawss states that the height of the hook-shaped prominence was perhaps 1/5 when first seen, and that its height “ increased to two minutes or more, as the moon’s progress revealed it more entirely.” The detached prominence “was sepa- * Notice of R. Ast. Soc., p. 55. + Account of the late Total Eclipse of the Sun, by R. C. Carrineton, pp. 6, 7, 10. t “ Le mouvements de ces derniéres relativement au bord de la lune, et surtout |’éloignement successif de d du bord obscur, avec lequel je la vis premiérement en contact m’ont convaincu qu’elles appartenaient au Soléil.” The letter d refers to his drawing of the detached prominence. See Plate XI., Fig. 9., No. 6.—Manuscript Letter to the Author, dated 26th January 1852. § Ast. Soc. Notice, p. 60. PMEb: op Go. | Ib., p. 67. ** Edin. New Phil. Journal, for October 1851, pp. 374, 375. VOL. XX. PART III. 6G 458 MR WILLIAM SWAN ON THE rated from the moon’s edge when first seen, and the separation increased as the moon advanced.”* My own observations of the prominences are accordant with those which have now been stated. A little after the commencement of the total phase, I determined their positions, and then left the telescope to make some other observations. On returning to the telescope, I found that the prominences on the moon’s western limb had increased very sensibly in height; and on watch- ing the hook-shaped prominence,—which I did until a few seconds before the end of the totality,—it seemed to rise from behind the moon, its base increasing in breadth, while the contour of the portions which were already visible, remained quite un- altered. Its motion, relatively to the moon, seemed to me quite sensible; but, although I may posssibly have been mistaken in this, I feel, no doubt whatever as to the striking difference between its height when first seen and that which it finally attained. Figs. 7 and 8, Plate XI., which are taken from a sketch made im- mediately after the total phase, represent this prominence as it was first and last seen. From its accidental resemblance to an object with whose form I happened to be familiar,} its shape was very distinctly impressed on my memory; and I feel satisfied that the change which took place in its appearance as the eclipse ad- vanced, was precisely such as would have happened to a body of permanent form belonging to the sun, from which the moon gradually receded and left more and more of it exposed. Numerous observers of the late eclipse, therefore, bear decided testimony to the fact, that the prominences situated on the side towards which the moon was moy- ing, were occulted by it, while those on the opposite side were gradually exposed ; and, at the same time, all are equally certain that the forms of those objects were in no other respect altered. I conceive, then, that unless we suppose they were deceived as to one or other of these points, we cannot hesitate to admit that the prominences are material objects, and that they exist in the sun. For if they were optical phenomena, it is quite inconceivable that the moon’s motion should alter their height alone, while it did not at the same time affect their forms. The discussion of the observations of the late eclipse seems, then, to lead to the following results :— 1. The red prominences are not caused by the telescopes used in observing the eclipse ; for they were seen with the naked eye. * Ast. Nachricht., No. 777, p. 157. yf 1S Sy. { The occultation of the prominences on the east side by the advancing moon, serves to explain some of the variations in the statements of different observers, as to their number. Mr LasseL1’s observations already cited, shew that an observer might be too late on the outlook to see some of the prominences on the east side. Mr Dunkin, Mr Jacxson, Mr Hinp, Mr Perrersson, and myself, all saw no prominences to the east of the sun’s vertex. At least three of these observers had their attention withdrawn from the red prominences by registering the time, and by making naked eye observations at the commencement of the total phase; while in Mr Dunxin’s case, the sun was covered with a cloud shortly after the commencement of the totality, and the prominences were not looked for until after it had passed away. RED PROMINENCES SEEN DURING TOTAL ECLIPSES OF THE SUN. 459 2. The red prominences cannot be regarded as optical phenomena, produced either by unequally heated strata of air, or by the action of the moon’s limb on the sun’s light ; for these hypotheses are inconsistent, both with the permanency of their forms, and with the similarity of their appearance as seen from stations dif- ferently situated in the moon’s shadow. 3. The discrepancies in the observations are as unfavourable to the supposi- tion that the prominences are optical phenomena, as to the hypothesis that they are material objects belonging to the sun. 4. The observed differences in the numbers and appearance of the prominences as seen from stations differently situated in the moon’s shadow, are, upon the whole, accordant with the effects which parallax would produce, if they existed in the sun. 5. The hypothesis that the prominences exist in the sun, seems to afford the only explanation of the facts, that the moon gradually occulted them on one side, and exposed them on the other, while their outlines remained unaltered. 6. On these grounds it is inferred, that the red prominences are material objects, actually belonging to the sun. , > 7 7e Ay. cs ; : Pras | a pie mn mnie barrabortig ; bes 1 “ ' 5 Dal ; Au dy enh % (nn ; A io : ' 6 cons a yay ot) daw nt fe si m 11a é sii sili ougey Aa } mae 7? oi | ae ly: ait Pe ones ‘fecommbaden ‘ chgopans ‘odd J «i ghd v4 y ew Ee dy toe ulid. 0h sks tus, aimaaltoeped: eth hceaheiel wwiceaey seats és y : per pemaeiicieties .~ a vig ee odd wes as — ” :' : epusqiguens ogld Ieapprioareniigs, ors xmcbegain subball naa wpe = 1196 RAL AA ae a Aa ot ai esau tn PAIRN iiboteixg Ln peathaiinend Seeerteabscer Dopegtae sale ty ts Peih- 7 rorya ng ‘pee grb dae Chik a nee edt & ars Srphe...t1 wife mw deigggbapsioniovenyvall 0h hia amy as yororts [vt Lipa etrulistta. nag. asl Soi dak gat eodee's beret bain, 1) ‘adam bush), eli shen, tho iyi _ Jaieeteie ota. 200 aie fit ier derusiiai eh, 35 peti. | : a he “cp otha obeohaeigyladag ~ rwis ‘ iy GPs mene one oi ie : adv hes ~ * yi ga y 1] — ais at yond , ne ee ee se so - .e — en” 7 ‘ ‘ ' Mile fa wnt ae my il ) ‘ “> nazis i PAZ (at) e Gwis LAS wad’ 2 pati a 40) re ® “tan 3! €.4) (yr y j B! ah c papas. eros} up ee. hn all ee ey ie ks haslisn Ron ‘fF ' ' 1 ad 7 Caw Us in aes “ei Th Aa? : es] ian p 4 He AS - x ri - i i, si ‘s ave My Elec? | ) , ant; a nt: ee ee Ve eee ee eae cian bate 7 Pe : BP, he Ty yr ‘ me tap a. apart’ Liv ah tehaneipteaentnl Ghar in ' r hs at ’ : P “4 = ? > onpae x, (are, i : ' “a nie <9 Paw a oo | Peer ere Satyr Tan 4 v ay ry t : - bi ® * ; ‘o 1a, Bride, onadly tack, obi ott eae seer lp cl oem eee een oil eae mit aLcoutlire aut bl) rusbevait in. (oeicraonnin eietita at. i i yout of , “ agury 41) (ito. 44 uit abat Aeite wash y “antremtina th; eh : i My daschd: serbia cate Irian 40 jlasierag thee Oe Cait ‘yas 1 eiaon {y 0 ad) Abba ha Sergi} mar eequCineen Ht. tod ustibrerr vt thea ¥7 mend nt or Spey Yea whoo teidt tant Mute os Aeron pe haty. 2 rat i ; . vas res i : ari) wit? tin ar pi? tote : ¥4 { ben Pad Ay nly anihecucrrure ppslenes rt) 0 < | ith earn ote acocttyind badelaierib pat geclemign sit tiaras. Pablo, orld. ai “al Nr, _ a) CARROT AD “Grune iia sd SL TLD VAT ty Jeilfe. huis, i f d+. tuenoo, Ole samrtiege seodt af ut} bata ~ gai hh xalon oat wna pala oni, J » a ; (ULE “AeA Teh ep QAP, Ladys itisaal (hes SER; or “t ; | ba he a : : fs ; >. ] ‘ ? ta ; 1 > \ ° ty é oy wi Ss f LiF a : vf 7 ry E ry thie 7 i *) . a4 >a : . . =f t 4 ‘ ss i in os Se “4 ; ey "7 , i . val * 7 y ¢ ; j - 4 i bs / ' , 7 \ ? e ; gent Fray “ai oi ery oe . A " SS } ; , > ‘ ; padat vo i Jit ie aka ge - < vhs ee ot ~~ e ( 475 ) 4 XXXI.—On the Dynamical Theory of Heat. Part V.* On the Quantities of Mechanical Energy contained in a Fluid in Different States, as to Temperature and Density. By Wititam Tuomson, M.A., Professor of Natural Philosophy in the University of Glasgow. (Read December 15, 1851.) 81. A body which is either emitting heat, or altering its dimensions against resisting forces, is doing work upon matter external to it. The mechanical effect of this work, in one case, is the excitation of thermal motions, and in the other, the overcoming of resistances. The body must itself be altering in its cir- cumstances, so as to contain a less store of work within it, by an amount precisely equal to the aggregate value of the mechanical effects produced: and conversely, the aggregate value of the mechanical effects produced, must depend solely on the initial and final states of the body, and is therefore the same, whatever be the intermediate states through which the body passes, provided the zndtial and jinal states be the same. 82. The total mechanical energy of a body might be defined as the mechanical value of all the effect it would produce, in heat emitted and in resistances over- come, if it were cooled to the utmost, and allowed to contract indefinitely or to expand indefinitely according as the forces between its particles are attractive or repulsive, when the thermal motions within it are all stopped ; but in our present state of ignorance regarding perfect cold, and the nature of molecular forces, we cannot determine this “ total mechanical energy” for any portion of matter, nor even can we be sure that it is not infinitely great for a finite portion of matter. Hence it is convenient to choose a certain state, as standard for the body under consideration, and, to use the unqualified term, mechanical energy, with reference to this standard state; so that the “ mechanical energy of a body in a given state,” will denote the mechanical value of the effects the body would produce in passing from the state in which it is given, to the standard state, or the mechanical value of the whole agency that would be required to bring the body from the standard state to the state in which it is given. . 83. In the present communication, a system of formule founded on proposi- * A preceding communication (April 21, 1851) published in the Transactions (Vol. xx., Part i.), under the title, “On a Method of Discovering Experimentally the Relation between the Mechanical Work spent, and the Heat produced by the Compression of a Gaseous Fluid,” will be referred to as Part IV. of a series of Papers on the Dynamical Theory of Heat; and the numbers of its sections will be altered accordingly, so that its first section will be referred to as § 61, and its 20th and last, as § 80. VOL. XX. PART III. 6M 476 PROFESSOR WILLIAM THOMSON ON THE tions established in the first part of my paper on the Dynamical Theory of Heat, and expressing relations between the pressure ofa fluid, and the thermal capacities and mechanical energy of a given mass of it, all considered as functions of the temperature and volume, and Carnovt’s function of the temperature, are brought forward for the purpose of pointing out the importance of making the mechanical energy of a fluid in different states an object of research, along with the other elements which have hitherto been considered, and partially investigated in some cases. 84. If we consider the circumstances of a stated quantity (a unit of matter, a pound, for instance) of a fluid, we find that its condition, whether it be wholly in the liquid state, or wholly gaseous, or partly liquid and partly gaseous, is com- pletely defined when its temperature, and the volume of the space within which it is contained, are specified (SS 20, 53,....56), it being understood, of course, that the dimensions of this space are so limited, that no sensible differences of density in different parts of the fluid are produced by gravity. We shall therefore consider the temperature, and the volume of unity of mass, of a fluid as the independent variables of which its pressure, thermal capacities, and mechanical energy, are functions. The volume and temperature being denoted respectively by v and ¢, let ¢ be the mechanical energy, p the pressure, K the thermal capacity under con- stant pressure, and N the thermal capacity in constant volume; and let M be such a, function of these elements, that or (§§ 48, 20), such a quantity that Mdv+N dt q . ; : yet : : sp lens may express the quantity of heat that must be added to the fluid mass, to elevate its temperature by dz, when its volume is augmented by dv. 85. The mechanical value of the heat added to the fluid in any operation, or the quantity of heat added multiplied by J (the mechanical equivalent of the thermal unit), must be diminished by the work done by the fluid in expanding against re- sistance, to find the actual increase of mechanical energy which the body acquires. Hence, (de, of course, denoting the complete increment of ¢, when v and ¢ are in- creased by dv and d?,) we have de=J (Mdv+Ndt)-pdv . 5 . ‘ : (3). Hence, accordiug to the usual notation for partial differential coefficients, we have de DYNAMICAL THEORY OF HEAT. 477 de dt Lastly, if we denote, as formerly, Carnot’s function of the temperature 7, by 4, we have ( § 21) = lig A donnie abs Daas pect eal al Mage LG dp _ qj7e™M : 0 6 : 5 A . : c (6). 86. The use that may be made of these formule in investigations of the physical properties of any particular fluid must depend on the extent and accuracy of the general data belonging to the theory of the mechanical action of heat, that are available. Thus, if nothing be known by experiment regarding the values of J and #, we may, in the first place, use equations (4) and (5), or the following de- duced from them (§ 20) by eliminating eg, dp. (aM aN . and equation (6), as tests of the accuracy of experimental researches on the pres- sure and thermal capacities of a fluid, on account of the knowledge we have from theory, that J is certainly an absolute constant, and that, in all probability if not with absolute certainty, we may regard pas independent of v, and as the same for all fluids at the same temperature; and, with experimental data of sufficient extent, we may use these equations as means of actually determining the values of J and #. No other way than this has yet been attempted for determining » ; and, if we except a conceivable but certainly not at present practicable mode of determining this element by experiments on thermo-electric currents, no other way is yet known. Carnot’s original determination of 4, was effected by means of an expres- sion equivalent to that of equation (6) applied to the case of a mass of air; and the determinations by CLaPEyRon, and those shewn in Table I. of my Account of Carnot’s Theory, were calculated by the formula which is obtained when the same equation is applied to the case of a fluid mass, partly liquid and partly in the state of saturated vapour (§ 55). | 87. As yet experiments have not been made on the pressure and thermal ca- pacities of fluids to a sufficient extent to supply data for the evaluation, even in the roughest manner, of the expression given for J by equation (7); and it may be doubted whether such data can even be had with accuracy enough to give as exact a determination of this important element as may be effected by direct experi- ments on the generation of heat by means of friction. At present we may regard J as known, probably within ,1, of its own amount, by experiments of this kind. 88. The value of J being known, equations (4) and (5) may be used for deter- mining the mechanical energy of a particular fluid mass in different states, from special experimental data regarding its pressure and thermal capacities, but not necessarily comprehending the values of each of these elements for all states of the fluid. The theory of the integration of functions of two independent variables 478 PROFESSOR WILLIAM THOMSON ON THE will, when any set of data are proposed, make it manifest whether or not they are sufficient, and will point out the methods, whether of summation or of analytical integration, according to the forms in which the data are furnished, to be followed for determining the value of ¢ for every value of v. Or the data may be such that, while the thermal capacities would be derived from them by differentiation, values of ¢ may be obtained from them without integration. Thus, if the fluid mass consist of water and vapour of water at the temperature 7, weighing in all one pound, and occupying the volume v,* and if we regard the zero or “ standard” state of the mass as being liquid water at the temperature 0°; the mechanical energy of the mass, in the given state, will be the mechanical value of the heat required to raise the ON g=n of it into vapour, diminished by the work done in the expansion from the volume A, to the volume ©; that is, we have temperature of a pound of water from 0° to7, and to convert phe (cr+L 2) SPOLA. ne The variables, c, L, and p (which depend on ¢ alone) in this expression have been experimentally determined by ReGNavtt, for all temperatures from 0° to 230°, and when ¥ is also determined, by experiments on the density of saturated steam, the elements for the determination of ¢ in this case will be complete. The expressions investigated formerly for M and N in this case (§ 54) may be readily obtained by means of (4) and (5 of § 84), by the differentiation of (8). 89. If Carnot’s function has once been determined by means of observations of any kind, whether on a single fluid, or on different fluids, for a certain range of dp temperatures, then, according to (6) of § 85, the value of = for any substance whatever, is known for all temperatures within that range. It follows that when the values of M for different states of a fluid have been determined experimentally, the law of pressures for all temperatures and volumes (with an arbitrary function of v to be determined by experiments on the pressure of the fluid at one particular temperature) may be deduced, by means of equation (6); or conversely, which is more likely to be the case for any particular fluid, if the law of pressures is com- pletely known, M may be deduced without farther experimenting. Hence the second member of (4) becomes completely known, the equation assuming the fol- lowing form when, for M, its value according to (6) is substituted :— * The same notation is used here, as formerly in § 54, viz. pis the pressure of saturated vapour at the temperature t, y the volume, and L the latent heat of a pound of the vapour, a the volume of a pound of liquid water, and c the mean thermal capacity of a pound of water between the tempera- tures 0 and ¢. A mass weighing a pound, and occupying the volume v, when at the temperature ¢, : : =A =i) must consist of a weight : 5 of vapour, and Y =: of water, Vea Tes DYNAMICAL THEORY OF HEAT. 479 a ee ee OY The integration of this equation with reference to v, leads to an expression for ¢, involving an arbitrary function of 7, for the determination of which more data from experiment are required. It would, for instance, be sufficient for this pur- pose, to have the mechanical energy of the fluid for all temperatures when con- tained in a constant volume; or, what amounts to the same (it being now supposed that J is known), to have the thermal capacity of the fluid in constant volume, for a particular volume and all temperatures. Hence, we conclude, that when the elements J and / belonging to the general theory of the mechanical action of heat are known, the mechanical energy of a particular fluid may be investigated with- out experiment, from determinations of its pressure for all temperatures and volumes, and its thermal capacity for any particular constant volume and all tem- peratures. 90. For example, let the fiuid be atmospheric air, or any other subject to the “gaseous” laws. Then if 7% be the volume of a unit of weight of the fluid, and 0 the temperature, in the standard state from which the mechanical energy in any other state is reckoned, and if p, denote the corresponding pressure, we have | p= "00 (1+E 9, ea and afm (75-2) de=P0% {== +84 } log 2 4 Bb V 0 Hence, if we denote by N, the value of N when v=, whatever be the tempera- ture, we have, as the general expression for the mechanical energy of a unit weight of a fluid subject to the gaseous laws, JE v t e=p)v, {a -(+Es) } tog e+ Reta A 2 x9. 91. Let us now suppose the mechanical energy of a particular fluid mass in various states to have been determined in any way, and let us find what results regarding its pressure and thermal capacities may be deduced. In the first place, by integrating equation (8), — as a differential equation with reference to t, for p, we find 1 t. a i Fa Awd _zf, “dt =f wat p=e a en Ss Re ae ag Pie tO), 0 where ¥ (v) denotes a constant with reference to ¢, which may vary with 2, and cannot be determined without experiment. Again, we have, from (5), (4), and (1), lde Se iias dp — : , - : : ie Kaige 1 de. dt 7 GP aiaimadeder _dp dv VOL. XX. PART III. ON 480 PROFESSOR WILLIAM THOMSON ON THE Hrom the first of these equations we infer that with a complete knowledge of the mechanical energy of a particular fluid, we have enough of data for determining for every state, its thermal capacity in constant volume. From equation (9) we infer, that with, besides, a knowledge of the pressure for all volumes and a parti- cular temperature, or for all volumes and a particular series of temperatures, we have enough to determine completely the pressure, and consequently also, accord- ing to equation (11), to determine the two thermal capacities, for all states of the fluid. 92. For example, let these equations be applied to the case of a fluid subject to the gaseous laws. If we use for _ its value derived from (9), in equation (10), we find * 1 wadt p= "0% (1+ EN +x (v)e" ; : 2 , ; d (12), where x (v), denoting an arbitrary function of v, is used instead of ¥ (v) —Fo%0" We conclude that the same expression for the mechanical energy holds for any fluid whose pressure is expressed by this equation, as for one subject to the gase- “ : d d 5 , : ous laws. Again, by using for 7? and 7 their values derived from (9), in equa- tion (11), we have 1 v s {—7- +89] NEN 0 —————— : ; . 5 13), oF FPo% a> dt -) a 4 F a {>* -Q+E)} wp, = = cas ee DE AAV K=Nyo +7 Py % eae, dt +ad+E? . (14). The first of these equations shews that, unless Mayer’s hypothesis be true, there is a difference in the thermal capacities in constant volume, of the same gas at the same temperatures for different densities, proportional in amount to the difference of the logarithms of the densities. The second compared with the first, leads to an expression for the difference between the thermal capacities of a gas in constant volume, and under constant pressure, agreeing with results arrived at formerly. (Account of Carnot’s Theory, Appendix iii., and Dyn. Th. of Heat, § 48.) 93. It may be, that more or less information, regarding explicitly the pressure and thermal capacities of the fluid, may have been had as the data for determining the mechanical energy ; but these converse deductions are still interesting, as shew- ing how much information regarding its physical properties, is comprehended in a knowledge of the mechanical energy of a fluid mass, and how useful a table of the values of this function for different temperatures and volumes, or an Empirical Function of two variables expressing it, would be, whatever be the experimental DYNAMICAL THEORY OF HEAT. 481 data from which it is deduced. It is not improbable that such a Table or Empi- rical Function, and a similar representation of the pressure, may be found to be the most convenient expression for results of complete observations on the com-: pressibility, the law of expansion by heat, and the thermal capacities of a vapour or gas. 94. The principles brought forward in a former communication “ Ona Means of discovering experimentally, &c.” (which is now referred to as Part IV. ofaseries of papers on the Dynamical Theory of Heat), may be expressed in a more con- venient, and in a somewhat more comprehensive manner than in the formule contained in that paper, by introducing the notations and principles which form the subject of the present communication. Thus, let ¢ be the temperature, and w the volume of a pound, of air flowing gently in a pipe (under very high pressure it may be) towards a very narrow passage (a nearly closed stopcock, for instance), and let p be its pressure. Let ¢’, w’, and p’ be the corresponding qualities of the air, flowing gently through a continuation of the pipe, after having passed the “rapids” in and near the narrow passage. Let Q be the quantity of heat (which, according to circumstances, may be positive, zero, or negative) emitted by a pound of air during its whole passage from the former locality through the narrow passage, to the latter; and let S denote the mechanical value of the sound emitted from the “rapids.” The only other external mechanical effect, besides these two, produced by the air, is the excess (which, according to circumstances, may be negative, zero, or positive) of the work done by the air in pressing out through the second part of the pipe above that spent in pressing it in through the first; the amount of which, for each pound of air that passes, is of course p’ u’—p wu. Hence, the whole mechanical value of the effects produced externally by each pound of the air, from its own mechanical energy, is JQ+Sipw—pu, . : f : ; : i : (15). Hence, if ¢ (2, ¢) denote the value of ¢ expressed as a function of the independent variables, v and ¢; so that (w, 7) may express the mechanical energy of a pound of air before, and ¢ (w’, ’) the mechanical energy of a pound of air after, passing the rapids; we have p (uv, t= (v, t)-{J Q+Stp'w-pu} . : : ‘ (16). 95. If the circumstances be arranged (as is always possible), so as to prevent the air from experiencing either gain or loss of heat by conduction through the pipe and stopcock,we shall have Q=0; and if (as is perhaps also possible) only a mechanically inappreciable amount of sound be allowed to escape, we may take S=0. Then the preceding equation becomes’ p(w’, C)= (u, )—-(p' wv —p uv) : : : : ; (17). 482 PROFESSOR W. THOMSON ON THE DYNAMICAL THEORY OF HEAT. If by experimenting in such circumstances it be found that / does not differ sen- sibly from ¢, MayEr’s hypothesis is verified for air at the temperature 7, and, as yw would then be equal to pw, according to BoyLe and Mariorve’s law, we should have Pw, )=>p (u, 0) which is in fact the expression of MayeEr’s hypothesis, in terms of the notation for mechanical energy introduced in this paper. If, on the other hand, 7’ be found to differ from ¢;* let values of p, p’, t, and i’ be observed in various experiments of this kind, and, from the known laws of density of air, let w and w’ be calculated. We then have, by an application of (13), to the results of each experiment, an equation shewing the difference between the mechanical energies of a pound of air in two particular specified states as to temperature and density. All the par- ticular equations thus obtained, may be used towards forming, or for correcting, a table of the values of the mechanical energy of a mass of air, at various tempera- tures and densities. 96. If, according to the plan proposed in my former communication (§ 72), the air, on leaving the narrow passage, be made to pass through a spiral pipe immersed in water in a calorimetrical apparatus, and be so brought back exactly to the pri- mitive temperature ¢, we should have, according to BoyLz’s and Mariorre’s law, p w—-pu=0; and if H denote the value of Q, in this particular case (or the quantity of heat measured by means of the calorimetric apparatus), the general equation (16) takes the form, p (u',)=h (u,)-(JH+8) . . A 2) gay: If in this we neglect S, as probably insensible, and if we litle for @ (u, t) and ¢ (w’, t) expressions deduced from (9), we find, A E u He (3—arrED | pelge . which agrees exactly with the expression obtained by a synthetical process, founded on the same principles, in my former communication (§ 76). * If the values of w I have used formerly be correct, ¢’ would be less than ¢, for all cases in which ¢ is lower than about 30° cent.; but on the contrary, if ¢ be considerably above 30° cent., ¢ would be found to exceed t. (See Account of Carnot’s Theory, Appendix II.) It may be shewn, that if they are correct, air at the temperature 0° forced up with a pressure of ten atmospheres towards a small orifice, and expanding through it to the atmospheric pressure, would go down in temperature by about 4°-4; but that if it had the temperature of 100° in approaching the orifice, it would leave at a temperature about 5°:2 higher; provided that in each case there is no appreciable expenditure of mechanical energy on sound. ( 483 ) XXXII.—On two New Processes for the detection of Fluorine when accompanied by Silica; and on the presence of Fluorine in Granite, Trap, and other Igneous Rocks, and in the Ashes of Recent and Fossil Plants. By Grorcr Witson, M.D. (Read April 19, 1852.) In several communications made to this Society and to the British Associa- tion, I have announced the results of a series of observations on the distribution of Fluorine throughout the mineral, vegetable, and animal kingdoms. To myself, the least satisfactory part of these investigations has been the inquiry into the presence of fluorine in plants, for I have been more frequently foiled than suc- cessful in my attempts to detect it in them. Others have not, apparently, been more successful. DAuBENy was as unable as SPRENGEL at an earlier period had been, to obtain evidence that the element under notice is present in vegetable structures; and Wixt of Giessen, the discoverer of fluorine in plants, speaks only of “traces” of it having been detected in barley. Later observers have not spoken more confidently concerning its abundance in vegetables ; and in the many ana- lyses of the ashes of plants which have recently been published, it seldom, if ever, finds a place. That one cause of this apparent rarity of fluorine in vegetables, is the small extent to which it occurs in them is certain ; but I have never doubted that the chief reason why it appeared to be so scanty a constituent of plants, was its occurrence along with silica, which makes its recognition very difficult. JI had given up, accordingly, all hopes of satisfactorily demonstrating its wide distribu- tion, till better processes than are at present in use, were devised for its de- tection when accompanied by silica. For the same reason I have thought it hitherto useless to endeavour to trace back fluorine from the plants, animals, natural waters, and more accessible strata which are the main seats of life at the present day, to those earlier rocks and geological formations which have furnished our soils, and have contributed the chief soluble matters which are found in the lakes, rivers, and seas of the globe. The more ancient rocks abound in silica, and, with our present processes, the prospect of discovering fluorine in trap and similar siliceous masses, was not encouraging. A representation, however, from Professor JAMESON, as to the im- portance attaching to the detection of fluorine in the most ancient rocks, led me to reconsider the geological and mineralogical interest which the inquiry possessed ; and within the last six weeks I have put in practice two methods of investigation, which I shall now explain. VOL. XX. PART III. 60 484 DR GEORGE WILSON ON NEW PROCESSES FOR FLUORINE, &c. The processes at present in use for the separation of fluorine from silica, are in many respects satisfactory ; but they imply the rejection of glass apparatus, and the use of vessels of platina, which, from their costliness, cannot be employed of any considerable size, and, from their opacity, render the observation of phe- nomena occurring within them impossible. They are thus inadmissible for opera- tions where large quantities of material must be dealt with ; and to the impossi- bility of employing glass and porcelain vessels, must be largely attributed the comparatively limited extent of our information as to the distribution of fluorine. The following processes, which, in the meanwhile, are offered only as qualita- tive (although I hope to succeed in rendering the second of them quantitative), may be carried on in the ordinary glass and porcelain vessels of the laboratory, and admit of everything visible being observed. They are applicable to all siliceous compounds or mixtures containing fluorine, provided it be present in the form of a fluoride which admits of decomposition by oil of vitriol at its boiling point. The first stage of the process consists, in both cases, in heating the silicated fluoride in a flask along with strong sulphuric acid, so as to occasion the evolution of the fluoride of silicon, Si F,. This gas is conducted by a bent tube into water, where it deposits a portion of gelatinous silica; and the liquid, after filtration (which, however, is not essential), is treated as follows :-— In the first process, | adopted one of Brerzetius’ well-known methods for the isolation of silicon. ‘The filtered liquid was neutralised with potass: and the resulting gelatinous precipitate of fluoride of silicon and potassium (2 Si F,, +3 KF), after being washed, was dried, and transferred to a small metallic crucible, in which it was heated with potassium, so as to separate and set free the silicon, and convert the whole of the fluorine into fluoride of potassium. This fluoride was then dissolved out by water, evaporated to dryness, and treated in the ordi- nary way with oil of vitriol, so as to evolve hydrofluoric acid, which could be made to record its evolution by the etching which its vapour occasioned on a plate of waxed glass, with lines written on it through the wax. This process is necessarily tedious, and is liable to several objections. The most serious of these is the impossibility of effecting the complete decomposition of the fluoride of silicon and potassium, by potassium, so as to liberate the whole of the silicon; and the risk of the latter undergoing oxidation into silica during the washing of the ignited mass. Accordingly, though this method gives good results, and has enabled me to detect fluorine in coal, in which I could not pre- viously detect more than the faintest traces of it, yet it almost unavoidably neces- sitates a loss of the element in question, and is much inferior in simplicity and certainty to the process which | am about to describe. In the second process, as in the first, the substance under examination is — heated with oil of vitriol so as to yield fluoride of silicon, which is conducted into ~ water. The resulting solution (with or without filtration) is neutralised with DR GEORGE WILSON ON NEW PROCESSES FOR FLUORINE, &c. 485 ammonia instead of potass, and then evaporated to dryness, which has the effect of rendering the silica produced insoluble. On digesting water on the residue, fluoride of ammonium is dissolved, and the solution requires only to be evaporated to dryness and moistened with sulphuric acid to give off hydrofluoric acid, which readily etches glass. The stages in the ammonia process are thus :— 1st, Distillation of the substance with oil of vitriol, so as to produce fluoride of silicon, Si F,. 2d, Neutralisation of the aqueous solution of the distillate, with ammonia in excess, so as to produce fluoride of silicon and ammonium, 2 S5if,+3 NH,F. 3d, Evaporation of the neutralised liquid to dryness, so as to separate silica, and render it insoluble. Ath, Exhaustion of the residue with water, and evaporation to dryness, so as to leave fluoride of ammonium. 5th, Moistening of the ammonio-fluoride with oil of vitriol, so as to liberate hydrofiuoric acid; which will act upon glass. I have tried this process with Aberdeen and Peterhead granite; with three trap rocks from the neighbourhood of Edinburgh, namely, basalt from Arthur Seat, greenstone from Corstorphine Hill, and clinkstone from Blackford Hill; with a deposit from the boiler of the Atlantic steamer, Canada; with a fossil bone; with the ashes of charcoal, of barley-straw, and of hay; and in all with such success that the applicability of the process to the end proposed is certain. The pieces of glass, etched by hydrofiuoric acid evolved from the substances referred to, which I lay upon the table, are not selected successful specimens, but repre- sent the whole of the trials made by the ammonia process. The etchings on the majority of them are as deep as could be obtained from pure fluorspar and oil of vitriol; and, with the experience which I have now acquired, I have no doubt that I shall be more successful in succeeding trials with vegetable ashes, which, for reasons to be presently mentioned, require more precautions than fragments of rock do. The examination of a hard crystalline mineral, such as granite, or an un- weathered trap, presents no difficulties. It must be reduced to a tolerably fine powder, and employed in considerable quantity. A little sulphurous acid is always evolved during the action of the oil of vitriol, from the dust which is gathered during a protracted process of powdering; but the presence of this acid in small quantity is of no importance, and the powdering of the rock is the most troublesome part of the investigation. It is otherwise with weathered granite and trap, which containc hlorides and carbonates, and give off hydrochloric and carbonic acids when treated with sul- phuric acid. These gaseous acids materially interfere with the processes described by the frothing which they occasion, and by their tendency to sweep away the hydrofluoric acid which may accompany them. In my earlier trials, accordingly, 486 DR GEORGE WILSON ON NEW PROCESSES FOR FLUORINE, &c. I treated the powdered pieces of rock with hydrochloric acid, and washed them with water, then dried them, and heated them with oil of vitriol. The prelimi- nary treatment, however, risked, and I have no doubt occasioned, the loss of the fluorides present in the mineral, which were soluble in water or in hydrochloric acid; and latterly I abandoned this process. J refer to it here only because it ex- plains certain of the less perfect etchings which are exhibited. In later trials, a simpler and more satisfactory process has been put in prac- tice. The powdered rock has been added to oil of vitriol in the cold, in small quantities at a time, so as to prevent any great rise in temperature. So long as the heat evolved is not considerable, there is no risk of fluorine escaping, either as hydrofluoric acid or as fluoride of silicon, whilst any chlorides or carbonates pre- sent are decomposed, and the hydrochloric and carbonic acids evolved, are carried away, before their escape can interfere with the evolution of fluorine. When the oil of vitriol is afterwards raised to its boiling-point, the fluoride of silicon is liberated, and little difficulty attends its collection and identification. The ashes of plants are somewhat less easily examined. They almost inva- riably contain charcoal, which occasions the evolution of sulphurous acid with hot oil of vitriol. Sulphurous acid, however, does not very materially interfere with the detection of fluorine, as it can be expelled by heating the distillate before adding ammonia, which is the process I have hitherto generally followed. It may also be converted into sulphuric acid by the cautious addition of nitric acid, and then its presence is quite immaterial. But in several quite successful trials no steps were adopted to separate the sulphurous acid. The specimen laid upon the table, of glass etched by fluorine from barley- straw, will illustrate the applicability of the process to plant-ashes largely charged with silica, and which yielded, with oil of vitriol, carbonic and hydrochloric acid, besides much sulphurous acid. The glass etched by the fluorine of charcoal-ashes is still more deeply cor- roded, although they were subjected to no preliminary process to remove the;vola- tile acids which they contained, or to set free or separate the sulphurous acid which they yielded. In truth, the ammonia process has succeeded with every substance upon which I have tried it. The worst result has been with the ashes of hay, but they had been washed with water and hydrochloric acid to remove chlorides and car- bonates ; and in former papers I have shewn that such washings remove fluorides. Notwithstanding this, the evidence of the presence of fiuorine in hay, afforded by the specimen, is such as has not hitherto (so far as | am aware) been afforded by any analyst, and the omission of the washings will, I have no doubt, yield a still more satisfactory result on a repetition of the analysis. The same remark applies to coal-ashes, by the fluorine of which I have only one etching to shew. It is not a favourable specimen; the ashes were washed with a considerable volume of DR GEORGE WILSON ON NEW PROCESSES FOR FLUORINE, &c. 487 hydrochloric acid and water; the product of distillation was tested by the less perfect potassium-process; and the lines etched by the hydrofluoric acid were drawn too fine. Experience has taught my assistants that the wax should be spread thin, and the lines through it be made with a broad point, if a distinct etching is to be obtained. But, withal, the results with coal-ashes are sufficiently marked. I have further tested the sufficiency of the ammonia process in the following stringent way. A fossil bone from the Himalayas, which I had already ascer- tained to contain a fluoride, and which was full of crystals of carbonate of lime, was reduced to powder, and mixed with powdered glass so as to add to it excess of silica. It was then subjected to the ammonia process, and has yielded an etching as deep as the purest fluorspar could have given with oil of vitriol. The result is so marked, that I should recommend the deliberate addition of silica to bodies suspected to contain fluorine, as a provision for permitting such substances to be analysed in glass vessels, in which the largest quantities may be subjected to examination without risk of missing the element in search, or per- mitting it to escape. Five points call for further notice. 1st, When a silicated fluoride, as I may, for the sake of brevity, call it, is distilled with oil of vitriol, the whole of the fluoride of silicon comes away as gas, as soon as the oil of vitriol has reached its boiling-point. It is not necessary, accordingly, to subject a body supposed to contain fluorine to any lengthened ebullition ; and, in the case of plant-ashes, it is desirable to arrest the boiling as soon as all the fluorine has been evolved, for protracted ebullition only occasions evolution of sulphurous acid. Besides the ultimate glass-etching, the escape of fluorine is rendered manifest by the appearance of a white gelatinous body in the water, through which the gas evolved (Si F,) is passed ; and by the production of a gelatinous, flocculent precipitate, when the solution of this gas is neutralised with potass. The coal-ashes gave all those results. 2d, It appears exceedingly probable, that much of the silica occurring in the forms of quartz, chalcedony, opal, sinter, and the like, which is generally sup- posed to have been deposited from aqueous or alkaline solution, has owed its origin to the decomposition of fluoride of silicon by water, or has otherwise been related to fluorine as its solvent or transferring agent. This, or rather the less precise notion of fluorine conveying silica, has been suggested by my friend Mr A. Bry- son, and by Dr H. Bucnanan, E.I.CS. 3d, The occurrence of fluorspar in drusy cavities in greenstone, along with silica, as in the specimens obtained from Bishopton, on the Clyde; the similar occurrence of apophyllite in the cavities of trap; the association of topaz, pyc- nite, lepidolite, and most of the other compound fluorides, with granite, gneiss, VOL. XX. PART III. 6 P 488 DR GEORGE WILSON ON NEW PROCESSES FOR FLUORINE, &c. and mica slate, will acquire additional significance from the discovery that fluorine occurs in the rocks which form their matrices. 4th, The presence of fluorine in plants is now rendered doubly probable, as it may enter them alike in combination with a metal such as potassium, sodium, or calcium, or in association with silica. 5th, The presence of fluorine in animals may now be fully accounted for; as it not only enters their bodies in the water they drink, but is contained in the vegetable food, by which, directly or indirectly, the whole animal kingdom is sustained. The prosecution of these views, however, will be taken up in succeed- ing papers. ‘i we eh Wes) ae ere ee Te} , é y ; ee fas Pa | : ; me 15100 be Ah Ae 2 eis re eat hae Oh a ; * y ‘ Fi s THE, 40 DTAGAR AT THE CAPE OF GOOD HOPE, L Peat JULY 1845. PLATE XIII. VOL.20 p.394 WForrest.s¢ ns Meee tas sab ( 489. ) XXXII. —Contribuitions to a Knowledge of the Phenomena of the Zodiacal Light. By Professor C. Prazzi SMYTH. “(Read pepe 7, 1848.) When preparing to make a night journey over one of the plains of South Africa, in the month of June 1843, a friend called my attention to the peculiar appearance of the sky in the west, as offering a very decided proof, “‘ agreeably with theory,” that there was no “ Solar atmosphere” to be seen at that season of the year. On looking in the direction mentioned, the last portion of the twilight was just visible, and forming a peculiarly level line above the place where the sun had set, for an extent in azimuth, of perhaps 40°, and at a height of about.5°. All the gorgeous colours which had attended the setting of the sun had long since vanished, and there only remained. sufficient light within the flattened arc described, to make the ‘space included between it and the horizon appear light blue, while all the rest of the sky had attained a deeper colour, nay was almost black, and thickly spangled with small as well as large stars. There .most decidedly was not then any symptom of the so-called ‘“ way of the twilight shooting upward.” But as soon as the last illuminated portion of the western sky had set, the phenomenon, 7. ¢., the zodiacal light, appeared in an, unmistakeable manner,:rising up in the ecliptic, to a height of 50°, with a breadth of perhaps 12° at the horizon; and forming, with the vast extent -of' its illuminated surface, and the regularity of its contour, one of the most remark- able objects in the starry sky. The form was that usually described, viz., a wedge pointing upwards, with curved sides, and of excessively indefinite outline; but still, as far as could be judged, free from any irregularities ; while the light, which was more delicate and transparent than that of the milky way, increased in intensity transversely from either side to the central longitudinal axis; and augmented also in the axis, from the apex downwards, until overpower ed by the haze on the horizon. Now, two circumstances worthy of notice, were pointed out by this night’s ob- servation, Jirstly, that persons did not always know exactly when to look for the zodiacal light, nor what sort of object to expect; and, secondly, that the theory was greatly in error; and, for an astronomical matter, grievously wrong... Both classes of mistakes may have been brought about in no small degree by the inju- dicious mixing up of erroneous theoretical and speculative views with the simple nomenclature of the phenomenon. All that can be asserted from a single obser- vation, and, perhaps indeed, from all the observations that have been made, up to the present time, is that a light appears in the zodiac, and if it be called “ the VOL. XX. PART III. 6Q 490 PROFESSOR PIAZZI SMYTH ON THE zodiacal light,” no idea except the visible fact itself is included. But to call it the “ Sun’s atmosphere,” is taking for granted a supposed fact which has never been proved, and is imagining the body to obey peculiar laws, to which it may not really be subject. Moreover, as in the case of a phenomenon which is so extremely faint as scarcely to be seen at all, a person may too easily persuade himself that he sees it as he ought to see it,—so there seemed to be much necessity for making further observations, which though they might prove, after all, to be not entirely free from errors of judgment and idea, yet would probably not be affected in the same way as those of other observers. The circumstances in which I was placed were very favourable, so far as the clearness of the sky, the purity of the atmosphere, and the advantage of geogra- phical position were concerned; but being engaged in the active duties of a trigo- nometrical survey, sometimes on the top of high mountains and sometimes in the plains below, the different character of the stations exercised too great an influence on the phenomenon to be observed, to allow of strict comparison being made be- tween the observations at the various places. But there was at least the possibi- lity of being able to determine a good method of making the observations, by en- deavouring to reduce to practice some plan by which the results should be expressed more in numbers than has generally been the case; and of ascertaining at least the degree of accuracy with which observations of place, 2. ¢., of AR. and Decl., could be made, in more or less favourable localities and seasons. I proposed to myself, therefore, to endeavour to determine each night the AR. and Decl. of the apex of the light; though the only method which was then avail- able, viz., observing the particular stars amongst which the point was situated, was only of use when there were large stars close by; since even if there had been star-maps to refer to in the desert, to identify the smaller ones, the phenomenon to be observed was not one that would bear close and direct investigation. It was only after having shut the eyes for some little time, or having turned them to some dark part of the sky or earth, that on suddenly directing them to the region of the zodiacal light, but not exactly to the middle of it,—it was seen of a well-defined figure ; for by looking straight at it, and still mcre by coming into contact with any artificial light, the situation of the apex appeared to vary many degrees, or could not be decided on at all. At length, therefore, in 1844, I made a little wooden instrument with equatorial motion, plain sights, and roughly divided circles; which being placed in position in some spot free from any artificial light, readily gave the means of determining the object sought. Then, by the sort of side glance above described, a good notion of the position of the apex being obtained, the plain sights were immediately pointed to the spot, the circles read off, and their index error obtained by reference to known stars on either side. This was usually done two or three times each night, and the mean has been entered in the accompanying table as a single observation. 491 PHENOMENA OF THE ZODIACAL LIGHT. “oc “ouoays A10 A ‘yQuUOW siz} Jo aed J9}}8[ 480 oY} Ul woos [OA ‘O{GISTA JONI “Hy sItq pue ‘Morreu ‘“suoy ‘suos A104 ‘OTqISIA SuTTTIO NT *IOJ POO] Ysnoy} ‘SUIUIOUL oY} UI UVES 40 NT ‘T]PA. Jou ynq “deeg ‘qjMo Ip Aaa suOTYRATESqO oy} tepuet snuseA jo uontsod pu ssouqy.st1q of} [OIA septs -oq §Avm AyTIUL oY} UE poyeed -U09 JST] Teovtpoz ayy jo xedy “YFUO Wet} Fo pus oT} SpIVMO} WO9G og 1G eS ON, ‘98 —CZ wOG (0G “UV pey “Wd 46 3e ‘G ‘09q UO poadosqo suroq xodv pouyep-[[t 9} Sasvod 0} JYSITIM} LOF UIT} OY} 1o}Je SUOT 4S9A\ OY} UL 4YYSIT jo A4yyuenb v ynq ‘tnFqQnop 410 A “qystiq 419 A ‘yjuour jo y1vd 4say ul use od at ‘snonordsuos 19 A. *BULUOAD OY} UT Mees 4eY} IO “IT "7 Jo uonsz0d Surpesead 10 ua94se \\ ‘SUIMIOUL OY} UL Woes VT} 10 “TT ‘7 Jo uoystod Sutmo]joy 10 uaoysemy HO syreMeyy &¢ Gg “Suoje rac) “482M 99 69 64 99 0G 6G “moTyes -u0oyo u1989seiy GL t= GG 2s Zilictan bo a0 ° ur ‘d “UV 2 G6 10s Ail 8 | 08 91 9+ de 31 1+ |% 6 | GG— |06 9T ROwen| Choo Pe | er 91 ° ‘wm ‘d “AV AVA " * “areld a a. a “OGL ms oni Oat “od 00ST OG 00¢9 ‘od 00gs “UreyUNO TT * “uel 0006 “ureyuNOPT " * Weld OOGT ‘urezyuNoTY WA ‘ule ‘UOIPLAIESYO JO edeI[ gq ‘Od | w0F yLT 32 { “16 PUL ‘MOE 4B “8 3%“ “PO y8 3% 1g “dog Sop Ga "yt ye 9 Ane wOF y9 78 G oun . . . . ‘ke judy pure youepy ‘Arvn1ga,T “GPST ‘req ula { Wd m0G ql 3? “OL * Wd ie 1a +8 Qs "Wd yg) 48 °Z “390 ‘qdag puv ysnsny . ‘Ayne * “hen ‘Aren.1qo,7 ‘PPS8L "+ Staqureydag * 4snsny . ‘Ane ‘oun ¢* ‘ST8I aye] 492 PROFESSOR PIAZZI SMYTH ON THE A few days after the last observation I left the Cape, and the passage thence by St Helena through the tropics, was so uniformly cloudy, that I was unable to obtain another satisfactory look at the zodiacal light, and ever since my residence in Edinburgh in the middle of a city glowing at night with gas, and reeking with smoke, and under a sky but rarely clear, and when it is so, not unfrequently illuminated by the Aurora Borealis, I have been equally unfortunate. To be able to make a good observation of the zodiacal light, the sky should be quite free from clouds, the air pure and transparent; not the slightest vestige of the twilight should remain, the milky way should be far from the neighbour- hood, the moon should not be visible, or the brighter planets, such as Venus and Jupiter. If these circumstances be secured, and a person look out at that period of the year, as hereinafter detailed, when the ecliptic makes a large angle with the horizon of the place of observation, he can hardly fail to see the phenomenon in the most marked degree. A beginner must be especially cautioned not to begin looking too soon in the twilight to discern the “‘ Sun’s atmosphere,” under the idea, happily, of catching it before all traces of the sun’s light on the horizon are completely gone; and he should also be forewarned of the immense influence which climate and geographical position have on the visibility and apparently on the form and size of the phenomenon. Thus, in 56° N. Lat., and still less further north, even were the elongation of the light E. and W., equal in every respect, it would still never appear equally visible, and would but seldom be seen either way. In the summer the twilight would render the sight impossible, and in winter, the sun’s path is too low and oblique. In the spring evenings, the light would be well seen, be- cause then the twilight is of a moderate length, and the zodiacal light rises at an angle to the horizon of 30° greater than the equator, and therefore does not set till long after the twilight has disappeared; but as the other end rises in the morning at that season, necessarily at an angle 30° less than that of the equator, the apex in its standing position, hardly rises above the mists of the horizon be- fore the twilight illumines the sky. In the month of September matters are just reversed, and the zodiacal light rising in the morning at a greater angle than the equator, is then well seen, but is not at all visible in the evening, when, from the standing position of the body, the apex sets very soon after the sun. And in these two short appropriate seasons, so many of the nights may be rendered untoward by clouds, strong moonlight, and other causes, that an opportunity of seeing the zodiacal light may even then but very rarely be enjoyed. Similarly in the southern hemisphere in 56° S. Lat., supposing also, as before, that the zodiacal light stretches out equally from the sun on every side in the plane of his equator, the two most favourable opportunities in the course of the year for viewing the body would be, in the evening in the month of September, and in the morning in the month of March. And that this would really be the case, the observations made in Lat. 33 S. sufficiently attest. PHENOMENA OF THE ZODIACAL LIGHT. 493 In order to give a clearer description of what may be expected to be seen, than can be conveyed in words alone, I have subjoined a number of drawings,* both of what the zodiacal light is, and what it is not, the latter being the great comet of 1668 and 1843, mistaken on both occasions for the more permanent members of the system. The object in the construction of the drawings has been, in so far as it was possible to be compassed by the small skill of the author, to give so complete a reproduction of all the attendant phenomena, and circumstances of climate or country, as to enable any one who looks at them, to form a tolerable idea, whether any of the accompanying conditions under which the original view was obtained, were likely to produce an erroneous judgment in the spectator, of the exact form and appearance of the zodiacal light. A larger portion of the land- scape has therefore been introduced, than would otherwise have been altogether appropriate in astronomical drawings. A more important addition is, however, that which I was advised to make by my friend Mr W. A. Capr.L, viz., the insertion in the margin of the circles of Right Ascension and Declination, which shew what particular projection has been employed, and serve to identify the stars, fix the latitude in which the ob- servations were made, the time at the instant, and to give an idea of the dimen-_ sions of the body under discussion, and the region of the sky in which it is found. To represent the eastern or western portion of the sky, in their perfection, or as would be thrown on paper by the camera lucida, as Mr Capett has shewn, the horizon should be defined by a straight line in the picture, and the E. or W. point must be in the middle of that line; then the eye of the spectator being directed toward it as such, the equator, being a great circle, will be represented by a straight line drawn through that point, and rising at an angle to the hori- zon, equal to the latitude of the place; and the meridian lines on the parallels of right ascension, being also great circles, must be expressed by straight lines cross- ing the equator at right angles; on the other hand, the parallels of declination being small circles, will appear as conoidal curves. A great circle becomes a straight line on the picture, since it is a plane passing through the eye, and the common section of this plane with the planes of the picture, is a straight line. A small circle is a conoidal curve on the picture, because a small circle is seen as a cone of which the apex is at the eye, and the common section of this cone with the plane of the picture is a conic section. The form of the conic section will vary as the inclination of the cone’s axis to the plane of the picture varies. In all the drawings given herewith, the line of sight is seldom directed exactly to the E. or W. points, but generally between them and the northern or (point of culmination for the southern hemisphere.) Were the spectator to face the * On account of the expense of first-class engravings, one of the drawings only has been put upon metal. This one, “ the appearance of the zodiacal light at the Cape of Good Hope, in July 1845,” will be found amongst the plates at the end of the volume. VOL. XX. PART III. OR 494. PROFESSOR PIAZZI SMYTH ON THE northern point exactly, then the equator would be represented by a straight line, parallel with the horizon, and elevated above it at an angle equal to the colati- tude of the place. And, according to the degree to which the spectator turns round from the E. or W. points towards the north, the inclination of the equatorial line will vary, from the angle of the latitude of the place, to perfect horizontality. This varied inclination of the equator has been strictly attended to in all the accompanying cases; but it has been found advisable for simplicity in practice, to represent the declination circles also by straight lines, for there is hardly any sensible difference caused thereby in the central region of the picture, where all the important part of the subject to be delineated, lies; and although the con- figuration of stars near the borders might not be such as would exactly appear to the eye of a spectator, or as they should be represented by the usual rules of per- spective, still the amount of discordance is so extremely small, that the unassisted eye would hardly perceive it; and, what is more important than having a repre- sentation perfectly similar, in the minutest particular, to that found in the re- tina,—the particular projection of the sphere which was actually employed, being inserted in the margin, gives just as good, and rather simpler, means, than would have been available on the other plan, for the identification of the stars. The application of instrumental measurement, hereinbefore described, to deter- mine the phenomena of the zodiacal light, is believed to be new; and the obser- vations so obtained, seem to shew very decidedly, especially those of October 1844, that numerical measures of the place of the apex of the light may easily be obtained,—with a probable error of not more than two degrees: so that vague estimations and notes of mere ideas should not be allowed to form the data in this particular branch of astronomy any longer. The general results to be deduced from the data given in the Table, are, 1st, That the zodiacal light is a body of a lenticular form, spread out nearly in the plane of the earth’s orbit, and extending almost equally from the sun in every direction. Were the ordinary European observations made about the time of the spring equinox the only ones existing, we should merely be entitled to conclude the existence of a one-lobed projection from the sun; but when we combine therewith the Cape observations, we find that the body is seen all through the year, and on both sides of the sun, of pretty nearly the same size and shape, viz., a curvilinear-sided wedge, in which the light continually increases from the borders towards the centre of the base, or the actual position of the sun; ap- pearances which can only be satisfied by a lenticular body seen in section. 2d, The zodiacal light is proved to be excentrically disposed about the sun, by the elongations observed east and west on the same day being different ; shew- ing, indeed, at various times an excentricity of from 35 to 75- 3d, The zodiacal light may also be considered to rotate about the sun, and to be brighter in some parts than in others; because it is observed to be of different lengths and degrees of brightness at corresponding periods in successive years. For PHENOMENA OF THE ZODIACAL LIGHT. 495 although such an effect might be produced by a periodical alteration in the size and general lustre of the body, still the supposition of such arapid material change in so large a member of the solar system, is extremely improbable: whilst this body’s revolving may be held to be necessary according to the principles of gravi- tation ; for otherwise the component particles would speedily fall into the sun; and that some portions are brighter than others, follows partly as a consequence of the observed unequal size of the two sides. Were the light stationary, then the greatest and least lengths and brightnesses should occur at the same time in suc- cessive years, because on arriving again at the same points of its orbit, the earth should again see the same parts of the zodiacal light pointing to the same direc- tion in space; but, as already stated, the contrary to this has been observed. The greatest elongation observed was 79°, and the least 50°, but from the ‘varying circumstances and positions in which the observations were made, the short period of time over which they extend, together with the small number of favourable opportunities, and the distance of the place from the equator, which these conditions afforded, no numerical results of much accuracy can be derived from them alone; but some advantage may be gained by comparing them with the results of former observers. The number, however, of these, 7. ¢., of actual observers, is comparatively small, and they are all very recent; for, strange to say, no notice of the zodiacal light is found amongst the writings of astronomers or natural philosophers until 1661. And indeed, when we consider that this phenomenon may be generally described as a broad and tall light seen in the western sky after sunset, and in the eastern before sunrise, with a length of about 60°, a breadth of 20°, combining with a brightness nearly equal to that of the milky way, a regular mathematical figure, which makes it far more remarkable, and rising, as it does, at a greater angle to the horizon, so as to be better seen in countries nearer the equator than ourselves, and being probably of as great antiquity as the sun itself,—truly it is astonishing that all these notabilia should have been passed over in the earlier ages of the world, when civilization flourished more to the south, and the men of ancient Athens and Babylon lived under a clear sky, in a genial climate, which invited rather than forbade the contemplation of the firmament by night. It re- mained, however, for the inhabitants of these cloud-vexed northern islands to be the first to take notice of the phenomenon, and so supply another instance of the indomitable perseverance of an iron race overcoming all the untoward obstacles of an unpropitious position, and rising superior to other races revelling in the most luxurious advantages of nature. Claims have been put up for KrrLer and Descartes, as being the original discoverers of the zodiacal light; but the passages in their respective works* * Kepier’s Epit. Astron. Copernicane, t. 1., p. 57; and t. ii., p. 893 ; Descartes, Principes, iii., Art. 136, and 137. 496 PROFESSOR PIAZZI SMYTH ON THE are so very meagre and obscure, that they require all the knowledge of the phe- nomenon acquired up to the present day, to be applied to make them mean anything. Marran, with whose theory Krpier’s fancy seems to agree, when discussing, in 1754, the history of the phenomenon, gives the German full credit ; but Humpotpt, in 1844, with different theoretical views, dismisses the case of his countryman in a very summary way. An earlier claim still has been brought forward, on account of the mention, in'a letter from RorumMann to TycHo Braue, that in the spring the twilight ceased not till the sun was 24° below the horizon ; and as the true twilight would have ceased long before the sun was so low,—it is contended that RorHmann must have seen the zodiacal light, though without remarking anything peculiar in it, or different from the ordinary course of the evening. So that the first satisfactory and clear description is still that of Cumprey in 1661, already alluded to. ‘‘ There is another thing,” says he, in his Britannia Baconica, p. 183, “ which I recommend to the observation of mathematical men ; which is, that in February, and for a little before and after that month (as I have observed for several years together), about six in the evening, when the twilight hath almost deserted the horizon, you shall see a plainly discernible way of the twilight, striking up towards the Pleiades, and seeming almost to touch them. It — is so observed any clear night, but it is best z/dc nocte. There is no such way to be observed at any other time of the year. But what the cause of it in nature should be, I cannot yet imagine, but leave it to further inquiry.” Here, then, is a clear and simple account of one phase of the phenomenon, marking it as a something unusual, as different from ordinary twilight, as con- stant in that anomalous difference, and therefore well worthy of being carefully inquired into. In his Travels in Persia in 1668,* CuarpIN mentions having seen the tail of the great comet of that year above the western horizon after sunset; the head being visible only in the southern hemisphere. Casstn1 and Marran, writing some years after, under the influence of the then new discovery of the zodiacal light, asserted that it must have been this which CHARDIN saw; and he is even made out by DeLamsre to have been the original discoverer of it. The comet of 1668 having, however, appeared again in 1843 (that is, they are supposed, with the greatest probability, to be identical; and if not identical, still they are at least both specimens of the comet genus), has given us the opportunity of determining whether Cuarpin’s description applies to the zodiacal light or to the comet, which though so very unlike each other, were not only confounded at the former appa- rition, but at the latter also; when the tail, as before, was the only part visible in the northern hemisphere. The slightest glance at the accompanying drawings * Hdit. de Langles, t. iv., p. 326; and t. x., p. 97. PHENOMENA OF THE ZODIACAL LIGHT. 497 of the two objects, however, will probably convince every one, that CHarp1n’s Persian expression “ niazouk,” or in French “ petit lance,” which was applied by the Persians to the phenomenon they saw, could only be considered as at all suitable in the case of the comet’s tail. In 1683, the subject was taken up by Domrnic Cassin1, and to him belongs the merit of first scientifically investigating the laws of the phenomenon, determining its cosmical nature, and giving it the appropriate name of the zodiacal light. His series of observations, extending over nearly six years, is still unrivalled; and if he is not correct in all his conclusions, it is chiefly because his observations were almost entirely confined to his own high northern latitude; and were therefore affected to a great and unknown extent by circumstances of climate and geogra- phical position. He had much wished to eliminate these effects by means of ob- servations made in the southern hemisphere, but unfortunately was not able to obtain any; and indeed those which have been made by the author, and recorded in this paper, are perhaps the first which have been published and brought to bear on the theory of the subject. Cassini’s conclusions were, that the zodiacal light is a flat luminous ring en- circling the sun, nearly in the plane of his equator, and is therefore seen always more or less in profile, and perfectly so at two periods of the year, April and August, when like Saturn’s ring, and for similar reasons, he supposed it to vanish to our sight; while the nonvisibility at any period between these two months, he con- sidered to be produced mainly by the overpowering effect of the lengthened sum- mer twilight. But these ideas, on being tested by the Cape observations, com- pletely fall to the ground; for during the whole period of invisibility to Cassini (caused in reality by the lengthened twilight of summer in his northern hemi- sphere), the phenomenon was most visible at the Cape, as winter then prevails in the southern hemisphere; and, indeed, the very reverse effect from that expected by Cassini should follow, when a transparent and oblate luminous ring is viewed in profile, for it will then be seen at its brightest, on account of all the infinitely small light-giving particles being brought closer together; so small are they, that they can by no means be distinguished separately, or when thinly scattered over the sky, but only make themselves sensible to the eye, and the telescope, when they are crowded together in a smaller space. The idea, moreover, of the zodiacal light being in the form of a 7ing at all, is discountenanced by the observed appear- ances, they being all conformable to the phenomena which would be afforded by a thin lenticular body, excentrically situated and revolving about the sun. Cassini's friend, M. Fatio, made observations of the zodiacal light about the same time, as did also M. Kircu, and Emmart, and Mr Dera. But the subject was not carried further, until taken up by Marran, in 1731, He was rather wild in his notion of the manner in which the body was formed, VOL. XX. PART III. 6s 498 - PROFESSOR PIAZZI SMYTH ON THE viz., by particles thrown off from the sun, in consequence of the rapidity of his rotation; nor was he very happy in his name of the “Sun’s atmosphere,” by which he led both himself and others to reason upon it, as if it were proved to be, and actually was of a kindred nature with the earth’s atmosphere. His conclu- sions, however, that the whole of the luminous body was of a lenticular form, nearly in the plane of the earth’s orbit, somewhat excentric with regard to the sun, and, indeed, with a rotation about that luminary, seem to be remarkably good. And his opinion, so far as the lenticular shape is concerned, is also held by OLBERs and by Sir J. Herscue., both of them observers. OLBERS in a letter to HumMBoLpT in 1833, says, “ What you tell me of the changes of brightness in the zodiacal light, and the causes to which, in the tropics, you ascribe such variations, has excited my interest the more, because I have been for a long time past particularly attentive every spring to this phenomenon in our northern latitudes. I, too, have always believed the zodiacal light to rotate; but I assumed it (contrary to Porsson’s opinion, which you communicate to me), to extend the whole way to the sun, increasing rapidly in intensity. The luminous circle which in total eclipses shews itself round the darkened sun, I have sup- posed to be this brightest portion of the zodiacal light. I have satisfied myself that the light is very different in different years, sometimes for several years being very bright and extended, and in other years scarcely perceptible. I have not myself been able to observe the sudden fluctuations in the light, probably on ac- count of the faintness with which it appears to us in this part of the world. You are certainly right in ascribing the rapid variations in the light of celestial objects, which you have perceived in the climate of the tropics, to changes taking place in our atmosphere, and especially in its higher regions. This shews itself in a more striking manner in the tails of great comets. Often, and particularly in the clearest weather, pulsations in the tails of comets are seen to commence from the head or nucleus as the lowest part, and to run in one or two seconds through the whole extent of the tail, which, in consequence, appears to lengthen several de- grees, and contract again. That these undulations, which engaged the attention of Ropert Hooke, and in later times of ScHroeTEr, and CuLapnt, do not take place in the cometary tails themselves, but are produced in our atmosphere, appears evi- dent if we reflect that the several particles of these cometary tails (which are many millions of miles in length) are at very different distances from us, and that the light from them can only reach our eyes at intervals of times which differ several minutes from each other. I will not attempt to decide, whether what you saw on the banks of the Orinoco, not at intervals of seconds, but of minutes, were actual coruscations of the zodiacal light, or whether they belonged solely to the upper strata of our atmosphere. Nor can I explain the remarkable lightness of entire nights, or the anomalous increase and prolongation of this light in the year PHENOMENA OF THE ZODIACAL LIGHT. 499 1831, particularly if, as it has been said, the aghtest part of these singular twi- lights did not coincide with the place of the sun below the horizon.” Sir Joun Herscuev’s views, published only five years ago, were called forth by the tail of the great comet of 1843 having been by some so pertinaciously mistaken for the zodiacal light. “ The zodiacal light,” said he, ‘as its name imports, invariably appears in the zodiac, or, to speak more precisely, in the plane of the sun’s equator, which is 7° inclined to the zodiac, and which plane, seen from the sun, intersects the ecliptic in longitude 78° and 258°, or so much in advance of the equinoctial points. In consequence, it is seen to the best advantage at, or a little after, the equinoxes, after sunset at the spring, and before sunrise at the autumnal equinox, not only because the direction of its apparent axis lies at those times more perpendicular to the horizon, but also because at those epochs we are approaching the situation in which it is seen most completely in section. « At the vernal equinox, the appearance of the zodiacal light is that of a pretty broad pyramidal, or rather lenticular, body of light, which begins to be visible as soon as the twilight decays. It is very bright at its lower or broader part near the horizon, and (if there be broken clouds about) often appears like the glow of | a distant conflagration, or of the rising moon, only less red; giving rise, in short, to amorphous masses of light, such as have been noticed by some as possibly ap- pertaining to the comet. At higher altitudes its light fades gradually, and is seldom traceable much beyond the Pleiades, which it usually however attains and in- volves; and (what is most to my present purpose) its axis at the vernal equinox is always inclined (to the nortward of the equator) at an angle of between 60° and 70° to the horizon; and it is most luminous at its base, resting on the horizon, where also it is broadest, occupying, in fact, an angular breadth of somewhere about 10° or 12° in ordinary clear weather.” The ring hypothesis of Cassini has, however, been followed in a greater or less degree, by La Piace, ScHERBERT, and Poisson, as well as by HumBowpr, who is an observer, and publishing in 1844 is the latest of all the authorities. His description of the general appearance of the light is most vivid and truth- ful, and can perhaps only be fully appreciated by those who have seen it under similar favourable circumstances. ‘“« Those who have dwelt long,”* says he, “ in the zone of Palms, must retain a pleasing remembrance of the mild radiance of this phenomenon, which, rising pyramidally, illumines a portion of the unvarying length of the tropical nights. I have seen it occasionally shine with a brightness greater than that of the milky way, near the constellation of Sagittarius ; and this not only in the dry and highly rarified atmosphere of the summits of the Andes, at elevations of thirteen to fifteen thousand feet, but also in the boundless grassy plains or Wanos of Venezuela, and on the sea-coast under the ever-clear sky of Cumana. The phenomenon is 500 PROFESSOR PIAZZI SMYTH ON THE one of peculiar beauty, when a small fleecy cloud is projected against the zodiacal light, and detaches itself picturesquely from the illuminated back-ground. A passage in my journal during a voyage from Lima to the West Coast of Mexico, notices such a picture. ‘For the last three or four nights (between 10° and 14° of north latitude), the zodiacal light has appeared with a magnificence which I have never before seen. Judging also from the brightness of the stars and nebulz, the transparency of the atmosphere in this part of the Pacific must be extremely great. From the 14th to the 19th of March, during a very regular interval of three quarters of an hour after the disc of the sun had sunk below the horizon, no trace of the zodiacal light could be seen, although the night was perfectly dark; but an hour after sunset, it became suddenly visible, extending in great brightness and beauty, between Aldebaran and the Pleiades, and, on the 18th of March, at- taining an altitude of 39° 5... Long narrow clouds, scattered over the lovely azure of the sky, appeared low down on the horizon, as if in front of a golden curtain, while bright varied tints played from time to time on the higher clouds: it seemed a second sunset. Towards that side of the heavens the light diffused appeared almost equal to that of the moon in her first quarter. Towards ten o’clock, in this part of the Pacific, the zodiacal light usually becomes very faint, and at mid- night I could only see a trace of it remaining. On the 16th of March, when its brightness was greatest, a mild reflected glow was visible in the east.’ ” He describes also several anomalous features, as that sometimes it did not appear for three-quarters of an hour after sunset, though the twilight had been for some time ended ; that then it appeared suddenly, and continued long of very ereat brightness; that at other times it would continue to shorten and lengthen many degrees in a few minutes, and have an undulatory sort of motion. But these peculiarities, when not accounted for by the atmospheric circumstances of which he himself takes notice, seem rather to be produced in the eye of the ob- server by reason of the extreme faintness of the object to be observed; by the length of time that a retina,—which has been initiated by watching the setting sun, or even when acted on by ordinary daylight,—requires to recover its full degree of sensitivenes; as well as by the deceptive phantasmagoric effect produced on the nerves when strained to a greater extent than they can well bear. Taking all the above facts into consideration, we are perhaps entitled to con- clude, on pretty good foundation, that the zodiacal light is an extremely oblate, lenticular, revolving body, nearly in the plane of the sun’s equator, rather excen- trically situated, of so vast a size as nearly to fill the whole orbit of the earth, and sometimes actually to reach it. But whether it does actually at the present time correspond exactly with the sun’s equator, and if it has always done so, and always will; whether the manifest changes in the intrinsic brightness, and the form and size of the light that have been observed, be due merely to a rotation of the excentric or oval body, or to a real periodical increase of the intensity of its PHENOMENA OF THE ZODIACAL LIGHT. 501 emanation, or an enlargement of its dimensions; and whether this be any con- comitant symptom with the appearance of spots on the sun, or magnetical dis- turbances on the earth,—are matiers still to be determined by observation. The physical constitution of the zodiacal light seems also well worthy of being inquired into. The most probable supposition is, that which makes it consist of innumerable small planetary particles revolving about the sun, and shining. by reflected, or not impossibly by direct light. Not impossibly, because while, on the one hand, the occasional crossing of the earth’s orbit by the extremer portions of the zodiacal light, has been by many held to be the origin of the shooting stars ; and many of them have been found to be, at the time of their incandescence, several hundred miles above the earth’s surface, and thus far above the limits of the atmosphere, whose friction might have imparted such a degree of heat to a body at a lower altitude, moving with a velocity of 1000 miles per minute ;—on the other hand, M. Maruizson has.recently made some most interesting experi- ments, in which the thermomultiplier shewed evident indications of radiant, and therefore direct heat, proceeding from the zodiacal light.* But in its present stage, the subject can only be profitably and successfully prosecuted in other climates, in countries where the twilight is shorter, where the ecliptic makes, all through the year, a larger angle with the horizon than here. and where there are clearer skies, and a more transparent atmosphere. As such conditions are well commanded by some of the magnetical and me- teorological observatories which have been lately established on a similar foot- ing to that of Makerstoun, in connection with the Royal Society of Edinburgh ; and as the species of phenomenon is one that belongs eminently to those de- partments,—we might expect ere long to enjoy much more intimate and exact knowledge of the laws and relations of this wondrous and extensive member of the solar system, if the Royal Society were to give its testimony that the pheno- menon was one of a nature worthy of scientific investigation ; as well as that all that has been done hitherto is insufficient, except for mere approximative pur- poses, and has been labouring under geographical disadvantages, which need not by any means continue to shackle observation in the present day. * Comptes Rendus, t. xvi., p. 687; Ap. 1843. VOL. XX. PART III. 6T t a | Ee ; | | A ‘aha iu pew 7 afthi a {i Ror i asa vs iin ci ees sent 5 e. rt , 2s mae) Fenidua init? Yr J ie Bu tig asir ce ‘hy Sangeae . ie . - . ie 4 oa ~ ‘ Pn i Test % . ° - \ ‘ ‘ - » ! Wie 4ny , } ’ . té 4 t } ee - ? r a | ay ] oo 4 : i ‘ ' P ‘ . : ‘ } + ~ a - vs é ' ’ a i at An . his Ral heli | a i - 4 wi te he . ist roy (itt ie Peis) OI ] ‘ Lf | € ‘ : ae as eee , > * y ‘ "| a bs] eat - A 4 ' Pen) - = \ . - yl 4 a " ie “AYWMUYON JO 1SVYOO “M “GNW1S! 3N@ NO N33S SY NOS HI dO ASdITOd WLOl Fel Are) 909d 0Z TON AIX FLY Td ee BOS27) | XXXIV.—On the Total Solar Eclipse of 1851. By Professor C. Piazzi Smyru. (Read December 1, 1851.) | - Eclipses are still, as they have ever been, very important phenomena for the astronomical observer; partly on account of the crucial test which they afford for the examination of the truth of the theory and calculation of the motions, real and apparent, of the Sun and Moon, partly also for the special opportunities which they furnish of inquiring into some of the arcana of the physical charac- teristics of those bodies. For the former purpose, a partial eclipse will serve almost as well as a total one; while the continued improvement of the observation of meridian passages is now raising these daily measures fully to the importance of the other occasional phenomena, as a test. of the theory.. But for inquiry into the physics of the Sun, a perfectly total eclipse of that body is necessary ; revelations may then happily be procured, which no observation of any other phenomena at any other time, can ~ hope to afford any suspicion of. As the occurrence however of a total eclipse near any inhabited and civilised region of the earth, is very rare; and as even when it does occur, the observation lasts ‘but for three short minutes,—the utmost extremity of importance attaches to the occasion in the eyes of all practical astronomers. So many circumstances, too, have to be noted, observed, and measured, within a’ few seconds, that’ it is necessary to adopt some systematic division of labour amongst a number of ob- servers, and for each to be previously practised and expert in his particular part. Much of this arrangement was organised for the eclipse of July 28, 1851; and while other observers were distributing themselves along various parts of the line of totality, I gladly seized the opportunity of occupying, in company with the Rev. T. R. Rosson, D.D., the western coast of Norway, where the path of the moon’s shadow first entered Europe. On the importance of the occasion being represented to the Commissioners of Northern Lighthouses, then sitting in Edin- burgh, that Board, who can so well appreciate science, and who have introduced so many of its more recondite appliances into their admirable establishments on the coasts of Scotland,—finding that their steam-vessel, the Pharos, would be engaged amongst the Shetland Isles about the time of the eclipse, most liberally undertook to convey Dr Ropinson and myself to the selected part of the Nor- wegian coast; a boon of so much the more importance, as that portion was un- visited, so far as we could learn, by any sort of vessels available to ordinary passengers. | _ Being taken across the North Sea, then, in this manner, and having been pro- VOL. XX. PART Ill. 6U 504 PROFESSOR PIAZZI SMYTH ON THE vided, through the Admiralty, with a recommendation from the Swedish ambas- sador to the local authorities, which opened the whole coast to us without let or hindrance, we landed on the Bue Island, north of Bergen, on the morning of the eclipse,—erected the instruments, many of which had kindly been lent to us by Admiral Sir F. Braurort, from the Hydrographical Department, and having the zealous co-operation of Messrs Commissioners Hunter, THomson, and UrquHart, Mr Secretary CunincHAM, and Mr ALAN StTevenson, the able Engineer of the Board, together with the officers of the vessel, we were enabled to detail a dis- tinct observer for each and every phenomenon that could well be expected during the obscuration. Our preparations, however, met the fate but too frequently suffered by astronomers in these northern regions, viz., that they were rendered futile through clouds; clouds so dense that nothing whatever was seen of the heavenly bodies during the middle of the eclipse. But we had a remarkably good opportunity of judging of the general effect of a total eclipse; and what with our partial expe- rience, and the impartiality with which we could judge of the observations of the more delicate phenomena by others, from not having any of our own to bring forward,—we are perhaps peculiarly qualified to point out, wherein observers may have failed in doing all that it is desired should be done on such an occasion, and how they may probably succeed another time. The general effect of a total eclipse, however interesting and instructive, as one of the most sublime phenomena in nature, may yet appear unconnected with the more scientific portion of the observations; and so it is directly, but indi- rectly it has the greatest influence. For its effects on the minds of men are so overpowering, that if they have never had the opportunity of seeing it before, they forget their appointed tasks of observation, and wz// look round during the few seconds of total obscuration, to witness the scene. Although it is not im- possible, but that some frigid man of metal nerve may be found capable of resist- ing the temptation, yet certain it is, that no man of ordinary feelings and human heart and soul, can withstand it. In the eclipse of 1842, it was not only the vo- latile Frenchman who was carried away in the impulses of the moment, and had afterwards to plead his being no more than a man, as an excuse for his unfulfilled part in the observations,—but the same was the case with the staid Englishman, and the stolid German. Nor was the history of this experience enough to guard against similar results on a second occasion; for in 1851, much the same unin- tended perversion of observation took place; and on asking a worthy American who had come with his instruments from the other side of the world, pointedly to observe this eclipse,—what he had succeeded in doing ?—he merely answered, with much quiet impressiveness, that if it was to be observed over again, he hoped that he would then be able to do something, but that as it was, he had TOTAL SOLAR ECLIPSE OF 1851. 505 done nothing, it had been too much for him. In fact, the general scene of a total eclipse, is a potent Siren’s song, which no human mind can withstand: and the only way in which its witcheries can be guarded against, is that by which Uxyssss passed the fatal shore in safety. Let, then, those who on a future occa- sion have to make the more accurate telescopic observations, surround themselves by some high wall, which shall prevent their seeing anything but a very small portion of the sky round about the sun and moon. And let those to whom the observation of the general effects may have been confided, be competent and pre- pared to put whatever they see, pictorially on paper, so that others may after- wards profit by their opportunity. First, as to this latter department, viz., the recording of the general effect. The result of my partial experience is, that during the progress of the earlier part of the eclipse, the observer may be sketching in a something of the general forms of the landscape, on six separate boards, giving 60° of azimuth to each, so as to include the whole panorama; or one long board properly supported may be better still, as there is no knowing beforehand where the most effective displays will take place. Moist water-colours in tin tubes and rough drawing-paper, I am disposed to consider, after much practice with all the varieties of water-colours, crayons, and oils, to be the most effective and convenient medium, all things con- sidered, for general field-work. Being seated then in an open place, with abundant paper-surface before him, the observer should have a powerful lamp, to throw its light on his work and the colours, which should all be mixed up beforehand, and arranged on a large pallet. Then on the instant that the total obscuration begins, and it is complete almost the instant that it begins, so well-defined is the shadow of the moon,—he should immediately put in the colours, shadows, and forms, at once and boldly, with a large brush; every stroke of which at the time, will enable his memory after- wards, to add multitudes of those little indescribable details, which together form the impression made on the eye; whose power was confessed at the time, but which are nevertheless easily and completely forgotten, unless actually seen again. But to be able to put in even the groundwork of these six pictures in so short a space of time as the total obscuration lasts, hardly three minutes, requires something more than the mere wish to be able to do them, though this is unhap- pily all that astronomers have generally taken with them to this most difficult problem in art. So difficult is it to paint a tolerable picture, even under the most favourable circumstances, that it has been a matter of frequent remark, that no amateurs have ever produced works capable of standing side by side with those of professional painters; but when there is further the excessive difficulty caused by the almost instantaneous disappearance of the scene, so as to necessitate its being painted from the memory rather than the fact,—it is not to be wondered at that none of our scientific books yet contain a tolerable representation of the 506 PROFESSOR PIAZZI SMYTH ON THE effects of a total eclipse; and that only those few persons who have actually seen it, really know what it is like. The phenomenon therefore, when seen, has, by its unexpected novelty, such a power of enchantment, as to hold all observers spell- bound. If astronomers, however, will only take the trouble, they may learn to give a good account of this most interesting subject. To no one who really tries to learn to draw, is the power wholly refused, and every one may by practice improve their memory, as applied to drawing, as well as to anything else. The test of the proper degree of skill having been arrived at, would be the taking of half- a-dozen views of the progress of a sunset, during a certain number of minutes; while to copy a picture after a one-minute view of it, would give the means of as- certaining afterwards what were the probable limits of that person’s errors in light, shade, and form, without some estimation of which no astronomical draw- ing should be considered presentable. No drawing can be made perfect, any more than a numerical observation can. The one cannot be depended on to the minutest feature inserted on the paper, nor the other to the smallest fraction of a division read off from the instrument. The question in either case must be, what is the extent to which dependence can be placed? By knowing that the ereatest probable error of Tycho Braune’s observations was 3’, KrpLer proceeded safely to deduce the elliptic theory of the planets: and if theories are ever to be based on astronomical drawings, the possible limits of error in every way must be ascertained, and published as anecessary appendage to the pictorial representation. T will not presume to say that I have arrived at the mark which is here pro- posed ; but I have practised myself in drawing from memory, as well as in hasty sketches from nature. My part, however, at Bue Island, was with a telescope, and but for the unexpected clouding of the sky, I might have seen nothing of the general effects; the clouds, however, absolving me from my special duty, enabled me at least to look round, and I hastily made pencil sketches of what I saw. These were coloured as soon as possible afterwards, and form a series of views, shewing the varying effects, through the short period of the totality, and in various directions. One of these views has been engraved with the present paper (Plate XIV.), and as far as one only can serve, may perhaps tend to give some- thing more of a local name and habitation in person’s minds, to the verbal de- scriptions of which there have been many good ones from various of the observers of 1851. I will only therefore add, that to understand the scene more fully, the reader must fancy himself on a small rocky island, on a mountainous coast, the weather calm, and the sky, at the beginning of the eclipse, 4, covered with thin and bright cirro-strati clouds. As the eclipse approaches, the clouds gradually darken, the rays of the sun are no longer able to penetrate through and through, and drench them in living light as before; but, as with clouds on an evening sky, they become TOTAL SOLAR ECLIPSE OF 1851. 507 darker than the background, on which they are projected. The air becomes sen- sibly colder, the clouds darker, and the whole atmosphere murkier. From moment to moment, as the totality approaches, the cold and the darkness advance apace; and there is something peculiarly awful and terribly convincing in the two different senses so entirely coinciding in their indications of an unprecedented fact being in course of accomplishment. Suddenly, and apparently without any warning, so immensely greater are its effects than those of anything else that had before occurred,—the totality supervenes, and darkness comes down. The shadow of the moon must evidently have a very well-defined termination ; and those who have seen a large eclipse, or even an annular one, have no idea what a total eclipse is like. Then suddenly came into view lurid lights and forms, as, on the extinction of the candles, a phantasmagoric picture, before unnoticed, may be made to appear prominently imposing in a darkened room. This was the most striking point of the whole phenomenon, and was precisely that which made the Norse peasants about us fly with precipitation, and hide themselves for their lives. Darkness was everywhere, in heaven and in earth, except where along the north-eastern horizon a narrow strip of unclouded sky pre- - sented a low burning tone of colour, and where some distant snow-covered mountains, beyond the range of the moon’s shadow, reflected the faint mono- chromatic light of the partially-eclipsed sun; and exhibited all the detail of their structure, the light and shade and markings on their precipitous sides, with an apparently supernatural distinctness. After a little time, the eyes seemed to get accustomed to the darkness, and the looming forms of objects close by could be discerned, all of them exhibiting a dull green hue; seeming to have exhaled their natural colours, and to have taken this particular one, merely by force of the red colour in the north. Life and animation seemed indeed to have now departed from everything around; and we could hardly but fear, against our reason, that if such a state of things were to last much longer, some dread- ful calamity must happen to us also. While the lurid horizon northward, ap- peared so like the gleams of departing light in some of the grandest of the works of Martin and Danpy, that one could not at the time, and in that presence, but believe, in spite of their alleged extravagances, that nature has opened up to the constant contemplation of their mind’s eyes, some of those magnificent revela- tions of power and glory, which others can only get a hasty glimpse of on occa- sions such as these. To this part of the scene the plate refers, and may, perhaps, be considered a successful work on the part of the engraver, Mr James F arp, in giving an idea in mere black and white, of the dark mysterious colouring of the scene. On other sides, rain clouds and falling rain, prevented any such striking effects as those just detailed, and within three minutes, the light of day was prevailing again. So much, then, for the general effects of this total eclipse, and may the next VOL. XX. PART III. 6x 508 PROFESSOR PIAZZI SMYTH ON THE one meet with a better artist, and may some more perfect plan, than mezzotint en- graving, be found for reproducing the drawings in all their colours, and cheap enough to admit of a whole series being published by any scientific society. The clouds already mentioned, prevented anything very interesting being done in the way of exact measurement, and what little was accomplished, having already appeared in the Memoirs of the Royal Astronomical Society of London, 1852, need not be repeated here. The most important subjects which presented themselves for observation to those under clear skies, were the corona, and the red pro- minences. Both may be spurious effects, and both may be real forms of matter in the neighbourhood of the sun, but of such faint illumination as only to be visible during the darkness of a total eclipse. Respecting the corona, Professor BADEN PowELt has produced such excellent imitations of it, by making dark bodies occult very bright points, and he has even shewn such a necessity for its existence to some extent, that what, with the exces- sive difference in the descriptions of different observers, and the absence of any crucial observations, we cannot consider that the corona has been proved to be anything real or material. On the other hand, we must not refuse the possibility of something of the sort, inasmuch as the best theory of the Zodiacal Light, re- presents it to be a nebulous mass, increasing in density towards the sun; but no part of the sky during the totality was dark enough to exhibit any such portion of the zodiacal light, as has ever been seen and recognised for it at night. The red prominences, however, are much more precise phenomena in them- selves, and have been better observed. Indeed, it may be considered, that they have been proved to lengthen on one side, and shorten on the other, during the eclipse, precisely in the drection in which they should do, on the supposition that they were true appendages of the sun, and that the moon was occulting them. This, however, is all, for other imaginable causes might produce such an appear- ance, and a difference of effect would only appear on comparing the accurately measured quantity and progress of the alteration of length, with the calculated motion of the moon. This, however, has not been done; and it is not a little surprising, that so many astronomers should have observed the phenomenon, and been contented with merely gazing. A few of them measured approximately the angular position of the prominences on the sun’s limb, but none measured the size and shape, and the rate of amount of increase or decrease. Indeed, the figures given by different observers, vary in the most incomprehensible way, and we can do no more than conclude, that something red was seen, and of a cosmical nature; but each person gives a different size and shape, and each person is quite certain that he is right. The observation doubtless may be, and indeed from this must be, very difficult ; and a person who has not seen these bodies, ought not perhaps to form any judg- ment. Butit must be apparent to every one, that almost every observer attempted TOTAL SOLAR ECLIPSE OF 1851. 509 to do too much, and with insufficient means. He tried to give an account of all the prominences all round the sun’s limb, as well as to observe the instants of beginning and ending of the totality, and judge of darkness over the landscape, &c., &c. ;—his main instrument being, too, a small telescope, with generally some inferior style of altitude azimuth mounting. Now, a little experience would shew, that a firm and clock-moved equatorial, with micrometer and lamp apparatus, is a sine gud non; and that with this appa- ratus an observer should confine himself to a single red prominence, and get a numerous series of measures of it throughout its period of visibility. On the records of such measures a safe theory might be erected. But, if we are never to see these red prominences, except during the very un frequent phenomenon of a total solar eclipse, ages may pass away before we know much, and if they be real, they must play some important part in the great mystery of the economy of the solar light and heat. Astronomers are bound, there- fore, to exert themselves to the utmost, in contriving methods which shall make these prominences visible at all times; and Mr James Nasmyru, C.H., having sug- gested to me a method by which he hoped the end in view might be effected, [lost . no time in putting it into execution. The method consisted in pointing a tele- scope to the sun from a dark room, and therein receiving the image of the field of view on the top of a box, painted black inside. A circular hole, a little larger than the sun’s image, being then made in the lid, the solar light passes through, is completely absorbed on the sides of the box, and the picture of the annular por- tion of the field, between its boundaries and the sun’s, 7.¢., the blue sky adjacent to the sun, can be examined at leisure, and in comparative darkness, so that a faint light projecting from the solar orb, anything in the shape of a ray or red promi- nence, would have much greater chance of being seen. Mr Nasmytu having no means at command to try his proposed experiment, I put it into execution myself in the Edinburgh Observatory. The shutters in the dome were furnished with screens and tubes, allowing no sunlight to enter the room, but what passed through the object-glass of the telescope; and this was 9 feet long, by 6 inches in diameter, was moved by clockwork, and carried near the eye- end, on an adjustable arm, a large light box lined with black velvet, and having a hole in the top. The image of the sky, in all but contact with the sun, was then received and examined on the surface of the lid round about the hole, into which the sun’s rays passed and were lost. So far as the apparatus was con- cerned, everything answered to admiration, for when the sun’s image was actually thrown into the dark box, the general illumination of the room was certainly much fainter than that of the air during the total eclipse. But notwithstanding this, and though I have tried it carefully on all the finest days of the autumn of 1851, and the summer of 1852, I have seen nothing of any prominent matter beyond the photosphere of the sun. The same negative 510 PROFESSOR PIAZZI SMYTH ON THE result was obtained when a circular plate was made to eclipse the sun’s image in the focus of the telescope, and I looked directly into the eyepiece. But hardly any other result could well be expected, as however dark the room might be kept by the apparatus employed, that in no wise checked the illumination of the atmosphere outside, in the apparent neighbourhood of the sun, the daylight, in fact; and this was always so bright, that no object of the reputed faintness of these red prominences could well appear on so luminous a background. There is only one way of getting over this difficulty; 7. ¢., taking the telescope to the top of a high mountain, above all grosser parts of the atmosphere. Other circumstances have lately compelled me to request leave from Government to take the Edinburgh Equatorial temporarily to the top of the Peak of Teneriffe; and if allowed to do so, it shall be one of my first cares to repeat this experiment. This mode undoubtedly would not be perfect, none would unless tried alto- gether above the limits of the atmosphere; but it would certainly be a great im- provement on anything done on the surface of the earth at the level of the sea, and might perhaps be found sufficient for the object in view. All travellers who have ascended high mountains, combine in speaking of the greater blackness of the sky witnessed in those elevated regions, as well as of the sun becoming more luminous and more concentrated as to his rays, and of stars becoming visible to the naked eye by day. Captain Hopes, at the height of 15,000 feet on the Himalayas, saw, with a two-inch object-glass, stars of the fifth magnitude in the open sunshine: but onthe Calton Hill, with the smoke of Edinburgh more or less diffused through the air, stars of the first magnitude are frequently in- visible, in our pale blue sky, to a six-inch object-glass; thus making a difference in favour of the mountain station, of at least 100 to 1. I have not myself had experience of such great heights, but have observed for months at the altitude of 6000 feet, and from the improvement in the transparency of the atmosphere up to that point, can well believe what has been related of the higher station. Thus far I have gone on the supposition that it was right and proper to attach great importance to the conclusions of the actual observers, that the red promi- nences were actual material bodies. This, however, has not been proved; and we cannot be too careful in guarding against the deceptive effects of objects close by. Now it is not difficult to suppose some partial diffractions of the sun’s light amongst the craggy mountains of the moon, during the total eclipse, which might make some rays diverge, and become visible in an anomalous manner. Accord- ingly, I introduced into the focus of the object-glass a small sphere, which was made to pass hefore and so eclipse the sun’s image, as in the natural pheno- . menon. The results were, that light of a pink colour was thrown off from the edge of the sphere, and in greater quantity as the polish of the surface was higher; in a complete ring if the surface was smooth, and in detached portions if the surface TOTAL SOLAR ECLIPSE OF 1851. 511 was crystallised. Balls of plaster of Paris, zinc, brass, transparent and opal glass, were tried: the best results were obtained with the last; when scratched with a diamond, there appeared only a little pink prominence here and there; often appearing exactly like those pictured by the eclipse observers. This pink light was, however, always thrown off from some object out of focus, though the visibly bounding line of the sphere might be in focus; and again, the light belonged to the ball as a centre, and not to the sun, seeming, therefore, to be a different phenomenon to the eclipse prominences; though the parallel direction of the rays grazing the moon’s edge, and the converging of those touching the ball’s, should be taken into consideration. A more similar experiment in this way, is to eclipse the sun behind a distant object; and for this purpose I placed a black tin screen on the top of Nelson’s Monument, and observed it from below with the naked eye and a small telescope. When the sun was completely eclipsed by the disc, there was much light of a spectrum character, with a preponderance to orange and red, thrown off beyond the edge, and this light was most abundant on that part of the circumference of the tin disc, to which, at the time, the sun was closest: thus bearing some sort . of relation to the observed fact of the lengthening of the red prominences on that side of the moon to which the sun was advancing. Anything transparent, as a bristle, on the edge of a disc, was particularly vivid, and some ropes in the neigh- bourhood were “glorified” over an extent of two degrees. This effect, too, was more marked the clearer and more transparent the atmosphere. With much haze in the air it vanished altogether; the disc and ropes then projecting themselves blackly on the bright sky behind. This would seem also to be in some measure in favour of the idea of a spurious origin at the moon’s edge for the eclipse pro- minences. The evidence, however, is so very uncertain, that few things would be more productive of advantage in the present state of the subject, than the repetition of all the experiments with a better instrument, either in the rarified atmosphere of the Peak of Teneriffe, as just mentioned, or that of some higher mountain: such observations, too, made at once, might tend to save and to utilise much valuable time on the occasion of the next total eclipse of the sun. VOL. XX. PART ITI. 6Y Mb bert ed a San a) Ae “ty pigiatios out rs baie (egho Sect ah i eos api: rete yey ‘nisoi sons ion: omni ag . é Misients &-ivbiod tre ssuttom sito haben eA ira ee Ea (oft 63 isle it1b! geist? abe idee nie st ie W's seoditiy wispy iN i= a daly 5994052 Uinipe Ree eee sha ‘Ak onl i FaeeGede hae Ss ‘ fee: a aitposduit ei rule viele al ve Neetiite® ee eT dD "ee al : hs i. Pago iho 4! U7 on Dov ophitiore?d sucabeinagny 4h ¥\ : i. fb sagen real + lo Dip ay Olina regitt “here Fai! with a, ty “Seow aioe ngrtttan } Byife 4aheol} api iri quilt site Ad ; ag Tash? tr ) ateNL in bebsiseld hers Herqhay ii a a6 wet Loerie : i Bled “tenet wt ARLEN Sane eae Aya als doth a nat vane “Hits 3603 Cy BS Ore ge dat tah by i+ eR ey balare ie WHT a fl a : 7 CAE iat sPidd eToeh Gy w Fire va’ bye" Be Melly se = on Mibsicien Pui at i ebrinant oi brian iont pan in tery ‘ ‘ } wv iva eo a igeaerlrdantn ap seth Op + rhs gla boda ¥ ameinsiaged * fi read ta phy ast me Bier eft faethe : aay Whebat , ; SHY “teh phe Ol) Mh Terie wring + to Wath ha re fii . mike wiasebeits Vio i op a a bait ae HOMETT ty ; ‘ bY PMT ey cP ea Wi eony ae ise) ny Sovran 4 ryad S usiw fede 8 4) “phd fee Wa s Tg son to, 4200) ‘eon aihianRi Raa Maneater ana 2" Le Re ae | : AY ei ag ATinsine! us PIT res sain pi! . shiairin hee a ar Peri mae ri ry habs D \ ‘ 1 Wii ue ~s va id 4 , { q ve rn ‘ 4 7 u 143 Shep i) UL: tae POTS AP utd FG ites 513 XXXV.—Observations on the Speculations of Dr Brown and other recent Meta- physicians, regarding the Exercise of the Senses. By Professor W. P. Axison. (Read 7th and 21st February 1853.) In offering to this Society a few remarks which have occurred to me on this fundamental department of Mental Physiology, I beg in the first place to explain, that my reason for doing so is merely this, that in consequence of certain un- guarded expressions, and, asI think, hasty reflections, the opinions of Dr Brown, and likewise of Sir JAMES MacxkintosH, and of Lord Jrrrrey, and other more recent writers on this subject, have been supposed to be irreconcileably at variance with those of Dr Rem and Mr Stewart; 2. ¢., with those which are usually called the leading doctrines, or essential characteristics, of the Scotch School of Meta- physics, in this fundamental department of the science. And when such difference of opinion is believed to exist among men of generally acknowledged talent, who have studied this subject, and nothing like an experimentum crucis can be pointed | out, to compel us to adopt one opinion and reject another,—the natural inference is, that there is something in the study itself, which renders it unfit for scientific inquiry,—that what is called the study of the Mental Faculties granted to our species is, in fact, only a record of the vacillations of human fancy and ingenuity, in the invention and demolition of hypotheses,—and that the subject is one on which it is in vain for our minds to dwell, with any hope of applying the principles of Inductive Science, and acquiring any insight into the laws of Nature, regulating the phenomena presented by the last and greatest of her works, similar to that which is the object and the reward of all other scientific inquiries. When, for example, we find it stated by Dr Brown, that on the first and most fundamental of all inquiries regarding the human mind,—that into the belief which attends the exercise of the Senses,—the creed of the sceptic, and of the orthodox philosopher of Dr Re1p’s School, consists, in fact, of the same two propositions,— ‘cand that what appeared to Dr Re1p and Mr Stewart to be the overthrow of a great system of scepticism on this subject, was nothing more than the proof that certain phrases are metaphorical, which were intended by their authors to be understood only as metaphors ;”—(Lectures, vol. i., p. 584); when we find this statement of ’ Dr Brown’s regarded by Sir James MackintosH as so just and important, that he says, “ the whole intellectual part of the philosophy of Brown is an open re- volt against the authority of Rein ;—Mr Srewarr had dissented from the language of Rerp, and departed from his opinions.on several secondary theories ; Dr Brown rejected them entirely,—very justly considering the claim of Rerp to the merit of detecting the universal delusion, which had betrayed philosophers into the belief that Ideas, which were the sole object of knowledge, had a separate existence, as VOL. XX. PART IV. 6 Z 514 PROFESSOR ALISON ON THE BELIEF a proof of his having mistaken their illustrative language for a metaphysical opinion ;”’—and when we remember the unparalleled popularity of Dr Brown’s Lectures since his death, which has no doubt led many to suppose that he is now regarded as the first authority on these subjects in Scotland;—when we find, again, Lord JEFFREY admitting that “ Dr Rerp’s subversion of the ideal system, or confutation of that hypothesis which represents the immediate objects of the mind in perception as certain images or pictures of external objects conveyed by the senses to the sensorium, had been performed with complete success;” but adding “ that after considering the subject with some attention, he has not been able to perceive how the destruction of the Ideal Theory can be held as a con- futation of those reasonings, which have brought into question the popular faith on this subject;” (Edinburgh Review, vol. iii, p. 281; or Contributions to Edinburgh Review, vol. ii., p. 604)—when, on the other hand, we find it stated by Sir Winit1am Hamiiton, that Dr Brown is, from first to last, in one and all of his strictures on ReEtp’s doctrine of Perception, wholly in error;” but, “‘ that nevertheless there are ambiguities and inconsistencies of Rem himself, in this the most important part of his philosophy, which ought to be exposed, and so deprived of their evil influence ;” (Works of Reid, p. 820)—“ and, in particular, that so far from confuting Idealism, the doctrine of Remp and Stewart affords it the best of,all possible foundations ;’ (Works of Reid, p. 820)—and, again, by MoreELt, that although Rem “ performed an inestimable service to philosophy, by shewing that certain simple processes must be viewed as ultimate and primi- tive facts in our constitution,—the benefit of which is still to be developed in coming generations,—yet that the false, or at least inadequate view which he has taken of the reflective method in mental philosophy, has caused a want of comprehen- siveness as to the legitimate objects or extent of philosophy at large ;” (Morell’s Philosophy, vol. ii., p. 61)—I think I have quoted enough to shew, that a general distrust of all speculations which led such men to such variety of opinion, and despondency as to the possibility of any fixed or useful principles being established, by scientific examination of the elementary mental processes to which they referred, is not unreasonable. And if, nevertheless, we hold, as I think we ought to do, by the maxim, ‘‘ that when Reason and Philosophy have erred, it is by themselves alone that their error can be corrected,’’—I trust it will not be deemed a useless or unprofitable discussion, to endeavour to shew that when the subject is calmly reviewed, and verbal ambiguities as far as possible avoided, there is.really no such difference of opinion among these authors, as will justify the strong expres- sions of dissent which I have quoted; but that the differences of opinion are either verbal only, or relate to matters ulterior to the main points of controversy, which have interested the human mind, in all ages, on this subject ; and, in parti- cular, ulterior to those on which it was the object of Rerp and Stewart to esta- blish fixed and satisfactory principles ; and that there are certain general truths ATTENDING THE EXERCISE OF THE SENSES. 515 in regard to the mental part of the process concerned in the exercise of the senses,—probably admitting of much more subtle analysis, and more learned discussion than I can presume to offer,—but already sufficiently certain and pre- cise, to constitute an important part of the science of Physiology ; and remarkably in accordance with all that has since been ascertained, as to the physical part of that process. As I was myself honoured in early life with the friendship both of Mr Srewarr and Dr Brown, and as I know well how much the former of these illustrious men was pained by finding that the latter, when succeeding him in the Chair of Moral Philosophy, had (as he afterwards expressed it) “given countenance to some doctrines, which, to more cautious and profound thinkers, appear to have a prac- tical tendency quite at variance with his known principles and opinions ;” (£/e- ments of the Philosophy of the Mind, p. 502)—although I believe that the natural partiality of Mr Srewarr to the studies to which he had devoted his life, had led him to exaggerate, in some degree, their practical importance,—still I feel much gratified at bemg able, as I think, in some measure to reconcile the appa- rently conflicting statements in their writings, and point out the misapprehensions —almost entirely on the part of Dr BRown—to which they may be traced. It will be generally admitted, that the first object of Rem and Stewart was to ascertain, by strict induction, the existence, and establish the authority, of certain Principles of Common Sense, as they were termed by Reip; Primary Ele- ments of Human Reason, or /undamental Laws of Human Belief, as they were termed by Stewart; Principles of Intuitive Belief, or Truths learned by Intuition, —perhaps the best name for them,—as they were since termed by Brown; which must be regarded as ultimate facts in the constitution of the human Mind, equally essential to all reasoning, to all scientific inquiry, to the acquisition of all practical knowledge, and to the daily business of life. Now the existence of such principles of Belief, and their authority, as ultimate facts in our mental constitution, are fully admitted by all the authors I have quoted; by no one are they more clearly and emphatically announced than by Dr Brown. “ Principles of intuitive belief,’ he says, “are essential to Philosophy in all its forms, as they are physically essential, indeed, to the very preservation of our animal existence.” ‘The belief of owr identity is not the result of any series of propositions ; but arises immediately, in certain circumstances, from a Principle of thought, as essential to the very nature of the Mind, as its powers of Perception or Memory, or as the power of Reasoning itself; on the essential validity of which, and consequently on the intuitive belief of some jirst truth on which it is founded, every objection to the force of these very truths themselves must ultimately rest. To object is to argue; and to argue is to assert the validity of aryument, and therefore of the primary evidence, from which the evidence of each succeeding proposition of the argument fiows. ‘To object to the authority of such primary 516 PROFESSOR ALISON ON THE BELIEF intuitive belief, would thus be to reason against reason,—to affirm and deny at the same moment,—and to own that the very arguments which we urge are un- worthy of being received and credited. “* Without some principles of immediate belief, then, it is manifest that we could have no belief whatever; for we believe one proposition because we discover its relation to some other proposition ; and we must ultimately come to some pri- mary proposition, which we admit from the evzdence contained in itself, or, to speak more accurately, which we believe from the mere impossibility of disbelieving a. All reasoning, then—the most sceptical, be it remarked, as well as the most dogmatical—must proceed on some principles which are taken for granted, not be- cause we infer them by logical deduction, but because the admission of these first principles is a necessary part of our intellectual constitution. *“* Every action of our lives is an exemplification of some one or other of these truths, as practically felt by us. Why do we believe that what we remember truly took place, and that the course of Nature will be in future such as we have already observed it? Without the belief of these physical truths, we could not exist a day, and yet there is no reasoning from which they can be inferred. “These prenciples of intuitive belief, so necessary for our very existence, and too important, therefore, to be left to the casual discovery of Reason, are, as it were, an eternal, never-ceasing voice from the Creator and Preserver of our being. The reasonings of men, admitted by some and denied by others, have over us but a feeble power, which resembles the general frailty of man himself. These internal revelations from on high are omnipotent, like their Author. It is impossible for us to doubt them, because to disbelieve them would be to deny what our very constitution was formed to admit.”—(Brown, p. 286.) The principle thus stated by Dr Brown, and some of the illustrations of it which he has given, seem to me to be worthy of all acceptation; but I beg to ask, how do they differ from the fundamental proposition of Dr Rrrp’s Philosophy of Com- mon Sense; long previously set forth, for example, in the following passage? If there is no essential difference, then I think it clear that Dr Brown ought to have distinctly intimated his acquiescence in this, which Dr Rem regarded as the cardinal point of his doctrine; and so far, by limiting and defining the province of reasoning, and that of simple observation in such inquiries, endeavoured to prevent useless labour, and irksome uncertainty, in future students of the same science. « All reasoning must be from First Principles; and for first principles no other reason can be given but this, that, by the constitution of our Nature, we are under a necessity of assenting to them. Such principles are parts of our constitution, no less than the power of thinking; Reason can neither make nor destroy them, nor can it do anything without them. «How, or when, I got such first principles, upon which I build all my rea- ATTENDING THE EXERCISE OF THE SENSES. 517 soning, I know not, for I had them before I can remember; but I am sure they are parts of my constitution, and that I cannot throw them off. That our thoughts and sensations must have a subject, which we call owrse/7f, is not an opinion got by reasoning, but a natural principle. That our sensations of touch indicate something external, extended, figured, hard or soft, is not a deduction of reason, but a natural principle. The belief of it, and the very conception of it, are equally parts of our constitution. If we are deceived in it, we are deceived by Him that made us, and there is no remedy.”—( Works of Retp, by Sir W. Hamitton, p. 130.) “IT beg,” he says farther, “to have the honour of making an addition to the sceptical system, without which I conceive it cannot hang together. I affirm that the belief of the existence of Impressions and Ideas, is as little supported by reason, as that of the existence of Minds and Bodies. No man ever did, or ever could, offer any reason for this belief. A thorough and consistent sceptic will never therefore yield this point; and while he holds it, you can never oblige him to yield anything else. “ To such a sceptic I have nothing to say; but of the semi-sceptics, I should beg to know, why they believe the existence of their own impressions and ideas ? The true reason I take to be, because they cannot help it; and the same reason will lead them to believe many other things.”—(Do., p. 130.) In quoting this last passage from Dr Rem, I think it right to say, that notwith- standing his distinct assertion here made, and supported by Mr Stewart, that the evidence of Consciousness (by which we are informed of the acts of our own minds) stands on exactly the same footing as that of Sense, and is equally open to the objections of the sceptic, it seems to me that the objection to that state- ment, made by several more recent authors, is well founded; because what we mean by objects of consciousness are certain changes or events which we feel within ourselves, and we cannot, without absurdity, assert, both that such a change exists, 2. ¢., that we feel it, and that we doubt its existence, which implies that it may not exist. To doubt the evidence of consciousness, therefore, is not merely to do violence to our understandings, but is to assert a contradiction in terms. This is thus stated by Lord JErrrey: “ Whatever we doubt, and whatever we prove, we must plainly begin with Consciousness. That only is certain—all the rest is inference. Our perceptions—not the existence of their objects—are what we cannot help believing.” —(Aeviem, vol. ili., p. 283.) And the same ground is © taken by Sir Wau. Hammtron thus: “ There is no scepticism possible touching the facts of consciousness in themselves. We cannot doubt that the phenomena of consciousness are real, in so far as we are conscious of them, because such doubt, being an act of consciousness, would contradict, and consequently annihilate itself: but all beyond the mere phenomena of which we are conscious, we may, without fear of self-contradiction at least, doubt.”—( Works of Rep, &c., p. 129.) VOL. XX. PART IV. 7A 518 PROFESSOR ALISON ON THE BELIEF But granting that this criticism is correct, the only alteration we need make on the passage last quoted from Ret is this, that, instead of asking the “ semi- sceptics why they believe in the existence of their impressions and ideas,” we should ask them, why they believe that the impressions and ideas of which they are conscious, are their own, or belong to the same persons as other mental changes which they remember. Here we become involved with the evidence of Memory and of Personal Identity, as to both of which Dr Brown expressly ad- mits, in passages already quoted, that they are to be ranked among the principles of Intuitive Belief; and with that slight correction, this passage from Dr Rem— closely approximating, as it obviously does, to that previously quoted from Dr Brown,—must have commanded his entire acquiescence. The reality and importance of these principles, regarded as ultimate facts in our mental constitution, is still more satisfactorily attested by Sir Wu. HamitTon, who has marshalled an array of authorities, such as any other man in this country might have in vain attempted, amounting to more than a hundred ancient and modern writers, all of whom, under certain varieties of expression, have announced and illustrated the same general proposition. Farther, not only have we this nearly uniform agreement of these philoso- phers in regard to the general statement of Rem, that “there are various acts of our minds, of which, when we analyse them as far as we are able, we find Belief to be an essential ingredient ;” but we have a special agreement, of all those whose opinion is thought of much weight, as to the fact of the exercise of the Senses being one of the occasions, in which evidence of this description, whether directly or indirectly, is at least uniformly and essentially concerned. The shortest and simplest account of Dr Ret’s doctrine on this subject is given by him in the following words: “The external senses have a double pro- vince, to make us feel, and to make us perceive. They furnish us with a variety of sensations, pleasant, painful, or indifferent; at the same time, they give us a conception, and an invincible belief of the existence of external objects. This con- ception of external objects is the work of Nature; the belief of their existence is the work of Nature; so also is the sensation that accompanies it. The conception and belief, which Nature produces by means of the senses, we call Perception.” He thus introduces the Intuitive Belief, simply as a part or accompaniment of the operation of the mind which results, in the healthy state, from an impression made on the senses, and a Sensation excited in the mind; and afterwards he enters on explanations in regard to the different qualities attributed to the material objects thus made known to us,—particularly as to the distinction of the Primary and Secondary qualities of matter, and the formation of the general notion or con- ception of Extension or Space; which, as he says, is no sooner formed, than it swells in the human mind to Infinity, as surely as the notion of Time to Eternity; and — ' affords, therefore, the simplest illustration of the essential distinction between ATTENDING THE EXERCISE OF THE SENSES. 519 Sensations felt in the mind, and Perceptions formed in the mind, in consequence of those sensations. But although he stated that he could trace the formation of our notions in regard to the external world no farther than the mental operations thus described, he distinctly admitted, as a general principle, the possibility, and approved the attempt, of farther analysis, if made under due precautions. “It must,’ he says, “ require great caution, and great application of mind, for a man that has grown up in all the prejudices of education, fashion, and philosophy, to unravel his no- tions and opinions, till he find out the simple and original principles of his constitution, of which no account can be given but the will of our Maker. «This may be truly called an analysis of the human faculties; and till this is performed, it is in vain we expect any just system of the mind,—that is, an enu- meration of the original powers and laws of our constitution, and an explication from them of the various phenomena of human nature. Success, in an inquiry of this kind, it is not in human power to command; but perhaps it is possible, by caution and humility, to avoid error and delusion. The labyrinth may be too intricate, and the thread too fine, to be traced through all its windings; but if we stop where we can trace it no farther, and secure the ground we have gained, | there is no harm done ; a quicker eye may in time trace vt farther.” —( Re, p. 99.) It is plain, therefore, that it was quite in accordance with Dr Reip’s views,— both with the principles which he thought he had established, and with his anti- cipations of the future progress of the science,—to attempt a farther and more minute analysis of the acts of Mind, attending the exercise of the Senses, by which we are assured of the existence, and informed of the properties of external things; and to endeavour to refer these, by a process of induction, to other and more general Laws of Mind. This, accordingly, has been attempted by several later writers. Mr Stewart maintained, and fortified himself by the opinion of Tureor, that in order to the formation of the notion of Externality, or independent exist- ence, in any object of perception, a repetition of the same sensations, under the same conditions, is necessary, and that then the formation of that notion,—the conclusion thus drawn as to the existence of a cause for our sensations, inde- pendent of ourselves, might be referred to the general Law of Mind,—analogous to the first Law of Motion, or the Inertia of Matter,—our belief “that the course of Nature is uniform, or will be in future such as we have already observed it.” Dr Brown went a step farther. He explicitly admitted the accuracy of the distinction drawn by Dr Rerp between Sensations and Perceptions, and the con- venience of the term Perception, as denoting an act of the mind, distinguishable from all others, but, as he thought, resolvable into others. “Iam far from wish- ing,” he says, “to erase the term Perception from our metaphysical vocabulary. On the contrary, I conceive it to be a very convenient one, if the meaning attached to it be sufficiently explained, by an analysis of the complex state of mind which 520 PROFESSOR ALISON ON THE BELIEF it denotes.” —(Lectures, vol. ii., p. 47.) And he made a very ingenious attempt (such as Dr Rem, from his expressions above quoted, I think, must have approved) to explain how the notion of the primary qualities of matter may be gradually formed, by the help of experience, in the mind. “Perception,” he says, ‘‘is only another name for certain associations and inferences which flow from other more general principles of the mind.”—(Vol. i., p 569.) He then goes on to explain how, by means of certain sensations, and particularly of those muscular sensations, consequent on the excitement of in- stinctive and voluntary muscular actions, which he has so ingeniously illus- trated, the notion of the qualities of matter may be gradually introduced into the human mind. He distinguishes the Primary Qualities of Matter, I think, more satisfactorily than Retr, or perhaps any other author has done, as the different modifications of Extension and Resistance ; “ the very notion of which combined,” he says, “ seems necessarily to indicate a material cause, or rather, is truly that which constitutes our very notion of Matter.”—(Vol. i., p. 574.) I am much inclined to think, although I would not state it as certain, that his very ingenious analysis of the mental acts suggesting this notion, as 2t is often sug- gested,—4. é., regarding it as the natural result of muscular sensations, repeatedly excited, and again obstructed, in different degrees, at different points, and for different periods of time,—is correct; if so, it affords as good an example as can be given, of what his friend Mr CampseEL. called “the mysterious, and almost miraculous subtilty of his mind.’ But I maintain with confidence, that it does not in the slightest degree invalidate the statement of Reip, as to the Belief which accom- panies this act of the mind being a case of that Intuitive Perception of Truth, which we have seen that Brown, equally as Ret, admitted as the foundation of all knowledge and all reasoning; and that for two reasons :— First, Dr Brown expressly admits, that the perception of the primary qua- lities of matter may take place without any such process of repeated muscular con- traction and reasoning thereupon ; and that it does so in the lower animals, in whom the very first complex act of perception may often be observed to be 7- stantaneous, and yet perfect, and its suggestions correct. ‘“ The calf and the lamb,” he says, ‘newly dropt into the world, seem to measure forms and distances with their eyes almost as distinctly as the human reason measures them after all the acquisitions of his long and helpless infancy.”—(Vol. ii., p. 70.) The well-known observation of the chicken and the spider shews that, in other classes of the lower animals, this primitive instinct, or suggestion, as he calls it, is still more obvious. It is therefore, as he states it, only a question of observa- tion and experiment, whether or not, in man as in other animals, Nature does communicate information by intuitive suggestion consequent on sensation,—which is neither contained in, nor logically deducible from, the sensation, but is, never- theless, correct. ATTENDING THE EXERCISE OF THE SENSES. 521 But secondly, the analysis which he offers of this act of mind, as usually per- formed by man, only professes to resolve the act, which Rerrp called Perception, and regarded as an ultimate fact, into other principles or laws of thought, which Dr Brown himself regards as ultimate facts; particularly into the principle that “ we must suppose a cause for all our feelings” (vol. i., p. 565) ; the “ enturtive belief” that what has been as an antecedent, will be followed by what has been as a consequent” (do., p. 514); the notion of Zime; the belief in the Suggestions of Memory (do., p- 553); and the principle of Association or Suggestion (do., p. 565). “I do not conceive,” says he, “that it is by any peculiar Intuition we are led to believe in the existence of things without. I consider this belief as the effect of that more general Intuition by which we consider a new consequent, in any series of ac- customed events, as a sign of a new antecedent, and of that equally general prin- ciple of association, by which feelings that have frequently co-existed flow together, and constitute afterwards one complex whole.”—(Vol. i., p. 518.) The fact that notions are formed in the Mind of the properties of Matter, per- fectly distinct from the sensations which excited them, and to be explained only by reference (sooner or later) to what we call Jntuztion, remains, therefore, as Rei stated it; and is indeed strongly illustrated and confirmed by the elaborate . analysis of the mode of their formation, attempted by Dr Brown. On the other hand, a fundamental part of the doctrine of Kant, as I under- stand it, and to which Sir Witt1am Hamitton is disposed to assent, is, that the notion of Extension or Space, which Mr Stewart thought it important to distin- guish from the other primary qualities, as what he called one of the Mathemati- cal affections of Matter, ought to be regarded as a necessary condition, or native element or form of thought; and that a belief in the existence of “an extended world, external to the mind and even to the organism, is not a faith blindly created, or instinctively determined, on occasion of a sensation; but exists in, or as a constituent of, Perception proper, as an act of Intuition or immediate know- ledge.” —( Collected Works of Ret, p. 883.) Whether this is really an improvement on the doctrine which he states, in connection with it, as that of Dr Rep | viz., “that on occasion of a Sensation, along with a notion or conception, constituting the Perception proper, there is blindly created in us, or instinctively determined, an invincible belief in its exist- ence” |, or whether this distinction is really verbal, I do not presume to decide; but I think it must be admitted, that this opinion is truly an addition to the statement of Rem, and does not stand opposed to it; inasmuch as Rerp says only, * that the conception and belief are the work of Nature;” and this, of course, does not exclude the evidence that may be adduced in favour of any particular mode, in which we may suppose that Nature accomplishes the work; as, indeed, we have already seen that both Stewart and Brown supposed it to be performed VOL. XX. PART IV. : (ee 522 - PROFESSOR ALISON ON THE BELIEF by help of the general law of belief in the continuance of the order of Nature, which it had not occurred to Rep to connect with it. But if there be, as I maintain, this perfect accordance between the principles of Dr Rep and the elaborate attempt of Dr Brown, as of other later authors, to analyse those operations of mind to which the term Perception has been restricted by both, we may be pretty wellassured that any difference of opinion among those authors, on this subject, can be of no great scientific importance; and may very probably resolve itself into one of those partial controversies, involving more or less of per- sonal jealousy, which, we must admit, have disfigured and retarded most sciences, We may next ask, then, how it should happen that Dr Brown should have thought himself justified in dwelling at great length on what he called an eztra- ordinary mistake made both by Rep and his followers, as to the evidence of Sense, and the scepticism of BERKELEY and Hume regarding it?—how he should have been led to infer, and been at such pains to prove, that there is no real dif- ference between the creed of the sceptic and that of the orthodox philosopher of Dr Rem’s school as to the evidence of sense; and how Sir James MackinTosH should have been led to assert the whole intellectual part of the philosophy of Brown to be, by reason of their difference on this very subject, an open revolt against the authority of Rei? The reason of this is, that both these authors, and other recent writers, as it appears to me, certainly misconceived and misrepresented the controversy as it was carried on during last century, in several particulars. I do not say that there may not have been partial mistakes on the part of Dr Rem, particu- larly as to the exact meaning of previous authors,—and certainly there is in his writings a diffuseness of style, and frequent repetition of statements which might have been more impressive if more condensed ;—but the chief misapprehensions affecting the principles which I have stated, were clearly on the side of Brown. I. It wasa palpable misconception on the part both of Dr Brown and Lord JErF- FREY, to attribute to Dr Rei the attempt to prove, by reasoning, the existence of the material world, in opposition to the scepticism of previous authors. Thus Dr Brown speaks of Retn’s “ supposed proof of the existence of a material world,” aS quite inadmissible (vol. ii., pp. 50, 51); and Lord Jerrrey speaks of his destruction of the Ideal Theory as “having been held as a demonstration of the real existence of matter.” —( Edinburgh Review, vol. iii., p. 281.) Whereas they ought to have observed that Rep had, in a few simple but weighty words, disclaimed, as expressly as it is possible to conceive, any intention of attempting, or belief in the possibility of obtaining, such proof. He says, “ Many eminent philosophers have laboured to furnish us with reasons for believing our senses ; but their reasons are very insufficient, and will not bear examination.”—(Collected Works, p. 328.) “ Man’s knowledge of what really exists, or ever did exist, comes by a@ channel — ATTENDING THE EXERCISE OF THE SENSES. 523 which is open to those who cannot reason. He is led to tt in the dark, and knows not how he comes by it.” ‘* The pride of philosophy has led some to invent vain theories to account for this knowledge; and others, who see this to be impracti- cable, to spurn at a knowledge which they cannot account for, and vainly endeavour to throw it off. But the wise and humble will take it as the gift of Heaven, and endeavour to make the best use of it.”—(Jdzd, p. 330.) Consistently with this statement, it is plain that Dr Retw’s object (as ex- pressly avowed by Mr Stewart, Phil. Essays, p. 551, published in 1810, prior to Dr Brown’s first course of Lectures on this subject), in this department of the science, could not be to prove by argument the existence of the material world, but only to refute the argument against it; and to put our belief in it on the foot- ing of one of those Intuitive principles, the existence of which we have seen that Dr Brown fully admitted and illustrated, as being essential to all knowledge and all reasoning, and tacitly admitted in all inquiries and all arguments; therefore, to put scepticism on this subject on the same footing as that of the “thorough and consistent sceptic, who will not believe in the suggestions of his own me- mory, or the identity of his own person,” to whom Dr Rep had explicitly avowed, that ‘‘ he had nothing to say ;” and whose scepticism, as we have seen, Dr Brown regarded in precisely the same light. IL. lt was quite a misconception to suppose that the creed of the sceptics of those days was merely, as Dr Brown states it, the negative proposition that the independent existence of the material world cannot be proved by reasoning,—or, as he expresses it, ‘“‘ that no argument can be offered to shew, by mere reasoning, the existence of external causes for our feelings.” —(Sketch of a System, &c., p. 143.) If this had been their principle, the words above quoted prove, that it must have commanded the entire acquiescence of Dr Rem. But their creed,—so plausibly supported, and so ingeniously deduced from the language of the most esteemed metaphysicians then generally known, as to havea practical bearing which we can hardly realise in this generation,—was the positive proposition, that Reasoning compels or necessitates our dishelieving that independent existence, as involving an absurdity. ‘ The opinion of the ablest judges, says Dr Rep (in his first work, published in 1764), when speaking of the reasoning of BrrKELrEy as to “ the evidence of the senses, seems to be, that these arguments neither have been nor can be confuted, atid that he has proved by unanswerable arguments, what no man in his senses can believe.” —(Collected Works, p. 101.) The object of Hume, says Mr Stewart, obviously was, “to inculcate a uni- versal scepticism ; not, as some have supposed, to exalt reasoning, in preference to our instinctive principles cf belief, but, by illustrating the contradictory conclu- sions to which our different faculties lead, to involve the whole subject in the 524 PROFESSOR ALISON ON THE BELIEF same suspicious darkness ;—not to interrogate Nature, with a view to the dis- covery of truth, but, by a cross-examination of Nature, to involve her in such con- tradictions as might set aside the whole of her evidence, as good for nothing.” (Phil. Essays, p. 56.) The argument of BERKELEY and Hume, although expressed in various terms, seems in substance to have been always this,—That we are made acquainted with any existence external to ourselves only by means of our own Sensations, 1. @., of certain acts or states of our own minds; or, as they usually expressed it, by zdeas in our own minds ; that any such external objects as exist must be the exact images or prototypes of these ideas or mental states, and that it is absurd to assert that an act or state of mind, whether called sensation or idea, can be the exact image or resemblance of any thing but another act of the same, or some other mind. The following passage from Mr Hume is given by Dr Ret, as the shortest and clearest exposition of the argument which he had anywhere found :— “« The universal and primary opinion of all men, that we perceive external objects, is soon destroyed by the slightest Philosophy, which teaches us, that nothing can be present to the mind but an image or Perception ;” (the distinction of which term from Sensation, was not recognised by Hume), “ no man who re- flects, ever doubted that the existences which we consider when we say this house, and that tree, are nothing but perceptions in the mind, and fleeting copies and re- presentations of other existences which remain uniform and independent. So far, then, we are necessitated by reasoning to depart from the primary instincts of nature, and to embrace a new system with regard to the evidence of our senses.” To the same purpose we have the explicit declaration of BERKELEY, “ that the existence of bodies, out of a mind perceiving them, is not only impossible, but a contradiction of terms.” _ This is not, as Dr Brown stated it, “ amere negative assertion, that the existence of external things cannot be proved by argument” (vol. i1., p. 55), but as Dr Rerp had said, a distinct positive assertion, that argument or reasoning does compel, or necessitate, our departing from the belief in that existence, as involving an absurdity or contradiction. It was these positive but puzzling, and even humiliating assertions, and these only, that Dr Rerp undertook to confute. Ill. It was quite a misconception to assert, as Dr Brown repeatedly and con- fidently did, that the term Ideas, in the language of Hume, or of any philosopher after Lockr, was to be understood on/y metaphorically or figuratively, as an ex- pression for acts or states of mind, and did not imply belief in the existence of anything intermediate between the mind and the external objects of sense. He shewed, indeed, that the term had been used occaszonally in that metapho- rical sense by various authors; which Dr Rem knew, and regarded as a proof of its ATTENDING THE EXERCISE OF THE SENSES. 525 being ambiguous, and therefore inconvenient. But we have already seen, that Mr lume expressly asserted that the existences which we consider when we speak of objects of sense, are ‘‘ fleeting copies and representations of other existences which remain uniform and independent ;” and his notion as to the nature of these fleet- ing copies is farther shewn in another passage, as follows,—‘‘ No external object can make itself known to the mind without the intervention of an image, and of these images the most obvious of the qualities is evtension.”—( Treatise on Human Nature, vol. ii., p. 416.) Has not Mr Locks expressly told us, says Mr Stewart, “ that the ideas of primary qualities of matter are resemblances of them ; and that their patterns do really exist in the bodies themselves ;’ and did not Mr Hume under- stand this doctrine in the most strict and literal meaning of words when he stated, ‘“‘ as one of its necessary consequences, that the mind either is no sub- stance, or is an extended and divisible substance, because the idea of eatension can- not be in a substance which is indwisible and uneatended ?”—(Phil. Essays, p. 553.) This is surely enough to shew that what Lockr and Hume called Ideas, had, according to them, a physical (not merely metaphorical) existence, and were essentially distinct from the mere acts or states of the mind itself. And as to | BERKELEY, we have the distinct admission of Dr Brown himself, that he evidently considered ideas ‘‘not as states of the individual mind, but as separate things ex- isting in it, and capable of existing in other minds, but in them alone.”—(Lect. vol. 1., p. 523.) On which he very justly afterwards observes, that “‘ a mind con- taining, or capable of containing, something foreign within itself, and not only one foreign substance, but a multitude of foreign substances at the same minute, is no longer that simple indivisible existence which we term spirit.”——(Lect., vol. 1., p. 525.) But these statements are obviously and irreconcileably inconsistent with. Dr Brown’s subsequent assertion, that the word Idea was used by all previous authors only metaphorically, and that in proving ideas not to be self-existent things, Rem had merely assumed as real what was intended as metaphorical. It is still more remarkable, that the notion which was taken up by Dr Brown, of the laneuage of Hume and Berxetry having been only metaphorical or figura- tive, is the very same as had been previously hazarded by Priestiey, and pre- viously answered, and shewn to be inconsistent, both with the language of these and other philosophers, and with his own language, by Mr Stewart in his Philo- sophical Hssays. “ The following strictures,” says Mr Stewart, “on Rerp’s reasonings against the Ideal Theory, occur in a work published by Dr Priestiey in 1774 :— -“ Before our author had rested so much upon this argument, it behoved him, I think, to have examined the strength of it a little more carefully than he seems to have done; for he appears to me to have suffered himself to be misled in the very foundation of it, merely by philosophers happening to call Ideas the cages of external things; as if this was not known to be a figurative expression, denoting, VOL. XX. PART IV. 7c 526 PROFESSOR ALISON ON THE BELIEF not that the actual shapes of things are delineated in the brain, or upon the mind, but only that impressions of some kind or other are conveyed to the mind by means of the organs of sense, and their corresponding nerves, and that between those impressions and the sensations existing in the mind, there is a real and necessary, though at present an unknown connecticn.” On this passage, Mr Stewart observes, “ To those who have perused the metaphysical writings of BerKELEy and of Hume, the foregoing passage cannot fail to appear much too ludicrous to deserve a serious answer. Where did he learn that the philosophers who have happened to call ideas the images of external things, employed this term as a figurative expression ?” He then contrasts it with some of the expressions of Locke and of Hump, which I have already quoted, and afterwards proceeds to shew, that it is utterly inconsistent with the following passage in a subsequent work of Dr PrigestLEy himself,—‘“ Whatever ideas are in themselves, they are evidently produced by external objects, and must therefore correspond to them ; and since many of the objects or archetypes of ideas are divisible, it necessarily follows, that the ideas themselves are divisible also. The idea of a man, for instance, could in no sense correspond to a man, which is the archetype of it, and therefore could not be the idea of a man, if it did not consist of the ideas of his head, arms, trunk, legs, &c. Jt therefore consists of parts, and is consequently divisible. And how is it possible that a thing (be the nature of it what it may) that is divisible, should be contained in a sub- stance, be the nature of it likewise what it may, that is indivisible.” Ifthe ‘* archetype of ideas have extension, the ideas expressive of them must have ex- tension likewise; and therefore the mind in which they exist, whether it be material or immaterial, must have extension also.” “No form of words,’’ says Mr Stewart, “ could have conveyed a more un- qualified sanction than he has here given to the old hypothesis concerning Ideas, —a hypothesis which he had before asserted to have been never considered by any philosopher but as a figurative mode of expression; and which, when viewed in the light of a theory, he had represented as an absurdity too palpable to deserve a serious refutation.” —(Phil. Essays, p. 554.) Mr Srewart afterwards refers, in the same work, to the passages which I shall presently quote from Dr Ret, as containing the true statement of his reply to the sceptical argument of BrerKELEY and Hume; founded, as he believed it to be, on the language of Locks, and of what have since been termed the Sensa- tional School of Metaphysicians; and farther refers to several prior authors, par- ticularly Baxter in this country, and D’ALEMBERT in France, as having stated and pointed out the importance of the same principle that Rep did, but without illustrating it sufficiently —(See Phil. Essays, Notes and Ilustrations, p. 55.) I cannot conceive that Dr Brown should have made the statements which I have quoted, and which Sir James Macxintosu and others have approved, as to ATTENDING THE EXERCISE OF THE SENSES. 527 the language of Hume and others having been merely metaphorical,—and should have pronounced, on that ground, the claim of Dr Rew to a refutation of their scepticism to have been inadmissible, without making the least reference to Mr Srewart’s answer to the very same objection when made by PrigstLey, and with- out mentioning the passages in Rem and other authors to which Mr Stewart had referred, as the true exposition of this argument,—ifhe had read or reflected on those passages in Mr Srewarvt’s writings; and yet they were published in his Philosophi- cal Essays in the summer of 1810, 2. ¢., some months before the first course of lec- tures which Dr Brown delivered as Professor of Moral Philosophy in Edinburgh. But those who are aware of the peculiar sensitiveness of Dr Brown’s physical con- stitution, of the painful effort which he made to prepare his lectures for that first course, and of his unwillingness at any subsequent time to revert to that part of his subject, on which indeed his lectures subsequently underwent only verbal alterations, will feel no difficulty in understanding, that one of Mr Stewart’s essays (the second in the volume of Philosophical Essays published in 1810), and the notes to it, may either not have been read, or read so hastily as to have been speedily forgotten by Dr Brown, and never recurred to his mind when he was _- either revising his lectures, or preparing the short abstract of this portion of them which was published only a few months before his death. It is only doing justice to the candour and discernment of the late Dr WELsH to observe, that in stating, in his life of Dr Brown, the argument drawn from what he considered to be only the metaphorical use of the term Idea, in opposition to Dr Reip’s argument, he took notice of what he termed “the defence of RxEtn’s views, contained, as if by anticipation, in Mr Srewarv’s Philosophical Essays,”— a. é., contained in a work published before Dr Brown’s lectures containing that argument were delivered, if not before they were written. It was perhaps un- fortunate that Dr Weusu merely referred to Mr Srewart’s argument, and to some of the extracts from former authors by which it was supported, without quoting them, or expressing any opinion of his own on the subject. (See Life of Dr Browy, p. 259.) And it is still more unfortunate that Mr Stewarr him- self, in the essay in question, and the notes to it, although he refers to the pas- sages in Reip’s writings, which I shall presently quote, as containing the true statement of his argument, did not quote any of his words. IV. But farther, keeping always in mind that Dr Rerp’s avowed object was, not to prove by reasoning the existence of the material world (which he expressly avowed to be impossible), but only to confute the argument which represented that belief as an absurdity, I would observe that it was quite a misconception to suppose, as both Dr Brown and Lord Jerrrey did, that “the destruction of the Ideal Theory” was what constituted “the confutation of the reasoning of BerkeLey and Hume.” Dr Rew was perfectly aware that the word Idea, in that 528 PROFESSOR ALISON ON THE BELIEF argument, might be used only metaphorically, as asserted by Dr Brown; and his answer to the argument is expressly so stated as to be equally applicable, whether the word is used in the literal or the metaphorical sense. His main argu- ment is directed, not necessarily against the supposition of intermediate exist- ences, called Ideas, but against the supposition that the material world, if it exists, must be the express image or representation of the mental acts by which we are made acquainted with it. It will be observed, that there is no absurdity in saying that a Sensation, or any other mental act, uniformly attends the impression on any of our organs, made by any particular external object or quality, that it indicates to us its ex- istence, and suggests to us, or enables us to form, a notion of its nature. The absurdity lies only in supposing, that any mental act can be the exact image or representation of anything but another mental act, in the same or another mind ; and Dr Rei was at pains to point out that his reply to this is independent of any particular meaning, and even of the use, of the word Idea. He says,—* To prevent mistakes, the reader must be reminded, that if by Ideas are meant only the acts or operations of our minds in perceiving, remem- bering, or imagining objects, ! am far from calling in question the existence of those acts ; we are conscious of them every hour of life, and I believe no man of a sound mind ever doubted of their existence.”— (Intellectual Powers, p. 197.) This shews that he was aware that the term Ideas might be used metaphori- cally, “ or as illustrative language” for acts or states of mind. Then he says, in stating his argument against Bishop BerKeLEy,—* That we have many Sensations by means of our external senses, there can be no doubt. and ifhe is pleased to call these Ideas, there ought to be no dispute about the meaning of a word.” ‘But,’ says Bishop BerKELey, “by our senses we have knowledge only of our Sensations or Ideas, call them which you will; and these, which are attributes of Mind, can have no resemblance to any qualities of a thing which is inanimate. J allow him to call them which he will, but I would have the word only in this sentence to be well weighed, because a great deal depends upon it. For if it be true that by our senses we have the knowledge of our sensations only, then his system must be admitted, and the existence of a material world must be given up as a dream.”—(Collected Works, p. 290.) Then he goes on to give the proof, that the mental act in question, however rapid, is more complex than it had been represented,—that our minds are so constituted as to form uniformly certain definite notions on occasion of certain sensa- ' tions being excited in us,—to draw certain inferences, or pass certain judgments, as to the existence and certain qualities of things external to ourselves,—that it is to these perceptions that the intuitive belief of independent existence is attached, —and that these we at once perceive, when our attention is fixed on them, to be es- sentially distinct from the sensations, and to resemble them im no particular. This per- ATTENDING THE EXERCISE OF THE SENSES. 529 ceived or felt dissimilarity of the Notions or Conceptions, as to external existences, whick are formed in the mind, from the Sensations which suggest or introduce them into the mind, is what both Remp and Stewart relied on, as the answer to the sceptical argument of Hume and BERKELEy ; and is not once noticed either by Dr Brown or Lord JErrrey. This argument is given at more length by Reip as follows :—“ It is true we have feelings of touch, which every moment present the notion of Extension or Space to the mind: but how they come to do so is the question; for those feel- ings do no more resemble extension, than they resemble justice or courage ; nor can the existence of extended things be inferred from those feelings, by any rules of reasoning ; so that the feelings we have by touch can neither explain how we get the notion, nor how we come by the belief, of extended things. “ What hath imposed upon philosophers in this matter is, that the feelings of touch, which suggest primary qualities, have no names, nor are they ever reflected upon. They pass through the mind instantaneously, and serve only to introduce the notion and belief of external things which, by our constitution are connected with them. They are natural signs, and the mind immediately passes to the thing signified, without making the least reflection upon the sign, or observing. that there was any such thing.” “Let a man press his hand against the table, he feels it hard. But what is the meaning of this? The meaning undoubtedly is, that he hath a certain feeling of touch, from which he concludes, without any reasoning, or comparing ideas, that there is something external really existing, whose parts stick so firmly together, that they cannot be displaced without considerable force. ** There is here a feeling, and a conclusion drawn from it, or some way suggested by it. The hardness of the table is the conclusion, the feeling is the medium by which we are led to that conclusion. Let a man attend distinctly to this medium and to this conclusion, and he will perceive them to be as unlike as any two things in nature. The one is a sensation of the mind, which can have no existence but in a sentient being, nor can it exist one moment longer than it is felt ; the other is in the table, and we conclude, without any difficulty, that it was in the table before it was felt, and continues there after the feeling is over. The one implies no kind of extension, nor parts, nor cohesion; the other implies all these. Both, indeed, admit of degrees, and the feeling, beyond a certain degree, is a species of pain, but adamantine hardness does not imply the least pain.”—( Collected Works, p. 125.) The substance of this argument is, that the external existences, or qualities of external objects, of which our knowledge is acquired by the senses, are not felt or apprehended by us as prototypes or patterns of the sensations, through which they are made known, but perceived to differ from them in every particular ; as in the case of the notion of Extension or Space, formerly mentioned,—formed during the exercise of various senses, 7. ¢., in consequence of the excitement of various VOL. XX. PART Iv. 7D 530 PROFESSOR ALISON ON THE BELIEF sensations, but which is no sooner apprehended than it “ swells in the human mind to Infinity,” to which notion certainly no human sensation can bear any resemblance; and no one has rightly apprehended the argument, or can be aware of the importance ascribed to it by Mr STrEwart, as opposed to what has been since called the Sensational School of Metaphysicians, who has not adverted to this absolute and essential disstmilarity of the sensations, from what Dr Rerp calls “the Perceptions,” and Dr Brown, the “ Associations and Inferences,” consequent on those sensations. Those who do advert to that dissimilarity must perceive that our conception of, and belief in, the external and independent existence of space and matter,—although a mental act, and a complex one, and involving one of those intuitive judgments, as to the existence and authority of which we have seen that Rem, STEwaRt, and Brown, are fully agreed,—is perfectly distinct from the sensation by which it is excited, and involves no such absurdity or con- tradiction in terms, as the assertion that a sensation or other mental act, can be the exact mage and representation of anything that is not mental; and therefore, that the sceptical argument of BERKELEY and Hume, founded on that supposed absurdity, and necessitating our departure, as Hume expressed it, from the in- stincts of nature, as to the evidence of the senses, falls to the ground. The same observation applies to the notice of this subject by Moreut, in his review of the Scottish Philosophy, who says, that Dr Rem “ does not appear to him to have dealt a complete and effective blow against Humn’s argument respect- ing the material world ;” because, he says, “the sceptic may urge, with no little force, that although we must admit the reality of our own personal or subjective ideas (i. e., of the objects of consciousness), yet it still remains to be proved, that our perceptions, however clear, and our beliefs, however strong they may be, in- ternally, have reference to any object out of, and distinct from ourselves.” Rem, he says, deprived himself of the “ power of answering this final argument, by maintaining that Perception is altogether an act of Mind. So long as perception is regarded as only a subjective process (7. e., an act of mind of which we are con- scious), and an idea defined to be the act of the mind in making itself acquainted with external things, we are unable to point out to the sceptic what he demands, viz., a clear passage from this subjective activity of the mind to the outward and material reality.” —(Morell’s Philosophy, vol. i., p. 287.) Now, if this author had rightly comprehended the argument of Remp,—which I apprehend he must have known only from the account of the controversy given by Dr Brown,—he would have known that Rem considered the clear passage from the act of Perception in the mind to the material reality, to be precisely similar to the passage from our consciousness of to-day to our recollections of yesterday ; 7. e., to rest on one of those principles of Intuitive belief, the existence and authority of which are admitted by himself and by Brown, as well as by Reip ; and to be from its own nature incapable of any other proof. ATTENDING THE EXERCISE OF THE SENSES. 531 But if he had rightly comprehended the argument of Hume and BERKELEY, he would have known, that they not only demanded a clear passage from the mind - to the material object, but maintained that it is absurd to assert that any such passage exists; because, as we have seen, they said that by our senses we have the knowledge only of our Sensations or Ideas, call them which we will, and nothing can possibly resemble a sensation, except another sensation in the same or another mind; to which assertion and consequent imputatién of absurdity it was that Dr REID opposed the fact in the natural history of the mind, that by our senses we have the act of Perception excited in our minds, involving, as all admit, an intui- tive belief ; and which, particularly in the case of the primary qualities of matter, is distinctly felt by us to be separate from the sensation by which it is excited, and utterly incapable of comparison with it. But it is equally obvious, that this perception and belief, being regarded as an ultimate fact, or as containing in itself an ultimate fact in our mental constitution, like every other wlé:mate fact, physical or moral, involves a mystery ; and one on which we must accustom our minds to dwell, if we would form to ourselves any clear notions as to the constitution of the human mind, or its connection with the Divine Mind. It is only by a kind of Instinct, as expressed by D’ALEMBERT, but it seems better to use the term Intuition,—“‘prior to Reason, and superior to reason, —that the human mind can overleap the gulf that separates the visible world, from the percipient soul.” I have already shewn that by the admission of Dr Brown himself, in all de- partments of human knowledge, we meet with such ultimate facts and principles of intuitive belief, any farther explanation of which can be given us only by “the great teacher, Death ;” and very little reflection is sufficient to shew that the only objects which we can propose to ourselves in any inquiry which lies on the con- fines of Matter and Mind,—in which both physical changes and mental acts are concerned,—are to ascertain the exact phencmena on each side of the line of de- marcation, the precise conditions under which they take place, and the precise laws by which they are determined,—the mode of union being beyond our com- prehension. But so restricting our objects of inquiry, we may confidently as- sert, that enough has been ascertained in regard to the mental operations con- sequent on the impressions on our senses, as well as to their physical conditions, to form an important body of science, and furnish conclusions of the highest interest. I think myself justified by what has been stated, in affirming that in so far as Dr Brown thought he had detected an essential error in the reasonings of Dr Reip on this subject, he had deceived himself; and that in so far as he made a real advance, in our knowledge of the manner in which the notion of the primary qualities of matter is formed in the human mind, he proceeded strictly in accord- ance with the principles of Rem and Srewarr; and therefore, that it is only 532 . PROFESSOR ALISON ON THE BELIEF retarding the progress of knowledge on the subject, to represent these authors as at variance with one another. In fact, it appears to me, that his doctrine on this subject, referring to the general Law of Belief in the permanence of the order of Nature, is substantially the same as that of Stewart and Turcot, and that the only real addition which he made to our knowledge on the subject, con- sists in explaining the province of the muscular sensations, as distinguished from those sensations that result merely from impressions on the cutaneous nerves, with which they had generally been confounded under the name of Sensations of Touch ; and in connection with them, the importance of the idea of Time, in communicating the information on which our notions of the Primary qualities of Matter are founded. This is the same distinction as is expressed by several French physiologists by the terms Tact and Toucher ; and it appears from the learned researches of Sir WILLIAM Hamiuton, that it had been clearly pointed out by various other authors, ancient and modern; but I have no doubt that it was original on the part of Dr Brown. In concluding these remarks on this part of the Philosophy of Dr Brown, | see no objection to my stating, what I am very certain was the case, that the re- pugnance which he felt towards the peculiar doctrines of Dr Rerp, was in reality not so much on the score of judgment as of ¢aste. His own taste in literature was peculiar,— it was founded in a great measure on the classical models,—and he was even more ambitious than Mr Stewart, of combining the reputation of a scholar and elegant writer with that of an acute metaphysician. The perfect simplicity of the language, the total absence of fancy, and the homeliness of many of the illustrations, in the writings of Dr Rem, were distasteful to him ; and I cannot but consider, therefore, his objections to the doctrines there laid down, as an illustration of the truth of the observation on his own scientific character, which I have often heard from my Father; who had the highest admiration, both of the acuteness of his intellect, and of the purity and elevation of his moral prin- ciples, but used to speak of him as the man of the most fastidious taste that he had ever known. It has been often observed, that the intellectual opinions, even of the men who take most pride in the exercise of their understandings, are very often more or less guided by their tastes and feelings; and in regarding the prejudice which may be detected in the writings of Dr Brown, against the phraseology and the doctrines of Rerp, as an instance of the reaction of independent thought against mere authority, and of cultivated taste against the imputation of vulgarity, I do not think I do injustice to the memory of either of these illustrious men. Sir WILLIAM Hamiuton, as I already mentioned, expresses himself strongly as to the doctrine of Rem regarding the formation of the notion of the primary qua- lities of matter, as so far from “being a confutation of Idealism, affording it the best of all possible foundations;” but then he explains this by saying that he ATTENDING THE EXERCISE OF THE SENSES. 533 means only “that simpler and more refined Idealism, which views in ideas only modifications of the mind itself,” 2. ¢., only what Dr Brown, in one passage already quoted, regarded the ideas of BERKELEY, viz. as a metaphorical way of expressing acts or states of the mind; in which sense Dr Rep, as we have already seen, said he did not object to the use of the term, although he preferred another phraseology ; and using it in that sense, we have seen that his argument against Hume and BrerkeELey is independent of any objection to the term. Dr Rep goes no farther in explaining the manner in which we acquire the knowledge of extension or space, than to say, that it is a Perception, or a notion suggested to the mind by certain of our sensations, distinctly formed in the mind, and in which, when we analyse it as minutely as we can, we find the be- lief of external independent existence to be an essential element. Sir WitLiaM HAMILTON considers the conception of Space to be a native form, or necessary con- dition of thought; but that we have an immediate perception of something ex- tended, 7. ¢., invested with this quality, and which is independent of us. (See Notes to pages 126 and 324 of Collected Works, Sc.) I cannot perceive that there is anything more than a verbal distinction be- | tween these forms of expression; but if there be a real improvement in the latter form, it seems to me that it is sufficiently provided for by Dr Retp’s admission, that a finer eye may trace the labyrinth farther than he has done; but that in the meantime “there is no harm done” in resting on the position of Rem as to that belief; and acquiescing in his reflection, that ‘‘if we are deceived in it, we are deceived by Him that made us, and there is no remedy.” It is stated by MorELL, and I believe is the opinion of others who have made a study of recent German works on metaphysics, that the works of Dr Rem and all other Scotch metaphysicians, although accurate, so far as theygo, in “ inves- tigating and classifying the more obvious phenomena of the mind, as they appear in the individual, are deficient in not having gone a step farther, and dis- covered the very laws of our mental constitution, on which our primitive beliefs rest; that they might have sought the groundwork of our universal notions in the depths of our own being, and thus referred all the principles of common sense, all the primary laws of belief, back to their source in the subjective forms of the understanding and the reason (Historical and Critical View, Sc., vol. ii., p- 64); that in investigating the mental phenomena, our object should be to discover, not merely the reality of certain principles, but their necessity,—not merely the law of operation, but the reason of that law” (Ditto, p. 53); and that this is to be done, not by mere induction, but “by scanning the contents of our consciousness by the power of reflection, whereby we are enabled to catch the very forms of our inward activity.”—(P. 52.) In forming this opinion, I cannot help thinking that this very learned and estimable author has deceived himself; and that no such advance has been made = VOL. XX. PART IV. (—E 534 PROFESSOR ALISON ON THE BELIEF since the time of Srewart and Brown, either in the mode of inquiry, or in the results of inquiry on the subject. But all that I wish to observe on that point is this, that those speculations avowedly relate to subjects ulterior to those on which Rerp and Stewart exerted their minds; that they do not stand opposed to the doctrines of REID or Stewart as to the exercise of the senses, and the mental acts thence resulting, but are regarded as an addition to these doctrines; and therefore, that, whether admitted or rejected, they ought not to interfere with our appreciation of the truth or importance of the principles regarding our mental constitution, which they had laid down, and which these authors substantially approve. | In particular, while I cannot but admire the sublimity of the Theological in- ferences which More. has stated as resulting from the study of the Mind as he directs it, I cannot think it necessary to go farther into the subject than Rem and STEWART had done, in order to draw from it inferences as satisfactory to the in- tellect, and as consoling to the heart of man, as can be drawn from any unassisted human contemplation or reflection. It is stated, indeed, by Moret, that the great argument of Natural Theology, drawn from the observed adaptation of means to ends,—of which I may observe, that the principle of the adaptation of the construction of animals to the conditions of their existence, so well illustrated since their time by Cuvier, Owen, and their follow- ers, 1s distinctly an example,—has been well set forth by all the Scottish School of Metaphysicians, from Rem to CHALMERS; but that two subjects connected with it ought to have been taken up more fully, viz., 1st, the origin of the idea of Ab- solute Power, or of the Divinity in the mind; and, 27, the relation of the Divine Power, or Energy, to Man on the one hand, and to Nature on the other.—(Modern Philosophy, vol. ii., p. 71.) The first of these, I think, may really be regarded as a defect in the philosophy of Dr Brown, who rested the great argument of Na- tural Theology exclusively on the observed adaptation of means to ends;—and did not admit as a part of that argument, the formation of the notion of Efficient Cause, as distinguished by Rerp and Stewart from Physical Cause ;—and that it was a defect seems to me distinctly shewn byan observation of his own, which I cannot reconcile with the doctrine which he had laid down on this subject. The passage to which I allude is that where he speculates, with his usual eloquence and fancy, on the emotions which would be excited in the human race if it were possible that they should come to maturity in a world of darkness, and the sun were then suddenly to arise on their sight. ‘ The very atheists of sucha world,” he says, “‘ would confess that there is a Power that can create.” Now he surely could not have maintained that this instantaneous inference would imply a process of reasoning, by which the supposed atheists might satisfy themselves that some particular object was in view, which could only be attained by an influence of the sun, and therefore saw in this sudden and striking change an adaptation of ATTENDING THE EXERCISE OF THE SENSES. O00 means to ends. If not, then this inference must be allowed to establish the fact of the observation of sudden and striking change introducing into the mind the notion of a “Power that can create;” and I cannot conceive that the notion arising in the mind from the contemplation of these circumstances, and which is here expressed by that term, excludes the idea of Arbitrary Will. If it includes that idea, it cannot be correctly expressed by the definition given by Dr Brown of Power, which he allowed to be a simple idea, formed by intuition, but was at great pains to prove to mean merely “ Invariable Sequence, having reference not only to the past, but to every future case.” (Observations on Cause and Lifect, p- 101.) I cannot help thinking, therefore, that this illustration is sufficient to establish the reality of the idea of Absolute Power, or of Efficient Cause, as dis- tinguished from Physical, which was maintained by Rew and Stewart, but contested by Brown. This criticism of Moret, therefore, I believe to be justly applicable to Brown, but certainly not to either of his predecessors. The second principle stated by Moret as having been neglected by the Scottish School of Metaphysicians, is so beautifully expressed by himself, that I cannot help quoting his words. The principle in question, he says, should be a comment “on the scriptural doctrine, that in Gop we live and move and have our being. This is a truth which has more meaning in it than the cursory reading of it gives us; it evidently has a reference to the mysterious dependence of the human spirit upon the Divine, shewing us that we are all emanations from the Divine Essence, and although gifted with a distinct personality, yet that we are but waves in the great ocean of existence, ever rolling onwards to our eternal home.’’—(More.t, vol. ii., p. 72.) Now if the doctrine of Rem and Stewart really excluded from the reflections of the metaphysician so elevating and consoling a train of thought as this, we might regard them as truly and lamentably defective; but I confidently main- tain, that all that is necessary is to let the mind dwell for a little on the principle of Intuitive Perception of Truth, illustrated by them as well as by Browy, and in connection with it, on the facts regarding our mental constitution which they have explained, in order to be satisfied of the truth and justice of the senti- ment which I have quoted, and which, indeed, in all ages has suggested itself to the most profound thinkers in this department of science. “ Intuition or Inspiration,” says Vicror Cousin, “is in all languages distinct from reflection or from Reasoning. It is the simple perception of Truth; I mean of essential and fundamental truths, without the intervention of any voluntary or personal act. This intuition does not belong to us. We are there, when the act is performed in our minds, simply as spectators, not as agents; all our action con- sists in having the consciousness of what is going on. Our perception of simple and primary truths may be separated, therefore, from the fallible reason of man, and referred to that Reason which is Universal, Absolute, Infallible, and Eter- 536 PROFESSOR ALISON ON THE BELIEF nal, beyond the limits of Space and Time, above all contact with error or disor- der,—to that Intelligence of which ours, or that which makes its appearance in us, is but a fragment,—to that Mind, pure and incorruptible, of which ours is only the reflection.” These are sentiments which adorn and dignify Science, but I beg to ask, whether they are not in exact accordance with the doctrines of all our esteemed Scottish metaphysicians,—nay, whether they may not be regarded as commen- taries on the simple text already quoted from Rein, that all our knowledge of what exists, or ever did exist, traced to its source, is found to come by a channel, which is open to those who cannot reason, 7. e. (the word reason being ambiguous), who cannot exert the voluntary power of Reasoning, but only yield to the influence of the faculty of Intuition implanted in their nature,—‘“ that we are led to it in the dark, and know not how we came by it,—and that the wise and humble will simply take it as the gift of Heaven, and try to make the best use of it.” Accord- ing to the doctrine of Rerp, all those mental acts in which Intuitive Belief is in- volved, and on which all knowledge is directly or indirectly founded, although we call them owrs, are ultimate facts in Nature, independent of our will, and beyond our comprehension ; and this conclusion, so far from humbling the human mind, establishes a more intimate connexion between man and his Creator than can be inferred from any other facts in nature. When we attend to the meaning, and trace the applications of this principle of Intuition, necessarily involved in the only account we can give of our per- ceptions, and of all our knowledge; when we observe the still more striking exercise of this power in animals, whose sensations suggest to them, prior to all experience, the true distance, direction, and size of external objects, certainly neither contained in, nor deducible by any process of reasoning from, the intima- tions of sense; when we reflect on the equally mysterious nature, and yet on the proved fidelity (in the healthy state) of the evidence of Memory, essential, not only to all reasoning, but to all definite voluntary action of men and animals; when we consider the nature and the tendency of those Instinctive propensities or Impulses, which are excited in us and in all animals during the exercise of the senses, and which are equally requisite and equally effective, in attaining objects essential to our existence, as are the vital properties of muscles and of nerves ;— in all these cases, we shall perceive that truths are made known to us ina manner | absolutely mysterious ;—by means of impressions on our senses, but ‘‘ no more con- tained in sense, than the explosion of a cannon in the spark that gave it fire.” And when we farther observe, that the actions which are prompted by the In- stincts and Volitions both of animals and of men, consequent on the knowledge thus acquired, are all conducive to certain important ends, intelligible to us after ob- servation and reflection, but scarcely ever in the contemplation of the agents at the moment, we can express these facts only by saying that both men and animals ATTENDING THE EXERCISE OF THE SENSES. da/ are the depositaries or recipients of certain portions of the knowledge, and the instruments of certain of the designs, of the superior Mind to which they owe their existence. And the “ creed of the sceptic,” shewing that it is by no exertion of our own reason, and indeed by no process of which we can give any account, that so many truths are made known to us, and so many useful acts suggested to us, becomes an essential part of the short and simple train of reasoning by which that connection is inferred, and which may be thus stated. Much of the knowledge which is part of the constitution of our minds, or which is awakened in us by the exercise of our senses, is not our knowledge; it is neither contained in our sensations, nor deducible by any reasoning from them, nor subject to our will, nor acquired by our experience or recollection; yet it is found to be accurate, and the possession of it to be useful and necessary to us. So also, many of the actions which we perform, which are fitted to the attain- ment of ends important to us, and obviously performed in anticipation of those ends, are not prompted by any such anticipation of ours. The will which per- forms them is ours, but the knowledge of their consequences, with a view to which they are performed, is not ours. “Man,” says Guizor, “is a workman, intelligent and free, but the work in which he is employed is not his; he sees the intention of it only when it has been so far accomplished, and even then, sees it only imper- fectly.” In so far, therefore, as the observation of these phenomena of our minds leads to an inference of Intelligence,—and if it does not, we have no grounds for ascribing intelligence to any of our friends or fellow-citizens,—it must be intelli- gence prior to ours, and superior to ours, and on which ours is dependent. It seems to me, that it is quite unnecessary to make any additions to the doctrine. which we have seen was the common doctrine of REtp, of Stewart, and of Brown, as to the existence and authority of the Intuitive Principles of Belief,—and hardly necessary to illustrate this farther than the two former authors had done,—to justify the whole of this inference. But farther, it is precisely the same inference which we find, if not so fully illustrated, at least distinctly expressed as resulting from the contemplation of our mental constitution, by much earlier authors. It was the same idea that was expressed by the three memorable words of Cicrro, “ Homo Rationis Particeps’” (not possessor); and by the positive assertion of PLato,— that nothing is more certain than that a part of every man’s mind existed before he did. Nay, in an earlier record than either of these, of the first metaphysical reflections of the human race, in those very words from the Book of Job which Dr Rep took as the motto of his Work on the Intellectual Powers, there is, as we are assured by an eminent Hebrew scholar, a meaning more exactly in accord- ance with the leading principle of Dr Retn’s Philosophy, than, in selecting that motto, he was probably aware. The words are, “ Who hath put wisdom in our inward parts?” but the more precise expression of the meaning, we are assured, is, VOL. XX. PART IV. 7¥F 538 PROFESSOR ALISON ON THE BELIEF Who hath given to our inward parts, or to our thoughts, the security of knowledge ? 2. e., What security have we of the truth or reality of knowledge, which we can trace no farther than certain impressions made on, and changes excited in, our own minds? and the only answer which the context will admit is, that we have no security but the will of our Maker, whereby our minds are so constituted, that Belief is an essential component part of the acts which they uniformly perform, or the states which they uniformly assume, under certain circumstances ; which in this as in other departments of knowledge, we can go no farther than to specify and describe. I may just add, that there are two questions in Physiology, which have at- tracted much attention of late years, and of which I think a just view cannot be taken, without a previous accurate discrimination of those mental phenomena which Dr Rerp distinguished as Sensations, Perceptions, Recollections, and Volun- tary Efforts. The first regards the appropriation of the larger masses of the nervous system to their specific uses; and jist, to those muscular movements which are generally now described as depending on the Reflex action of the Spinal Cord, e. ¢., those concerned in Respiration, Deglutition, and the various actions associated with those, and which have been ascertained, particularly by the experiments of FLourEns, to have no dependence on the hemispheres of the Brain or Cerebellum ; and, accordingly go on, even for months together, in animals of which both the brain and cerebellum have been extirpated ; so that the term Refiex Spinal Action may be properly applied to them, instead of the older term Sympathetic Action, by which they were long previously distinguished. But it is equally certain, and was indeed established long ago, by Dr Wuyrvt, that another principle is here concerned, which goes so far in explanation of the fact, not only that muscular contractions are excited by this reflex action in these circumstances, but that those muscles are se- lected for this purpose, which are capable of performing the motions, and successions of motion, requisite for the particular end to be attained in each case,—one set of motions, e.g., for breathing, another for coughing, another for deglutition, another for vomiting, &c. That principle is the existence and the peculiarity of the Sen- sation, preceding and attending the performance of each of these motions. The proof of this is, that in many of these cases, the same sensation may be excited by im- pressions made on the sensitive nerves of different parts, in each of which the same reflex or sympathetic movement follows; while in others, different sensa- tions result from varied impressions made on the sensitive nerves of the same parts, and in these different reflex actions are excited. It appears, therefore, that it is by the sensations preceding and attending them, that the nature and inten- sity of these reflex movements are determined, at least in the ordinary exercise of these functions ; and that those parts of the nervous system, and those only, which are found to be essential to those movements, must be those which are concerned . Ce ae eee ee ee ATTENDING THE EXERCISE OF THE SENSES. 539 in the mental act of Sensation ; which term is now habitually used in Physiology, in exactly the same sense as Dr Reip understood it.* Accordingly, I think it may be confidently asserted,—although many physio- logists speak of reflex actions as not necessarily connected with sensation,—that the correct expression of these phenomena was truly given by Cuvirr, in his Re- port to the Academy of Sciences on the Memoir of FLourENs in 1822,—that an animal of which brain and cerebellum have been destroyed, and the medulla oblongata only remains in the cranium, is still capable of feeling Sensation, and of performing those acts which are immediately linked with sensation; and, in- deed, is dependent on sensations for the preservation of its life, which, in these cir- cumstances has been preserved for many months,—because it still breathes, and still swallows what is put into its mouth, &c.; but that, in these circumstances, it has no recollection of past sensations, shews none of its usual habits, cannot seek for food, or even avoid obstacles placed in its way; in short, is reduced to a state of stupor, more or less profound. In such an animal, of course, those judgments consequent on sensations, to which both Dr Rei and Dr Brown gave the name of Perceptions, and all more strictly Mental recollections and acts consequent on these, are manifestly suspended; and thus we acquire the certainty that the dis- tinction of Sensations and Perceptions, which we have seen to be of so much im- portance when considered metaphysically, is fully confirmed by physiological in- quiries, and, I may add, by researches in Comparative Anatomy; which have proved that the Cerebro-Spinal Axis is the part of the animal structure which fur- nishes the conditions, and supplies the instrument, of the ones et of mental phe- nomena; and the Brain and Cerebellum, superimposed on that structure within the skull, are those which minister in like manner to the other. This is, in fact, the only conclusion, as to the appropriation of these different parts of the larger masses of the nervous system to different acts or states of mind, which has ye tbeen satis- factorily established; and if we regard it, as I think we may, as an important guide to farther inquiries as to the use of the different portions of the physical instrument concerned in Thought, we ought also to regard it as an important indication of the value of the distinctions among the acts of thought, with which these different portions of the nervous system are connected. The other question is, as to the degree of modification which the exercise of the Senses, as well as other mental acts may undergo, in several anomalous conditions of the living body, especially in that to which the term Somnambulism, Extase, or Clairvoyance, has been applied. On this subject, which can only be elucidated by very carefully-conducted observations,—always likely to be impeded by peculiar * See Observations on the Physiological Principles of Sympathy, by the present Author, in Edinburgh Medico-Chirurgical Transactions, vol, 11. 540 ON THE BELIEF ATTENDING THE EXERCISE OF THE SENSES. sources of fallacy, especially by that extraordinary propensity to deception which medical men so continually encounter in this part of their studies,—it would be wrong in me, not having had sufficient opportunities for making such observa- tions, to pronounce any decided opinion; but I think it only due to the memory of Dr Rerp to point out, that in one part of his writings he has distinctly asserted, —and indeed, consistently with his principles, could not fail to perceive,—the possibility of such a modification of the exercise of the senses, as has been ex- pressed by the term Clairvoyance; and left it, therefore, as a question to be de- cided simply by experience, whether or not such modification may occur. “Our power of perceiving external objects is limited in various ways, and particularly in this, that without the organs of the several senses, we perceive no external object. We cannot see without eyes, nor hear without ears; and it is not only necessary that we should have these organs, but that they should be in a sound and natural state. *« All this is so well known from experience, that it needs no proof; but it ought to be observed, that we know it from experience only. We can give no reason for it, but that such is the will of our Maker. No man can shew it to be impossible for the Supreme Being to have given us the power of perceiving exter- nal objects without such organs. ‘“‘If a man were shut up in a dark room, so that he could see nothing but through one small hole in the shutter of a window, would he conclude that the hole was the cause of his seeing, and that it is impossible to see in any other way? Perhaps, if he had never in his life seen but in this way, he might be apt to think so; but the conclusion is rash and groundless. He sees, because Gop has given him the power of seeing; and he sees only through this small hole, because his power of seeing is circumscribed by impediments on all other hands.”— (ReE1D’s Collected Works, p. 246.) On this passage we have the following note by Sir Witt1am Haminton :— ** However astonishing, it is now proved beyond all rational doubt that, in certain abnormal states of the nervous organism, perceptions are possible through other than the ordinary channels of the senses.” This is expressing a decided opinion on the question, on which I have said that I do not think myself qualified to judge; but I beg to express my perfect concur- rence with Sir Witut1am Hamiuron in thinking, that, consistently with the prin- ciples of Dr Rerp, it is a question on which no @ priorz opinion is admissible, and which observation and experiment alone can decide. ( 541 ) XXXIV.—Summation of a Compound Series, and its Application to a Problem in Probabilities. By Bisnop TERRor. (Read 21st February 1853.) The series proposed for solution in the following paper is— (m—q.m—q—-1l..... m—qt+pt+1)x(1.2.3...... q) +(m~q—1.m—q—-2...m—q+p) x(2.3.4 .....q+1) os GD) GD See ts ee aa 1 x(m—p.m—p+1..m—p+q+t1) The law of this series is manifest. Each term is the product of two factorials, the first consisting of p, and the latter of g factors. And in each successive term, the factors of the first factorial are each diminished by one, and those of the latter increased by one. met therewbe!a Series, XV i4 X28 Vo 4 fae eee ee X, Y where, Y,=Y,+4,,Y,=Y,+4,=Y,+4,+4,, and so on. Then the series=X, x Y, +X,.x Y,+4, +X,» x War A, PA, &c. = 2 yx Vi Ku, x Ay + 2 hug KAS Wee. where x X, means the sum of all the terms of X from X, to X, inclusive. Let us then, in the first place, take the differences of the second factorials— (ae! Ne SEE ORC HT err as (eS ORE eee q)-4 eA hig L(y sau tay, (ie) Ce a rn q+1).¢ &e. &e. Hence the sum of the whole series= x(m—q.m—q-1l....... m—prg+i)-112.3 2.004 g—l.q +3(m—q—-1.m—q-2..... Ft) ae Ce ieee ee q-9 (B) +3 (m—q—2.m—q—3..... m—p+q—-l).3-4.5 wa gt+l1l.g &e. &c. VOL. XX. PART IV. UG 542 BISHOP TERROT ON THE SUMMATION OF A COMPOUND SERIES, Integrating then each line separately, we have the sum ws Sebi 0s Epa a AN NG Qe 6 altel ce m—p+t¢Fl xd 2.3.5 0-4. q-1 The — p+i™—G-m—q-1....... m—pt+qx2.3.4.....6. q KC) sg por ae p+ m—q—1.m—q—2 .:>. m—p+q—1x3.4.5....... q+ &e. &e. If again we treat this form as we have done the original, by taking the differences of the second factorials as they now stand, and again integrating, we reproduce the sum in the form q-q—-1 pe sek pr lipe2 = g+2.mogst ) prot ee ss q—2 D Se as i Se a a Sate ; (D) prlip+2- qri. Qisge ree AEA ens m—p+qx2.3.4....q— &c. &e. ; It appears, then, that we may continue this differentiation on the one side q times, and integration on the other g+1 times; and that at each succeeding operation, an additional next lower factor will be introduced into the numerator of the fractional coefficient, and an additional next highest into the denominator. And after q differentiations, the last factorials will all become unity; and, the middle factorial having acquired an additional higher factor at each of g+1 inte- grations, we have for the sum of the series— 9-9 = ligmeain. rewk ptl.pt+2 ....pt+qt y Xmt+i.m arigeternae m—qtpt+l1 \ Ve ey HH: The Problem in Probabilites to which the foregoing summation is applicable, is the following :— Suppose an experiment concerning whose inherent probability of success we know nothing, has been made p+q times, and has succeeded p times, and failed q times, what is the probability of success on the p+q+1"" trial. This Problem is interesting, because it tends to the discovery of a rational measure for those expectations of success which constitute the motive for a large portion of human actions. The force of such expectations commonly depends, not upon reason, but upon temperament; and, according, as a man is naturally sanguine or the reverse, so in all the contingencies of life, does he over-estimate or under-estimate the chances in his favour. | It would be going much too far to think, that we can give an algebraic formula, by the application of which a’ man may, in every practical case, correct his natural tendency to error, and arrive at a strictly rational amount of expectation. AND ITS APPLICATION TO A PROBLEM IN PROBABILITIES. 543 All that we can say is, that experience has led dispassionate men to come to nearly the same ae as the mathematician: for while he asserts the probability of success to be , they act upon the supposition that the probabilities of ea success and failure are proportioned to the number of experienced cases of success and failure : and when either p or q¢ isa large number, that is, when the experience is great, the conclusion and the supposition coincide. In order to realise the Problem, we shall use the ordinary illustration, and suppose that a bag contains m balls in unknown proportions of black and white, but all either black or white; that p white and qg black balls have been drawn, and that it is required to find the probability of drawing a white at the p+q+1'% drawing. The Problem as thus stated, admits of four varieties. 1. m may be given, and the balls drawn may have been replaced in the bag. 2. m may be given, and the balls drawn not replaced. 3. m may be infinite or indefinite, and the balls replaced. 4. m may be infinite or indefinite, and the balls not replaced. Of these, the 3d is the only case which I find solved in the treatises which I have consulted. I propose to solve the 2d case, and therein the 4¢2; and, in conclusion, to make an attempt at the solution of the 1s¢ case. To render the observed event, that is, the drawing of p white and q black balls (or E), possible, the original number of whites may have been any number from m—g to p inclusive, and the number of blacks any number from ¢ to m—p. Let us call the hypothesis of m—gq white and q¢ black, H, . and m—q-—1 white and q+1 black, H,, &c. m— = m—q-1....m—q—-—pt1x1.2.3.....q* Then H, gives for probability of E ap IN Re GIG aI or, calling the denominator A, H, gives + -m—q.m—q-l..... m—q—pt1xl.2.3..... gq (a) H, gives + »m—g—1.m—g—2 ee epee gil (By) CE) Jake gives + +m—g—2.m—g—3 oa. mm gp—bx B04 2s ig 2) (y) &e. &e. _ Now, a+@++¥, &c. by the former proposition (E) if ike eee ea aes 1 rei 7 oat py od" ig apices p-q+l -. probability of i= ee ear anes ara, * The coefficient (U of Gattoway’s Treatise), expressing the number of different ways in which p white and q black balls can be combined in p+q trials, is here omitted. This is immaterial, a as it disappea: the expression ———————— 1 Pp rs in Pp atB+y ca 544 BISHOP TERROT ON THE SUMMATION OF A COMPOUND SERIES, Pel ota oe eee pt+qtl m+1l.m.... nip gti IedeBasgs ei a es ee But the probability of a white at p+ q+1'™ drawing on H, is a = . probability of white derived from H, is ‘ ptl.pt2....p+qtl m+l.m....m—p—qx1.2.3.... a (m—q.m—q-—1...m—q—p)x(1.2.3...¢) (G) So probability from H, m: pt+l....ptqtl ~m+til.m....m—p—qx1.2.3... ; x (m—q—1.m—q—2...m—q—p—l) x (2.3--¢+1) And so for all the other hypotheses in succession. Now this series, omitting for the present the consideration of the fraction which is a factor common to them all, is a series of the same form as that summed in the last proposition, only that now p+1 must be substituted for p. We have therefore the whole probability of a white at p+ q+1™ drawing at Pt pee oe : jee Rates . ~ mtil.m...m—p—qxl.2...q > p+2...ptgqt2 pt+1 (H) m+l.m... ile oak Lang EO Note.—It may be worth observing, that, had we summed the original series in Prop. 1. upwards instead of downwards, we should have got for a first factor 102 MBIA! OHS ys tek are Feigao ee which must therefore pki pea that these fractions are equal may be proved independently, for if we divide each by 1.2.3...px1.2.3...9, we have on both sides the same quotient 1 LPs i. ptoet ea - There now remains for solution only the first case of the problem in chances, that is, to find the probability of drawing a white ball, when m the number of balls is given, and p white and g black have already been drawn and returned. The main object in this case is to sum the series m—1" x1'+m—2" x2... Boma OU eee (a This may be done much as in the preceding case, by taking the successive differences of the right-hand factors till the differences vanish, and multiplying the successive terms of the last or g+1'* row of differences into the g+1'" summa- tion of the successive terms of the series (1+2”. . . +m—1")+(14+2?... +m—2?), &c.. This may be sufficiently explained by going through the operation in a low —_ particular case. Let p=2, g=3. AND ITS APPLICATION TO A PROBLEM IN PROBABILITIES. 545 Then the series written perpendicularly is m—1" x1 See xd x,m—1" x1 z,m—1" x1 zn —1" x1 2) x8) slim 2" x7 3,m—2 x 6 3m —2! x5 2m—2? x 4 m—3" x27 = 3,m—3"x19 = Xm—3"x12 = %m—3?x6 = 3m—3" x1 m—4A" x 64 3,m—4? x 37 xm—4” x 18 zm —4" x 6 m—5"x125 3m—5" x61 3m —5!” x 20 33m —5" x 6 &c. &e. &c. &e. The value of the different sigmas is easily found by the method of finite dif- ferences. Generally, since the differences of 1%, 2%, 3°, &c., always vanish in the g+1'™ line and after the g* term of it, the general expression is See a Se mee! ay). dy 4 gs d,, d,, d,, &c., signifying the 1st, 2d, 3d, &e., terms of the g+1™ row of differences. * This summation may be applied to find the probability in the case now under consideration, for it expresses the a+ 6+ ¥, &c., of the preceding case. Applying it as we did the value of 2+ 6 ++, &c., there found, we shall find the probability of a white ball at the p+q+1™ trial to be ee dy Se SO ithe) Ge Sau M— Oe sa as mae a dma If m be infinite, the expression becomes CAs eas ty eet m (L+d,... . dy)-2q4, MP? M3q41 mM? But if 2 be a quantity varying between the limits 0, 2, 3, Seg eps ax _ptl a? Sel fieag FF Be And by continuation Sie Gale, gE SU Oe cE I ap Cae (L) m3or1mP p+2.pt+3....ptqt2 ptpt2 We have thus found the probability in every case of the problem; the 2d and Ath at H, for the result, being independent of m, must be true for an infinite as well as for a finite number. The Ist case is solved at K, and the 3d at L. VOL. XX. PART IV. Voagel XXXVII.—On the Optical Phenomena and Crystallisation of Tourmaline, Titanium, and Quartz, within Mica, Amethyst, and Topaz. By Sir Davin Brewster, K.H., D.C.L., F.R.S., and V.P.R.S. Edin. (With a Plate.) (Read 4th January 1853.) The existence of certain minerals imbedded in others,—the optical phenomena which they exhibit,—their form and mode of distribution, and the mechanical in- fluence which has been exerted during their formation on the mineral that con- tains them, are among the most curious and instructive facts in physical science. The dissemination of perfectly-formed crystals of titanium, both in the form of ttanite and anatase, in Brazilian crystals of quartz, is a fact so well known that I shall take no farther notice of it, but shall proceed to give an account of a series of facts of a much more general and interesting character, which I have had occasion to observe, during an extensive examination of minerals, undertaken with a different object. 1. On the Distribution of Tourmaline in Mica. When fluids and condensed gases are imprisoned in the cavities of topaz and other hard minerals, they retain their place till some powerful agent releases them from confinement, or till heat gives them such an expansive force as to burst the mineral. In mica, however, where the laminz of which it is com- _ posed are held together by a very feeble cohesive force, the fluids in their cavi- ties, and the extraneous materials which were present at their formation, have experienced no difficulty in quitting their place, and spreading themselves be- tween the plates of the mineral. Tourmaline and quartz, though thus distributed between the laminze of mica subsequent to its crystallisation, have yet found a place in it contemporaneously with the crystallisation of the mica itself. In this case they are large crystals, equivalent in thickness to many laminee, and may be taken out and subjected to examination. Some of the crystals of tourmaline are so large, indeed, that I have used them with their own natural faces as analysing prisms ; and the quartz crystals, which are amorphous, and very irregularly formed, occupy a still greater space. In both cases, however, the tourmaline and the quartz, when taken out, leave large openings in the laminee, and have greatly disturbed the structure of the mica around them. The crystals of tourmaline thus formed in the mica, have almost always the faces of the flattened hexagonal prism parallel to the lamine of the mica. I have found, however, a few cases in which the flat summit of the hexagonal prism is parallel to the laminz. The crystallisations of quartz have also the axis of the prism, or its hexagonal faces parallel to the lamine. VOL. XX. PART IV. rag 548 SIR DAVID BREWSTER ON THE OPTICAL PHENOMENA OF The other crystals of tourmaline which I have discovered in mica have a very different character: They have been formed subsequently to the crystallisation of the mica, and exist only between its laminze. I have not been able to discover any cavities in mica containing fluids or gases, but I have found thousands from which the fluids and gases have escaped,—the one crystallismy into hexagonal plates of tourmaline, and the other separating the laminze, or running between them, and carrying along with it minute portions of crystallisable matter. The hexagonal crystals thus formed have their faces perpendicular to the axis of double refraction, which is the axis of the prism; and what is peculiarly in- teresting, the fluid from which they were formed has insinuated itself between several of the lamine, and the different plates of tourmaline which they formed have, of course, the sides of the hexagon incoincident. Sometimes these crystals extend to different distances from the centre of the original cavity, and are occa- sionally formed round it in a circular group. See Plate XV., Fig. 1. : The centre of the cavity from which these crystals have been projected is oc- cupied by a spherical group of granular or capillary crystals, which is generally very opaque, though such groups sometimes exhibit, in particular spots, double refraction, and a speck of light is occasionally seen through the centre of the group. In some cases I have observed these very thin hexagonal plates without this opaque centre; and they have probably been formed by a portion of the fluid projected to a distance between faces of easy cleavage. The black spherical group already mentioned has its outward surface bristled with points, which are the extremities of the crystals radiating from its centre ; and in one fine specimen to be farther described, it is surrounded with a ring of less opacity than the nu- cleus, and analogous to what is common in circular crystals. See Fig. 1. The thin plates thus formed between the laminze, whether hexagonal or pris- matic, are always of a faint brownish yellow, which at an increased thickness be- comes green; and so exceedingly thin are these plates, especially those farthest from the nucleus, that with a power of 400, it is often very difficult to see their terminal lines. In order to convey an idea of these phenomena, I have given a drawing in Fig. 1 of a very interesting one, where the prismatic crystal nearest the black central group is a bright green in all azimuths with polarised light, surrounded with three or four larger prismatic yellowish plates, growing fainter both in tint and outline as they recede. In some cases the crystals are brown, and in others beautifully dichroitic, being bright green and pink in the different azimuths of | polarised light. As considerable forces must have been in operation during the production of these phenomena, we may expect to see the effects of them upon the surrounding mica. We accordingly observe the polarisation produced by pressure round almost all of these crystalline groups. Rents and other marks of violence are dis- PLATE XV. VoL XX. hoy. Soe. Irans 2 546. : il | | WHLizars. so TOURMALINE &c., WITHIN MICA AND OTHER MINERALS. 549 tinctly seen in the mica, and cracks or luminous streaks often occur in the tourmaline plates themselves. I have observed, too, in portions of the mica where I cannot find any cavities or crystals, distinct luminous sectors of polar- ised light, which could only be produced by a force emanating from their centre. This force may have been that of gas discharged from some neighbouring cavity, and driven by change of temperature to some other part of the mica plate; and in the following remarkable phenomenon we may perhaps find some evidence in favour of this opinion. Plates of mica contain many beautiful systems of Newton’s rings, occupying a circular space where the laminze have been separated by some cause or other, and where, of course, there must be either air or some gaseous body. The colours of the first order are at the circumference of the circular space where the laminz are in optical contact, and the higher orders of colour extend towards, and often to the centre of the space. Now it is a curious fact, that wherever there is a cavity which has projected its fzd and probably gaseous contents, it is situated in the circumference of one of these circular spaces. When two cavities have been near each other, the circular spaces unite and lose their form, and when the cavi- ties have been more numerous, the circular spaces unite into very irregular shapes. That these circular hollows or spaces between the laminz have been produced by something which has issued from the cavity to which they are so constantly related, cannot admit of a doubt. That it has not been a fluid is evi- dent, and therefore it must have been a gas, which is either there still, or has escaped through some minute openings between the lamine, where optical contact has been restored.* There are some specimens of mica in which the crystals of tourmaline are large and opaque, and exhibit phenomena which I believe have not been recog- nised in any other mineral. The most interesting specimen of this kind I owe to Professor FLEMING, who pointed out to me one of the peculiarities which it con- tains. This specimen is accurately represented, of the natural size, in Fig. 2. The largest of the five crystals is 0°28 of an inch broad, and the smallest 0:08 of an inch. Their thickness cannot greatly exceed the thousandth of an inch, and yet it is with difficulty that the strongest sun-light can be seen through them. The form of the smallest is a perfect hexagon, and in the rest the same form is more or less distinct. In'the oval crystal there are numerous holes, and in all of them there are numbers of rectilineal cracks parallel to the sides of the hexagon, and some of them so narrow that light can scarcely pass through them. When we look at the sun through one of these crystals, a curious optical phenomenon is seen, a luminous hexagonal surface, composed of lines of light, parallel to the * A fluid even may have thus escaped, and the’ circular hollow remained as before. In support of this opinion, see Edinburgh Transactions, vol. x., p. 11; but especially vol. xvi., p. 13 ; or Phil. Mag., vol. xxxi., p. 101, August 1847. 550 SIR DAVID BREWSTER ON THE OPTICAL PHENOMENA OF sides of the hexagon, and six beautiful radiations, like those of the Asterial Sapphire, perpendicular to the sides of the hexagon. The existence of these rectilineal fissures is an important fact in crystallogra- phy. It proves that the crystals were in a soft state after they had attained their present form; and that, in the process of induration, the fissures were produced by the shrinking of the tourmaline, in the same manner as similar fissures are produced during the induration of clay. In the mica which surrounds some of the crystals, there is the appearance of considerable disturbance; but I can find no trace of any cavity from which the tourmaline may have been ejected in a fluid state. The faces of these crystals are not everywhere in optical contact with the mica, and it is very probable that they could be removed without any adhering mica, as I have occasionally found crystals of tourmaline that were moveable between the lamine. In the same specimen which contains these tourmalines, and in others, I have found, what I believe has never before been observed, the woolly filaments of the Penicillum glaucum of Linx, with its sporules scattered about between the laminee, and sometimes beautifully moniliform, as in the Penicillum glaucum obtained from milk by M. Turrin.* 2. On the Distribution of Titanium in Mica. In examining a remarkable specimen of mica from Irkutsk, in Siberia, I found t2taniwm between the lamineze in varieus forms, sometimes in amorphous plates, sometimes in a powdery state adhering to the mica, and most frequently in beautiful dendritic forms, of various degrees of thickness. At a thickness of about the hundredth of an inch, the titanium, in all these forms is opaque; but at less thicknesses, it has a brownish transparency, becoming almost perfectly transparent at thicknesses which do not seem to exceed the 2000th part of an inch. In Fig. 3 I have given a drawing of an opaque group executed for me with minute accuracy by my celebrated friend Mr HarpincEer of Vienna, during his residence in Edinburgh. The transparent groups are much more beautiful than the opaque ones, the crystalline ramifications having the most diversified forms, resembling often regular organisations. When the mica is removed from above the titanium, so that only an exceed- ingly thin film of it is left, the reflected light is extremely brilliant, and consists of the most splendid colours. These colours, which have always the form of the titanium, are those which are produced by the thin film of mica which covers the titanium, and are not produced, as has been supposed, by a vacuity in the mica. In some specimens of mica from Bengal, the imbedded titanium is spread out * See Comptes Rendus, tom. v., p. 822, 1837, Dec. 11. TOURMALINE, &c., WITHIN MICA AND OTHER MINERALS. 551 in a very irregular manner from a nucleus, sometimes having the form of a thin film; sometimes of oriental characters ; and sometimes it is disseminated in grains so extremely minute, that the flame of a candle seen through it is surrounded with a halo of five or six perfectly-formed coloured rings. 3. Distribution of Quartz in Mica. In mica from various localities, I have found large crystallisations of quartz, the quartz replacing the mica. I have never even once met with a regular crystal of quartz; and what is curious, all the crystalline masses of it which I have exa- mined have their axis of double refraction in the plane of the laminz of mica. In some very large specimens of Bengal mica given to me by Mr Swinton, I have found layers of quartz, several inches in area, and about the 200th of an inch thick. The two surfaces of the plates are exceedingly inequal and corrugated, owing to the circumstances under which they were formed, but they possessed regular double refraction, and gave the colours of polarised light. 4. Distribution of Titanium in Amethyst. While examining, many years ago, along with the late Marquis of Norrn-— AMPTON, several bags of amethyst which had been imported into Scotland from the Brazils, we were surprised to observe a number of fine pyramidal crystals, which seemed to have a powdery matter distributed through their mass. Upon more narrowly examining these crystals, I found that this dust formed an inner pyramid, all the faces of which were parallel to the faces of the pyramid of ame- thyst. When two parallel faces were ground upon the pyramid, and perpendi- cular to its axis, the particles of dust were seen by the microscope to consist each of several spicular crystals of titanium, crossing one another at angles of 60° and 30°, and forming distinct groups. In one crystal there were two interior pyra- mids composed of these groups; and it will be seen, from the explanation which I shall presently give of this phenomenon, that there may be any number of such pyramids. As the crystals of amethyst are supposed to have been produced by the gradual enlargement of a small crystal placed in an amethystine solution, we have only to assume that a solution containing titanium has been introduced into the ame- thystine solution at different times during the growth of the crystal. The small crystals of titanium will deposit themselves on each of the surfaces of the pyra- mid; and when the whole of the introduced titanium has been thus deposited, the enlargement of the amethyst will go on, leaving a pyramid of titanium crys- tals in its interior. Ifa second solution of titanium is introduced, a second pyra- mid of its particles will be formed in the same manner; and this process may be repeated any number of times. If we now suppose that the amethystine solution is exhausted, just when the VOL. XX. PART IV. 7K 552 SIR DAVID BREWSTER ON THE OPTICAL PHENOMENA OF titanium solution has deposited all its crystals, the completed crystal of amethyst will have its outer surfaces covered with spicular crystals of titanium, or the pyra- mid of titanium groups will be on the very outside of the pyramid of amethyst. I had the good fortune to find such a crystal, in which the coat containing the titanium is laid like varnish on all the faces of the pyramid, but only on the upper end of three of them; the lower end of these three faces having lain on the solution protected from the deposition of the titanium. This crystal is, I believe, unique, and possesses the great interest of exhibiting the very process by which it was formed. The two phenomena which I have just described are shewn in Figs. 4 and 5. 5. Distribution of Titanium in Brazil Topaz. In examining a great number of very imperfect crystals of Brazil topaz, I found many which contained crystals of titanium of a brilliant scarlet colour, with a tinge of yellow. These crystals were perfectly transparent, and occurred in seven different forms. 1. In flat amorphous plates, which were highly transparent. 2. In hexagonal plates, lying in different planes. 3. In transparent lines running in different directions, and, though continuous, lying in different planes. 4. In lines running inwards from the margin of the specimen, and terminating in small flat plates. See Fig. 6. 5. In the most remarkable symmetrical forms like sceptres or maces, resem- bling some of those symmetrical cavities which I had previously found in the white topazes of New Holland.* See Fig. 7. 6. In some specimens the plates of titanium are actually bent, as in Fig. 8. 7. In little groups of transparent circular plates of a scarlet colour, and hay- ing concentric rings. When light is reflected from the separating faces of the titanium and topaz, it is almost completely polarised; and at greater angles than that of maximum polarisation, colours of singular brilliancy cross the reflected images. These colours are doubtless connected with the fact, that at some of these faces there are three images of a luminous object seen by reflexion, one of the two outer ones being polarised oppositely to one of the double middle images, as in the case of the multiplication of images in composite crystals of calcareous spar.t 6. On the Crystals and Cavities in Garnet. In the greater number of the crystals of garnet which I have had occasion to exa- mine, I have found many crystals and cavities, and much amorphous matter. In * See Edinburgh Transactions, 1826, vol. x., Plate XX. + See Phil. Trans., 1815, Plate XV., Fig. 2. TOURMALINE, &c., WITHIN MICA AND OTHER MINERALS. 553 one specimen, in particular, the included crystals form a larger mass than the garnet, which is merely a cement for holding them together. These crystals have various crystalline forms, while some are amorphous, though regularly crystallised in their interior. All these crystals are doubly refracting, and give the colours of polarised light from their small size. In another specimen, many of the crystals, in the form of hexagons and rhombic plates, are opaque, and exhibit by polarised light the remarkable pheno- menon, which I had never before seen, of having luminous edges, so that when the rest of the crystal and all the field of view is dark, we observe hexagons and rhombs, and other geometrical figures, depicted in lines of red light. It is not easy to ascertain the cause of this singular appearance, because we cannot see the form of the crystals where the light exists; but I have no doubt that the lumi- nous lines consist of light depolarised by reflexion from the sides of the hexagonal and rhombic plates, because the illuminating pencil is much larger than the crys- tals, and the crystals much smaller than the pupil of the eye, so that light must be reflected from the prismatic faces of the hexagons and rhombic plates, if they have sufficiently broad faces, and that light so reflected must enter the pupil of the eye. - In this specimen and in others there are many spherical cavities, surrounded with sectors of polarised light, and also several amorphous masses of matter, round which there is also polarised light,- indicating, as all the phenomena of the crystals do, that the matter of the garnet must have been in a soft state, and com- pressed by some force emanating from these cavities. In another specimen of garnet, a large fissure in its interior is occupied with granular matter, which must have issued either from a burst cavity containing a fluid or a gas, or both; but what is very interesting, and what I have never ob- served in any other mineral, the matter has, in several places, formed circular crystals of singular beauty, some being very simple, and others very composite. St LEoNARD’s COLLEGE, St ANDREWS, December 11, 1852. : er et oe ct s 1 a a 1 Ln a Sha Nees Cha & ‘ eee ee “ ¢ 4 » ad - ; ’ ; ‘ ; va La < a (aa 2 ae ; ; % 2S I he eed ie ghd ne ada : ; ‘ Hl , h re ee -: _— , ” A - ® as ay ah e aee A St Oe er * ages”, uit oe — ‘ wee ns : TAY S Leh oe tts IA i er ee ieee ee oa AUNEMD rs 7 —_ : - ‘ i 2 ' ‘" Si 4 fy fay Panui! ad ; : af a oe ‘ aS ¥ ' * - Pir iy ree Lint ta bic, r : au 4 i ‘ : ; P t | : . 5 ; . ne OO ’ ~ ’ ’ | ; nah Bee - t a 4% hey HF \ ieee a] A +i © ‘ ; | Meee —_% ‘ - ‘ j | S ‘ di yely He . +s ; 4 j i i ‘J pe - | a A . 3 ; we rs 7 i : *, ry “ ¥ * ; . U { xX isa ; { 5 A) tae : - f 4 . ‘ rez . ‘ ¥ , , : | ‘ ~~ * ( 555) XXXVIII.--On the Production of Crystalline Structure in Crystallised Ponders, by Compression and Traction. By Sir Davip Brewster, K.H., D.C.L., F.R.S., V.P.R.S. Edin., and Associate of the Institute of France. (Read 7th March 1853.) The influence of compression and dilatation in producing the doubly refract- ing structure in solids of all kinds, whether crystallised or uncrystallised, which do not possess it, and in modifying that structure in all crystals which do possess it, has been long known; but with this class of phenomena, those which I am about to describe have no connection whatever. In the course of experiments on the double reflexion and polarisation of light . which I discovered in the chrysammates of potash and magnesia, mureaide, and other crystals, I was surprised to find that these substances could be spread out upon glass by hard pressure, like grease or soft wax, and that in the case of chry- sammate of potash and other bodies, when the powder could scarcely be distin- guished from snuff, I obtained a transparent film, exhibiting the phenomena of double refiexion and polarisation from its surface, as perfectly as if I had been using a large crystal. In subsequently repeating these experiments, and examining, under polarised light, the film thus produced by compression and traction, I was surprised to ob- serve that the streaks and separate lines of the film, as well as the film itself, had regular axes of double refraction, as if they were regularly crystallised portions of the substance under examination. These streaks and capillary lines, which were often of extreme minuteness, did not appear to consist of insulated particles merely dragged into a line, but when the substance possessed the new property in per- fection, the lines of polarised light were continuous, and the crystallographic as well as the optical axes of the particles were placed in that line. In other cases, where the experiment was less successful, the insulation of the particles was easily recognised, though the general mass of them was crystallographically arranged. In making these experiments, the natural crystalline powder, or the particles of the crushed crystal, may be placed, either upon a polished glass surface, or upon a piece of glass ground on one side. In those cases where the substance is soft, the polished surface is preferable, but when the powder is hard and considerable pres- sure necessary, it is better to place it upon the ground surface of a piece of glass, VOL. XX. PART IV. rai 556 SIR DAVID BREWSTER ON THE PRODUCTION OF as the particles are detained between its minute elevations, and submit more readily to the combined force of pressure and traction. When the powder is thus placed, I take a polished and elastic knife, and with its broad point I compress and drag the powder in a given direction, till there is the appearance of a polished surface on the compressed substance. In general, I have used both the smooth and the rough glass, and have frequently obtained results with the one, which were not given by the other. If we now place the plate of glass in a polarising microscope, with the field dark, we shall find that the streaks and lines produced by traction have, in cer- tain substances, regular neutral and depolarising axes, as if they were prismatic crystals of the substance under examination. With the chrysammate of magnesia, a red powder with specks of yellow reflected light, the phenomena are peculiarly splendid ; the natural colours of the substance, which vary greatly with the thick- ness of the streaks and films, being combined with the different tints which they polarise. As the crystals of this substance possess unusual reflexion, this pro- perty is displayed in the crystallised streaks produced by traction; and the superficial colours which they reflect, vary with the azimuth which the plane of incidence forms with the plane passing through the axis of the prism. The remarkable property which I have now described, I have found, in a greater or a less degree, in the following crystals :— Chrysammate of magnesia. Platina and magnesia, cyanuret of. of potash. ... and barytes, cyanuret of. Hydro-chrysammid. ... potassium, cyanuret of. Murexide. ... ammonia, chloride of. Aloetinate of potash. Potash, oxymuriate of. Aloetinic acid. : ... chromate of. Oxamide. Urea, nitrate of. Palmine. Sulphur. Palmic acid. Camphor. Amygdaline. Cinchonine. Tannin, pure. ... Sulphate of. Quinine, pure. Meconic acid. acetate of. Brucine, sulphate of. sulphate of. Morphia, acetate of. muriate of. Tin, iodide of, phosphate of. Cerium, oxide of. ... citrate of. Parmeline. Cacao butter. Lecanorine. Veratric acid. Indigo, red. Esculine. Theine. Silver, cyanide of. acetate of. Ammonia, oxalate of. sulphate of. Soda, chromate of. Lead, iodide of. CRYSTALLINE STRUCTURE BY COMPRESSION AND TRACTION. 557 Strychnine, sulphate of. | Mercury, oxymuriate of. acetate of. Tsatine. Soda, native nitrate of. | Alizarine. Berberine. Manganese, sesquioxide of. Mucic acid. | Lead, protoxide of. Solanine. Tungstic acid. Asparagine. Chromo-oxalate of potash. In submitting other crystals to the influence of compression and traction, I have found great numbers which do not exhibit the least trace of transparent streaks and lines, the separate particles being merely dragged into lines, and ex- hibiting only a quaquaversus polarisation. On the other hand, there is another class of crystals, whose powders or particles are forced into distinct and transpa- rent streaks and lines in which the individual particles have a quaquaversus polarisation, and no trace of a prismatic arrangement. As these crystals have a peculiar relation to those in the preceding list, I shall enumerate the most im- portant of them in the following table; that is, those in which the powder has been dragged into transparent and. continuous streaks and lines, resembling exter- nally portions of a solid body; for it is only by a comparison of the physical, or perhaps the chemical qualities of the two classes of bodies, that we can expect to explain the new property which is possessed only by one of them. Hydrate of potash, pure. Soda, acetate of. Indigotic acid. Mercury, prussiate of, Urea. see muriate of. Citric acid. se sulphuret of. Silver, nitrate of. Barytes, acetate of. Meconine. Zine, chromate of. Napthaline. ... sulphate of. Soda, nitrate of. Cobalt, sulphate of. Potash and copper, sulphate of. Magnesia and soda, sulphate of. Soda, phosphate of. Borax. As both compression and traction are necessary in producing the transparent streaks and lines in both classes of the substances I have enumerated, it became interesting to ascertain what effect was produced by each of these forces acting separately, and which of them was chiefly influential in developing the doubly refracting arrangement exhibited by the substances that possessed it. The force of compression was undoubtedly the agent in forcing the separate particles into optical contact, while that of traction drew them into a line, and tended to dilate the film in the direction of that line, and to draw its particles from each other; or overcome their attraction of aggregation in that direction. It is quite possible, too, that these forces may have exercised some influence in modifying the doubly refracting structure of the substance under examination ; but as such a question has no bearing upon our present subject, I have not at- tempted its solution. 558 SIR DAVID BREWSTER ON THE PRODUCTION OF Without expecting any very interesting result, I submitted to examination several of the soft solids which possess double refraction, such as bees’ waz, oil of mace, tallow, and almond soap. The last of these substances, though in common use, is a very remarkable one. Owing to its particles not being in optical contact, it has a fine pearly lustre, and may be drawn out into long and slender strings. Upon laying a portion of it on glass, it has a quaquaversus polarising structure, with a tendency to form circular crystals, but when it is drawn out into strings, and laid upon glass, these strings have neutral and depolarising axes, like the streaks formed by compression and traction. In the present case, it is by traction alone, that this crystalline arrangement of the particles is produced. In oil of mace and tallow, a similar effect is produced by compression and traction. With bees’ waz, the depolarising lines are still better displayed, and the effect is considerably increased by mixing the bees’ wax with a small quantity of rosin. As the preceding experiments place it beyond a doubt, that the optical or crystallographic axes of anumber of minute particles are dragged by pressure and traction into the same direction, so as to act upon light like regular crystals, it became interesting to discover the cause of phenomena which certainly could not have been anticipated from any theoretical principle with which we are acquainted. The primary force, and indeed the only apparent one exerted in these experiments, is a mechanical force; but it is not improbable that a secondary force, namely, that of electricity. may be generated by the friction which accom- panies the forces of pressure and traction. That such a force is excited with certain crystals will not admit of a doubt ; but even if it were developed in every case, this would not prove that electricity was the agent in producing the pheno- mena under consideration. In subjecting asparagine to compression and traction, I observed, upon placing it in the polarising microscope, that its particles were moving about under an electrical influence, but in no other case did the same phenomenon present itself to me. The experiments with soft solids, but especially those made with the almond soap, exclude the supposition that the electricity of friction is the cause of the crystalline arrangement of its particles; though it is not improbable that the sliding of the particles upon one another, as produced by traction, and their mutual separation, as in the case of tearing asunder mica or paper, may produce enough of electricity to have some share in giving the same direction to the axes of the particles. When a portion of almond soap is placed upon glass, the axes of its particles lie in every direction, and have no tendency to assume the crystalline arrange- ment. The forces of aggregation emanating from three rectangular axes, are not strong enough to overcome the inertia, as we may call it, arising from the natural quaquaversus adhesiveness of the substance, and from the water interposed be- CRYSTALLINE STRUCTURE BY COMPRESSION AND TRACTION. O09 tween its particles; but when the portion of soap is drawn out into a thread, these resistances to crystalline arrangement are diminished; elementary prisms, or crystals whose length is greater than their breadth, will have a tendency to place their greatest length in the line of traction, and all lateral obstruction to the play of its natural polarities being to a great extent removed, when the substance is drawn into a capillary thread the molecules will have free scope to assume their natural crystalline arrangement. The application of these views to the powders and particles of hard crystals, is not so readily apprehended; but when we consider that the pressure brings the molecules of the substance within the sphere of their polarities, and that the force of traction reduces the compressed film into separate streaks and lines, like the threads of the almond soap, we have reason to conclude, that even in hard substances the atoms. when released from their lateral adhesions, and brought into narrow lines, will assume the crystalline arrangement. In the course of these experiments, I have observed, in some cases where the crystalline arrangement was very imperfectly effected, a tendency in the atoms to quit their position, as if they were in a state of unnatural constraint, like the par- ticles of silex and manganese in certain kinds of glass which experience a slow de- composition. If this should prove to be the case, either partially or generally, which time only can shew, it will doubtless arise from the non-homologous sides of the elementary atoms having come into contact, a condition of the crystalline lines perfectly compatible with the existence of neutral and depolarising axes, and of the colours of polarised light, provided that the non-homologous sides in contact deviate from their proper position, either 90° or 180°. If we cut a plate of mica, for example, into two pieces, and combine them by turning one of them round 90° or 180°, polarised light transmitted through them perpendicularly, will exhibit the same colours as when they were in their natural position, and also the same neutral and depolarising axes. If the polarised light is transmitted obliquely, the hemitropism of the combination, as we may call it, will be in- stantly discovered by the difference of colour of the two plates. St LEONARD’S COLLEGE, ST ANDREWS, February 25, 1853. VOL. XX. PART IV. 7M ‘ . } t eer Sd Vim “teh v 4 = y £ “s ‘ ‘ ) ‘ TS arti ae Modes sas EY vue 5 ee VS Oh ee bap FW RID ME A : 1 athe ‘eit Aa ory Tey hee; ey aye es hide st ‘> Avy Cane ratohee Dig Tell (ih 2957 bre PP ier ing Sih) rite Meee heh | sar SNS aad ab if oN a Pere Ee OES fi A tua Gag? he ee ek Re nee yt) Bre cL . " hy inn OW ae Ene a Hs Re Ge ba é . Oo 5% » ga eS A, aba Reh i at, aia? Bd dae nd die 1 tie (ibis TRAD) |) ae eee a pa ee ay inieoeia ethane Tita Bey eae rag a A ; gc UNS A ehOg ahs Paria ed MOIRA T: Sey gi adh Balad geese Ry aca oN ace Nea Cal, re ob Medan ie and ea ps: Viel teulaigi ay nina “tele else as a Ai Oe eo vee ee ee kere re > such aa b ; ; ay ‘ t \ 7 Alida ° A vom, | Ae > irleeiatfal te aris bditegr jaa on ext at cbs ea a bal he's DRE (rin hie | | St eee eet ; q f ‘ ole ae nik ta eee Satchel | See eee a STARA) PA ON Sa leet A Seat ty CS es oa an ee PES e cea Wie a eae fies OAT. Lube alo . | ere tates ites) 02: , + ' Ay ef et) ae oie ead ; try atch : > ye ‘ Tat 2c Pine ea i ~ ‘ y 5 ook prt wake dyn «St. | ) ? ; wie 2 Ata ol a m4 - bores Tr A Me j ya win ti! 7" 1. “IS c3 i a . ‘ a ( 561 ) XXXIX.—On the Absolute Zero of the Perfect Gas Thermometer ; being a Note to a _ Paper on the Mechanical Action of Heat. By W1ttiaAM JoHN Macquorn RANKINE, C.E., F.R.S.E., F.R.S.S.A., &c. (Read January 4, 1853.) Temperature being measured by the pressure of a perfect gas at constant density, the absolute zero of temperature is that point on the thermometric scale at which, if it were possible to maintain a perfect gas at so low a temperature, the pressure would be null. The position of this point is of great importance, both theoretically and prac- tically; for by reckoning temperatures from it, the laws of phenomena depending on heat are reduced to a more simple form than they are when any other zero is adopted. As we cannot obtain any substance in the perfectly gaseous condition (that is to say, entirely devoid of cohesion), we cannot determine the position of the abso- — lute thermometric zero by direct experiment, which furnishes us with approxi- mate positions only. Those approximate positions are always too high; because the effect of cohesion is to make the pressure of a gas diminish more rapidly with a diminution of temperature, than if it were devoid of cohesion. As a gas is rarefied, the cohesion of its particles diminishes, not only in absolute amount, but also in the proportion which it bears to the pressure due to heat. The gas, therefore, approaches more and more nearly to the stateo f a perfect gas as its density diminishes; and from a series of experiments on the rate of increase of its elasticity with temperature, at progressively diminishing densities, may be calculated the positions of a series of points on the thermometric scale, approach- ing more and more nearly to the true absolute zero. By observing the law which those successive approximations follow, the true position of the absolute zero can be determined. Having performed this operation by means of a graphic process, soon after the publication of the experiments of M. Recnavutt on the elasticity and expansion of gases, I stated the result in a paper on the Elasticity of Vapours (Hdinburgh New Philosophical Journal, July 1849), and also in a paper on the Mechanical Action of Heat (Trans. Royal Soc. Edin. vol. xx., Part 1), viz., that the absolute zero is 274:6 centigrade degrees, or 494-28 degrees of FAHRENHEIT, or 462:28 degrees below the ordinary zero of FAHRENHEIT’S scale. VOL. XX. PART IV. 7N \ below the temperature of melting ice ; 562 MR W. J. M. RANKINE To enable others to judge of the accuracy of this result, I shall now explain the method by which it was obtained, annexing a copy of the diagram used. Let E denote the mean rate of increase, per degree, between the freezing and boiling points, of the pressure of a gas whose volume is maintained constant. Then the reciprocal of this coefficient, = > 1s an approximation to the number of degrees below the freezing point, at which the absolute zero is situated. The experimental data in the following table were copied from the memoirs of M. Recnavut on the Expansion of Gases. The numbers in the first column designate the series of experiments. The second column contains the pressures of the gases at the freezing point. The third column contains the mean coefficients of increase of pressure per centigrade degree, between 0° and 100° centigrade. The fourth column contains the reciprocals of those coefficients, with the negative sign, being approximate positions of the absolute zero, in centigrade degrees, below —" the temperature of melting ice. carbonic acid. The gases employed were atmospheric air and Pressure at Coefficient of in- oe ae eee 0° Centigrade | crease of Elasticity BY ‘ ie aan a een No. in with Temperature TE ONE Te = EBTCLS Atmospheres. =H: == E CARBONIC ACID. 1 09980 | 0-0036856 —271:33 2 1:1857 0:0036943 —270°63 3 9:2931 0:0037523 — 266:°50 4 4:7225 0:0038598 — 259-08 de 0-°1444 0-0036482 — 274-11 2. 0:2294 0:00365138 — 273°88 3. 0°3501 0-0036542 — 273°66 4. 0:4930 0:0036587 —273°32 5. 0-4937 00036572 — 273-43 6. 1:0000 0:0036650 — 27285 7s 2°2084 00036760 — 272°03 8. 2°2270 0-0036800 — 271-74 9. 2°8213 0-0036894 — 271-05 10 4°8100 0-:0037091 —269°61 I I SS SES ATMOSPHERIC AIR. ON THE MECHANICAL ACTION OF HEAT. 563 The approximate positions of the absolutezero contained in this table were laid down on the diagram, in which they are marked by crosses. The longitudinal divisions represent centigrade degrees divided into tenths; the transverse divisions, atmospheres of pressure at 0° centigrade, also divided into tenths. The positions of the crosses indicate at once the pressures in the second column of the table, and the approximate zeros in the fourth ; and the numbers affixed to them correspond with those in the first column. As the effect of cohesion is greater, and more easily eliminated, in carbonic acid gas than in atmospheric air, the determination of the true absolute zero was made from the experiments on the former gas. It will be observed that the ap- proximate positions of the absolute zero for carbonic acid lie nearly in a straight line. A straight line (dotted in the diagram) having been drawn so that it should as nearly as possible traverse them, was found to intersect the line corresponding to the zero of pressure, that is, to the state of perfect gas, at a point on the scale of temperatures 274°6 centigrade degrees below the temperature of melting ice; which point was accordingly taken as the true absolute zero of the perfect gas thermometer. So far as their irregularity permits, the experiments on atmospheric air con- firm this result, for the approximate positions of the absolute zero deduced from them, evidently tend towards the very same point on the diagram with those deduced from the experiments on carbonic acid. The values of the coefficient of dilatation and of increase of pressure, of a per- fect gas, per degree, in fractions of its volume and pressure, at the temperature of melting ice, are accordingly,— For the Centigrade Scale = 0:00364166 at 2746 1 = 0:00202314 For FAHRENHEIT’S Scale 494-98 = rd ew AIRS Th ( 565) XL.—On the Mechanical Action of Heat. By Wittiam Joun Macquorn RANKINE, Civil Engineer, F.R.S.E., F.R.S.S.A., &c. (Read January 17, 1853.) Section VI.—A REVIEW OF THE FUNDAMENTAL PRINCIPLES OF THE MECHANICAL THEORY OF HEAT; WITH REMARKS ON THE THERMIC PHENOMENA OF CURRENTS oF ELASTIC FLUIDS, AS ILLUSTRATING THOSE PRINCIPLES. (Article 46.) I have been induced to write this Section, in continuation of a paper on the Mechanical Action of Heat, by the publication (in the Philosophical Magazine for December 1852, Supplementary Number) of a series of experiments - by Mr Joune and Professor Witx1am THomson, on the Thermal Effects expe- rienced by Air in rushing through small Apertures. Although those authors express an intention to continue the experiments on a large scale, so as to obtain more precise results; yet the results already obtained are sufficient to constitute the first step towards the experimental determination of that most important function in the theory of the mechanical action of heat, which has received the name of Carnot’s Function. By the theoretical investigations of Messrs CLausius and THomson,—which are based simply on the fact of the convertibility of heat and mechanical power, the determination of their relative value by Mr Jouts, and the properties of the function called temperature, without any definite supposition as to the nature of heat,—Carnor’s function is left wholly indeterminate. By the investigations contained in the previous sections of this paper, and in a paper on the Centrifugal Theory of Elasticity,—in which the supposition is made, that heat consists in the revolutions of what are called Molecular Vortices, so that the elasticity arising from heat is in fact centrifugal force,—a form is assigned to CarnoT’s function; but its numerical values are left to be ascertained by expe- riment. The recent experiments of Messrs JouLe and Tomson serve (so far as the degree of precision of their results permits) at once to determine numerical values of Carnot’s function for use in practice, and to test the accuracy with which the phenomena of heat are represented by the consequences of the hypothesis of molecular vortices, from which the investigation in this paper sets out. VOW. XX. PART Iv. 70 566 MR W. J. M. RANKINE ON THE Sus-Section 1.—Properties of Expansive Heat. (47.) To shew more clearly the nature of the questions, towards the decision of which these experiments are a step, I shall now briefly review the fundamental principles of the theory of heat, and the reasoning on which they are based ; and the object of this being illustration rather than research, I shall use algebraical symbols no farther than is absolutely necessary to brevity and clearness, and shall follow an order of investigation, which, though the same in its results with that pursued in the previous sections of this paper, is different in arrangement. By a mind which admits as an axiom, that, in the present order of things, physical power cannot be annihilated, nor produced out of nothing, the law of the mutual convertibility of heat and motive power must be viewed as a necessary corollary from this axiom, and Mr Joute’s experiments, as the means of deter- mining the relative numerical value of those two forms of power. By a mind which does not admit the necessity of the axiom, these experiments must be viewed also as the proof of the law. This law was virtually, though not expressly, admitted by those who intro- duced the term Latent Heat into scientific language; for when divested of ideas connected with the hypothesis of a subtle fluid of caloric, and regarded simply as the expression of a fact, this term denotes heat which has disappeared during the appearance of expansive power in a mass of matter, and which may be made ~ to reappear by the expenditure of an equal amount of compressive power. (48.) Without for the present framing any mechanical hypothesis as to the nature of heat, let us conceive that unity of weight of any substance, occupying the bulk V under the pressure P, and possessing the absolute quantity of thermo- metric heat whose mechanical equivalent is Q, undergoes the indefinitely small increase of volume d V; and let us investigate how much heat becomes latent, or is converted into expansive power, during this process; the thermometric heat being maintained constant, so that the heat which disappears must be supplied from some external source. During the expansion d V, the body, by its elastic pressure P, exerts the me- chanical power PdV. Part of this power is produced by molecular attractions and repulsions; and although this part may be modified by the influence of heat upon the distribution of the particles of the body, it is not the direct effect of heat. The remainder must be considered as directly caused by the heat pos- sessed by the body, of which the pressure P is a function; and to this portion of the power developed, the heat which disappears during the expansion must be equivalent. To determine the portion of the mechanical power Pd V which is the effect of heat, let the total heat of the body, Q, be now supposed to vary by an indefinitely MECHANICAL ACTION OF HEAT. 567 small quantity dQ. Then the mechanical power of expansion Pd V will vary by the indefinitely small quantity dQ x 7G Ea This is the development of power for the expansion dV, caused by each indefi- nitely small portion dQ of the total heat possessed by the body; and conse- quently, the whole mechanical power for the expansion d V due to the whole heat possessed by the body Q, is expressed as follows :— Q55-¢¥ - ae mets pe Seine ener and this is the equivalent of the heat transformed into mechanical power, or the latent heat of expansion of unity of weight, for the small increment of volume dV, at the volume V and total heat Q. Now a part only of this power, viz.— PdV is visible mechanical energy, expended in producing velocity in the expanding body itself, or.-in overcoming the resistance of the bodies which enclose it. The remainder (@55-P) av A Say iolgteiao: lice. nae is therefore expended in overcoming molecular attraction. Molecular attraction depends on the density and distribution of the particles of the body; and is consequently a function of the volume and total heat of unity of weight. It is therefore possible to find a potential S, being a function of V and Q, of such a nature, that the difference between its two values gos corresponding respectively to two sets of values of the volume and total heat (V,, Q, and V,, Q,), shall represent the power which is the equivalent of the heat consumed in overcoming molecular attraction, during the passage of the body from the volume V, and heat Q, to the volume V, and heat Q,. The form of the expression (68) shews that this potential has the following property :— ee mee ean) St SoSr ay The integration of which partial differential equation gives the following value for the potential of molecular action :— s=/ (@t5-P)av+o@ Sf aie ens. c7g5) ? (Q) being some unknown function of the heat only, and the integral being taken as if the heat Q were constant. The heat which disappears in overcoming molecular action, during a small 568 MR W. J. M. RANKINE ON THE increase of total heat dQ, while the volume remains constant, is expressed as follows :-— 2 qHtd={ 4 a pays o(@}aQ x. ae the heat Q being treated as a constant in the integration. If we now investigate the entire quantity of heat, both sensible and latent, which is consumed by a body during a simultaneous small change of total heat dQ and volume d V, we find the following results :— Sensible heat (which retains its condition) . : : : =dQ Latent heat, or heat which disappears in overcoming molecular action 5 dQ + = dV Latent heat equivalent to the visible mechanical effect . : Pay The amount being . dQ+d.S+PdV=(1 +3) dQ+ (ov?) dV= (72.) (1+ Tp 1V+9'Q) 49.5% Toe This formula expresses completely the relations between heat, molecular action, and expansion, in all those cases in which the expansive power developed, P dV, is entirely communicated to the bodies enclosing the substance which ex- pands. (49.) The following coefficients are contained in, or deducible from it. The ratio of the cima heat at constant volume to the real specific heat :— Ky, , ==1 sprite. dVie(@Q) . 4. es The coefficient of aie heat a ee at constant heat :— dS a gikacaes 75 d 5 The ratio of the specific heat at constant pressure to the real specific heat is found as follows. To have the pressure constant, we must have (74.) dP dP EP. GS ELG Ieee Nau adig Pk eng SUE Car yeaa TP av consequently the ratio in question is dP Ker. dS, (es dO, EP d 5. (u 5 (75.) _ (aa) MECHANICAL ACTION OF HEAT. 569 (50.) In order to investigate the laws according to which heat is converted into mechanical power, in a machine working by the expansion of an elastic body, it will be convenient to use a function P= oa 4V (@= const.) of such a nature that the difference between two of its values, corresponding to dif- ferent volumes of the body at the same total heat, represents the ratio of the heat converted into power by expansion between those volumes, to the given constant total heat. I shall call this function a heat-potential. Introducing this function into Equation 72, we find, for the total heat con- sumed by a body during the increase of total heat dQ, and the expansion d V, dQ+d.8+PdV=(1+9'.@)) dQ+Qa-¥ PP Oia War hag (observing that d.B= SydQ+ Ty, aV= ( aoe) ag Pav) Let us now suppose that the body changes its volume without either losing or gaining heat by conduction. This condition is expressed by the equation 0=(14+¢'.Q)dQ+Qd.F from which we deduce the following, -d.F= tO aq Be aE which expresses the following theorem :— When the quantity of heat in a body 1s varied by variation of volume only, the variation of the heat-potential depends on the heat only, and is independent of the ‘volume. In order that a machine working by the expansive power of heat may produce its greatest effect, all the heat communicated from external bodies should be em- ployed in producing expansive power, and none in producing variations of the quantity of heat in the body; for heat employed for the latter purpose would be wasted, so far as the production of visible motion is concerned. To effect this, the body must receive heat by conduction, and convert it into expansive power, while containing a certain constant quantity of heat Q,; give out by conduction heat produced by compression, while containing a smaller constant quantity of heat Q,; and change between those two quantities of thermometric heat by means of changes of volume only, without conduction. For this purpose a cycle of operations must be performed similar to that described by Carnot; as fol- lows :— (I.) Let F, be the initial value of the heat-potential; let the body expand at the constant heat Q,, till the heat-potential becomes F,. Then the heat received and converted into expansive power is H,=Q, Fs—F,) VOL. XX. PART IV. ie 570 MR W. J. M. RANKINE ON THE (II.) Let the body further expand without receiving or emitting heat, till the : quantity of heat in it falls to Q,; the heat-potential varying according to Equation 77, and becoming at length F,. The heat converted into expansive power in this operation is Q,—2 (III.) Let the body be compressed, at the constant heat Q,, till the heat-poten- - tial becomes F,,; a quantity differing from the initial heat-potential F, by as much as F, differs from F,. In this operation the following amount of power is recon- verted into heat, and given out by conduction :— H,=Q, (Fce— Fp) (IV.) Let the body be further compressed, till the heat-potential returns to F,, its original value. Then, by the power expended in this compression alone, with- out the aid of conduction, the total heat of the body will be restored to its original amount, exactly reversing the operation II. At the end of this cycle of operations, the following quantity of heat will have been converted into mechanical power :— H—Hj—@, (3 -F)—@, @—E,) but it is obvious that the difference between the heat-potentials is the same in the first and third operations; therefore, the useful effect is simply H, —H,=(Q,—Q,) Fs Ey) while the whole heat expended is, ; 2 GES H,=Q, (Fs—F,) Hence, the ratio of the heat converted into mechanical effect, in an expan- - swe machine working to the greatest advantage, to the whole heat expended, is the same with that which the difference between the quantities of heat possessed by the expansive body during the operations of receiving and emitting heat, respectively, bears to the quantity of heat possessed by it during the operation of receiving heat ; and is independent of the nature and condition of the body. This theorem is thus expressed symbolically,— Hy Ho Effect _Q-a, H, Heat Expended = Q, ; : ‘ : ; - 79.) (51.) When a body expands without meeting with resistance, so that all its expansive power is expended in giving velocity to its own particles, and when that velocity is ultimately extinguished by friction, then a quantity of heat equi- valent to the expansive power is reproduced. The heat consumed is expressed by taking away the term representing the expansive power, Pd V, from the expression 72, the remainder of which consists merely of the variation of actual heat, and the heat expended in overcoming molecular attraction, viz. :— a it MECHANICAL ACTION OF HEAT. o71 gore s- (1+5,) 40 +2 av= ewontamnlal + (of§-P)ev This expression is a complete differential, and may be written thus :— a(Q+8)=d { Q+9(@ + (Q atg-1) fray | acy (Q being treated as a constant in performing the integration / Pd V). Its integral, Q+S, the sum of the heat of the body, and of the potential of its molecular actions, is the same quantity which I have denoted by the symbol vy in the 10th article of a paper on the Centrifugal Theory of Elasticity, and whose differences are there stated to represent the total amount of power which must be exercised on a body, whether in the form of expansive or compressive power, or in that of heat, to make it pass from one volume and temperature to another. This integral corresponds also to the function treated of by Professor WILLIAM Txomson in the fifth part of his paper on the Dynamical Theory of Heat, under the name of “ Total Mechanical Energy.” (52.) We have now obtained a system of formule, expressing all the relations between heat and expansive power, analogous to those deduced from a considera- tion of the properties of temperature, by Messrs CLausius and THomson, and from the Hypothesis of Molecular Vortices in the previous sections of this paper; but, in the present section, both the theorems and the investigations are distinguished from former researches by this circumstance;—that they are independent, not only of any hypothesis respecting the constitution of matter, but of the properties, and even of the existence, of such a function as Temperature; being, in fact, simply the necessary consequences of the following DEFINITION OF EXPANSIVE HEAT. Let the term Expansive Heat be used to denote a kind of Physical Energy con- vertible nith, and measurable by, equivalent quantities of Mechanical Power, and augmenting the Expansive Elasticity of matter, in which tt is present. (52 A.) It is further to be remarked, that the theorems and formulee in the pre- ceding articles of this section are applicable, not only to heat and expansive power, but to any two directly convertible forms of physical energy, one of which is actual, and the other potential. They are, in fact, the principles of the conversion of energy in the abstract, when interpreted according to the following definitions of the symbols. . Let Q denote the quantity of a form of actual physical energy present in a given body ; 572 MR W. J. M. RANKINE ON THE V, a measurable state, condition, or mode of existence of the body, whose tendency to increase is represented by P, a force, depending on the condition V, the energy Q, and permanent pro- perties of the body; so that P dV is the increment of a form of potential energy, corresponding to a small increment d V of the condition V. Let dS be the quantity whereby the increment of potential energy Pd V falls short of the quantity of actual energy of the form Q, which is converted into the potential form, by the change of condition d V. Then, as in Equation 69 d8$ dP cv 0 ae an equation from which all those in the previous articles are deducible, and which comprehends the whole theory of the mutual conversion of the actual form of energy Q, and the potential form of P dV, whatsoever those forms may be, when no other form of energy interferes. The application of these principles to any form or any number of forms of actual and potential energy, is the subject of a paper read to the Philosophical Society of Glasgow, on the 5th January 1853, and published in the Philosophical Magazine for February 1853. Sus-SECTION 2.—Properties of Temperature. (53.) Still abstaining from the assumption of any mechanical hypothesis, let us proceed a step beyond the investigation of the foregoing articles, and in- troduce the consideration of temperature; that is to say, of an arbitrary function increasing with heat, and having the following properties. Definition of Equal Temperatures. Two portions of matter are said to have equal temperatures, when neither tends to communicate heat to the other. Corollary. All bodies absolutely destitute of heat have equal temperatures. The ratio of the real specific heats of two substances, is that of the quantities of heat which equal weights of them possess at the same temperature. Theorem. The ratio of the real specific heats of any pair of substances, is the same at all temperatures. For, suppose equal weights of a pair of homogeneous substances to be in con- © tact, containing heat in such proportions as to be in equilibrio. Then, let additional MECHANICAL ACTION OF HEAT. 573 portions of each substance, of equal weight, and destitute of heat, be added to the original masses ; so that the quantities of heat in unity of weight may be dimi- nished in each substance, but may continue to be in the same ratio. Then, if the equality of temperature do not continue, portions of heat which were in equilibrio must have lost that equilibrium, merely by being transferred to other particles of a pair of homogeneous substances, which is absurd. Therefore, the temperatures continue equal. It follows, that the quantity of heat in unity of weight of a substance at a given temperature, may be expressed by the product of a quantity depending on the nature of the substance, and independent of the temperature, multiplied by a function of the temperature, which is the same for all substances. Let 7 denote the temperature of a body according to the scale adopted; x, the position, on the same scale, of the temperature corresponding to absolute privation of heat; %, a quantity depending on the nature of the substance, and independent of temperature. Then the quantity of heat in unity of weight may be expressed as follows:— Q=k ().7--k) : : : : : : (81.) (54.) If we introduce this notation into the formula (79) which expresses the proportion of the total heat expended, which is converted into useful power by an expansive machine working to the best advantage, the quantity &, peculiar to the substance employed, disappears, and we obtain Carnot’s THEOREM, as modified by Messrs Ciausius and THomson, viz.,—that this ratio is a function solely of the temperatures at which heat is received and emitted respectively, and is indepen- dent of the nature of the substance; or symbolically, Effect _%— te .T,—.T, | (82) Heat Expended Q, .7,—-.K (55.) Let us now apply the same notation to the formula (67) for the latent heat of a small expansion d V at constant heat, viz :— we have evidently at and consequently, the heat which disappears by the expansion d V is Qog:¢v== Leesa ae cai 941) 1721S ohn jneiyitwnc £899 from which formula the specific quantity has disappeared. Now, in the notation of Professor THomson we have y.tT—-h kK J ig) VE Teed VOL. XX. PART IV. 7Q 574 MR W. J. M. RANKINE ON THE where J is JouLE’s equivalent, and ya function of the temperature, the same for all substances, to be determined empirically ; and consequently, 1 hyp. log. ervey [Tuas 1 [tude ce Gpeceyh nati s) . : A 84.) [ude ( me Byrn tale aT e These expressions will be recognised by those who have studied Professor Taom- son’s papers on the Dynamical Theory of Heat. By introducing the value given above of the quantity of heat in unity of weight, into the formule of the preceding articles of this section, they are at once transformed to those of Professor THomson, and in particular, the formule 79 and 82 become the following :— . Lf wae Lf was Lf ude * Effect of Machine _ Ee. ae peel Heat Expended Sus-SECTION 3.—On the Hypothesis of Molecular Vortices. (56.) The use of a Mechanical Hypothesis in the Theory of Heat, as in other branches of physics, is to render it a branch of Mechanics, the only complete phy- sical science; and to deduce its principles from the laws of Force and Motion, which are better understood than those of any other phenomena. The results of the investigations in the preceding part of this section are con- sistent alike with all conceivable hypotheses which ascribe the phenomena of heat to invisible motions amongst the particles of bodies. Those investigations, however, leave undetermined the relation between tem- perature and quantity of heat, except in so far as they shew that it must follow the same law of variation in all substances. By adopting a definite hypothesis, we are conducted to a definite relation be- tween temperature and quantity of heat; which, being introduced into the formule, leads to specific results respecting the phenomena of the mutual transformation of heat and visible mechanical power; and those results, being compared with experiment, furnish a test of the soundness of the hypothesis. Thus the hypothesis of Molecular Vortices, which forms the basis of the in- vestigations-in the first five sections of this paper, and in a paper on the Centri- fugal Theory of Elasticity, leads to the conclusion, that, if temperature be mea- * It is to be observed, that in Professor Tuomson’s notation, heat is supposed to be measured by an arbitrary unit, whose ratio to a unit of mechanical power is denoted by J ; while in this paper, the same unit is employed in expressing quantities of heat and of mechanical power. MECHANICAL ACTION OF HEAT. 575 sured by the expansion of a perfect gas, the total quantity of heat in a body is simply proportional to the elevation of its temperature above the temperature of absolute privation of heat ; or, in the notation of the preceding article, Venn Hiei T= Land Cai ie)”. é : : : . . (86.) * being the real specific heat of the body. If this value be substituted for the quantity of heat Q, in all the formule, from 67 to 80 inclusive, which are founded simply on the definition of expansive heat, it reproduces all the formule which, in this and the other paper referred to, have been deduced directly from the hypothesis. In the sequel I shall apply one of these formulze to the calculation, from the experiments of Professor THomson and Mr Jour on the heating of currents of air by friction, of approximate values of the absolute temperature corresponding to total privation of heat, that the mutual consistency of those values may serve as a test of the soundness of the hypothesis, and the accuracy of the formule deduced from it. (57.) Before proceeding further, it may be desirable to point out how far this hypothesis agrees with, and how far it differs from, that proposed by Mr Hrra- PATH and Mr WateErsTon, which supposes bodies to consist of extremely small and . perfectly elastic particles, which fly about in all directions with a velocity whose half-square is the mechanical equivalent of the heat possessed by unity of weight, and are prevented from dispersing by their collisions with each other and with the particles of surrounding bodies. Let v be the velocity of motion, then ye 5778 represents the heat possessed by unity of weight, expressed in terms of the force of gravity. The expansive pressure due to such motions is found by conceiving a hard, perfectly elastic plane of the area unity to be opposed to the collision of the par- ticles, and calculating the pressure which would be required to maintain its posi- tion against them. If all the particles were to strike and rebound from such a plane at right angles, the pressure would be represented thus: ee Vl : he Me where V is the volume which contains so many particles as amount to unity of weight. But the particles are supposed to fly in equal numbers in all directions. Then if @ denote the angle of incidence on the plane sin 0d 0 Tr S,* sin6.a6 represents the proportion of the whole particles which fly in those directions which make the angle 6 with the normal to the plane. Of this proportion, again, = sinOd0 576 MR W. J. M. RANKINE ON THE the fraction cos @ only strikes the plane; while the force of the blow also is less than that of a normal blow in the ratio cos@: 1. Hence the mean force of col- lision is J? cos? Osind.a0=2 0 3 of the force of a perpendicular collision; so that the expansive pressure is repre- sented by mre tial Pal gst wy Sh AR VEL Sul & Hence, according to this hypothesis, we should have for a perfect gas pd Ae PV =3Q or the product of the pressure and volume of a mass of a perfect gas equal to two- thirds of the mechanical equivalent of its total heat. It is known, however, that the product of the pressure and volume of a mass of sensibly perfect gas is only about four-tenths of the equivalent of its total heat. The hypothesis, therefore, requires modification. By supposing the particles to attract each other, or to be of appreciable bulk compared with the distances between them, the ratio in question is diminished ; but either of these suppositions is inconsistent with the perfectly gaseous con- dition. It appears to me, that, besides this difficulty connected with the gaseous con- dition, there exists also great difficulty in conceiving how the hypothesis can be applied to the solid condition, in which the particles preserve definite arrange- ments. The limited amount of time and attention, however, which I have hitherto bestowed on this hypothesis, is not sufficient to entitle me to pronounce whether these difficulties admit of a solution. (58.) The idea of ascribing expansive elasticity to the centrifugal force of vortices or eddies in elastic atmospheres surrounding nuclei of atoms, originated with Sir Humppry Davy. ‘The peculiarity of the view of the hypothesis taken in this paper consists in the function ascribed to the nuclei or central physical points of the atoms, which, besides retaining the atmospheres round them by their attraction, are supposed, by their actions on each other, to constitute the medium which transmits radiant heat and light; so that heat is radiant or ther- mometric, according as it affects the nuclei or their atmospheres. In this form the hypothesis of Molecular Vortices is not a mere special suppo- sition, to elucidate the theory of expansive heat, but becomes connected with the theory of the elasticity of matter in all conditions, from solid to gaseous, and with that of the transmission of radiations. I have already investigated mathematically the consequences of this hypo- thesis by two different processes, which are necessarily somewhat complicated. MECHANICAL ACTION OF HEAT. 577 When the question, however, is confined to the relations between tempera- tures and quantities of heat, a more simple process may be followed, analogous to that which has been applied in the preceding article to the hypothesis of Mole- cular Collisions. If a mass of elastic fluid, so much rarefied that the effect of molecular attrac- tion is insensible, be entirely filled with vortices, eddies, or circulating currents of any size and figure, so that every particle moves with the common velocity 2, then, if the planes of revolution of these eddies be uniformly distributed in all possible positions, it follows, from reasoning precisely similar to that employed in the preceding article, that the pressure exerted by the fluid against a plane, in consequence of the centrifugal force of the eddies, has the following value in terms of gravity :— Sa te AO ME eo eA EC ae Ss or two-thirds of the hydrostatic pressure due to the velocity of the eddies w; V being, as before, the volume occupied by unity of weight. It is, however, reasonable to suppose, that the motion of the particles of atomic _ atmospheres does not consist merely in circulating currents; but that those cur- rents are accompanied with a certain proportionate amount of vibration,—a kind of motion which does not produce centrifugal force. To these we have to add the oscillations of the atomic nuclei, in order to obtain the mechanical equivalent of the whole molecular motions; which is thus found to be expressed for unity of weight by boo = Re A DRY, wy Ts atey e Sep k being a specific coefficient. Hence it follows (denoting a8 by N), that the ex- pansive pressure due to molecular motions in a perfect gas, is equal to the mecha- nical equivalent of those motions in unity of volume multiplied by a specific constant Babee s monda tala Gelert, fi... S-oxcexiggy The coefficient N has to be determined by experiment; its value for atmo- spheric air is known to be between 0°4 and 0°41. In order to account for the transmission of pressure throughout the molecular atmospheres, it is necessary to suppose them possessed of a certain amount of inherent elasticity, however small, varying proportionally to density, and inde- pendent of heat. Let this be represented by h = then P= OQ + ~ Sa ree | ak (O05 is the total pressure of a perfect gas. VOL. XX. PART IV. 7R 578 MR W. J. M. RANKINE ON THE Equilibrium of heat and pressure between portions of two different perfect gases in contact requires that the pressures independent of heat, and the pres- sures caused by heat, shall separately be in equilibrio. Let the suffixes @ and 6 be used to distinguish quantities relative to two different substances in the per- fectly gaseous condition. Then the first condition of equilibrium is expressed as follows :— (+) (a= (+) (ey > tal) Oe oe ee that is to say, the densities of two perfect gases in equilibrio are inversely propor- tional to the coefficients of elasticity of their atomic atmospheres. The second condition is expressed as follows :— (8) «= Ao which, being taken in connection with the first condition, gives F9) @:-=(GV)O 0 Wes Now by Equation 90, we have N gh 'g z Oe se ie L Hence the condition of equilibrium of heat between two perfect gases is (=) @ = (FS) Os ui: o ah consequently, temperature may be measured by the product of the pressure and vo- lume of a perfect gas, divided by a coefficient, which is proportional to the volume of the gas at a standard pressure and temperature. Temperatures thus measured are reckoned from the point known as the zero of gaseous tension, or absolute zero of a perfect gas thermometer, 274°-6 cen below the temperature of melting ice. Let V, denote the volume of unity of weight of a perfect gas, at a standard pressure P,, and absolute temperature 7,; then any other absolute temperature has the following value :— PV 7; a To P, Vv, — PV, (N Q+h) . . . . . (94.) while the absolute temperature of total privation of heat is h K=T ><> 94 A. T PV, ( ) Hence it appears that quantity of heat in unity of weight bears the following relation to temperature,— Q=4@V-= oe ae MECHANICAL ACTION OF HEAT. 579 in which, if we substitute the symbol of real specific heat, Pavia Coe eee 8) we obtain the formula already given (86) for the relation between heat and tem- perature.* (59.) The introduction of the value given above of the quantity of heat in terms of temperature, into the formula 67, gives for the latent heat of a small expansion d V at constant temperature (r= 0) av CORE cco Rees aoe.) The formule 79 and 82, for the proportion of heat rendered available by an expansive engine working to the greatest advantage, becomes cote Sci ih GON Ala atc i ois anh OE) or the ratio of the difference between the temperatures of receiving and emitting heat, to the elevation of the former temperature above that of total privation of heat. This is the law already arrived at by a different process in Section V. of this paper. When the same substitution is made in Equation 80, which represents the total energy, whether as heat or as compressive power, which must be applied to unity of weight of a substance to produce given changes of heat and volume, the following result is obtained :-— d.¥=dQ+d.S= { & rf eee fT dV lar 2 +{-mF-P lav f =a. {tr+f(7) (c-»F.-1) feav} Le (Oo) As it cannot be simplified, it is unnecessary here to recapitulate the investi- gation, which leads to the conclusion that the functions f(7) and /’ (7) have the following values :— 2 2 f()=4N (hyp. log. 7 + —) 5 f" ()=kN (F-5) ne In sar ieg onal We have thus reproduced Equation 26 of the paper formerly referred to, on the Centrifugal Theory of Elasticity. . The coefficient of the variation of temperature in the first form of Equation 99 is the specific heat of the substance at constant volume. Denoting this by Ky, the formula becomes d.v=K,.dr+{ (rn) SP hav eee (100) * See Appendix, Note A. 580 MR W. J. M. RANKINE ON THE Sup-Secrion 4. Thermic Phenomena of Currents of Elastic Fluids. (60.) When a gas previously compressed is allowed to escape through small apertures, as in the experiments of Mr Joute and Professor THomson, and has its velocity destroyed entirely by the mutual friction of its particles, without im- pediment from any other substance, and without conduction of heat to or from any other substance; then its condition is expressed by making d.¥ =0 that is to say, 1 CP2, dP -dr=g- fr. —— —«5)av ha hiecane If we assume (as is really the case in the experiments) that the specific heat of the gas at constant volume does not sensibly vary within the limits of the experiments as to temperature and volume, so that Ky is sensibly constant, and also that the variation of temperature is very small as compared with the absolute temperatures, then we have the following approximate integral :— 1 Vag, bo Eke. Yed P ate late (G3) av—f 7 av} ga ne which represents the cooling effect of an expansion from the volume V, to the volume V.. If it weré possible to obtain any substance in the state of perfect gas to be used in experiments of this kind, the first integral in the above expression would disappear, because, for a perfect gas, dP _P ie ir and as the other term is negative, the result would be a slight heating effect. As no gas, however, is perfect, and as a always exceeds = the mode of reducing the experimental data is to calculate the value of the first term, which represents the effect of cohesion, from the known properties of the gas, to subtract from it the actual cooling, and from the remainder to compute values of x, the tempera- ture of absolute privation of heat, according to the following formula :— dL, SAGE ial aa? (G->)av-(-a9) pe ul Ye ties Ge ola tuilyie Sea ined oR GRE Ke vy, aT When the gas is nearly perfect, as in the case of atmospheric air, it is unne- cessary to take into consideration its deviation from the perfect condition in com- puting the integral in the denominator; whose approximate value is found to be MECHANICAL ACTION OF HEAT. 581 W. : Ro - hyp. log oe =N - hyp. log vt nearly (7 being nearly constant), and K, nearly = k. The value of the integral in the numerator is found as follows :— The Centrifugal Theory of Elasticity indicates that the pressure of an imper- fect gas may be represented by the following formula :— Vi A A, =)= $A |. 1 2. (004) where V, is the volume in the perfectly gaseous state, at a standard pressure P,,, and Polis temperature 7,, and A,, A,, &c., are a series of functions of the ve sity, to be determined empirically. prom this formula it is easily seen that ge PaP, y{— a0 4 “ah + &. } mae ss! > os, Mes(EOS:) T 7 1 email oe Ge Ore = Ne so that the first term in the numerator of the expression (103) has the following value :— dP _P Pao ee NO BO Ae aS. G =)av eco: Paves [Favs de. } - 106.) in which an = N7, nearly. Vv In order to represent correctly the result of M. Recnavutt’s experiments on the elasticity and expansion of gases, it was found sufficient to use, in the for- mula for the pressure (104), the first three terms; and the functions of the den- sity which occur in these terms, as determined empirically from the experiments, were found to have the following values, in which the unit of volume is the theoretical volume of unity of weight of air under the pressure of one atmosphere, at the temperature of melting ice,* and the values of the constants are given for the centigrade scale. ane ; ~=a eM : : : - (107.) Com. log b = 3°8181545; Com. log a = 0:3176168. Hence it appears that the integrals in the formula (106) have the following values :— vo A ILM 23 ; 2 Vv, A 5 10 a T 1\ % if yd V=20.. (<7) A (7) . (107 A.) Vv, Vi in which the common logarithms of the constants are * This unit of volume is greater than the actual volume of air, under the circumstances described, in the ratio of 1:00085 to 1. VOL. XX. PART IV. 7s 582 MR W. J. M. RANKINE ON THE Com. log 25 = 21101845 ; log 5” . “= 3-4017950; To a and these values suit any scale of temperatures. In calculating, for use in these formule, the densities = from the observed pressures, it is sufficiently near the truth, in the case of air, to use the approxi- mate equation \ ie: = - P (in atmospheres). The common logarithm of r,, the absolute temperature of melting ice, for the centigrade scale, is 24387005. The constant N for atmospheric air is 0:4 nearly; therefore Com. log (N x hyp. log 10) = 1:9642757. _ The following, therefore, is the approximate value of the formula (103), to be used (with the numerical constants already given) in reducing the experiments of Mr Jouve and Professor THomson on atmospheric air, so as to obtain approximate values of the absolute temperature of total privation of heat :— K= { Nis; (~ 5 (=) ee : P*)—2(%) " Ay; })) (as) } T -- N hyp. log 10 x A. com. log = : : : : > 0s In using this formula, the mean absolute temperature should be taken as the value of r. The following table shews the values of the quantity x, computed from ten mean experimental data, taken respectively from the first ten series of experi- ments described in the recent paper of Messrs JouLE and Tuomsov, in the supple- mentary number of the Philosophical Magazine for December 1852. The tempe- ratures in the table, for the sake of convenience, are reduced to the centigrade scale, because that scale has been used throughout the previous sections of this paper. The final pressure in each case was that of the atmosphere. 583 MECHANICAL ACTION OF HEAT. Se ee a ae ‘é FL-Z If 86-1 ZL-0 Wer 9:36 18-91 GIT { ee ee ure, ‘¢ 8G5-G 696-0 C8e-1 eF-0 36-6 9-G6G 13-8 9-¢ { pare UeoT ZO LT Z9-0 66-0 18-0 FB 6-363 F081 oie { Ee ue uvoy €89-1 &F-0 99-0 86:0 ¥68-1 £366 L8-L1 FI { Rae aS a“ wea d CEE. 62-1 18-G 26-0 OF-F F616 1Z-G eI is i ea oe ueayy d 180:4 81-1 81-G 00-1 IL-F 0-812 68-¢ F-8 e 18. ate Jo uvoyy d. 60-6 £6-0 6F-1 92-0 50-8 1-18 6S-L1 9.¢ Fe te chee MASSE ‘squountied 1-1 88-0 QT 18-0 86-F G-198 TELL ¥-9 { : pee ee . tod. 80-1 BF-0 02-0 - 86:0 $93 9-GF8 IT-TL — | ‘poyou yon {" pa ee mee T f d 8-1 F6-0 OL-T 94-0 19-2 ¥-066 11-91 -poqou ONT { By OMIT ad jo uvoy ‘apeastueg : ' ; oprisijue, ‘apeistquag ‘soroqdsouy ‘epeaSiqueg “puooes ‘yeayy JO UOT]eATI f : ‘© aanyereduie aod sayout “‘SLNAWIUGA XT T2107, 70 srneeeteae douereBr(T ca tanto ‘Surjoog ur rai aqnjosqy at ‘ganyereduray, | orqno ut ett 10 UAAWAN GNV salugg eynposqy oy} “% Jo Senne Tenpy Tent [eur ary Jo AyWuend son[e@A oyeunxoaddy BEV IO) 584 MR W. J. M. RANKINE ON THE Professor THomson and Mr Jou.e have expressed the opinion, which is un- doubtedly correct, that those experiments in which the largest quantities of air were used were the least liable to error from disturbing causes, such as the con- duction of heat. Now it may be observed in the preceding table, that the calculated values of k are generally greatest, and the discrepancies amongst them least, for the experi- ments in which most air was used. To illustrate this, the results of the last eight series are arranged below in the order of the quantities of air employed. Cubic inches per second, 1:4 2°8 56 56 6-4 8-4 11:2 11:2 Values of kK, . . . . 1683 1-762 2:09 2:228 151 2:087 2:adaed4 It is further to be remarked, that the discrepancy between the highest and the lowest of the values of x is 2°345 — 1°08 = 1°:265 centigrade: a quantity which corresponds to a difference of less than one three-hundredth part in computing the proportion of heat converted into mechanical power by any or- dinary expansive engine, according to the formula (98), which has been deduced from the hypothesis of Molecular Vortices. The experiments, therefore, may be considered as tending to prove, that the formule deduced from this hypothesis are sufficiently correct for practical pur- poses; and also as affording a strong probability that the principles to which it leads are theoretically exact, and that the temperature of absolute privation of heat is a real fixed point on the scale, somewhat more than two centigrade de- grees above the absolute zero of a perfect gas-thermometer (which is, of course, an imaginary point); that is to say, about 2724 centigrade degrees, or 49034 degrees of FAHRENHEIT, below the temperature of melting ice. If these conclusions be correct, it follows, that when the temperatures T, and T,, between which an expansive engine works, are measured from the ordinary zero points of the centigrade and of FAHRENHEIT’s scales respectively, the follow- ing are the utmost proportions of the total heat expended which it can be made to convert into mechanical power :— I T, = T, For the centigrade scale, T2795 | j : . . (109.) For FAHRENHEIT’S scale _T,-T, ; > T+ 458h In the fifth section of this paper, where a comparison is made between the actual duty of theCornish engine at Old Ford, as determined by Mr WicksTEEp, and the greatest possible duty which could be obtained from a given quantity of heat by a theoretically perfect engine working between the same temperatures, the constant « is treated as being so small that it may be neglected in practice. MECHANICAL ACTION OF HEAT. 585 If the value of « is really 2°:1 centigrade, as computed above, the calculated maxi- mum theoretical duty in Section V. is too small by about one one-hundred-and- ninetieth part of its amount,—a quantity of no practical importance in such cal- culations. (61.) It may be anticipated, that when Mr Joute and Professor Tomson shall have performed experiments on the thermic phenomena exhibited by air in more copious currents, and by gases of more definite composition, and more simple laws of elasticity, much more precise results will be obtained. When a gas deviating considerably from the perfectly gaseous condition, or a vapour near the point of saturation, is employed, it will no longer be sufficiently accurate to treat the specific heat at constant volume as a constant quantity, nor the cooling effect as very small. It will therefore be necessary to employ, for the reduction of the experiments, the integral form of equation (99); that is to say, O=ave=a{ hr+&Ne«(hyp.logr + 2) + +(@-of -1)f Pav} =h(n—n) +a f'(rg,-P)av 4 dP k fe? fs cedV—uN(a- < + ahyp. log ) } be octsiF ucoultOn (62.) Preliminary to the application of this equation, it is necessary to deter- mine the mechanical value of the real specific heat k. Supposing the law which connects the pressure, density, and temperature of the gas to be known, it is suf- ficient for this purpose to have an accurate experimental determination, either of the apparent specific heat at constant pressure for a given temperature, or the velocity of sound in the gas under given circumstances. First, let us suppose that the apparent specific heat at constant pressure is known. The value of this coefficient (Centrifugal Theory of Elasticity, art. 12) is 2) K, a+ —o{ Xe Vo De ane S | = EET | ~a¥ In order that the lower limit of the integral may correspond with the condition of perfect gas, it is convenient to transform it into one in terms of the density. Let D be the weight of unity of volume, then ad? P Di 7b ar dV= — mee op ARM tgs Sa hata ee If, then, we have the pressure of the gas under consideration expressed by the the following approximate formula :— VOL. XX. PART IV. (heat 586 MR W. J. M. RANKINE ON THE p= Hate * sen The following will be the values of the functions of the pressure which enter into the above equation :— EPI Py Nhat) lay hes B P,V Oa! BV 12 e? 2 w PP yen ea TR pope 1c pam AS ga > [paige OP ate Joa: Be es era ia A dae ee aeWe TBD) oP bie Tai Tg: = qarna (11 B,) (i) (8) LOREID EPCS aoe _aP *OOPiirm ye egal Das a ea aaa adv T, LL ee Uae ee ek To illustrate the application of these formule, let us calculate the difference between the real specific heat, and the apparent specific heat, at constant pressure, of carbonic acid gas, at the temperature of melting ice, and at the density which, if the gas were perfect, would correspond to a pressure of one atmosphere at the temperature of melting ice. Let this density be denoted by D,, and its reciprocal by V,. As the constants have been deduced from M. Reanautt’s experiments, the calculations will be made in French measures and for the latitude of Paris. The actual density of carbonic acid at 0° centigrade, and under one atmosphere of pressure, exceeds the theoretical density, in the perfectly gaseous state, in the ratio of 1:0065 to 1 nearly. Hence the height of a homogeneous atmosphere of actual carbonic acid at 0° centigrade being. : : : 5225°5 metres | the corresponding height in the state of perfect gasisP,V, = 52595 ,, and ue = 19°53 metres per centigrade degree = 62°84 feet. The functions which express the influence of density on the deviation of car- bonic acid gas from the perfectly gaseous state, have the following values :— D D be D,: Ae. D,: when Com. log b = 3:1083932 ; Com. log a = 0-3344538 bi (111 C.) DA, =; De 4b .D. 2) ee D d D =26 cabs (3 aD Mee cena 17 For the purposes of a first approximation, we may assume that the value of x MECHANICAL ACTION OF HEAT. 587 already found is sufficiently near the truth, viz., 2°°1 centigrade; so that, in the present instance r—x=272°'5 centigrade. Then we find the following results when r=7,, and D=D,; Metres. Feet. T—K Py Vo . “= per centigrade de ree, : 7 : ; 0°145 0:48 HK 7 P g g ; é (tT — K) ox = 4s _ 3 : : Ube ; 0-150 0:49 Sum = K, — & = excess of apparent specific heat at constant volume PE Pp above real specific heat, : : : A 3 0:295 0:97 cal (7 — kK) d 7 = difference between apparent specific heats at con- TV stant volume and at constant pressure, - 19°565. 64:19 K, —k = excess of apparent specific heat at constant pres- sure above real specific heat, : ; . 19:860 65:16 | 2 of the above quantities are of course the corresponding quantities for FaHREN- HEIT’S scale. ; Secondly, If the velocity of sound in the gas is given, let this=w. Then we know that Bee ene ais ah dae coun 2c ye nC in which dP_ Ped AD 1d. A, =P, V, = + ae = un iene ae aT A) So that from the velocity of sound we can calculate the ratio of the specific heats at constant pressure and at constant volume. Let this ratio be denoted by y¥, and let K, =k +c; K, =k +e; then : Sear ce _¢—vV¥e ittem ep é amd Ry y—1 in which ¢ and ¢ are to be calculated as above.* (112 B.) (63.) In using the formula (110) for a gas whose pressure is represented by the formula, aA a A Pantpt{ 7 + A, — =} the integrals may be transformed so as to be taken, with respect to the density, as in the preceding article. Thus we obtain * See Appendix, Note B. 588 MR W. J. M. RANKINE ON THE 9 : | ye irae. Me s (*--P)aD=-P, Vv a{? pad — Pap} dt D2 aP, Wal aP Pav= i oa D=—P,V, (= byp. tally ) eye For carbonic acid, the first of these formulze becomes simply \ (2 a >) _ 5 ( ES } Bey te 'e See ad and the second, .. » CEIBSA,) 1 D af) D +P Vo | = hyp. log ine ae -—%) } tLAsGow, 27th December 1852. AP PEN DIX. Note A (to Article 58). Since this section was read, the theoretical views relative to the relation between heat and temperature contained in it and the ' previous sections of this paper, have received a strong confirmation by the publi- cation by M. Recnavtt of the fact, that he has found the specific heat of air to be sensibly constant at all temperatures from —30° centigrade to +225°, and at all pressures from one to ten atmospheres (Comptes Rendus, 18th April 1853); so that equal lengths on the scale of the air thermometer represent equal quanti- ties of heat. Note B (to Article 62). Until very recently, there existed no exact experi- mental determination of the specific heat of any gas. The specific heat of air at constant pressure, as compared with that of water, was calculated theoretically in the previous part of this paper, from JouLe’s equivalent and the velocity of sound, and found to be 0°24. This value has since been confirmed very closely by Mr Jouun’s experiments, whese mean result was 0°23, and still more exactly by M. Reenavyr’s experiments, already referred to, which give the value 0°2379. The following table shews the results of the application of the formule of this paper to the specific heats of five different gases at constant pressure, selected from M. Recnavut’s table (Comptes Rendus, 18th April), as being those in which the velocity of sound can be computed, and has been determined experimentally. The table shews also a comparison of the calculated and observed velocities of sound. This table appeared originally, in French measures, in the Philosophical Magazine for June 1853: the metres are here reduced to feet. Kp, Ky, and Ky, are expressed in feet of fall per centigrade degree. Kw (JOULE’s equivalent) = 1359°6. MECHANICAL ACTION OF HEAT. 589 EXPERIMENTAL Data. THEORETICAL RESULTS. VELOCITY OF SOUND aT 0° CEnT. = AOS cocoa eae a K, |Kp-t-K [By Theory,| °Y OPse™ REGNAULT.| REGN. P Ee Cay v pa ypPy eneory:| vation. Observers. a Wenn! aren 0 ween, acres aaron pene eee { 26214:4 |0-2379 | 330°6| 96:0 | 234:°6 |1:-4094| 1090-4 |1090°5 | Bravais & Martins. 1090-1 | Mout & Van Berk. Oxygen, . . | 23710°4 6-2182| 303-2| 86-8 | 216-4 |1:-4014/1036-4 | 1042-3 | Durone. Hydrogen, . |378819-0|3°4046 |4731-0 |1388-0 |3343:0 [14150 | 4153°3 |4165-1 | Dutone, Carbonic oxide, | 27097-8 |0:2479 | 344:5| 99-25)! 245-25 |1-4047 | 1106-8 | 1107-0 | Dutone. Carbonic acid, | 17144°7 |0:2169| 300-7| 64:2 | 236-5 |1:2714| 837-55} 858-28) DuLone. The real specific heat of carbonic acid gas is 235°5 feet of fall per centigrade degree. That of the other gases does not differ from the apparent specific heat at constant volume by an amount appreciable in practice. VOL, XX. PART IV- 7U 591 XLI.—On Mitric Acid as a Source of the Nitrogen found in Plants. By Greorce Witson, M.D. (Read 4th April 1853.) The source from which plants obtain nitrogen, which is now recognised as one of their most important elements, has, from the first recognition of its importance, been matter of dispute. Latterly, however, chemists and physiologists have pretty unanimously come to the conclusion, that a large (perhaps the largest) part of the nitrogen of vegetables is derived from ammonia; whilst much discus- sion has been carried on as to the question, Is any part of their nitrogen yielded by nitric acid? The most able advocate in this country of the claims of ammonia is Dr Gre- cory. The most able advocate of the claims of nitric acid is Professor JoHnsTon of Durham, and the opposite conclusions to which accomplished chemists like © these have come in reference to the point in dispute, have perplexed botanists, who know not which view to prefer. The extent to which they are pressed by this dilemma, has been so strongly represented to me by Dr Batrour, that I have engaged to bring the subject, as I now do, before this Society. I shall sedulously avoid discussing the question in a polemical spirit; and, as the shortest and most satisfactory way of doing justice to the rival views, I shall select Dr Grecory’s clear and concise statement, as representing the opinions of those who deny that nitric acid is part of the food of plants; and then proceed to state what appear to me conclusive proofs that nitric acid does supply plants with nitrogen. Dr GreGory writes thus:—‘ Let us now attend to the nitrogen of plants. This, as already stated, is supplied to wild plants entirely by the air, and, so far as we know, only in the form of ammonia. Some authors have held that nitric acid furnishes nitrogen to plants, and that this acid is formed in the air by thunder-storms, and carried down by the rain. And they point to the occur- rence of nitric acid in springs in proof of this. Now it is true that nitric acid is formed in thunder-storms, but in very minute quantity, whereas ammonia is, and must be, present in the air at all times. Indeed there is reason to believe that the nitric acid of storms is produced by the oxidation of the ammonia of the air, as in nitrification, where ammonia is oxidised into nitric acid and water NH,+0,=NO,,3 HO; so that even if nitric acid did yield nitrogen to plants, that nitrogen would be derived from ammonia. This would account, too, for the small amount of nitric acid formed. For if it were produced_by the action of elec- tricity on the nitrogen and oxygen of the air, there seems to be no reason why it VOL. XX. PART IV. ix 592 DR GEORGE WILSON ON NITRIC ACID should not be formed in very large quantity; while ammonia forms less than one-10,000th of the air, perhaps much less. Nitric acid is only found in springs where decaying organic matter is near them, as in towns, and is formed from the ammonia produced in their decay, by the same process as in nitrification. Besides, while we have no proof that plants decompose nitric acid, which it is certainly possible they may do, we know that many plants, such as tobacco and sunflower, actually produce nitric acid, or, at least, do not destroy that which enters them.’* Thus far Dr Grecory. I at once concede to him that plants are largely in- debted to ammonia for the nitrogen found in them; and in support of the belief that they are also indebted to nitric acid for their nitrogen, I adduce the follow- ing proofs. Firstly, The production of nitric acid in the atmosphere during thunder- storms, is a certain, not a questionable fact ; and the scale on which it is pro- duced is such as to necessitate its recognition as a portion of the azotised food of plants. That this should have been questioned is perhaps not strange, for the newly-discovered truth that ammonia is generally present in the air, could scarcely fail to throw into temporary oblivion the equally important truth that nitric acid is generally present there also. The name of the great living chemist LiresieG is identified with the one discovery, and the name of the great dead chemist CAVENDISH with the other; and we must not grudge that greater interest should be felt by most in the doings of the living philosopher. But assuredly it is not necessary to set the two truths against each other, as if they were mutually in- compatible, or in any respect contradictory. On the other hand, I believe that they are complementary, and form an essential and manifest part of that harmo- nious adjustment which we everywhere perceive guarding plants and animals against imperfect nourishment or decay. In the year 1781, CAVENDISH addressed himself to the task of answering this question, among others, “ Why does the passage of an electric spark through a confined portion of air, cause a diminution in its volume?”+ ‘He did not give a categorical reply to this question till 1785, when he published his discovery that a mixture of two measures of nitrogen and five measures of oxygen can be entirely converted into nitric acid, by sending a succession of electric sparks through it.{ He had observed the fact, however, in 1781, in the course of the famous experi- ments which led to the discovery of the composition of water.—a truth to which I refer, because an impression is prevalent, that the conversion of a mixture of nitrogen and oxygen into nitric acid by the electric spark, can only be effected with great difficulty, whereas the undesired and unintended production of this acid, in trials instituted with a totally different object in view, was the chief * Grecory’s Organic Chemistry, Third Edition, p. 466. Phil. Trans., 1784, p. 119, + Ibid, 1785, p. 372. p + »P AS A SOURCE OF THE NITROGEN FOUND IN PLANTS. 593 cause of the delay which attended the announcement that water is not a simple body. CAvVENDISH’s later experiments were repeated by a Committee of the Royal Society at his own request, and with entire success ;* and if any one is slow to repose faith in chemical experiments made in 1785, let me remind him that Farapay has shewn that every time a friction electric machine is in action, the truth of CAVENDISH’s observations may be proved, by no more complex device than the stretching of a piece of paper wetted with solution of potass, across the interval separating two surfaces, between which electric sparks are passing. The potass is quickly changed into nitrate of potass.t Resting upon these observations of CAVENDISH and Farapay, I urge the con- clusion, that every lightning flash must convert a portion of the air into nitric acid ; and that in tropical regions where thunder-storms prevail, this acid must be produced largely and almost constantly. Secondly, As for the proposition that the ammonia of the atmosphere is con- verted by simple oxidation, as in the process of nitrification at the surface of the earth, into nitric acid, I might leave~it unconsidered, for my concern is simply with nitric acid, not with its source. |! am quite prepared to admit the probabi- lity of atmospheric ammonia undergoing conversion into nitric acid; for although one condition essential to nitrification in the soil, namely, the presence of an alkali or alkaline earth is wanting, yet, from what is known of the intense oxid- ising power of ozone, we may well believe that when it is developed in the air, as it so certainly and frequently is, it will compel the conversion of ammonia into nitric acid. It will presently, indeed, appear, that, from the recent researches of Barrat, it is probable that nitric acid is generated in the atmosphere at the expense of ammonia. If this, however, be the case, then we must acknowledge that, in addition to thunder-storms, a force is constantly at work in the air pro- ducing nitric acid; and further, that this force is constantly removing from the atmosphere the ammonia on which plants are supposed to be solely dependent for nitrogen. No data exist from which we can compute, with even an approximation to accuracy, the amount of nitric acid produced by thunder-storms all the world over. It is certainly, however, considerable, as compared with the amount of ammonia in air, and with the amount of nitrogen required by plants. It is further uncertain how far temperate regions profit by the nitric acid developed by the storms of tropical latitudes; but from the known effects of the winds, and of the diffusive force of gases, in spreading through the atmosphere substances added to one part of it, we cannot doubt that when the heavy rains which so frequently follow thunder-storms, do not at once transfer to the earth the nitric acid which they have produced, it will be conveyed, either free or combined, to immense distances from the spot where it was developed. But upon * Phil. Trans., 1788, p. 261. + Electrical Researches, vol. i., pp. 90, 91. 594 DR GEORGE WILSON ON NITRIC ACID this point I do not dwell; for I am content with the alternative conclusion, that the nitric acid of thunder-storms either descends at once to the earth, and feeds the most luxuriant vegetation known to us; or that it is diffused through the en- tire atmosphere, and is available for the nutrition of the plants of all lands. Thirdly, Rain-water is often found to contain nitric acid in combination with different bases. The most recent observations on this point with which I am acquainted, are those of M. Barrau, communicated to the French Academy, and approved by a committee of that body. If Barrat’s results are confirmed, and are not found to be exceptional, they will compel us to acknowledge a much larger proportion of nitric acid, as normally present in the atmosphere, than is generally imagined. His researches were made on the water collected in the rain-gauges of the Observatory of Paris in 1851 and 1852. The following are his general conclusions :— “1°. During one year, reckoning from July 1, 1851, to June 30, 1852, there fell at Paris a quantity of nitrogen in combination, equal to 20:04 lbs. avoirdu- pois to the English imperial acre; namely, 11:13 lbs. in the condition of nitric acid, and 8°91 lbs. in the condition of ammonia.* «2°. The quantity of ammonia which fell during that period amounted to 12:29 Ibs. to the acre. « 3°. The quantity of anhydrous nitric acid which fell during the same period amounted to 41-24 Ibs. to the acre. | « 4°. The quantity of ammonia diminished in the months during which the quantity of nitric acid increased. «5°. The quantity of nitric acid increased whenever the weather became stormy. «6°. During the months only of February, March, April, and June, the quantity of nitrogen in the form of nitric acid, was a little less than the quantity of nitrogen in the form of ammonia.’’+ These observations apply to rain-water collected in the neighbourhood of a great city, and do not admit of direct comparison with the purer rain-water of the open country; but they are very remarkable, not merely as shewing that rain brings down nitric acid as well as ammonia, but that, in certain places at least, it contains more nitric acid than ammonia. And although a given weight of ammonia contains three times the amount of nitrogen which the same weight * There is some mistake in Barrat’s numbers, for the statements in the first paragraph do not agree with those in the second and third; as the numbers, however, for nitrogen are calculated from the observed quantities of nitric acid and ammonia, the figures representing these are assumed as the correct ones. If so, the quantity of ‘‘ nitrogen in combination” is equal to 20°81 lbs. per acre; that of the nitrogen in nitric acid is 10°69 Ibs.; and that of the nitrogen in ammonia, 10°12 lbs. These, ac- cordingly, are the numbers which should appear in the first paragraph of Barrat’s conclusions. + Comptes Rendus pour 27 Septembre 1852, p. 431. AS A SOURCE OF THE NITROGEN FOUND IN PLANTS. 595 of nitric acid does; yet, as in the numbers I have quoted, the weight of acid exceeds that of alkali three and a-half times, it appears that, so far as we have quantitative observations on the matter to refer to, a larger amount of nitrogen is offered to plants in rain-water, in the form of nitric acid, than in that of ammonia. I have separated the question of the occurrence of nitric acid in rain-water, from that of its development in the atmosphere by oxidation, and by electricity ; because it is not certain that the whole of the nitrates found in rain-water have been produced by a process like that of nitrification, or by the action of lightning- discharges on the air. Since rain-water is found to contain common salt, lime, magnesia, and the like, which have been raised into the atmosphere from the earth, or from the bodies of water at its surface, we cannot refuse to credit that nitre may be elevated in the same way. I might go further, for attention has long been directed to the fact, that there isa marked loss during the evaporation of solutions of common nitre, in consequence of that salt, although not volatile in the dry state, undergoing volatilisation along with the vapour of water. This is a secondary point, but it is important, as shewing that, apart altogether from oxidation, and from thunder-storms, there is a source from which the atmosphere . everywhere may receive compounds of nitric acid. Fourthly, \t has been known for more than a century, that many springs contain nitrates. Fifthly, % is now universally admitted, that wherever nitrogenous vegetable or animal matter is exposed to the air along with alkaline bases, ammonia is developed, and then oxidised into nitric acid, which combines with the bases. Now, those conditions are extensively realised all over the globe, both in culti- vated and uncultivated tracts of land; and in the warmer regions of the earth, where decomposition proceeds with greatest rapidity, the production of nitre in the soil is constant and immense. India alone furnishes Great Britain with all the nitre needed for her gunpowder. Siathly, The most marked nitrous districts of India are celebrated for their fertility, provided a due supply of water is furnished to them. Seventhly, The alkaline nitrates dissolved in water, and not employed in too strong solutions, have been found greatly to quicken the growth of plants; and the nitrate of soda which, from its cheapness, is the most accessible, is daily coming into greater use among our farmers. In the current number of the Journal of the Royal Agricultural Society,* will be found the last of a series of papers on this sub- ject, in which the virtues of nitrate of soda in increasing the amount of wheat yielded by a field manured with it, are placed by Mr Pusry above those of ammonia. It has been asserted, indeed, that alkaline nitrates are serviceable to plants only by furnishing them with alkalies; but I know not by what arguments it is proposed to defend this opinion. It is at variance with the experience of farmers, who find nitrate of soda, as Mr Pusry reports,} a powerful fertiliser where common = Vol, xu. Part u., p. 366. + Ibid. p. 349. VOL. XX. PART IV. 7Y 596 DR GEORGE WILSON ON NITRIC ACID salt is of no avail. But it is needless to enlarge upon this, for even if it were con- ceded that soda is the more important constituent of nitrate of soda, considered as a fertiliser, it is manifest that it must make a difference to a plant whether soda be supplied to it combined with carbonic, hydrochloric, sulphuric, or nitric acid ; and that in the case of nitrate of soda, the plant must in some way dispose of the nitric acid before it can avail itself of the soda; so that the question must be answered, What becomes of the nitric acid which enters plants ? To this, one reply is offered in the quotation which I commenced by reading. The presence of nitrates in tobacco, sunflower, and certain other plants, is thought to shew that if they do not even possess the power of producing nitric acid, they at least cannot decompose it. But surely this is proving too much. For if the presence of undecomposed nitric acid in a plant shews that it cannot decompose that acid, then the presence of ammonia shews that it cannot decompose ammonia, and the presence of undecomposed sulphuric acid shews that it cannot decompose this acid; and for the same reason, as plants all contain undecomposed chlorides, carbonates, water, and carbonic acid, it should be held that they can decompose none of these. In short, it should be contended that a plant can decompose no- thing, and that its existence is a chemical contradiction. If we refuse to draw this conclusion in the case of the other oxides and acids which are found in plants, we must extend our refusal to nitric acid, which is circumstanced exactly as the others are. As for the opinion that plants may produce nitric acid, it is quite possible that they can, although for reasons to be presently mentioned it does not seem likely that they generally do; but it would be unwise to speak confidently on the matter. The only conclusion certainly deducible from the presence of nitrates in plants is, that at least nitric acid does not act injuriously on them. Thus far, then, it has been I think satisfactorily shewn— Firstly, That nitrates are largely offered to plants, both as they grow wild and as they are artificially cultivated. Secondly, That plants do not refuse the nitrates thus offered them. Thirdly, That the nitrates which enter plants do not, if properly diluted, do injury to any class of them; whilst, Fourthly, They largely promote the growth of many of the most important among them. It remains to inquire, Can plants decompose nitric acid, and avail themselves of its nitrogen? I can offer no direct or demonstrative proof that plants possess the power of effecting this decomposition. Direct proof is not to be had in the matter, but the following powerful considerations may be urged in support of the belief that plants can decompose nitric acid. From the moment of the discovery that water is the oxide of hydrogen, chemists perceived that the great characteristic function of a living plant, con- sidered as a piece of chemical apparatus, was to deprive oxides of their oxygen, AS A SOURCE OF THE NITROGEN FOUND IN PLANTS. 597 or to deoxidise them. The earliest teachers of this doctrine, CavENDIsH, Wart, Mevusnizr, and Lavoisier, supposed this deoxidising power to be chiefly expended upon water. At a later period, when the fact that carbonic acid is an oxide of carbon was discovered, and PriEsTLEY’s experiments on the conversion of fixed air into free oxygen, by the green leaves of plants in the presence of sunshine, were recalled, the deoxidising powers of a plant were supposed to be mainly expended on carbonic acid. At present, we should decline to say whether this acid or water was most the subject of deoxidation in plants; and we should add to those oxides, sulphuric acid, as constantly undergoing separation into its ele- ments. To such a conclusion we are driven by the fact, that whilst unoxidised sulphur is found in many of the constituents of plants, sulphates are the only compounds of sulphur which are found entering them. Whatever else, however, is doubtful, this is certain, and is acknowledged by chemists of every school, viz., that a plant is like a blast-furnace, which the sun kindles every day into full action; and that no oxide can pass through such an apparatus, without risking the loss of all its oxygen. With what consistency, then, can it be contended, that water, carbonic acid, and sulphuric acid, cannot pass through a plant in the presence of sunshine, without being deprived in whole or in part of their oxygen, but that the much more easily deoxidised nitric acid, in the same circumstances, will not suffer deoxidation? It might as well be affirmed that a blast-furnace may be competent to reduce the refractory oxide of iron, and yet be incompetent to reduce the easily reducible oxide of lead. No one I think will deny, that out of a plant, sulphates are deprived of oxygen with much more difficulty than nitrates are; if, however, the deoxidising force at work within a plant can deprive sulphates of their oxygen, @ fortiori it can deprive nitrates of their oxygen, and we must concede their deoxidability and deoxida- tion. But further, the alkaline nitrates which are the medium of the introduction of nitric acid into plants, will certainly within them separate more or less com- pletely into acid and alkali, and let the former become free. Those who contend that nitrate of soda profits plants only in so far as it contains soda, imply by this statement that the nitric acid is set free from the soda, and in some way disposed of. All chemists, moreover, will acknowledge that the large amount of fixed alkaline bases found present in every plant in union with organic acids, compels us, what- ever theory we hold, to look upon these acids developed within the plant, as having taken the place of the inorganic or mineral acids which accompanied the bases into its structure. Nitric acid must therefore be often set free within vegetable organ- isms; and when set free, must more rapidly than any uncombined inorganic oxide which is present in plants, suffer instant deoxidation. This proposition, I think, needs no proof. Uncombined carbonic or sulphuric acid, cannot be deoxidised by any known artificial process, so as to separate its oxygen as free gas. Water can be made to yield free oxygen only by a powerful voltaic eurrent,—by an intense 598 DR GEORGE WILSON ON NITRIC ACID, &c. white heat, assisted by platina,—or by chlorine and its congeners, with their affi- nities for hydrogen exalted by sunshine: but nitric acid is the frailest of oxides. It not only parts with oxygen to the immense majority of metals, and of metallic and organic compounds, but the simple application of heat deoxidises it ; and sun- light, which so greatly intensifies the inherent deoxidising power of a plant, can, without the co-operation of its complex organic apparatus, compel nitric acid to undergo deoxidation. If, therefore, sunlight alone can deoxidise nitric acid, sunlight, co-operating with a powerful deoxidising apparatus, will not be less efficacious; and those chemists who declare that a plant can deoxidise water, carbonic acid, and sul- phuric acid, but cannot deoxidise nitric acid, are uttering the paradox, that the more easy the decomposition of an oxide is, the more difficult does a plant find it to be to decompose it; so that if it be exceedingly susceptible of deoxidation, then the plant, whose greatest chemical power is a deoxidising one, cannot deoxidise it at all. No one, I think, would articulately defend such a doctrine. The opposite con- clusion is surely the just one, that if nitric acid be conveyed into plants, it will be reduced by loss of oxygen finally to the condition of nitrogen, and as such be as available for the production of azotised vegetable compounds as the nitrogen of ammonia. Teachers of chemistry appear to be reluctant to admit two sources of nitrogen for plants, because it complicates their statements, and multiplies their formule ; but the partial representations of truth, to which all teachers are compelled, how- ever catholic in spirit, can never justify the expression of one-sided views, as the counterpart of the multiform unity of Nature. Those, moreover, who have been - accustomed to trace back all azotised vegetable compounds to ammonia, need only postulate that nitric acid having been deoxidised into nitrogen, that element unites with hydrogen to form ammonia before any organic compound is developed ; and thereafter they may carry out the ammonia theory as before. Such a con- version of nitric acid into ammonia is not hypothetical, for it can be readily ef- fected by diluting the acid largely with water, and dissolving zinc in it. It would more consist-with the modesty of true science, to be less dogmatic than we generally are on the phenomena which occur within the inscrutable re- cesses of a living plant; and to admit the probability of its being able to employ as food various azotised, as well as other compounds. If, however, we are re- quired to reduce to its simplest chemical expression the conclusion which our present science warrants regarding the inorganic origin of the nitrogen so essential to plants, we must not say that only ammonia, or only nitric acid, is its source, but that both are; or, in a word, that the chief mineral or inorganic representa- tive and parent of the nitrogenous constituents of plants and animals is the Nitrate of Ammonia. ( 599 ) XLII.—Some Observations on Fish, in relation to Diet. By Joun Davy, M.D., F.R.S. Lond. & Edin., Inspector-General of Army Hospitals, Sc. (Read 18th April 1853.) What are the nutritive qualities of fish, compared with other kinds of animal food? Do different species of fish differ materially in degree in nutritive power ? Have fish, as food, any peculiar or special properties? These are questions, amongst many others, which may be asked, but which, in the present state of our knowledge, I apprehend it would be difficult to answer in a manner at all satisfactory. On the present occasion, I shall attempt little more than an opening of the inquiry, and that directed to a few no —chiefly those alluded to in the fore- going queries. 1. Of the Nutritive Power of Fish. The proposition probably will be admitted, that the nutritive power of all the ordinary articles of animal food, at least of those composed principally of mus- cular fibre, or of muscle and fat, to whatever class belonging, is approximately denoted by their several specific gravities, and by the amount of solid matter which each contains, as determined by thorough drying, or the expulsion of the aqueous part, at a temperature such as that of boiling water, not sufficiently high to effect any well-marked chemical change. In the trials I have made, founded on this proposition, the specific gravity has been ascertained in the ordinary hydrostatical way ;—the portions subjected to trial, in the instance of fish, have been taken from the thicker part of the back, freed from skin and bone, composed chiefly of muscle. And the same or similar portions have been used for the purpose of determining their solid contents, dried . in platina or glass capsules of known weight, and exposed to the process of drying till they ceased to diminish in weight. The trials on the other articles of diet, made for the sake of comparison, both as regards specific gravity (excepting the liquids), and the abstraction of the hygroscopic water, or water capable of being dissipated by the degree of tem- perature mentioned, have been conducted in a similar manner. The balance used was one of great delicacy, at home, or a small portable one, when from home, of less delicacy, yet turning readily with one-tenth of a grain. The results obtained are given in the following tables. In the first, on some different species of fish; in the second, on some other articles of animal food. I have thought it right, whenever it was in my power, to notice not only the time when the fish were taken, but also the place where they were procured,—not VOL. XX. PART IV. 7Z 600 DR DAVY’S OBSERVATIONS ON FISH, always so precise as I could wish,—as both season and locality may have an in- fluence on their quality individually. must be understood, that, in the instance of sea-fish, they were from the nearest seaport. Species of Fish. When the place mentioned is inland, it Place where got, and Time. Turbot, Rhombus maximus, Brill, R. vulgaris, . Haddock, Gadus cglofinas Hake, G. merlucius, Pollack, G. pollachins, Whiting, Merlangus vulgaris, Common Cod, Morrhua vulgaris, | Red Cunard! Trigla cuculus, Dory, Zeus Fallen; Mackerel, Scomber Leora Sole, Solea vulgaris, Do. do., Thornback, Raia agin Salmon, Salmo salar, Sea-Trout, S. erioz, Charr, S. wmbla, Trout, S. fario, Do. do. Smelt, S. eperlanus, Eel, Anguilla latirostris, TaBLe I. sae] ae 1062 20°3 1061 20-2 1056 20-2 1054 17°4 1060 19°3 1062 21:5 1059 19-2 1070 22-9 1043 37-9 1065 23-0 1064 91-1 1061 99-9 1071 29-4 sels 41-2 1056 De) 1053 99-5 1050 18-7 1060 19:3 1034 33-6 TasieE II. March, Liverpool. October. Penzance. August. Ambleside. October. Penzance. October. Penzance. March, Chester. April. Ambleside. October. Penzance, October. Penzance. October. Penzance. February. Ambleside. February. Ambleside. October. Penzance. March. River Boyne, Ireland. { Fresh run from the sea. June. Ambleside. November. Windermere. March. Lough Corrib, Ireland, Weight about 3 lb., in good condition. October. River Brathay. A { small fish of about 2 oz. March. Liverpool. June. Ambleside. Kinds of Food. Solid Matter, Place and Time. Specific Gravity. per cent. Beef, sirloin, 1078 26:9 March. Ambleside. Veal, loin, 1076 22 November. Ambleside. Mutton, leg, 1069 26°5 November. Ambleside. Pork, loin, 1080 30°5 January. Ambleside. aa scOMpOE RE of beet an} nae 86:25 Victualling-yard, Portsmouth. Common fowl, Tescsh 1075 pt November. Ambleside. Grey Plover, breast, : 1072 30:1 November. Ambleside. Cow’s milk, new, Before the 1031 11-2 Ne eee cream had separated, White of hen’s egg, 1044 13°9 Yolk of the same, 1032 45:1 IN RELATION TO DIET. > Got These results I would wish to have considered merely as I have proposed in introducing them, viz., as approximate ones. Some of them may not be perfectly correct, owing to circumstances of a vitiating kind, especially the time of keeping. Thus, in the case of the whiting, which was brought from Chester, its specific gravity, and its proportion of solid matter may be given a little too high, owing to some loss of moisture before the trials on it were made. Casting the eye over the first table, it will be seen that the range of nutritive power, as denoted by the specific gravity, and the proportion of solid matter, is pretty equable, except in a very few instances, and chiefly those of the salmon and mackerel. The one ex- hibiting a high specific gravity, with a large proportion of solid matter; the other, a low specific gravity, with a still larger proportion of matter, viz., muscle and oil, and, in consequence of the latter, the inferior specific gravity.